Cd-17-major Project Report.pdf 365x5s

Project Report On DESIGN OF RETAINING WALL FOR A MINOR BRIDGE

A project report submitted in the partial fulfillment of Requirement for the award of the degree of

Bachelor of Technology In Civil Engineering By SIRIPURAM ANUSHA

(09241A0157)

M.BALAKOTESHWARI

(09241A0160)

R.SABITHA RAJ

(09241A0195)

A.SWETHA

(09241A01A7)

Under the guidance of Mrs.C.Lavanya Assistant Professor, Department of Civil Engineering.

GOKARAJU RANGARAJU INSTITUTE OF ENGINEERING AND TECHNOLOGY BACHUPALLY, KUKATPALLY, HYDERABAD-500090

2012-2013 1

GOKARAJU RANGARAJU INSTITUTE OF ENGINEERING AND TECHNOLOGY, HYDERABAD

CERTIFICATE This is to certify that the dissertation entitled “DESIGN OF RETAINING WALL FOR A MINOR BRIDGE” is a bonafide project work done under the guidance of Mrs. C.LAVANYA , Assistant Professor in the Department Of Civil Engineering, GOKARAJU RANGARAJU INSTITUTE OF ENGINEERING AND TECHNOLOGY, Hyderabad.

Project done by

Mrs.C.Lavanya Guide

SIRIPURAM ANUSHA

(09241A0157)

M.BALAKOTESHWARI

(09241A0160)

R.SABITHA RAJ

(09241A0195)

A.SWETHA

(09241A01A7)

Prof.Dr.G.Venkata Ramana HOD Civil Engineering

2

External Examiner

STUDENT DECLARATION We hereby declare that the project entitled “DESIGN OF RETAINING WALL FOR A MINOR BRIDGE” is the work done by us during the academic year 2012-13. This project report is submitted in partial fulfillment of the requirements for the award of degree of bachelor of technology in CIVIL ENGINEERING from JNTU, Hyderabad.

SIRIPURAM ANUSHA

(09241A0157)

M.BALAKOTESHWARI

(09241AO160)

R.SABITHA RAJ

(09241A0195)

A.SWETHA

(09241A01A7)

3

ACKNOWLEDGEMENT Salutations to our beloved and highly esteemed institute “Gokaraju Rangaraju Institute of Engineering and Technology” for having well qualified staff and labs furnished with necessary equipment and computers. Firstly we would like to express our deep sense of gratitude towards Dr. G.Venkata Ramana, Head of the Department, Civil Engineering for giving us the opportunity to do an industrial oriented project work. We would also like to thank our project guide, Mrs.C.Lavanya, Assistant Professor, Department of Civil Engineering at Gokaraju Rangaraju Institute of Engineering and Technology for always being available when we required her guidance. Special thanks to all our team for this team work and other friends for their .

4

CONTENTS

PAGE NUMBER

1. Introduction

1

2. Objective of the project

3

3. Site location

4

3.1 Bridge definition

4

3.2 Classification of bridges

5

3.3 Bridge specifications

6

4. Soil strata analysis

7

4.1 Type of soil

8

4.2 Properties of soil

8

5. Effect of wall movement on earth pressure

12

6. Retaining wall

13

6.1 Types of retaining walls

13

7. Tests

17 7.1 Standard compaction test

17

7.2 Direct shear test

25

7.3 Unconfined compressive test

34

8. Estimation of safe bearing capacity

42

8.1 Factors influencing bearing capacity

43

8.2 Terzaghi’s bearing capacity theory

43

8.3 Effect of shape of Foundation

48

8.4 Summary of Shape factors

49

8.5 Factor of safety

49

8.6 Calculation of safe bearing capacity

50

5

9. Design considerations for a retaining wall

52

9.1Wall Deformations And Earth Pressures

52

9.2 Backfill Material

52

9.3 Gravity Retaining Walls

53

9.4 Design

54

10. Deg of retaining wall

57

Existing section

58

Trial section 1

59

Trial section 2

64

Trial section 3

69

11. Conclusion

75

12. Bibliography

76

6

LIST OF FIGURES Fig.3

Existing Minor Bridge

4

Fig 4.1

Moorum soil

8

Fig. 5

Effect of Wall Movement on Earth Pressure

13

Fig 6.1.1

Gravity Retaining Wall

14

Fig 6.1.2

Cantilever Retaining Wall

15

Fig. 6.1.3

Counter-fort Retaining Wall

15

Fig. 6.1.4

Piling Wall

16

Fig. 6.1.5

Anchored Retaining Wall

16

Fig. 7.1.1

Fig. 7.1.2

Fig. 7.1.3

Fig.7.2.1

Fig. 7.2.2

Compaction Mould and Rammer Compacting the soil sample

Scraping

Direct Shear Apparatus

Components of Direct Shear Mould

7

18

20

20

25

26

Fig. 7.2.3

Fig.7.2.4

Fig.7.2.5

Fig.7.2.6

Fig.7.3.1

Fig.7.3.2

Fig. 7.3.3

Fig.7.3.4

Fig. 7.3.5

Fig.7.3.6

Components of Direct Shear Apparatus

Proving Ring

Load applied on Soil Sample

Sample conditions before and after the test

Unconfined Compression Test Apparatus

Sample Extractor

Cylindrical Mould

Extracted soil sample

Load applied on soil specimen

Soil Specimen after failure

28

28 29

30

35

36

37

37

38

39

Fig. 8.1

Main components of a structure including soil

42

Fig. 8.2.2

Terzaghi’s concept of Footing with five distinct failure zones in foundation soil

45

8

Fig. 8.2.3

Fig.9.3.1

Fig. 10.1

Fig. 10.2

Terzaghi’s Bearing Capacity Factors for different ϕ

Gravity Retaining wall

Existing section of Retaining wall

Trial section1

48

53

58

59

Fig. 10.3

Trial Section2

64

Fig. 10.4

Trial section 3

69

Fig.10.5

Retaining wall being constructed

74

9

LIST OF TABLES

Table No.1 Table No.2 Table No.3

Standard Compaction Test Readings Direct Shear Test Readings

22 31

Unconfined Compression Test Readings Bearing Capacity Factors For Different Φ

40

Table No.5

Load Details Of The Trial Section 1

60

Table No.6

Load Details Of The Trial Section 2 Load Details Of The Trial Section 3

65

Table No. 4

Table No.7

10

47

70

LIST OF GRAPHS

Graph showing the variation Graph 1

of moisture content and dry

24

density in compaction test

Graph showing variation of Graph 2

normal load and shear stress in direct shear test.

11

33

ABSTRACT Structures which are used to hold back a soil mass are called retaining structures. Our project is to design retaining wall for a minor bridge. As the metro rail project is running through Miyapur, there is a need for the extension of 4 lane carriage way to 6 lane carriage way. But the carriage way includes a minor bridge, which too has to be extended for facilitating the traffic flow. Thus, this project focuses on the design of retaining wall for the modified section of the minor bridge. Retaining walls are the structures designed to restrain soil to unnatural slopes. They are used to bound soils between two different elevations in areas of terrain possessing undesirable slopes. They are also used in areas where the landscape needs to be shaped severely and engineered for more specific purposes like hillside farming or roadway overes. They are also used in bridge abutments and wing walls. The design of structures like retaining wall requires the knowledge of the earth pressure acting on the back of the wall because of the soil backfill in with it. Hence relation between the earth pressure on the retaining wall and strains within a backfill is a prerequisite. The project also includes the estimation of safe bearing capacity of soil and its properties, earth pressure calculations and design criteria of a modified section of a retaining wall. The design criteria includes: check for stability against sliding, overturning and bearing capacity.

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1. INTRODUCTION A soil mass is stable when the slope of the surface of the soil mass is flatter than the safe slope. At some locations where the space is limited, it is not possible to provide flat slope and the soil is to be retained at a slope steeper than the surface one. In such cases, a retaining structure is required to provide lateral to the soil mass. Retaining walls are relatively rigid walls used for ing the soil mass laterally so that the soil can be retained at different levels on the two sides. Generally, the soil masses are vertical or nearly vertical behind the retaining structure. Thus, a retaining wall maintains the soil at different elevations on its either side. In the absence of a retaining wall, the soil on the higher side would have a tendency to slide and may not remain stable. However for a minor bridge of span 15 m a retaining wall is constructed without considering the slope factor but only the soil properties. The project concentrates on the deg of a retaining wall located on National Highway-9; Pune- Hyderabad via Miyapur. The road in this region is extended for two lanes, from four lane road way to six lane road way to accommodate free traffic flow because of metro railway construction process. The minor bridge located in this region is also to be extended. Thus, our project is been cleared with the design of a retaining wall to this bridge on one side and hence replicating it to remaining. Structures which are used to hold back a soil mass are called retaining structures. Retaining walls, sheet pile walls, crib walls, sheeting in excavations, basement walls, etc., are examples of retaining structures. A retaining wall helps in maintaining the ground surface at different elevations on either side of it. Without such a structure, the soil at higher elevation would tend to move down till it acquires its natural, stable configuration. Consequently, the soil that is retained at a slope steeper than it can sustain by virtue of its shearing strength, exerts a force on the retaining wall. This force is called the earth pressure and the material that is retained by the wall is referred to as backfill. The gravity retaining wall is the simplest type of retaining wall along with other common types of retaining walls such as the cantilever, and the counterfort walls. The design of structures like a retaining wall requires the knowledge of the earth pressure acting on the back of the wall because of the soil backfill in with it. 13

The magnitude of earth pressure itself, on the other hand, is a function of the magnitude and nature of the absolute and relative movements of the soil and the structure. Problems such as these, where structure is in with the soil mass and the behavior of each one is influenced by that of the other, are classed as soil-structure interaction problems. Often, the earth pressures are statistically indeterminate and hence pose problems in evaluation. In some cases, the desired accuracy in determination cannot be achieved. But knowledge of the relationship between the earth pressure on the retaining wall and strains within a backfill is a prerequisite for the solution of earth pressure problems. The design of the retaining structure requires determination of the magnitude and line of action of the lateral earth pressure. The magnitude of the lateral earth pressure depends upon a number of factors, such as the mode of the movement of the wall, the flexibility of the wall, the properties of the soil, and the drainage conditions. It is a soil-structure interaction problem, as the earth pressure depends on the flexibility of the wall. The design has been accomplished with few tests which we have done in the college laboratory. The results extracted were used in the design. The site being in a hard rocky soil strata, we got very high safe bearing capacity. Hence, two more sections apart from actual section according to standard specifications were also evaluated for economic reasons with increased safety factor. The definition of minor bridge, retaining wall and their types, tests and tests results with brief procedure were explained in this report in addition to the safe bearing capacity of the ground, designed sections and their evaluations for safety conditions.

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2. OBJECTIVE OF THE PROJECT Our Project focuses on design of retaining wall for a minor bridge. The project, deg of retaining wall for a minor bridge is the consequence of road widening due to prestigious metro rail project. In the construction course of metro railway, a four lane road way has to be extended to six lanes, to avoid the occurrence of traffic problems. As there is a minor bridge existing there it should also be extended as a part of road widening. The idea behind our project is to design a modified section of existing retaining wall for the extension of the bridge. Before deg part, all the soil properties which include dry density, optimum moisture content, cohesion, shear strength parameters were evaluated by conducting corresponding tests. The safe bearing capacity of the ground is then calculated with the test results. Taking existing retaining wall as an example each modified section has been analysed for stability against bearing capacity, sliding and overturning with the reduced dimensions according to the area of the total project so as to make it economical.

15

3. SITE LOCATION The site is located opposite to Talkie Town, Miyapur on Pune-Hyderabad section of NH-9. The figure here shows the existing minor bridge.

cc Fig 3 Existing Minor Bridge

3.1 BRIDGE A bridge is a structure built to span physical obstacles such as a body of water, valley, or road, for the purpose of providing age over the obstacle.In other words Bridge is a structure having a length of above 6 m between the inner faces of dirt walls for carrying traffic or other moving loads over a depression or obstruction such as channels,raods,railways etc. There are 16

many different designs that all serve unique purposes and apply to different situations. Bridges can be categorized in several different ways. Common categories include the type of structural elements used, by what they carry, whether they are fixed or movable, and by the materials used and by the span of bridge..In this project we carried out work for deg of retaining wall for a minor bridge.

3.2 CLASSIFICATION OF BRIDGES Classifications based on span of bridge are categorized as follows.

3.2.1 MINOR BRIDGE A Major Bridge is a bridge having a total length of upto 60 m.This is a cross drainage structure consisting of 4 piers and 2 abutments currently in this project.Centre to centre span between piers is 3m.Total length of the bridge is 15m and hence called minor bridge.Retaining walls are otherwise called Wing walls which are ed to the two abutments.Type of retaining wall existing at this site is gravity retaining wall or gravity wing wall.

3.2.2 MAJOR BRIDGE A Major bridge is a bridge having a total length upto 60m.These can also be a cross drainage structures. It includes all other bridge structures including large or complex culverts. Major bridges are typically built from site-specific drawings, but can also be built from standard girder drawings. Typically major bridges are river crossings, highway interchanges or railway crossings.

3.2.3 CULVERT Culverts are cross drainage structures having a total length upto 6m or less between the inner faces of dirt walls or extreme vent way boundaries measured at right angles thereto. A large number of culverts are needed for taking care of the streams crossing the railway lines. A culvert is a cutting under or beside a road which allows water to drain, rather than pooling and making road conditions hazardous.

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3.3 SPECIFICATIONS •

The work shall be carried out as per M.O.R.T & Hs (Ministry of Road Transport and Highways)

•

The work will be governed by design considerations & specifications contained in IRC codes of practice for roads/bridges.

•

The materials of construction shall be governed as per relevant I.S codes.

•

The grading, size, quality of coarse aggregates shall be strictly as per “Specifications for Road and Bridge works” M.O.R.T & Hs and relevant I.R.C codes.

•

The size, quality of aggregates and mixing etc for plain concrete and R.C.C works shall be as per “Specifications for Road and Bridge works” and relevant I.S codes

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4. SOIL STRATA ANALYSIS For any type of retaining wall design it is necessary to evaluate the engineering properties of soil mainly the strength parameters as all retaining walls serve to hold back a vertical or near vertical face of soil that would, without adequate retention, cave, slump or slide to a more natural slope. Therefore the following parameters need to be assessed 4.1 Type of soil 4.2 Properties of soil 4.2.1. Safe bearing capacity 4.2.2. Dry density 4.2.3. Optimum moisture content 4.2.4. Shear Strength parameters 4.2.4.1 Cohesion 4.2.4.2 Angle of internal friction 4.2.5. Unconfined Compressive strength of soil 4.2.6. Lateral Earth Pressures

19

4.1. TYPE OF SOIL Soil is composed of particles of broken rock (parent materials) which have been altered by physical, chemical and biological processes that include weathering (disintegration) with associated erosion (movement).Soil existing at our site is Moorum. Moorum means powdered rock. It consists of small pieces of disintegrated rock or shale, with or without boulders. These are products of decomposition and weathering of the pavement rock. Visually these are similar to gravel except presence of higher content of fines. Site is completely a rocky area with this type of granular soil. Generally Moorum soil possess maximum dry density and therefore good strength.

Fig 4.1 Moorum

4.2. PROPERTIES OF SOIL 4.2.1. SAFE BEARING CAPACITY In geotechnical engineering, bearing capacity is the capacity of soil to the loads applied to the ground. The bearing capacity of soil is the maximum average pressure between the foundation and the soil which should not produce shear failure in the soil. Ultimate bearing 20

capacity is the theoretical maximum pressure which can be ed without failure; allowable bearing capacity is the ultimate bearing capacity multiplied by a factor of safety. Sometimes, on soft soil sites, large settlements may occur under loaded foundations without actual shear failure occurring; in such cases, the allowable bearing capacity is based on the maximum allowable settlement. Terzaghi’s Bearing Capacity theory is used in this project to calculate safe bearing capacity of soil which can be further used to evaluate stability analysis of retaining wall. 4.2.2. DRY DENSITY This is one of the important strength parameters need to be calculated. It can be determined from Standard Compaction Test. The safe and economic design of retaining wall depends on the dry density of surrounding soil. Bearing capacity of soil in turn depends on dry density of the soil. If the soil is not having sufficient dry density the structure built on it couldn’t carry loads. To make it strengthened soil is stabilized which will be expensive. Hence dry density of oil is the important parameter for any structure. Dry density of soil can be achieved by Compaction. Compaction is the process of increasing the density of the soil by packing the solid particles closer together by reducing the volume of the air. The degree of compaction is measured in of dry density, γd. The dry density after compaction depends on; •

type of soil

•

water content of the soil

•

amount of effort supplied by the compactive equipment

4.2.3. OPTIMUM MOISTURE CONTENT The optimum moisture content for a specific compactive effort is the moisture content at which the maximum density of soil is obtained. The optimum moisture content is an important control parameter of the soil base construction. This is also an outcome of Standard Compaction Test. Dry density and Optimum moisture content results are required to conduct further tests like direct shear and unconfined compression test. The optimum moisture content is an important control parameter of the soil base construction. Compaction is a process that brings about an increase in soil density or unit weight, accompanied by a decrease in air volume. There is usually no change in water content. The degree of compaction is measured by dry unit weight 21

and depends on the water content and compactive effort (weight of hammer, number of impacts, weight of roller, number of es). For a given compactive effort, the maximum dry unit weight occurs at an optimum water content. 4.2.4. SHEAR STRENGTH PARAMETERS The shear strength of a soil is a function of: The particle shape -- (Angular vs. rounded) The gradation of the soil (Poor vs. well graded) The soil density (Loose vs. dense) The amount and types of fines The pore pressure u and how the rate of loading affects it 4.2.4.1. COHESION This is the shear strength parameter which is determined from direct shear test. Shear strength is a term used in soil mechanics to describe the magnitude of the shear stress that a soil can sustain. The shear resistance of soil is a result of friction and interlocking of particles, and possibly cementation or bonding at particle s. Soil derives its shear strength in two forms - Cohesion and angle of internal friction. Cohesion is the interlocking strength between the soil particles. It is stress independent component.

4.2.4.2. ANGLE OF INTERNAL FRICTION Internal Friction angle (φ) is the measure of

the shear strength of soils due to friction. It is

stress dependent component. This is due to frictional resistance due to particles. The mechanical strength of soil is an important concept in considering (and predicting) soil behavior. We use strength to represent the reaction of a soil to an applied force. Highstrength soils resist deformation (compaction especially), break-up (shearing and shattering), and slippage. However, high-strength soils also resist root penetration and exploration. Strength is imparted to a soil by virtue of: 22

•

cohesive forces between particles; and

•

frictional resistance met by particles that are forced to slide over one another, or move from interlocked positions.

4.2.5. COMPRESSIVE STRENGTH OF SOIL The unconfined compressive strength (qu) is defined as the compressive stress at which an unconfined cylindrical specimen of soil will fail in a simple compression test. In addition, in this test method, the unconfined compressive strength is taken as the maximum load attained per unit area, or the load per unit area at 15% axial strain, whichever occurs first during the performance of a test. 4.2.6. LATERAL EARTH PRESSURES Retaining walls shall be designed to withstand lateral earth and water pressures, the effects of surcharge loads; the self-weight of the wall Lateral earth pressure is the pressure that soil exerts against a structure in a sideways, mainly horizontal direction. The common applications of lateral earth pressure theory are for the design of ground engineering structures such as retaining walls, basements, tunnels, and to determine the friction on the sides of deep foundations. These are of three types: •

At rest Earth pressure

•

Active Earth Pressure

•

ive Earth Pressure

The above specified earth pressures are used according to the situation i.e according to the movement of the wall and the soil pressure acting on it.

5. EFFECT OF WALL MOVEMENT ON EARTH PRESSURE When the wall is rigid and unyielding, the soil mass is in a state of rest and there are no deformations and displacements. The earth pressure corresponding to this state is called the earth pressure at rest. If the wall rotates about its toe, thus moving away from the backfill, the soil mass expands, resulting in a decrease of the earth pressure. This is a consequence of the 23

mobilization of shearing resistance in a direction opposing the movement of the earth mass. When the wall moves away from the backfill, a portion of the backfill locates next to the retaining wall tends to break away from the rest of the soil mass and tends to move downwards and outwards relative to the wall. Since the shearing resistance is mobilized in directions away from the wall, there is a resultant decrease in earth pressure which continues, until, at a certain amount of displacement, failure will occur in the backfill and slip surfaces will be developed. At this stage, the entire shearing resistance has been mobilized. The forces acting on the wall at this stage does not decrease anymore beyond this point even with further wall movement. This force is called the active earth pressure. On the other hand, if the wall is pushed towards the backfill, the soil is compressed and the soil offers resistance to this movement by virtue of its shearing resistance. Since the shearing resistance builds up in directions towards the wall, the earth pressure gradually increases. If this force reaches a value which the backfill cannot withstand, failure again ensues and slip surfaces develop. The pressure reaches a maximum value when the entire shearing resistance has been mobilized and does not increase any more with further wall movement. This pressure is called the ive earth pressure. The active earth pressure and ive earth pressure develop corresponding to two limiting states of equilibrium. The soil mass is said to be in a state of plastic equilibrium at these two stages. A small increase in stress at this stage will cause a continuous increase in the corresponding strain- a condition known as plastic flow.

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Fig. 5 Effect of Wall Movement on Earth Pressure

6. RETAINING WALL A retaining wall is a structure that retains holds back any material usually earth and prevents it from sliding or eroding away. It is designed so that to resist the material pressure of the material that it is holding back.

6.1 TYPES OF RETAINING WALLS There are four common types of retaining walls. They are 6.1.1 Gravity Retaining wall 6.1.2 Cantilever Retaining Wall 6.1.3 Counter-fort Retaining Wall 6.1.4 Piling Retaining wall 6.1.5 Anchored Retaining Wall

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6.1.1 GRAVITY RETAINING WALL It is that type of retaining wall that relies on their huge weight to retain the material behind it and achieve stability against failures. Gravity Retaining Wall can be constructed from concrete, stone or even brick masonry. Gravity retaining walls are much thicker in section. Geometry of these walls also help them to maintain the stability. Mass concrete walls are suitable for retained heights of up to 3 m. The cross section shape of the wall is affected by stability, the use of space in front of the wall, the required wall appearance and the method of construction.

Fig 6.1.1 Gravity Retaining Wall

6.1.2 CANTILEVER RETAINING WALL A cantilever retaining wall is one that consists of a wall which is connected to foundation. A cantilever wall holds back a significant amount of soil, so it must be well engineered. They are the most common type used as retaining walls. Cantilever wall rest on a slab foundation. This slab foundation is also loaded by back-fill and thus the weight of the back-fill and surcharge also stabilizes the wall against overturning and sliding.

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Fig 6.1.2 Cantilever Retaining Wall

6.1.3 COUNTER-FORT RETAINING WALL Counter fort walls are cantilever walls strengthened with counter forts monolithic with the back of the wall slab and base slab. The counter-forts act as tension stiffeners and connect the wall slab and the base to reduce the bending and shearing stresses. To reduce the bending moments in vertical walls of great height, counter forts are used, spaced at distances from each other equal to or slightly larger than one-half of the height Counter forts are used for high walls with heights greater than 8 to 12 m.

Fig. 6.1.3 Counter-fort Retaining Wall

6.1.4 PILING RETAINING WALL Sheet pile retaining walls are usually used in soft soils and tight spaces. Sheet pile walls are made out of steel, vinyl or wood planks which are driven into the ground. For a quick estimate the material is usually driven 1/3 above ground, 2/3 below ground. Taller sheet pile walls will 27

need a tie-back anchor placed in the soil a distance behind the face of the wall that is tied to the wall, usually by a cable or a rod. Anchors are then placed behind the potential failure plane in the soil.

Fig. 6.1.4 Piling Wall

6.1.5 ANCHORED RETAINING WALL An anchored retaining wall can be constructed in any of the aforementioned styles but also includes additional strength using cables or other stays anchored in the rock or soil behind it. Usually driven into the material with boring, anchors are then expanded at the end of the cable, by mechanical means. This method is very useful where high loads are expected, or where the wall itself has to be slender.

Fig. 6.1.5 Anchored Retaining Wall

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7. TESTS CONDUCTED TO EVALUATE SOIL PROPERTIES The following tests have been conducted in order to evaluate the given soil properties. 7.1 Standard Compaction Test 7.2 Direct Shear Test 7.3 Unconfined Compression Test

7.1 STANDARD COMPACTION TEST

Purpose: This laboratory test is performed to determine the relationship between the moisture content and the dry density of a soil compacted in a mould of given size.

Significance: Mechanical compaction is one of the most common and cost effective means of stabilizing soils. An extremely important task of geotechnical engineers is the performance and analysis of field control tests to assure that compacted fills are meeting the prescribed design specifications. Design specifications usually state the required density (as a percentage of the “maximum” density measured in a standard laboratory test), and the water content. In general, most engineering properties, such as the strength, stiffness, resistance to shrinkage and imperviousness of the soil, will improve by increasing the soil density. The optimum water content is the water content that results in the greatest density for a specified compactive effort. Compacting at water contents higher than (wet of) the optimum water content results in a relatively dispersed soil structure (parallel particle orientations) that is weaker, more ductile, less pervious, softer, more susceptible to shrinking, and less susceptible to swelling than soil compacted dry of optimum to the same density. The soil compacted lower than (dry of) the optimum water content typically results in a flocculated soil structure (random particle orientations) that has the opposite characteristics of the soil compacted wet of the optimum water content to the same density.

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Equipment: 1. Proctor mould having a capacity of 944cc with an internal diameter of 100mm and effective height of 127.3mm. The mould shall have a detachable collar assembly and a detachable base plate. 2. Rammer 3. Sample extruder 4. Straight edge 5. Graduated cylinder 6. Mixing tools such as mixing pan, spoon, spatula, etc. 7. Moisture tins

Fig. 7.1.1 Compaction Mould and Rammer

Procedure: 1. About 3kg of air-dried, pulverized soil ing 4.75mm sieve is taken. Thoroughly mix the sample with sufficient water to dampen it. 2. The mould is cleaned, dried and greased lightly. 3. The mass of the empty mould with the base plate, without collar, is taken. 4. The collar is then fitted to the mould.

30

5. The mould is placed on a solid base and filled with fully matured soil to about one-third its height. 6. The soil is compacted by 25 blows of the rammer, weighing 2.6kg, with a free fall of 310mm. 7. The blows are evenly distributed over the surface. The soil surface is scratched with a spatula before the second layer is placed. 8. The mould is fitted to about two-thirds height with the soil and compacted again by 25 blows. 9. Likewise, the third layer is placed and compacted. 10. The third layer should project above the top of the mould into the collar by not more than 6mm. 11. The collar is rotated to break the bond between the soil in the mould and that in collar. 12. The collar is then removed, and the soil is trimmed off flush with the top of the mould. 13. The mass of the mould, base plate and compacted soil is taken and thus the mass of compacted soil is determined. 14. The bulk density of the soil is computed from the mass of the compacted soil and the volume of the mould. 15. Representative soil samples are taken from the bottom, middle and top of the mould for determining the water content. 16. The soil is removed from the mould. 17. More water is added to the soil so as to increase the water content 2-3%. It is thoroughly mixed and allowed to mature. 18. The test is repeated and the dry density and water content are determined. 19. Continue this series of determination until there is either a decrease or no change in the wet unit weight of compacted soil.

31

Fig. 7.1.2Compacting the soil sample

Fig. 7.1.3 Scraping

32

Analysis: 1. Calculate the moisture content of each compacted soil specimen. 2. Compute the wet density in grams per cm3 of the compacted soil sample by dividing the wet mass by the volume of the mold used. 3. Compute the dry density using the wet density and the water content determined in step 1. Use the following formula:

γd= γ / (1+w) Where w = moisture content in percent divided by 100, and ρ = wet density

Formulae: Wet density (gm/cc) = weight of compacted soil/944 Dry density = Wet density/ (1+w) Where “w” is the moisture content of the soil.

Observations: Diameter of the cylinder = 10 cm Height of the cylinder = 12 cm Volume of the cylinder = 944 cc Weight of the empty cylinder = 2219 gm

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TABLE.NO.1 : STANDARD COMPACTION TEST READINGS

Details

1

2

3

Water to be added (%)

8

10

12

Weight of water to be added (gm)

240

300

360

Weight of cylinder + compacted

4151.36

4250.48

4294.85

Weight of compacted soil (gm)

1932.36

2031.48

2075.86

Container No.

6

12

14

Weight of Container + wet soil

99

105

98

Weight of container + dry soil (gm)

94

100

92

Weight of empty container (gm)

49

52

48

Water content (%)

6.8

9.2

12.8

Wet density (gm/cc)

2.047

2.152

2.199

Dry density (gm/cc)

1.915

1.97

1.949

soil(gm)

(gm)

34

Calculations: 1. For 8% water, Wet density = Weight of compacted soil / 944 = 1932.36/944 = 2.047 gm/cc Dry density = Wet density / (1+w) = 2.047 / (1+0.068) = 1.915 gm/cc 2. For 10% water, Wet density = Weight of compacted soil / 944 = 2031.48 /944 = 2.152 gm/cc Dry density = Wet density / (1+w) = 2.152 / (1+0.092) = 1.97 gm/cc 3. For 12% water, Wet density = Weight of compacted soil / 944 = 2075.86/944 = 2.199 gm/cc Dry density = Wet density / (1+w) = 2.199 / (1+0.128) = 1.949 gm/cc

35

Graph 1: 1. Plot the dry density values on the y-axis and the moisture contents on the x-axis. 2. Draw a smooth curve connecting the plotted points.

Fig Graph showing the variation of moisture content and dry density in compaction test

Result: From the graph, Maximum Dry Density of the Moorum soil = 1.97 gm/cc 36

Optimum Moisture Content = 10.8 %

7.2 DIRECT SHEAR TEST Purpose: This test is performed to determine the consolidated-drained shear strength of the given soil. The shear strength is one of the most important engineering properties of a soil, because it is required whenever a structure is dependent on the soil’s shearing resistance. The shear strength is needed for engineering situations such as determining the stability of slopes or cuts, finding the bearing capacity for foundations, and calculating the pressure exerted by a soil on a retaining wall.

Fig.7.2.1 Direct Shear Apparatus

Significance:

37

The direct shear test is one of the oldest strength tests for soils. In this laboratory, a direct shear device will be used to determine the shear strength of a soil (i.e. angle of internal friction (φ)). From the plot of the shear stress versus the horizontal displacement, the maximum shear stress is obtained for a specific vertical confining stress. After the experiment is run several times for various vertical-confining stresses, a plot of the maxi mum shear stresses versus the vertical (normal) confining stresses for each of the tests is produced. From the plot, a straight-line approximation of the Mohr-Coulomb failure envelope curve can be drawn and φ is determined.

Equipment: 1. Direct shear device 2. Load and deformation dial gauges 3. Balance 4. Spatula

Fig. 7.2.2Components of Direct Shear Mould

Procedure: 1. A soil specimen of size 60x60x25 mm is taken. 2. The base plate is attached to the lower half of the box. A porous stone is placed in the box. 38

3. The upper grid, porous stone and the pressure pad are placed on the specimen. 4. The box is placed inside the large container and mounted on the loading frame. 5. The upper half of the box is brought in with the proving ring. 6. The loading yoke is mounted on the steel ball placed on the pressure pad. 7. The dial gauge is fitted to the container to give the shear displacement. 8. The other dial gauge is mounted on the loading yoke to record the vertical movement. 9. The locking pins are removed and the upper half of the box is slightly raised with the help of spacing screws. 10. The space between two halves is adjusted, depending upon the maximum particle size. 11. The normal load is applied to give a normal stress of 25kN/m2. 12. Shear load is then applied at a constant rate of strain. For undrained tests, the rate is generally between 1.0 mm to 2.0 mm per minute. 13. The sample shears along the horizontal plane between the two halves. 14. The readings of the proving ring and the dial gauge are taken every 30 seconds. 15. The test is continued till the specimen fails. The failure is indicated when the proving ring dial gauge begins to recede after having reached the maximum. 16. At the end of the test, the specimen is removed from the box and its water content is found. 17. The test is repeated under the normal stress of 50,100, 200 and 400 kN/m2. The range of the normal stress should cover the range of loading in the field problem for which the shear parameters are required. 18. Readings are noted down carefully. Set the dial gauges zero, before starting the experiment.

Mechanism: 1. The direct shear test uses a box split into top and bottom halves. 2. The bottom half is fixed while the top half can slide. 3. A constant normal force P is applied to the top of the box while a shearing force T is gradually applied to one side. 4. As the shear force increases, the lateral displacement is measured.

39

5. The normal force divided by the cross sectional area of the box is the normal stress and the shear force T divided by the area is the shear stress.

Fig. 7.2.3Components of Direct Shear Apparatus

Fig.7.2.4 Proving Ring

40

Fig.7.2.5 Load applied on Soil Sample

Analysis: 1. Calculate the density of the soil sample from the mass of soil and volume of the shear box. 2. Convert the dial readings to the appropriate length and load units and enter the values on the data sheet in the correct locations. Compute the sample area A, and the vertical (Normal) stress sv. sv=Nv/A Where Nv = normal vertical force, and sv = normal vertical stress 3. Calculate shear stress (t) using t = Fh / A Where Fh= shear stress (measured with shear load gage) 4. Plot the horizontal shear stress (t) versus horizontal (lateral) displacement (∆H). 5. Calculate the maximum shear stress for each test. 6. Plot the value of the maximum shear stress versus the corresponding vertical stress for each test, and determine the angle of internal friction (φ) from the slope of the approximated Mohr-Coulomb failure envelope. 41

Fig.7.2.6 Sample conditions before and after the test

Formulae: Shear stress = (Proving Ring Reading * calibration) / area of container 1 division of proving ring reading= 0.3797 kg

Observations: Dimensions of shear box = 6x6 cm

42

TABLE.NO.2: DIRECT SHEAR TEST READINGS

S. No.

Normal

load Normal stress Proving (kg/cm2)

(kg)

reading

ring Shear stress (kg/ cm2) (proving ring reading x calibration/ area of container)

1.

0.5

0.5

6.4

0.33

2.

1

1

14.4

0.78

3.

1.5

1.5

18.8

1.03

Calculations: Maximum Dry Density, γd = 1.97 gm/cc Optimum moisture content = 11% Volume of the mould, V = 6*6*2.5 = 90 cc 1.97= weight/ 90 Weight of sample to be taken = 1.97*90 = 178.3 gm Water to be added = 178.3 * 0.11 = 19.6 ≈ 20 ml (1) Normal stress = 0.5 kg/cm2 Proving ring reading = 6.4 = (6*5) + 4 = 34 Area of mould = 6*6 = 36 cm2

43

Shear stress (τ1) = (34*0.3797)/36 = 0.33 kg/cm2 (2) Normal stress = 1 kg/cm2 Proving ring reading = 13.6 = (13*5) + 6 = 71 Area of mould = 6*6 = 36 cm2 Shear stress (τ2) = (71*0.3797)/36 = 0.75 kg/cm2 (3) Normal stress = 1.5 kg/cm2 Proving ring reading = 18.8 = (18*5) + 8 = 98 Area of mould = 6*6 = 36 cm2 Shear stress (τ3) = (98*0.3797)/36 = 1.03 kg/cm2

44

Graph 2:

Fig: ; Graph showing variation of normal load and shear stress in direct shear test.

Result: Shear strength of the given soil sample is 0.03 kg/ cm2

45

7.3 UNCONFINED COMPRESSIVE STRENGTH TEST

Purpose: The primary purpose of this test is to determine the unconfined compressive strength, which is then used to calculate the unconsolidated undrained shear strength of the clay under unconfined conditions. According to the ASTM standard, the unconfined compressive strength (qu) is defined as the compressive stress at which an unconfined cylindrical specimen of soil will fail in a simple compression test.

Significance: For soils, the undrained shear strength (su) is necessary for the determination of the bearing capacity of foundations, dams, etc. The undrained shear strength (su) of clays is commonly determined from an unconfined compression test. The undrained shear strength (su) of a cohesive soil is equal to one-half the unconfined compressive strength (qu) when the soil is under the φ = 0 condition (φ = the angle of internal friction). The most critical condition for the soil usually occurs immediately after construction, which represents undrained conditions, when the undrained shear strength is basically equal to the cohesion (c).This is expressed as: Su = c = qu/2 Then, as time es, the pore water in the soil slowly dissipates, and the Inter-granular stress increases, so that the drained shear strength (s), given by s = c + s’tanφ , must be used. Where s’ = inter-granular pressure acting perpendicular to the shear plane; and s’ = (s - u), s = total pressure, and u = pore water pressure; c’ is drained shear strength parameter.

Equipment: 1. Compression device 2. Load and deformation dial gauges 3. Sample trimming equipment 4. Balance 46

5. Moisture can.

Fig.7.3.1 Unconfined Compression Test Apparatus

Procedure: 1. Sample is prepared at the desired water content and dry density. 2. It is compacted in three layers in a cylindrical tube of standard dimensions. 3. In this type of unconfined compression testing machine, a proving ring is used to measure the compressive force. 4. There are two plate, having cone seating for the specimen. 5. The specimen is placed on the bottom plate so that it makes with the upper plate. 6. The dial gauge and proving ring are set to zero. 7. Compressive load is applied to the specimen by turning the handle. 8. As the handle is turned, the upper plate moves downward and causes compression. 9. The handle is turned gradually so as to produce an axial strain of ½ % to 2 % per minute. 10. The shearing is continued till the specimen fails.

47

11. The compressive force is determined from proving ring reading and axial strain from dial gauge reading.

Fig.7.3.2 Sample Extractor

48

Fig. 7.3.3Cylindrical Mould

Fig.7.3.4 Extracted soil sample

49

Analysis: 1. Convert the dial readings to the appropriate load and length units, and enter these values on the data sheet in the deformation and total load columns. (Confirm that the conversion is done correctly, particularly proving dial gage readings conversion into load) 2. Compute the sample cross-sectional area A0 = π d2/4 3. Compute the strain, e =∆ L / L0 4. Computed the corrected area, A' = A0 / (1- e) 5. Using A’, compute the specimen stress, sc = P/ A’ (Be careful with unit conversions and use constant units). 6. Compute the water content, w%. 7. Plot the stress versus strain. Show qu as the peak stress of the test. Be sure that the strain is plotted on the abscissa. 8. Draw Mohr’s circle using qu from the last step and show the undrained shear strength, su = c (or cohesion) = qu/2.

Fig. 7.3.5 Load applied on soil specimen

50

Fig.7.3.6 Soil Specimen after failure

Formulae: •

1 Proving Ring Reading = 0.3839 kg

•

Strain = (Compression Dial Reading) / Initial Height of sample

•

Axial load = Calibration x 1 Proving Ring Reading

•

Compressive stress = (Axial load/Area)

Observations: Diameter of the sample = 3.8 cm Initial height of the sample = 7.8 cm Area of cross-section = 11.34 cm2

51

TABLE.NO.3: UNCONFINED COMPRESSION TEST READINGS Compression Strain Area dial reading

c

(mm)

Proving

Axial

A/(1-c )

ring

(kg)

(cm2)

reading

2

load Compressive stress (kg/cm2 )

(div) 50

0.641

11.413

0.7

0.26873

0.02354

100

1.282

11.487

0.8

0.30712

0.02673

150

1.923

11.562

1.8

4.9907

0.4316

200

2.564

11.638

2.6

6.1424

0.5277

250

3.205

11.715

3.3

6.9102

0.5898

300

3.846

11.79

3.6

8.0619

0.6837

350

4.487

11.872

4.4

9.2136

0.776

400

5.128

11.95

5.4

11.1331

0.9316

450

5.769

12.034

5.6

11.9009

0.9888

500

6.41

12.11

6.2

12.2848

1.0144

550

7.051

12.2

6.6

13.8204

1.1328

600

7.692

12.28

7.2

14.2043

1.1567

650

8.33

12.37

7.7

16.1238

1.3034

52

Calculations: Maximum Dry Density, γd = 1.97 gm/cc Optimum moisture content = 11% Cross-sectional Area of sample = (π*d2)/4 = (π*3.82)/4 = 11.34 cm2 Volume of the sample = ((π*d2)/4)*h = ((π*3.82)/4)*7.8 = 11.34*7.8 = 88.46 cm3 Density = weight / volume 1.97 = weight / 88.46 Weight of sample to be taken = 1.97*88.46 = 175 gm Water to be added = 175 * 0.11 = 19.36 ≈ 20 ml

Result: •

Maximum unconfined compressive strength of given soil (qu ) = 1.303 kg/cm2

•

Shear strength of given soil (qu/2) = 0.6515 kg/cm2

53

8. ESTIMATION OF SAFE BEARING CAPACITY Foundation is that part of the structure which is in direct with soil. Foundation transfers the forces and moments from the super structure to the soil below such that the stresses in soil are within permissible limits and it provides stability against sliding and overturning to the super structure. It is a transition between the super structure and foundation soil. The job of a geotechnical engineer is to ensure that both foundation and soil below are safe against failure and do not experience excessive settlement. Footing and foundation are synonymous.

Bearing capacity is the power of foundation soil to hold the forces from the superstructure without undergoing shear failure or excessive settlement. Foundation soil is that portion of ground which is subjected to additional stresses when foundation and superstructure are constructed on the ground. The following are a few important terminologies related to bearing capacity of soil.

Super Structure

Ground Level

Foundation

Foundation Soil

Fig. 8.1 Main components of a structure including soil

54

8.1 Factors influencing Bearing Capacity Bearing capacity of soil depends on many factors. The following are some important ones. 1. Type of soil 2. Unit weight of soil 3. Surcharge load 4. Depth of foundation 5. Mode of failure 6. Size of footing 7. Shape of footing 8. Depth of water table 9. Eccentricity in footing load 10. Inclination of footing load 11. Inclination of ground 12. Inclination of base of foundation

8.2 Terzaghi’s bearing Capacity Theory Terzaghi (1943) was the first to propose a comprehensive theory for evaluating the safe bearing capacity of shallow foundation with rough base.

8.2.1 Assumptions 1. Soil is homogeneous and Isotropic. 2. The shear strength of soil is represented by Mohr Coulombs Criteria. 3. The footing is of strip footing type with rough base. It is essentially a two dimensional plane strain problem. 4. Elastic zone has straight boundaries inclined at an angle equal to Φ to the horizontal. 5. Failure zone is not extended above, beyond the base of the footing. Shear resistance of soil above the base of footing is neglected. 55

6. Method of superposition is valid. 7. ive pressure force has three components (PPC produced by cohesion, PPq produced by surcharge and PPγ produced by weight of shear zone). 8. Effect of water table is neglected. 9. Footing carries concentric and vertical loads. 10. Footing and ground are horizontal. 11. Limit equilibrium is reached simultaneously at all points. Complete shear failure is mobilized at all points at the same time. 12. The properties of foundation soil do not change during the shear failure

8.2.2 Limitations 1. The theory is applicable to shallow foundations 2. As the soil compresses, Φ increases which is not considered. Hence fully plastic zone may not develop at the assumed Φ. 3. All points need not experience limit equilibrium condition at different loads. 4. Method of superstition is not acceptable in plastic conditions as the ground is near failure zone.

56

Fig. 8.2.2 : Terzaghi’s concept of Footing with five distinct failure zones in foundation soil

8.2.3 Concept A strip footing of width B gradually compresses the foundation soil underneath due to the vertical load from superstructure. Let qf be the final load at which the foundation soil experiences failure due to the mobilization of plastic equilibrium. The foundation soil fails along the composite failure surface and the region is divided in to five zones, Zone 1 which is elastic, two numbers of Zone 2 which are the zones of radial shear and two zones of Zone 3 which are the zones of linear shear. Considering horizontal force equilibrium and incorporating empirical relation, the equation for ultimate bearing capacity is obtained as follows. Ultimate bearing capacity, q f = cN c + γDN q + 0.5γBN γ If the ground is subjected to additional surcharge load q, then q f = cN c + (γD + q) N q + 0.5γBN γ

57

Net ultimate bearing capacity, q n = cN c + γDN q + 0.5γBN γ − γD q n = cN c + γD ( N q − 1) + 0.5γBN γ

[

Safe bearing capacity, qs = cNc + γD( N q − 1) + 0.5γBNγ

] F1 + γD

Here, F = Factor of safety (usually 3) c = cohesion γ = unit weight of soil D = Depth of foundation q = Surcharge at the ground level B = Width of foundation Nc, Nq, Nγ = Bearing Capacity factors

“Net safe bearing capacity” is the net soil pressure which can be safely applied to the soil considering only shear failure. It is obtained by dividing the net ultimate bearing capacity by a suitable factor of safety. qns

=

qnu / F

Net ultimate bearing capacity is the net increase in pressure at the base pf the foundation that causes shear failure of the soil. It is equal to gross pressure minus overburden pressure. qnu = qu - γDf

58

TABLE NO.4 BEARING CAPACITY FACTORS FOR DIFFERENT Φ ϕ

Nc

Nq

Ng

N'c

N'q

N'g

0

5.7

1.0

0.0

5.7

1.0

0.0

5

7.3

1.6

0.5

6.7

1.4

0.2

10

9.6

2.7

1.2

8.0

1.9

0.5

15

12.9

4.4

2.5

9.7

2.7

0.9

20

17.7

7.4

5.0

11.8

3.9

1.7

25

25.1

12.7

9.7

14.8

5.6

3.2

30

37.2

22.5

19.7

19.0

8.3

5.7

34

52.6

36.5

35.0

23.7

11.7

9.0

35

57.8

41.4

42.4

25.2

12.6

10.1

40

95.7

81.3

100.4

34.9

20.5

18.8

45

172.3

173.3

297.5

51.2

35.1

37.7

48

258.3

287.9

780.1

66.8

50.5

60.4

50

347.6

415.1

1153.2

81.3

65.6

87.1

59

\

Fig. 8.2.3 : Terzaghi’s Bearing Capacity Factors for different φ

8.3 Effect of shape of Foundation

The shape of footing influences the bearing capacity. Terzaghi and other contributors have suggested the correction to the bearing capacity equation for shapes other than strip footing based on their experimental findings. The following are the corrections for circular, square and rectangular footings. Circular footing q f = 1 .3cN c + γ DN q + 0 .3γ BN γ

60

Square footing q f = 1.3cN c + γDN q + 0.4γBN γ

Rectangular footing

B B q f = (1 + 0.3 )cN c + γDN q + (1 − 0.2 )0.5γBN γ L L

8.4 Summary of Shape factors Table 7.2 gives the summary of shape factors suggested for strip, square, circular and rectangular footings. B and L represent the width and length respectively of rectangular footing such that B < L.

Table 7.3 : Shape factors for different shapes of footing Shape

sc

sq

sγ

1

1

1

Square

1.3

1

0.8

Round

1.3

1

0.6

B (1 + 0.3 ) L

1

B (1 − 0.2 ) L

Strip

Rectangle

8.5 Calculation of safe bearing capacity •

For a square footing, qu = 1.2 c Nc + q Nq + 0.4 γ B Nγ Nc , Nq, Nγ are bearing capacity factors. 61

Nq

=

a

=

Nc

=

Nγ

=

Kp

=

e

= coefficient of ive earth pressure.

8.6 Factor of Safety It is the factor of ignorance about the soil under consideration. It depends on many factors such as, 1. Type of soil 2. Method of exploration 3. Level of Uncertainty in Soil Strength 4. Importance of structure and consequences of failure 5. Likelihood of design load occurrence, etc. Assume a factor of safety F = 3, unless otherwise specified for bearing capacity problems.

62

From direct shear test graph, Cohesion, c = 300 kg/ m2 Angle of shear resistance Ø= 330 49’ For Ø= 330 49’ Nc = 52.6 Nq = 36.5 Nγ = 30.0

Result Ultimate bearing capacity, qu = 202.18 t/ m2 Net ultimate bearing capacity, qnu = 198 t/ m2 Net safe bearing capacity, qns = 198/3 = 66.06 t/ m2

63

9. DESIGN CONSIDERATIONS FOR RETAINING WALLS 9.1 WALL DEFORMATIONS AND EARTH PRESSURES Earth pressures are a function of both the type and magnitude of wall deformations. In cohesion less soils, deflections of the order of 0.001H and 0.05H are required to develop active and ive pressure, respectively, and the order of0.04H to develop active pressure in cohesive soils. Deflections needed to develop ive pressure in cohesive soils are not exactly defined. Most retaining walls of the gravity type are normally designed for active pressure. However, certain categories of retaining walls are restrained at the top and are not free to tilt, as for example, basement walls restrained by floor slabs and bridge abutments restrained by the deck structure. In such cases, the earth pressure at rest should be used in the design. Compacting of a backfill against a rigid wall will result in an increase in the K0 value. In the design of a gravity wall, the ive resistance in front of the toe is usually ignored unless the wall base is founded at a considerable depth below grade level.

9.2 BACKFILL MATERIAL Wherever there is a choice, clean, granular backfill material should be preferred because the computed active earth pressures are more reliable in such cases and there is less likelihood of hydrostatic pressure build-up under adequate provision of drainage. Some forms of filter material should be used just behind a retaining wall to preclude pore water pressure development within the backfill. The water collecting in the filter is led away weep holes which are provided within the section of the retaining wall. It may be noted that when the nature of backfill changes from a free drainage to one having water table at the top of the wall, the lateral pressure will more than double. Even a change from a simple ‘wet’ condition to a fully saturated condition may increase the lateral pressure by 20 to 30 percent. Hence, it is much more desirable to provide suitable drainage than to design a retaining wall for the larger pressure which will be induced if the backfill does not readily drain. Clay backfills should be avoided as far as possible, essentially because they are susceptible to swelling and shrinkage during rainy and summer seasons, respectively. Swelling is 64

likely to cause unpredictable earth pressures and wall movements while shrinkage may lead to tension cracks in soil. The cracks may subsequently get filled with water, adding considerably to the lateral pressure.

9.3 GRAVITY RETAINING WALLS As in design of all other structures, a trial section is first chosen and analyzed. If the stability checks yield unsatisfactory results, the section is changed, and rechecked. Figure shows the general proportions of a gravity retaining wall of overall height H. the top width of the stem should be at least 0.3m for proper placement of the concrete in the stem. The depth, D, of the foundation below the soil surface should be at least 0.6m. The base width of the soil is generally between 0.5H to 0.7H; with an average height of 2H/3.

Fig.9.3.1 Gravity Retaining wall

65

The earth pressure can be computed using Rankine’s theory or Coulomb’s theory. For using Rankine’s theory a vertical line AB is drawn through the heel point A. it is assumed that Rankine active condition exist along vertical line AB. However, the assumption for the development of Rankine’s conditions along AB is theoretically justified only if the shear zone bounded by the line AC is not obstructed by the stem of the wall, where AC makes an angle η with the vertical, given by η= (450 + i/2) - φl/2 - sin-1(sin i/ sin φl) where i is the angle of surcharge. The angle α which the line AC makes with the horizontal is given by, α= (450+ φl/2) – i/2 + sin-1(sin i/ sin φl) when i=0, the value of α is equal to (450+ φl/2) While checking the stability, the weight of soil (Ws) above the heel in the zone ABC should also be taken into consideration, in addition to the earth pressure on the back face (Pa), the forces to be considered are only Pa (coulomb) and the weight of the wall (Wc). In this case, the weight of the soil (Ws) is not to be considered separately. Once the forces acting on the wall have been determined, the stability is checked using the procedure shown in the preceding section. For convenience, the section of the retaining wall is divided into rectangles and triangles for the computation of weight and determination of the line of action of the weights.

9.4 DESIGN The earth pressure is computed using Rankine’s theory on the vertical plane AB, provided the shear zone bounded by the line AC is not obstructed by the stem of the wall. The line AC makes an angle η with the vertical given by the equation, η= (450 + i/2) - φl/2 - sin-1(sin i/ sin φl) Figure below shows the forces acting on the wall. The Rankine pressure Pa acts at an angle i with the horizontal. It is resolved into vertical and horizontal components Pv and Ph, as shown. The 66

ive pressure Pp is generally neglected. For convenience, the weight of soil (Ws) over the slab is divided into two parts. Likewise, the weight of stem is divided into two parts. a) Factor of safety against sliding The factor of safety against sliding may be expressed as Fs = Σ FR /Σ Fd Where Σ FR =sum of the horizontal resisting forces, and Σ Fd =sum of horizontal driving forces hence the final equation is, Fs= ((ΣV) tan φ2 + bc2 + Pp) / (Ph) where b = base width, ΣV = sum of all vertical forces; Wc, Ws, Pv Pv = Pa sini, Ph = Pa cosi Pp = ive force in the front of the wall = ½ Kp2γ2D2 + 2c2 Kp21/2 D where c2, γ2 and φ2 are parameters of the foundation soil. The factor of safety can also be determined from the equation Fs = µRV / RH Where RV and RH are vertical and horizontal reaction forces µ = coefficient of friction between base of the wall and the soil = tan 2φ/3 A minimum factor of safety of 1.5 against sliding is generally recommended.

67

b) Factor of safety against overturning The wall must be safe against overturning about toe. The factor of safety against overturning is given by F0 = ΣMR / ΣM0 Where ΣMR = sum of the resisting moments about toe, ΣM0 = sum of the overturning moments about toe. The only overturning force is Ph, acting at a height of H/3 M0 = Ph * H/3 The resisting moments (MR) are due to weights of the soil and the concrete. The vertical components of pressure Pv also helps in resisting moment. Its resisting moment is given by Mv = Pv * b The factor of safety against overturning is usually kept between 1.5 and 2. c) Factor of safety against bearing capacity failure The sum of vertical forces acting on the base is equal to ΣV. The horizontal force is Ph. the resultant force(R) is given by R = ((ΣV)2 + (Ph)2)0.5 The net moment of these forces about toe B is given by ΣM = ΣMR – ΣM0 The distance xl of the point E, from the toe, where R strikes the base is given by xl= ΣM / ΣV hence, the eccentricity e of R is given by

68

e = b/2 - xl if e > b/6, the section should be changed as it indicates tension. The pressure distribution under the base slab is determined as Pmax = (ΣV/b) * (1+ (6e/b)) Pmin = (ΣV/b) * (1- (6e/b)) The factor of safety against bearing failure is given by Fb = qna / Pmax Where qna= allowable bearing pressure. Generally, a factor of safety of 3 is usually specified, provided the settlement is also within the allowable limit.

69

10.

DESIGN OF THE RETAINING WALL

By considering the above design procedure and keeping in view of soil analysis, the existing section should be modified and reconstructed. The Existing section of Retaining wall is shown in the figure below.

EXISTING SECTION 0.55 m

3.68 m

1m

0.55 m

1.5 m

3.05 m

Fig. 10.1 Existing section of Retaining wall

70

0.5 m

TRIAL SECTION 1

0.55 m

2.245 m

0.5 m

1m

0.5 m

0.5 m 1.6 m

0.5 m

2.6 m

Fig. 10.2 Trial section1

71

TABLE NO. 5 : LOAD DETAILS OF THE TRIAL SECTION 1 s. no

I

Components

Load

Moment Lever arm at sill sill

at Lever arm at floor level

Moment at floor level

Above sill level:-

1

Heel side triangular portion 0.50*0.5*2.245*2.3 1.291

2

0.717

0.926

1.767

2.281

0.275

0.781

1.325

3.763

0

0

1.05

0

Rectangular portion 0.55*2.245*2.3 =

3

2.84

Toe side triangular portion 0.5*0*2.245*2.3 = 0 Total

4.131

1.707

6.044

Below sill level:II 4

Trapezoidal footing a

Rectangular portion 1.05*1*2.3

b

2.415

1.575

3.804

0.633

0.867

0.549

2.99

1.3

3.887

0.5*3.245*2

3.245

2.123

6.89

Total

13.414

Triangular portion 1*0.5*1*2.3

5

Final footing 2.6*0.5*2.3

6

Weight of earth

21.174

72

Check for the stresses at sill level:xl= ΣM / ΣV =1.707/ 4.131 = 0.413 m e = (b / 2) - xl = (1.05/2) – 0.413) = 0.112 m b / 6 = 0.175 m e 3 Thus, safe against bearing failure Where qna = allowable bearing pressure. Check for stresses at foundation level:xl = ΣM / ΣV = 15.13 / 9.283

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= 1.6 e = -((b / 2) - xl) = -((2.6/2) – 1.6) =0.3 b/6 = 2.6/6 =0.433 e 3 Thus, safe against bearing failure Where qna = allowable bearing pressure. Check for sliding failure:Fs = µRV / RH = (0.674*10.169) / 3.245 = 2.11 >1.5 Thus, safe against sliding 74

Where RV and RH are vertical and horizontal reaction forces µ = coefficient of friction between base of the wall and the soil = tan φ (where φ = 340) Check for overturning failure:The wall must be safe against overturning about toe. The factor of safety against overturning is given by F0 = ΣMR / ΣM0 = 14.248 / 6.89 = 2.073> 2 Thus, safe against overturning Where ΣMR = sum of the resisting moments about toe. ΣM0 = sum of the overturning moments about toe.

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TRIAL SECTION 2

0.55m

2.245 m

0.5m

1m

0.5 m

0.25 m 0.7 m

2.5 m

Fig. 10.4 Trial section 2

76

0.5 m

TABLE NO.7 : LOAD DETAILS OF TRIAL SECTION 2 S. no Components

Load

Lever Moment arm at sill sill

at Lever arm at floor level

Moment at floor level

I Above sill level:-

1

Heel side triangular 1.29 portion 0.5*0.5*2.245*2.3= Rectangular portion 2.839 0.55*2.245*2.3 =

2

Total

0.716

0.923

1.66

2.15

0.275

0.78

1.225

3.47

4.129

1.703

5.62

Below sill level:II 4

Trapezoidal footing a

Rectangular portion 1.05*1*2.3

b

2.415

1.475

3.56

0.805

0.716

0.576

2.875

1.25

3.593

0.25*3.245*2

1.6225

2.122

3.44

Total

11.846

Triangular portion 0.7*0.5*1*2.3

5

Final footing 2.5*0.5*2.3

6

Weight of earth

16.789

77

Check for the stresses at sill level:xl = ΣM / ΣV = 1.703/4.129 = 0.412 m e = xl – b/2 = 0.412-(1.05/2) = 0.113 m b / 6 = 1.05/6 =0.175 m e 3 Thus, safe against bearing failure Where qna = allowable bearing pressure.

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Check for stresses at foundation level:xl = ΣM / ΣV =16.789/10.223 =1.642 m e = - ((b / 2) - xl) = - ((2.5/2) – 1.642) =0.392 m b/6 = 2.5/6 = 0.416 e < b/6 Thus, safe against tension Maximum stress, Pmax = (ΣV/b) * (1+ (6e/b)) = (10.223/2.5)*(1+6*0.392/2.5) = 7.93 t/m2 Minimum stress, Pmin = (ΣV/b) * (1- (6e/b)) = (10.223/2.5)*(1-6*0.392/2.5) = 0.24 t/m2 < 53 t/m2 for M20 grade concrete Factor of safety against bearing capacity, Fb = qna / Pmax = (66 / 7.93) = 8.32> 3; safe against bearing failure Where qna = allowable bearing pressure. Check for sliding failure:Fs = µRV / RH

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= (0.674*10.223) /1.6225 = 4.24 >1.5 Thus, safe against sliding Where RV and RH are vertical and horizontal reaction forces µ = coefficient of friction between base of the wall and the soil = tan φ (where φ = 340) Check for overturning failure:The wall must be safe against overturning about toe. The factor of safety against overturning is given by F0 = ΣMR / ΣM0 = 16.78/3.44 = 4.87> 2 Thus, safe against overturning Where ΣMR = sum of the resisting moments about toe ΣM0 = sum of the overturning moments about toe

80

TRIAL SECTION 3 0.55m

2.245 m

0.5 m 1m 0.25 m

0.4m 0.7 m

2.4 m

Fig. 10.3 Trial Section 3

81

0.5 m

TABLE NO.6 : LOAD DETAILS OF TRIAL SECTION 3 s. no

Components

Load

Moment Lever arm at sill sill

at Lever arm at floor level

Moment at floor level

I Above sill level:1

2

Heel side triangular portion 0.5*0.5*2.245*2.3 1.29 = Rectangular portion

0.716

0.923

1.66

2.15

0.55*2.245*2.3 =

2.839

0.275

0.78

1.225

3.47

Total

4.129

1.703

5.62

Below sill level:II 4

Trapezoidal footing a

Rectangular portion 1.05*1*2.3

b

2.415

1.475

3.562

0.805

0.716

0.576

2.76

1.2

3.312

0.25*3.245*2

1.622

2.123

3.44

Total

11.731

Triangular portion 0.5*0.7*1*2.3

5

Final footing 2.4 *0.5*2.3

6

Weight of earth

16.51

82

Check for the stresses at sill level:xl = ΣM / ΣV = 1.703/4.129 = 0.412 m e = (b / 2) - xl = (1.05/2) – 0.412 = 0.525 – 0.412 = 0.113 m b / 6 = 0.175 m e 3 Thus, safe against bearing failure Where qna = allowable bearing pressure.

83

Check for stresses at foundation level:xl = ΣM / ΣV = 16.512/11.731 = 1.407 m e = -((b / 2) - xl ) = 1.407 – 1.2 =0.207 m b/6 = 2.4/6 = 0.4 m e 3 Thus, safe against bearing failure Where qna = allowable bearing pressure. Check for sliding failure:Fs = µRV / RH

84

= (0.674*10.109)/1.622 = 4.205 >1.5 Thus, safe against sliding Where RV and RH are vertical and horizontal reaction forces µ = coefficient of friction between base of the wall and the soil = tan φ (where φ = 340) Check for overturning failure:The wall must be safe against overturning about toe. The factor of safety against overturning is given by F0 = ΣMR / ΣM0 = 13.07/3.44 = 3.79 > 2 Thus, safe against overturning Where ΣMR = sum of the resisting moments about toe ΣM0 = sum of the overturning moments about toe

85

Result The width of the foundation for the third trial section is less when compared to other two sections. Hence, among the three trial sections, the third trial section is economical.

Fig.10.5 Retaining wall being constructed

86

CONCLUSION The project, deg of retaining wall for a minor bridge is the consequence of prestigious metro rail project. In the construction course of metro railway, a four lane road way has to be extended to six lanes, to avoid the occurrence of traffic problems. The minor bridgein this course also has to be extended. We took existing four lane retaining wall as an example and designed retaining wall for the six lane road way. Each section has been analyzed for failure against sliding, overturning, tension and bearing capacity. After doing trials for many sections, we got a section satisfying all the safety conditions, approximating the standard dimensions of a gravity retaining wall. The location of minor bridge being in rocky strata, with moorum soil, we got a high bearing capacity value. Taking this as a reference, we also designed two economical sectionswith reduced dimensions. Hence, apart from the main modified section other two sections can also be considered to make the project economical, which is the main philosophy behind the project.

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BIBLIOGRAPHY

1. Soil Mechanics and Foundation Engineering by “Dr.K.R.Arora” 2. Irrigation Engineering And Hydraulic Structures by “S.K.Garg” 3. www.nptel.iitm.ac.in 4. www.wikipedia.com 5. www.aboutcivil.com 6. http://elearning.vtu.ac.in 7. http://engineering.sdsu.edu

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