Rp-h103 4j6pw

45 it is therefore required to check the possibility that the established high-low criterion will not trigger local buckling at a lower moment. To do this, a FE-model capable of modelling this failure mode should be established and; a) Reproducing the capacity for D/t=45 b) Determine the capacity for the actual D/t c)

Apply this reduction (i.e. b/a) to the DNV local buckling capacity for D/t=45

“The capacity” is the moment peak for given axial loads and pressures (basically the MSd without safety factors). By applying the reduction, any offset in models is avoided. If the difference between the DNVOS-F101 capacity at D/t=45 deviates significantly from the FE results at this D/t value, this needs to be assessed and the difference identified. For D/t<15 a similar exercise is required, but it is not required to analyse any high-low trigger mechanism.

5.2

Fatigue

The fatigue damage due to vessel motion shall be checked based on the analyses time series for all relevant scenarios. In practice, a few of the critical sea states will be used for fatigue calculations unless some time consuming installation operations are planned for where less conservative sea states may be added. In case the vessel cannot feed out pipe (construction difficulties or operational restraints) a maximum hold time or a minimum lay speed (“slow lay”) shall be established. This shall ensure acceptable fatigue damage or ECA criterion. For ultra-deep water installation additional fatigue may be caused by VIV along the catenary. The VIV may also imply a larger equivalent diameter with associated increase in static drag force that results in change in configuration that should be considered. For installation outside industry experience this should be evaluated. The fatigue shall comply with the fatigue criterion in DNV-OS-F101 Sec. 5 D800. Even if a ECA may give higher fatigue capacity than the SN-curve, a fatigue capacity beyond the SN-curve is not allowed. The split of allowable design fatigue damage during installation, temporary as-laid phase and operational phase shall be agreed on with purchaser and based on the highest safety class during the three phases. For a pipeline where e.g. 50% of the design fatigue capacity can be utilized during the installation and which is classified as safety class medium (high) during the operational phase this will correspond to a damage ratio of 50% / 6 (10) of the characteristic fatigue capacity.

DNV GL – Report No. 2014-0185, Rev. 3 – www.dnvgl.com

Page 32

A common split of fatigue capacity between installation, as laid and operation is 10%, 10% and 80% but depend on the need for fatigue capacity in the different phases. For a pipeline resting on the seabed with limited need for fatigue capacity in the operation phase (i.e. no free spans or buried pipeline), the split between installation, as laid and operation could be 80%, 10% and 10%.

5.3

Fracture

If the installation strains and operational nominal strains exceed 0.4%, or if some DNV-OS -F101 Appendix A (A107) requirements are not fulfilled, a fracture assessment (ECA) of these shall be performed in compliance with DNV-OS-F101 Appendix A. Note that the fracture assessment for installation need to include system effects, i.e. the weakest weld (largest defect) needs to be considered.


Page 33

6

SERVICEABILITY LIMIT STATE CRITERIA Tensioner

6.1

The primary objective of this criterion is to ensure that there is sufficient shear capacity between tensioner and steel pipe to ensure that the specified loads can be transferred. The tensioner slippage and squeeze must be checked to ensure that the pipe can be held safely in the tensioners including under any contingency scenarios. These checks depends on a number of factors such as the equipment, the contingency scenarios, the tensioner pad geometry and friction coefficient. The list below can be considered as a check list of the various verifications that are required but ultimately the operator and the installation contractor must ensure that the pipe can be held without any damage whilst in the tensioner. •

Squeeze Pressure The primary objective of this criterion is to ensure that sufficient squeeze exists to give the required friction transfer to the pipe to fulfil the top tension required. The shear capacity shall be verified for all relevant interfaces (i.e. between tensioner and outer coating layer as well as between subsequent coating layers). A certain squeeze pressure is required by tensioner to ensure sufficient axial friction transfer to the pipe. This shall be limited to avoid damage of coating and pipeline excluding coating indentation due to friction pads. This calculation is specific to the vessel, based on weather (temperature and humidity), tensioner pads and the pipe spooling facility which may add contaminants to the pipe.

•

Holding Capacity Holding capacity is a measure of the maximum tension it can

•

Maximum Pulling Capacity is critical with respect to enabling recovery of a product. The installation contractor should therefore specify tensioner capacity pulling in product, ing for friction between mechanical components and within the hydraulic system of the tensioner.

•

Tolerance of Grip Force In order to ensure that tensioner grip force capacity is sufficient to maximum product tension, the tolerance of the grip force for the maximum setting should be specified. The tolerance of the tensioner grip force setting will typically increase as the grip force decreases, eventually causing the tensioner to struggle to maintain an even load. Therefore, the installation contractor should specify the minimum grip force that the tensioner(s) can maintain, together with the corresponding tolerance. As the grip force capacity tends to decrease over time, specified minimum grip force should for increased mechanical friction and frictional losses in the hydraulic system over time.

•

Tensioner Pad Tensioner pad material and geometry (i.e. length and relative angle between the surfaces of the tensioner pads and the surface of the product) affects the distribution of the applied grip force through the cross-section of the product. While steel pads are robust with respect to wear, the applied grip force is localized to the points of between the pad and the product. Polymer pads, on the other hand, will deform and distribute the applied force over a larger sector of the circumference, but are less robust with respect to wear. The installation contractor should therefore specify geometry and material properties of the tensioner pads.


Page 34

6.2 6.2.1

Coating General

A thick coating could be at risk at cracking under high strain such in reeling, especially under cold temperature and shall be evaluated.

6.2.2

Concrete Crushing

The primary objective of this criterion is to ensure sufficient weight of the pipeline as installed. Consider spalling of the concrete coating. The primary objective of weigh coating is to give weight to the pipeline to keep it stable on the seabed during operation. The increased submerged weight will also assist in curve stability and residual lay tension during installation. As a secondary objective, the weight coating may also provide additional impact resistance. The purpose of the concrete crushing criterion is therefore typically to ensure that it will be attached to the pipe but no to ensure its structural strength. In case no other data is available the following criterion should be used:

γ cc ⋅ e mean ≥ e cc

DNV-OS-F101 Eq. 13.15

(6-1)

DNV-OS-F101 Eq. 13.16

(6-2)

where

e mean = −

D + e axial 2⋅ R

γcc

1.05 safety factor for concrete crushing

εcc

limit mean strain giving crushing of the concrete.

All strains shall be taken as negative, reflecting compression. The mean over bend strain at which concrete crushing first occurs depends on the pipe stiffness, the concrete strength and thickness, the axial force and the shear resistance of the corrosion coating. Crushing occurs at lower mean over bend strains for lower concrete strength, lower axial force, higher pipe stiffness and higher shear resistance. If no other information is available, concrete crushing may be assumed to occur when the strain in the concrete (at the compressive fibre in the middle of the concrete thickness) reaches -0.2%. The use of steel outer diameter is to adjust for partial sliding between concrete and steel pipe. For concrete coating of 40 mm thickness or more, together with asphalt corrosion coating, a conservative estimate of εcc is -0.22% for 42" pipelines and -0.24% for 16" pipelines, with linear interpolation in between, see Figure 6-1.


Page 35

Maximum compressive strain

0.245% 0.240% 0.235% 0.230% 0.225% 0.220% 0.215%

12

16

20

24

28

32

36

40

44

Nominal outer diameter [inch]

Figure 6-1

Maximum compressive strain in concrete coating to avoid crushing (spalling) For concrete coating of minimum 40 mm thickness and asphalt corrosion coating

This criterion is typically applied on the S-lay ramp and reference is made to Ness /5/ when applied on other applications. Further, the criterion is based on asphalt corrosion coating with low shear transfer capacity that may be non-conservative for other types of corrosion coating.

Residual Ovality

6.3 6.3.1

General

The primary objective of this criterion is to ensure that the pipeline meets the specified requirement to residual ovality on the seabed during operation. The DNV-OS-F101 line pipe specification states typically a maximum ovality of 1.5% which applies for the as delivered pipe. For ultra deep water projects 0.5% is commonly specified pushed by the collapse requirement of the pipe. Ovality is defined as:

o=

Dmax − Dmin D

DNV-OS-F101 Eq. 5.14

(6-3)

Additional ovality may be introduced during construction or operation in case the pipe experience yielding. DNV-OS-F101 states that this residual ovality shall be less than 3% during the operation life in order to allow for this potential additional ovality. This limit can be increased given that (ref. DNV-OSF101 5D1100): •

a corresponding reduction in moment resistance has been included

•

geometrical restrictions are met, such as pigging requirements

•

additional cyclic stresses caused by the ovalisation have been considered

•

tolerances in the relevant repair system are met

If acceptable ovality is larger than 3% this should be stated in the design basis. Plastic strains that can increase the ovality may have been caused during installation due to: •

Reeling and straightening


Page 36

•

Plastic strains on stinger

•

Plastic strains in sag-bend

Large plastic strains, several cycles

6.3.2

The following calculation procedure may be used for the residual ovality calculation after several plastic strain cycles during reeling. Appendix C presents the background of the calculation procedure. The residual ovality due to bend cycle 𝑖𝑖 is:

𝑜𝑜𝑚𝑚𝑚𝑚𝑚𝑚,𝑖𝑖 = �1 + 𝑘𝑘𝑜𝑜,𝑖𝑖 � ∙ �𝑜𝑜𝑟𝑟𝑟𝑟𝑟𝑟,𝑖𝑖−1 + 𝑜𝑜𝐷𝐷𝐷𝐷𝐷𝐷,𝑖𝑖 �

𝑘𝑘𝑜𝑜,𝑖𝑖

(6-4)

𝑜𝑜𝑟𝑟𝑟𝑟𝑟𝑟,𝑖𝑖 = 𝑜𝑜𝑟𝑟𝑟𝑟𝑟𝑟,𝑖𝑖−1 + 𝑘𝑘𝑜𝑜,𝑖𝑖 ∙ �𝑜𝑜𝑚𝑚𝑚𝑚𝑚𝑚,𝑖𝑖 − 𝑜𝑜𝑟𝑟𝑟𝑟𝑟𝑟,𝑖𝑖−1 �

(6-5)

= Residual ovality factor at bend cycle 𝑖𝑖.

= Maximum ovality at bend cycle 𝑖𝑖.

𝑜𝑜𝑚𝑚𝑚𝑚𝑚𝑚,𝑖𝑖

= Residual ovality at bend cycle 𝑖𝑖.

𝑜𝑜𝑟𝑟𝑟𝑟𝑟𝑟,𝑖𝑖

𝑜𝑜𝑟𝑟𝑟𝑟𝑟𝑟,𝑖𝑖−1 = Residual ovality at bend cycle 𝑖𝑖 − 1,

= 𝑜𝑜𝑟𝑟𝑟𝑟𝑟𝑟,0 at 1st bend cycle (= manufacturing ovality).

= DNV-OS-F101 prediction ovality at cycle 𝑖𝑖 = 𝑜𝑜𝐷𝐷𝐷𝐷𝐷𝐷,𝑖𝑖 = 0.03 ∙ (1 + 𝐷𝐷/120𝑡𝑡) ∙ �2𝜖𝜖𝑏𝑏,𝑖𝑖 ∙ 𝐷𝐷/𝑡𝑡�

𝑜𝑜𝐷𝐷𝐷𝐷𝐷𝐷,𝑖𝑖

2

= Bending strain in cycle 𝑖𝑖.

𝜖𝜖𝑏𝑏,𝑖𝑖

The factor 𝑘𝑘𝑜𝑜,𝑖𝑖 must be established based on full scale bend tests and/or finite element analyses and will depend on pipe diameter, wall thickness, bending strain, back tension, coating etc. A value in the range

0.25 to 0.35 for the first cycle and 0.05 to 0.15 for subsequent cycles is suggested for thin coated pipes with diameter in the range 12”-16” and D/t in the range of 15 to 20.

6.3.3

Moderate plastic strains (typically on stinger)

Residual ovality resulting from plastic bending over a stinger 𝜖𝜖𝑏𝑏 and the point load from the stinger

rollers 𝑅𝑅 can be estimated from:

𝒐𝒐𝒓𝒓𝒓𝒓𝒓𝒓 = �𝒌𝒌𝜹𝜹 ∙

𝑘𝑘𝛿𝛿 = 1 +

𝐷𝐷−0.6 2

𝟐𝟐 𝟐𝟐 ∙ 𝜹𝜹𝑬𝑬𝑬𝑬,𝑹𝑹 𝑫𝑫 𝑹𝑹 𝟐𝟐 ∙ 𝑫𝑫 𝝐𝝐𝒃𝒃 + �𝜶𝜶 ∙ �𝟏𝟏 + �+ ∙ 𝝐𝝐𝒃𝒃 � � ∙ � � + 𝒐𝒐𝟎𝟎 �∙� 𝑫𝑫 𝜷𝜷 ∙ 𝒕𝒕 𝑹𝑹𝒀𝒀 ∙ 𝒌𝒌𝒓𝒓 𝒕𝒕 𝝐𝝐𝒄𝒄,𝒎𝒎𝒎𝒎𝒎𝒎

, 𝛿𝛿𝐸𝐸𝐸𝐸,𝑅𝑅 = 1.2 ∙

𝑅𝑅

𝑡𝑡∙𝐸𝐸

𝐷𝐷 1.22

∙� � 2∙𝑡𝑡

, 𝑘𝑘𝑟𝑟 =

𝐷𝐷

14∙𝑡𝑡

, 𝛼𝛼 = 0.03, 𝛽𝛽 = 130, 𝑅𝑅𝑌𝑌 = 3.9 ∙ 𝑓𝑓𝑦𝑦 ∙ 𝑡𝑡 2

𝜖𝜖𝑐𝑐,𝑚𝑚𝑚𝑚𝑚𝑚 = 𝜖𝜖𝑐𝑐,𝐷𝐷𝐷𝐷𝐷𝐷−𝑂𝑂𝑂𝑂−𝐹𝐹101 ∙ �1 − �

𝐷𝐷 𝑅𝑅 ∙ � 80 ∙ 𝑡𝑡 𝑅𝑅𝑌𝑌

(6-6)

(6-7)

This approach is a modification of the approach presented in ref. /7/, and it should be noted that it is based purely on finite element analyses and not ed by physical tests. The point load effect may be waived in case of V-rollers with an angle of at least 30 degrees if the loading of these is symmetric, see also Sec. 5.1.3 and Appendix B.6.

6.4

Rotation

The primary objective of the rotation check is to ensure a controlled installation and position of the pipe on the seabed. This does not rule out rotation. The potential for pipeline rotation from the vessel to the seabed due to curvature, in-line components with CoG above the pipeline neutral axis and hydrodynamic forces shall be evaluated and judged versus the consequence of rotation. In case the potential and related risk is too large, the rotation shall be


Page 37

controlled such that the load effects are acceptable or that the position on the seabed is ensured. Reference is made to Endal /4/.

Curve stability

6.5

The objective of the curve stability criterion is to ensure that the pipeline can be laid along the intended route with its specified route curves. The maximum bottom tension shall be low enough to ensure that the proposed route can be laid. The safety margin may be linked to the: •

Criticality

•

Lateral slopes

•

Pipeline penetration into the seabed

•

Uncertainty and variation in soil properties

Lower lay radius may be achieved by turning bollards or other such devices may be designed to allow a tight radius to be installed. For normal lay (no slopes or high consequences) the following criterion should be used:

H bottom ,max ≤

Rmin ⋅ ( f LB ⋅ Wsub + FR )

γ

⋅

DNV-RP-F109 Eq. 4.1

(6-8)

Where γ

is 1.1

Hbottom,max See comments below The bottom tension in Eq. (6-8), Hbottom,max, should be the maximum bottom tension. In case alternative formulations are used, variations in soil resistance, both axial and lateral, should be included in the considerations (typically presented with lower bound, Best Estimate and upper bound values). This may also include 'break out factors' and 'residual factor's. Alternative characterisation of the bottom tension should also include evaluations of the dynamics of the whole laying configuration.

Residual curvature

6.6

The objective of the residual curvature evaluation is to include the effect of residual curvature on the global configuration and local buckling capacity during operation. Residual curvature after installation may be caused by insufficient straightening (during reeling installation) or by plastic strains introduced in overbend or sag bend. Sometimes, residual curvature is introduced on purpose e.g. to trigger global buckling, to adapt to uneven topography, to enable direct tie .See Endal et al /19/ and Endal and Nystrøm /20/. The primary requirement regarding permanent deformation during construction, installation and repair is the resulting straightness of the pipeline. This shall be determined and evaluated with due considerations of effects on: •

instability

•

positioning of pipeline components e.g. valves and Tee-ts

•

operation.

Guidance on how this may be considered for operational design, based on engineering judgment, is shown in Appendix E. As an alternative to the simplified method outlined in Appendix E, the effect of global or local residual curvature in the pipeline can be included in the as-laid and operational conditions analyses.


Page 38

Residual lay tension

6.7

The objective of the residual lay tension criterion is to ensure compliance with the configuration used for the design during operation. •

The maximum bottom tension shall be low enough to comply with the design bottom roughness analyses e.g. avoiding excessive free-spans etc.

•

Change in lay tension has to ensure that the residual lay tension requirements are not exceeded, i.e. lower bound axial soil resistance shall be used as bases for the length before the lay tension is increased.


Page 39

7

LIMIT STATE CRITERIA: INSTALLATION EQUIPMENT AND INSTALLATION AIDS Pull-in Winch Capacity

7.1

A winch is typically rated according to its static line pull, which is a measure of the maximum static tension that the winch can pull. Design resistance in relation to a capacity check of the winch may vary depending on the standard applied in design and certification. In order to ensure that a pull-in winch has sufficient capacity, it shall be ensured that its specified static line pull exceeds the maximum pull-in load, considering relevant tolerances and sensitivities as specified in the Analysis Guideline, ref. /1/. In addition to the tension capacity of the winch, pull-in speed at maximum line pull shall be considered, as this may limit the pull-in operation. The number of layers on the drum shall also be taken into , as this may affect both the pull speed and pull load considerably. A test to that a winch is capable of pulling the required load is recommended. The code break in relation to a product pull-in operation is illustrated in Figure 7-1. ISO 13628-2 ISO 13628-5 DNV-OS-H102

ISO 19901-6 DNV-OS-H205 c

= 1.15

c

= 1.3

MACHINERY DIRECTIVE DNV-OS-E301

PRODUCT

END FITTING/ TERMINATION

PAD-EYE PULL-IN HEAD

PULL-IN WINCH

Figure 7-1 – Code break in relation to pull-in operations

Installation/Hang-off Clamp Capacity

7.2

Maximum allowable squeeze load on the product shall be considered in design of friction clamps. Special attention shall be paid to creep of polymer materials in both product (e.g. sheaths and fillers) and clamp liner/pads, if applicable, in order to ensure sufficient squeeze load over time. Minimum required squeeze load (alternatively minimum required track length) to prevent slippage between clamp and product shall be established by applying a safety factor of 1.5, considering, as applicable: -

maximum installation tension, established according to the Analysis Guideline, ref. /1//

-

minimum friction coefficient between the product’s tensile components and its externals, and between the externals and the clamp, whichever is lower

-

change in product diameter due to tension, internal pressure, hydrostatic pressure and creep


Page 40

-

effect of temperature, e.g. on expansion/contraction, creep rate etc.

The friction factor applied in design shall for wet conditions, including flooding of the crosssection, if applicable. Documentation ing the choice of friction factor shall be available. Further guidance related to design of clamps is given in API 17L1. Note that design of friction clamps according to DNV-OS-H102 requires the application of a material factor of 1.4 (to for uncertainty in the friction factor) in addition to functional and environmental load factors. Furthermore, if failure of a single critical clamp component, e.g. strap or bolt, will lead to uncontrolled slippage and/or loss of the product, an additional consequence factor shall be applied according to DNV-OS-H205. Also note that DNV-OS-H102 specifies requirements to testing and documentation of the friction factor. The structure and lift point(s) of an installation clamp or a temporary hang-off clamp shall be designed according to ISO 19901-6 or DNV-OS-H205 applying the maximum installation loads determined according to the Analysis Guideline, ref. /1/. A clamp ing a dynamic load during installation shall be evaluated with respect to fatigue. Sufficient fatigue life, ing for contingency operations, shall be ensured for the duration of relevant operations assuming conservative loading conditions. The radial load applied by the clamp to the product cross-section typically increases friction and/or restricts relative movement between internal product components. Restricting the clamp at the vessel interface will thus result in stress concentrations that in turn may lead to premature fatigue failure of the product. Unless restriction of the clamp can be avoided, a fatigue assessment shall be performed to evaluate the need for a bend stiffener, bend restrictor or radius controller. If sufficient fatigue capacity cannot be demonstrated, detailed analyses and/or tests shall be carried out to ensure that premature fatigue failure is avoided. In general, the following fatigue criterion shall be satisfied: 𝐷𝐷𝑓𝑓𝑓𝑓𝑓𝑓 ∙ 𝐷𝐷𝐷𝐷𝐷𝐷 ≤ 𝛽𝛽

where

Dfat is accumulated fatigue damage according to the Miner-Palmgren rule DFF is the design fatigue factor

β is allowable fatigue damage during installation Maximum allowable fatigue damage shall be determined by applying a design fatigue factor (DFF) as specified in the relevant design code. Tensioner holding capacity for axial load will be reduced if there also acts a rotational force (torque) on the pipe. Rotational torque in the pipe will arise during laying of horizontal curves and with residual curvature in the pipeline.

7.3

Maximum Dynamic Sling Load, Steel Wire and Fibre Ropes

Lifting equipment shall be designed according to a recognized lifting standard, e.g. ISO 19901-6 or DNVOS-H205. The general design format applied in these standards is LRFD, for which the design load effect shall not exceed the design resistance (capacity): 𝐿𝐿𝐷𝐷 < 𝑅𝑅𝐷𝐷 DNV GL – Report No. 2014-0185, Rev. 3 – www.dnvgl.com

(7-1)

Page 41

For steel wire ropes and fiber ropes, the design load effect is the maximum dynamic sling load, i.e. the characteristic load effect determined according to the Analysis Guideline, ref. /1/, while the design resistance is given as:

where

𝑅𝑅𝐷𝐷 =

𝑀𝑀𝑀𝑀𝑀𝑀 𝛾𝛾𝑠𝑠𝑠𝑠

γsf

(7-2)

is a safety factor determined as the product of several partial factors

Relevant partial safety factors shall be taken according to the relevant lifting standard, e.g. ISO 19901-6 or DNV-OS-H205. These safety factors for reduction in strength due to e.g. splicing, bending around sheaves, snatch blocks or similar. Note that for well planned, one time pull-in operations to an onshore or offshore facility, the consequence factor may be discarded provided that the conditions stated in section 7.5are satisfied. A manufacturer’s certificate corresponding to the requirements in EN 10204, type 3.1 (or type 3.2) shall be provided for wire ropes used for slings and grommets. A 3.2 certificate (as defined in EN 10204, issued/endorsed by a recognized Certifying Body) is required by DNV-OS-H205 for slings or grommets made of steel wire ropes using a material factor of less than 1.5. Fibre rope certification shall follow the principles indicated in DNV-OS-E303. The design format for structural steel components in lifting applications is described in section 7.5.

Safe Working Load, Rigging

7.4

Safe working load (SWL) is a term generally used as a reference for the strength of shackles and is normally determined by the manufacturer or a Certifying Body. The required minimum SWL for applied shackles shall be determined according to a recognized lifting standard, e.g. ISO 19901-6 or DNV-OSH205. According to DNV-OS-H205, maximum allowable dynamic load in a shackle shall not be taken greater than the minimum of: -

SWL*DAF

-

MBL/3.0

-

Documented “Proof Loading” (including safety factor, ref. DNV-OS-H205)

A manufacturer’s certificate and proof load certificate signed by a recognized Certifying Body shall be provided for each shackle.

7.5

Lifting Capacity, Structural Steel Components

The structure and lift point(s) of terminations, end fittings, pull-in heads and installation aids ing the weight of a suspended product and/or an end termination assembly during installation shall be designed according to ISO 19901-6 or DNV-OS-H205. The following criterion should be satisfied:

where

𝐿𝐿𝐷𝐷 ≤ 𝑅𝑅𝐷𝐷

(7-3)

𝐿𝐿𝐷𝐷 = 𝐿𝐿𝐶𝐶 ∙ 𝛾𝛾𝐷𝐷 ∙ 𝛾𝛾𝐶𝐶

(7-4)


Page 42

𝑅𝑅𝐷𝐷 =

𝑅𝑅𝐶𝐶 𝛾𝛾𝑅𝑅

(7-5)

The characteristic load effect shall be determined according to the Analysis Guideline, reference /1/, while design resistance shall be determined according to the relevant design code. The consequence factor shall be taken according to the following (see also ISO 19901-6 and DNV-OSH205): -

γC = 1.3 for lift points including attachment (e.g. welds) to object, including attachment between end termination/fitting and bullnose (if applicable) as illustrated in Figure 7-1, and

-

γC = 1.15 for the structural elements ing the lift.

For well planned, one time pull-in operations to an onshore or offshore facility, the consequence factor may be discarded provided that the following conditions are satisfied (see also DNV-OS-H206): -

a risk assessment of the operation has been carried out to evaluate potential consequences of winch and winch wire failure, and

-

it can be documented that a failure of the end termination/fitting, pull-in head or installation aid will not cause personnel injury, environmental pollution or damage to vessel, installation equipment or other installations, and

-

necessary contingency procedures are in place, ed by analyses as appropriate.

Note that the skew load factor specified in DNV-OS-H205, API RP 2A and ISO 19901-6 applies to lifts using several slings and is therefore not relevant with respect to design of pull-in heads. The skew load factor is meant to for a possible load increase in a sling due to differences in sling lengths caused by manufacturing tolerances (see DNV-OS-H205 for further guidance related to out-of-plane loads). In design of pull-in heads and pad-eyes, maximum relative wire angle shall be considered according to the Analysis Guideline, reference /1//. The code break in relation to a product pull-in operation is illustrated in Figure 7-1.


Page 43

8 /1/

References Guideline for Installation of Rigid and Flexible Pipelines, Umbilicals and Subsea Power Cables – Analyses, DNV GL Report no 2014-0183

/2/

Guideline for Installation of Flexible Pipes, Umbilicals and Subsea Power Cables – Limit State Criteria, DNV GL Report no 2014-0184

/3/

Collberg, Leif; Aronsen, Kristoffer; Palmer, Andrew; Hahn, Guillermo Benefit of Partly Displacement Controlled Condition in Sagbend. Cancun : ASME, 2003. OMAE2003-37376

/4/

Endal G., Ness O. B., Verley R., Holthe K. and Ramseth S; Behaviour of Offshore Pipelines Subjected to Residual Curvature During Laying, Proceedings of OMAE'95 conference, Copenhagen, Denmark

/5/

Ness O. B. and Verley R.; Strain Concentrations in Pipelines with Concrete Coating: An Analytical Model, Proceedings of OMAE'95 conference, Copenhagen, Denmark

/6/

Torselletti, Enrico, et al., Submarine Pipeline Installation t Industry Project: Global Response Analysis Of Pipelines During S-Laying. Hamburg : OMAE2006-92377.

/7/

Torselletti, Enrico, et al, Submarine Pipeline Installation JIP:Strength and Deformation Capacity of Pipes ing Over The S-Lay Vessel Stinger. Hamburg : ASME, 2006. OMAE2006-92378

/8/

Brown, G., Tkaczyk, T. and Howard, B. (2004);Reliability Based Assessment of Minimum Reelable Wall Thickness for Reeling, IPC04-0733, Calgary, Alberta, Canada

/9/

Martinez, Michael & Brown, George Evolution of Pipe Properties during Reel-Lay Process: Experimental Characterisation and Finite Element Modelling, OMAE2005-67074, Halkidiki.

/10/

Denniel, S., Tkaczyk, T., Howard, B., Levold, E. and Aamlid, O. On the Influence of Mechanical and Geometrical Property Distribution on the Safe Reeling of Rigid Pipelines OMAE2009-79344 Honolulu, USA

/11/

Denniel, S., Tkaczyk, T., Howard, B., Levold, E. and Aamlid, O. The Development of a Refined Assessment Procedure for the Pipeline Reeling Process Using Reliability and Finite Element Techniques OMAE2009-79348 Honolulu, USA

/12/

Smith, D., Tkaczyk, T., Denniel, S. Reliability Based Assessment of Minimum Wall Thickness for Reeling – a Focus on Cold Worked Pipe OMAE2011-49389, Rotterdam

/13/

Karjadi, E.; Smienk, H.; Boyd, H.; Aamlid, O. Extended Reel-Ability of New Aegir Reeling Vessel Based on Reliability Based Assessment and Bending Tests Program, OMAE2012-83061, Rio de Janeiro.

/14/

Smienk, H.; Karjadi, E.; Vazquez, G.; Doherty, P. and Dooley, P. DCV Aegir Pipelay Installation Analyses and Capabilities, OMAE2013-10262 Nantes.

/15/

Karjadi, E.; Boyd, H.; van Rooijen, R.; Demmink, H. and Balder, T. Development on Aegir Reeling Pipeline Analyses by Test Validation, OMAE2013-10365 Nantes.

/16/

Karjadi, E.; Smienk, H. Reliability Assessment Approach for DCV Aegir Pipeline Installation Analyses, OMAE2014-24507 San Francisco.

/17/

Vitali L., Torselletti E., Bruschi R., Spinazzè M., Brunetto L.; Bending Capacity of Pipes Subject to Point Loads, OMAE2003-37222 Cancun, Mexico

/18/

Hertz, D.L and Farinella, A.C Shore A Durometer and Engineering Properties

/19/

Endal, G., Giske, S.R., Moen K., Sande, S.; “Reel-Lay Method to Control Global Pipeline Buckling Under Operating Loads” OMAE2014-24062


Page 44

/20/

Endal, G. and Nystrøm, P.R.; "Benefits of generating local residual curvature during Reel- and S-lay installation", OPT 2015


Page 45

APPENDIX A ON-REELING ANALYSES


A-1

A.1 Introduction The design approaches described below intend to ensure a sufficient safety margin with respect to buckling during on-reeling and due to stength mismatch due to inherent variation in yield stress and thickness from one t to another. The bending moment required to bend the strong pipe must be provided by the weaker trailing pipe and the weaker pipe fails if the moment required to bend the stronger pipe is higher than the moment capacity of the weaker pipe. Additional symbols used in this appendix to those defined in Section 1.8 are given in Table A-1. Table A-1

Symbols

Symbol

Description

fy,strg

Yield stress for the strong leading pipe t.

fy,weak

Yield stress for the weak trailing pipe t.

Δ𝑓𝑓𝑦𝑦

Yield stress mismatch; = 𝑓𝑓𝑦𝑦,𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 − 𝑓𝑓𝑦𝑦,𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 .

𝑓𝑓𝑦𝑦,𝑎𝑎𝑎𝑎𝑎𝑎

1

Average yield stress = � 𝑓𝑓𝑦𝑦,𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + 𝑓𝑓𝑦𝑦,𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 �. Can be taken as expected yield stress 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 + 2𝜎𝜎𝑓𝑓 . 2

Project specific data or other relevant experience can be used if avalable.

𝑡𝑡𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

Wall thickness for the strong leading pipe t.

Δ𝑡𝑡

Wall thickness mismatch; = 𝑡𝑡𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 − 𝑡𝑡𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 .

𝑡𝑡𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤

Wall thickness for the weak trailing pipe t.

𝑡𝑡𝑎𝑎𝑎𝑎𝑎𝑎

Average wall thickness = � 𝑡𝑡𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + 𝑡𝑡𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 �. Can be taken as nominal wall thickness 𝑡𝑡𝑛𝑛𝑛𝑛𝑛𝑛 . Project

𝜎𝜎𝑡𝑡

1 2

specific data or other relevant experience can be used if avalable.

Standard deviation of wall thickness over a cross sectional area. Statistics investigated by DNV GL indicate that the standard deviation of wall thickness averaged over a cross section can be taken as 60% of the standard deviation of individual measurements and the latter can be taken as as 1/3 of the negative fabrication tolerance. Project specific data or other relevant experience can be used if avalable.

𝜎𝜎𝑓𝑓

Standard deviation of yield stress averaged over a cross sectional area. DNV GL has no data on which the relation between standard deviation of individual measurements and standard deviation of values averaged over a cross sectional area. Statistics investigated by DNV GL indicate the standard deviation of individual measurements can be taken as 3.3% of yield stress for CMn steels and 4.1% of yield stress for 13Cr steel. Project specific data or other relevant experience can be used if avalable.

𝛽𝛽 𝛼𝛼ℎ

Safety index which value depends on the chosen safety level, Ref. Table A-3 Note that this guideline is only considering the case where the weaker t is trailing the stronger t, i.e. one tail in the distribution. The hardening factor, ratio between yield stress and ultimate strength, Ref. Table A-2. Project specific data or other relevant experience can be used if avalable.

𝛼𝛼ℎ′

The gradient in the relationship between yield stress and the hardening factor, i.e. 𝛼𝛼ℎ′ = (𝛼𝛼ℎ,𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 − 𝛼𝛼ℎ,𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 )/Δ𝑓𝑓𝑦𝑦 , Ref. Table A-2. Project specific data or other relevant

DReel

(Inner) Diameter of the reel

T

Back tension

experience can be used if avalable.


A-2

A.2 Design Equation For on reeling of empty pipelines, the approach given in DNV-OS-F101:2013 Sec. 5 D608 may be applied. DNV-OS-F101:2013 Table 4-5 specifies 𝛾𝛾𝑐𝑐 = 0.82 for a continuously stiff ed pipe, whereas FE

analyses performed according to the procedures specified below have shown that a sufficient safety level for straight pipes with homogeneous properties and tolerances within the limits given by DNV-OS-F101 is obtained with 𝛾𝛾𝑐𝑐 = 0.77.

Finite element analyses have shown that a high hardening factor is detrimental for the buckling strength, and with supplementary requirement for plastic deformation (P), DNV-OS-F101:2013 Sec. 7 I 303 allows

a maximum value of 0.90 for 𝛼𝛼ℎ . The values in Table A-2 have been calculated as the mean value plus one standard deviations from a large amount of material tests. These are considered sufficiently

conservative since one would expect a t with low yield stress, and thus a low hardening factor, to buckle. Hence, if no specific information is available, these can be used in design. Table A-2

Hardening factor

450 / X65 – SML

𝜶𝜶𝒉𝒉 [-]

485 / X70 – SML

0.90

13%Cr - SML

0.80

Material

0.87

Specification of supplementary requirement S for sour service may result in a higher value for the hardening factor. Back tension T is assumed to fulfil the following criterion: 𝑇𝑇 ≥ 1.5 ∙

𝑓𝑓𝑦𝑦 ∙(𝐷𝐷−𝑡𝑡)2 ∙𝑡𝑡 𝑅𝑅𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

(A.1)

This equation, including the factor 1.5, is based on general experience from the industry


A-3

A.3 Design by FE Analyses A.3.1 Introduction Relevant references to this section are Refs. /8/ to /16/. This section decribes a design approach aiming to document sufficiently low probabaility for buckling when reeling a specific pipeline onto a specific reel diameter. If one wants to minimise wall thickness for on reeling, the same approach can be applied but iterations on wall thickness are required. The design approach described below consists of two main steps: 1. Establish the failure curve, i.e. how large mismatch is required for the pipe to fail, and 2. Determine the probability that this degree of mismatch to occur.

A.3.2 Failure curve A.3.2.1 Introduction The failure curve is established based purely on finite element analyses. A representative FE model where a weak t is trailing a strong t with varying mismatch in yield stress Δ𝑓𝑓𝑦𝑦 and wall thickness Δ𝑡𝑡

is run until the points of failure are established to a satisfactory degree of accuracy. Based on the results from these FE analyses, one can establish a curve in the Δ𝑓𝑓𝑦𝑦 /𝑓𝑓𝑦𝑦 and Δ𝑡𝑡/𝑡𝑡 space as indicated in Figure A-1. Experience has shown that this failure curve is well represented by a straight line, so the mismatch

values can be chosen along the two axes in this coordinate system. However, it is adviced also to run at least one series of FE analyses with mismatch in both yield stress and wall thickness to this. The point where the failure curve crosses the axes are here denoted Δ𝑡𝑡Δf=0 and Δ𝑓𝑓Δt=0 , respectively It is convenient to scale the x and y axes with 1/�√2 ∙ 𝜎𝜎𝑓𝑓 � and 1/�√2 ∙ 𝜎𝜎𝑡𝑡 �, respectively and introduce the two

variables 𝛽𝛽𝑓𝑓 = Δ𝑓𝑓Δ𝑡𝑡=0 /�√2 ∙ 𝜎𝜎𝑓𝑓 � and 𝛽𝛽𝑡𝑡 = Δt Δf=0 /�√2 ∙ 𝜎𝜎𝑡𝑡 �, where 𝜎𝜎𝑓𝑓 and 𝜎𝜎𝑡𝑡 are the standard deviations of yield stress and wall thickness averaged over the pipe cross section.

The easiest way of reducing the probability for buckling and high peak strains for a certain pipe on a given vessel is to increase back tension, but sorting ts with respect to wall thickness and yield stress to reduce maximum mismatch is also viable. Note that these Guidelines do not consider residual ovality in the as-installed pipe after the whole reeling process. Mesh sensitivity should be performed to confirm that the calculated strain is representative as an average value.

A.3.2.2 Buckling Normally, a buckle can easily be detected visually, but as guidance, the following acceptance criteria for “global” bending strain 𝜖𝜖𝑔𝑔 , averaged over one diameter pipe length from the weld into the weak t,

and total ovality 𝑜𝑜 can be applied to avoid local buckling: 𝑡𝑡

𝜖𝜖𝑔𝑔 ≤ 1.2 ∙ − 0.01 and 𝑜𝑜 ≤ 0.10 𝐷𝐷

(A.2)

A.3.2.3 Peak Strains

Finite element analyses have shown that high local strains will often occur in a pipe that es the acceptance criteria above. It is thus adviced that the absolute value of the strains are kept below 5% when averaged over the area covered by the wall thickness and an axial length equal to pre-straining – and tensile test specimen length (not more than 75 mm) with the peak in the middle.


A-4

If the strains do not meet this criteria then strain aging tensile tests according to Supplementary P in DNV-OS-F101 should be performed. High local strains in the weld material needs to be assessed through adequate ECA.

A.3.3 Probability of mismatch The probability of mis-match is calculated based on a pure probabilistic assessment. If one assumes that the yield stress and wall thickness are normal distributed, the difference in, e.g. wall thickness, Δ𝑡𝑡 = 𝑡𝑡𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 − 𝑡𝑡𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 will be normal distributed with mean value equal to zero and standard deviation equal to

√2 ∙ 𝜎𝜎𝑡𝑡 . The probability that Δ𝑡𝑡 is larger than the standard deviation multiplied by the safety index 𝛽𝛽 is Φ(−𝛽𝛽):

P�Δ𝑡𝑡 > √2 ∙ 𝛽𝛽 ∙ 𝜎𝜎𝑡𝑡 � = 𝑃𝑃 �𝑁𝑁(0,1) >

√2∙𝛽𝛽∙𝜎𝜎𝑡𝑡

Similarly along the yield stress axis:

P�Δ𝑓𝑓𝑦𝑦 > √2 ∙ 𝛽𝛽 ∙ 𝜎𝜎𝑓𝑓 � = 𝑃𝑃 �𝑁𝑁(0,1) >

√2∙𝜎𝜎𝑡𝑡

� = 𝑃𝑃(𝑁𝑁(0,1) > 𝛽𝛽) = Φ(−𝛽𝛽)

√2∙𝛽𝛽∙𝜎𝜎𝑓𝑓 √2∙𝜎𝜎𝑓𝑓

(A.3)

� = 𝑃𝑃(𝑁𝑁(0,1) > 𝛽𝛽) = Φ(−𝛽𝛽)

(A.4)

In reality, a combination of mismatch in wall thickness and yield stress will obviously occur, and it is assumed that any combination where Δ𝑡𝑡 = √2 ∙ 𝛽𝛽 ∙ 𝜎𝜎𝑡𝑡 ∙ 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 and Δ𝑓𝑓𝑦𝑦 = √2 ∙ 𝛽𝛽 ∙ 𝜎𝜎𝑓𝑓 ∙ 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠, 𝛼𝛼 ∈ {0, 𝜋𝜋/2}for the first

quadrant in the figure below, have the same probability of occuring. Hence, the probability that a

combination of mismatches, L, lies outside the failure curve, R, can then be estimated by the shortest

distance from origin to the failure curve. Considering one single t, the probability for a buckle PoB1 is thus: 𝑃𝑃𝑃𝑃𝑃𝑃1 = 𝑃𝑃(𝐿𝐿 > 𝑅𝑅) = 𝑃𝑃(𝑁𝑁(0,1) > 𝛽𝛽) = Φ(−𝛽𝛽)

(A.5) n

The probability that one out of n t buckles PoBn can be estimated by 1 – (1 – PoB1) . Note that the consideration above only considers failure of a weak t trailing a strong. Allthough the opposite (3rd quadrant in the figure below) has a larger capacity, it does contribute to the probability of failure. Furthermore, from equal sided triangles in Figure A-1 it can be shown that the safety index is given by the following formula if the failure curve is assumed to be perfectly straight: 𝛽𝛽 =

𝛽𝛽𝑓𝑓 ∙𝛽𝛽𝑡𝑡

�𝛽𝛽𝑓𝑓2 +𝛽𝛽𝑡𝑡2


(A.6)

A-5

6 ing Failing

5

Failure curve

Normalized wall thickness mismatch

Series4 4

3

2

1

0 0

1

2

3

4

5

6

Normalized yield stress mismatch, Figure A-1

Failure surface and safety index

Selecting mismatch values along the two axis in the figure above may lead to unrealistic values, e.g. wall thickness less than the minimum acceptable, yield stress below SMYS and hardening factors above 0.90. However, no lower limit is set here since the assumption of mismatch in one parameter only is hypothetical, and the exceedance will occure with combined mismatch with much lower values. Table A-3

Safety index

Exceedance probability

10-2

10-3

10-4

10-5

Safety index, β

2.32

3.09

3.71

4.26

It is industry practice to apply safety class low with a nominal target probability of 10-3 during installation (β = 3.09), but DNV-OS-F101:2013 Sec. 5 D610 states that “ “A higher probability of failure corresponding to a serviceability limit state may be allowed during the installation phase provided that: •

aids to detect buckle are provided

•

repair of potential damage is feasible and may be performed during laying

•

buckle arrestors are installed if the external pressure exceeds the initiation propagating pressure.”


A-6

Input to the FE model is thus as given in Table A-4, the values for the hardening factor given in Table A2 refers to average yield stress. Table A-4

Input to FE model

Parameter Wall thickness Yield stress Ultimate strength Hardening factor

Weak t 1 𝑡𝑡𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 = 𝑡𝑡𝑎𝑎𝑎𝑎𝑎𝑎 − ∙ Δ𝑡𝑡 2 1 𝑓𝑓𝑦𝑦,𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 = 𝑓𝑓𝑦𝑦,𝑎𝑎𝑎𝑎𝑎𝑎 − ∙ Δ𝑓𝑓𝑦𝑦 2 𝑓𝑓𝑦𝑦,𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 𝑓𝑓𝑢𝑢,𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 = 𝛼𝛼ℎ,𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 1 𝛼𝛼ℎ,𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 = 𝛼𝛼ℎ,𝑎𝑎𝑎𝑎𝑎𝑎 − ∙ 𝛼𝛼ℎ′ ∙ Δ𝑓𝑓𝑦𝑦 2

Strong t 1 𝑡𝑡𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑡𝑡𝑎𝑎𝑎𝑎𝑎𝑎 + ∙ Δ𝑡𝑡 2 1 𝑓𝑓𝑦𝑦,𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑓𝑓𝑦𝑦,𝑎𝑎𝑎𝑎𝑎𝑎 + ∙ Δ𝑓𝑓𝑦𝑦 2 𝑓𝑓𝑦𝑦,𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑓𝑓𝑢𝑢,𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 𝛼𝛼ℎ,𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 1 𝛼𝛼ℎ,𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 𝛼𝛼ℎ,𝑎𝑎𝑎𝑎𝑎𝑎 + ∙ 𝛼𝛼ℎ′ ∙ Δ𝑓𝑓𝑦𝑦 2

One should be aware that a warm field t coating, that may thus be very soft, will introduce additional stiffness mismatch. When the steel pipe is bent well into its plastic region, the stiffness of a thick coating may be significant compared to the tangent stiffness of the steel pipe. This effect may be especially important for the field ts with normally softer material that also may be warm and thus affect the steel properties. Also derating of the heated steel pipe should be considered. For counter bored pipes, the counter bore depth should be considered as an additional parameter with uncertainty, see ref. /17/. Normally, a buckle will be discovered visually during on-reeling, but this may be otherwise if the pipe has a thick coating. A finite element (FE) model must be established with the objective to document safe on-reeling. The potential failure mechanism is buckling of a weak pipe t that is trailing a stronger pipe t during on-reeling. The model must thus be capable of predicting local buckling of the pipe cross section in the vicinity of the transition between two ading pipe ts. This will normally require shell - or solid elements in this critical region. Apart from this, beam elements may be used. Reference is made to the benchmark example in next section. The FE code must be capable of describing: -

large rigid body motions,

-

non-linear material properties and

-

surfaces.

Essential properties that should be considered in the FE model are as a minimum the following: -

Pipe diameter (including coating if relevant)

-

pipe steel wall thickness,

-

pipe steel material (non-linear),

-

pipe weight (including weight of coating and content if relevant),

-

back tension,

-

reel drum radius,

-

tensioner angle,

-

aligner radius,

-

horizontal distance between reel drum and aligner/tensioner,

-

vertical distance between reel drum and aligner/tensioner, vertical distance between aligner/tensioner and rollers on land.


A-7

Figure A-2 shows a schematic figure of a very simple vessel configuration (however not showing the whole span towards the rollers on land).

Pipe modelled with shell elements, weak t trailing strong t Pipe modelled with beam elements

Reel drum diameter

Tensioner angle

Aligner radius Aligner vertical distance

On-reeling tension

Aligner horizontal distance

Figure A-2

Schematic on-reeling configuration

The part of the pipe that is modelled by shell or solid elements, and thus capable of predicting local buckling, shall represent two steel pipe ts, one weak trailing a stronger. This mismatch in strength/stiffness is introduced through differences in wall thickness and yield strength. If the pipeline experiences plastic deformations through the tensioner/aligner, the shell elements shall also be modelled in this part. It is known that variability in ultimate strength 𝑓𝑓𝑢𝑢 is lower than the variability in yield stress. For reeling,

this is a beneficial effect that can be ed for through the hardening factor which gives the yield stress to ultimate strength ratio.

FE analyses have shown that a low hardening factor (high 𝑓𝑓𝑢𝑢 to 𝑓𝑓𝑦𝑦 ratio) is beneficial, and material tests

show in general that this hardening factor decreases for decreasing yield stress. This can be ed for in the FE analyses by specifying a lower hardening factor for the weak t according to the dependency given in Table A-5. Table A-5

Hardening factor as a function of yield stress

Carbon 450/X65

𝜶𝜶′𝒉𝒉 [MPa-1]

Carbon 480/X70

2∙10-4

13%Cr

9∙10-4

Material

5∙10-4

If a theoretical material model, e.g. of the Ramberg-Osgood type, is applied, yield stress and ultimate strength should be taken at 0.5% and 10% strain, respectively. Stress-strain curves from relevant tests may be used if avalable.


A-8

A.4 Design by Experience Safe on-reeling can be documented by experience, however, unrealistically many similar projects are needed to document a probability of failure in the range 10-2 to 10-3. If a data base is established to collect experience, all relevant data, see above, should be included.

A.5 Reeling Example A.5.1 Introduction This example case is set up to work as a guideline example for validation of reeling FE-models. The important input parameters and their background are presented along with actual modelling results. For better understanding of the model, this should be considered in combination with the design theory presented in Section A.3. All of this can then be used to validate an FE-model. This example is analysed in Abaqus version 6.13.2.

Α.5.2 FE-model design The following main assumptions / simplifications were made: •

A strong pipe is followed by a weak pipe.

•

Symmetry conditions utilized, i.e. half the cross section is modelled.

•

The stiffness of all surfaces was set to 100 kN/m/m.

The parameters used in the analys is listed below. Table A.6

Summary of material input parameters

Parameter Pipe diameter Average wall thickness Average yield stress Average ultimate strength Hardening factor Change in strain hardening CoV of wall thickness CoV of yield stress Youngs modulus

Symbol

Value

D

323.9 mm

𝑡𝑡𝑎𝑎𝑎𝑎𝑎𝑎

17.26 mm

𝑓𝑓𝑦𝑦,𝑎𝑎𝑎𝑎𝑎𝑎

481.8 MPa

𝛼𝛼ℎ

0.87

𝑓𝑓𝑢𝑢,𝑎𝑎𝑎𝑎𝑎𝑎

553.8 MPa

𝛼𝛼ℎ′

5·10-4 0.60⋅3.3% = 1.98% 0.80⋅3.3% = 2.64% 207GPa

Poisson ratio

0.3

Steel density

7850 kg/m3

Reel radius

7.5m

Aligner radius

10m

Horizontal distance reel to aligner

28m

Vertical distance reel to aligner

2.3m

Tensioner tilt angle

9 deg

Nominal strain on reel

2.11%


A-9

The wall thickness is calculated from Eq. (5.31) in DNV-OS-F101 with safety class low: 𝑡𝑡𝑎𝑎𝑎𝑎𝑎𝑎 = 323.9𝑚𝑚𝑚𝑚⋅ �0.01 + 0.02114 ∙

0.871.5 0.78

∙ 0.82 ∙ 1.2 ∙ 2.0� = 17.26𝑚𝑚𝑚𝑚

(A.7)

The plastic material model is made using a Ramberg-Osgood curve fit to yields stress at 0.5% strain and ultimate stress at 10% strain. The vessel geometry input is presented schematically in Figure A-3 and the FE model shown in Figure A-4. The pipe model consists of two parts. The first part is modelled using shell elements to be able to for local buckling, while the second part is modelled using beam elements.

Pipe modelled with shell

Pipe modelled with

elements, weak t

beam elements

trailing strong t

Tensioner angle Reel drum

= 9°

Aligner

diameter = 15m

radius =10m Back tension Aligner vertical distance = 2.3m

Aligner horizontal distance = 28m

Figure A-3

Reel and aligner geometry

The overall length of the pipe model (shells and beams) is 150m. The model includes a horizontal surface to simplify the model in of applying load (back tension).

Figure A-4

Finite element model geometry


A-10

The loads specified in the model are gravity and back tension. The back tension is set to 250kN/2 = 125kN, i.e. larger than what is calculated based Eq. (A.1): 𝑇𝑇 = 1.5 ∙

𝑀𝑀𝑝𝑝

𝑅𝑅𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

= 1.5 ∙

(0.3239−0.01726)2 ∙0.01726∙480.8∙106 𝑁𝑁 7.5𝑚𝑚∙2

= 78.0𝑘𝑘𝑘𝑘

(A.8)

where MP and Rreel are plastic moment and reel radius respectively. The divisor 2 is introduced because only half the cross section is modelled. However, the back tension used in the model is 250kN, to get a lower probability of failure. This is a measure that can be taken into consideration as long as the tension level used is within the range for the reeling vessel. The boundary condition between the surfaces are based on element to surface . The pipe elements have pairs with reel, aligner, tensioner and . The detailed pipe (shell elements) are in with the reel, while beam elements are in with aligner, tensioner and . The detailed pipe is modelled as a half pipe and therefore boudary conditions are applied to all nodes in the “half plane” to prevent displacement out of plane to simulate the complete cross section. The tensioner makes sure the correct curvature is obtained over the alinger, while the surface is present to make the convergency more efficient and make it easier to apply the back tension. All surfaces are frictionless with a vertical stiffness of 100 kN/m/m. As mentioned, the model consists of both beam and shell elements. The shell element details are as follows: •

S8R5 shell elements.

•

Total length of 16m.

•

Symmetry, half the pipe is modelled.

•

Weld, weak and strong t properties.

•

Mesh: Circumferential direction: A total of 24 elements (for half the cross section). The mesh is refined in the area where with the reel is expected, i.e the circumferrencial element length is not uniform. Longitudinal direction: 54 girths of elements have strong t properties and 90 girths elements have weak t properties. A refinement is made towards the weld, see Figure A-5


A-11

Figure A-5

Mesh refinement in proximity to the weld

The beam element details are as follows: •

PIPE31 beam elements

•

Total length of 134m.

•

Section properties: The properties of the beam elements correspond to weak t properties. As only half the pipe cross section is modelled in the shell element section, the wall thickness of the beam elements has been manipulated so that the beam elements give the same bending stiffness as the shell element section.

•

The material density associated with the beam elements has been manipulated to give a unit length weight corresponding to the weight of the shell element section (weak t).

•

Mesh: Element length of 0.5m.

The analysis procedure is described for one particular pipe reeled on one particular reel vessel. i.e. the reel and pipe geometry are given, and the probability of exceedance and failure curve is extracted from analyses for this set up. The following methodology has been used: •

For pipe diameter and thickness together with reel radius a certain “strain on reel” level is calculated together with a criterion for allowable average strain, see Section A.3.

•

Properties for weak and a strong t are then determined, and a FE analysis is performed. FEanalyses for different Δt and Δfy values are run. The mismatch in thickness and mismatch in strength is run independent of each other, i.e. either Δt different from zero and Δfy equal to zero or vica verca.

•

Based on the strain criterion find the maximum allowable mismatch for both thickness and strength, and then establish the failure surface in the normalised Δt vs Δfy space, see Figure A-6.

•

As a control, some cases (minimum one ing and one failing) with both mismatch in thickness and strength should be run to show that the fail surace is linear.

•

Calculate the corresponding safety index, β, and the probability of failure using the fail surface, see Section. A.3.


A-12

A.5.3Results Two acceptance criteria are checked in this example: The average strain over a distance one OD, maximum of tensile strain on extrados (12 o’clock) and

-

compressional strain on intrados (6 o’clock) less than 1.2⋅𝑡𝑡/𝐷𝐷 – 0.01 = 5.4% (ovality was well below

10% for all the analysed cases), and Peak strain less than 8%

-

The results based on the average strain criterion are shown in Table A.7 and Figure A-6. Analyses that did not meet the acceptance criterion are marked with red crosses, and analyses that ed the criterion are marked green dots. The red line is the failure line, defined from the largest mismatches that did not fail. The calculated probability of failure is 7.55·10-5 for a single t and 7.52·10-3 for 100 ts (system effect). Table A.7

Probablity of buckling based on average strain

Maximum Δ𝑓𝑓Δ𝑡𝑡=0 [MPa]

93.0

𝛽𝛽𝑓𝑓 = Δ𝑓𝑓Δ𝑡𝑡=0 /�√2 ∙ 𝜎𝜎𝑓𝑓 �

5.17

Maximum Δ𝑡𝑡Δ𝑓𝑓=0 [mm]

2.65

𝛽𝛽𝑡𝑡 = Δ𝑡𝑡Δ𝑓𝑓=0 /�√2 ∙ 𝜎𝜎𝑡𝑡 �

5.48

𝛽𝛽 = 𝛽𝛽𝑓𝑓 ∙ 𝛽𝛽𝑡𝑡 ∙ �𝛽𝛽𝑓𝑓2 + 𝑃𝑃𝑃𝑃𝑃𝑃1 = Φ(−𝛽𝛽)

−1/2 𝛽𝛽𝑡𝑡2 �

3.76 8.44E-05 8.41E-03

βt [-]

∆t/t [%]

𝑃𝑃𝑃𝑃𝑃𝑃100 = 1 − (1 − 𝑃𝑃𝑃𝑃𝑃𝑃1 )100

∆fy/fy [%] Figure A-6

βf [-]

FE results establishing the failure surface for the averange strain criterion

Below, in Figure A-7 and Figure A-8, pictures of the buckle present in the weak t after on-reeling are shown. The pictures are showing the largest allowable mismatch in thickness and yield strength with respect to the average strain criterion. Some ovality is seen, but this may be considered acceptable. Note however, the peak strain in the models shows values of 9.5% and 8.3% which is considered high. It is worth mentioning that the 8% limit would need thorough documentation and testing to be applied in a real setting.


A-13

Figure A-7

Up close picture of buckle in weak t for the largest allowable mismatch in

thickness for the average strain criterion

Figure A-8


yield strength for the average strain criterion


A-14

The results based on the peak strain criterion are shown in Table A.8 and Figure A-9, the calculated probability of failure is 2.24·10-4 for a single t and 2.22·10-2 for 100 ts (system effect). Table A.8

Probablity of buckling based on peak strain

Maximum Δ𝑓𝑓Δ𝑡𝑡=0 [MPa]

88.0

𝛽𝛽𝑓𝑓 = Δ𝑓𝑓Δ𝑡𝑡=0 /�√2 ∙ 𝜎𝜎𝑓𝑓 �

4.89

Maximum Δ𝑡𝑡Δ𝑓𝑓=0 [mm]

2.40

𝛽𝛽𝑡𝑡 = Δ𝑡𝑡Δ𝑓𝑓=0 /�√2 ∙ 𝜎𝜎𝑡𝑡 �

4.97

𝛽𝛽 = 𝛽𝛽𝑓𝑓 ∙ 𝛽𝛽𝑡𝑡 ∙ �𝛽𝛽𝑓𝑓2 + 𝑃𝑃𝑃𝑃𝑃𝑃1 = Φ(−𝛽𝛽)

−1/2 𝛽𝛽𝑡𝑡2 �

3.49 2.46E-04 2.43E-02

βt [-]

∆t/t [%]

𝑃𝑃𝑃𝑃𝑃𝑃100 = 1 − (1 − 𝑃𝑃𝑃𝑃𝑃𝑃1 )100

∆fy/fy [%] Figure A-9

βf [-]

FE results establishing the failure surface for the peak strain criterion

Below in Figure A-10 and Figure A-11 it is shown pictures of the buckle present in the weak t after on-reeling. The cases shown are for the largest allowable mismatch in thickness and yield strength with respect to the peak strain criterion. The results based on peak criterion could be much more “conservative” for other geometries than what is outlined in this example.


A-15

Figure A-10


thickness for the peak strain criterion

Figure A-11


yield strength for the peak strain criterion


A-16

APPENDIX B STINGER ROLLER EVALUATIONS


B-1

B.1 Introduction The present appendix describes a FE model which takes into effect of inclined and straight roller as well as rollers with rubber. The results are compared towards the reduction factor for point loads given in DNV-OS-F101. The work was previously performed, without inclined or rubber coated rollers, by Snamprogetti, see ref. /17/ (confidential) and ref. /7/. A typical lay ramp is shown in Figure B-1. The following load scenarios were considered: •

Horizontal roller box with and without a rubber layer, Ref. Figure B-2b.

•

V-shaped roller boxes without rubber layer, Ref. Figure B-2a.

Figure B-1 Picture of a typical roller-box over the lay ramp (bilancino-tilting box), ref. /17/

Figure B-2 - Schematic representation of different roller shapes, ref. /17/.

B.2 Scenarios for the FE Analyses Table B-1 summarises the analyses and combination of axial and roller forces which were run. The cases have been chosen with typical values for axial tension and roller reaction forces that the 𝐷𝐷 of 15 to 45 where the pipeline is subject to under installation with S-lay. The analyses were chosen for 𝑡𝑡


B-2

outer diameter is kept constant and the thickness is changed. The input values for the FE analyses are shown in Table B-1. Definition of Ry and Ny are given below: 𝑅𝑅𝑦𝑦 = 3.9 ∙ 𝑓𝑓𝑦𝑦 ∙ 𝑡𝑡2 2 𝑁𝑁𝑦𝑦 = 𝑓𝑓𝑦𝑦 ∙ 𝜋𝜋 ∙ (𝐷𝐷 − 𝑡𝑡) ∙ 𝑡𝑡

(B.1) (B.2)

where

R

is the applied roller force

N

is the applied axial force

t2 𝑓𝑓𝑦𝑦

is the characteristic wall thickness as specified in DNV-OS-F101 is the yield strength

D

is the outer diameter.

Table B-1: Analysed cases. D

D/t

[mm]

t

fy

fu

[mm]

[MPa]

[MPa]

N/Ny

N

R/Ry

[kN]

R [kN]

762

15

50.8

450

535

6%

3065

0%

0

762

15

50.8

450

535

6%

3065

15 %

679

762

15

50.8

450

535

6%

3065

30 %

1359

762

15

50.8

450

535

24 %

12258

0%

0

762

15

50.8

450

535

24 %

12258

15 %

679

762

15

50.8

450

535

24 %

12258

30 %

1359

762

30

25.4

450

535

6%

1587

0%

0

762

30

25.4

450

535

6%

1587

15 %

170

762

30

25.4

450

535

6%

1587

30 %

340

762

30

25.4

450

535

24 %

1587

0%

0

762

30

25.4

450

535

24 %

6348

15 %

170

762

30

25.4

450

535

24 %

6348

30 %

340

762

45

16.93

450

535

6%

1070

0%

0

762

45

16.93

450

535

6%

1070

15 %

75

762

45

16.93

450

535

6%

1070

30 %

151

762

45

16.93

450

535

24 %

4281

0%

0

762

45

16.93

450

535

24 %

4281

15 %

75

762

45

16.93

450

535

24 %

4281

30 %

151

B.3 Description of the FE Model B.3.1 Introduction Two different approaches were used to study the effect of rubber on roller and the effect of inclining the roller. To study the effect of rubber on the roller, a horizontal roller was made of solid elements. When investigating the effect of inclining the roller, the roller was modelled as an analytical rigid surface. The inclined analytical roller was angled at 30° giving a relative angle of 120° for a V-roller. Figure B-3 and Figure B-4 show the assembly of the two FE-models.


B-3

B.3.2 Geometry, boundary conditions and load application Symmetry in two directions was used, see Figure B-3 and Figure B-4. The lengths of the pipes were modelled five times the outer diameter. Abaqus’s ZSYMM and XSYMM were applied at the respective symmetry boundaries (see global coordinate system in Figure B-3 and Figure B-4). The pipe end on the opposite side of the roller end was coupled to a reference point located at the cross section centre, with a cylindrical coordinate system, see Figure B-6. The coupling was set to restrain displacements in U2 and U3 directions as well as rotation in UR1 and UR3 directions. The reference point (centre node at the pipe end) was constrained in the vertical (global Y) direction; see Figure B-3 and Figure B-4 for global coordinate system. The principal drawing of Figure B-5 summarises the boundary conditions and applied loads for undeformed and derformed state.

Figure B-3 FE-model for horizontal roller with and without rubber layer

Figure B-4 FE-model with analytical rigid roller

Figure B-5 - Principal drawing of the boundary conditions and applied loads at undeformed and deformed state

For the solid roller, the roller centreline of Figure B-7 was coupled to a reference point constrained in all directions expect for the vertical (global Y) direction. The roller force (R) was applied in the vertical (global Y) direction to the reference point. For the analytical rigid roller, the roller force (R) was applied to its reference point in the vertical (global Y) direction.


B-4

Figure B-6 - Coupling on pipe end

Figure B-7 – Coupling on roller

Roller force, axial force and rotation were applied. The loads were applied in the following steps. 1. An initial vertical roller force was applied to established . The initial force was 1% of the force applied in step 3. 2. The axial force, N, was then applied horizontally in the global coordinate system. 3. The total roller force, R, was applied. 4. The pipe was bent to failure by applying rotation at the pipe end.

The axial load was applied as a load in the global z-direction. This implied that the axial load at the symmetry point, where the capacity was determined, was constant and not affected by the rotation of the pipe. The load at the pipe end will then be the vector sum of the “axial load” and the point load reaction. On a stinger, the axial load will follow the rotation of the cross section and hence the reaction force at the stinger will increase as the rotation increase. The case shown here, with a horizontal axial force will therefore simulate the point load of an un-rotated system. The applied loads (axial and vertical) are scaled with respect to the symmetry in the model, i.e. 25% of the roller reaction and 50% of the axial force from Table B-1 is applied.


B-5

It is also clear that a “too small” point load will give a load at the pipe end that is close to horizontal and that this will cause a moment at the symmetry plane that reduced the applied moment, hence the failure of the pipe occurs at the pipe end instead of the symmetry plane for some cases.

B.3.3 Material model The material properties are given in Table B-2 and the stress strain curve according to the RambergOsgood equation as shown in Eq. B.3-B.5. Table B-2 - Material data Symbol

Stress

Symbol

Strain

Yield

σy

450 MPa

εy

0.5%

Ultimate

σu

535 MPa

εu

10%

σn 

σ ⋅ 1 + Ay ⋅  n εn = σ E   y 

 σ  log  ε u − u  E  n= log(σ u

Ay =

   

n −1

   

σ    ε y − y  E  

(B.3)

(B.4)

σy)

εy ⋅E −1 σy

(B.5)

σn and εn are nominal stress and strain respectively The true stress and strain was then calculated as follows:

σ t = σ n ⋅ (1 + ε n )

(B.6)

ε t = ln(1 + ε n )

(B.7)


B-6

650

True stress [MPa]

600 550 500 450 400 350 300 0

0.02

0.04

0.06

0.08

0.1

0.12

Plastic strain Figure B-8 - Stress-strain curve implemented into Abaqus

Figure B-8 compares the material model with the model of ref. /17/. LAYING CRITERIA X65 MAXIMUM STEEL STRESS-STRAIN CURVES Y/T=0.84

700

7.0E+08

600

6.0E+08

500

5.0E+08 Stress (Pa)

Stress [MPa]

Engineering

400 300 200

True

100

Nominal 0.02

0.04

0.06

0.08

6.0E+08 5.0E+08

4.0E+08

4.0E+08 3.0E+08

3.0E+08 2.0E+08

0 0

True

0.1

2.0E+08

1.0E+08

1.0E+08

0.0E+00 0.0% 0.2% 0.4% 0.6% 0.8% 1.0%

0.0E+00 0.0%

1.0%

2.0%

3.0%

4.0%

Total strain Material model of this study

5.0%

6.0%

7.0%

8.0%

9.0%

10.0%

Strain

Material model of study from ref. /17/

Figure B-9 - Comparison of material model of this study and ref. /17/

B.3.4 Mesh The pipe used in relation to the solid roller was modelled with 7107 linear quadrilateral elements of type S4R. The mesh is shown in Figure B-10. Fine mesh was used for the 0.1∙D long circumferential area close to the symmetry axis and then increased over 1∙D in axial direction. The pipe used in relation to the analytical rigid roller was made of 31900 elements of the same type. The mesh was homogenous in all

directions. This mesh was considered fine and sensitivity of the mesh was performed by approximately doubling the element size two times. The results are shown in Figure B-16.


B-7

Figure B-10 – Meshed pipe and solid roller


Figure B-11 – Meshed pipe for analytical roller

B-8

B.3.5 Roller Model The solid roller is shown in Figure B-12. The solid roller was modelled with outer diameter of 406mm. Symmetry was used as for the modelling of the pipe. Abaqus’s ZSYMM and XSYMM are applied at their respective symmetry boundaries (see global coordinate system in Figure B-3). The effect of a 30mm rubber layer has been modelled, see Figure B-12. The rubber layer has been modelled as linear elastic material with Young’s modulus of 50 MPa and Poisson’s ratio of 0.3. The Young’s modulus was decided based on ref. /18/for a 95 Shore A rubber material. The Young’s modulus was chosen as approximate and assumed to capture any effect due to the large difference in stiffnes between steel and rubber. In the cases where only a steel roller were modelled, the 30 mm layer was modelled as linear elastic with Young’s modulus of 207,000 GPa. The center of the roller was modelled as linear elastic steel for all analyses.

Figure B-12– Roller geometry.

Figure B-13 and Figure B-14 shows the meshed roller. The solid roller model was made of linear hexahedral elements of type C3D8R. Enhanced hour glass control was applied to the rubber of the roller. Adaptive mesh was used with 5 sweeps every increment for the steps when full roller force was applied as well as when the rotation was applied at pipe end. Smaller mesh was used in the initial region between pipe and roller. The meshed region of initial is shown in Figure B-14.


B-9

Figure B-13 - Meshed Roller, horizontal

Figure B-14 – Mesh at initial area

B.3.6 The normal properties were modelled as “hard” with pressure-overclosure and augmented Lagrange constraint enforcement method. The tangential behaviour is modelled with penalty friction formulation. Frictionless tangential is assumed between the pipe and analytical rigid roller. A frictional coefficient of 0.4 was used between pipe and solid roller.

B.4 Validation of the FE-model The FE-model was compared to the model described in the report of Bruschi et al, Ref /17/. The case in Table B-3 was compared. Abaqus 6.13 has been used for this study. Table B-3: Input for validation analysis. OD

ID

t

[mm]

[mm]

[mm]

1098.4

1016

41.2

D/t 26.7

σY(0,5%)

σU(10%)

[MPa]

[MPa]

450

535

Y/T

NSTEEL

N/NY

[kN] 0.84

4000

0.063

RY

Reaction

[kN]

[kN]

2979

500

R/RY 0.168

The model used in this report was compared and found to match the results from ref. /17/ in of bending moment versus curvature plot as shown in Figure B-15 for the case given in Table B-1. The curves fit well except from at curvatures larger than 0.04/m. However, the peak moments (moment capacities) are similar.


B-10

Figure B-15 Bending moment versus curvature for results of ref. /17/ and the present report.

Mesh convergence was performed for the pipe modelled in relation to the analytical rigid roller. A “coarse”, “medium” and “fine” mesh was investigated by approximately halving/doubling the element size. The coarse mesh was made by 2000 elements, while 8000 elements were used for the medium mesh and 31900 was used for the fine mesh. The result from the sensitivity is shown in Figure B-16. The effect of the different meshes is small. When studying the effect of inclined roller an analytical rigid surface was used to model the roller because the convergence of such surfaces was found favourable with respect to modelled solid surfaces. When studying the effect of rubber coating solid elements was needed for modelling the rubber, and therefore a bare steel roller was also made with solid elements to work as a comparison for the effect of rubber coated roller. The reason why the analytical rigid roller was not used as benchmark towards the rubber coated roller was because it yields small differences with respect to the bare steel solid roller, see comparison in Figure B-17. This is the reason why the horizontal roller moment capacity is not identical between Table B-5 and Table B-6.


B-11

7.00E+06

Bending moment [Nm]

6.00E+06 5.00E+06 4.00E+06 DT30-Coarse 3.00E+06

DT30-Medium DT30-Fine

2.00E+06 1.00E+06 0.00E+00 0

0.05

0.1

0.15

0.2

0.25

Curvature (averaged over 1D) [1/m] 𝑫𝑫

Figure B-16 – Mesh convergence for pipe model with horizontal analytical rigid roller, =30, 𝒕𝒕

N=Ny∙6%, R=Ry∙30%

7.0E+06

Bending moment [Nm]

6.0E+06 5.0E+06 4.0E+06 DT-30 Rigid roller

3.0E+06

DT-30 Solid roller

2.0E+06 1.0E+06 0.0E+00 0

0.05

0.1

0.15

0.2

0.25

Curvature (averaged over 1D) [1/mm] Figure B-17 - Comparison of FE-model with horizontal solid roller and horizontal analytical 𝑫𝑫 rigid roller, =30, N=Ny∙6%, R=Ry∙30% 𝒕𝒕


B-12

B.5 Results B.5.1 Introduction At the symmetry plane the moment applied to the free end (caused by the enforced rotation) and the moment caused by the horizontal load work in opposite directions. The vertical load on the free end (i.e. the roller point load) and the moment applied to the free end work in the same direction. This means that depending on the ratio between the vertical and horizontal load and the deformation of the pipe, the maximum bending moment in the pipe could either be at the free end or at the symmetry plane (intention). Those combinations for which the maximum bending moment occurred at the free end are not reported, the analyses highlighted in green in Table B-4 failed at the roller. Table B-4 – Successful analyses without rubber coating (green rows) D

D/t

[mm]

t

fy

fu

[mm]

[MPa]

[MPa]

N/Ny

N

R/Ry

[kN]

R [kN]

762

15

50.8

450

535

6%

3065

0%

0

762

15

50.8

450

535

6%

3065

15 %

679

762

15

50.8

450

535

6%

3065

30 %

1359

762

15

50.8

450

535

24 %

12258

0%

0

762

15

50.8

450

535

24 %

12258

15 %

679

762

15

50.8

450

535

24 %

12258

30 %

1359

762

30

25.4

450

535

6%

1587

0%

0

762

30

25.4

450

535

6%

1587

15 %

170

762

30

25.4

450

535

6%

1587

30 %

340

762

30

25.4

450

535

24 %

1587

0%

0

762

30

25.4

450

535

24 %

6348

15 %

170

762

30

25.4

450

535

24 %

6348

30 %

340

762

45

16.93

450

535

6%

1070

0%

0

762

45

16.93

450

535

6%

1070

15 %

75

762

45

16.93

450

535

6%

1070

30 %

151

762

45

16.93

450

535

24 %

4281

0%

0

762

45

16.93

450

535

24 %

4281

15 %

75

762

45

16.93

450

535

24 %

4281

30 %

151

This section shows the difference in moment capacity due to: •

Rubber coated rollers in horizontal position.

•

Rollers in inclined position

Moments are reported at the symmetry plane where the roller force is applied. Curvatures are reported as the average over 1D inwards from the symmetry plane. The bending moment capacity of the inclined roller model and the horizontal roller model including rubber are normalised with the bending moment capacity of the horizontal roller model without rubber coating and compared with the point load reduction factor αpm. The respective results are shown in Section B.5.2 and Section B.5.3.


B-13

B.5.2 Effect of rubber coated rollers in horizontal position Mp,steel gives the moment Mp,rubber gives the moment capacity

The maximum moment capacities from the analyses are shown in Table B-5. capacity when the whole roller is modelled with steel properties.

when the rubber layer is modelled. As seen in the table, one analyses failed to complete and the results are not reported. CR,H gives the effect of the rubber. Values above one give a positive effect. αpm CR,h is the reduction factor from point loads, in accordance to DNV-OS-F101, multiplied with the positive effect from rubber. It can be seen that there is a marginal positive effect modelling the rubber. The reduction factors for point loads, positive effect of modelling the rubber as well as αpm ∙CR,H is plotted in Figure B-19. Figure B-18 shows a picture when the rubber is being compressed. Table B-5 - Analyzed cases for horizontal solid roller

D mm

D/t -

t mm

N/NY -

N kN

R/RY -

R kN

αpm -

Mp,steel kNm

Mp,rubber kNm

CR,H -

αpm CR,H -

762

15

50.8

6%

3065

30 %

1359

0.965

13408

Failed

Failed

Failed

762

30

25.4

6%

1587

30 %

340

0.931

6275

6355

1.013

762

45

16.9

6%

1070

30 %

151

0.896

3893

3912

1.005

0.943 0.901

Figure B-18– Deformed rubber


B-14

1.20 1.15 1.10 Factor

1.05 1.00

Rubber/steel

0.95

Multiplied

0.90

αpm

0.85 0.80 10

20

30

40

50

D/t Figure B-19 - Moment capacity ratio plot versus reduction factor 𝜶𝜶𝒑𝒑𝒑𝒑 from DNV-OS-F101

B.5.3 Effect of inclined rollers The objective of the analyses with inclined roller was to show the effect of the pipe resting on two points in the cross section (as should be the case along most of the stinger) where the reaction from one roller contradicts the ovality caused by the other roller. Figure B-20 plots the bending moment over the averaged curvature for the successful analyses. It can be seen the positive effect inclining the roller. The maximum moment capacities from the analyses are shown in Figure B-20 and given in Table B-4.

Mp,H gives the moment capacity when the roller is modelled horizontal. Mp,I gives the moment capacity when the rollers are inclined. CI is the effect of inclining the roller, i.e. the ratio between moment capacity of inclined roller model to the moment capacity of horizontal roller model. Values above one give a positive effect. αpm ∙CI is the reduction factor from point loads, in accordance to DNV-OS-F101, multiplied with the positive effect from inclined rollers. The reduction factor for point loads, , CI (positive effect of inclining the roller), as well as αpm ∙CI are plotted in Figure B-21. Values where αpm ∙CI are above

one indicated that the reduction factor due to point loads might be neglected. αpm ∙CI are larger than one for all analyses, except for 𝑫𝑫𝒕𝒕=45 where the factor is 0.99.


B-15

1.60E+07 1.40E+07

Bending moment [Nm]

1.20E+07 1.00E+07

DT15 DT15 - Inclined roller

8.00E+06


6.00E+06


4.00E+06 2.00E+06 0.00E+00 0

0.1

0.2

0.3

0.4

0.5

Curvature (averaged over 1D) [1/m] Figure B-20– Bending moment versus curvature averaged over one diameter

Table B-6 - Analyzed cases for analytical rigid roller

D mm

D/t -

t mm

N/NY -

N kN

R/RY -

R kN

αpm -

Mp,H kNm

Mp,I kNm

CI -

αpm ∙CI

762

15

50.8

6%

3065

30 %

1359

0.965

13009

13793

762

30

25.4

6%

1587

30 %

340

0.931

6259

6783

762

45

16.9

6%

1070

30 %

151

0.896

3955

4377

1.060 1.084 1.107

1.023 1.009 0.992


B-16

1.20 1.15 1.10 Factor

1.05 1.00

Inclined roller/Straight roller

0.95

Multiplied

0.90

αpm

0.85 0.80 10

20

30

40

50

D/t Figure B-21 - Moment capacity ratio plot versus reduction factor 𝜶𝜶𝒑𝒑𝒑𝒑 from DNV-OS-F101

B.6 Conclusion

The effect of two opposing reaction points balance the negative effect of a point force and it is therefore recommended to •

Use the existing formulation when the major force is ed by one roller only

•

Not include the point load reduction factor when carried equally by the two V-rollers.

It is further assumed that the two V-rollers are balanced in the upper and middle section of the over bend but not close to the stinger tip. The effect of V-rollers not located exactly at the same point along the pipe axis has not been studied.


B-17

APPENDIX C RESIDUAL OVALITY CALCULATIONS


C-1

C.1 Residual ovality calculations for reeling Figures C-1, C-2 and C-3 below are taken from Refs. /13/ and /15/, and include results from FE calculations and measurements from full scale tests. The dashed blue line is calculations performed by DNV GL using Eq. (6-4) and (6-5) in the main body of this guideline with 𝑘𝑘𝑜𝑜,1 = 0.30 and 𝑘𝑘𝑜𝑜,1+ = 0.10 for Figures C-1 and C-2 and with 𝑘𝑘𝑜𝑜,1 = 0.35 and 𝑘𝑘𝑜𝑜,1+ = 0.15 for. The values used by HMC are given in Figure 22 in ref. /13/. 7.0 % 6.0 %

Ovality [%]

5.0 % 4.0 % 3.0 % 2.0 % 1.0 % 0.0 % 0

2

4

6

8

10

12

14

16

18

20

Load step Figure C-1 Ovality during reeling, ref./14/, D = 355.6mm, t = 20.6mm, Rreel = 8.0m 10.0 % 9.0 % 8.0 %

Ovality [%]

7.0 % 6.0 % 5.0 % 4.0 % 3.0 % 2.0 % 1.0 %

HMC formulation

0.0 % 0

2

4

6

8

10

12

14

16

18

20

Load step Figure C-2 Ovality during reeling, ref./14/, D = 323.9mm, t = 12.7mm, Rreel = 8.0m


C-2

14.0 % 12.0 %

Ovality [%]

10.0 % 8.0 % 6.0 % 4.0 % 2.0 %

HMC formulation

0.0 % 0

2

4

6

8

10

12

14

16

18

20

Load step Figure C-3 Ovality during reeling, ref./14/, D = 406.4mm, t = 21.4mm, Rreel = 8.0m


C-3

Figure C-4 and Figure C-5 below are taken from ref. /9/ and include results from FE calculations and measurements from full scale tests. The dashed blue line is calculations performed by DNV GL using Eq. (6-4) and (6-5) in the main body of this guideline with 𝑘𝑘𝑜𝑜,1 = 0.30 and 𝑘𝑘𝑜𝑜,1+ = 0.10. Note that in Figure C-5 the experimental results are only shown up to load step 8 to the very right in the figure. 5.0 % HMC formulation

Ovality [%]

4.0 %

3.0 %

2.0 %

1.0 %

0.0 % 0

1

2

3

4

5

6

7

8

Load step Figure C-4 Ovality during reeling, ref. /9/, D = 457.2mm, t = 23.8mm, Rreel = 9.75m

2.4 % HMC formulation 2.0 %

Ovality [%]

1.6 %

1.2 %

0.8 %

0.4 %

0.0 % 0

1

2

3

4

5

6

7

8

Load step Figure C-5 Ovality during reeling, ref. /9/, D = 273.1mm, t = 14.3mm, Rreel = 9.75m


C-4

C.2 Residual ovality calculations - Stinger Ref. /7/ presents a formula for residual ovality for a pipe ing over an S-lay stinger. If the direct effect of the roller load and initial ovality are neglected and the same notation as above is applied, this formula reads: (C-1)

𝑜𝑜𝑚𝑚𝑚𝑚𝑚𝑚,𝑖𝑖 = 𝑜𝑜𝑟𝑟𝑟𝑟𝑟𝑟,𝑖𝑖−1 + 𝑜𝑜𝐷𝐷𝐷𝐷𝐷𝐷,𝑖𝑖 𝑜𝑜𝑟𝑟𝑟𝑟𝑟𝑟,𝑖𝑖 =

𝜖𝜖𝑏𝑏,𝑖𝑖 𝜖𝜖𝑐𝑐

∙ 𝑜𝑜𝑚𝑚𝑚𝑚𝑚𝑚,𝑖𝑖 𝑡𝑡

𝜖𝜖𝑐𝑐 = � − 0.01� ∙ � 𝐷𝐷

(C-2)

0.85 1.5 𝛼𝛼ℎ

�

∙ 𝛼𝛼𝑔𝑔𝑔𝑔

The blue dashed graph in Figure C-6 below is based on Eq. (6-4) and (6-5) in the main body of this guideline (𝑘𝑘𝑜𝑜,1 = 0.10) whereas the green dashed curve is based on Eqs. C-1 and C-2. 0.40%

HMC formulation

0.35%

Saipem/Statoil formulation

Ovality [%]

0.30% 0.25% 0.20% 0.15% 0.10% 0.05% 0.00% 0

1

2

3

4

Load step Figure C-6 Ovality over stinger, Refs. /7/and /13/, D/t = 20, 𝝐𝝐𝒊𝒊 = 0.5%


C-5

APPENDIX D CALIBRATION OF STINGER CRITERION


D-1

D.1 Introduction The load controlled condition for pipe subjected to bending moment and effective axial force (zero pressure) is in DNV-OS-F101 states as 2 2

(D.1)

|𝑀𝑀𝑆𝑆𝑆𝑆 | 𝑆𝑆𝑆𝑆𝑆𝑆 �𝛾𝛾𝑚𝑚 𝛾𝛾𝑆𝑆𝑆𝑆 + �𝛾𝛾𝑚𝑚 𝛾𝛾𝑆𝑆𝑆𝑆 � � ≤1 � 𝑀𝑀𝐾𝐾 𝑆𝑆� 𝐾𝐾

�𝐾𝐾 and 𝑆𝑆� where 𝑀𝑀𝑆𝑆𝑆𝑆 and 𝑆𝑆𝑆𝑆𝑆𝑆 are the design moment and effective axial force, and 𝑀𝑀 𝐾𝐾 represents design capacities.

� and 𝑀𝑀𝑆𝑆𝑆𝑆 = 𝛾𝛾𝐹𝐹 𝛾𝛾𝑐𝑐 𝑆𝑆� where 𝑀𝑀 � and 𝑆𝑆� are the For pipeline installation it is proposed to define 𝑀𝑀𝑆𝑆𝑆𝑆 = 𝛾𝛾𝐹𝐹 𝛾𝛾𝑐𝑐 𝑀𝑀

bending moment and effective axial force estimated from finite element analysis. A margin of safety is obtained from the product of safety factors 𝛾𝛾𝑚𝑚 𝛾𝛾𝑆𝑆𝑆𝑆 𝛾𝛾𝐹𝐹 𝛾𝛾𝑐𝑐 . The safety factor 𝛾𝛾𝑐𝑐 is calibrated to meet a required probability of failure when the other safety factors are defined as 𝛾𝛾𝑚𝑚 = 1.15, 𝛾𝛾𝑆𝑆𝑆𝑆 = 1.00 and 𝛾𝛾𝐹𝐹 = 1.2.

D.2 Summary of results

A condition load effect factor of 𝛾𝛾𝑐𝑐 = 0.8 is recommended. The full set of safety factors is tabulated in Table D-1.

Table D-1 Safety factors to be used in the load controlled limit state Target PoF 10-2

𝜸𝜸𝒎𝒎

𝜸𝜸𝑺𝑺𝑺𝑺

1.15

1.0

𝜸𝜸𝑭𝑭

1.2

𝜸𝜸𝒄𝒄

0.8

The calibration procedure is presented in the following sections. NB! The use of 𝛾𝛾𝐹𝐹 = 1.2 implies that the calibration covers system effect, and it is assumed in the

probabilistic modelling that the distribution of load effect (bending moment and effective axial force) includes system effect, i.e. represents the expected worst load during installation.

D.3 Limit state formulation The probability of failure is estimated from the limit state equation below. Failure will occur for 𝑔𝑔 ≤ 0 where

2

where

|𝑀𝑀| 𝑆𝑆 2 𝑔𝑔 = 𝑋𝑋𝑚𝑚𝑚𝑚𝑚𝑚 − � +� � � 𝑀𝑀𝐾𝐾 𝑆𝑆𝐾𝐾

𝑀𝑀𝐾𝐾 = 𝛼𝛼𝑝𝑝𝑝𝑝 𝛼𝛼𝑐𝑐 𝜎𝜎𝑦𝑦 (𝐷𝐷 − 𝑡𝑡)2 𝑡𝑡 𝑆𝑆𝐾𝐾 = 𝛼𝛼𝑐𝑐 𝜎𝜎𝑦𝑦 𝜋𝜋(𝐷𝐷 − 𝑡𝑡) 𝑡𝑡

(D.2)

(D.3) (D. 4)

The variables entering the limit state are presented in Table D-2. Distributions representing the uncertainty in these variables are given in Table D-5.


D-2

Table D-2 Limit state variables Variable

Description 𝑋𝑋𝑚𝑚𝑚𝑚𝑚𝑚

Empirical factor (model uncertainty)

𝑀𝑀

Applied moment

𝑆𝑆

Effective axial force

𝛼𝛼𝑐𝑐

Flow stress parameter

𝐷𝐷

Outer diameter

𝑀𝑀𝐾𝐾

Moment capacity

𝑆𝑆𝐾𝐾

Effective axial force capacity

𝜎𝜎𝑦𝑦

Yield stress (temperature de-rated)

𝑡𝑡

Wall thickness

𝛼𝛼𝑝𝑝𝑝𝑝

Plastic moment reduction factor ing for point load

D.4 Design equation The design equation is based on Eqn. (D.6) using estimated input values and safety factors. The design should satisfy 2 2

Where

|𝑀𝑀𝑆𝑆𝑆𝑆 | 𝑆𝑆𝑆𝑆𝑆𝑆 �𝛾𝛾𝑚𝑚 𝛾𝛾𝑆𝑆𝑆𝑆 + �𝛾𝛾𝑚𝑚 𝛾𝛾𝑆𝑆𝑆𝑆 � � ≤1 � 𝑀𝑀𝐾𝐾 𝑆𝑆� 𝐾𝐾 2 �𝐾𝐾 = 𝛼𝛼� 𝑀𝑀 �𝑓𝑓 𝑝𝑝𝑝𝑝 𝛼𝛼 𝑐𝑐 𝑦𝑦 (𝐷𝐷 − 𝑡𝑡𝑛𝑛𝑛𝑛𝑛𝑛 ) 𝑡𝑡𝑛𝑛𝑛𝑛𝑛𝑛

𝑆𝑆� �𝑓𝑓 𝐾𝐾 = 𝛼𝛼 𝑐𝑐 𝑦𝑦 𝜋𝜋(𝐷𝐷 − 𝑡𝑡𝑛𝑛𝑛𝑛𝑛𝑛 ) 𝑡𝑡𝑛𝑛𝑛𝑛𝑛𝑛 𝑓𝑓𝑦𝑦 = �𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 − 𝑓𝑓𝑦𝑦,𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 � ⋅ 𝛼𝛼𝑈𝑈


(D.5)

(D.6) (D.7) (D.8)

D-3

The input parameters to the design criterion are shown in Table D-3. Table D-3 Design variables Variable

Description 𝑀𝑀𝑆𝑆𝑆𝑆

Design moment

𝑆𝑆𝑆𝑆𝑆𝑆

Design effective axial force

𝛼𝛼 �𝑐𝑐

Estimated flow stress parameter

𝑓𝑓𝑦𝑦

Design yield stress

�𝐾𝐾 𝑀𝑀

Design moment capacity

𝑆𝑆� 𝐾𝐾

Design effective axial force capacity

𝛼𝛼� 𝑝𝑝𝑝𝑝 𝑓𝑓𝑦𝑦,𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆

Estimated plastic moment reduction factor ing for point load

Yield stress de-rating value Specified minimum yield stress

𝛼𝛼𝑈𝑈

Material strength factor

𝑡𝑡𝑛𝑛𝑛𝑛𝑛𝑛

Nominal wall thickness

𝛾𝛾𝑆𝑆𝑆𝑆

Safety class resistance factor

𝐷𝐷

Outer diameter (assumes that exact value is known)

𝛾𝛾𝑚𝑚

Material resistance factor

The calibration of 𝛾𝛾𝑐𝑐 will rely on the following design assumptions for pipeline installation. Table D-4 Assumptions with respect to pipeline installation

Variable

Assumed value Pressure

Zero differential pressure is assumed. It is possible to extend the calibration to also include pressure (internal and/or external).

𝑀𝑀𝑆𝑆𝑆𝑆

� where 𝑀𝑀 � is the estimated moment load (mean value). 𝛾𝛾𝑐𝑐 is the 𝑀𝑀𝑆𝑆𝑆𝑆 = 𝛾𝛾𝐹𝐹 𝛾𝛾𝑐𝑐 𝑀𝑀

𝑆𝑆𝑆𝑆𝑆𝑆

𝑆𝑆𝑆𝑆𝑆𝑆 = 𝛾𝛾𝐹𝐹 𝛾𝛾𝑐𝑐 𝑆𝑆� where 𝑆𝑆� is the estimated effective axial force load (mean value).

𝛾𝛾𝑚𝑚

𝛾𝛾𝑆𝑆𝑆𝑆 𝛾𝛾𝐹𝐹

condition load effect factor that will be studied further in the calibration, and 𝛾𝛾𝐹𝐹 is a functional load effect factor. 𝛾𝛾𝑚𝑚 = 1.15

𝛾𝛾𝑆𝑆𝑆𝑆 = 1.0 (Safety class low) 𝛾𝛾𝐹𝐹 = 1.2

D.5 Calibration model The probability of failure for pipelines designed according to the criterion in Eqn. (D.9) (with equality) is estimated as 𝑃𝑃𝑃𝑃𝑃𝑃

= 𝑃𝑃 �𝑔𝑔 < 0� �𝛾𝛾𝑚𝑚 𝛾𝛾𝑆𝑆𝑆𝑆

2 2

(D.9)

|𝑀𝑀𝑆𝑆𝑆𝑆| 𝑆𝑆𝑆𝑆𝑆𝑆 + �𝛾𝛾𝑚𝑚 𝛾𝛾𝑆𝑆𝑆𝑆 � � � � 𝑀𝑀𝐾𝐾 𝑆𝑆𝐾𝐾

where 𝑔𝑔 is the limit state function given in Eqn. (D.6). The parameters entering the limit state (Eqn. (D.6)) are assumed to follow the distributions in Table D-5.


D-4

Table D-5 Limit state distributions Variable

Distribution 𝑋𝑋𝑚𝑚𝑚𝑚𝑚𝑚

𝑋𝑋𝑚𝑚𝑚𝑚𝑚𝑚 ~𝑁𝑁(1.0, 0.3).

𝑀𝑀 *

�, 𝐶𝐶𝐶𝐶𝑉𝑉𝑀𝑀 � , 𝐶𝐶𝐶𝐶𝑉𝑉𝑀𝑀 = 4%, 𝜌𝜌𝜎𝜎 ,𝑀𝑀 = 0.9 𝑀𝑀~𝑁𝑁�1.06 ⋅ 𝑀𝑀 𝑦𝑦

𝑆𝑆 * 𝛼𝛼𝑐𝑐

𝛼𝛼𝑝𝑝𝑝𝑝 𝜎𝜎𝑦𝑦 𝐷𝐷 𝑡𝑡

For nonzero pressure 𝑋𝑋𝑚𝑚𝑚𝑚𝑚𝑚 ~𝑁𝑁�𝜇𝜇𝑋𝑋𝑚𝑚𝑚𝑚𝑚𝑚 = 1.0 + 0.15𝑞𝑞ℎ , 𝐶𝐶𝐶𝐶𝑉𝑉𝑋𝑋𝑚𝑚𝑚𝑚𝑚𝑚 = 0.3(1 + 2𝑞𝑞ℎ )�. 𝑆𝑆~𝑁𝑁�1.06 ⋅ 𝑆𝑆� , 𝐶𝐶𝐶𝐶𝑉𝑉𝑆𝑆 �, 𝐶𝐶𝐶𝐶𝑉𝑉𝑆𝑆 = 𝐶𝐶𝐶𝐶𝑉𝑉𝑀𝑀 𝛼𝛼𝑐𝑐 ~𝑁𝑁�𝛼𝛼 �, 𝑐𝑐 𝐶𝐶𝐶𝐶𝑉𝑉𝛼𝛼𝑐𝑐 � , 𝐶𝐶𝐶𝐶𝑉𝑉𝛼𝛼𝑐𝑐 = 3% 𝛼𝛼𝑝𝑝𝑝𝑝 = 𝛼𝛼� 𝑝𝑝𝑝𝑝 (fixed)

𝜎𝜎𝑦𝑦 ~𝑁𝑁 �1.06 ⋅ 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 − 𝑓𝑓𝑦𝑦,𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 , 𝐶𝐶𝐶𝐶𝑉𝑉𝜎𝜎𝑦𝑦 �, 𝐶𝐶𝐶𝐶𝑉𝑉𝜎𝜎𝑦𝑦 = 4% for 𝛼𝛼𝑈𝑈 = 1.0 𝐷𝐷 = 𝐷𝐷 (fixed)

𝑡𝑡~𝑁𝑁(𝑡𝑡𝑛𝑛𝑛𝑛𝑛𝑛 , 𝐶𝐶𝐶𝐶𝑉𝑉𝑡𝑡 ), 𝐶𝐶𝐶𝐶𝑉𝑉𝑡𝑡 = 3%

* The bias of 1.06 corresponds to the difference between mean yield stress and SMYS, and comes from using SMYS in the FE analysis of 𝑀𝑀. The

increase in bending moment due to increased yield stress is relevant as the design allows plastic (nonlinear) bending moment response. In this scenario the load effect is also strongly correlated with the yield stress of the material, and a correlation coefficient of 0.9 is applied. The distribution of 𝑆𝑆 is assumed to be equal to the distribution of 𝑀𝑀.

In order to evaluate the conditional probability in Eqn. (D.13), the limit state in Eqn. (D.6) can be written as 2

�| � 2 �𝐾𝐾 |𝑀𝑀 |𝑀𝑀| 𝑀𝑀 𝑆𝑆 𝑆𝑆� 𝐾𝐾 𝑆𝑆 𝑔𝑔 = 𝑋𝑋𝑚𝑚𝑚𝑚𝑚𝑚 − � ⋅ ⋅ +� ⋅ ⋅ � � �| 𝑀𝑀𝐾𝐾 𝑀𝑀 �𝐾𝐾 |𝑀𝑀 𝑆𝑆� 𝑆𝑆𝐾𝐾 𝑆𝑆� 𝐾𝐾

(D.10)

� |/𝑀𝑀 �𝐾𝐾 ) is obtained by �𝐾𝐾 and 𝑆𝑆� /𝑆𝑆 A relationship between estimated moment and axial force utilization (|𝑀𝑀 rearranging the design criterion in (D.9) and using the design values for moment and effective axial force.

2 �| |𝑀𝑀 1 𝑆𝑆� = �1 − �𝛾𝛾𝑚𝑚 𝛾𝛾𝑆𝑆𝑆𝑆 𝛾𝛾𝐹𝐹 𝛾𝛾𝑐𝑐 � � �𝐾𝐾 𝛾𝛾𝑚𝑚 𝛾𝛾𝑆𝑆𝑆𝑆 𝛾𝛾𝐹𝐹 𝛾𝛾𝑐𝑐 𝑀𝑀 𝑆𝑆� 𝐾𝐾

Note that the above expression is only valid for 𝛾𝛾𝑚𝑚 𝛾𝛾𝑆𝑆𝑆𝑆 𝛾𝛾𝐹𝐹 𝛾𝛾𝑐𝑐

(D.11)

𝑆𝑆� 𝑆𝑆� 𝐾𝐾

� , 𝑋𝑋𝑀𝑀,𝐾𝐾 = 𝑀𝑀𝐾𝐾 /𝑀𝑀 �𝐾𝐾 , ≤ 1. Defining 𝑋𝑋𝑀𝑀 = 𝑀𝑀/𝑀𝑀

𝑋𝑋𝑆𝑆 = 𝑆𝑆/𝑆𝑆� and 𝑋𝑋𝑆𝑆,𝐾𝐾 = 𝑆𝑆𝐾𝐾 /𝑆𝑆� 𝐾𝐾 and using Eqn. (D.15) in Eqn. (D.14) gives

2

2 2 |𝑋𝑋𝑀𝑀 | 1 𝑆𝑆�𝐹𝐹 𝑋𝑋𝑆𝑆 𝑆𝑆�𝐹𝐹 𝑔𝑔 = 𝑋𝑋𝑚𝑚𝑚𝑚𝑚𝑚 − � ⋅ �1 − �𝛾𝛾𝑚𝑚 𝛾𝛾𝑆𝑆𝑆𝑆 𝛾𝛾𝐹𝐹 𝛾𝛾𝑐𝑐 � � + � ⋅ � � 𝑋𝑋𝑀𝑀,𝐾𝐾 𝛾𝛾𝑚𝑚 𝛾𝛾𝑆𝑆𝑆𝑆 𝛾𝛾𝐹𝐹 𝛾𝛾𝑐𝑐 𝑋𝑋𝑆𝑆,𝐾𝐾 𝑆𝑆� 𝑆𝑆� 𝐾𝐾 𝐾𝐾

(D.12)

Hence, the probability of failure given that the design criterion is satisfied can be calculated for a given �𝐾𝐾 ) as axial force utilization (𝑆𝑆�𝐹𝐹 /𝑆𝑆 2 2

2

|𝑋𝑋𝑀𝑀| 1 𝑆𝑆�𝐹𝐹 𝑋𝑋𝑆𝑆 𝑆𝑆�𝐹𝐹 𝑃𝑃𝑃𝑃𝑃𝑃 = 𝑃𝑃 �𝑋𝑋𝑚𝑚𝑚𝑚𝑚𝑚 − � ⋅ �1 − �𝛾𝛾𝑚𝑚 𝛾𝛾𝑆𝑆𝑆𝑆 𝛾𝛾𝐹𝐹 𝛾𝛾𝑐𝑐 � � + � ⋅ � � < 0� 𝑋𝑋𝑀𝑀,𝐾𝐾 𝛾𝛾𝑚𝑚 𝛾𝛾𝑆𝑆𝑆𝑆 𝛾𝛾𝐹𝐹𝛾𝛾𝑐𝑐 𝑋𝑋𝑆𝑆,𝐾𝐾 𝑆𝑆�𝐾𝐾 𝑆𝑆�𝐾𝐾

By defining the design axial force utilization as ℎ = 𝛾𝛾𝑚𝑚 𝛾𝛾𝑆𝑆𝑆𝑆 𝛾𝛾𝐹𝐹 𝛾𝛾𝑐𝑐 𝑃𝑃𝑃𝑃𝑃𝑃 = 𝑃𝑃 �𝑋𝑋𝑚𝑚𝑚𝑚𝑚𝑚 − �

𝑆𝑆�𝐹𝐹 , 𝑆𝑆� 𝐾𝐾

the failure probability can be expressed as 2

2 |𝑋𝑋𝑀𝑀 | 𝑋𝑋𝑆𝑆 2 2 �1 − ℎ � + � � ℎ � < 0� 𝑋𝑋𝑀𝑀,𝐾𝐾 ⋅ 𝛾𝛾𝑚𝑚 𝛾𝛾𝑆𝑆𝑆𝑆 𝛾𝛾𝐹𝐹𝛾𝛾𝑐𝑐 𝑋𝑋𝑆𝑆,𝐾𝐾 ⋅ 𝛾𝛾𝑚𝑚 𝛾𝛾𝑆𝑆𝑆𝑆 𝛾𝛾𝐹𝐹𝛾𝛾𝑐𝑐


(D.13)

(D.14)

D-5

for ℎ ∈ [0,1]. The parameters 𝑋𝑋𝑀𝑀 , 𝑋𝑋𝑀𝑀,𝐾𝐾 , 𝑋𝑋𝑆𝑆 and 𝑋𝑋𝑆𝑆,𝐾𝐾 represents uncertainty in moment and effective axial force (load and capacity). The distributions of these parameters are given in Table D-6 below, with coefficients of variation (CoV) taken from Table D-5.

Table D-6 Distributions used for conditional failure probability Variable

𝑋𝑋𝑀𝑀 *

𝑋𝑋𝑀𝑀,𝐾𝐾 𝑋𝑋𝑆𝑆

𝑋𝑋𝑆𝑆,𝐾𝐾 𝑋𝑋𝛼𝛼𝑐𝑐

𝑋𝑋𝜎𝜎𝑦𝑦 𝑋𝑋𝐼𝐼𝐼𝐼 𝑋𝑋𝑡𝑡

𝑋𝑋𝛼𝛼𝑝𝑝𝑝𝑝

Distribution

Comment

𝑋𝑋𝑀𝑀 ~𝑁𝑁(1.06, 𝐶𝐶𝐶𝐶𝑉𝑉𝑀𝑀 ), 𝜌𝜌𝑋𝑋𝜎𝜎𝑦𝑦 ,𝑋𝑋𝑀𝑀 = 0.9

�. Uncertainty in applied moment load. 𝑋𝑋𝑀𝑀 = 𝑀𝑀/𝑀𝑀

𝑋𝑋𝑆𝑆 ~𝑁𝑁(1.06, 𝐶𝐶𝐶𝐶𝑉𝑉𝑆𝑆 )

Uncertainty in effective axial force. 𝑋𝑋𝑆𝑆 = 𝑆𝑆/𝑆𝑆�

𝑋𝑋𝑀𝑀,𝐾𝐾 = 𝑋𝑋𝛼𝛼𝑝𝑝𝑝𝑝 ⋅ 𝑋𝑋𝛼𝛼𝑐𝑐 ⋅ 𝑋𝑋𝜎𝜎𝑦𝑦 ⋅

2 𝑋𝑋𝐼𝐼𝐼𝐼

⋅ 𝑋𝑋𝑡𝑡

𝑋𝑋𝑆𝑆,𝐾𝐾 = 𝑋𝑋𝛼𝛼𝑐𝑐 ⋅ 𝑋𝑋𝜎𝜎𝑦𝑦 ⋅ 𝑋𝑋𝐼𝐼𝐼𝐼 ⋅ 𝑋𝑋𝑡𝑡 𝑋𝑋𝛼𝛼𝑐𝑐 ~𝑁𝑁�1.0, 𝐶𝐶𝐶𝐶𝑉𝑉𝛼𝛼𝑐𝑐 �

𝑋𝑋𝜎𝜎𝑦𝑦 ~𝑁𝑁 �1.06/𝛼𝛼𝑈𝑈 , 𝐶𝐶𝐶𝐶𝑉𝑉𝜎𝜎𝑦𝑦 �

𝑋𝑋𝐼𝐼𝐼𝐼 = 1.0 (fixed) 𝑋𝑋𝑡𝑡 ~𝑁𝑁(1.0, 𝐶𝐶𝐶𝐶𝑉𝑉𝑡𝑡 )

𝑋𝑋𝛼𝛼𝑝𝑝𝑝𝑝 = 1.0 (fixed)

Uncertainty in moment capacity.

Uncertainty in effective axial force capacity.

�𝐶𝐶 . Uncertainty in flow stress parameter. 𝑋𝑋𝛼𝛼𝑐𝑐 = 𝛼𝛼𝐶𝐶 /𝛼𝛼 Uncertainty in yield stress.

𝑋𝑋𝜎𝜎𝑦𝑦 = 𝜎𝜎𝑦𝑦 /𝑓𝑓𝑦𝑦 ≥ 𝑁𝑁�1.06/𝛼𝛼𝑈𝑈 , 𝐶𝐶𝐶𝐶𝑉𝑉𝜎𝜎𝑦𝑦 � with equality for 𝑓𝑓𝑦𝑦,𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = 0. Uncertainty in inner diameter. Assumed negligible. Uncertainty in wall thickness. 𝑋𝑋𝑡𝑡 = 𝑡𝑡/𝑡𝑡𝑛𝑛𝑛𝑛𝑛𝑛 .

Uncertainty in point load moment capacity reduction. Assumed negligible.

* As the design allows plastic (nonlinear) bending moment response the correlation between bending moment and yield stress is modelled using a correlation coefficient of 0.9. For elastic response the correlation should be removed together with the bias of 1.06 (1.0 can be applied)

D.6 Calibration results The parameters used in the calibration are listed in Table D-7 below. Table D-7 Values used in calibration Variable

Value

Comment

𝐶𝐶𝐶𝐶𝑉𝑉𝑀𝑀

4%

Uncertainty in applied moment load

𝐶𝐶𝐶𝐶𝑉𝑉𝑆𝑆

Uncertainty in effective axial force

𝐶𝐶𝐶𝐶𝑉𝑉𝛼𝛼𝑐𝑐

𝐶𝐶𝐶𝐶𝑉𝑉𝑆𝑆 = 𝐶𝐶𝐶𝐶𝑉𝑉𝑀𝑀 3%

Uncertainty in flow stress parameter

𝐶𝐶𝐶𝐶𝑉𝑉𝜎𝜎𝑦𝑦

4%

Uncertainty in yield stress

𝐶𝐶𝐶𝐶𝑉𝑉𝑡𝑡

3%

Uncertainty in wall thickness

𝛼𝛼𝑈𝑈

1.0

Material strength factor

𝛾𝛾𝑚𝑚

1.15

Material resistance factor

𝛾𝛾𝑆𝑆𝑆𝑆

1.0

Safety class resistance factor (safety class low)

𝛾𝛾𝐹𝐹

1.2*

Load effect factor

𝛾𝛾𝑐𝑐

1.11/(1.15*1.2)

Condition load effect factor

ℎ

[0,1]

Design axial force utilization

* A load effect factor of 1.2 representing system effect is applied. It is assumed that the load distribution covers the worst system load (expected largest load during installation).

From the probabilistic analysis a total safety margin of 1.11 is required to obtain a failure probability in the order 1-2%. 𝛾𝛾𝑐𝑐 can thus be taken as 𝛾𝛾𝑐𝑐 = 1.11 /𝛾𝛾𝑚𝑚 𝛾𝛾𝑆𝑆𝑆𝑆 𝛾𝛾𝐹𝐹 𝛾𝛾𝑐𝑐 ≈ 0.8. The safety margin of 1.11 is illustrated

in Figure D-1 which shows an example of bending moment versus rotation from an FE analysis of pure bending of a pipe.


D-6

Figure D-1 Illustration of moment response to pure bending of a pipe

D.7 Comments to the applied load effect distribution In the calibration of 𝛾𝛾𝑐𝑐 the load effect is modelled with a bias of 1.06 (equal to the bias in yield stress)

and correlated with the yield stress (correlation coefficient of 0.9). This modelling choice was selected to best represent the material behaviour at high bending moment utilisation, and is based on the

assumption that an increase in yield stress will produce a corresponding increase in bending moment response for a given applied load. This formulation may differ from how bending moment versus moment capacity traditionally has been considered in probabilistic analyses, where it is often assumed that using SMYS in design will under predict the capacity only. The safety margin obtained in this manner is hence relevant for elastic moment response (low utilisation). To evaluate the current calibration of 𝛾𝛾𝑐𝑐 against such a model the

correlation and the 1.06 bias on bending moment was removed. The failure probability from this analysis is shown as a function of design axial force utilisation in Figure D-2. The total safety margin required to achieve the target failure probability becomes 1.155 which implies a 𝛾𝛾𝑐𝑐 factor of 𝛾𝛾𝑐𝑐 = 1.155 / 1.06 ⋅

𝛾𝛾𝑚𝑚 𝛾𝛾𝑆𝑆𝑆𝑆 𝛾𝛾𝐹𝐹 𝛾𝛾𝑐𝑐 ≈ 0.79 which happens to correspond well with the selected 𝛾𝛾𝑐𝑐 of 0.8.


D-7

Figure D-2 Failure probability – uncorrelated yield stress and bending moment response The normalised mean value (predicted mean / characteristic value) and coefficient of variation on bending moment response is established based on the analyses performed in “Laying criteria, Development of a design guideline for submarine pipeline installation, Rev.2, LF-E-72502”. Here a normalized mean value of around 1.08 is proposed for combined functional and environmental loads, together with a CoV in the range 1%-12%. The 8% bias (mean of 1.08) is explained by using SMYS in the characteristic or normalised load effect, where the mean yield stress is 1.08 ⋅ 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆. The positive bias

and larger CoV values are related to analyses where the moment capacity utilisation is low or moderate. For higher moment utilisation the load effect bias approaches unity and the coefficient of variation is

reduced. The bending moment uncertainty applied in the calibration is selected to represent the larger moment capacity utilisations, by excluding the analyses performed where the pipeline response is in the elastic region. In this manner the load effect uncertainty applied in the probabilistic model is relevant in the vicinity where failure may occur. An unbiased normal distribution with a 4% CoV was selected to for the calibration of 𝛾𝛾𝑐𝑐 .

D.8 Extension to multiple loads with different CoV This section considers the possible extension of the calibration procedure to establish a load condition factor for other load scenarios with different load effect uncertainty, possibly defined through superposition of bending moments. In order to apply the formulation in DNV-OS-F101 for such scenarios the load condition factor 𝛾𝛾𝑐𝑐 may be calibrated as a function of load effect CoV, 𝛾𝛾𝑐𝑐 = max{𝑎𝑎(1 + 𝑏𝑏 ⋅ 𝐶𝐶𝐶𝐶𝑉𝑉 ), 𝑐𝑐},

where 𝑎𝑎, 𝑏𝑏 and 𝑐𝑐 are constants. If the sum of a finite number of loads are considered (for instance

functional, environmental etc.), such that 𝑀𝑀 = ∑𝑀𝑀𝑖𝑖 , 𝑆𝑆 = ∑𝑆𝑆𝑖𝑖 and all 𝑀𝑀𝑖𝑖 and 𝑆𝑆𝑖𝑖 are assumed independent, normally distributed and nonnegative, then the correct design moment becomes

�𝑖𝑖 = 𝛾𝛾𝐹𝐹 ⋅ 𝑎𝑎 �∑𝑀𝑀 �𝑖𝑖 + 𝑏𝑏�∑�𝑀𝑀 �𝑖𝑖 𝐶𝐶𝐶𝐶𝑉𝑉𝑖𝑖 �2 � 𝑀𝑀𝑆𝑆𝑆𝑆 = 𝛾𝛾𝐹𝐹 𝛾𝛾𝑐𝑐 ∑𝑀𝑀

(D.15)

�𝑖𝑖 , 𝛾𝛾𝑐𝑐,𝑖𝑖 = 𝑎𝑎(1 + 𝑏𝑏 ⋅ 𝐶𝐶𝐶𝐶𝑉𝑉𝑀𝑀 ) 𝑀𝑀𝑆𝑆𝑆𝑆 = ∑𝛾𝛾𝐹𝐹 𝛾𝛾𝑐𝑐,𝑖𝑖 𝑀𝑀 𝑖𝑖

(D.16)

It is also possible to make use of the formulation in OS-F101, which is given as


D-8

The DNV-OS-F101 version of design moment is conservative, as can be seen from the triangle inequality

�𝑖𝑖 + 𝑏𝑏�∑�𝑀𝑀 �𝑖𝑖 𝐶𝐶𝐶𝐶𝑉𝑉𝑖𝑖 �2 � ≤ 𝛾𝛾𝐹𝐹 ⋅ 𝑎𝑎�∑𝑀𝑀 �𝑖𝑖 + 𝑏𝑏∑�𝑀𝑀 �𝑖𝑖 𝐶𝐶𝐶𝐶𝑉𝑉𝑖𝑖 � � = 𝑀𝑀𝑆𝑆𝑆𝑆,𝑂𝑂𝑂𝑂−𝐹𝐹101 𝑀𝑀𝑆𝑆𝑆𝑆 = 𝛾𝛾𝐹𝐹 ⋅ 𝑎𝑎 �∑𝑀𝑀

(D.17)

The same argument applies also to design effective axial force.

Note that this expression for 𝛾𝛾𝑐𝑐 can be applied also when 𝐶𝐶𝐶𝐶𝑉𝑉𝑀𝑀 ≠ 𝐶𝐶𝐶𝐶𝑉𝑉𝑆𝑆 , as the design equation still will be

valid for ℎ = 0 and ℎ = 1, and a value of 0 < ℎ < 1 will result in a lower failure probability. Hence, if the bending moment and effective axial force are defined as 𝑀𝑀 = ∑𝑀𝑀𝑖𝑖 and 𝑆𝑆 = ∑𝑆𝑆𝑖𝑖 where all 𝑀𝑀𝑖𝑖 and 𝑆𝑆𝑖𝑖 are

nonnegative, independent and normally distributed with possibly different coefficients of variation of 𝐶𝐶𝐶𝐶𝑉𝑉𝑀𝑀𝑖𝑖 for 𝑀𝑀𝑖𝑖 and 𝐶𝐶𝐶𝐶𝑉𝑉𝑆𝑆𝑖𝑖 for 𝑆𝑆𝑖𝑖 , then the design format in Eqn. (D.9) can be applied with

�𝚤𝚤 , 𝛾𝛾𝑐𝑐,𝑀𝑀 = 𝑎𝑎(1 + 𝑏𝑏 ⋅ 𝐶𝐶𝐶𝐶𝑉𝑉𝑀𝑀 ) 𝑀𝑀𝑆𝑆𝑆𝑆 = ∑𝛾𝛾𝐹𝐹 𝛾𝛾𝑐𝑐,𝑀𝑀𝑖𝑖 𝑀𝑀 𝑖𝑖 𝑖𝑖 𝑆𝑆𝑆𝑆𝑆𝑆 = ∑𝛾𝛾𝐹𝐹 𝛾𝛾𝑐𝑐,𝑆𝑆𝑖𝑖 𝑆𝑆�𝚤𝚤 , 𝛾𝛾𝑐𝑐,𝑆𝑆𝑖𝑖 = 𝑎𝑎(1 + 𝑏𝑏 ⋅ 𝐶𝐶𝐶𝐶𝑉𝑉𝑆𝑆𝑖𝑖 )

(D.18) (D.19)

D.9 Discussion The calibration of the load condition factor 𝛾𝛾𝑐𝑐 for pipeline installation relies on a probabilistic model that covers uncertainties related to load effects relevant for pipeline installation together with respective capacities and model uncertainties. The relevance of the calibration relies on the validity of these

distributions and underlying assumptions. Some key items related to the selected distributions and modelling assumptions are discussed in this section. -

Load uncertainty: The distribution of bending moment and effective axial force is assumed to cover the total load effect from the combination of static and dynamic loads.

-

System effect: The capacity in the probabilistic model represents the pipe capacity at a random cross section. If the load distributions are also selected to represent the loads that will affect a random location at any time during the installation, the probability of failure becomes the probability of failure at a random pipe location. Based on this probability it is possible to derive the failure probability for the entire pipeline during installation by considering it as a series (weakest link) system. That is, the probability that the pipeline will fail at some location during installation. Another approach is to apply an extreme value distribution for the load. If the load distribution represents the worst load that affect a random pipe location, then under the assumption that failure will most likely occur for the worst load, the system probability of failure is estimated directly from the probabilistic model. In the current calibration the system effect is handled in this manner. The current calibration is based on two assumptions. First, the load effect distribution represents the worst expected combination of static and dynamic loads. The second assumption is that the failure probability for smaller more likely load combinations is negligible compared to the probability of failure during the worst expected load, even though an average load is applied to a larger set of pipe cross sections. Hence, the system failure probability is dominated by the variation in load and not the variation in capacity at different pipe cross sections.


D-9

-

Material yield stress: The yield stress is modelled as a normal distribution with mean equal to 1.06 ⋅ 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆. The calibration considers high utilisation of the bending moment capacity, and in such

a model the bias of 1.06 on yield stress will not produce an additional safety margin as the

applied bending moment is modelled with a corresponding bias of 1.06. An earlier version of the calibration performed in this guideline considered a model relevant for small/moderate bending moment utilisation, where the dependency between yield stress and applied bending moment was not included. Also, a bias of 1.08 was selected in the yield stress distribution. As presented

in Section D-7, the margin of safety required in such a model was 1.155 which implies a required condition load effect factor of 𝛾𝛾𝑐𝑐 = 1.155 / 1.08 ⋅ 𝛾𝛾𝑚𝑚 𝛾𝛾𝑆𝑆𝑆𝑆 𝛾𝛾𝐹𝐹 𝛾𝛾𝑐𝑐 ≈ 0.77.

D.10 PROBAN input file The probabilistic analysis was performed using the software PROBAN. The PROBAN input file used for the calibration is presented below.

%% %% OS-F101 Combined loading - zero pressure, pipeline installation (stinger bending load) %% %% Calculates P(Fail | Design criterion fulfilled), used to calibrate Gamma_c %% % --------------------------------------------------------% Random variables % --------------------------------------------------------CREATE VARIABLE CoV_M 'CoV of moment load' FIXED 0.04 % Relevant for high utilisation CREATE VARIABLE CoV_S 'CoV of axial force load' FUNCTION Product ( ONLY 1.0 CoV_M ) CREATE VARIABLE CoV_ac 'CoV of flow stress parameter' FIXED 0.03 CREATE VARIABLE CoV_sy 'CoV of yield stress' FIXED 0.04 CREATE VARIABLE CoV_t 'CoV of wall thickness' FIXED 0.03 CREATE VARIABLE L_Bias 'Load effect bias' FIXED 1.06 CREATE CREATE CREATE CREATE CREATE

VARIABLE VARIABLE VARIABLE VARIABLE VARIABLE

Alpha_U Mean_sy Gamma_m Gamma_SC Gamma_F

'Material strength factor' 'Yield stress distribution mean' 'Material resistance factor' 'Safety class resistance factor' 'Load effect factor'

FIXED 1.00 FUNCTION Division 1.06 Alpha_U FIXED 1.15 FIXED 1.0 FIXED 1.2

CREATE VARIABLE h

'Design axial force utilisation'

FIXED 0.2

CREATE CREATE CREATE CREATE CREATE

VARIABLE VARIABLE VARIABLE VARIABLE VARIABLE

X_ac X_sy X_ID X_t X_apm

'Flow stress parameter' 'Yield stress' 'Inner diameter' 'Wall thickness' 'Point load reduction'

DISTRIBUTION Normal Mean-CoV 1.0 CoV_ac DISTRIBUTION Normal Mean-CoV Mean_sy CoV_sy FIXED 1.00 DISTRIBUTION Normal Mean-CoV 1.0 CoV_t FIXED 1.00

CREATE CREATE CREATE CREATE

VARIABLE VARIABLE VARIABLE VARIABLE

X_M X_S X_MK X_SK

'Moment load' 'Axial force load' 'Moment capacity ' 'Axial force capacity '

DISTRIBUTION Normal Mean-CoV L_Bias CoV_M DISTRIBUTION Normal Mean-CoV L_Bias CoV_S FUNCTION Product ( ONLY X_apm X_ac X_sy X_ID X_ID X_t ) FUNCTION Product ( ONLY X_ac X_sy X_ID X_t )

CREATE VARIABLE X_mod 'Model uncertainty' DISTRIBUTION Normal Mean-CoV 1.0 0.03 % Zero pressure % --------------------------------------------------------% Correlation % --------------------------------------------------------ASSIGN CORRELATION ( ONLY X_M X_sy ) NORMALIZED 0.9 % --------------------------------------------------------% Functions % --------------------------------------------------------CREATE FUNCTION LimSta 'Limit state' FORMULA ( ONLY X_mod 'Model uncertainty' X_M_fra '|X_M| / X_MK' X_S_fra 'X_S / X_SK' h 'Design axial force utilisation' gam_M 'Total safety factor - moment' gam_S 'Total safety factor - axial force' ) ( 'X_mod - ((X_M_fra/gam_M)*(1-h**2) + ((X_S_fra*h/gam_S)**2))**2' ) % --------------------------------------------------------% Calibration % --------------------------------------------------------CREATE VARIABLE Gamma_c 'Condition load effect factor' FIXED 0.8043 % ---------------------------------------------------------


D-10

% Temp variables % --------------------------------------------------------CREATE VARIABLE X_M_abs 'Absolute value of X_M' CREATE VARIABLE X_M_fra '|X_M| / X_MK' CREATE VARIABLE X_S_fra 'X_S / X_SK' CREATE VARIABLE gam_M 'Total safety factor - moment' Gamma_c ) CREATE VARIABLE gam_S 'Total safety factor - axial force' Gamma_c ) % --------------------------------------------------------% Limit state % --------------------------------------------------------CREATE VARIABLE G 'Limit state value' CREATE EVENT FAIL 'G < 0 '


FUNCTION FUNCTION FUNCTION FUNCTION

Abs X_M Division X_M_abs X_MK Division X_S X_SK Product ( ONLY Gamma_m Gamma_SC Gamma_F

FUNCTION Product ( ONLY Gamma_m Gamma_SC Gamma_F

FUNCTION LimSta X_mod X_M_fra X_S_fra h gam_M gam_S SINGLE G < 0.0

D-11

APPENDIX E EFFECT OF RESIDUAL CURVATURE ON SEABED


E-1

E.1 INTRODUCTION An increased utilisation on the stinger as allowed by this guideline may introduce plastic strains that in turn will cause a residual bending moment. The implication of this during installation (e.g. twist during installation) and operation (straightening moment) shall be agreed with operator in order to allow such high utilisation. The effect of the build in bending moment due to residual curvature and axial force for further loading can be ed for either by proper modelling on the residual curvature in the in-place analyses or by a simplified approach. This appendix presents a procedure for a simplified approach by calculating a reduction in bending moment capacity of a pipe that has been laid according to the S-lay method and plastically bent on the stinger. The calculation steps are as follows, reference is also made to Figure Ε.1: 0:

Establish the non-linear moment strain curve.

1:

Calculate the pipe’s characteristic strain capacity εc/γε.

2:

Calculate the plastic (residual) strain due to bending over the stinger εs,res.

3:

Calculate the reduced strain capacity:

4:

The reduction in bending moment capacity to be subtracted from the capacity Mp given in DNV-OS-

𝜀𝜀𝑐𝑐

𝛾𝛾𝜀𝜀

− 𝛾𝛾𝐹𝐹 ∙ 𝜀𝜀𝑠𝑠,𝑟𝑟𝑟𝑟𝑟𝑟 .

F101 is then found from the strain moment curve: 𝜀𝜀

𝜀𝜀

Δ𝑀𝑀𝑝𝑝,𝑟𝑟𝑟𝑟𝑟𝑟 = 𝑀𝑀 � 𝑐𝑐 � − 𝑀𝑀 � 𝑐𝑐 − 𝛾𝛾𝐹𝐹 ∙ 𝜀𝜀𝑠𝑠,𝑟𝑟𝑟𝑟𝑟𝑟 �. 𝛾𝛾𝜀𝜀

𝛾𝛾𝜀𝜀


E-2

In the following an illustrative example is presented in which the following parameters are assumed: Pipe diameter:

D=

508.0mm

Wall thickness:

t=

15.9mm

Yield stress:

fy =

450MPa

Strain on stinger:

εs =

0.45%

The steps for a load-controlled condition are as follows, see also Figure E.1: 0:

Establish a moment - bending strain relationship, typically by a FE analysis. In the following a “Murphey-Langner” relationship is used:

𝜀𝜀 = 1:

𝐷𝐷 𝑀𝑀 𝑀𝑀𝑏𝑏 𝑀𝑀 𝑛𝑛 � + �𝐾𝐾𝑏𝑏 − � � � �, 𝐸𝐸𝐸𝐸 𝑀𝑀𝑏𝑏 2 𝐸𝐸𝐸𝐸

where 𝐾𝐾𝑏𝑏 =

𝑡𝑡

The strain capacity according to DNV-OS-F101 is: 𝜀𝜀𝑐𝑐

𝛾𝛾𝜀𝜀

= 0.78 �

15.9 508

𝐷𝐷

𝐷𝐷

= 6.16 ∙ 10−5 𝑟𝑟𝑟𝑟𝑟𝑟/𝑚𝑚𝑚𝑚, 𝑀𝑀𝑏𝑏 = 𝑓𝑓𝑦𝑦 𝐷𝐷2 𝑡𝑡 �1 − 0.002 𝑡𝑡 � = 1728𝑘𝑘𝑘𝑘𝑘𝑘, 𝑛𝑛 = 16 − 0.07 = 13.8

𝐷𝐷2

− 0.01� ⋅

0.93−1.5 ⋅0.88 2.0

𝑡𝑡

= 0.819%.

2:

Bending strain on the stinger is 0.45%, and with linear unloading:

3:

𝜀𝜀𝑠𝑠,𝑟𝑟𝑟𝑟𝑟𝑟 = 𝜀𝜀𝑠𝑠 −

𝐸𝐸𝐸𝐸

⋅

𝐷𝐷 2

= 0.45% − 0.246% = 0.204%.

Calculate the reduced strain capacity: 𝜀𝜀𝑐𝑐

4:

𝑀𝑀𝑠𝑠

𝛾𝛾𝜀𝜀

− 𝛾𝛾𝐹𝐹 ∙ 𝜀𝜀𝑠𝑠,𝑟𝑟𝑟𝑟𝑟𝑟 = 0.819% − 1.2 ⋅ 0.204% = 0.574%.

The reduction in bending moment capacity to be subtracted from the capacity Mp given in DNV-OSF101 is then found from the strain moment curve: 𝜀𝜀

𝜀𝜀

Δ𝑀𝑀𝑝𝑝,𝑟𝑟𝑟𝑟𝑟𝑟 = 𝑀𝑀 � 𝑐𝑐 � − 𝑀𝑀 � 𝑐𝑐 − 𝛾𝛾𝐹𝐹 ∙ 𝜀𝜀𝑠𝑠,𝑟𝑟𝑟𝑟𝑟𝑟 � = 1626𝑘𝑘𝑘𝑘𝑘𝑘 − 1561𝑘𝑘𝑘𝑘𝑘𝑘 = 65𝑘𝑘𝑘𝑘𝑘𝑘 . 𝛾𝛾𝜀𝜀

𝛾𝛾𝜀𝜀

The plastic bending moment capacity from DNV-OS-F101; α𝑐𝑐 ∙ 𝑀𝑀𝑝𝑝 can be calculated to be 1828kNm, so the 65kNm reduction constitutes 3.6% of this. 1800 1600

Moment [kNm]

1400 1200 1000 800 600 400 200 0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Strain [%]

Figure E. 1

Illustration of design check and residual capacity


E-3

APPENDIX F SAG BEND EVALUATIONS


F-1

F.1 Introduction The fundamental limit state for pipeline installation in the sag bend is the combined loading criterion, considering Moment, pressure and axial load. In DNV-OS-F101 there are two formulations for this limit state; load controlled and displacement controlled condition. The displacement controlled allows in general a higher utilisation and the study focus on if the conditions in the sag bend can be considered being load or displacement controlled. Normally, for a load controlled condition, safety factors are determined based on the uncertainty in the load and capacity. Applied to the sag bend, it is not obvious what to apply as the load will depend on the capacity as explained later in this appendix. On this basis, a study is performed on the behaviour of the sag bend during installation in order to assess the conservatism and possible relaxation of the safety factors here. The evaluated failure mode for the sag bend in this report is the local buckling – combined loading criteria in the presence of external over pressure. As it is the sag bend that is in focus, a catenary configuration (i.e. without stinger) is used but the result should apply to S-lay, J-lay and reel-lay.

F.2 Hypothesis The evaluated failure mode for the sag bend in this report is the local buckling – combined loading criteria in the presence of external over pressure. The load controlled formulation of this failure mode in DNV-OS-F101 is given in Eq. (F.1) (F.1)

This limit state criterion is valid when the uncertainty is on the load and that the load is independent on the deformation, like a weight on a cantilever. If the load is displacement controlled, i.e. that the load is governed by applied deformations, the limit state from DNV-OS-F101 in Eq. apply. (F.2)

For a slender structure the curvature in the sag bend will generally follow the catenary solution, which is independent on the stiffness of the pipe (given that it can still be considered “slender”).


F-2

Depth

Depth

This is, however, only valid if the stiffness is uniform along the pipe. In case a hinge is introduced, the configuration as well as the moment will be slightly changed; this is illustrated in Figure F-.

Weak link

Lay back length

Moment

Moment

Lay back length

Lay back length Equal stiffness Figure F-1

Lay back length With weak link (exaggerated)

Sketch of sag bend performance with and without link

The curvature, or strain for a given length, in the weak link increases due its reduced stiffness. Hence, the moment diminishes. In a hypothetical example, imagine a case where the bending moment for the nominal pipe is larger than the weak link capacity. The introduction of the weak link would reduce the bending moment below the capacity limit. The hypothesis is therefore that there could be an “equilibrium point” where the capacity of the weak link matches the moment. This is the hypothesis to be explored in this study. What is special with installation is that this is not “one” configuration (as for a SCR) but a configuration that moves along the pipeline. The maximum curvature in the sag bend will move along the pipeline as the installation progress and failure will occur where the pipeline is weakest. This will occur close to where the maximum plastic variation is largest, i.e. close to a weld between to pipe ts, similar to the on-reeling process described in Appendix A.


F-3

Hence, the sag bend configuration to be considered will be where you have a “weak link” or largest plastic capacity variation that will affect both the capacity and load effect.

F.3 FE-model Finite element models are established in the Abaqus FE-program and analysed to study the hypothesis. The model is based on pipe elements with non-linear material and large deformations. The model will therefore not capture ovalisation of the cross section, and hence cannot be used for capacity predictions where collapse will contribute to the capacity reduction. Away from the capacity point they are, however, considered to be appropriate. To capture the true behaviour close to the capacity point detailed model with shell elements and ovality have to be used. Prior to the analyses reported here, several simplified models are analysed to get a general impression of the behaviour. The presented analyses are expected to be representative when the pipe can be considered “slender”, i.e. in a water depth more than 1000-1500 diameters. A summary of the properties are given in Table F-1. Table F-1

Investigated cases parameters variation

Parameter

Symbol

Value

Unit

Diameter

D

678.8

mm

Water depth

WD

1000 (1473 D)

m (-)

1500 (2210 D) Steel grade

-

X65

-

Yield Stress

YS

450

MPa

427.5 405 Tensile Strength

YT

535

MPa

508 481 Wall thickness

T

34.6

mm

32 30 Diameter to thickness ratio

D/t

19.6 (nominal)

-

Five different models are analysed; one with nominal properties throughout the model and four with weak links. The weak links is a limited section of the catenary which has reduced stiffness. In the present analyses this is achieved either with reduced yield and tensile strengths or with reduction in wall thickness. Two weak link models have reduction in yield and tensile strength and two have reduction in wall thickness; see

Table F-2. These are analysed in both 1000 m water depth and 1500 m water depth.


F-4

Table F-2

Analysed models

Model

Denotation

Yield stress

Tensile strength

Thickness

Base case

BM

450

535

34.6

Weak link – yield 5%

YS95

427.5

508

34.6

Weak link – yield 10%

YS90

405

481

34.6

Weak link – Thickness 5%

T32

450

535

32

Weak link – Thickness 10%

T30

450

535

30

The weak link is located at the point of the maximum bending moment. This location changes in the different base configurations studied. The extent of the weak link is also studied. While a 12 m length is adopted in most cases Section F 5.3 presents a comparison with a shorter weak link length, 3 m. As the sag bend is the focus of the study, no over bend is modelled. The pipe is modelled on a flat seabed with formulation and the end is then lifted to the water surface with a horizontal force applied to it. This is identical to the bottom tension and henceforward be refereed by it. The bottom tension is then reduced until a maximum bending strain of 0.15%, 0.2%, 0.3% or 0.5% is achieved for the base case model. The corresponding bottom tension is then applied to the other models as well. The different configurations are shown in Figure F- and Figure F-3.


F-5

Figure F-2

Model configurations of the uniform models for four different bottom tensions at

1000 m water depth

Figure F-3

Model configurations of the uniform models for four different bottom tensions at

1500 m water depth

The load case for 0.5% results in a negative bottom tension. For such a case there is really not a catenary solution and it is therefore purely dependent on the bending stiffness of the pipe. This is undesirable in practice as the compression will increase the moment in the sag bend (and burning additional fuel to achieve this) and that compression may cause global buckling of the pipeline on the sea bed. The case is, however, kept as an extreme reference case.


F-6

F.4 Results Some basic results for the five models in the two water depths and four bottom tensions are shown in Table F-3 and Table F-4. Corresponding results are given in Figure F- through Figure F-. Table F-3 Model

Summary of analyses at 1000 m water depth Water depth Case Bottom tension [kN]

BM

Max moment [kNm] Max strain Lay back distance [m]

YS95

Max moment [kNm]

Yield

Max strain Lay back distance [m]

YS90

Max moment [kNm]

Yield


T32

Max moment [kNm]

Thickness


T30

Max moment [kNm]

Thickness



1000 m 0.15%

0.2%

0.3%

0.5%

305

155

67.7

-10

3237

4379

5234

5874

-0.148%

-0.207%

-0.304%

-0.526%

495

346

238

112

3240

4370

5180

5790

-0.148%

-0.213%

-0.357%

-0.696%

495

346

238

110

3240

4370

5090

5650

-0.147%

-0.220%

-0.431%

-0.943%

495

346

240

108

3120

4270

5100

5720

-0.153%

-0.223%

-0.373%

-0.747%

497

349

240

112

3050

4180

4950

5550

-0.158%

-0.237%

-0.436%

-0.996%

499

351

240

109

F-7

Table F-4 Model

Summary of analyses at 1500 m water depth Water depth

1500 m

Case

0.15%

0.2%

0.3%

0.5%

315

184

76.8

-1

3178

4168

5086

5693

-0.151%

-0.202%

-0.305%

-0.499%

564

413

265

125

3172

4115

4893

5270

-0.150%

-0.205%

-0.319%

-0.448%

564

414

268

140

3172

4101

4823

5177

-0.150%

-0.211%

-0.383%

-0.571%

564

414

267

139

3072

4019

4831

5211

-0.156%

-0.214%

-0.336%

-0.472%

567

416

269

142

3162

3940

4708

5076

-0.162%

-0.228%

-0.395%

-0.605%

568

417

270

142

Bottom tension [kN] BM

Max moment [kNm] Max strain Lay back distance [m]

YS95

Max moment [kNm]

Yield


YS90

Max moment [kNm]

Yield


T32

Max moment [kNm]

Thickness


T30

Max moment [kNm]

Thickness



F-8

The moment and strain along the catenary for the four strain cases are shown in Figure F- to Figure F-11.

Figure F-4

Moment and strain along the catenary for 0.15% strain in base case, 1000 m

Figure F-5



F-9

Figure F-6


Figure F-7



F-10

Figure F-8


Figure F-9



F-11

Figure F-10


Figure F-11



F-12

F.5 Discussion of weak link influence F.5.1 Configuration

The first observation is that the catenary (configuration) is not largely affected by introduction of a weak link as the bottom tension and lay back distance are not largely affected. This means that the presence of a weak link will have limited effect upon the global configuration and its main contribution is a local reduction in pipe capacity. The limited variation in bottom tension and lay back distance are due the local, i.e. at the weak link location, change in configuration.

F.5.2 Load and weak link capacity

The local pipe capacity is closely linked to the discussion on load controlled versus displacement controlled which is illustrated in Figure F-. The two lines illustrate two different moment-curvature relationships with moment on the y-axis. The moment-curvature relationship is taken from a short model with uniform properties. The solid line corresponds to nominal properties, while the dashed line corresponds to the weak link properties.

Moment

For a fully load controlled case the bending moment of the weak t will remain constant as the nominal/base case, moving from point 0 to point B. While in a fully displacement controlled the strain will remain constant, moving from point 0 to point A. A partial displacement controlled case will be in between points A and B, e.g. moving from point 0 to point C, and the degree of displacement control could be estimated by the slope of the ��⃗ 0𝐶𝐶 vector.

Curvature Moment-curvature relationship of nominal and weak t

Figure F-12 Illustration of load controlled and displacement controlled behaviour with the introduction of a weak link

The results from the analyses of the model for 1000 m water depth are shown in Figure F- and for the 1500 meter depth in Figure F-. The dots illustrate the different bottom tensions, i.e. stain cases, for the different models. The solid lines correspond to the moment-curvature relationship for the nominal properties and for the weak links.


F-13

Figure F-13 Moment-curvature curves in 1000 m water depth for base case and 4 weak links and moment-curvature points for the four strain cases

Figure F-14 Moment-curvature curves in 1500 m water depth for base case and 4 weak links and moment-curvature points for the four strain cases


F-14

F.5.3 Effect of weak link length

Figure F- shows the bending moment reduction in the YS09 case for a weak link of 12m (YS09_12) and a weak link of 3m (YS09_3) and a clear difference can be seen, which increases with increasing strain case. From Figure F-16 it is noted that the actual difference between the two weak link lengths are small compared to the total predicted value.

Figure F-15 Bending moment variation with weak link length, 1000m water depth

Figure F-16 Bending moment in sag bend for the different cases, 1000m water depth From Figure F-16 it can also be observed that the bending moment variation with the strain case is very similar for base case and weak link cases as the curves are almost parallel. The bending moment behaviour with strain case change is the nearly the same regardless of the weak link. However one can


F-15

note the reduction in bending moment with the introduction of the weak link, which is expected to be reflected in strain. Figure F- shows that the strain difference is fairly sensitive with the weak link length as the strain case increases.

Figure F-17 Compressive axial strain variation with weak link length, 1000m water depth From Figure F- it can also be observed that the strain variation with strain case is unique with the weak link.

Figure F-18 Compressive axial strain in sag bend for the different cases, 1000m water depth


F-16

The observations regarding bending moment and compressive axial strain predictions with the introduction of a weak link indicates that bending moment presents the lowest variation.

F.5.4 Equilibrium Connecting the dots from Figure F- and Figure F- with its respective base case will give the vector similar to Figure F-. An example is shown in Figure F- for the weak link YS90 and 0.5% strain case. In the example shown, the vector is constructed connecting the base case point (0) and the weak link YS90 case point (C) for the same strain case. 0 C

Figure F-19 Illustration of slope vector, results for 1000 m are used

The derivative/slope of these lines (0C) is reported in Table F-5 and Table F-6. The trend is that the slope of the constructed vectors becomes flatter as the nominal strain case increases. I.e. increasing the strain case approximates the behaviour to load control. The same trend is found in both water depths.


F-17

Table F-5 Model Load case

Influence of weak link, 1000 m water depth Equilibrium derivative from base case model (Moment/curvature) [Nm²] 0.15%

0.2%

0.3%

0.5%

T32

-5.02E+08

-4.51E+07

-3.25E+07

-1.59E+07

T30

-5.02E+08

-2.27E+07

-3.64E+07

-1.73E+07

YS95

-9.13E+08

-2.51E+08

-6.41E+07

-2.29E+07

YS90

-7.66E+08

-2.39E+08

-7.15E+07

-2.27E+07

Table F-6 Model Load case

Influence of weak link, 1500 m water depth Equilibrium derivative from base case model (Moment/curvature) 0.15%

0.2%

0.3%

0.5%

T95

1.27E+09

-5.97E+08

-4.48E+08

2.63E+08

T90

1.27E+09

-2.29E+08

-1.11E+08

-2.34E+08

YS95

-8.02E+08

-4.52E+08

-2.95E+08

5.33E+08

YS90

-6.72E+08

-3.22E+08

-1.44E+08

-1.98E+08

For small bending strains the stiffness is less important. The configuration follows more closely the catenary solution. The introduction of a weak link reduces the moment, the vector is more vertical, and it approximates to displacement control, as predicted by the hypothesis. When determining the safety factor, an assessment of the probability of the capacity being less than the load is carried out as stated in the introduction of this appendix. If the load is larger than the capacity, the pipe fails. As seen in this example above, this may not be the case as the equilibrium is reached for a lower load. As long as this lower load is less than the capacity of that weak link, it is not failing. Hence, there will always be equilibrium. To avoid failure, this equilibrium has to be for a curvature less than the curvature capacity of the weak link. This curvature capacity is given in DNV-OS-F101 by Eq. (F.3) (F.3)

Neglecting the pressure part, the strain capacity is a function of D/t only, and not the yield stress. I.e. for a weak link created by the reduction of yield stress only, the capacity will not be affected. If the weak link is created by a reduction of thickness, the capacity will be reduced. Hence, if a weak link is introduced in a configuration with small strains, it will be very much displacement controlled and equilibrium at a lower moment will be reached and a larger safety level than foreseen in the calibration of the safety factors can be assumed. On the other side, if the utilisation in the sag bend is larger, i.e larger strains, the moment/curvature difference vector becomes more flat and a smaller reduction in moment is expected. So the larger the strains the closer to a load controlled case it is.


F-18

F.5.5 Conclusion

In general the equilibrium in the sag bend can be illustrated by Figure F-. The red curve is the displacement controlled strain capacity and depend on the thickness only. It can be seen that a given load moves closer to the capacity with the introduction of a weak link. If the capacity curve and the weak link response curve are known, the weak link capacity will be defined where the two curves meet, see schematics in Figure F-. The challenge is that the green line is not fixed but depends on the utilisation in the sag bend, as seen by the two different green curves in Figure F-. The degree of conservatism in the load controlled in sag bend assumption depends on the utilisation in the sag bend. The higher utilisation the more load controlled and less conservative is the assumption.

Figure F-20 Weak Link design schematics Although the capacity is defined by one curve, the analysis presented in the previous sections show that the weak link response curve is a family of curves, function of: -

Material strength (YS and TS); Dimensional tolerance (wall thickness and diameter); Weak Link length; and Layback (the position in the moment-strain nominal curve).

It is recommended to maintain the current practice to use a nominal pipe and check this for a load controlled combined loading criterion as the moment tends to be quite fixed when introducing the weak link. However, in special applications, a modified design capacity can be used based on a model with a representative weak link model combined with a displacement controlled criteria. For this application, the following aspects need to be considered: • •

A representative weak link needs to be calculated. Guidance can be found in the reeling procedure in Appendix A. In presence of high utilisation of the collapse capacity, the weak link model needs to represent the true behaviour i.e a shell element model with representative ovality is required.

A fair amount of engineering judgement is required to adequately predict the collapse capacity.


F-19

About DNV GL Driven by our purpose of safeguarding life, property and the environment, DNV GL enables organizations to advance the safety and sustainability of their business. We provide classification and technical assurance along with software and independent expert advisory services to the maritime, oil and gas, and energy industries. We also provide certification services to customers across a wide range of industries. Operating in more than 100 countries, our 16,000 professionals are dedicated to helping our customers make the world safer, smarter and greener.

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