Bridge Substructure Analysis & Design

ABSTRACT

The analysis and design of all the components of even the most simple bridge

type can be a fairly laborious and cumbersome job especially with respect to the various

elements of the bridge substructure. For bridges located on major perennial rivers, resort

will have to be made to deep foundations like wells or pile foundations, the design of

which involves lengthy computational effort. The bridge engineer should be equipped

with a handy computational tool with the help of which he can quickly and reliably

determine the suitability of various layouts and configuration of the sub-structure before

finalizing the most optimum design of the substructure. In this thesis and attempt has

been made to develop a P.C. based software on VB.Net platform for the analysis and

design of substructure for bridges with simply-supported spans. The computer

programme includes the analysis and of wall-type and circular piers and includes the

option for the complete analysis and design of two-types of deep foundations on the basis

of the relevant IS Codes of Practice: Well foundations and pile foundations. The pile

foundations can be analyzed and designed for both river and non-river bridge crossings

and the user is presented the option of two types of piles for use in the foundations:

under-reamed piles particularly for non-river bridge foundations and bored cast-in-situ

circular piles. A noteworthy feature of the program is that lateral load analysis of both

free and fixed-head piles can be carried out by the user in line with the recommendations

of the relevant IS Codes. The user friendly and interactive program assists the user in the

selection of preliminary dimensions of the well foundation, the safety of which is

checked of the elastic state of the soil surrounding the well and at ultimate loads.

Structural design of the critical well components like well curb, steining and well cap is

incorporated in the software. The results for foundation design obtained from the

program have been validated with long-hand calculations present in the Appendix.

CONTENTS

Chapter No. Title Pg. No.

Chapter-1 INTRODUCTION

1.1 Introduction 1

1.2 Objective of the Thesis 3

1.3 Scope of the Work 3

1.4 Organization of the Thesis 3

Chapter-2 PIERS & PIER CAPS

2.1 Introduction 4

2.2 Types of Piers 4

2.3 Procedure for Analysis of Pier 6

2.4 Conclusions 9

Chapter-3 WELL FOUNDATIONS

3.1 Introduction 10

3.2 Types of Well Foundations 10

3.3 Elements of a Well Foundation 12

3.4 Analysis and Design of Well Foundation 14

3.4.1 Determination of Maximum Scour Depth 14

3.4.2 Loads for Well Foundation Design 16

3.4.3 Stability Analysis of Well Foundations 16

3.4.4 Design of Well Curb 21

3.4.5 Design of Well Steining 22

3.4.6 Design of Bottom Plug 23

3.4.7 Design of Well Cap 23

3.5 Conclusions 25

Chapter-4 PILE FOUNDATIONS

4.1 Introduction 26

4.2 Design of Pile Foundations 29

4.2.1 Under-reamed Piles 29

4.2.2 Bored Cast-in-situ Piles 30

4.2.3 Numbers, Spacing and Arrangement of Piles 35

4.2.4 Safe Bearing Capacity of Pile Groups 37

4.2.5 Distribution of load between Vertical Piles of

Pile Group 39

4.2.6 Lateral load analysis of Piles 40

4.2.7 Structural Design of Pile 42

4.2.8 Settlement of Pile Group 44

4.2.9 Design of Pile Cap 46

4.3 Conclusions 48

Chapter-5 SOFTWARE FEATURES

5.1 Introduction 49

5.2 Functions Layout of the Software 49

5.2.1 Selection and Input of Parameters used for

Analysis and Design of Foundations 50

5.2.2 Analysis of Pier 53

5.2.3 Estimation of Scour Depth for Foundation

Design 53

5.2.4 Analysis and Design of Well Foundation 55

5.2.5 Analysis and Design of Pile Foundation 62

5.3. Conclusions 73

Chapter-6 RESULTS AND DISCUSSION

6.1 Introduction 74

6.2 Problem on Well Foundation 74

6.3 Problem on Pile Foundation 103

6.4 Conclusions 128

Chapter-7 CONCLUSIONS

7.1 Conclusions 129

7.2 Scope for Further Work 129

Chapter-8 REFERENCES 130

APPENDIX A SUPPORTING LONG HAND CALCULATIONS FOR THE

ILLUSTRATIVE PROBLEM ON WELL FOUNDATION 132

APPENDIX B SUPPORTING LONG HAND CALCULATIONS FOR THE

ILLUSTRATIVE PROBLEM ON PILE FOUNDATION 164

LIST OF TABLES

Table.

No. Title Pg.No.

2.1 Value of constant K for Pressure Intensity due to Water Current 7

2.2 Permissible Stresses in Concrete 9

3.1 Silt factors for Sandy beds, IRC: 78-20008 15

3.2 Values of the constant Q for square or rectangular wells 20

4.1 Bearing Capacity Factor, 33

4.2 Value of coefficient of horizontal soil stress ( 33

4.3 Safe loads for under-reamed piles 35

4.4 Values of the constant (kN/m3) 41

4.5 Values of the constant K (kN/m2) 41

A-1 Calculation of Maximum Shear forces bearings 141

A-2 Stresses due to horizontal shear force at bearings 141

A-3 Summary of Stresses due to various forces acting on the Pier 142

A-4 Resultant Compressive Stresses at Point “A” & “B” on Pier 143

A-5 Resultant Tensile Stresses at Point “A” & “B” on Pier 143

A-6 Horizontal shear force at bearings & moments at the base of foundation 148

A-7 Seismic moment due of mass of bridge components & Live load 148

B-1 Calculation of Maximum Shear forces at bearings 168

B-2 Stresses due to horizontal shear force at bearings 169

B-3 Summary of Stresses due to various forces acting on the Pier 169

B-4 Resultant Compressive Stresses at “A” & “B” on Pier 170

B-5 Resultant Tensile Stresses at “A” & “B” on Pier 170

B-6 Moment about longitudinal axis in pile cap from the critical section 182

B-7 Calculation of two-way shear force 184

B-8 Calculation of one-way shear force at critical section along L-L axis of

bridge

185

LIST OF FIGURES

Fig.

No. Title Pg. No.

2.1 Typical Shapes of Piers 5

3.1 Different Shapes of Well 11

3.2 Typical Section of Well Foundation 12

4.1 Piles Classification on the basis of load transfer mechanism 26

4.2 Uplift Piles 27

4.3 Use of piles in scourable beds 27

4.4 Piles in expansive soils can control seasonal movements 28

4.5 Free Standing Pile Group 29

4.6 Piled Foundation 29

4.7 Load resisting mechanism in a pile 31

4.8 Bearing Capacity Factor, for bored piles 32

4.9 Adhesion factor for cohesive soils 34

4.10 Typical arrangement of piles in a group 36

4.11 Determination of the depth of fixity of the pile 42

4.12 Reduction factors for free-head and fixed-head piles 43

4.13 Computation of Settlements for End Bearing Piles & Friction Piles 45

4.14 Critical section for moment & one-way shear 47

4.15 Critical section for two-way shear 47

4.16 Typical detailing of reinforcement in a pile cap 47

5.1 Flow Chart of preliminary dimensioning of pier 51

5.2 Flow Chart for Analysis of Pier 52

5.3 Flow Chart for calculation of Maximum Scour Depth 54

5.4 Flow Chart for calculation of soil resistance 56

5.5 Flow Chart for calculation of soil resistance at ultimate loads 58

5.6 Flow Chart for design of Well curb 59

5.7 Flow Chart for design of Well steining 60

5.8 Flow Chart for design of Well Cap 61

5.9 Flow Chart for soil details 63

5.10 Flow Chart for calculating safe bearing Capacity of bored cast-in-situ pile 65

5.11 Flow Chart for calculating safe bearing Capacity of an under-reamed Pile 66

5.12 Flow Chart for calculation of SBC of group of bored cast-in-situ piles 68

5.13 Flow Chart for calculation of SBC of group of under-reamed piles 69

5.14 Lateral load capacity of Under-reamed Pile 70

5.15 Lateral load capacity of Bored Cast-in-situ pile 71

5.16 Design of Pile Cap 72

6.1 Details of Soil layers in Ground 104

A-1 Pier Section in longitudinal direction of bridge 133

A-2 Water Pressure Details 137

A-3 Location of “A” & “B” on pier 142

A-4 Diagram of a Well Foundation 145

A-5 Diagram of Well curb 146

A-6 Diagram of Bottom Plug 146

A-7 Load dispersion area in well cap 158

A-8 Moments in well-cap when freely supported 160

A-9 Moments in well-cap when fully clamped 161

A-10 Reinforcement Details of Well Cap 163

B-1 Pier Section in transverse direction of bridge 164

B-2 Location of “A” & “B” on Pier 170

B-3 Effective overburden pressure on pile 172

B-4 Arrangement of Piles in Foundation 174

B-5 Settlement of End bearing piles 180

B-6 Reinforcement details of Pile Cap 186

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CHAPTER 1

INTRODUCTION

1.1 INTRODUCTION

Thomas B. Macaulay once said: “Of all inventions, the alphabet and the printing press

alone, excepted, those inventions which abridge distance have done the most for the

civilization of our species”. Since ancient times, bridges have been the most visible testimony

to the contribution of engineers. Bridges have always figured prominently in human history.

They enhance the vitalities of the cities and aid the social, cultural and economic

improvements of the locations around them.

Bridge is a structure providing passage over an obstacle without closing the way

beneath. The required passage may be for a road, a railway, pedestrians, a canal or a pipeline

and the obstacle to be crossed may be a river, a road, railways or a valley. The portion of the

bridge structure below the level of the bearing and above the founding level is generally

referred to as the substructure. The design of bridge substructure is an important part of the

overall design for a bridge and affects to a considerable extent the aesthetics, the safety and

the economy of the bridge. Bridge substructure are a very important part of a bridge as it

safely transfers the loads from the superstructure to the earth in such a manner that the

stresses on the soil are not excessive & the resulting deformations are within the acceptable

limits.

The selection of the foundation system for a particular site depends on many

considerations, including the nature of subsoil, location where a bridge is proposed to be

constructed i.e. over a river, road, or a valley, etc. & the scour depth. A bridge may have

either have the following types of foundations:

1. Well foundations: It is the most common type of foundation in India for both road &

railway bridges. Such foundation can be sunk to great depths and can carry very heavy

vertical and lateral loads. Well foundations can also be installed in a boulder stratum. It is a

massive structure and is relatively rigid in its structural behavior.

2. Pile foundations: It consist of relatively long and slender members, called piles which are

used to transfer loads through weak soil or water to deeper soil or rock strata having a high

bearing capacity. They are also used in normal ground conditions for elevated road ways.

The analysis and the design of all the components of a bridge particularly with

reference to the bridge substructure can become a very lengthy and laborious task if the

calculations are attempted manually. A design engineer would like to try various

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configurations, shapes and sizes of the principal components of a bridge before finalizing the

most optimum combination on the basis of safety, economics and aesthetics of the elements

of the super-structure and the sub-structure. At the same time, in spite of the best efforts

during sub-soil investigations, many uncertainties always exist with respect to the sub-soil

conditions which may be encountered at pier and foundation locations. Unexpected sub-soil

conditions may require a significant redesign of the foundation or in extreme cases the

foundation type may have to be changed from for example an open-footing to a pile or a well

foundation. For the above eventualities, it is desirable that a quick, handy and reliable

computational tool should be available to the design engineer for the analyses and design of

bridge sub-structure in general and well and pile foundations in particular.

In this thesis an attempt has been made to develop P.C. software package in the

VB.Net platform for the analysis and design of sub-structures for concrete bridges with

simply supported spans.

Analysis of the super-structure for loads transferred to the sub-structure is included in

the software. Two IRC loading categories: Class AA and Class A are considered for super-

structure analysis. The option for single lane and two lanes of traffic is included. The user is

provided with the option of two types of concrete piers: wall-type and hammer-head type

with a circular shaft. The analysis and design of both these types of piers is included in the

software. In the software, the option is provided for two types of deep foundations: well and

piles. Well foundations are essentially meant for river-bridge crossings where as the option

for pile foundations take care of pile analysis and design for both non-river and river bridge

crossings. The analysis of the well foundation is carried out as per the relevant IRC code for

the resultant axial, lateral loads and moments transferred from the super-structure for the

following two conditions: (1) The soil surrounding the well is in an elastic state (2) At

ultimate load conditions. The program includes check on thickness of the bottom plug and the

analysis and design of the critical components of a well viz. well curb, well steining and well

cap. Practical considerations related to construction of wells are examined through a check on

the sinking effort developed in the well. Two types of piles are available for design of pile

foundations: (1) Under-reamed piles and (2) Bored cast-in-situ circular piles. Under-reamed

piles are essentially meant for non-river bridge crossings and their design for vertical and

lateral loads has been carried out as per recommendations of IS: 2911. The software includes

the analysis and design of both free-head and fixed-head bored cast-in-situ circular piles in

cohesion less as well as cohesive soils. A noteworthy feature of the software is the lateral

load analysis of the pile as per the relevant IS Code. The design of the pile foundation

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concludes with check on group behavior including settlement analysis and structural design

of the pile and the pile cap.

1.2 OBJECTIVE OF THE THESIS

Development of an interactive user-friendly software for the analysis and design of

substructures of RCC bridges with simply supported spans for river as well as non-river

bridge crossings.

1.3 SCOPE OF THE WORK

The analysis of the simply supported super-structure has been carried out for only two

loading classes: Class AA and Class A. Two type of piers are included in the software: wall-

type and hammer-head type with a circular shaft. Besides gravity loads, lateral loads due to

wind, earthquake and hydro-dynamic effect are considered in the analysis. The well

foundation analysis is performed at both elastic and ultimate state. The analysis and design of

pile foundation is restricted to under-reamed and bored cast-in-situ piles in both cohesionless

and cohesive soils for vertical as well as lateral loads. Structural design of piles and pile-cap

is included in the software. The software does not have the option of generating detailing and

working drawings of the bridge sub-structure.

1.4 ORGANIZATION OF THE THESIS

The introduction to the thesis & the scope of present work together with the

organization of thesis is contained in Chapter 1.

Chapter 2 discusses about the piers in substructure. It contains the details &

summarizes the available literature on pier. The steps for analysis for pier are

explained in this chapter.

The knowledge base of well foundation is provided in Chapter 3, following the

procedure for analysis of well foundation & design of various components of the well.

Chapter 4 includes the literature review on pile foundations & discusses the analysis

& design steps of pile foundations.

The features & limitations of the software developed as the part of thesis work are

being explained in Chapter 5. The functioning of various modules of the software are

explained in the form of flow chart, in the same chapter.

The application of the proposed software to the analysis & design of typical well

foundation and pile foundation is presented in Chapter 6.

The conclusions from the present study are discussed in Chapter 7.

References form the last part of this thesis.

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CHAPTER 2

PIERS & PIER CAPS

2.1 INTRODUCTION

Piers are substructures located at the ends of bridge spans at intermediate points

between the abutments. The function of the piers is two-fold: to transfer the superstructure

vertical loads to the foundation and to resist all horizontal and transverse forces acting on the

bridge. Piers are generally constructed of masonry or reinforced concrete. Being one of the

most visible components of a bridge, the piers contribute to the aesthetic appearance of the

structure. They are found in different shapes, depending on the type, size and dimensions of

the superstructure and also on the environment in which the pier is located.

The pier cap (also known as the bridge seat) is the block resting over the top of the

pier or the abutment. It provides the immediate bearing surface for the support of the

superstructure at the pier location, and disperses the strip loads from the bearings to the

substructure more evenly. The pier cap is given an offset of 75 mm beyond the edge of the

pier. This offset prevents rain water from dripping down the sides and ends of the pier and

also improves the appearance of the pier. Minimum thickness provided to the pier cap is 225

mm for spans of up to 25 m, otherwise 300 mm.

2.2 TYPES OF PIERS

Typical shapes of piers commonly used in practice are as shown in Fig. 2.1. They can

be solid, cellular, trestle or hammer-head types. Solid and cellular piers for river bridges are

provided with semicircular cut-waters to facilitate and streamlined flow and to reduce the

scour. Solid piers can be of mass concrete or of masonry for heights of up to 6 m and spans

up to about 20 m. Hammer-head type piers are increasingly used in urban elevated highway

applications, as it provides slender substructure with open and free-flowing perception to the

motorists using the road below. It is also used for river crossings with skew alignment, which

will result in least obstruction to passage of flood below the bridge. Cellular, trestle, hammer-

head types are suitable for heights above 6 m and spans over 20 m. In trestle type piers,

concrete hinges have been recently introduced between the top of column and the bent cap in

order to avoid moment being transferred from deck to the columns. Reinforced concrete

framed types of piers as shown in Fig. 2.1 (e) have also been used in recent years. Such piers

lead to economy in cost of superstructure as it reduces the span length of girders on either

side of pier, but at the same time it will accumulate debris and floating trees from the stream

flow. Two expansion joints formed on each pier will result in riding discomfort.

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(a) Solid Pier

(b) Cellular Type Pier

(c) Trestle R.C. Pier (d) Hammer-head Type Pier

(e) Framed Type Piers

Fig. 2.1 Typical Shapes of Piers

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Minimum top width of pier is kept 600 mm more than the out-to-out dimension of the

bearing plates, measured along the longitudinal axis of the superstructure. Length of pier

should not be less than 1200 mm in excess of the out-to-out dimension of the bearing plates

measured perpendicular to the axis of the superstructure. The bottom width of pier is usually

larger than the top width so as to restrict the net stresses within the permissible values. It is

normally sufficient to provide a batter of 1 in 25 on all sides for the portion of pier between

the bottom of the pier cap and the top of the well or pile cap, as the case may be.

2.3 PROCEDURE FOR ANALYSIS OF PIER

Analysis of pier is carried out considering various forces and loads transmitted from

the superstructure and forces acting directly on the pier. Following are the loads and forces to

be resisted by a pier:

1. Dead load:

Dead load of superstructure and substructure above the base level of pier.

2. Live load:

This consists of Live load of traffic passing over the bridge. Effect of eccentric

loading due to live load should also be considered.

3. Buoyancy:

Buoyancy has the influence of reducing weight. In masonry or concrete structure, the

buoyancy effect through pore pressure may be limited to 15 percent of full buoyancy

on the submerged portion.

4. Wind load:

Wind load is considered on the live load, superstructure and the part of the

substructure above the base of pier or water level, whichever is higher. It acts on the

area of the bridge in elevation and is thus always taken to be acting laterally to the

bridge only. This force could be considered as per recommendations of IS:8752.

5. Horizontal forces due to water current:

Horizontal force due to water current is considered on that part of substructure that

lies between the water level and the base of pier. The water current pressure is given

by Equation 2.1

, (2.1)

where, = intensity of pressure in kN/m2 due to water current,

K = a constant having different values for different shapes of piers.

The values of this constant for different pier shapes are present in

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Table 2.1

V = velocity of current in m/sec at the point where pressure intensity

is being calculated.

It is assumed that the velocity distribution in stream is such that V2

is

maximum at the free surface of water, zero at the deepest scour level and varies

linearly in between them. Also the maximum velocity of flow is assumed to be equal

to times the velocity of the current.

Table 2.1: Value of constant K for Pressure Intensity due to Water Current

SHAPE K – Values

Square ended piers 1.50

Circular piers 0.66

Piers with semi-circular cut-waters 0.66

Piers with triangular cut-waters 0.5 to 0.9

Trestle type piers 1.25

For calculating the pressure on the pier, the angle which the current makes

with the axis of the pier should be taken into account. Generally, the maximum

variation in the angle of water current to the transverse axis of the bridge is taken as

20°. Thus, the pressure along the axis of the pier and transverse to it is respectively

given by,

(2.2)

(2.3)

6. Centrifugal forces:

Centrifugal forces are taken into account, when the bridge is located on a curve.

7. Longitudinal forces:

Longitudinal forces are caused due to tractive effort caused through acceleration of

the driving wheels, braking effect due to application of brakes to the wheels &

frictional resistance offered to the movement of free bearings due to change of

temperature. Braking effect is invariably greater than the tractive effort, and as a

result the tractive effort of vehicles is neglected.

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8. Seismic forces:

Seismic force acts on all loads, which posses mass at their centre of gravity. Seismic

forces acting in horizontal direction, along longitudinal and transverse axis of the

bridge are considered. Forces acting in the vertical directions are comparatively small,

and are hence neglected. During earthquake, water in river will apply hydrodynamic

force on the submerged portion of pier. Seismic forces are considered to act only in

one direction at a time.

All the above loads are classified into different loading cases as discussed below.

1. Normal (N) Case loading: It includes dead load, live load, buoyant force, wind load,

forces due to water current, centrifugal forces, braking force/tractive force &

horizontal shear force at hinge bearings due to the effect of braking force, wind load.

2. Temperature (T) Case loading: It includes loads due to frictional restraint to

temperature movement at bearings.

3. Seismic (S) Case loading: It includes seismic forces acting in horizontal forces

acting in horizontal direction.

Considering the probability of earthquake with other forces, it is generally assumed

that earthquake and wind forces will not occur simultaneously and so only one can be

considered at a time. Taking all the case loading into accounts, pier is analyzed for three

different load combinations: Normal (N) Case, Normal and Temperature (N + T) Case &

Normal, Temperature and Seismic (N + T + S) Case.

Longitudinal forces acting on the bridge like braking effort/tractive effort, frictional

resistance at the bearings and seismic forces acting on live load and bridge superstructure will

produce horizontal shear force at the bearings. The horizontal shear force will be calculated

for different load combinations as discussed above, and later is incorporated into their

respective case of load combinations.

Stresses developed into the pier due to different loads and forces are calculated

individually, and the resultant maximum stress acting on the pier is worked out for different

load combinations. The resultant maximum stress for each load combination should be within

the permissible stress limits. For brick masonry in cement mortar, permissible compressive

stress is 1 MPa and permissible tensile stress is 0.10 MPa. In stone masonry, compressive

stress is limited to 1.5 MPa and tensile stress is limited to 0.10 MPa. Permissible stresses for

concrete are given in Table 21 of IS: 456-20001, for different grades of concrete. Table 2.1

shows the permissible stresses for plain concrete used in bridge analysis and design.

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Table 2.2: Permissible Stresses in Concrete

Grade of

Concrete

Permissible Stresses in Concrete (in MPa)

For Compression For Tension

M 10 2.5 -

M 15 4.0 0.6

M 20 5.0 0.8

M 25 6.0 0.9

M 30 8.0 1.0

M 35 9.0 1.1

M 40 10.0 1.2

M 45 11.0 1.3

M 50 12.0 1.4

IRC: 6-20006 allows the increase in permissible stresses of concrete for different load

combinations. For Normal and Temperature (N + T) case i.e. when the effect of temperature

is considered, permissible stress can be increased by 15 percent. Finally, for Normal,

Temperature and Seismic (N + T + S) case permissible stress can be exceeded by 50%. If the

maximum stresses in piers for the worst loading combination are more than the permissible

stress, it is required to redesign the piers in order to bring maximum stresses within the

permissible limit.

2.4 CONCLUSIONS

The types and the features of piers and pier caps usually employed for bridge

crossings have been briefly discussed together with analysis methodology and permissible

stresses for design.

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CHAPTER 3

WELL FOUNDATIONS

3.1 INTRODUCTION

Well foundations have their origin in India & have been used for hundreds of years

for providing deep foundation to important buildings and bridges. Well foundations were

freely used during the Moghal Period for bridges across the major rivers. Moghal monuments

including Taj Mahal are built on well foundations. Well foundations provide a solid &

massive structure. This foundation has maximum sectional modulus for a given cross-

sectional area. Wells can resist large horizontal forces & vertical loads even when the

unsupported length is large in scourable river beds. A well foundation is monolithic and

relatively rigid in its structural behaviour.

3.2 TYPES OF WELL FOUNDATIONS

Different types of wells in common use are shown in Fig. 3.1 The controlling factors

in selecting the shape of the well foundation are: the base dimensions of pier or abutment, the

ease with which the well can be sunk, cost, considerations of tilt and shift, ease of sinking and

the magnitude of the forces to be resisted by the foundation. Circular wells are used most

commonly and the mains points in their favour are their strength, simplicity in construction

and ease of sinking. However, in terms of the lateral stability for a given cross-sectional area,

circular wells offer the least resistance against tilting when compared with other sections.

Circular wells also suffer from the disadvantage that in the case of large oblong piers, the

diameter of a circular well becomes excessive which renders them uneconomical besides

creating obstruction to the flow of water.

Two or three independent circular, square or rectangular wells in section suitably

connected can be used for supporting long piers. Such wells are called tied wells. Tied wells

of different shapes are preferred to avoid relative tilts between wells. Double-D shaped and

dumb-bell shaped wells are the most commonly used shapes of tied wells. Double octagonal

well is also a monolithic well consisting of two circular dredge holes. On account of its

shape, the flexural stresses developed in the steining are relatively less compared to a double-

D shape. However, sharp corners of double octagonal wells produce grater scour.

Rectangular wells are generally adopted for bridge foundations having shallow depths. They

can be adopted very conveniently where the bridge is designed for open foundations and

change to well foundation becomes necessary during the course of construction on account of

adverse conditions such as excessive inflow of water and silt into the excavation. For piers of

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very large sizes, wells with multiple dredge holes are used. Wells of this type have been used

for the towers of the Howrah Bridge.

(a) Circular well (b) Double-D well

(c) Double octagonal well (d) Double rectangular well

(e) Dumb-bell (f) Rectangular well

(g) Multiple dredge-hole well

Fig. 3.1 Different Shapes of Well

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3.3 ELEMENTS OF A WELL FOUNDATION

A well foundation is a type of foundation which is generally built in parts at the

surface and sunk to its final position, where it forms the permanent foundation. Fig. 3.2

shows a typical section of a circular well foundation.

Fig. 3.2 Typical Section of Well Foundation

(a) Well-cap:

It is a RCC slab laid at the top of the well steining to transmit the loads and moments from

the pier to the well or wells below. Shape of well cap is same as that of well with a possible

overhand of 150 mm all-around to accommodate lengthy piers. It is designed as a two-way

slab with partial fixedity at supports. The top of the well cap is usually kept at the bed level in

case of rivers with seasonal flow or at about the low water level in case of perennial rivers.

Thickness of well cap is usually between 1500 mm to 2000 mm.

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(b) Steining:

It is the main body of the well which transfers load to the base of the foundation. Steining is

normally of reinforced concrete. Minimum grade of concrete used in steining is M20 with

cement content not less than 310 kg/m3. To facilitate well sinking an off-set of 75 mm to 100

mm is provided in well steining at its junction with the well curb.

The thickness of well steining should not be less tan 500 mm nor less than that given

by Eq. 3.1.

(3.1)

where, t = minimum thickness of concrete steining, m,

D = external diameter of circular well or dumb bell shaped well or smaller

plan dimension of twin D well, m,

L = depth of well in m below L.W.L. or top of well cap whichever is greater,

K = a constant depending on the nature of subsoil and steining material (taken

as 0.30 for circular well and 0.039 for twin – D well for concrete steining

in sandy strata and 10% more than the corresponding value in the case of

clayey soil).

(c) Well curb:

It is the wedge shaped RCC ring beam located at the lower portion of the well steining

provided to facilitate sinking. Well curb carries cutting edge for the well and is made up of

reinforced concrete using controlled concrete of grade M25. The cutting edge usually consists

of a mild steel equal angle of side 150 mm. In case blasting in anticipated, the outer face of

the well curb should be protected with 6 mm thick steel plate and the inner face should have

10 mm thick plate up to the top of the curb and 6 mm plate further up to a height of 3 m

above the top of the curb.

(d) Bottom plug:

After the well is sunk to the required depth, the base of the well is plugged with concrete.

This is called the bottom plug. It acts like an inverted dome supported by the steining on all

the sides and transmits the load to the subsoil and acts as a raft against soil pressure from

below. Minimum grade of concrete used in bottom plug is M15. Thickness of bottom plug

should not be less than the half of dredge-hole diameter nor less than the value calculated in

Eq. 3.2.

, (3.2)

where, W = total bearing pressure at the base of well,

14 | P a g e

fc = flexural strength of concrete in bottom plug,

, and,

= Poisson‟s ratio for concrete, 0.18 to 0.20.

(e) Top plug:

The top plug is an unreinforced concrete plug, generally provided with a thickness of about

600 mm beneath the well cap to transmit the loads from the pier to the steining. Minimum

grade of concrete used in top plug is M15.

The space inside the well between the bottom of the top plug and the top of bottom

plug is usually filled with clean sand, so that the stability of the well against overturning is

increased. While this practice is good in case of wells resting on sand or rock, the desirability

of sand filling for wells resting on clayey strata is doubtful, as this increases the load on the

foundation and may lead to greater settlement. In the latter case, the sand filling is done only

for the part of well up to scour level, and remaining portion is left free.

(f) Intermediate plug:

As discussed above, for wells resting on clayey strata, it is not preferable to fill the space

inside the well completely with sand. In such cases, sand filling is not done or sand is filled

up to the scour level. A concrete plug covering the filling is usually provided, known as

intermediate plug. Usually, thickness of intermediate plug is taken as 500 mm.

3.4 ANALYSIS AND DESIGN OF WELL FOUNDATION

In order to design the well foundation, maximum depth of scour should be determined

first since the maximum scour depth decides the depth of the well foundation.

3.4.1 DETERMINATION OF MAXIMUM SCOUR DEPTH

The codes IRC: 78-20008 and IS:3955-1967

5 recommend that the maximum scour

depth in a stream should be ascertained, whenever possible, by actual soundings at or near the

site proposed for the bridge, during or immediately after a flood before the scour holes have

had time to silt up appreciably. In case actual soundings are not possible, depth of scour in

stream can be ascertained using theoretical methods taking into account the velocity of

stream, characteristics of the river bed materials, and many other factors.

The IRC: 78-20008 recommended formula for calculating the mean depth of scour

below High Flood Level (HFL) for natural channels flowing over scourable bed is as follows:

, (3.3)

where, Db = Design discharge per meter width of effective linear waterway, m3/ms,

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= , Q is the design discharge in the stream in m3/s

and

is the linear waterway, m,

Ksf = Silt factor for a representative sample of the bed material obtained up

to the level of the anticipated deepest scour, and,

= 1.76 , dm is the median size of the bed sediments in mm.

Table 3.1 presents the IRC: 78-20008 recommended values of silt factor for various

types of sandy beds for ready reference and adoption.

Table 3.1: Silt factors for Sandy beds, IRC: 78-20008

The normal scour depth for natural streams in alluvial beds can also be calculated

using Lacey‟s formula given below:

, (3.4)

where, d = Normal depth of scour below highest flood level for regime conditions in

a stable channel, m.

Q = Designed discharge, m3/s and,

f = Lacey‟s silt factor for a representative sample of the bed material. This

can be determined from Table 3.1.

The scour depth with maximum value, obtained from any of the formulae as discussed

above will be considered as , the mean scour depth for design of foundation.

As per the recommendations of IRC: 78 – 20008, at the noses of piers, the maximum

depth of scour, dmax, is taken as twice of mean scour depth, .

(3.5)

Type of bed material

Coarse silt

Silt/fine sand

Medium sand

Coarse sand

Fine bajri and sand

Heavy sand

0.04

0.081 to 0.158

0.233 to 0.505

0.725

0.988

1.29 to 2.00

0.35

0.5 to 0.6

0.8 to 1.25

1.5

1.75

2.0 to 2.42

16 | P a g e

The well foundation shall be taken to such a depth that it is safe against scour. Apart

from this, the depth of the well foundation should also be sufficient from considerations of

bearing capacity, settlement stability and suitability of strata at the founding level. Invariably,

the well foundation in all cases shall be taken down to a depth which will provide sufficient

grip. The grip length below the anticipated maximum scour level shall not be less than 1/3rd

the maximum anticipated depth of scour below H.F.L.

3.4.2 LOADS FOR WELL FOUNDATION DESIGN

After determining the depth of the well foundation, the dimensions of well and its

different components are empirically assumed.

The following loads are considered for the analysis and design of well foundation:

1. Dead load

2. Live load

3. Buoyancy

4. Wind load

5. Horizontal force due to water current

6. Centrifugal forces

7. Longitudinal forces

8. Seismic forces

9. Horizontal shear forces at bearings due to longitudinal forces and seismic forces

10. Forces due to tilt and shift.

The loads mentioned above are discussed in Section 2.2 of Chapter 2. These loads are

calculated with respect to the bridge superstructure and substructure and correspondingly, the

total vertical load, the total horizontal forces acting along the longitudinal direction and the

transverse direction of bridge and the moments about the transverse and longitudinal axis of

the bridge are obtained for the design of the well foundation. Moments due to shift and tilt of

wells are also be included in the analysis of the well.

3.4.3 STABILITY ANALYSIS OF WELL FOUNDATIONS

The stability of well foundation under the action of lateral loads, particularly large

magnitudes of seismic forces, depends on the passive resistance of the soil on the sides and

the base of the well. As the lateral load increases for a given magnitude of the vertical load,

the soil deformation increases disproportionately when compared with the deformation at

initial loading. Under the combined action of vertical and lateral loads the mechanism of

sharing the applied loads between the sides and the base of the well also gets significantly

modified. Hence, the behaviour of the soil at ultimate loads is different form that at the elastic

17 | P a g e

stage which is assumed to prevail under vertical loading. The IRC: 45-19727 therefore

specifies two checks, one for soil pressures under working loads and the other for the factor

of safety available with respect to ultimate strength of the surrounding the well.

As per IRC: 45-19727, the resistance of the soil surrounding the well is checked using:

a. Elastic theory

b. Plastic theory (also called as Ultimate Resistance Method)

The following assumptions are made in computing soil pressure using elastic theory:

i. The soil surrounding the well and below the base is perfectly elastic, homogeneous

and obeys Hooke‟s law

ii. Under design loads, the lateral deflections are so small that the unit soil reaction „p‟

increases linearly with increasing lateral deflections „z‟. Hence p = KHz

where, KH is the coefficient of horizontal subgrade reaction at the base.

iii. The coefficient of horizontal subgrade reaction increases linearly with depths in the

case of cohesionless soils.

iv. The well is assumed to be a rigid body, subjected to an external unidirectional

horizontal force „H‟ and moment „M‟ at scour level.

As a consequence of the above assumptions, the pressure distribution is parabolic on the sides

of the well and linear at the base.

The elastic theory gives the soil pressure in the sides and the base of the well under

design loads. However, to determine the actual factor of safety against failure it is necessary

to calculate the ultimate soil resistance which is done by assuming plastic behaviour of the

soil at ultimate loads. For checking the ultimate load capacity of the well foundation, the

applied loads are multiplied by suitable load factors for various load combinations and the

ultimate resistance is reduced by appropriate under-strength factors and the two are then

compared.

A step-wise description of these two methods of analysis of well foundations is given

below:

Both the above methods are applicable if the well foundation is resting on

non-cohesive soil like sand and is surrounded by the same soil below the maximum scour

level.

The above methods should not be used for analysis if the depth of embedment of the well

is less than 0.5 times the width of foundation in the direction of the principal lateral forces.

18 | P a g e

1. ELASTIC THEORY

STEP 1: Determine the values of W, H and M under combination of normal loads

without wind and seismic loads

where, W = total downward load acting at the base of well, including self weight of

well

H = external horizontal force acting on the well at scour level

M = total applied external moment about the base of well, including those

due to tilts and shifts,

STEP 2: Compute and and ;

where, (3.6)

= moment of inertia of base about an axis normal to the direction of

horizontal forces and passing though the C.G. of the well.

= moment of inertia of the projected area in elevation of the soil mass

offering lateral resistance = ;

L = projected width of the soil mass offering lateral resistance multiplied by

the appropriate value of shape the factor. The value of shape factor for

circular wells shall be taken as 0.9. For square or rectangular wells

where the resultant horizontal force acts parallel to the principal axis, the

shape factor shall be unity and where the forces are inclined to the

principal axis, a suitable shape factor based on experimental results is

used.

D = depth of well below scour level,

m = KH/K; Ratio of horizontal to vertical coefficient of sub grade reaction at

base of well. In the absence of values for KH and K determined by field

tests m shall generally be assumed to be unity,

= coefficient of friction between the sides of the well and the soil

= , where δ is the angle of wall friction between well and the soil,

α = for a rectangular well,

= for a circular well.

STEP 3: Ensure the following:

(3.7)

19 | P a g e

(3.8)

where, ,

= coefficient of friction between the base of the and the soil. It

shall be taken as

= angle of internal friction of soil.

STEP 4: Check the elastic state

(3.9)

where, = density of the soil (submerged density to be taken when under water or

below water table)

= passive and active pressure coefficients to be calculated using Coulomb‟s

theory, assuming „δ‟, the angle of wall friction between well and soil to

be equal to , but limited to a value of .

(3.10)

(3.11)

STEP 5: Calculate (3.12)

where, & = maximum and minimum base pressures, respectively,

A = area of the base of well,

B = width of the base of well in the direction of forces and moments,

P = M/r,

STEP 6: Check i.e. no tension, and,

& allowable bearing capacity of soil.

STEP 7: If any of the conditions in Step 3 or Step 4 is not satisfied, then the grip length of

the well may be increased and all the calculations are revised. If the conditions in Step 5 are

not satisfied then, either the grip length of the well or the diameter of the well is increased.

STEP 8: The above steps are repeated for load combinations containing seismic and wind

loads separately.

20 | P a g e

2. ULTIMATE RESISTANCE METHOD

STEP 1: Check that , (3.13)

where, W = total downward load acting at the base of well, taking appropriate load

factors as per the combinations given below:

1.1D

1.1D + B + 1.4(WC + EP + W or S)

1.1D + 1.6L

1.1D + B + 1.4(L + WC + EP)

1.1D + B + 1.25(L + WC + EP + W or S)

where, D = dead load

L = live load including barking load and other forces related to live load

B = Buoyancy

WC = water current force

EP = earth pressure

W = wind force

S = seismic force

A = area of the base of well

= ultimate bearing capacity of soil below the base of well (taking a factor

of safety of 2.5).

STEP 2: Calculate the base resisting moment, Mb, at the base of well using the following

equation:

Mb = QWB , (3.14)

where, B = width, in the case of square and rectangular wells measured parallel to

the direction of forces and diameter for circular wells

Q = a constant whose values are given in Table 3.2 below for wells with a

square or a rectangular base. A value of 0.60 is taken for circular wells

= angle of internal friction of soil.

Table 3.2 Values of the constant Q for square or rectangular wells

D/B 0.5 1.0 1.5 2.0 2.5

Q 0.41 0.45 0.50 0.56 0.64

21 | P a g e

The ultimate moment of resistance of the well sides due to the passive resistance of

the soil, , is calculated next.

(3.15)

where, = density of soil (submerged density to be taken for soils under water or

below the water table),

L = projected width of the soil mass offering resistance. In case of circular

wells, it shall be 0.9 times the well diameter

= passive and active pressure coefficients to be calculated using Coulomb‟s

theory, assuming „δ‟, the angle of wall friction between the well and the

surrounding soil to be equal to but limited to a value of .

STEP 3: The ultimate moment of resistance of the well sides due to friction, , is

calculated

(i) For rectangular wells,

(3.16)

(ii) For circular wells,

(3.17)

STEP 4: The total ultimate moment of resistance of the well is taken as Mt

Mt = 0.7(Mb + Ms + Mf) (3.18)

Where 0.7 is the strength reduction factor

STEP 5: Check Mt M

where, M = Total applied external moment about the plane of rotation of the well

taking appropriate load factors as per combinations given vide step 1.

STEP 6: If the conditions in Steps 1 and 5 are not satisfied, the well shall be redesigned.

3.4.4 DESIGN OF WELL CURB

When the well is dredged during the process of sinking, the curb cuts through the soil

under the action of the dead weight of the steining including kentledge, if any and hence hoop

tension is developed in the well curb. The well curb has to be designed for the hoop tension.

Total hoop tension, (3.19)

where, N = running load of the well steining on the curb,

d = mean diameter of well steining,

= angle of beveled edge of well curb with horizontal, and,

µ = coefficient of friction between soil and concrete of curb.

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A minimum reinforcement of 72 kg/m3 is provided in the well curb. The

reinforcement is provided in the form of rings distributed along the perimeter of the well

curb, the rings being enclosed within stirrups.

3.4.5 DESIGN OF WELL STEINING:

Before designing the section of the steining, the stresses in the steining are calculated

at the level of maximum scour.

(3.20)

(3.21)

where, W = total vertical load acting up to the maximum scour depth,

A = area of cross-section of well steining,

M = Resultant moment due to various loads as considered during analysis

of well at maximum scour level

Z = Section modulus of well steining.

The stresses should be within the permissible limits. Permissible limit of stresses for

different grades of concrete can be obtained from Table 2.2. If the stresses exceed the

permissible limits, the thickness of the well steining has to be increased.

A minimum thickness of the steining, tmin, given by the following equation is required

to avoid the excessive kentledge during sinking of the well.

Thickness, (3.22)

where, d = external diameter of well,

= density of concrete, and,

f = skin friction acting on the curved surface area of the well,

=

where, = coefficient of friction between soil and concrete,

KA = coefficient of active earth pressure

= submerged density of soil on the sides of steining

h = height of well.

After performing the checks for stresses and thickness of steining, the reinforcements

in the steining are calculated. The vertical reinforcements in the steining should not be less

than 0.12 percent of the gross sectional area of the actual thickness provided for the steining.

The vertical reinforcement should be equally distributed on both the faces of the steining. The

23 | P a g e

vertical reinforcement should be tied up with hoop steel not less than 0.04 percent of the

volume per unit length of the steining.

3.4.6 DESIGN OF BOTTOM PLUG

The bottom plug has to be checked for minimum thickness given by the following

equations,

(For circular wells), (3.23)

(For rectangular wells), (3.24)

where, r = radius of well at the base

q = unit bearing pressure against the base of the well

= flexural strength of concrete used in bottom plug

b = short side of well

α = short side/long side ratio of well.

3.4.7 DESIGN OF WELL CAP

A well cap is needed to transfer the loads and moments from the pier to the well. The

shape of the wall cap is normally kept the same as of the well with a possible overhang of

150 mm. The top of the well cap is usually kept at about the low water level in case of

perennial rivers. The well cap is designed as a two-way reinforced concrete slab resting over

the top of well. The support conditions are taken partially restrained.

The design of the well cap is carried out by assuming that the load from the pier acts

on an imaginary circle having an area equal to the area of dispersion of the loads transferred

from the pier to the well cap.

Since the well-cap is assumed to be partially restrained by the steining, the moments in

the well-cap are calculated for circular patch loading and for U.D.L. (self-weight of well cap)

for the following two conditions:

(1) Well cap freely supported on steining

(2) Well cap fully clamped on steining

Condition 1: Well cap freely supported on the steining

Take, Poisson‟s ratio of concrete,

w = weight of well cap per unit area

V = vertical load acting on the well-cap

h = effective diameter of well-cap,

& are the radial and the tangential moments in well-cap, respectively.

24 | P a g e

In the first instance, the moments in the well cap due to vertical loads transferred from the

pier and the self weight of the well cap are determined.

(i) Moments beneath loaded area due to circular patch loading

(3.25)

(3.26)

d = diameter of equivalent circular patch loading

(ii) Moments beneath unloaded area due to circular patch loading

(3.27)

(3.28)

At support, d = h; = 1

The radial and tangential moments in the well cap due to U.D.L. are given by

(3.29)

(3.30)

At centre, d = 0; = 0


Condition 2: Well cap fully clamped at support

(i) Moments beneath loaded area due to circular patch loading

(3.31)

(3.32)

d = diameter of equivalent circular patch loading

(ii) Moments beneath unloaded area due to circular patch loading

(3.33)

(3.34)



(3.35)

25 | P a g e

(3.36)



If is the resultant moment per metre length of the pier, then maximum reactive moment at

the support =

Hence, the maximum moment at the centre of the well cap due to moments

transferred form pier =

The maximum moment at the edges of the well cap due to moments transferred from

pier = .

The resultant moments for the design of the well-cap section at mid-span and at

supports can be found out as follows.

Mcentre = (Mean radial moment due to patch loads beneath the loaded area)

+ (Mean radial moment due to U.D.L. at the centre of well-cap)

+ (moment at the centre of well cap due to moments transferred from pier)

Medge = (Mean radial moment due to patch loads beneath unloaded area)

+ (Mean radial moment due to U.D.L. at the support of well-cap)

+ (moment at the edges of well cap due to moments transferred from pier)

Hence, the reinforcement at the centre of the well-cap is calculated for the moment Mcentre

and the reinforcement at the edges of well-cap is calculated for the moment Medge. Half of the

main tension reinforcement at the centre and at the support sections of the well cap is

provided on the compression face. All reinforcement in the well-cap is provided as an

orthotropic mesh.

The well-cap is finally checked for punching shear as per IS: 456-20001.

3.5 CONCLUSIONS

The role and the features of well foundations have been discussed in this chapter. This

stability analysis of well foundations has been explained and the design of various

components has been briefly reviewed.

26 | P a g e

CHAPTER 4

PILE FOUNDATIONS

4.1 INTRODUCTION

Piles are relatively long and slender members used to transfer loads through weak soil

or water to deeper soil or rock strata having a high bearing capacity. Piles are usually

installed in clusters/group to provide foundations for bridges. A pile foundation may have

vertical piles or batter piles or a combination of vertical and batter piles. Well foundations are

provided to the bridges, only when soils with high bearing capacity are available at the

shallow depths in ground, in order to resist loads and moments transferred by well to the soil.

It is not preferable to use well foundations, when low bearing strata like clay is present in the

ground up to greater depths.

The uses of piles for bridge foundations are justified in the following cases:

(a) The upper soil strata are too compressible or too weak to support the heavy vertical

reaction transmitted by the superstructures and piers. In this instance, piles serve as

extensions of piers to carry the loads to deep, rigid stratum such as rock. Such piles

are called as point or end bearing Piles. If a rigid stratum does not exist within

reasonable depth, the load must be gradually transferred, mainly by the friction, along

the pile shafts. Piles transferring loads to soil by skin friction through its lateral

surface area are called as Friction Piles.

(a) Point Bearing Piles (b) Friction Piles

Fig. 4.1 Piles Classification on the basis of load transfer mechanism

27 | P a g e

(b) Piles are also frequently required because of relative inability of other foundations to

transmit inclined, horizontal, or uplift forces and overturning moments. As the name implies,

uplift piles are used for resisting uplift forces on foundations.

Fig. 4.2 Uplift Piles

(c) Pile foundations are often required when scour around the foundations can cause

erosion in spite of presence of strong, incompressible strata (such as sand, gravel, etc.) at

shallow depths. In such cases, piles can be particularly effective in bypassing scourable strata

and transferring loads to in erodible soil.

Fig. 4.3 Use of piles in scourable beds

(d) In areas where expansive or collapsible soil extends to considerable depth below the

ground, pile foundations may be needed to ensure safety against undesirable seasonal

movements of foundations.

28 | P a g e

Fig. 4.4 Piles in expansive soils can control seasonal movements

Piles can be classified according to the materials of which they are made of. The main

materials used in makings piles are timber, reinforced concrete and steel. Reinforced concrete

piles are generally used in pile foundations for bridges. Concrete piles are either precast or

cast-in-situ. Precast piles are installed into the ground by drilling, while cast-in-situ piles are

bored pile. Under-reamed pile is a special type of bored pile having one or more bulbs. With

the presence of under-ream, substantial bearing or anchorage is available. These piles find

application in widely varying situations in different types of soils where foundations are

required to be taken down to a certain depth. Diameters of bulbs are usually 2 to 3 times the

diameter of the pile shaft. The under-ream increases the load carrying capacity of the pile.

Such piles are claimed to be useful and economical in expansive soils like black cotton soils

of India, where shrinkage and swelling of clays rules out the use of shallow spread footings.

Piles in foundations are usually installed in a group. The top of the piles are connected

together with a stiff reinforced concrete slab called pile cap. All the piles are projected atleast

50 mm in the concrete of the cap.

A pile group having pile cap standing clearly above the ground is know as a free

standing pile group. Free standing pile groups are used in river bridge crossings, where the

top of the pile cap is usually kept at the level of L.W.L. A pile group in which the pile cap

rests on the soil, partially or is fully buried below ground level is known as piled foundation.

In a piled foundation, the pile cap may, under certain soil conditions, help in transmitting a

part of the load to the soil on which it rests. Piled foundations are generally used for elevated

highways and flyovers where pile cap is fully buried inside the ground to provide space for

the roadways.

29 | P a g e

Fig. 4.5 Free Standing Pile Group Fig. 4.6 Piled Foundation

4.2 DESIGN OF PILE FOUNDATIONS

If pile foundations are to be used for river bridge crossings, then the maximum scour

depth for the stream has to be determined. The calculation of maximum scour depth is

discussed in Section 3.3.1 of Chapter 3. For river bridge crossings, the top of the pile cap is

placed at the level of L.W.L., while for non-river bridge crossings, the pile cap is fully buried

into the ground with its top placed at ground level. Later, the forces and moments acting at

the top of pile cap i.e. at the base of pier are calculated, during the analysis of pier. After

calculating the forces and moments at the base of pier, the axial loads in the piles due to

applied forces and moments are determined for an assumed size and configuration of piles in

a pile group. The assumed pile properties are subsequently checked for safety.

4.2.1 UNDER-REAMED PILES

The diameter of under-reamed piles in bridge applications is generally not taken less

than 300 mm. The length of the pile is selected as per the nature of the soil strata. For

example, if a weak layer is underlain by a strong stratum at a reasonable depth, the length of

the pile is so chosen such that the penetration of the pile into the strong stratum (bearing

stratum) is a minimum of 5 times the pile diameter or width. On the other hand, if the weak

layer extends to a considerable depth, the length of pile is so chosen as to obtain adequate pile

capacity through skin resistance.

The design of under-reamed piles can be carried out with the aid of Table 1 of IS:

2911(Part III) – 19804. Table 1 of IS: 2911(Part III)

– 1980

4 which is reproduced in toto as

Table 4.3 in this thesis is a useful guide for selecting important parameter w.r.t. under-reamed

piles viz. Diameter of pile shaft and under-ream, length of pile number of under-reams and

the capacity of a selected configuration of under-reamed pile in compression, tension and

30 | P a g e

lateral load carrying capacity. Usually a suitable value is selected as the diameter of the pile

shaft. The diameter of the under-ream is taken as 2.5 times the diameter of pile shaft. Piles

can have one or more than one under-reams, but it is not advisable to have more than two

under-reams on one pile without ensuring their feasibility in strata needing stabilization of

boreholes by drilling mud. For piles up to 300 mm diameter, the spacing between consecutive

under-reams should not exceed 1.5 times the diameter of the under-ream. For piles of

diameter greater than 300 mm, spacing can be reduced to 1.25 times the stem diameter. The

top-most under-ream should be at a minimum depth of 2 times the under-ream diameter

below the ground. In expansive soils, the top-most under-ream should not be less than 1.75 m

below ground level. Clearance between the underside of pile cap embedded in the ground and

the top under-ream should be minimum 1.5 times the under-ream diameter. Columns (3) &

(4) of Table 4.3 provide minimum length for single and double under-reamed piles,

respectively.

After fixing the dimensions of the under-reamed pile, the load bearing capacity of a

single under-reamed pile is estimated. The pile capacity is compared with the maximum load

expected on the pile to ensure an adequate margin of safety.

4.2.2 BORED CAST-IN-SITU PILES

The safe bearing capacity of a pile can be determined from its ultimate bearing

capacity, by using a suitable factor of safety. The methods available to estimate the ultimate

capacity of a single pile in compression can be grouped into the following categories:

i. Static-in-situ test.

ii. Static analysis,

iii. Dynamic analysis,

The static-in-situ test, popularly known as pile load test, is the only direct method for

determining the allowable load on piles. It is considered to be the most reliable of all the

approaches, primarily due to the fact that it is an in-situ test performed on a pile of prototype

pile dimension. Pile load test is a costly test and is used to confirm whether the actual pile

installed in the filed can take the load predicted by static or dynamic analysis. Dynamic

analysis is used for determining ultimate capacity of driven piles. Static analysis, which is

based on „soil mechanics‟ approach provides approximate estimates of pile capacity, as

values of a number of parameters appearing in the static formulae are assigned empirically.

For bored piles, static analysis is performed. A brief description of static analysis of piles is

presented next.

A pile when loaded, transfers the load through skin friction along the length of the

31 | P a g e

pile and through point bearing at the tip of the pile.

Thus, the ultimate capacity of a pile may be obtained as,

, (4.1)

where,

= total skin frictional resistance,

= total point bearing resistance,

= unit skin frictional resistance,

= unit point resistance,

= lateral surface area of the pile, and,

= area of the pile tip.

Fig. 4.7 Load resisting mechanism in a pile

The unit frictional resistance, and the unit point bearing resistance, , depend on

many factors such as the type of soil, method of installation and the pile material. Of these,

the method of pile installation affects the pile capacity significantly, and also makes the

estimation of pile capacity more complex. In order to clearly identify the effect of pile

installation and account for the same, it is convenient to discuss separately the case of piles in

cohesion-less soils and cohesive soils.

32 | P a g e

Piles in Cohesion-less soil:

As suggested in Eq. 4.1, the pile capacity can be obtained as the sum of point bearing

resistance and skin friction resistance.

Point Bearing Resistance:

The unit point bearing resistance in cohesion-less soil is given by,

, (4.2)

where, = effective overburden stress at the level of the pile tip,

B = diameter or width of pile,

= density of the soil,

= shape factor, 0.4 for square or rectangular piles, and,0.3 for

circular piles, and,

& = bearing capacity factors.

The second term in Eq. 4.2, is usually neglected, particularly in the case of

long piles, as this constitutes an insignificant part of the total capacity. The first term in Eq.

4.2 implies that the base resistance increases linearly with depth. The bearing capacity factor,

is a function of the angle of internal friction of soil, , and its value can be obtained from

Fig. 1 of IS: 2911 (Part 1) – 19793, reproduced here as Fig. 4.8. The bearing capacity factor,

can also be read off from Table4.1.

Fig. 4.8 Bearing Capacity Factor, for bored piles.

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Table 4.1 Bearing Capacity Factor, ,

Angle of internal friction of soil

( , in ( ° )

0 0.00

5 0.45

10 1.22

15 2.65

20 5.39

25 10.88

30 22.40

35 48.03

40 109.41

45 271.76

50 762.89

Skin Frictional Resistance:

The unit skin frictional resistance at any depth, z, below the ground level may be

obtained as follows

, (4.3)

where, = the effective overburden stress at the depth considered,

= angle of wall friction of the material of the pile,

= of the angle of friction of soil( )

= coefficient of horizontal stress.

The value of depends on the soil properties and the method of installation of the

pile. The appropriate value of can be selected from Table 4.2

Table 4.2 Value of coefficient of horizontal soil stress (

Installation Method

Driven piles, large displacement 1 to 2

Driven piles, small displacement 0.75 to 1.25

Bored and cast-in-situ piles 0.70 to 1

Jetted piles 0.50 to 0.70

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Here, . (4.4)

Piles in cohesive soils:

The point bearing resistance and the skin frictional resistance of a pile in cohesive soil

i.e. clay, can be determined as follows:

Point Bearing Resistance:

The unit point bearing resistance is obtained as follows,

, (4.5)

where, = undrained cohesion at the pile tip, and,

= bearing capacity factor, generally taken as 9.

Skin Frictional Resistance:

The unit skin resistance is obtained as follows,

, (4.6)

where, α = adhesion factor.

The adhesion factor depends on the cohesive strength of the soil. It can be obtained

from Fig. 4.9.

Fig. 4.9 Adhesion factor for cohesive soils

The safe bearing capacity of a bored pile can be computed by dividing the ultimate

bearing capacity of the pile by an appropriate factor of safety. The minimum factor of safety

for static analysis is 2.5.

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Table 4.3 Safe loads for under-reamed piles

4.2.3 NUMBERS, SPACING AND ARRANGEMENT OF PILES

The number of piles required in bridge foundation is obtained by dividing the total

vertical load acting on the foundation by the safe bearing capacity of a single pile.

The spacing of piles shall be considered in relation to the nature of ground, the types

of piles and the manner in which the piles transfer the load to the ground.

Generally, the centre-to-centre spacing of under-reamed piles in a group should be at

least 1.5 times the diameter of the under-ream.

For bored cast-in-situ piles, a minimum spacing of 2.5 times the diameter of pile is

recommended for piles deriving their capacities mainly from the end bearing stratum (end

bearing piles). On the other hand, piles deriving their bearing capacity primarily from friction

(friction piles) shall be sufficiently apart to ensure that the zones of soils from which the piles

derive their support do not overlap to such an extent that their bearing values are reduced.

Generally the spacing in such case shall not be less than 3 times the diameter of the pile.

The arrangement of piles in a foundation depends upon the number of piles to be

installed in the foundation. Wherever conditions permit, the piles should be arranged in the

most compact geometric form in order to keep the stresses in the pile cap to a minimum.

Some geometric forms are shown in Figure 4.10.

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Fig. 4.10 Typical arrangement of piles in a group

Piles in foundation can be arranged in a grid pattern, where the spacing between the

piles in longitudinal as well as transverse direction of the bridge remains the same.

After fixing the arrangement of piles in a group, the dimensions of the pile cap are

determined. A clear overhang of 100 mm to 150 mm should be provided in the pile cap

beyond the edge of the outermost pile in the group.

A minimum of three piles shall be provided in pile group. If the numbers of piles

provided in the foundation are three, then the connection of the pile cap with the piles is

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assumed to be hinged connection i.e. pile cap can transmit only forces and not the moments,

from pier to the piles. If the number of piles in the pile group exceeds three, then a rigid

connection is provided between the piles and the pile cap i.e. the pile cap is able to transmit

both forces and moments, from pier to the piles.

The group capacity of piles is found by assuming the pile group to behave as a deep

footing.

4.2.4 SAFE BEARING CAPACITY OF PILE GROUPS

The group capacity of piles may be found assuming the pile group to behave as one

deep footing.

4.2.4(a) GROUP OF BORED CAST-IN-SITU PILES

The ultimate bearing capacity of the pile group in can be estimated as follows:

Pile Group in cohesion-less soil

For a pile group in sand, the values of the different parameters used for estimating the

ultimate bearing capacity of the pile group can be calculated as follows:

(4.7)


, (4.8)

where, = the effective overburden stress at the depth considered,

= angle of friction of soil, and,

, (4.9)

= lateral surface area of the block enclosing the piles in the group,


, and, (4.10)

where, = undrained cohesion at the bottom of pile group, and,

= bearing capacity factor, generally taken as 9,

= base area enclosing all the piles in group.

For Pile Group in cohesive soil

For pile group in clay, the values of different parameters used in estimating ultimate

bearing capacity of pile group can be calculated as follows:


, (4.11)

where, = undrained cohesion at the bottom of pile group,

= lateral surface area of the block enclosing the piles in the group,

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, and, (4.12)

where, = bearing capacity factor, generally taken as 9,

= base area enclosing all the piles in group.

The safe bearing capacity of the pile group shall be taken as the smaller of the two

values given below:

where, n = number of piles in group,

= ultimate bearing capacity of a single pile,

= ultimate bearing capacity of the pile group as estimated above,

FOS = Factor of Safety, generally taken as 3.

4.2.4(b) GROUP OF UNDER-REAMED PILES

For under-reamed piles with a spacing of 2 times the diameter of the under-ream, the

safe bearing capacity of the pile group will be equal to the safe load on an individual pile

multiplied by the number of piles in the group. For piles at spacing of 1.5 times the diameter

of the under-ream, the safe bearing capacity of the pile group will be equal to 90 percent of

the safe load on an individual pile multiplied by the number of piles in the group.

The safe bearing capacity of a pile group shall be greater then the actual load

acting on the pile foundation. The vertical load acting on the foundation will also include the

weight of pile cap. If the load acting on the foundation exceeds the safe bearing capacity of

the pile group, then the piles are redesigned or the numbers of piles in the group are increased

or the spacing between the piles is increased. In case of under-reamed piles, the number of

under-reams on each pile can also be increased to extend the safe load limit of the pile group.

Safe bearing capacity of the pile group is then re-estimated to check whether it is greater than

the loads acting on foundation.

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4.2.5 DISTRIBUTION OF LOAD BETWEEN VERTICAL PILES OF PILE GROUP

The load acting on an individual pile is obtained from the elastic theory by using the

following method:

, (4.13)

where, Qi = load on ith pile,

= Total vertical load acting on the foundation

n = Total number of piles in group,

= Moment acting at the soffit of pile cap about longitudinal axis of

bridge

= Moment acting at the soffit of pile cap about transverse axis of

bridge

= distance of the centre of ith pile from the centre of gravity of pile

group, measured parallel to transverse axis of bridge

= distance of the centre of the ith pile from the centre of gravity of pile

group, measured parallel to longitudinal axis of bridge

= summation of squares of distances of the centres of all the piles from

the centre of gravity of pile group measured parallel to transverse axis of

bridge

= summation of squares of distances of the centres of all the piles from

the centre of gravity of pile group measured parallel to longitudinal axis

of bridge

If the calculated load on a pile exceeds its safe bearing capacity then the piles are

required to be redesigned. The option is that, the number of piles or the spacing between piles

can also be increased to reduce the maximum load acting on the piles. In the case of under-

reamed piles, the number of under-reams can be increased to increase the safe load limit of

the pile.

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4.2.6 LATERAL LOAD ANALYSIS OF PILES

It is assumed that all the piles in a group share equally the lateral load acting on the

foundation.

4.2.6 (a) LATERAL LOAD ANALYSIS OF BORED CAST-IN-SITU PILES

When the length of a pile is more than ten times its diameter it is classified as a long

pile and flexural behaviour governs the response of the pile to lateral loads. A majority of the

piles used in bridge practice belong to this category.

Generally, three types of boundary conditions are encountered in long piles namely

(a) free-head pile, (b) fixed-head pile, & (c) partially-restrained head pile. In the case of free-

head pile, the lateral load may act at or above the ground level and the pile head is free to

rotate without any restraint. A fixed-head pile is free to move only laterally but rotation is

prevented completely, whereas a pile with partially restrained head moves and rotates under

restraint. If the number of piles in group is 3 or less, then the piles are considered as free-head

piles. If the number of piles in group exceeds 3, the piles are considered as fixed-head piles.

The following procedure is followed for finding the lateral load capacity of a pile.

i. The relative stiffness factor T or R as the case may be, is found.

(for piles founded in sand and normally loaded clays), (4.14)

(for piles founded in pre-loaded clays), (4.15)

where, E = Young‟s modulus of the pile material,

. For concrete piles, = (in MPa), (4.16)

where, fck is the 28-days characteristic compressive strength of .concrete,

I = second moment of inertia of the pile cross-section, in m4,

The values of the soil constants and K are presented in Table 4.4 and 4.5

respectively.

ii. Form Fig. 4.11, the depth of fixity, Lf, of the pile assumed as an equivalent cantilever

is found as a function of the ratio or where L1 is the unsupported length of the

pile. For non-river bridge crossings where in the piles are completely embedded in

ground where in the piles are completely embedded in ground, L1 = 0. As shown in

Fig. 4.11, the total length of equivalent cantilever is obtained as the summation of L1

and Lf.

iii. Knowing the total length (L1 + Lf) of the equivalent cantilever, the lateral load

capacity of a pile is calculated from the following equations

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, (for free head piles), (4.17)

, (for fixed head piles), (4.18)

where, Y is the limiting lateral deflection of pile head taken as 5 mm for bridge

substructures.

Table 4.4 Values of the constant (kN/m3)

SOIL TYPE Value of , (kN/m

3)

Dry Submerged

Loose sand 2600 1460

Medium sand 7750 5260

Dense sand 20760 12450

Very loose sand under

repeated loading - 410

Very soft organic soil - 110-270

For normally loaded

clays

Static loads

Repeated loads

-

-

450

270

Table 4.5 Values of the constant K (kN/m2)

Unconfined

Compression

Strength, in kN/m2

Range of values of

K, in kN/m2

Probable value of

K, in kN/m2

20 – 40 700 – 4200 775

100 - 200 3200 – 6500 4880

200 - 400 6500 – 13000 9770

> 400 - 19546

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Fig. 4.11 Determination of the depth of fixity of the pile

4.2.6 (b) LATERAL LOAD CAPACITY OF UNDER-REAMED PILES

The safe lateral load of an under-reamed pile can be obtained from columns (16) and

(17) of Table 1 of IS: 2911 (Part III)4 – 1980, which is reproduced as Table 4.3 in this thesis/.

It may be noted from Table 4.3 that the lateral loads cannot be increased or decreased with

change in the pile length. At the same time for piles with multi-under reamed the allowable

lateral load values should not exceed those given in column (17) of Table 4.3.

4.2.7 STRUCTURAL DESIGN OF PILE

As pointed out earlier, the fixed or free-head pile is treated as an equivalent cantilever

for lateral load analysis. The fixed end moment (MF) of the equivalent cantilever is higher

than the actual maximum moment (M) expected in the pile. The design moment for the pile is

obtained by multiplying the fixed end moment of the equivalent cantilever by a reduction

factor, m, obtained from Fig. 3 of IS: 2911 (Part 1)-19793

or from Fig. 5 of IS: 2911 (Part III)

– 19804. The two figures are reproduced in Fig. 4.12 of this thesis for ready reference.

The fixed end moment of the equivalent cantilever is given by:

, (for a free-head pile) (4.19)

, (for a fixed head-pile) (4.20)

The design moment for the pile, M = m (MF) (4.21)

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(a) For Free Head Piles

(b) For Fixed Head Piles

Fig. 4.12 Reduction factors for free-head and fixed-head piles

The pile is designed as a RCC column for the maximum vertical load P and moment

M.

The area of longitudinal reinforcement provided in the pile should not be less than 0.4

percent of the gross-sectional area of pile.

The longitudinal reinforcement is confined by lateral ties i.e. transverse

reinforcements. The diameter and the spacing of the lateral ties should be provided as per the

requirements of IS 456: 20001.

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4.2.8 SETTLEMENT OF PILE GROUP

According to Terzaghi and Peck (1967)21

, the total settlement of a group of driven or

bored piles under a safe design load not exceeding one-third to one half of the ultimate group

capacity can generally be estimated roughly as that of an equivalent raft foundation. The

deformation and compressibility properties of the soil beneath the equivalent raft foundation

can be estimated from empirical correlations with the results of field tests, plate load tests,

etc. or from the laboratory tests on undisturbed soil samples of cohesive soils. The settlement

estimates should also be checked by pile load tests for possible extrapolation to group

behaviour.

Since the use of elastic theory for determination of vertical stresses in the soil

surrounding and below the pile tips is extremely laborious for practical cases, approximate

methods are proposed. These methods are briefly discussed below:

(i) For friction piles, the vertical load acting on the foundation is placed on a fictitious raft

footing located at from the bottom of the piles, where Lf is the penetration of the pile

into the ground. Plan dimensions of the raft are determined on the basis of a 1H : 2V

dispersion of load as shown in Fig. 4.13 (b) & (c). .

(ii) For point bearing piles in dense sand-gravel deposits, the fictitious raft is placed at

from the bottom of the piles, where Lf is penetration of the pile into the soil layer where the

pile tip is situated. Plan dimensions of the raft are determined on the basis of a 1H : 2V

dispersion of load as shown in Fig. 4.13 (a). .

The soil at or below the fictitious raft must carry the applied loads without excessive

deformation. In some cases the settlements calculated by the above methods are smaller than

the measured values. However, these simple approximations give sufficient information for

determining the supporting strength of the lower strata of the soil.

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(a) End Bearing Piles

(b) Friction pile, with pile cap embedded (c) Partially embedded friction piles

into the ground

Fig. 4.13 Computation of Settlements for End Bearing Piles & Friction Piles

Settlement of pile group in cohesionless soil

On the basis of the raft analogy, a preliminary estimate of the settlement of a pile

group in cohesionless soil can be made.

The settlement of the pile group in a soil layer can be estimated from the following

equation proposed by De-Beer and Martens method (1957)22

.

, (4.22)

where, Si = settlement of the layer considered,

H = height of layer,

= mean effective overburden pressure for the layer,

= average increase in vertical stress in the layer due to footing load. This

may be obtained assuming 1H : 2V load dispersion

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C = constant of compressibility,

, (4.23)

where, = average static cone penetration resistance for the layer considered.

Settlement of pile group in cohesive soils

For piles in normally consolidated clays, the settlement is given by,

, (4.24)

where, Si = settlement of the layer considered,

H = height of layer,

= mean effective overburden pressure for the layer,

= average increase in vertical stress in the layer due to footing load. This

may be obtained assuming 1H : 2V load dispersion,

= compression index, and,

= void ratio in the clay layer corresponding to the effective in-situ

overburden pressure.

For piles in pre-consolidated clays, the settlement is given by

, (4.25)

where, = pre-consolidated pressure of the layer considered.

From serviceability considerations, the settlement of pile group should not exceed 50

mm.

4.2.9 DESIGN OF PILE CAP

Pile cap is a structural member that ties a group of piles together. Plan dimensions of

the pile cap are decided from the spacing between the piles and their arrangement in the

group. Piles should be well arranged in a group so that the centroid of the group coincides

with the line of action of load. A clear overhang of 100 mm to 150 mm beyond the edge of

the outermost pile is given to the pile cap. The thickness of pile cap is usually governed by

the shear developed in the pile cap. Pile caps can also be designed using the truss analogy.

A clear cover of 50 mm is provided to the reinforcement in pile cap.

As shown in Fig. 4.14, the critical section for moment in the pile cap is at the face of

the pier.

The pile cap is also checked for both, one-way shear & two-way shear. The critical

section for one-way shear in the pile cap is located at a distance equal to effective depth „d‟

47 | P a g e

away from the face of the pier, Fig. 4.14. For two-way shear, the critical section is located at

a distance of half of the effective depth „d‟, from the face of pier, Fig. 4.15.

Fig. 4.14 Critical section for Fig. 4.15 Critical section for

moment & one-way shear two-way shear

When the vertical load from the pier is transferred to the centroid of the piles through

inclined internal coverage struts in the pile cap, large tension forces are induced in the

reinforcements of the pile cap. The component of the thrust in the inclined concrete struts

acting in the horizontal direction away from the pile-cap has a tendency to create “bursting

forces” in the pile cap. Therefore, it is desirable to configure the concrete in the pile cap with

suitable “bursting reinforcement”, usually 12 mm diameter closed rings at 150 c/c along the

depth of the pile cap, Fig. 4.16.

Fig. 4.16 Typical detailing of reinforcement in a pile cap.

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4.3 CONCLUSIONS

The features, analysis methodologies and the design of piles for vertical as well as

lateral loads have been discussed in this chapter. The analysis and design of pile caps has

been briefly reviewed.

49 | P a g e

CHAPTER 5

SOFTWARE FEATURES

5.1 INTRODUCTION

A software has been developed in the Visual Basic.Net platform for the analysis and

design of bridge piers and foundations. The analysis and design of both well and pile foundations

is incorporated in the software. The details and features of the software along with its functions

layout are presented in this Chapter. Interactive feature are incorporated in the software which

provides guidelines to the user for the input of every data. The software provides ample of

flexibility to the user for selecting suitable data.

Some of the important user friendly aspects of the software developed are as follows:

1. The analysis and design calculations are explained sequentially with the help of

appropriate diagrams

2. Alert messages are given by the software if the user misses to input the required data in

any of the form pages.

3. In case any of the analysis or design requirements are not satisfied the software will

prompt the user with appropriate alternatives.

The limitations of the software developed are as follows:

1. Simply supported spans are assumed for the superstructure

2. Only the following live load categories are included in the software: Class A and Class

AA loading

3. The functions of the software are limited only up to the analysis of the pier. Software

does not incorporate the structural design of piers. Also software can perform analysis of

only two types of piers: wall type pier and hammer-head type piers

4. Software can work out for circular well foundation, bored cast-in-situ & under-reamed

piles only.

5.2 FUNCTIONS LAYOUT OF THE SOFTWARE

The tasks performed by the software are partitioned into various modules. The

computations done in each module & the functioning of the modules are presented in the form of

flow charts as explained below.

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5.2.1 SELECTION AND INPUT OF PARAMETERS USED FOR ANALYSIS AND

DESIGN OF FOUNDATIONS

Initially, the software will ask the user to select the type of foundation whose analysis and

design is to be performed. The option of pile foundations is provided for river bridge crossings

and for elevated roadways. The user will be asked to select any one type of bridge: river bridge

crossing or non-river bridge crossing. The option of well foundations is provided for river bridge

crossing. For well as well as and pile foundations in river bridge crossing, the user will be asked

to input values of maximum mean velocity of stream, High Flood Level (HFL), Low Water

Level (LWL), mean diameter of river bed particle & submerged density of soil at the site where

the proposed foundation is to be provided. The option for use of different type of material in the

pier is included in the software is included in the software. The user will be asked to input other

relevant parameters like depth of girder, span, dead load on each girder, area of superstructure,

type and width of carriageway & seismic zone, etc...

The flow chart for the preliminary dimensioning of the pier is presented in Fig. 5.1 If a

wall type pier is selected then as per the bearing spacing and plan dimensions of the bearings, the

minimum required top width and length of the pier (without cutwater) is calculated. Software

will not perform the next stage of calculations unless the input value of top width and length of

pier (without cutwater) is greater than the minimum requirements. Later, the user is prompted to

enter the batter of the pier so as to calculate the bottom width of the pier. Length of pier cap of

walled type pier is calculated from the top length of pier. If a hammer-head type of pier is

selected by the user then the user is asked to input the diameter and height of the pier shaft

Length of pier cap is calculated from bearing spacing and dimensions. The user will be asked to

enter the thickness of the rectangular and the tapered portion of the pier cap.

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Fig.5.1 Flow Chart of preliminary dimensioning of pier

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Fig. 5.2 Flow Chart for Analysis of Pier

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5.2.2 ANALYSIS OF PIER

The flow chart for the analysis of the pier is presented in Fig. 5.2. After deciding the

preliminary dimensions of pier and pier cap, the software will perform the analysis of pier for the

various forces acting on the pier. For both well and pile foundations in river bridge crossing, the

pier is analysed for flood condition i.e. water level is at HFL. Stresses for various types of forces

acting on pier due to dead load on pier, eccentric live load, longitudinal forces, water current in

river, buoyant force, wind load, seismic force and shear forces at the bearings are computed.

These loads are categorized into three loading categories: Normal (N) Case, Temperature (T)

Case & Seismic (S) Case. Stresses in pier due to N Case, T Case and S Case loading are

computed separately. Subsequently, the resultant stresses in the pier due to the following load

combinations are calculated: N case, N+T Case, N+T+S case. These resultant stresses are

compared with the permissible limits. If the stresses are within the permissible limits, the pier is

safe and the pier will be analyzed next for no water condition. However if the resultant stresses

exceed the permissible limit, then the software will direct the user to a page where the pier will

be redesigned in order to withstand the stresses safely.

5.2.3 ESTIMATION OF SCOUR DEPTH FOR FOUNDATION DESIGN

For both well and pile foundations in river-bridge crossings, the scour depth is required to

be calculated for determining the founding levels. The flow chart for calculation of maximum

scour depth is shown in Fig. 5.3.

To ensure a sufficient margin of safety in the scour depth calculations, the software

multiplies the design discharge by a flat value of 1.30 to get the discharge for calculation of the

normal depth of scour. The software calculates the normal scour depth using two formulae:

formula suggested in IRC: 78-20008 & Lacey’s formula.

Linear water-way in calculated form the equation . Knowing the linear

water-way L, Db is calculated. The silt factor in both the equation is taken as 1.76 , where

dm is the median size of the bed sediments, in mm.

The higher of the two values of the normal scour depth is used for calculating the

maximum scour depth. The normal scour depth is multiplied with two to get the of maximum

scour depth at the nose of the pier.

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Fig. 5.3 Flow Chart for calculation of Maximum Scour Depth

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5.2.4 ANALYSIS AND DESIGN OF WELL FOUNDATION

The analysis and design of well foundation follows the designing of the pier. The user is

prompted to select the preliminary dimensions of the ell based on empirical rules.

5.2.4.1 ANALYSIS OF WELL FOUNDATION

The resistance of soil surrounding the well foundation is determined in its elastic state

and at ultimate loads to check whether the soil will be able to resist the force and moments

transferred by the well foundation.

The flow chart for calculation of soil resistance using elastic theory is presented in Fig.

5.4.

The flow chart for calculation of soil resistance at ultimate loads is presented in Fig. 5.5.

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Fig. 5.4 Flow Chart for calculation of soil resistance

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5.2.4.2 STRUCTURAL DESIGN OF WELL

Once the safety of the selected preliminary size of the well has been established in the

elastic state and at ultimate loads, the structural design of the following components of the well

is performed next by the software: Bottom plug (check on thickness provided), well curb,

steining and well cap. The design aspects for these components have been explained in detail in

an earlier chapter. The flow charts for the structural design of well curb, steining and well cap

are presented in Figs. 5.6,5.7 and 5.8 respectively.

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Fig. 5.5 Flow Chart for calculation of soil resistance at ultimate loads

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Fig. 5.6 Flow Chart for design of Well curb

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Fig. 5.7 Flow Chart for design of Well steining

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Fig. 5.8 Flow Chart for design of Well Cap

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5.2.5 ANALYSIS AND DESIGN OF PILE FOUNDATION

Before proceeding to the analysis of pile foundation, the software will prompt the user to

supply details of the sub-soil investigations. The user will be required to input details of the

numbers, the type and the engineering properties of the soil layers at the site where the pile

foundation is to be constructed. Particularly, care will be required to enter the relevant properties

of cohesive soils and the user will be required to make a distinction between pre-consolidated

and normally consolidated clays. The flow chart for soil details is show in Fig. 5.9. The software

will first run the loop to enter details of soil layers, and subsequently, the user will be asked to

enter details about the first layer. User will be asked to enter the height of first layers, density of

soil & type of soil. If the soil is sandy, then the user will be asked to enter the angle of internal

friction and the average cone resistance of the soil layer (qc). If soil is clay then software will

ask user to enter the undrained cohesion of soil (cu) and the compression index of clay. Further,

the user will be asked to select the type of clay. If the clay is pre-consolidated, then pre-

consolidation pressure will have to be entered. Similarly, the loop will run again so as to enable

the user to enter the details of next soil layer. The loop will be terminated when details of all the

layers are entered.

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Fig. 5.9 Flow Chart for soil details

5.2.5.1 ANALYSIS OF PILES

(a) Bored cast-in-situ circular piles

The user will have to enter the diameter and the length of the pile. Thereafter, the

software will perform the calculations for estimating the safe bearing capacity of the pile. The

procedure for calculation of the ultimate bearing capacity of the pile in cohesive as well as

cohesion less soils has been explained in detail in Chapter 4. The computed ultimate bearing

capacity is divided by a factor of safety of 3 to get the safe bearing capacity of the pile. The flow

chart for calculation of the safe bearing capacity of a bored cast-in-situ pile is presented in

64 | P a g e

Fig.5.10.

(b) Under-reamed piles

The user will be asked to select the diameter of pile stem and the number of under-reams

on each pile. For the selected diameter of the pile stem, the length of pile specified in Table 1 of

IS: 2911(Part III) – 19804 is noted. This pile length is stored in “L”. If the number of under-

reams selected for the pile is less than or equal to two, then for the user specified diameter,

number of under-reams & length “L”, the safe vertical load for the under-reamed pile is read

from Table 1 of IS: 2911(Part III) – 19804. However, if the number of under-reams specidified

by the user exceeds two, then the safe vertical load for the pile is extrapolated with the help of

the incremental values given in Table 1 of IS:2911 (Part III) – 19804.

The procedure for obtaining the safe vertical load of an under-reamed pile is presented in

the flow chart in Fig. 5.11.

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Fig. 5.10 Flow Chart for calculating safe bearing Capacity of bored cast-in-situ pile

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Fig. 5.11 Flow Chart for calculating safe bearing Capacity of an under-reamed Pile

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5.2.5.2 SAFE BEARING CAPACITY OF PILE GROUP

After calculating the single pile capacity, the safe bearing capacity of the pile group is

calculated.

(a) Pile groups with bored cast-in-situ piles

The software will calculate the vertical load acting on the foundation. The pile

dimensions are then entered by the user in software. As discussed in the previous section, the

software will calculate the ultimate bearing capacity of a single pile and from it the safe bearing

capacity of the pile. Dividing the total vertical load on the foundation by the safe bearing

capacity of one pile will give the total number of piles required in the foundation. The software

will ask the user to enter the total number of piles. The number of piles provided will be accepted

only if it is greater than total number of piles required. For analysis, the pile group is considered

to act as a deep footing in soil. The software will then run the loop file to calculate pile group

capacity. The software will start with soil layer 1. If layer 1 is sand then Qs & Qp will be

calculated as per the formulae of sand, while if it is clay then the formulae of clay will be used to

calculate values of Qs & Qp. The loop will run again and calculate Qs & Qp for the second layer,

as per the soil type. In this manner the software will calculate the value of Qs & Qp for each layer

of the soil. Finally, Qs & Qp for all the soil layers are added together to obtain the value of Qg;.

Qg,safe is obtained by dividing Qg by 3. If Qg is more than the total number of piles provided *

ultimate bearing capacity of each pile (Q) / 3, then Qg,safe will be equal to the total number of

piles provided * ultimate bearing capacity of each pile (Q) / 3.

The values of Qg,safe finally obtained is the safe bearing capacity of the pile group. The

flow chart for calculating the safe bearing capacity of pile groups made of bored cast-in-situ

circular piles is presented in Fig. 5.12

(b) For under-reamed piles

The flow chart of Fig. 5.13 explains the complete procedure to compute safe bearing

capacity of under-reamed pile. User is required to enter diameter of pile stem, number of under-

reams on each pile & spacing between piles. Diameter of under-ream is taken as 2.5 times the

diameter of pile stem. If the spacing between piles is less than two times the under-ream

diameter, then the safe bearing capacity of pile group is taken as 90% of safe bearing capacity of

single pile X number of piles in foundation. While if spacing is more than or equals to two times

the under-ream diameter, then the safe bearing capacity of pile group is taken as safe bearing

68 | P a g e

capacity of single pile X number of piles in foundation.

Fig. 5.12 Flow Chart for calculation of SBC of group of bored cast-in-situ piles

69 | P a g e

Fig. 5.13 Flow Chart for calculation of SBC of group of under-reamed piles

5.2.5.3 LATERAL LOAD ANALYSIS OF PILES

The lateral load capacity of the piles has to be determined so as to ensure that the

foundation can safely resist all design lateral loads. The flow chart for the lateral load analysis of

an under-reamed pile is given in Fig. 5.14.

(a) Under-reamed piles

For the given under-reamed pile selected by the user, the lateral load capacity is directly

read-off from the values given in Table 1 of IS: 2911 (Part III)-1980 and compared with the

lateral load apportioned to each pile. If required the under-reamed pile parameters are revised to

ensure safety. The flow chart for the lateral load analysis of under-reamed piles is given in Fig.

5.14. The detailed procedure for lateral load analysis of a bored cast-in-situ pile has been

explained in Chapter 4 and the flow chart for the same is shown in Fig. 5.15.

5.2.5.4 DESIGN OF PILE CAP

As shown in the flow chart of Fig. 5.16 the plan dimensions of the pile cap are computed

according to the arrangement and layout of piles in the group. Thereafter, the user will be asked

to enter the overall depth of the pile cap. Subsequently, the effective depth of pile cap is

70 | P a g e

calculated. Later, the moment in the pile cap is calculated considering the critical section to be

located at the face of pier. For calculated moments, the area of steel required in pile cap is

calculated. Then, the user will be asked to select the diameter of bars to be used in pile cap and

enter the desired spacing between the reinforcement. For the selected bar diameter and spacing,

area of steel to be provided in the pile cap is calculated. Further, the pile cap is checked for one-

way shear and two-way shear. If it fails, effective depth of pile cap will be increased.

Figure 5.14 Lateral load capacity of Under-reamed Pile

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Figure 5.15 Lateral load capacity of Bored Cast-in-situ pile

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Figure 5.16 Design of Pile Cap

73 | P a g e

5.3 CONCLUSION

The features of the software developed in theVB.Net platform for the analysis and design

of bridge sub-structure have been explained with relevant flow charts in this chapter. Some of the

interactive features of the program which facilitate the work of the user have been highlighted.

74 | P a g e

CHAPTER 6

RESULTS AND DISCUSSION

6.1 INTRODUCTION

The features & the functioning of various modules of the software developed for analysis

and design of bridge substructure has been discussed in the previous chapter. To illustrate the

practical application of the software, analysis and design of the well foundation and pile

foundation is performed for the assumed parameters. The long hand calculations of the problem

will be done, which are compared with the results of software, to verify the output of the

software developed in the thesis work.

6.2 PROBLEM ON WELL FOUNDATION

The analysis of the well foundation and design of various components of well are being

performed. The details required for the analysis and design of well foundation are given below:

DETAILS REGARDING BRIDGE SUPERSTRUCTURE

Dead load on each span: 1500 kN

Depth of simply supported girder: 2 m

Span of simply supported girder: 16 m

Type of Carriage way: Two lane carriage way

Clear carriage way width: 7.5 m

Area of bridge superstructure: 70 m2

Type of live load acting on bridge: Class A loading

BEARING DETAILS

Type of bearing used in bridge: Sliding bearings of Teflon on Stainless Steel

Centre-to-Centre distance between bearings along longitudinal axis of bridge (S1): 900

mm

Centre-to-Centre distance between bearings along transverse axis of bridge (S2): 5500

mm

dimension of bearing along longitudinal axis of bridge: 300 mm

dimension of bearing along transverse axis of bridge: 400 mm

OTHER DETAILS

Maximum mean velocity of stream: 4 m/sec

Maximum discharge of stream: 4500 m3/sec

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Weighted mean diameter of river bed particle: 0.505 mm

High Flood Level (H.F.L.): 459.5 m

Low Water Level (L.W.L.): 455.5 m

Bridge is located in seismic zone II

Angle of internal wall friction of soil ( : 37°

Submerged density of soil (γsub): 14 kN/m3

DETAILS OF PIER

Type of Material used in Pier: Reinforced Concrete

Grade of Concrete used in Pier: M25

Type of Pier used in bridge: Wall Type Pier

Type of cut-water provided to pier: Circular cut-water

Height of Pier: 7 m

Batter provided to pier: 1 in 20

PIER CAP DETAILS

Thickness of pier cap provided: 500 mm

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6.3 PROBLEM ON PILE FOUNDATION

The analysis of pile foundation design of pile and pile cap are being performed. The long

hand calculations are compared with the results of software to verify the output of software. The

detail used in analysis and design of foundation is given below:

DETAILS REGARDING BRIDGE SUPERSTRUCTURE

Dead load on each span: 1500 kN

Depth of simply supported girder: 2 m

Span of simply supported girder: 16 m

Type of Carriage way: Single lane carriage way

Clear carriage way width: 5 m

Area of bridge superstructure: 70 m2

Type of live load acting on bridge: Class AA loading

BEARING DETAILS

Type of bearing used in bridge: Sliding bearings of Teflon on Stainless Steel

Centre-to-Centre distance between bearings along longitudinal axis of bridge (S1): 1000

mm

Centre-to-Centre distance between bearings along transverse axis of bridge (S2): 4500

mm

dimension of bearing along longitudinal axis of bridge: 300 mm

dimension of bearing along transverse axis of bridge: 400 mm

GROUND PROFILE

Elevation of Ground Level: 453.4 m

Details of soil layer present in ground

For soil layer 1, Height of layer: 7 m

Type of soil: Normally Consolidated Clay

Density of soil: 17 kN/m3

Undrained Cohesion, Cu: 120 kN/m2

Compression Index: 0.3

For soil layer 2, Height of layer: 9m

Type of soil: Sand

Density of soil: 23 kN/m3

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Angle of internal friction, = 36°

Average static cone resistance: 2800 kN/m2

Fig. 6.1 Details of Soil layers in Ground

OTHER DETAILS

Bridge is located in seismic zone III

Type of Bridge: Non-river Bridge Crossing

DETAILS OF PIER

Type of Material used in Pier: Reinforced Concrete

Grade of Concrete used in Pier: M25

Type of Pier used in bridge: Hammer-head Type Pier

Height of Pier: 8 m

Diameter of Pier: 4 m

PIER CAP DETAILS

Thickness of rectangular portion of pier cap: 500 mm

Thickness of tapered portion of pier cap: 500 mm

128 | P a g e

6.4 CONCLUSIONS

The analysis and design of well foundation and pile foundation for the provided details have

been performed. The software generates the output of result with diagrammatic representation.

All the guide line are given to user where necessary. The output of the software is compared with

the long hand calculations of the problem. The output of software resemble with the results of

long hand calculations. Hence, it is concluded that the software provides accurate results and

with in the short period of time.

129 | P a g e

CHAPTER 7

CONCLUSIONS

7.1 CONCLUSIONS

The following conclusions are drawn on the basis of the software development work

related to analysis and design of bridge structures carried out for this thesis.

1) It is possible to develope user friendly, interactive and handy computational tools for the

analysis and design of bridge sub-structure sing readily available software platforms.

2) The proposed software can be particularly useful for the design optimisation of bridge

foundations particularly in the context of unexpected sub-soil conditions encountered

during construction. The program equips design engineers with a handy and convenient

software tool to quickly reconfigure and analyse and design bridge foundation in

response to field conditions for best performance and economy.

7.2 SCOPE FOR FURTHER WORK

The capabilities of the software developed can be further expanded to include the

following additional aspects of substructure analysis and design:

1) The superstructure analysis for continuous spans on different types of bearings and of

different configuration can be included so as to broad-base the scope of application of the

software.

2) Options for pier design can be included for varying geometry pier. Option for analysis

and design of pier cap of hammer-head type of piers using strut-and-tie models can be

included in the software.

3) Options for different arrangement and layouts of pile in a pile group can be included in

the software

4) The software can be interfaced with standard CAD packages like AUTOCAD for

generating detailing and working drawings of the bridge sub-structure.

130 | P a g e

CHAPTER 8

REFERENCES

1. IS: 456 2000; “Plain and Reinforced Concrete – Code of Practice (Fourth Revision)”;

BIS, New Delhi.

2. IS: 875 (Part 3) – 1987; “Code of Practice for Design Loads (Other than Earthquake) for

buildings and structures”; BIS, New Delhi.

3. IS: 2911 (Part I/Sec 2) – 1979; “Code of Practice for Design and Construction of Pile

Foundations, Concrete Piles, Bored Cast In-situ Piles (First Revision)”; BIS, New Delhi.

4. IS: 2911 (Part III) – 1980; “Code of Practice for Design and Construction of Pile

Foundations, Under-reamed Piles (First Revision)”; BIS, New Delhi.

5. IS: 3955 - 1967; “Code of Practice for Design and Construction of Well Foundations”;

BIS, New Delhi.

6. IRC: 6 – 2000; “Standard specifications and code of practice for road bridges, Section:

II, Loads and Stresses (Fourth Revision)”; The Indian Road Congress, New Delhi.

7. IRC: 45 – 1972; “Recommendations for estimating the resistance of soil below the

maximum scour level in the design of well foundations of bridges”; The Indian Road

Congress, New Delhi.

8. IRC: 78 – 2000; “Standard specifications and code of practice for road bridges, Section:

VII, Foundations and Substructure”; The Indian Road Congress, New Delhi.

9. SP: 16 (1980); “Design Aids For Reinforced Concrete to IS: 456-1978”; BIS, New

Delhi.

10. SP: 34 (S & T) (1980); “Hand Book on Concrete Reinforcement and Detailing”; BIS,

New Delhi.

11. Saran, S. (1996); “Analysis and Design of Substructure - Limit State Design (Second

Edition)”; Oxford & IHB Publishing Co. Pvt. Ltd., New Delhi.

12. Victor, D. J. (1973); “Essentials of Bridge Engineering (Fifth Edition)”; Oxford & IBH

Publishing Co. Pvt. Ltd., New Delhi.

13. Jain, A. K. (1993); ”Reinforced Concrete – Limit State Design (Fourth Edition)”; Nem

Chand & Bros., Roorkee, Fourth Edition.

14. Pillai, S. U. & Menon, D. (1999); “Reinforced Concrete Design”; Tata McGraw Hill,

New Delhi.

131 | P a g e

15. Das, B. M. (2004); “Principles of Foundation Engineering (Fifth Edition)”; Brook/Coles

Pub. Co., CA.

16. Singh, V. (1981); “Wells and Caissons (Second Edition)”; Nem Chand & Bros., Roorkee

17. Prakash, S. (1979); “Analysis and Design of Foundations And Retaining Structures”;

Sarita Prakashan, New Delhi.

18. Arora, K. R. (2003); “Soil Mechanics And Foundation Engineering (Sixth Edition)”;

Standard Publishers Distributors, New Delhi.

19. Ramamrutham, S. (2005); “Theory of Structure (Eighth Edition)”; Dhanpat Rai

Publishing Company (P) Ltd., New Delhi.

20. Holzner, S. (2005); “Visual Basic .Net Programming Black Book”; Paraglyph Press,

USA.

21. Terzaghi, K. And Peck, R. B. (1976); “Soil Mechanics in Engineering Practice”; John

Wiley and Sons Inc., New York.

22. De Beer, E. And Marten (1957); “Method of Computation on Upper limit for the

Influences of Heterogeneity of Sand Layers in the Settlement of Bridges”; Proc. 4th

Int.

Conf. On SMFE, London, Vol. 1.

23. www.iricen.gov.in , website of Indian Railway Institute of Civil Engineering, Pune.

132 | P a g e

APPENDIX – A

SUPPORTING LONG HAND CALCULATIONS FOR THE

ILLUSTRATVIE PROBLEM ON WELL FOUNDATION

Minimum top width of pier required = bearing spacing along longitudinal axis + bearing

dimension along longitudinal axis + 600 mm

= 900 + 300 + 600

= 1800 mm

Top width of pier provided: 1800 mm (= minimum top width of pier required. Hence OK.)

Minimum desirable length of pier (without cut-water) = bearing spacing along transverse axis

+ bearing dimension along transverse

axis + 1200 mm

= 5500 + 400 + 1200

= 7100 mm

Length of pier provided (without cut-water): 7100 mm (= minimum desirable length of pier.

Hence OK.)

Batter provided in pier: 1 in 20

Hence, bottom width of pier = = 2500 mm

PIER CAP DETAILS

Span of bridge is 16 m i.e. less than 25 m. Hence, minimum thickness of pier cap should be 250

mm.

Thickness of pier cap provided: 500 mm (> 250 mm. Hence OK.)

Width of pier cap = top width pier cap + (2 * 75)

= 1800 + 150

= 1950 mm

Length of pier cap = length of pier (including cut-water) + (2 * 75)

= 7100 + 1800 + 150

= 9050 mm

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Fig. A-1 Pier Section in longitudinal direction of bridge

ANALYSIS OF PIER

Now, after deciding the dimensions of pier & pier cap, the pier is analyzed for various

forces & stresses are calculated due to these forces.

CALCULATION OF STRESSES IN PIER

The stresses developed in pier due to various forces acting on it are calculated as below:

1. Stresses due to dead load & self weight of Pier

Dead load from superstructure of bridge = 2 X 1500

= 3000 kN

Area at the top of pier =

= 15.33 m2

Area at the bottom of pier =

= 22.66 m2

Area at the middle of pier =

= 18.9 m2

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Pier Volume =

=

= 132.52 m3

Pier cap volume =

= 8.82 m3

Total volume = 132.52 + 8.82 = 141.34 m3

Hence, total weight of pier & pier cap =

Stresses due to dead load of superstructure & weight of pier & pier cap =

= 288.34 kN/m2

2. Stresses due to eccentricity of live load

Moment of Inertia about X axis i.e. T-T axis of bridge, Ixx

Moment of Inertia about Y axis i.e. L-L axis of bridge, Iyy

(a) Due to eccentric live load about transverse axis of bridge

Vertical live load on pier, producing maximum stress about transverse axis = 763 kN, &

Moment due to live load eccentricity about transverse axis of bridge, producing maximum stress

about transverse axis = 180 kNm

Stress at the base of pier due to eccentricity of live load about transverse axis

=

=

= 53.84 kN/m2

or 13.57 kN/m2

(b) Due to eccentric live load about longitudinal axis of bridge

Vertical live load on pier, producing maximum stress due about longitudinal axis = 395 kN,

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Moment due to live load eccentricity about transverse axis of bridge, producing maximum

about longitudinal axis = 969 kNm

Stress at the base of pier due to eccentricity of live load about longitudinal axis

=

=

= 46.85 kN/m2

or -11.94 kN/m2

NOTE: The stresses acting at the base of pier due to live load eccentricity is calculated with the

use of program prepared in Microsoft Excel Worksheet.

3. Stresses due to longitudinal forces

(a) Due to tractive effort or braking forces

Braking effect is invariably greater than tractive effort. Hence, braking effort is considered.

Longitudinal force of Class A load = 0.2 X 486 X 2

= 194.4 kN

Moment at the base = 194.4 X 11

= 2138 kNm

Stress at the base of pier due to braking effort =

=

=

(b) Due to resistance at bearings

Coefficient of friction on the left side of bearing = 0.05

Coefficient of friction on the right side of bearing (reducing 5%) = 0.0475

Assume the combination of dead load & live load acting on the left side bearing and dead load

on right side bearing

Maximum live load reaction acting on the left side bearing = 648 kN

(as calculated from the program based on Excel Worksheet)

Total resistance to sliding on the left side bearing = 0.05 X (1500 + 648) = 107 kN &

Total reacting on the right side bearing = 0.0475 X 1500 = 71.25 kN

Unbalanced force = 36 kN

Moment due to unbalanced force at the base of pier = 36 X 7.8 = 282 kNm

136 | P a g e

Stress at the base of pier = = = 31.56 kN

4. Stresses due to water current

Maximum scour depth due to river stream will be calculated.

Discharge, Q = 4500 m3/sec

Linear water-way,

Db = , here Q is increased by 30%

=

= 17.98 m

According to the formula recommended by IRC: 78-20008,

Mean scour depth,

where, 1.76 = 1.76 = 1.25

= 8.54 m

And as per the Lacey’s formula,

Normal depth of scour,

where, 1.76 = 1.76 = 1.25

The scour depth calculated from the formula recommended by IRC: 78-20008 is greater.

Hence maximum score depth is computed from the scour depth as per the formula recommended

by IRC: 78-20008.

Maximum scour depth = 2 X = 17.07 m

Intensity of pressure, ,

=

= 10.67 kN/m2

To account for possible variation in water current direction, assume maximum angle change in

current direction of 20°

Hence, considering the change of 20° in direction of water current,

137 | P a g e

Pressure along longitudinal axis of bridge =

= 2.81 kN/ m2

& Pressure along transverse axis of bridge =

= 9.42 kN/ m2

Total Pressure along transverse axis of bridge = 10.67 + 9.42 = 20.09 kN/ m2

(a) (b)

Fig. A-2 Water Pressure Details (a) in transverse direction & (b) in longitudinal

direction of bridge

Moment about longitudinal axis of bridge

Pressure at HFL = 20.09 kN/ m2

& Pressure at LWL = 15.38 kN/ m2

lever arm of resultant pressure from the base of pier =

= 2.09

Moment at the base of pier =

Stress about longitudinal axis at the base of pier =

=

=

138 | P a g e

Moment about transverse axis of bridge

Pressure at HFL = 2.81 kN/ m2

& Pressure at LWL = 2.15 kN/ m2

lever arm of resultant pressure from the base of pier =

= 2.09

Moment at the base of pier =

Stress about transverse axis at the base of pier =

=

=

5. Stresses due to effect of buoyancy

Width of pier at HFL = 2.1 m

Area of pier at the HFL =

Hence, submerged volume of pier =

Net buoyant force = 82 X 10 X 0.15 = 123 kN

Stress due to buoyant force = =

6. Stresses due to wind load

(a) Area of superstructure as seen in elevation = 70 m2

The height of exposed surface of bridge structure, when water level is at HFL = 5.8 m

For 5.8 m, the intensity of wind load is taken as 0.72 kN/ m2

Hence, Total wind force = 70 X 0.72 = 50.4 kN/ m2

(b) Considering the wind load acting on moving live load having magnitude of 3 kN/m & acting

at 1.5 m above road way,

Wind force against the moving load = 16 X 3 = 48 kN

(c) Total wind force as in (a) & (b) above = 48 + 50.4 = 98.4 kN

(d) Minimum limiting load on deck at 4.5 kN/m = 16 X 4.5 = 72 kN

(e) Minimum limiting load on at 2.4 kN/m2 on exposed surface = 2.4 X 70 = 168 kN

Since force in (e) is maximum, this will be adopted. This force will be assumed to act at the

bearing level for the purpose of calculating the moment at the base of pier.

139 | P a g e

Moment at the base of pier = 168 X 8.8 = 1478.4 kNm

Stress at the base of pier =

=

=

7. Stresses due to seismic effect

(a) Seismic moment acting at the base of pier due to the masses of bridge component & live load

Seismic moment at the base of pier, due to mass of pier

=

Maximum live load acting on the pier, for Class A train = 791 kN

(as calculated from the program coded in Excel Worksheet)

Total dead load of superstructure = 2 X 1500 = 3000 kN

& Mass of pier cap = 221 kN

Hence, total seismic moment due to mass of bridge components

= ((791 X 11) + (3000 X 8.8) + (221 X 7.25)) X 0.1 + 1084

= 4755 kNm

Total seismic moment due to mass of pier about longitudinal axis = 4755 kNm &

Total seismic moment due to mass of pier about transverse axis

= ((3000 X 8.8) + (221 X 7.25)) X 0.1 + 1084

= 3885 kNm

(b) Moment due to hydrodynamic forces

For hydrodynamic force along longitudinal direction

H = 4 m, a = 4.8 Therefore,

For seismic zone II,

For value of , &

= 71 kN

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Moment at the base of pier about transverse axis

= 110 kNm

For hydrodynamic force along transverse direction

H = 4 m, a = 1.25 Therefore,


For value of , &

= 10 kN

Moment at the base of pier about longitudinal axis

= 6.5 kNm

Now,

Resultant stress due to seismic effect about transverse axis =

=

=

Resultant stress due to seismic effect about longitudinal axis =

=

=

8. Stresses due to horizontal shear forces

Maximum horizontal shear force at roller support is calculated for N Case, N + T Case &

N + T + S Case. For these maximum shear forces, resultant stresses at the base of pier are

calculated for different load combinations.

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Table A-1 Calculation of Maximum Shear forces bearings

No. Forces At hinge

support At roller support

1 Vertical Reaction due to dead load, kN 750 750

2 Vertical Reaction due to live load, kN

(when live load at roller support is max.) 176 323

3 Total Vertical Reaction, kN 926 1073

4 Maximum horizontal force at roller

support, due to resistance at bearings, kN ---

0.05 X 1073 =

53.7

5 Braking force at bearing level, kN 48.6 48.6

6 Resultant horizontal forces, at roller

support for N Case loading, kN --- 48.6


support for N + T Case loading, kN ---

48.6 + 53.7 =

102.3

8

Resultant horizontal forces, at roller

support for N + T + S Case loading, kN

(No braking force)

---

(1500 X 0.1) +

((323+176) X 0.1)

+ 53.7 = 253.7 kN

Table A-2 Stresses due to horizontal shear force at bearings

No. Load Combination Shear Force, kN Moment, kNm Stress, kN/m2

1 N Case 48.6 379

2 N + T Case 102.3 798

3 N + T + S Case 253.7 kN 1979

Table A-3 shows the summary of stresses calculated due to various forces acting on the

pier.

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Table A-3 Summary of Stresses due to various forces acting on the Pier

No. Loads

Stresses due to

vertical forces, kN/m2

Stresses due to

moment about

transverse axis of

bridge, kN/m2

Stresses due to

moment about

longitudinal axis of

bridge, kN/m2

DRY FLOODS DRY FLOODS DRY FLOODS

1 Dead load & self

weight 288.34 288.34 -- -- -- --

2 Eccentric live load 33.67 33.67

3

Longitudinal force

(1) Braking effort -- -- -- --

(2)Bearing resistance -- -- -- --

4 Wind load -- -- -- --

5 Water current -- -- -- --

6 Buoyancy -- -5.43 -- -- -- --

7 Seismic effect -- --

The summary of stresses due to horizontal shear forces is given in Table A-2.

Now, considering stresses due to all the forces as calculated above, we will compute the

resultant maximum stresses at “A” & “B” on pier for different load combinations. The location

of “A” & “B” on pier are shown in Fig. A-3.

The resultant compressive & tensile stresses acting at point “A” & “B” on pier for

different load combinations are shown in Table A-4 & Table A-5 respectively.

Fig. A-3 Location of “A” & “B” on pier

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Table A-4 Resultant Compressive Stresses at Point “A” & “B” on Pier

No. Loads

Resultant compressive stress at

“A” on pier, MPa


“B” on pier, MPa

DRY FLOOD DRY FLOOD

1 N Case 0.380 0.385 0.624 0.640

2 N + T Case 0.380 0.385 0.743 0.759

3 N + T + S Case 0.479 0.485 1.309 1.338

Table A-5 Resultant Tensile Stresses at Point “A” & “B” on Pier

No. Loads

Resultant compressive stress

at “A” on pier, MPa

Resultant compressive stress

at “B” on pier, MPa

DRY FLOOD DRY FLOOD

1 N Case 0.231 0.216 0.02 -0.0072

2 N + T Case 0.231 0.216 -0.081 0.108

3 N + T + S Case 0.132 0.116 -0.649 1.338

COMPARISION OF MAXIMUM STRESSES IN PIER WITH THEIR PERMISSIBLE LIMITS

The maximum compressive and tensile stresses in pier calculated for different load

combinations are compared with their permissible limits as shown below:

Permissible compressive stress for M25 grade of concrete = 6 MPa (as per Table 21 of IS: 456-

20001) & Permissible tensile stress for M25 grade of concrete = 0.15 X 6 MPa = 0.9 MPa

Maximum compressive stress under “N” Case loading = 0.64 MPa < 6 MPa. Hence,

Safe.

Maximum compressive stress under “N + T” Case loading = 0.759 MPa < 6.9 MPa

(15% increase). Hence, Safe.

Maximum compressive stress under “N + T + S” Case loading = 1.338 MPa < 9 MPa


Maximum tensile stress under “N” Case loading = 0.0072 MPa < 0.9 MPa. Hence, Safe.

Maximum tensile stress under “N + T” Case loading = 0.081 MPa < 1.035 MPa (15%

increase). Hence, Safe.

Maximum tensile stress under “N + T + S” Case loading = 0.649 MPa < 1.35 MPa (50%


144 | P a g e

ANALYSIS OF WELL FOUNDATION

Now, the dimensions of different components of well foundation are decided.

Maximum scour depth = 17.1 m (as calculated previously)

Maximum scour level = 442.4 m

Unsupported length of well is LWL – Maximum scour level = 455.5 – 442.4 = 13.1 m

Providing the grip length of 10 m, the height of well is 23.1 m.

Diameter of well is assumed 12000 mm

Thickness of well cap = 1200 mm

Thickness of top plug = 500 mm

Minimum thickness of steining = = 1730 mm

Thickness of steining = 1750 mm > 1730 mm. Hence, OK.

Height of well curb = 2750 mm

Height of steining = 23.1 – 1.2 – 2.75 = 19.15 m

Diameter of dredge hole = 12000 – (2 X 1750) = 8500 mm

Thickness of bottom plug = 2750 + 500 + 1000 = 4250 mm

Sand filling is done in well foundation up to the soffit of top plug

Density of sand filled in dredge hole = 24 kN/m3

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Fig. A-4 Diagram of a Well Foundation

Thereafter, the vertical and horizontal forces & moments acting at the base of the

foundation is calculated

CALCULATION OF FORCES & MOMENTS AT THE BASE OF WELL FOUNDATION

Water level is considered at HFL. Hence all the vertical load and horizontal forces are calculated

accordingly.

Calculation of Vertical load at the base of foundation

1. Total Dead load from superstructure = (2 X 1500) = 3000 kN

2. Live load reaction acting at the base of foundation = 791 kN (As calculated from the program

prepared on Microsoft Excel Worksheet)

3. Weight of pier & pier cap = 2492 + 221 = 2713 kN

4. Weight of well cap =

5. Weight of top plug =

146 | P a g e

6. Weight of Steining =

Volume of Well curb=

+

= 97.82 m3

7. Weight of well curb = 1467 kN

Fig. A-5 Diagram of Well curb

8. Weight of bottom plug =

= 4520 kN

9. Weight of sand filling =

Fig. A-6 Diagram of Bottom Plug

Therefore, total vertical load acting at the base of well = 45508 kN

Calculation of Horizontal forces & Moments at the base of foundation

1. Due to water current (Refer Fig. A-2)

Moment about longitudinal axis =

= 26679 kNm

Moment about transverse axis =

147 | P a g e

= 2282 + 3153

= 5495 kNm

Force along transverse axis =

= 1372 kN

Force along longitudinal axis =

= 262 kN

2. Due to braking effect

Braking force acting at the base of pier = 194 kN

Moment at the base of pier = 6623 kNm

3. Due to resistance at bearing






(as calculated from the program prepared on Excel worksheet)

Total resistance to sliding on the left side bearing = 0.05 X (3000 + 1296) = 214 kN &



Moment due to unbalanced force at the base of pier = 72 X 30.87 = 2231 kNm



The height of exposed surface of bridge structure, when water level is at HFL = 5.8 m





Wind force against the moving load = 16 X 3 = 48 kN

(c) Total wind force as in (a) & (b) above = 48 + 50.4 = 98.4 kN

148 | P a g e

(d) Minimum limiting load on deck at 4.5 kN/m = 16 X 4.5 = 72 kN





5. Due to eccentricity of live load

Moment due to live load eccentricity about transverse axis of bridge = 179.8 kNm

.Moment due to live load eccentricity about longitudinal axis of bridge = 968.9 kNm

6. Due to horizontal shear forces at bearing level

Table A-6 Horizontal shear force at bearings & moments at the base of foundation

No. Load Combination Shear Force, kN Moment, kNm

1 N Case 48.6 1500

2 N + T Case 102.3 3158

3 N + T + S Case 253.7 kN 7831

7. Due to seismic effect

(a) Seismic moment due to mass of bridge components & live load

Table A-7 Seismic moment due of mass of bridge components & Live load

No. Force

Seismic force acting at the

centroid of component,

kN

Moment,

kNm

1 Live load 79.1 2694.9

2 Dead load of superstructure 300 9561

3 Pier cap 22.1 668.8

4 Pier 249.3 6656

5 Well Cap 203.6 4574

6 Top Plug 42.6 920

7 Steining 1616 19899

8 Well curb 146.7 251.3

9 Bottom Plug 371.4 579.7

10 Sand fill 1440 17748

149 | P a g e

Considering the forces and moments as calculated above,

Total moment about longitudinal axis = 63524.5 kNm

& Total moment about transverse axis = 60829.6 kNm

(b) Moment due to hydrodynamic forces

For hydrodynamic force along longitudinal direction

H = 17.1 m, a = 6 m Therefore,


For value of , &

= 943.4 kN

, &

Net force on well =

Net moment at the base of well =

For the hydrodynamic force on pier

H = 17.1 m, a = 4.8 Therefore,


For value of , &

= 647.47 kN

Resultant hydrodynamic pressure on the pier =

Moment at the base of well =

Total moment at the base of well about transverse axis of bridge = 6093 kNm

For hydrodynamic force along transverse direction

H = 17.1 m, a = 1.25 Therefore,


For value of , &

150 | P a g e

= 55.49 kN

Moment at the base of well =

Total moment at the base of well = 4925 + 105 = 5030 kNm

6. Due to tilt & shift

Moment due to tilt = = 5634 kNm

Moment due to shift = = 2317 kNm

The forces and moments as computed by software are as follows:

Total vertical load acting at the base of well foundation W = 45515 kN

Horizontal force along longitudinal axis of bridge, HLL = 630.8 kN

Horizontal force along transverse axis of bridge, HTT = 6754.9 kN

Moment acting at the base of well about longitudinal axis, MLL = 104160 kNm

Moment acting at the base of well about transverse axis, MTT = 17692 kNm

Now, the resistance of the soil surrounding the foundation is determined by elastic theory &

ultimate resistance method & is checked whether the soil surrounding the foundation is able to

resist the forces and moments transferred by the well foundation.

ELASTIC THEORY

STEP 1: The value of W, H & M is determined as follows:

Values of total vertical force W, resultant horizontal force H & resultant moment M

acting at the base of pier is calculated considering seismic effect & neglecting the wind effect on

bridge. Seismic effect along transverse direction is critical. Hence the forces & moments are

calculated considering the seismic effect along transverse direction.

W = 45508 kN

HLL = 630.3 kN & HTT = 6749.3 kN

MLL = 104146 kNm & MTT = 17696 kNm

The values of forces and moments as calculated by the software are

W = 45515 kN

HLL = 630.8 kN & HTT = 6754.9 kN

MLL = 104160 kNm & MTT = 17692 kNm

151 | P a g e

The results of long hand calculations and as generated by software are almost same.

Hence, we will continue the problem considering the force and moments as generated by

software.

Hence, W = 45515 kN

STEP 2: Compute

Take, m = 1,

Hence,

= 2254.5 m4

STEP 3: Ensure the following

Both the conditions are satisfied.


152 | P a g e

= 46.86

Hence, the condition is satisfied

STEP 5: Calculate

> 675 kN/m2.

Hence, Safe.

& 77.7 kN/ m2

> 0. Hence, Safe.

All the above five steps are repeated for loads with combination of wind load &

neglecting seismic effect

STEP 1: The value of W, H & M is determined as follows:

W = 45508 kN

MLL = 40945.43 kNm & MTT = 17696 kNm

The values of forces and moments as calculated by the software are

W = 45515 kN

HLL = 630.8 kN & HTT = 1537.4 kN

MLL = 40945.91 kNm & MTT = 17692.86 kNm

The results of long hand calculations and as generated by software are almost same.

Hence, we will continue the problem considering the force and moments as generated by

software.

Hence, W = 45515 kN

153 | P a g e

STEP 2: Compute

Take, m = 1,

&

Hence, &

= 2254.5 m4

STEP 3: Ensure the following

Both the conditions are satisfied.


= 19.78

Hence, the condition is satisfied

154 | P a g e

STEP 5: Calculate

> 675 kN/m2.

Hence, Safe.

& 259.65 kN/ m2

> 0. Hence, Safe.

6.2.2.3 ULTIMATE RESISTANCE METHOD

STEP 1: Check that ,

W = 1.1 DL + 1.6 LL

= (1.1 X 44724) + (1.6 X 791)

= 50461.6 kN

Hence, condition is satisfied

STEP 2: Calculate Mb &

Calculate Mb = QWB

For ratio , Q = 0.262, (as obtained from Table 3.2 of Chapter 3)

W = 50461.6 kN

Mb = QWB = 0.262 X 50461.6 X 12 X = 119552 kNm

= 162509 kNm

155 | P a g e

STEP 3: Calculate

= 91211.52 kNm

STEP 4: Calculate Mt = 0.7(Mb + Ms + Mf)

Mt = 0.7(119552 + 162509 + 91211.52) = 261291 kNm

STEP 5: Calculate ,

= 132066 kNm

Mt . Hence, OK.

DESIGN OF COMPONENTS OF WELL FOUNDATION

DESIGN OF WELL CURB

Well curb is designed for hoop tension,

N =

Referring to Fig. A-5,

, ,

Value of hoop tension being less, minimum reinforcement is provided in well curb

Volume of well curb = 97.819 m3

Reinforcement required in well curb = Minimum reinforcement in well curb

= 72 X 97.819

= 7043 kg

= (7043/7850) m3

= 0.8972 m

3

Provide 50 nos. of 25 mm dia.bar rings distributed along the perimeter of the well curb

& 80 nos. of 16 mm dia. bar stirrups enclosing the perimeter of well curb

Volume of rings =

Volume of stirrups =

156 | P a g e

Total volume of reinforcement provided = 0.9121 m3 > 0.8972 m

3 . Hence, OK.

16 mm dia. anchor bars are provided at 300 mm c/c

DESIGN OF WELL STEINING

Before designing the section of steining, stresses in steining are calculated at the level of

maximum scour as shown below:

Moment at the section of steining about longitudinal axis = 9881 kNm

Moment at the section of steining about transverse axis = 41869 kNm

Vertical load acting on the section at the level of maximum scour, W = 19001 kN

Area of section =

Z =

Hence,

& . Hence, Safe.

Required area of vertical reinforcement in steining = 0.12 % of gross sectional area of

steining

= 0.0676 m2 = 67622 mm

2

Area of steel required on both the faces of steining = 67622 mm2

Area of steel required on one face of steining = 33811 mm2

Using 16 mm dia. bars in vertical reinforcement,

Spacing of 16 mm dia. bars required =

Effective depth of steining = 1750 – 50-8 = 1692 mm

Spacing provided = 150 mm <

Hence, 16 mm dia. bars of vertical reinforcement is provided at 150 mm c/c

Required volume of hoop steel in steining =0.04 % of volume of steining / unit length

of steining

157 | P a g e

= 0.02254 m3

= 2.254 X 107 mm

3

Area of steel required on both face of steining = on each face

Area of steel required on each face = 350

Using 10 mm dia. bars in hoop reinforcement,

Spacing of 10 mm dia. bars required =

Spacing provided = 220 mm <

Hence, 10 mm dia. bars of hoop reinforcement is provided at 220 mm c/c

The thickness of steining is checked for requirement of excessive kentledge during

sinking of well.

Thickness,

where, kN/m2

Hence, excessive kentledge is required for sinking the well

DESIGN OF WELL CAP

Over all depth of well cap = 1200 mm

Effective depth = 12000-50-12.5 = 1137.5 mm

Vertical load on well cap = 7325.5 kN

Self weight of well cap = 25 X 1.2 = 30 kN/m2

Moment at the base of pier, about transverse axis = 8768 kNm

Moment at the base of pier, about longitudinal axis = 1309.6 kNm

Resultant moment, M = =8865.3 kNm

The load from the pier is dispersed at an angle of 45° to the well cap, throughout its

effective depth. Area of load dispersion is calculated,

Dispersion width = 2500 + (2 X effective depth of well cap) = 4.775 m

Length of dispersion = 9.6 + (2 X effective depth of well cap) = 11.875 m < Diameter of well

cap. Hence, OK.

158 | P a g e

Maximum dispersion width available = a

Mean length of dispersion =

Fig. A-7 Load dispersion area in well cap

Hence, dispersion area = 11.44 X 4.775 = 54.636 m2

Diameter of equivalent circle i.e. circle of patch loading = 8.34 m

Since the well-cap is assumed to be partially restrained by the steining, the moments in the

well-cap are calculated for circular patch loading and for U.D.L. (self-weight of well cap) for the

following two conditions: Well cap freely supported on steining & Well cap fully clamped on

steining

Condition 1: Well cap freely supported on steining

(i) For moments beneath loaded area due to circular patch loading

159 | P a g e

Hence, = 833.1 kNm

(ii) For moments beneath unloaded area due to circular patch loading


Hence,




Condition 2: Well cap fully clamped at support

(i) For moments beneath loaded area due to circular patch loading

(ii) For moments beneath unloaded area due to circular patch loading


160 | P a g e




(a) Moments due to Patch load (b) Moments due to Self weight load

Fig. A-8 Moments in well-cap when freely supported

161 | P a g e

(a) Moments due to Patch load (b) Moments due to Self weight load

Fig. A-9 Moments in well-cap when fully clamped

Maximum moment at the centre of well cap due to moments transferred form pier

= , where

=

Maximum moment at the edges of well cap due to moments transferred from pier

= .

=

Total moment at the centre of well-cap

Due to patch loads =

Due to self weight of well cap =

Due to moment from pier & superstructure =

Hence, total sagging moment = 1469 kNm &

total hogging moment = 780.4 kNm

Total moment at the support of well-cap

Due to patch loads =

Due to self weight of well cap =

Due to moment from pier & superstructure =

Hence, total hogging moment = 486.16 kNm &

Total hogging moment at the centre of well cap = 780.4 kNm

162 | P a g e

Total sagging moment at the centre of well cap = 1469 kNm &

Total hogging moment at the support of well cap = 486.2 kNm

Now, the reinforcement of the well cap is calculated.

Bottom reinforcement of the well cap will be designed for total sagging moment at the

centre of well cap = 1469 kNm

0.515%

28 mm dia. bars are used at the bottom of well cap,

Spacing required for 28 mm dia. bars =

Spacing provided to 28 mm dia. bars = 100 mm <

Top reinforcement of the well cap will be designed for total hogging moment at the

centre of well cap = 780.4 kNm

0.262%

25 mm dia. bars are used at the top of well cap,



Hence, 25 mm dia. bars at 150 mm c/c is provided at the top of well cap & 28 mm dia.

bars are provided at 100 mm c/c is provided at the bottom of well cap.

163 | P a g e

Check for Punching Shear

Total vertical load acting on the well cap = 3533 + 3000 +791 = 7324 kN

Hence, Shear stress acting on the well-cap =

Maximum shear stress for M25 Grade concrete =

Hence, Safe

Fig. A-10 Reinforcement Details of Well Cap

164 | P a g e

APPENDIX – B

SUPPORTING LONG HAND CALCULATIONS FOR THE

ILLUSTRATVIE PROBLEM ON PILE FOUNDATION

Width of pier cap = 4000 mm

Length of pier cap = Bearing Spacing(S2) + dimension of bearing along transverse axis +

1200

= 4500 + 400 + 1200

= 6100 mm

Fig. B-1 Pier Section in transverse direction of bridge

ANALYSIS OF PIER

Now, the pier is analyzed for various forces acting on it.

CALCULATION OF STRESSES IN PIER

The stresses developed in pier due to various forces acting on it are calculated as below:

1. Stresses due to dead load & self weight of Pier

Dead load from superstructure of bridge = 2 X 1500

= 3000 kN

Pier Volume =

165 | P a g e

=

= 100.53 m3

Volume of tapered portion of Pier cap =

Volume of rectangular portion of Pier cap =

Total volume of pier & pier cap = 122.83 m3

Hence, total weight of pier & pier cap =

C/s area of pier = 12.57 m2

Stresses due to dead load of superstructure & weight of pier & pier cap =

= 483.1 kN/m2

2. Stresses due to eccentricity of live load

Moment of Inertia about X axis i.e. T-T axis of bridge, Ixx

= Moment of Inertia about Y axis i.e. L-L axis of bridge, Iyy

(a) Due to eccentric live load about transverse axis of bridge

Vertical live load on pier, producing maximum stress about transverse axis = 385 kN, &

Moment due to live load eccentricity about transverse axis of bridge, producing maximum stress

about transverse axis = 192.5 kNm

Stress at the base of pier due to eccentricity of live load about transverse axis

=

=

= 61.27 kN/m2

or 0 kN/m2

(b) Due to eccentric live load about longitudinal axis of bridge

Vertical live load on pier, producing maximum stress due about longitudinal axis = 397.5 kN,

& Moment due to live load eccentricity about transverse axis of bridge, producing maximum

stress about longitudinal axis = 377.6 kNm

Stress at the base of pier due to eccentricity of live load about longitudinal axis

=

166 | P a g e

=

= 91.73 kN/m2

or -28.47 kN/m2

NOTE: The stresses acting at the base of pier due to live load eccentricity is calculated on

program made in Microsoft Excel Worksheet.

3. Stresses due to longitudinal forces

(a) Due to tractive effort or braking forces

Braking effect is invariably greater than tractive effort. Hence, braking effort is considered.

Longitudinal force of Class AA load = 0.2 X 400

= 80 kN

Moment at the base = 80 X 12.5

= 1000 kNm

Stress at the base of pier due to braking effort =

=

=

(b) Due to resistance at bearings






(as calculated on program prepared in Microsoft Excel Worksheet)

Total resistance to sliding on the left side bearing = 0.05 X (1500 + 385) = 94.25 kN &



Moment due to unbalanced force at the base of pier = 23 X 9.3 = 213.9 kNm

Stress at the base of pier = = = 34.04



167 | P a g e

The height of exposed surface of bridge structure = 10.3 m





Wind force against the moving load = 1.2 X 3 = 4.2 kN

(c) Total wind force as in (a) & (b) above = 68.57 kN

(d) Minimum limiting load on deck at 4.5 kN/m = 1.2 X 4.5 = 5.4 kN





Stress at the base of pier =

=

=

5. Stresses due to seismic effect

(a) Seismic moment acting at the base of pier due to the masses of bridge component & live load

Lever arm of tapered portion of pier cap from the base of pier =

Hence, total seismic moment due to mass of bridge components & live load about longitudinal

axis = ((397.5 X 12.5) + (305 X 8.75) + (252.5 X 8.3) + (252.5 X 8.3) + (2513 X

4) + (1500 X 10.3 X 2)) X 0.1

= 5068.7 kNm

Total seismic moment due to mass of bridge components & live load about transverse axis

= ((305 X 8.75) + (252.5 X 8.3) + (252.5 X 8.3) + (2513 X 4) + (1500 X 10.3 X 2)) X 0.1

= 4571.8 kNm

Resultant stress due to seismic effect about transverse axis =

=

=

168 | P a g e

Resultant stress due to seismic effect about longitudinal axis =

=

=

6. Stresses due to horizontal shear forces

Maximum horizontal shear force at roller support is calculated for N Case, N + T Case &

N + T + S Case. For these maximum shear forces, resultant stresses at the base of pier are

calculated for different load combinations.

Table B-1 Calculation of Maximum Shear forces at bearings

No. Forces At hinge

support At roller support

1 Vertical Reaction due to dead load, kN 750 750

2 Vertical Reaction due to live load, kN

(when live load at roller support is max.) 0 385

3 Total Vertical Reaction, kN 750 1135

4 Maximum horizontal force at roller

support, due to resistance at bearings, kN --

0.05 X 1135=

56.75

5 Braking force at bearing level, kN 40 40


support for N Case loading, kN -- 40


support for N + T Case loading, kN --- 40+ 56.75= 96.75

8

Resultant horizontal forces, at roller

support for N + T + S Case loading, kN

(No braking force)

---

(1500 X 0.1) +

(397.5X 0.1) =

189.75

169 | P a g e

Table B-2 Stresses due to horizontal shear force at bearings

No. Load Combination Shear Force, kN Moment, kNm Stress, kN/m2

1 N Case 40 372

2 N + T Case 96.75 899.78

3 N + T + S Case 189.75 2294.76

Table B-3 shows the summary of stresses occurring due to various forces acting on the

pier, as calculated above.

Table B-3 Summary of Stresses due to various forces acting on the Pier

No. Loads

Stresses due to

vertical load,

kN/m2

Stresses due to

moment about

transverse axis

of bridge,

kN/m2

Stresses due to

moment about

longitudinal axis of

bridge, kN/m2

1 Dead load & self weight 483.1 -- --

2 Eccentric live load 31.45 30.63 60.1

3

Longitudinal force

(a) Braking Effort -- --

(b)Due to resistance at bearing -- --

4 Wind load -- -- 275.4

5 Seismic effect --

The summary of stresses due to horizontal shear forces is given in Table B-2.

Now, considering stresses due to all the forces as calculated above, we will compute the

resultant maximum stresses at “A” & “B” on pier for different load combinations.

Fig. B-2 shows the location of “A” & “B” on pier.

170 | P a g e

Fig. B-2 Location of “A” & “B” on Pier

The resultant compressive & tensile stresses acting at “A” & “B” on pier for different

load combinations are shown in Table B-4 & Table B-5 respectively.

Table B-4 Resultant Compressive Stresses at “A” & “B” on Pier

No. Loads Resultant compressive stress at




1 N Case 0.85 0.763

2 N + T Case 0.85 0.886

3 N + T + S Case 1.38 1.845

Table B-5 Resultant Tensile Stresses at “A” & “B” on Pier

No. Loads Resultant compressive stress at




1 N Case 0.179 0.264

2 N + T Case 0.179 0.152

3 N + T + S Case -0.352 -0.708

COMPARISION OF MAXIMUM STRESSES IN PIER WITH THEIR PERMISSIBLE LIMITS

The maximum compressive and tensile stresses in pier calculated for different load

combinations are compared with their permissible limits as shown below:

Permissible compressive stress for M25 grade of concrete = 6 MPa (as per Table 21 of IS: 456-

20001) & Permissible tensile stress for M25 grade of concrete = 0.15 X 6 MPa = 0.9 MPa

171 | P a g e

Maximum compressive stress under “N” Case loading = 0.85 MPa < 6 MPa. Hence,

Safe.

Maximum compressive stress under “N + T” Case loading = 0.886 MPa < 6.9 MPa (15%


Maximum compressive stress under “N + T + S” Case loading = 1.845 MPa < 9 MPa


Maximum tensile stress under “N + T + S” Case loading = 0.708 MPa < 1.35 MPa (50%


ANALYSIS AND DESIGN OF PILE FOUNDATION

The pile cap in foundation is embedded into the ground such that the top of pile cap is at

ground level. The thickness of pile cap is assumed as 1500 mm. Piles used in the foundation are

bored cast-in-situ pile.

The diameter of pile is taken as 900 mm & pile length is taken as 13 m.

SAFE BERING CAPACITY OF PILE

To estimate the safe bearing capacity of pile, the ultimate bearing capacity of pile is

calculated. Static formulae are used in estimating ultimate bearing capacity of pile:

Ultimate bearing capacity of a pile

,

The pile is penetrated into the two soil layers. Hence, its ultimate bearing capacity is

dependent on the properties of both the soils,

For soil layer 1

Skin frictional resistance due to soil layer 1,

As the soil layer 1 is Clay,

, where α = adhesion factor, is obtained from Figure 4.9 of Chapter 4

= 0.415

undrained cohesion of soil, = 120 kN/m2

&

= 774.78 kN

172 | P a g e

Fig. B-3 Effective overburden pressure on pile

For soil layer 2


As the soil layer 2 is Sand,

,

Effective overburden pressure at top of the soil layer 2,

Effective overburden pressure at pile tip,

Effective overburden pressure at mid of the pile penetration in soil layer 2, ,

=

=0.7, for Bored cast-in-situ piles

173 | P a g e

Hence,

= 16.41

= 348.03 kN

Point bearing resistance of pile,

For sand,

,

where,

For , value of bearing capacity factor (obtained from Fig. 1 of IS: 2911 (Part 1)

– 19793)

= 10413.5

Area of pile at the tip,

= 6624.8

Hence, Ultimate bearing capacity of a pile

= 774.78 + 348.03 + 6624.8

= 7747.6 kN

Taking Factor of safety as 3, safe bearing capacity of pile,

= 2583 Kn

174 | P a g e

ARRANGEMENT OF PILES IN FOUNDATION

Total vertical load acting on the pile foundation = Dead load from the superstructure + Live

load acting on the bridge + weight of pier +

weight of pier cap

= 3000 + 3070.8 + 397.5

= 6468.3 kN

Number of pile required in foundation =

Number of piles provided in the foundation = 36

Fig. B-4 Arrangement of Piles in Foundation

Piles are arranged in grip pattern, having six rows of pile and six columns of pile along

transverse and longitudinal axis of bridge

Minimum spacing between piles = 3 X diameter of pile

= 2700 mm

Spacing between the piles provided = 2700 mm

Hence, the dimensions of pile cap is calculated considering clear over hang of 150 mm

from outermost pile,

Length of pile cap = (2700 X 5) + 900 + 300 = 14700 mm

175 | P a g e

Width of pile cap = (2700 X 5) + 900 + 300 = 14700 mm

DISTRIBUTION OF LOADS ON PILE

Load on pile ith pile Qi

Moment & is calculated at the soffit of pile cap,

Considering the seismic effect along longitudinal direction

Moment about longitudinal axis of bridge, = Eccentric moment due to live load about

longitudinal axis

= 377.6 kNm

Moment about transverse axis of bridge, = Eccentric moment due to live load about

longitudinal axis + Moment due to braking effort

+ Moment due to resistance at bearings +

Moment due to horizontal shear force +

Moment due to seismic effect

= 192.5 + 1120 + 248.4 + 2665 + 6090.2

= 10316 kNm

Vertical load acting on the pile foundation, Q = 14571.7 kN

Pile at distance from the longitudinal and transverse axis of bridge

respectively, is carrying the maximum load.

Hence, load on the pile Qi

= 499 kN <

SAFE BEARING CAPACITY OF PILE GROUP

Ultimate bearing capacity of pile group,

The pile group is penetrated into the two soil layers. Hence, its ultimate bearing capacity is

dependent on the properties of both the soils.

For soil layer 1


As the soil layer 1 is Clay,

, But for pile group

176 | P a g e

Undrained cohesion of soil, = 120 kN/m2

Plan dimensions of pile group are,

Length of pile group = (2.7 X 5) + 0.9 = 14.4 m

Width of pile group = (2.7 X 5) + 0.9 = 14.4 m

= 38016 kN

For soil layer 2


As the soil layer 2 is Sand,

,

For pile group, , Hence,

Effective overburden pressure at mid of the pile group penetration in soil layer 2, ,

\

Hence,

= 38.26

= 16528 kN

Point bearing resistance of pile group,

For sand,

,

where,

177 | P a g e

For , value of bearing capacity factor (obtained from Fig. 1 of IS: 2911

(Part 1) – 19793)

= 10413.5

Area of pile group at the bottom,

= 2159343

Hence, Ultimate bearing capacity of a pile group

= 38016 + 16528 + 2159343

= 2213887 kN

Safe bearing capacity of pile group shall be taken as smaller of the two values given below:

Hence, the Safe bearing capacity of pile group is kN > Total vertical load acting on the

pile. Hence, Safe.

LATERAL LOAD ANALYSIS OF PILE

The lateral load capacity of the pile is estimated as per the layer of soil situated at the

ground level as it will have the major contribution in the lateral load capacity of pile.

As the top most soil layer is normally consolidated clay,

,

where, E = = 25000 MPa

I = m4 &

= 450 kN/m3, for normally loaded clays

Hence, T = 4.47

As the pile is completely embedded into the unscourable ground,

178 | P a g e

From Figure 2 of IS: 2911 (Part 1)-19793, depth of fixity Lf = 9.72 m

Here, number of piles provided in foundation is 36 i.e. more than 3

The pile head is considered as fixed head pile

Lateral load capacity of fixed head pile is calculated as,

where, Y = limiting lateral deflection of pile head,

= 5 mm, for bridge substructures

kN

Actual lateral acting on the pile is 49.1 kN < 52.59 kN Hence, Safe.

The fixed end moment of the equivalent cantilever is given by:

, for fixed head pile

Reduction factor, m as obtained from Figure 3 of IS: 2911 (Part 1)- 19793 is 0.82

Hence, the actual maximum moment, M = m (MF)

= = 209.6 kNm

STRUCTURAL DESIGN OF PILE

Axial load acting on pile, P = 499 kN

& Moment acting on pile, M = 209.6 kNm

&

Referring to SP:16 (1980)9,

For & d’/D = 0.10

0.005

Hence,

Area of steel required =

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Minimum area of steel = 0.4% of gross-sectional area of pile

=

Minimum area of steel governs,

Provide 20 mm dia. bars as longitudinal reinforcement in pile

Number of 20 mm dia. bars required =

Hence, 9 bars of 20 mm diameter are provided in piles as longitudinal reinforcement

Lateral ties of 6 mm are provided at the spacing of 300 mm

Diameter of lateral ties i.e. 6mm , and,

6 mm.

Spacing between lateral ≯ 900 mm, and,

ties ≯ 320 mm, and,

≯ 300 mm.

SETTLEMENT OF PILE GROUP

The point bearing resistance of pile has major contribution in bearing capacity of pile.

Hence, the piles are considered as end bearing piles.

As shown in Fig. B-5, the fictitious raft is situated in sand layer at the depth of 12 m

depth below ground level. On the basis of 1H : 2V dispersion of load, the plan dimensions of raft

are decided as:

Length of raft = 14.4 + 5 = 19.4 m

Width of raft = 14.4 + 5 = 19.4 m

The soil below the raft is sand. Hence, De-Beer and Marten method (1957)22

is used for

estimating settlement of pile group in sand.

where, = mean effective overburden pressure for the layer,

=

= =31.82 kN/m2

C =

180 | P a g e

= 27.8

Fig. B-5 Settlement of End bearing piles

Permissible settlement for pile foundations = 50 mm > 28 mm. Hence, Safe

DESIGN OF PILE CAP

Length of pile cap = 14.7 m & width of pile cap = 14.7 m

Depth of pile cap = 1500 mm

Effective depth of pile cap = 1500 – 60(reinforcement cover) = 1440 mm

The critical section for bending moment is at the face of pier.

Moment in the pie cap about the transverse axis of bridge, MTT = 21428 kNm.

0.308%

< . Hence, OK.

Provide 25 mm dia. bars in pile cap,

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Moment in the pie cap about the longitudinal axis of bridge, MLL = 16634 kNm.

(as obtained from table B – 6)

0.236%

< . Hence, OK.

Provide 25 mm dia. bars in pile cap,



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Table B-6 Moment about longitudinal axis in pile cap from the critical section

NUMBER X- CO-ORDINATE

OF PILE Y- CO-ORDINATE

OF PILE LOAD

ON PILE

MOMENT FROM FACE OF PIER

ON INDIVIDUAL PILE

1 1.35 6.75 496.4043474 0

2 1.35 4.05 460.0163404 0

3 1.35 1.35 423.6283333 0

4 1.35 -1.35 387.2403263 0

5 1.35 -4.05 350.8523192 0

6 1.35 -6.75 314.4643122 0

7 4.05 6.75 497.7363404 1020.359498

8 4.05 4.05 461.3483333 945.7640833

9 4.05 1.35 424.9603263 871.1686689

10 4.05 -1.35 388.5723192 796.5732544

11 4.05 -4.05 352.1843122 721.9778399

12 4.05 -6.75 315.7963051 647.3824255

13 6.75 6.75 499.0683333 2370.574583

14 6.75 4.05 462.6803263 2197.73155

15 6.75 1.35 426.2923192 2024.888516

16 6.75 -1.35 389.9043122 1852.045483

17 6.75 -4.05 353.5163051 1679.202449

18 6.75 -6.75 317.1282981 1506.359416

TOTAL MOMENT

16634.02777

183 | P a g e

Check of two-way shear

The critical section for two way shear is effective depth/2 i.e. 720 mm away from the face

of pier. The two- way shear developed in pile cap is as calculated in Table B-7.

Hence, for two-way shear

Shear force = 12952 kN

Nominal Shear Stress =

Permissible shear stress, , where

& > Nominal shear stress. Hence OK.

Check of one-way shear

The critical section for one way shear is effective depth i.e. 720 mm away from the face

of pier. The one - way shear developed in pile cap is as calculated in Table 6.14.

For shear force acting at the critical section along transverse axis of bridge



As per Table 23 of IS: 456-20001, for 0.34% steel,

Permissible shear stress, . Hence, OK.

For shear force acting at the critical section along longitudinal axis of bridge



As per Table 23 of IS: 456-20001, for 0.26% steel,

Permissible shear stress, < . Nominal Shear Stress. Hence, OK.

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Table B-7 Calculation of two-way shear force

NO. X- CO-ORDINATE


OF PILE LOAD

ON PILE CONTRIBUTION OF

PILE IN SHEAR FORCE

1 1.35 6.75 496.4043474 496.4043474

2 1.35 4.05 460.0163404 460.0163404

3 1.35 1.35 423.6283333 0

4 1.35 -1.35 387.2403263 0

5 1.35 -4.05 350.8523192 350.8523192

6 1.35 -6.75 314.4643122 314.4643122

7 4.05 6.75 497.7363404 497.7363404

8 4.05 4.05 461.3483333 461.3483333

9 4.05 1.35 424.9603263 424.9603263

10 4.05 -1.35 388.5723192 388.5723192

11 4.05 -4.05 352.1843122 352.1843122

12 4.05 -6.75 315.7963051 315.7963051

13 6.75 6.75 499.0683333 499.0683333

14 6.75 4.05 462.6803263 462.6803263

15 6.75 1.35 426.2923192 426.2923192

16 6.75 -1.35 389.9043122 389.9043122

17 6.75 -4.05 353.5163051 353.5163051

18 6.75 -6.75 317.1282981 317.1282981

19 -1.35 6.75 495.0723545 495.0723545

20 -1.35 4.05 458.6843474 458.6843474

21 -1.35 1.35 422.2963404 0

22 -1.35 -1.35 385.9083333 0

23 -1.35 -4.05 349.5203263 349.5203263

24 -1.35 -6.75 313.1323192 313.1323192

25 -4.05 6.75 493.7403616 493.7403616

26 -4.05 4.05 457.3523545 457.3523545

27 -4.05 1.35 420.9643474 420.9643474

28 -4.05 -1.35 384.5763404 384.5763404

29 -4.05 -4.05 348.1883333 348.1883333

30 -4.05 -6.75 311.8003263 311.8003263

31 -6.75 6.75 492.4083686 492.4083686

32 -6.75 4.05 456.0203616 456.0203616

33 -6.75 1.35 419.6323545 419.6323545

34 -6.75 -1.35 383.2443474 383.2443474

35 -6.75 -4.05 346.8563404 346.8563404

36 -6.75 -6.75 310.4683333 310.4683333

TOTAL SHEAR

12952.58667

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Table B-8 Calculation of one-way shear force at critical section along L-L axis of bridge

X- CO-ORDINATE


OF PILE LOAD

ON PILE CONTRIBUTION OF

PILE IN SHEAR FORCE

1 1.35 6.75 496.4043474 0

2 1.35 4.05 460.0163404 0

3 1.35 1.35 423.6283333 0

4 1.35 -1.35 387.2403263 0

5 1.35 -4.05 350.8523192 0

6 1.35 -6.75 314.4643122 0

7 4.05 6.75 497.7363404 497.7363404

8 4.05 4.05 461.3483333 461.3483333

9 4.05 1.35 424.9603263 424.9603263

10 4.05 -1.35 388.5723192 388.5723192

11 4.05 -4.05 352.1843122 352.1843122

12 4.05 -6.75 315.7963051 315.7963051

13 6.75 6.75 499.0683333 499.0683333

14 6.75 4.05 462.6803263 462.6803263

15 6.75 1.35 426.2923192 426.2923192

16 6.75 -1.35 389.9043122 389.9043122

17 6.75 -4.05 353.5163051 353.5163051

18 6.75 -6.75 317.1282981 317.1282981

19 -1.35 6.75 495.0723545 0

20 -1.35 4.05 458.6843474 0

21 -1.35 1.35 422.2963404 0

22 -1.35 -1.35 385.9083333 0

23 -1.35 -4.05 349.5203263 0

24 -1.35 -6.75 313.1323192 0

25 -4.05 6.75 493.7403616 0

26 -4.05 4.05 457.3523545 0

27 -4.05 1.35 420.9643474 0

28 -4.05 -1.35 384.5763404 0

29 -4.05 -4.05 348.1883333 0

30 -4.05 -6.75 311.8003263 0

31 -6.75 6.75 492.4083686 0

32 -6.75 4.05 456.0203616 0

33 -6.75 1.35 419.6323545 0

34 -6.75 -1.35 383.2443474 0

35 -6.75 -4.05 346.8563404 0

36 -6.75 -6.75 310.4683333 0

TOTAL SHEAR

4889.187831

186 | P a g e

Fig. B-6 Reinforcement details of Pile Cap

Bridge Substructure Analysis & Design

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