Sname Jack Up Site Assessment Recommended Practices Copy 1h4z6g

<3.6~(Hsrp) However in shallow water the wave steepness can increase to 1112 or more, leading to a zero-upcrossing period Tz as low as 2.8 ~(Hsrp) . This is because the wave height increases and wave length decreases for a given Tz. Note: If a JONSW AP spectrum is applied the response analysis should consider a range of periods associated with Hsrp based on the most probable value of Tp plus or minus one standard deviation. However it should be ensured that the assumptions made in deriving the spectral period parameters are consistent with the values used in the analysis. Alternatively, applicable combinations of wave height and period may be obtained from a scatter diagram determined from site specific measurements; in this case specialist advice should be obtained on a suitable spectral form for the location. To avoid the need for analyses of several wave periods a practical alternative is to use a 2 parameter spectrum with y = 1.0 in combination with the site specific most probable peak period. 3.5.4

For stochastic/random wave force calculations, the short-crestedness of waves (i.e. the angular distribution of wave energy about the dominant direction) may be ed for when site-specific information indicates that such effects are applicable. In all cases the potential for increased response due to short-crested waves should be investigated. The effect may be included by means of a directionality function F(a), as follows: ST]T](f, a)

=

a

= =

F(a)

=

ST]T](f).F(a)

where; angle between direction of elementary wave trains and dominant direction of the short-crested waves. ST]T](f, a) directional short-crested power density spectrum. = directionality function. F( a) and, in the absence of more reliable data: 1t

C.Cos 2na for - -

2

1t

:$ a:$ -

2

where; n

C

=

power constant constant chosen such that: 1tI2 L F(a) .da = 1.0 -1tI2

The power constant n, should not normally be taken as less than: n = 2.0 for fatigue analysis n = 4.0 for extreme analysis

Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002

Page 18

3.5.5

Where the natural period of the jack-up is such that it may respond dynamically to waves (Section 7.3), the maximum dynamic response may be caused by wave heights or seastates with periods outside the ranges given in Sections 3.5.1.2 and 3.5.3. Such conditions shall also be investigated to ensure that the maximum (dynamic plus quasistatic) response is determined.

3.5.6

For fatigue calculations (Section 7.4), the long term wave climate may be required. For the purposes of the fatigue analysis the long-term data may be presented deterministically in of the annual number of waves predicted to fall into each height/period/direction group. Alternatively the probability of occurrence for each seastate (characterized by wave energy spectra and the associated physical parameters) may be presented in the form of a significant wave height versus zero-upcrossing period scatter diagram or as a table of representative seastates.

3.6

Current

3.6.1

The extreme wind driven surface current velocity shall be that associated with the assessment return period wind, seasonally adjusted if appropriate. When directional information regarding other current velocity components is available the maximum surface flow of the mean spring tidal current and the assessment return period surge current, seasonally adjusted if appropriate, shall be vectorially added in the down-wind direction and combined with the wind driven surface current as indicated in Section 3.6.2. If directional data are not available the components shall be assumed to be omnidirectional and shall be summed algebraically. Note: A site specific study will normally be required to define the current velocity components.


3.6.2

Page 19

The current profile may be expressed as a series of velocities at certain stations from seabed to water surface. Unless site specific data indicates otherwise, and in the absence of other residual currents (such as circulation, eddy currents, slope currents, internal waves, inertial currents, etc.), an appropriate method for computing current profile is (see Figure 3.1): Vc

=

V t + Vs + (Vw - Vs) [(h+z)/h], for Izl

~

h and Vs < Vw

for Izl > h or V5 ~ V W where; Vc= current velocity as a function of z. Note that a reduction may be applicable according to Section 4.5. Vt = downwind component of mean spring tidal current. Vs = downwind component of associated surge current (excluding wind driven component). wind generated surface current. In the absence of other data this may conservatively be taken as 2.6% of the 1 minute sustained wind velocity at 10m. h = reference depth for wind driven current. In the absence of other data h shall be taken as 5 meters. z = distance above still water level (SWL) under consideration (always negative). Vt)

I

Vw

2

Vs

[)

Figure 3.1 - Suggested current profile 3.6.3

In the presence of waves the current profile should be stretched/compressed such that the surface component remains constant. This may be achieved by substituting the elevation as described in Section 4.4.2. Alternative methods may be suitable, however mass continuity methods are not recommended. The current profile may be changed by wave breaking. In such cases the wind induced current could be more uniform with depth.

3.6.4 For a fatigue analysis, current may normally be neglected.


Page 20

3.7

Water Levels and Airgap

3.7.1

The water depth at the location shall be determined and related to lowest astronomical tide (LAT). The relationship between LAT and Chart Datum is discussed in the Commentary.

3.7.2

The mean water level (MWL) related to the seabed shall be expressed as the mean level between highest astronomical tide (HAT) and lowest astronomical tide (LAT) i.e.: MWL =(RAT + LAT)/2

3.7.3

The extreme still water level (SWL) shall be expressed as a height above LAT, and shall be the sum of; Mean high water spring tide (MEWS) + 50 year extreme storm surge (see Note 1). unless reliable data indicates that an alternative summation is appropriate.

3.7.4

When lower water levels are more onerous the minimum still water level (SWL) to be considered in the loading calculations shall be the sum of: Mean Low Water Spring Tide (MLWS) + 50 year negative Storm Surge.

3.7.5

The Airgap (see Note 2) is defined in Section 3.2 of the GUIDELINE as the distance between the underside of the hull and LAT during operations. It shall be not less than the sum of: Distance of the extreme still water level (SWL), from Section 3.7.3, above LAT + 50 year extreme wave crest height associated with Hmax as defined in Section 3.5.2 (see Note 1), + 1.5m Clearance to the underside of the hull (or any other vulnerable part attached to the hull, if lower). See Commentary. Notes: 1. Section 3.2.1 of the GUIDELINE recommends that values for a return period of no less than 50 years be applied, even if a lower return period is used for other purposes. 2. The definition of Airgap used herein differs from that used in other areas of offshore engineering where the Clearance used here is often defined as Airgap. In areas subject to freak waves a higher airgap may be applicable.

3.8

Temperatures The lowest average daily air and water temperatures shall be compared with the steel design temperature limits of appropriate parts of the jack-up. If these are not met, suitable adjustments should be made to the properties applied in the strength assessment.

I


3.9

Page 21

Marine Growth Where existing marine growth is not to be cleaned between locations or where the operation is to last long enough for significant growth to occur, the influence of growth on the leg hydrodynamic properties should be considered as stated in Section 4.2.3 of the GUIDELINE. Where applicable, location specific data should be obtained. In the absence of such data, default values for thickness and distribution are given in Section 4.7.3.

3.10

Leg Length Recommendations regarding the reserve leg length are given GUIDELINE.

3.11

In

Section 3.3 of the

Geotechnical and Geophysical Information Adequate geotechnical and geophysical information must be available to assess the location and the foundation stability. Aspects which should be investigated are shown in Table 3.1 and are discussed in more detail in the referenced Sections. The information obtained from the surveys and investigations set out in Sections 3.12 to 3.16 is required for areas where there is no data available from previous operations. In areas where information is available it may be possible to reduce the requirements set out below by use of information obtained from other surveys or activities in the area. See Section 2.4 of the GUIDELINE.

3.12

Bathymetric Survey

3.12.1 An appropriate bathymetric survey should be supplied for an area approximately 1 kilometer square centered on the location. Line spacing of the survey should typically be not greater than 100 meters x 250 meters over the survey area. Interlining is to be performed within an area 200 meters x 200 meters centered on the location. Interlining should have spacing not exceeding 25 meters x 50 meters. 3.12.2 Further interlining should be performed if any irregularities are detected. 3.13

Seabed Surface Survey

3.13.1 The seabed surface shall be surveyed using sidescan sonar or high resolution multi beam echosounder techniques and shall be of sufficient quality to identify obstructions and seabed features and should cover the immediate area (normally a 1 Ian square) of the intended location. The slant range selection shall give a minimum of 100% overlap between adjacent lines. A magnetometer survey may also be required if there are buried pipelines, cables and other metallic debris located on or slightly below the sea floor.


Page 22

REFERENCE METHODS FOR EVALUATION & PREVENTION SECTION(S) Installation problems

- Bathymetric survey

3.12

Punch-through

- Shallow seismic survey - Soil sampling and other geotechnical testing and analysis

3.14 3.16 6.2.6

Settlement under storm loadinglBearing failure

- Shallow seismic survey - Soil sampling and other geotechnical testing and analysis - Ensure adequate jack-up preload capability

3.14 3.16 6.2.6 6.3

Sliding failure

- Shallow seismic survey - Soil sampling and other geotechnical testing and analysis - Increase vertical footing reaction - Modify the footing(s)

3.14 3.16 6.3.3

Scour

- Bathymetric survey (identify sand waves) - Surface soil samples and seabed currents - Inspect footing foundations regularly - Install scour protection (gravel bag/ artificial seaweed) when anticipated

3.12 3.15 6.4.3

Seafloor instability (mudslides)

- Side scan sonar, shallow seismic survey - Soil sampling and other geotechnical testing and analysis

3.13 3.14 3.16 6.4.4

Gas pockets/ Shallow gas

- Digital seismic with attribute analysis processing (shallow seismic)

3.14 6.4.5

Faults

- Shallow seismic survey

3.14

Metal or other object, sunken wreck, anchors, pipelines etc.

- Magnetometer and side scan sonar - DiverlROV inspection

3.13

Local holes (depressions) in seabed, reefs, pinnacle rocks or wooden wreck

- Side scan sonar - DiverlROV inspection

3.13

Legs stuck in mud

- Geotechnical data - Consider change in footings - Jetting

3.14 3.16

Footprints of previous jack-ups

- Evaluate location records - Consider filling/modification of holes as necessary

3.12 3.13 6.4.2

Table 3.1 - Foundation risks, methods for evaluation and prevention


Page 23

3.13.2 Where seabed obstructions such as pipelines and wellheads are known to be present, sufficient infonnation to enable safe positioning of the jack-up is required. In some cases an ROV or diver's inspection may be required in addition to a sidescan sonar survey. 3.13.3 Seabed surface surveys can become out-of-date, particularly in areas of construction/drilling activity or areas with mobile sediments. Good judgment should be used regarding the applicability of all surveys, especially with regard to validity. In open locations the maximum period for the validity of seabed surveys for debris and mobile sediment conditions should be determined taking of local conditions. For locations close to existing installations seabed surveys for debris and sediment conditions should, subject to practical considerations, be undertaken immediately prior to the arrival of the jack-up at the location. 3.14

Geophysical Investigation - Shallow Seismic Survey

3.14.1 The principal objectives of the shallow seismic survey are: To determine near surface soil stratigraphy. This requires correlation of the seismic data with (existing) soil boring data in the vicinity. To reveal the presence of shallow gas concentrations. Due to the qualitative nature of seismic surveys it is not possible to conduct analytical foundation appraisals based on seismic data alone. This requires correlation of the seismic data with soil boring data in the vicinity through similar stratigraphy. 3.14.2 A shallow seismic survey should be performed over an approximately 1 kilometer square area centered on the location. Line spacing of the survey should typically not be greater than 100 meters x 250 meters over the survey area. Equipment should normally be capable of giving detailed data to a -depth equal to the greater of 30 meters or the anticipated footing penetration plus 1.5 to 2 times the footing diameter. Further guidance on seismic surveys is given in reference [2]. 3.14.3 The survey report should include at least two vertical cross-sections ing through the location showing all relevant reflectors and allied geological information. The equipment used should be capable of identifying reflectors of 0.5m and thicker. 3.15

Surface Soil Samples The site investigation should be sufficient to identify the character of the soil surface and allow evaluation of the possibility of scour occurring. (See Commentary to Section 6.4.3)


3.16

Page 24

Geotechnical Investigations

3.16.1 Site specific geotechnical testing is recommended in areas where any of the following apply: the shallow seismic survey cannot be interpreted with any certainty, significant layering of the strata is indicated, the location is in a new operating area, the area is known to be potentially hazardous. 3.16.2 A geotechnical investigation should comprise a minimum of one borehole to a depth equal to 30 meters or the anticipated footing penetration plus 1.5 to 2 times the footing diameter, whichever is the greater. All the layers should be adequately investigated and the transition zones cored at a sufficient sampling rate. The number of boreholes required should for the lateral variability of the soil conditions, regional experience and the geophysical investigation. When a single borehole is made, the preferred location is at the center of the leg pattern at the intended location. 3.16.3 "Undisturbed" soil sampling and laboratory testing and/or in-situ cone penetrometer testing may be conducted. Other recognized types of in-situ soil testing may be appropriate such as vane shear and/or pressure meter tests. 3.16.4 The geotechnical report should include borehole logs, cone penetrometer records (if appropriate) and documentation of all laboratory tests, together with interpreted soil design parameters. Design parameters should be selected by a competent person. For the methods recommended in Section 6, the design parameters should include profiles of undrained shear strength and/or effective stress parameters, soil indices (plasticity, liquidity, grain size, etc.), relative density, unit weight and, where applicable, the over consolidation ratio (OCR). Additional soil testing to provide shear moduli and cyclic/dynamic behavior may be required if more comprehensive analysis are to be applied or where the soil strength may deteriorate under cyclic loading.


Page 25

GLOSSARY OF - ASSESSMENT INPUT DATA

3

C d f F(a) h HAT ~et

Hmax

Hs Hsrp Io(y)

LAT MHWS MLWS MWL n q ST]T](f)

ST]T](f,a)

SWL

Tass Tp Tz Vc Vs Vt Vw

z

= = = = = = = = = = =

= = = = = = = = = = = = = = = = = = = = = = = = = = =

Constant in expression for F(a). Water depth. Wave frequency. Directionality function C.Cos 2na Reference depth for wind driven current. 5.0 m in the absence of other data. Water depth at highest astronomical tide. Reduced wave height which may be used for deterministic wave force calculations, allowing for the conservatisms of higher order wave theories. 1.60 Hsrp The individual extreme wave height for a given return period defined as the wave height with an annual probability of exceedence of lIreturn period (e.g. the 50 year return period Hm has a 2% annual probability of exceedence). Where local data is not available: Hmax = 1.86 Hsrp (for non-tropic revolving storm areas), Hmax = 1.75 Hsrp (for tropical revolving storm areas.) When Hmax is used for airgap calculations the minimum return period for Hsrp is recommended as 50 years, even if a lower return period is used for other purposes. Significant wave height (meters), including depth/asymmetry correction, according to Section 3.5.1.1. The assessment return period significant wave height for a three hour storm. Parameter depending on y used in the expression for ST]T](f). Water depth at lowest astronomical tide. Height of mean high water spring tide above LAT. Height of mean low water spring tide above LAT. Mean water level related to the seabed. Power constant in expression for F( a).

20r4. Exponent in expression for ST]T](f). exp(-(Tpf-I )212(i) Power density spectrum of long crested wave surface elevation as a function of frequency, f. (16Io(Y)rlHs~p(Tpf)-5exp(-1.25/(Tpf)4)f Power density spectrum of short-crested wave surface elevation as a function of frequency, f. ST]T](f).F( a) Height of extreme still water level above LAT. MHWS + 50 year storm surge. MLWS + 50 year negative storm surge (if more onerous). Wave period associated with Hmax (also used with ~et). Peak period associated with Hsrp (also used with Hs). Zero-upcrossing period associated with Hsrp (also used with Hs). Current velocity as a function of z. Downwind component of surge current. Downwind component of mean spring tidal current. Wind generated surface current. 2.6% of 1 minute sustained wind velocity at 10m, in the absence of other data. Distance above still water level used in determination of V c.


Page 26

GLOSSARY OF - ASSESSMENT INPUT DATA (Continued)

3 a

=

y

=

(j

= = =

Angle between direction of elementary wave trains and dominant direction of short-crested waves. Peak enhancement factor used in expression for STlTl(f). For JONSW AP spectrum varies between 1 and 7 with a most probable average value of 3.3. Constant in expression for q 0.07 for T pf <= 1 0.09 for Tpf > 1


Page 27

4

CALCULATION METHODS - HYDRODYNAMIC AND WIND FORCES

4.1

Introduction

4.1.1

The models, methods and coefficients given in this Section are matched to represent a consistent method such that the whole Section should be considered together. No force coefficients should be used unless they correspond to a particular stated analysis method.

4.1.2

The environmental forces may be determined according to the recommendations of this Section based on the dimensions of the and the environmental criteria as described in Section 3 (wind speed, wave height and period and current velocity and profile).

4.1.3

Since differences in shape, proportions and even detail can result in considerable differences in the resultant forces, rational data from model testing may be used by the assessor at his discretion subject to the conditions of Section 4.7.6.

4.2

Wind Force Calculations

4.2.1

For wind load application according to Section 5.7.2, the wind force for each component (divided into blocks of not more than 15m vertical extent), F wi , may be computed using the formula: FWi = PiAWi where; Pi = the pressure at the center of the block. AWi = the projected area of the block considered. and the pressure Pi shall be computed using the formula: Pi = 0.5 P (Vref)2 Ch Cs where; 3 p = density of air (to be taken as 1.2224 kglm unless an alternative value can be justified for the location). V ref = the 1 minute sustained wind velocity at reference elevation (normally 10m above MWL), see Section 3.4.1. Ch = height coefficient, as given in Section 4.2.2. Cs = shape coefficient, as given in Section 4.2.3. Note: The wind area of the hull and associated structures (excluding derrick and legs) may normally be taken as the profile area viewed from the direction under consideration.

Page 28


4.2.2

Ch may be derived from the wind velocity profile;

vz

=

V ref (ZlZref) lIN

vz

=

the wind velocity at elevation Z.

Vref

= the 1 minute sustained wind velocity at elevation above MWL), see Section 3.4.1.

N

=

where;

Zref

(normally 10m

10 unless site specific data indicate that an alternative value of N is appropriate.

Hence:

Alternatively, the approximate coefficients shown in Table 4.1 may be applied. The height is the vertical distance from the still water surface to the center of area of the block considered. Blocks which have a vertical dimension greater than 15 m shall be subdivided, and the appropriate height coefficients applied to each part of the block.

Height m 0- 15 15 - 30 30 - 45 45 - 60 60 - 75 75 - 90 90 - 105 105 - 120 120 - 135 135 - 150 150 - 165 165 - 180 180 - 195

Height coefficient

Ch 1.00 1.18 1.30 1.39 1.47 1.53 1.58 1.62 1.66 1.70 1.74 1.77 1.80

Table 4.1 - Height coefficients

In deriving Table 4.1 the wind velocity used to obtain Ch for the block below 15.0m is the Vref value. For all other blocks the Ch value is that for the mid-height of the block. When using Table 4.1 the wind velocity is derived from Section 3.4.1 for a reference height of 10m above the still water.

Recommended Practice jor Site Specific Assessment oj Mobile Jack-Up Units Rev 2, Jan 2002

4.2.3

Page 29

Shape coefficients shall be derived from Table 4.2; Type of member or structure Hull side, (flat side)

Shape coefficient

Cs 1.0, based on total projected area

Deckhouses, jack-frame structure, sub-structure, drawworks house, and other abovedeck blocks Leg sections projecting above jack-frame structure and below the hull

Isolated tubulars pedestals, etc.)

1.1, based on the total projected area (i.e. the area enclosed by the extreme contours of the structure) Cs = CDe as determined from Section 4.6, except that marine growth may be omitted. AWi determined from De and section length.

(crane 0.5

Isolated structural shapes 1.5, based on member projected (angles, channels, box, 1- area sections) Derricks, crane booms, flare The appropriate shape coefficient towers (open lattice sections for the concerned applied to 50% of the total only, not boxed- in sections) projected profile area of the item (25% from each of the front and back faces) Shapes or combinations of shapes which do not readily fall into the above categories will be subject to special consideration Table 4.2 - Shape coefficients 4.3

Hydrodynamic Forces

4.3.1

Wave and current forces on slender having cross sectional dimensions sufficiently small compared with the wave length should be calculated using Morison's equation. Note: Morison's equation is normally applicable providing:

A > 5Di where; A = wavelength and Di

=

reference dimension of member (e.g. tubular diameter)

Morison's equation specifies the force per unit length as the vector sum: LlF

=LlFdrag + LlFinertia = 0.5 P D CD Vn IVn I+ P CM A Un

where the of the equation are described in the following.

Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Page 30 Rev 2, Jan 2002 4.3.2 To obtain the drag force, the appropriate drag coefficient (CD) is to be chosen in combination with a reference diameter, including any required additions for marine growth, as described in Section 4.7.

The Morison's drag force fonnulation is: ~drag 0.5 P Co D Vn Vn

I I

=

where; ~drao0

=

P

= = = =

Co Vn D

drag force (per unit length) nOlmal to the axis of the member considered in the analysis and in the direction of vn. mass density of water (nonnally 1025 kglm3 ). drag coefficient ( CDi or COe from Section 4.6-7). relative fluid particle velocity resolved nonnal to the member axis. the reference dimension in a plane nonnal to the fluid velocity Vn (= Di or De from Section 4.6-7).

=

Note: The relative fluid particle velocity, vn, may be taken as: Vn = Un + V Cn - U t n where; un + V Cn

=

fn

=

U

= =

the combined particle velocity found as the vectorial sum of the wave particle velocity and the current velocity, normal to the member axis. the velocity of the considered member, nonnal to the member axis and in the direction of the combined particle velocity. 0, if an absolute velocity is to be applied, i.e. neglecting the structural velocity. 1, if relative velocity is to be included. May only be used for stochastic/random wave force analyses if: uTnlDi ~ 20 where u particle velocity V C + nH/fz Tn first natural period of surge or sway motion and Di = the reference diameter of a chord.

= =

=

Note: See also Section 7.3.7 for relevant damping coefficients depending on u. 4.3.3

To obtain the inertia force, the appropriate inertia coefficient (C M ) is to be taken in combination with the cross sectional area of the geometric profile, including any required additions for marine growth, as described in Section 4.7.


4.3.3

Page 31

The Morison's inertia force fonnulation is: ~inertia

=

P CM A Un

~inertia

=

p

= = = =

inertia force (per unit length) nonnal to the member axis and in the direction of Un. mass density of water (nonnally 1025 kglm 3). inertia coefficient. cross sectional area of member ( =Ai or Ae from Section 4.6) fluid particle acceleration nonnal to member.

where;

CM A

Un 4.4

Wave Theories and Analysis Methods

4.4.1

For deterministic analyses an appropriate wave theory for the water depth, wave height and period shall be used, based on the curves shown in Figure 4.1, after HSE [3]. For practical purposes, an appropriate order of Dean's Stream Function or Stokes' 5th (within its bounds of applicability) is acceptable for regular wave survival analysis.

4.4.2

For random wave (stochastic) analyses, it is recommended that the random seastate is generated from the summation of at least 200 component Linear (Airy) waves of height and frequency determined to match the required wave spectrum. The phasing of the component waves should be selected at random. The extrapolation of the wave kinematics to the free surface is most appropriately carried out by substituting the true elevation at which the kinematics are required with one which is at the same proportion of the still water depth as the true elevation is of the instantaneous water depth. This can be expressed as follows:

z

,= z-S

1+ Sf d

where; z z

,

S d

= =

The modified coordinate to be used in particle velocity fonnulation The elevation at which the kinematics are required (coordinate measured vertically upward from the still water surface) = The instantaneous water level (same axis system as z) = The still, or undisturbed water depth (positive).

This method ensures that the kinematics at the surface are always evaluated from the linear wave theory expressions as if they were at the still water level, Wheeler (1969) [4] (see Figure C4.4.2 in the Commentary). 4.4.3

If breaking waves are specified according to Figure 4.1, it is recommended that the wave period is changed to comply with the breaking limit for the specified height.


Page 32

. . .------r__----.. .

0.030 ...-----~-----""P"'-----

The boundaries given are approximate and depend on the pUIpose of the analysis beingperfonned. It is accepted that refraction and diffiaction analysis will usually will be based on linear theory.

DEEPWATER BREAKING LIMIT Hm ax/ L =0.14

J....~"".,...,

0.025 - 4 1 - - - - - - I - - - - - - 4 - - - - - - - - , l , . . " . E : . . - - - - f - - - - - - - I

H max

~

gT as s

0.020 .......-----'-----..111~-__h"""___::~--__+-""''---___,,''""f__----__1

0.015 ....---T----,h~-__:;I~-__h~---.,..._t------t_----___1

0.010

ooI---+_........--+-I--+_ _~-----r_:S~T~O=KE=S~5_t_-__,;:><:::___-_t OR SlEAM FUNCTION

3

0.05 .......+-.....~-+----,I#-------+--------+------f----:D""E==E""P---I WATER WAVES

INTERMEDIATE DEPTIiWAVES

~INEARJAIRY OR STREAM FUNCTION CD

0~~~----P---------_r--------~~--------._--~----_4

o

0.02

0.04

1) None of these theories is theoretically correct at the breaking limit. 2) Wave theories intended for limiting height waves should be referenced for waves higher than O.9Hb when stream function theory may underestimate the kinematics. 3) Stream function theory is satisfactory for wave loading calculations over the remaining range of regular waves. However, stream function programs may not produce a solution when applied to near breaking waves or deep water waves 4) The order of stream function theory likely to be satisfactory is circled. Any solution obtained should be checked by comparison with the results of a higher order solution. S) The error involved in using Airy theory outside its range of applicability is discussed in the background document.

0.08

0.06

d

0.10

Nomenclature 2

Dimensionless wave steepness

HmaxlgTass d/gTass Hmax Hb d

2

=

Tass L g

=

Dimensionless relative depth Wave height (crest to trough) Breaking wave height Mean water depth Wave period Wave length (distance between crests) Acceleration due to gravity

Figure 4.1 - Range and validity of different wave theories for regular waves, (after HSE [3])


Page 33

4.5

Current

4.5.1

The current velocity and profile as specified in Section 3.6 shall be used. Interpolation between the data points may be required and linear interpolation is recommended for simplicity.

4.5.2

The current induced drag forces are to be determined in combination with the wave forces. This is to be carried out by the vectorial addition of the wave and current induced particle velocities prior to the drag force calculations.

4.5.3

The current may be reduced due to interference from the structure on the flow field of the current, Taylor [5]. The current may be reduced as follows (see Commentary):

where;

= the current velocity to be used in the hydrodynamic model, Vc should be not taken as less than O.7Vf. V f = the far field (undisturbed) current. CDe = equivalent drag coefficient, as defined in 4.6.5. De = equivalent diameter, as defined in 4.6.5. DI = face width of leg, outside dimensions. Vc

4.6

Leg Hydrodynamic Model

4.6.1

The hydrodynamic modeling of the jack-up leg may be carried out by utilizing 'detailed' or 'equivalent' techniques. In both cases the geometric modeling procedure corresponds to the respective modeling techniques described in Section 5.6.4. The hydrodynamic properties are then found as described below: Detailed' model All relevant are modeled with their own unique descriptions for the Morison term values with the correct orientation to determine Vn and Un and the corresponding CoD =CDjD j and CMA =CMj1tD?14, as defined in Section 4.7. 'Equivalent'model The hydrodynamic model of a bay is comprised of one, 'equivalent' vertical tubular located at the geometric center of the actual leg. The corresponding (horizontal) Vn and Un are applied together with equivalent CoD = CDeDe and CMA = CMeAe, as defined in Sections 4.6.5 and 4.6.6. The model should be varied with elevation, as necessary, to for changes in dimensions, marine growth thickness, etc. Note: The drag properties of some chords will differ for flow in the direction of the wave propagation (wave crest) and for flow back towards the source of the waves (wave trough). Often the combined drag properties of all the chords on a leg will give a total which is independent of the flow direction along a particular axis. When this is not the case it is recommended that the effect is included directly in the wave-current loading model. If this is not possible it is recommended that:


Page 34

1. Regular wave detenninistic calculations use a value appropriate to the flow direction under consideration, noting that the flow direction is that of the combined wave and current particle motion. 2. An average drag property is considered for random wave analyses which are solely used to determine dynamic effects for inclusion in a final regular wave deterministic calculation which will be made on the basis of 1. above. 3. The drag property in the direction of wave propagation is used for random wave analyses from which the final results are obtained directly. 4.6.2

Lengths of are normally taken as the node-to-node distance of the in order to for small non-structural items (e.g. anodes, jetting lines of less than 4" nominal diameter). Large non-structural items such as raw water pipes and ladders are to be included in the model. Free standing conductor pipes and raw water towers are to be considered separately from the leg hydrodynamic model.

4.6.3

The contribution of the part of the spudcan above the seabed should be investigated and only excluded from the model if it is shown to be insignificant. In water depths greater than 2.5 Hs or where penetrations exceed 112 the spudcan height, the effect of the spudcan is normally insignificant.

4.6.4

For leg structural , shielding and solidification effects should not normally be applied in calculating wave forces. The current flow is however reduced due to interference from the structure on the flow field, see Section 4.5.3.

4.6.5

When the hydrodynamic properties of a lattice leg are idealized by an 'equivalent' model description the model properties may be found using the method given below: The equivalent value of the drag coefficient, C De , times the equivalent diameter, De, to be used in Section 4.3.2 for CDei of the bay may be chosen as: CDe De = De ~ CDei The equivalent value of the drag coefficient for each member, CDej, is determined from: [sin2~i + COS2~i sin2 <Xi ]3/2 CDi D iIi CDei

=

Des

where; C Di

=

Di

=

drag coefficient of an individual member (i) as defined in Section 4.7. reference diameter of member 'i' (including marine growth as applicable) as defined in Section 4.7.

equi valent diameter of leg, suggested as ~ (L. D i \ / s length of member 'i' node to node center. length of one bay, or part of bay considered. angle between flow direction and member axis projected onto a horizontal plane. angle defining the member inclination from horizontal (see Figure ~i = 4.2). Note: L indicates summation over all in one leg bay De Ii S <Xi

= = = =


Page 35

The above expression for CDei may be simplified for horizontal and vertical as follows: Vertical (e.g. chords): Horizontal : FLOW DIRECTION

Figure 4.2: Flow angles appropriate to a lattice leg (after DNV Class Note 31.5, February 1992, [6])

4.6.6

The equivalent value of the inertia coefficient, C Me , and the equivalent area, Ae, to be used in Section 4.3.3, representing the bay may be chosen as: CMe

=

equivalent inertia coefficient which may normally be taken as 2.0 when using Ae

Ae

=

equivalent area of leg per unit height =(LAili)/s

Ai

= equivalent area of element = nn?/4

Di

=

reference diameter chosen as defined in Section 4.7

For a more accurate model the CMe coefficient may be determined as:

where; 2

2

2

A.I. Ae s

=

[1 + (sin f3i + cos f3i sin Uj)(C Mi _ 1)]

=

the inertia coefficient of an individual member, CMi is defined in Section 4.7 related to reference dimension D i.

_1_1

Note: For dynamic modeling the added mass of fluid per unit height of leg may be determined as pAi(Cmi - 1) for a single member or pAe(CMe - 1) for the equivalent model, provided that Ae is as defined above.

Page 36


4.7

Hydrodynamic Coefficients for Leg

4.7.1

Hydrodynamic coefficients for leg are given in this Section. Tubulars, brackets, split tube and triangular chords are considered. Hydrodynamic coefficients including directional dependence are given together with a fixed reference diameter Di. No other diameter should be used unless the coefficients are scaled accordingly. Unless better information is available for the computation of wave and current forces, the values of drag and inertia coefficients applicable to Morison's equation should be obtained from this Section.

4.7.2

Recommended values for hydrodynamic coefficients for tubulars «1.5m diameter) are given in Table 4.3 based on the data discussed in the commentary.

Surface condition Smooth Rough

}

CDi 0.65

CMi 2.0

1.00

1.8

I

See Note

Table 4.3: Base hydrodynamic coefficients for tubulars Note: The smooth values will normally apply above MWL + 2m and the rough values below MWL + 2m, where MWL is as defined in Section 3.7.2. If the jack-up has operated in deeper water and the fouled legs are not cleaned the surface should be taken as rough for wave loads above MWL + 2m. See Commentary. 4.7.3

When applicable, marine growth is to be included in the hydrodynamic model by adding the appropriate marine growth thickness, to, on the boundary of each individual member below MWL + 2m where MWL is as defined in Section 3.7.2 i.e. for a tubular Di = DoriginaI + 2tm. Site specific data for marine growth is preferred (see Section 3.9). If such data are not available all below MWL + 2m shall be considered to have a marine growth thickness tm = 12.5 mm (i.e. total of 25 mm across the diameter of a tubular member). Marine growth on the teeth of elevating racks and protruding guided surfaces of chords may normally be ignored. The effects of marine growth may be ignored if anti-fouling, cleaning or other means are applied, however the surface roughness is still to be taken into (see Commentary).

Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Page 37 Rev 2, Jan 2002 4.7.4 The in-line force due to gussets in any vertical plane shall be determined using a drag coefficient:

C Di =2.0 applied together with the projected area of the gusset visible in the flow direction, unless model test data shows otherwise. This drag coefficient may be applied together with a reference diameter Di and corresponding length Ii chosen such that their product equals the plane area, A = Dili and Di = Ii (see Figure 4.3). In the equivalent model of Section 4.6 the gussets may then be treated as a horizontal element of length Ii , with its axis in the plane of the gusset. C Mi should be taken as 1.0 and marine growth may be ignored.

tVisible Part

Figure 4.3: Gusset plates

Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Page 38 Rev 2, Jan 2002 4.7.5 For non-tubular geometries (e.g. leg chords) the appropriate hydrodynamic coefficients may, in lieu of more detailed information, be taken in accordance with Figures 4.4 or 4.5 and corresponding formulas, as appropriate. Ci

t)

~

WlDj= 1.4 2.5

l5

E 2.. 0 ~

e

t)

1.5

CI

1.0

~ ..::

......... ~ .. W/Dj =1.1 ROUGH

0.5 0.0

SMOOTH

+------,------,.----1 30

60

90 ANGLE

e

Figure 4.4: Split tube chord and typical values for Cm For a split tube chord as shown in Figure 4.4, the drag coefficient CDi related to the reference dimension D j = D+2tm, the diameter of the tubular including marine growth as in Section 4.7.3, maybe taken as:

where;

8

=

Angle in degrees, see Figure 4.4

Coo =

The drag coefficient for a tubular with appropriate roughness, see Section 4.7.2. (Coo = 1.0 below MWL+2m and Coo =0.65 above MWL+2m.)

=

The drag coefficient for flow normal to the rack (8 = 90°), related to projected diameter, W. COl is given by:

CD!

1.8

C Ol

= { l.4+~(W/Dj) 2.0

1.2 < 1.8 <

W/D j <1.2 W ID j <1.8 W/Dj

The inertia coefficient CMj = 2.0, related to the equivalent volume nD j 2/4 per unit length of member, may be applied for all heading angles and any roughness.

Page 39


Q

0

~ 2.5

w

W!D=1.07

~ 2.0 D

o

1.5

~

1.0

u

~

0.5 O~--'----.---.----r---r-~

o

30

60

90

120

150 180 ANGLES

Figure 4.5: Triangular chord and typical values of C.Qi. For a triangular chord as shown in Figure 4.5, the drag coefficient CDi related to the reference dimension Di =D, the backplate width, may be taken as: CDi =CDprCS) Dpr(S) I Di where the drag coefficient related to the projected diameter, C Dpn is determined from: 1.70 S = 0° 1.95 S = 90° CDpr = 1.40 S = 105° 1.65 S =180°-So 2.00 S =180° Linear interpolation is to be applied for intermediate headings. The projected diameter, Dpr(S), may be determined from: DCOS(S) 0 < S < So Dpr(S) = W sin(S) + 0.5Dlcos(S)1 So < 8 < 180 - So { Dlcos(S)1 ; 180- 8 0 <8<180 The angle So, where half the rackplate is hidden, 8 0 =tan- 1(D/(2W». The inertia coefficient CMi = 2.0 (as for a flat plate), related to the equivalent volume of nDi2/4 per unit length of member, may be applied for all headings and any roughness. 4.7.6 Shapes, combinations of shapes or closely grouped non-structural items which do not readily fall into the above categories should be assessed from relevant literature (references to be provided) and/or appropriate interpretation of (model) tests. The model tests should consider possible roughness, Keulegan-Carpenter and Reynolds number dependence. 4.8

Other Considerations Local load effects will normally have been addressed at the design stage. Should the wind or current and/or wave height parameters at the location exceed those applicable at the design stage further consideration may be required. The Commentary provides further details and references to calculation methods.


4

Page 40

GLOSSARY OF - CALCULATION METHODS HYDRODYNAMICS AND WIND FORCES

=

AWi A Ae Ai Co COe CDi Coo COl COpr CM C Me C Mi Ch Cs d D De Di DI Dpr FWi Hs Ii Pi tn

= = = = = = = =

= = = = =

= = =

=

= =

=

= =

=

=

s tm Tn Tz u Un Un Vn Ven Vf V ref Vz W

=

z z' Z 'Zref ex <Xi f3i LWdrao LWinertia

=

=

= =

= = = = =

=

= =

=

b

=

= =

=

= = =

=

Projected area of the block considered in wind computations. Cross sectional area of member. Equivalent area of leg per unit heifht =(L Ai Ii )/s. Equivalent area of element = 1t Di 14. Drag coefficient. Equi valent drag coefficient. Drag coefficient of an individual member, related to D i. The drag coefficient for chord at direction e =0°. The drag coefficient for flow normal to the rack, e = 90°. The drag coefficient related to the projected diameter. Inertia coefficient. Equi valent inertia coefficient. Inertia coefficient of a member, related to D i. Height coefficient for wind. Shape coefficient for wind related to projected area. The mean, undisturbed water depth (positive). Member diameter or backplate width. Equivalent diameter of leg. Reference dimension of individual leg . Face width of leg, outside dimensions. The projected diameter. Wind force for block i. The effective significant wave height (Section 5.5.1.3). Length of member 'i' node to node center. Wind pressure at the center of block i. Velocity of the considered member, normal to the member axis and in the direction of the combined particle velocity. Length of one bay, or part of bay considered. Marine growth thickness. First natural period of sway motion. The zero-upcrossing period associated with Hs. Wave particle velocity. Wave (only) particle velocity normal to the member. Wave particle acceleration normal to the member. Total (relative) flow velocity normal to the member. Current velocity to be used in the hydrodynamic model, normal to member. Far field (undisturbed) current. One minute sustained wind velocity at elevation 'Zref. Wind velocity at elevation Z. Dimension from backplate to pitch point of triangular chord or dimension from root of one rack to tip of other rack of split-tubular chord. Coordinate measured vertically upward from the mean water surface. Modified coordinate to be used in particle velocity formulation. Elevation measured from the mean water surface. Reference elevation for wind speed. Indicator for relative velocity, 0 or 1. Angle defining flow direction relative to member. Angle defining the member inclination. Drag force per unit length. Inertia force per unit length.

Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Page 41 Rev 2, Jan 2002 4 GLOSSARY OF - CALCULATION :METHODS HYDRODYNAMICS AND WIND FORCES (Continued)

sp 8 80 A

= = = = =

The instantaneous water surface elevation (same axis system as z). Mass density of water or air. Angle in degrees of water particle velocity relative to the chord orientation. Angle at which half rackplate of Do chord is hidden tan- l (D/(2W» Wave length.

=


Page 42

5

CALCULATION METHODS - STRUCTURAL ENGINEERING

5.1

General Conditions

5.1.1

Structural calculations should be carried out in accordance with the following sections.

5.1.2

A range of environmental approach directions and storm water levels should be considered, such that the most onerous (i.e. that leading to the extreme maximum and/or minimum loading) is determined for each assessment check {strength of each major type of element (chord, brace, etc.), overturning stability, foundation capacity, horizontal deflections, holding system, etc.}.

5.1.3

In deterministic calculations the most critical wave phase position(s) should be considered for each case identified under 5.1.2. Normally the phase giving maximum base shear and/or overturning moment will be found critical for overturning, leeward leg stresses, leeward leg foundations and windward leg foundations.

5.1.4 For fatigue calculations it may be necessary to determine the load or stress ranges, and hence other phase positions may also need to be considered. 5.2

Seabed Reaction Point For independent leg jack-up units, the reaction point for horizontal and vertical loads at each footing shall be situated on the geometric vertical axis of the leglspudcan, at a distance above the spudcan tip equivalent to: a) Half the maximum predicted penetration (when spudcan is partially penetrated), or b) Half the height of the spudcan (when the spudcan is fully, more than fully penetrated). If detailed information exists regarding the soils and spudcan the position of the reaction

point may be calculated. (Brekke et al, [7]) 5.3

Foundation Fixity

5.3.1

For analyses of an independent leg jack-up unit under extreme storm conditions the foundations may normally be assumed to behave as pin ts, and so are unable to sustain a bending moment. Analysis and practical experience suggest that this may be a conservative approach for bending moment in the upper parts of the leg in way of the lower guides.

5.3.2 In cases where the inclusion of rotational foundation fixity is justified and is included in the structural analysis, it is essential that the nonlinear soil-structure interaction effects are properly taken into . The model should include the interaction of rotational, lateral and vertical soil forces.

I


5.3.3

Page 43

Methods of establishing the degree of fixity of rotational restraint, or fixity, at the footings are discussed further in Section 6.3.4 and the Commentary to Section 6. Upper or lower bound values should be considered as appropriate for the areas of the structure under consideration.

5.3.4 For checking the spudcans, the leg-to-can connection and the lower parts of the leg, appropriate calculations considering soil-structure interaction shall be carried out to determine the upper bound can moment. These areas may be checked assuming that a percentage of the maximum storm leg moment at the lower guide (derived assuming a pinned footing) is applied to the spudcan together with the associated horizontal and vertical loads. This percentage would normally be not less than 50%. For such simplified checks the loading on the spudcan may be modeled assuming that the soil is linear-elastic and incapable of taking tension. 5.4

Leg Inclination The effects of initial leg inclination should be considered. Leg inclination may occur due to leg-hull clearances and the hull inclination permitted by the operating manual. Thus the total horizontal offset due to leg inclination, 0,., may be determined as:

where; OT =Total horizontal offset of leg base with respect to hull.

0 1 =Offset due to leg-hull clearances. O2 =Offset due to maximum hull inclination permitted by the operating manual. If detailed information is not available, OT should be taken as 0.5% of the leg length

below the lower guide. The effects of leg inclination need be ed for only in structural strength checks. This will normally be accomplished by increasing the effective moment in the leg at the lower guide by an amount equal to the offset OT times the factored vertical reaction at the leg base due to dead, live, environmental, inertial and p-~ loads. 5.5

p-~

5.5.1

The p-~ Effect occurs because the jack-up is a relatively flexible structure and is subject to lateral displacement of the hull (sidesway) under the action of environmental loads. As a result of the hull translation the line of action of the vertical spudcan reaction no longer es through the centroid of the leg at the level of the hull. Consequently the leg moments at the level of the hull are increased over those arising from a linear quasi-

Effects


Page 44

static analysis by an amount equal to the individual leg load P times the hull translation, D. This additional moment will cause additional deflection over that predicted by standard linear-elastic theory. The increased deflection is a function of the ratio of the applied axial load to the Euler load. Furthennore the shift in the hull center of gravity due to the hull translation will increase the overturning moment (or decrease the righting moment). Consequently the axial loads in the leeward leg(s) will increase and the axial loads in the windward leg(s) will reduce. The consequences of the above are: a) Increased hull deflections (which will increase the linear-elastic P-8 moments). b) A redistribution of base shears (in global axes) such that the increase in lower guide moment is reduced in the leeward leg(s) and increased in the windward leg(s). 5.5.2

An analysis using a standard linear elastic (small displacement) finite element program will not allow for these effects. The following Sections describe techniques which may be used to for the P-MEuler effects. The large displacement methods are the most accurate, but require more rigorous analysis. The geometric stiffness methods are simpler and generally of sufficient accuracy.

5.5.3

Large displacement methods; These methods are part of a number of finite element (F.E.) programs. In such methods the non-linear (large-displacement) solution is obtained by applying the load in increments and iteratively generating the stiffness matrix for the next load increment from the deflected shape (nodal deflections) of the previous increment. Some F.E. programs offer an intermediate solution in which the deflected geometry from an initial linearelastic solution is used as the input to the final 'corrected' solution.

5.5.4

Geometric stiffness methods,·

5.5.4.1 These methods are also available within a number of F.E. programs. A linear correction is made to the element stiffness matrix based on the axial load present in the element. Iteration is also required for this solution procedure. 5.5.4.2 A simplified geometric stiffness approach allows incorporation of P-L\ effects in a standard linear-elastic F.E. program without recourse to iteration (refer to Commentary for derivation). In this approach a correction tenn is introduced into the global stiffness matrix prior to analysis. When the analysis is complete the hull deflections, leg axial loads and leg bending moments will include the P-L\ effects. The derivation of the method is described in appendix C5.A of the Commentary.


Page 45

The correction term is: -PgIL where; Pg = Total effective gravity load on legs at hull. This includes the hull weight and weight of the legs above the hull. L = The distance from the spudcan reaction point to the hull vertical center of gravity. This single (negative) value is incorporated into the global stiffness matrix by attaching a pair of orthogonal horizontal translational earthed spring elements to a node representing the hull center of gravity and entering the negative value for each of the spring constants. Some F.E. packages allow direct matrix manipulation. The negative stiffness term at the hull will produce an additional lateral force at the hull proportional to the structural deflection. The resulting (additional) base overturning moment will be equal to the gravity load times the hull displacement. The additional lateral load (due to the negative stiffness term) will cause an overprediction of the base shear (in global axes). Typically this is not critical. However, the base shear at each leg can be reduced by an amount equal to the difference between the total base shear and the shear due to the applied loads (both in global axes) divided by the number of legs. 5.5.4.3 An alternative geometric stiffness approach is given below. Here the P-~ effects are determined by amplifying the linear-elastic displacement (excluding P-~) as follows:

where; ~

=

the approximate displacement including P-~. 8s = the linear-elastic first order hull displacement. P = the average axial load in the leg at the hull (i.e. the total leg load at the hull divided by the number of legs). PE = Euler buckling load of an individual leg.(See Section 7.3.5 for general formulation). Corrections can then be made to a global linear-elastic solution by manually adding P-~ moments to the results. The P-~ moments are computed using the amplified deflection, ~, and P'S adjusted to for this. (This approach is not strictly valid because it ignores the fact that the deflection of all the legs at the hull must be approximately equal. The imposition of this constraint will lead to a redistribution of the global base shear between the legs.) Ignoring the redistribution will generally be conservative for leeward leges) and their foundation loads and non- conservative for windward leges) and their foundation loads.


5.6

Structural Modeling

5.6.1

Introduction

Page 46

It is important that the structural model accurately reflects the complex mechanism of the

jack-up. For most jack-up configurations the load distribution at the leg-hull interface is not amenable to manual calculation, therefore, it is necessary to develop a Finite Element (F.E.) computer model. A number of different modeling techniques can be used to depict the jack-up structure. The recommended techniques are summarized below and their applicability and limitations are discussed in more detail in Section 5.6.3. a) Fully detailed model of legs and hull/leg connections with detailed or representative stiffness model of hull and spudcan. b) Simplified lower legs and spudcans, detailed upper legs and hull/leg connections with detailed or representative stiffness model of hull. c) Equivalent stiffness model of legs and spudcans, equivalent hulllleg connection springs and representative beam-element hull grillage. d) Detailed leg (or leg section) and hull/leg connection model. Section 5.6.3 and Table 5.1 outline the limitations of the various modeling techniques and should be referenced to ensure that the selected models address all aspects required for a specific assessment.

5.6.2

General Considerations In the elevated condition the most heavily loaded portion of the leg is normally between the upper and lower guides and in way of the lower guide. The stress levels in this area depend on the design concept of the jack-up. A specific jack-up design concept can be described by the combination of the following components (see Commentary Figure

C5.5): a) With or without fixation system, b) Fixed or floating jacking system, c) Opposed or unopposed pinions. In units having fixation systems the transfer of moment between the leg and the hull is largely by means of a couple due to vertical loads carried from the chord into the fixation or jacking system.

Where a fixed or floating jacking system is fitted (and there is no fixation system) the transfer of moment between the leg and the hull is partly by means of a couple due to horizontal loads carried from the chords into the upper and lower guides. In this case and when the chord/guide occurs between bracing nodes significant local chord bending moments are normal.


Page 47

If the jacking system has unopposed pinions local chord moments will arise due to: the horizontal pinion load component (due to the pressure angle of the rack/pinion). the vertical pinion load component acting at an offset from the chord neutral axis. The modeling of the various design aspects is critical and recommended modeling techniques are outlined in the following sections. The Commentary provides detailed information regarding the combination of the above three components for current jack-up units. 5.6.3

Applicability and Limitations It is most desirable to fully model the jack-up when assessing its structural strength. Very

often assumptions and simplifications such as equivalent hull, equivalent leg, etc. will be made in the process of building the model. In view of this, various levels of modeling described in a) through d) below may be used. It should be noted that some of these methods may have limitations with respect to the accuracy of assessing the structural adequacy of a jack-up and when simplified models, such as those described in (c) and (d) are used it may be appropriate to calibrate against a more detailed model. a) Fully detailed 3-leg model

The model consists of 'detailed legs', hull, hulllleg connections and spudcans modeled in accordance with 5.6.4(a),5.6.5, 5.6.6 and 5.6.7, respectively. The results from this model can be used to examine the preload requirements, overturning resistance, leg strength and the adequacy of the jacking system or fixation system. b) Combination leg 3-leg model

The model consists of a combination of 'detailed leg' for the upper portion of legs and 'equivalent leg' for the lower portion of the legs modeled in accordance with 5.6.4. The hull, hulllleg connections and spudcans are modeled in accordance with 5.6.5, 5.6.6 and 5.6.7 respectively. The results from this model can be used to examine the preload requirements, overturning resistance, leg strength and the adequacy of the jacking system or fixation system. c) Equivalent 3-stick-leg model

The model consists of 'equivalent legs' modeled in accordance with 5.6.4(b), hull structure modeled using beam elements in accordance with 5.6.5, leg to hull connections modeled in accordance with 5.6.6 and spudcans modeled as a stiff or rigid extension to the equivalent leg. The results from this model can be used to examine the preload requirements and overturning resistance. This model may also used to obtain the reactions at the spudcan or internal forces and moments in the leg at the vicinity of lower guide for application to the 'detailed leg' and hulllleg model (d) which should be used to assess the strength of the leg in the area between lower and upper guides.

Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 d) Single detailed leg model

Page 48

The model consists of a 'detailed leg' or a portion of a 'detailed leg' modeled in accordance with 5.6.4(a), the hulllleg connection modeled in accordance with 5.6.6 and, when required, the spudcan modeled in accordance with Section 5.6.7. This model is to be used in conjunction with the reactions at the spudcan or the forces and moments in the vicinity of lower guide obtained from Model (c). The results from this model can be used to examine the leg strength and the adequacy of the jacking system or the fixation system.

Model Type a b c d

I

IT

Global Loads

Overturning Checks

y Y y -

Y Y Y -

Applicability (see Note 1) ill IV V Global Leg Foundation Leg Member Checks Loads Loads

Y Y Y -

Y Y Y -

vn

VI Pinion! Fixation System Loads

Hull Element Loads

Y Y y

2 2 -

Y Y y

Legend: Y = Applicable = Not applicable Notes: 1. Large displacement and dynamic effects to be included where appropriate. 2. VIT, hull stresses will only be available from more complex hull models. Table 5.1 - Applicability of the suggested models 5.6.4

Modeling the Leg

The leg can be modeled as a 'detailed leg', an 'equivalent leg' or a combination of the two. The 'detailed leg' model consists of all structural such as chords, horizontal, diagonal and internal braces of the leg structure and the spudcan (if required). The 'equivalent leg' model consists of a series of colinear beam elements (stick model) simulating the complete leg structure. It is recommended that the leg model(s) be generated in accordance with the following: a) 'Detailed Leg' Model

The coordinates of the ts for this model are to be defined by the intersection of the chord and brace centerlines. For ts where there is more than one brace, it is unlikely that there will be one (1) common point of intersection between the braces and chord. In this instance, it is usually sufficient to choose an intermediate point between the chordlbrace centerline intersections. Gusset plates normally need not be included in the structural leg model, however their effects may be taken into in the calculation of member and t strength checks.

Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 b) 'Equivalent Leg' Model

Page 49

The leg structure can be simulated by a series of colinear beams with the equivalent cross sectional properties calculated using the formulas indicated in Figure 5.1 or derived from the application of suitable 'unit' load cases (see Commentary C5.5) to the 'Detailed Leg' model described in 5.6.4 (a). Where such a model is used, detailed stresses, pinion loads, etc. will be derived either directly or indirectly from a 'detailed model'. c) 'Combination Leg' model

To facilitate obtaining detailed stress, pinion loads, etc. directly, a 'detailed leg' model can be generated covering the region between the guides, and extending at least 4 bays below and, where available, at least 4 bays above this region. The remainder is then modeled as an 'equivalent leg'. Care is required to ensure an appropriate interface and consistency of boundary conditions at the connections. The 'detailed leg'/'equivalent leg' connection should be modeled so that the plane of connection remains a plane after the leg is bent. Note: The leg stiffness used in the overall response analysis may for a contribution from a portion of the rack tooth material. Unless detailed calculations indicate otherwise, the assumed effective area of the rack teeth should not exceed 10% of their maximum cross sectional area. When checking the capacity of the chords the chord properties should be determined discounting the rack teeth. 5.6.5

Modeling the Hull

The hull structure should be modeled so that the loads can be correctly transferred to the legs and the hull flexibility is represented accurately. Recommended methods are given below: a) Detailed Hull Model

The model can be generated using plate elements in which appropriate directional modeling of the effect of the stiffeners on the plates should be included. The elements should be capable of carrying in-plane and, where applicable, out-of plane loads. b) Equivalent Hull Model

Alternatively, the hull can be modeled by using a grillage of beams. Deck, bottom, side shell and bulkheads can be used to construct the grillage. The properties of the beam can be calculated based on the depth of the bulkheads, side-shell and the 'effective width' of the deck and bottom plating. Attention should be paid to the inplane and torsional properties due to the continuity of the deck and bottom structures. 5.6.6

Modeling the HulllLeg Connection

The hulllleg connection modeling is of extreme importance to the analysis since it controls the distribution of leg bending moments and shears carried between the upper and lower guide structures and the jacking or fixation system. It is therefore necessary that these systems are properly modeled in of stiffness, orientation and clearance. For the 'Equivalent 3-stick-Ieg model'


Page 50

a simplified derivation of the equivalent leg-hull connection stiffness may be applicable. For jack-ups with a fixation system, the leg bending moment will be shared by the upper and lower guides, the jacking and the fixation systems. Normally the leg bending moment and axial force due to environmental loading are resisted largely by the fixation system because of its high rigidity. Depending on the specified method of operation, the stiffnesses, the initial clearances and the magnitude of the applied loading a portion of the environmental leg loading may be resisted by the jacking system and the guide structures. Typical shear force and bending moment diagrams for this configuration are shown in Figure 5.2. For jack-ups without a fixation system, the leg bending moment will be shared by jacking system and guide structure. For a fixed jacking system, the distribution of moment carried between the jacking system and guide structure mainly depends on stiffness of the jacking pinions. Typical shear force and bending moment diagrams this design are shown in Figures 5.3 and 5.4.

the leg the for

For a floating jacking system, the distribution of leg bending moment carried between the jacking system and guide structure depends on the combined stiffness of the shock pads and pinions. Typical shear force and bending moment diagrams for this design are shown in Figure 5.5. The hull/leg connection should be modeled considering the effects of guide and system clearances, wear, construction tolerances and backlash (within the gear-train and between the drive pinion and the rack). The following techniques are recommended for modeling hull/leg connections (specific data for the various parts of the structure may be available from the designers data package): Detailed modeling a) Upper and Lower Guides - The guide structures should be modeled to restrain the chord member horizontally only in directions in which guide occurs. The upper and lower guides may be considered to be relatively stiff with respect to the adjacent structure, such as jackcase, etc. The nominal lower guide position relative to the leg may be derived using the sum of leg penetration, water depth and airgap. It is however recommended that at least two positions are covered when assessing leg strength: one at a node and the other at the midspan. This is to allow for uncertainties in the prediction of leg penetration and possible differences in penetration between the legs. The finite lengths of the guides may be included in the modeling by means of a number of discrete restraint springs/connections to the hull. Care is required to ensure that such restraints carry loads only in directions/senses in which they can act. Alternatively the results from analyses ignoring the guide length may be corrected, if necessary, by


Page 51

modification of the local bending moment diagram to allow for the proper distribution of guide reaction, see Figure 5.6. b) Jacking Pinions - The jacking pinions should be modeled based on the pinion stiffness specified by the manufacturer and should be modeled so that the pinions can resist vertical and the corresponding horizontal forces. A linear spring or cantilever beam can be used to simulate the jacking pinion. The force required to deflect the free end of the cantilever beam a unit distance should be equal to the jacking pinion stiffness specified by the manufacturer. The offset of the pinion/rack point from the chord neutral axis should be incorporated in the model. c) Fixation System - The fixation system should be modeled to resist both vertical and horizontal forces based on the stiffness of the vertical and horizontal s and on the relative location of their associated foundations. It is important that the model can simulate the local moment capacity of the fixation system arising from its finite size and the number and location of the s. d) Shock Pad - Floating jacking systems generally have two sets of shock pads at each jackcase, one located at the top and the other at the bottom of the jackhouse. Alternatively shock pads may be provided for each pinion. The jacking system is free to move up or down until it s the upper or lower shock pad. In the elevated condition, the jacking system is in with the upper shock pad and in the transit condition it is in with the lower shock pad. The stiffness of the shock pad should be based on the manufacturer's data and the shock pad should be modeled to resist vertical force only. It should also be noted that the shock pad stiffness characteristics may be nonlinear. e) Jackcase and associated bracing - The jackcase and associated bracing should be modeled based on the actual stiffness since it has direct impact on the horizontal forces that the upper guide can resist. Note: Where the hull is not modeled it is normally suitable to earth the base of the jackcase and associated bracing, the foundations of the fixation system and the lower guide structures at their connections to the hull. Simple modeling f) For applications such as those described in Section 5.6.3 c) (Equivalent 3-stick-Ieg model) a simplified representation of the hull to leg connection is required. In this

instance the rotational stiffness may be represented by rotational springs and, where applicable, horizontal and vertical stiffnesses by linear springs. Where these are derived from a more detailed modeling, as described above, it is important that suitable loading levels (typical of the cases to be analyzed) are selected so that the effects of clearances, etc. do not dominate the result. Hand calculations may also be applicable. See Section C5.5 in the Commentary.


5.6.7

Page 52

Modeling the Spudcan

When modeling the spudcan, rigid beam elements are considered sufficient to achieve an accurate load transfer of the seabed reaction into the leg chords and bracing in the area between upper and lower guides. It should be noted that, due to the sudden change in stiffness, rigid beams can cause artificially high stresses at the leg to spudcan connections. Hence the modeling and selection of element type should be carefully considered when an accurate calculation of chord stresses is required in this area. For a strength analysis of the spudcan and its connections to the leg it may be appropriate to develop a separate detailed model with appropriate boundary conditions. 5.7

Load Application The loads and load effects to be included in the analysis, with their designators used in Section 8 in ( ), comprise: a) Self weight and non-varying loads (0), variable and drilling loads (L). b) Wind loads (E). c) Hydrodynamic wave-current loads (E). d) Inertial loads due to dynamic response (On). e) Second order effects (associated with D,L,E & Dn). These are discussed in tum below.

5.7.1

Self weight. variable and drilling loads

Depending on the initial positions of the legs with respect to guide clearances, and the operation of the jacking and fixation systems (if fitted), the distributed hull loading and stiffness will lead to hull sagging which may impose bending moments on the legs which remain present for the remainder of the period on location. Such moments should be considered in the site assessment analyses, and will be larger in shallow waters where the leg extension below the hull is small and consequently the leg bending stiffness is higher. To correctly capture these effects the hull loads should be applied to the model in such a manner as to represent their correct vertical and horizontal distribution. If dynamic analyses are to be performed all weights should be represented by means of masses together with vertical gravitational acceleration. It is generally appropriate to apply these masses by means of factored element self-weight with additional correction masses applied as necessary to obtain the correct total mass and center of gravity. Alternatively, it may be sufficient to apply point masses at the node points of the model. It is noted that an F.E. model with distributed hull stiffness and loading will incorporate

hull sag effects if the hull and variable gravity loading is 'turned on' with the unit defined in its initially undeflected shape at the operating airgap. It should be


Page 53

verified that the amount of hull sag moment arising is applicable, given the operating procedures pertaining to the unit. It may be necessary to apply corrections to the final results for any discrepancies in the hull sag induced loadings. Further guidance is given in Section 5.3.3 of the Commentary.

5.7.2

Wind loads The wind loading on the legs above and below the hull may be applied as distributed or nodal loads. Where nodal loads are used a sufficient number of loads should be applied to reflect the distributed nature of the loading and it should be ensured that the correct total shear and overturning moment is applied on each leg. Similarly the wind loading on the hull and associated structure may be applied as distributed or nodal loads. The application should ensure the correct total shear and overturning moment is applied to the hull.

5.7.3

Hydrodynamic wave-current loads The wave-current loading on the leg and spudcan structures above the mudline may be applied as distributed or nodal loads. Where nodal loads are used the application should ensure the correct total shear and overturning moment on each leg, and reflect the distributed nature of the loading.

5.7.4 Inertial loads due to dynamic response When the dynamic approach (see Section 7) leads to the explicit determination of an inertial loadset, this should be applied to the hull model. In simpler dynamic approaches the inertial load may be represented by a single lateral point loading acting at the hull center of gravity, or by a number of point loads applied to other parts of the hull having the same line of action. In more complex approaches a more complete distributed load vector may be applied to the hull and legs.

5.7.5

Second order effects Methods for including P-Li effects are described in Section 5.5.

-. !=i

'"I1

en

VI

~

.

FIG 5.1.a

FIG.S.1.b _. - - - -

'.

~

EQUIVALENT SHEAR AREA FOR TWO DIMENSIONAL LATTICE STRUCTURES EQUIVALENT SHEAR AREA. ISTRUC rURE

4~

A.

(i "\ I

;;~

5

C.

,

,

(I+V) sh 2

A Qi =

h'

d'

At> N

+ 8Av

A.

0'

" fN 3L,,) B.

(l+v~ sh 2

AQi =

---_ ....-

/.

~~

l

~~~~l]

d3

53

4Ao

12AC

E.

AQi=

3

S3 d h -+--+-2Ao 6 AC 2 Av

s II

\~i

,

I

3

--h

--~9

Y

mAC,

AQy= AQz- -fAOi Iy .. IZ-"I2 ACi h 2 Ir .. "I~ AQi h 2

h

I

I

Oi

I

I

Y

I

AACi '"

/

',AQi

" ~ " '.!"

'~/

'"

...~ ~ .- '

i ~ ~

'"'0 ~

l4.

~.

~ "'I V:l ~.

A-4 ACi AQy. AQz == 2 AOi Iy'" Iz .. ACi h 2 IT-AQi h 2 A-4 ACi AQy_ AQz .. 2 AOi Iyatlz =ACi h2 IT- AQj h 2

~ ~ (')

'S; (') ;x:..

~ ~

~

~

;:::,;

~~

~~

J'V~

i:i'~

;::$"I:::j

,,..!,2

,

'....!.a

I

h

~~

48 (l+v)Ia

AQi=

I

c.

(l+v) sh 2

V'

I

,

/

A"3 ACi

Z

- NAC ""3 -i=l,N

V

I

I

Ar.1

I I

'NO OF ACTIVE BAYS

~

~] I'..

D.

'<.'

,

Z

~

'<

C~~KH3 I

53 d3 --+-6AC 2AO

h

~~

B.

(I+v) sh 2

AQi = )

EQUIVALENT SECTION PROPERT ES OF 3-~ LA"TICE LEGS EQUIVALENT PROPERTIES. LEG.

Sl

!.si. ) 'Iid

(1+.!! s Ie

I

Note: l.)AQi IS DETERMINED FROM 5.1a. 2.) THE STIFFNESS PROPERTIES ARE THE SAME FOR ALL DIRECTIONS UNLESS THE CHORDS HAVE DIFFERENT AREAS.

<:::> ....

3.) ACi MAY HAVE TAKEN AS THE CHORD AREA INCLUDING A CONTRIBlITION FROM THE RACK TEETH. (SEE NOTE TO SECfION 5.6.4.)

N~

4.) THE FORMill.AE WILL BE INACCURATE IF SIGNIFICANT OFFSETS EXIST BETWEEN BRACE WORK POINTS. 5.) FOR BRACING ACCORDING TO 5.1.a.C THE EQUIVALENT BEAM END ROTATIONS WILL NOT BE ACCURATE; lHIS MAY BE IMPORTANT IF THIS MODELLING IS USED IN CONJUNCTION WITH ROTATIONAL FOUNDATION STIFFNESS.

o? ~

~


Page 55

;;;:

2

I-

<.I

....

I-

UI

III

Z

a:

a: ::::I u

'"

:>

!: 0

~

UI ;;;I Q

a:

~

Z

:Ii 0

:& <' Z

15

z:

IU

II

"-

a:

..: 1&1 :r::

~

...

III

CIJ

Z

I I

II

I J J I

1 '\

Figure 5.2: Leg shear force and bending moment - jack-ups with a fixation system


Page 56

z

0 j: (.)

<

..... ';I:

'"

II: II:

~

I-

z:

Ia.I

:10 0

(.)

::E

UI

<:)

;;0.

0« ~

0

tW

;;)

Q

Z

is Z

II::

'" Ia.I :t:

en

IU

.........

% OR

Z

I·

II

Ii

;

1 i

"".

It

c:t

".'"

ILl

10

JZ W

I II

I

; ~ z

;; w m

11

11\

Go.

o

Ia.I

oGo.

a.

o

Figure 5.3: Leg shear force and bending moment - jack-ups without a fixation system and having a fixed jacking system with opposed pinions


Page 57

z

0 j: C) 0(

l-

I-

lit

III

II:: II::

0

z:

:)

IJ w

Z

5!

:!

0

z:

> < is Z

~ C ~

III :::J

0

a:

<

III

",'"

a:

....C

l: I/)

...

%

II Z

II

II

""

",'"

'",-ID

• J

i

Figure 5.4: Leg shear force and bending moment - jack-ups without a fixation system and having a fixed jacking system with unopposed pinions


Page 58

z:

0

i= 0

c( ~

I-

=

Z

Ilol

II.!

:r

lie

til: 0

= :IE

"

(,,)

Z

1&1 :0-

« C z

~ III I-

a:

.= <£ '"

101 ::!

11.1 ::t:

II:

..,x:

l-

II

II

III

II

mD~

III "-

0

.

I

i . ; I

!

11.1

Z

:LI

~

...0

=

«

CIJ

w

I~

Q

a.

z o o

l:

tI)

J:

'-I"

%

1 I I

j: C

o

D-

IU

CIJ

f"l ~

#

j

~

It>

III II .

'

I I I : 1....1--'-.....r.--,........~

, ,

I i

IH

ill !B

, 11 I I I I I I , I , I , . '11-r-t-"-l..Ll......l..l.J~..LU..l..l-.LJ-L-kJ.-*

C'

o

~

u

..,c

~,

..

',:.~ ~~ .'"

KKKKKKkJ<J<J< J<J
I

..

lit

ez

;: Q

:u

en

o

iL II.

... ,: .' ,,'

I Z

.

1&1

.....'-.";

o 5

" II: III

~ ....

o

Figure 5.5: Leg shear force and bending moment - jack-ups without a fixation system and having a floating jacking system


Page 59

2Pfh

Bending of chord member may be derived by simple beam element analysis

s

2P/h

p

h

Guide positions

S'

Bending of chord member may be derived by simple beam element analysis

lified distribution

"!fguide reactions

Figure 5.6: Correction of point ed guide model for finite guide length (AfterDNV Class Note 31.5,1992 [6])


5

Page 60

GLOSSARY OF · STRUCTURAL ENGINEERING A ACi

= =

AD AQi AQy AQz Av d

= = = = = =

D Dn E h h IB

O2

= = = = = = = = = = = = = = = = =

P P PE Pg

= = = =

s

= = = = = =

~

IT Iy Iz L L N OT

01

{}s

!!.

v

Equivalent axial area of a leg for stiffness calculations. Area of chord including a contribution from the rack teeth (see note to Section 5.6.4.) Axial area of an inclined brace. Equivalent shear area of a leg face. Equivalent shear area of a leg in y direction. Equivalent shear area of a leg in z direction. Axial area of a brace perpendicular to the chords. Length of inclined brace or face to face distance between chords for lattice structures without inclined braces. Self weight and non-varying loads. Inertial loads due to Dynamic response. Environmental loads. Distance between chord centroids. Length of guide. Second moment of area of 'brace'. Second moment of area of longitudinal girder. Equivalent torsional constant of leg about longitudinal axis. Equivalent second moment of area of leg about y-y axis for stiffness calculations. Equivalent second moment of area of leg about z-z axis for stiffness calculations. Variable loads. Distance from the spudcan reaction point to the hull vertical center of gravity. Number of bays, used in determination of equivalent shear area AQ. Total horizontal offset of leg base with respect to hull 0 1 +0 2 Offset of leg base with respect to hull due to leg-hull clearances. Offset of leg base with respect to hull due to maximum hull inclination permitted by the operating manual. Average axial load in the legs at the hull (total leg load divided by number of legs). Guide reaction. Euler buckling load of an individual leg. Total effective gravity load on legs at hull, including the hull weight and weight of legs above hull. Leg bay height (distance between brace nodes). Linear elastic first order displacement of hull. Approximate hull displacement including P-L1 effects {}s /(1 - PIPE) Poissons ratio for the material 0.3 for steel.

Recommended Practicefor Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002

Page 61

6

CALCULATION METHODS· GEOTECHNICAL ENGINEERING

6.1

Introduction

6.1.1

Section 6 addresses three groups of geotechnical areas of concern which are discussed in the following subsections: 6.2 Prediction of footing penetration during preloading. 6.3

Jack-up foundation stability after preloading.

6.4 Other aspects of jack-up foundation performance during or after preloading. 6.1.2

Where geotechnical analyses are performed they should be based on geotechnical data obtained from a site investigation incorporating soil sampling and/or in-situ testing (see Section 3.16).

6.1.3

Uncertainties regarding the geotechnical data should be properly reflected in the interpretation and reporting of analyses for which the data are used.

6.1.4 The majority of spudcans are effectively circular in plan but other spudcan geometries are not uncommon. Typical spudcan designs are illustrated in Figure 6.1. The bearing capacity formulas given in this section are consistent with 'circular' spudcan footings without skin-friction on the leg. Due consideration should be given to the tapered geometry of most spudcans for bearing capacity assessment. Note: which are not defined in the text may be found in the Glossary to this Section. 6.2

Prediction of Footing Penetration During Preloading

6.2.1

Analysis Method

The conventional procedure for the assessment of spudcan load/penetration behavior is given in the following steps: 1. Model the spudcan.

2. Compute the vertical bearing capacity of the footing at various depths below seabed using closed form bearing capacity solutions and plot as a curve. 3. Enter the vertical bearing capacity versus footing penetration curve with the specified maximum preload and read off the predicted footing penetration. For conventional foundation analyses the spudcan can often be modeled as a flat circular foundation. The equivalent diameter is determined from the area of the actual spudcan cross section in with the seabed surface, or where the spudcan is fully embedded, from the largest cross sectional area. Foundation analyses are then performed for this circular foundation at the depth (D) of the maximum cross sectional area in with the soil. (See Figure 6.2). Alternative shapes, e.g. tubular legs, should be treated as appropriate.

Page 62


r

2.83m

17. 8m

4

Figure 6.1: Typical spudcan geometries

Figure 6.2: Spudcan foundation model

10.lm


Page 63

The depth of spudcan penetration is usually defined as the distance from the spudcan tip to the mudline. It is therefore necessary to correct for this when referring to the analytical foundation model. The possibility of soil back-flow over the footing should be considered when computing bearing capacity. In very soft clays complete back-flow may occur whereas in firm to stiff clays and granular materials, where limited footing penetration may be expected, the significance of back-flow diminishes. Back-flow in clay may be assumed not to occur if:

Nc us D~- y'

where, in this case, Cus is taken as the average undrained cohesive shear strength over the depth of the excavation, N is a stability factor and y' is the submerged unit weight of the soil. Conservative stability factors in uniform clays, as a function of excavation depth and diameter, are summarized in Figure 6.3. Alternative stability factors are given in the Commentary. For spudcan penetration analyses it is recommended that conservative criteria are used and the excavation depth be considered as the depth to the maximum spudcan bearing area. Both the bearing capacity analyses and the above back-flow analysis are based on simple solutions developed for other geotechnical purposes or foundation conditions. These differences should be recognized and are discussed further in the Commentary. The equations given in the following sections may be considered with or without soil back-flow over the footing. The additional load from back-flow on the footing increases the maximum penetration. In general two cases can be distinguished: Immediate back-flow Hole side walls collapse after the installation phase. For deeply penetrated footings the effect of side wall collapse after preloading will be to significantly reduce the ultimate vertical bearing capacity of the foundation. Where relevant this phenomenon should be considered. For spudcan penetration analyses the ultimate vertical bearing capacity, Fv, may be determined at a series of spudcan penetration depths according to the criteria given in Sections 6.2.2 to 6.2.6.


Page 64

Undrained shear strength

C

C

T

.D

'B. 2

D

y'

1

I~

:

_._._._._:

u

+

D_._._._... _._._._.

constant strength profile

Nonnal consolidation strength profile

9

iz 8

v-- l----M;;crhof (1972) /

5 4

1/

o

V

/

Unstable: D~ Nc'us_

2

4 ~

I I

6

D Diameter B

8

I

10

12

--4

Figure 6.3: Stability factors for cylindrical excavations in clay 6.2.2

Penetration in Clays

The ultimate vertical bearing capacity of a foundation in clay (undrained failure in clay,


Page 65

Po'

tt t

A,V ~B~

~B~

No backflow of soil

Full backflow of soil

Figure 6.4: Spudcan bearing capacity analysis

6.2.3

Penetration in Silica Sands The ultimate vertical bearing capacity of a circular footing resting in silica sand or other granular material can be computed by the following equation; Fv =(0.5 y'B Ny Sy dy + Po' Nq Sq dq)A The maximum preload is equal to the ultimate vertical bearing capacity, F v , taking into the effect of backflow, Fo'A, and the effective weight of the soil replaced by the spudcan, y'V (see Commentary) i.e.: VLo =Fv - FaA + y'V See Figures 6.4 and note that the -F'aA + y'V should always be considered together. Typically observed load-penetration data for large diameter spudcans suggest that reduced friction angles may be applicable for this analysis method. To for this it is appropriate to reduce the laboratory derived by 5°. Further recommendations on the selection of values are given in the Commentary together with a discussion regarding the use of alternative bearing capacity factors.

6.2.4

Penetration in Carbonate Sands Penetrations in carbonate sands are highly unpredictable and may be minimal in strongly cemented materials, or large, in uncemented materials. Extreme care should be exercised when operating in these materials. Further discussion regarding these soil conditions is provided in the Commentary.

6.2.5

Penetration in Silts It is recommended that upper and lower bound analyses for drained and undrained

conditions are performed to determine the range of penetrations. The upper bound solution is modeled as a loose sand and the lower bound solution as a soft clay. Cyclic loading may significantly affect the bearing capacity of silts. See discussion in Commentary.

I

Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 6.2.6 Penetration in Layered Soils

Page 66

Three 'basically different foundation failure mechanisms are considered m spudcan predictions in layered soils: 1. General shear. 2. Squeezing. 3. Punch-through. The first failure mechanism occurs if soil strengths of subsequent layers do not vary significantly. Thus an average soil strength (either Cu or <1» can be determined below the footing. The footing penetration versus foundation capacity relationship is then generated using criteria from Sections 6.2.2 through 6.2.5. Criteria for the other two failure mechanisms (squeezing and punch-through) are given below. The last condition is of particular significance since it concerns a potentially dangerous situation where a strong layer overlies a weak layer and hence a small additional spudcan penetration may be associated with a significant reduction in bearing capacity. 6.2.6.1 Squeezing of clay

On a soft clay subject to squeezing overlaying a significantly stronger layer (Figure 6.5), the ultimate vertical bearing capacity of a footing given by Meyerhof [8] is: For no back-flow conditions: Fv=A{(a+

bB T

I.2D

+ B ) cu + Po'} ~A{Ncscdecu+Po'}

and for full back-flow conditions:

bB 1.2D + - - ) c u} + Vy' ~ A{Nc Sc de cu} + Vy' T B where the following squeezing factors are recommended: a =5.00 b =0.33 and C u refers to the undrained shear strength of the soft clay layer. Fv = A{(a + -

:, st~ong soil I4--B~

No bacldlow of soil

, strong soil jif-B~


Figure 6.5: Spudcan bearing capacity analysis - squeezing clay layer

I I

Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Page 67 Rev 2, Jan 2002 It is noted that the lower bound foundation capacity is given by general failure in the clay

layer (right hand side of equation), and that squeezing occurs when B ~ 3.45T(l +l.lDIB). The upper bound capacity (for T<
13

See Figure 6.6. For the evaluation of punch-through potential for deep footings, and to achieve compatibility with the equations used for homogeneous clays, the following equations are recommended: For no back-flow conditions: Fv =A {3 H

13

Cu,t

+ Ne Se (1 + 0.2 D+H B ) Cu,b + Po'} ::;; A(Ne Se de Cu,t + Po')

and for full back-flow conditions:

H B

Fv =A [3 -

Cu,t

+ Ne Se (1 + 0.2

D+ H, N ' ) Cu,b] + YV ::;; A e Se de Cu,t + YV B

·.

Po'

A,V

***

Cu,t

Cub ,

A,V H

Strong cla~ Weak clay

1'4 Ilol B No backflow of soil

:t

Strong clay Weak clay

I'f

Ilol B Full backflow of soil

Figure 6.6: Spudcan bearing capacity analysis - finn clay over weak clay

I

Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Page 68 Rev 2, Jan 2002 6.2.6.2 It is noted that the condition (finn clay over soft clay) can also be "man-made" as in some clays artificial crusts can fonn during delays in the installation procedure. Caution is therefore required in situations where soil sampling/testing is perfonned from a jack-up prior to preloading.

6.2.6.3 Punch-through: Sand overlying clay The ultimate vertical capacity of a spudcan on a sand layer overlying a weak clay layer can be computed using: For no back-flow: Fv = Fv,b - A Hy' + 2

H

B (Hy' + 2 p'o) Kstan<j> A

and for full or partial back-flow: Fv =Fv,b - A Hy' - A I y' + 2 H (Hy' + 2 p'o) Kstan<j> A B where; Fv,b

is determined according to Section 6.2.2 assuming the footing bears on the surface of the lower clay layer, with no back-flow. .

See Figure 6.7. The coefficient of punching shear, K s, depends on the strength of both the sand layer and the clay layer. For practical purposes a lower bound for the tenn Ks tan<j>, applicable to the onset of punch-through, can be approximated by: Ks tan<j> =: 3culBy' An alternative analysis method is described in the Commentary.

:::::: :

::::::,::::::: ::::::::::..

.. ... .

:;:::..

:

.:. .:

Po'

**t

I

A,V

"'.:::

A,V

: :

.:.

,:'::.

I

I

~B---JII

No backHow of soil


Figure 6.7: Spudcan bearing capacity analysis - sand over clay

Y=P'o D


Page 69

6.2.6.4 Three Layered Systems The foundation bearing capacity for a spudcan resting on three soil layers can be computed using the squeezing and punch-through criteria for two layer systems. Firstly the bearing capacity of a footing with diameter B resting on top of the lower two layers is computed. These two layers can then be treated as one (lower) layer in a subsequent two layer system analysis involving the (third) upper layer. For further explanation see Figure 6.8. Analysis 2 Qv

Layer I

Analysis 1 Qv

Layer 2

Layer 3

Use 2 layer bearing capacity procedures for both analyses Analysis 2

Analysis 1

Layer lover (Layer 2 and 3)

Layer 2 over layer 3

Figure 6.8: Spudcan bearing capacity analysis - three layer case


6.3

Foundation Stability Assessment

6.3.1

Approach

Page 70

The overall foundation stability may be assessed using a phased method with three steps increasing in order of complexity (See Figure 6.9): - Step 1

Preload and Sliding Check (Section 6.3.2). The foundation capacity check is based on the preloading capability. Sliding of the windward leg is also checked. Loads from pinned footing analysis.

- Step 2

Bearing Capacity Check.

Step 2a

Bearing capacity check (Section 6.3.3), based on resultant loading, assuming a pinned footing. (see Section 5.3.1). Also check sliding.

Step 2b

Bearing capacity check (Section 6.3.4),including rotational, vertical and translational foundation stiffness.

- Step 3

Displacement Check (Section 6.3.5). The displacement check requires the calculation of the displacements associated with an overload situation arising from Step 2b.

Any higher level check need only be performed if the lower level check fails to meet the foundation acceptance criteria given in Section 8.3. The following sections give details regarding the three phased acceptance procedure. However, there are certain aspects which are not covered in these sections which may require further consideration. Some of the more common ones are listed below: - Soils where the "long term" (drained) bearing capacity is less than the "short tenn" (undrained) capacity. This may be the case for overconsolidated cohesive soils (silts and clays) with significant amounts of sand seams. - Where soil back-flows over the spudcan after the preload installation phase, (silts, clays). - If a reduction of soil strength due to cyclic loading occurs. This can be of particular

significance for silty soils and/or carbonate materials. - If an increase in spudcan penetration occurs, due to cyclic loading, where a potential

punch-through exists.

- In soils with horizontal seams of weak soils located beneath the spudcan it is recommended that the lateral bearing capacity/sliding stability of the foundation is verified. If any of the above circumstances exist further analysis is required.

In the case of partial spudcan embedment, (e.g. sandy soils), additional footing embedment may result in a considerable increase in bearing capacity.


Page 71

erlonn structlJ!"al analysis assuni~ pirned footi~. See Section 5.

-

-

-

-

SUggested path to shoW decisIon mt to ~t Ulit based (rI. sirrple analysis

method

OK

PeriOI'Dl structural analysis 1 - - - - - - - 1 assuni~ mnent fixity with I---,--+--"

I

~

elastic vertical ard horiz-
_____~

I

~~~_1~ _ _ _ _ _ _ J

I I I

r--------I

~~--~~~

I

Perfonn structural lnIlysis assuuire fu[l non-linear fOUl::lation stiffnesses_ See 6.3.5

I

L ___ _

Fou-dIIti on NOT shOW'l

to be Acceptabl e

Figure 6.9: Foundation stability assessment

Fardati(rl

Acceptable

Page 72


6.3.2

Ultimate bearing capacity for vertical loading - Preload Check (Step

1)

Except as discussed in 6.3.1, when the horizontal load is small, the ultimate vertical bearing capacity under extreme conditions is assumed to be the same as the maximum footing load during preloading, (VuJ The minimum requirements for VLo are given in Section 8.3.1.3 or 8.3.2 as applicable.

6.3.3

Bearing Capacity/Sliding Check - Pinned footing (Step 2a) A reduction in vertical bearing capacity, Fv, of a footing occurs when it is simultaneously subjected to horizontal loading, QH, and moment loading, QM. The latter is ignored in Step 2a analyses as the footings are considered to be pinned. The verticalfhorizontal capacity envelope, FVH, for sands and clays may be generated according to the following criteria, however, further discussion with regard to the analytical applicability is provided in the Commentary.

6.3.3.1 Ultimate Verticallhorizontal bearing capacity envelopes for spudcanfootings in sand: The general ultimate verticallhorizontal bearing capacity envelope for jack-up footings in sand is as follows: FVH ::: A (0.5 y' B Ny Sy iy dy + Po'Nq Sq iq dq) During the preloading phase it may be assumed that no horizontal load acts on the foundation and that the ultimate vertical bearing capacity of the soil is in equilibrium with the applied footing installation load, V 10. The applied footing installation load should include the effect of back-flow and spudcan buoyancy i.e. VLo ::: Fv - Fo'A + y'V. In this instance the inclination factors assume values of unity and the remaining telTI1S may be defined. Substituting for iq and iy the appropriate relationship may be written for generation of the foundation capacity for combined vertical and horizontal loading as:

This may be solved by the use of assumed values for (FHlFvH ) designated (FHlFvH )* . For example use (FHlFvH )* ::: 0.00,0.04,0.08,0.12, etc. For these values corresponding FVH values may be determined. The correct FH values may then be determined as FVH and (FHlFvH )* are known, e.g. for (FHlFvH )* ::: 0.12, FH* ::: 0.12 FVH*. The corrected horizontal capacity, FH, may then be given as: FH ::: FH* + 0.5y' (kp - ka ) (hI + h2) As The sliding capacity envelope of a footing in sand is given by: FH ::: FvHtan[) + 0.5y' (kp - ka) (hI + h2) As where [) is the steel/soil friction angle which for a flat plate, [) ::: surfaced conically shaped spudcan [)::: <1>.

<1> -

5°, and for a rough


Page 73

6.3.3.2 Ultimate verticallhorizontal bearing capacity envelopes for spudcan; footings in clay The general equation for the horizontal and vertical bearing capacity envelopes for footings in clay is as follows: FVH = A [(Ne Cu Se de ie) + Po' Nq Sq iq dq] Substituting for the inclination factors for a circular footing the equation may be written as: FVH = A {Ne C u Se de [1 - (1.SFH*lNeAc u)] + Po' Nq Sq (1 - FH*IFVH)1.5 dq} The ultimate bearing capacity envelope under inclined loading may be determined by substituting values of FVH and solving for FH*. FH may then be given as: FH = FH* + (c uo + cUl)As Footing sliding capacity in clay: When 0 ::; Qv ::; 0.5 Fv the sliding capacity in clay may be conservatively assumed constant, determined by: FH = Ac uo + (c uo + cuDAs

6.3.3.3 Ultimate verticallhorizontal bearing capacity envelopes for spudcanfor spudcanfootings on layered soils. The above formulas (Sections 6.3.3.1 through 6.3.3.2) can also generally be used to make a conservative estimate of the ultimate FvWFH relationship for layered soils by considering failure through the weakest zones in such a soil profile. The bearing capacity of layered soils may be determined using the principles of limiting equilibrium analysis or the finite element method.

6.3.3.4 Settlements resulting from exceedence of the capacity envelope Vertical settlement andlor sliding of a footing can occur if the storm load combination is in excess of the (FvWFH) resistance envelope computed for the spudcan at the penetration achieved during installation. Such settlements can result in a gain of (FVWFH) bearing capacity, e.g. in silica sands. However, the integrity of the foundation may decrease in the situation where a potential punch-through exists, e.g. where dense sand overlies soft clay. More thorough analyses are required for complex andlor potentially dangerous foundation conditions of the type listed in Section 6.3.1.

6.3.4

Footing with moment fixity and vertical and horizontal stiffness (Step 2b) Foundation fixity is the rotational restraint offered by the soil ing the foundation. The degree of fixity is dependent on the soil type, the maximum vertical footing load during installation, the foundation stress history, the structural stiffness of the unit, the geometry of the footings and the combination of vertical and horizontal loading under consideration. Inclusion of foundation fixity in an assessment incorporates a check on bearing capacity in of vertical and horizontal (sliding) capacities. The amount of rotational fixity is

I


Page 74

not directly involved in a checking equation, but it serves to modify the forces (beneficially) in both the foundation and structure. The bearing and sliding checks are performed implicitly through the use of the yield function and explicitly through the bearing capacity and sliding checks described in Section 6.3.3. Uncertainties in soil properties should be considered when including fixity in assessments. Where data reliability is uncertain, an upperllower bound sensitivity analysis should be performed. For performing structural analysis, horizontal and vertical spring stiffnesses should be included in addition to the rotational stiffness (see Section 5.3). The springs should be applied to the spudcan point as defined in Section 5.2. The calculation of fixity should be based on factored environmental loading including dead, live, environmental, inertial and p-~ loads. 6.3.4.1 Calculation procedures ing for moment fixity - See also 6.3.4.6

The interaction of vertical, horizontal and rotational forces has been modeled based on a plasticity relationship (References C6 [48] through [52]). The plasticity relationship can for moment softening at high load levels, unloading behavior and workhardening effects. This type of foundation modeling is preferable if foundation fixity is to be included directly in a time-domain analysis. For a pseudo-static analysis, a simplified application of this full plasticity analysis is described in this section. This simple approach can be used to create moment loads on the spudcan by inclusion of a simple linear rotational spring to generate moments at the spudcan. The moment thus induced on the spudcan is limited to a capacity based on the yield interaction relationship among vertical (Qv), horizontal (QH) and moment (QM) loads acting at the spudcan. This simple procedure is described in the following steps: 1. Include vertical, horizontal and (initial) rotational stiffnesses (linear springs) to the

analytical model and apply the gravity and factored metocean and inertial loading. 2. Calculate the yield interaction function value using the resulting forces at each spudcan. For extreme wave analysis, the result will likely indicate the force combination falls outside the yield surface. In this case, reduce the rotational stiffness (arbitrarily) and repeat the analysis. 3. Continue with step 2 until the force combination at each spudcan lies essentially on the yield surface. If the moment is reduced to zero, and the force combination is still outside the yield surface, then a bearing failure (either vertical or horizontal) is indicated. 4. If a force combination initially falls within the yield surface, the rotational stiffness must be further checked to satisfy the reduced stiffness conditions in Section 6.3.4.3. The following sections are applicable to traditional spudcan designs. Information on spudcans fitted with skirts can be found in references C6 [48] through [51].

II

Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Page 75 Rev 2, Jan 2002 6.3.4.2 Ultimate Vertical/horizontal/rotational capacity interaction; function for spudcan footings in sand and clay

For shallow embedment for both sand and clay, the yield interaction is defined by the following expression:

16 [F~ J[1- F~ ][1-F;: ]-[~:J [~:J =0

where VLo is taken to be equal to the vertical spudcan load achieved during preloading and HLo and MLo are defined as follows: For sand:

For clay:

HLo

= (C l 1 C 2)(VLo 14) = O.l2VLo

MLo

=C lVLo B/4 = 0.075VLoB

HLo MLo

=cuoA + (cuo + Cui) As = O.IVwB

with C l = 0.3, C 2 =0.625

Note that in the above expression for the yield surface, if a load combination (QV,QH,QM) satisfies the equality then (QV,QH,QM) = (FVHM, F HM , FM). The load combination (QV,QH,QM) lies outside the yield surface if the left-hand side is less than zero. Conversely, the load combination lies inside the yield surface if the left-hand side is greater than zero. An alternative expression of the yield surface gives the maximum spudcan moment as a function of the horizontal and vertical loads. Thus, for a given vertical and horizontal load combination, the moment at a spudcan cannot exceed the value defined below.

F=MLDH ~Jl- ~~][I- ~~] -[ ~:JT' M

Embedded footings in clay achieve greater moment and sliding capacities as compared to shallow penetrations in clay. For fully or partially penetrated spudcans, the yield surface at FVHMNLo<0.5 can be expressed as:

]2 =0 [ F ]2 - [F f2 M Lo

10- ~ . flHLo

M

where;

f, =

a+ a{ ~ ] 2(1 -

f2 = fl where suction (i.e. uplift resistance) is available, = 4[

F~ ]

[1- F;: ] where suction cannot be relied upon

a = 1.0 for soft clays =

0.5 for stiff clays (see over)


Page 76

a s for the degree of adhesion. Engineers may want to consider a values within the range 0.5-1.0 depending on site specific soil data, spudcan/soil interface roughness, etc. An a value less than 0.5 may be considered for situations such as a hard clay at the surface. In this case, the standard form of the yield surface should be considered. There is no existing data for deeply embedded footings in sand. The application of the yield surface calibrated to shallow penetrations will likely be conservative for the deep penetration case. 6.3.4.3 Estimation of rotational, vertical, and horizontal stiffness

An initial estimate for rotational stiffness, K3, which is applicable for a flat spudcan without embedment (Winterkom [10]) under relatively low levels of load is given below: G B3 K3 = r , flat spudcan with no embedment 3(1- v) Values for K3 for other cases are given in the Commentary. The selection of the rotational shear modulus, Gn is discussed in the Commentary (Note for the recommended values based on Dean, the appropriate units are kN-mlrad.) An upper or lower bound value should be selected as appropriate for the analysis being undertaken. For clays susceptible to cyclic degradation (OCR ~ 4) the soil rotational stiffness, calculated from the degraded static soil properties, may be multiplied by a factor of 1.25, Anderson [18]. If the load combination of (Qv,QH,QM) lies outside the yield surface, the linear rotational

stiffness at the spudcan must be reduced until the load combination lies on the yield surface. The reduction in stiffness is arbitrary and requires iterative analyses.

It should be noted that if the initial load combination (QV,QH,QM) lies outside the yield surface, the final value of the rotational stiffness is determined only by the requirement that the generated moment at the spudcan falls on the yield surface. If the load combination of (QV,QH,QM) lies inside the yield surface, the initial estimate of rotational stiffness should be reduced by a factor, fro The reduction factor is equal to unity when the moment and horizontal forces are zero. It is given by the following expression:

where rf is the failure ratio defined by:

Note that rf > 1.0 implies that the load combination (Qv,QH,QM) lies outside the yield surface. Under such conditions, the reduced stiffness factor is not applicable.

I


Page 77

For fully embedded foundations in clays at vertical load ratio FVHMNLo < 0.5, the failure ratio may be expressed as:

r,=

{[~J +[f~JT

where fl and f2 are as defined in Section 6.3.4.2 above, but replacing FVHM with Qv. Vertical and horizontal stiffnesses can be estimated from the Boussinesq elastic solutions for a rigid circular plate on an elastic half-space (assuming no embedment): 2G v B Vertical stiffness, KI = ---'-(I-v)

I6G h B(1-v) Horizontal stiffness, K2 = ---!!..--'----'(7 - 8v) Advice on the selection of appropriate values for Gy and Gh may be found in the Commentary. 6.3.4.4 Extension of the yield surface for additional penetration

On seabeds of silica sands, conical spudcans which are not fully seated may show a plastic moment restraint due to further penetration. The effect may be taken into for legs with QVNLo > O. The moment capacity Mp associated with further penetration is estimated as the minimum of Mps and Mpv, calculated as follows: M ps =0.075 B VLo(DIB)3 Mpv =0.15 B FVHM in which B is the plan diameter of the effective area after preload, and D is the plan diameter of the area when the spudcan is fully seated. The combined capacity should be checked against the modified yield function:

16[F~:HI-F~] [l_F~] -[~:J-[~J =0 For additional penetration of spudcans in clay, references C6 [49] and [52] provide workhardening modifications to the yield surface equations. Updated stiffnesses are determined through plasticity principles. 6.3.4.5 Deep Footing Penetration

For deep footing penetrations, typically experienced in soft clay conditions, the calculation of foundation fixity may be augmented with the inclusion of the lateral soil resistance on the leg due to soil back-flow over the spudcan. This lateral soil resistance is effectively added to the rotational elastic stiffness of the spudcan (as determined in Section 6.3.4.3), (Brekke [7]). The lateral soil resistance may be modeled based on concepts proposed by Matlock [17] for lateral soil resistance of piles. The jack-up leg may be modeled as an equivalent pile for purposes of determining "p-y", or load-deflection curves. The diameters of the individual (i.e., leg chords and braces) give appropriate characteristic dimensions for determining the p-y curves. The p-y curve for each member

Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Page 78 Rev 2, Jan 2002 is summed to form a p-y curve for the entire leg. Only one face of each leg should be assumed to be in with the soil and contribute to lateral resistance.

Given a set of p-y curves for the leg, the lateral force-deflection along the entire embedded leg section is thus determined. Typically, equivalent springs at each bay elevation are used to simplify the calculations. 6.3 .4.6 Calculation procedures ing for moment fixity - further details Structural analyses should for rotational, horizontal and vertical stiffnesses at all spudcans. The jack-up is then acceptable if the following conditions are met: 1.

Structural conditions satisfy acceptance criteria outlined in Section 8.1.

2.

Factored foundation loads Qv, QH satisfy, as applicable, the bearing capacity criteria in Sections 8.3.2 or 8.3.1.5.

3.

Factored foundation loads Qv, QH, QM satisfy the appropriate unfactored yield surface criterion from Section 6.3.4.2 or 6.3.4.4. Factored foundation loads exceeding this requirement are permitted provided that the soil-structure interaction model adopted accurately captures the expansion of the foundation yield surface after first yield, and that the large-displacement effects of associated structural displacements are taken into .

4.

The analysis ensures load & displacement compatibility between the foundation and the structure.

5.

The location is not prone to, or is protected from, scour so that the assumed fixity is assured.

Fixity may be included in the response simulation in three ways (Refer to Figure 6.11 below): 1.

By conservatively considering effects of changes to seabed boundary reactions only and ignoring any reduction in the dynamic response with pinned footings. In this approach quasi-static analyses are used in the iterations of the procedure given in Section 6.3.4.1 to derive the foundation rotational and horizontal secant stiffnesses with loadings obtained from the pinned foundation case including dynamics. This approach is not applicable if the inclusion of fixity brings the natural period closer to the wave period.

2.

By considering linearised fixity in SnOF or more detailed dynamic calculations and then carrying out a final quasi-static analysis with non-linear fixity using the procedure of Section 6.3.4.1. If this approach is adopted, care should be taken to ensure that the natural period with fixity does not fall at a cancellation point in the wave force transfer function (Sections 7.3.5.2, 7.3.5.4, C7.4 & Fig C7.1). Typically the initial linearised rotational stiffness for the dynamic analysis may be taken as 80% of value determined from the formulation in the first paragraph of Section 6.3.4.3. When this stiffness is adjusted to avoid wave force cancellation, the adjusted value may lie anywhere between 0% and 100% of the value from Section 6.3.4.3. This simplified approach does not capture the temporary reductions in stiffness which occur during plasticity events, but also does not capture the increased damping that is associated with these events; these two effects are considered to be largely self-cancelling. Given that care is taken to avoid wave force cancellation effects, it is


Page 79

considered that the dynamic response will be determined at a level which is either realistic or conservative. For further discussion of approaches which may be used to avoid cancellation and reinforcement effects refer to the Commentary Section C7.4. 3.

By considering the effects of the foundation fixity on both the dynamic response and the seabed reactions. This approach is more complete and may require a complex iterative calculation procedure. The following outline procedure may be adopted: a) Use a time-domain dynamic analysis to determine structural response and foundation loadings at each time step. b) Compute the foundation behaviour using a non-linear elasto-plastic model, such that at each time step the plastic and elastic portions of the behaviour are captured. If desired, this model may include hysteresis. This will likely require an iterative procedure. c) When plasticity occurs, the responses will be influenced by the load history. Consideration should be given to ensuring that the methodology used to determine the extreme values provides stable results. In cases where the analysis is intended to provide final results (rather than DAF's for application in subsequent analysis step) it may be appropriate to perform analyses for differing wave histories, and then determine the extremes from a procedure such as that given in C7.B.2.4.


'

Not OC

~------I

Page 80

.......--+-Ilk1it NOT acceptable

RU1 new d)InInic response 8'lal)'Sis usi~ Latest f~tion stlffnesses ard cletermir-e new inertial loadset

Perfom ~;·static ~ analysis incltl:tiJ"Q inertial toadset

calculate new rotational stiffnesses based CIn load CCJlbination (Q". QH' ~) (See 5ectiClnS 6.3.4.1 &6.3.'.2)

~"""'----1

Perlonn Step 3

Unit acceptable

Figure 6.10: Calculation procedure to for foundation fixity

Recommended Practice for Site Specific A ssessment of Mobile Jack-Up Units Rev 2, Jan 2002 Assume elastic spudcan response QM =K3• • Qv = K)· v' QH = K 2•

Page 81

h.

Not OK

Unit NOT acceptable

(Section 6.3.4.6 Option 1) Run iterative structural analysis using current inertialloadset and de-grade foundation stiffness until spudcan loads fall within foundation yield surface. Section 6.3.4.1

Simplified (Section 6.3.4.6 Option 2) Select initiallinearised fixity

Run dynamic analysis using linearised fixity and determine wave force transfer functions.

No

Select revised linearised fixity &lor change hull mass. Run non-linear elasto-plastic soil timedomain analysis and determine DAF from a number of differing storm simulations. Use resulting DAF to determine new inertial loadset. (Section 6.3.4.5 Option 3) Unit NOT acceptable

Unit acceptable

Figure 6.11: Calculation procedure to for foundation fixity


6.3.5

Page 82

Displacement Check (Step 3) Structural model with nonlinear soil response included When a Step 2 assessment results in an overload situation, Step 3 may be used to calculate the associated displacements and rotations from a full nonlinear loaddisplacement foundation model. The procedure should for the load redistribution resulting from the overload and displacement of the spudcan(s). The displacements derived from the analysis should be checked against the allowable displacements of the spudcans and should satisfy the following requirements: The spudcan vertical and horizontal displacements should not lead to unacceptable overturning or strength checks. The resulting rotation of the unit should neither exceed the limitations defined by the operating manual nor lead to the possibility of with any adjacent structure.


6.4

Other Aspects of Jack-Up Unit Foundation Perfonnance

6.4.1

Leaning Instability

Page 83

Leaning instability of jack-ups can occur during preloading operations in soft clays where the rate of increase in bearing capacity with depth is small. In deep water a potentially unsafe condition (comparable to a punch-through situation) may occur. However, the potential for such incidents may be discounted if appropriate installation procedures are adopted. These may, for example, include preloading the footings individually. Further discussion on leaning instability is included in the Commentary. 6.4.2

Footprint Considerations

The seabed depressions which remain when a jack-up is removed from a location are referred to as 'footprints'. The form of these features depends on several factors such as the spudcan shape, the soil conditions, the footing penetration achieved and the method of extraction. The shape, and the time period over which the fonn will exist, will also be affected by the local sedimentary regime. The positioning of spudcans very close to, or partially overlapping, footprints is not recommended. The difference in resistance between the original soil and the disturbed soil in the footprint area and/or the slope at the footprint perimeter, may cause the spudcans to slide towards the footprint. The resulting leg displacements could cause severe damage to the structure and, at worst, could lead to catastrophic failure. The situation could be complicated by the proximity of a fixed structure or wellhead. The following two operational sequences may be considered: a) Installation of an identical jack-up design to that previously used at a particular location: If a jack-up with identical footing geometry to the unit previously used is to be

installed, the re-positioning should not cause problems provided that the jack-up is located in exactly the same position as for the previously installed unit. Thus the footings would lie in the existing footprints. It is therefore necessary to ensure that reliable records are obtained of the exact location of existing footprints in relation to the well/jacket. If the new spudcan positions are not located directly over the footprints sliding of the

legs may occur with the potential consequences described above. b) Installation of a jack-up of different design to that previously used at a particular location: It is unlikely for two jack-up designs to have similar footing geometries.

It is therefore probable that it will not be possible to locate the spudcans exactly within the existing footprints. However, it may be possible to carefully position the jack-up on a new heading, and/or with one footing located over a footprint with the others in virgin


Page 84

soil, to alleviate the potential for spudcan sliding. Again reliable records of existing footprint locations (and depths) are required. Where it is not possible to locate the jack-up to avoid spudcan-footprint interaction special attention is required to minimize the potential sliding problem. Consideration may be given to infilling the footprints with imported materials. The material selection should recognize the potential for material removal, by scour, and the differences of material stiffness. Further discussion is included in the Commentary. 6.4.3

Scour Scour may occur when a footing or other object is installed on the seabed, and its presence causes increased local current velocities. The phenomenon is usually observed around spudcans which are embedded to a shallow level in granular materials at locations with high current velocities. Scour may partially remove the soil from below the footing, resulting in a reduction of the ultimate bearing capacity of the foundation and any seabed fixity. This is normally a gradual process and the effects of the reduced bearing capacity may not be apparent until during storm loading when (rapid) downward movement of the leg may occur. The effects of scour are potentially more severe when it occurs at a location where a potential for punch-through exists. There is no definitive procedure for the evaluation of scour potential and emphasis must usually be placed on previous operational experience. Further guidance is given in the Commentary. If scour is recognized to be a potential problem, then preventative measures should be

implemented. These should be adopted on a trial basis and include: a) Gravel dumping prior to installation provided the selected gravel gradation will not cause damage to the jack-up footing. b) Installation of artificial seaweed. c) Use of stone/gravel dumping, gravel bags or grout mattresses after installation.

Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 6.4.4 Seafloor Instability

Page 85

Seafloor instability may be caused by a number of mechanisms which may be interactive or act independently. The most frequent types of instability result in large scale mass movement, in the form of mudslides or slope failures. Such phenomena are often associated with deltaic deposits, and it is recommended that the advice of local experts is obtained when such situations are encountered. Liquefaction, or cyclic mobility, occurs when the cyclic stresses within the soils cause a progressive build up of pore pressure. The pore pressure within the profile may build up to a stage where it becomes equal to the initial average vertical effective stress. Foundation failure may result depending on the extent of pore pressure developed. Such failures may be manifested as continued foundation settlements or large scale failure of the soil mass as described above. In areas where liquefaction is known to be possible its potential must be assessed. For further guidance refer to the Commentary. 6.4.5

Shallow Gas

Gas in soils may originate from biogenic degradation or thermogenic diagenesis. Gas charged sediments may result in hazards during site investigation soil borings, reduced bearing capacity, unpredictable foundation behavior (due to seabed depressions or gas accumulations under the spudcans) and complications with shallow drilling operations, including blowouts. The presence of gas charged sediments may be identified by geophysical digital high resolution shallow seismic surveys using attribute analysis techniques. Any gas concentration should be avoided if it is located above the primary casing shoe level (generally 20 inch or 18.75 inch diameter casing) or the conductor pipe shoe level which are determined during the drilling program design. This is because neither of these holes are drilled under BOP control and, therefore, there is a risk of seabed cratering around the well which could result in the undermining of the footings in the event of a blowout. Of lesser risk is the potential for gas migration from depth to the surface outside the casing. Although this occurrence is uncommon the potential should not be discounted.


6.4.6

Page 86

Spudcan - Pile Interaction

For jack-ups located in close proximity to pile-founded platfonns, soil displacements caused by the spudcan penetration will induce lateral loading into the nearby piles. The amount of soil displacement will depend on the spudcan proximity (spudcan edge-to-pile distance), the spudcan diameter and penetration. If the foundation materials comprise either a deep layer of homogeneous finn to stiff clay or sand and if the proximity of the spudcan to the pile is greater than one spudcan diameter, then no significant pile loading is expected. When the proximity is closer than one spudcan diameter, then analysis by the platfonn owner is recommended to determine the consequences of the induced pile loading. Guidance regarding the analytical procedures available for assessing these spudcan induced pile loads is given in the Commentary.


6

Page 87

GLOSSARY OF - CALCULATION METHODS. GEOTECHNICAL ENGINEERING A

b Cu CuI

Cuo

cus Cu,b Cu,t

C1 C2

de

=

Spudcan effective bearing area based on cross-section taken at uppermost part of bearing area in with soil (see Figure 6.2). = Spudcan laterally projected embedded area. = Bearing capacity squeezing factor. = Adhesion. = Effective spudcan diameter at uppermost part of bearing area in with the soil (for rectangular footing B = width). = Bearing capacity squeezing factor. = Undrained cohesive shear strength at D + B/4 below mudline. = Undrained cohesive shear strength at spudcan tip. = Undrained cohesive shear strength at maximum bearing area (D below mudline). = Undrained cohesive shear strength at DI2 below mudline. = Undrained cohesive shear strength - lower clay below spudcan. = Undrained cohesive shear strength - upper clay below spudcan. : } Constants used in computation of HLo and VLo for sand.

= = = =

=

= = =

= = = = =

= =

= FVH FVHM FM

= =

=

Gv

=

Gh Gr

= =

h

hI

= =

=

= = = = =

Bearing capacity depth factor. 1 + 0.4 (DIB) for DIB ~ 1. 1 + 0.4 arctan (DIB) for DIB > 1. Bearing capacity depth factor. 1 + 2tanq,(1- sinq,)2 DIB for DIB ~ 1 1 + 2tanq,(1- sinq,)2 arctan(DlB) for DIB > 1 Bearing capacity depth factor = 1. Distance from mudline to spudcan maximum bearing area. Factor used in yield surface equation for embedded footings on clay. Factor used in yield surface equation for embedded footings on clay. Reduction factor on stiffness. Effective overburden pressure due to back-flow at depth of uppermost part of bearing area. Horizontal foundation capacity. Horizontal foundation capacity in combination with moment. Vertical foundation capacity. Ultimate vertical bearing capacity assuming the footing bears on the surface of the lower (bottom) clay layer with no back-flow. Vertical foundation capacity in combination with horizontal load. Vertical foundation capacity in combination with horizontal and moment load. Moment capacity of foundation. Shear Modulus for vertical loading. Shear Modulus for horizontal loading. Shear Modulus for rotational loading. Distance from rotation point to reaction point. Embedment depth to the uppermost part of the spudcan, (if not fully embedded =0). Spudcan tip embedment depth. Distance from spudcan maximum bearing area to weak strata below. (C I/C 2)(Vr.ol4), C I =0.3, C2 =0.625 (sand) Ac uo +(c uo + cuI)As (clay) Inclination factor (for q, =0). 1 - mPH/ACuNc

I


6

Page 88

GLOSSARY OF - CALCULATION METHODS. GEOTECHNICAL ENGINEERING (Continued)

=

iy I ka kp K 1,K2,K3

Ks L

m=

M1.o

Mpv n N Nc Nq Ny

Po' QH QM Qv rf Sc Sq Sy

T V V1.0 ex 8

Ov &t y'

e

<j> v

Inclination factor. = (1 - FHlFvH)m = Inclination factor. = (1 - FHlFvH)m+1 Height of soil column above spudcan. = Active earth pressure coefficient (for Cu = 0) = tan 2(45-<j>/2) = ive earth pressure coefficient = 1lka = Stiffness factors. = Coefficient of punching shear. = Foundation length, for circular foundation L=B. For strip footing - inclination in direction of shorter side. = (2 + BIL)/(1 + BIL) For strip footing - inclination in direction of longer side. (2 + IJB)/(1 + IJB) For circular footing = 1.5 = C 1VwB/4, C 1 =0.3 (sand) = O.lVwB (clay) = moment capacity associated with further spudcan penetration under environmental loading (equal to minimum ofMps and Mpv). = moment capacity when further spudcan penetration leads to fully seated spud conditions. = moment capacity under further spudcan penetration, when the actual vertical force is too low to reach fully seated conditions. = Iteration factor, ~ 2. = Stability factor. = Bearing capacity factor (taken as 5.14). Bearing capacity factor e7ttantan 2(45 + <j>/2) = Bearing capacity factor =2(Nq + l)tan<j> = Effective overburden pressure at depth, D, of maximum bearing area. = Applied factored horizontal load. = Applied factored moment load. = Applied factored vertical load. = Failure ratio. = Bearing capacity shape factor =(1 + (NqINc)(BIL» = Bearing capacity shape factor =1 + (BIL)tan<j> = Bearing capacity shape factor =1 - 0.4(B1L) ( = 0.6 for circular footing under pure vertical load). Thickness of weak clay layer underneath spudcan. = Volume of soil displaced by spudcan. = Maximum vertical foundation load during preloading. = Adhesion factor = 1.0 for soft clays, = 0.5 for stiff clays. = Steel/soil friction angle - degrees, ( -5::;;8::;;<j». = Vertical displacement of foundation. = Horizontal displacement of foundation. = Submerged unit weight of soil. = Foundation rotation - radians. = Angle of internal friction for sand - degrees. = Poisson's ratio.

=

=

=

I


Page 89

7

CALCULATION :METHODS· DETERMINATION OF RESPONSES

7.1

General

7.1.1

The response of a jack-up unit is determined by combining the applied loading with a structural model to determine the internal forces in the and the reactions at the foundations. These are compared with the resistances available to take up these loads to determine the safety of the unit. The loads consist of fixed loads (self weight and nonvarying loads) and variable loads (see Section 3.2) together with hydrodynamic and wind loadings (see Section 4). The structural modeling is described in Section 5. The foundation resistance is described in Section 6. Section 8 provides the structural resistance and a methodology to check the adequacy of the various resistances to the acceptance criteria.

7.1.2

Two aspects of the response are to be distinguished and assessed separately. These are: a) The extreme response. The maximum calculated response to the design environment occurring at a particular instant in time, which is compared with the acceptance criteria. See Sections 7.2 and 7.3. b) Fatigue. The cumulative effect of stress/strain cycling, which is used to estimate the fatigue lives of steel components (see Section 7.4).

7.1.3

For typical jack-up assessments, the time-varying nature of the wave loading will amplify the quasi-static responses and must be considered. The extreme response can be assessed either by a quasi-static analysis procedure (Section 7.2) including an inertial loadset (Section 7.3.6) or by a more detailed dynamic analysis procedure (Section 7.3.7).

7.1.4

The dynamic amplification of the quasi-static response may not be significant for a given set of location parameters. The magnitude of the dynamic response is primarily influenced by the amount of wave energy at or near the natural period of the jack-up. The distribution of wave energy is at a maximum at the peak wave period and reduces for other periods. Thus the single most important parameter in the determination of the dynamic amplification of responses is the separation of the natural period of the jack-up from the peak period of the wave spectrum. Generally a large separation will produce a small dynamic amplification. As the separation decreases, the dynamic amplification will increase. These conclusions may be modified by effects such as wave-load cancellation and wave-current induced harmonics.

7.1.5

For many applications, the dynamic amplification may be determined using a simple, but empirical, method. This simple method is detailed in Section 7.3.6.1. Caution is advised when relying solely on results using this simple method. Specific guidance on the limitations of the method is given in Section 7.3.6.1.


Page 90

Because of its simplicity, the method detailed in Section 7.3.6.1 is recommended for an initial evaluation of the dynamic amplification. If the dynamic amplification is determined to be relatively small (see Section 7.3.6.1), or, if acceptance criteria are met, then random dynamic analysis is not required. 7.1.6 For many applications the dynamic effects may be included through the addition of an inertialloadset (see Section 7.3.6.1) to the environmental loads in a quasi-static analysis procedure. In this approach the inertial loadset may be determined using a simplified model of the jack-up. An appropriate detailed model of the jack-up may then be used to determine the detailed responses when the inertial loadset is applied together with the quasi-static environmental loads. 7.1.7

Appropriate combinations of gravity loads, wave/current loads and wind loads shall be applied as required by the acceptance criteria in Section 8. Load application is described in Section 5.7. Section 5.1 requires that the analysis is carried out for a range of environmental headings with respect to the unit such that the most onerous loading(s) for each major type of element in the structural system is(are) determined. The checks cover: Limit State Check

Section

Response Parameters(s)

Load Component L no.e"

1

D Strength of elements Overturning stability Foundation capacity: - preload - sliding

8.1 8.2 8.3 8.3.1 8.3.1

- bearing

8.3.213

- displacement

8.3.4

Horizontal deflection Holding system loads

8.4 8.5

Dn

E

Element load vectors" Overturning moment Stabilizing moment

Y 5 Y

min y+ 5 Y

Vertical leg reaction Vertical & Horizontal leg reactions Vertical, Horizontal (& moment) leg reactions Leg footing displacements and reactions Hull displacement. Holding system loads vectors

Y Y

Y

Y

max Y

Y

Y

Y Y

Y

Y Y

Y Y

y6

y6

Y

Y

Y

y6

y6

Y

Y

Y Y

y" yo

Y" Y"

Y y

y

I

Y

where D, L, E and Dn are defined in the glossary at the end of section 7.

•

Notes: 1. In all instances the responses are evaluated including the effects of deformation under dead loads (hull sag) and large displacement (P-~) effects. 2. Placed at most onerous center of gravity position. 3. The effects of leg offset to be added after global response analYSis (see Section 5.4). 4. Consider minimum live (variable) load if this is more onerous. 5. Must be included in response calculation so P-~ effects are included. 6. Worst case combination required.

I

7.2

Quasi-Static Extreme Response with Inertial Loadset

7.2.1

The most common method of analysis adopted for the determination of extreme responses is the deterministic, quasi-static wave analysis. Such an analysis shall be carried out in accordance with all relevant requirements of Sections 3 to 6. The maximum wave loading is determined by 'stepping' the maximum wave through the structure. The maximum wave is defined in Section 3.5.1.2 and the methodology


Page 91

for calculating the wave loading is described in Section 4.3. Various methods for determining the inertialloadset are given in Section 7.3.6. Load cases and combinations are discussed in Section 7.1.7. 7.2.2 The spudcan-foundation interface should normally be modeled as a pin t. The inclusion of a degree of fixity is to be justified on a case by case basis. If foundation fixity is included it should generally be represented by a combination of horizontal, vertical and rotational springs (which may be coupled) at the spudcan, rather than by a rotational spring alone. (See also Sections 5.3, 6.3.4 and 7.3.5.2). 7.3

Dynamic Extreme Response

7.3.1

Factors Governing Dynamics

Dynamic amplification of the structural response must be taken into (see Figure 7.1). Determination of dynamic response requires the incorporation of two separate items in the analysis: a) The dynamic characteristics of the structural system formed by the jack-up on its foundation, b) The characteristics of the environmental excitation. 7.3.2

The Structural System

7.3.2.1 The characteristics of the structural system are governed by the following aspects: a) The mass and mass distribution of the jack-up. This includes structural mass, mass of equipment and variable load on board, added mass due to the surrounding water and marine growth (if applicable), etc. The magnitudes and effective centers of mass of the various mass contributions are to be accurately determined. b) The overall (global) structural stiffness. This includes stiffness contributions from bending, shear deformation and axial straining of the legs, the leg to hull connections, the hull and the spudcan-foundation interface (if applicable). c) The damping. Damping contributions arise from the structural components and their connections, the water surrounding the legs and the soil underneath/around the spudcans. For further discussion of damping refer to Section 7.3.7. 7.3.2.2 The jack-up on its foundation represents a multi degree-of-freedom system. If the dynamic behavior is to be investigated in some detail it should also be modeled as such. The model may contain a number of nonlinear elements, notably the leg to hull connections and the spudcan-foundation interfaces. The influence of gravity (P-LVEuler) on the effective sway stiffness should be considered (see Section 5.5).

Page 92


Detennine highest newel period of jack-t.p. Tn' See SectIon 7.3.5

Datemire peak

~iod.

Te •

of wave spectrun for extreme se8State ard T!I&&' the period associated wlm-the lIBl(ilUll ~ (sections 3.5.1.2 &3.5.3)

Perf0l'Il randall d\lr&nic analysis See section 7.3.7

Nont inear tine darain sinulation

Use !DOl' method to

detemrine

~riodic

DAF

fl'Clll.TI'I ai-d O.9T . g1 see :;ection 7.3 •.

AccOU'lting for nongaussian effects use means and stardard deviations to estimate:

Aj:pI.y to 8R:,rqJdate structural rix!et wi th WIM:/current & wird

loads in CfJIISi -static a"lBlysis procedJ-e.

I f necessary. 8A'l Y nlSUlts to mre deta; led mdel to obtain finaL results

Analyse time series ard use ..,

appropriate method to directly predict:

CaJP.:lre with ~; stat IC respcinSe fran sane procectJre wi th zero 118SSeS. Obtain inertial loadset so

that .standard CfJiIS;· statIc responses are arplifiecl by sane factor as randan (J.IaS i-stat i C responses

1f necessary, aj:pl Y results to mere detailed IIlIOdel to obtain final results

y

ST(P Jack·L.p

suitable for this site

ST(P Jack'~ not

suitable for this site

1 The selected responSe wi LL nomally be base shear. This is usually detennined fr.an a siaple structural natel ard 2 an edditiorel ~i-static analysis is ~irecl to include partial load tac;tors & to determine detailed results. If this path is adopted, the appl icati~ of partial lead factors my be difficult.

Figure 7.1: Recommended approach to determine extreme dynamic responses


Page 93

Due to the fact that the mass of the hull dominates the mass distribution, the global dynamic behavior of the jack-up may in some cases be determined from an idealized single degree-of-freedom system (see Section 7.3.6.1). Structural modeling at various levels of complexity is discussed in Section 5.6.

7.3.3

The Excitation

7.3.3.1 The characteristics of the environmental excitation are controlled by the fluctuating nature of the environmental factors - wind, current and waves. Currents change slowly compared with the natural periods at which jack-ups may oscillate and may hence be considered to be a steady phenomenon. Variations in wind velocity cover a wide range of periods, but the main wind energy is associated with periods which are considerably longer than the natural periods of jack-up oscillations. Therefore, in connection with jack-ups, the wind may generally be represented as a steady flow of air. The periods of waves typically lie between some 2-3 sec and some 20 sec. Since typical jack-up natural periods fall within this range, the primary source of excitation is from waves. Sea waves are generally not regular but random in nature unless swell is predominant. This has important implications which should be considered for both the dynamic excitation and the resulting dynamic response. As waves and currents interact these two environmental factors should be considered in combination when generating time varying hydrodynamic drag forces according to Section 4.3. 7.3.3.2 For the simplified dynamic analysis method of Section 7.3.6.1 based on a regular-wave deterministic quasi-static analysis the wave period is chosen to be 0.9Tp where Tp is the peak period of the wave spectrum for the extreme sea state. For random analyses (see Sections 7.3.6.2 and 7.3.7) the most probable peak period (Tp) of the wave spectrum for the extreme seastate will normally be selected when a 2 parameter Pierson-Moskowitz spectrum is used (Hs and Tp from site specific data and y = 1 in Section 3.5.3). If a JONSWAP spectrum is used it is recommended that the peak period is considered to vary between plus and minus one standard deviation from the most probable peak period (Tp). Where the jack-up is sensitive to the wave period it is recommended that the range described in Section 3.5.1.2 or 3.5.3 is investigated as appropriate. In a deterministic calculation waves with a period close to the natural period of the jackup will give the largest dynamic amplification. It is therefore recommended that the wave associated with the highest natural period of the jack-up is also investigated.

7.3.4

The Dynamic Analysis A flow chart indicating the recommended dynamic analysis approach is shown in Figure 7.1.

Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Page 94 Rev 2, Jan 2002 An initial estimate of the dynamic amplification can be obtained using the empirical methods described in Section 7.3.6.1.

Techniques for performing random dynamic analyses can be categorized as frequency domain methods or time domain (simulation) methods or hybrids thereof; see Section 7.3.7.

7.3.5

The Natural Period(s)

7.3.5.1 The natural period of the jack-up on its foundation in the fundamental (or first) mode of vibration is an important indicator of the degree of dynamic response to be expected. The first and second vibrational modes are nearly always the surge and sway modes. The natural periods of these vibrational modes are usually close together; which of the two is the higher depends on which direction is less stiff. Where the period varies with environmental heading, care should be taken that the period used is applicable to the environmental direction being considered in the analysis. The third vibrational mode is normally a torsional mode, the three-dimensional effects of which may be important, in particular for environmental attack directions where the legs and hence wave loads are not symmetric about the direction of wave propagation. 7.3.5.2 If available, a finite element structural model containing the mass and stiffness properties of the jack-up may be used to obtain the various natural periods and mode shapes. This model should include the stiffness of the legs, hull and hull/leg connections according to Sections 5.6.4 to 5.6.6. If a finite element model containing only stiffness properties is available, then the global sway stiffness for the required headings may be determined by applying lateral unit loads to the hull. Normally the foundation will be considered pinned. This assumption may however be unconservative for situations in which: 1. The structure natural period is within a cancellation region of the base shear transfer function (see Commentary Section C7.4). 2. Significant foundation nonlinearities are expected at higher loading levels typical of dominant wave frequencies but not at lower loading levels typical of inertial frequencies. If either of these situations occur, and detailed foundation modeling is not available, it is recommended that the DAF's be calculated with fixity included and are then applied to a pinned model for response calculations.

Where the foundation stiffness is included, lateral and vertical translational springs should be included together with the rotational springs. fu any case the limitations on foundation loading according to Section 6.3.4 must be verified.

Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Page 95 Rev 2, Jan 2002 7.3.5.3 If such a capability is not available, the fundamental mode period may be estimated from the system described by:

an equivalent mass representing the mass of the jack-up and its distribution as referred to in Section 7.3.2; the equivalent mass is equal to the mass of the hull plus a contribution from the mass of the legs, including added mass, and is located at the center of gravity of the hull. an equivalent spring representing the combined effect of the various stiffnesses mentioned in Section 7.3.2. The period is determined from the following equation applied to one leg: Tn = 2n ~(Me / Ke) where; Tn

Me

= highest (or first mode) natural period. = effective mass associated with one leg. =

M hull

N

M M +MIa+ _l_b N 2 full mass of hull including maximum variable load. ~

= = number of legs.

Mia = mass of leg above lower guide (in the absence of a clamping mechanism) or above the center of the clamping mechanism. Mlb

= mass of leg below the point described for MIa, including added mass for the submerged part of the leg ignoring spudcan. The added mass may be determined as Aep(C Me - 1) per unit length of one leg (for definitions of Ae and CMe see Section 4.6.6); p mass density of water.

=

Ke

= effective stiffness associated with one leg (for derivation, refer to Commentary).

When the soil rotational stiffness Krs at the spudcan-foundation interface is zero this may be re-written:

Krs

= rotational spring stiffness at spudcan-foundation interface.

Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Page 96 Rev 2, Jan 2002 Krh rotational stiffness representing leg to hull connection stiffness (see below).

Fr

=

=

factor to for hull bending stiffness. 1

{1+ ::} IH

= representative second moment of area of the hull girder ing two legs about a horizontal axis normal to the line of environmental action.

E

= Young's modulus for steel.

A

= axial area of one leg (equals sum of effective chord areas, including a contribution from rack teeth - see Note to Section 5.6.4).

As

= effective shear area of one leg (see Figure 5.1).

I

= second moment of area of the leg (see Figure 5.1), including a contribution from rack teeth (see Note to Section 5.6.4).

Y

= distance between center of one leg and line ing centers of the other two legs (3 leg unit). = distance between windward and leeward leg rows for direction under consideration (4 leg unit)

Fg

= geometric factor. = 1.125 (3 leg unit), 1.0 (4 leg unit)

Fy

= factor to for vertical soil stiffness, K ys , and vertical leg-hull connection stiffness, KYh (see below). =

1

EA EA} {1+--+-LKvs LKvh Fh

= =

factor to for horizontal soil stiffness, Khs , and horizontal leg-hull connection stiffness, Khb (see below). 1 EAs EAs} {1+ 2.6LK +--"-2.6LK hs hh length of leg from the seabed reaction point (see Section 5.2.1) to the point separating MIa and Mib (see above).

L

=

P

=

the mean force due to vertical fixed and variable loads acting on one leg.

g

= =

MhuIlg N acceleration due to gravity.


PE

a

= = =

Page 97

Euler buckling load of one leg. a 2EI the minimum positive non-zero value of aL satisfying: (Krs + Krb )aEI } tan(aL) = { (aE1)2 - (KrsKrh) Thus:

=

=

=

=

=

=

when Krs 0 and Krh 00, aL TCl2 and hence: n 2 EI PE=-4L2 when Krs 00 and Krh 00, aL 1t and hence n 2 EI PE = L2 The hull to leg connection springs, K rh , Kvh and Khh represent the interaction of the leg with the guides and ing system and for local member flexibility and frame action. They should be computed with respect to the point separating MIa and M Ib , as described above. The following approximations may be applied: Khh 00 Kvh = effective stiffness due to the series combination of all vertical pinion fixation system stiffnesses, allowing for combined action with shockpads, where fitted. Unit with fixation system: Krh combined rotational stiffness of fixation systems on one leg. Fnh2kf where; Fn = 0.5, three chord leg; = 1.0, four chord leg h distance between chord centers. kf combined vertical stiffness of all fixation system components on one chord. Unit without fixation system: Krh rotational stiffness allowing for pinion stiffness, leg shear deformation and guide flexibility. k u=--_ d 2 __ Fnh2kj+ _ _ _

=

orl

= = = = = =

1 + (2.6k u d lEAs)

where; h

= distance between chord centers (opposed pinion chords) or pinion pitch

points (single rack chords). combined vertical stiffness of all jacking system components on one chord. d distance between upper and lower guides. ku total lateral stiffness of upper guides with respect to lower guides. As = effective shear area of leg. 7.3.5.3 The above equations for estimating the fundamental natural period are approximate and ignore the following effects: kj

= = =

more realistic representation of possible fixity at the spudcan-foundation interface in the form of (coupled) horizontal, vertical and rotational spring stiffnesses.

I

Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Page 98 Rev 2, Jan 2002 three dimensional influences of the system as compared with the two-dimensional single leg model.

7.3.5.4 Due to uncertainty in the parameters affecting the natural period the calculated natural period(s) will also be uncertain. The natural period(s) used in the dynamic analysis should be selected such that a realistic but conservative value of the dynamic response is obtained for the particular application envisaged. Care should be taken to ensure that the maximum dynamic amplification is not selected as coincident with a cancellation period causing minimum environmental loading. The potential for increased response due to shortcrested waves should be considered (see Section 7.3.7.5). For further details refer to the Commentary Section C7.4 and Figure C7.1.

7.3.6

Inertial Loadset Approaches In inertial loadset approaches the dynamic response is represented in a global quasi -static response model by either a distributed inertialloadset or an equivalent point load applied at the hull center of gravity. The inertial loadset may be derived from the simple approach described in Section 7.3.6.1 or from the more complex methods discussed in Sections 7.3.6.2 and 7.3.6.3.

7.3.6.1 The classical SDOF analogy This representation assumes that the jack-up on its foundation may be modeled as an equivalent mass-spring-damper mechanism; see Section 7.3.2. The (highest) natural period of the vibrational modes may be determined as described in Section 7.3.5. The torsional mode and corresponding three-dimensional effects cannot be included in this representation. The single degree-of-freedom (SnOF) method is fundamentally empirical because (1) the wave-current loading does not occur at the mass center and (2) the loading is nonperiodic (random) and non-linear. It should also be noted that all global and detailed response parameters are not equally amplified. The method described below will generally lead to a reasonable approximation of the jack-up's real behavior and has been calibrated against more rigorous methods. The following cautions are noted when using the SnOF method: 1. If the ratio of the jack-up natural period to the wave excitation period, Q, is less than 0.5 and the current is 'relatively small' the SDOF method should give reasonably accurate results when compared to a more rigorous analysis. 2. If Q is greater than 0.5, the relative position of the jack-up natural period within the base shear transfer function should be checked. If the natural period falls near a wave force peak, then the SDOF method may be unconservative because it ignores forcing at other than the full wave excitation period. Note that the calculation of natural periods should include a range of periods to for a reasonable estimate of foundation fixity (see Section 7.3.5.2). 3. The SDOF method may be unconservative for cases-with relatively high currents. If the results of the assessment are close to the acceptance criteria further detailed analysis is recommended.

I


Page 99

The ratio of (the amplitudes of the) dynamic to the quasi-static response as a function of frequency (<0) or period (T) of steady state, periodic and sinusoidal excitation is calculated as the classical dynamic amplification factor (DAF):

where; Q

~ T Tp Tn

Wave Excitation frequency <0 Jack - up natural frequency
=

The damping parameter ~ in this model represents the total of all damping contributions (structural, hydrodynamic and soil damping). For the evaluation of extreme response using the SDOF method a value not exceeding 0.07 is recommended. The calculated DAF from the SDOF method is used to estimate an inertial loadset which represents the contribution of dynamics over and above the quasi-static response in accordance with Figure 7.1. This inertial loadset should be determined as follows and applied at the hull (center of gravity) in the down-wind direction: Fin = (DAP - 1) BSAmplitude where; Fin = Magnitude of the inertial loadset for use in conjunction with the SDOF method. BSAmpIitude = Amplitude of quasi-static Base Shear over one wave cycle. = (BS(Q _S)Max - BS(Q -S)Min)/2 BS(Q _S)Max = Maximum quasi-static wave/current Base Shear. BS(Q _S)Min = Minimum quasi-static wave/current Base Shear. Note: The above equation is part of a calibrated procedure and should not be altered. A more general inertialloadset procedure, using the results from random analysis, is described in Section 7.3.6.3. 7.3.6.2 Other SDOF approaches

An alternative use of the SDOF method is to apply the entire DAP function for all frequencies (periods), rather than a single point DAF at one frequency. The closed-form frequency domain solution given in C7.B.2.2 of the Commentary is one such approach. This method reflects the random wave plus current excitation more correctly. Execution of this procedure is as per the relevant parts of Section 7.3.7.

I


Page 100

7.3.6.3 Inertialloadset based on random analysis The inertial loadset may be derived from random frequency or time domain analysis according to the recommendations of Section 7.3.7. The inertialloadset should be such that it increases the responses of the deterministic quasi-static analysis by the same ratios as those determined between the random quasi-static (zero mass) analysis and the random dynamic analysis (see Figure C7.B.l) In such cases the structural model (used for dynamic analysis) may be simplified and does not need to contain all the structural details, but will nevertheless be a multi degree-of-freedom model. The approach to the modeling and determination of the inertial loadset is described further in the Commentary, Section C7.B.2. The inertial loadset can be determined to model the effect of dynamic amplification in a more realistic manner as required. The simplest alternative uses a single point force to match inertial overturning moment effects as shown in the Commentary, Section C7.B.2. However the use of a distributed inertial loadset is considered more representative and will therefore provide a more accurate description of the component dynamic amplification effects as well as global response amplification. The distribution of the loadset is based on the fundamental sway modes and mass distribution. Note that the use of a distributed inertial loadset is recommended for units where a significant proportion of the total mass (including fluid added mass) acts at a location other than the hull center of gravity. The mathematical procedure for calculation of the distributed loadset is given in Figure 7.2. A brief description of the calculation process is as follows:

Step 1 Perform random response analysis using a wave attack direction along the selected main axis (x or y) and establish the global response dynamic amplification factors for base shear and overturning moment, whereby the dynamic amplification factors are defined as DAF3 = MP:MEdynlMP:MEstatic. Step 2 Establish a set of two simultaneous equations using combinations of 2-D mode shapes, nodal masses and unknown modal scalar, which match the inertial base shear and moment along the selected main axis. Solve this equation set to determine the two modal multipliers. Step 3 Establish the (2-D) inertial loadset Fin by a combination of the selected structural mode shapes (

Page 101

JACK-UP

7f-_ _ _.• Mass (MJ)

L

Lever 3ID1 or

+

massj=hj _~_ _..F;...;;.o~oting

Level Mass distribution

First bending mode (
Figure 7.2 - Procedure for calculation of distributed inertialloadset (2-D response)

7.3.7

Detailed Dynamic Analysis Methods Fully detailed random dynamic analysis will be necessary indicated in Figure 7.1. Random dynamic analysis may be performed in the time or in the frequency domain.

7.3.7.1 The waves may be modeled as a linear random superposition model which is fully described by the wave spectrum (see Section 3.5.3). The statistics of the underlying random process are gaussian and fully known theoretically. An empirical modification around the free surface may be needed to for free surface effects. This, together with the fact that drag forces are a nonlinear (squared) transformation of wave kinematics, makes the hydrodynamic force excitation always nonlinear. As a result, the random excitation is non-gaussian. The statistics of such a process are generally not known theoretically, but the extremes are generally larger than the extremes of a corresponding gaussian random process. For a detailed investigation of the dynamic behavior of a jackup the non-gaussian effects must be included. A number of procedures for doing this are presented in the Commentary. 7.3.7.2 The spudcan-foundation interface should normally be modeled as a pin Jomt in the absence of justifiable site-specific foundation fixity information, but see Section 7.3.5.2. If foundation fixity is included, it should be represented by a combination of horizontal, vertical and rotational springs. Coupling of the springs is preferable. In any case the limitations on foundation loading according to Section 6.3.4 must be verified. 7.3.7.3 When the random displacements of the submerged parts are small and the velocities are significant with respect to the water particle velocities the damping is not well represented by the relative velocity formulation in Morison's equation, which will tend to overestimate the damping and underpredict the response. A criterion for determining the applicability of the relative velocity formulation is given in Section 4.3.2.

Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Page 102 Rev 2, Jan 2002 7.3.7.4 Table 7.1 summarizes appropriate percentages of global critical damping for the various damping sources which should be summed to provide the total global damping as a percentage of critical damping.

Damping source Structure, holding system, etc. Foundation Hydrodynamic

Notes:

Global damping not to exceed (% of critical damping) 2% 2% or 0%(1) 3% or 0%(2)

1. Where a non-linear foundation model is adopted the hysteresis foundation

damping will be ed for directly and should not therefore be included in the global damping. 2. In cases where the relative velocity formulation may be used (a = 1 in Section 4.3.2) the hydrodynamic damping will be ed for directly and should not therefore be included in the global damping. Table 7.1 - Recommended damping from various sources

7.3.7.5 The effects of directionality and wave spreading may be considered in any dynamic analysis. It is recommended that a comparison be made between the Base Shear Transfer Function (BSTF) for the chosen 2-D (long crested/unspread) analysis direction and the 3D (short crested/spread) BSTF to determine whether the selected direction is unconservative. Optimally the direction of the 2-D seastate should be chosen to obtain a match with the 3-D BSTF for the entire wave spectrum. If this is not possible the match between the spread and unspread BSTFs should be good at the natural period. A 3-D BSTF, H 3D, can be generated from a set of 2-D BSTFs, H2D, by the following expression: 2ft

f[H 2D (0l,9)Y cos 2n(9)d9 o

where: Ol

9 n

= Wave excitation frequency = Angle between 2-D BSTF and dominant direction of 3-D BSTF = Power constant of spreading function ~

2.0 for fatigue analysis :;::: 4.0 for extreme analysis A simple approximation to the incorporation of wave spreading into inertial load calculations is to perform a 2-D analysis with the wave approach angle which is between the two approach angles which give the maximum and minimum forces at the cancellation and reinforcement points (see Figure C7.1 in the Commentary).


Page 103

7.3.7.6 Tables 7.2 and 7.3 respectively identify the most important factors associated with each type of analysis method and with each approach to detenruning the extreme responses. Further details of the methods are provided in the Commentary.

7.3.8

Acceptance Criteria The results of a dynamic extreme response analysis shall be assessed against the acceptance criteria described in Section 8. The required load factors should be introduced when combining the component loads into total load combinations.


Method Frequency Domain

Time Domain

Recommendations Consider linearization assumptions with respect to: - wave-current loading (quadratic dependence on particle velocity and finite wave ht). - structural non-linearity. Generate random sea from at least 200 components and use divisions of equal frequency. Note: fewer frequency components may be used provided that the divisions are shown to be sufficiently small around the wave period, the natural period & periods associated with reinforcement and cancellation. Generate random sea from at least 200 components and use divisions of generally equal energy. It is recommended that smaller energy divisions are used in the high frequency portion of the spectrum, which will generally contain the reinforcement and cancellation frequencies. Each wavelet should be taken to disperse with its own linear dispersion relationship [12] Check validity of wave simulation: - correct mean wave elevation - standard deviation (Hs 14) ± 1% - -0.03 < skewness < 0.03 - 2.9 < kurtosis < 3.1 - Max crest elevation (Hsf4)."j{2In(N)} -5% to +7.5% where N is the number of cycles in the time series being qualified, N == Duration 1 T z

=

=

Integration time-step less than the smaller of: Ti20 where;

or

T/20

=

the zero-upcrossing period of the wave Tz spectrum Tn the jack-up natural period (unless it can be shown that a larger time-step leads to no significant change in results)

=

Avoid transients in 'run-in' (~100 secs). Ensure simulation length OK for method chosen to determine the Most Probable Maximum Extreme (MPME) response(s). Note: The MPME is defined in Table 7.3 Table 7.2 - Recommendations for application of dynamic analysis methods (see Commentary)

Page 104

I


Method General

Frequency Domain Time Domain

Recommendations Define the Most Probable Maximum Extreme (MPME) as the extreme with a 63% chance of exceedence (typically this is the mode or highest point on the probability density function (PDF)).This is approximately equivalent to the 111000 highest peak level in a 3-hour stonn. Use mean & standard deviation to determine drag-inertia parameter and use Figure C7.B.6 in Commentary Section C7.B.2.1. Use mean & standard deviation to determine drag-inertia parameter and use Figure C7.B.5 or Figure C7.B.6 in Commentary Section C7.B.2.1. Simulation time of at least 60 minutes usually required to obtain stable standard deviation. or Fit Weibull distribution to distribution, for 3-hour probability level. Take results as average of MPME's from;;::: 5 simulations. Each input wave simulation to be of sufficient length for recommendations of Table 7.2 to be met (usually at least 60 minutes). See Commentary C7.B.2.3. or Use multiple 3-hour simulations and use Gumbel distribution on the extreme from each simulation. Sufficient simulations (usually at least 10) are required to obtain stable MPME of responses. See Commentary C7.B.2.4. or Use Winterstein's Hermite polynomial model, with improvements by Jensen if Kurtosis> 5. Simulation of sufficient duration to provide stable skewness and kurtosis of responses (nonnally in excess of 180 minutes). See Commentary Section C7.B.2.5.

Table 7.3 - Recommendations for determining MPME (see Commentary)

Page 105

II


7.4

Fatigue

7.4.1

General

Page 106

The fatigue of jack-ups should be considered for all new locations and operations. Jackups are mobile structures, generally operating in a wide range of water depths, therefore the location of the fatigue sensitive areas may vary (see Section 7.4.3). This means that fatigue damage at any member/t or other component may not occur equally throughout the life of the unit and tends to complicate the fatigue problem. If the original analysis carried out for the unit demonstrates that lives of critical

components are adequate then a unit may not require a separate analysis if on location for a period of less than one year provided that adequate proof from a recent inspection exists showing that the unit is behaving as originally predicted. If no original analysis and/or inspection proof is in existence then a separate analysis may

be required for all operations in excess of one year. In extreme cases six months may be more appropriate if this period contains the rough winter season. Alternatively a recent assessment inspection, or proof that such an inspection (including detailed NDT) has been carried out may serve as a demonstration of the adequacy of the unit. 7.4.2

Fatigue Life Requirements

A fatigue analysis, if undertaken, should ensure that all structural components have (remaining) fatigue lives of more than the greater of four times the duration of the assignment or 10 years. Different (reduced) fatigue life requirements may be justified for certain items on a case by case basis where structural redundancy or ease of access for inspection and repair permit. 7.4.3

Fatigue Sensitive Areas All structural subject to fatigue loading are to be checked in the analysis, with emphasis on the following areas, which are likely to be the most critical. However; other areas should also be studied if they are potentially more critical: a) The leg and ts in the vicinity of the upper and lower guides for the operating leg/guide location(s). b) The rack teeth of the chord. c) The leg and ts adjacent to the waterline. d) The jack-frame/jackhouse and associated areas of the hull. e) The leg and ts in the vicinity of the leg to spudcan connection. f) The spudcan to leg connection. Records of inspections, damage and repair for the unit may provide guidance in the selection of critical areas.


Page 107

As mentioned the fatigue analysis should consider all loading conditions that may occurduring the period under consideration and for items c) through f) the cumulative damage due to transit loadings should also be included. 7.4.4

General Description of Analysis Suitable approaches to the analysis may be found approaches may be applied.

In

reference [13].

Equivalent


7

Page 108

GLOSSARY OF - DETERMINATION OF RESPONSES A As BS d D DAF Dn E E Fg Fh Fin Fn Fr Fv g h

!LIe! Hmax

Hs Hsrp H2D H3D I

IH kf kj ku

Ke Khh Khs Krh Krs Kvh Kvs L L

= Equivalent axial area of a leg (see Figure 5.1), including contribution from rack teeth (see note to Section 5.6.4). Effective shear area of one leg. = Base Shear. = Distance between upper and lower guides. = Self weight and non varying loads. = Dynamic Amplification Factor. = Inertial loads due to Dynamic response. = Environmental loads. = Young's modulus for steel. = Geometric factor = 1.125 (3 leg unit), 1.0 (4 leg unit) = Factor to for horizontal soil stiffness, Khs , and horizontal leg-hull connection stiffness, K hh . Magnitude of inertialloadset. = 0.5, three chord leg; = 1.0, four chord leg = Factor to for hull bending stiffness. = Factor to for vertical soil stiffness, Kvs, and vertical leg-hull connection stiffness, Kvh . = Acceleration due to gravity. = Distance between chord centers or pinion pitch points. = The wave height to be used for detenninistic waveforce calculations, allowing for conservatisms in the theoretical predictions of higher order wave theories. = 1.60 Hsrp = The maximum detenninistic wave height. = 1.86 Hsrp , generally. = 1.75 Hsrp, in Tropical Revolving Storm areas. = Significant wave height (meters), including depth/asymmetry correction, according to Section 3.5.1.1. = The assessment return period significant wave height for a 3 hour stonn. = 2-D base shear transfer function. = 3-D base shear transfer function. = Second moment of area of the leg (see Figure 5.1) including contribution from rack teeth (see note to Section 5.6.4). = Representative second moment of area of the hull girder ing two legs about a horizontal axis normal to the line of environmental action. = Combined vertical stiffness of all fixation system components on one chord. = Combined vertical stiffness of all jacking system components on one chord. = Total lateral stiffness of upper guides with respect to lower guides. = The effective stiffness associated with one leg. = Horizontal stiffness of leg-hull connection, generally infinite. = Horizontal stiffness at the spudcan-foundation interface. = Rotational stiffness representing the leg-hull connection. = Rotational stiffness at the spudcan-foundation interface. = Vertical stiffness of leg-hull connection. = Vertical stiffness at the spudcan-foundation interface. = Variable loads. = Length of leg from the seabed reaction point (see Section 5.2.1) to the point separating MIa and M Ib .

=

=

I


7

Page 109

GLOSSARY OF - DETERMINATION OF RESPONSES (Continued) M Me MhulJ MIa

= = = =

M Ib

=

MPME

=

n

= ~ ~

N N P

= = = =

PE T Tass Tn Tp Tz y

= = = = = = = = = =

Nodal masses. Effective mass associated with one leg. Full mass of hull, including variable load. Mass of a leg above lower guide (in the absence of a clamping mechanism) or above the center of the clamping mechanism. Mass of leg below the point described for MIa, including added mass for the submerged part of the leg. Most Probable Maximum Extreme response(s). The extreme response with a 63% chance of exceedence; approximately equal to the 1/1000 highest peak level in a 3-hour storm. Power constant of spreading function. 2.0 for fatigue analysis. 4.0 for extreme analysis. Number of legs. Number of cycles. The mean force due to vertical dead weight and variable load acting on one leg. MhuI1g N Euler buckling load of one leg. a 2EI O.9Tp • Wave period associated with Hmax (also used with lLiet). Natural period of jack-up (subject to the precautions of Section 7.3.5.4). Peak period associated with Hsrp (also used with Hs). Zero-upcrossing period of the wave spectrum. Distance between center of one leg and line ing centers of the other two legs (3 leg unit). Distance between windward and leeward leg rows for direction under consideration (4 leg unit). The minimum positive non-zero value of aL satisfying: (Krs + Krh )aEI } tan(aL)= { --~2--~--( uBI) - (K rs Krh )

a 13 <j>},<j>2

Q

P

e <0

~

= = = = = = = = =

Scalar multiplier used in establishing 2-D Fin. Scalar multiplier used in establishing 2-D Fin' Structural mode shapes. wiroo. =TniT. Mass density of water. Angle between 2-D BSTF and dominant direction of 3-D BSTF. Wave excitation frequency = 27r1T. Jack-up natural frequency = 27rlTn. Damping ratio or fraction of critical damping.


8

Page 110

ACCEPTANCE CRITERIA The acceptance checks in the following sections cover: Structural strength (Section 8.1), Overturning stability (Section 8.2), Foundation capacity (preload, bearing, sliding displacement and punch-through) (Section 8.3), Horizontal deflections (Section 8.4), Loads in the holding system (Section 8.5), Loads in the hull (Section 8.6) and The condition of the unit (Section 8.7).

In each check the factored resistance should equal or exceed the factored load. Thus the general form of the check is: L(Factored loads) -.:.....-----.:.-.$ 1.0 Factored resistance For some checks, where load and resistance vectors are considered, it may be necessary to address the interaction between the n different components. The form of the check then becomes: ~ { L(Factored loads in component i) } ~fn $1.0 i=1 Factored resistance to component i The required load factors are as follows: YI = 1.00 - Applies to non-varying weight loads (D) Y2 = 1.00 - Applies to maximum or minimum variable loads (L) applicable to check being carried out Y3 = 1.15 - Applies to environmental loads (E); (provisional - see Section 1.8); Y4 = 1.00 - Applies to dynamic loads (Dn) in combination with Y3 It is assumed that the jack-up is built to recognized standards, and has been maintained as required to continue to meet those standards (see Sections 2.4.2 and 8.7). Any deterioration should be taken into in the assessment. 8.1

Structural Strength Check Note: Figure 8.1 provides a flowchart for member strength assessment.

8.1.1

Introduction

8.1.1.1 Code Basis

The main basis for the structural strength check is the AISC 'Load and Resistance Factor Design (LRFD) Specification for Structural Steel Buildings' [14]. The AISC LRFD specification has been interpreted and, in some cases, modified for use in the assessment of mobile jack-up unit structures. Interpretation of the code has been necessary to enable a straight-forward method to be presented for the assessment of beam-columns of non 'I' section. Development of the code has been necessary in two areas as described below: a) A method has been established for dealing with sections constructed of steels with different material properties. b) A method has been established for the assessment of beam columns under biaxial bending to overcome a conservatism which has been identified in the standard AISC LRFD equations.

II


Page 111

!EMlER STRENGTH ASSES9ENT USING FACTCRB> LOADS

fail

fail .......- - - - - - - - - - '.......-i Assess to 8.1.5

T

8~1.4.2

8.1.4.3a) ca!p8Ct & ncu:a!p8Ct secti oos

~---------t

8.1.4.3b) slerder sectioos

8.1.4.4

T

ASSESS TO 8.1.4.1

8.1.4.5

8.1.4.6a) ........--1 Ca!p8Ct sectioos

L..-_ _. - - - _ - - - '

8.1.4.6b) non-

"'-'--1 Ca!p8Ct sections

L -_ _.---_---'

fail 8.1.4.6c)

'-----......------1 slerder sections 8.1.4.7

Figure 8.1: Flow chart for member strength assessment


Page 112

One particular type of member geometry which is not covered at all by AISC LRFD is the high Rlt ratio tubular which usually has ring frame and/or longitudinal stiffeners. Recommendations for checking such are given in Section 8.1.5 where the is referred to an applicable code and guidance is given on suitable load and resistance factors. The resistance factors used in the AISC LRFD specification have been adopted. In addition to checking the strength of , it may be necessary to check the strength of ts between . Recommendations for t checking are given in Section 8.1.6 where the is referred to an applicable code and guidance is given on suitable load and resistance factors. 8.1.1.2 Limitations

The structural strength check assessment described here is limited by the following criteria: a) The geometry of structural components and , as defined in 8.1.2, must fall reasonably within the categories described in that section. b) In accordance with AISC LRFD Specification, Chapter A Para. A5, the minimum specified yield stress of the strongest steel comprising the components and should not exceed: 65 ksi (448 MN/m2) if (elasto-)plastic structural analysis is used to determine the member loads. For slender geometries plastic structural analysis is precluded, even if the yield stress is below 65 ksi. 100 ksi (690 MN/m2) if elastic structural analysis is used to determine the member loads. For higher strength steels within the holding system, refer to Section 8.5. It should also be noted that the assessment has been tailored towards the types of analysis normally carried out for jack-ups. The detailed recommendations which follow focus particularly on closed section brace and chord scantlings in truss type legs. Geometries outside the limits of Sections 8.1.2 - 8.1.4 may be checked in accordance with the recommendations of Section 8.1.5. Notes: 1. Of necessity, many of the equations presented in Section 8.1 are dimensional. Such equations are quoted firstly in metric units (MN, m, MN/m 2 etc.) and then in { } in North American imperial units (kips, inches, ksi, etc.). 2. Where the member geometry may contain components of part-tubular shape it is appropriate to consider their dimensions in of radius and thickness (rather than diameter and thickness), and hence relevant equations have been converted to this format.

Page 113


3. The AISC LRFD source equations/text are identified between [ ]. 4. The in the equations are defined where they appear. provided at the end of Section 8.

8.1.2

A glossary is also

Definitions

8.1.2.1 Structural and Components a) Structural For the purposes of strength assessment, it is necessary to consider the structure as comprised of structural . Typically each structural member could be represented by a single finite element in an appropriate finite element model of the structure. Examples of would include braces and chords in truss type legs, box or tubular legs and plating which forms a piece of structure for which the properties can readily be calculated. The strengths of structural are to be assessed according to Section 8.1.4 with the exception of structural exceeding any of the following provisions which should be assessed according to Section 8.1.5. i)

A plain tubular with Rlt > 44,815IFy {Imperial: 6,500IFy} [Table A-F1.1]

ii) Any tubular with ring stiffeners with or without longitudinal stiffeners. iii) Tubulars with longitudinal stiffeners where; Rlt> 1l,3751Fy

{Imperial: 1,650IFy} [Table B5.1]

b) Structural Components A structural component is defined as a part of a structural member (see Figure 8.2). Typically, structural components are pieces of plating or tubulars such as the plates, splittubulars and rack pieces forming a jack-up chord, or the stringers on a . Note that it is not always appropriate to consider fundamental structural parts as components. A plain tubular, for example is better analyzed as a member. A component should not consist of more than one material.

8.1.2.2 Stiffened and Unstiffened Components A component which is stiffened along both edges is denoted a stiffened component. A component which is ed along only one edge is denoted an unstiffened component. Typically all the components forming parts of chord sections may be regarded as stiffened.


Page 114

8.1.2.3 Compact, noncompact and slender sections Steel sections are divided into compact sections, noncompact sections and sections with slender compression elements. Compact sections are capable of developing a fully plastic stress distribution before the onset of local buckling. Noncompact sections can develop the yield stress in compression components before local buckling occurs, but will not resist inelastic local buckling at the strain levels required for a fully plastic stress distribution. Slender compression components buckle elastically before the yield stress is achieved. Where a distinction is required between these categories, appropriate limiting slenderness ratios have been stipulated.

8.1.3

Factored Loads Factored loads in structural components and are to be determined in accordance with the previous sections, using the most onerous condition for each structural component or member. Each structural component or member should be checked for the factored load vector Q (Le. axial load, moments and, if applicable, shears and torsion) where; Q =YI.D + Y2.L + Y3(E + Y4. Dn) and Y1 = 1.0 Y2 = 1.0 Y3 = 1.15 (provisional. see Section 1.8) Y4 = 1.0 D = Member load vector due to the weight of structure and non-varying loads including: Weight in air including appropriate solid ballast. Equipment. Buoyancy. Permanent enclosed liquid. L

= Member load vector due to the maximum variable load (gravity adds to environmental loads) or minimum variable load (gravity opposes environmental loads) positioned at the most onerous center of gravity location applicable to extreme conditions as specified in Section 3.2.

E

=

The extreme member load vector due to the assessment return period wind, wave and current conditions (including associated large displacement effects).

Dn = Member load vector due to the inertial loadset which represents the contribution of dynamics over and above the quasi-static response as described in Section 7.3.6 (including associated large displacement effects).

II

Page 115

Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 8.1.4 Assessment of - excluding stiffened and high Rlt ratio tubulars 8.1.4.1 General interaction equations

I

Each structural member within the scope of Section 8.1.2 shall satisfy the following conditions:

If PulG>aPn > 0.2

r n [{ r {M n 1

P s[{ M + {M

_u_+_ (/>aPn

9

else

uex lA,M nx

uey lA,Mny

< 10 -'

[Eq. Hl-la]

1

~+ 2(/JaPn

Muex lA,M nx

+ ~ lA,Mny

<10 -'

[Eq. Hl-lb]

where;

I I

Po

= =

Muex,Muey

=

effective applied bending moment determined in accordance with Section 8.1.4.4 (tension) and 8.1.4.5 (compression).

Mox,Moy

nominal bending strength determined in accordance with Section 8.1.4.6.

G>a

= =

b

=

II

= Exponent for biaxial bending, a constant dependent on the member cross

Pu

applied axial load nominal axial strength determined in accordance with Section 8.1.4.2 (tension) and 8.1.4.3 (compression).

Resistance factor for axial load = 0.85 for [Eq. E2.1] compression and 0.90 for tension [Eq. D1.1]. Resistance factor for bending =0.9 [Ch. F1.2] section geometry, determined as follows: i)

For purely tubular , II = 2.0

ii)

For doubly symmetric open section , II

=1.0

I I

iii) For all other geometries, the value of II may be determined by analysis as described in Section 8.1.4.7 but shall not be less than 1.0. In lieu of analysis, a value of II equal to 1.0 may be used.

The interaction equations can be used in a reduced form if one or two of the three load ratio tenns in the equation are zero.

Alternatively, the more complex interaction formulations given in Section C8.1.4.7 the Commentary may be used where applicable.

ofl


Page 116

8.1.4.2 Nominal Axial Strength of a Structural Member in tension Pn For a member comprising more than one component, the nominal tensile strength lies between the maximum individual tensile strength of anyone component, and the sum of all the individual tensile strengths. The nominal tensile strength of a tension component shall be the lower value from the following equations: a) P ni = FyiAi b) P ni = % FuiAi where; Ai = area of component Fyi = specified minimum yield stress of component (or specified yield strength where no yield point exists) FUi = specified minimum tensile (ultimate) strength of component P ni = component nominal axial tensile strength This assumes that for in jack-up units the net section is equal to the gross section [Eq's. D1.1 and D1.2]. The total member nominal tensile strength shall be: Pn =Fmin~Ai with the resistance factor t = 0.90 where F min is the smallest value of Fyi or %Fui of all the components.

[Eq. Dl.l]

Note: If for any component the nominal strength is significantly different from the nominal strengths of other components, the formulation above may be conservative and alternative rational methods may be applied. An example is given in the Commentary.

8.1.4.3 Nominal Axial Strength of a Structural Member in Compression P n So long as local buckling of the components of a member is not the limiting state, the member can be treated for global loads only. Should local buckling dominate, the loads in the components must be considered. Therefore, in determining the nominal axial strength of a member in compression, a local buckling check must first be applied. Check: Local buckling The structural components which make up the cross section of a compact or noncompact section must satisfy the following criteria [Table B5.1]: i)

For rectangular components stiffened along both edges b/ti ~ 625/ ~(Fyi - Fr) {Imperial: b/ti ~ 238/ ~(Fyi - Fr) }

Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 ii) For rectangular components stiffened along one edge

b/ti::;; 250/ ~(Fyi) iii)

Page 117

{hnperial: b/ti::;; 95/ ~(Fyi) }

For tubular sections {hnperial: Rlti::;; 1650IFyd R1ti ::;; 113801Fyi where; bi = width of a rectangular component thickness of a rectangular component or tube wall ti R = outside radius of the tube or tubular component residual stress due to welding (114 MPa, {16.5 ksi}) Fr

containing rectangular and tubular sections which do not meet this criteria are considered to be slender and are treated in 8.1.4.3 b) for local buckling. a) Strength assessment for Compact and Noncompact Sections The nominal axial strength of a structural member subject to axial compression and within the above stipulated restrictions regarding cross section shall be determined from the following equations: [Eq. E.2.1] Pn = A Fer /..2 [Eq. E2.2] Fer = (0.658 e ) Fyeff

Fa = {O~;7} Fyoff where; A

=

Ae = 1

=

r E Fyeff

= = =

K

=

For Ae > 1.5

[Eq. E2.3]

gross area of section (excluding rack teeth of chords)

~ {F;; },v, for max. Ktfrfrom all directions

[Eq. E2.4]

unbraced length of member: - face to face for braces - braced point to braced point for chords - longer segment length of X-braces (one pair must be in tension, if not braced out of plane) radius of gyration, based on gross area of section. material Young's modulus (200,000 MN/m2 {29,000 ksi}). effective material yield stress, to be taken as the minimum of (specified) yield stress or 5/6 (ultimate stress) of all components in the member unless rational analysis shows that a higher value may be used. effective length factor. Figure 8.3 provides generally recommended values for K. For the specific case of jack-up truss legs, the value of K shall be taken as follows [Table C-C2.1], unless alternative values are shown applicable by rational analysis: Assumed boundary conditions 1.0 pinned-pinned Chord K-Braces & span breakers 0.8 }{ between pinned-pinned X-Braces 0.9 and fully built-in 2.0 pinned-sliding Complete legs


Page 118

b) Strength Assessment for with Slender Components The nominal axial strength of a structural member subject to axial compression and outside the restrictions for a) above shall be determined from the following equations.

where; Q(0.658 QA.e2)Fyeff for Ae.JQ ::; 1.5

Fer = Fer

=

0.877} "T! Fyeff

[Eq. A-B5-11]

for Ae.JQ > 1.5

{

[Eq. A-B5-13]

where Ae is defined in Section 8.1.4.3 a) and Q is determined from the following: i)

For comprising entirely of stiffened components [A-B5.3.b and A-B5.3.c]: = Qa Q where; [Eq. A-B5-1O] Qa = AefA and Ae is the section effective area found from: Ae = L bei ti (excluding rack teeth of chords) with bei

= 85~i {1vfi

. b {Impenal: ei

=

Jf:}

170 (b i ItJ fi

< b. -

I

i 326t 64.9} r;- {1r;- ::; b i } vfi (b i I tJvfi [Eq A-B5-7]

and fi is the calculated elastic stress in the component where, for the analysis, the is based on the actual cross sectional area but with elastic section modulus and radius of gyration based on effective area. ii)

For comprising of stiffened and unstiffened components [A-B5.3.b and A-B5.3.c]:

where Qa is determined from Section 8.1.4.3 b) i) but with the additional check that fi for the stiffened component must be such that the maximum compressive stress in the unstiffened component does not exceed t,FyeffQs with 0.90.

=

I

Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Page 119 Rev 2, Jan 2002 Qs is the lowest value for all components in the member which are stiffened along one edge determined from the following:

For 2501.JF: < b/ti < 4601.JF: {Imperial: 951.JF: < b/ti < 1761.JF: } Qs

=1.415 - 0.00166(b/ti) .JF: {Imperial: 1.415 - 0.00437(b/ti)

[Eq. A-B5-3]

{Imperial: b/ti ~ 176/ .jF; }

For b/ti;;::: 4601 ~Fyi Qs

.JF:}

=137,900/[Fyi(b/til {Imperial: Qs

=20,000/[Fyi(b/til}

[Eq. A-B5-4]

Note: The implication of this section is that the critical components in the member will be the unstiffened components. If these buckle, then the assumed buckling lengths and hence strengths for the stiffened components will then be wrong, hence invalidating the original assumptions. This assumes that the un stiffened components are placed in the member to reduce the buckling length of the major components. iii)

For comprising a tube alone and: 1l,375IFy < Rlt < 44,815IFy {Imperial: 1,650IFy < Rlt < 6,500IFy }

Q

=

3790

FyCR I t)

550

2

---+3

{Imperial: Q

2

= FyCR I t) +"3} [Eg. A-B5-9]

8.1.4.4 Effective Applied Moment/or in Tension; Mue (Mue;x,Muey)

In many cases, the effective applied moments used in the interaction equations will not be equal to applied moments obtained in a structural analysis. This can be due to the type of structural model and lor the effective length effect on buckling. The following procedures shall be followed for the determination of the effective applied moment. The effective applied moment for a member under axial tension shall be taken to be equal to the applied moment from an analysis including global P-L\ effects and ing for local loading.


Page 120

8.1.4.5 Effective Applied Moment/or Compression ; Mue (Mue;x,Muey) The effective applied moment for a member under axial compression shall be taken to be: Mue B Mu [Eq. H1.2] where; Mu is the applied moment determined in an analysis which includes global P-Mhullsway effects and s for local loading. When eccentricity is not incorporated in the model, the equation for Mue should be modified to include pue due to the eccentricity, e, between the elastic and plastic neutral axes. Note: When the member considered represents the leg the requirement to include P-A effects in the global analysis means that the provisions of ii) below apply. and i) Where the individual member loads are determined from a first order linear elastic analysis i.e. the eqUilibrium conditions were formulated on the undeformed structure, (For example a linear analysis of a detailed truss type leg, using external loads determined from a second order analysis of a simplified global model): C B = m ~ 1.0 [Eq. Hl-3] (l-Pu /PE ) where: P E = (1ir AE)/(Kti with K ~ 1.0 and PE is to be calculated for the plane of bending. A is defined in Section 8.1.4.3 a) and r is the radius of gyration for the plane of loading. Cm = a coefficient whose value shall be taken as follows [Ch. H1.2a]:

=

i)

For not subject to transverse loading between their s in the plane of bending Cm = 0.6 - 0.4 (M1IMZ) [Eq. Hl-4] where MIIMZ is the ratio of the smaller to the larger moments at the ends of that portion of the member unbraced in the plane of bending under consideration. MIIMZ is positive when the member is bent in reverse curvature, negative when bent in single curvature.

ii) For subjected to transverse loading between their s, the value of Cm can be determined from rational analysis. In lieu of such analysis, the following values may be used: For whose ends are restrained against sidesway Cm =0.85 For whose ends are unrestrained against sidesway Cm =1.0 ii)

Where the individual member loads are determined from a second order analysis i.e. the equilibrium conditions were formulated on the elastically deformed structure so that local P-A loads were also included in the analysis: B

=

1.0

Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 8.1.4.6 Nominal Bending Strength; Mn (Mnx. Mny)

Page 121

The calculation of nominal bending strength is based on the plastic properties of the section. The practice allows for hybrid sections built up from components of different yield strengths. Standard techniques shall be applied to obtain a section plastic moment in the absence of axial load, Mp , based on the individual component values which are the lesser values of Fyi and 5/6 FUi (an example is given in the Commentary). Lateral torsional buckling and local buckling of components must be considered. If both tensile and compressive yielding occur during the same load cycle, it shall be demonstrated that the structure will shake down without fracture. Check: Lateral torsional buckling (Not applicable to tubulars) The cross sectional geometry of a member subjected to bending shall be examined for susceptibility to the limit state of lateral torsional bucking. The member cross section must satisfy the following criteria for compact sections for the nominal bending strength to be assessed under Sections 8.1.4.6 a) or 8.1.4.6 b). {Imperial: 4/ry ~ 3750 ~(JA) / Mp } [Table A-Fl.!] where;

Lb

=

Laterally unbraced length; length between points which are either braced against lateral displacement of the compression flange or braced against twist of the cross section.

ry

= = =

Radius of gyration about the minor axis.

A J

Cross sectional area. Torsional constant for the section

Sections which do not satisfy this criteria are susceptible to lateral torsional buckling and are treated as having slender compression components as in Section 8.1.4.6 c). Check: Local buckling The cross sectional geometry of a member subjected to bending is to be examined for susceptibility to the limit state of local bucking. If local buckling is deemed to be the limit state, the nominal bending strength shall be reduced in accordance with the following paragraphs. with particularly slender components are covered in Section 8.1.4.6c). For this check it is necessary to identify web components and flange components. This can be done by visual inspection, with knowledge of the major and minor axes. For example, in a split-tubular, opposed rack chord, the rack plate would be a suitable web component, and the split tubulars flanges. For a teardrop chord, the rack and side plates would be web components, and the back plate the flange. In cases of doubt, components shall be checked as both web and flange.


Page 122

a) Compact Sections For in which all the components sections satisfy the following [Table B5.1]: i) For rectangular components stiffened along both edges b/ti :::; Ap where; Ap

=

500/ ~(Fyi)

{Imperial: Ap = 190/ ~(Fyi) }

ii) For rectangular components stiffened along one edge b/ti :::; Ap where; Ap

=

170/ ~(Fyi )

{Imperial: Ap = 65/ J(Fyi) }

iii) For tubular sections

2R1t where; Ap

:::; Ap :::;

14270IFyi

{Imperial: Ap :::; 20701Fyi}

The nominal bending strength is given by the plastic bending moment of the whole section [Eq-A-F1-1] Mn = Mp where Mp is derived as discussed above. Note: Where significant plastic hinge rotations are required the section must remain stable after rotation through an appreciable angle. In such cases, to achieve this requirement, the limitations of ii) and iii) above should be reduced to: ii) Ap =

135/ J(Fyi)

iii) Ap:::;

1l000IFyi

{Imperial: Ap = 52/ J(Fyi ) } {Imperial: Ap:::; 16001Fyi}

b) Noncompact Sections For in which all the components do not satisfy the previous criteria but satisfy the following [Table B5.1]: i) For rectangular components stiffened along both edges b/tj :::; Ar where; Ar

=

625/ ~(Fyi - Fr)

{Imperial: Ar = 238/ ~(Fyi - Fr) }

I

2

Fr = 114 MN/m {16.5 ksi} residual stress ii) For rectangular components stiffened along one edge b/tj :::; Ar where; {hnperial: Ar= 106/ ~(Fywj -Fr)}

Ar

Fywj = web component yield stress. Fr = 114 MN/m2 {16.5 ksi} residual stress. iii) For tubular sections

2R1t where; Ar

:::;

Ar

:::;

61850IFyi

I


Page 123

The nominal bending strength is given by an interpolation between the plastic bending moment and the limiting buckling moment: Mn

=

A-A} Mp - (Mp- Mr) { A _; r

where; Mp h

= =

A Ap Ar Mr

= is is is

P

[Eq. A-F1.3] h

Section Plastic Moment. subscript referring to the component which produces the smallest value of Mn. bit or 2R1t as applicable for component h. determined for component h from 8.1.4.6 a). determined for component h from 8.1.4.6 b). the limiting buckling moment of the section defined as follows:

For bending of non-tubular sections about the major axis, the lesser of Mr = FI S (flange buckling) [Table A-Fl.I] Mr = ReFyfjS (web buckling) [Table A-Fl.I] where; FI = the smaller of (Fyfj - Fr) and Fywj S = minimum section elastic modulus for plane of bending under consideration. For bending of non-tubular sections about the minor axis; Mr = FyfjS (flange buckling)

[Table A-Fl.I]

For bending of tubular sections:

[Table A-Fl.I]

Mr =

ar m

{2068

R It

+F}S Y

II II

300 {Imperial: Mr = {- + Fy }S} RI t

= yield stress of flange component. = hybrid girder reduction factor [A-G2] = 1.0 if components are of the same material otherwise: 3 = [12 + ar (3m - m )] 1(12 + 2 ar) <=1.0 = ratio of total web area to area of compression flange. = ratio of web component yield stress to flange component yield stress which gives smallest value of Re.

c) Slender Sections The nominal bending strength of including components which do not satisfy the above criteria for compact and noncompact sections or for lateral torsional buckling shall be determined in accordance this section.

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The nominal bending strength of a member is given by the limiting flexural bending moment: Mn = S Fer where S is the elastic section modulus for the plane of bending under consideration and Fer is the lowest value from (where appropriate): i) Doubly symmetric (lateral torsional buckling) Fer

=

6.895 CbXj J2 {I + Xj2X2 }!f2 /.. 2/..2

[Table A-F1.1(b)]

. CbXj J2 { XI 2X2 }!f2 {Impenal: Fer = /.. 1 + 2/..2 } where; Cb

=

= X2 = E = G = J = A = Iy = Sx = Cw = /.. = ry = Xl

1.75 + 1.05(M/M2) + 0.3(M/M2i ~ 2.3 where MI is the smaller and M2 the larger end moment in the unbraced member; MIIM2 is positive when the moments cause reverse curvature. (1tIS) .J(EGJA I 2) (4CwlIy)(Sx/GJ)2

Modulus of elasticity (200,000 MN/m2 {29,000 ksi}). Shear modulus of elasticity (77,200 MN/m2 {II ,200 ksi}). Torsion constant for section. Cross-sectional area (excluding rack teeth). Second moment of area of section about minor axis. Elastic section modulus for major axis bending. Warping constant.

LJry Radius of gyration about the minor axis

ii) Singly symmetric (lateral torsional buckling) Fer

=

where;

B1

=

B2 = h

Ie Cb

[Table A-F1.1(c)]

= = =

r

2.25 {{ ::) -1}{~J{; 25 {1-(:: )}{ ~J e; }

web depth. second moment of area of compression flange about the section minor axis as for doubly symmetric sections.


iii)

Doubly and singly symmetric (flange local buckling)

Fer = 77,220().} where; ')... = b/ti for flange(s) iv)

Page 125

For tubular (Local buckling) Fer = 33,610/(RJt) where; R = radius of tubular t = wall thickness of tubular

[Table A-Fl.l(g)] {Imperial: Fer = 1l,2001')...2}

[Table A-Fl.!] {Imperial: Fer = 4,875/(RJt)}

8.1.4.7 Determination of n for non-tubular sections The general interaction equation requires that applied bending moments are resolved into components in two perpendicular axes (X, Y). For elaborate sections such as chords, these axes may be selected on the basis of section geometry and not on load incidence. Therefore neither of these axes need be coincident with the angle of load. The use of the exponent 11 is necessary to ensure that the effective nominal bending strength of the section is not significantly influenced by this choice of axes. To determine a suitable value of 11 the following process is applied: 1. For angles q = 0°, 30°, 45°, 60°, 90°, to the X-axis, obtain the allowable bending strengths Mnq. 2. Assume loads incident at angle q=30°, the limiting bending moment in the absence of axial load is Muq =Mnq. When the section is non-compact Mnq is a function of Mr and a suitable analysis in line with that of Section 8.1.4.6 b), should be applied in determining Mr for non-principal axes. 3. Resolve this limiting moment into limiting components M'uex and M'uey about the X and Y axes: M'uex =Muq cos q M'uey = Muq sin q 4. The interaction ratio for the (X,Y) axis pair is required to give the same result as if the X-axis were lined up with the q-axis: i.e.

I

Since Mnx and Mny are by definition Mnq for q = 0° and 90° respectively and so are known, the only unknown in the above identity is 11. This can be determined from the graph in Figure 8.4 or by numerical means if preferred. Figure 8.4 is based on the ratio MuqlMnq being equal to unity, and will produce conservative results when axial loads are present. 5. Step 4 yields a value of 11 suitable for loads from 30° to the X-axis. Steps 2 to 4 are repeated for q =45° and 60° to obtain a range of values of 11. 6. The value of 11 for use in subsequent assessment· shall be the least of the above determined values, but not less than 1.0.

I


Page 126

This method includes some approximation. Since bending will not be along or perpendicular to a plane of symmetry, deflection will not necessarily be at the same angle as the applied moment. This effect is second order. Note: An alternative, more detailed approach, involving modified interaction equations is presented below for a number of typical chord configurations. 8.1.4.8 Plastic Interaction Curve Approach

Alternatively, interaction equations and curves for generic families of chords are presented in Figures C8.1.8 - C8.1.11 in the Commentary. These are taken from Dyer [19] and based on the interaction approach proposed by e.g. Duan & Chen [20]. It should be noted that the curves and equations are based on axial load applied at the 'center of squash' which is defined as the location at which the axial load produces no moment on the yielded section. For chords without two axes of symmetry (triangular and tubular with offset rack) this is offset from the elastic centroid when the section is comprised of materials of differing yield strengths. Before a section is checked it is necessary to correct as appropriate moments by the axial load times the offset distance between the elastic centroid (used in the structural analysis) and the 'center of squash'. This offset, together with other geometric data for the of each family of chord is presented in Tables C8.l.1 to C8.1.4 in the Commentary. The effective applied moment may then be calculated from: Muex = BxCMux + Pu.ey) Muey = ByCMuy + Pu.ex) The interaction equations are based on ultimate capacity. It is therefore necessary to introduce the required resistance factors. This is achieved by defining: Py = F1. a.Pn Mpx = Fz·b.Mnx Mpy = Fz.b.Mny where; FI = 1.0, unless alternative values are justified by analysis. Fz =1.0, unless alternative values are justified by analysis. The ratio of PulPy, MuexlMpx and MueylMpy shall be determined for the condition under consideration. The should then enter the plastic interaction curves with the MuexlMpx and MueylMpy ratios. The allowable value for PulPy may then be determined. A measure of the interaction ratio can then be obtained as the ratio between the actual and allowable values of PulPy. The should note that the equations for sections with only one axis of symmetry depend on the sign of the moment about the Y-Y axis (given in the Figures). The sign convention should be observed with care. The equations are based on lower bound data from each family of chord shape and will therefore tend to be conservative. More accurate results will be obtained from the individual consideration of the chord in question. [NOTE: At present Figures C8.l.8 - C8.1.11 in the Commentary cover only fully plastic section strength considerations, and their use for a beam-column member is based on the assumption that the member being evaluated is sufficiently short/compact that elasto-plastic stability (buckling at large strains) is not a consideration. Violating


Page 127

this assumption may lead to errors on the unsafe side. Updated infonnation covering elasto-plastic stability may be generated in the future, and should preferentially be used for member evaluations.]

8.1.5 Assessment orother member geometries It is recommended that other member geometries are assessed using the relevant provisions of AISC LRFD [14] or, for stiffened or high Rlt ratio shell , the DNV Rules for fixed offshore installations in conjunction with the DNV Classification note on Buckling Strength Analysis of Mobile Offshore Units [15].

For these geometries, the nominal strength/resistance factors shall be the same as given in the relevant codes, but the load cases and factored loads should be determined in accordance with Section 8.1.3 rather than using the factors in the reference.

8.1.6 Assessment of member ts It is recommended that the assessment of ts of which fonn a truss structure be carried out in accordance with AISC LRFD [14] or API LRFD [16] as appropriate for the t under consideration. The factored loads should be detennined in accordance with Section 8.1.3, rather than using the factors in the references.

Rack plate component Split tubular components

Side plate components

Rack plate component Back plate component OPPOSED RACK SPLIT TmJULAR CHORD MEMBER SECTION

TRIANGULAR TYPE CHORD MEMBER SECTION

Figure 8.2: Typical and components

I


(a)

I

~,...

(b)

(e)

Cd)

~t~

,

,,~ rh

t

,

, ,,

I I

I

I

I

Buckled shape of column is shown by dashed line

j

!

j

I

,

I

1

\

• •

(e:

~ \

\ \

I

I

\

t

77,(

,

m'fT

1

,

(f)

l ,p 12~ ~!) , I I

I

I

I

I

I

I

I

I

I

I

I

/

)

\

",?>

I

I I

L

,

\

Page 128

I

I

I

t'

I

I

I

11';( Im;r.t

lbeoretical K value

0.5

0.7

1.0

1.0

2.0

2.0

Recommended design value when ideal 0000:tions are approximated

0.65

0.80

1.2

1.0

2.10

2.0

E:Kl condition code

.ur-

Rotation fixed and translation fixed

V

Rotation frte and trao.slation

FlfA

?

ti~ed

Rotation find and translation free Rotation (ree and translation free

Figure 8.3: Effective Length Factors (from AISC-LRFD [14])

.8

6+---+---~--+-~~~

~: J5+---+--4-~k1

[

.4+---+---~--+-~~--+---~--~~~--fT--+

.7

.8

Figure 8.4: Chart for Determination of n

.9

1


Page 129

8.2

Overturning Stability

8.2.1

For independent leg jack-ups the assumed overturning axis shall be the most critical axis ing through any two spudcan reaction points as defined in Section 5.2.

8.2.2

The overturning moment shall be calculated from the components of environmental loading, resolved normal to the overturning axis, times the vertical distance from the point of action of the component to the overturning axis. The overturning stability should be checked for the overturning moment Mo caused by the following factored loads: Mo = Y3(ME + Y4.M Dn) where; (provisional - see Section 1.8) Y3 = 1.15 Y4 = 1.0 ME = The extreme overturning moment due to the assessment return period wind, wave and current conditions (see note). MDn = The dynamic overturning moment due to the inertial loadset which represents the contribution of dynamics over and above the quasi-static response as described in Section 7.3.6 (see note).

8.2.3

The unit shall be shown to satisfy the following overturning requirements: Mo :s; 1.Mo + 2.ML + 3.Ms where; Mo = The stabilizing moments due to weight of structure and non-varying loads (at the displaced position resulting from the factored loads - see note) including: - Weight in air including appropriate solid ballast. - Equipment. - Buoyancy. - Permanent enclosed liquid. ML The stabilizing moment due to the most onerous combination of minimum variable load and center of gravity applicable to extreme conditions as specified in Section 3.2 (at displaced position - see note). Ms = The stabilizing moments due to seabed foundation fixity (these shall not be taken into unless specific calculations for the location and the spudcan concerned show that a significant contribution from seabed fixity may be expected). <1>1 R.F. for dead load moments (Mo) 0.95 <1>2 = R.F. for live load moments (Md = 0.95 <1>3 R.F. for seabed moments (Ms) 0.95

=

=

=

=

Note: It may be convenient to consider the reduction in dead and live load stabilizing moment caused by the displacement resulting from the factored loads as an increase in the overturning moment, rather than as a reduction in the stabilizing moment.

II


Page 130

8.3

Foundation assessment The foundation assessment shall be carried out in a step-wise manner until the requirements of the current stage are satisfied when it is not necessary to proceed further. The philosophy is described in Section 6.3 and shown in Figure 6.9.

8.3.1

Step 1 - Preload and Sliding checks Step 1a - Preload check

8.3.1.1 A preload check shall be used to the adequacy of the leeward leg foundation. The acceptance criteria for the windward leg are discussed in Section 8.3.1.5. 8.3.1.2 The preloading capability should be checked for the vertical leg reaction Qv caused by the following factored loads:

where; = 1.0 = 1.0 (provisional - see Section 1.8) = 1.15 = 1.0 VD = Vertical leg reaction due to the weight of the structure and non-varying loads including: Weight in air including appropriate solid ballast. Equipment or other objects. Buoyancy. Pennanent enclosed liquid. VL = Vertical leg reaction due to maximum variable load positioned at the most onerous center of gravity location applicable to extreme conditions as specified in Section 3.2. VE = Extreme vertical leg reaction due to the assessment return period wind, wave and current conditions (including associated large displacement effects). VOn = Vertical leg reaction due to the inertial loadset which represents the contribution of dynamics over and above the quasi-static response as described in Section 7.3.6 (including associated large displacement effects).

YI Yz Y3 Y4

8.3.1.3 The preload capacity shall be shown to be sufficient to satisfy the following requirements:

where;

= % = = VLo

Vertical leg reaction during preloading R.F. for foundation capacity during preload 0.9 (see Commentary)

II

Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Page 131 Rev 2, Jan 2002 8.3.1.4 In dense sands (Le. with maximum bearing area not mobilized) and in clayey soils the

preload check may be applied if the leeward leg horizontal reaction QH < 0.1 VLo (with QH determined in accordance with the equations of Section 8.3.1.5). For a spudcan fully embedded in sand the preload check may be applied if the leeward leg horizontal reaction QH < 0.03VLo. In all other cases a pinned condition bearing capacity check of the foundation shall be carried out in accordance with Section 8.3.2 (see Commentary). 8.3.1.5 Step Ib - Sliding Resistance - Windward Leg(s) a) The sliding capacity of the windward leges) should be checked for the horizontal leg reaction QH caused by the following factored loads: QH = Y3(HE + Y4. H Dn) in association with: Qv = YI.V O + Y2. VL + Y3(VE+ Y4. VDn) where; YI = 1.0 Y2 = 1.0 (provisional. see Section 1.8) Y3 1.15 Y4 = 1.0 HE, VE

The extreme horizontal and vertical leg reactions due to the assessment return period wind, wave and current conditions (including associated large displacement effects).

H on ,VDn =

The horizontal and vertical leg reactions due to the inertialloadset which represents the contribution of dynamics over and above the quasi-static response as described in Section 7.3.6 (including associated large displacement effects).

Vo

=. Vertical leg reaction due to the weight of the structure and non-varying loads including: Weight in air including appropriate solid ballast. Equipment or other objects. Buoyancy. Permanent enclosed liquid.

VL

=

Vertical leg reaction due to the minimum variable load positioned at the most onerous center of gravity location applicable to extreme conditions as specified in Section 3.2.

b) The foundation shall be shown to satisfy the following capacity requirements: QH ~ <J>Hfc.FH where; FH = foundation capacity to withstand horizontal loads when load Qv is acting Hfc

= R.F. for horizontal foundation capacity (see Commentary). = 0.80 (effective stress - sand/drained). = 0.64 (total stress - clay/undrained).

II


8.3.2

Page 132

Step 2a - Capacity check - pinned foundation

8.3.2.1 The bearing capacity of the leeward leg should be checked for the leg reaction vector QVH, relative to the still water leg reaction vector, caused by the following factored loads: QVH YI.VHo + Y2. VHL + Y3(VHE + Y4. VHDn)

=

where;

YI Y2 Y3 Y4

= = = =

1.0 1.0 1.15 1.0

VHo

=

Vector of vertical and horizontal leg reaction due to the weight of structure and non-varying loads (allowing for structural deformation) including: Weight in air including appropriate solid ballast. Equipment or other objects. Buoyancy. Permanent enclosed liquid.

VHL

=

Vector of vertical and horizontal leg reaction (allowing for structural deformation) due to maximum variable load positioned at the most onerous center of gravity location applicable to extreme conditions as specified in Section 3.2 (including associated large displacement effects).

VHE

=

Vector of extreme vertical and horizontal leg reaction due to the assessment return period wind, wave and current conditions (including associated large displacement effects).

(provisional - see Section 1.8)

= Vector of vertical and horizontal leg reaction due to the inertial load set

VHon

which represents the contribution of dynamics over and above the quasistatic response as described in Section 7.3.6 (including associated large displacement effects). 8.3.2.2 The leeward leg foundation shall be shown to satisfy the following capacity requirements: QVH ~ c!>vH .FVH where; FVH

=

c!>vH

=

foundation capacity to withstand combined vertical and horizontal loads taken as a vector from the still water load vector in the same direction as QVH.

R.F. for foundation capacity (see Commentary). = 0.90 - Maximum bearing area not mobilized. 0.85 - Penetration sufficient to mobilize maximum bearing area.

=

8.3.2.3 The windward leg foundations should be checked according to the requirements of Section 8.3.1.5.

II


8.3.3

Page 133

Step 2b - Capacity check - with foundation fixity

8.3.3.1 The foundation capacity of the leeward and windward legs should be checked for the leg reaction vector, including the associated can moment, QVHM, relative to the still water leg reaction vector, caused by the following factored loads: QVHM = Yl.VHMD + Y2.VHML + Y3(VHME + Y4. VHMDn) where;

VHJ\,1D

= = = = =

VHML

=

Vector of vertical and horizontal leg reaction and spudcan moment (allowing for structural deformation and large displacement effects) due to maximum (leeward leg) or minimum (windward leg) variable load positioned at the most onerous center of gravity location applicable to extreme conditions as specified in Section 3.2.

VHME

=

Vector of extreme vertical and horizontal leg reaction and spudcan moment due to the assessment return period wind, wave and current conditions (including associated large displacement effects).

VHJ\,1Dn

=

Vector of vertical and horizontal leg reaction and spudcan moment due to the inertial loadset which represents the contributions of dynamics over and above the quasi-static response as described in Section 7.3.6 (including associated large displacement effects).

Yl Y2 Y3 Y4

1.0 1.0 1.15 (provisional. see Section 1.8) 1.0

II

Vector of vertical and horizontal leg reaction and spudcan moment due to the weight of the structure including non-varying loads (allowing for structural deformation and large displacement effects) including: Weight in air including appropriate solid ballast. Equipment or other objects. Buoyancy. Permanent enclosed liquid.

8.3.3.2 The leg reaction vector QVHM shall be checked to satisfy the yield surface as defined in 6.3.4. 8.3.3.3 The windward and leeward leg foundations shall also be shown to satisfy the bearing capacity and sliding capacity requirements of 8.3.2.

I I


8.3.4

Page 134

Step 3 - Displacement check If the factored loads on any footing exceed the factored capacity discussed above a further assessment may be performed in order to show that any additional settlements and/or the associated additional structural loads are within acceptable limits. See Section 6.3.5.

8.3.5

Punch-through The selection of factors of safety against punch-through should be made using sound engineering judgment, ing for the accuracy of the available soil data and the magnitude of any possible sudden penetration (see Commentary). When the possibility of punch-through exists during the installation and preloading phases it may be applicable to consider the magnitude of possible sudden penetration in comparison with the structural capability of the unit to resist punch-through. If the possibility of punch-through remains once the unit has been installed on location and elevated to the operational airgap the evaluation should for long term effects (e.g. cyclic degradation).

8.4

Horizontal Deflections When working close to or over a platform the assessor shall, if required by the platform owner, provide the extreme deflections of the jack-up to the platform owner (see Section 5.5.1 of the GUIDELINE).

8.5

Loads in the Holding System

8.5.1

The holding system (elevation and/or fixation system) is deemed to be the system which forms the load path connecting the hull to the legs.

8.5.2

The loads in the holding system shall not exceed those specified by the manufacturers, unless the basis of the limitations and the equivalent reference stress levels are stated, when the factored applied load may be compared with the ultimate capacity multiplied by a R.F. (q,) of 0.85.

8.5.3

he stresses in the structural connecting the holding system to the hull shall be in accordance with the requirements of Section 8.1.

8.6

Hull

8.6.1

It is assumed that the jack-up hull is designed and built to the structural/scantling requirements of a recognized Classification Society and carries a valid Class Certificate.

8.6.2

For jack-ups where 8.6.1 does not apply it shall be shown that the hull has adequate strength to withstand appropriate combinations of dead load, variable load, environmental load, deflections, preload conditions and dynamics effects.


8.7

Page 135

Structure Condition Assessment The objective of the site specific assessment is to ensure an appropriate level of structural reliability of the jack-up in the elevated condition. To achieve this, must be taken of any deterioration in the jack-up structure (see Section 1.3.4 of the GUIDELINE). The condition of the structure is the responsibility of the owner and is deemed to be satisfactory if the jack-up has valid class certification as described in Section 2.4.2. Normally the owner can thus provide the assessor with all the information required to satisfy the structure condition requirement.

In special cases (usually at the option of the operator), an on site structural inspection may be required to assess the condition of the jack-up. Guidance for such an on site structural inspection is given in the Commentary. In the event that the results of this inspection reveal deterioration of the structure, due of such deterioration shall be taken into in the assessment.


8

Page 136

GLOSSARY OF . ACCEPTANCE CRITERIA ar A

= = = = = = =

Ratio of total web area to area of compression flange. Cross sectional area of a member (excluding rack teeth). Section effective area (excluding rack teeth). Ae Area of a component in a member. Ai bei Effective width of a component. Width of a rectangular component. bi B,B},B 2 Factors used in determining Mu for combined bending and compressive axial load. Moment amplification factors. II Bx,By = Cb = Bending coefficient dependent on moment gradient. Cm = Coefficient applied to bending term in interaction formula for prismatic dependent upon column curvature caused by applied moments. Cw = Warping constant. D = Dead load vector due to the self-weight of the structure and non-varying loads. Do = The load vector due to the inertial loadset which represents the contribution of dynamics over and above the quasi-static response (including associated large displacement effects). e = Eccentricity between elastic and plastic neutral axes. e , ex, ey = Eccentricity between elastic and plastic neutral axes. II E Load due the to assessment return period wind, wave and current conditions = (including associated large displacement effects). E of elasticity (200,000 MN/m2 {29 ,000 ksi} ). Modulus = fi = Component compressive stress. Fer = Critical stress. FH = Foundation capacity to withstand horizontal loads when Qv is acting. Fmio components (in a member). = The smaller value of Fyi and (5/6)Fui of all the 2 MN/m ). Residual stress due to welding (114 Fr = FVH = Foundation capacity to withstand combined vertical and horizontal loads. FVHM = Foundation capacity to withstand combined vertical, horizontal and moment loads. Fy = Minimum specified yield stress or specified yield strength. Fyh = Minimum yield stress or specified yield strength of component with highest bit ratio. Fyeff = Effective material yield stress for consideration of axial buckling. FYi = Minimum specified component yield stress or specified yield strength. Fywj = Minimum specified web yield stress or specified yield strength. Fyfj = Minimum specified flange yield stress or specified yield strength. FUi = Component material ultimate strength. G = Shear modulus of elasticity. h = Subscript referring to the component which produces the smallest value of Mo. h = Web depth. H Do = Horizontal leg reaction due to inertialloadset representing dynamics. HE = Horizontal leg reaction due wind wave and current. Ie = Second moment of area of compression flange. I = Second moment of area of section. Ix = Second moment of area of section about major axis. Iy = Second moment of area of section about minor axis. J = Torsional constant for the section.

I


8

GLOSSARY OF - ACCEPTANCE CRITERIA (continued)

K

= = = =

1

L Lb m MD MDn ME ML Ms Mn,Mnx , Mny Mnq

Me Mp Mpx Mpy Mr Mu M ue, Muex, Muey M'uex, M'uey Muq MI M2 PE Pu Pn P ni Py q Q Q Qa QH Qs Qv QVH QVHM r rx ry R Re

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

Page 137

Effective length factor. Unbraced length of member; face to face for braces, braced point to braced point for chords. The load vector due to the maximum or minimum variable load positioned at the most onerous center of gravity location applicable to extreme conditions. Laterally unbraced length; length between points which are either braced against lateral displacement of compression flange or braced against twist of the cross section. Ratio of web component yield stress to flange component yield stress which gives smallest value of Re. Stabilizing moment due to self weight. Overturning moment due to inertialloadset representing dynamics. Extreme overturning moment due to wind, wave and current. Stabilizing moment due to most onerous combination of variable load and center of gravity. Stabilizing moment due to seabed foundation fixity. Nominal bending strength. Allowable bending strength about axis q. Factored overturning moment. Section plastic moment. Plastic moment capacity about member x-axis. Plastic moment capacity about member y-axis. Limiting buckling moment of section. Applied moment determined in an analysis which includes global and s for local loading.

II P-~

Effective applied bending moment. Limiting components of applied bending moment. Assumed limiting bending moment about axis q in absence of axial load. Smaller end moment of a member. Larger end moment of a member. Euler buckling strength. Applied axial load. Nominal axial strength. Component nominal axial strength. Axial yield strength. Angle of load heading with respect to defined X axis. Factored load vector. Full reduction factor for slender compression components. Reduction factor for slender stiffened compression components. Factored horizontal leg reaction. Reduction factor for slender unstiffened compression components. Factored vertical leg reaction. Factored leg reaction vector of vertical and horizontal loads. Factored leg reaction vector of vertical, horizontal and moment loads. Radius of gyration. Radius of gyration about the major axis. Radius of gyration about the minor axis. Outside radius of the tube or tubular component. Hybrid girder reduction factor.

effects

II


8

Page 138

GLOSSARY OF - ACCEPTANCE CRITERIA (continued)

t ti VD VDn VE VL

= = = = = = = = =

VLo VHD VHDn

= = =

VHE VHL

= =

VHMD VHMDn

= =

VHME

=

VHML

=

XJ,X2

= = = = = = = = = = = = = = = =

S Sx Sy

~

Y YI Y2 Y3 Y4 A,Ac Ap Ar

II

a t, c Hfc

= = =

=

p t

Elastic section modulus. Elastic section modulus for major axis bending. Elastic section modulus for minor axis bending. Thickness of tubular member or tubular section. Thickness of a rectangular or tubular component.. Vertical leg reaction due to self weight. Vertical leg reaction due to inertialloadset representing dynamics. Vertical leg reaction due wind wave and current. Vertical leg reaction due to maximum or minimum variable load at most onerous center of gravity. Vertical leg reaction during preloading. Vector of vertical and horizontal leg reaction due to self weight. Vector of vertical and horizontal leg reaction due to inertialloadset representing dynamics. Vector of vertical and horizontal leg reaction due wind wave and current. Vector of vertical and horizontal leg reaction due to maximum variable load at most onerous center of gravity. Vector of vertical, horizontal and moment leg reaction due to self weight. Vector of vertical, horizontal and moment leg reaction due to inertial loadset representing dynamics. Vector of vertical, horizontal and moment leg reaction due wind wave and current. Vector of vertical, horizontal and moment leg reaction due to maximum or minimum variable load at most onerous center of gravity. Beam buckling factors. Component plastic modulus. Load factor. Load factor for dead load vector. Load factor for variable load vector. Load factor for environmental load vector. Load factor for inertial load vector due to dynamic response. Column slenderness parameter. Limiting slenderness parameter for compact component. Limiting slenderness parameter for noncompact component. Exponent for biaxial bending. Resistance factor. Resistance factor for axial load. Resistance factor for bending. Resistance factor for axial load (compression). Resistance factor for foundation to withstand horizontal loads when Qv is acting. Resistance factor for foundation during preload. Resistance factor for axial load (tension). Resistance factor for foundation to withstand combined vertical and horizontal loads. Resistance factor for foundation to withstand combined vertical, horizontal and moment loads.

Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Page 139 Rev 2, Jan 2002 8 GLOSSARY OF - ACCEPI'ANCE CRITERIA (continued) <1>1 <1>2 <1>3

= Resistance factor for dead load moments (MD). = Resistance factor for live load moments (ML). = Resistance factor for seabed moments (Ms).


Page 140

REFERENCES 1

Carter D.J.T. (1982), Estimation of Wave Spectra from Wave Height and Period', I.O.S. Report No. 135.

2

Compiled by P. Walker (1990), The UKOOA Surveying and Positioning Committee 'Technical Notes for the conduct of Mobile Drilling Rig Site Surveys (Geophysical and Hydrographic)'.

3

Health and Safety Executive, Petroleum Engineering Division (1990), 'Offshore Installations; guidance on design and construction' (and subsequent amendments).

4

Wheeler J.D. (1969) 'Method for Calculating Forces Produced by Irregular Waves', Proceedings 1st Offshore Technology Conference, Houston. (OTC 1006).

5

Taylor P.H. (1991), 'Current Blockage - Reduced Forces on Offshore Space-Frame Structures' Proceedings 23rd Offshore Technology Conference, Houston. (OTC 6519).

6

Det Norske Veritas, Classification Note 31.5, 'Strength Analysis of Main Structures of SelfElevating Units', February 1992.

7

Brekke J.N., Murff J.D., Campbell R.B., and Lamb W.e., (1989) 'Calibration of Jackup Leg Foundation Model Using Full-Scale Structural Measurements', Proceedings 21st Offshore Technology Conference, Houston. (OTC 6127).

8

Meyerhoff G.G. and Chaplin T.K., The Compression and Bearing Capacity of Cohesive Layers', Br. J. Appl. Phys, No 4, 1953.

9

Brown J.D., and Meyerhoff G.G., Experimental study of Bearing Capacity in Layered Soils', Proc. 7th ICSMFE, Vol 2, 1969.

10

Winterkorn H.F. and Fang H.Y. (1975) 'Foundation Engineering Handbook', Van Nostrand Reinbhold Company.

11.1 Noble Denton & Associates Limited (1987), Foundation fixity of jack-up units, t Industry Study', Volumes I and ll. 11.2 Noble Denton & Associates Limited (1988), Foundation fixity of jack-up units, t Industry Study, extra work'. 12

Sarpkaya T. and Isaacson M. (1981), 'Mechanics of Wave Forces on Offshore Structures', Van Nostrand Reinhold Company.

13

Det Norske Veritas, Classification Note 30.2, 'Fatigue Strength Analysis for Mobile Offshore Units', August 1984.

14

American Institute of Steel Construction, 'Specification for Structural Steel Buildings Load and Resistance Factor Design', September 1986.


Page 141

REFERENCES (Continued)

15

Det Norske Veritas, 'Rules for Classification of Fixed Offshore Installations', July 1989, Part 3, Chapter 1, Section 6B and associated Class Note 30.1, 'Buckling strength analysis of Mobile Offshore Units', October 1987.

16

American Petroleum Institute, 'Draft Recommended Practice for Planning, Deg and Constructing Fixed Offshore Platforms - Load and Resistance Factor Design' (RP 2A-LRFD), First Edition, December 1989.

17

Matlock H. (1970), "Correlations for Design of Laterally Loaded Piles in Soft Clay", Proceedings Offshore Technology Conference (OTC 1204).

18

Andersen K.H. (1992), "Cyclic effects on Bearing Capacity and Stiffness for a Jack-up Platform on Clay", NGI Oslo report 913012-1, Rev 1.

19

Dyer A.P., "Plastic Strength Interaction Equations for Jack-Up Chords", MSc Thesis, Dept of Mechanical Engineering, Univ. of Sheffield, Nov. 1992.

20

Duan L., Chen W.-F., "A Yield Surface Equation for Doubly Symmetrical Sections", Engineering Structures, Vol 12, pp. 114-119, April 1990.

Recommended Practice jar Site Specific Assessment oj Mobile Jack-Up Units Rev 2, Jan 2002 ~

ACCEPTANCE CRITERIA dynamic extreme response foundation assessment holding system loads horizontal deflections hull overturning stability plUlCh-through structural strength check structure condition assessment

10,110-135 102 130 134 134 134 129 134 110 135

ADDED MASS

35,91,95,100

AIRGAP

15,20

AIRY WAVE TIIEORY

15,31

AlSC-lRFD CODE

1l0,112,113

ASSOCIA1ED WAVE PERIOD

15

AXIAL AREA chord leg

49 54

AXIAL LOAD at leg/hull connection duetoP-~

50 44

AXIAL SIRENG1H compact and noncompact sections slender sections structural member in compression structural member in tension

117 118 116 116

BASE SHEAR 1RANSFER RJNCTION

9O,94,98-99,I02-103

BATHYME1RIC SURVEY

21,22

BEARING CAPACITY bearing capacity check, foundation stability penetration in carbonate sands penetration in clays penetration in layered soils penetration in silica sands penetration in silts settlements resulting from exceedence of capacity envelope soil back-flow

61-82 72,132 65 64

BENDING MOMENT bending moment diagrams for leg bending moment due to foundation

66-69

65 65 73 63

55-58 42

Page 142

Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 INDEX (Continued) Subject

BENDING SfRENGTH compact sections noncompact sections slender sections

121-125 122 122-123 123 -125

BIAXIAL BENDING EXPONENT

125 -128

BOREHOLE INVESTIGATION

24

BREAKING WAYES

19,31

CENTER OF ORAVITY

13,14,114,129-134

COMPACf SECTIONS definition nominal axial strength nominal bending strength

114 116 121

CONEPENIROMETER TESTING

24

CREST ELEVATION

15,20

CURRENT

18-19,33 29-30,33 93 39 53,90 19,33 19 33,34 18 18,19 18,19 18,19,33

drag forces environmental excitation other considerations load application profile stretching structure interference surface current surge tide velocity DETAILED LEG MODELING hydrodynamic structural

33-39 4&52

DETERMINISTIC ANALYSIS dynamic wave analysis extreme response determination hydrodynamic modeling wave height for wave theories

31,42 93 90 34 15 31

DIRECTIONALITY directionality fimction for spreading effects on dynamic response

14 17

102

DISPLACEMENT CHECK, FOUNDATION ASSESSMENT

70,81,134

Page 143

Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 INDEX (Continued) ~

DRAG COEFFICIENTS equivalent drag coefficient gusset drag coefficient split tube chord drag coefficient triangular chord drag coefficient tubular drag coefficient

33-39 34-35 37 38 39 36

DRAG FORCE

30,33

DYNAMIC AlV1PLIFICATION dynamic amplification factor

89,91,93,98-100 98,99

DYNAMIC ANALYSIS application of dynamic analysis methods c1osed-fonn frequency domain analysis damping dynamic amplification dynamic amplification factor environmental excitation equivalent mass-spring-damper system extreme response fixation system frequency domain method inertialloadset JONSWAP spectrum maxirnwn response most probable maxirnwn natural period nonlinear elements Pierson-Moskowitz spectrum random analysis regular wave (detenninistic) analysis single degree of freedom analogy structural system damping masses springs stiffness time domain methods

89-107 104 99 91,98,101 89,91,93,94,98 98,99 93 95,98 89,92, 104, 105 46,48,49-51,55-58,97 94,100-101,104,105 52,53,89-91,98-101 16-17,93 18 100-101, 104-105 18,90,93,94-99 91 1693 90,93,94,100-103 93 98,99 91 91,98,101 91,95 95 91,94 94,101,104-105

EFFECTIVE LENGTH effective length factor

117 117,128

~ONMENTALDATA

14-21

(see also WIND, WAVE and CURRENT)

directionality return period return period for airgap ~ONMENTALEXCITATION

EQUIVALENT LEG MODELING hydrodynamic structural

14,17 10,14 15,20 93

33 47,49,54

Page 144

Recommended Practice/or Site Specific Assessment o/Mobile Jack-Up Units Rev 2, Jan 2002 INDEX (Continued) Subject

~

EXTREME (MPME) RESPONSE

89,92,104

EXTREME STll.L WATER lEVEL

20,42

FACTORED LOADS for foundation stiffness detennination foundation checks ovectuming check structural strength check

110 74 130-134 129 114

FACTORED RESISTANCE foundation checks overturning check structural strength check

110 130-134 129 115

FATIGUE analysis environmental data for life requirements sensitive areas

89,106-107 42,107 17-18,19 106 106

FIXATION SYSTEM modeling rotational and vertical stiffness shear force and bending moment diagrams

48,49-51 97 55-58

FIXITY degree of fixity foundation capacity with horizontal and vertical stiffness rotational foundation fixity (stiffness)

42-43 43,91,94 133 75,% 42-43,73-75,76,95

FOO1PRINTS

22,79

FOUNDATION ASSESSMENT capacity check foundation fixity pinned foundation displacement check horizontal leg reaction preload check sliding resistance vertical leg reaction

130-134 132 133 132 134 133 130 131

FOUNDATION ANALYSIS bearing capacity displacement check moment fixity footprints leaning instability other considerations partial spudcan embedment preloading penetration preloading check

61-86

46

125 61-81,1~134

70,81,134 73-81 22,83 83 70 70 61-69 70-72,130-131

Page 145

Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 INDEX (Continued)

Page 146

FOUNDATION ANALYSIS (Continued) scour seafloor instability shallow gas sliding check spudcan-pile interaction

22,84 85 22,85 70,72-73,131 86

FREQUENCY OOMAIN ANALYSIS closed-foan frequency domain analysis

92,94, 101-103, 104 - 105 100

GEOTECHNICAL ANALYSIS leg penetration analysis method carbonate sands clay layered soils silica sands silts spudcan geometries spudcan fotmdation model

61-86 61-69 61-63 65 64 66-69 65

GEOTECHNICAL SURVEYS bathymetric survey borehole investigation cone penetrometer testing geotechnical investigation seabed smface survey shallow seismic survey soil sampling use of geotechnical data

21-24 21,22 24 24 24 21-23 22,23 22 61

GUIDES

46,49-51,59

GUSSETS

37,48

HEIGEIT COEFFICIENT FOR WIND LOADING

28

HOlDING SYSTEM LOADS

46,49,134

HORlZONTAL DEFLECTIONS

134

HORlZONTALIEG REACTION, FOUNDATION ASSESSMENT

131- 133

HUlL acceptance criteria detailed hull model equivalent hull model functional loads loading

134 49 49 13 52

HULlJlEG CONNECTION MODELING equivalent system fixation system guides

46,47,49-51 49,51 50,51 49-51,59

65

61,62 62


Subject HUll.JlEG CONNECfION MODELING (Continued) jackcase jacking system modeling considerations shock pads

51 50,51 49-51 51

HUlL MODELING detailed hull model equivalent hull model

49 49 49

HYDRODYNAMIC COEFFICIENTS gussets marine growth non-rubulars other shapes rough ttJbulars smooth ttJbulars split tube chord triangular chord rubulars

36-39 37 21,30,36 38 39 36 36 38 39 36

HYDRODYNAMIC LOADS deterministic/regular wave analysis chagforce fluid-structure interaction inertia force Morison's equation slender stochastidrandom wave height/spectra wave kinematic extrapolation

29-31,53 15,31 30 30,98 30-31 29,30,31,33,36 29 15,16-17,31 31

INERTIA inertia coefficients inertia force (wave) inertialloadset

35,36,37,38-39 30 52,53,89,90,98 - 101

~CTIONEQUATIONSFORMEMBER~

115,119, 125

JACKING SYSTEM

46,49-51,55-58

LARGE DISPLACEMENT ANALYSIS (see NON-LINEAR ANALYSIS) lEANING INSTABILITY

79

lEG'CAN CONNECfION

43

lEG'HULLCONNECfION (seeHUIlJl.EG CONNECTION) lEG INa..INATION

43

Page 147


lEG MODELING hydrodynamic added mass

buoyancy ~edlegnKrleling

drag coefficients equivalent leg nKrleling inertia coefficients member lengths non-structural items shielding solidification spudcan nKrleling strucnJral combination leg nKrleling ~ed leg nKrleling equivalent leg nKrleling member lengths single detailed leg model spudcan nKrleling

lEG PENETRATION analysis method carbonate sands clay layered soils silica sands silts

35,91,94 13 33-34 33-39 33-35 35,36-37,38-39 34 34 34 34 34 49 46-52 4749,54 48 48 52

61-63 65 64 66 65 65

lEG RESERVE

21

LOAD AND RESISTANCE FACfOR DESIGN, SIRUCfURAL S1RENGTII

110-113,127

LOADS application to structural model combinations current hull (fimctional)

hydrodynamic inertialloadset P-d

52-53 90 53,90 13,52 29-31,53 52,53,89,90,98 - 101 4345,52,53

wind27-29,53

LOCAL BUCKLING

116,121

MARINE GROWTIl

21,30,36

MASS-SPRING-DAMPER SYSTEM

95,98-100

MAXIMUM HEIGHf, WAVE

14

MEAN WATER lEVEL

20

MINIMUM STllL WATER lEVEL

20

Page 148

Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 INDEX (Continued) Subject MOMENT bending moment capacity bending moment due to foundation fixity bending moment diagrams for leg can moment effective applied moment in compression in tension hull sag moment leWhull connection moment lower guide moment due to leg inclination overturning moment P-Llmoment second moment of area (legs)

121-125 42 55-58 129,133 120

119 52-53 46,49-51 43 90,100,129 4345 54

MORISONS EQUATION

29,30,31,33,36

MOST PROBABLE MAXIMUM

100 - 101, 104 - 105

NATURAL PERIOD

90,93, 94 - 99

NONLINEAR MODELING METIIODS non-linear elements

44,77 87

NON-STRUCfURAL ITEMS, LEG MODELING

34

NON-TUBULARS, HYDRODYNAMIC COEFFICIENTS

38-39

OVERTURNING STABll..ITY axis moment

124

P-Ll

geometric stiffness modeling methods linear-elastic displacement amplification loads manual addition ofP-Ll moments non-linear modeling methods

10,129 44,45,90, 129 4345 44 45 52,53 45 44

PERIOD natural return

18,90,93,94 - 99 14,15,20

wave associated peak zero-upcrossing

15 16-17,90,99 17

PINIONS

46-47,49-51,55-58,134

PLASTIC ANALYSIS plastic moment plastic stress distribution

112 121,122

114

Page 149

Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 INDEX (Continued) Subject PRELOAD foundation assessment foundation stability leg penetration during

90,110 130,131

PUNCH-THROUGH

134

QUASI-STATIC ANALYSIS

44,89,90,93,98 -100

RACKTEErn fatigue stiffuess due to marine growth on

100 49 36

70-72 61-69

RANDOM WAVE ANALYSIS (see STOCHASTIC ANALYSIS) REFERENCE LEVEL, WIND

14,27,28

REGULAR WAVE ANALYSIS (see DEIERMINISTIC ANALYSIS) RESERVE LEG LENGTH RESISTANCE FACTORS foundations holding system overturning structural

21

130-131

134 129 115

RESPONSE ANALYSIS

89-107

RETIJRN PERIOD

14,15,20

SCOUR

22,80

SEABED REACTION POINT

42

SEABED SURFACE SURVEY

21

SEAFLOOR INSTABILITY

81

SHAlLOW GAS

22,81

SHAlLOW SEISMIC SURVEY

22,23

SHAPE COEFFICIENTS FOR WIND LOADING

29

SHEAR FORCE DIAGRAMS

55-58

SHIELDING

34

SHOCK PADS

50,51

SHORTCRESTEDNESS (WAVE SPREADING)

17-18,98,102-103

Page 150


SIGNIFICANT WAVE HEIGHT

14,15,17

SINGlE DEGREE OF FREEDOM ANALOGY

98-99

SLENDER SECTIONS hydrodynamic loads structural considerations

29 114, 118 , 123 -125, 127

SLIDING CHECK

70,72-73, 130-l31

SMOOTH VALVES, HYDRODYNAMIC COEFFICIENTS FOR roBULARS

36

SOIL SAMPLING

23,24

SOLIDIFICATION

34

SPECIRUM (WAVE) JONSWAP Pierson-Moskowitz

16-18 16-17,93 16-17,93

SPLIT roBE CHORD, HYDRODYNAMIC COEFFICIENTS

38

SPUOCAN modeling partial spudcan embedment spudcan foundation model spudcan geometries spudcan-pile interaction

34,52 70

62 61,62

86

STIFFNESS due to chord rack

for natural period estimation geometric stiffness modeling methods

49 95-98 44

STOCHASTIC ANALYSIS dynamic analysis hydrodynamic modeling kinematic extrapolation wave height for (scaled) wave spectra wave theory

93,94,100,101,104,105 34 31 15 16-17 31

STORM DIRECTIONS, RANGE OF

42

STRUCTURAL ANALYSIS fatigue analysis foundation fixity general conditions leg inclination load application

42-53 18,42,107 42-43,73-81 42 43 52-53 43-45 42 89 -105 42 46-52

P-~effects

range of storm directions response analysis seabed reaction point structural modeling

Page 151


STRUCTURAL definitions structural strength check

113 110-127

STRUCTURAL MODELING combination 3-leg model combination leg model detailed hull model detailed 3-leg model detailed leg model equivalent 3-stick-Ieg model equivalent hull model equivalent leg model fixation systems general considerations jacking systems jack-case and bracing leg-hull connection modeling model applicability pinions rack tooth stiffuess shock pad single detailed leg model spudcan modeling

46-52 47 49 49 47 48 47 49 49 46,51 46-47 46,51 51 49-51 47 47,51 49 51 48 52

STRUCTURAL STRENGTH CHECK AISCcode axial strength structural member in compression structural member in tension bending strength biaxial bending exponent compact sections axial strength bending strength effective applied moment in compression in tension effective length factors factored loads factored resistance interaction equations local buckling limitations load and resistance factor design member ts noncompact sections axial strength bending strength other geometries resistance factors

110-127 101-126,127 116-119 116 121-125 125,128 114 116 -119 121 - 125 120 119 117,128 110-114 110, 115, 127 115 116-119,121-125 112-113 110-111,127 127 122 117 122 127 112,115,127,134

Page 152


STRUCTIJRAL STRENGTII CHECK. (Continued) slender sections axial strength bending strength structural components - stiffened and unstiffened structural structural strength check torsional buckling (lateral) yield stress STRUCTIJRAL SYSTEM (FOR DYNAMICS) damping

masses stiffness

114 118-119 123 -125 113 113 110-127 121 112,114,117 91-93 91,102 91,95 94,95-98

STRUCTIJRE CONDmON ASSESS:MENT

10,135

STRUCfURE INTERFERENCE, CURRENT

33,34

TEMPERATURE - AIR AND WATER TIIREE lEG MODEL combination 3-leg model detailed 3-leg model equivalent 3-stick-Ieg model

20

TIME DOMAIN ANALYSIS

94,101,104,105

TRIANGULAR CHORD, HYDRODYNAMIC COEFFICIENTS

39

TIJBULARS, HYDRODYNAMIC COEFFICIENTS

36

VERTICAL lEG REACTION, FOUNDATION ASSESSMENT

130-133

WATER lEVEL chartdatmn extreme still water level lowest astronomical tide mean water level minimtnn still water level

20 20 20 20 20 20

WAVES Airy wave theory breaking waves crest elevation directionality function extreme wave height freak waves kinematic extrapolation maximmn height

14-18 15,31 19,31 15,20 17,102 14 20 31 14,15

47 47 47

period

associated peak retmn zero-upcrossing

15 16-17 14,15,20 16-17

Page 153


WAYES (Continued) shortcrestednes (spreading) significant height significant height (scaled)

17,98,102-103 14 15,17

spectrum

JONSWAP Pierson-Moskowitz steepness

16-17,93 16-17,93 17

WEIGH!'

center of gravity minimwn elevated weight WIND

force calculation height coefficient load application profile reference level shape coefficient velocity

13,14,114,129 - 133 13 14,27-29 27-29 28 53 14,28,29 14,27-28 29 14,27-28

YIElD STRESS

112,114,117

YIEl..D SURFACE, FOUNDATION FIXITY

74-75

ZERO-UPCROSSING WAVE PERIOD

16-17

Page 154

COMMENTARIES TO RECOMMENDED PRACTICE FOR SITE SPECIFIC ASSESSMENT OF MOBILE JACK-UP UNITS FIRST EDITION -MAY 1994 (REVISION 2 - JAN 2002)

Rev Rev I

Issue Date May 1997

Rev 2

Jan 2002

Details Changes made to pages 12, 28, 31, 82, 88, 115, 125, 152, 168, 173, and 188. Revised areas indicated by sidelines thus: I Changes made to pages. ]]3,115,128,129,144,161,173 Revised areas indicated by double sidelines thus: II

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002

Page 2

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 PREAMBLE

Page 3

These Commentaries to the Recommended Practice for Site Specific Assessment of Mobile JackUp Units (PRACTICE) have been written to provide background information, ing documentation, and additional or alternative calculation methods as applicable.

The reader should recognize that the information presented herein should only be taken in conjunction with the PRACTICE and that the cautions and limitations discussed in Section 1 of the PRACTICE apply.


Page 4

CONTENTS SECTION TITLE

PAGE NO

C3

COMMENTARIES TO ASSESSMENT INPUT CONDITIONS

12

C3.3

ENVIRONMENTAL CONDITIONS - GENERAL

12

C3.4

WIND

12

C3.5

WAVES C3.5.1 Determining Wave Heights for Regular and Irregular Wave Analysis C3.5.1.1 Significant Wave Height for Stochastic Irregular Waves Analysis. C3.5.1.2 Wave Height for Regular Wave Analyses C3.5.3 Alternative formulation for wave spectrum. C3.5.4 Spreading

13

C3.7 WATER LEVELS AND AIRGAP Glossary of for Section C3 References for Section C3

20 21 22

C4

COMMENTARIES TO CALCULATION METHODS - HYDRODYNAMIC AND WIND FORCES

23

C4.1

INTRODUCTION

23

C4.2

WIND FORCE CALCULATIONS

23

C4.3

HYDRODYNAMIC FORCES C4.3.1 General C4.3.2 Drag forces C4.3.3 Inertia forces

24

C4.4

WAVE THEORIES C4.4.1 General C4.4.2 Regular wave analysis C4.4.3 Irregular wave analysis

27

C4.5

CURRENT C4.5.1 General C4.5.2 Combination with wave particle velocities C4.5.3 Reduction of current by the actuator disc formula C4.5.4 Current stretching

31

C4.6

LEG HYDRODYNAMIC MODEL C4.6.1 General C4.6.2 Length of C4.6.3 Spudcan C4.6.4 Shielding and Solidification C4.6.5 Equivalent drag coefficient C4.6.6 Equivalent Inertia coefficient

32

Page 5

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 CONTENTS (Continued) SECTION TITLE

PAGE NO

C4.7

HYDRODYNAMIC COEFFICIENTS FOR LEG C4.7.1 General C4.7.2 Hydrodynamic Coefficients for Tubulars C4.7.2.1 General C4.7.2.2 Literature survey and recommended values C4.7.2.3 Marine Growth dependence C4. 7.2.4 Definition of relevant parameters C4.7.2.5 Dependence on roughness C4.7.2.6 Keulegan Carpenter number dependence C4.7.2.7 Reynold's number dependence C4. 7.3 Marine Growth Thickness C4. 7.4 Hydrodynamic Coefficients for Brackets C4.7.5 Hydrodynamic Coefficients for Chords C4.7.5.1 Split tube chords C4.7.5.2 Triangular chords C4.7.6 Other shapes

34

C4.8

OTHER CONSIDERATIONS

58

Glossary of for Section C4

59

References for Section C4

61

Appendices to Section C4 C4.A Example of Equivalent Model Computations C4.B Comparison cases to assess implications of PRACTICE formulation C4.C Comparison of test results for chords

66 70 75

CS

COMMENTARIES TO CALCULATION METHODS - STRUCTURAL ENGINEERING

78

C5.1

INTRODUCTION

78

C5.2

GENERAL

78

C5.3

GLOBAL RESPONSE

79

C5.4

DISCUSSION OF THE LEG-HULL CONNECTION

80

C5.5

DETERMINATION OF PROPERTIES FOR EQUIVALENT MODELLING OF LEG AND LEG-HULL CONNECTION

82

C5.6

LOAD APPLICATION

84

C5.7

EVALUATION OF FORCES

84


89

Appendices to Section C5 C5.A Derivation of alternative geometric stiffness formulation for P-Ll effects

90

Page 6

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 CONTENTS (Continued) SECTION TITLE

PAGE NO

C6

COMMENTARIES TO CALCULATION METHODS - GEOTECHNICAL ENGINEERING

98

C6.1

INTRODUCTION

98

C6.2

PREDICTION OF FOOTING PENETRATION DURING PRELOADING C6.2.1 Analysis method for leg penetration prediction C6.2.2 Penetration analysis for clays C6.2.3 Penetration analysis for silica sands C6.2.4 Penetration analysis for carbonate sands C6.2.5 Penetration in silts C6.2.6 Penetration analysis for layered soils C6.2.6.1 Squeezing of clay C6.2.6.3 Punch-through: Dense sand over soft clay C6.2.7 Summary

98

C6.3

FOUNDATION STABILITY ASSESSMENT C6.3.3 & C6.3.4 Bearing capacity for inclined loading

111

C6.4

OTHER ASPECTS OF JACK-UP UNIT INSTABILITY C6.4.1 Leaning instability C6.4.2 Footprint considerations C6.4.3 Scour C6.4.4 Seafloor instability C6.4.6 Spudcan-pile interaction

118

GlOSSary

of for Section C6

120


121

C7

COMMENTARIES TO CALCULATION METHODS - DETERMINATION OF RESPONSES

126

C7.1

INTRODUCTION

126

C7.2

QUASI-STATIC EXTREME RESPONSE WITH INERTIAL LOADSET

126

C7.3

CONSIDERATIONS AFFECTING THE DYNAMIC RESPONSE

126

C7.4

SELECTION OF APPROPRIATE EXCITATION PERIOD

128

C7.5

METHODS FOR DIRECT DETERMINATION OF THE DYNAMIC RESPONSES

129

Appendices to Section C7 C7.A Derivation of jack-up stiffness equation C7.B Details of appropriate dynamic analysis methods C7.B.l Analysis methods C7.B .1.1 Frequency domain methods C7.B.l.2 Time domain methods C7.B.2 (see overleaf)

132

143


Page 7

CONTENTS (Continued) SECTION TITLE Appendices to Section C7 (continued) C7.B.2 Methods for determining the MPM C7.B.2.1 Use of drag-inertia parameter (or equivalent) determined from mean and standard deviation of a frequency or time-domain analysis. C7.B.2.2 Fit Weibull distribution to results of a number of time-domain simulations to determine responses at required probability level and average the results. C7.B.2.3 Fit Gumbel distribution to histogram of peak responses from a number of time-domain simulations to determine responses at required probability level. C7.B.2.4 Apply Winterstein's Hermite polynomial method to the results of time domain simulation(s).

PAGE NO 143 145 146

14S

149

C8

COMMENTARIES TO ACCEPTANCE CRITERIA

162

C8.0

BACKGROUND TO PARTIAL LOAD FACTORS CS.O.l General C8.0.2 Fundamental Question CS.0.3 Solution C8.0.3.1 Probabilistic Description of Input C8.0.3.2 Limit States C8.0.3.3 Response Model C8.0.3.4 Safety Index vs. Safety Factor C8.0.3.5 Reference or Target Safety Level C8.0.3.6 Derivation/Calibration of Safety Factors

162

C8.1

STRUCTURAL STRENGTH CHECK CS.1.1 Introduction C8.1.2 Definitions C8.1.3 Factored loads C8.1.4 Assessment of - excluding stiffened and high D/t ratio tubulars CS.l.4.1 General interaction equations C8.1.4.213 Nominal Axial Strength C8.1.4.4/5 Effective Applied Moment CS.1.4.6 Nominal Bending Strength C8.1.5 Assessment of - other geometries

165

C8.3

FOUNDATION ASSESSMENT

184

C8.7

STRUCTURE CONDITION ASSESSMENT CS.7.1 Introduction CS.7.2 Scope of condition assessment C8.7.3 Condition monitoring

186


188


190

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 CONTENTS (Continued)

Page 8

LIST OF FIGURES C3.5.1

C4.7.18 C4.7.19 C4.7.20

Comparison of wave crest elevation predicted skewness and observed data at 70m in the North Sea. Oscillating drag coefficient vs. motion amplitude to diameter ratio xolD for given reduced velocities. Range of validity of different wave theories. Surface elevation, and velocity profiles for deterministic regular waves. Linearization w.r.t. wave heights. Comparison between measured and computed forces on a pile up to free surface Drag coefficient for rough cylinders at high Reynold's number Drag coefficient for post critical Reynolds numbers for rough cylinders. Effect of roughness on drag coefficient and vortex shedding frequency for post-critical Reynolds numbers. Recommended values for the drag coefficient as function of relative roughness. Drag coefficient dependence on KC number. Drag coefficient dependence on KC-number for clean cylinders of the Ocean Test Structures. Drag coefficient dependence on KC-number for barnacle covered cylinders of the Ocean Test Structure. Recommended drag coefficient dependence on KC for cylinders in waves, at high Reynolds numbers. Suggested Reynolds dependence in existing guidance. Reynolds dependence of drag coefficient in test results. Reynolds dependence of drag coefficient. Recommended values for Reynolds dependence for different values of relative roughness, KC>40. Definition of directions and dimensions for a split tube chord. Drag coefficient at 90° related to the rack width W. Alternative interpolation formulations fit to data. Comparison with some current practices for regular wave analysis. WID 1.24 and the scaling regular/irregular =0.7, valid below MWL+2.0m. Definition of dimensions and angles for a triangular chord. Drag coefficients for basic sections in uniform flow. Comparison between TEES test results and the PRACTICE.

C4.A.l C4.A.2

Model of a bay for test purposes Square bay with triangular chords

66 68

C4.C.l

Comparison of PRACTICE formulation with model tests, ratio WID 1.08 Comparison of PRACTICE formulation with model tests, ratio WID 1.10 Comparison of PRACICE formulation with model tests, ratio WID 1.13 Comparison of PRACTICE formulation with model tests, rack WID 1.18 Comparison of PRACTICE formulation with model tests, rack WID 1.24

75

C4.3.1 C4.4.1 C4.4.2 C4.4.3 C4.7.1 C4.7.2 C4.7.3 C4.7.4 C4.7.5 C4.7.6 C4.7.7 C4.7.8 C4.7.9 C4.7.1O C4.7.11 C4.7.12 C4.7.13 C4.7.14 C4.7.15 C4.7.16 C4.7.17

C4.C.2 C4.C.3 C4.C.4 C4.C.5

=

= = = = =

16 26 29 30 30 42

44 44 45 45 47 47 48 48 49 49 50 50 53 53 54 54

56 57 57

75 76 76 77


Page 9

LIST OF FIGURES (continued)

C5.1 C5.2 C5.3 C5.5 C5.6 C5.7 C5.8 C5.9

Responses/reactions from first order analyses P-~ and leg inclination effects Contribution of second order effects to first order responses Representative leg-hull connection Leg-hull connection component combinations Guide clearances Jacking system backlash Types of leg guide arrangement Unopposed and opposed pinion arrangements

85 85 86 86 87 87 87 88 88

C5.A.l C5.A.2

Analysis model Load application

94 94

C6.1

Comparison of bearing capacity analytical procedures for shallow foundations and jack-ups. Stability factors for cylindrical excavations in clay. Conical footing bearing capacity - problem definition and notation. Depth of failure zone in sand Spudcan bearing capacity analysis - sand over clay - load spread method. Foundation bearing failure modes. Verticallhorizontalload envelopes for footings in clay. Foundation combined verticallhorizontalloading on sand - comparison of design criteria and observed data. Verticallhorizontalload envelopes for footings in sand. Vertical load-displacement curves for leeward and windward legs.

98

C5A

C6.2 C6.3

C6A C6.5 C6.6 C6.7 C6.8 C6.9 C6.1O

99 101 107 109 110 112 114 114 117

C7.1

Periods for wave force cancellation and reinforcement as a function of leg spacing.

131

C7.A.l

Graphical solution of equation (24)

140

C7.B.1 C7.B.1

Part 1 - Procedure for determining inertialloadset Part 2 - Procedure for determining (distributed) inertial loadset Time domain procedure for determining mean and standard deviation. Frequency domain procedure for determining mean and standard deviation. Procedure for estimating the extreme response. Procedure for determining the mpm-factor of the static response. Ratio C R of most probable maximum to standard deviation as a Function of drag-inertia parameter K for N =1000 peaks. Comparison between the normalized spectra S11(oo), Sc»(oo) and SPM(ro)

151 152

C7.B.2 C7.B.3

C7.BA C7.B.5 C7.B.6 C7.B.7 C8.0.1 C8.l.1 C8.l.2

Link between safety factor and safety index Stress-strain curve - ultimate strength much bigger than yield strength. Stress-strain curve - yield strength close to ultimate strength.

153 154 155 157 160 160 164 169 169


Page 10

LIST OF FIGURES (continued) CS.1.3 CS.1.4

CS.1.5 CS.1.6 CS.1.7 CS.1.S CS.1.9 CS.1.l0 CS.1.l1

Stress-strain curves for two component member for which addition of nominal strengths is permissible. Stress-strain curves for two component member in which one component fractures before the other is loaded to its nominal strength. Stress-strain curves for components of example member. Example hybrid chord section. Fully plastic stress distribution. Interaction equations/curves for tubular chords with double central racks. Interaction equations/curves for split tubular chords with double central racks. Interaction equations/curves for tubular chords with offset double racks. Interaction equations/curves for triangular chords with single racks.

169 170

170 172 172 175 17S

ISO IS2

LIST OF TABLES C3.5.1 C3.5.2 C4.7.1 C4.7.2 C4.7.3 C4.7.4 C4.A.l C4.A.2

C4.A.3

C4.A.4 C4.A.5 C4.B.l C4.B.2

=

Regular Wave Analysis Normalized Results, CDeDe 5.13 over the full depth. Scaling Factor Yd on loads to comply with Airy Wheeler in Irregular Seas. Survey of Relevant Literature on CM - and CD-values for Tubulars. Recommended Roughness Values for Tubulars. Recommended Hydrodynamic Coefficients for Tubulars. Comparison of Drag Coefficients for Simple Sections and Chord CDpr Evaluated From tests. Computations of Equivalent model for heading 0° to be used in Site Assessment for z < MWL +2m, chord WID = 1.13. Computations of Equivalent model for heading 0° to be Compared with Model Test Results, Chord WID = 1.13, Model Scale 1:4.264. Computations of Equivalent model for heading 30° to be Compared with Model Test Results, Chord WID = 1.13, Model Scale 1:4.264. Square Bay with Triangular Chords, Equivalent Model to be used in Site Assessment z < MWL + 2m. Square Bay with Triangular Chords, Equivalent Model to be used in Comparison with Test Results, Model Scale 1:4.256. Comparison including wave height scaling, water depth = 30m, Hsrp 10m. Comparison including wave height scaling, water depth 90m, Hsrp = 14m.

=

=

14 15 37 43 43 56 66 67

67

6S 69 72 73


Page 11

LIST OF TABLES (continued)

C5.A.1 C5.A.2 C6.1 C6.2 C6.3 C6.4 C6.5 C6.6 C7.1 CS.l.1 CS.l.2 CS.l.3 CS.l.4

Verification of Simple Procedure for P-~ Effect with Exact Solution. Wave Loading Case. Verification of Simple Procedure for P-~ Effect with Exact Solution. Wind Loading Case.

93

Ne' factors as a function of embedment, rate of increase of shear strength with depth and roughness, cone angle 30°. Ne ' factors as a function of embedment, rate of increase of shear strength with depth and roughness, cone angle 60°. Ne ' factors as a function of embedment, rate of increase of shear strength with depth and roughness, cone angle 90°. Ne ' factors as a function of embedment, rate of increase of shear strength with depth and roughness, cone angle 120°. Ne ' factors as a function of embedment, rate of increase of shear strength with depth and roughness, cone angle 150°. Ne ' factors as a function of embedment, rate of increase of shear strength with depth and roughness, cone angle 180°. Recommended combinations of the structural system and environmental excitation models for a dynamic analysis. Data for tubular chords with double central racks. Data for split tubular chords with double central racks. Data for tubular chords with offset double racks. Data for triangular chords with single racks.

103

93

103 104 104 105 105 130 176 179 lSI IS3


C3

Page 12

COMMENTARIES TO ASSESSMENT INPUT CONDITIONS

C3.3 ENVIRONMENTAL CONDITIONS· GENERAL The PRACTICE does not permit the use of full t probability (assessment return period) environmental data. Nevertheless some of t probabilities is permitted as noted below: Seasonally adjusted data may be used if appropriate (Section 3.3.1). Note: When seasonal data are specified, the data should not be divided into periods of less than one month and the values so calculated should generally be factored such that the extreme for the most severe period equals the all-year value for the required assessment return period. Where directional data are available, these may be considered (Section 3.3.1). Note: When directional data are specified, the data should normally not be divided into sectors of less than 30° and the directional values so calculated should generally be factored such that the extreme for the most severe sector equals the omnidirectional value for the required assessment return period and season where applicable. In certain areas 30° sectors may be inappropriate; caution should be exercised if an assessment heading falls marginally outside a sector with higher data. The downwind (vector) component of the maximum surface flow of the mean spring tidal current is specified rather than the maximum spring tidal current (Section 3.6.1). Site specific infonnation may be used to determine an appropriate combination of wind driven and surge currents (Section 3.6.1). C3.4

WIND The PRACTICE selects the 1 minute sustained wind for determining the wind loadings on the jack-up. In some instances the wind data will be supplied only for an alternative averaging period. The conversion to the 1 minute sustained value can not be uniquely defined as the conversion can be a function of various parameters, including the wind speed itself. In the absence of site specific data the following formula may be applied [1], providing that the design stonn is of longer duration than the supplied averaging period (the supplied averaging period may exceed the storm duration in areas of the world where the extreme winds are due to squalls, thunderstorms, etc.): Vref

=

t

Vs[1 - 0.047In( ~)] ts

where; Vref = wind velocity for reference averaging period required by PRACTICE (1 minute). Vs = wind velocity for supplied averaging period, ts. tref = averaging period required by PRACTICE (l minute). ts = averaging period for supplied wind velocity~

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 C3.5 WAVES

Page 13

C3.5.1 Determining Wave Heights for Regular and Irregular Wave Analysis The wave heights utilized by the PRACTICE for wave load calculations are related to the return period significant wave height for a three-hour stonn, Hsrp. The PRACTICE however recognizes that this data may not always be available to the assessor and therefore provides relationships between Hsrp and H max , the individual extreme wave height for the assessment return period with an annual probability of exceedance of lIreturn period. The assessment return period is nonnally taken as 50 years in which case Hmax(so) is the wave height with a 2% annual probability of exceedance. Hsrp and the associated period are nonnally determined through a direct extrapolation of measured or hindcast site specific significant wave heights. Hmax may be determined either from an extrapolation of the distribution of individual wave heights over the assessment return period or by the application of a multiplication factor to Hsrp. It is noted that the 'extreme wave height' of a regular wave, Hmpm , determined from a 3hour stonn segment is the most probable maximum (MPM) wave height, defined as the distance from the extreme crest to the following trough. Using this definition, the MPM wave height from the 3-hour stonn segment is given by: Hmpm

=

1.68 Hsrp

This relationship is confinned by the data of [2] for individual stonns. However, Hmpm must not be confused with Hmax and must not be used to determine the value of Hsrp on which an assessment is based. This is because Hmax includes site specific considerations of potentially longer durations of stonns (including build up and decay) and the additional probability contributions of other return period stonns (i.e. 20, 30, 40, 100-year, etc., return period stonns). Consequently the ratio HmaxlHsrp is larger than the ratio Hmpn/Hsrp. A consequence of the site specific nature of the derivation of Hmax is that there is no unique relationship between Hmax and Hsrp applicable to all areas of the world. Thus, if a specified return period maximum wave height is given at a particular location there is no consistent way to derive Hsrp without knowledge of how the maximum (Hmax) wave height was derived originally. Average factors between Hsrp and Hmax have been derived for a North Sea and a Gulf of Mexico location for a 50-year return period. Without further infonnation, the North Sea factors can be generalized to any non-tropical revolving stonn area and the Gulf of Mexico factors can be generalized to tropical revolving stonn areas. These factors are: Environmental Conditions Tropical revolving stonns Non-tropical stonns

HmaxlHsro 1.75 1.86


Page 14

The Dean's stream function/Stoke's fifth order theories predict higher peak than trough amplitudes, increasing the maximum velocities and the wetted surface compared with the Airy theory. In Figure C4.4.2 the difference in the profiles is illustrated. Using the same specified wave height this difference may be seen in of the overturning moment, base shear or deck displacement. A number of computations were performed to determine the differences due to wave kinematics on selected Jack-up designs. Some results are summarized in Tables C3.5.1 and C3.5.2. See also Appendix C4.B.

Table C3.5.1 Regular wave analysis normalized results, ~eDe =5.13 over the full water depth Theory

Airy Const. Airy Wheeler Stoke's fifth Dean's stream Airy Const. Airy Wheeler Stoke's fifth Dean's stream

Overt. moment MNm

Dean's overturning! other

3.577

91.607

1.74

7.5

3.266

82.782

1.93

15/14

10.22

5.211

156.16

1.02

15114 15114 28/16 15115 28/16 15/14 28.16 15/14 28/16

10.42 7.5 14.0 7.5 14.0 8.41 19.17 8.41 19.33

5.243 2.916 14.121 2.563 13.446 3.171 18.264 3.161 18.136

159.45 160.83 677.69 138.80 636.53 180.80 976.62 180.30 972.54

1. 1.12 1.44 1.30 1.53 1.00 1.00 1. 1.

Water depth m

Wave H:T m:sec

30

15114

7.5

15114

70

Crest amp. m

Base shear MN


Page 15

In Table C3.5.2 the deterministic analysis is based on application of a various Hmax to Hs relationships. The Stochastic analysis refers to extreme values determined from time domain analyses by fitting a three parameter Weibull distribution to the response peaks and reading the extreme as the 0.999 fractile, approximating a three hour storm extreme.

The results show dependence on the choice of wave kinematics differing with wave height. Table C3.5.2 Scaling factor yd on loads to comply with Airy Wheeler in irregular seas, [11]. BASE SHEAR:

Airy Wheeler

Stochastic irregular seas 1) Deterministic 2) regular waves 3) 4) OVERTURNING MOMENT: Stochastic irregular seas 1) Deterministic 2) regular waves 3) 4)

Airy No stretch

Airy Constant

1.00 0.79 0.66 0.71

1.03 0.84 0.69 0.75

0.83 0.69 0.56 0.61

1.00 0.81 0.67 0.72

1.10 0.93 0.76 0.83

0.790.69 0.56 0.61

Stokes fifth

0.66 0.66 0.66 0.92

0.66 0.66 0.66 0.93

Water depth 110m, Hs = 13.0m, Tp =Tass = 17.0 sec, uniform current V = 0.4 mls 1) Hmax = 1. 86Hs 2) crest as Stokes 3) Hmax = 1.86Hs * 1.07 except Stokes. 4) Hmax = 1.60Hs (pRACTICE recommendation) Wheeler stretching basis for normalized results, i.e.: Airy Wheeler stochastic load = Yd (other load)

C3.5.1.1 Significant Wave Height for Stochastic Irregular Waves Analysis. Only Airy theory is currently applicable together with a stochastic irregular seas analysis, and in Section 4.4 the Wheeler stretching is recommended for describing the kinematics to the instantaneous surface. It is accepted that the increasing assymetry described by higher order theories such as

Stokes is appropriate. The asymmetry can also be seen in recorded data as skewness of the waves, as shown in Figure C3.5.1. Since Airy theory has certain limitations, a practical way to compensate for the assymetry is to increase the significant wave height used as input to the force computations. In order to show that a scaling of significant wave height is appropriate, and to determine the absolute values of the scaling factors, one needs to decide which theory is correct at a given wave condition. Based on the

Commentaries to Recommended Practice for Site Specific Assessment of Page 16 Mobile Jack-Up Units Rev 2, Jan 2002 good fit to test results in wave tank measurements, [6], the Wheeler stretching is found to be a best fit. However, due to the asymmetry of wind generated ocean waves in shallow water, this agreement is judged to be valid only for large water depths. In [7] it is also indicated that a higher peak than trough is appropriate. Here it is assumed that the significant wave height should have a scaling factor close to 1.0 for Wheeler stretching at 110m using irregular wave analysis. At shallower water depths a scaling factor in excess of 1.0 should be due to the wave asymmetry. In [8] a scaling of wave crests is suggested based on the Stokes wave profiles. Comparisons are made both with data for North Sea conditions (d 70 m), see also Figure C3.5.1, and shallow waters (d == 5.0 m) in the Baltic Sea implying that this may be a general model. A correction proportional to wave steepness is deduced which shows fair agreement with the data.

=

0.3 ~

~ 4>

I

0.2

3-4 I

f

§

'"

:>

0.076 2996 1021

2-3

#l .:

<1"

Hs (m)

<2

C')

'"'"4>

Tp:s)

4-5

, I

0.1

4>

5-6

I

~ 4>

:>

ti

0.04

0.06

'·IU

18-11

u·u u-u

1:1-14 14-15

0.105 0.102 0.107 2.974 2966 2.671 194 61 1 0.121 0.118 0.088 3.001 3.007 2.912 43 59 11 0.184 0.147 0.111 2991 3.001 2.912 3 33 11 0.194 0.135 0.148 2.674 3.021 2.934 1 20 9 0.126 u.r14 U.I4l! 2.936 2978 3.018 1 2 3

7-8

0.209 0.141 2.815 3.086 2 3

0.08

Average Steepness keJ'l

8-,

6-7

0.0 0.02

7-11

8-9

0.168

3.096 1

9-10

0.256 2.548 1

Figure C3.5.1 - Comparison of wave crest elevation predicted skewness and observed data at 70 m in the North Sea [8] The crest height correction formula may be simplified neglecting the higher order to be [8]: 11/11 == 1. + 0.6 U3 + 0.5 (
= = = = =

crest elevation by Stokes crest elevation by Airy 2.5 D2 Hs / T/ '
The data and the model indicate that the skewness, U3, is about 0.08 - 0.2 for large seastates at 70 m water depths giving a correction of


Page 17

1.05-1.12 on the crest height compared with a linear model. The forces on a Jack-up structure increase proportionally as the square (or more) of the elevation. Applying a correction for the square of the bias in wave crest the correction for 70m should be in the range 1.10-1.25, depending on wave steepness. By combining the above suggested formulae a correction for the Wheeler stretching in a stochastic analysis may be deduced as: Hs

=

1.0 + 1.5 D2 Hsrp / Tp2

The D2 factor includes a dependence on the wave number for individual; waves. This is not suitable for the purpose of inclusion in the PRACTICE, since there is no unique wave number for a seastate. The elevation is not the only parameter to be considered and others; are: the depth attenuation over water depth, the profiles are not similar in horizontal directions, and forces at some distance lose correlation. This gives a different scaling than that deduced from the wave crest height only. Based on the above a significant wave height for stochastic/irregular wave analysis using Airy waves and Wheeler stretching is recommended as: Hs

=

[1 + 10 HsfT/ exp(-d/25) ]Hsrp

This removes the direct link to the Stokes profile as suggested in [8], but contains the linear dependence on steepness and a depth dependence with an exponential decay. Further, by inserting the limited range of wave steepness specified in Section 3.5 the scaling may be further simplified. Assuming a peak enhancement factor of y = 3.5, the peak period may be approximated as TpfTz =1.3, giving a range for 0.046 < HsfTp2 < 0.057 for all areas. A ratio HsfT/ =0.05 is therefore introduced, such that the significant wave height is recommended as: Hs

=

[1 + 0.5 exp(-d/25)] Hsrp

The scaling factor should be limited to a water depth above, say 25m. A similar scaling on wave height for AirylWheeler stretching is currently being applied indirectly in design specifications, [9], where it is stated that the wave heights according to Airy should be two times the peak amplitude predicted by the Stokes wave profile. The above scaling is an approximation. It would be more correct to for the wave asymmetry directly in the generation of the sea surface elevation by, for example, the methods indicated in [8]. The significant wave height Hsrp could then be applied directly. Scaling for other stretching techniques combined with Airy waves may be deduced for stochastic, irregular waves and based on computational comparisons for different wave heights and water depths. However, this will not give exactly the same force profile over the leg and discrepancies in force prediction will occur. Such scaling is therefore not included in the PRACTICE.

Commentaries to Recommended Practice for Site Specific Assessment of Page 18 Mobile Jack-Up Units Rev 2, Jan 2002 For computational comparisons using this wave height scaling, see also Appendix C4.B. C35_12 Wave Height for Regular Wave Analyses The selection of wave height to be applied in a particular analysis approach (regular or irregular waves) is recommended based on matching the loads resulting from the combination of the wave height and kinematics models, as recommended in Section 4.4. The scaling of wave heights is introduced as an alternative to the scaling of drag coefficients, using the wave height relation Hmax = 1.86Hs • For regular wave analyses the wave asymmetry is properly ed for, but the irregularity of the sea surface and the wave spreading may not be modeled properly. As indicated in Tables C3.5.1 and C3.5.2 a reduction factor is required to give similar forces as predicted by an irregular seas simulation if Hmax = 1.86Hs . In [3] a reduction of the drag coefficient by a factor 0.7 is chosen and in [4] a reduction of wave kinematics is chosen. Classification societies generally specify lower CD values than specified in Section 4 and these apply to regular wave analyses. Considering that the computations with regular waves are made with a kinematics model that has been documented in [5] to be somewhat conservative a reduction factor is appropriate to arrive at realistic force estimates. Accepting that a scaling factor on kinematics is applicable, a practical way of implementing this in the PRACTICE is to reduce the wave height to be used for force computations in regular wave analyses. This may be more practical than using a factor on kinematics as most software on the market does not include such a scaling factor. Equivalent wave heights are suggested as: lLIet

= 1.60Hsrp

The scaling factors on kinematics may be implemented assuming that the load effect is proportional to wave height to the power 2.2, ing that CD'S should not be scaled. As a comparison with previous practices the relationship lLIet ::::: 1.60Hsrp may also be compared with the reduction of CD by a factor 0.7 as recommended in [3] in combination with the wave height Hmax =1.86Hs . By assuming that load effects are proportional to the ratio of wave heights to the power 2.2, the scaling becomes (1.60/1.86)2.2 = (0.86)2.2 = 0.72, indicating that this is not lower than current practice. The computational results of Table C3.5.2 indicate also that scaling of 0.66 would give similar static forces as the irregular seas simulation at large water depths. See also Appendix C4.B for a comparison of the computational results, related to other practices. C3.5.2 The wave heights specified in the PRACTICE for use in airgap determination will be generally applicable. Special consideration may, however, be required in areas subject to Freak Waves or where the 1.5m clearance will not be adequate to cover the increase in wave height associated with higher return period waves. It should be noted that certain regulatory bodies require the use of higher return period waves (e.g. 10,000 years) for the determination of airgap requirements.

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 C3.5.3 Alternative formulation for wave spectrum

Page 19

The following alternative, and rather restrictive, representation of the wave spectrum by the power density of wave surface elevation S1111(f) as a function of wave frequency may be used: ST111(f) = ag2(21t)-4(f)-sexp(-1.25/(Tpf)4)f where; a g q cr

= = = =

Hmo Tp f Y

= = = = =

equilibrium range parameter =0.036 - 0.0056Tpf ~Hmo2 acceleration due to gravity exp(-(Tpf_I)2/2cr2) spectral peakwidth parameter = 0.07 for T pf <= 1 = 0.09 for Tpf > 1 estimate of Hs significant wave height (meters) spectral peak period (seconds) frequency (Hz) peak enhancement factor exp(l/0.287[1-0.1975aTp4/Hmo2

n

The above definition yields a Pierson-Moskowitz spectrum when y = 1 and Tp = 5-V(Hs) with Tp in seconds and Hs in meters. C3.5.4

Spreading The PRACTICE provides a formulation which may be used to incorporate the effects of wave spreading in the analysis. The power constants recommended [10] imply that the extreme seastate is close to long-crested, and that there is therefore little angular distribution of wave energy about the mean direction. It should be noted that where significant spreading exists it may be non-conservative to assume a long-crested sea. In [4] a reduction formula is suggested which reduces the velocity by a factor 'primarily

ing for wave spreading': urectfu = -V[(2n+l)/(2n+2)] where; 2 n = the exponent in the cos De spreading function at T p' u = the computed velocity for long crested waves, = the reduced horizontal velocity. Ured For a range of the spreading exponent, 2 < n < 3, the range of the scaling is 0.91 < Ured/u < 0.94. This corresponds to a reduction of the forces by a factor ranging from 0.8330.875. To use such a spreading factor in reducing overall forces on a structure is debatable, and especially so for jack-up structures. There may be cases where the inclusion of the spreading in irregular seas results in higher forces for some headings. If the leg spacing corresponds to a wave period, inducing opposing wave forces for different legs coinciding with the first resonance period, the forces will in fact be amplified when spreading is included. For jack-ups where the resonance period may often be as high as 4-7 sec., the effect of wave spreading is believed to reduce forces. However, the size of the reduction is dependent on the structure.

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 C3.7 WATER LEVELS AND AIRGAP

Page 20

The PRACTICE references water depths to lowest astronomical tide (LAT). In some instances the water depth may be referenced to Chart Datum. It is modem practice for these reference levels in hydrographic surveys to be the same, however caution should be exercised when using older data or navigation charts and the relation of Chart Datum to LAT should be checked and any necessary corrections applied. See also the Section C3.5.2 regarding wave heights for airgap determination.

Page 21

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev!2, Jan 2002

GLOSSARY OF FOR SECTION C3 CDeDe d D2 f g H ILtet

= = = = = = =

Hmax = Hmpm =

equivalent drag coefficient times effective diameter. water depth. depth attenuation. frequency (Hz). acceleration due to gravity. wave height. reduced wave height which may be used in deterministic/regular wave force calculations. maximum wave height for a given return period; used for airgap calculations. wave height associated with Hsrp equivalent to the height between the extreme crest and the following trough. estimate of Hs significant wave height (meters). scaled significant wave height to be used in irregular seas simulation (meters). significant wave height for assessment return period. wave number. the exponent in the CosnS spreading function at T p.

Hmo Hs Hsrp k n q Snn(f) tref ts T Tp Tz u Ured V Vref Vs

= = = = = = = = = = = = = = =

power density of wave surface elevation as a function of wave frequency. wind averaging period required by PRACTICE (1 minute). wind averaging period for supplied wind velocity. wave period (seconds). peak period in wave spectrum (seconds). zero-upcrossing period of wave spectrum (seconds). the computed velocity for long crested waves. the reduced horizontal velocity. current. wind velocity for reference averaging period required by PRACTICE (1 minute). wind velocity for supplied averaging period, tu.

a

= = = =

equilibrium range parameter =0.036 - 0.0056Tp / ~Hmo

a3 ~

Y Yd 11s 11 (J

exp(-(Tpf-l)2/2~)

= = = =

2

skewness. kurtosis. peak enhancement factor exp(1I0.287[1-0.1975aTp4/Hmo2 and Hmo in meters. scaling of drag forces. crest elevation by Stokes. crest elevation by Airy theory. spectral peakwidth parameter = 0.07 for T pf <= 1 0.09 for Tpf > 1

n, for Tp in seconds

=

=

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 REFERENCES FOR SECTION C3

Page 22

1

Det Norske Veritas, Classification Notes No 30.5, 'Environmental Conditions and Environmental Loads', H!3vik, March 1991.

2

Heideman J.C. and Schaudt K.J., 'Recommended Equations for Short-term Statistics of Wave Heights and Crest Heights', 1 April 1987.

3

'Practice for the Site Specific Assessment of Jack-up Units', By Marine Technology division, SIPM, EDP-5, The Hague, May 1989.

4

American Petroleum Institute, proposal for an update of the API-RP2A, 'Hydrodynamic Force Guidelines for U.S. Waters', received 6 February 1992.

5

L. Skjelbreia and J .A. Hendricksen, 'Fifth-order Gravity Wave Theory', Proceedings of Seventh Conference on Coastal Engineering, 1961, pp. 184-196.

6

J.E. Skjelbreia, G. Berek, Z.K. Bolen, O.T. Gudmestad, J.e. Heideman, R.D. Ohmart, N. Spidsoe and A. Torum, 'Wave Kinematics in Irregular Waves', OMAE, Stavanger, 1991.

7

Health and Safety Executive, Petroleum Engineering Division, 'Offshore Installations: Guidance on Design, Construction and Certification', London, 1990.

8

S.R. Winterstein, E.M. Bitner-Gregersen and K. Ronold, 'Statistical and Physical Models of Nonlinear Random Waves', OMAE, Volume IT, Safety and Reliability, Stavanger, 1991, pp.23-31.

9

OJ. Andersen, E. Frland and S. Haver, 'Design Basis, Environmental Conditions, Statfjord', Statoil Report no. F&U-ST 88007, Stavanger, April 25, 1988.

10

S. Haver, 'On the Modelling of Short Crested Sea for Structural Response Calculations', EurOMS, Trondheim, 20-22 August 1990.

Other project reports and related technical notes: 11

D. Karunakaren, 'Scaling of Hydrodynamic Loads According to Computational Models', Technical memo no. 710762, SINTEF, Trondheim, July, 1991.

Commentaries to Recommended Practice for Site Specific Assessment of Page 23 Rev 2, Jan 2002 Mobile Jack-Up Units C4 COMMENTAruffiSTOCALCULATIONMETHODS-HYDRODYNANnCAND WIND FORCES C4.1

INTRODUCTION The main objective of this Section is to provide documentation of the numbers, methods and formulations of the Section 4 of the PRACTICE. This Section is limited to considering Jack-Up specific methods for wind loading on legs and hulls and hydrodynamic forces acting on the legs under the action of waves and current. Typical jack-up leg designs consist of legs with an open lattice frame structure with typical member dimensions of O.25-1.0m in diameter. A special feature are the racks fitted to the chord elements for jacking purposes. The fact that jack-ups are mobile will also limit the marine growth. The models, methods and coefficients for computing the forces are considered together in the development of PRACTICE Section 4, and represent a consistent method such that the whole Section should be considered in its entirety. This means that no coefficients should be taken from this Section or Section 4 of the PRACTICE unless the corresponding method is applied. The Section is organized such that the main sub-sections have the same numbers as the corresponding section in the PRACTICE. This means that Section C4.2 in this report corresponds to section 4.2 in the PRACTICE and so on.

C4.2

WIND FORCE CALCULATIONS The wind force acting on each block of the jack-up is obtained by mUltiplying the pressure (which s for the elevation and shape of the block - see C4.2.2 and C4.2.3 respectively) by projected area. The total wind force on the jack-up can then be obtained by summing the wind forces over all the blocks. Shielding effects are not normally included in the calculation, except that the wind area of the hull and associated structures (excluding derrick and legs) may normally be taken as the profile area viewed from the direction under consideration. The wind speed varies with height since the boundary layer friction (which in increased by the roughness of the sea surface) retards the wind near the sea surface. The lower layers then retard those above them, resulting in increasing velocity above the sea level, until the retarding forces reduce to zero. A wind profile is normally used to represent the variation of wind speed with respect to height. The PRACTICE recommends a power law of 10 (N =10) to represent the wind. The wind speed measured at 10m above the mean sea level is normally used as the reference in defining the wind speed profile. Alternatively, the height coefficients (Ch) listed in Table 4.1 can be used to determine the wind speed at various heights. Where a block has a vertical extent of more than 15m, it is recommended that it is subdivided and the appropriate height coefficients are applied to each part of the block.

Commentaries to Recommended Practice for Site Specific Assessment of Page 24 Mobile Jack-Up Units Rev 2, Jan 2002 The shape coefficients for various typical components of a jack-up are given in Table 4.2. Items with 'solid' faces are treated as individual blocks. A different approach is used for open lattice structures, such as derricks, crane booms, helideck structure, flare booms and raw water towers, etc. Here Table 4.2 recommends the use of 50% of the total projected profile area of the item (e.g. 50% of the product of the derrick width overall and the vertical extent of block under consideration) in association with the appropriate shape coefficient for the isolated shapes comprising the lattice. For leg structures, the equivalent hydrodynamic coefficients on lattice legs may be taken from Section 4.6. These will generally be the same as those for clean legs in large velocities and long waves and hence the smooth values are generally recommended. C4.3

HYDRODYNAlv1IC FORCES

C4.3.1

General Jack-up leg sections are complex structures, usually made of slender . The best engineering tool available for computation of hydrodynamic forces is Morison's equation. However, the limitations of Morison's equation should be recognized. For single large diameter /legs, which may be an alternative to lattice legs, more appropriate theories and formulations for the inertia forces should be applied. MacCamy and Fuch's [60] corrections on the inertia coefficients of vertical elements may be an alternative for those structures. A limitation on the application of Morison's equation to predict wave loads is implemented. The limitation is set to: A> 5Di (4.3.1) where; A = wave length and Di = reference dimension of individual leg (within a lattice leg). The above limitation implies that the should be small compared with the waves. Morison's equation [30] is an empirical relation given by a drag term plus an inertia force term as: 2 M' = M'drag + M'inertia =0.5 P CD D IU x IU x + P CM (1tD /4) Ux (4.3.2) where; CD = the drag coefficient. CM = the inertia coefficient. ux, Ux = the horizontal water particle velocity and acceleration. D = the tubular diameter. P = the density of fluid surrounding the tubular. The above equation was established to be used for vertical circular cylinders in waves, but has later been modified and generalized to for current, inclined and relative velocity and acceleration. These extensions are further defined for use in the PRACTICE and discussed in the following sections.

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 C4.3.2 Drag forces

Page 25

For the drag part of the equation the extension from Morison's original formula is made as: ~drag = 0.5 P CD D I vn I Vn (4.3.3) where Vn is now introduced as the relative particle velocity normal to the local member axis including current, taken as: (4.3.4) where; Un + Ven = the combined particle velocity from wave and current by vectorial summation normal to the member considered. t n = the velocity of the considered member normal to its axis and in the direction of the combined particle velocity. a = 0, if an absolute velocity is to be applied, i.e. neglecting the structural velocity. 1, if relative velocity is to be included. May only be used for stochastic/random wave force analyses if: Ured =

where; u Tn Di

= =

uTnIDi ~ 20.

particle velocity, first natural period of surge or sway motion the reference diameter of a chord.

In the above definition of combined velocity, current is included.

This should be acceptable as the member does not distinguish between the velocity due to current or wave motions. The backflow of the wake is different in combined wave and current fields, (KC dependence) but this has a small influence on the prediction of the largest force in an extreme wave for single of diameters typical for jack-ups, see Section C4.7.2.6. For inclined the above definition implies that the procedure to arrive at the force components is first to determine the particle velocity component normal to the member axis, then determine the force normal to the member axis and thereafter to determine the force components in the global directions. This implies that the force component along the member is neglected. On the inclusion of the relative velocity there has been some reluctance to directly accept the extension to the original Morison's equation. Intuitively the extension should be correct using the same argument as for current forces as the member only experiences the flow field ing locally. However, the displacements of the are quite small and there has been few data to such an extension as pointed out in [34]. In [55] test results show that for small amplitude motions the damping may be overpredicted when the relative velocity is included. However, for a typical jack-up, with member diameters less than 1m and natural periods around 5.0 seconds, the sensitivity to member displacement is not large because the parameter U red = uTnlD i =:: 20 or more in an extreme sea state, see Figure C4.3.1. In addition, the Christchurch bay test results show that the relative velocity formulation gives good prediction of the inine loading [44], 'correctly predicting the important hydrodynamic damping at the resonant frequency'. From this it may be concluded that the relative

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 velocity formulation is probably applicable for jack-up structures. introduced to avoid any significant overprediction of damping.

Page 26 A limitation is

The reduced velocity Ured may be computed for a wave height equal to the significant wave height and using the first natural period normally corresponding to the fixed condition soil parameters. In practical cases it is suggested to evaluate Ured for a majority of close to the sea surface, and to include relative velocity either for all or no . The relative velocity formulation is in effect similar to the inclusion of damping reaction forces. All predictions of damping are uncertain, and compared with other damping estimates the relative velocity formulation is judged to be reasonably well estimated. This additional damping from the relative velocity formulation should be considered when choosing the structural/proportional damping coefficient. A low structural damping should be considered when the relative velocity is included. A procedure to combine the forces on several individual into one member with equivalent diameter and drag coefficient to be used with the horizontal water particle velocities is discussed in Section 4.6. 2.4 2.2 2.0 1.8

1.6

-

1A

dd

1.2 1.0

_46_

0.8

-

0.6

OA 0.2 0.0

-0.2 -0.4

Xo/D

Figure C4.3.1 Oscillating drag coefficient vs. motion amplitude to diameter ratio xJD for given reduced velocities [55]

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 C4.3.3 Inertia forces

Page 27

These forces are not dominant for extreme loads of typical jack-up lattice legs. A more comprehensive model could be applied to include relative accelerations (noting that in this case the added mass should not be included in the structural model). In the RP the fonnulation is given as: 2 (4.3.5) ~inertia = P eM (1tD /4) Un where; ~inertia = nonnal force per unit length of member (in this case the member is vertical and the force horizontal). p = density of fluid surrounding the tubular. CM = inertia coefficient. D = diameter of the member. = water particle acceleration nonnal to the member. un This implicitly defines how to treat inclined . However, for inclined the horizontal force may alternatively be determined by ing for the inclination on the added mass part of the inertia force, but not on the Froude-Krylov part of the force. The horizontal inertia force is hence computed as: 2 ~inertiaH = p1tD /4 [(CM-1)sin2~i + 1] un (4.3.6) where ~i is the angle between the particle acceleration and the element orientation as defined in Figure 4.2. It should be noted that the vertical particle acceleration will also provide a horizontal component on inclined braces. For global force calculations this will generally be unimportant as the loadings on different braces at different angles will tend to cancel out. C4.4.

W AVB THEORIES

C4.4.1

General In general there are two different computational methods with corresponding suitable wave theories; Deterministic regular wave analysis, and Stochastic irregular or random wave analysis. For the deterministic regular wave analysis all fonnulated wave theories may be chosen from a mathematical point of view. For shallow waters however, the choice of wave theory is limited to those properly predicting wave asymmetry and the corresponding change in wave kinematics. For the stochastic irregular wave analysis only the linear Airy wave theory, or variations of Airy theory are suitable. Airy wave theory does not fully describe the wave kinematics behavior since this wave theory implies symmetric waves, which are not always applicable for shallow water. This will limit the application of this type of analysis to deeper and intennediate water depths and is considered further in Section 3.5.1, see Appendix C4.B.

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 C4.4.2 Regular wave analysis

Page 28

Currently there are a number of wave theories that are applied in the analysis of jack-up platforms. In most cases the deterministic computations are performed using Stokes fifth order [42] or Dean Stream function [40] theories. The Dean Stream function theory shows the best fit to test results, [40,41], for shallow water waves. The difference in overall forces from these two wave theories will however be small at large to intermediate water depths and for low wave steepnesses. Figure C4.4.1 is included in the PRACTICE in a linear scale to guide the selection of the appropriate wave theory for deterministic analyses. Only the Dean stream and Stokes wave theory are recommended here in order to limit the range of possible choices, reducing the scatter in wave force predictions. C4.4.3

Irregular wave analysis For the irregular waves analysis, Airy's wave theory is the only possible choice using the principle of sum of independent wave components as implied in standard irregular seas time domain simulation and frequency domain solutions. For both the Dean Stream and Stokes wave theories there are implicit phase dependencies between wave components at different frequencies. To for changes in wetted surface a modification of the Airy wave theory is required, introducing the surface elevation as a parameter in the kinematics. A number of such stretching methods have been proposed in literature. One simple method, the Wheeler stretching method [37], compares well with test results in model tank measurements [38]. Even for the Wheeler stretching method there exist different variations. The chosen definition is that originally suggested in [37], to substitute the true elevation at which the kinematics are required with one which is at the same proportion of the mean water depth. This can be expressed by: z'

=

where; z

=

z' ~ d

= = =

z-~ 1+~/ d

(4.4.1)

The elevation at which the kinematics are required. (Coordinate measured vertically upward from the mean water surface) modified coordinate to be used in particle velocity formulation The instantaneous water level (same axis system as z) the mean, or undisturbed water depth (positive)

This method causes the kinematics at the surface to be evaluated from linear theory expressions as if they were at the mean water level. If a frequency domain analysis is to be applied in extreme response predictions, it is

recommended to use linearization with respect to a finite wave height, Hmax defined in 3.5.1, however damping should be linearized using a lower wave height. Stochastic linearization implies the use of a unit wave height and when combined with the assumption of Gaussian statistics the extreme response may be underpredicted, see Figure C4.4.3. For fatigue computations stochastic linearization, [51], is recommended as fatigue damage is not dominated by the extreme wave heights, however consideration should be given to local loads arising from the finite wave height.

I

Page 29


0.05 "'---""I"---~----""--~!"'""'--"""'----""'!----""--~

0.02

The boundaries given are approximate and depend on the purpose of-the analysis being perfonned. It is accepted that refraction and diffraction analysis will usually will be based on linear theory.

0.01 ....-----+----+-----+Hb

0.005~---~----+----~~~~~~~-,.~---4_---~--~

SHALLOW WA1ER

STOKES 5

B:RE:AKmG LIMIT Hm ax/d= 0.78

ORS1EAMFUNCTION

CD

0.002 ..----I\-17T71Jr---.;-7f.---I---I--::~-iiiiiiiiiiiil

0.001 "'I-----+--#---++--i

0.0002

~----4---~+---+-~~~~~----+-----~---~r---~

LlliEARJAIRY OR STREAM FUNCTION

0.0001

+---

3 DEEP W.ATER

INI'ERMEDIATE DEPTH WAVES

WAVES

---r----.... ---....,---t 0.05 0.1 0.2 0.02

0.00005 .....- - -.....- -.....r-I;..--....- - -.... 0.001 0.002 0.01 0.005

d

gTa s s 2

Notes 1) None of these theories is theoretically correct at the breaking limit. 2) Wave theories intended for limiting height waves should be referenced for waves higher than O.9Hb when stream function theory may underestimate the kinematics. 3) Stream function theory is satisfactory for wave loading calculations over the remaining range of regular waves. However, stream function programs may not produce a solution when applied to near breaking waves or deep water waves. 4) The order of stream function theory likely to be satisfactory is circled. Any solution obtained should be checked by comparison with the results of a higher order solution. 5) The error involved in using Airy theory outside its range of applicability is discussed in the background document.

Nomenclature

Hmax/gTass 2

2

= Dimensionless wave steepness

dlgTass

= Dimensionless relative depth

Hmax

= Wave height (crest to trough)

Hb d

Tass L

g

= Breaking wave height

= Mean water depth = Wave period

= Wave length (distance between crests) = Acceleration due to gravity

Figure C4.4.1 : Range of validity of different wave theories [52,58]


Wave length, I Period T

-Airy's theory - sinusoidal wave folUl

Figure C4.4.2 : Surface elevation, and velocity profiles for detenninistic regular waves

FDLinear

~------------------~------------~H

DRAG FORCE OVERESTIMATED DRAGFORCE UNDERESTIMATED

Figure C4.4.3 : Linearization w.r.t. wave heights [47]

Page 30

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 C4.5. CURRENT

C4.5.1

C4.5.2

Page 31

General The current specified for a specific site is to be included as specified in section 3.6 of the PRACTICE. Interpolation between the data points may be required and linear interpolation is recommended for simplicity. Combination with wave particle velocities It should be emphasized that the wave and current velocities are to be treated together,

as a sum of separate force contributions will significantly underestimate the hydrodynamic forces. C4.5.3

Reduction of current by the actuator disc formula The current velocity will be reduced due to the presence of the structure in the current flow field. An estimate of the reduction of the steady flow velocity may be found by [53]: (4.5.1) VcNr = [1 + ~(CDiDi)/4Wrl ~ 0.7 where; Vc = the reduced current velocity to be used in analysis. Vr = the observed far field current. COi = the drag coefficient of an element i. Di = the element diameter of element i. W = the width of the structure. Several limitations of the above relation are discussed in [53,56] and a lower limit to the reduction of the current velocity is suggested to be 0.7. The above equation contains a sum of COi and diameters Di, but is not explicit with respect to inclined . The summation ~CoiDi is similar to the computation of the equivalent drag coefficient and diameter, CoeDe, in Section 4.6 of the PRACTICE, where member inclination is ed for. Since the equation should be considered for separate groups of elements [53], it suggested to apply the formula for each leg and use the following format: (4.5.2) Vc = Vr [1 + CoeDJ(4D 1)r l = the current velocity to be used in the hydrodynamic model, Vc where; Vc should not be taken less than 0.7Vf . Vr = the far field (undisturbed) current. COe = equivalent drag coefficient, as defined in 4.6.6. De = equivalent diameter, as defined in 4.6.6. = face width of leg, outside dimensions. DI For structures where the hydrodynamic geometry varies significantly with depth, the blockage factors can be computed for different depths. In view of the reduced drag above MSL (due to lack of marine growth) it may be appropriate to calculate current blockage for the stretched part of the current above MSL separately.

C4.5.4

Current stretching It is suggested to let the profile follow the surface elevation by changing the coordinate system similarly to that of the Wheeler stretching defined by equation 4.4.1. The current profile is recommended in Section 3.6.2.

I

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 C4.6. LEG HYDRODYNAMIC MODEL

C4.6.1

Page 32

General The hydrodynamic modeling of the leg of a jack-up may be carried out by utilizing either 'detailed' or 'equivalent' techniques. In both cases the geometric orientation of the elements are ed for. The hydrodynamic properties are then found as described below: Detailed Model' All relevant are modeled with their own unique descriptions for the Morison term values and with correct orientation to determine Vn and un and the corresponding drag coefficient times diameter CoD =CDjD j and inertia coefficient times sectional area CMA =Cmi1tD?14, as defined in Section 4.7. 'Equivalent Model' The hydrodynamic model of a bay is comprised of one, 'equivalent', vertical tubular to be located at the geometric center of the actual leg. The corresponding (horizontal) Vn and un are to be applied with equivalent CoD = CDeDe and CMA = CMeAe, given in 4.6.5 and 4.6.6. The model should be varied with elevation, as necessary, to for changes in dimensions, marine growth thickness, etc.

C4.6.2

Length of Lengths of are normally to be taken as node-to-node distance of the , in order to for small non-structural items.

C4.6.3

Spudcan A criteria for considering the spudcan is suggested such that the effect of the wave and current forces on the spudcan may normally be neglected at deep water or deep penetrations. However, there may be special cases with e.g. large spudcans in combination with high currents that should be considered also outside the suggested criteria.

C4.6.4

Shielding and Solidification Shielding is normally neglected for computations of the hydrodynamic model as presented herein. The shielding is dependent on KC- and Re- numbers. Since it is difficult to quantify shielding, and shielding in waves is less than in constant flow [45,62], shielding is neglected. The same criteria are used for solidification as for shielding such that both effects should be considered if advantage is taken due to shielding in wave and current loads. According to [56] shielding is recommended to be neglected for SID :::; 4 for an array of elements, where S is the outer diameter of the array and D is the diameter of individual elements. This is also considered in [45]. If information on shielding is obtained from experiments, care should be taken to distinguish between shielding and the effect discussed in C4.5.3. These effects are different, but could possibly be confused in tests on small models in large tanks. Solidification is an increase of wave forces due to interference from objects 'side by side' in the flow field. This is normally not included in the hydrodynamic coefficient formulation for jack-ups since shielding is also neglected. Jack-up rigs are usually

Commentaries to Recommended Practice for Site Specific Assessment of Page 33 Mobile Jack-Up Units Rev 2, Jan 2002 space frame structures with few parallel elements in close proximity so that this effect is usually not important. In [45] solidification effects are quantified for two elements and for a group of elements. The drag coefficient may increase 100% if two tubulars are placed side by side, or be reduced for a group of elements, e.g. a conductor array, where shielding is also present. The effect is less than 10% in the worst direction and is therefore suggested omitted in the PRACTICE, when: A/At < 0.5 where; As = sum of projected areas for all in the considered plane At = the total projected envelope area of the considered plane. Solidification should be considered if shielding is included. C4.6.5

Equivalent drag coefficient In order to comprise the information on drag forces for individual of a lattice leg into an equivalent vertical member over the bay length s, a fixed diameter and a directional dependent drag coefficient is specified. This model s for the geometrical orientation of the individual . In this model the principle of no shielding and no blockage is assumed. The equivalent diameter is recommended such that the inertia coefficient normally will follow without any further computations. The equivalent drag coefficient, CDe , times the equivalent diameter, De, is specified. If another reference diameter De is preferred, the product of CoeDe should in any case be equal to that specified in Section 4.6.5 of the PRACTICE. The expression for COei may be simplified for horizontal and vertical as follows: Vertical member (e.g. a chord) CDei = CDi (D/De) 3 Horizontal member CDei = sin a; CDi (Dil/Des)

C4.6.6

Equivalent Inertia coefficient The equivalent value of the inertia coefficient, CMe, and the equivalent area, Ae, to be used in Section 4.3.3, representing the CMA chosen as: C Me = may normally be taken as equal to 2.0 when using Ae = 1.0 for flat plates (brackets). Ae = equivalent area of leg per unit height =(L Ai li)/s. Ai = equivalent area of element =1t D?14. Di = reference diameter as defined in Section 4.7. The reference diameters Di and corresponding area of member Ae, are chosen such that the use of an inertia coefficient C Me = 2.0 or C Me = 1.0 is consistent with the inertia forces for chords and brackets respectively. A conservatism is present since the inertia coefficient for rough tubulars is set to 1.8 and there is no reduction of forces for inclined . For normal lattice leg designs the conservatism


Page 34

will not play any significant role as the drag forces are dominant. The inertia force will also be dominated by chords due to their larger diameter, such that the conservatism is judged to be insignificant for extreme wave forces. If, however, a more accurate model is wanted an alternative is given using the individual member inertia coefficients, as specified in Section 4.7 of the PRACTICE, and including the effect of inclined . The C Me coefficient is then determined by the summation shown in Section 4.6.6 of the PRACTICE. This model is in closer agreement with the 'detailed model'. It should be stressed that the coefficients must be defined together with their reference dimensions D i .

As comments to this fonnulation the following may be observed: for horizontal with flow along the length axis the inertia coefficient is: C Mei = 1.0 for a vertical rough tubular the inertia coefficient will be: C Mei 1.8 for other vertical the inertia coefficient will be: C Mei = 2.0 for other flat plates (brackets) the inertia coefficient will be: C Mei = 1.0

=

C4.7

HYDRODYNAMIC COEFFICIENTS FOR LEG

C4.7.1

General The coefficients determined herein are based on tests where the particle velocities and accelerations are measured simultaneously as the forces, usually in a controlled environment. This is the logical way to determine the loading coefficients. However, the important result in engineering is the overall forces predicted by the Morison's equation over the Jack-up legs. Since some wave theory has to be applied, which does not perfectly predict the wave particle motions in all cases, additional scaling is suggested in Section 3.5 of the PRACTICE, see also Appendix C4.B. This is important to consider when reading this chapter as the stated coefficients may be somewhat larger than those applied in other recommendations or classification rules.

C4.7.2

Hydrodynamic Coefficients for Tubulars

C4.7.2.1 General; There exists a wealth of data on hydrodynamic coefficients (drag and inertia coefficients) for tubulars, mainly from model tests. A number of model tests have been performed in wind tunnels, others in oscillating water environment or in steady water flow, while (to our knowledge) only a few model tests have been performed in a wave environment. In addition a few full scale tests have been reported.

In the following section (Section C4.7.2.1-7) an overview is given of the literature that has been applied for the purpose of recommending values for the hydrodynamic coefficients of jack-up platforms.

Page 35 Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 Before choosing the appropriate hydrodynamic coefficients for tubular parts of jack-up platfonns the following questions have to be answered: Are the coefficients to be used for a fatigue analysis or an ultimate strength analysis? Are the tubular parts smooth or rough, and if they are rough what is the roughness to be applied? The parameters to be considered in determining the hydrodynamic coefficients are; Keulegan-Carpenter number

KC

=

Reynolds number

Re

=

Relative roughness

=

UmT D UD v k D

where; k D Urn T U

v

= = = = = =

roughness height diameter maximum orbital particle velocity wave period flow velocity at the depth of the considered element. kinematic viscosity of water (v:::: 1.4 X 10-6 m2/sec, t =10°C)

Concerning the first question above, it is important to determine the range of Reynolds numbers and Keulegan-Carpenter numbers of interest. Both the drag coefficient CD and the inertia coefficient C M are dependent on the Reynolds number and the KeuleganCarpenter number. In the ultimate strength case one is interested in the CD and CM coefficients in relatively long and steep waves, i.e. wave steepness S = H/A in the range 1110-1115. A typical ultimate strength case may for example be, a tubular with diameter D = 0.3 m standing in a seastate with average zero-upcrossing period Tz = 10 secs. (A = 156 m) and significant wave height Hs = 13.0 m. The representative water particle velocity for this wave will be: H s 1t Uw = -=4.1 mls. Tz Assuming a current velocity Uc of about 1.0 mis, the total water particle velocity will be U = Uw+Uc = 5.1 mls. This results in the following Reynolds number and Keulegan-Carpenter numbers (close to the water surface): UD 6 UT Re = = 1.1 10 , KC = - z = 170

v

D

This means that in the ultimate strength case we are dealing with high KC-numbers and post-critical Re-numbers. Sarpkaya (see for example [4]) uses a parameter ~ =RelKC to describe the test environment. In the ultimate strength environment described above, the value of ~ is approximately 6500.

Commentaries to Recommended Practice for Site Specific Assessment of Page 36 Mobile Jack-Up Units Rev 2, Jan 2002 A typical fatigue case may for example be the same tubular in a seastate with Tz = 6 secs. (A = 56 m) and Hs = 5.6 m. In this case the representative water particle velocity will be Uw = Hs1TfI'z = 2.9 m1s. In the fatigue case, current is not part of the water particle velocity, which is to be applied. This results in the following Reynolds number and Keulegan Carpenter number (close to the water surface): KC

=

58.

This means that post-critical Re-numbers and relatively high KC-numbers are also to be dealt with in the fatigue case. Sarpkaya's ~ parameter has a value ~ = 10860 for the described fatigue case. It may be concluded that, in general, for jack-up tubulars, the following ranges of Renumbers and KC-numbers will be of interest: Re-numbers: Ultimate Strength, Fatigue, KC-numbers: Ultimate Strength, Fatigue,

roughly from Re == 1.0x106 - 4.5 X 106 roughly from Re == 0.5x106 - 1.0 X 106 KC> 100 KC == 25 - 60

Since quite a large amount of the literature survey is dealing with papers written by Sarpkaya, the following range of Sarpkaya's ~-parameter may be regarded to be of interest: ~ == 6000 - 20000 (depending on the KC-number). The answer to the second question concerning the roughness of the tubulars will depend largely on type of paint used and the smoothness of the steel surface, whether the tubular is new or has been in the water for quite some time (marine growth), or whether the tubular mainly stays in air, etc. Smooth cylinders are defined as cylinders having a roughness kID < 0.0001, while rough cylinders are assumed to have a roughness kID > 0.004 (i.e. highly rusted steel kID == 0.005-0.01). Marine roughness due to marine growth implies a roughness in the range kID == 0.01-0.15.

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 C4.7.2.2 Literature Survey and Recommended Values

Page 37

In Table C4.7.1 a survey result is presented of relevant literature with respect to inertia

coefficients (C M ) and drag coefficients (CD) for tubulars. Of course, there exists more relevant literature than that presented in Table C4.7.1, but it should give a reasonably representati ve overview. Table C4.7.1 : Survey of Relevant Literature on CM and Co values for Tubulars Source

Geometric Shape Re-Number KC-number

Co

CM

Comments

-K~~i~g~~-----S~~~thCyii~d~;-0:i~oj-i(l-----25~50-----ij~i'-s-------ij---i:8----S~b~Criti~-~i------

0.1 105

Carpenter 1958 [1]

>100

1.0-1.2

2.4-2.6

Sarpkaya 1976 [2]

Smooth Cylinder >0.5 106 >0.7 106

20-40 60-100

0.6-0.7 0.6-0.7

1.7-1.8 1.7-1.9

Sand

Rough Cylinders kID =0.005 >0.5 106 kID =0.01

20-40

1.5-1.7 1.6-1.8

1.2-1.4 1.2-1.4

and Critical Flow. Low Re-numbers. Post-Crit. Oscillating Flow. Post-Crit. Oscillating

____________________________________________~:? ~_~ _ ~ _______~: ~_-_~ :~____ !'!?_~ _______________ _

_~?~~~~~~~ __ ~ _=::_ 9:~?

kID = 0.005 kID = 0.01 Roughened kID = 0.02 Hogben Smooth Cylinder >1.0 106 et al. 1977 [3] Rough Cylinders kID =0.0002 >1.0 106 Survey Paper kID =0.002 >0.5 106 State of kID =0.01 >0.5 106 the Art kID =0.05 >0.1106 Sand

-S~k~y~-

60-100

>25

>25 >25 >25 >25

1.4-1.6 1.5-1.6 1.6-1.7 =0.6

1.5-1.7 1.4-1.6 1.4-1.6 =1.5

Post-Crit. Flow.

0.6-0.7 =1.0 =1.0 =1.25 1977

----S~~~th -Cyii~d~; --;,o."i -i06--------- 2540------O'-6~O'-8 -------i :5---i :7--- -criti~-~ -~ ----------

et al. 1982 [4] -S~k~y~-

Rough Cylinder kID =0.01

et al. 1985 [6]

>0.1106

25-40

1.5-1.7

1.0-1.2

Super-Crit. Oscillating Flow. ~ =4000.

----S~~~th -Cyii~d~; -~."i"i()6" --------25~40 -----0."7~0'-8 ------ -i ~5---i ~~i --- criti~-~i -~ ----------

et al. 1984 [5]

-S-~k~y~-

Post-Crit. Oscillating Flow. Post-Crit. Flow.


=0.15 106

60

0.6-0.65

1.5-1.6

=0.1106 =0.15 106

25-40 60

1.4-1.5 1.4-1.5

1.4-1.6 1.5-1.6

=0.21 106

50

1.4-1.5

1.2-1.3

Super-Crit. Oscillating Flow. ~ =2500.

----R~~gh- Cyii~d~~- --oj~oj- icf -----2540 -----i '-4~i.-s -------i :o~-i:3- --- criti~-~i -~ ---------kID =0.01

Super-Crit. Oscillating Flow.

-----------------------------------------------------------------------------------------------------~-:::!?-~~-----------


Page 38

_~~~!~~________ g~
According to Sarpkaya, available data with current + oscillatory flow substantiate the fact that drag coefficients obtained from tests at sea in general will be smaller than those obtained under laboratory conditions. Smooth Cylinder 0.2-0.3 106 Sarpkaya 20-25 0.6-0.7 1.6-1.8 Super-Crit. 1985 [7] Oscillating Flow. ~ = 11240.

-S~k~y~-

---- S~~~th -Cyii~d~; -;0.-5 -i
1985 [8], 1986 [9]

>0.5 106

>50

0.6-0.7

1.6-1.8

>0.5 106 >0.5 106

25-40 >50

1.4-1.8 1.4-1.6

1.2-1.4 1.3-1.5

Survey Articles

Rough Cylinder kID = 0.02

-N~th

S~~~th -Cyii;;ci~;- -~.-5-

----------

io6-------- --

--~ -- ------ 0~4~0.-5

Oscillating Flow.

-------------------

S~p~;~crii.--

1982 [10]

------

Steady Flow. Rough Cylinder kID =0.02

00

kID>O.1

00

Smooth Cylinder 0.15-0.2 106 Rough Cylinder kID = 0.02 kID>O.1

0.15-0.2 106 0.15-0.2 106

0.9-1.0 1.0-1.2

Post-Crit. Steady Flow.

15-25

0.3-0.6

0.8-1.4

15-25 15-25

0.6-1.0 1.0-2.0

0.4-1.0 0.8-2.3

Super-Crit. Oscillating Flow.

There is very large scatter in the data presented by Nath. -B~~~~-----S~~~th-Cyii~d~;-O:i5~Oj-i06-----~20-------0~6~oj------i4~-i:5-----S~p~;iP~~t~-------

et al. 1985 [11]

Crit. Flow, Regular Waves.

The authors present results for random waves as well, but it is difficult to draw any conclusion from these results. -K~~-~-~~-----S~~~th-Cyii~-ci~~-O~5~-i~o-iOo------20~40------O:5~O.6-------j~6---i~8----P~~t~crit.----------

et al. 1987 [12]

Chaplin 1988 [13]


0.5-1.0 106

kID =0.0042

0.5-1.0106

Smooth Cylinder =0.2 106

20-40 =50 20-40 =50 =20

1.1-1.4 1.1-1.2 0.9-1.3 0.9-1.1 0.6-0.7

1.3-1.7 1.6-2.3 1.3-2.1 1.6-2.1 1.4-1.5

Oscillating Flow. Large Scatter in CM-values.

SuperlPostCrit. Oscilla-

-----------------------------------------------------------------------------------------------------~~~~-~

Source i)~~i~~-

Geometric Shape Re-Number KC-number

CD

CM

Page 39

Comments

-------S~~~th -Cyii~d~~-- -;0.-5- i06-- ----- --- -~20- ------0~6~0.7 -------i ~5~-i i ---P~~t~crit.- ---------

et aI. 1990 [14]

Flow, Reg. Waves. Smooth Cylinder >0.5 106

Post-Crit. Flow. Random Waves. The authors conclude that for smooth cylinders and KC>4, drag and inertia coefficients in periodic waves may be used to represent average CD- and CM - values in random waves.

i~d~~~-

------

busch et al. 1983 [15]

S~~~th -Cyii~d~~-

Rough Cylinder kID = 0.02

==18

--;i-6-i06-------- ----;;,- -- ---->1.0106

0.5-0.7

~.6

1.5-1.7

----------------------

P~~t~crit.-

---------

Steady Flow (Steady Tow).

00

0.9-1.1

Smooth Cylinder > 1.0 106 Rough Cylinder kID = 0.02 > 1.0 106

>30

0.6-0.7

1.6-1.7

>30

1.4-1.5

1.1-1.3

Smooth Cylinder > 1.0 106 Rough Cylinder kID = 0.02 > 1.0 106

20-40

0.6-0.8

1.4-2.0

20-40

1.0-1.8

1.0-1.9

Smooth Cylinder > 1.0 106 Rough Cylinder kID = 0.02

60-90

Post-Crit. Oscillating Flow. (Forced Motion). Post-Crit. Random Flow (Forced Motion).

Post-Crit. Random Flow 1.0-1.4 (Forced 1.1-1.4 60-90 Motion). The random tests show relatively large spread especially for the lower KC-numbers (20-40). iod~~~

0.6-0.8

1.5-1.7

------ -S~ooth -Cyii~-ci~i--;i .-0- i06-------- -- -;6i) ------O'-65~(i 75----i j~-i ~7----Po~t~crit'- ---------

busch et aI.

Random Flow (Forced

Rough Cylinder

_! ~~~ _(! ~L ___ ~?~:g~g_~ ________ ~~:.~ _~_~~ __________ ~~g_______ L! ~_1_:.~ _______!: ~_-_~ :?___ }~~~~i_
0.95-1.05 1.0-1.1 1.15-1.25

=>

Post-Crit. Steady Flow (Steady Tow). Sand Rough.

kID =0.049 kID = 0.098

1.15-1.25 1.3-1.4

=>

Pyramids

kID = 0.067 "Rough" Cylinder kID = 0.00012 ==0.5 106

1.2-1.3

=>

0.6-0.9

1.3-1.6

Mussels Post-Crit. Random Waves.

Rough Cylinder kID = 0.005 kID =0.0095 kID =0.025

6

>0.8 10

---------------------------------------------------------------------------------------------------------------------------

Klopman et al.

_!~~~_(!~l

==15

_____________________________________________________________________________________________________________ _

Commentaries to Recommended Practice for Site Specific Assessment of Page 40 /,1~~j!l!Jq~~~ gR _f!'!J!~____________________________________________ ~~y. ~,_ !.f!!': _?QQ~ ______________________________ _ Source Geometric Shape Re-Number KC-number Co CM Comments --------------------------------------------------6-----------------------------------------------------------------------Heideman Smooth Cylinder >0.2 10 15-30 0.5-1.2 Post-Crit. >0.2 106 >30 0.6-0.8 1.2-1.9 Random Waves. et al. 1979 [19] Rough cylinder Ocean Test 6 kID~.03-0.05 >0.210 15-30 0.9-1.8 Structure. >0.2106 >30 0.8-1.3 0.9-1.7 Large spread for lower KC-numbers « 30). Authors state that for large KC-numbers (> 30), smooth cylinder CD approaches an asymptote CD = 0.68, while rough cylinder CD approaches an

_

_~~~~~C?!~_ ~R _~_ ~:g: !~~~~ _t'~tf?~~~!~ _~_ ~~~~ ~l!~~~?~~l!~: __________________________________________ _

Nath 1988 [20]

Wolfram & Theophanatos 1990 [21]

-R~~-hk~-

Rough Cylinder Barnacles: kID = 0.073 kID = 0.104 Artificial Hard Fouling: kID =0.078 Rough Cylinder Mussels: kID =0.075 kID = 0.085 Mixed Hard Fouling: kID = 0.076 Kelp: kID = 1.25 kID = 2.5 Sea Anemones: kID = 0.16

00 00

00

00 00

00

00 00

00

0.95 0.98-1.2

0.98-1.2 1.22 1.26

Post-Crit. Steady Flow.

Post-Crit. Steady Flow. Post-Crit. Steady Flow.

1.11 1.51 1.69 1.35

------S~~~th -Cyii~d~~-- >3.-5- i06----------- -~ --- --- --O'-65~O~ 75----------------P~~t~crit'- ---------

1961 [22]

Steady Flow Wind Tunnel.

-Miii~~---------S~~~th-Cyii~d~;-;3.-6-io6------------;;,--------O.-60~O~65----------------p~~t~crit.----------

1976 [23] Rough Cylinder kID = 0.0004 Sand kID = 0.0009 Roughened kID = 0.0014 kID = 0.0021 kID = 0.0031 kID = 0.0050 Pearl kID = 0.015 Barley kID = 0.023 kID =0.044 Dried kID = 0.042 Peas kID = 0.063 i)~~~-~;;

------

et al. 1982 [24]

S~~~th -Cyii~-ci~~

Rough Cylinder kID = 0.0004 kID = 0.0014 kID = 0.0028

Steady Flow Wind Tunnel. >3.0 106

00

>0.5 106

00

>0.5 106

00

->3.-5 -i06------ -----

::::D. 80 0.8-0.9 0.8-0.9 0.9-1.0 1.0-1.1 1.0-1.1 =1.1 =1.1 1.1-1.2 1.1-1.2 1.2-1.4

-~ -- ----- - ~-.6-

---------------------

Post-Crit. Steady Flow Wind Tunnel P~~t~crit'-

---------

Steady Flow Wind Tunnel >2.0 106

00

::::D;8 ::::D. 88 ::::D. 92

Commentaries to Recommended Practice for Site Specific Assessment of Page 41 Mobile Jack-Up Units Rev 2, Jan 2002 In addition to the literature review presented in Table C4.7.1, an interesting and useful overview of existing literature is presented in a survey report prepared by Advanced Mechanics Engineering Limited for the Health and Safety Executive [25]. The literature review presented in Table C4.7.1 shows that the test results at different facilities agree reasonably well with respect to the drag coefficients for smooth cylinders in post-critical flow. The majority of tests show CD values between 0.6 and 0.7, both for the lower KC range for fatigue (25-60) and the higher KC range for ultimate strength. The suggested CD value for smooth tubular elements (kID < 0.0001) in post-critical flow is therefore chosen to be CD = 0.65. For rough cylinders the spread between the individual tests with respect to CD values is considerably larger. Especially Sarpkaya [2] operates with very high post-critical CD values for rough cylinders. It should be noted that none of the values obtained by the other authors referenced in Table C4.7.1 the Sarpkaya values in the post-critical region. The differences between individual tests may partly be due to the different types of post-critical flow (different test conditions) and to the non-uniform definition of roughness used by the different authors. One should also bear in mind that the wave particle velocities decrease with increasing depth below the water surface, which might mean a transition from the post-critical regime to the super-critical or even critical regime. This will result in a reduction in CD values for smooth cylinders (although in the lower Re-number part of the critical regime it may result in an increase in CD values, but here the water particle velocities are so low that the resulting contribution to the overall drag force will be significantly smaller than the contributions higher up on the cylinder). For the rough cylinders the critical regime occurs at lower Re-numbers and there is no reduction in the drag coefficient in the super-critical regime. For large roughnesses an increase in the drag coefficient has in fact been reported in this regime [3, 32]. Based on the literature survey presented in Table C4.7.1 and the discussion above, the drag coefficient for rough cylinders (roughness kID>0.004) is chosen equal to Co = 1.0, both for the ultimate strength and the fatigue cases. C4.7.2.3 Marine Growth dependence Rust and hard marine growth has been found to behave in essentially the same manner as artificial hard roughness, but a surface with hard marine growth behaves quite differently from a surface with soft marine growth. Another point of consideration is that different types of marine growth on a submerged tubular may dominate at different depths below the sea surface. The use of anti-fouling coating will at least delay the development of marine growth but after a few years the anti-fouling coating becomes less effective. Regularly cleaning of the tubulars is another possible way to limit the development of marine growth. In Table 4.3, Section 4.7.2 of the PRACTICE, it is assumed that severe marine growth is not allowed. This is in accordance with the operational profile of mobile jack-up rigs, with cleaning of legs at intervals preventing severe marine growth.

Commentaries to Recommended Practice for Site Specific Assessment of Page 42 Rev 2, Jan 2002 Mobile Jack-Up Units The main contribution to forces is in the surface region, such that the extension of the marine growth below the surface zone is not important for the overall forces. The paint will in addition be somewhat roughened when exposed to the salt water for a longer period. Above the marine growth region the use of values for a smooth cylinder has been recommended. This is mainly based on the fact that the marine growth will be limited to the region below MWL + 2m, limiting the roughness above this region. In addition measurements also indicate that the wave forces in ocean waves are less than predicted by use of a constant Co [39, 31], see also Figure C4.7.1

Based on this it is recommended that the value CD for a smooth surface (CD =0.65) is generally used for the legs above MWL + 2m and the value for a rough surface below MWL + 2m (CD =1.0), as stated in Table 4.4 of the PRACTICE. HURRICANE CARLA Wave No. 06887 - 018 SEPT. 10, 1961 H=39Ft. T= 13 Sec. L= 676 Ft. -----------,~

.

~/'",""...,. /' ~

I ~

Stokes sth(CD= 0.7)

/ /

I ~~I

I

I J

I I • !

I i I

I

taO

I

:

200

100

Figure C4.7.1 Comparison between measured and computed forces on a pile up to free surface [39, 31] C4.7.2.4 Definition of relevant parameters The drag coefficient (CD) for tubulars, may be considered as a function of roughness (kID), Keulegan-Carpenter number (KC) and Reynolds number (Re) as an alternative to Table 4.3. This explicit dependence is intended to be used in cases where there is more detailed knowledge, first of all on the roughness and in addition on the flow conditions around the at a specific site. A definition of these governing parameters are included in section C4.7 .2.1. C4.7.2.5 Dependence on roughness The roughness may be ed for explicitly if the roughness is documented to be of an intermediate value compared with the smooth and rough kID values assumed above. Recommended values for the roughness, k, may be found from table C4.7.2.

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 Table C4.7.2 Recommended Roughness Values for Tubulars [45] Surface Steel, new uncoated Steel, painted Steel, highly rusted Marine growth

Page 43

k (meters) 5.0E-5 5.0E-6 3.0E-3 5.0E-3 - 5.0E-2

Several authors have presented, in graphical form, the Co dependence on the relative roughness kID at post-critical Re-numbers. Figure C4.7.2 presents a graph from Miller [23], showing the variation of CD with varying kID based on several model experiments at post-critical Re numbers. Figure C4.7.3 and Figure C4.7.4 show similar graphs presented by respectively Wolfram et al [21] and Pearcey et al [28]. Based on the available data with respect to the dependence of CD on kid, the expressions presented in Equation (4.7.1) have been proposed to describe this dependence for the purpose of the PRACTICE. The drag coefficient COi may then be obtained from Equation (4.7.1): C DsmOOth =0.65 ; CDi(kID) = COsmooth * (236 + 034 Log,o (k I D)); {C ; Drough =1.0

kiD < 0.0001 0.0001 < kiD < 0.004 0.004 < kiD

(4.7.1) A graphic representation of Equation (4.7.1) is shown in Figure C4.7.5. With respect to the inertia coefficients for smooth cylinders, all the references from Table C4.7.1 report post-critical C M values lower than the asymptote CM =2.0. The C M values lie mainly in the range 1.6 - 1.7. However the question is whether (in general) some inertia contribution has been included in the drag forces used for the CD determination. This would mean that the CD values are slightly overestimated and the CM values slightly underestimated. At the same time, since both fatigue and ultimate strength imply Keulegan-Carpenter numbers >25, it is the drag dominated region which is of most interest and the chosen CM values are not really critical. Based on this argument the inertia coefficient for smooth cylinders in the post-critical regime is set equal to the asymptotic value CM =2.0. The CM values for rough cylinders, are in general reported to be slightly lower than the CM values for smooth cylinders. Based on the same argument as used for the smooth cylinders, the inertia coefficient for rough cylinders in the post-critical regime is set equal to CM = 1.8. A summary of the recommended values for the hydrodynamic coefficients for tubulars is given in Table C4.7.3. Table C4.7.3 : Recommended Hydrodynamic Coefficients for Tubulars Tubular Smooth (k!D O.004) Intermediate kID

CDi 0.65 1.0 Equation 4.7.1

CMi 2.0 1.8 2.0

Page 44


~ ~

1.2

SZECHENY

1.0

I ~~~~

r:::l

U

0.8

1:: .....0

-0 ....

Q)

:.0

l~

0.6

~

Q)

0

Range of "In Service" Marine Roughness

6

U

~

10 <6x10

0.4

4

5

5

-+1(

I-<

Q

5 x 10 < Re < 6 x 10

5 x 10 < Re < .I~ 6 X 10 6

6.

0.2

0 0

0

Achenbach Sand

6

} NMI

Simulated Marine Rouglmess

10-3

10.4

,.1

10. 1

10 ·2

Relative Roughness kiD Figure C4.7.2 Drag coefficient for rough cylinders at high Reynold's number, [23]

o -

Ci

U ~ (J)

2.00

/::,. X • •

1.75

o

\1

1.50

•

1.25

o

0

-0

U

~ 1-1

Achenbach (beads) Achenbach (pyxamids) Rodenbuschetal Miller (peas) Miller (barle YJ Math (sand) Math (barnacles) Math (ert. roughness) LRfCIT (cubes)

X

()

(J)

OTS Dam

<>

'..-1

~ ~

Present Dam Pearceyelal

-

1.00

___ - -x- _----

0

~

- o .... -

.... -"'

J) ... -

v

2

3

r:I-

"

..... " " 0

IID[J

V

o

0

~

x

0

Q

0.75 0.50 2

3

456789

2

10-

456789

Relative Roughness kiD Figure C4.7.3 Drag coefficient for post critical Reynolds numbers for rough cylinders, [21]

10-1

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 0.3

Page 45

® •.•.•.•.•.•.•............•.• 9-..... ........

S

.@ .•••••••

0.2

". ' •. (iL

1.4 ",®

1.2 0.1

::)'!KUUHAL NUMlIE,K

1.2

(PRESENT TESTS)

1.0

0

1.0

. •

f{

0.8

,~'

CD e------------ -- ----'- -------

0.6 0.4

MAXIMUM VALUJ£ UF l"U::;T· t;tUTlt;AL t;}

®

HIGEST TEST, REYNOLDS NUMBER

•

10.6

l"KJ::::;J:'.NTTJ£::;T::;

0.4

MAxrr.ruM VALUE

HIGHEST TEST, REYNOLD5 NUMBER MEAN CURVE

0

CD 0.6

x

•

0.2

--~--------- ----•••.•••••-

0.8

10.4

10')

}

0.2

MILLER (REF1.2)

0

.:.1

10·:$

10.1

10

Figure C4.7.4 Effect of roughness on drag coefficient and vortex shedding frequency for post-critical Reynolds numbers, [28] CD smooth = 0.65 CD smooth * (236 + 0.34 Log 10 CD rough =1.0

; 1110000 >kID >kID>1I10000 kID> 11250

(k/D» ;11250

0.2 ". /MARlNEGROWTH

/ ............ ~:'. '>:'" k .\'.¥

1.0 C Di (kID)

"

0.8 0.6

\,JH:[:~~S;:~...... ....

0.4

kID 1.0F.-O:i

1.0E-04

1.0E-03

1.0E-02

1.0E-0l

Figure C4.7.5 Recommended values for the drag coefficient as function of relative roughness

". ~"

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 Keulegan-Carpenter number dependence.

Page 46

In post-critical conditions, for KC-numbers lower than say 30-40, there seems to be some dependence of the drag coefficient on the KC-number, at least for rough cylinders. For smooth cylinders this KC-dependence is more uncertain. The Christchurch Bay Tower (CBT) results for a clean cylinder reported by Bishop [26], for example, show this dependence for smooth cylinders, and so do the results reported from the Ocean Test Structure (OTS) [19]. Wolfram and Theophanatos [21], and the SSPA results reported by Rodenbusch and Gutierrez [15], do not show this dependence for smooth cylinders. For rough cylinders in post-critical conditions, the KC-dependence of the drag coefficient for KC-numbers lower than say 30-40, seems to be a more generally observed trend, as in [15, 19,27] amongst others. It must be emphasized that for decreasing KC-numbers «30) the (post-critical) conditions will gradually be more inertia dominated and less drag dominated, implying an increasing uncertainty in the reported CD- values.

Figure C4.7.6 shows CD as a function of the KC-number for cylinders in waves from [52]. Figures C4.7.7 and C4.7.8 show in a similar way CD as a function of KC-number for respectively a clean cylinder and a rough barnacle covered cylinder of the Ocean Test Structure COTS [19]) as presented in [25]. Based on the discussion above and the results reported in the literature the explicit KCdependence presented in Equation (4.7.2) may be included in the computations in addition to the roughness dependence: 1.45 ; KC
Page 47


--1/20 ·---1/1~O

• ---,.

-'... ....

.•• -1/1~GO··-......

""'''',

'"" 1.0

Ifl

0.5

"

'" ' ....

'... "

........

...

........-... --- ------- --- .. _-------- .. _----

-"'- ... _-

OUGRJ.M BAScO ON lOGARITHIC IHTERPOLA nON BfT'WfEH k/D.1I20 #.NO

k/l)-v1ooao

o

o

20

10

30

40

KC

Figure C4.7.6 Drag coefficient dependence on KC number, [52] Q

3.0 ,..-_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _--,

C,)

; E-o

C,)

o

/ ' NUMeeR OF

~ 2.0

H~LF

WAVE C'(CI..!;S

3SS_+ CJ

1.0

.-0-+--'-6-=6---------- Co-- (l.68

0.0

i-w_ _J...-_ _.L.-_ _..I....-_ _.I.-_ _-'--_ _. . I . . - _ - J

o

10

20

30

40

50

60

70

KC

Figure C4.7.7 Drag coefficient dependence on KC-number for clean cylinders of the Ocean Test Structures, [19,25]

Page 48

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 :::) 3.0

I

u

~

I

~

NUMSER OF HALF WAve CYCI..ES

745

{J

"~'EiHOO I MEAN

~ U

o

1271

2.0

~

•

~~7

.457

IN r

-0-

181

'-

1.0

tOJ

r

I

~16"----------CO \

0.0 '--_ _I--._

o

___lL~_--.Jl'__

10

20

_

-

METHOD II MEAN

___lLI..._.._

30

1.0

tl_..__

___i

___I.L'___ _ _ _

40

50

70 KC

60

Figure C4.7.8 Drag coefficient dependence on KC-number for barnacle covered cylinders of the Ocean Test Structure, [19, 25J

rJ 1 . 6 i + - - - - - - ' - - - - - - - - ' - - - - - - . . L . - ' - - - - - t - ............. Kd.01 ~ ••••• Kd .001 ~

.... ..... Kd .0001

1.4

~

..............

u 1.2

o

~ 1.0

00.

"

"

'------. --------

.

'.

'"

'.

.

"

-----~ ... . .. '

•

O.g-

...

_-

•

...

...

oj.

••

I

--- --- ---

0.6 0.4 +-...,........,.....-..,....-..---r--.----,.--..---,...,........-.--..--.....-.,-...,.--,--..,....--,--r 40 30 o 10 20

KC

Figure C4.7.9 Recommended drag coefficient dependence on KC for cylinders in waves, at high Reynolds numbers

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 Reynold's number dependence

Page 49

As previously discussed the drag coefficient is dependent on the Re-number and this has been reported by several authors [3, 32] (Figures C4.7.11 and C4.7.12) and is reflected in some guidance on load computations, e.g. [29,33] (Figure C4.7.1O). However, the use of test results reducing Co in the critical region is not relevant for practical purposes as the roughness kID<1I100000 implied in the curve for smooth cylinders is not applicable for jack-up structures. The change in the Reynolds dependence with respect to roughness is quite large and it is therefore not possible to recommend one single curve for this dependence. The recommended set of curves shown in Figure C4.7.13 are mainly based on a functional fit to the test results presented in [32] and in addition the drag coefficient in the critical regime is set to minimum of CD = 0.45. Test results have indicated lower CD values, but only in the ideal conditions of test facilities. A recommended set of curves are given in Figure C4.7.13, complying with the roughness dependence of Figure C4.7.5 at large Reynolds numbers. Using the curve for roughness kID = 0.01 there is no reduction below CD = 1.0 for Reynolds numbers above 105, which s the use of a constant CD in the PRACTICE. .. ..

.. CD

I~

.\ t\/

-_.

\.

I"'V . . .~

;.:--

\

_\\

0.5

. .-

\

"\. \\ \. .'\\ L "- W }\

1.0

__

.- ---....,_.

~

L

~.'a"

Y,

1.1'l~·-

l/

V-;:~I~_ ...

7

~

I

/SMOOIIJ-.--- -

o 10

4

,0

105

10

Re

7

10

Figure C4.7.10 Suggested Reynolds dependence in existing guidance, [33] CD

-.,

1.2 i

i

1.0 0.,8 0.,6

Ii

I'

,

,- - . ,

i'

-,...

\"'\.\ ~~ ~ /1-" ·1 .

\

~I!J

.

--~t

, k.fOalD

0..4 - f - - ,-

0.2

r'I"--H~1

!\\ X~~ V JI,'J ~ h4' ..." rl. :fS..OOTI<

V~

/'

- -I"-

iT ~'

r-- ~

- =-

,

Uf

, '.

111,/0 -01 J

i

111111, ___ . 10.

6

Reynolds Numbe% (Re)

Figure C4.7.11 Reynolds dependence of drag coefficient in test results, [3] ,

Page 50


0.4

+----TJ~_f.&:II-+_.,...---~--------_t-+__t_--_+--_t

0.2

+----+--.f-~_+_--__I_--_.,;.__+-4--l----l----I

4

Re 4 Drag coefficient Co of rough circular cylinders in steady incident flow for ditf'erent surface roughn~ss values kiD (k =average height of surface roughness, D ~ cylinder diameter,' Rn = U-P / v, u_= incident flow velocity.) ll) kiD = 110 . 10-5 ; 0, kiD ..:.. 450' 10-:5; D, kID = 900· 1O-~;-# Page & Warsap (1929), (Achenbach, 1971).

2.10

4

6

8

10.5

2

4

6

8

10°

2

Figure C4.7.12 Reynolds dependence of drag coefficient, [32]

CD ~ ..:. := :: ::- -- ,

.

1.2

,

~

--

....

"" ..... ';~~

10

"

'I.'

.. ,

0.8

,

'.

............. Kd.Ol

"

.... e

•

,

• • • • • III

••••• Kd.OOl ,. ..... Kd,OOOl

... " .

Kd.OOOOl

. . . . . . ..

I ) ' " .'

:

\_.'

: ~. .

." I

I

I

I

0.6

-"

0.4

I

I J'"

'-

- .:: .: . : --..;--0'

-

..,

...

~

.-

0.2

0.04--------,.------,.-------+ 1.0E+04

1.0E+05

1.0E+06

Re

1.0E+07

Figure C4.7.13 Recommended values for Reynolds dependence for different values of relative roughness, KC>40

Commentaries to Recommended Practice for Site Specific Assessment of Page 51 Mobile Jack-Up Units Rev 2, Jan 2002 C4.7.3 Marine Growth Thickness In addition to the effect on the roughness the effective diameter should be increased to for marine growth. Here it is recommended to increase the radius by 12.5 mm (i.e. diameter increased by 25mm) over the full water depth for tubulars. C4.7.4

Hydrodynamic Coefficients for Brackets These are treated as flat plates implying that a CDi = 2.0 and C Mi = 1.0 is to be applied (considering the area associated with CM as that of the circumscribed circle). For convenience the PRACTICE proposes that brackets are included as horizontal in the hydrodynamic model to assure proper directional dependence of forces. Shielding may be considered according to Figure 4.3 of the PRACTICE.

C4.7.5

Hydrodynamic Coefficients for Chords

C4.7.5.1 Split tube chords In considering the test results for split tube chord data the following aspects are considered: The tests are almost always performed with a smooth cylinder section. Most of the tests are performed in stable current or wind conditions. The first aspect is the most important, also indicated by the test results evaluation of the tubulars presented in Section C4.7.2. The drag coefficient for smooth tubulars is about COsmooth = 0.65, while for rough cylinder this increases to CDrough = 1.0. The second aspect on stable flow conditions should not affect the results very much as the KC values are very high in extreme load evaluations. However, the test result in [63] showed higher values in waves than in stable current. This has not yet been fully explained, but comparisons made in [25] indicates that test results in waves from flume experiments overpredict the drag forces. A number of test results [62] have been considered, from wind tunnel tests and towing in water, when evaluating hydrodynamic coefficients for split tube chords. The drag coefficient is first estimated for the directions 0° and 90° as defined in Figure C4.7.14. The drag coefficients for 0° are dominated by the tubular part and no particular effect of the rack on the drag coefficient is seen from the tests. That is, for typical dimensions of the tubular diameter and rackplate thickness t, D/t » 1.0, tests show values of about Co ::= 0.65. This indicates that the drag coefficients chosen for the tubular are also valid for the split tube chord for the 0° direction. In order to be consistent with the roughness dependence of the drag coefficient for tubulars, the drag coefficient in the marine growth region is increased due to roughness to C Drough = 1.0 for8=0°. For the 90° direction the drag coefficient should be similar to that of a flat plate for large WlDi ratios, CDplate = 2.0. However, test results seem to indicate that the CD values for this direction referring to the mean rack width W, are, on average, about 1.8, see Figure C4.7.15. The suggested drag coefficient in the PRACTICE is therefore set to be 1.8 for small WlDi ratios, increasing to 2.0 for large WlDi ratios. The interpolation between these two numbers is based on engineering judgment.

Commentaries to Recommended Practice for Site Specific Assessment of Page 52 Mobile Jack-Up Units Rev 2, Jan 2002 The drag coefficient for the wave flow normal to the rack, related to the rack width W, is recommended as: 1.8 1.4+ W 13D j { 2.0

W/Dj <1.2

1.2<W ID j <1.8 1.8 < WID j < 2.0

(4.7.3)

For the interpolation between the directions 0° and 90° a number of formulations are available, but since there were a number of test results available, a best fit of a new formulation was decided. The following interpolation formula were found to fit the data best, see Appendix C4.C, and at the same time be flexible with respect to the drag coefficient for rough and smooth surfaces at 0°:

where~

Coo = is the drag coefficient for the chord at 6 = 0° and is to be taken as that of a tubular with appropriate roughness, see Section C4.7.2 i.e. Coo = 0.65 above MWL + 2.0m and Coo = 1.0, below MWL+2.0m. Possible dependence on KC and Re numbers as for a tubular. CD! = The drag coefficient for flow normal to the rack (6 = 90°), related to the projected diameter (the rack width W). Explicit dependence on KC may be taken according to Figure C4.7.9, but is normally not relevant for extreme loading conditions. Dependence on kID or Re may normally be neglected. The above formulation was derived based on the assumption that the chord behaves like a tubular up to a direction where the rack enters the flow field, and from there and up to 90° the chord acts as a flat plate. In addition to the above formulation two other formulations were tested as shown in Figure C4.7.16. Equation 4.7.4 gave an excellent fit with the observed drag coefficients for a smooth tubular and is therefore recommended to be used for split tube chords. Interpolation formula similar to those used in [29] and [46] are compared in Figure C4.7.17 with Equation 4.7.4, for a regular wave analysis. There is some difference in the direction close to 90°, but the number of test results behind the PRACTICE formulation is believed to justify the change.

Page 53


I+----w---..

D

1 Figure C4.7.14 Definition of directions and dimensions for a split tube chord

o 3.04-------~------~--------------~--------r

u

~

~

2.5

u

D_-------

C D1 FROM PRACTICE

o

~

Ir

c I---~----

I

a

I

r

1.5

t

1.0

t

4-_,........,--.---r-....,...---.,.........,--r-...,--..--..--r-...,----..,.....,--~.....-...._:__ I

1.0

1.2

1.4

1.6

20

1.8

wm

Figure C4.7.15 Drag coefficient at 90° related to the rack width W

Page 54


Q

U

2j

~

20

~

8

..-

., ~ A

~

.....

IS ,

"

."

,. '" " '"

...

•

",'

,,' 4

/

./

10

-~ ../.

"

I--...::....;-....--·--~- "

"

-'

'"

"

"/a

0.5

0.0

+-_____.,.._____......._____ o

30

~

60

90 ANGlE

e

Figure C4.7.16 Alternative interpolation formulations fit to data

~20 -.------------------------------------_~-~

..-.... PRACTICE , ..... SHELL

,/

I"~

",/

,/

--

".."...-

.. •...•.. DNV

"..--

"/'" -'-'-'-' .-.-~.-.-.-.-.-'.-'

" ". ,..,.,'

LO

",.-

...,.,.

••~.: :;;;0'

.-:;.

s

n.s •

o

/

'"

'"

"

-'~

~/

;----------~.r-------~.r-----------,

o

30

60

90

ANGLE

e

Figure C4.7.17 Comparison with some current practices for regular wave analysis [29], [46]. WID =1.24 and the scaling regular/irregular =0.7, valid below MWL + 2.0m

Commentaries to Recommended Practice for Site Specific Assessment of Page 55 Mobile Jack-Up Units Rev 2, Jan 2002 For the inertia coefficient the theory [32] indicates CM = 2.0 for a smooth tubular related to the projected diameter and CM = 1.0 for an isolated flat plate. However, when the plate is considered in conjunction with the split tube sections eM = 2.0 is appropriate for the combined section. For a rough tubular as indicated in Table 4.4 of the PRACTICE, the inertia coefficient should be about 1.8 in the marine growth region. However, since the inertia forces will not contribute much to the extreme forces on the legs, the inertia coefficient was set to 2.0 related to the width of the chord measured over the tubular, i.e. at 0°. This is a simple solution and will be conservative in the direction of the tubular for a rough surface and unconservative in the direction of the rack and on average correct. This formulation will also be consistent with the simplified modeling of the leg section where the reference diameter Di is the dimension D and using CMe = 2.0. For large rack to diameter ratios WID, it may however be considered appropriate to modify Creduce) the inertia coefficient such that it s more correctly for the combination of the contributions from the flat plate and tubular components. C4.7.5.2 Triangular chords For triangular chords (Figure C7.4.18) little test data are available. Some currently applied formulae for drag coefficients of more basic sections were therefore used in addition to the test results to improve the background for the actual chosen values. Drag coefficients related to two typical shapes are given in [45], as shown in Figure C4.7.19, for a triangular box section and two plates mounted normally on each other. A triangular chord is a combination of these cross sections. The numbers at different directions are compared in Table C4.7.4. The drag coefficients were determined by vectorial summation of drag forces in direction 1 and 2 according to Figure C4.7.19. To relate the drag coefficient to a fixed dimension Di = D the back plate width is chosen. A fixed dimension and directional dependent drag coefficient is convenient for modeling purposes. The drag coefficient related to this fixed diameter may be computed as: C Di = CDpr(8) * D pr(8) I Di where; CDpr(8) = the drag coefficient referenced to the projected diameter. 1.70 8 =0° 1.95 8=90° 1.40 8 = 105° = 8 = 180°-8 0 1.65 2.00 8 = 180° D pr(8) = the projected diameter of the chord determined as:

reOS(S)

W sin(8) + D 121cos(8)1 nlcos(8)1

0< 8 < 8 0 8 0 < 8 < 180 - 8 0 180 - 8 0 < 8 < 180

D pr(8)

=

80

= the angle where half the backplate is hidden behind the rackplate, determined as 8 0 = tan- 1(D/2W).

C7.9)


Page 56

Table C4.7.4 Comparison of drag coefficients for simple sections and chord CQru: evaluated from tests.

CDpr:

e

-L 1451

/::../451

0 45 90 135 180

1.7 2.5 2.2 1.5 2.0

1.3 1.8

PRACTICE 1.70 1.825 1.95 1.50 2.00

1.3 1.8

(WID = 1.1)

As a basis for the suggested drag coefficients the results available from TEES [67] and DHL [61,62] were considered together with the recommendations in [46]. The drag coefficients recommended in the PRACTICE are compared with the TEES test results in Figure C4.7.20. The inertia coefficient CMj = 2.0 may be applied for all directions, related to the equivalent volume of 1tD j 2/4 per unit length, where D j = D, the backplate dimension. This assumes that the outline cross sectional area is approximately 1tD/14. If the rack width is not of similar size to the backplate dimension, a more detailed consideration of the inertia coefficient should be made if the loadings on the leg are not drag dominated i.e. if the results are sensitive to the choice of inertia coefficient. Explicit dependence on KC may be taken according to Figure C4.7.9, but is normally not relevant for extreme loading conditions. Dependence on kID or Re may normally be neglected.

W-----+l.\ :'

:~

Figure C4.7 .18 Definition of dimensions and angles for a triangular chord C4.7.6

Other shapes For other shapes, or groups of elements, see e.g. [45].

Page 57

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 Table Cl Shape coefficient for irregular cross sections.

Profile

It

]]6 II

t

C S1

CS2

0

180

2.0 1.2 -1.6 -1.1 -1.7

2.2 -2.4 0

0 80

1.8 -1.3

0 0

0 45 90 135

.t:~::I'

(deg.)

0.9

pdZ

·t:U>~ .. t. 0.876

Figure C4.7.19 Drag coefficients for basic sections in uniform flow [45] 5

3.0-l-------I-------lL..----....I-----.

C)

• ~

TJ::!iT~ULT

PRACTICE

,o.~ 1.5 c

1.0 ". 0.5

O.O-lo----,r----,.r----,-----r.----"1---1

o

30

60

90

120

150

180

ANGLE

e

Figure C4.7.20.a : Marathon LeTourneau 116C is

3.0

• ..-....

0

~

......

2.5

0

.~

tz::

t:1

2.0

0 0

0

~

TEST RESULT PRACTICE

1.5 1.0 0.5

o

30

60

90

120

150

ANGLE

180

e

Figure C4.7.20.b : Marathon LeTourneau Gorilla Figure C4.7.20 Comparison between TEES test results and the PRACTICE

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 C4.8 OTHER CONSIDERATIONS

Page 58

For the most critical individual leg the possibility of local vortex induced vibrations should be evaluated. This check will normally be covered at the design stage. However, if the site conditions of wind or current and/or wave height exceed those used for design such a check may be required. This is because vortex induced vibrations may lead to very high local stresses and a major contribution to fatigue loading. Vortex induced resonance will not normally be occur if: S < 0.2 for tubulars < 0.145 for flat plates where; S = [(fi Di)!Vn], the Strouhal number Vn = flow velocity normal to the member n I = diameter of member fi = fundamental vibration frequencies of member (in Hz). Further information and bounds for S above which vortex shedding will not occur may be found in [45] and [59].

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 GLOSSARY OF FOR SECTION C4

= = = = = = = = = = = = COi = COpr(S) = CDrough = COsrnooth = Ch = CM = CMe = CMei = = = = = CMi = d = D = De = Di = DJ = Dpi 8) = fi = Hs = k = kID = KC = Ii = N = = tn A Ae Ai As At Co Coo COl COe C Oei

Re s S S S T Tn Tz u Un un ux, Ux U Uc Urn

= = = = = = = = = = = = = = =

Page 59

cross sectional area of member. equivalent area of leg per unit hei:¥ht = (1: Ai Ii )/s. equivalent area of element = 1t Di /4. sum of projected areas for all in the considered plane. total projected envelope area of the considered plane. drag coefficient. The drag coefficient for chord at direction S = 0°. The drag coefficient for flow normal to the rack, S = 90°. equivalent drag coefficient. equivalent drag coefficient of member i C Oi (D/De) (vertical member) 3 sin
Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 GLOSSARY OF FOR SECTION C4 (Continued) Ured Uw Vn Ve Ve

=

Ven Vf W

= =

= = =

W

=

Xo

= = =

Z

z' Z

= <Xi = P = Pi = ~draa = ~inertia = ~inertiaH = A = v = 8 = 8 = P = a.

0

0

~ ~o

=

Page 60

reduced particle velocity for regular waves, Ured = uTnlD. particle velocity by waves. total flow velocity nonnal to the member. the reduced current velocity to be used in analysis. the current velocity to be used in the hydrodynamic model, Ve should not be taken less than O.7Vf. current velocity nonnal to member used in the hydrodynamic model. far field (undisturbed) current. dimension from backplate to pitch point of triangular chord or dimension from root of one rack to tip of other rack of split -tubular chord. the width of the structure. motion amplitude used in consideration of the applicability of the relative velocity fonnulation. coordinate measured vertically upward from the mean water surface. modified coordinate to be used in particle velocity fonnulation. elevation measured from the mean water surface. indicator for relative velocity, 0 or 1. angle defining flow direction relative to member. RelKC parameter to describe the test environment. angle defining the member inclination. drag force per unit length. inertia force per unit length. horizontal inertia force per unit length. wave length. kinematic viscosity. angle in degrees for waves relative to the chord orientation. angle where half the backplate is hidden behind the rackplate. mass density of water or air. the instantaneous water surface elevation (same axis system as z) the wave crest (same axis system as z).


Page 61

1

Keulegan, G.H., Carpenter, L.H., 'Forces on Cylinders and Plates in an Oscillating Fluid', Journal of Research of the National Bureau of Standards, Volume 60, No.5, May 1958.

2

Sarpkaya, T., 'In-Line and Transverse Forces on Smooth and Sand-Roughened Cylinders in Oscillatory Flow at High Reynolds Numbers', Naval Postgraduate School, Report NPS-69 SL 76062, 1976.

3

Hogben, N., Miller, B.L., Searle, J.W., Ward, G., Estimation of Fluid Loading on Offshore Structures', Proc. Institution Civil Engineers, Part 2, 1977.

4

Sarpkaya, T., 'Wave Forces on Inclined Smooth and Rough Circular Cylinders', Offshore Technology Conference, Paper OTC 4227,1982.

5

Sarpkaya, T., Bakmis, c., Storm, M.A., 'Hydrodynamic Forces from Combined Wave and Current Flow on Smooth and Rough Circular Cylinders at High Reynolds Numbers', Offshore Technology Conference, Paper OTC 4830, 1984.

6

Sarpkaya, T., Storm, M.A., 'In-Line Force on a Cylinder Translating in Oscillatory Flow', Applied Ocean Research, Volume 7, No.4, 1985.

7

Sarpkaya, T., 'Force on a Circular Cylinder in Viscous Oscillatory Flow at Low KeuleganCarpenter Numbers', Journal of Fluid Mechanics, Volume 165, 1986.

8

Sarpkaya, T., 'Past Progress and Outstanding Problems in Time-Dependent Flows about Ocean Structures', Proc. of Separated Flow around Marine Structures, The Norwegian Institute of Technology, Trondheim, Norway, 1985.

9

Sarpkaya, T., 'On Fluid Loading of Offshore Structures - After Ten Years of Basic and Applied Research', Offshore Operations Symposium, 9th ETCE, New Orleans, 1986.

10

Nath, J.H., 'Heavily Roughened Horizontal Cylinders in Waves', Proceedings of BOSS, 1982.

11

Bearman, P.W., Chaplin, J.R., Graham, J.M.R., Kostense, J.K., Hall, P.P., Klopman, G., The Loading on a Cylinder in Post-Critical Flow Beneath Periodic and Random Waves', Proceedings of BOSS, 1985.

12

Kasahara, Y., Koterayama, W., Shimazaki, K., 'Wave Forces Acting on Rough Circular Cylinders at High Reynolds Numbers', Offshore Technology Conf., Paper OTC 5372,1987.

13

Chaplin, J.R., 'Loading on a Cylinder in Uniform Oscillatory Flow: Oscillatory Flow', Applied Ocean Research, Vol.lO, No.3, 1988.

14

Davies, M.J.S., Graham, J.M.R., Bearman, P.W., 'In-Line Forces on Fixed Cylinders in Regular and Random Waves', Society for Underwater Technology, Volume 26: Environmental Forces on Offshore Structures and Their Prediction, 1990.

15

Rodenbusch, G., Gutierrez, c.A., 'Forces on Cylinders in Two-Dimensional Flows', Report BRC13-83, Shell Development Co., 1983.

Part I - Planar

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 REFERENCES FOR SECTION C4 (Continued)

Page 62

16

Rodenbusch, G., Kallstrom, c., 'Forces on a Large Cylinder in Random Two-Dimensional Flows', Offshore Technology Conference, Paper OTC 5096, 1986.

17

Theophanatos, A., Wolfram, J., 'Hydrodynamic Loadings on Macro-Roughened Cylinders of Various Aspect Ratios', Journal of Offshore Mechanics and Arctic Engineering, Volume 111, No.3, 1989.

18

Klopman, G., Kostense, J.K., 'The Loading on a Vertical Cylinder in Random Waves at High Reynolds Numbers', Water Wave Kinematics, pp. 679-699,1990.

19

Heideman, J.C., Olsen, O.A., Johansson, P.I., 'Local Wave Force Coefficients', Civil Engineering in the Oceans IV, ASCE, 1979.

20

Nath, J., 'Biofouling and Morison Equation Coefficients', Proceedings 7th. International Conf. on Offshore Mechanics and Arctic Engineering, 1988.

21

Wolfram, J., Theophanatos, A., 'Marine Roughness and Fluid Loading', Society for Underwater Technology, Volume 26: Environmental Forces on Offshore Structures and Their Prediction, 1990.

22

Roshko, A., 'Experiments on the Flow Past a Circular Cylinder at Very High Reynolds Number', Journal of Fluid Mechanics, Volume 10, Part 3,1961.

23

Miller, B.L., The Hydrodynamic Drag of Roughened Circular Cylinders', Transactions RINA,1976.

24

Pearcey, H.H., Cash, RF., Salter, 1.J., 'Flow Past Circular Cylinders: Simulation of FUllScale Flows at Model Scale', NMI Report R131, 1982.

25

'Roughness and Vortex Shedding Effects for Cylinders in Flume and Real Sea Waves', Report for the Health and Safety Executive by Advanced Mechanics Engineering Limited, 1991.

26

Bishop, J.R., 'An Analysis of Peak Values of Wave Forces and Particle Kinematics from the Second Christchurch Bay Tower', NMI Report R180, 1985.

27

Bishop, J.R., 'Wave Force Experiments at the Christchurch Bay Tower with Simulated Hard Marine Fouling', Report No. OTI 89 541, HMSO, 1989.

28

Pearcey, H.H., Matten, RB. and Singh, S., 'Fluid Forces for Cylinders in Oscillatory Flow Waves and Currents when Drag and Inertia Effects Are Present Together', BMT Report to the Health and Safety Executive OT-0-86-011, 1986.

29

Det Norske Veritas Rules for the Classification of Fixed Offshore Installations.

30

J.R Morison, M.P O'Brien, J.W. Johnson, S.A. Schaaf, The Forces Exerted by Surface Waves on Piles', J. of Petro Techn., American Inst. of Mining Engrs., Vol. 189, 1950, p149154.

31

S.K. Chakrabarti, 'Hydrodynamics of Offshore Structures', Springer Verlag, Berlin, Hedelberg, 1987.

32

O.M. Faltinsen, 'Sea Loads on Ships and Offshore Structures', Cambridge University Press, Trumpington Street, Cambridge, 1990.


Page 63

33

BSI Code of Practice No.3, Chapter 5, Part 2, 'Wind Loads', September 1972

34

J.H. Vugts, 'A Review of Hydrodynamic Loads on Offshore Structures and Their Fonnulation', BOSS'79, Imperial College, London, England, August 1979

35

E.J. Laya, J.J. Connor and S.Shyam Sunder, 'Hydrodynamic Forces on Flexible Offshore Structures', Journal of Engineering Mechanics, Vol. 110, No.3, 1984.

36

S.R Winterstein, E.M. Bitner-Gregersen and K. Ronold, 'Statistical and Physical Models of Nonlinear Random Waves', OMAE, Volume IT, Safety and Reliability, Stavanger, 1991, pp.23-31.

37

J.D. Wheeler, 'Method for Calculating Forces Produced by Irregular Waves', OTC, paper no. 1006, Dallas, Texas, 1969.

38

J.E. Skjelbreia, O. Berek, Z.K. Bolen, O.T. Oudmestad, J.C. Heideman, R.D. Ohmart, N. Spidsoe and A. Torum, 'Wave Kinematics in Irregular Waves', OMAE, Stavanger, 1991.

39

RO. Bea and N.W. Lai, 'Hydrodynamic Loadings on Offshore Platforms', OTC paper no 3064, May, 1978,pp. 155-168.

40

RO. Dean and P.M. Aagaard, 'Wave Forces: Data Analysis and Engineering Calculations', Journal of Petroleum Technology, March 1970, 105-119.

41

J.R Chaplin and T.P Flintham, 'Breaking Wave Forces on Tubulars', 3rd International Jackup Conference, City University, London, September 1991.

42

L. Skjelbreia and J.A. Hendricksen, 'Fifth-order Gravity Wave Theory', Proceedings of Seventh Conference on Coastal Engineering, 1961, pp. 184-196.

43

OJ. Andersen, E. F~rland and S. Haver, Design Basis, Environmental Conditions, Statfjord, Statoil Report no. F&U-ST 88007, Stavanger, April 25 1988.

44

RC.T. Rainey, 'Christchruch Bay Tower Compliant Cylinder Project, Final Summary Report and Conclusions', OTH-90-139, WS Atkins Engineering Sciences, Surrey, January, 1991.

45

DNV Classification note 30.5, 'Environmental Conditions and Environmental Loads', July 1990.

46

'Practice for the Site Specific Assessment of Jack-up Units', By Marine Technology Division, SIPM, EDP-5, The Hague, May 1989,

47

WAJAC, Veritas Sesam Systems Report no. 82-6108, H~vik, Dec. 1984.

48

N. Pharr Smith, D.B. Lorenz, C.A. Wendenburg and J.S. Laird, 'A Study of Drag Coefficients for Truss Legs on Self-Elevating Mobile Offshore Drilling Units', SNAME Tansactions, Vol. 91, 1983, pp. 257-273.

49

N. Pharr Smith and C.A. Wendenburg, 'A study of Drag Coefficients', The Jack-Up Drilling Platfonn, Ed. L. Boswell, City University, London, 1989.


Page 64

50

Yoshiharu, Ideguchi, 'Legs Drag Coefficients of Enhanced 30DIC Jack-Up Rig', TSU Research Laboratories Technical Research Center, Nippon Kokan K.K. Report No. 822117, June 1982

51

Borgman, L.E., 'Random Hydrodynamic Forces on Objects', Annals of Mathematical Statistics, Vol. 38., 1967, pp. 37-51.

52

Atkins Engineering Services, 'Fluid Loading on Fixed Offshore Structures', 1990.

53

Taylor, P., 'Current Blockage - Reduced Forces on Steel Platforms in Regular and Irregular Waves with a Mean Current', Offshore Technology Conference, OTC 6519, Houston, 1991.

54

Heideman J.e. and Schaudt K.J., 'Recommended Equations for Short-term Statistics of Wave Heights and Crest Heights', 1 April 1987

55

Moe, G. and Verley, R.L.P, 'Hydrodynamic Damping of Offshore Structures in Waves and Currents', The Offshore Technology Conference, OTC 3798, Houston, 1980.

56

American Petroleum Institute, proposal for an update of the API-RP2A, 'Hydrodynamic Force Guidelines for U.S. Waters', received 6. February 1992.

57

The Norwegian Petroleum Directorate, 'Regulation for structural design of loadbearing structures intended for exploitation of petroleum resources', 1988.

58

Health and Safety Executive, 'Offshore Installations: Guidance on design, construction and certification', London, 1990.

59

N.D.P. Barltrop, A.J. Adams, Dynamics of Fixed Marine Structures', Third Edition, Butterworth Heinemann, 1991.

60

MacCamy R.S., Fuchs R.A., 'Wave Forces on Piles: A Diffraction Theory", U.S. Army Corps of Engineers, Beach Erosion Board, Tech. Memo No 69, Washington DC, 1954.

om 90 322,

Other project reports related and technical notes: 61

G.H.G. Lagers, 'Morison Coefficients of Jack-Up Legs', MSC report 1005, Schiedam, The Netherlands, February 1990.

62

G.H.G. Lagers, 'Collected Morison Coefficients of Jack-Up Leg Elements', MSC report 1715, Schiedam, The Netherlands, June 1991.

63

S.Th. Schurmans et. aI., DHL, Wave Forces on Jack-Up Legs', Delft Hydraulics measurement report 8603-1505, Delft, 1990.

64

A.

65

~seth

~ken,

'Review ofDHL test data', Veritec report no. 91-3372, H!2Svik, 1991.

R.M., Arnesen Y., 'Check of data reduction of DHL data', DNVC report No 921054, H!2Svik, August 1992.


Page 65

Other project reports related and technical notes (continued): 66

D. Karunakaren, 'Scaling of Hydrodynamic Loads According to Computational Models', Technical memo no. 710762, SINTEF, Trondheim, July, 1991.

67

N.P. Smith, TEES Test Data, Extract, December 6, 1991.

Page 66

Commentaries to Recommended Practice for Site Specific Assessment of Rev 2, Jan 2002 Mobile Jack-Up Units APPENDIX C4.A : EXAMPLE OF EOillVALENT MODEL COMPUTATIONS

Pipe 0 70x4 (typ)

1178.8 (typ)

I~

Pipe Ji' 25x2

.1

2345

Figure C4.A.1 Model of a bay for test purposes

Table C4.A.1 Computations of eguivalent model for heading 0° to be used in site assessment for z < MWL + 2m, chord WID = 1.13. Uj

~i

cos ... *)

CDi

Di

Ii

CDi*Di*ltcos ...

Chords:

1 2 3

(30) (30) (90)

90. 90. 90.

1.0 1.0 1.0

1.0 1.0 2.124

.65 .65 .65

5.0 5.0 5.0

3.25 3.25 6.90

Inclined braces

4 5 6 7 8 9

-30 -30 30 30 90 90

26.7 -26.7 26.7 -26.7 26.7 -26.7

0.25 0.25 0.25 0.25 1.0 1.0

1.0 1.0 1.0 1.0 1.0 1.0

.30 .30 .30 .30 .30 .30

11.2 11.2 11.2 11.2 11.2 11.2

0.84 0.84 0.84 0.84 3.36 3.36

10 11 12

-30 30 90

O. O. O.

0.125 0.125 1.0

1.0 1.0 1.0

span breakers

s C De *De = LCDjDjl j /s De = ~(LDj21j / s) C De = 4.82/1.58 C Me *)

Geometric factor, see Section 4.6.6 the PRACTICE

0.06 5.0 .10 0.06 .10 5.0 0.50 5.0 .10 LCDi*Di*li*cos ... = 24.10

=5.0m =4.82

=158} = 3.05 equivalent model =2.0 [sin2~i

+ COS2~i sin2Uj]3f2

Page 67 Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 Table C4.A.2 Com12utations of eguivalent model for heading 0° to be com12ared with model test results, chord WID = 1.13, model scale = 1:4.264

i

Uj

Chords:

1 2 3

(30) (30) (90)

90 90 90

1.0 1.0 1.0

Inclined braces

4 5 6 7 8 9

-30 -30 30 30 90 90

26.7 -26.7 26.7 -26.7 26.7 -26.7

10 11 12

-30 30 90

o. o. o.

span breakers

cos ... *)

f3i

s = 1.178 = 0.842 C De *De 2 = LD j 1j Is De C De = .842/0370 C Me

=

CDi

Coi*Di*li*cos ...

Di

Ii

0.65 0.65 2.124

.152 .152 .152

1.178 1.178 1.178

0.1164 0.1164 0.3803

0.25 0.25 0.25 0.25 1.0 1.0

0.65 0.65 0.65 0.65 0.65 0.65

.07 .07 .07 .07 .07 .07

2.628 2.628 2.628 2.628 2.628 2.628

0.02899 0.02899 0.02899 0.02899 0.11957 0.11957

0.125 0.125 1.0

0.65 0.65 0.65

1.173 .025 .025 1.173 1.173 .025 LCoi*Di*li*cos ...

0.00238 0.00238 0.01906 = 0.992

C De *D e =359

0370}

= 2.277 equiv. model = 2.0 (model scale)

D,

C De C Me

= 158 }

= 2.277 equiv. model = 2.0 (full scale)

Table C4.A.3 Com12utations of eguivalent model for heading 30° to be com12ared with model test results, chord WID = 1.13, model scale = 1:4.264 1

Uj

Chords:

1 2 3

(60) (60) (30)

90 90 90

Inclined braces

4 5 6 7 8 9

0 0 60 60 30 30

10 11 12

60 60 30

span breakers

s = 1.178 C De *D e =0.843 = iLD21. Is De = .843) 0.370 C De C Me

cos ... *)

f3i

CDi

Di

Ii

Coi*Di*li*cos ...

1.0 1.0 1.0

1.663 1.663 0.65

.152 .152 .152

1.178 1.178 1.178

0.2978 0.2978 0.1164

26.7 -26.7 26.7 -26.7 26.7 -26.7

0.091 0.091 0.716 0.716 0.254 0.254

0.65 0.65 0.65 0.65 0.65 0.65

.07 .07 .07 .07 .07 .07

2.628 2.628 2.628 2.628 2.628 2.628

0.01088 0.01088 0.08561 0.08561 0.03037 0.03037

o. o. o.

0.650 0.650 0.125

0.65 0.65 0.65

1.173 .025 1.173 .025 1.173 .025 LCDi*Di*li*cos ...

0.01239 0.01239 0.00238 = 0.9929

=

0370}

= 2.278 equiv. model = 2.0 (model scale)

C De *D e =359

D,

C De C Me

= 158 }


Page 68


Pipe 054"x4"

38 (typ)

800.8 (typ:

1895.3

Figure C4.A.2 Square bay with triangular chords

Table C4.A.4 Sguare ba:\:: with triangular chords 2 Eguivalent model to be used in site assessment z < MWL + 2m. Ii

1.0 1.0 1.0 1.0

1.65 1.65 1.79 1.79

.71 .71 .71 .71

3.4 3.4 3.4 3.4

3.983 3.983 4.321 4.321

40.2 40.2 40.2 40.2

0.2689 1.0 1.0 0.2689

1.0 1.0 1.0 1.0

.32 .32 .32 .32

10.6 10.6 10.6 10.6

0.912 3.392 3.392 0.912

0 90 90 0

o. o. o. o.

0.091 1.0 1.0 0.091

1.0 1.0 1.0 1.0

.32 .32 .32 .32

11.2 11.2 11.2 11.2

0.0 3.584 3.584 0.0

13 14

45 45

o. o.

0.354 0.354

1.0 1.0

.23 .23

11.4 11.4

2.622 2.622

15

90.

o.

1.0

2.0

.98

1 2 3 4

45 45 135 135

90 90 90 90

5 6 7 8

0 90 90 0

Side Horiz

9 10 11 12

span breakers brackets

Inclined braces

Coi*Di*li*cos ...

Di

J3i

Chords:

cos ... *)

COi

<Xi

s = 3.4 = 11.63 C De *De = ~(~Di\ / s) De = 11.63/ 230 C De C Me

=

0.98 ~Coi*Di*li*cos ...

230} equivalent model

= 5.06 =2.0

1.921 =39.550

Page 69 Commentaries to Recommended Practice for Site Specific Assessment of Rev 2, Jan 2002 Mobile Jack-Up Units Table C4.A.5 Sguare bay with triangular chords) Eguivalent model to be used in comparison with test results) model scale 1:4.256.

eOi

Di

Ii

1.0 1.0 1.0 1.0

1.65 1.65 1.79 1.79

.167 .167 .167 .167

0.8008 0.8008 0.8008 0.8008

0.2207 0.2207 0.2989 0.2989

0.2689 1.0 1.0 0.2689

0.65 0.65 0.65 0.65

.076 .076 .076 .076

2.481 2.481 2.481 2.481

0.0330 0.1226 0.1226 0.0330

o. o. o. o.

0.091 1.0 1.0 0.091

0.65 0.65 0.65 0.65

.076 .076 .076 .076

2.628 2.628 2.628 2.628

0.0 0.1298 0.1298 0.0

45 45

o. o.

0.354 0.354

0.65 0.65

.054 .054

2.680 2.680

0.0333 0.0333

90.

o.

1.0

2.0

.231 0.231 SCDi*Di*VCOS ...

= 1.7836

<Xi

f3i

1 2 3 4

45 45 135 135

90 90 90 90

5 6 7 8

0 90 90 0

40.2 40.2 40.2 40.2

Side Horiz.

9 10 11 12

0 90 90 0

span breakers

13 14

brackets

15

Chords:

Inclined braces

s = 0.8008 C De *D e =2.227 2 De = 1.1 /s C De = .227/0.542 C Me

YLD

cos ... *)

= 0542}

= 4.1 09 equi v. model = 2.0 (model scale)

C De *D e De C De C Me

COi*Di*li*cos ...

0.1070

= 9.48

= 2307}


Commentaries to Recommended Practice for Site Specific Assessment of Page 70 Mobile Jack-Up Units Rev 2, Jan 2002 APPENDIX C4.B: COMPARISON CASFS TO ASSESS IMPLICATIONS OF PRACTICE FORMULATION Computations are perfonned on a 'simplified model' with no mass. The irregular and regular wave results are computed according to the PRACTICE, Section 3 and 4. These computations are made to asses the implications of changes made concerning drag coefficients and wave kinematics fonnulations compared with previous practices. The significant wave height is chosen as judged realistic for the two water depths investigated: Water depth 30m: significant wave height

Hsrp = 10m

Water depth 90m: significant wave height

Hsrp= 14m

The period range specification is taken from PRACTICE, Section 3.5:

~(11.8Hs) < T < ~(19.5Hs) 3.5~(Hs) < Tz < 3.6.J(H s ) The current and current profile is often site dependent. The current is here set be constant over the water depth, extrapolated to sea surface. The example design for the computations is defined by: Three legs, split tube chords, Diameter chord (tubular) Rack width Diameter of braces length of braces per m. height leg spacing leg diameter

Dc W Db lb xleg Dr

= = = = = =

O.7m, O.8m, O.3m, 13.44m, 50m 10m

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 Particulars for two existing practices and the PRACTICE

Practice I: Irregular waves: d 1 cos Co *0.3 *13.44 *0.6 = 2.419 Tubular 1.0 Chord 1 2.114 *0.7 *1.0 *1.0 = 1.479 Chord 2,3 1.279 *0.7 *2.0 *1.0 = 1.790 5.688 CoJ)e

PRACTICE: cos d CD *13.44 1.0 *0.3 *0.6 = 2.419 2.057 *0.7 *1.0 * 1.0= 1.440 1.056 *0.7 *1.0 *2.0 = 1.478 5.338 z < 1.5m 4.491 z> 1.5m

kinematics according to Delta stretching

Wheeler stretching

Regular waves: Stokes' fifth

Stokes' fifth (regular)

*0.3 *13.44 *0.6 = 1.693 Tubular 0.7 Chord 1 1.486 *0.7 *1.0 *1.0 = 1.040 Chord 2,3 0.896 *0.7 *2.0 *1.0 = 1.254 CoeDe = 3.989 No shielding assumed

No shielding for waves Reduction of current by a factor 1/[1 + CoeDef(4Dl)] = 0.88

Practice II: Regular waves: Stokes' fifth Tubular 0.64 *0.3 *13.44 *0.6 = 1.548 Chord 1 1.307 *0.7 *1.0 *1.0 = 0.915 *1.0 = 1.362 Chord 2,3 0.973 *0.7 *2.0 = 3.825 CDeDe Irregular waves: Airy with constant stretching = 3.825 * 1.3

= 4.973

Page 71

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 Table C4.B.l Comparison including wave height scaling, Water depth =30 m, Hm2 =10 m. Case

Environment HIT

Page 72

Current

Base Shear Overturning Moment

mlsec 0.0

:MN 5.58

143

1.0

8.03

197

0.0

5.42

139

1.0

7.70

189

0.0

3.18

108

1.0

6.89

145

0.0

4.90

115

0.88

6.96

157

0.0

5.95

122

0.88

7.88

154

HlTz m and sec Regular waves Practice I

MNm

18.6/14.0

H =Hmax = 1.86 Hsro Regular waves Practice IT

18.6/14.0

H =Hmax =1. 86 Hsro Irregular waves Practice IT

10.0/11.0

Hs =Hsrp Regular waves PRACTICE

H =!Liet =0.86 Hmax Irregular Waves PRACTICE Hs =[1+.5exp(-d125)] *HgJL

16.5/14.0

11.84/11.0

Page 73

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 Table C4.B.2 Comparison including wave height scaling, Water depth =90 m, Hsm =14.0 M. Current

Base Shear Overturning Moment

18.6/16.5

mlsec 0.0

MN 9.82

668

26.0/16.5

0.5

12.30

819

18.6/16.5

0.0

9.41

641

26.0/16.5

0.5

11.79

785

14.0/13.0

0.0

11.22

747

14.0/13.0

0.5

13.11

859

23.14/16.5

0.0

8.90

578

23.14/16.5

0.44

11.20

709

Irregular Waves PRACTICE

14.34/13.0

0.0

9.12

573

Hs = [1+.5exp(-d125)] *Hsro

14.34/13.0

0.44

10.80

671

Case

Environment

Hff HJTz m and sec Regular waves Practice I

MNm

H = Hmax = 1.86 Hsro Regular waves Practice II

H = Hmax = 1.86 Hsro Irregular waves Practice II

Hs = Hsro Regular waves PRACTICE

H = lLIet = 0.86 Hmax

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 Comments to the results

Page 74

The results for both the 30m and 90m water depth cases in Tables C4.B.l and C4.B.2 show improved agreement between regular and irregular wave force calculations for the PRACTICE methodology as compared to Practice ll. The main differences between Practice II and the PRACTICE are that: the PRACTICE uses a reduced wave height for regular wave analysis instead of a reduced drag coefficient. the PRACTICE includes a shallow water wave height correction to be applied to the significant wave height used in irregular wave analysis. The shallow water wave height correction term is described and justified in C3.5.1.1. The effect of wave asymmetry in shallow water in Practice II is included only by a conservative kinematics model above the mean water level for an irregular wave analysis. Other practices give no consideration to shallow water effects in irregular wave analysis. The agreement between regular and irregular wave forces is better at the 90m water depth case than for the 30m water depth case. However, the correction term for shallow water cases is justified as compared to the Practice II results.

Page 75

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 APPENDIX C4.C : COMPARISON OF TEST RESULTS FOR CHORDS Split tube chords compared in the following rack ratio WID F&G 1.08 1.10 NKK 1.13 MIMC 1.18 MSC 1.24 MIMC Q

2.0 ~---------------..,

(.)

~ ~

o(.)

15

o

~

l.()

0.5

0.0

..f.-----"""I""-----..------i {)

30

60

90 ANGLE e

Figure C4.C.l : Comparison of PRACTICE formulation with model tests, ratio WID 1.08, [48]

=

:l (.)

--_.. -

2.5

Eo<

~

(.)

§

2.0

U 0

~

u

I.S

1.0

"

0";

0.0

0

30

60

90 ANGLE

e

Figure C4.C.2 : Comparison of PRACTICE formulation with model tests, ratio WID 1.10, [50]

=


2.5

c

U

f-4

~u

~0

2.0 c

U

0

~1.5

c

~

1.0 c c

c

0.5

O.O+------r-------.....-------~

o

30

60

90 ANGLEe

Figure C4.C.3 : Comparison of PRACTICE formulation with model tests, ratio WID 1.13, [49]

=

2.5 c

U

....Z ~

~0

20 c

U

0

~

1.5 c

1.0 c c

0.5

0.0

1-------"T"""-----...... ~----___4 30 60 90

o

ANGLEe

Figure C4.C.4 : Comparison of PRACTICE formulation with model tests, rack WID 1.18, [511

=

Page 76

Page 77


2.5-r---------------------, c

D

[J

1.0 c

c

0.5

O.O+--------r-------~-----~

o

30

90

60

ANGLE

e

Figure C4.C.5 : Comparison of PRACTICE formulation with model tests, rack Will = 1.24, [49]

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 C5 COMMENTARY TO CALCULATION METHODS - STRUCTURAL ENGINEERING C5.1

Page 78

INTRODUCTION The application of the procedures and techniques given in Section 5 is consistent with the guidance given in the other sections of the Recommended Practice (pRACTICE). Furthermore, it is assumed that the of the PRACTICE is familiar with the general philosophy and design/assessment approach specifically applicable to jack-ups. To provide additional guidance to the analyst less familiar with these procedures and to also ensure consistency of application by all s, this commentary has been prepared. In general, the structural modeling for the assessment of a jack-up must achieve the following objectives for both the static and (where applicable) dynamic responses: • • •

C5.2

Realistic global response (i.e. displacement, base shear, overturning moments, etc.) for the unit under the applicable environmental and functional loads. Represent the correct linear and non-linear characteristics of the leg, leg-hull connection and the leg-foundation interaction. Sufficient detail to allow for detailed assessment of the adequacy of the leg structure, structural/mechanical components of the jacking system and the foundation.

GENERAL Prior to beginning the actual modeling of the jack-up unit the analyst should ensure that all data necessary to perform the assessment is available. Refer first to the accompanying "Guideline for Site Specific Assessment of Mobile Jack-up Units" and Section 3 of the PRACTICE - Assessment Input Data for guidance on the data needed and for the rationale as to why they are important to the assessment procedure. Once these data are collected it would also benefit the analyst to review Section 4 Calculation Methods - Hydrodynamics and Wind Forces and Section 6 - Calculation Methods - Geotechnical Engineering of the PRACTICE. This will serve not only as confirmatory check to assure the completeness of the data being collected for the analysis, but will also allow the analyst to evaluate the level of analysis techniques to be used in light of the computer software available. It is important that the analyst anticipate the complete scope of the assessment in of the level of quasi-static and dynamic analyses which may be required. This will allow the analyst to optimize the structural modeling and reduce the duplication of effort. In the remaining sections of this Section of the Commentary the analyst is guided through the overall structural modeling of a jack-up for the following: (1)

Quasi-static analysis procedures

(2)

Assessment criteria procedures

For guidance on dynamic analysis techniques, refer to Section 7 of the PRACTICE.

Page 79


This Commentary has been focused on providing a general discussion of key points and their impact/importance on the final assessment results. Thus it is important that if additional detail is required, the analyst refer to appropriate technical references or the jack-up designer for further guidance. C5.3

GLOBAL RESPONSE

C5.3.1

In the analysis of jack-ups the global response is developed by appropriate combination/modeling of both the first order (linear) response and the second order (non-linear) response. The first order response of a jack-up can be derived from models of varying degrees of complexity as discussed in Section 5.6 of the PRACTICE. Please refer to Figure C5.1 for the resulting response/reactions which are derived from a first order analysis.

C5.3.2

The effects noted in Section 5.4 - 5.5 of the PRACTICE (e.g. leg inclination, P-M should be determined and combined with the forces generated by the first order analysis. These effects have been shown to be significant (in varying degrees of importance) in the assessment of jack-ups based on the specific circumstances of the jack-up and the specific site conditions being considered. The actual treatment/derivation of the response is highly dependent on the modeling complexity chosen and the computer software analysis packages available to the analyst. The guidance given in Sections 5.4 - 5.5 of the PRACTICE allows for this needed flexibility in addressing the full spectrum of approaches by allowing for implicit incorporation of these second order effects by using the appropriate non-linear modeling capabilities of the computer software or by explicit addition of a conservative incorporation of these effects by approximate/simplified hand calculations. Please refer to Figure C5.2 for further representation of the effects of P-~ and leg inclination and Figure C5.3 as to the applicable contribution of these second order effects that are required to be incorporated with the first order response. It should be noted that the PRACTICE recommends that P-~ effects are included throughout the assessment. It also recommends that the effects of initial leg inclination are included only at the end of the analysis in the structural strength checks (by means of an additional applied moment). The derivation of the alternative geometric stiffness approach to of the PRACTICE is given in Appendix C5.A.

C5.3.3

P-~

of Section 5.5.4.3

Although the "Recommended Practice" gives guidance as to simplified calculations that can be performed for P-~ and leg inclination, no specific guidance has been given for the additional moment caused by hull sagging. When a unit is installed on location the legs will normally engage the seabed with the hull ed by its own buoyancy in a hogged condition. Subsequently, with the hull slightly clear of the water, preload ballast will be taken on board thus preloading the legs to achieve their final penetration. This will normally lead to an extreme hull sagging condition. Finally the preload ballast is dumped and the hull elevated to the required airgap for the location. In this condition the hull will be sagging under self weight and variable loads.


Page 80

As explained in Section 5.7 of the PRACTICE, the leg shear and bending moments caused by hull sagging are very dependent on leg guide clearances, the design of the jacking system, operational parameters and the modeling used in the analysis. A simplified approach for a conservative quantitative assessment is to assume that 25 to 50 percent of the theoretical hull sagging moment at the lower guide is seen in practice. This may be ed for in a global model by reducing the distributed hull mass by 75 to 50 percent and applying the residual mass as point masses on the hull adjacent to the connections to the legs. This procedure is not applicable when hull stresses are required. A more thorough method is to apply self equilibrating pairs of forces/moments across the spring connections between hull and legs:

i

An alternative approach is to allow a relaxation of the horizontal seabed restraint by means of prescribed displacements. C5.4

DISCUSSION OF THE LEG-HULL CONNECTION In addition to the importance of understanding the global response of the jack-up, it is

important that the analyst has a full appreciation of the leg-hull interface. A representative leg-hull connection is shown in Figure C5.4. The basic function of the leg-hull connection is to provide for a transition of forces between the leg and hull via: 1)

the upper and lower guide which transfer bending moments by a set of horizontal forces

and 2) a jacking system and/or fixation system which transfers vertical load and bending moment via a set of vertical forces. Section 5.6.6 gives guidance on the detailed modeling requirements for each of the following components: • • • • • • •

upper and lower guides jacking pinions fixed jacking system floating jacking system fixation system shock pads jackcase and associated bracing


Page 81

The various combinations of the above components to create the leg-hull connections on typical jack-ups now in service are given in Figure C5.5. Close attention to the leghull connection should be given by the analysts to ensure a thorough understanding of the jacking system so that proper modeling is realized. The number of key variables which must be properly incorporated are: • bending, shear and torsional stiffness of the leg between the upper and lower guide • axial, bending, shear and torsional stiffness of the jackcase stiffness of the upper and lower guides • amount of clearance/tolerance of the legs within the guides (see Figure C5.6) • amount of backlash in the jacking system (see Figure C5.7) • type of leg guide arrangement (see Figure C5.8) • rack/pinion arrangement (opposed versus unopposed pinions) (see Figure C5.9) When ing for the effects of clearances (e.g. between guides and leg) in simpler models there are several approaches available: • For estimates of extreme behavior, use a 'secant stiffness' approach, so t~at the springs used provide a realistic displacement for the load/deflection levels expected. Thus the equivalent stiffness will include any slack behavior: p °typicd ~

•

o

Equivalent

1

An alternative to the above, which is less sensitive to the initial estimate of load and deflection, is to use a pair of self equilibrating applied forces to represent the slack so that the spring is initially under a compressive load Po, where Po =

koo:

p k

Note: When using the methods above any spring with true tensile loading must be manually released. •

For natural frequency calculations, providing that the gaps do not open and close, the use of the stiffness for closed gaps is appropriate.

Commentaries to Recommended Practice for Site Specific Assessment of Page 82 Mobile Jack-Up Units Rev 2, Jan 2002 C5.5 DETERMINATION OF PROPERTIES FOR EQUIVALENT MODEIllNG OF LEG AND LEG-HUlL CONNECTION C5.5.1

Equivalent leg stiffness The determination of stiffnesses for the equivalent leg model referred to in Section 5.6.4b) of the PRACTICE may be accomplished the following means: •

Hand calculations using the formulae presented in Figure 5.1 (after DNV, with corrections). Provided that there are no significant offsets between the brace work points these will be reasonably accurate for cases A (sideways K bracing), C (X bracing) and D (Z bracing); case B (normal K bracing) should be used with caution as the values of equivalent shear area and second moment of area are dependent on the number of bays being considered. If the leg scantlings change in different leg sections this can be ed for by calculating the properties for each leg section and creating the equivalent leg model accordingly.

•

The application of unit load cases to a detailed leg model in accordance with Section 5.6.4 a) of the PRACTICE. The following load cases should be considered, applied about the major and minor axes of the leg: - Axial load. This is used to determine the axial area, A, of the equivalent beam according to standard theory: FL FL ~=-=>A=E~ AE where; ~ = axial deflection of cantilever at point of load application F = applied axial end load L = length of cantilever (from rigid to point of load application) E = Young's modulus - Pure moment applied either as a moment or a couple. This is used to derive the second moment of area (I) according to standard beam theory: ML2 ML2 ML ML 0=--=>1=-- and 8=-=>1=2EI 2£0 EI E8 where; 0 = lateral end deflection of cantilever at point of load application M = applied end moment 8 = end slope of cantilever at point of load application It should be noted that the value of I resulting from the two equations may differ somewhat.

- Pure shear, P, applied at the end of the leg which may be used to derive I according to standard beam theory: PL2 PL2 8=-=>1=2EI 2E8


Page 83

Using either this value of I, or a value obtained from the pure moment case, the effective shear area, As, can then be determined from: PL3 PL 7.8PLI 8 = 3EI + AsG => As = 3EI8 _ PL3 where; G =shear modulus =El2.6 for poissons ratio of 0.3 C5.5.2

Equivalent leg-hull connection stiffness The determination of stiffnesses for the equivalent leg-hull connection model referred to in Section 5.6.6 t) of the PRACTICE may be accomplished the following means: •

Hand calculations using the formulae presented in Section 7.3.5.3 of the PRACTICE.

•

The application of unit load cases to a detailed leg model in combination with a detailed leg-hull connection model in accordance with Sections 5.6.4 a) and 5.6.6 a)-e) of the PRACTICE. Unit load cases are again applied, as described in C5.5.1. In this instance the differences between the results from the detailed leg model alone (see C5.5.1) and the detailed leg plus leg-hull connection model allow the effective stiffness of the connection to be determined: Axial load. This is used to determine the vertical leg-hull connection stiffness, Kvh from the axial end displacements of the detailed leg model, D., and the axial end displacements of the combined leg and leg-hull connection model, D.c, under the action of the same loading, F: Kvh

=

F/(D..c-D.)

Pure moment applied either as a moment or a couple. This is used to derive the rotational connection stiffness, Krh from either the end slopes, 8 and 8c , or the end deflections, Sand Sc, of the two models under the action of the same end moment, M: Krh

=

M/(8c-8)

or

Krh

=

MU(Sc-S)

Pure shear which may be used to determine the horizontal leg-hull connection stiffness, Khh, in a similar manner, ing for the rotational stiffness already derived. Normally the horizontal leg-hull connection stiffness may be assumed infinite. If the model contains nonlinearities due to the inclusion of gap elements care should be taken to ensure that suitable levels of 'unit' loading are applied such that the derived stiffness is applicable to the analysis to be undertaken.

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 C5.6 LOAD APPUCATION

Page 84

Section 5.7 of the PRACTICE indicates appropriate methods for applying the various loads to the analytical model(s). The importance of capturing the distributed nature of the self weight and distributed loadings is emphasized.

C5.7

EVALUATION OF FORCES This Commentary is directly applicable for the structural modeling of jack-ups for either quasi-static or dynamic analysis. Key points which impact the final conclusions drawn from the assessments of jack-ups have been emphasized to complement the guidance given in the PRACTICE. A successful analysis will conclude with a set of forces which can then be used in the final evaluation of the adequacy of the unit the specific site, as contained in Section 8.0 - Assessment Criteria. The specific areas of review include: • • •

•

Structural Strength Check (see Section 8.1 of the PRACTICE). Overturning Stability (see Section 8.2 of the PRACTICE). Foundation Assessment (see Section 8.3 of the PRACTICE): Bearing Capacity Sliding Resistance. Other Responses of Interest (see Sections 8.4, 8.5 and 8.6 of the PRACTICE respectively): Horizontal Deflection Holding Capacity of the Jacking System Hull Strength (if required).

Care should be taken to ensure that the appropriate load factor is reflected in the determination of the load set applied during the analysis. This allows for direct use of the resulting loads in the assessment formulation.

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 PORT BOW

1

STARBOARD

Wmd induced

shear---M-

Fnvironmcntal--L---I~ ..I

approach direction

iL~:"'.-+--'----l

Vertical Reaction HORIZONTALREACnONS

- Wmd load component - Wave load component

VERTICAL REACTIONS

- Wind load component - Wave load component - SclfWeight component

Figure CS.l : Responses/reactions from first order analyses DECK SWAY

tp NON VERTICAL LEGS

r

OT - Horizontal offset 01

L

- Hull leg clearances

O2 - Hed of platfOlDl

, 0;-

tp

Figure CS.2 : p-~ and leg inclination effects

Page 85


Wmd induced shear

---+/

20d Order axial torce from P·Dclta effect (Delta P)

1

2nd Order moment from p. Delta effect (Delta M)

t---=,"----r--

Lower guide position

Leg length from lower guide to base (llg)

Wave induced shear

Lcver(Lcv) --'"--.......--..1...--'WmdForce Reaction + Wave Force Reaction + Deck Sagging

Base ofleg

lOTALBASE SHEAR REAC1ION Wmd Force Reaction

+ Wave Force Reaction + DcltaP

TOTAL BASE AXIAL FORCE

Figure C5.3 : Contribution of Second Order Effects to First Order Responses

Jacking system inducing:

e Fixation System e FIXed or Floating Jacking System with Shock Pads e Jacking Pinions (Opposed or Unopposed) eJackcasc

"

Lower guide

M

Fv

Figure C5.4 : Representative leg-hull coimection

Page 86

Page 87


l

LEG· HULL CONNECTION

I

I

I

l

I

I

I

Opposed pinacs

I

I Fixed

jecki%Jg system

F & G L780 II L'l8OV _G.... i.~kG;"'1

I

I

Fix alien system

•

I

I

1 Fixed

jaclcing

jacking

system

system

Floati:lg jacking system

(MSC C1'I6) CJ46) (WSCCJ3l)

I Opposed pmions

I

• I

I I Unopposed pinons j I

J

jacking

Floating jacking

jacking

system

system

system

Fixed

/lIodec3CD:

~tSicaa(IoISC

ElrIoaO

I

I

I

I

I

I

I

Flolling

NoIliIl3

I pm..,. I

U""!'POsed

I No fixation system

~o!~~CJ!Il) v..t1lota

VioIG......

Fixed

-.. .1l6C

.supcr:m -GaiI&

Guslo

MSCCJ/i2

1 Flolling jacking system

examplesd Wlilsinthi. category

Figure C5.5 : Leg-hull connection component combinations

Guide tolcrancc.

Figure C5.6 : Guide clearances backlas

Effect of backlash

NB:

Additional backlash may arise due to slack in gear train, clearances between floating elevating system and shockpads etc. Figure C5.7 : Jacking system backlash

I


Guiding types

Tangential

Radial

Combined

~~--------------------~v~----------------------J/ Guiding

Figure C5.8 : Types of leg guide arrangement

Rack types

Page 88

single sided

opposed racks

Figure C5.9 : Unopposed and opposed pinion.arrangements

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 GLOSSARY OF FOR SECTION C5

A As E F G I

Khb Krb Kvh

= = = = = =

p 0

= = = = = =

oe

=

I:!

=

I:!e

=

8 8e

= =

L M

Page 89

axial area of equivalent beam. effective shear area of equivalent beam. Young's modulus. applied axial end load. shear modulus =El2.6 for poissons ratio of 0.3. second moment of area of equivalent beam. horizontal leg-hull connection stiffness. rotational leg-hull connection stiffness. vertical leg-hull connection stiffness. length of cantilever (from rigid to point of load application). applied end moment. applied end shear. lateral end deflection of cantilever at point of load application for detailed leg model alone. lateral end deflection of cantilever at point of load application for detailed leg plus leg-hull connection model. axial deflection of cantilever at point of load application for detailed leg model alone. axial deflection of cantilever at point of load application for detailed leg plus leghull connection model. end slope of cantilever at point of load application for detailed leg model alone. end slope of cantilever at point of load application for detailed leg plus leg-hull connection model.

Commentaries to Recommended Practice for Site Specific Assessment of Page 90 Mobile Jack-Up Units Rev 2, Jan 2002 APPENDIX CS.A - DERIVATION OF ALTERNATIVE GEOMETRIC STIFFNESS FORMULATION FOR P-A EFFECTS C5.A.l SUMMARY The method described below allows a simple procedure for incorporating P-A effects in a jack-up structural analysis. The advantage of this simple procedure is the ability to include such effects without the necessity to adopt the iterative procedures required by other methods. This method is accurate in determining the global response parameters, including hull displacement and base overturning moment. It is also accurate in determining the leg moment below the lower guide (usually the most critical part of the leg). In its simplest form the procedure will conservatively predict the shear in the legs (by roughly 10%). However leg shear is rarely a controlling factor in structural assessments; therefore this difference is insignificant. C5.A.2 DESCRIPTION OF THE METHOD It is assumed that a structural computer model of a jack-up is used to determine the

effects of applied loads. Typically, a 'static' wave load is applied to a structural model, and resulting deflections, forces and moments are determined. Note, however, that the method can be similarly applied to dynamic analysis. (The method may not be permitted by some software packages which 'prohibit' the use of a negative spring stiffness). The incorporation of P-A effects in the structural analysis is accomplished by including a correction term in the global stiffness matrix of the structure. When an analysis is performed with the correction term included, the resulting deflections, etc. will include P-A effects. Note that since the global stiffness matrix is modified before the analysis, no subsequent changes to the matrix are required (i.e. no iterations are required in the solution). The correction term to the global stiffness matrix is determined by a simple hand calculation: The correction term is: where; Pg

-PgIL

=

Effective hull gravity load. This includes hull weight and weight of the legs above the hull. L = The distance from the spudcan point of rotation to the hull center of gravity.

This single (negative) value is then incorporated into the global stiffness matrix of the jack-up structural model. This can be accomplished in various ways depending on the software in use. Typically, an orthogonal pair of horizontal translational earthed spring elements can be attached to a node representing the hull center of gravity, and the negative value is entered for each of the spring constants. Some software packages allow direct matrix manipulation. The effect of the negative stiffness is to produce an additional overturning load at the hull. The overturning moment produced by this lateral load about the base is equal to the overturning moment caused by the vertical load (of hull and legs above the hull) times the deflection of the hull. Thus, the effect of the translation of the vertical load is incorporated as a lateral force couple.

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 C5.A.3 BASIS FOR THE METHOD

Page 91

The P-Ll effect is a consideration of the displacement of the structure under the applied loads. In its most general form, the solution considers the displacements of each element of the structure under loading. This is typically called a 'large displacement' solution. In this general procedure, the deflections of the structure are used to reform the stiffness matrix, which is then used to recalculate the displacements. While this is analytically correct, there is a requirement to resolve the stiffness matrix several times for each loading condition. If the overall structural displacements are not very large, approximate solutions may be

used. Typically, approximate solutions are valid if tane = e, where e is the rotation of the structure about its base. These approximate 'solutions are known as 'geometric stiffness' solutions. The classical column moment magnification or 'Euler amplification' term is an example. The simple method presented here is another example. A comparison of these two methods is given in Section C5.AA and the derivation is presented in Section C5.A.5. The P-Ll effect for jack-up structures is manifested as a change in lateral stiffness of the individual legs, given a change in the axial load in each leg. For jack-ups the change in axial load in each leg is caused by the application of the gravity loading and environmental loading. As shown in Section C5.A.5, the net effect on the P-Ll of the axial load changes in each leg due to the environmental loading will cancel out. Thus, for overall structural response, only the gravity load need be considered in the calculation of P-Ll effects. The reduced stiffness will then affect the response to environmental loadings. C5.AA VERIFICATION AGAINST 'EXACT' SOLUTION

Verification of this simple procedure was made against an 'exact' solution. In this case, the 'exact' solution was performed using analysis software which s for large displacements. In this procedure, the displaced configuration of the structure is used to update the stiffness matrix, and iteration is used to converge on a given solution. Verification was performed using a jack-up structural model as shown in Figure C5.A.1. The leg chord, horizontal and diagonal are modeled as individual elements. The hull (in this case) is assumed to act as a rigid body. The hull to leg connection included leg clamping devices. These were modeled along with the leg guides. For the purpose of this verification the detailing of the hull and leglhull connection is not important. The spudcans were modeled as 'pinned'. Loading of the model was accomplished as shown on Figure C5.A.2. Loadings due to wave and wind (and dynamic inertial) were considered separately to the behavior under the two separate types of loading. The loading direction was towards the bow in both cases. For each case, a vertical load was applied at the hull center of gravity. It is interesting to note that the vertical load is necessary for solution using 'exact' large displacement methods, but is not needed to obtain a solution using the simple method.


Page 92

A summary of the comparison results is given on Tables C5.A.l (wave load) and C5.A.2 (wind load). Verification with these two load cases was done separately, since the loading occurs on different parts of the structure. The level of loading is arbitrary. Values assumed here are greater than used in the site assessment of this particular jackup. Discussion of the individual response parameters from Tables C5.A.l and C5.A.2 is given below. C5.A.4.1 Global Response Parameters The fundamental response quantities of deck displacement and overturning moment agree to within 1%. The base shear for the simple method is not correct since it includes the additional (fictitious) lateral force applied to the hull. The difference between the total applied force and the base shear is the additional lateral force applied at the hull. In theory the moment due to the vertical load (P-~ moment) should be replaced by a lateral force couple, i.e. lateral loads at the hull and base. Reduction of the base shear (in global axes) by this additional lateral force at the hull will equate the global base shear with the applied load.

C5.AA.2 Windward and Leeward leg parameters The values for individual leg axial load and moment at the lower guide agree to within 1%. These quantities are the most critical parameters for structural assessments. The distribution of global base shear among the individual legs is not as accurately matched by the simple method. For each leg, the lateral stiffness is decreased by increasing axial load. Thus, the distribution of global base shear will depend on the axial load present in each leg. The simple method, since it lumps the effects of all legs into one correction term, cannot accurately predict the shear re-distribution among the legs. This lack of re-distribution of global base shear loading is not generally important to a structural assessment. The amount will depend on the level and type of loading (wave or wind). For the two cases given, 1% and 5% of the total base shear load (in global axes) is shifted from the leeward leg to the windward legs. When the leg base shears are not corrected, the simple method conservatively overpredicts the shear in the legs. Since shear force is not as critical as the leg bending moment this conservatism is not very restricti ve. If a correction is desired, the added lateral load at the hull can be subtracted in equal

fractions from the leg spudcan reactions (in global axes). Note that, for the case of the windward leg, this will slightly under-predict the 'correct' global shear reaction.

Page 93 Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 TABLE C5.A.l - VERIFICATION OF SIMPLE PROCEDURE FOR P-Ll EFFECT WITH EXACT SOLUTION - WAVE LOADING CASE Exact Sim~le No P-Ll Method Solution Global res~onse ~arameters Hull displacement (inches) 24.7 21.6 24.5 3 Base OTM (Kip-ft x 10 ) 227. 253. 251. Base shear (kips) 711. 780. 711. (Added lateral load at hull, kips) (69.)

Windward leg ~arameters Axial force (kips) Shear at spudcan (kips) (Corrected by 69/3 = 23 kips) Moment at lower guide (Kip-ft x 103) Leeward leg ~arameters Axial force (kips) Shear at spudcan (kips) (Corrected by 69/3 = 23 kips) Moment at lower guide (Kip-ft x 103) Shear transferred from leeward leg to windward legs due to P-Ll (kips)

3638. 250. 48.

5477. 212. 57.

3524. 272. (249.) 56.

3534. 254.

5706. 235. (212.) 65.

5685. 204.

o.

56.

65. 8.

TABLE C5.A.2 - VERIFICATION OF SIMPLE PROCEDURE FOR P-L1 EFFECT WITH EXACT SOLUTION - WIND LOADING CASE Exact Sim~le No P-Ll method Solution Global res~onse ~arameters Hull displacement (inches) 44.9 51.4 51.0 Base OTM (Kip-ft x 103) 541. 490. 545. Base shear (kips) 1055. 1055. 1198. (Added lateral load at hull, kips) (143.) Windward leg ~arameters Axial force (kips) Shear at spudcan (kips) (Corrected by 143/3 = 48 kips) Moment at lower guide (Kip-ft x 103) Leeward leg ~arameters Axial force (kips) Shear at spudcan (kips) (Corrected by 143/3 = 48 kips) Moment at lower guide (Kip-ft x 103) Shear transferred from leeward leg to windward legs due to P-Ll (kips)

2538. 352. 124.

7803. 352. 124.

2300. 399. (351.) 141.

2318. 375.

8279. 400. (352.) 141.

8242. 305.

o.

141.

140. 47.


Page 94

z x

(BowLeg)

Figure C5.A.l - Analysis model

I Wind = 1055 kips ~

-j2m "".

-$-------

L=4592' Wave. =711 kips

:J,;. (BowLeg)

Figure C5.A.2 - Load application

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 CS.A.S DERIVATION OF THE SIMPLIFIED CORRECTION TERM

Page 95

Centroid of area under moment diagram

Z-L 1t

Beam Deflection

Asswncd sinc CUlVC

Moment diagram (due to secondary bending only)

Ref.: Salmon and Johnson, 'Steel Structures', p 620.

Yo Yl

= =

Deflection without axial load, P Additional lateral deflection due to axial load, P

To calculate Yh take moment of MlEI diagram between and midspan

Yl

= P(Y~;Yl) {~ }{~}

L

I I

-J.-._ _ _ _

1-._ _

Rearranging:

Yl

=

Centroid of area unde~ moment diagram Area under moment diagram

4pe

(Yo + Yl) n 2EI

using:

n 2EI

(with k =2)

PE

=

Yl

=

P (Yo + Yl)PE

=

{ PIPE } Yo I-PIPE

Yl

(kL)2

Total lateral deflection: Ymax

Ymax

=

Yo + Yl

=

PIPE } Yo + Yo { 1- PIPE

=

YO{l-:,pJ I

I

I

'Euler amplification' term


Page 96

Detennine effect on stiffness

H

Define Ko =

Lateral stiffness without axial load, P

Yo 3EI L3 H

= Define KI =

Lateral stiffness with axial load, P

Ymax

~{l-~} Yo P

=

E

K+-P[:~]}

=

= Ko _p{3EI}{~} L3 n2EI

{~*P} n L

= Ko-

2

Conclusion: Effective lateral stiffness reduced by P

=

axial load in one leg

Note: This is based on assuming a sine curve for deflection. Repeat calculations assuming a linear deflection (rather than a sine curve):

YI =

P( Y~; Y1) {~}{ 2~ }

I

I

1 . . -_ _

I

L -_ _..L..-_ _ _ _

Rearranging:

Centroid of area under moment diagram Area under moment diagram

pe

YI = (Yo + YI) 3EI

{PL'/3EI }

YI = Yo 1 _ PL2 / 3EI Ymax = Yo + YI Ymax =

Yo { 1 I

PL~ / 3EI} I

1 . . -_ _ _ __

Amplification for linear assumption

Detennine effect on stiffness H Define Ko = Lateral stiffness without axial load, P

Yo

=

3EI


Define Kl =

H

Page 97

Lateral stiffness with axial load, P

Ymax

P = Ko-L

Conclusion: Based on linear deflection assumption, lateral stiffness is reduced by -PIL term. This is the usual approximation of geometric stiffness. Effect on total jack-up stiffness: KE =

Kel + Kez + Ke3 sum of individual leg stiffnesses (neglects hull rotation)

For each leg: P = P gravity + P environment KE

=

=

12 1 12 1 (Pgl + Pel)] + [koz - - 2 - (PgZ + P eZ )] + ... n L n L 12 1 12 1 (kol + koz + ko3) - - 2 - (Pal + PaZ + Pa3) - - 2 - (Pel + P eZ + P e3 ) nL <> <> <> nL [kol -

-2 -

Assume net vertical environmental load (Pel + P eZ + P e3) = 0 KE

= (LKoD - -n122 -PLG

,

where Pa is total gravity load only

If linear deflection assumption is made: PG KE = (LKoD-L

Commentaries to Recommended Practice for Site Specific Assessment of Rev 2, Jan 2002 Mobile Jack-Up Units C6 COMMENTARY TO CALCULATION METHODS . ENGINEERING C6.1

Page 98 GEOTECHNICAL

INTRODUCTION This Commentary is compiled to Section 6 of the PRACTICE and should only be used as a reference document in conjunction with the text of the PRACTICE. A Glossary of used for the Geotechnical Engineering Analysis is included at the end of this Commentary.

C6.2

PREDICTION OF FOOTING PENETRATION DURING PRELOADING

C6.2.1

Analysis Method for Leg Penetration Prediction The equations in Sections 6.2.2 and 6.2.3 may be applied for estimating the penetration of the spudcan during preloading. In this case the backflow and contribution of the spudcan buoyancy (due to the weight of soil replaced by the spudcan) will have a direct effect on the penetration depth. Hence the effect of backflow and spudcan buoyancy should be included in the calculations. Predictions of spudcan penetration are based on a direct application of conventional bearing capacity formulae for shallow circular flat foundations. However, the analysis methods for shallow foundations and spudcan penetration predictions are fundamentally different as illustrated in Figure C6.1. Conventional foundation analyses for a circular footing at depth D firstly comprise the determination of the ultimate bearing capacity, F v, at this depth and subsequently computing the vertical displacement of this footing, zu, which is required to mobilize this resistance. Thus the analyses consist of a strength analysis followed by a deformation analysis. Q..

'mm~ ___ ~@l ~I;r Displacement, z

+ Conventional analyse:s for shallow foundation i.ns1alJ.e:d at dc:pth D: 1. Compute: ultimate load Qv 2. Dc:tc:nninc: displacemc:nt Xu to re:ach Qv

Q..

~I----L-~--1\:::. ·:··1 Spudcan penc:tration D

~ Conventional anaIyse:s for spudcan at pene:tration D. 1. Compute: dtimatc: load Qv

Figure C6.1 : Comparison of bearing capacity analytical procedures for shallow foundations and jack-ups


Page 99

In a spudcan penetration analysis the deformation at ultimate resistance (i.e. the spudcan penetration D) is taken as an input and from this the associated soil resistance is directly computed. The conventional analysis consist of only one step using the same bearing capacity criteria as for the former shallow foundation analyses. The incompatibility between these approaches is generally ed for by the application of empirical corrections to classical bearing capacity formulations. These empirical corrections are generally introduced by the selection of appropriate soil strength parameters. It is also noted that these corrections for other significant differences between conventional shallow foundations and spudcans, such as: 1. Spudcans are relatively smooth (steel) and (semi) conical whereas the other footings are usually rough (concrete) and flat. 2. Spudcan foundations stress soil which, during installation, has been subjected to large strains, whereas conventional foundations are placed on soil which has not failed. Also for conventional foundations the soil may have improved due to "pre-design" foundation loads causing increased strength by consolidation. 3. Spudcans are an order of magnitude larger than most conventional foundations. For the conservative evaluation of the hole backflow the PRACTICE recommends that the stability factors of Meyerhoff [1] are used. However, for normally consolidated clay profiles the Britto and Kusakabe [2] curve may be more appropriate (see Figure C6.2). It should be noted that the expression in Section 6.2.1 is based on static hole stability. In reality, during penetration of the spudcan the soil will probably flow along the spudcan upwards on to the top of the spudcan. Hence, the hole stability derived from the expression provided in Section 6.2.1 may be too optimistic. lhI<:Immod. _heel' sImlgtlI

T T'

1)

t..ll. ....... }

~

~ 2

1t

+

1) •••••••••••••..

Constant strength Normal consolidation

strength profile

profile

r--'--~J=:::::j:===t===:J=:::::t-

Z 8

~

~ 7

.~

Britto and Kusakabc [2J (less conservative approach, useful for nounally consolidated clayprofilc.)

'---+--+-Mcycmof. [IJ . . th (conservative approach as given m c PRACTICE main tcxt)

1--~........,,4--+--+--+---I

:s

~6~~-~-+-~--+-~ UlISIobl. : D

Ncu 7"

40~-+2-~4~-+6-~-~~1·2 Depth Width

D

'B ----..

Figure C6.2: Stability factors for cylindrical excavations in clay

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 C6.2.2 Penetration Analysis For Clays

Page 100

For the selection of undrained shear strength, cu, it is recommended that the mean value to a depth of half a spudcan diameter beneath the level where the maximum spudcan diameter is in with the soil is used (Young [3]). This method is applicable if the shear strength values up to one diameter below the spudcan do not vary more than 50 percent from the average value (after Skempton [4]). If significant Cu variations occur, then the bearing capacity should be computed using a method for layered soil conditions. Analytical solutions are available for computing the bearing capacity of footings on clay with increasing shear strength with depth (Davis and Booker, [5]); Salencon and Matar, [6]; Houlsby and Wroth, [7]). These methods give bearing capacities less than those reSUlting from the use of Skempton's [4] and Vesic [8] relationships. Empirical correction factors for the Skempton [4] and the Davis and Booker [5] methods are recommended by Endley et al [9]. However these empirical methods take no of the spudcan equivalent cone angle, the spudcan roughness factor or the depth of spudcan embedment of the uppermost part of the bearing area below the soil surface. An alternative bearing capacity factor Ne ' has been developed which takes these factors, and that of increased shear strength with depth, into . In this case the ultimate bearing capacity of a spudcan in clay can be expressed by: Fv = {cuoNe' + Po'} A The maximum preload, VLo , is equal to the ultimate vertical bearing capacity, Fv, taking into the effect of backflow, Fo'A, and the effective weight of the soil replaced by the spudcan, y'V i.e.: VLo = Fv - FaA + y'V noting that the -FaA + y'V should always be considered together. Table C6 provides values for Ne' which is an alternative dimensionless bearing capacity factor dependent on: (a) The equivalent cone angle of the spudcan~. For spudcans with multiple cone angles, the equivalent cone has a base equal to the base of the largest component and a volume equal to the total volume of the components, (b) The roughness factor for the spudcan surface ex, (c) The depth of embedment of the uppermost part of the bearing area below the soil surface D, (d) The rate of increase of the undrained shear strength with depth below the spudcan "p" (see Figure C6.3). The alternative non-dimensional bearing capacity factors "Ne '" shown in Tables C6.1 to C6.6 have been derived using a computer program which is able to calculate lower bound (conservative) collapse loads for both axisymmetric and plane strain foundations. Vertical bearing capacity has been computed for all combinations of the following parameters:

Page 101


UNDRAINED STRENG'IH PROFILE i

i

i+-R i

,i ,

Soil:

1\>= 0; l' =0; Tresca Yield Criterion

Footina Base Level

............. ___ .................. __ .. c-...•............ _............................ .

Cuo = Com+ ~

Undrained Footing J Soil Adhesion = au ; Roughness Factor ct = ao/Cu

Figure C6.3: Conical footing bearing capacity - problem definition and notation Cone angle, Footing embedment depth, Roughness factor,

~

=

30°,60°,90°, 120°, 150°, 180°.

DIR

=

0.0, 0.2, 0.5, 1.0, 2.0, 5.0.

ex

=

0.0,0.2, 0.4, 0.6, 0.8, 1.0

(where ex =0.0 for fully smooth and 1.0 for fully rough)

Rate of increase of clay shear strength with depth, p2R1cum =0.0, 1.0, 2.0, 3.0,4.0, 5.0. The effects of the depth of embedment and the rate of increase of shear strength with depth are expressed by use of the dimensionless factors D/2R and p2R1cum , where Cum is the undrained strength at the soil surface (equal to Cua - Dp assuming a linear variation of strength with depth) and R is the radius of the spudcan. Values of the dimensionless factor Nc' are given in Tables C6.1 to C6.6 for the range: ~ = 30° to 180° ex = 0.0 to 1.0 D/2R = 0.0 to 2.5 ; p2R1cum = 0.0 to 5.0 The factors are calculated assuming a linear variation of undrained strength with depth. The best fit to the profile of undrained strength between the depth of the lowermost point of the maximum bearing area and one radius below that point should be used in deriving the value of p. In the model a field of slip lines is formed between the footing and the horizontal free soil surface. This type of "general shear" failure mechanism is appropriate for the shallow footing penetrations being considered. At larger embedments, however, the slip lines do not propagate to the surface as the "local shear" failure mechanism becomes


Page 102

critical (i.e. it gives a lower bearing capacity). A transition from general to local shear failure may be predicted at footing embedments between 6R and SR. The greatest embedment considered in the tables is 5R, so the general shear bearing capacity factors are still appropriate for this depth. Therefore Table C6.6 should not be extrapolated to higher values of D12R, since the bearing capacity factor does not increase significantly with further embedment. Values for DI2R = 2.5 should be used for large embedments. Although a footing may be fully rough (a = 1.0), full adhesion is only mobilized at the cone surface when ~ ~ 900 • For cone angles greater than 90 0 , only partial friction is mobilized. In general, if the roughness factor is a, full friction is mobilized only when ~ < 1t - sin-lao This relationship may be derived using Mohr's Circle. For the selection of appropriate roughness factors the results of mathematical models (Noble Denton [lOaD suggest that the presence of a sharp secondary cone, forming the tip of spudcan, tends to cause "rough" behavior. Rough blunt spudcans behave in a similar manner to flat circular plates but more pointed spudcans behave as neither fully rough nor fully smooth and have intermediate roughness factors of between a =0.3 to 0.5. In the absence of detailed information, and as an approximation, a value of a =0.4 may be appropriate for typical "double cone" spudcan shapes. For further information regarding this alternative method for bearing capacity analysis in clay reference should be made to Houlsby [11, 12, 13], Koumoto [14] and Houlsby [15]. It is noted that footing penetration predictions are generally made using shear strength data from simple laboratory tests such as torvane, pocket penetrometer, motorvane and/or unconfined compression tests. Strength values from such tests are generally lower than those of higher quality in-situ or laboratory tests, particularly if samples for the latter tests are obtained from push/piston sampling rather than the percussion sampling method. It is likely that the former testing methods may yield low bearing capacity values for

very sensitive clays and/or strongly strain softening clays. Engineering judgment is required in such cases to assess the likely footing penetration. It is noted that in some clays, following remolding during spudcan penetration, the

shear strength may increase over a short time period. For certain clays the strength may be regained in a matter of hours. In such cases, a crust of stronger material may develop underneath the spudcan and this crust may then be underlain by weaker clay. In this condition a potential punch-through situation could occur during subsequent reloading. Several actual failures have been attributed to this type of soil behavior (Young et al., [3D. For soils where this type of strength hardening (thixotropy) is possible caution should be exercised as interruptions during the preloading operations could lead to severe consequences. For the conservative assessment of the effects of cyclic loading on clay foundations the following vertical bearing capacity reduction factors may be applied to the capacities calculated from static soil properties (Andersen [16D: Leeward leg vertical bearing capacity reduction factor

=

1.0

Windward leg vertical bearing capacity reduction factor = O.S

TABLE C6.1 30 degrees cones D Cuo p2R p2R

60 degrees cones D p2R p2R Guo

---

-

---

---

Cum

R

Cum

Cuo

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.00 1.00 1.00 1.00 1.00

0.00 0.00 0.00 0.00 0.00 0.00

4.61 4.80 5.05 5.41 5.98 7.12

5.51 5.70 5.94 6.29 6.85 7.98

6.38 6.56 6.80 7.14 7.70 8.81

7.22 7.40 7.63 7.79 8.51 9.61

8.03 8.20 8.43 8.76 9.29 10.38

8.78 8.95 9.18 9.50 10.03 11.10

0.0 0.0 0.0 0.0 0.0 0.0 1.0 1.0 1.0 1.0 1.0 1.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.10 1.25 1.50 2.00 3.50

1.00 0.91 0.80 0.67 0.50 0.29

7.53 7.45 7.38 7.28 7.20 7.34

9.02 8.89 8.73 8.55 8.38 8.39

~g

TABLE C6.2 Fv/(Acuo) factors Roughness

10.46 10.27 10.05 9.78 9.51 9.39

11.84 11.61 11.32 10.98 10.61 10.37

13.19 12.90 12.55 12.14 11.68 11.30

14.46 14.13 13.72 13.24 12.68 12.19

---

-

Cum 0.0 0.0 0.0 0.0 0.0 0.0 1.0 1.0 1.0 1.0 1.0 1.0

\)"~ :::::.~

FvliAcuo) factors Roughness

(\)

(\)

R

---

---

Cum

Guo

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.00 1.00 1.00 1.00 1.00

0.00 0.00 0.00 0.00 0.00 0.00

4.45 4.68 4.98 5.41 6.07 7.33

4.96 5.19 5.50 5.90 6.55 7.81

5.45 5.67 5.96 6.37 7.01 8.25

5.90 6.12 6.40 6.81 7.43 8.66

6.32 6.53 6.81 7.21 7.84 9.05

6.69 6.90 7.18 7.57 8.18 9.39

~~

8.87 8.89 8.91 8.94 9.03 9.39

(\)

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.10 1.25 1.50 2.00 3.50

1.00 0.91 0.80 0.67 0.50 0.29

5.81 5.92 6.04 6.20 6.43 6.97

6.51 6.59 6.70 6.84 7.05 7.55

7.15 7.23 7.30 7.41 7.58 8.08

7.77 7.83 7.88 7.96 8.12 8.54

8.34 8.38 8.42 8.47 8.59 8.98

2.0 2.0 2.0 2.0 2.0 2.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.20 1.50 2.00 3.00 6.00

2.00 1.67 1.33 1.00 0.67 0.33

10.45 9.65 8.89 8.20 7.60 7.37

12.51 11.53 10.58 9.67 8.87 8.44

14.51 13.33 12.19 11.09 10.10 9.48

16.44 15.08 13.76 12.47 11.30 10.18

18.31 16.79 15.27 13.80 12.45 11.44

20.10 18.40 16.72 15.08 13.54 12.35

2.0 2.0 2.0 2.0 2.0 2.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.20 1.50 2.00 3.00 6.00

2.00 1.67 1.33 1.00 0.67 0.33

7.14 6.92 6.74 6.59 6.55 6.99

8.02 7.73 7.50 7.29 7.20 7.49

8.84 8.49 8.18 7.91 7.76 8.03

9.60 9.21 8.84 8.53 8.33 8.50

10.32 9.88 9.46 9.09 8.83 8.95

10.99 10.50 10.03 9.61 9.30 9.37

3.0 3.0 3.0 3.0 3.0 3.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.30 1.75 2.50 4.00 8.50

3.00 2.31 1.71 1.20 0.75 0.35

13.36 11.51 9.98 8.74 7.79 7.40

15.98 13.76 11.89 10.33 9.11 8.46

18.56 15.92 13.72 11.87 10.39 9.51

21.03 18.02 15.49 13.36 11.64 10.52

23.42 20.05 17.21 14.80 12.83 11.49

25.71 22.00 18.85 16.18 13.98 12.42

3.0 3.0 3.0 3.0 3.0 3.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.30 1.75 2.50 4.00 8.50

3.00 2.31 1.71 1.20 0.75 0.35

8.49 7.77 7.24 6.82 6.60 6.99

9.54 8.70 8.03 7.56 7.27 7.47

10.50 9.56 8.80 8.21 7.85 8.01

11.42 10.38 9.53 8.86 8.44 8.49

12.29 11.14 10.20 9.45 8.94 8.94

13.10 11.85 10.82 10.00 9.43 9.36

4.0 4.0 4.0 4.0 4.0 4.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.40 2.00 3.00 5.00 11.00

4.00 2.86 2.00 1.33 0.80 0.36

16.27 13.10 10.83 9.11 7.91 7.40

19.46 15.68 12.87 10.77 9.26 8.47

22.57 18.14 14.86 12.38 10.57 9.52

25.62 20.54 16.79 13.96 11.84 10.54

28.52 22.86 18.66 15.47 13.06 11.52

31.32 25.08 20.44 16.91 14.23 12.46

4.0 4.0 4.0 4.0 4.0 4.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.40 2.00 3.00 5.00 11.00

4.00 2.86 2.00 1.33 0.80 0.36

9.83 8.51 7.61 6.97 6.64 6.86

11.02 9.52 8.44 7.74 7.31 7.45

12.16 10.48 9.26 8.41 7.90 8.00

13.24 11.38 10.04 9.08 8.49 8.48

14.26 12.22 10.75 9.69 9.01 8.94

15.18 13.00 11.41 10.26 9.51 9.35

5.0 5.0 5.0 5.0 5.0 5.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.50 2.25 3.50 6.00 13.50

5.00 3.33 2.22 1.43 0.83 0.37

19.18 14.48 11.46 9.37 7.98 7.40

22.94 17.33 13.64 11.08 9.35 8.47

26.61 20.06 15.75 12.77 10.68 9.53

30.20 22.72 17.80 14.38 11.97 10.56

33.63 25.29 19.78 15.94 13.21 11.55

36.92 27.75 21.68 17.43 14.40 12.48

5.0 5.0 5.0 5.0 5.0 5.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.50 2.25 3.50 6.00 13.50

5.00 3.33 2.22 1.43 0.83 0.37

11.17 9.14 7.90 7.08 6.66 6.85

12.52 10.23 8.78 7.84 7.32 7.44

13.83 11.26 9.63 8.55 7.94 7.99

15.06 12.25 10.43 9.24 8.53 8.47

16.20 13.15 11.17 9.86 9.06 8.93

17.26 13.99 11.87 10.45 9.56 9.35

~~ (") t:l ~ ~.

C ~~

-. ~

(\)

(")

C

~ ~

;:::

f} t:l...

~

......

~.

'C..,"> V:l

~

~ (\) (")

'S;

~(") ~

(\)

-0:::

~

~t'-.) ~ ~

~~ ;::: (\) ~ t'-.);:::

C ......

~~

~

'"-

~

TABLE C6.3 90 degrees cones D Cuo p2R p2R

TABLE C6.4 Fv/(Acuol factors Roughness

120 degrees cones D Cuo p2R p2R

---

-

---

---

Cum

R

Cum

Cuo

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.00 1.00 1.00 1.00 1.00

0.00 0.00 0.00 0.00 0.00 0.00

4.64 4.90 5.22 5.68 6.37 7.65

5.02 5.28 5.59 6.03 6.71 8.03

5.36 5.61 5.93 6.36 7.05 8.32

5.67 5.91 6.23 6.66 7.32 8.60

5.95 6.18 6.49 6.92 7.58 8.86

6.17 6.41 6.71 7.14 7.79 9.05

1.0 1.0 1.0 1.0 1.0 1.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.10 1.25 1.50 2.00 3.50

1.00 0.91 0.80 0.67 0.50 0.29

5.57 5.74 5.94 6.16 6.50 7.25

6.05 6.21 6.38 6.61 6.93 7.57

6.47 6.62 6.79 6.99 7.30 7.94

6.87 7.00 7.16 7.36 7.64 8.25

7.22 7.36 7.50 7.68 7.95 8.53

2.0 2.0 2.0 2.0 2.0 2.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.20 1.50 2.00 3.00 6.00

2.00 1.67 1.33 1.00 0.67 0.33

6.46 6.41 6.41 6.40 6.54 7.16

7.03 6.94 6.88 6.88 6.99 7.49

7.54 7.43 7.35 7.29 7.37 7.86

8.01 7.88 7.76 7.69 7.73 8.18

3.0 3.0 3.0 3.0 3.0 3.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.30 1.75 2.50 4.00 8.50

3.00 2.31 1.71 1.20 0.75 0.35

7.36 6.99 6.70 6.54 6.56 7.12

8.00 7.57 7.24 7.04 7.02 7.46

8.59 8.10 7.73 7.47 7.41 7.83

9.14 8.60 8.17 7.88 7.78 8.15

~g

Fv/IAcuo ) factors Roughness

~~

......:.~

---

-

---

---

Cum

R

Cum

Cuo

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.00 1.00 1.00 1.00 1.00

0.00 0.00 0.00 0.00 0.00 0.00

4.96 5.23 5.57 6.04 6.74 8.07

5.25 5.52 5.85 6.31 7.01 8.32

5.51 5.77 6.10 6.55 7.24 8.55

5.73 5.99 6.31 6.76 7.44 8.75

5.92 6.17 6.49 6.93 7.61 8.90

6.05 6.30 6.62 7.05 7.72 8.99

7.53 7.65 7.79 7.97 8.21 8.78

1.0 1.0 1.0 1.0 1.0 1.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.10 1.25 1.50 2.00 3.50

1.00 0.91 0.80 0.67 0.50 0.29

5.69 5.89 6.12 6.39 6.80 7.52

6.04 6.24 6.45 6.72 7.10 7.82

6.36 6.55 6.76 7.01 7.37 8.08

6.65 6.82 7.02 7.27 7.61 8.29

6.89 7.07 7.26 7.48 7.82 8.49

7.09 7.26 7.45 7.66 7.97 8.61

8.45 8.28 8.14 8.03 8.06 8.47

8.82 8.65 8.46 8.35 8.33 8.72

2.0 2.0 2.0 2.0 2.0 2.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.20 1.50 2.00 3.00 6.00

2.00 1.67 1.33 1.00 0.67 0.33

6.38 6.41 6.46 6.56 6.80 7.43

6.79 6.80 6.83 6.91 7.12 7.72

7.16 7.16 7.17 7.22 7.40 7.99

7.50 7.47 7.46 7.49 7.65 8.21

7.80 7.75 7.72 7.74 7.87 8.41

8.04 7.97 7.94 7.92 8.03 8.53

9.65 9.05 8.59 8.24 8.11 8.44

10.08 9.45 8.94 8.57 8.39 8.46

3.0 3.0 3.0 3.0 3.0 3.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.30 1.75 2.50 4.00 8.50

3.00 2.31 1.71 1.20 0.75 0.35

7.04 6.84 6.71 6.66 6.81 7.38

7.51 7.27 7.09 7.02 7.11 7.68

7.93 7.65 7.45 7.34 7.41 7.95

8.31 8.00 7.76 7.63 7.67 8.17

8.66 8.31 8.05 7.88 7.89 8.38

8.93 8.57 8.27 8.08 8.06 8.51

~

(:5

4.0 4.0 4.0 4.0 4.0 4.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.40 2.00 3.00 5.00 11.00

4.00 2.86 2.00 1.33 0.80 0.36

8.22 7.49 6.94 6.63 6.57 7.05

8.96 8.11 7.50 7.15 7.03 7.44

9.64 8.68 8.01 7.58 7.43 7.81

10.25 9.22 8.48 8.01 7.80 8.13

10.82 9.70 8.92 8.38 8.14 8.42

11.33 10.14 9.29 8.72 8.42 8.67

4.0 4.0 4.0 4.0 4.0 4.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.40 2.00 3.00 5.00 11.00

4.00 2.86 2.00 1.33 0.80 0.36

7.70 7.20 6.88 6.72 6.80 7.39

8.22 7.66 7.28 7.08 7.12 7.66

8.69 8.07 7.65 7.42 7.41 7.93

9.11 8.44 7.98 7.71 7.68 8.15

9.49 8.77 8.27 7.97 7.90 8.36

9.81 9.03 8.53 8.18 8.08 8.49

5.0 5.0 5.0 5.0 5.0 5.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.50 2.25 3.50 6.00 13.50

5.00 3.33 2.22 1.43 0.83 0.37

9.11 7.87 7.12 6.70 6.57 7.03

9.93 8.55 7.71 7.22 7.04 7.42

10.66 9.17 8.24 7.67 7.44 7.80

11.35 9.74 8.72 8.09 7.82 8.12

12.00 10.26 9.17 8.47 8.16 8.41

12.56 10.75 9.57 8.82 8.44 8.66

5.0 5.0 5.0 5.0 5.0 5.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.50 2.25 3.50 6.00 13.50

5.00 3.33 2.22 1.43 0.83 0.37

8.35 7.52 7.01 6.77 6.80 7.34

8.91 7.99 7.43 7.13 7.12 7.64

9.43 8.43 7.81 7.47 7.42 7.91

9.89 8.82 8.15 7.77 7.69 8.14

10.31 9.18 8.45 8.03 7.91 8.34

10.67 9.95 8.72 8.25 8.09 8.48

~

~;::s

~

..,..., :::!

~.

~~

-.

cs-

~~

t;j ~ ~ C

~ ~ ~

;::s

~

t::l..

i

~ .......

~. ~

~ "'! ~ ~.

~ ~

~

'5;

~~ ~ ~

.....

-.:: ~

~ ~ ~

~~

;::s

~

W~ 0 .......

~~

"'tl

~ ~

.....

~

TABLE C6.6

TABLE C6.5 150 deQrees cones D Cuo p2R p2R --R Cuo Cum Cum

---

180 deQrees cones D Cuo p2R p2R R Cuo Cum Cum

Fv/(Acuo) factors Roughness

---

---

0.0

0.2

0.4

0.6

0.8

1.0

---

~g

FvlAcuo ) factors Roughness

c::.--~ :::::.~ (I)

---

(I)

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.00 1.00 1.00 1.00 1.00

0.00 0.00 0.00 0.00 0.00 0.00

5.32 5.60 5.94 6.41 7.13 8.46

5.55 5.82 6.16 6.62 7.32 8.65

5.74 6.00 6.34 6.80 7.49 8.81

5.89 6.16 6.49 6.94 7.62 8.93

6.01 6.26 6.59 7.03 7.71 8.99

6.05 6.30 6.61 7.05 7.72 8.99

0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.00 1.00 1.00 1.00 1.00

0.00 0.00 0.00 0.00 0.00 0.00

5.69 5.97 6.31 6.79 7.49 8.82

5.86 6.13 6.47 6.93 7.63 8.94

5.97 6.24 6.57 7.02 7.70 8.99

6.03 6.29 6.61 7.05 7.71 8.99

6.05 6.30 6.61 7.05 7.71 8.99

6.05 6.30 6.61 7.05 7.71 8.99

1.0 1.0 1.0 1.0 1.0 1.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.10 1.25 1.50 2.00 3.50

1.00 0.91 0.80 0.67 0.50 0.29

5.94 6.16 6.41 6.71 7.13 7.91

6.22 6.43 6.67 6.96 7.36 8.12

6.46 6.67 6.90 7.18 7.57 8.31

6.67 6.87 7.09 7.36 7.73 8.44

6.84 7.04 7.25 7.51 7.86 8.56

6.97 7.15 7.36 7.60 7.95 8.61

1.0 1.0 1.0 1.0 1.0 1.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.10 1.25 1.50 2.00 3.50

1.00 0.91 0.80 0.67 0.50 0.29

6.25 6.48 6.74 7.05 7.47 8.26

6.47 6.69 6.94 7.24 7.64 8.32

6.65 6.87 7.11 7.39 7.79 8.52

6.79 7.00 7.23 7.51 7.88 8.60

6.90 7.10 7.32 7.58 7.93 8.61

6.95 7.14 7.35 7.60 7.94 8.61

2.0 2.0 2.0 2.0 2.0 2.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.20 1.50 2.00 3.00 6.00

2.00 1.67 1.33 1.00 0.67 0.33

6.50 6.59 6.69 6.84 7.11 7.81

6.82 6.90 6.98 7.10 7.35 8.01

7.11 7.16 7.23 7.34 7.57 8.21

7.35 7.40 7.45 7.54 7.74 8.35

7.57 7.59 7.63 7.70 7.89 8.47

7.73 7.74 7.76 7.82 7.99 8.53

2.0 2.0 2.0 2.0 2.0 2.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.20 1.50 2.00 3.00 6.00

2.00 1.67 1.33 1.00 0.67 0.33

6.73 6.85 6.98 7.15 7.45 8.16

6.98 7.08 7.20 7.36 7.63 8.27

7.20 7.30 7.39 7.53 7.78 8.43

7.39 7.46 7.55 7.67 7.90 8.50

7.53 7.59 7.66 7.76 7.96 8.53

7.63 7.68 7.72 7.80 7.98 8.53

3.0 3.0 3.0 3.0 3.0 3.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.30 1.75 2.50 4.00 8.50

3.00 2.31 1.71 1.20 0.75 0.35

7.03 6.94 6.88 6.91 7.10 7.76

7.40 7.27 7.18 7.18 7.35 7.97

7.72 7.56 7.45 7.43 7.57 8.16

7.98 7.81 7.68 7.63 7.75 8.31

8.24 8.03 7.88 7.81 7.90 8.43

8.43 8.21 8.03 7.94 8.00 8.49

3.0 3.0 3.0 3.0 3.0 3.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.30 1.75 2.50 4.00 8.50

3.00 2.31 1.71 1.20 0.75 0.35

7.16 7.13 7.15 7.21 7.43 8.13

7.45 7.40 7.37 7.42 7.62 8.23

7.69 7.62 7.58 7.61 7.78 8.38

7.91 7.81 7.75 7.75 7.90 8.46

8.08 7.96 7.88 7.86 7.97 8.49

8.21 8.07 7.96 7.91 7.99 8.49

4.0 4.0 4.0 4.0 4.0 4.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.40 2.00 3.00 5.00 11.00

4.00 2.86 2.00 1.33 0.80 0.36

7.55 7.23 7.02 6.95 7.09 7.72

7.94 7.58 7.34 7.23 7.34 7.94

8.30 7.89 7.62 7.49 7.56 8.13

8.58 8.16 7.86 7.70 7.75 8.29

8.88 8.40 8.07 7.88 7.90 8.41

9.10 8.59 8.23 8.01 8.00 8.47

4.0 4.0 4.0 4.0 4.0 4.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.40 2.00 3.00 5.00 11.00

4.00 2.86 2.00 1.33 0.80 0.36

7.56 7.38 7.26 7.25 7.44 8.09

7.87 7.64 7.50 7.46 7.61 8.19

8.15 7.89 7.71 7.65 7.77 8.36

8.38 8.09 7.89 7.80 7.89 8.44

8.58 8.26 8.03 7.92 7.97 8.47

8.73 8.39 8.13 7.98 8.00 8.47

5.0 5.0 5.0 5.0 5.0 5.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.50 2.25 3.50 6.00 13.50

5.00 3.33 2.22 1.43 0.83 0.37

8.05 7.46 7.13 6.99 7.09 7.70

8.48 7.83 7.45 7.27 7.34 7.93

8.86 8.16 7.74 7.53 7.56 8.12

9.19 8.44 7.99 7.74 7.75 8.27

9.48 8.69 8.20 7.93 7.91 8.40

9.74 8.90 8.37 8.07 8.01 8.46

5.0 5.0 5.0 5.0 5.0 5.0

0.0 0.2 0.5 1.0 2.0 5.0

1.00 1.50 2.25 3.50 6.00 13.50

5.00 3.33 2.22 1.43 0.83 0.37

7.94 7.56 7.34 7.27 7.43 8.07

8.27 7.85 7.59 7.49 7.60 8.18

8.57 8.10 7.81 7.68 7.77 8.35

8.83 8.32 8.00 7.84 7.89 8.43

9.05 8.50 8.15 7.96 7.97 8.46

9.23 8.64 8.25 8.02 8.00 8.46

~~

~, § (I).

~""C

~~ _.

~

(I)

~

C

~ ~

(I)

~

f} $:l....

i

~

I

...... ;::;. (I)

~ ""! ~ ....... (I)

~ (I) ~

'S

~~ ~

(I)

..:

........

~

""""

(I)

~~

~ (I) ~ t'-.)~

C) ......

~~ '"tI

~

(I)

........

&;

Page 106

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 C6.2.3

Penetration Analysis For Silica Sands Various bearing capacity and shape factors are given in the literature for the analysis of bearing capacity in silica sand. The method described in the PRACTICE text is that of Vesic [8]. However, of particular relevance is the method proposed by Brinch Hansen [17] which is also in common use particularly where the angle of internal friction has been determined for plane strain conditions. Fv =A (0.5 y' B NydySy + Po' Nq Sq dq) where; Ny = 1.5(Nq - 1) tan Nq = e7ttan tan 2 (45° + <1>/2) Sq = 1 + BIL sin dy = 1 Sy = (1 - O.4BIL) dq = 1 + 2tan (1 - sin values for the sand indicated values in the range of 30° to 40°. Observed penetrations were significantly larger than the values would indicate for both the Vesic and Brinch Hansen methods. Analyses by various researchers (Graham, [18]; James, [19]; Kimura, [20]) suggest that reduced values be used to for these "scale effects" . In view of these observations it is recommended that laboratory triaxial test values should be reduced by 5° for the prediction of large diameter footing penetrations in silica sands, i.e. design triaxial - 5 ° If laboratory test data are unavailable the following design values may be applicable:

=

DESIGN PARAMETERS FOR COHESIONLESS SiliCEOUS SOIL* Density Very Loose Loose Medium Loose Medium Dense Medium Dense Dense Very Dense Dense Very Dense

* See notes overleaf

Soil Description Sand Sand-Silt Silt Sand Sand-Silt Silt Sand Sand-Silt Sand Sand-Silt Gravel Sand

Ny 2.6

NQ 3.9

20

5.4

6.4

25

11

11

30

22

18

35

48

33


*

Page 107

NOTE: "Sand-Silt" includes those soils with significant fractions of both sand and silt. Strength values generally increase with increasing sand fractions. For spudcans on sand the effects of cyclic loading may be to either increase or decrease the pore water pressure. Positive excess pore water pressure will weaken the soil and in severe cases may cause partial fluidization. Negative excess pore water pressures may temporarily strengthen the soil. Approximate methods are available for the assessment of excess pore water pressure development and associated foundation settlement (Dean [20D.

The following qualifications apply: 1. Footing penetrations in a thick layer of clean silica sand are usually minimal with

the maximum diameter of the spudcan rarely coming into with the soil. It is therefore not usual to consider the effects of soil backflow in this situation. 2. If various sand layers occur to 1.5 B below the footing depth an average value for <1>' can be selected using the graph developed by Meyerhof [22] as shown in Figure C6.4. Considering the overall inaccuracy in the prediction of footing penetration in sand, this refinement does not generally influence the accuracy of the prediction. 3. Emphasis should be placed on the identification and analyses of potential punchthroughs into a clay layer (or a silt layer which may behave undrained).

tel4--B·--.-tllrl

4

-~

10

V

/

/

-'

30 20 40 Angle ofintcmal friction, degrees·

50

Figure C6.4 : Depth of failure zone in sand

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 C6.2.4 Penetration Analysis For Carbonate Sands

Page 108

Relatively large footing penetrations have been reported for uncemented carbonate materials despite high laboratory friction angles (Dutt, [23]). This may be attributed to either the high compressibility of these materials or low shear strengths due to high voids ratio and a collapsible structure. The leg penetration is governed by both strength and deformation characteristics of foundation soils as noted in Commentary 6.2.1. The compressibility of carbonate sands is relatively higher than for silica sands. Hence, greater penetrations should be expected for carbonate sands relative to silica sands despite the similar or even higher laboratory friction angles. This is ed by both experimental (Poulos, [24]) and theoretical (Yeung, [25]) studies on model foundations. The predictions of footing penetrations in carbonate sands are likely to be performed to a lower degree of accuracy compared with those for silica sands. The conventional method is to use the plasticity based formulation for bearing capacity of shallow foundations in sand. However, friction angles to be used in the formulae should be considerably smaller than laboratory values to (in an artificial manner) for the soil behavior. C6.2.5

Penetration in Silts Cyclic loads imposed in silty fine sands/silt foundations may cause liquefaction due to the generation of excess pore water pressures. In this situation foundation settlements would be anticipated. Conservative assessments of reduced bearing capacities and increased settlements should be conducted as appropriate.

C6.2.6

Penetration Analysis For Layered Soils

C6.2.6.l Sgueezing of Clay For a squeezing clay layer the resistance on the footing cannot become larger than the resistance of the layer underneath the soft clay layer. Thus there is a limit to the squeezing process. C6.2.6.3 Punch-through: Dense Sand Over Soft Clay Traditionally the bearing capacity of a footing on a thin sand layer overlying soft clay has been computed according to the method developed by Hanna and Meyerhof [26] as described in the PRACTICE. This method appears to provide reasonable predictions of the ultimate resistance at the onset of punch-through, however it may overpredict the resistance after the initiation of punch-through as the soil shear planes then approach the vertical and the assumed modeling is then incorrect. The approximation Kstan<j> == 3culBy' is a lower bound applicable to the onset of punch-through. The reference paper provides more accurate data for Ks. An alternative method is that in which a load spread is considered through the upper sand layer, as illustrated in Figure C6.5. In this model the bearing capacity of the foundation is assumed to be equal to the bearing capacity of the foundation projected onto the lower layer. This method allows capacity ranges to be developed for a range of load

Page 109


spread gradients. Thus for a load spreading under a slope of l:n, the ultimate bearing capacity of a circular foundation is given by: Fv = FV,b- W where; Fv = ultimate bearing capacity of footing (with diameter B and area A at depth D). FV,b = ultimate bearing capacity of fictitious footing (with diameter [B + 2H1n] and area (1 + 2H1nB)2A, at the top of the soft clay layer. W = weight of soil "plug" in between footing and fictitious footing. = [1 + 2H1(nB)] 2ARy'

Dense

r

sand , t4-- t! -----+t :

weak clay

.",

fi,b l

No backflow of soil

---+t i iFull '" t4-backtlow of soil

Qv = Qv,b-W

Qv= Qv,b-W-AI'f~

:...

t!'

~

tl

B'

..:

Figure C6.5 : Spudcan bearing capacity analysis - sand over clay load spread method This method, using n = 3, has been recommended by Young, [27] for jack-up foundations. However, comparison with model test data (Jacobsen, [28]; Higham, [29]; Craig, [30]) suggest a range from n = 3 to 5. Conversely, actual spudcan penetration data are available which suggest a higher spread, i.e. smaller n values, (Baglioni, [31]). Hence it is suggested that this method would provide reasonable, but conservative, results if a lower bound value n = 5 be used. However, it is noted that both observations of model test data and results of numerical analyses reveal that soil punching failure occurs along vertical surfaces. Thus, although this method can provide reasonable quantitative estimates on leg penetration, it may not be based on a physically correct model. The same comment applies to the previously referenced Hanna and Meyerhof method which is based on failure along a truncated cone surface. This is unlike the observed vertical shear surface. However, the ultimate resistance computed when punching shear is initiated generally gives reasonable agreement (and is acceptably conservative) compared with actually observed data. It is noted that this method generally provides reasonable estimates of ultimate soil

resistance at the onset of punch-through. However, significant underpredictions of soil resistance have been reported by Baglioni, [31]. Conversely the method appears to overpredict soil resistance after punch-through has initiated as suggested by Craig, [32].


Page 110

Craig, [30] observed in centrifuge model tests that a sand plug underneath the spudcan is pushed with relatively little lateral deformation into the underlying clay for prototype offshore conditions. It is suggested that be taken of the frictional resistance on this sand plug when penetrating the clay. C6.2.7

Summary The various soil failure mechanisms considered in this section are illustrated in Figure C6.6. The current status on analytical methods for punch-through (Section C6.2.6) is that the widely used methods, discussed above, (i.e. the load spread method and the Hanna and Meyerhof method) show (different) discrepancies with observed data. However, both methods allow prediction of a lower bound resistance at the initiation of punch-through.

A) "Conventional" bearing capacity failure: unifonn soils.

C) Squeezing.

B) "Conventional" bearing capacity failure: layered soils.

D) Punch-through

E) Punch - through + conventional bearing capacity failure

F) Punch - through + Squeezing

Figure C6.6 : Foundation bearing failure modes

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 C6.3 FOUNDATION STABILITY ASSESSMENT

Page 111

C6.3.3/4 Bearing capacity for inclined loading Introduction Fonnulae for combined vertical (PVH, FvHM ), horizontal (PH, FHM) and moment (PM) capacity on shallow foundations in unifonn soils have been suggested by various researchers. Those due to Vesic [8] and Brinch Hansen [17] are commonly used for offshore applications and are included in API RP2A [33] and DNV [34] guidelines respectively. It should be noted that the equations are applicable to shallow penetrations. Any contribution of horizontal soil resistance on the embedded legs is ignored. In case of deep penetrations the horizontal resistance may be significant, especially when the jack-up leg comprises a single tubular or box section or when the spudcan is provided with skirts around the can perimeter. The following section is an overview of the recommended criteria for spudcan foundations. It is noted that the analytical procedures apply to a flat footing in which all load/resistance is transmitted through its base. The influence of horizontal resistance on vertical areas (e.g. footing cone or vertical surfaces above the base) can either be assessed separately or ignored. Reasons for discluding the latter resistance component are discussed below. 1. Uncertainty of the area between the spudcan and soil due to the shape of the foundations or due to removal of foundation material by scour. 2. Soil strengths and stiffnesses may be significantly reduced as a result of material remolding during unit installation. 3. The ultimate shear resistance along the foundation base is generally mobilized at a significantly smaller displacement than that required to mobilize the ive soil resistance. It is noted that the combined loading problem is generally solved in a simplistic and

generally conservative manner. For layered soil conditions and/or complex footing configurations it may be helpful to assess the ultimate foundation capacity using finite element techniques. Such analyses are particularly relevant for the assessment of displacements associated with combined loads (level 3 analyses). The equations of Sections 6.3.3.1 and 6.3.3.2 may be used to calculate the bearing capacity of the soil beneath the spudcan under inclined loading. The expressions provide correlation between the vertical soil bearing capacity the associated horizontal soil bearing capacity. In this case the effect of backflow and spudcan buoyancy shall be included in the spudcan loading. The total vertical load during stonn conditions may comprise: dead, live and environmental loads including associated P-Ll effects backflow spudcan buoyancy (due to weight of soil displaced by the spudcan)

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 Unifonn Clay Clay pinned foundation

Page 112

~:

A comparison of the Vesic [8] and Brinch Hansen [17] criteria for surface footings in clay shows that the latter are slightly more conservative than the fonner (i.e. the Brinch Hansen results show a reduced capacity compared with those given by the Vesic approach). The Brinch Hansen criteria appear to provide a lower bound to finite element analysis results and (model) test data reported by Noble Denton [lOb] and by Santa Maria [35]. The relationship between maximum vertical capacity (FVH) and horizontal soil capacity (FH) for a circular surface footing in clay is graphically presented in Figure C6.7. The graph has been non-dimensionalized by dividing FVH and FH by the maximum vertical soil capacity Fvmax (which occurs when FH = 0). Also shown is a curve for deep footings where DIB;;:::2.5. For spudcans founded on overconsolidated clay (OCR;;::: 4), cyclic degradati
T D

1 ~

•••• 1:-.. ~

Brinm Banscn~ ~ DNV ~4]

...~

"'\ ~

.6

,

\

.4

Surtace

"Deep":

(*~2~ , , ,,

.2

0.04

0.08

0.12

0.16

0.20

~

Figure C6.7 : Verticallhorizontalload envelopes for footings in clay

Commentaries to Recommended Practice for Site Specific Assessment of Rev 2, Jan 2002 Mobile Jack-Up Units Clay foundation with moment fixity CFM > 0):

Page 113

The FvWFH envelope reduces in size if an overturning moment is applied in addition to horizontal and/or vertical loading. Reference is made to Brinch Hansen [17] or to DNV [34]. Some guidance can also be obtained from Santa Maria [35]. Uniform Sand Pinned sand foundation 0): The FvWFH envelope reduces in size if an overturning moment is simultaneously applied. Reference is made to Vesic [8] and API RP2A [33] for details on the computation procedure. Further guidance can be obtained from Tan [39].

II

Page 114

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 C6.3.3/4

FVH

-

-+

1.0

FvlllOX

O. •

••

0.8

Test data various researchers (primarily strip footings)

-

DNV criteria (all footings) API criteria (strips lower bOllldJ [] circular footings upper bound)

0.7 0.6 0.5

•

0.4 0.3

•

0.2

••

0.1 0

0

0.1 0.2 0.3

0.4

0.5

0.6 0.7

0.8 09

1.0

FH

F;ma"!' Figure C6.8 : Foundation combined verticallhorizontalloading on sand - comparison of design criteria and observed data

1 1 D

F

t

1.0 ~--r---.-----'---.----,

F~ ~~---_ ' ____ O.S

~--+----"""""",-+--"-""<"-_-I_- , , - - + - - - 1

~

Surfa '-"""" "de· Vesic [SJ 0.6 t----+---t-~\_+_--+"'"t-,- I APIRP 2A [33] (D =oo)

}

I)

0.4 t----t---t---tl---+-/-:/'--I

0.2

/

,/ t----t---t/~~_l:_r....:.~.- + - - 1

o~~~,,_-,~~_,,·_··_··_··~-·_··_--_~·~_~_~ ~~ o

0.Q4

0.06

0.12

0.16

0.20

FVmax

Figure C6.9 : Verticallhorizontalload envelopes for footings in sand

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 C6.3.3/4 Clay & Sand Foundations with moment fixity (FM2:...ffi

Page 115

Section 6.3.4.6 describes three methods by which fixity may be included in the analysis. The intennediate method, using linear fixity, is an approach that was not previously encomed. It is now included as the more detailed methods are not readily available to most analysts. It must however be noted that the linear rotational stiffness must be selected with care to ensure that wave force cancellation effects do not drive the resulting DAF's. Refer to C7.4. Elastic Spring Stiffnesses - Sand and Clay The elastic stiffness factors are calculated assuming full of the spudcan with the seabed. If the vertical load is insufficient to maintain full as the moment increases then reduced stiffnesses should be used. The stiffness factors are derived for a homogeneous, linear, isotropic soil. Choice of the appropriate shear modulus should take into the expected stress level and strain amplitude. Selection of Shear Modulus, G, in clay When determining the secant rotational stiffness, K3, the shear modulus may be taken as G =IrCu. In extreme response analysis, it is recommended that the following be used: G/c u = 50 for overconsolidated clays, with an overconsolidation ratio greater than 10. G/c u 100 for overconsolidated clays, with an overconsolidation ratio between 4 and 10. G/c u = 200 for nonnally consolidated clays, with an overconsolidation ratio less than 4.

=

It is clear that lower Ir values may develop in certain regions of the soil. However, the rotational stiffness is an integrated result of near and far field soil stiffness. Furthennore, the secant stiffness will be reduced by a stiffness reduction factor, fro The recommended Ir values are therefore considered reasonably conservative. For applications involving small strain beneath the spudcan, such as in a structural fatigue analysis, a higher Ir should be used. Typical Ir values for small strains may range from the order of 200-400 for overconsolidated clays to 800-1000 for nonnally consolidated clays according to Wroth [40] and Andersen [36]. Selection of Shear Modulus in Sand For calculating the soil stiffness during extreme loading conditions the following empirical expressions for shear moduli for vertical (Oy), horizontal (Gh ) and rotational loading (Gr) may be used, Dean [41]: Gv Gh Gr

= =

=

36,600 + 24.9 (VuJA) 1,100 + 5.6 (VuJA) 4,100 + 11.5 (VuJA)

where Gv, Gh and Gr are in kN/m 2, VLo is the maximum preload applied to the foundation by the spudcan in kN and A is the plan cross sectional area in m2 • The above expressions have been deduced from the re:-evaluation of load excursions perfonned in centrifuge tests. A total of 522 load excursions were examined, 111 from 11 centrifuge tests perfonned on loose sand, 316 from 18 medium dense sand tests and 96 from 6 dense sand tests. Recent work perfonned by Dean [42], in which

Commentaries to Recommended Practice for Site Specific Assessment of Page 116 Mobile Jack-Up Units Rev 2, Jan 2002 unpublished data from centrifuge tests were inspected resulted in the following expressions for dense sand: G v = 1,500 (VuJA)O.55 Gh = 150 (VuJA)O.55 Gr 600 (VuJA)O.55 where G v , G h , G r and VuJA are in kN/m2 •

=

For rotational stiffness, the Dean [42] fonnulation of Gr is recommended. Dean's inspections of the loose sands show a lower stiffness than for dense sand. Preliminary analyses have indicated that the elastic shear modulus for loose sand might be based upon the same expression as for dense sand, but reduced using a factor f( e) where: (2.973- e)2 fCe) = (1+ e) where e is the voids ratio. The above expressions may be seen in Hardin [43]. Using this expression a shear modulus, G Loose, for a loose sand would be related to the corresponding shear modulus GDense, for dense sand by: G"",

=

{:i~:;}

Gn-

where; fCe.) fCeD)

=

value of fCe) for loose sand value of fCe) for dense sand

Effect of Embedment of the Spudcan on the Elastic Spring Stiffness A study of the effect of embedment of flat plate and conical type footings has been performed by Bell [42] to demonstrate the effect of penetration depth on the translational and rotational spring stiffnesses. In order to take the embedment into the elastic spring stiffness derived from the Boussinesq equations may be multiplied by the depth factor~. The results of the study are summarized in the table below. In the table ~l' ~ and ~ represent the depth factors for the vertical spring stiffness, horizontal spring stiffness and the rotational spring stiffness, respectively. Case 1 represents an open hole above the spudcan, case 2 a back-filled hole. ~l

DIR 0.5 1.0 2.0 4.0

Case 1 1.15 1.28 1.42 1.59

Case 2 1.21 1.41 1.70 2.00

~

Case 1 1.33 1.44 1.51 1.61

Case 2 1.49 1.71 1.92 2.06

~3

Case 1 1.28 1.43 1.51 1.57

Case 2 1.64 2.05 2.31 2.41

A voidance of numerical problems An analysis in which the spudcan is considered as pinned to the seabed is equivalent to the assumption that KI and K2 are infinite and K3 is zero. In any analysis taking into foundation fixity CK3 non-zero) it is recommended that the effects of KI and K2 are considered, as they will tend to decrease the sway stiffness, and hence increase the natural period and second order effects. As a first approximation elastic springs are

I

Commentaries to Recommended Practice for Site Specific Assessment of Page 117 Mobile Jack-Up Units Rev 2, Jan 2002 recommended. In some instances the vertical deformations resulting from the inclusion of such springs may be large, and could compromise the numerical accuracy of the solution. A possible method of reducing the absolute value of the deflections is given overleaf. Load

Load

V~

r----------r-------------

VLo~--------~-------------

V mox 1--------+1.

VJJ

Leeward leg displacement

Wmdwardleg displacement

Figure C6.1O : Vertical load-displacement curves for leeward and windward legs With reference to Figure C6.1O, consider the windward and leeward legs as follows: Leeward leg Vmax= VO+VE

Windward leg V min = Vo - V E

where~

Vo

VE

=

Vertical reaction due to dead load = Vertical reaction due to environmental load (and any change from the variable load level used in computing V0)

The deflection due to environmental load alone ~d can be derived as: ~d

~d

=

The modified vertical spring stiffness K* y is then:

K*y = Ky

Vn +VE VE

K*y = Ky

VO-VE VE

where;

Kv

= KI from the PRACTICE = 2GD/(I-v)

For further information regarding foundation stiffness evaluation reference should be made to Bell, [44].

Commentaries to Recommended Practice for Site Specific Assessment of Page 118 Rev 2, Jan 2002 Mobile Jack-Up Units C6.4 OTHER ASPECTS OF JACK-UP UNIT FOUNDATION PERFORMANCE C6.4.1

Leaning Instability A lower bound estimate of the leaning stability can be perfonned using the theory of Hambly [45]. However, it should be recognized that such estimates have proven to be generally conservative due to the omission of beneficial effects such as spudcan fixity and lateral soil resistance on the legs. The potential for jack-up unit leaning instability may largely be discounted if appropriate installation procedures are adopted.

C6.4.2

Footprint Considerations Installing a jack-up with its spudcans near or adjacent to existing footprints, or zones of weaker material (naturally infilled spudcan footprints) may induce soil failure. Mathematical models are available for the evaluation of ground stability in such situations and, in particular, finite element techniques are becoming more widely used. It is not possible to advise on a minimum acceptable distance between the proposed

spudcan locations and existing footprints as this will depend on several parameters. These parameters include the soil conditions, the depth and configuration of the footprints, the degree of soil backfill during and after spudcan removal, the elapsed time since the last installation, the spudcan geometry and foundation loading. As a general guideline it is usually acceptable for a spudcan to be installed at a minimum distance (from the edge of the bearing area to the edge of the footprint) of one diameter measured at the spudcan bearing area. However, in soft clay conditions, with consequentially deep footing penetrations, the situation may be complicated by the fact that the footprints may have larger diameters than the spudcans. Also in dense sand or stiff clay conditions, where shallow footprints are unlikely to influence the integrity of the spudcan foundations, the above guideline may be conservati ve. C6.4.3

Scour The seabed is susceptible to scour when the shear stresses induced by fluid flow exceed a certain value and/or when turbulent intensity of the flow is sufficiently large to lift individual grains and entrain these in the flow. Both wave action and currents can induce scour although in deep water, the effect of wave action on seabed scour is negligible. The following parameters are important for the assessment of scour potential: a) Seabed material - size, shape, density and cohesion b) Flow conditions - current velocity, wave-induced oscillatory velocities interaction of waves and currents c) Shape, size and penetration of jack-up footing. Methods are available to determine whether significant scour is likely under waves and currents. These generally proceed by considering the velocities near the seabed and by calculation of the shear stresses. Guidance is given with regard to the assessment of scour potential in the US NCEL [46] Marine Geotechnical Engineering Handbook.

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 C6.4.4 Seafloor instability

Page 119

Seafloor instability may be caused by a number of mechanisms and where the potential for unstable ground conditions is recognized it is recommended that expert local advise is obtained. In areas where liquefaction is known to be possible its potential must be assessed.

Liquefaction, or cyclic mobility, occurs when the cyclic stresses within the soils cause a progressive build up of pore pressure. The pore pressure within the profile may build up to a stage where it becomes equal to the initial average vertical effective stress. Foundation failure may result depending on the location and extent of pore pressure developed in the soil. The rate and degree of pore pressure build up will depend on three factors: a) The loading characteristics; that is, the amplitude, period and durations of the different cyclic loading components b) The cyclic characteristics of the soil deposits c) The drainage and compressibility of the strata comprising the soil profile. The cyclic loads may be induced by environmental or mechanical means, or by the oscillatory ground accelerations imposed during earthquake conditions. If appropriate soil conditions prevail, the potential for cyclic mobility should be

considered for a wide variety of load cases. Of particular interest is the windward footing during storm conditions, where reduced vertical load and increased horizontal load may theoretically induce lateral sliding or bearing failure. C6.4.6

Spudcan - pile interaction Where it is recognized that jack-up footings may adversely effect the piles of an adjacent structure it will be necessary to assess the implications. Procedures such as that proposed by Siciliano [47] may be used for deeply embedded footings in clay. Otherwise, if adequate soil data is available, mathematical modeling techniques, such as finite element modeling, could be used to assess the significance of the spudcan-pile interaction.


Page 120

GLOSSARY OF FOR SECTION C6 au A B

= = =

B' Cu Cui Cum Cuo d

= = = = = = = = = =

dq ely D e e(e) feed feeD) FH FM Fo' Fy FY.b F YH Fymax G Gy Gh Gr GLoose GDense H

Ir I ks kv K 1,K2,K3 ~I ~2 ~

K*v L

Adhesion. Spudcan effective bearing area. Effective spudcan diameter at uppermost part of bearing area in with the soil (for rectangular footing B width). Increased effective spudcan diameter -load spread method. Undrained cohesive shear strength. Undrained cohesive shear strength at spudcan tip. Undrained cohesive shear strength at mudline. Undrained cohesive shear strength at max bearing area. Critical depth of failure below spudcan in sand. Bearing capacity factor = 1 + 2tanq,(1- sinq,i DIB. Bearing capacity factor 1. Distance from mudline to spudcan maximum bearing area. Voids ratio. = Voids ratio factor. Voids ratio factor for loose sand. Voids ratio factor for dense sand. Horizontal foundation capacity (envelope). Foundation moment capacity (envelope). Effective overburden pressure due to backfill at depth of the uppermost part of the bearing area. Vertical foundation capacity. Vertical bearing capacity of fictitious footing on the surface of the lower (bottom) clay layer with no backfill. Vertical foundation capacity when horizontal load is present. Maximum vertical soil resistance (occurs when FH 0). Shear modulus. Shear modulus for vertical loading. Shear modulus for horizontal loading. Shear modulus for momentlrotationalloading. Shear modulus for loose sand. Shear modulus for dense sand. Distance from spudcan maximum bearing area to weak strata below. Coefficient relating undrained shear strength to shear modulus. Height of soil column above spudcan. Coefficient of punching shear. Vertical foundation stiffness (= KI). Vertical, horizontal and rotational stiffness. Stiffness factor on vertical stiffness to for embedment. Stiffness factor on horizontal stiffness to for embedment. Stiffness factor on rotational stiffness to for embedment. Modified vertical foundation stiffness. Foundation length, for circular foundation L B.

=

=

= = = = = = =

= = = = = = = = = = = = = = = = = = =

=

=

GLOSSARY OF CONTINUED ...


Page 121

GLOSSARY OF FOR SECTION C6 (Continued) n N , Nc Nq Ny

OCR

Po'

= = = = =

= =

=

Inverse slope of load spreading (slope of spread 1:n). Stability factor. Alternative bearing capacity factor for normally consolidated clays. Bearing capacity factor e1ttan4Ptan 2( 45 + q,/2). Bearing capacity factor 2(Nq + 1) tanq, for Vesic analysis [8] = 1.5(Nq - 1) tanq, for Brinch Hansen analysis [17]. Over consolidation ratio. Effective overburden pressure at spudcan base level (i.e. depth of maximum bearing area). Factored vertical leg reaction. Factored horizontal leg reaction. B/2. Bearing capacity shape factor = 1 + (B1L)tanq,. Bearing capacity shape factor (1 - O.4BIL). 0.6 for circular footing under pure vertical load). Thickness of weak clay layer underneath spudcan. Embedded spudcan volume. Vertical reaction due to dead load. Vertical reaction due to environmental load (and any change from the variable load level used in computing VD). Maximum vertical foundation load during preloading. Maximum footing reaction on leeward leg. Minimum footing reaction on windward leg. Weight of soil plug (load spread method) [1 + 2H1(nB)] 2ARy'. Vertical foundation settlement for conventional bearing capacity analysis. Vertical displacement required to mobilize capacity Fv.

=

=

T V VD VE

= = = = = (= = = = =

VLo Vmax Vmin W z zu

= = = = = =

a

= Roughness factor = au/c u.

Qv QH R Sq

sy

p

~d

y' q, q,' v

p

= = = =

=

=

The equivalent cone angle of the spudcan. Vertical deflection due to environmental load. Submerged unit weight of soil. Angle of internal friction for sand - degrees. Angle of internal friction for sand - degrees, dependent on d/B ratio. Poisson's ratio. Rate of increase of cohesive shear strength with depth.


Page 122

1

Meyerhof G.G. (1972), "Stability of Slurry Trench Cuts in Saturated Clay", Proceedings of the Speciality Conference on Performance of Earth and Earth ed Structures, ASCE, pp. 1451-1466.

2

Britto A.M., Kusakabe, Osanu (1983) "Stability of Axisymmetric Excavations in Clays", Journal of Geotechnical Eng., Vol 109, No.5.

3

Young A.G., Rernmes B.D., Meyer B.J., (1984) "Foundation Performance of Offshore Jack-Up Drilling Rigs" Journal of Geotechnical Engineering, Vol. 110, No.7, pp. 841-859.

4

Skempton A.W. (1951), "The Bearing Capacity of Clays", Building Research Congress.

5

Davis E.H., Booker J.R., (1973), "The Effect of Increasing Strength with Depth on the Bearing Capacity of Clays", Geotechnique Vol. 23, No.4, pp. 551-563.

6

Salencon J., Matar M., (1982), "Capacite portante des Foundations superficielles circulaires", Journal de Mecanique theorique et applique, Vol. 1, No.2, pp. 237-267.

7

Houlsby G.T., Wroth C.P., (1983), "Calculation of Stresses on Shallow Penetrometers and Footings", Proc. IUTAM Symp. on Seabed Mechanics, Newcastle, pp. 107-112.

8

Vesic A.S., (1975), "Bearing Capacity of Shallow Foundations", Foundation Engineering Handbook (H.F. Winterkorn and H.Y. Fang, eds.), 121-147, Van Nostrand.

9

Endley, S.N., Rapoport, V., Thompson, P.J., and Baglioni, V.P. (1981), "Prediction of Jack-up rig Footing Penetration", OTC, Houston, OTC 4144.

lOa Noble Denton & Associates (1987), "Foundation Fixity of Jack-up Units, t Industry Study", Volumes I, II. lOb Noble Denton & Associates (1988), "Foundation Fixity of Jack-up Units, t Industry Study, Extra work", Volume ill. 11

Houlsby G.T., Wroth C.P., (1982), "Determination of undrained strengths by cone penetration tests", Proceedings of the Second European Symposium on Penetration Testing / Amsterdam.

12

Houlsby G.T., Wroth C.P., (1982), "Direct Solution of Plasticity Problems in Soils by the Method of Characteristics", Proceedings of the Fourth International Conference on Numerical Methods in Geomechanics, Edmonton, Canada.

13

Houlsby G.T., (1982), "Theoretical Analysis of the Fall Cone Test" Geotechnique 32, No. 2, 111-118.

14

Koumoto T., Kaku K. (1982), "Three-Dimensional Analysis of Static Cone Penetration" Proceedings of the Second European Symposium on Penetration Testing, Amsterdam.


Page 123

15

Houlsby G.T. (1991), "Bearing Capacity Factors for Conical Footings on Clay - Comments on Derivation of Factors", presented to Jack-Up Working Group Foundations SubCommittee, London.

16

Andersen K.H. (1988), "A Review of Soft Clay under Static and Cyclic Loading", Invited lecture, International Conference on Engineering Problems of Regional Soils, Being, China.17Brinch Hansen J., (1970) "A Revised and Extended Formula for Bearing Capacity", Bulletin No. 28, Danish Geotechnical Inst., Copenhagen.

18

Graham J., Stuart J.G. (1971), "Scale and Boundary Effects in Foundation Analysis", Journal of the Soil Mechanics and Foundation Division, ASCE, Vol. 97, No. SMll, November, pp. 1533-1548.

19

James RG., Tanaka H. (1984), "An Investigation of the Bearing Capacity of footings under Eccentric and Inclined Loading in Sand in a Geotechnical Centrifuge", Proc. Symp. Recent Advances in Geotechnical Centrifuge Modelling, University of California, Davis, pp. 88115.

20

Kimura T., Kusakabe 0., and Saitoh K. (1985), "Geotechnical Model Tests of Bearing Capacity Problems in Centrifuge", Geotechnique, Vol. 35, No.1, pp. 33-45.

21

Dean E.T.R (1991), "Some Potential Approximate Methods for the Preliminary Estimation of Excess Pore Water Pressures and Settlement-Time Curves for Submerged Foundations subjected to Time Dependent Loading", Cambridge University Engineering Department, CUEDID-SoilsffR240.

22

Meyerhof G.G. (1984), "An Investigation of the Bearing Capacity of Shallow Footings on Dry Sand", Proceedings 2nd ICSMFE, Rotterdam.

23

Dutt RN., Ingram W.R (1988), "Bearing Capacity of Jack-up Footings in Carbonate granular Sediments", Proceedings of the International Conference on Calcareous Sediments, Perth, pp. 291-296.

24

Poulos H.G., Chua E.W. (1985), "Bearing Capacity of Foundations on Calcareous Sand", Proceedings 11th ICSMFE, San Francisco, Vol. 3, pp. 1619- 1622.

25

Yeung S.K., Carter J.P. (1989), "An Assessment of the Bearing Capacity of Calcareous and Silica Sands", International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 13, pp. 19-26.

26

Hanna A.M., Meyerhof G.G. (1980), "Design Charts for Ultimate Bearing Capacity of Foundations on Sand Overlying Soft Clay", Canadian Geotechnical Journal Vol. 17.

27

Young A.G., Focht J.A. Jr. (1981), "Subsurface Hazards Affect Mobile Jack-up Rig Operations", Sounding, McClelland Engineers Inc., Houston, Texas, Vol. 3, No.2, pp. 4-9.

28

Jacobsen M., Christensen K.V., Sorensen C.S. (1977), "Gennemlokning of Tynde Sandlag (Penetration of Thin Sand Layers)", Vag-och Vattenbyggaren 8-9, Sweden.


Page 124

REFERENCES FOR SECTION C6 (Continued) 29

Higham M.D. (1984), "Models of Jack-up Rig Foundations:", M.Sc. Thesis, University of Manchester.

30

Craig W.H., Chua K. (1990), "Deep Penetration of Spudcan Foundations on Sand and Clay", Geotechnique, VoL 40, No.4, pp. 541-556.

31

Baglioni V.P., Chow G.S. Endley S.N. (1982) "Jack-up Rig Foundation Stability in Straified Soil Profiles", Proceedings, 14th OTC, Houston, OTC 4408.

32

Craig W.H., Higham M.D. (1985), "The Applications of Centrifugal Modelling to the Design of Jack-up rig Foundations". Proceedings Offshore Site Investigation Conference, VoL 3. ISBN 0-86010-668-3.

33

API RP2A (1989), "API Recommended Practice for Planning, Deg, and Constructing Fixed Offshore Platforms", API Recommended Practice 2A (RP2A) 18th Edition, Washington.

34

Det Norske Veritas (1977), "Rules for the Design and Inspection of Offshore Structures, Appendix F, Foundations", H'vik, Reprint with corrections (1980).

35

Santa Maria P.E.L. de (1988), "Behavior of Footings for Offshore Structures under Combined Loads", Ph.D. Thesis, Oxford University.

36

Andersen K.H. (1992), "Cyclic effects on Bearing Capacity and Stiffness for a Jack-up Platform on Clay", NGI Oslo report 913012-1, Rev 1.

37

Brekke J.N., Murff J.D., Lamb W.e. (1989) "Calibration of Jackup Leg Foundation Model Using Full-Scale Structural Measurements", Proceedings Offshore Technology Conference, Houston, (OTC 6127).

38

Matlock H. (1970), "Correlations for Design of Laterally Loaded Piles in Soft Clay", Proceedings Offshore Technology Conference (OTC 1204).

39

Tan F.S.e. (1990), "Centrifuge and Theoretical Modelling of Conical Footings in Sand", Ph.D. Thesis, Cambridge University.

40

Wroth et al. (1979), "A Review of the Engineering Properties of Soils with Particular Reference to the Shear Modulus", Cambridge University Engineering Department. Report No 1523/84.1SM049/84.

41

Dean et aL (1992a), "A New Procedure for Assessing Fixity of Spudcans on Sand", Andrew N Schofield and Associates Ltd., Cambridge, for t Industry Jack-Up Committee.

42

Dean et aL (1992b), "A New Procedure for Assessing Fixity of Spudcans on Sand - Further Notes", Andrew N Schofield and Associates Ltd., Cambridge, for t Industry Jack-Up Committee.

43

Hardin B.O., and Dmevich V.P. (1972), "Shear Modulus and Damping in Soils: Design Equations and Curves", J. Soil Mech. Foundation Division, ASCE Vol 98, SM7, 667-692

44

Bell R.W. (1991), "The Analysis of Offshore Foundations Subjected to Combined Loading", MSc. Thesis presented to the University of Oxford.


Page 125

45

Hambly E.C. (1985), "Punch-through Instability of Jack-up on Seabed", Journal of Geotechn. Eng., ASCE, Vol. 111, No.4.

46

US NCEL (1985), "Handbook for Marine Geotechnical Engineering". Deep Ocean Technology, Naval Civil Engineering Laboratory, Port Hueneme, CA 93043.

47

Siciliano R.J., Hamilton J.M., Murff J.D. (1990), "Effect of Jackup Spudcans on Piles", Proceedings Offshore Technology Conference (OTC 6467).

48

Dean, et al. (1995), "Centrifuge Modelling of 3-Leg Jackups with Non-Skirted and Skirtedl Spuds on Partially Drained Sand", Proceedings Offshore Technology Conference, Houston, (OTC 7839).

49

Wong P.C. and Murff J.D. (1994),"Dynamic Analysis of Jack-up Rigs Using Advancedl Foundation Models", Proceedings OMAE, Houston, paper 94-1315

50

Svano and Tjelta (1993),"Skirted Spudcans - Extending Operational Depth and bnproving Performance", 4th City University Jack-up Platform Conference, London.

51

Baerheim (1993),"Structural Effects of Foundation Fixity on a Large Jack-up", 4th Cityl University Jack-up Platform Conference, London.

52

Van Langen and Hospers (1993),"Theoretical Model for Determining Rotational Behaviorl of Spudcans", Proceedings Offshore Technology Conference, Houston, (OTC 7302).

I

Commentaries to Recommended Practice for Site Specific Assessment of Page 126 Rev 2, Jan 2002 Mobile Jack-Up Units C.7 COMMENTARY TO CALCULATION METHODS - DETERMINATION OF

RESPONSES C7.1

INTRODUCTION The main objective of this Section is to provide documentation of the considerations applied to the recommendations given in the Recommended Practice (pRACTICE) concerning the determination of extreme responses. The PRACTICE recommends that extreme response determination should always follow a procedure which always considers the potential dynamic magnification of the jack-up's behavior.

C7.2

QUASI-STATIC EXTREME RESPONSE WITH INERTIAL LOAD SET Section 7.2 of the PRACTICE recommends that quasi-static responses are normally determined by stepping the design wave through the structure. The extreme response is obtained by combining the quasi-static wave-current loading with wind loads, dead loads, etc., and an inertial loadset to represent the loading due to dynamic response. This method approximates the random nature of wave excitation and implicitly assumes that the extreme response is uniquely related to the occurrence of the extreme wave. As an alternative to the deterministic quasi-static design wave analysis a probabilistic quasi-static random wave analysis may be used. This procedure is identical to a random dynamic analysis procedure with the dynamic effects suppressed. Where software permits, suppression may be achieved by setting all jack-up vibrational masses to zero; see Section 7.3 of the PRACTICE. The significant wave height used for the random wave analysis should include a water depth correction as shown on Section 3.5.1 of the PRACTICE.

C7.3

CONSIDERATIONS AFFECTING THE DYNAMIC RESPONSE The following considerations are relevant: a) The highest natural period of the jack-up, in absolute , in relation to the environmental excitation periods. For the present purpose the highest natural period (Tn) is used as the single indicator representing the properties of the structural system for the given application. The environmental excitation is due to sea waves and may contain energy at periods in the range 2-3 to some 20 seconds. The energy content in the wave spectrum at the lower end of this period range is controlled by wave saturation and is independent of the geographical location. Experience has shown, and theoretical calculations , that the dynamic magnification may be neglected if the highest natural period does not exceed 2.5 seconds. The extent of the upper end of the period range, and its energy content, varies significantly with the geographic location, an important indicator being the peak period (Tp) of the wave spectrum of the extreme sea state. If Tn > 0.5 Tp the dynamic behavior becomes increasingly significant and complex, which always demands an appropriate dynamic analysis. Tn may be determined in accordance with Section 7.3.5 of the PRACTICE. The derivation of the equations is given in Appendix C7.A. The derivation of Tn and Tp are therefore critical to the dynamic analysis. Considerations for the calculation of Tn and Tp are given in Section C7.4.

Commentaries to Recommended Practice for Site Specific Assessment of Page 127 Mobile Jack-Up Units Rev 2, Jan 2002 b) The magnitude of the dynamic magnification, relative to the quasi-static response. Engineering calculations are subject to inherent (in)accuracy as a result of uncertainties/inaccuracies in calculation methods and input data. Therefore, if the magnitude of the dynamic contribution remains smaller than some 5%, it may be considered to be covered by the overall margins included in the engineering assessment criteria in Section 8 of the PRACTICE, without explicitly quantifying and including the dynamic effect. For this evaluation, the magnitude of the dynamic contribution may be estimated by the Dynamic Amplification Factor (DAF) of an idealized single degree-of-freedom system in accordance with Section 7.3.6.1 of the PRACTICE. If the DAF < 1.05, dynamic magnification may be neglected. c) As the dynamic responses to periodic and random excitations can be significantly different, the random nature should (where possible) be retained in the modeling of the excitation. The simplified method described in Section 7.3.6.1 implicitly assumes periodic excitation. C7.3.7

Free surface corrections for frequency domain spectral wave load analysis When using frequency domain spectral techniques, the wave forces are evaluated using linear kinematics up to the mean water level only. Thus the force in the wave crests may be underestimated. The underestimation is perhaps further compounded by the drag force linearization. To primarily for the effects if inundation, but also partially to correct any errors in the drag linearization, empirical factors (FSE's) may be derived to adjust the wave induced force and overturning moment obtained from a frequency domain spectral analysis. By way of an example, the maximum wave force and overturning moment on a pile group (representing jack-up legs) and ing for free surface effects and drag force non-linearity, have been compared with the wave load on the same pie group when ignoring the sea surface variability and using linearized drag force. This yields separate FSE's for shear and overturning moment which may be used to make an initial correction for the above effects. Such factors are dependent on the kinematic stretching algorithm assumed. Using Wheeler stretching for a drag-dominated jack-up of typical size gives:

.fIT, + ~}

FSEs FSEr

2

=

{I

2d

.fIT,{1+~}2 2 2d

where; FSEs = FSET = d H =

the base shear correction factor the overturning moment correction factor water depth the most probable maximum wave height (Hmax or Hmpm)

Similar expressions may be derived for different wave stretching algorithms.

Commentaries to Recommended Practice for Site Specific Assessment of Page 128 Mobile Jack-Up Units Rev 2, Jan 2002 C7.3.7 For a jack-up subjected to wave and current loading these factors should be used to scale the MPM responses prior to combination with the mean (wind) response to form MPME.

C7.4

SELECTION OF APPROPRIATE EXCITATION PERIOD Sections 7.3.3, 7.3.6, 7.3.7 and 7.4 of the PRACTICE require that an appropriate selection of excitation period is made. In making the selection consideration should be given to the position of the natural period(s) in relation to the cancellation and reinforcement points in the global wave loading of the jack-up which is important for the magnitude of any dynamic wave magnification. Cancellations and reinforcements in global loading are due to spatial separation of the wave load attracting legs and may be different for different wave directions. The global loading may be characterized by the total horizontal wave loading or overturning moment; cancellation and reinforcement of points for these may appear at slightly different wave periods. Figure C7.1 presents the periods at which first and second cancellations and reinforcements occur in the total wave loading. It is valid for the main wave directions of 3 and 4 -legged jack-ups in water depths exceeding 30m. The calculation of natural period(s) is subject to uncertainty as a result of uncertainty in the parameters affecting the natural period. In order to avoid the possibility of underconservative dynamic amplification factors, it is important to investigate the relationship between the jack-up natural period and the cancellation and reinforcement points in the transfer functions relating wave height to base shear and overturning moment [1]. The range of possible natural period(s) should be bracketed and compared with the relevant cancellation/reinforcement points in the global wave loading. The natural period(s) used in the dynamic analysis should be selected such that a realistic but conservative value of the dynamic response is obtained for the particular application envisaged, avoiding maximum dynamic amplification to coincide with minimum environmental loading. Figure C7.1 may be used for a first evaluation of the position of the calculated natural period(s), but it is recommended that the definitive selection of natural period(s) be based on the shape of the global horizontal wave loading (base shear) and overturning moment transfer functions calculated for the actual application under consideration. When the natural period occurs at a cancellation point in the transfer functions, the mass or stiffness should be adjusted in a logical manner to move the natural period away from the cancellation point. If the analysis is for pinned footings with maximum hull mass, then the adjustment

should be made by reducing the hull mass (within the normal range) and/or by introducing a degree of rotational fixity at the seabed. If the analysis is for a case with footing moment fixity, then the adjustment would most

logically be made by varying the degree of rotational fixity at the seabed. To minimise cancellation effects, it is suggested that the dynamic analysis may be carried out for a single wave heading along an axis which is neither parallel nor normal to a leg line. Thus, for a 3-legged unit with equilateral leg positions and a single bow leg, suitable analysis headings would be with the environment approaching from


Page 129

C7.4

approximately 15° or 45° off the bow. The dynamic amplification factors (DAP's) should be determined for one, or both, of these headings, with suitably adjusted natural period. The DAP's (or more conservative DAP's) may then be applied to the final quasi-static analysis for all headings and hull weight cases with, when applicable, nonlinear fixity iteration according to Section 6.3.4.1 of the Practice.

C7.5

METHODS FOR DIRECT DETERMINATION OF THE DYNAMIC RESPONSES Section 7.3.7 of the PRACTICE outlines some of the considerations which are relevant to direct methods for determining the dynamic responses. Appendix C7.B provides further details of appropriate methodologies, together with flowcharts indicating their implementation. An overview of the applicability of various modeling combinations is given in Table C7.1 (overleaf). For applications incorporating linearised foundation fixity in the dynamic analysis, the methodology of Appendix C7.B.2.1 is recommended using the time domain approach per Appendix C7.B.l.2. For applications incorporating non-linear foundation fixity in the dynamic analysis, the methodology needs to be selected with care, to ensure stable results. When the analysis is used solely to determine DAP's it is probable that a time domain simulation of appropriate duration using the approach per Appendix C7.B.l.2 will be sufficient with the extremes determined using the methodology of Appendix C7.B.2.l. However, if the analysis is to be used to directly determine the extremes of other responses, then the methodology of Appendix C7.B.2.4 is recommended using the time domain approach per Appendix C7.B.l.2. This is because the results from the noninear fixity analysis (where non-linear foundation response occurs) are dependent upon the load history experienced by the foundations. Consequently, the analysis should be carried out for a number of load histories in order to determine a reliable extreme value.


Analysis Level

Simple full results not available directly

Linear

Model of the Environmental Excitation (alwavs nonlinear) Random Frequency Time Periodic domain Domain A B

Nonlinear

Unsuitable

Linear

Generally not recommended

Structural Model

SDOF

MDOF Nonlinear

Complex full results available

Page 130

Linear MDOF Nonlinear

Generally not recommended

Unsuitable C E

D C

E

D

Notes: A -

Combines a simplistic model of the structural system with a simplistic model of the excitation.

B -

Is a refinement of case A. It remains simplistic to execute and lends itself to both frequency and time domain methods. In the latter method the main nonlinearities in the excitation can be retained and therefore non-gaussian effects in the random response can be ed for. Same limitations as for case A.

C -

Is a simplification of case D, if linear modeling of the structural system is a sufficiently accurate representation.

D -

Is the more complete and accurate representation of reality, but also the most complex. This is a necessary combination for a detailed evaluation of the dynamic behavior of a jack-up. Both random time and frequency domain methods can be used; the latter requires some approximation in the form of appropriate linearization of nonlinear and, therefore, the former are the most suitable.

E -

Incompatible combination.

Table C7.1 : Recommended combinations of the structural system and environmental excitation models for a dynamic analysis


Page 131

Wavp. Pp.riod in ItP.lation to Wave !,'orce Cancellation and ReinforcemeDt 12 11

10

-.

"

----I

I

-

.....---.. ..1.

~~--

9

-

~-'

H

II>

'tl 0

-c CI c..

'"

> cu

~

_1Y---~

5

4

.--.-~.-

----..

... .

...---T

v--.

1,...--..............

5

~

----- >--1 .....---r -h----r-=:- .-..-----'-----~ ._-

7

~

~--

r~.----r

3

;,--

2

o o

20

10

30

40 ~S~acinJr

.. 1st Wave Fllrce Canc:eUauon Waterdepth :: 30 m -()- 2nd Wave Fon:e

CaDCellation Wsteniepth ;. 30 m

£I'

50 [m I

70

60

80

90

..- 1st WavE Force lal Wave Foree :ReinCorcem~nt Cancellation Waterdepth ~60 m Waterdepth .. 30 m

-.. 2nd Wave Force

Reinfon:emeDt

Waterdepth ~30m

Nate: See sketches below for definll.lons.

WAVE (1) \

Horizontal Wave Force on _Jack-up Ri~

\

WAVE (1) _ _

WAVE (2)

t--- Leg Spacing -

T lot

.. .. s::

WAVE (1)

U

4-Leiif!d Ril'

c.

In

bIl

1

,.:i

1 -

Wave Frequency

Wtlve Peried

-

I

WAVE (1)

Figure C7.1 : Periods for wave force cancellation and reinforcement as a function of leg spacing

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 APPENDIX C7.A - DERIVATION OF JACK-UP STIFFNESS EQUATION

Page 132

To determine the natural period of a jack-up, the effective lateral stiffness seen by a horizontal load acting at the level of the jack-up hull is required. To determine this stiffness the following effects which cause hull lateral deflections are considered: 1. bending of the legs, leg-soil and leg-hull rotational stiffness. 2. shear defonnation of the legs. 3. axial defonnation of the legs. 4. hull bending defonnation. 5. horizontal soil and leg-hull connection stiffness. 6. vertical soil and leg-hull connection stiffness. 7. second order P-~ or Euler amplification. Effects 4, 5 and 6 may readily be considered by means of modifications to tenns in the stiffness equation that can be derived for effects 1,2 and 3. Taking each effect in turn:

1. Bending of the legs, leg-soil and leg-hull rotational stiffness. Consider one leg as shown in the Figure: F E v I E,v E,As

As L Krh

L

Krs Mh Ms The bending equation may be written for any section z-z as: Mzz = F.z - Ms substituting the general equation of flexure:

a2 x

EI az 2 = -M zz = Ms - Ez

hence:

Apply the boundary condition: Hence:

ElMs B =OandA=-K rs

ax

Ms z=O x=O - = -

,

'az

Krs

shear transmitted from the hull Young's modulus Poisson's ratio second moment of area of leg effective leg shear area length considered leg-hull connection rotational stiffness = leg-soil connection rotational stiffness = moment on leg-hull spring = moment on leg-soil spring

= = = = = = =

Page 133

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 The deflection at any point is then given by: Ms .Z2 F.z 3 Ms .z.EI EIx = - - - + --"--

2

6

(1)

Krs

To detennine Ms, apply the boundary condition: z = L, Mb

ax =Mh=F.L - Ms, -a z

Krh

also from (1):

ax az

Ms.Z

F.z 2

Ms

EI

2EI

K rs

F.L2

ms

2EI

K rs

-=-----+Thus when z

=L:

ax Ms.L az - EI

Mh

F.L- Ms

-------+-------"-

Krb -

Krb

rearranging:

(2)

The deflection XLB at x Ms .L2 x

-

LB -

2EI

=L, due to bending is (from (1)): Ms.L

F.e

K rs

6EI

+-----

Rearranging and substituting from (2), the effective bending stiffness, KB obtained thus:

=F/xLB, at z =Lis

e 6EI

-1

e

KB--

6EI

After rearrangement and manipulation:

3EI/e

KB = ---,,-------:3L

3(EI)2

(3)

Page 134

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 2. Shear defonnation of the legs.

Considering the shear force at any section zz is constant, the deflection XzzS due to shear is: Xzzs = F.z/(As·G) but: G = E/{2(1 + v)} and, for steel, v = 0.3 hence: Xzzs

=2.6F.z!(As.E)

(4)

and the shear stiffness, K s , when x = Lis: F As.E Ks=-=-XLS 2.6L

(5)

3. Axial defonnation of the legs. A) Consider a 3-leg jack-up, and assume that the legs are placed at the vertices of an equilateral triangle. The shear applied to the hull is 3F, i.e. F acting on each leg. - - -..... 3F

A A

A

L

---y-

x

Case 2

Case 1 3.F.L - 3.Mu - R.Y =0 thus:

3.F.L - 3.Mu - R.X =0 thus:

R

=

R

=

Oaxial

=

applying Hook's law: Oaxial

=

3(EL - Ms )L A.E.Y

The resulting hull rotation is: Shull = 3.Oaxia1l(2.Y) 9(EL- Ms)L = 2A.E.y2

=

3(EL- M s)L A.E.X

2.oaxiallX 6(EL- M s)L = A.E.X2

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 and the horizontal hull deflection is: ~horz = 8hul1.L ~horz = 8hulI .L 9(F.L- M s)L2 6(F.L- Ms )L2 = = 2A.E.y2 A.E.X2 If X

Page 135

yJ3 =Y/cos30 = -2-

9(F.L-MJL2 = ~horz 2A.E.y2 i.e. assuming an equilateral hull, the two loading directions yield the same horizontal displacement at the hull: 9(F.L - Ms )L2 (6) = 2A.E.y2 B) Consider an N-Iegjack-up, where N = 4, and assume that the legs are placed in two parallel rows. The shear applied to the hull is NF, i.e. F acting on each leg. Applying similar methods as above: ~horz

=

4(F.L- M s)L2 A.E.y 2

(7)

where Y is the distance between the windward and leeward leg rows. Comparing equations (6) and (7), it can be seen that (6) is a factor, Fg , of: Fc>e = (9/2)/4 = 1.125 larger than (7). The effective horizontal stiffness due to axial deformation, K A , rearranging (7), including Fg and substituting for Ms from (2) is: KA

= =

F ~horz·Fg

A.E.y2 14FgL2

{L L' } L- {IlL} Krh + 2EI

Krs + Krh + EI

=

A.E. y2 14FgL3

{E1 L} {El EI } K rs +"2

-+L+Krs Krh

(8)

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 4. Hull bending deformation.

Page 136

Assume that the hull can be represented by equivalent beams ing the legs, of typical bending stiffness IH :

I

2 I

y If it is assumed that the hull deflects in double-curvature under the influence of the moments transmitted by the leg-hull connection springs, and that the rotational deflections at the two sides are equal (the side with higher stiffness has two legs acting on it) we can write, for one half of the beam: M.(Y /2)

e

=

E.I H

Hence the hull rotational stiffness Khu1h = Mle = 2E.lHIY If this stiffness is considered as acting in series with the leg-hull connection spring Krh , the modified stiffness is:

K 1I(_I_+_I_J Krb K rh

'

=

hull

Rearranging, and substituting for Khull gives: K rh ' =

Krh/(1 +

Y.Krh

)

2E.I H Hence the modification factor Fro to be applied to the leg-hull connection stiffness, Krh , to for hull flexibility is: 1 (9)

=

{I+

Y.Krh }

2E.I H

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 5. Horizontal soil leg-hull connection stiffness.

Page 137

The horizontal soil and leg-hull connection stiffnesses, Khs and Kbh, may be considered to act in series with the lateral stiffness due to leg shear deformation (AsGIL). The combined stiffnesses is then: Ks'

=

( L 1 1)

11 - - + - + AsG Khs Khh

rearranging, gives: Ks'

=

AsG AsG (AsGIL)/(l + - - + - - ) LKhs LKhh

=

(AsGIL)(l +

As·E + As·E ) 2.6L.K hs 2.6L.K hh

If it is considered that the modified leg deformation stiffness Ks' is linked to the unmodified value by a factor, Fh: 1

=

(10)

6. Vertical soil and leg-hull connection stiffness. The vertical soil and leg-hull connection stiffnesses, Kvs and K vh , may be considered to act in series with the axial stiffness due to leg axial deformation (AE/L). The combined stiffnesses is then: =

1I(~+_1_+_1-J AE

Kvs

Kvh

rearranging: =

AE AE (AE/L)/(l + - - + - - ) LKvs LKvh

If it is considered that the modified leg deformation stiffness KA ' is linked to the unmodified value by a factor, Fv: 1 (11) l+_AE +_AE } { L.Kvs L.Kvh

=

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 7. Second order P-L\ or Euler amplification.

Page 138

The deflection will (approximately) be amplified by a factor (1 - [PIPED due to second order effects. The Euler load, P E, may be derived as follows, ing for the soil and leg-hull connection rotational springs: ~p

E,I

L

z z

P E I L Krh

== == == == ==

Krs

==

Mh Ms Xh

== == ==

axial load in leg Young's modulus second moment of area of leg length considered leg-hull connection rotational stiffness leg-soil connection rotational stiffness moment on leg-hull spring moment on leg-soil spring hull deflection

The bending equation may be written for any section z-z as: Mzz == P.x -Ms substituting the general equation of flexure:

iPx

EI-2 ==

-Mzz == Ms - P.x

ax az

Ms E.I

az

hence: 2

P.x E.I

-+ -=2 let Jl2 == PIE.! hence:

aaz x + Jl - (x - p) Ms =0 2

ry

(12)

2

The solution to (12) is:

pMs

(13)

ax . + JlB.CosJlZ az == -JlA.SmJlz

(14)

x == A.CosJlz + B.SinJlZ +

differentiating (13):

When z == 0, x == 0 and hence, from (13), A == -MsIP Ms When z == 0, -a = and hence, from (14) B == MsI(Jl.Krs )

ax

z

Thus: and:

Krs

-Ms Ms. Ms x = --.CosJlZ+--.SmJlZ+P JlK rs P JlM s . Ms -ax =--.SmJlZ + - .CosJlZ

az

P

Krs

(15) (16)

Commentaries to Recommended Practice for Site Specific Assessment of Page 139 Mobile Jack-Up Units Rev 2, Jan 2002 Apply boundary conditions at leg-hull interface to derive the equation yielding the Euler load: Whenz=L, and

ax = az x =Xh

Mh Krh

(17) (18)

also

(19)

From (16) and (17): Mh ~s Ms -=--.Sin~+-.Cos~ Krh P Krs From (15) and (18): Ms Ms Ms Xh= --.Cos~+--.sin~+P J.LK rs P Substituting (21) into (19) gives: P.M s Mh= -Ms.Cos~+--.Sin~ IlK rs Mh P hence: = --.Sin~- Cos~ Ms IlKrs Rearranging (20) gives: Mh J.LK m Km -=--.Sin~+-.Cos~ Ms . P Krs Equating the (22) and (23): Sin~

(21)

(22)

(23)

P IlKm ---} =Cos~{Km 1 + -} {Il.K rs P K rs {

or:

(20)

TanJ.1L =

I + Km}

K rs _P _ { Il·K P rs

IlKm}

(24)

Notes: 1. When Krs = 0, and Krh = 00, (24) reduces to Tan~ = 00 i.e. ~ = rrJ2, 3rrJ2, 5rrJ2, ... The smallest finite value satisfying (24) is rrJ2, thus J.1L = rrJ2 and 112 = P/(EI) hence: PE =JiEI I (4L2)

Page 140 Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 2. When Krs = 00, and Krh = 00, (24) reduces to Tan~L = 0 i.e. ~L = 0, n, 2n, 3n, ... Rejecting the first value (~L = 0) as this give PE = 0, the smallest value satisfying (24) is ~L=n

hence: PE

= n2EII L2

3. For finite values of Krs and Krh the Euler load may be determined using a graphical solution. For example: 2.65 X 10lO Nmlrad Krs 5.30 x 10lO Nmlrad Krh 2.10 x lOll N/m2 E I 7.45 m 4 L 100m From equation (24) the LHS = Tan~L = Tan100~ (Note (Krs + Krh )~EI theRHS = (~EI)2 - (Krs .K rh )

~

is in radians/m)

124.4/J 2448~ 2 -1.4045 Plotting these as shown in Figure C7.A.1 the smallest non-zero value in the example is ~1 = 0.018248. Thus the Euler crippling load is: PE = (0.018248iEI or, in the more general form: PE = 0.337389n2EI/ L2

10

\ \

8 6 4

2

fu(]t )

0 -2 -4

-6 -8

....",., 0

/

J

r

,

•

I'-..

~ ~

1'-1

-0.01 ......... ........

ol~

~

/

I

:li2 ~

0.03

i'Jr' (\ 1\

f Ii

-

~.

,£

'~~

I(

\

-10

"

(radlm)

LHS-Eqn. (24) -

RHS-Eqn. (24)

Figure C7.A.1 Graphical solution of equation (24)

"h6

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 COMBINING EFFECTS 1 TO 7 ABOVE:

Page 141

For the leg under consideration, all the effects can be combined by considering the components as springs in series, thus Ke, the effective spring stiffness for one leg is deduced from: 1 1 1 1 -=-+-+Ke KB Ks KA where the stiffness K B , Ks and KA are derived in (3), (5) and (8). Rearranging and including the Euler amplification effect:

=

3L 3(EI)2 4 LKrsKm lEI EI -+L+Krs Km

--

3EII rJ

=

2.6L

--

EI L -+Krs 2 EI EI -+L+Krs Krh

3(EI) 2 3EI 3L 3(EI) 2 -3 L3K + 2L2 7.81 4Fg L 4 LKrsKm rs +--+ IEI EI EI As.L2 AEy2 EI -+L+-+L+Krs Krh Krs Krh

Commentaries to Recommended Practice for Site Specific Assessment of Page 142 Mobile Jack-Up Units Rev 2, Jan 2002 If the correction to Krh , As and A which are Fr, Fh, and Fv as defined in (9), (10) and (11) respectively are included:

If the foundation is effectively pinned, and Krs = 0, the equation can be simplified as follows

(multiply top and bottom of central term in denominator by Krs , and then set Krs =0):

3EI[1_~] K

IJ

=

e

1+

12Fg I 2

P E 3EI

+

7.81

+

2

FyAY FrLK rh Fh.As.L If the foundation and leg-hull connection are effectively encastre, and Krs =Krh =00, the equation can be simplified as follows (note that the Fr term to incorporate hull stiffness has vanished, as its definition relies on a finite value of Krh ; if an alternative definition were applied, its effect could be retained).

12EI[l_~] L3 P

=

K e

1+

24Fg I 2

E

31.21

+

2

FyAY Fh.As.L In the absence of any of the for effects other than bending (i.e. setting A and As to infinity), this further reduces to 12EIIL3 , which is as expected for a beam, encastre at each end, with one end free to slide.

Commentaries to Recommended Practice for Site Specific Assessment of Page 143 Mobile Jack-Up Units Rev 2, Jan 2002 APPENDIX C7.B - DETAll.S OF APPROPRIATE DYNAMIC ANALYSIS l.\1ETHODS Section 7.3.6.1 of the PRACTICE provides a simple approach to determining the dynamic response, based on the SDOF approximation. Sections 7.3.6.2 and 7.3.7 of the PRACTICE outline more complex approaches and some specific recommendations are included in Tables 7.1, 7.2 and 7.3. It should be noted that the basic analysis may be carried out in either the frequency or time domain and that there are then a number of approaches for determining the required most probable maximum (MPM) response which is defined in Table 7.3 of the PRACTICE as the mode value (or highest point on the PDF with a 63% chance of exceedance). This corresponds to a 111000 probability level in a 3-hour storm. The recommended, more complex, analysis methods are described below, together with appropriate methods of determining the MPME. These may be summarized as follows: C7.B.1

Analysis Methods

C7.B.1.1 Frequency Domain Methods: Use entire RAO (DAP) from simplified SDOF model. Use RAO from multi-degree-of-freedom (MDOF) model, with appropriate linearizati on. Frequency domain methods require the linearization of the wave-current drag loading. It is recommended that the statistical (or least squares) linearization procedure formulated by Borgman is adopted [L.E. Borgman, 'Ocean Wave Simulation for Engineering Design', Civil Engineering in the Oceans, ASCE conference, San Francisco, September 1967]; other forms of linearization may not adequately handle the current velocity, wave induced particle velocity and the structures velocity (if a relative velocity formulation is used). Table 7.2 of the PRACTICE makes some additional recommendations regarding the generation of the random seastate. C7.B.1.2 Time Domain methods: Use simplified SDOF model. Use MDOF model. Time domain simulations require a suitable generation of the random seastate, that the validity of the generated seastate is checked, and that the time-step for the solution of the equations of motion is sufficiently small. It is also necessary to ensure that the duration of the simulation(s) is sufficient for the method being used to determine the MPME. Specific recommendations are given in Tables 7.2 and 7.3 of the PRACTICE. C7.B.2

Methods for Determining the MPME It should be noted that the simpler modeling approaches will not lead directly to the MPME of all quantities of interest. For example, SDOF based models will provide directly only the MPME hull displacement; simpler multi-degree-of-freedom models may provide the MPME of total leg loads, but will not lead directly to loads in individual of a truss-leg.

Commentaries to Recommended Practice for Site Specific Assessment of Page 144 Rev 2, Jan 2002 Mobile Jack-Up Units As a means of circumventing this difficulty the analysis may be used solely to determine the inertial loadset which represents the contribution of dynamics over and above the quasi-static response (see Figure C7.B.l). The inertialloadset is then applied to a structural model of appropriate complexity together with all the quasi-static loads (due to wind, wave!current, weight, etc.) and the required responses determined. The simplest inertial loadset uses a single point load at deck level. The magnitude of this force is calculated to match the inertial overturning moment effects as shown on the right hand side of figure C7.B.l (blocks 18,23, 24, and 25). It is possible to refine this loadset to match both base shear and overturning moment inertial effects by simply determining the magnitude of the loadset to match the inertial base shear and then applying this loadset (single point load) at an elevation such that the inertial overturning moment is matched. However, the use of a distributed inertial loadset is considered more representative and will, in tum, result in a more accurate description of the component dynamic amplification effects as well as the amplification of global responses. The distribution of the inertial loadset is based on the fundamental sway modes and the mass distribution and is determined so that both the global base shear and overturning moment responses are matched. Figure C7.B.l (on the left hand side) outlines how a distributed loadset (2-dimensional response) is determined based on the first two fundamental bending modes (in the same direction) and the mass distribution. An alternative to the inertialloadset approach is to use transfer functions to link known responses with other required responses (for example to determine leg member loads from total leg loads). The derivation of such transfer functions requires the use of appropriately detailed models. Where non-linearities are significant the transfer functions are not linear (and cannot be linearized) and may vary, for example, as a function of the level of leg load(s). The following methods are recommended for determining the MPME: Use of drag-inertia parameter (or equivalent) determined from mean and standard deviation of a frequency or time-domain analysis. Fit Weibull distribution to results of a number of time-domain simulations to determine responses at required probability level and average the results. Fit Gumbel distribution to histogram of peak responses from a number of timedomain simulations to determine responses at required probability level. Apply Winterstein's Hermite polynomial method to the results of time domain simulation(s). Further details of the approaches are given below:

I

Commentaries to Recommended Practice for Site Specific Assessment of Page 145 Mobile Jack-Up Units Rev 2, Jan 2002 C7.B.2.1 Use ordrag-inertia parameter (or equivalent) determined from mean and standard deviation ora frequency or time-domain analysis This procedure relies on the identification of the two components of the total dynamic response, i.e. the quasi-static and the 'inertial' parts. The 'inertial' part is the amplification of the quasi-static part due to dynamic effects, and should not be confused with inertial wave loading. The procedure requires the detennination of the basic statistical parameters of the mean, J..l, and the standard deviation (excluding the mean), cr, of the required response variable(s). In general the root-mean-square, RMS, -:;:. cr, unless J..l = O. The notation MPMR is used to refer to the most probable value of the response minus the mean response, R(t) - J..lR, for a given storm duration. When the mean is included the MPM value is referred to as the most probable maximum extreme of R(t) and denoted by MPMER. The response quantity of interest is indicated by the general notation R; this can be any quantity which is related to the random wave excitation (e.g. base shear BS, overturning moment OTM, etc.) Where necessary to distinguish between different forms of response a second subscript is used as follows: 's' for (quasi-)static, 'i' for inertial and 'd' for total dynamic (quasi-static plus inertial) response. The procedure for estimating the extreme response is shown on Figure C7.B.4, and requires the means and standard deviations of the (overall) dynamic and quasi-static response, and the standard deviation of the 'inertial' response. These can be determined from time domain simulations (Figure C7.B.2) or frequency domain analyses (Figure C7.B.3). Figures C7.B.5 or C7.B.6 form an input to Figure C7.B.4. These Figures are based on [SIPM EPD/51152 Dynamic Analysis and Estimation of Extreme Responses for Jack-Ups', August 1991].

Commentaries to Recommended Practice for Site Specific Assessment of Page 146 Mobile Jack-Up Units Rev 2, Jan 2002 C7.B.2.2 Fit Weibull distribution to results of a number of time-domain; simulations to determine responses at required probability level and,' average the results. This procedure requires a suitable length time domain simulation record for each quantity of interest. The input seastate record should be checked for 'Gaussianity'. Guidance is given in Tables 7.2 and 7.3 of the PRACTICE. The procedure requires the following steps. Step 1 The signal record is first analyzed to calculate the mean, J..lR, as: n

LR(tJ

J..l R where R(tj) ti n

=

= = =

i-...:.l_ _ ..:..

n

time history of signal time points number of useable time points in simulation (discounting the run-in)

Step 2 The individual point-in-time maxima are next extracted according to the following criteria: A maximum occurs at ti if: R(ti-I) < R(tD and R(tj+I) ~ R(tj) Suppose Nmax maxima are found in the extraction. Step 3 From the Nmax maxima, the mean of the signal, J..lR, is subtracted and the maxima R(max,i) are ranked into 20 blocks having mid-points in ascending order. The blocks all have the same width and the upper bound of block 20 is taken as being 1.01 x the largest value, the lower bound of the first block being zero. A distribution of maxima observations is then found, using for each block the Gumbel plotting position in order to obtain the best possible description of the distribution for large values of R. If each block has nj maxima, the cumulative probability Fi to be plotted against the mid point for block i is then given by: j=i-l

)=1

F; =[(1+ Ln)Ln)O.5 /(N max +1) j=O

where no =O.

j=O

Commentaries to Recommended Practice for Site Specific Assessment of Rev 2, Jan 2002 Mobile Jack-Up Units

Page 147

C7.B.2.2 Step 4.a A Weibull distribution is fitted against the cumulative distribution of the maxima as defined under Step 3 (see Steps 4.b to 4.d). The 3-parameter Weibull cumulative distribution function is defined as:

F(R;a,j3,y)

=

F(R;a,j3,y)

= = =

-{R2

I -exp .[

n

where;

a

13 and

y a,j3,CR-y)

probability of non-exceedance scale parameter slope parameter = threshold parameter > 0.0

Step 4.b Only data points R(max,i), corresponding to a probability of non-exceedance greater than a threshold value of 0.2 are used to fit the Weibull distribution, i.e. only the points: [ R(max,i) {

N max - i + N max

I}]

for i>0.2 x Nmax

Notice that R(max,i) are in ascending order. Step 4.c For each of these points, the deviations between the Weibull distribution and the values R(max,i) (transformed to Weibull scales) are calculated as: Oi In[ -In {l-FCR(max,i),a,j3,y)}] - !3[ln(r(max,i)-Y) -InCa)]

=

Step 4.d The parameters a,j3,y are now estimated by a non-linear least square technique, i.e. Nmax 2 0 i is minimized i=O.2Nmax The procedure may be based on a Levenberg-Marquardt algorithm, using the parameters of a 2-parameter Wei bull distribution (found by the maximum likelihood method) as initial estimates.

L

Step 5 The MPM value R MPM is found as the value of R for which: 1 F(R,a,j3,y) 1- { 3 hours }

=

N max· simulation duration Step 6 The total extreme MPM value, R MPME is found as: J..lR + RMPM R MPME where J..lR the mean value of R established in Step 1 R MPM (excluding the mean) established in Step 5.

=

=

Step 7 The procedure is repeated for each required response parameter.

= the

MPM value

Commentaries to Recommended Practice for Site Specific Assessment of Page 148 Rev 2, Jan 2002 Mobile Jack-Up Units C7.B.2.3 Fit Gumbel distribution to histogram of peak responses from a number oftime-domain simulations to determine responses at required probability level. The basic assumption of this method is that the 3-hour extreme values follow a Gumbel distribution:

P''(x)

= exp [-exp{_ x ~

\jI}]

where; = the probability that the 3-hour maximum will not exceed value x. = location parameter = scale parameter

The following steps are followed for each required response parameter: Step 1 Extract maximum (and minimum) value for each of 10 3-hour response signal records. Step 2 A Gumbel distribution is fitted through these 10 maxima/minima. This is done using the maximum likelihood method, yielding \II and K. Step 3 The Most Probable Maximum Extreme is found according to:

MPME

=

\jI -

K

In {- In{P" (MPME))}

with; p3h

(MPME) = 0.37

The 0.37 lower quantile is used because the extreme of recurrence of once in 3 hours will have a probability of exceedance of 0.63 (= 1 - 0.37). In this case it can be seen that:

MPME

=\11

Step 4 The procedure of Step 3 is similarly applied for minima.

Commentaries to Recommended Practice/or Site Specific Assessment 0/ Page 149 Rev 2, Jan 2002 Mobile Jack-Up Units C7.B.2.4 Apply Winterstein's Hermite polynomial method to the results of time domain simulation(s). For Gaussian processes, analytical results exist for the determination of the MPM values (e.g. MPM wave height = 1.86 x significant wave height). For general noninear, non-gaussian, finite band-width processes, approximate methods are required to generate the probability density function of the process. The method proposed by Winterstein [Winterstein S.R., 'Non-Linear Vibration Models for Extremes and Fatigue', Journal of Engineering Mechanics, Vol. 114, No 10, 1988] fits a Hermite polynomial of gaussian processes to transform the non-linear, non-gaussian process into a mathematically tractable probability density function. This has been further refined by Jensen [Jensen, J.J. Dynamic Amplification of Offshore Steel Platform Responses due to Non-Gaussian Wave Loads', The Danish Center for Applied Mathematics and Mechanics Report No 425, May 1991, Submitted to Journal of Structural Engineering, ASCE] for processes with large kurtosis. This procedure requires a suitable length time domain simulation record for each quantity of interest. The input seastate record should be checked for 'Gaussianity'. Guidance is given in Tables 7.1 and 7.2 of the PRACTICE. The calculation procedure to determine the maximum of a time series, R(t), in duration T is as follows: Step 1 Calculate the following quantities of the time series for the parameter under consideration: Il = mean of the process 0" = standard deviation a3 = skewness C4 = kurtosis Step 2 Hence construct a standardised response process, Z = (R - Jl)/O". Using this standardised process, calculate the number of zero-upcrossings, N. In lieu of an actual cycle count from the simulated time series, N =1000 may be assumed for a 3-hour simulation. Step 3 Compute the following quantities from the characteristics of the response parameters identified earlier: h3 = a 3 1[4+2~{1+1.5(a4 -3)}]

= [~{1+ 1.5(a K

=

4 -

3)} -1] 118

Commentaries to Recommended Practice for Site Specific Assessment of Page 150 Mobile Jack-Up Units Rev 2, Jan 2002 Step 3 It is necessary to seek a more accurate result by determining the solution of the following equations for C I , C2 and C3: cr2 cr3a3 4 cr CX4

2 2 = C l + 6C I C3 + 2C2 + 15Cl = C2(6C/ + 8cl + 72C I C 3 + 270Cl) 2 4 4 2 4 = 60C2 + 3C l + l0395C3 + 6oc l 2cl + 4500C 2 Cl + 630C l Cl + 936C l clc 3 + 3780c l cl + 60C l 3C 3

using as initial guesses: CI C2 C3

= = =

crK(1-3h4) crKh3 crKh4

with cr, K, h3 and h4 from above. Following the solution for CJ, C2 and C 3, the values for K, h3 and h4 are computed as follows: K h3 h4

= = =

(C I + 3C3)/cr C2/( crK) C3/( crK)

Step 4 The most probable value, U, of the transformed process is computed by the following equation:

u

=

210

ge

(N' simulation3 hours J time (in hours)

Where U is a Gaussian process of zero mean, unit variance.

Step 5 The most probable maximum, transformed back to the standardised variable, z, is then given by: 2 ZMPM K[U + h3(U - 1) + h4(U3 - 3U)]

=

Step 6 Finally, the most probable maximum extreme in the period T, for the response under consideration, can be computed from the following equation: RMPME Il + crZMPM

=

;:S:(J

C)

C)

~~

Notes with Figure C7.B.1 - Part 1

two global responses are necessary:) R Is base shear BS, denoted S, and ( overturning moment OlM, denoted T

General

::::.:~ ~

('")

=

=

=(DAF3s - 1) mpmess F11&~

M11

=(DAF3T -1) mpmeTs

~

Establish a set of 2 19 simultaneous equations of 2-D mode shapes, nodal masses and (unknown) model scalars

M11 1

Determine equivalent 23 Inertial force F21 at deck level producing M1i F2i M11/h

M11

~

=

20

~ ~

8 ~

~

~

!} ~ ~ ~.

~

~

.., ~ ~

~ ~

'$

Ae blocks 17 and 18: The input to these blocks is obtained from Figure C7.B.4 ~ ('") (blocks 14, 15 and 16). Note that DAF3T will be greater ~ ~ than DAF3s. This is in agreement with experience and.N ~ ~ ~ ed by theory. Ae block 19: An outline calculation of the distribution of F1 i over height § ~ is given in Figure C7.B.1 (Part 2). N ~ Ae block 23: The force F2i follows directly from the increase in OTM ~ and the height h at which F2i is applied above the N <..::;., effective hinge or fixation points of the legs Therefore this does not require knowledge of the mass distribution and mode shape. Ae block 24: The excess F3i in representing the dynamic base shear is calculated as general verification. If F3i is found to be relatively large compared to the dynamic base shear it is recommended to follow the path on the left instead of the path on the right. A criterion for this should be set by the ; as a suggestion the excess should not be greater than up to 5% of the dynamiC base shear.

2

Solve the equations of block 19 to determine the scalars Q; and ~

+a,p Calculate the Inertial load set Ifn using the equation Fin a.q>lM + Pq>2M

~

:::

~

By contrast, the path on the right chooses to match the dynamic overturning moment by an inertial force in the form of a point load at deck level. This is a very reasonable approximation of the inertial loadset, for cases where the mass of the hull is much larger than the masses of the legs and the mode participation factor (the relative horizontal displacement of the vibrating jack-up) is also largest at the deck elevation. The inertial point load thus determined is again not equal to the difference in dynamiC and static base shears; generally it overmatches the dynamic base shear. In this case the remaining excess force is not compensated for (as was possible for the path on the left) and must be accepted as an element of some conservatism.

choose to match either F11 and M11 or Just M11 ~M11

Fll

+

The figure shows two possible paths. The path on the left through blocks 19 to~ 22 matches the dynamic base shear and the dynamic overturning moment, by ~ making up the difference between the dynamic and static base shears by a~. distributed inertial force. This distributed inertial force is established by an t;j appropriate combination of structural mode shapes and lumped masses. The basis for the calculation is that the base shear and overturning moment inertial effects are simultaneously matched and combined in phase with the quasi-static loads such that the levels of total global response are maximized.

Determine Increase In 18 OTM due to dynamic effect M11 mpmeTd - mpmeTs

~

~;::J. I

17 Determine increase In BS due to dynamic effect F11 mpmesd - mpmess

~

S:i'~

F21 21

24

F11

Determine excess In BS as conservatism F31 F21- F11

~

I

=

=

I

+Fin 22

25

Loadset Is point load F2i at deck level

Loadset Is distributed load vector Fin --

- -

-

-

---

-

i

F21

.-

Figure C7.B.l, Part 1 - Procedure for determining inertialloadset

~

~ ...... v. ......


Page 152

JACK-UP

7f-----. Mass (Mj)

Mass distribution

+

Fust bending mode (
Notes with Figure C7.B.1 - Part 2 Procedure for Determining (Distributed) Inertial Loadset. The extreme inertial load will generally be three dimensional in nature. It should be noted that vertical dynamic response effects are not normally significant for storm conditions. It is assumed that the response of the Jack-up under combination of wave/current and inertial loading will be in-line with the applied wave and current actions. Hence a 2-D response is considered along one of the global structural axes. The first two bending sway modes (i.e. global modes rather than local leg bending modes) acting along the selected axis are combined to form a pair of simultaneous equations which match both inertial base shear and overtuming moment. Base shear is given by the product of mass and assumed acceleration profile, and overtuming moment by the product of mass, assumed lateral acceleration profile and lever arm above footing level i.e.

where

M1i F1i M1 i F1 i $1 $2 M Z a and J3

a$1 MZ+J3«1>2MZ a$1 M+J3«1>2M is the global inertial overtuming moment (zero mean) is the global inertial base shear (zero mean) is the first global swaylbending mode shape is the second global swaylbending mode shape is a matrix of structural masses is a vector of pOint elevations above footing level are scalars

(1 )

Global inertial responses are calculated from the global response OAFs generated by the dynamic analyses, combined with the design wave and current load i.e. F1i = (DAF3s-1)mpmess M1i = (DAF3r-1)mpmers (2) where OAF3Ts is the global overtuming moment OAF (using mpme responses) DAF3s s is the global base shear OAF (using mpme responses) M1i is the maximum design wave and current overtuming moment F1 i is the maximum design wave and current base shear mpmess is the most probable maximum extreme static shear mpmers is the most probable maximum extreme static overtuming moment The simultaneous equations (1) are solved for scalar multipliers a and 13, which are used to calculate the inertial load set i.e. Fin = a $1 M + 13 «1>2 M (3) • In its current format, Fin is a distributed load vector consisting of horizontal forces applied to each pOint mass in the structure. Equations (1) to (3) can be readily adapted such that the inertial load is fully three dimensional in nature, by using the first and second global (3-0) sway modes along both horizontal axes, and extending equation set (1) to 4 components.

I I

Jack-up structures exhibit several unique properties which allow the use of a simplified inertial load set calculation procedure. For the majority of units, approximately 80% of the total system mass (including added fluid mass) effectively acts at the hull COG. In addition, the mass and stiffness distribution results in the ratio of the first and second bending/sway mode periods for each principal direction being in excess of 5. This leads to the resonant component of response being largely confined to the fundamental modes in each direction (sway and surge), with a potential contribution from the first torsional mode (yaw). On this basis, and assuming torsion can be ignored, equation set (1) can be reduced: M1 i aOtiMHZH F1i aOtiMH (4) where OH is the first mode shape ordinate at the hull COG MH is the point mass acting at the hull COG ZH is the elevation of the hull COG above footing level We can clearly relate the second of equations (4) with the inertial load set given in Section 7.3.6.1 of the Practice.

Figure C7.B.1, Part 2 - Procedure for determining

Page 153

1

2

Perform quasi-static lime domain sirnulaUon to determine Ule response Rs (t)

Perform dynamtc time domain simulation to determine the response Re' (t)

R(t'. !j. • )

Subtract tho tVliO to determin e the time series of tha "inertial" response R i (t) = Rd(t) - Rs(t)

3

Ai (t) Perform statistical 4 analysis on R.. (1) to determine mean and std. dev.cr R5 ~ • o static response

IlI1

Perform stat~stical s analysis on R i (t) to determine mean ~lR' and std. dev.aflj Of "inertia!"' response

Perform statislical G anafysis on Rd (l) to determine mean Jl'Rd nr.d s.ld. dev'O'Rd of dynamic response

Specific notes with Figure C7.B.2 General The procedure for estimating the extreme response due to hydrodynamic loading shown in Figure C7.B.4 requires knowledge of the mean and the standard deviation of the quasi-static and dynamic responses, and the standard deviation of the "inertial" response. A time domain procedure may be used to determine these. Re blocks 4, 5, 6:

The mean of the "inertial" response is not used in the procedure. In most cases the mean of the static response will be (approximately) equal to the mean of the dynamic response. Therefore, the mean of the "inertial" response will be (approximately) zero. This may serve as a check on the simulations performed. However, under certain conditions the means may truly be different. this can most clearly be seen when relative velocities (Le. the wave indUCed water particle velocity minus the structure's velocity) are used to perform the dynamic simulation.

Figure C7.B.2 Time domain procedure for determining mean and standard deviation


Page 154

Perlorm dynamic 2 frequency domain analysis

Perfonn quasi-static frequency domain analysis to delennine mean J.I. As of stalic response ~nd stalic transfer luncLion HR , (.,) under iineruised wave + currenlloadinQ

10 determine mean llR.

I---

of dynamic response and dynamic lransi.r function HAd''') under tinearised

wave + current loading

Perlorm complex number 3

~_H....;"'_~

subtraction to determine 'ineniar' transferfune1ion

~

HR;(OJ) • HR. (OJ)' HR,(OJ)

. - - - - , . - - - - - 'i ItAi Perform spectral analysis on HRJro) to determine std. dev. of static response aRlO

Perform spectral analysis on H R, «(I) to determine Sid. dev. of "iner1ial' response URi

HAd

Perform spectral analysis on HR. ("')

to determine std. dev. of dynamic response O'Ad

1 6) Specific notes with Figure C7.B.3 General The procedure for estimating the extreme response due to hydrodynamic loading shown in Figure C7.B.4 requires knowledge of the mean and the standard deviation of the quasi-static and the dynamic responses, and the standard deviation of the "inertial" response. A frequency domain procedure may be used to determine these. In order to reflect the interactions between the current velocity, the absolute wave induced water particle velocity and the structure's velocity (if a relative velocity formulation is adopted) and to linearize the associated drag loading adequately it is necessary to adopt a statistical or least squares linearization procedure as first formulated by Borgman (see Ref. below). Other forms of linearization in frequency domain analysis cannot handle these interactions. For the least square linearization procedure, there only is a mean response in case of a non-zero current. The magnitude of the mean depends on the value of the current velocity and on the standard deviation of the wave induced (horizontal) water particle velocity, both taken at the same elevation z, and subsequently integrated over the full water depth. The wave induced water particle velocity may be the absolute or the relative velocity, depending on which of these is more appropriate for the case considered. The transfer functions HRs(OO) and HRd(OO) between the response and the water surface elevation are similarly dependent on both the wave induced (horizontal) absolute or relative velocities and the current velocities at various elevations. The means mRs and mRd and the transfer functions HRs(OO) and HRd(W), are therefore a function of the sea state and the current sued in the environmental definition. Re block 3:

The transfer function representing the difference between the dynamic and the quasi-static response is only notionally associated with "mass inertial" forces (not to be confused with inertial wave loading). The difference may additionally be due to damping forces and any effect causing (frequency dependent) phase differences between HRd(OO) and HRs(OO). (e.g. associated with multi degree of freedom system responses).

Re blocks 4, 5, 6:

The spectral analyses operate on the transfer functions HRx(W), which by definition represent the time varying part of the response minus the mean, i.e. Rx(t)-I.I.Rx, A similar note on the mean values of the various responses as given with Figure C7.B.2 should be made here. The mean value of the "inertial" response cannot be determined in a frequency domain analYSis and is not required either. However, the fact remains that in most cases the mean of the static response will be (approximately) equal to the mean of the dynamic response. This should again serve as a useful check 0 the analyses performed. From the above general note it can be seen that both means will only be non-zero if there is a current present. When relative velocities are used in the analysis of the dynamic problem the interaction between the current and the relative velocity may be different for the dynamic and the static case, resulting in realistically different mean values.

Reference: L.E. Borgman "Ocean wave simulation for engineering design" Civil Engineering in the Oceans, ASCE conference, San Francisco, September 1967

Figure C7.B.3 Frequency domain procedure for determining mean and standard deviation


rcr:1

).I~

°Ri

Page 155

@

CfF.d I

(jRd O'Ri

I

Calculate correlation coe!f.

CJMS

e·

Dete~mfne Dynamic Amplification Factor 1

O'~

DAFt R

PR =

(j~ - (j~s - O'~ 2GR.<1~

.-

°AII

aRc! =(jRI 9

10

De:ermine mpm-factor for static response Rs

mpm-fac:or for the "inertial" ~esponse RI is assumed to be 3.7

(se9 fig- 4)

1

mpm R C Ai - - - - 3 . 7

rnp~.

CR~=-GAS

._. C R5

Estimate mpm for dynamfc response "

(jll~

{mpm~d)Z - (CRs(jIls)Z + (CRjGRJ +

:

I

i I I

c~

;

PR

2

+ 2P~

i I

O'Ri

;

I

°

I'll

(eFts 0'1'1.) (C",O'fl.)

12

Determine'Dtnamic Amplification Factor 2

CAs Or-s

13

mpmRd DAF2 R = - mpmR•

mpm:>ld

Detenrine mpm·factor ror dynamic response Rd

~Rd

mpm'ld CRd = ...(j-

f1lprn rld

fW

:=--

CAsO'Rs

CAd

'--_.

en. Ons

IlAo

.4

I,

Deterrnioe mpm extrema for 5 tatic response mpme Rs

•

0''''(1

IlRS + C RS

I~

Determine mpm e~treme for dynamic response mpmeRd ==).Irk! + C nd (inc

(lAs

16

mpme n•

Delermirte Dynawic Amplilica:ion Factor 3

mplTc"'d

II'1'meRd DAF3!'1"'---

mpmeRs

Figure C7.BA Procedure for estimating the extreme response

......

(j~4

!lRri


Page 156

Specific notes with Figure C7.B.4 Re block 7: The correlation coefficient pR is theoretically a value between -1 and +1. For virtually all arplications to offshore structures problems it is expected that: Rd > 02RS + 02Ri so that 0 < pR < 1. For rR = 0, zero correlation, the quasi-static and "inertial" responses do not influence one another and will be well separated in the frequency domain. This is generally only to be expected for relatively low natural periods which fall in the (very) high frequency tail of the wave spectrum and where HRs(ro) is also very low. Under these circumstances the variance (or mean square) of the full dynamic response is equal to the sum of the variances of the quasi-static response and the "inertial" response: 02Rd 02RS + 02Ri Geometrically, this means a direct addition of non-overlapping areas of the two parts of the response spectrum. For rR 1, full correlation, the quasi-static and "inertial" responses are fully dependent on one another. The two parts of the response spectrum overlap strongly and will not really be distinguishable. This will increasingly be the case for high natural periods, considerably closer to the peak of the wave spectrum and therefore associated with a region of significant wave energy, and where HRs(ro) is also having appreciable values. Under these circumstances the standard deviation (instead of the variance) of the full dynamic response is equal to the sum of the standard deviations of the quaSi-static response and the "inertial" response: ORd =ORs + ORi Re blocks 8,12,16: Several definitions of the dynamic amplification factor OAF are in use. The purest and most meaningful definition is believed to be OAF1, the ratio of the standard deviations of the dynamic and static responses (block 8), i.e. after eliminating the means which are not affected by dynamic magnification. If the static and the dynamic processes are both gaussian, or to an equal degree non-gaussian, then OAF2 OAF1; however, this will not be the case in general. The ratio OAF3 of the most probably maximum extremes, including the means, is a practical overall measure of the increase in response due to dynamics. Re block 9: The mpm-factor for an arbitrary non-gaussian response is not known. As an engineering postulate it is assumed that this is equal to the mpm-factor for Morison type wave loading on a cylindrical element of unit length. The factor for a nominal number of 1000 peaks (corresponding approximately with a 3 hr storm duration) then varies between the extremes of 3.7 (for inertial wave loading only and hence a gaussian process) and 8.0 (for drag waver loading only and consequently a strongly non-gaussian process). It can be determined on the basis of a drag-inertia parameter or the kurtosis of the response, as shown in Figure C7.B.5 with its associated notes. Note that the factor 8.0 is different from the previously used factor of 8.6. This is due to the fact that in this report the most probably maximum is conSistently used as a predictor for the maximum of a random process. The previous factor 8.6 referred to the expected maximum instead of the most probably maximum. Re block 10: The mpm-factor for the "inertial" part of the response is associated with the dynamic behavior and predominantly of a purely narrow banded resonant nature. Experience has shown (and theory s this) that such lightly damped dynamic processes tend towards gaussianity so that a mpm-factor of 3.7 is a reasonable and confident assumption for engineering purposes. Re block 11: The relationship between the mpm-values is entirely analogous with the relationship between the standard deviations from which the correlation coefficient is determined. However, while it is theoretically proven equation for the standard deviations, it is an engineering postulate for the mpm-values. Re blocks 14,15: It should be recalled that the procedure depicted in Figures C7.B.2 to C7.B.6 is aimed at estimating the extreme short-term response due to hydrodynamic loading only (see General Note 1). Therefore, the effect of wind should be excluded from the most probably maximum extreme static and dynamic responses in block 14 and 15, respectively. Wind is assumed to produce a static load and a static response, and not to influence the dynamic behavior. To determine the ultimate response the mean response due to wind should be determined separately and added to mpmeRs and mpmeRd.

o

=

=

=

Notes to Figure C7.BA

Commentaries to Recommended Practice for Site Specific Assessment of Rev 2, Jan 2002 Mobile Jack-Up Units

Sa

Page 157

9b

Determine std. dey. of static response under hydrodynamic drag

Determine std. deY. of static response under hydrodynamic inertia loading only

loading only (JRs(Cm- 0)

(JRS(CCS

-

0)

calculate drag-inertia parameter for the static response K Rs

Estimate

C RS

from

D - 8.0 O'RS(C m - 0) M .. 3.7 (JRs(Cd .. 0) S2 _

O'~(Cm - 0) + (J~s(Cd .0)

~8

_.

O'Rs(Cm- 0) O'As (Cd" 0)

y

9cI

Read CRs from

Figure C7.8.6

Figure C7.B.5 Procedure for determining the mpm-factor of the static response

Page 158


Specific notes with Figure C7.B.5 Re blocks 9a and 9b: These standard deviations may be obtained from separate time domain simulations in the same manner as shown in Figure C7.B.2 (blocks 1 and 4) or, altematively, from separate frequency domain analyses as shown in Figure C7.B.3 (blocks 1 and 4). The mean values are not required and neither is it necessary to subtract dynamic and static response time series or transfer functions, respectively. Re block 9c: The drag-inertia parameter is defined as the ratio of the magnitude of the drag force to the magnitude of the inertia force due to waves. All relationships given below are valid for the case of zero current, which is used as the basis for the whole procedure in view of the engineering approximations involved. For an element of a circular cylinder of diameter D and unit length, subjected to a periodic wave, the drag-inertia parameter then becomes:

1

K

1

( - P Cd D J!) 1 ( - Cm P 1t D2 a) 2

4

2C d v

2

(1 )

7tC m Da Where v and a are the velocity and the acceleration normal to the element, respectively. As both v and a depend on the wave parameters (wave height, wave period, waterdepth) and the elevation at which the element is located, it is obvious that K is also a function of depth, waterdepth, wave height and wave period. therefore, the theoretical definition of K is only meaningful for Morison wave loading per unit length of the element. The definition of K can be generalized to random instead of periodic wave conditions by replacing the deterministic normal velocity v by the standard deviation of the random normal velocity (Jv and replacing the deterministic normal acceleration a by the standard deviation of the random normal acceleration (Ja. Equation (1) then becomes: K

2C d o v

2 (2)

7tC m D(Ja Using a statistical or least squares linearization procedure in the frequency domain, as developed by Borgman (see notes with Figure C7.B.3), it can be shown that for the wave force on an element of a single member the standard deviations of the two parts of the wave force are as follows:

= = ..J8I":.

(JR(C m 0) 1/2 P Cd D.d (JR(Cd = 0) = p C m.1/41t D2 .(Ja These relationships can be used to determine (J} and (Ja, which can then be substituted into equation 2 to result in:

K

In V-;· (JR

OR (C m = 0)

(3)

(Cd = 0)

With R being the wave force per unit length in a random sea. Equation (3) may subsequently be generalized to apply to any other local or global response R selected for interest. It will be clear that such a generalization is purely an engineering postulate and not founded on theoretical reasoning. It is an attempt to incorporate the important but unknown non-gaussian effects on the maximum response through the assumed similarity with the wave loading process for which the non-gaussian statistics are known. Yet another way to determine the drag-inertia parameter K for a generalized response R is by using the kurtosis of R. The kurtosis is defined through the expected values of the second and fourth order moments of the time simulations of R, Le.: K E {R'1 1 [E {~}f (4) For Morison wave loading per unit length of member the relationship between K and the kurtosis k is (see Ref. 2 below):

4 2 10SK + 18K + 3 K

(3K

2

+ 1)2

or in the inverse form:

Notes to Figure C7.B.5

(Sa)


Page 159

K

(5b)

While K varies between 0 (inertia loading only) and infinity (drag loading only) K ranges from 3 to 35/3. It may now be assumed that the same relationship holds for an arbitrary response variable R. Therefore, if the kurtosis of R is know the corresponding drag-inertia parameter K can be determined. If this is done, separate time domain Simulations for the standard deviations in blocks 9a and 9b are not required but the route through block 93 cannot be follOWed. One enters the diagram in block 9c and must read CRs from Figure C7.B.6 as per block 9d. Both the kurtosis and the drag-inertia parameter may be subject to appreciable statistical variability and their determination may require time domain simulations of substantial length; see Ref. 2 below. Re blocks 9d and ge:

Figure C7.B.6 (referred to in block 9d) is equivalent to the figure that was derived by Brouwers and Verbeek and presented in Ref. 1 below as well as in Figure A1 of the SIPM - Practice (EP 89-0550). However, this latter figure presented the ratio of the expected value of the extreme to the standard deviation for a 1000 peaks, rather than the mpm-factor CR which is the ratio of the most probable maximum value of the response to the standard deviation, which is used in this report. Therefore, Figure C7.B.6 has been recalculated in accordance with Ref. 3 and now truly presents the mpm-factor CR. It should be noted that the figure is valid for a narrow band process, the corresponding ratios for a broad band process being somewhat smaller. Therefore, CR is a slightly conservative estimate for the mpmfactor. This is in accordance with the general principles underlying a simplified engineering method and is well within the accuracy of the overall procedure. An altemative and practical method to estimate K is to apply the engineering assumption for estimating the most probably maximum value of the dynamic response, as used in block 11 of Figure C7.B.4, to separate responses due to hydrodynamic drag loading only and inertia loading only, replacing Rs from block 9 and Ri from block 10, respectively. These two hydrodynamic loading components are fully uncorrelated and so are the responses caused by them; hence the correlation coefficient r = O. Further, the mpm-factor for a totally drag dominated Morison force is 8.0 and for a totally inertia dominated Morison force it is 3.7. With these substitutions the ~uation in block 11 of Figure C7.B.4 becomes: 2 mpmR {8.0 OR (Cm = 0)}2 + {3.7 OR (Cd O)}

=

=

For zero correlation the standard deviation of the overall response is obtained from the equation: 2 OR = {OR (Cm 0)}2 + {OR (Cd = 0)}2 (see note with block 7 of Figure C7.B.4). These are the equations presented in block ge. The comments made with regard to conservatism included in the route through block 9d remain equally valid here. Its determination in block 9c could therefore, strictly speaking be avoided. The input of KRs into block 93 of Figure C7.B.5 is symbolic, representing the implicit use through ORs (C m 0) and ORs (Cd 0), resulting directly from blocks 9a and 9b. In practical applications it is recommended that both routes through block 9d and 93 are followed as a check on the calculations.

=

=

Reference 1: J.J.H. Srouwers and P.H.J. Verbeek "Expected fatigue damage and expected extreme response for Morison-type wave loading" Applied Ocean Research, Vol. 5, No.3, 1983, pp. 129-133 Reference 2: P.M. Hagemeijer "Estimation of drag/inertia parameters using time-domain simUlations and the prediction of the extreme response" Applied Ocean Research, Vol. 12, No.3, 1990, pp. 134-140. Reference 3: J.J.M. Saar Extreme values of Morison-type processes" Report EP 90-33365, October 1990. To be published shortly in Applied Ocean Research

Notes to Figure C7.B.S (cont.)

=

Page 160


/

7 6

~~

~

/

5

V J

4

.......

3

0.01

0.1

10

1

K

100

The equation for the curve is Ref. 3, Specific notes with Fig. C7.B.5

CR

=

. CR < B C R

3.72/.fA (6.91+D)/C

(K < 0.135) (K < 0.135)

If

Where A, B, C and D are functions ofk as follows: A 3K2 + 1

=

B

11

[(2K)~(3K2 +1) ]

~(3K2 + 1) }

C

[

D

l/(8K2)

(2K)

Figure C7.B.6 Ratio CB, of most probable maximum to standard deviation as a function of drag-inertia parameter K for N = 1000 peaks

roD

-

: S~(co) : Sn (co)

--

. SPI4(CO)

~

2

,

,,

I

, ,, , ,, , ",

,

, ,

,\

\

1S=7s

\~ o

o

2

3

ro (radJs)

Figure C7.B.7 Comparison between the normalized spectra Sn(ro), Sm(ro) and S~(ro)


Page 161

REFERENCES FOR SECTION C7 1.

Parker G.J. (1997), 'Calibration of an SDOF-Based Dynamic Analysis Procedure Including Non-Linear Foundation Fixity', Sixth International Conference The Jack-Up Platfonn, Design Construction and Operation, City University, London.

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 CS COMMENTARIES TO ACCEPTANCE CRITERIA

CS.O

BACKGROUND TO PARTIAL LOAD FACTORS

CS.O.l

General

Page 162

Reliability analysis was used in the derivation of load effect factors which are presented in the PRACTICE. All factors associated with strength or resistance have been derived either from consensus (e.g. weight in overturning) within the JUWG or from other relevant codes (e.g. AISC LRFD). The philosophy used in the derivation of the load effect factors is discussed below. Further references on the technique etc. are given in [1], [2], [3] and [4]. CS.O.2

Fundamental Question When a jack-up is offered for operation at a marginal location, a number of issues such as overturning stability, soil capacity and leg strength are addressed to ascertain the fitness for purpose of the jack-up. In all these assessments, it is necessary to establish an acceptable safety margin (or safety factor) between load and resistance. The question is, how do we establish, quantitatively, the safety factor required for the performance assessment?

CS.O.3

Solution Loads and resistances are not uniquely defined due to physical, statistical and methodological uncertainties. Acceptance of this fundamental principle has led to the understanding that the use of safety factors merely assists in maintaining a level of safety. Furthermore, the true goal of assessment is to achieve as consistent a level of safety as possible when the safety factors are just satisfied. This demonstrates the need to perform reliability analysis which would provide a framework to link the safety factors to the safety levels. The various key stages of the analysis are described below:

CS.O.3.1 Probabilistic Description oflnput The code calibration project was performed in two stages. In Stage 1, sensitivity studies were performed to identify the key parameters which influence the response of a jack-up [5], [6]. These showed that significant wave height (Hs), peak period (Tp), drag diameter (CoD), tidal current (VT ) and the permissible interaction ratio for structural elements were important items. The reliability studies, [2], showed that the significance of Tp, CoD and VT was not critical and therefore the variability in these parameters was ignored in Stage 2 studies, [3]. However, it was clear that the largest value of the responses varied between different realizations of the same seastate and it was therefore necessary to for this variability. Thus in the final stages of the study, Hs, the variability in the largest value in a storm and the permissible interaction ratio were considered as variables. The following table summarizes the variables and associated probability distributions used in Stage 2 studies [3]: Parameter Significant Waveheight, Hs Largest value in a storm Permissible Interaction Ratio

Distribution Gumbel Poisson Log-normal

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 CS.0.3.2 Limit States

Page 163

Three limit states, namely, overturning, preload and leg strength were considered. These limit states are recognized to possess some degree of reserve of safety from actual failure. As the PRACTICE is focused upon component failures, and target safety levels were determined from average safety levels of exemplary rigs (see section CS.0.3.5 below), reaching any of the selected limit states does not indicate "true" failure. This is not significant to the code calibration. CS.O.3.3 Response Model A major objective of the JUWG has been to develop as comprehensive an analysis method as possible which reflected the behavior of jack-ups in the elevated condition. The developed method was applied to derive the response parameters required for the reliability analysis. It must be noted that time domain analysis was performed in order to properly capture all the non-linearities in jack-up loading and response. The following table summarizes the key facts associated with the simulations and analysis methodology: • • •

• • • • • • • • • •

0.5s time step used in simulations 3 hour simulations used for MPM 1 hour simulations with correction for response surfaces Hs increased by factor [1 + O.5e<-dl30)]* 75% of max. variable load used in reliability analysis P-Ll effects included Hull Sag and Flexibility included Pinned Foundations Initial leg inclination included in leg strength evaluation. Relative velocity Morison's equation used 4% critical damping (plus damping from above) Jonswap spectrum used Winterstein [7], Juncher Jensen [S] used for MPM .

* This is changed to [1 + 0.5e<-dl25)] in the current draft of the PRACTICE. The following response model, which linked Hs to the safety index (or probability) of exceeding the given limit state in that Hs was derived from three simulations with different but large (near 50-year return) Hs:

f3 =A + B.Hs + C.H/ Once this link was established, then using the probability distribution of the annual extremes of significant wave height, the probability of limit state exceedance in anyone year (or the annual safety index) was computed. CS.0.3.4 Safety Index vs. Safety Factor By repeating the procedures described in CS.O.3.3 for different values of the resisting quantities such as righting moment, permissible interaction ratio and preload a rigllocation specific link between safety factor and safety index was generated (e.g. see Figure CS.O.l). This then permitted the evaluation of the required safety factor for a specified level of safety.

Page 164

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 C8.0.3.5 Reference or Target Safety Level

No absolute target or reference safety level was imposed. Instead, the four rig/location combinations which were, on average, considered to be close to the limit were analyzed using reliability techniques and the target safety level obtained by averaging the individual safety levels achieved by each rig. This process is described graphically in Figure CS.O.l. The process was repeated for each of the limit states considered.

It is not possible to directly compare safety levels achieved by the exemplary rigs with safety levels of other offshore structures. However, the safety levels achieved are broadly comparable.

Average f3 used as target

Safety Factor Figure 8.0.1 : Link between safety factor and safety index

m)

C8.0.3.6 Derivation/Calibration of Safety Factors As noted in section C8.0.3.5, four exemplary rig/location combinations were analyzed using reliability techniques. The reliability analysis was further extended to tropical cyclone locations by simply modifying the statistical distribution of the environmental parameters to reflect the greater variability. The spread in the safety index vs. safety factor curves was shown to be due to the varying levels of dynamicity of the four different rig/location combinations and the environmental variability between North Sea and tropical cyclone locations. The response quantities were split into quasi-static and dynamic components in order to investigate the potential for reducing the spread in safety levels across rigs and locations. The objective of the optimizing function was to minimize the squared difference between the achieved safety index and the target safety index. This approach did show a reduction in spread of safety levels with the use of partial factors, however, as the initial safety index spread itself was small, the decision was taken to adopt a single load factor which minimized the spread whilst maintaining the target safety level as discussed in section C8.0.3.5.

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 CS.l STRUCTURAL STRENGTH CHECK

CS .1.1

Page 165

Introduction Code Basis

Currently, the most widely used codes for structural strength assessment for the offshore industry are based on "working stress design". Examples of commonly used codes are AISC ASD [9] and API RP2A [10]. Due to a number of inadequacies of these codes, there has been a move by their authors to replace them with the "Load and resistance factor design (LRFD)" approach. Although AISC and API allow use of both the "working stress" and LRFD codes in parallel, it is their intention to phase out the "working stress" methods in the future. To follow the trend in the industry, it was decided that the structural strength assessment code to be used in the PRACTICE should also be based on LRFD. Both the AISC LRFD [11] and API LRFD [12] codes were reviewed as bases for jack-up structural assessment. It was decided that the AISC LRFD should be used as the basis for the PRACTICE, for

the following reasons: i) API LRFD covers tubular thoroughly but refers the to AISC LRFD for non-tubular . Since non-tubular are commonly encountered in jack-ups, AISC LRFD offers the greater applicability. ii) Although a limit state code, the equations used in API LRFD are expressed in of stresses and not loads. This would cause difficulties in the integration of AISC LRFD with API LRFD for use in assessment computer programs for the non-tubular cases (see (i)). iii) A parametric study of the two codes for tubular produced results for the AISC LRFD equations (including the n exponent discussed below) similar to those for the API LRFD code. For analysis of a structure using the LRFD approach, it is necessary to define the structure more comprehensively. Certain characteristics which occurred in jack-up structures which could be fitted in with the AISC "working stress" codes had to be dealt with specifically for AISC LRFD. Whether the treatment of these characteristics was correct in the AISC "working stress" code was doubtful and hence the use of LRFD has not created additional problems but has highlighted inadequacies of the previously accepted codes. Particular points of concern include local buckling limit states, hybrid beam-columns and biaxial bending. For the PRACTICE it was desirable to produce a code simple to use, unambiguous and as close as possible to AISC LRFD to avoid the need for validation. Except for the sections on shell , the code uses the same equations as given in AISC LRFD apart from two areas of extension, relating to beam-column biaxial bending and hybrid beam-columns, discussed below. For instance, the same ranges of Dlt ratios have been used as specified in AISC to define the different ranges of limit state. These ranges may not be instantly recognizable since they been given in of Rlt ratios in many places. This is considered more appropriate for jack-up which may contain

Commentaries to Recommended Practice for Site Specific Assessment of Page 166 Mobile Jack-Up Units Rev 2, Jan 2002 partial tubular sections for which a section radius is a more meaningful quantity than a diameter.

Most sections are drawn from the numerous chapters and appendices in AISC LRFD and are placed in a logical sequence. In some cases it has been necessary to interpret which equations are applicable especially in the area of local buckling for beamcolumns. AISC LRFD does not cover very high O/t ratio tubes and tubes with stiffeners, so reference has been made to relevant sections of a different code. The "ONV Rules for Classification - Fixed Offshore Installations" [13] was selected as the most suitable, since this is a limit state code. This document refers the to "ONV Classification Notes - Note 30.1" [14] for obtaining member resistances or strengths. Some guidance on the use of these notes is given in section C8.1.S. Hybrid beam-columns

Hybrid beam-columns are quite common in jack-ups such as chords with high yield stress racks welded to lower yield stress plate constructions. The treatment of hybrid beams of this nature is not adequately covered in AISC LRFD and hence it has been necessary to state rules dictating the method for establishing the axial and bending strengths of such beam-columns. The methods described are based upon engineering understanding of the problem and have been made as straight forward as possible. Limitations

The first limitation, (a) has been stated as a warning that the code given in the PRACTICE must be restricted to the type of geometries as described in section 8.1.4. The intention has been to cover all of the geometries likely to be encountered in jackups although there may be some exceptional cases. If this is so, the must refer to AISC LRFD [11]. One notable exception could be 'I' type sections which are sometimes used in jack house frames. Since AISC LRFD is oriented towards the assessment of 'I' type sections, it is reasonably straight forward to use. It is recommended that the equations given in Appendix H are used for 'I' sections since these should give less conservative results than the general equations in Chapter H. The limitation (b) is stated in AISC LRFD [11] for the reasons that experimental validation has not been carried out for steels with higher yield stresses than 100 k.sj. The equations may not be valid for higher yield stresses although there does not appear to be any theoretical reason for this to be the case. However, if higher yield stress steels are to be assessed using the practice, it will be necessary to validate the equations for whatever yield stress is used in the design. Currently steels with yield stresses greater that 100 k.s.i. are not generally encountered in jack-ups with the exception of the mechanical components in the holding system which are to be treated under other assessment criteria.

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 CS.1.2 Definitions

Page 167

Structural and Components The definitions of and components have been stated so that the appropriate analysis method can be used for a particular type of geometry. The emphasis of the assessment is on structural , for which loads and properties must be known. Components are assessed only when the section is identified as being prone to local or lateral torsional buckling. This type of specification is in keeping with conventional jack-up analysis procedures in which chord scantlings are modeled as single beams; the modeling of the individual plates not being necessary.

CS.1.3

Factored Loads The load factors used in AISC are inappropriate for jack-up analysis since these have been derived for land based buildings. The derivation of load factors specific to jackups is discussed in Section CS.O.

CS.l.4

Assessment of - excluding stiffened and high D/t ratio tubulars

CS.l.4.1 General interaction equations The treatment of biaxial bending in AISC LRFD tends to be conservative for beamcolumns laterally ed at both ends. This is most apparent when assessing a tubular member. The bending strength of the tube must be the same in all directions, but this is not reflected in the AISC LRFD equations. The linear addition of x- and yaxis bending moment in effect reduces the nominal bending strengths in all cases of biaxial bending. For example, a tubular member subject to bending in a plane at 45° to the x-axis has in the AISC LRFD code a nominal strength of 71 % of that for uniaxial bending in the x- or y- planes. The problem is not confined to tubulars, as most sections would have a reduction in nominal strength on of this linear addition. Only for 'I' sections does AISC LRFD allow a more liberal formulation. In the AISC ASD formulation, such a problem does not arise, as the stress points are considered explicitly. Since optimal design is required for jack-ups, and since previous ASD-based design did not suffer from this problem, it was considered necessary to remove the conservatism for the PRACTICE. The general interaction equations have therefore been modified from the AISC LRFD equations.


Page 168

In deriving a suitable form the problem for the tubular was considered first. Clearly, since the tubular has equal bending strength in all directions, the correct actual bending moment should be the vectorial sum of the x- and y-axis bending moments. Expressed as a unity check equation for bending only:

{ M }2 {M _-,u:::.x_

(hMnx

+

}2 < 10

uy

bMny

_.

and with the addition of axial load (for Puf aPn > 0.2)

I

P

8

_u_+_

•• p,

9

[{.bMJ M

ux

+

2J- <10

{.bM,,} _. Mu

2

2

y

Since most jack-up chords are closed sections with high torsional stiffnesses similar to tubulars, the logical step was to formulate a similar equation which had the ability to for sections not exhibiting circular symmetry. This was carried out by using a generalized exponent l'J to form the two equations given in the PRACTICE. One of the equations is given below as an example (for Puf aPn > 0.2). This resembles the formulation in the AISC LRFD for I sections, although the exponent l'J has a different determination procedure.

With l'J = 1.0, the equations revert to the standard AISC LRFD equations, and hence a conservative assessment can be made. However, if the limit is required with more accuracy, then it is necessary to determine the value for 11 (discussed later). If the nominal bending strengths Mux and Muy are the same and 11 = 2.0, then this would imply that the section has equal bending strength in all directions. A value to l'J = 00 implies that the bending capacities in the x- and y-axes are independent of each other. Favorable interaction between, for example, the -Mx and +My moments acting on triangular chords with a single rack cannot be reproduced by the above equation. In such cases recourse to the section-specific interaction surface is recommended (see Section CS.l.4.7).

Page 169 Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 C8.1.4.2 Nominal Axial Strength C8.1.4.3 Whereas the nominal axial strength of tension of one material are fully catered for in the AISC LRFD code, some interpretation was required hybrid beamcolumns. The basic measure of tensile strength is O.9Fyj, but in certain cases this value may be unacceptably close to the ultimate strength. Therefore the provision is introduced that the factored strength is the lesser of O.9Fyi and O.75Fui. This ensures that an acceptable margin is applied to each component as illustrated in Figures C8.1.1 and C8.1.2. stress

r----.(----0.9Fy i -0.75Fui

st:rain

Figure C8.1.1 : ultimate strength much bigger than yield strength

~--------------

strain

Figure C8 .1.2 : yield strength close to ultimate strength

For hybrid a nominal strength is required that takes into the properties of each component. If there is no likelihood of fracture of anyone component then an addition of the nominal strengths of each component is appropriate for the member (Figure C8.1.3.).

(c:tressj component 1 Fnl

;----1'

max nominal component strength

__---:{ component 2

lowest strain level for component fracture

strain

Figure C8.1.3 : Stress/strain curves for two component member for which addition of nominal strengths is permissible

Commentaries to Recommended Practice for Site Specific Assessment of Page 170 Mobile Jack-Up Units Rev 2, Jan 2002 However it is conceivable that fracture of one component may take place at a strain level below that at which another component is loaded to its nominal strength (Figure CS.1.4.). stress x. component 1

I I

component 2

I I I I component fracture

max nominal component strength Figure CS.l.4 : Stress/strain curves for two component member in which one component fractures before the other is loaded to its nominal strength. For such an eventuality it is stipulated that the strength of the whole section is that for the weakest component, applied across the whole section, so that:

=

Pn FminLAj

This formulation is suitable when component materials are similar. When material properties differ widely from component to component then the formulation may be over conservative, and a rational analysis may be preferred. An example follows.

Example Consider a member in tension. The section consists of a rectangular portion of steel 1 sandwiched between two rectangular portions of steel 2. The areas occupied by steels 1 and 2 are both half the total section area A. By symmetry the section is balanced. !';t:ndn 1 eve 1 s

stress

r- for

component 1

xl

II II

p

IT

I I I I

component fracture

1

~--1-----Ir-X

~n2---

.£

1

.£

I I I I I I

COllponen L. 2

I I I strain

11

p

Figure CS.l.5 : Stress/strain curves for components of example member


Page 171

Consider the portion of steel 1 as component 1 and the portions of steel 2 as component 2. The stress/strain plots of the materials (Figure CS.1.5.) show that the strain level for component 1 to reach its nominal strength is well below that for fracture of 2. The ductility of 2 means that the component can a stress of just over Fn2 for strains up to those at which component 1 reaches its nominal capacity. Therefore, a less conservative nominal strength for the member is: P n = FnIAl2 + Fn2A12 Because the section is balanced, plastic deformation of 2 does not induce any extra loads or moments on the member. Were the section not balanced, then this would not be true. It is essential that such aspects are considered in a rational analysis of strength. CS.1.4.4 Effective Applied Moment CS.1.4.5 The PRACTICE allows for structural analyses of a range of levels of sophistication. In some, it may be necessary to manipulate the calculated moment to produce a more "true" value for application in the PRACTICE. This leads to the use of the effective applied moment for with compressive axial loads. Adjustments for tensile axial loads are not considered significant. P-~ effect produces an extra moment on a leg under hull sway, and that this moment should be included in the structural analysis. The similar, local P-~ effect on the individual of truss leg must also be included, directly in the structural analysis, or by use of the B term. If for a truss, the structural analysis includes the local P-~ effect then no manipulation is required. If the local P-~ is not included, for example through a linear elastic analysis of the leg segment, then the amplifier B is required. For many non-truss leg cases there is no local P-~ effect, such as for a jack-up with large diameter tubular legs.

It has been noted that the

The use of the single B term differs from that in the AISC LRFD code. There, the first order moment is separated into two parts: a moment assuming no lateral deflection of the frame Mnb and a moment attributed only to lateral deflection MIt. Then the effective applied moment is the sum of BIMnt and B2Mlt , where BI is similar to B in the PRACTICE ~md B2 is a second coefficient. It is important to note that both these moments are first order, and do not include P-~. The use of BI and B2 is to simulate the P-~ effects at local and global level respectively. Therefore, in the PRACTICE the calculated applied moment is not the same as the Mu in the AISC LRFD code. The use of Mue=B Mu performs the necessary step of adding the local which already includes global P-~.

P-~

moment to the calculated moment

Note that in a plastic analysis, yielding can take place within the and bending moments can hence be redistributed. The types of analysis to be used for the structural assessment of jack-ups are to be elastic analyses where yielding does not take place, so this aspect is not covered. For reference, AISC LRFD states their code is only valid for plastic analysis if material yield stresses do not exceed 65 k.s.i.

Page 172

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 C8.1.4.6 Nominal Bending Strength

The calculations of nominal bending strength for compact and noncompact sections require knowledge of the plastic moment capacity of the section. For a section composed of uniform material this is given by the lesser of: Mp=FyZ and Mp =5/6FuZ where Z is the plastic section modulus. For hybrid sections there is more than one set of material properties to consider. Standard techniques are recommended for evaluation of Mp and an example is provided below. Example Consider the simplified problem of a square rack section (component 1) of properties: FyI = 700 MN/m2 Ful = 828 MN/m 2 ; Fy' = 828 x 5/6 = 690 MN/m2 connected to a solid square chord section (component 2) of properties: Fy2 = 345 MN/m2 Fu2 = 485 MN/m2 Fy' = 485 x 5/6 = 404 MN/m 2 as shown in Figure C8.1.6 below. The nominal strengths are the lesser of the Fyi and 5/6Fuj, namely: component 1 strength = 690 MN/m2 component 2 strength = 345 MN/m2 Dimensions are as marked. z O.lm

o. 400m----+-~~-r-ra.300m

O.3m O.aOOm 0.3m

Figure C8.1.6 Example hybrid chord section

--L-I--+--r--~

345 690

stre s·s

(MN/m2)

Figure C8.1.7 Fully plastic stress distribution

On the assumption that the strain for component 1 to be loaded to its nominal strength is not sufficient to lead to fracture of component 2, the plastic stress distribution for pure bending is as shown in Figure C8.1.7. The Plastic Neutral Axis is a distance Zo from the back face of the chord component, such that: 345 x 0.3 x Zo = 345 x 0.3 x (O.3-zo) + 690 x 0.1 x 0.1 i.e. Zo = 0.183 m The section plastic moment is then: Mp = 345 x 0.3 x 0.183 x (0.183/2) + 345 x 0.3 x 0.117 x (0.117/2) + 690 x 0.1 x 0.100 x (0.117 + 0.100/2) = 3.59 MNm

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 CS.1.4.7 Detennination of n

Page 173

I

Determination of the correct value of 11 is carried out by calculation of the nominal strength of the member about axes other than the x-and y-axes. This can be done in the normal manner based on the effective plastic section modulq.s with reductions for local buckling if applicable. Although a beam will not necessarily bend in the same plane as the applied moment when the bending plane is at an angle to the orthogonal axes, it is not expected that the capacity will be greatly affected. Once the nominal bending strength has been calculated for a few angles between the xand y-axes, the value for 11 can be calculated using the graphical procedure given in the practice, or by an iterative procedure. A successful iterative procedure was found to be by the use of the coupled equations, setting a = M'uexlMnx and b = M'ue/Mny: In(l- bTJi) 11i+l

=

Ina with the accelerating step: 11i+2 = 0.5(11i+l + 11i) and the initial value 11 = 1.5. The three angles which were chosen, 30°,45° and 60° give a good spread over the 90° range. It is not the intention to fit a curve through all the values from the three angles but merely find the lowest value to 11. This may still make the equation conservative although considerably less so than for 11 =1.0. Plastic Interaction Curve Approach Alternatively, interaction equations and curves for generic families of chords are presented in Figures CS.1.S - eS.1.l1. The offset distance between the elastic centroid (used in the structural analysis) and the 'center of squash', together with other geometric data for the of each family of chord is presented in Tables CS.1.1 to CS.1.4.

II


CS.1.5

Page 174

Assessment of - other geometries For high D/t ratio tubulars, reference is made to the DNV Rules for Fixed Offshore Installations, as these are based on a suitable LRFD format. Care must be taken to adapt the usage factors in the Rules to the correct resistance factor format. The buckling strength of shells is best described in of buckling stress. For this reason, the stress to cause buckling in the shell must be determined and compared with the stresses caused by the factored loads. Since the analysis model usually gives the overall member loads, it is necessary to calculate the stresses in the shell. It may be possible, with caution, to allow the analysis model to also calculate membrane stresses. The detailed stress formulations in the DNV Class note 30.1 are amenable to some simplification. For example, the pressure loading may usually be omitted, since high D/t tubulars in jack-up legs are generally flooded. For beam-column interaction, the effects from global axial buckling are added to the effects of local buckling due to flexural bending. Global buckling effects in bending such as lateral-torsional buckling only occur in sections in which the stiffness out of plane is less than the stiffness in the plane of bending. Thus tubular and rectangular sections, hollow or otherwise, in which the depth is less than or equal to the width do not suffer lateral torsional buckling.


Page 175

_-+_ _ +~y~~ve My

Strength Interaction Equations

{( ~J +(::JT ~lOO For (pIPy)

~ 0.6:

Mpy = For (PlPy) > 0.6:

r Mo+o{;:,)r

M p< = hlp. { co{

M p<

=

~:, )

1.71Mp. (1- :, )

M py = 1.39Mpy ( 1- :, ) Figure CS.l.S Interaction equations/curves for tubular chords with double central racks.


Page 176

Chord Dimensions - Tubular Chord with Central Double Racks

L2. t2. Fy2

All dimensions are in millimeters, Yield Stresses are in MPa <--- Yield --->

Design

Stress Fy2 Fy3

L1

t1

L2

t2

D

t3

Fy1

BMC JU-300-CAN (Zapata Scotian) 991

127

o

o

914

44 48 52 34 26 34 42 28 30 31 32 33 35 36 38 40 44 34 38 42

690

0

690

5532

690

690

690

4500 Btm 3 bays 4100 Top 3 bays 4050 Middle bays

700

685

650 700'

700

685

700

700

685

650

CFEM T2001 (Hitachi Redesign)

960

18

121

140

960

CFEM T2005

650

20

108

140

800

Bay Ht

or 5050

• Note: Early CFEM T2005 designs use 650 MPa steel for tube, later designs use 700 MPa steel. ... continued

Table eg.1.! Data for tubular chords with double central racks


Page 177

<--- Yield --->

Design CFEMT2600

MODEC200 MODEC300

MODEC 400 (Trident 9) Hitachi K1025/31/32

Hitachi K1026 (Neddrill4) Hitachi K105617

ETA Robray 300 (Asia Class)

ETA Europe Class

L1

t1

L2

t2

D

650

20

120

140

800

15 27 450 25 28 15 20 27 60 115 690 20 20 35 18 900 18 18 20 20 950 18 18 20 1000 28 30 30 30 30 60 60 627 10 11 13 14 16 17 19 25 32 627 38 51

102

127 559

102

127 559

450

t3

Fy1

33 700 35 38 40 41 43 45 47 49 50 51 52 55 56 57 58 27 490

Stress Fy2 Fy3 Bay Ht 700 700 6000

690 490

5486

490

690

490

5486

30 490 35 35 32 690 36 50 40 42 32 690 36 42 47 690 50 52 60

690

490

6200

690

690 5160

690

690 4360

730

690 4600

34 34

40 40 40 40 40 102

127 800

100

127 900

100 127 950 130 178 1000

64

60 127 127 762

22

690

690

4000 690 5486

140

22

690

690

690 5486

64

140 762

64

76 89 102 114 127

Table CS.l.1 (Continued} Data for tubular chords with double central racks


Page 178

N

'-,

1

i

o·

I.~

'""i

v~-~~--litT-y-j- + ve My

Strength Interaction Eguations

where;

M'px

=

P J2.25

M px ( 1 -P y

M'py

=

P J1.85 M py 1 -P ( y

Figure C8.1.9 Interaction equations/curves for split tubular chords with double central racks.


Page 179

Chord Dimensions - Split Tubulars with Double Central Racks

D

..

Hi

~

_ _ Ll, tl. Fyl

t3

H2

All dimensions are in millimeters, Yield Stresses are in MPa

Design

F & G L780 (Lower bays) F & G L780 (Upper bays) F & G L780 m2 (Lower bays) F & G L780 m2 (Upper bays) F & G L780 m5 (Monitor) F & G L780 m5 (Monarch) F & G L780 m6 MSC CJ62 (Lower bays) MSC CJ62 (Upper bays) MSC CJ50 (1) MSC CJ50 (2) Technip TPG 500 (1) Technip TPG 500 (2) Technip TPG 500 (3) Technip TPG 500 (4) Technip TPG 500 (5) Technip TPG 500 (6)

L1

t1

D

12

t3

L4

t4

Y1

H1

H2

400

152 127 152 127 178 178 178 210 210 210 210 160 160 160 160 160 160

381 381 381 381 381 381 584 600 600 520 520 680 680 680 680

25 25 32 32 81 81

25 25 32 32 57 51 38 48 40 25 35 61 37 37 37 37 37

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 510

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 30

0 0 0 0 51 51 95 75 75 0 0 20 55 36 30 19 19

191 191 191 191 178 178 292 270 270 260 260 340 340 340 340 340 340

165 191 165 191 178 178 292 270 270 260 260 340 340 340 340 340 340

400 400 400 401 401 611 650 650 550 550 722 722 722 722 722 722

680 680

83 65 55 25 25 75 75 62 58 50 50

Yield Stress Fy1 Fy2 Bay Ht

621 621 621 621 690 690 690 690 690 690 690 690 690 690 690 690 690

Table CS.l.2 Data for split tubular chords with double central racks

690 450 690 517 690 690 690 690 690 690 690 540 540 540 540 540 540

3658 3658 3658 3658 4267 4267 5486 6927 6927 5608 5608 6000 6000 6000 6000 6000 6000

Page 180


-I.Z

I

+ve Mx


{(:.J +(::Jf = ~+ r}

where;

-(:,

M'"

WhenMx~O:

~ = 18 + 2{ :, ) + ~ :,

and M'px = When Mz

$1.00

~

r-

5.{ :, )'

P ) 1.12 } 111.12 Mpx 1- { ( Py

=

1.8

and for (PlPy) ~ 0.25:

M 'px -

-Mpx

for (PlPy) > 0.25:

M 'px --

-~+-(O.7~Py -~r}

Figure C8.1.10 Interaction equations/curves for tubular chords with offset double racks.

Page 181

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 Tubular Chords with Offset Double Racks

L2

Fy2

Ll

All dimensions are in millimeters, Yield Stresses are in MPa

Design

Levingston 011-C

<--- Yield ---> Stress Fy1 Fy2 Fy3 Bay Ht Yena Ycos

D

t1

L1

L2

914

29 33 32 35 32

305

906

127

0

483 621

0

4826

305 1047

127

0

690 690

0

4877

305 1046

127

0

690 690

0

5650

29 29 32 36 30 32

305 1046 305 1046

127 127

0 0

690 690 690 690

0 0

190

882

127

0

690 690

0

4672 5050 5050 5050 5500

30 30

190 300

890 882

130 127

0 0

690 690 690 690

0 0

300

854

127 13

690 690 690

5500 4800 5090 5090 5090 5260

292

881

127

690 690

5461

Levingston 111

1016

Mitsui JC-300 (Key Hawaii)

1016

t2 t3

34 35 Mitsui 100ft (Key Bermuda)

1016 1016

Hitachi Drill-Hope

762

Hitachi C-150 (lie Du Levant) Hitachi K1040/44/45

762 900

66

30 35 42 Hitachi K1060 (Sagar Lakshmi) 900

30

84 75 73 68 78

73 66 57 55

60 77 77

100 16 90 15 73 0 68 0 78 0 0 66 0 0 0 73 0 66 0 57 0 55 0 60 0 77 0 77 0

60 84

84

77 83 68 89 82

77 83 68 89 82

60

31 32

34 Robc0350-C

876 876 864 864

29 38 29 32

0

0

E

Table CS.l.3 Data for tubular chords with offset double racks

0 0 0 0 0 0 0 0 0

Most of leg Towage Section

..

Btm 2 bays Rest of leg

Btm 3 bays

.

Rest of Leg


x

Py


{(~':I::=~r +(:.JT where;

K=

and

~{ :, ) + o.{ :,

M'~=Mpy{l-(

When (M,fMpJ H:

+

:,r}

+-(:,f}

M'" = M p

and ~= 1.45

When (M,IM,J < K:

ro.{:,)'

$100

,+ -(:,r'" f04

M' po< = - M p

and~= 145 +23{ :,) +4.{:,

r

Figure e8.l.11 Interaction equations/curves for triangular chords with single racks

Page 182

~g g.~ ::::.:~

13, tJ,Fy3 IA,t4,Fy4

~

~

~§

(')

""t

~ ~.

~

R

I Y2

~ ...... ~

i.-Xl---J

>-+>

g All dimensions are in millimeters, Yield Stresses are in MPa 8". l2 Design

l1

t1

Yi

::E

::+. ; .....

~

(i'

~

n

~

;::s

§

~

N~

o~

::3p..... (')

t2

l3

t3

l4

t4

l5

t5

t6

X1

Y1

Y2

Y3

~

<-------- Yield Stress --------> Fy1

Fy2

Fy3

Fy4

Fy5 Bay Ht Yena Ycos

E

~ ""t V)

~.

711 711 711 Marlet Standard (1" side plates) 711 Marlet Standard (1.5" side plates) 711 Marlet Standard + side stiffeners 711 Marlet Std 116 (1 "x4" rack stiffeners) Marlet 116 North Sea (1 "x4"+ 1"x12" stifnrs) 711 Marlet 116 (1"x4"+1.5"x12" stifnrs) 711 Marlet 116 Juneau (2"x4"+ 1"x12" stifnrs) 711 Marlet Gorilla (150-88) 813 Marlet Super 300 813 813 Marlet 300 Slant 711 711 leToumeau 150 (3/4" side pi) LeTourneau 150 (1.125" side pi) 711 711 LeTourneau 150 (1.5" side pi) LeTourneau 46,47 559 LeTourneau 4,9 559 750 Mitsubishi MD-T76J Gusto 1-off: (Maersk Endeavour) 800 800 800 Gusto 1-off: (Maersk Explorer) 800 800 800 800 711 BMC 1-off design (Trident 7) Marlet Standard (3/4" side plates)

n Marlet Standard (7/8" side plates)

rJ>

§

~~

C

5" a

~ ~

JQ

~

(')

~I::)

1

~

t:1 Pl S' Chord Dimensions - Triangular Chords with Single Rack

~

~

N~

......

-

....~~

t6 Fy6

n 00

§

~'"

~ ~

51 51 51 51 51 51 51 51 51 76 76 76 64 51 51 51 44 51 50 60 90 110 76 64 51 51 38

466 466 466 466 466 466 466 466 466 573 607 607 441 466 466 466 432 565 574 592 534 488 535 549 562 562 356

19 22 25 38 19 19 19 19 19 57 38 38 38 19 29 38 13 13 25 30 40 50 38 38 32 29 19

213 213 213 213 213 213 213 213 213 222 222 222 213 213 213 213 178 197 225 283 283 283 279 279 279 279 279

127 127 127 127 127 127 127 127 127 140 140 140 127 127 127 127 89 102 125 127 127 127 127 127 127 127 127

0 0 0 0 0 102 102 102 102 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 25 25 25 51 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 127 0 305 305 305 0 0 305 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 25 0 25 38 25 0 0 51 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 25

236 236 236 236 236 236 236 236 236 248 268 268 218 236 236 236 166 178 226 359 331 307 337 344 351 351 264

457 457 457 457 457 457 457 457 457 600 600 600 457 457 457 457 432 533 575 443 443 443 453 453 453 453 204

0 0 0 0 0 524 524 524 524 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 211 0 118 124 118 0 0 296 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

483 483 483 483 483 483 483 483 483 483 483 483 414 414 414 414

483 483 483 483 483 483 483 483 483 483 483 483 414 414 414 414

587 587 587 587 587 587 587 587 587 620 620 620 414 620 620 620

? ?

? ?

? ?

687 687 620 620 620 620 620 620 690 690 690 690 690 690 690 690

687 620 620 620 690 690 690 690

?

?

?

0 0 0 0 0 483 483 483 483 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 483 0 483 483 483 0 0 483 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

3408 3408 3408 3408 3408 3408 3408 3408 3408 5113 5113 5113 2556 2556 2556 2556 3408 3430 3456 4800 4800 4800 4539 4539 4539 4539 3353

259 259 260 262 260 278 276 277 290 302 298 327 245 259 259 262 224 286 315 284 255 244 268 282 297 297 197

279 279 279 279 279 296 291 291 304 323 323 346 245 302 303 298 224 286 315 284 255 244 268 282 297 297 197

20 20 19 17 19 18 15 14 14 21 25 19 0 43 44 26 0 0 0 0 0 0 0 0 0 0 0

~ ~ (')

'5i (')

~

'"'" ~

~ ~

;::s

..... .Q,

o? ~

.....

00 tJ.J

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 C8.3 FOUNDATION ASSESSMENT

Page 184

The intention of the foundation capacity checks of steps 1 and 2 (Sections 8.3.1 and 8.3.2/8.3.3 of the PRACTICE) is to safeguard against foundation failure. Foundation failure will, in most cases, manifest itself through excessive spudcan vertical and/or horizontal displacements which may cause local or global instability of the jack-up. Local instability occurs when a leg becomes overstressed, with global instability as a consequential effect. Global instability may occur through overturning which will then cause leg overstress. The key to preventing either type of failure mode is to safeguard against excessive spudcan displacements. Since it is difficult to accurately compute the displacements (as proposed in Step 3, Section 8.3.4 of the PRACTICE, the checks of steps 1 and 2 are performed by comparing the bearing capacity with the extreme combinations of load, including applicable partial factors. In steps 1 and 2a the loads are computed assuming pinned footings. In step 2b the check allows for fixity. Selection ofthe Resistance Factors (j) The resistance factor is intended to cover uncertainties in the estimation of the bearing capacity. In foundation engineering it is common to adopt in the range 111.25 - 1/1.30 (0.80 - 0.77) when the capacity is determined on the basis of available soil data and analytical predictions. For a jack-up there is however additional information available in of the preload applied at installation, which generally justifies the use of a higher resistance factor.

During preloading the spudcan foundation experiences loading similar, but not identical to the conditions of the leeward leg during the extreme event. Taking this information into , there is greater certainty in the upper part of the bearing capacity curve applicable to bearing failure than in the lower part applicable to sliding failure. However, some uncertainty still remains for the foundation capacity in bearing applicable to the leeward leg determined from the preload value. This uncertainty is due to factors such as: effect of cyclic loading effects of consolidation and creep loading rate effects There is at present insufficient information available to fully quantify the likely distribution in the actual foundation capacity curve. In the study performed by NGI [17] it is concluded that cyclic degradation effects on clay are significantly larger for the leeward leg than for the windward leg. It is also noted that the case of a spudcan which has not penetrated sufficiently to mobilize the maximum available bearing area should be differentiated from the case where the maximum bearing area is utilized. This is because in the former case a small additional penetration will lead to a increase in capacity as a result of the increase in bearing area. On the basis of the above arguments the following resistance factors are proposed: Step la - preload, vertical load alone: <1>=0.9

See note overleaf


Page 185

Note: Section 8.3.1.4 of the PRACTICE requires that the vertical and horizontal load check of step 2a is made when the horizontal leg reaction at the leeward leg exceeds prescribed limits, depending on the penetration and soil. This is because the simplistic check in Step 1a is based on the proven ultimate vertical bearing capacity during preloading and it is therefore assumed that the extreme footing load is the same as the maximum footing load during preloading. This implies that the horizontal loading on the spudcan under extreme conditions is small and it is therefore appropriate to limit the combined horizontal and vertical loading to the values permitted under Step 2. In the selection of the limits for Step 1a two penetration cases can be distinguished: full embedment to maximum bearing area in foundation layer, partial embedment in the foundation layer. For full spudcan embedment in sand the lateral soil resistance at a vertical load of O.9VLo is approximately O.03VLo. Additional penetration may increase the soil resistance, but to increase the horizontal resistance to O.lVLo the additional penetration will be in the order of 10% of the spudcan diameter and outside tolerable limits. In the case of partial penetration of the spudcan in sand (i.e., full bearing area not mobilized), any additional penetration will result in a significant increase of bearing capacity due to the rapid increase in the bearing area. An increase in embedded area of approximately 10% will increase the horizontal capacity to O.lVLo· In clayey soils the requirement of QH < 0.1 V10 is met if the ratio of the spudcan laterally projected area to bearing area, AsiA is in the order of 0.3. Step 1b - sliding, vertical and horizontal load vector: Hfc = 0.8 (effective stress - sand/drained) = 0.64 (total stress - clay/undrained) Step 2a - bearing, vertical and horizontal load vector: vH = 0.9 (maximum bearing area not mobilized) = 0.85 (maximum bearing area mobilized) Step 2b - vertical, horizontal and moment load vector: vHM = vH from step 2a for leeward legs = Hfc from step 1b for windward legs Selection of safety factors against punch-through Where the potential for punch-through foundation failure is recognized, detailed consideration regarding foundation integrity will be required. Methods have been proposed for punch-through installation procedures and acceptability criteria but are omitted from this document as they remain ambiguous, (Rapaport [18], Senner [19]).

Some jack-up designs are more able to tolerate rapid leg penetration than others and if the magnitude of the potential leg plunge is acceptable then installation could be possible even though punch-through is predicted during preloading. Significant investigation will be required in such circumstances and it is recommended that each potential punch-through situation is assessed on its own merit both at preloading and, should the potential for punch-through remain after installation, for the elevated operational and survival conditions.

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 CS.7 STRUCTURE CONDITION ASSESSMENT CS.7.1

Page lS6

Introduction Where an on-site structural inspection is required Section CS.7.2 provides guidance as to how this may be carried out. Section CS.7.3 provides guidance on monitoring the structural condition during an assignment.

CS.7.2

Scope of Condition Assessment The aim of a condition assessment is to the condition of the structural components and details that are essential for the ultimate strength of the jack-up in the elevated condition and to confirm that the condition of the jack-up structure is in line with the assumptions made in the site specific analysis. Structural details to be assessed can be identified based on general considerations (see [20]), or on the results of site specific calculations and/or fatigue considerations. Condition assessment may comprise four steps with increasing involvement as described below. It is necessary that step 1 should always be completed and steps 2, 3 and 4 should be carried out as necessary to validate the condition of the jack-up.

Step 1 - Review of existing records The review should initially cover the existing certificates and operating/inspection records. These should provide details of any incidents (indications of damage and subsequent repairs). Step 2 - Visual inspection A general visual inspection is carried out to confirm the rig is in a good state of repair and well maintained. The inspection should focus on the critical structural components and will include checks for missing , mechanical damage, corrosion, etc. Normally this will only cover above water areas and should include a selection of the fatigue sensitive areas listed in Section 7.4.4. The visual inspection may be carried out by the same team visiting the unit for a precontract inspection (safety, drilling, etc.). However it is required that qualified personnel should be part of that team.

Step 3 - Close Visual inspection Close visual inspection of key structural areas may be required if the condition can not be validated based on the review of existing records (step 1) and the general visual inspection (step 2). Hence the close visual inspection should focus on specific areas or details that may be in doubt. If fatigue is a consideration, it is recommended that, following steps 1 and 2, a selection of the fatigue sensitive areas should be subjected to close visual inspection. These close visual (weld) inspections should cover a number oflocations from each of the groups of fatigue sensitive areas identified in Section 7.4.4. This should possibly be followed with an MPI inspection as outlined below.

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 C8.7.2 Step 4 - Detailed inspection

Page 187

Detailed inspection may be required in special cases and in case of inconclusive findings after completion of the three steps above. The detailed inspection is seen as a continuation of the visual inspection and hence is aimed at confirming that the condition of some specific details are sound for the intended operation. The major concern is the ultimate strength of the unit. Local damage with no significance for the planned mode of operation need not be assessed, but should be recorded for inclusion in future maintenance work. The scope of the inspection may include some NDT (e.g. MPI) and these inspections must be carried out by qualified personnel. The NDT will normally cover areas of specific concern. It may also be necessary to provide some spot checks of fatigue sensitive areas. In this case it is recommended that MPI checks should, as a minimum, be made at a selection of areas from each of the groups of fatigue sensitive locations identified in Section 7.4.4. If defects are found it may be necessary to expand the scope of the inspection so that the

full extent of the damage can be assessed. C8.7.3

Condition Monitoring The condition of the jack-up structure should be monitored during the assignment. This is to ensure the continuation of the overall structural integrity during the operations. The requirements for condition monitoring may be based on the approach outlined in steps 1 through 4 above. The operating and maintenance records kept by the owner are the primary source of input for the independent condition monitoring and it should be possible to validate the condition of the unit by reviewing these records at any time during the operation. It is not expected that, for normal operations, the scope of the condition monitoring should extend beyond step 1. It is noted that records should be kept for future reference.


Page 188

GLOSSARY OF FOR SECTION C a A

A A

= = = =

Ai As

= = b = B = B = Bl = B2 = C = CoD = d = D = Fmin = Fnl = Fn2 = FUi = Fy = F'Y = Fyi = FI = F2 = Hs = K = Ll,L2,etc. = MIt = Mnt = Mnx = Mny = Mp = Mpx = Mpy = M'px = M'py = Mu = Mue = Mux,Muex= Muy,Muey= Mx = My = P,Pu = Pn = Py =

M'uexlMnx used in detennination of 11. constant in quadratic expression for~. cross sectional area. effective spudcan bearing area based on cross-section taken at uppermost part of bearing area in with the soil. cross sectional area of component i. laterally projected embedded area of spudcan. M'ueylMny used in detennination of 11. constant in quadratic expression for ~. moment amplification factor. moment amplification factor applicable to M nt. moment amplification factor applicable to Mit. constant in quadratic expression for ~. product of drag coefficient and associated diameter. water depth (m). diameter of tubular member. strength of weakest component. nominal strength of component 1. nominal strength of component 2. material ultimate strength for component i. material yield strength. effective material yield strength =5FJ6. material yield strength for component i. factor used in computer axial capacity for plastic interaction. factor used in computer moment capacity for plastic interaction. significant wave height. parameter in chord strength interaction relationship. length of chord component 1,2, etc. moment attributed only to lateral deflection. moment excluding lateral deflection. nominal bending strength about member x-axis. nominal bending strength about member y-axis. plastic moment capacity. plastic moment capacity about member x-axis. plastic moment capacity about member y-axis. effective allowable x-axis bending capacity used in strength interaction equations. effective allowable y-axis ending capacity used in strength interaction equations. applied bending moment. effective applied bending moment. effective applied bending moment about member x-axis. effective applied bending moment about member y-axis. applied bending moment about member x -axis. applied bending moment about member y-axis. applied axial load. nominal axial strength. axial yield strength.

I

I

Commentaries to Recommended Practice for Site Specific Assessment of Mobile Jack-Up Units Rev 2, Jan 2002 GLOSSARY OF FOR SECTION C8 (Continued) t tl,t2,etc. Tp

VT zo Z

f3 ~

11 a

t,

Hfe

vH vHM

= = = = = =

Page 189

wall thickness of tubular member. thickness of chord component 1, 2, etc. peak period associated with Hs. tidal current velocity. distance between plastic neutral axis and back face of chord. plastic section modulus.

safety index. exponent in chord strength interaction relationship. exponent in bending interaction relationship. resistance factor. resistance factor for axial load. resistance factor for bending. foundation resistance factor - sliding. foundation resistance factor - bearing under the action of vertical and horizontal loads. = foundation resistance factor - bearing under the action of vertical, horizontal and moment loads.

= = = = = = = =


Page 190

1

Ahilan RV., Baker M.J., Hoyle M.J.R and Robinson N.J., "Reliability Based Development of Jack-up Assessment Criteria". Presented at the Tenth Structures Congress (ASCE), San Antonio, Texas, April 13-15, 1992.

2

Noble Denton Consultancy Services Limited. "Jack-up Assessment Criteria", Stage 1 Report, L15709INDCSIRVA (Rev. 2) London, dated 28th February 1992.

3

Noble Denton Consultancy Services Limited. "Jack-up Assessment Criteria", Stage 2 Report, L16268INDCSIRVA (Rev. 1), London, dated 8th January 1993.

4

Ahilan RV., Baker M.J. and Snell RO., "Development of Jack-up Assessment Criteria using Probabilistic Methods". OTC7305, Houston, Texas, 1993.

5

Noble Denton Consultancy Services Limited. "Jack-up Assessment Criteria - Interim Scope of Work Items 1.1 to 1.4 on Reliability Analysis". Report No. L15323INDCSIRVA (Rev. 2) London, dated 4th March 1991.

6

Noble Denton Consultancy Services Limited. "Jack-up Assessment Criteria - Statement of Variable Selection". Report No. L15670INDCSIRVA (Rev. 0), London, dated 12th September 1991.

7

Winterstein, S. "Nonlinear Vibration Models for Extremes and Fatigue", J. Engineering Mechanics, ASCE, Vol. 114, October 1988.

8

Juncher Jensen J., "Dynamic Amplification of Offshore Steel Platform Responses due to Non-Gaussian Wave Loads", Danish Center for Applied Mathematics and Mechanics Report No. 425, May 1991.

9

Manual of Steel Construction - Allowable Stress Design - Ninth Edition, AISC, 1989.

10

Recommended Practice for Planning, Deg and Constructing Fixed Offshore Platforms - API RP2A, Eighteenth Edition, 1 Sept 1989.

11

Load and Resistance Factor Design Specification for Structural Steel Buildings, AISC, 1 Sept 1986.

12

Draft Recommended Practice for Planning, Deg and Constructing Fixed Offshore Platforms - Load and Resistance Factor Design API RP2A - LRFD First Edition, 1 Sept 1989.

13

Rules for Classification - Fixed Offshore Installations, Det Norske Veritas H'vik, July 1991.

14

Buckling strength analysis of Mobile Offshore Units - Classification Notes- Note 30.1, H'vik, October 1987.

15

Dyer A.P., "Plastic Strength Interaction Equations for Jack-Up Chords", MSc Thesis, Dept of Mechanical Engineering, Univ. of Sheffield, Nov. 1992.

16

Duan L., Chen W.-F., "A Yield Surface Equation for Doubly Symmetrical Sections", Engineering Structures, Vol 12, pp. 114-119, April 1990.

17

Norwegian Geotechnical Institute, "Cyclic Effects on Bearing Capacity and Stiffness for Jack-Up Platforms on Clay', Report 913012-1, May 1992.


Page 191

18

Rapaport V., Alford J., (1987) "Pre-loading of Independent Leg Units at Locations with Difficult Seabed Conditions." Conference title: Recent developments in jack-up platfonns - design, construction and operation. The City University, London.

19

Senner D.W.F., (1992) "Analysis of Long Tenn Jack-up Rig Foundation Perfonnance." Offshore Site Investigation and Foundation Behavior. SUT International Conference, London.

20

Sliggers P.G.F., "SIPM Practice for Site Specific Structural Fitness for Purpose Assessment of Jack-Up Rigs", Paper 21979, SPElIADC Conference, Amsterdam, 11-14th March 1991.

This page is intentionally left blank

EXAMPLE ("GO-BY") CALCULATIONS USING RECOMMENDED PRACTICE FOR SITE SPECIFIC ASSESSMENT OF MOBILE JACK-UP UNITS

PRELIMINARY ISSUE MAY 1994

Rev Preliminary Issue

Issue Date May 1994

Details Substantive changes from April '93 Draft are indicated by sideline thus: I as an aid to s, but neither the authors nor SNAME make any warranty as to the accuracy of such notations.

NOTES: 1. During the production of these sample calculations, the PRACTICE changed in a variety of ways. The text was updated to match the fist issue ofthe PRACTICE (1994), however not all the calculations were revised. Since the issue of this document, the PRACTICE has been subject to two revisions (Rev 1, 1997 and Rev 2, 2002). Consequently neither the text nor the calculations of this document are fully aligned with Rev 2 of the PRACTICE. 2. The is therefore advised to treat this document as providing useful guidance that must however be treated with caution and judgment.

Example ("Go-by") Calculations for a Typical Jackup

Page 2

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994

Page 3 Introductory Comments

INTRODUCTORY COMMENTS

General Points This go-by document serves to blaze a trail through the analysis methods in the PRACTICE. These methods have been applied to a hypothetical jack-up, the "Typical Jack-up 2", and this document provides a set of engineer's notes on the analysis. Most of the options available have been covered. It is intended that an engineer endeavoring to perform an analysis of a unit according to the PRACTICE can look up the relevant section(s) of this document to find sample calculations. Details ofthe Typical Jack-up 2 unit are provided in appendix A.

During the production of these sample calculations, the PRACTICE changed in a variety of ways. It has been possible to update the text according to these changes, but not to revise all the calculations. Consequently a study using the same input data might not arrive at the same final answers. It should also be noted that at a number of stages, for example in some of the detailed dynamic response determinations, purely illustrative numbers have been used. The PRACTICE employs partial load and resistance factors which, at the time of production of this document, had not been finalized. Therefore, artificial load factors of 1.0 were used throughout, however the resistance factors employed are in accordance with PRACTICE except for the overturning check. The should have little trouble in applying other values. It is anticipated that the this document will be fully updated in the future. Sections

in need of significant updated are generally identified. How to Use the Document The flowchart of figure 2.1 of the PRACTICE (the FLOWCHART) shows the general analysis route, and provides the basic structure ofthe go-by document. This is reproduced at the appropriate part of the calculation sequence. By following each box in the FLOWCHART, the go-by document is conveniently compartmentalized. To address anyone item in a FLOWCHART box, the can flick through the text until corning to a reproduction of the relevant box, and start to follow the calculations from there. It is not recommended that the picks up calculations at other points in the middle of the text. While the order of the FLOWCHART is obeyed, the route through the PRACTICE to complete each FLOWCHART item is in order of convenience. Where alternative paths are available to complete an action, these are marked and placed one after the other. Throughout the document roadsign-like symbols have been added to assist the in navigating the analysis options. The document is best read with the PRACTICE open for reference.

I



Navigation Within the Document The go-by document begins with the first section of the PRACTICE and proceeds to the point at which the FLOWCHART is encountered. Each subsequent calculation step begins with a reproduction of the relevant FLOWCHART box, which is often accompanied by a few explanatory comments. In most cases, this is followed by "local route card", which is of the form of: WIND LOADS - route Introduction Wind Force Calculations or Model Tests

4.1 4.2 4.7.6

The local route card is a more detailed list of the sections to be followed in the completion of an item of the FLOWCHART, and shows the major choices available. Similar cards appear at other points in the text as considered beneficial. At key points "high level" instructions are given, for example advising the when an item is complete and the next FLOWCHART entry should be started. These are identified by the upturned triangle:

Within the items of the FLOWCHART, there is a choice of routes to analysis and these have been followed up, one after the other. A road sign like format has been adopted to show the points where routes diverge, and to label the turn-off points for each option. Examples include:

~

detailed methods

followed by ...

C7.2

7.2

Once all the options have been discussed, a convergent route sign of similar form is given. Smaller labels are provided for minor route choices and short turn-offs. Whereas the major FLOWCHART items are tackled in an obedient order, the actions within each item are tackled in the most appropriate order at the time. A few other symbols are used, as referenced in the key below.



Key to Symbols: The following types of symbol appear in the go-by document.

Top level navigational instruction, for example showing where an item in the overall assessment has been completed, or where a level of assessment has been concluded.

Initial route Read introduction objectives Follow FLOWCHART

1 2 fig 2.1

"Local route sign" showing the general route(s) available to achieve an item in the overall FLOWCHART.

Reference to an entry in the route card above. Placed in margm.

detailed methods C7.2

Point at which the analysis route divides into options which are separately labeled within the PRACTICE.

7.2

Indicator of start of a separately labeled option, as directed by the signpost immediately above. Option terminates at the next similar sign, or at the sign ... 5.5.3

5.5.4

V

Point at which separately labeled options converge onto the same route again.

l

Reference to an entry in the route card which carries on an identified option.

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 7.2.2

I


Point at which a minor division in the analysis route occurs. This is usually within a sub-section.

A I OPTION)

Minor option in the route as introduced by the above sign. Terminated either by a similar sign or by the sign ...

Point at which minor route divisions re-converge.

Reference to source of further information in the PRACTICE.


Page 7 Initial Steps

INITIAL STEPS IN THE ANALYSIS OF THE TYPICAL JACK-UP 2

Initial route Read introduction objectives Follow FLOWCHART

o 1.1

l. 2. fig 2.1

INTRODUCTION The PRACTICE is for use with the GUIDELINE. Section 1.4.1 of the GUIDELINE states: "Where a jack-up is to be employed in conditions well within its design capacity and existing calculations in accordance with the RECOMMENDED PRACTICE are available, the site specific assessment may be undertaken by appropriate comparisons between the parameters used in the calculations and those applicable to the new location. Otherwise, engineering calculations of various degrees of complexity are required to justify that the jack-up can be safely used at the location." For this document it is assumed that the latter case applies and that recourse to the PRACTICE is necessary to justify the safe use of the unit.

1.3

Alternative practices within the framework of the GUIDELINE are permissible.


o


OBJECTIVES

2.1

The following areas are covered: geometric suitability structural adequacy foundation adequacy overturning stability.

2.3

There are no local regulations to be met for this analysis.

2.4.1

An accurate representation of the condition of the unit is available for this study.

2.4.2

The jack-up can be assumed to be in sound mechanical and structural condition.

2.4.4

Three levels of assessment are available: comparison with existing assessments application of simple methods application of complex methods These are hierarchical. Satisfying a simple assessment method is adequate. Otherwise a more complex method may be attempted. Foundations are to be assessed.

It is now appropriate to start using the

FLOWCHART in figure 2.1, as reproduced overleaf. Upside down triangles give "top-level" instructions in this GO-BY document.



Overall analysis FLOWCHART as given in figure 2.1 of the PRACTICE

Cbtain jack-"" data, Sectim 3.1. Establish proposed Weights and C.ofG.'s Section 3.2. Cbtain Environmental data, Sections 3.3, j.4, 3.5 & 3.6. Cbtain Geotechnical data, Sections 3.11 - 3.16.

Will 'other aspects' limit suitability: - HydrodynamicsSecSectfm 4.8. - Foundations tim 6.4. - Cordition o~ unit, Sectim 8.7

Yes

Preventative measures avai lable and wi II be adtecl? Yes

No

I

Determine airgap, Sectim 3.7 (or as dictated by other considerations, if higher). Estimate leg penetrations (based m maxinun preload), Sectim 6.2.

No

I I~~UBLE I No

liS adeq.Jate

leg length avai lable? Section 3.10. Yes

Yes

I

1

Assess foundation Sections 6.3 &8. j •

a<

No

IAWL icable calculations according to PRACTICE exist and show acceptability? Sectim 2.4.4.

Choose to calculate req.Jired preload ard re-assess penetratim and leg length?

I

Yes

No

l Not a<

I

Establ ish wind loads Sectim 4.2, hydrodynamic coefficients, Sections 4.6 & 4.. t Prepare analysis models, Sectim 5.

J

IDetermine responses (e.g. SOOF method), Section 7/Figure 7.1. I IAssess structure and overturning, Sections 8.1, 8.2, 8.5, 8.6 & 8.7.~()( ()(

lit legreq.Jired, re-assess penetration I Not ()( length, Sections 6.2 3.10. &

&

()(

IAssess foundation, Sections 6.3 & 8.3/Figure 6.9. J Not ()( ()(

/If applicable, check horizontal deflections, Sectim 8.4.

I

Not ()(

()(

Choose roore detai led: - Response calculation (Section 7/Figure 7.1>. - Res~e calculation inc uding foundatim fixity (Sectlon'7/Figure 7.1 & Section 6.3/Figure 6.10). No UNIT

I SUITABLE J Figure 2.1 - Overall flow chart for the assessment

I

UNIT UNSUITABLE

-

Yes




Page 11 Collect Data

COLLECT DATA FOR THE TYPICAL JACKUP 2

Obtain jack-up data, Section 3.1. Establish proposed Weights and C. of G.'s, Section 3.2. Obtain Environmental data, Sections 3.3,3.4,3.5 & 3.6. Obtain Geotechnical data, Sections 3.11 - 3.16.

~

The first item in the FLOWCHART involves data collection. The references are well itemized, and so no local route sign is required.

OBTAIN JACK-UP DATA

~

Rig data

3.1.1

Following the GUIDELINE the following data is collected: Rig type Drawings & specifications Weights Pre loading capability Materials Design parameters/ deviations Relevant modifications

3.1.2

Typical Jackup 2 (original data pack) (original data pack) (original data pack) (original data pack) none none

The original data pack acts as the operations manual for this study. ESTABLISH PROPOSED WEIGHTS AND C of Gs

[22]

Functional Loadings

3.2.1

It is assumed that this study represents a survival assessment.

3.2.2

Maximum elevated weight: (100% variable load) Minimum elevated weight: (50% variable load)

6800 t 5800 t

The weight distribution can be deduced from plans and the original data package. For both cases, survival C. LCG: 16.0m VCG: O.Om tolerance: ± 1.5m

of G. is fwd. of aft legs centers. port oflongitudinal C L . either way.



3.2.2 (cont) Information is not currently available on: substructure and derrick position hook, rotary or setback loads. However the above C. of G.'s incorporate the substructure and derrick. Weight of one leg excluding can: Weight of footing spudcan:

880 t 200 t

Determine C. of G. of dry leg + spudcan: height of can 6.25 m leg length excl. can: 93.75 m [880( 6.25 + li (93.75)) + 200(li (6.25))] VCG above can tip 880+ 200 43.87m Determine buoyancy of legs and can: Buoyancy per unit length

=

displaced weight of one bay/length of one bay 1.025 x enclosed volume of one bay + 3.75m 3.232 tim

Obtain buoyant upthrust on can. Assume can is flooded. = 200 t Mass of can For density of steel of7.856 t/m 3 , volume of steel in can 20017.856 = 25.46 m 3 displaced volume of water. so buoyant upthrust 1.025 x 25.46 26.1 t

3.2.3

To meet an overturning requirement it is permitted that water can be added to the hull weight (bear in mind). [not used]



OBTAIN ENVIRONMENTAL DATA

@]

Environmental Conditions - General 50 year return period extreme conditions are to be used here. Wind, wave and current act in the same direction, and at the same time as the extreme water level. No directional data is to be used here.

B

Wind

3.4.1

The 50 year, 1 minute sustained wind at 10m above sea level is 39.0m/s.

3.4.2

In the absence of further information, the 111 Oth power law of Sections 3.4.2/4.2.2 will be used.

rn

3.4.3

4.2.2 There is no requirement for the jackup to be altered between operating and survival modes.

~

Waves

Hsrp 8.6 m specified Hmax 16.0 m specified ( 1.86 Hsrp O.K.; also O.K. for airgap calcs per 3.5.2) 3.5.1.1 } These are specific applications ofH to be considered in the 3.5.1.2 } course of the analysis. 3.5.1.2 Tass= 13.0 s specified. Check: 3.44~Hsrp = 10.1 s} Tass lies within range just. 3.5.1 3.5.1

3.5.3

4.42 ~Hsrp = 13.0 s } A JONSWAP spectrum has been specified. In-house programs cater for this spectrum. We have here specific values ofT p and Tz, so the peak enhancement factor is defined Tp = 12.4 s } Tp/Tz = 1.305 Tz 9.5 s } so by interpolation, y= 2.77 Check range of Tz: 3.2~Hsrp 9.38 s so Tz is within range.

3.6~Hsrp 10.56 s According to the note to 3.5.3, a range of periods should be considered, or a 2 parameter spectrum should be used with the same peak period. Here, consider a single JONSW AP period only. 3.5.4

Short crestedness should be investigated (see also 7.3.7.5). Here, for example purposes, ignore spreading.

3.5.5

If dynamics is significant, watch out for other seastates with large dynamic response.



~

Current The specification of the current profile is surface current bottom current

2 m/s 2 m/s

} }

block profile

This supersedes all of 3.6.1 and 3.6.2. Stretch profile to get same surface component in waves. See section 4.4.2 4.4.2

OBTAIN GEOTECHNICAL DATA

~

Geotechnical and Geophysical Information. It is assumed that the unit is to operate in areas for which there is considerable experience ofthe geotechnical conditions. Two locations are to be considered, with the soil conditions of 1) homogeneous sand and 2) homogeneous clay as follows:

38°

"I

0.011 MN/m 3

Sand: (locn 1)

triaxial friction angle submerged unit weight

Clay: (locn 2)

submerged unit weight "I 0.009 MN/m undrained cohesive shear strength varies linearly from cu 0.040 MN/m2 at surface to Cu = 0.080 MN/m2 at depth of 10m

3

It is not necessary to go through sections 3.12 to 3.16 for a site where there is operating experience.

All the items in this box of the FLOWCHART have now been carried out. Skip the "other aspects" box (outside the scope) and go to the box for air gap & penetrations

Page 15 Other Aspects


OTHER LIMITING ASPECTS OF THE ANALYSIS

I

Will 'other aspects' limit suitability: Hydrodynamics, Section 4.8 Foundations, Section 6.4 Condition of unit, Section 8.7

~

The unit should be assessed for the other limiting aspects as identified in the FLOWCHART box. These, however, are outside the scope of this document and so are not considered further. The following analysis assumes that these aspects are not limiting.


Page 16 Other Aspects


Page 17 Airgap & Penetration

DETERMINATION OF AIRGAP AND PENETRATION I

Determine airgap, Section 3.7 (or as dictated by other considerations, ifhigher). Estimate leg penetrations (based on maximum preload), Section 6.2.

The actions in this item of the main FLOWCHART concern leg length demands. Their completion is straightforward and so no local route sign is required.

DETERMINE AIRGAP

6

Water levels and Airgap

3.7.1

Lowest astronomical tide:

25 m above sea bed.

3.7.2

Highest astronomical tide:

28.5 m above sea bed.

Mean water level MWL = 12(28.5 + 25) = 26.75 m MHWS + surge 3.5 + 1.5 = 5.0 m above LAT 5 + 26 = 31.0 m above seabed

3.7.3

Extreme SWL

3.7.4

For cases where lower water levels are more onerous, minimum SWL = MLWS + (-ve) surge This information is not immediately available. Wait and see whether it crops up. [in the end the MLWS was not used in this analysis]

3.7.5

Determine minimum airgap above LAT: clearance extreme SWL crest height augap

1.50 m 5.00 m 11.03 m 17.53 m

(see below)

From 3.5.2 a maximum wave height of 16m is applicable for airgap calculations. The required format of this information is as a 50 year extreme crest height. (4.4.1) The wave crest height is to be found from an applicable wave theory according to 4.4.1. Refer to figure 4.1. } H/gT2 Hmax = 16.0 m 0.0096 } Tass 13. s g 9.81 mls } d/gT 2 0.018 d 30 m } This indicates that the seventh order stream function should be used. An in-house program using stream function gives: C50

=

11.03 m


Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 ESTIMATE LEG PENETRA nONS

A penetration of 1.25m has already been specified for this assessment, for either soil type, corresponding to an experience-based approach. Although not necessary for this analysis, the penetration calculation sections are now considered. 16.21

Prediction of Footing Penetration During Preloading

6.2.1

Looking for an equilibrium position between vertical footing load and bearing capacity of the footing. Investigate backflow; there can be no back flow since D = 0.0 for 1.25m penetration. Now obtain the vertical capacity ofthe footing at various levels of penetration and match against the vertical footing load (during preload). The sections 6.2.2 to 6.2.6 give ways of deriving the vertical footing capacity for a range of soil types. Here only uniform clays and uniform silica sands are considered in detail.

6.2.2 to 6.2.6 @2>Penetration in Clays For an undrained clay foundation as defined earlier ("locn 2"):

=

L.



6.2.2 (cont) This leaves the cu , A and V which are dependent on the penetration depth. A given depth will have unique values of each of these , and so the variation of Qu with penetration depth can be plotted:

penetration h2 The level of penetration is found by substituting the preload footing vertical reaction during preload Vp for Qu, and reading offthe penetration depth h 2. Here, the footing reaction during preload is SO.734 MN, so the above procedure amounts to finding the depth at which: 6.117 cwA + 0.009 V = SO.734 Ifh2 indicates complete embedment, the above formulation will require revision, but the same principles of equilibrium apply.

~Penetration in Silica Sands The silica sand identified earlier ("locn 1") is characterized by:



~Penetration in Carbonate Sands Basically this is not a mainstream calculation.

~Penetration in Silts Obtain range of capacities from loose sand to soft clay and refer to illustrations above.

~Penetration in Layered Soils (Outside the scope of this document) penetration

,

A value of airgap and a value of penetration are now obtained. Now check there is sufficient leg length.


Page 21 Leg Length

ASSESSMENT OF LEG LENGTH

I

Is adequate leg length available? Section 3.10.

The foregoing calculation of penetration and airgap will determine how much leg reserve there is for a given water depth. The availability ofleg length should be checked against this, and if there is insufficient reserve the unit is not recommended for use. In some such cases it may be possible to refine the penetration analysis, or use less preload so that the calculated leg length reserve can be made acceptable.

IS ADEQUATE LEG LENGTH AVAILABLE?

[]JQJ

Refer to section 3.3 of the guideline. A leg length reserve of 1.5m is recommended. For this unit:

fixed factors (keel to u.G.): airgap above LAT: water depth (LAT): penetration:

19.00 m 17.53 m 25.00 m 1.25 m

total length used:

62.78 m

Leg length: reserve:

100.00 m 37.22 m

Therefore the unit has plenty of leg length in reserve.

With adequate leg length the analysis can proceed to a comparison with existing calcs. Otherwise refinements to the penetration calculation should be considered, or other suitable preload levels and the check repeated.


Page 22 Existing Conditions

REVIEW EXISTING CALCULATIONS

I

Applicable calculations according to PRACTICE exist and show acceptability? Section 2.4.4

If there has been an historic study on the same type of unit at a similar location it may be appropriate to draw conclusions from it for the current assessment. This is the lowest level of application ofthe PRACTICE as mentioned in 2.4.4.

APPLICABLE CALCULATIONS ACCORDING TO PRACTICE EXIST AND SHOW ACCEPTABILITY? There have been no analyses of this unit at this location according to the PRACTICE. Therefore acceptability cannot be demonstrated at this stage.

W EXT ITEM

Had there been a previous study according to the practice in which the above calculated parameters had been as severe, or more severe, and for which the unit had been acceptable for the relevant assessment checks, then no further analysis would have been necessary and the unit would have been acceptable.

Because this was not so, the higher order studies of section 2.4.4 must be carried out. All the following items in the flow chart apply to either the simple or the detailed methods of 2.4.4.

Page 23 Wind load / hydro


ESTABLISH WIND LOADS AND HYDRODYNAMIC COEFFICIENTS

~stablish wind loads, Section 4.2, Hydrodynamic coefficients

Sections 4.6 & 4.7.; Prepare analysis models, Section 5,

1

This item of the FLOWCHART contains two sizable amounts of work. It is therefore presented in two parts. Here the wind loads and hydrodynamic coefficients are tackled.

WIND LOADS - route Introduction

4.1

Wind Force Calculations or Model Tests

4.2 4.7.6

ESTABLISH WIND LOADS Only use the wind loads determined in section 4 with the environmental loads also determined in section 4. The section has been designed to produce a matching load set. Mixing parts of section 4 with other sources may lead to errors. Wind forces may be obtained from calculations or from model tests. Wind force Model / \ calcs Tests 4.7.6 ~ ~ 4.2

I

§Model tests for wind loads Model tests must consider: roughness Keulegan-Carpenter number dependence Reynolds number dependence It is not appropriate here to carry this option further.


Page 24 Wind load I hydro

E)Wind Force Calculations This section gives a method for deriving the wind force on any block or structure of the unit above the SWL. The force is given in relation to a reference windspeed V ref, to the area of the block projected normal to the Vref, and to coefficients Cs and Ch which for shape and elevation respectively. There are two options for obtaining the Ch • Note that "shielding effects are not normally included in the calculation". This is because a profile area viewed from the direction under consideration is to be used. For the typical jackup 2, p 1.2224 kg/m 3 <4.2.1> Vref = 39.0 m/s (1 min sustained at 10m) The application of loads is left to the . For this calculation the wind force on the structure above the SWL shall be partitioned into: force on hull structure

+ force on legs above hull + force on legs, hull to SWL total wind force above SWL Wind force on hull structure: By treating the hull structure as a single block, the force on the hull structure can be written in the form: Force where A

hull

is an effective area for the hull. The corresponding moment about the SWL is

Moment

=

Y2p V

2 refAhullZhull

where Zhull is the effective moment arm. From this subsection we can calculate an effective area and moment arm from the numerous contributions ofthe projected areas of the blocks making up the hull structure. The following procedure is applied here. Identify major blocks in the hull structure. The descriptions in Table 4.2 can be used here with outboard profiles and general arrangements. Measure projected areas of blocks and their effective arms above the SWL for the elevated position.



-

Obtain height coefficients for the blocks either from Table 4.1 or from the equation C h = (Z/ZrefifN with N = 10 here.

I Option>

Use Table 4.1 to get height coefficients.

The blocks are subdivided so that no blocks straddle the height divisions in Table 4.1. The Ch are applied accordingly.

I Option>

Obtain height coefficients from equation.

Blocks are subdivided so that none has vertical dimension greater than 15m. The Ch are obtained for the elevations of the centers of effort of the blocks. All elevations below 15m shall be treated as if the elevation were 10m. 4.2.3

d. Obtain shape coefficients from Table 4.2. e. Calculate the sum of the projected areas to get A hull .

4.2.1

f.

Calculate the wind forces on each block and add them up. Calculate the wind moments on each block and add them up. Take the ratio of the two sums to obtain Zhull.

The above procedure is applied in a spreadsheet. Summary results for the jack-up hull excluding legs are: heading

wind force

(0)

(t) 2539 2637 2104

0 60 90

wind moment reSWL (tm) 61504 70180 51325

arm above SWL (m) 26.05 26.62 26.24

efftve. area (m 2 ) 2540 2836 2104

arm above keel (m) 15.69. 16.26. 15.88.

Wind force on exposed leg sections: The procedure for calculating the wind forces on the exposed leg sections is identical to that for the hull structure, except that shape coefficients shall be computed from section 4.6. GOT04Ji6 (hydro model to get ~ C s) .J,..

From the leg calculation, values of C s can be found under the heading C De for the equivalent leg with no marine growth.



4.2.1 (cont) HYDRODYNAMIC COEFFICIENTS -route Leg Hydrodynamic Model Hydrodynamic Coefficients for Leg alternative route: Model tests

4.6 4.7

4.7.6

ESTABLISH HYDRODYNAMIC COEFFICIENTS The parts of section 4 relevant to this calculation are 4.6 and 4.7. Sections 4.3 to 4.5 need not be considered in detail until later, but it may be useful at this stage to be aware of their content. The use of model tests to establish coefficients is permitted as an option.

Leg I Model hydro Testi\model

§

Model Tests for Hydrodynamic Coefficients Model tests must consider: roughness Keulegan-Carpenter number dependence Reynolds number dependence

o

For this document it is not appropriate to carry this option further.

4.6.1

The form of the hydrodynamic model depends on the nature of the modeling technique applied down the line. The must decide whether a detailed representation of all leg is to be applied in the structural model (the detailed model), or whether an equivalent model of a single tubular is to be used for the leg. In the 5.6.4 hydrodynamic model calculation, details of all are considered in both approaches, so it is not difficult to change from one modeling approach to another. Section 5.6.4 gives details of the structural modeling options.

Leg Hydrodynamic Model

[!JI



Use node to node member lengths. Check whether there are any large, non structural items to be included. Identify any free standing pipes or water towers requiring their own modeling. There are no non-structural items identified for the legs of this unit. There are no freestanding pipes or water towers.

4.6.3

Check for the contribution of the part of the spudcan above the seabed: 30m ) depth> 2.5 Hs, so spudcan (i) water depth (SWL) 21.5m) contribution insignificant 2.5Hs = 2.5 x 8.6 (ii) penetration spudcan height

1.25m ) 6.25m)

penetration < liz spudcan height, but check (i) overrides.

In the absence of further information, it is taken that the spudcan contribution to hydrodynamic loading is negligible. 4.6.4

Shielding and solidification effects are not normally considered. There is no reason to override this here. Interference is applied to the current, as detailed later in section 4.5.3. 4.5.3

0Hydrodynamic Coefficients for Leg : 4.7.2

For this unit there is no specification of anti-fouling measures, and so it is assumed that the are rough below MWL+2m. From 3.7.2 we have MWL = 26.75m. Hydrodynamic details for tubular : horizontal braces:

length outer diameter

8.680m 0.350m

diagonal braces:

length outer diameter

5.736m 0.350m

internal spanbreakers: length outer diameter for all of the above: above MWL + 2m, CD above MWL + 2m, CM below MWL + 2m, CD below MWL + 2m, CM

4.340m O.lOOm 0.65 2.00 1.00 1.80

The unit has not had previous operation and so there is no likelihood of roughness occurring beyond the above stated limits. 4.7.3

There is no site-specific information on marine growth thickness, and so a thickness of 12.5mm is to be applied to all below MWL + 2m. Chords excepted, as noted below. There is no documentation of anti-fouling measures for this unit.



For gusset plates, use Co = 2.0 with projected visible area. Represent the visible area A j as an arbitrary (but representative) length lj, and an effective diameter Di, such that Aj = IjD j. Apply Cm values as in table 4.3. For this unit it is convenient to treat the gussets attached to a chord as a single item . .J,.. 0° Define directions on each chord as demonstrated. Visible dimensions are calculated as summarized in the following table. Select lj = 1.575m.

e

visible width (0) (m) 0 0 0.084 30 0.l14 45 0.l54 60 90 0.250 From symmetry the 4.7.5

Dj visible projected area A area (m 2 ) (m2 ) (m) 0 0 0 0.0424 0.0367 0.0233 0.0374 0.0698 0.0589 0.0885 0.0562 0.0885 0.143 0.0909 0.l65 values for 180° - e equal the values for

e, for e > 90°.

The chords ofthis unit are of geometry covered by Figure 4.5 and the subsequent equations. backplate to pitchpoint length W backplate width D

=

=

1.2m 1.0m

From 4.7.3, marine growth on the teeth ofthe racks and on the guided surfaces is to be ignored. In this case, the guides are at either side of the back plate and so Wand D do not change with marine growth. There is no variation in C Opr and so marine growth does not affect the chord hydrodynamic properties. Set the reference dimension Dj = D = 1.00m. For local directions as defined for the gussets, the following member drag coefficients are obtained:

eco) 0 15 30 45 60 75 90 105 120 135 150 165 180

DprCm) 1.000 0.966 1.033 1.202 1.289 1.289 1.200 1.289 1.289 1.202 1.033 0.966 1.000

For all headings the chord CMj

=

C Opr 1.700 1.742 1.783 1.825 1.867 1.908 1.950 1.400 1.472 1.543 1.615 1.888 2.000

COj 1.700 1.683 1.842 2.l94 2.407 2.459 2.340 1.805 1.897 1.855 1.668 1.824 2.000

2.0. This does not change for marine growth.


Page 29 Wind load I hydro

All leg are now covered.

The necessary calculation for the detailed leg is now complete. If required the information can be combined in an equivalent leg model as described in the option below. Instructions applicable to both cases follow the equivalent leg model.

equivalent leg 4.6.5

~

Equivalent leg model An equivalent leg model comprising a single tubular of effective hydrodynamic properties may be constructed from the detailed member hydrodynamic information. For each different type of bay, overall parameters are derived as follows: effective diameter: effective drag coefficient:

CDe

=

L CDei

effective inertia coefficient

CMe

=

L CMei

with

s

bay height Clj angle in horizontal plane of member axis from flow direction ~i angle of member axis from horizontal. Ae = effective area ofleg = nD/14 and other symbols as defined above.

Using these relationships, spreadsheets were set up. Summary results for this unit follow. Zero degrees heading is defined as parallel to the axis of symmetry of a chord cross-section. The leg exhibits triangular symmetry.

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 4.6.5 (cont)

(1)

for no marine growth (above MWL+2m)

Heading (0)

0 30 45 60 (2)


De (m) 2.24 2.24 2.24 2.24

C De

Ae (m2) 3.94 3.94 3.94 3.94

3.41 3.58 3.85 4.00

C Me 1.85 1.85 1.85 1.85

for 12.5mm marine growth (below MWL+2m) Heading (0)

0 30 45 60

De (m) 2.31 2.31 2.31 2.31

C De

Ae (m 2 ) 4.18 4.18 4.18 4.18

3.90 4.06 4.32 4.47

C Me 1.78 1.78 1.78 1.78

End of equivalent leg option

4.2J

~

There is now sufficient information to calculate the wind loads on the exposed leg sections by use of an equivalent leg, using C s = C De and projected width De. Before progressing to the next item, conclude data collection for the wind loading. 4.7.6

4.7

V l Hydrodynamic coefficients and wind forces are now determined. Go on to the next action in the FLOWCHART box i.e. analysis models.


Page 31 Analysis models

PREPARE ANALYSIS MODELS

Establish wind loads, Section 4.2, Hydrodynamic coefficients, Sections 4.6 & 4.7. Prepare analysis models, Section 5

1 The second action in this FLOWCHART box is now considered. The action refers to analysis models, but it was found to be easier just to establish the structural models at this stage, having read through the other sections 5.1 to 5.4. Sections 5.5 and 5.7 on load application crop up when tackling the response calculations.

STRUCTURAL MODELS - general route Introduction Observe general considerations Select model(s) Construct models

5.6.1 5.6.2 5.6.3 5.6.4 to 5.6.7

PREPARE ANALYSIS MODELS For most jack-up configurations it is necessary to develop a Finite Elements computer model. The choice is between + Type a: most detailed and complete model + Type b: like type a but with more simplified legs. + Type c: simplest 3 leg model + Type d: detailed model of one leg Features discussed in this section of relevance to the typical jackup 2 are: There is a floating jacking system without a fixation system. Therefore there is a couple due to horizontal loads from chords touching upper and lower guides. Watch out for bending moments being locally high. The jacking system comprises unopposed pinions, and so locally high chord bending moments come in through vertical and horizontal offsets of pinion reactions W.r.t chord centerlines.



On the basis of the descriptions of the model types and the considerations in 5.6.2, selection of appropriate analysis models can be made. The following checks are required for this study: overturning, foundation, leg member loads, pinion system loads. The models which would satisfy these requirements are, from table 5.1: • • •

Type a Type b Type c with type d

It has been decided that the most suitable models for application in this office are the equivalent 3 stick leg model (type c) in conjunction with the single detailed leg (type d). It is appropriate to calibrate the leg properties in the 3 leg model against the characteristics of the detailed single leg model.

GOTO selected model route( s)

a+b c/d

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 5.6.3 a) Fully detailed 3 leg model

Detailed Leg Hull Hull/leg connection Spudcan

Page 33 Analysis models 5.6.4a 5.6.5 5.6.6 5.6.7

This modeling technique has not been used for this study. However, many of the notes for model types c and d are applicable, and appropriate reference is made to these. See notes for model type d. See notes for model type c. When constructing the hull model, accommodation must be made for the jackhouse connections, and the lower guide connections to the leg. A grillage model must therefore have beams which connect with the roots ofthe jack house model. It will be necessary to add in links from the grillage to the lower guide connection points. These should have stiffnesses representative of the local hull structure. See notes for model type d. Instead of earthing the jackhouse and lower guide connections, these can be linked in to the hull grillage or plate model. Connections as applied in model type d are usually appropriate. See those notes. References to the spudcan section are OK for this model.

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 5.6.3 b) Combination leg 3 leg model

Combination Leg Hull Hull/leg connection Spudcan

Page 34 Analysis models 5.6.4c 5.6.5 5.6.6 5.6.7

This modeling technique has not been used for this study. However, many of the notes for model types (c) and (d) are applicable, and appropriate reference is made to these. The notes on the hull sub-model and hull/leg connection sub-model as given for model type (a) also apply and are reproduced for this model type. The connection between the two leg model parts is such that "the plane of connection remains a plane after the leg is bent" 1

5 .6 .4c I Leg model

5.6.4a

Construct a detailed leg sub-model as for the model type d, but for a length extending from at least 4 bays below the lower guide to at least 4 bays above the upper guide, or the top of the leg (whichever comes first).

5.6.4b

Using this length of detailed leg sub-model, clamp one end and apply 'unit' loadcases to determine equivalent leg beam properties. Set up colinear beam sub-models for the remaining lengths of each leg above and below the guides.

5.6.4c

Make connections between the portions of leg by rigid links from the three chords to the equivalent leg beam. This will ensure the boundary condition described in 5.6.2. Note that in these regions, spurious stresses may emerge from the response calculations. See notes for model type c. When constructing the hull model, accommodation must be made for the jackhouse connections, and the lower guide connections to the leg. A grillage model must therefore have beams which connect with the roots of the jack house model. It will be necessary to add in links from the grillage to the lower guide connection points. These should have stiffnesses representative of the local hull structure. See notes for model type d. Instead of earthing the jackhouse and lower guide connections, these can be linked in to the hull grillage or plate model. Stiff or rigid equivalent beams will be sufficient to meet the recommendations for this model. See model type c.


Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 Equivalent leg Hull Hull/leg connection

5.6.3 c) Equivalent 3 stick leg model

5.6.4b 5.6.5 5.6.6

The simple 3 leg model (type c) will be used to obtain global loads, such as spudcan reactions, and intemalleg loads at the lower guide. If detailed leg strength checks are to be performed, the model type (d) will also be required. In constructing the simple 3 leg model (type c) fairly detailed modeling of the hull/leg connection will be necessary to determine effective stiffnesses. If a type (d) detailed leg model is to be used later, it might also be used for this part of the calculation. Therefore it would be more efficient to construct the type (d) model first. Model ... type 1 - -..... " (d) I

.011

.... "'III~

5.6.4

I5.6.4l

The appropriate leg sub-model is the 'equivalent' leg, comprising a series of colinear

~ beam elements as described in 5.6.4b.

Note that the modeling of the legs here is tied in with the hydrodynamic coefficient modeling of equivalent legs. 5.6.4b

DJ

To determine the required properties ofthe equivalent beams there is a choice of methods.

IOPTION> Apply formulae contained in Figure 5.1. The unit has a leg side of type B ('K-brace'). Therefore the equivalent shear area of one side is: (1 + v)sh

AQi

= ~+~_~(N3 Ao

where

s N L

h d AD Av Ac l.e.

2

8A v

3.75m Lis = 48.75/3.75 48.75 8.68m 5.74m 2 0.0183m 0.0183m2 0.1 93m2

NA c

3

_. Li

2

J

l=l,N

bay height 13.0 active leg length * to be revised side width diagonal length diagonal section area horizontal section area chord section area


Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 5.6.4b (cont)

The leg cross section is type A (triangular), and so:

I.

OPTION

>

0.579 m 2 0.0331m2 7.10 m 4 0.451 m 4

3 ACi YzAQi lhAci h2 'l4AQih2

leg area leg shear areas leg 2nd mom. area leg torsional mom.

Get cross sectional properties of leg by application of 'unit' load cases to the detailed leg.

.

If a detailed leg model is available it is possible to use it to determine the equivalent leg cross sectional properties. The technique is to fully clamp the leg model at one end so that there is no hull or jackhouse involvement, and to apply loads at a known distance away. By comparing deflections with a simple beam model of the same length, under the same loads, effective beam properties can be deduced. L

wi V

~I
V

~

E.A.I,~

6z

y

-

y

-1

wi II

p

<-

-1

P

To

For the calculations below, L = 48.75m (*to be revised), E = 200x1 06 kN/m2 and G = E/2.6. The leg properties are here assumed to be symmetrical. Leg sectional area: Apply P = 10000 kN, W load application. A

=

=

0, M

=

PLlEoz

o.

Obtain leg vertical deflection =

oz at the point of

0.581m2

Leg 2nd Moment of Area: Apply P = 0, W = 0, M of load application.

=

86800 kNm. Obtain leg horizontal deflection Oh at the point

= ML2/2Eoh

=

6.85m2


Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 5.6.4b (cont)

Leg shear area: Apply P = 0, W = 10000 kN, M load application.

= O.

Obtain leg horizontal deflection ~ at the point of

WLIE

AQy

2

= A Qz = Oh _ (wI! 13EI) = 0.025m

5.6.2c

In accordance with the recommendations for the spudcan modeling, nominally stiff beam properties are put in for the length of the legs corresponding to the spudcan. Use the following: 10 m 2 4 100 m 4 100 m 2 1m

5.6.5

There are two recommended techniques available for modeling the hull structure. Jackup models incorporating a hull model may use either, depending on the preference of the .

III ~

I

OPTION>

Construct hull using plate elements.

This is the more detailed of the modeling techniques and is likely to reproduce hull flexibility and stressing with the greater accuracy. A model can be set up representing bulkheads, decks, top, bottom and sides with equivalent plate properties to for stiffeners, spacers, etc.

I OPTION>

Generate grillage of beams.

The hull flexibility can be represented by constructing a grillage of beams with properties chosen to represent the flexibilities ofthe hull. This method involves some approximation and certain aspects may not be modeled properly, for example in-plane shear stresses. However, the overall flexibility is adequate for the application of the 3 leg stick model, and use of the detailed single leg model with hand calculations is expected to be of sufficient accuracy for this unit. The first stage is to establish the geometry of the grillage. This is based on the plan of bulkheads and plate sides, and is shown in figure 1a. Next, properties are to be assigned to the equivalent beams. It is appropriate to assign sectional areas, second moments of area in plane and out of plane, and the torsional second moments of area. A typical calculation is as follows. Assign long, beam-like portions of the structure, following a bulkhead or like which can represent the web. An effective width of the beam-like component can be deduced from inspection of the plan, such that most of the plan area is assigned to beams with mInImUm



Figure 1a. 3 Stick Leg Model (showing hull beam grillage)

Figure 1b. Division of Hull Structure into Equivalent Beams

-_. __ ._,


Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 5.6.5 (cont)

overlap (figure 1b). If this web is too large, a limit such as effective width ~ where t is the 'web' thickness might be appropriate. For example, a beam section to represent the sides of the unit is: f--8.5m

-----t

~ ~20mmthick

25mmthick

y

8m

4x

\ AH

2.67m

Area Ixx Iyy Itors

0.872 m 2 4 10.32 m 5.61 m 4 (see below) (see below)

~ \.- 40mm thick

Some standardizations and adjustments may be appropriate. It is noted that the PRACTICE does not advocate use of nominally high in-plane stiffnesses, but does advise that attention is paid to this aspect; as the beams will be effectively constrained against bending in the plane ofthe hull (by the deck plating) increase Iyy to say 50m4. For the torsional properties, the overall torsional moment of area of the hull is estimated and divided up between the beams. Transverse cross section at full width:

8m

11

25mm thick }jI

f-

20mm thick 40mm thic~

20mm thick --t

--7-4-.-6m---"~

Overall torsional stiffness of a box section (not from RP): 4A2 It = L(b / t) for plates of thickness t, width b and box enclosed area A. Therefore for the above section, It = 250 m4. This is apportioned equally between the 4 four longitudinal beams, such that each has torsional second moment of area It = 60m . Performing the above calculations for each beam produces a hull model which matches the requirements of 5.6.5b.



~ The hull/ leg connection model can now be put in. This unit has a floating jacking system with no fixation system. A simplified derivation of the equivalent leg-hull connection stiffness is applicable. Modeling shall consider the effects of: + guide and system clearances, stiffness and clearance. + wear + construction tolerances + backlash 5.6.6f

Construct simple (conservative) model of interface. This comprises springs to represent vertical, horizontal and rotational stiffnesses. The derivation of the spring stiffnesses is left fairly open. Guidance is available in the Commentary on how to do some of the modeling. The "extreme importance" ofthe hull/leg connection modeling has already been stressed. C5.4 From C5.4, the following are key variables: + bending, shear, torsion ofleg + axial bending, shear, torsion of jackhouse + stiffness of upper and lower guides + clearance/ tolerance of legs within guides + backlash in jacking system + type of leg guide arrangement + rack/pinion arrangement. Hand calculation of effective springs for stick leg model Model the interface as follows: Moment M applied produces rotation Q radians, and is resisted by: upper guide stiffness lower guide stiffness pinion stiffness shockpad stiffness shearing of leg

«upper guide

pinion set

lower guide»

All clearances and backlash is assumed to be taken up. From the equations in 7.3.5.3 an approximate rotational stiffness for this leg/hull connection is:

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 5.6.6f (cont)


chord centers spacing combined elevation system stiffness (see below) relative stiffness of guides dist. between upper and lower guides shear area of leg modulus of elasticity of leg material

where

A corresponding estimate of vertical stiffness is Kz 3 ke

h d E Aq

Here,

8.68m 15 m 200 x 106 kN/m 0.0368 m 2

Relative stiffness of upper & lower guides:

-0 F-

Assume all flexibility comes from comer posts. Ignore flexibility of hull behind lower guide. ku 3F/(3 as shown 3(3EI/L3) 3x3x200x 106 X 1.0/(0.150)3 5.4 X 1011 kN/m

III Note that in reality the jackframe bracing will contribute significantly to the stiffness, and should also be taken into . Combined stiffness of fixation system:

c h o r

Three pinion stiffnesses act with the compressed shock pad stiffness to produce ke 4kp k s k =-----'-e ks +4kp

d

Effective acting shockpad stiffness = 80 000 kN/m Single pinion stiffuess = 200 000 kN/m giving ke Thus we get

=

73 x 10 3 kN/m

45 x 106 kNm/rad 220 x 10 3 kN/m



For comparison, the values obtained from analysis using unit loads to a detailed leg and connection model were: ko 23 x 106 kNm/rad kz = 200 X 10 3 kN/m The hand calculated stiffness is conservative on the upper leg. Differences in ko may be due to the modeling of the action points of the pinion springs, to gaps operations and to leg bending. A high horizontal stiffness is assumed i.e. kT = 109 kN/m CHECKLIST FOR HULL/LEG stiffness jacking system orientation clearances guide, clearances Wear construction tolerances backlash

OK? y y no no no no no

Obtain hull/leg connection springs from application of unit loadcases to the detailed leg. The procedure is similar to that used to get equivalent leg stiffnesses. Here the full detailed leg model (type d) is used with its hull/leg connection model and compared to a single beam with springs at its roots.

The spring is assumed to be acting at the level of the lower guide at the leg centroid. Loads are applied at the effective penetration. The distance between the spring position and load application point is L.



The leg stiffness properties are assumed to be known. Here we have L 48.75 m * to be revised A 0.581 m 2 I 6.85 m 4 E 200 x 106 kN/m2 Vertical spring stiffness, kz: Apply P = 10000 kN, W = 0, M = O. Obtain total vertical deflection at point ofload application Oz = 0.054m Portion of <>z due to leg compression = PLiEA = 0.0042 m portion of Oz due to spring compression = 0.054 - 0.0042 = 0.0498 kz = Force/defln = 1000010.0498 = 2.0xl0 5 kN/m. Rotational spring stiffness, ko: Apply P = 0, W = 0, M = 86800 kNm. Obtain total horizontal deflection at point of load application ~ = 0.250m Portion of oh due to leg bending = ML212EI = 0.0631 m Portion of oh due to spring rotn. = 0.250 - 0.0631 = 0.187 m ko = Moment/rotn

=

CHECKLIST FOR HULLILEG jacking system stiffness orientation clearances guide, clearances Wear construction tolerances backlash

86800 x 48.7510.187 = 23 x 106 kNm/rad OK? y y y y y y y

assuming detailed leg model is OK

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 5.6.3 d) Single detailed leg model.

Detailed leg Hull/leg connection Spudcan


5.6.4 5.6.4a 5.6.6 5.6.7

15.6.4.1 Guidelines on the construction of a leg model are noted as follows. Model the following: chords, horizontal braces, diagonal braces, internal braces. Loads will be applied near the spudcan so include a spudcan model. 15.6.4a

IDefine ts coordinates as intersections of chord and brace centerlines.

Simplify

some intersections. Ignore gusset plates. Set up mesh geometry The leg consists of a single basic unit (one bay) repeated 25 times: Component list 3 chord sections 3 horiz. braces 6 diag. braces 3 internal spanbreakers

side of length 8.68m defined by horizontal / - - - \ - spanbreakers meet intersects. (chord at horizontals centroids midpoints offset by O.06m) ilin ~ diagonals intersect horizontals at I midpoints. with spanbreakers Bay height of 3.75m I defined by chord/ horizontal intersects. --- diagonals meet chords at same point as horizontal braces. Offsets ignored

\ J' _V_

1

Bottom bay begins 6.25m above the can tip. Properties of The properties of the do not vary up the leg. Chords:

Area Iyy Izz AQ Itors

0.193 0.0115 0.026 0.106 0.02

m2 m4 m4 m2 m4

y

z.• ) \ .. z y

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 5.6.4a

Horizonta1/ diagonal braces: Outside diameter 0.350 m wall thickness 0.035 m Internal spanbreakers: outside diameter thickness

0.100 m 0.006m

Material properties: modulus of elasticity density

200 x 106 kN/m 2 7860 kg/m 3

Checklist for detailed leg Chords included Horizontal braces Diagonal braces Internal braces Spudcan ts coordinates modeling Gusset plates ignored

~


OK? y y y y no y y

Construct hull/leg connection model For this unit the leg bending moment is shared by the jacking system and the guide structure, with the shock pad and pinion stiffness affecting the bending moment distribution. Guidance notes: jacking system to be properly modeled in of stiffness, orientation, clearance. consider effects of guide and system clearances consider effects of wear consider effects of construction tolerances consider effects of backlash at gear train and between pinion and rack.

5.6.6a

Upper and Lower guides Guide : Upper and lower guides restrain movement parallel to back plate of chords and towards the rack as shown. These can be represented by gaps in these directions. It is appropriate to set the gaps at the correct positions with respect to the chord beam position as constructed (as

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 5.6.6a (cont)


opposed to the chord centroid). Between chord beam and gaps place springs of stiffnesses derived below.

.L

T

Guides are to be stiff with respect to the adjacent structure, so put in nominally high spring stiffnesses, in all directions since the gaps for degrees of freedom.

~

~

Iw • wH-

/\ (leg)

6

so, for guide springs, kx = ky = kz = 10 kN/m

guide model

Lower guide position: Nominal position is derived using the sum of leg penetration, water depth and air gap. Cover two positions: one at a node and the other at the mid-span. Guide lengths:

IOPTION> IOPTION>

Model guide length by a set of spring connections to hull

2m length

Model guide by a single spring connection to hull, and for length in bending moment diagram.

Here, put single connections at positions of centers of guides. 5.6.6b

Jacking pinions Use manufacturer's specified stiffness: 200,000 kN/m at pitch point for this unit. Single rack pinions resist deflection normal to the tooth, i.e. vertically and horizontally parallel with the rack. Sliding possible across rack. Use linear springs. Incorporate offset of pitch point from chord neutral axis.

The pinion connection is modeled as a stiff link from the chord to represent the offset of the pitch point from the chord beam axis. A gap is positioned at the position of the pitch point and orientated with the normal to the tooth surface at that point. Springs are used to represent the pitch tooth and pinion stiffness. The gaps can be sized to represent the total clearance due to backlash, wear and tolerances. pinion gap = O.OIm

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 5.6.6c

The unit has no fixation system.

5.6.6d

Shock pads


Shock pads are positioned at the top and the bottom of each pinion stack. The pads act in compression. It is assumed that the upper pads are always in compression. The shockpads have no lateral stiffness however the pinion stack is restrained horizontally, at top and bottom, in the jack-frame. Manufacturer' effective shockpad stiffuess = 80000kN/m Nonlinear characteristic is not available. Model as shown: zero length gap so pad takes only compression. Laterally stiff. shock pad spring (linear but nonlinear preferred) 4-high pinion model (see above), rigidly linked sliding for uncompressed pad with gap and spring to allow for load reversal 5.6.6e

Jackcase and associated bracing For this construct a representative beam structure. This is shown in figure 2. The beam positions are such that the centroids of the jack posts are in the correct positions, as are the centroids of the horizontal and diagonal bracing . Some interpretation of beam positions has been performed at the top comers ofthe jackcase to fit in guide connections. Beam properties are drawn from the plans: vertical jack post beams:

all other beams

I tors

0.150 m 2 4 1.0 m 4 1.0 m

Area Ix = Iy I tors

0.115 m 2 0.031 m 4 4 0.015 m

Area Ix = Iy

Torque equalization is discussed later. CHECKLIST FOR HULL/LEG jacking system stiffness Orientation Clearances guide, clearances Wear construction tolerances Backlash

OK? y y y y y y y


Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 Figure 2. F.E. Model of HulllLeg Interface

PINION SPRINGS

LOWER GUIDE

@ ~

o

:r::

u

o

:r::

u



It is assumed here that the flexibility of the structure adjacent to the lower guide is incorporated in the lower guide connection springs.

The model is earthed at the roots of the jackhouse, and at the lower guide connections. 5.6.7

Spudcan Model the spudcan with rigid links since we are not studying lower leg strength here. Define a node on the leg section centroid at the elevation of the effective penetration, as used for the 3 leg model pin-point. This will facilitate application of base loads. Link the spudcan node to the bottom nodes of each chord by rigid links. modeling routes

Structural models are now set up. Note their application with seabed reaction point and fixity (5.2, 5.3), and leg inclination (5.4). Now move on to the next item in the FLOWCHART

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 DETERMINE RESPONSES OF UNIT

Page 50 Determine Responses

I

Determine responses (e.g. SDOF method), Section 7/Figure 7.1.

I

Choose more detailed: Response calculation (Section 7/Figure 7.1). Response calculation including foundation fixity (Section 7/Figure 7.1 & Section 6.3/Figure 6.10).

---+

All the options for determining the unit response are considered in this section including the SDOF method, the frequency domain and time domain detailed dynamic approaches. The hierarchy of modeling techniques is represented in the commentary C7.5, which can be referenced when a "more detailed response calculation" is required.

RESPONSES - general route General Quasi-static response Dynamics preparations

Determine natural period (s) Determine dynamic response: inertial loadset approaches or detailed dynamic analysis

7.1 7.2 (C7.2) 7.3.1 7.3.2 7.3.3 7.3.4 7.3.5 7.3.6 7.3.7

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 DETERMINA nON OF RESPONSES


@]

General

7.1.1

Loads consist of:

7.1.2

Consider separately the extreme response (sections 7.2 and 7.3), and fatigue (section 7.4). A fatigue analysis is outside the scope of this study.

7.1.3

Assess the extreme response by quasi-statics with inertialloadset or by dynamics. For typical jack-up assessments, the time-varying nature of the wave loading will amplify the quasi-static responses and should be considered.

7.1.4

The separation between the natural period of the unit and the peak period of the wave spectrum indicates the need for a dynamic assessment.

dead and live loads, section 3.2 wind and hydrodynamic loads, section 4

Consider this when the natural frequency has been obtained. 7.1.5

Note that there is no guarantee that the simple method of 7.3.6.1 will "adequately represent results of a more rigorous analysis of any given site".

Use the simple method of7.3.6.1 to evaluate the need for dynamic analysis. 7.1.6

It is acceptable to apply dynamic effects as an inertial loadset (see 7.3.6.1) obtained

from a simple model. A detailed model can then be used to get the responses. 7.1. 7

Select load combinations according to the requirements of section 8. The following categories of response evaluation are required: Dead load, D: Live load, L: Extreme load E:

weight in air, ballast, equipment, buoyancy, permanent enclosed liquid. Variable load (maximin) placed at most onerous c of g. Assessment return period wind, wave, current load with associated PLl

Inertial load Dn:

Contribution of dynamics over and above the loads above, including associated PLl. (not applicable to quasi-statics)

These are applied for the assessment criteria as detailed in the table in 7.1.7.

Example ("Go-by") Calculations for a Typical Jackup Page 52 Determine Responses Preliminary Issue, May 1994 7.1.7 (cont) The next most useful stage in the calculation is the determination of the quasi-static response. The nature of the assessment check is such that a quasi-static response is required as well as a fully dynamic response, although with a unit partial factor on dynamic component Y4 = 1.0, it is possible to by- the quasi-static. The main method of obtaining the quasi-static response is according to section 7.2, with the more detailed methods discussed in the commentary, C7.2.

~

detailed methods C7.2

7.2

Refer to commentary for more detailed approaches. These resemble the detailed dynamic approaches which are explored later in this document, but with unit mass artificially set to zero.

o

Quasi-Static Extreme Response with Inertial Loadset

7.2.1

Apply deterministic, quasi-static design wave according to all the relevant requirements of sections 3 to 6. Specific sections are drawn out below.

(3.5.1 )

From 3.5.1, Hsrp = 8.6m, and Hmax = 16.0m. It is correct here to use 3.5.1.2 for the deterministic analysis, so that a reduced wave height is used. Thus: Hdet = 1.60 Hsrp = 13.8m An appropriate wave kinematics model is to be selected using section 4.4.1:

(4.4.1)

Refer to figure 4.1. = 16.0m

}H / gT2

= 0.0096

d / gT2

= 0.018

= 13.s = 9.8 1m / s = 30m

This indicates that the seventh order stream function should be used. (4.3)

Hydrodynamic forces.

(4.3.1)

Check for applicability of Morison's equation: wavelength tubular diameter

z

200m (from theory) for the extreme wave, 125m (from theory) for the significant wave. 0.35m

Therefore the wavelength is greater than five times the reference diameter and so Morison's equation is applicable.

Example ("Go-by") Calculations for a Typical Jackup Page 53 Preliminary Issue, May 1994 Determine Responses (4.3.2) This formulation for the drag force is used in the in-house programs. The CD and D are calculated elsewhere. The velocity term Vn is a variable within the programs. Determine the value of a to be used (relative particle velocity or not): u = Vc + 1tBs / Tz Tn = 45s D. =10 i.e. a = 1. I

= 2 + 1t(S.6 / 95) = 4.S} uT _0

= 22> 20

Dj

•

(4.3.3)

This formulation for the inertial fluid force is used in the in-house programs. CM and A are given elsewhere. Un is a variable within the programs.

7.2.2

The spudcan-foundation interface should normally be modeled as a pin t unless there is justification for using fixity, however 7.3.5.2 notes that under some circumstances the pinned assumption may be non-conservative. pinned 1\ fixity foot ~~

fOOY

I Pinned

From 5.2, the reaction point is 0.625m above the can tip. Simple s are to be put into the finite element 3 stick leg model.

------..>

I.------FiX-i ty

Include foundation fixity, if justifiable, as a combination of horizontal, vertical and rotational springs. (5.3.2)

Include nonlinear rotational, lateral and vertical soil springs.

(5.3.3)

Upper and lower bound values should be considered as appropriate for the areas of structure under consideration.

(6.3.4)

Degree of fixity depends on: - soil type - spudcan characteristics - maximum vertical footing load during installation - foundation stress history - structural stiffness of unit - geometry of footings - stress levels and load conditions under consideration Apply springs at seabed reaction point. From 5.2 this is 0.625m above the can tip

(6.3.4.1) Estimation of foundation fixity Fixity is assessed by considering whether the footing load combination falls within the yield surface or not. The quantity rf is a measure of whether the load combination falls within the

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 (6.1.4.1) (cont) surface or not, so that: rf ~ 1 load combination outside yield surface (no fixity) rf ::; 1 load combination lies within yield surface (fixity)


Because the degree of fixity will affect the footing load set for a given environmental load condition, an iterative approach must be adopted to find the equilibrium position. In application of the method, separate types of treatment will be necessary for "snapshot" analysis (quasi-static plus inertia) and for time domain analysis involving numerous loadsteps.

I 1\

time domain snapshot analysis ~~ analysis "snapshot" For a single point in time it is possible to iterate to a solution of a level fixity for a given set of environmental loads. SELECT INITIAL LEVEL OF FIXITY If zero fixity is initially preferred then the footing is modeled as a pin-point, and structural response calculations are carried out. With the resultant load set, the failure ratio rf is determined and foundation springs derived as required. This is discussed as an example later. An analysis where a pinned footing lead to foundation assessment failure would follow this path in the "Response calculation including foundation fixity" part of the FLOWCHART. The recommended course of action if there is reason to expect foundation fixity is to assume a failure ratio of zero (rf = 0) which enables full fixity. The calculation of the required rotational, horizontal and vertical spring stiffnesses in such an approach is now carried out for the unit, with the two soil types. In preloading, assume a vertical footing load of 50000kN on each leg. Rotational spring stiffness: The rotational spring stiffness K3 is given by: G B3 K =fx-.:..-f3 3(1- v) f

where the effective spudcan diameter is B = 7m, and:

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 (6.3.4.1) (cont) For sand (drained): Gr 660 S' 660x(VLo/A) v 0.2 = -rr/ln( l-rf)

Page 55 Determine Responses - LOWER BOUND 214285 kN/m

2

0

30625 kNmlrad For clay (undrained): Gr 39 cu 39 x47 v 0.5 1 - rf

- LOWER BOUND 1833 kN/m

2

o

419146 kNmlrad Horizontal and Vertical spring stiffnesses: These are given by the expressions 2G y B vertical K =-I I-v 16G h B(1- v) horizontal K2 = x fr 7-8v For sand: 1500(VLo/A) = 487000 kN/m 2 Gy so

so

KJ

8522000 kN/m

Gh

150(VLo/A)

K2

808000 kN/m

For clay: Gv so

so

1833 kN/m2

KJ

51324 kN/m

Gh

1833 kN/m 2

K2

34216 kN/m

48700 kN/m

2

(lower bound)

(lower bound)

With footing springs established the snapshot response calculation can be carried out, new footing loads obtained and new springs determined. Convergence of these load iterations indicates when the correct fixity has been applied and the assessment can be continued

Example ("Go-by") Calculations for a Typical Jackup Page 56 Preliminary Issue, May 1994 Determine Responses (6.3.4.1) REVISION OF FIXITY USING CALCULATED FOOTING LOADSET (cont) In this example it is assumed that the first round of the fixity calculation has been performed i.e. using the above spring stiffnesses, a response calculation has been carried out. First the footing load set is inspected for its position against the yield surface. Suppose from the SDOF quasi static plus inertia approach, the following D+L+E+Dn loadset was obtained: Qv

QH QM i) For sand:

32500 kN 330 kN 22010 kNm 50000 kN as above 0.12 VLo 6000 kN 0.075 B V Lo 26250 kNm 0.92 < 1.0 so the point is within the yield surface

then

and so fr(calc) = 0.36, giving a new fr = 0.68. Using this value, spring stiffnesses are reevaluated and the procedure is repeated until convergence is obtained. ii) For clay The in the failure ratio equation are HLo M Lo

cuoA = 40 x 154 (assuming the (c uo + cUl)As 6160 kN term is small and can be 0.1 VLoB conservatively ignored) 35000 kNm

This gives rf = 0.69, and so the same procedure described for sand should be followed.

For time domain calculations two approaches are offered.

~B

[XlB

Run a pinned case dynamics. Using spring stiffnesses obtained by quasistatic response calculations, make conservative adjustments to the seabed reactions only. Start with springs calculated from a quasi-static response evaluation. Put these into the dynamic model and perform a time domain calculation to get the characteristic seabed reactions (e.g. most probable maximum). Using these characteristic reactions, evaluate new spring stiffnesses and repeat until convergence is obtained.

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 (6.3.4.1) (cont) snapshot/dynamic


V +

V + (5.1.2)

end of footing options

Consider a range of headings to pick out the most onerous for each assessment case. For the three leg stick model, apply loads at 0°,30°,60°,90°, 120°, 150°, 180° for the full unfactored quasi-static load (D + L + E)Pi1 to pick out the worst heading for each assessment.

definition of headings w.r.t Bow

(5.1.3)

For each loadcase the wave is to be stepped through the model structure to find the worst phase. This can be done using the in-house program STA TLOAD, which identifies max horizontal force on the leg. Run for 20s in 0.25 steps to pick out most severe instant, then apply those loads in the Finite Element simulations.

(5.7.1)

Application of Dead Loads: Dead loads comprise weights. To model this a gravitational acceleration is applied to the FE model which shall have suitable masses and densities. The hull dead weight is 4800t. This is applied via a scaled hull beam element density with lump masses applied at leg center nodes to ensure the correct center of gravity (less than 10% of total mass in lump masses). The requisite weight is to be achieved by first putting in guessed densities, allowing the FE package to evaluate the modeled mass and then adjusting the scaling and lump masses before re-running. The center of gravity of the dead load is not available, but is assumed to lie within the range specified for dead plus live load below.

(C5.3.3) As a conservative measure apply 50% of hull sag derived in this way at suitable stages of the analysis The leg weight in air (excluding spudcan) is 880t which is applied as an effective leg density. Buoyancy of 3.232 tim is subtracted from the dry leg weight per unit length in determining an effective buoyant leg density. The spudcan dry weight is 200t and the buoyant upthrust has been calculated as 26.1 t, so an effective buoyant spudcan element density is obtained.


Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 (C5.3.3) (cont) For modeled leg area ofO.581m2 ,

dry leg buoyant leg buoyant can

wtllength

effective density

(tim)

(tlm 3 )

9.387 6.155 27.82

16.157 10.594 47.883

Application of Live loads: The maximum variable load is 2000t, and the minimum variable load is 1000t. In conjunction with the dead hull load, the hull center of gravity has a range of positions: 16m forward of aft leg centers ± 1.5m Om transverse of CL ± 1.5m The four "comer" positions shall be considered for each case, and the most onerous positions shall be used in the subsequent analyses. The weight modeling shall be performed in the same way as for the dead load, with hull masses and densities scaled up as required. Application of Environmental loads: (5.7.2)

Wind loads are applied as nodal point loads to the three leg stick model. The distribution is adequately covered by applying loads at three elevations: for the legs below the hull, for the hull and for the legs above the hull. The total loads for each heading and associated elevations are integrated in the in-house program NEWS TOWA. This procedure will ensure correct total shear and overturning moment on each leg due to wind, and correct leg loads near the hull. For the program, the equivalent leg model is used with the effective hull areas as calculated earlier in this document. A more sophisticated model might consider individually every element and member in the hull and legs, but this is not necessary here. sample: heading 60°

(5.7.3)

item legs above hull hull legs below hull

wind force 143.5t 296.5t 4.1t

arm above can tiQ 79.9m 57.9m 4 1. Om

legs above hull hull legs below hull

122.3t 296.5t 3.5t

79.9m 57.9m 40.9m

The in-house program STATLOAD will be used to generate nodal loads up the legs (approximately ten nodes per leg) representative of the correct load distribution. The loads from the instants of maximum total horizontal hydrodynamic load shall be applied in the finite element model for each heading. The equivalent hydrodynamic leg model derived earlier is used in the three leg model. More detailed modeling may be preferred.

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 (5.7.3) sample: (cont) hydro heading item force (kN) maximum horiz. 16732 60 -380 minimum horiz. maximum horiz. minimum horiz.

120

(5.7.5) (5.5.1)

time in wave cycle (s) 11.25 4.75 1.50 5.50

Second order effects can be considered in a number of ways. large displ.

I

A

methods~~

5.5.3

§

13807 -516


geometric stiffness methods 5.5.4

Large displacement methods The in-house FE package includes the large displacement option, and so this shall be used to include P~ effects

B

Geometric stiffness methods

~IOPTION

>

[Xl

>

IOPTION

Add orthogonal, horizontal spring elements between the hull center node and earth, with negative spring constant of stiffness -P/L. This won't work on our software. Amplify linear-elastic displacement by os/(l-P/PE) manually, and calculating additional P~ moment. This is not employed here. 5.5.3

5.5.4.

V ~

It is assumed that the full set of analyses as detailed above has been carried out and that

the most onerous cases have turned out to be 60°, maximum variable for preload and member strength, and 120°, minimum variable for overturning and sliding. These will be considered in detail below. It is not held to be constructive to provide excessive and ultimately unhelpful results for

other cases. In reality the above cases have been selected from a preliminary analysis. For accuracy, refine the storm headings to be perpendicular to leg centers i.e. apply headings 61.7° and 118.3°.

Example ("Go-by") Calculations for a Typical Jackup Page 60 Determine Responses Preliminary Issue, May 1994 5.5.4 Apply the following sequence ofload cases: (cont) D dead load only D+L dead and live load (D + L+ E)P~ dead, live, environmental load with associated P~ effects. To obtain the component parts of the response parameters for section 8, vectorially subtract the equivalent parameters from these runs e.g. subtract the D run leeward base vertical from the D+L run leeward base vertical to obtain the L response parameter. The following table summarizes the results of these analyses. Note that the directions of the load vectors are not written here, but may need to be considered at a later stage. Minimum hull, heading at 118.3° (overturning, sliding)

footing reactions: vertical (kN) 1 2 3 shear (kN) 1 2 3

D+L+E

D+L

D

L

E

15653 33425 36420 4221 6949 6801

29042 27418 29042 139 129 139

25680 24337 25680 115 107 115

3362 3081 3362 24 22 24

-13389 6007 7378 4359 6887 6721

Maximum hull, heading at 67.7° (structural strength, preload)

footing reactions: vertical (kN) 1 2 3 shear (kN) 1 2 3 lower guide loads: moment (kNm) 1 2 3 vertical (kN) 1 2 3 shear (kN) 1 2 3

D+L+E

D+L

D

L

E

23898 23520 47981 7990 8125 4995

32436 30530 32436 162 152 162

25680 24337 25680 115 107 115

6756 6193 6756 47 45 47

-8538 -7010 15545 8081 8196 4832

213350 207270 232680 19038 19417 43499 140 64 4311

7166 6680 7166 27991 26085 27991 162 152 162

5051 4708 5051 21235 19892 21235 115 107 115

2115 1972 2115 6756 6193 6756 47 45 47

211320 216450 225520 -8953 -6668 15508 111

207 4146

Page 61 Example ("Go-by") Calculations for a Typical Jackup Detennine Responses Preliminary Issue, May 1994 5.5.4 (cont) The only surprise in these results is the leeward leg shear (leg3) at the lower guide from the Environmental load (E) at 67.7°. This is very large due to the wave phasing. It happens that almost all the hydrodynamic loading appears on the other two legs, and so the base reaction is almost entirely reacted by lower guide shear. The displacements of the unit are not checked using partial factors, and so need only be considered after dynamics later. To obtain the full set of required parameters for quasi-static response assessment, the member load vectors are to be detennined. For this, some of the results from the three stick leg analyses above are applied to the detailed leg model. It is appropriate at this stage, before structural strength checks are carried out, to add in

extra lower guide moment due to leg offset. application below.

This is discussed in the detailed leg

Note that for the more complex three leg model with truss sections in the vicinity of the lower guide, the critical member load vectors would mostly be available by now, but adjustment would be necessary to for the leg offset. This might be by hand corrections or by application of additional leg moments to the model. Application of loads to detailed leg model wjackh.

in-

d

.... ... . swl h

Y d r 0

-

"/\

....

"/\ "/\

-

I

footing reacts.

With the detailed model that has been set up earlier it is possible to apply nodal loads in some detail, and there is considerable flexibility in the method required. For example, with the jackhouse and lower guides providing earth, footing reactions can be applied to the spudcan at the level of the effective pin-point, hydrodynamic loads can be applied to nodes up the leg with magnitUde varying to represent reality, and wind loads can be distributed among nodes above the sea water level and clear of the hull. Member densities can be scaled to accommodate buoyancy within a gravitational field.

Here, however there is some knowledge on the critical parts of the unit and so a simpler modeling technique is preferable. The critical are known to be in the region of the hull/leg connection. To correctly generate member load vectors in this region, a small number of discrete nodal loads can be applied, so long as they are applied some distance away from the hull. A distance of 4Y:z bays above or below the area between the guides is suitable to allow the loading to distribute around the critical area correctly. Two leg positions are to be considered: one with lower guide level with a horizontal brace, and one with lower guide level with a chord mid-span. To avoid repetition, only the latter is discussed here. Note that to ensure the most accurate load distribution in

Page 62 Example ("Go-by") Calculations for a Typical Jackup Determine Responses Preliminary Issue, May 1994 5.5.4 (cont) the hull region, the elevations of some of the environmental loads must be adjusted for the different positions. Pinion equalization: It is specified that pinions are equalized in the still water condition (D + L). This can be done by a number of FE modeling techniques, for example iterative stretching and compressing pinion springs until equal net spring loads are obtained under the still water condition. Here, to avoid excessive attention to detail a simplified approach is adopted.

The loads in the pinion model springs are noted for the D + L case, and the deviations from the overall average pinion model spring load obtained. These deviations are then added to or subtracted from the D + L + E simulation spring loads, to produce an approximate "equalized" load set. This approach does not represent the redistribution of loads onto or off the guides, as would be produced by true equalization. Gravitational loads: The detailed leg model is to be placed in a gravitational field. This means that if the member densities are suitably set up, the variation in loads due to self weight will be modeled. Since we are interested in the region near the hull, the leg material density is iteratively adjusted until the weight of a single bay equals the expected value for the dry leg. As the model is not earthed at its footing, a compensating load is required. Vertical loads are to be applied at the horizontal bracing/ chord junctions 412 bays below the lower guide, such that the load at the lower guide is correct. Therefore the weight of the modeled unit below the load application point must be ed. This is done by applying a single vertical point load at the center of the spudcan model. The additional moment due to P~ is built into the lower guide loads from the 3 leg model run, and so linear elastic analysis is performed. Lower guide loads: Loads are applied to create the correct lower guide axial load. The lower guide vertical loads are added to the weight of the 412 bays of leg and distributed evenly between the three chord nodes for this. The lower guide shear load is applied 412 bays below the lower guide, is distributed evenly between the three chord nodes, and is resolved into appropriate components based on the 3 leg model output. The lower guide moment derived from the three leg model has to be adjusted in a number of ways. Firstly the above application of shear load in itself generates lower guide moment, which has to be vectorially subtracted. Secondly, the 50% of the hull sag calculated in the three leg model runs has to be vectorially

Page 63 Example ("Go-by") Calculations for a Typical Jackup Determine Responses Preliminary Issue, May 1994 5.5.4 (cont) subtracted. Thirdly, the additional moment due to leg offset has to be added on. It is assumed that this is acting in the most onerous direction, namely the resultant direction after all of the foregoing adjustments. (5.4)

In the absence of further information, the offset is 0.5% of the length of leg below the lower guide: offset = 0.005 x 44.61 * = 0.22m *to be revised

additional moment = seabed reaction x 0.22m This applies to the D and (D + L) load cases as well. The resultant moment after all adjustments is applied by means of vertical couples across the three load application nodes. Wind loads: The wind loads on the hull and the legs below the hull are built into the lower guide loads. The loads above the hull are applied to ensure correct modeling of upper guide reactions. Loads are applied to two nodes on each chord. The elevation of the effective wind force on a single leg above the hull is expressed as a height above the lower guide. The wind force is distributed between the two sets of nodes which straddle this ideal elevation, so that the correct effective arm above the lower guide is applied. Application to the unit: For the detailed leg runs, the following load sets were applied: spudcan vertical ing force

=

93,733 kN D+L

D

D+L+E

loads applied 4Y:z bays below the lower guide: vertical (MN) shear (MN) moment (MNm)

22.788 0.115 @62.2° 6.313 @62.2°

29.544 0.163 @62.3° 8.070 @62.2°

45.052 4.311 @60.5° 167.624 @61.0°

0.0

0.0

0.469 @61.3° 79.9m above can tip

wind forces: force (MN) elev'n (m)

7.2

C7.2

V .J,.

7.3

Dynamic Extreme Response

Example ("Go-by") Calculations for a Typical Jackup ~minary Issue, May 1994


This document is arranged to indicate a progress route considering all the options on the way, one after the other. The PRACTICE allows for repetition of stages of analysis, albeit at different levels of complexity, so that parts of this go-by document may be encountered twice, especially for dynamic response calculation. 7.3.1 7.3.2

7.3.2.1

Reading through these sections provides a useful introduction to various aspects. Certain information is discussed which will be required during the calculation, whether using finite elements or not. It is logical to prepare this information now. a) - The structural and equipment mass, and the variable loads are the same as used for the quasi static analysis procedure. - Added mass has to be included. For the equivalent leg model, the added mass per unit length ofleg is: Aep(C Me - 1) = 4.18(1.025)(1.78 - 1) = 3.34 tim Note that this should not be permitted to conflict with the buoyancy modeling. b) - The stiffness of legs, leg to hull connections and spudcan-foundation interfaces should be modeled. This has already been investigated in the setting up of leg models. c) - Damping is discussed in 7.3.7. It has already been decided that the relative velocity formulation is to be used, although for some methods this is not practicable. A nonlinear foundation model is not in use at this stage. Therefore the applicable percentage of critical damping is: structure, etc. foundation hydrodynamic

2% 2% 0% with relative velocity 3% without relative velocity

For this document the global dynamic behavior will be obtained using the 3 leg stick model, and where required, detailed analysis completed using the single detailed leg model. Detailed modeling for dynamic analysis may be preferred, but this is outside the current capability ofthis office.

Example ("Go-by") Calculations for a Typical Jackup Page 65 Preliminary Issue, May 1994 Determine Responses 7.3.3.1 Current may be steady. Wind may be represented by a steady flow of air. Wave and current should be considered in combination (4.3), as has been done in the quasi static analysis so far. (4.3)

For the time-varying random seastate analyses the in-house jackup suite of programs applies the required form ofloading, assuming an equivalent leg model.

7.3.3.2

Wave period data for each analysis type is available. Use the range of periods in 3.5.1.2 or 3.5.3 at a suitable stage.

7.3.4

Refer to the flowchart in figure 7.1. For an initial estimate of dynamic amplification go to 7.3.6.1. For random dynamic analysis go to 7.3.6.3/7.3.7. But first get the natural period.

~

The Natural Period(s) The natural period(s) may be determined either by a finite element structural model, or by equation.

equation 7.3.5.3

1

7 .3 .5 .2

>

finite elements 7.3.5.2 Finite element approach:

The three leg stick model is sufficient to meet the requirements of this paragraph. Derivation of sway stiffnesses from a detailed model has been discussed earlier in setting up the three leg model. A similar approach could be employed for a detailed three leg model, or for a model with foundation stiffness. For natural period calculations, small displacements are assumed, and so nonlinear P~ effects are ignored. The added mass of the model is built in by adjusting the effective member densities of the appropriate sections of equivalent leg: mass/length of dry leg added mass

9.387 t/m 3.34 t/m

for leg area effective leg density

0.581 m 2 , 16157 kg/m3

effective leg + added mass density

=

(9.387 + 3.34) x16157 9.387 21906 kg/m3

Page 66 Example ("Go-by") Calculations for a Typical Jackup Determine Responses Preliminary Issue, May 1994 7.3.5.2 (cont) The spudcan is assumed flooded. It both carries a volume of water and displaces a volume of water. spudcan steel volume spudcan enclosed volume spudcan dry mass

200 t

mass of water enclosed in spudcan

(288-25)xl.025 270 t

added mass displaced by spudcan assuming CM = 2.0

288(1.025)(2 - 1) 295 t 200 + 270 + 295

total dynamic mass

=

765 t

For 6.25m of spudcan model length, and 0.58lm2 area, effective dynamic spudcan density

= 210 670kg/m3

Buoyancy is omitted from this calculation. Damping is not necessary. The hull weight is for the D + L load, maximum hull case.

mode

freguency (Hz)

Qeriod(s)

sway

0.223

4.48

surge

0.226

4.42

yaw

0.287

3.48

}

See attached figures 3a,3b,3c

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 Figure 3. First 3 Natural Modes of Vibration of Unit

..........

-

-

........


Page 68 Detennine Responses

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 17.3.5.3) Approach using equations

The fundamental period is estimated as Tn = 21t ~M e / Ke , where M

= e

Now, MIa Mlb

N So

M hull + M + M Jb N Ja 2 Mhul\ = 6800 t (100-1.25-25-15.36-3)x9.387 = 520 t (1.25+25+ 15.36+3)x21.906xO.581 t 1066 3 3320 t

Also, for zero soil rotational stiffness:

3EI

Ke = Now,

[1-

~]

x=-------=------==-------=

e [1+

E I L P PE

12Fg I 3EI 7.81] 2+ + 2 AFy Y FrLK rh AsFhL = 200xl0 6 kN/m 2 7.10 m4 43.985 m 113 Mhul\g 6 = 0.022 X 10 kN aEI 0.687 x 106 kN with a defined as the solution of (Krs + Krh )aEI } --'--=-2- = " ' - - { (aEI) - (K Krh ) rs Krs 0.0

tanaL = with

Krh

k u"----_ d 2 __ Y2h2k + ___

1+(2.6k ud/EAq) 4.52 x 10 7 kNm/rad for h 8.68 m 3 kJ 73 x 10 kN/m ku 5.4 X 1011 kN/m d = 15. m Aq = 0.03675 m2 so that a = 0.022 J

Fg A Fy

1.125 0.579m 1

1+ EA + EA } { LKyS LKYh 0.07680 for K ys = 00 K yh = 3kj

=

219 x 103 kN/m

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 7.3.5.3 Y 48.41m 1 YK 1 + -rh2EIH 0.89 for Estimated IH = 44 m 4


1

{ =

1+

EAs +--=---EAs} 2.6LK hs 2.6LK hh

1

for

K hs

=

00

Khh

=

00

Thus we get an effective stiffness

Ke

=

9.485

X

103 kN/m

and so the estimated natural period is: Tn

21t.J332019485

Tn

3.72 s

7.3.5.4

The estimates from the two methods for natural period are 4.5s and 3.7s, which are about the same order, but demonstrate the uncertainty described in this section.

(7.1.4)

A check of figure C7.1 indicates that the second reinforcement peak of the wave force transfer function occurs at around 4 seconds. As this is close to the estimate of the natural period the SDOF method (7.3.6.1) may be unconservative. However, since 11 = 0.36 there is a relatively large separation between the natural period and the peak of the wave spectrum so the difference should be relatively small. Tn "'" 4 s) Tp"'" 12.4 s)

11 = Tn/(0.9Tp)

=

0.36

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 DETERMINE DYNAMIC RESPONSE


The first division in the dynamic response calculation is between inertial loadset approaches and detailed dynamic analysis approaches. The latter tend to be the more complete, but complicated. detailed dynamic analyses 7.3.7

1

7 .3 .6

>

inertial loads 7.3.6 Inertial Loadset Approaches

These approaches represent additions to the quasi-static loads determined earlier. Inertial loads may be applied either a distributed loadset or by an equivalent point load at the hull center of gravity. Here the latter is preferred. For a simple approach go to 7.3.6.1. For more complex approaches go to 7.3.6.2.

other methods 7.3.6.2 SDOF 7.3.6.1 7.3.6.9 The classical SDOF analogy. This is the recommended first approach to evaluating the dynamic response, and is quick and simple. Calculate the DAF:

Tn/T, where

~

0.33 0.07 from (7.3.2.1)

3.7s (manual calculation) 0.9Tp = 11.2 seconds.


Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 7.3.6 (cont) 1 DAF ~[(1- Q2)2 + (2SQ)2] 1.12

This is greater than the lower threshold of 1.05 in the commentary. In other words, dynamics is worth further investigation.

If dynamics can be ruled out at this stage then Dn = 0 and all the response parameters required for the assessment have been obtained. Then go the next entry in the FLOWCHART Determine inertialloadset: To obtain Fin it is again necessary to inspect the hydrodynamic force data in the inhouse program STATLOAD. 118.3° heading:

so

13.807 X 103 kN -0.516 x 103 kN

maximum hydrodynamic load minimum hydrodynamic load

BS(Q-S)Max BS(Q-S)Min

BSAmplitude

=

7.162

X

3

10 kN

(1.12 - 1) x 7.162

X

10 3 = 860 kN

61.7° heading: BS(Q-S)Max = BS(Q-S)Min so

16.732 x 103 kN -0.380 x 103 kN

maximum hydrodynamic load minimum hydrodynamic load BSAmplitude

and Fin

=

8.556

X

3

10 kN

(1.12 - 1) x 8.556

X

103 = 1026 kN

These loads should now be applied through the hull center of gravity along with the D + L + E loads from the quasi-static analysis in a response calculation including second order sway effects, to generate the (D + L + E + Dn)P L\ response. Vectorially subtracting the (D -+- L -+- E)P L\ response parameters from these results yields the Dn for application in the assessment criteria. To apply the loads through the center of gravity, the hull model is modified slightly to include a structural node at the c. of g.

I


Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 7.3.6 Results of 3 leg model simulation: (cont) Minimum hull, heading at 118.3 0 (overturning, sliding) Hull displacement for fullioadset

footing reactions: vertical (kN) 1 2 3 shear

(kN)

1 2 3

=

0.71m

D+L+E

D+L+E+Dn

Dn

15653 33425 36420

14778 32819 36901

- 875 394 481

4221 6949 6801

4539 7216 7077

318 267 276

Maximum hull, heading at 67.7 0 (structural strength, preload) Hull displacement for fullioadset = 0.84m D+L+E

D+L+E+Dn

Dn

23898 23520 47981

23315 23046 49038

-583 -474 1057

1 2 3 lower guide loads: moment (kNm) 1 2 3

7990 8125 4995

8360 8474 5303

370 349 308

207270 213350 232680

224139 229322 249238

16869 15972 16558

vertical (kN)

1 2 3

19417 19038 43499

18830 18558 44551

-587 -480 1052

shear

1 2 3

64 140 4311

313 439 4619

249 299 308

footing reactions: vertical (kN) 1 2 3 shear

(kN)

(kN)

Page 73 Example ("Go-by") Calculations for a Typical Jackup Determine Responses Preliminary Issue, May 1994 7.3.6 (cont) As for the quasi-static analysis, the lower guide loads and wind loads on the legs above the hull are applied in a detailed leg model to obtain the required Dn member load vectors for the structural strength assessment. D + L+ E + Dn loads applied 4Y2 bays below the lower guide: vertical shear moment

(MN): (MN): (MNm):

46.105 4.619 @ 60.6° 178.493 @ 60.6°

wind force: force elevation

(MN): (m):

0.469 @ 61.3° 79.9 m above the can tip

17.3.6.213> Other approaches to obtaining an inertialloadset

An inertial load set method using the entire SDOF DAF function for all frequencies is described in appendix C7.B.2.2. This is discussed under detailed dynamic methods later. IOPTION) The determination of an inertial loadset from more complex random dynamic approaches is illustrated as follows. It is assumed that quasi-static and dynamic MPM responses have been

note:

calculated for both base shear and overturning moment. Values are as follows (from drag-inertia time domain approach): base shear: mpmeRd 9000 kN mpmeRs 8500 kN overturning: mpmeRd 818440 kNm mpmeRs 779804 kNm These base shears are hypothetical, and are provided for illustration. Follow the instructions in Section 7.3.6.3/figure 7.2 or in figure C7.B.l part 2. Note: The following is based on an earlier simplified procedure and is to be updated. 17: F1i 9000 8500 500 kN 18: M1i = 818440 - 779804 = 38636 kNm Choose to match F 1 19: Apply Fb as: 200 kN through hull centroid 100 kN through each leg centroid

I

Example ("Go-by") Calculations for a Typical Jackup Page 74 Preliminary Issue, May 1994 Determine Responses 7.3.6 elevation of hull centroid above can tip = 44.98m (cont) elevation of buoyant legs centroid above can tip = 44.18m 20:

M2i = 200(44.98) + 300(44.18) = 22250 kN

21:

M3 i = 38636 - 22250 = 16386

22:

Apply M3i as a point load through the centroid (a couple across the leg centers might be preferable).

inertial loadset approaches

v.J,. Once the required response parameters have been obtained then the next entry in the FLOWCHART may be engaged. More detailed analysis methods are in 7.3.7.


Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 17.3.7 Detailed Dynamic Analysis Methods.

>

Several detailed dynamic analysis methods are now considered. It is expected that in many analyses, this section can be called upon to produce responses of increasing levels of sophistication. The table in C7.5 provides an indication of their hierarchy.

The following details apply to all methods. although the underlying statistics are gaussian, the nonlinear forcing makes the excitation non-gaussian, and this must be included. the spudcan-foundation interface should be modeled as a pin t, except when fixity has been justified. Here it is assumed that fixity is not justified. the relative velocity formulation has already been shown to apply in this case. From table 7.1, total global damping (% of critical) has already been determined as 4%. (both details in the quasi-static response section). A Jonswap spectrum with peak enhancement factor of 2.77 has already been identified. For random analyses the significant waveheight in 3.5.1.3 is applied: [1 + Yzexp( -d/25)]Hsrp 9.9 m for d Hsrp =

30m 8.6m

The first decision to be made is whether to perform calculations in the frequency or time domains.

I

frequency 1\ time domain ~~ domain

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 7.3.7 (cont) frequency domain analysis


Detailed frequency domain analysis options considered here are the drag-inertia parameter approach and the closed form solution, both found in the Commentary.

The notes on loading in table 7.2 should be observed. for frequency domain calculations, linearization of the wave-current loading and the structural response will be necessary. the wave spectrum shall be divided into equal frequency slices (at least 200) for the calculations. Obtain the most probable maximum responses as directed in table 7.3. The MPM has a 63% chance of being exceeded by the maximum of anyone three hour storm. Within a three hour storm, this level is reached by one in one thousand peaks on average. There are two options for frequency domain analysis. Appendix C7.B.

)C7.B)

draginertia parameter C7.B.2.1

I

A

closed form solution C7.B.2.2

First go to the commentary



C7.B.2.1 drag-inertia parameter The first step is to obtain the quasi-static part and the inertial part of the total dynamic response, calculating the means and standard deviations. This is done in the frequency domain using Figure C7.B.3. Assuming a frequency domain analysis has been carried out, the mean quasi static and dynamic responses are available, as are the corresponding transfer functions between wave elevation and response parameter. These transfer functions are for the required wave and current loading. The inertial transfer function can be obtained as indicated. Spectral analysis techniques will yield the standard deviations of quasi-static, inertial and dynamic responses as indicated.

With the above information the method in Figure C7.B.4 produces the extreme response. This has been carried through in the time domain examples later; the capability to produce the required frequency domain calculations was not available in this office at the time of production of the Go-by document.


Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 C7.B.2.2 closed form solution

This is the application of the method proposed by Jensen and Pedersen ofthe University of Denmark.

Step 1 Illustrative maxima and minima from the time histories of overturning moment are tabulated below for a range of waveheights with the assessment current loading. The periods have been constrained to fit the relationship: T = 1 + 4.lH°.4 Note that for the calculations, a value H' = 0.86H has been input to be consistent with Section 3.5.1.2 of the PRACTICE. H(m) 14.2 8.0 0.0

H'(m) 12.21 6.88 0.0

ill} 12.85 10.4

OTMmax (kNm) 599060 243705 99385

OTMmin (kNm) -13 343 21 109 99385

Step 2 These data points are used to obtain the coefficients Ai in a cubic expansion. The notation Yo is used for overturning moment. Yomax (T = 12.85s) Yomin (T = 12.85s) Yomax (T = lO.4s) Yo(H = 0) Hence,

Ao + 7.1 AI + 50.41 A2 + 357.9 A3 = 599060. 357.9 A3 = -13343. Ao - 7.1 AI + 50.41 A2 Ao + 4.0 AI + 16.00 A2 + 64.0 A3 = 243705. 99385. Ao

Yo(t) = 99385. + 24343.h(t) + 3838.h2(t) + 372.6 h\t)

This gives satisfactory values for response maxima in the expected range of wave periods, but is not accurate for the minima, as can be seen by investigating Yomin(T = lO.4s). Here we are only interested in the maxima, so the approximation will suffice. To obtain the coefficients ai, divide the coefficients Ai by (Hsl4)i a stochastic sea: Yo(t) = 99390. + 52340.U(t) + 17740.U2(t) + 3703 U\t)

=

(8.6/4.0)i, giving for

This yields the percentiles of the quasi-static response on substitution of suitable percentiles of the standard normal process U(t). (7.3.7)

The most probable maximum peak value in a 3 hour storm has a 111000 probability of occurrence.

(C7.B)

With a Rayleigh distribution of peaks, the value ofU corresponding to the 111000 peak is U = .J2ln 1000 = 3.72. Substituting this in the above equation gives: MPM Quasi-static Response (excluding wind) = 729200.kNm

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 Step 3


We have already calculated the dynamic characteristics of the unit which are: natural period 4.48 s i.e. COo = 1.402 radls damping ratio ~o = 0.07

Accepting the wave spectrum modeling strategy in this step gives the parameters {Og = 21t/Tp = 0.507 and ~g = 0.222.

The dynamic response is obtained by inputting the above in the program MOMENTS by J Juncher Jensen. This delivers the statistical moments of the response process: mean variance skewness kurtosis

117100 kNm 14.49 x 109 (kNm)2 0.6283 5.739

With these, the program constructs the dynamic response process as a cubic polynomial in the standard normal process U(t): yet) = 107900. + 98020.U(t) + 9204.U2(t) + 6825 U3(t) Substituting again U = 3.72 for the 111000 peak gives: MPM dynamic response (excluding wind) = 949900 kNm and a dynamic amplification factor of 9490001729200 = 1.30. Wind can be added in with little difficulty. freq.

domain

V ~

With all response parameters required for the assessments obtained by either of the above detailed methods, this of the response calcs is complete. Go to the next entry in the FLOWCHART

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 time domain analysis


There are several ways of performing detailed time domain analysis. Some are costly on computing time, and so economies have been made to reduce the number of simulations actually carried out for the sample calculations. Observe the guidelines on loading in table 7.2: A random sea has been generated using 200 divisions ofthe spectrum with equal energy content. Checks on validity: mean elevation 0.0 standard deviation 2.577 Hsig/4 2.55 skewness -0.034 kurtosis 3.03 MPM crest 9.426 (Hsig/4)J21n(n) 8.79

OK

m m m

) )

m m

) )

OK OK OK

OK

W AVE SIMULAnON MEETS CHECKS Select the integration timestep: T / 20 = 0.48S} . T: / 20 = 0.24s tlmestep of 0.25s selected Avoid transients by skipping 150s of response simulation. Select simulation length: This depends on the method selected and the quantities used. For example a calculation using Winterstein's polynomials will require stable mean, standard deviation, skewness, kurtosis and zero upcrossing frequency, whereas the drag-inertia parameter approach merely requires stable mean and standard deviation. To avoid excessive demand on the in-house computing facilities all of the sample calculations have been performed on a one hour simulation. In some cases, this is insufficient for an accurate analysis, but it was held to produce sufficiently realistic results for sample calculations. Perform simulations as required in table 7.3: Simulations were carried out using the in-house nonlinear random dynamics suite of programs. In these, P-delta effects are included in the dynamic response by generating additional moments due to structure weight applied at the deflected position at the previous timestep. Combined wave/current particle velocities were used in determining the hydrodynamic loading on the legs. All other loads are applied as for the quasi-static plus inertial analysis approach.

Example ("Go-by") Calculations for a Typical Jackup Page 81 Preliminary Issue, May 1994 Determine Responses C7.B Four approaches to detailed dynamic time domain analysis are recommended:

drag-inertia parameter Weibull distribution Gumbel distribution Winterstein

C7.B.2.1 C7.B.2.3 C7.B.2.4 C7.B.2.5

C7.B.2.1 drag-inertia parameter At least 60 minutes of simulation are likely to be necessary. Obtain means and standard deviations of the quasi-static and dynamic responses, and the standard deviation of the inertial part, according to figure C7.B.2. Two simulations can achieve this: one with full dynamic response, and one with only the quasi-static response to the waves. Following the approach in C7.2, the latter is obtained by repeating the full dynamic simulation, but using a model with negligible vibrational masses. In all four simulations are required: full dynamic, quasi static, quasi-static with Cm= 0,

quasi-static with Cd

=

O.

Check that the simulation length is suitable: Response mean and standard deviation should be stable. The following overturning moments were obtained after 2500s of simulation and after 3600s of simulation: after 2500s

after 3600s

dynamic

(kNm) mean std.dev. (kNm)

411100 101900

411200 102300

q-static

(kNm) mean std.dev. (kNm)

410080 46990

410090 46520

These results appear to be stable, and so the simulation length is suitable for this method. Using Figure C7.B.2 an inertial time series is obtained from the difference between the dynamic and quasi-static time senes. This has a negligible mean and a standard deviation of 116900 kNm. Further preliminary processing is to be carried out according to C7.B.5. The following overturning moments are obtained from the quasi-static simulations for zero Cd and zero Cm:

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 C7.B.2.1 6762 Cd = 0 std.dev. (kNm) Cm = 0 std.dev. (kNm) 45929


These results show the relatively high importance of the drag part of the response. Obtain CRs from box ge. D = 367432 kNm} M = 25019 kNm Crs = 7.93 S =46424 kNm

IVII OPTION> Obtain C, from box 9d. .J,..

The drag-inertia parameter K Rs = 1.0474 From figure C7.B.6, Crs = 7.5 Now apply the method in Figure C7.B.4. 7:

PR

-0.493

8:

DAFI

2.20

9:

C Rs

7.93

10:

CRi

3.7

11 :

mpmRd

407240kNm

12:

DAF2

1.104

13:

CRd

3.98

14:

mpmeRs

779804 kNm

15:

mpmeRd

818400 kNm

16:

DAF3

1.049

By this method we get the overturning moment extremes: 818400 kNm D + L + E + Dn D+L+E 779804 kNm 38596 kNm 2 2 It is noted that here aD < a/ + ai , which for a regular wave would imply a phase lag of over 90 degrees. This is not yet fully understood.



The distribution (of peaks) is matched to a Wei bull distribution. Over five storms shall be used. Simulation length shall be checked.

C7.B.2.3 Weibull distribution

As for the Gumbel illustration, one storm of duration one hour has been used to generate the sample values. The storm has already been checked for Gaussianity. The 1: 2: 3:

simulation has already been shown to meet the requirements of table 7.2. The mean of the response is 411200 kNm. There are 298 maxima in the sample. The maxima are placed into 20 groups of magnitude between 0.0 and 925564 kNm (maximum peak 916400 kNm) to generate a distribution of peak values. e.g.

band 0.0 46279 92557 138836 185114 231392 277670 323948 370227 416505 462783 509061 555339 601618 647896 694174 740452 786730 833009 879287 4:

no. of peaks 46278 to 92556 138835 185113 231391 277669 323947 370226 416504 462782 509060 555338 601617 647895 694173 740451 786729 833008 879286 925564

68 77 56 37 23 13 7 4 2 1 1 0 1 1 2 1 2 0 1 1

p.d.f. 0.2282 0.2584 0.1879 0.1242 0.0772 0.0436 0.0235 0.0134 0.0067 0.0033 0.0033 0.0000 0.0033 0.0033 0.0067 0.0033 0.0067 0.0000 0.0033 0.0033

The parameters in the Wei bull distribution are obtained by deriving the start values, evaluating the error OJ and minimizing the sum of the Oj2 e.g. by a "Levenberg-Marquardt algorithm".

The in-house program RANEX generates parameters as follows: a 117858 kNm ~ 1.2756 Y 26536 kNm

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 C7.B.2.3 (cont) 5: Obtain Rmpm as the solution of F(Rmpm,a,~,y)


= 1 - 1/(298(3/1)) = 0.99888

I.e.

Rmpm = 555914 kNm 6: 7:

Rmpme = 967114 kNm No other response parameters are to be considered here.

According to table 7.3, at least five MPME values calculated in this way should be averaged. The above method yields corresponding values for the quasi-static simulations, from which the Dn response parameters can finally be separated.

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 C7.B.2.4 Gumbel distribution


Multiple simulations are required with stable kurtosis for this option.

Generate ten 3-hour response simulations. Here, for the sample calculations the method is tested using just one one-hour storm, with ten artificial random variations in the extreme response. Check stability of kurtosis: kurtosis in OTM after 2500s 4.766 ) after 3600s 4.165 ) In a proper analysis this would not be accepted as showing stability of kurtosis. However, the results of the storm are accepted for this illustration. 916400 kNm Maximum overturning moment in the storm: A further nine random perturbations about this value are taken for the illustration: 930006 kNm 909750 kNm 925709 kNm 899009 kNm 880288 kNm 949545 kNm 876094 kNm 965402 kNm 967038 kNm Apply the maximum likelihood method to get the parameters \j1 and K. The cumulative distribution F3h (x) is in one variable x, with two parameters \j1 and K. The probability density function fx(x) is:

dF 3h (x) dx (l/k)exp[-e- V - v] where v = f(x;\j1, K)

(x-\j1) -K-

say

The likelihood estimator method defines a function L which takes into the assumption that the likelihood of obtaining a particular sample Xi is proportional to the pdf at Xi. We have ten samples of Xi here. We define L(x], .... ,XlO;\j1,K) = logeTI f(x i , \j1, K) i

This function can define a surface over \j1, K space. Its maximum turning point defines the maximum likelihood estimator in \j1 and K. Therefore, solve for \j1 and K:

~~dL = 0)

-=0 dK

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 C7.B.2.4 (cont) These eventually boil down into two simultaneous equations:


10

L exp[-(xj - 'JI / K] = 1 j

10

L[(X j

-

'JI / K][I- exp[-(Xj - 'JI) / K] = 10

j

Using a program to solve these for the ten overturning moments,

'JI K

Hence, MPME

906750 kNm 27400 906750 - (27400)ln[-ln(0.37)] 906908 kNm

A similar procedure will generate the quasi-static MPME, and so the Dn overturning moment can be obtained.


Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 C7.B.2.5 Winterstein option

This approach requires one simulation for a given parameter of interest.

The input seastate has been checked for Gaussianity. The method requires stable skewness, kurtosis and zero upcrossing rate in addition to the mean and standard deviations which were checked in the drag-inertia parameter approach. As before, the values for the simulation are checked against those for a shorter interval. after after quantity 2500s 3600s skewness kurtosis rate/upcross

0.5708 4.766 0.0732

0.4815 4.165 0.0739

These would NOT normally be accepted as showing sufficient convergence, and a longer simulation time would then be required. Here, the results are expected to show representative patterns, and so the simulations are used FOR ILLUSTRATION. The method is applied in the in-house program MOSAP, which generates the quantities as follows:

K

full dynamic 411200 kNm 102300 kNm 0.4815 4.165 266 0.0739 S-l 0.0309 0.0658 0.0365 0.992

5

U mpm

3.8186

6

ZMPM

6.276

7

R MPMe

1053172 kNm

step 1

2

3 4

quantity mean std. dev. skewness kurtosis upcross rate

fl

a U3

N Yo

S h3

14

quasistatic 410900 kNm 45320 kNm 1.713 8.425 334 0.09278 S-l [since the kurtosis of this simulation exceeds 5.0, it is necessary to apply the more complete solution of J Juncher Jensen, which yields ... 788190 kNm

Example ("Go-by") Calculations for a Typical Jackup Page 88 Preliminary Issue, May 1994 Determine Responses C7.B.2.5 With step 7 the required quantities are obtained, and the Dn part of the response can be separated. detailed timeseries methods

With all response parameters required for the assessments obtained by any of the time domain methods, this of the response calc. is complete. Go to the next entry in the FLOWCHART

freq'vtime dom. dom.

All detailed dynamic analysis methods have now been considered.


Page 89 Assess structure/O.T.

STRUCTURAL AND OVERTURNING ASSESSMENT

Assess structure and overturning, Sections 8.1, 8.2, 8.5 & 8.6.

~ This is the first part of the load and resistance assessments. Foundations are considered in the next FLOWCHART item. Failure of the unit at this stage leads either to more detailed response determination or to unsuitability of the unit.

Structure assessment - route Leg Overturning Holding system Holding structure Hull 8

8.1 8.2 8.5 8.5 (8.1) 8.6

ASSESSMENT CRITERIA In the following assessments the load are functions of the factored load set and the response are functions of the factored resistance vector. The load set is generally in intermediate parameters, for example overturning moment or member loads, as opposed to wave height. Load functions can be as simple as base vertical reactions, or as complex as member unity checks. Dividing the factored load vector function by the factored resistance vector function gives the unity check for each limit state. The unit is assumed to meet the relevant building standards.

~

Structural Strength Check (applied to leg ) The flowchart in figure 8.1 of the PRACTICE may be followed to obtain the in the member strength equations.

8.1.1.1

Code Basis This section gives guidance on where to find assessment formats suitable for geometries outside the code. If checking high Rlt tubulars (possibly with stiffeners) go to 8.1.5 as directed below. If checking ts, follow the guidance in 8.1.6 as directed below.


Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 8.1.1.2

The geometrical requirements of8.1.2 must be satisfied, or else go to 8.1.5 as directed below. The minimum yield stress in the must not exceed the stipulated limits. Here, elastic finite element analysis was used to determine the member loads, and so the specified minimum yield stress of the strongest component material must not exceed 690 MN/m2 . horizontal braces: 450 MN/m2 450 MN/m2 diagonal braces: 700 MN/m2 chords: 240 MN/m2 internal braces: Technically, the chords exceed the stipulated limit, but only by a very small amount, so make the decision to apply the code. If the original AISC code were metric it would probably have accepted the chords. Check that using closed section brace and chord scantlings in truss-type legs: OK.

8.1.2

Definitions The following elements are to be classified as : chord lengths between bracing junctions diagonal, horizontal and internal bracings between bracings junctions are to be assessed according to 8.1.4 unless their geometry falls into the classifications in this section. i)

Check Rlt of plain tubulars. For horizontal and diagonal bracings:

Rlt 44815/Fy

5. 100.> Rlt

Rlt 44815/Fy

8.3 187.> Rlt

Therefore assess these elements to 8.1.4. For internal bracings: Therefore assess these elements to 8.1.4. ii)

None of the tubulars has ring stiffeners

iii)

None of the tubulars has longitudinal stiffeners.

The following are to be treated as structural components: backplates in chord sideplates in chord racks in chord

stiffened component stiffened component unstiffened component

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 8.1. 3


Factored Loads The load vector for a member comprises the axial load, the bending moments, and possibly the shear loads and torsional moment. Load vectors are to be obtained for each ofthe D,L,E and Dn cases (as carried out in the detailed leg model analysis), and combined to give a factored load vector. From a preliminary survey of the load vectors, the following are to be considered in full detail: compression chord spanning the lower guide tension chord in the bay below the bottom pinion horizontal bracing opposite the bottom pinion. These are now considered in tum.


8.1.3 (cont)


COMPRESSION CHORD SPANNING LOWER GUIDE

Highest bending moments are at the lower guide node. Note that according to 5.6.6 a) the bending moments should be adjusted to for the finite guide length, but this is not carried out here for a conservative check.

Load vector: case

axial (MN)

Myy(MNm)

Mzz(MNm)

D

-7.603 -2.416 -19.187 -1.208

0.013 0.064 6.281 0.439

0.059 0.021 -3.500 -0.375

L E Dn

For the following partial load factors: "{I = 1.0 "{2 = 1.0 "{3 = 1.0 "{4 = 1.0 The factored load vector becomes: axial load: moment Myy: momentM zz :

30.414 MN compression 6.797MN 3.795 MN

where the y-axis runs parallel to the rack plate.


8.1.3 (cont)


TENSION CHORD BELOW BOTTOM PINION

Highest loads are at the lower end of this member.

Load vector: case

axial (MN)

Myy(MNm)

Mzz (MNm)

D L E Dn

-5.911 -2.013 16.138 1.098

1.236x10-3 0.390x10-3 7.809x10-3 -1.390x10-3

0.270 0.l20 2.766 0.l90

For the following partial load factors: "{I = 1.0 "{2 = 1.0 "{3 = 1.0 "{4 = 1.0 The factored load vector becomes: axial load: momentM yy : momentM zz :

9.312 MN tension 0.008 MN 3.346 MN

where the y-axis runs parallel to the rack plate.


8.1.3 (cont)


HORIZONTAL BRACE AT LEVEL OF LOWEST PINION Highest loads are at the end of the member attached to the chord. This is the most severely loaded tubular.

Load vector: case

axial CMN)

MyyCMNm)

Mzz CMNm)

D

-0.840 -0.376 -5.595 -0.347

-0.023 -0.011 -0.196 -0.011

-0.0064 -0.0029 -0.0390 -0.0026

L E Dn

For the following partial load factors: 'YD 1.0 'YL 1.0 'YE 1.0 'YDn 1.0 The factored load vector becomes: axial load: moment Myy: moment Mzz:

7.158 MN compression -0.241 MN -0.051 MN

The should now go to the assessment section identified for the member in question. If no specific direction has been given to another section at this stage, assessment should be to the provisions in 8.1.4.

excluded geometries ts .... _+--.... ~ , 8.1.6 8.1.5 ....

""',.

8.1.4



Assessment of - excluding stiffened and high Rlt ratio tubulars

v

The structure of this section is well set out in the flowchart in figure 8.1. Several of the subsections are mutually exclusive, depending on whether the member is in tension or compression, etc.

Therefore it was decided that the most useful format of the GO-BY document would be to take typical and follow their options through. This is done below for the three critical identified above.

The in the general interaction equations are obtained in subsequent subsections. Once these are obtained, the analysis returns to 8.1.4.1. The examples include both non-tubular and tubular .

e

non-tubular in compression non-tubular in tension tubular in compression


Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 Axial load Axial strength Eff. moment load Bending strength Exponent 11 Assessment

member in compreSSIOn

8.1.4.1 8.1.4.3 8.1.4.5 8.1.4.6 8.1.4.7 8.1.4.1

Example 1. Compression chord member This is the member spanning the lower guide node, as described earlier.

0pu

=

30.414 MN compression from detailed leg model.

In the interaction equations, the x-axis corresponds to the model z-axis, i.e. parallel to the backplate. The y-axis is parallel to the rackplate. §]Nominal axial strength for a member in compression Check the components for local buckling. the backplate is stiffened along two edges. Bi 1.00 m ti 0.065 m Fyj 700 MN/m2 Fr 114 MN/m2 b j / tj

= 15.4}component not suscepitble

625/ ~Fyj - Fr = 25.8

to local buckling

the sideplates are stiffened along two edges. 0.90 m Bj tj 0.040 m Fyj 700 MN/m2 Fr 114 MN/m2 b j / tj

=

625/ ~Fyj - Fr

= 25.8

22.5} component not suscepitble to local buckling

the rack is stiffened along one edge. Assume no rack teeth contribution. 0.40 m Bj tj 0.14 m Fyj 700 MN/m2 b j / tj

250/

=

.JF::

2.8} component not suscepitble

= 9.4

to local buckling

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 8.1.4.3 (cont)

Page 97 Assess structure/G.T.

Thus none of the components in the section fails the check for local buckling, and so the strength in 8.1.4.3 a) applies. Had any of the components in the section failed this check, the strength in 8.1.4.3 b) would have been applicable. member with slender components I-------.~ 8.1.4.3b [not applicable here]

Pn

=

A Fer

where A and Fer are obtained as follows. A Fer

0.193 m 2 ?

E

1.0 3.75 m (brace point-brace point) .J0.0115/0.193 = 0.244m minimum 700 MN/m 2, assuming that Fy is less than 5/6 Fu for this material (information not available) 3 200x 10 MN/m 2

Ae

: {F~IT

K t

r FYeff

r

= 0289

since Ae < 1.5, (A. 2)

Fer

[0.658 ' ]FYeff

And so, Pn

=

676 MN/m2

130MN

~ Effective Applied Moment for in Compression Mue =

B Mu for each of the X,y headings.

where Band Mu are defined as below. First check the suitability of the analysis. - yes global P~ included? local loads included? - yes member represents leg? - no The modeling matches the description in i).



Therefore, Mux and Muy are the applied loads identified above. B Crn/(1 - Pu/P e) ;?: 1.0 for each direction.

Pu

31.41 MN n 2r/AE/(Kt)2 = n 2r/AE/(Kt)2 =

Pex Pey Crnx ? C rny ?

3636 MN 1609 MN

The member is loaded by the lower guide between ends. For a centrally loaded member, restrained at its ends (?), a value of 0.85 is appropriate. 0.85 0.85

Crnx C rny so, Bx By

--+ --+

0.857 < l.0, so set Bx 0.87 < l.0, so set By

1.0 1.0

Muex = 3.795 MNm MJID' = 6.797 MNm

Thus

18.1.4.6 1Nominal Bending Strength Apply standard techniques to get Mp (calculated for zero axial load). There is just one material in the section. It is assumed that Fy is limiting, and not 5/6F u For no axial load, Mpx Mpy =

44.23 MNm 21.0 MNm

Check for susceptibility to Lateral Torsional Buckling. Lb r J A

=

Lb I r

3.75 m 0.244 m 0.043 m 4 0.193 m 2

= 15.4

}section is not susceptible to lateral torsional 25680~(JA) IMp = 12.6 minimum buckling. Continue with this section.



Had the section failed this check then it would have had slender components and 8. 1A.6c) would have been applicable from here. member with slender components f - - - - - -... ~ 8.1.4.6 c ""'~ [not applicable here]

Check for local buckling of the components. The following are identified as web components: rack, sideplates. The following are identified as flange components: backplate. Try the criteria for compact sections: backplate component, stiffened along two edges. b 1.00 m t = 0.065 m bit < Ap, so component meets compact 2 section check. Fy 700 MN/m

Ap

5001.JF:

=

19

sideplate component, stiffened along two edges. b 0.90 m 0.04m bit> Ap so component does not meet t the compact section check. 19 as above Ap Therefore, try the noncompact section check. The backplate will this and so need not be further checked. 2 Fr 114 MN/m Ar 6251 ~[Fy - Fr] bit < Ar so component meets the 25.8

non-compact section check.

rack component, stiffened along one edge. B 0040 m bit < Ar so component meets the O.l4m 2781 ~r-[F-yw---F-r] non-compact section check ==

11.5

All components in the section have now been checked, and so the member is noncompact. The nominal bending strength follows in the same subsection. For non-compact sections the nominal bending strength is given by:



for the most slender component (sideplate): bit

22.5 19. Ar 25.8 Mrx min[(Fyw - Fr)Sx, Re FyfS x] 24.4MNm for Fr 114 MN/m2 Sx 0.0416 m 3 Fyf = Fyw = 700 MN/m2 Re 1.0 similarly, Mry 16.03 MNm Hence: Mnx 34.0 MNm Mny = 18.4 MNm

Ap

=

~ Determine 11

t

For this member a value of11 can be determined by analysis, either from this subsection, or from equations in the commentary. Alternatively a conservative value of 1.0 maybe used.

IOPTION) Apply conservative

11

=

1.0

IOPTION) Derive suitable value from method in 8.1.4.7. 1.

For illustration only the angles q = 0°, 60°, 90° are tackled. Allowable bending strengths are as follows: q = 0° Mng = 34.0 MNm q = 60° Mng = 30.9 MNm (see below) q = 90° Mng = 18.4 MNm Method for getting Mng for q = 60°: graphically determine the plastic neutral axis for the angle of bending and zero axial load, and obtain MpqMpg = 46.2 MNm calculate the elastic buckling strength Mrg for the angle of bending. Mrg = 16.5 MNm Since the section is known to be noncompact, the same equation as applied above for Mnx shall be used to get Mng.

2.

Set Mug = Mng = 30.9 MNm for q = 60°

3.

Resolve:

M'uex M'uey

30.9 cos 60° 30.9 sin 60°

15.45 MNm 26.76 MNm



8.1.4.1 4. Solve for 11: (cont)

{26.8}11}~

15.4}11 + {{ 34.0 18.4 I.e. 0.45411 + 1.451 11

=

1.0

But this does not have a solution for 1.0 ::::; 11 : : ; 2.0 . ... This section to be revised/expanded. Refer to equations in commentary. ... To be expanded.

~With all the in the interaction equations determined, assessment of the member can be completed. Pu Pn <Pa Muex Muey Mnex Mney b

11

30.41 130 0.85

) ) )

MN MN

Pu/<PaPn = 0.275> 0.2

3.80 MNm 6.80 MNm 34.0 MNm 18.4 MNm 0.9 1.0 (only available result - conservative)

So, check 0.275

+~{ 0.1241.0 + 0.4101. 0}XO 9

0.275 + 0.475

=

0.75 < 1.0

OK.

Thus the member es the strength assessment criterion.


Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 Axial load Axial strength Eff. moment load Bending strength (Exponent 11 Assessment

member in tension

8.1.4.1 8.1.4.2 8.1.4.4 8.1.4.6 8.1.4.7) 8.1.4.1

Example 2. Chord member in tension This is the member below the lowest pinion, as described earlier. 8.1.4.1

Pu

9.312 MN tension from detailed leg model. 1.0

as determined for the compressed chord above.

In the interaction equations, the x-axis corresponds to the model z-axis, i.e. parallel to the backplate. The y-axis is parallel to the rackplate.

~Nominal axial strength for a member in tension As before, it is assumed that Fy is less than (5/6)Fu for the chord materials, as no value for Fu is available. No contribution from rack teeth is considered. For the member, Pn

=

FyminI.Ai

= 700 x 0.193 = 135.1 MN 18.1.4.4 1Effective Applied Moment for in Tension that: - analysis includes global P~ - local loading is ed for

O.K. O.K.

Therefore effective loads equal applied loads: Muex = 3.346 MNm Muey = 0.008 MNm

I

18.1.4.6 Nominal Bending Strength As for the chord member in compression: Mnx 34.0 MNm Mny = 18.4 MNm

§ ] With all the in the interaction equations determined, assessment of the member can be completed.


Pu Pn

= =

10.49 MN} 135 MN Pu / <PaPn = 0.086 < 0.2 0.90 MN

Muex Muey Mnex Mney

<j)b

11

=

3.35 MNm 0.008 MNm 34.0 MNm 18.4 MNm 0.9 1.0 (only available result - conservative)

So, check 0.077 { - + 0.1091.0 + 0.00051.0 } 111.0

2.0

0.038

+ 0.110 = 0.148 < 1.0

OK.



Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 Axial load Axial strength Eff. moment load Bending strength Exponent 11 and Assessment

tubular in compressIOn


8.1.4.1 8.1.4.3 8.1.4.5 8.104.6 8.104.1

Example 3. Compressed tubular brace This is the horizontal brace at the level of the lower guide, as described earlier. 7.158 MN compression from detailed leg model. 2.0 as the member is purely tubular. In the interaction equations, the x-axis corresponds to the model z-axis, and the y-axis is as modeled.

~Nominal axial strength for a member in compression Check the tubular for local buckling. R 0.175 m t 0.035 m Fyi 450 MN/m2 R/ t

5.0 } component not susceptible = 25.3 to local buckling =

11380/ FYi

Thus the tubular does not fail the check for local buckling, and so the strength in 8.104.3 a) applies. Had any of the components in the section failed this check, the strength in 8.104.3 b) would have been applicable. member with slender components 8.1A.3b ... ,. [not applicable here] 1------6~

Pn

= A Fer

where A and Fer are obtained as follows. A Fer

0.0346 m

2

? K t

0.8 4.34m

r

0.112m

(brace point center-brace point center This is more conservative)

Page 105 Example ("Go-by") Calculations for a Typical Jackup Assess structure/O.T. Preliminary Issue, May 1994 assuming that Fy is less than 8.1.4.3 F Yeff = 450 MN/m2, 5/6 Fu for this material (information not available) 3 200 x 10 MN/m2 E Kt{F

~ff

f1t

}X = 0.468

since Ae < 1.5 , 411 MN/m2

(A 2)

Fer

[0.658 ' ]FYeff

And so, Pn = 14.2 MN

~ Effective Applied Moment for in Compression Mue

BMu

=

where Band Mu are defined as below. First check the suitability of the analysis. global Pd included? - yes local loads included? - yes member represents leg? - no The modeling matches the description in i). Therefore, Mux and Muy are the applied loads identified earlier. B Cm/(l - Pu/Pe) ~ 1.0 for each direction.

Pu

7.16 MN 2 1t r2AE/(Kt)2 Pex 71.2 MN 2 1t r2AE/(Kt)2 Pey 71.2 MN Cmx ? Cmy ? The member is not loaded between s, so C mx

= 0.6 - 0.4(M]/M 2) 0.6 - 0.4(0.0482/0.0509) 0.6 - 0.4(0.107/0.241)

C my so, Bx By

---+ ---+

> 0.245 < 1.0, so set Bx = 1.0 > 0.469 < 1.0, so set By = 1.0

Thus Muex Muey

0.051 MNm 0.241 MNm

0.222 0.422



18.1.4.6 1Nominal Bending Strength Apply standard techniques to get Mp. There is just one material in the section. It is assumed that Fy is limiting, and not 5/6Fu For no axial load, Mp

=

1.569 MNm for all headings

Check for susceptibility to Lateral Torsional Buckling. Lb r J A

4.34 m O.l12m 8.698 x 10-4 m4 0.0346 m 2 38.75 90.0

25680J(JA) IMp

) ) )

section is not susceptible to lateral torsional buckling.

Continue with this section. Had the section failed this check then it would either be noncompact or would have had slender components and sections 8.1.4.6 b) or c) would have been applicable from here. member with slender components 1------.~ 8.1.4.6 c or "III'" non-compact sections 8.1.4.6 b) Check for local buckling of the section. The entire tubular is considered as a component for this check. Try the criteria for compact sections: R 0.175 m t 0.035 m Fy 450 MN/m 2 7140lF y

tubular meets compact section check.

15.9

The member has been shown to be compact. The nominal bending strength follows in this subsection. For compact sections the nominal bending strength is given by Mn = Mp: Mnx 1.569 MNm Mny = 1.569 MNm

Page 107 Assess structure/O.T .

Example ("Go-by") Calculations for a Typical Jackup . Preliminary Issue, May 1994 8.1.4.1

With all the in the interaction equations determined, assessment ofthe member can be completed.

Pu

=

Pn

=

7.16 MN} 14.24 MN Pj<PaPn

= 0.622 > 0.2

0.85 Muex Muey Mnex Mney

=

0.051 0.241 1.569 1.569 0.9 2.0

MNm MNm MNm MNm

So, check 0.591 +

~{0.0362°+0.1712°r2.o

9 0.591 + 0.155

= 0.75 < 1.0

OK.


examples

1.

This concludes the strength assessment examples. The go-by document returns to its original exploration of all avenues.



~

Overturning Stability

8.2.1

The critical heading for overturning was determined at an early stage to be 118.3°. For this there are two leeward legs.

8.2.2

Overturning moments are to be worked out from components of environrnentalloads applied at suitable elevations. Footing reactions contain this information along with the P 8 effects, and so are used here. To calculate the overturning moment, multiply the windward leg footing vertical reaction by the perpendicular arm to the overturning axis (for no footing fixity moment).

;'

,/I;' Overturning ./

".

Axis •

Leg centres at footing

Using the reactions from the quasi-static + inertial analysis, ME VI x 48.41 648.2 MNm ) Mon = V I x 48.41 42.4 MNm ) For partial load factors: YE 1.0 YOn = 1.0 Factored load Mo

8.2.3

1.0[648.2 + (1.0)42.4] 690.6 MNm

Stabilizing moments are calculated in the same way, compensating for the sign of the vertical footing reaction. Mo VI x 48.41 1243.2 MNm ML VI x 48.41 162.8 MNm Ms = 0 For partial resistance factors:
Mo/factored resistance

(1.0)1243.2 + (1.0)162.8 + (1.0)0. 1406 MNm =

0.49 < 1.0

Therefore the unit es the overturning stability assessment.



~

Loads in the holding system

8.5.1

The holding system for this unit comprises the pinions and the jackhouse structure.

8.5.2

Maximum specified holding capacity of the pinions

=

4.904 MN per pinion.

A factored ultimate capacity may also be used. The specification is 80% of yield. With a factor of 0.85, Factored yield capacity of pinions = (4.904/0.8)0.85

=

5.210 MN

The maximum pinion load for the D + L + E + Dn load cases is at 61.3, with the maximum hull. Maximum load from FE model: Adjustment for load equalization maximum pinion load

4.06 MN -0.08 MN 3.98 MN

Therefore, neither the factored yield capacity, nor the specified maximum capacity detailed in the data pack are exceeded. 8.5.3

~

It is a straightforward process to analyze the in the FE representation of the jackhouse, according to 8.1. This has not been included in this document to avoid excessive repetition.

Hull

8.6.1

Here it can be taken that all relevant Class Certificates apply. (i.e. none for a hypothetical model!).

8.6.2

A detailed hull model including plate elements would be amenable to a detailed strength analysis. Extreme loads could be determined from a simpler structural model, and applied via portions of leg model, in reverse of the application of loads to a detailed leg model.

The structure has now been assessed and overturning stability considered. The unit meets both requirements, and so foundations should now be assessed. Had the unit failed, a more detailed response calculation would have been appropriate. If that were not possible the unit would have been unsuitable.



Page 111 Assess foundation

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 ASSESSMENT OF FOUNDATION

I

Assess foundation, Sections 6.3 & 8.3/Figure 6.9

The second part of the assessment concerns the foundation stability. If the unit gets this far and es the foundation assessment, then the only remaining check is (if required) a limit on allowable displacement. Rather than produce a local route sign, the flowchart in figure 6.9 is referenced.

8.3

Foundation Assessment Section 6.3 is referenced for this section. The flowchart in Figure 6.9 may be followed at this stage.

~

Step 1 - preload check for leeward leg. From the quasi-static analysis with inertialloadset, leeward leg vertical loads are as follows: VD 25.68 MN VL 6.76MN VE 15.54 MN V Dn 1.06 MN For the following partial load factors, 11 1.0 12 1.0 13 1.0 14 1.0 the factored load is Qv

(1.0)25.68 + (1.0)6.76 + (1.0)15.54 + (1.0)1.06 49.04MN

The vertical leg reaction during preloading is as follows. max. load permissible through jacks buoyant leg weight =

The resistance factor for foundation capacity = 0.9

41.19 MN 9.54MN 50.73 MN



Hence

=

0.9 x 50.73

=

45.66 MN

Therefore Qv >
[not yet applicable here]

8.3.1.4

The bearing capacity check has already been engaged, and so there is no need to carry out this check. The bearing capacity check depends on the footing model. If a pinned footing has been used then 8.3.2 is applicable. Ifa degree of footing fixity has been used then 8.3.3 is applicable.

I

fixity pinned foot /\ 8.3.2 ~~ 8.3.3

§

Bearing Capacity Check - pinned foundation (leeward leg)

8.3.2.1

The vectors of horizontal and vertical leg reaction are required for each load case. We have the following reactions [vertical (MN), horizontal (MN)]: VHo = [25.680,0.115] VH L [ 6.756,0.047] (max. hull, leeward leg) [ 15.545, 4.832] VH E VHOn [1.057,0.308] For the following partial load factors: "(1 1.0 "(2 1.0 "(3 1.0 "(4 1.0 The factored load vector is: QVH = [49.038 MN, 5.302 MN] The resistance term is the foundation capacity to withstand combined vertical and horizontal loads, FvH , which is obtained in 6.3.3 for the particular soil types.



I

ffi

sand 6.3.3.1

~

clay 6.3.3.2

other 6.3.3.3 F VH for footing in sand. During installation the maximum bearing capacity is equal to the footing load. However, here a penetration of 1.25m is specified and this will determine the bearing capacity. For this penetration there is no overburden pressure at spudcan base level i.e. Po' = 0, so the capacity load envelope is described by: FVH = 12A)"BNys"dy[1 - (HJVd*]m+l in this equation are evaluated as follows: = 154m2 A )" .011 MN/m2 B 7.0m L 7.0m

where,

Using the above relationships the following table of capacities is obtained: (FH/FvH)*

FVH

0.0 0.04 0.08 0.15 0.25 0.35 0.50

277.5 250.6 225.3 185.0 135.0 94.5 49.1

FH* (MN) 0.0 10.0 18.0 27.8 33.8 33.1 24.6

FH 0.06 10.1 18.1 27.8 33.8 33.1 24.6



The above table represents the unfactored foundation load capacity vector. Along side it has been marked the factored load capacity envelope, for a resistance factor
According to figure 6.9 ofthe PRACTICE the unit shall now be checked for windward leg sliding.

Figure 4. Bearing Capacity Envelope and Loads

V (MN)

300

.- -- --

--- -

Unfactored Load Capacity

--I /

200

Factored Load Capacity ........ ........................

........

100

Still Water Load

-10

Factored Load

--- ---o 10

20

30 H(MN)


1

6 .3 .3 .2

>


FVH for footing in clay.

For this penetration there is no overburden pressure at spudcan base level i.e. Po' = 0, so the capacity load envelope is described by:

in this equation are evaluated as follows: 154 m 2 5.14 0.047 MN/m 2 1 + (NqBlNcL) = 1.19 since N q = 1.0 for an undrained clay (

A Nc Cu

Sc

de

From this there exists a direct relationship between vertical foundation capacity and horizontal foundation capacity. The horizontal foundation capacity is obtained from:

where

FH

FH* + As(c uo + CuI)

As

2.125 m 0.040 MN/m2 0.040 MN/m 2

2

Cuo CuI

Now apply the resistance factor G>vH 0.9 V Lo = 49.038 MN, i.e. V Lo

=

=

0.9. The required vertical capacity is

54.49 MN

For this, there is no sensible solution ofH L , and it is concluded that the unit does not have sufficient capacity to meet the factored loads for the leeward leg.

1

>

6 .3 .3 .3

F VH for footing in layered soils.

(Outside the scope of this document.) pinned foot



~ Bearing Capacity Check - with foundation fixity Factored loads for the case of a footing with moment fixity are treated in much the same way as for the pinned foot, except that the moment footing load is part of the vector QVHM. The load factors are applied to the magnitudes ofthe load vectors, when expressed relative to the still water case. The foundation capacity to withstand vertical, horizontal and moment loadings FVHM is defined by the yield surface function encountered in the fixity calculations. To apply the resistance factors to this, the points on the yield surface must be written as vectors from the still water reaction 10adset, and then reduced in magnitude accordingly. The factored load and resistance check is then

where rds defined by the equation in 6.3.4.1. No results for an analysis with fixity are available, so numerical values are not presented here. leeward leg

V +

From figure 6.9 the next step is to perform the sliding check on the windward 1eg(s). When the unit fails on the leeward leg checks it is necessary to perform a structural analysis including fixity at the footing, or to use a more detailed dynamic response method. This is discussed later.

~tura1 analysis with

1 .

fIxity 6.3.4



~ Sliding resistance of the windward leg The most critical case for windward leg sliding is minimum hull, storm heading 118.3°, where there is just one windward leg. From the quasi-static analysis with inertialloadset, we have the following windward leg reactions horizontal vertical

HE Hon Vo VL VE VOn

4.359 0.318 25.680 3.362 -13.389 -0.875

MN MN MN MN MN MN

The following are the partial load factors: 11 1.0 12 1.0 13 1.0 14 1.0 and so the following factored loads are obtained: horizontal vertical

Qv

(1.0)[ 4.359 + (1.0)0.318] 4.677 MN in association with (1.0)25.680 + (1.0)3.362 - (1.0)13.389 - (1.0)0.875 14.778 MN

The resistance term is a horizontal foundation capacity FH when the vertical load Qv is acting. From figure 6.9 values ofF H are obtained from 6.3.3 for the various soil types.

I

sand 6.3.3.1

ffi l.

clay 6.3.3.2

other 6.3.3.3

1

>

6 .3 .3 . 1

F H for footing in sand.

A horizontal sliding capacity HL is given for a vertical load V L. FH = FvHtan () + 'i'2y(kp - ka)(h l + h2)As where parameters are defined for sand earlier, except for () =

= 33° for a flat



6. 3.3.1 The FVH here is deduced to be the factored vertical load, QV, so the horizontal resistance becomes: sliding 14.778 tan 33° + 0.0579 9.655 MN

FH

uc=horizontal load/(0.8*vertical laod*tan(o-5))

The resistance factor for sand is < 1.0 0.8x9.655 Therefore the unit meets the sliding criterion for sand. With a satisfactory footing under the leeward leg, the foundation is acceptable. FH for footing in clay. A horizontal sliding capacity for a footing in clay is given by FH

= ACul + (c uo + cUl)As

where the are as defined for clay earlier. This expression is valid for a range of vertical loads FYH such that

where FYH is the ultimate vertical bearing capacity in the presence of horizontal load. For the assessment, the factored vertical load Qy must lie within this range. It is therefore necessary to determine FyH . The relevant expression for F YH is found in the penetrations calculation in 6.2.2, allowing for backflow and displaced soil: (6.2.2) where, in addition to parameters assigned earlier, Fo' V

o. (no back-flow)

FYH

44.4 MN

YlF YH

=

19.9 m 3

so that and 22.2 MN> QL = 14.8 MN

Therefore the expression for horizontal capacity is applicable. FH

=

6.33 MN

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 (6.2.2)


With a resistance factor for clay of
- - - = 1.55 > 1.0

Therefore the unit does not meet the criterion for sliding in clay. Structural analysis including fixity moments at the footing is now required. FVH for footing in layered soils. (Outside the scope of this document). windward leg

W +

The foundation assessment for pinned footing is now complete. Depending on its outcome, the should either check displacements, or perform a more detailed analysis. Summary for this unit: (sand soil) step 1 - preload FAIL) ) step 2a- bearing (pinned) sliding Action: go on to displacement check. There are no requirements to look at displacement, so UNIT IS ACCEPTABLE FOR THIS SOIL TYPE. Summary for this unit: (clay soil) FAIL) step 1 - preload step 2a- bearing (pinned) FAIL) sliding FAIL Action: determine fixity and repeat analysis, or use results of more detailed dynamic analysis




APPENDIX A Data Pack for Typical Jack-Up Number 2

Page 121 Appendix A

Example ("Go-by") Calculations fora Typical Jackup Preliminary Issue, May 1994

Page 122 Appendix A

JACK-UP OPERATIONS COMPARATIVE STUDY OF ASSESSMENT PROCEDURES

TYPICAL JACKUP NUMBER 2 - DATA SHEET

PRINCIPAL PARTICULARS Dimensions Length overall Beam overall Longitudinal leg centers Transverse leg centers Number oflegs Overall leg length Leg chord pitch centers Bay height Distance between guide CL's

66.660m 74.624m 51.000m 55.000m 3, K-braced 100.000m 10.000m 3.750m 15.000m

Weights Hull Hull lightship (inc. eqt) Cantilever etc. Maximum variable Maximum elevated hull weight Survival C of G:

4000t 800t 2000t 6800t

LCG:

21.500m

TCG:

1.500m

Legs One leg, excluding can Footing can Total weight of a single leg

880t 200t 1080t

forward of AP (14.500m fwd of center-line of aft legs) to starboard of center-line


Page 123 Appendix A

TYPICAL JACKUP NUMBER 2 - DATA SHEET (CONT 1) Elevating System The elevating system is a four-high single rack system, thus providing 4 pinions per chord or 12 pinions per leg. Maximum holding capacity Effective stiffness

SOOt/pinion

200000 kNlm

(this is O.S of the load at which yielding was observed in a test) in the direction normal to the pinion tooth and with respect to the mounting at the neutral axis of the comer post (from the same tests)

The pinion sets may be torque equalized in the 'still water' condition. Each set of four pinions is ed within the comer post by shock pads top and bottom with an effective stiffness of SOOOOkN/m each. Either top or bottom pad acts alone on anyone chord. Comer 'post' & pinion stack Each have the following properties: Axial area Second moment of area Torsional constant

0.150 m2 1.000 m4 1.000 m4

(all axes)

The centroid of each section is located at the nominal chord pitchline. Nominal Clearances The rack guide clearance Back plate guide clearance The pinion/rack clearance

0.010 m +1-0.010 m 0.010 m

in the plane of the rack (no restraint normal to the rack plane) in the plane of the plate (no restraint normal to the plane of the back plate) in the vertical direction including backlash in gears through to the brake.

Available Preload The maximum available preload that can be applied through the jacks is given below. The values given for contributions from the hull, equipment, variable and preload water. Bow leg Stem legs

4000 4200

tonnes tonnes each

Page 124 Appendix A

Example ("Go-by") Calculations for a Typical Jackup Preliminary Issue, May 1994 TYPICAL JACKUP NUMBER 2 - DATA SHEET (CONT 2) THE DESIGN STORM

including tide and surge

Maximum still water depth Tidal rise Storm surge (Water depth chart datum)

30.0 3.5 1.5 25.0

m m m m

Maximum wave height Period associated with max wave Significant wave height Peak wave period Zero-up crossing period

16.0 13.0 8.6 12.4 9.5

m secs m secs secs

One hour mean wind One minute mean wind Three second gust

33.3 m/sec 39.0 m/sec (at 10.0 m ref. level) 45.6 m/sec

Surface current Current at the seabed

2.0 m/sec 2.0 m/sec

Based on previous experience of a similar footing on a nearby location the penetration of the spudcan tip is expected to be 1.25m below the seabed.

'"dm

:x~ :=:3 >-;

]000

1

~

!

3>0

s·

~

8'"

... ~

...

L------,

;11

ca

I~

III

..--

8

~

:

...... 0

""+1----

~ ~~I .. )12:._""'-11 J

~

~,.-,

Derrick l'uuwDr~ frGm ......_Flill feced Sections

~

0

~

0-

~

n

~'< ~0 '<

e:..

...... 0

GO '"

\OE..

'" ~

\O~ .j:::.

::to

§ ~

"'" :s .,;,

0' >-;

....

BEAM ELEVATIOM

~

....,

:a-.o e:.. .....

! ,1"

II

~·I

bI~j~ lu~ ca ~

-=0

"" '"

'" '" ~~

~

--STERN ELEVATION

115011

Hot es;-

'UII dimtnsiDns in IIIt:res.

TYPICAL JACK -UP Ng 2

PLAN VIEW

1:"I~lior dru.l~

oI.or

h

na ....e:

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~
ElEVATION 8-8

TVPICAl JACK-UP "22 LEG DETAILS WURiBI1'I

~RG

:g"'O (1)

H' 2i?

~

8.~ ;;< .......... >~

>-em ;><

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g..Pl _. "0 lack fromr l D~~.. ~ulde uni( II .. ~tla ,hett fDr d, t~il.1 \

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