BEHAVIOUR OF LATERALLY LOADED PILES IN LAYERED SOIL · 2019-04-28 · 2.4.1 Broms method 15 2.4.2 Beam-on-elastic foundation approach 22 2.4.3 Beam-on-winkler foundation 23 2.4.4

BEHAVIOUR OF LATERALLY LOADED PILES IN LAYERED SOIL

by

Mohammad Shazzath Hossain

A thesis submitted to the Department of Civil Engineering,

Bangladesh University of Engineering and Technology,

Dhaka, in partial fulfillment of the degree of

MASTER OF SCIENCE IN CIVIL ENGINEERING (Geotechnical)

BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY

2014

ii

The thesis titled "BEHAVIOUR OF LATERALLY LOADED PILES IN

LAYERED SOIL" Submitted by Mohammad Shazzath Hossain, Roll No.

100704250(P), Session 2007, has been accepted as satisfactory in partial fulfillment

of the requirement for the degree of Master of Science in Civil Engineering

(Geotechnical) on September 16, 2014.

BOARD OF EXAMINERS

Dr. Syed Fakhrul Ameen Chairman Professor (Supervisor) Department of Civil Engineering BUET, Dhaka - 1000.

Dr. A.M.M. Taufiqul Anwar Member Professor and Head (Ex-officio) Department of Civil Engineering BUET, Dhaka - 1000.

Dr. Md. Jahangir Alam Member Associate Professor Department of Civil Engineering BUET, Dhaka-1000

BA- 3580 Col. Md Wahidul Islam, psc Member Deputy Commandant (External) Quadirabad Cantonment Natore

iii

ACKNOWLEDGEMENTS

The author is indebted to his supervisor Dr. Syed Fakhrul Ameen, Professor,

Department of Civil Engineering, Bangladesh University of Engineering and

Technology (BUET), for his inspiration, encouragement, continuous guidance,

patience, generosity and important suggestions throughout the various stages of this

research. It could not have been completed without his kind guidance, dedication and

close supervision during the study. Having vast working experiences, knowledge on

most recent analysis methods’ and finite element software, Dr. Syed Fakhrul Ameen

has greatly helped to make the study very easy and smoothly.

The author also expresses his profound gratitude to Dr. A.M.M Taufiqul Anwar,

Professor and Head, Department of Civil Engineering, BUET, Dhaka, for his valuable

corrections and suggestions during preparation of proposal and writing of this thesis.

The author gratefully acknowledges the constructive criticisms and valuable

suggestions made by Dr. Md. Jahangir Alam. The author also gratefully

acknowledges the valuable suggestions and corrections made by Col. Md Wahidul

Islam. Thanks to the Kuril Flyover Project Authority for their kind cooperation and

excellent support regarding the pile lateral load test and giving important documents

related to the sub soil of the project site.

The author gratefully acknowledges to his wife for great patience, continuous support

and encouragement to complete the study.

iv

ABSTRACT

Piles are relatively long, slender members that transmit foundation loads through soil strata of low bearing capacity to deeper soil or rock strata having a high bearing capacity. High rise structures supported by piles need analysis for lateral loading due to earthquake and wind. Piles are frequently subjected to lateral forces and moments, for example, in quay and harbor structures, where horizontal forces are caused by the impact of ships during berthing and wave action; in offshore structures subjected to wind and wave action and in transmission-tower foundations, where high wind forces may act.

Pile lateral capacity can be analyzed using conventional statical approach. The linear spring model may be adopted in case where soil strains are small. Under extreme pile loading condition it is important to make use of a non-linear soil spring model referred to as ‘p-y’ curve. Considerable effort has been put into the refinement of p-y curve formulations on the basis of measurement of the behavior of laterally loaded piles.

Frequently the pile is embedded in layered soil which consists soft clay layer over stiff clay. Some authors proposed dimensionless solutions for ultimate lateral capacity of piles in layered soils. It is noted that there are limited literature reporting on pile behavior under lateral loading in layered soil.

In this study pile lateral capacity for free headed and fixed headed condition are presented. Piles embedded in homogeneous soil and layered soils are analyzed and the results are discussed. Soil is defined series of non linear spring having different spring constant for different soil shear strength. Piles are embedded in soil having different soil shear strength in different layers. Layered soils like soft clay layer over stiff soil of different thickness are analyzed. Piles are long pile of diameter 500 mm, 600 mm, 750 mm and 1000 mm.

From the analysis of piles embedded in homogeneous soil it is seen that as the soil shear strength, diameter and allowable head deflection increases, corresponding lateral capacity increases. For a soft layer over laying a stiff layer, larger diameter piles are more effective than smaller diameter piles.

v

Table of Contents

ACKNOWLEDGEMENTS iii

ABSTRACT iv

TABLE OF CONTENTS v

LIST OF FIGURES viii

LIST OF TABLES xiii

NOTATION xvii

CHAPTER 1: INTRODUCTION 1

1.1 General 1

1.2 Background of the study 2

1.3 Objectives of the study 3

1.4 Methodology 3

1.5 Organization of the thesis 4

CHAPTER 2: LITERATURE REVIEW 5

2.1 General 5

2.2 Structures subjected to lateral loads 6

2.3 Load transfer mechanisms and failure modes of laterally

loaded piles

7

2.4 Analysis methods 15

2.4.1 Broms method 15

2.4.2 Beam-on-elastic foundation approach 22

2.4.3 Beam-on-winkler foundation 23

2.4.4 Elastic continuum approach 24

2.5 Mechanics concerning response of soil to lateral loading 25

2.5.1 General 25

2.5.2 Modulus of subgrade reaction 26

2.5.3 Subgrade modulus related to piles under lateral

loading

29

2.5.4 Theoretical solution by skempton for subgrade

modulus of soil

30

2.5.5 Empirical equations for estimating ks 32

2.5.6 Concept of p-y curves 33

vi

CHAPTER 3: ANALYSIS AND RESULTS OF LATERALLY

LOADED PILES

39

3.1 Introduction 39

3.2 Methodology of analysis 39

3.3 Steps for analysis of piles embedded in soil 42

3.4 Allowable lateral load for piles embedded in homogeneous

soil

44

3.5 Allowable lateral load for piles embedded in homogeneous

Soil neglecting head 1.5 m soil shear strength

46

3.6 Graphical form of piles in homogeneous soil 48

3.7 Results of piles embedded in layered soil 58

3.8 Graphical form of piles in layered soil 77

3.9 Lateral capacity of piles using Broms method 89

CHAPTER 4: DISCUSSION 90

4.1 General 90

4.2 Pile embedded homogeneous soil 90

4.2.1 Free headed piles 90

4.2.2 Fixed headed piles 98

4.2.3 Comparisons between free headed & fixed headed

piles

105

4.2.4 Free headed piles neglecting head 1.5 m soil shear

strength

107

4.2.5 Fixed headed piles neglecting head 1.5 m soil shear

strength

111

4.3 Piles embedded in layered soil 117

4.3.1 Free headed and fixed headed piles 117

4.3.2 Comparison between pile lateral capacity for free

head and fixed head condition

119

4.3.3 Comparison between pile maximum moment for

free head and fixed head condition

121

4.3.4 Comparison between pile lateral capacity for free

head and fixed head condition for stiff soil of

70 kpa lying below soft soil

123

vii

4.3.5 Comparison between pile maximum moment for

free head and fixed head condition

126

4.3.6 Comparison between pile capacity of stiff soil of

50 kpa and 70 kpa below soft soil

126

CHAPTER 5: CASE STUDY: LATERAL PILE LOAD TEST

OF KURIL FLYOVER PROJECT AT DHAKA

127

5.1 Introduction 127

5.2 Over view of the project 127

5.3 Location of the pile lateral load test area 128

5.4 Test equipment and instruments 133

5.4.1 Test equipment for load application 133

5.4.2 Test equipment for measurement 133

5.5 Test procedures 136

5.6 Computer analysis using soil spring 138

5.7 Comments 140

CHAPTER 6: CONCLUSION 141

6.1 General 141

6.2 Conclusion 141

6.3 Recommendations for future study 142

REFERENCES 143

APPENDIX A: GRAPHS FOR FREE HEADED AND FIXED

HEADED PILE CAPACITY AND MOMENT

146

viii

List of Figures

Fig. 2.1: Load Transfer Mechanism of Axially Loaded Piles

Fig. 2.2: Transfer Mechanism of Laterally Loaded Piles

Fig. 2.3: Load transfer mechanism for vertically loaded pile group

Fig. 2.4: Illustration of overlapping zones creating additional load on piles

within a group

Fig. 2.5: Kinematics of Rigid Piles

Fig. 2.6: Kinematics of Flexible Piles

Fig. 2.7: Kinematics of a vertically loaded pile group

Fig. 2.8: Kinematics of a laterally loaded pile group

Fig. 2.9: Broms Earth Pressures for Cohesive Soils

Fig. 2.10: Broms Pressure, Shear, Moment Diagrams for Cohesive Soils

Fig. 2.11: Broms Pressure, Shear, Moment Diagrams for Cohesionless Soils

Fig. 2.12: Ultimate lateral resistance of short pile in cohesive soil

Fig. 2.13: Ultimate lateral resistance of long pile in cohesive soil

Fig. 2.14: Charts for calculation of lateral deflection at ground surface of

horizontally loaded pile in cohesive soil (after Broms 1964)

Fig. 2.15: Lateral Loading Near Surface Passive Wedge Geometry and Soil-Pile Forces(after Reese, 1958)

Fig. 2.16: Description of experiment leading to definition of subgrade modulus. Fig. 2.17: Implementation of Winkler Spring Concept for Laterally Loaded Pile

Problem

Fig. 2.18: Definition of p-y Concept with a) Pile at Rest; b) Pile after Load Applied(after Dunnavant, 1986)

Fig. 2.19: Typical Family of p-y Curves Response to Lateral Loading (after

Dunnavant, 1986)

Fig. 2.20: Figure 2.20: Deflections, slopes, bending moments, shearing forces, and soil reactions for elastic conditions (after Reese and Matlock).

Fig. 2.21: Characteristic Shape of p-y Curve for Soft Clay ( Static Loading ) (after Matlock, 1970)

Fig. 3.1: Location of spring (a) Considering full depth of soil effective

(b) Neglecting top 1.5 m soil

Fig. 3.2: Load vs deflection graph showing spring constant & pult

Fig. 3.3: Pile Capacity vs Soil Undrained Shear Strength for 6 mm deflection

ix



Fig. 3.6: Pile Moment vs Soil Undrained Shear Strength for 6 mm deflection





















Fig. 3.26a: Pile Max Moment Location vs Soil Undrained Shear Strength for 6

mm deflection

Fig. 3.26b: Pile Max Moment Location vs Soil Undrained Shear Strength for 12

mm deflection

Fig. 3.26c: Pile Max Moment Location vs Soil Undrained Shear Strength for 25

mm deflection

Fig. 3.26d: Pile Max Moment Location vs Soil Undrained Shear Strength for 6

mm deflection

Fig. 3.26e: Pile Max Moment Location vs Soil Undrained Shear Strength for 12

mm deflection

x

Fig. 3.26f: Pile Max Moment Location vs Soil Undrained Shear Strength for 25

mm deflection

Fig. 3.27: Pile Capacity vs Depth of soft soil for 6 mm deflection



Fig. 3.30: Pile Moment vs Depth of soft soil for 6 mm deflection









Fig. 3.38a: Pile Capacity vs Depth of soft soil for 6 mm deflection

Fig. 3.38b: Pile Capacity vs Depth of soft soil for 12 mm deflection

Fig. 3.38c: Pile Capacity vs Depth of soft soil for 25 mm deflection

Fig. 3.38d: Pile Moment vs Depth of soft soil for 6 mm deflection

Fig. 3.38e: Pile Moment vs Depth of soft soil for 12 mm deflection

Fig. 3.38f: Pile Moment vs Depth of soft soil for 25 mm deflection

Fig. 3.38g: Pile Capacity vs Depth of soft soil for 6 mm deflection

Fig. 3.38h: Pile Capacity vs Depth of soft soil for 12 mm deflection

Fig. 3.38i: Pile Capacity vs Depth of soft soil for 25 mm deflection

Fig. 3.38j: Pile Moment vs Depth of soft soil for 6 mm deflection

Fig. 3.38k: Pile Moment vs Depth of soft soil for 12 mm deflection

Fig. 3.38l: Pile Moment vs Depth of soft soil for 25 mm deflection








xi






Fig. 4.1: Pile Embedded in Homogeneous soil

Fig. 4.2: Deflected Shape of Pile

Fig. 4.3: Soil Reaction Diagram

Fig. 4.4: Pile Bending Moment Diagram

Fig. 4.5: Pile lateral capacities with its head Deflection for 10 kpa soil shear

strength


strength

Fig. 4.7: Pile lateral capacities with its head Deflection for 50 kpa soil shear strength


strength

Fig. 4.9: Pile Embedded in Homogeneous soil

Fig. 4.10: Deflected Shape of Pile

Fig. 4.11: Soil Reaction Diagram

Fig. 4.12: Pile Bending Moment Diagram


strength


strength


strength


strength

Fig. 5.1: Perspective view of Kuril Fly Over

Fig. 5.2: Location of lateral load test

Fig. 5.3: Location of soil test bore hole

Fig. 5.4: Bore Log of 19


xii


Fig. 5.7: Excavated & piles are open for test setup

Fig. 5.8: Setup systems for testing the piles

Fig. 5.9: Hydraulic jack setup for application of lateral load on piles

Fig. 5.10: Dial gauge reading are recorded

Fig. 5.11: Instrument set-up for applying lateral load to the pile

Fig. 5.12: Load vs Deflection graph (load test and computer analysis)

xiii

List of Tables

Table 2.1: Summary of Procedure in Developing p-y Curves for clay soil

(Matlock, 1970)

Table 3.1: Pile analysis data for homogeneous soil

Table 3.2: Values of spring constant & pult of different Clay soil.

Table 3.3: Allowable horizontal loads on pile for free head condition

Table 3.4: Allowable horizontal load on pile for fixed head condition

Table 3.5: Allowable horizontal load on pile for free head condition neglecting

top 1.5 m soil

Table 3.6: Allowable horizontal load on pile for fixed head condition neglecting

top 1.5 m soil

Table 3.7: Values of spring constant & pult for analysis of different layer of soil.

Table 3.8: Allowable horizontal load on pile for free head condition



top 1.5 m soil


top 1.5 m soil




top 1.5 m soil


top 1.5 m soil




top 1.5 m soil


top 1.5 m soil


xiv



top 1.5 m soil


top 1.5 m soil



Table 4.1: Lateral capacity of 1 m diameter long pile embedded in soils of

different shear strength with different head deflections.

Table 4.2: Lateral capacity of different diameter of long pile embedded in soils

having Shear strength 10 kpa with different head deflections.

Table 4.3: Lateral capacity and maximum moment of long pile embedded in

soils of different shear Strength with different head deflections.

Table 4.4: Lateral capacity and maximum moment of different diameter of long

pile embedded in soils of shear Strength 10 kpa with different head

deflections.




of shear Strength 10 kpa with different head deflections.


soils of different shear strength with different head deflections.



deflections.

Table 4.9: Relationship between lateral capacities of free headed and fixed

headed piles of diameter 1 m.

Table 4.10: Relationship between lateral capacities of free headed and fixed

headed piles of different diameter.

Table 4.11: Relationship between maximum moments of free headed and fixed




xv




soils of different shear Strength with different head deflections.



deflections.

Table 4.15a: Relationship of lateral load capacity and maximum moment of free

headed plies considering full depth and neglecting head 1.5 m of soil.






soils of different shear strength with different head deflections.



deflections.

Table 4.19a: Lateral load capacity and maximum moment of fixed headed plies

for considering full depth and neglecting head 1.5 m of soil.

Table 4.19b: Location of pile maximum moment from head of pile for considering

full depth.

Table 4.19c: Location of pile maximum moment from head of pile for neglecting

head 1.5 m of soil.

Table 4.20: Pile lateral load with thickness of soft soil for free head condition (6

mm top deflection). (soft soil, cu = 10 kpa and stiff soil,

cu = 50 kpa)

Table 4.21: Pile lateral load with thickness of soft soil for fixed head condition

(top 6 mm deflection). (soft soil, cu = 10 kpa and stiff soil,

cu = 50 kpa)

Table 4.22: Pile maximum moment with depth of soft soil for free head condition

head deflection 6 mm (soft soil, cu = 10 kpa and stiff soil, cu = 50

kpa)

xvi

Table 4.23: Pile maximum moment (Negative moment) with respect to depth of

soft soil for fixed head condition. (soft soil, cu = 10 kpa and stiff soil,

cu = 50 kpa)

Table 4.24: Pile lateral load with depth of soft soil for free head condition (6 mm

top deflection). (soft soil, cu = 10 kpa and stiff soil, cu = 50 kpa)

Table 4.25: Pile lateral load with depth of soft soil for fixed head condition (6

mm head deflection). (soft soil, cu = 10 kpa and stiff soil,

cu = 50 kpa)

Table 4.26: Pile maximum moment with depth of soft soil for free head

condition, 6 mm head deflection. (soft soil, cu = 10 kpa and stiff soil,

cu = 50 kpa)

Table 4.27: Pile maximum moment (Negative moment) with depth of soft soil

for fixed head condition & 6 mm head deflection. (soft soil, cu = 10

kpa and stiff soil, cu = 50 kpa)

Table 5.1: Load and deflection from lateral pile load test

Table 5.2: Spring value and ultimate soil resistance for computer analysis

Table 5.3: Load and deflection results from computer analysis

xvii

NOTATION

b = Width cu = Undrain Cohesion D = Pile diameter Ep = Modulus of elasticity of the pile Es = Young’s modulus of the solid EpIp = Flexural rigidity of the pile H = Lateral load of pile Ip = Moment of inertia of the pile Iρ = Influence coefficient kh = Coefficient of horizontal subgrade reaction Kp = Rankine coefficient of passive earth pressure ks = Coefficient of subgrade reaction N = Standard Penetration Resistance Value Nc Nq Nγ= Bearing capacity factor p = Soil reaction per unit length of the pile pu = Ultimate soil resistance

q = Foundation pressure

qa = Allowable foundation pressure

qf = Failure stress

qu = Ultimate foundation pressure

sm = Mean settlement of foundation y = Soil deflection y50 = Soil displacement at one-half of ultimate soil resistance z = Depth σ' = Effective vertical stress at depth γ = Unit weight of soil (use buoyant weight below water) φ = Angle of internal friction of soil μs = Poisson’s ratio of the soil

µ = Poisson’s ratio of the solid

ϵ = Strain of soil ϵ50 = Strain at one half the ultimate soil resistance γ' = Effective Soil Unit Weight for Soil under Water

1

CHAPTER 1

INTRODUCTION

1.1 General

Piles are relatively long, slender members that transmit foundation loads through soil strata

of low bearing capacity to deeper soil or rock strata having a high bearing capacity. They

are used when for economic, constructional or soil condition considerations it is desirable

to transmit loads to strata beyond the practical reach of shallow foundations. Piles are also

used to anchor structures against uplift forces and to assist structures in resisting lateral and

overturning forces.

After selecting materials for the pile foundation to make sure of durability, the

designer begins with the components of loading on the single pile or the pile group.

With the axial load, lateral load, and overturning moment, the engineer must ensure

that the single pile, or the pile group, is safe against collapse and does not exceed

movements set by serviceability. High rise structures supported by piles need analysis

for lateral loading due to earthquake and wind.

Piles are frequently subjected to lateral forces and moments, for example, in quay and

harbor structures, where horizontal forces are caused by the impact of ships during

berthing and wave action; in offshore structures subjected to wind and wave action

and in transmission-tower foundations, where high wind forces may act.

Design for lateral loading typically controls the diameter of drilled shafts for highway

bridges, high rise buildings and may also control the embedded length for some types

of structures such as retaining walls, noise walls, and sign or light standard

foundations. Thus, an evaluation of lateral loading is required during planning and

preliminary design. A more complete analysis of lateral loading conditions is required

for final design including structural design;

An adequate factor of safety against ultimate resistance and an acceptable deflection

at service load criteria must be satisfied in the design of such pile foundations.

2

The behavior of laterally loaded deep foundations depends on stiffness of the pile and

soil, mobilization of resistance in the surrounding soil, boundary conditions (fixity at

ends of deep foundation elements), and duration and frequency of loading.

For analyzing the pile behavior the diameter of the pile as well as its material &

stiffness property is very important including the surrounding soil in which the pile is

embedded to take the design lateral load coming from the superstructure from wind or

earth quake forces.

In practical the soil is not homogeneous over the depth. It contains various soil layers

like soft soil over stiff soil or loose soil over hard soil or soft to stiff soil in increasing

depth. In this condition the evaluation of the behavior of the pile response of different

soil layer is very important to design the foundation and the superstructure.

1.2 Background of the Study

Frequently pile is embedded in layered soil which may consist soft clay lying over

stiff clay. Information about the lateral behavior of piles in layered soil profiles is

very limited. Poulos gave dimensionless solutions for ultimate lateral capacity of a

pile in two layered cohesive soil profile. Davisson & Gill, Reese, Rollins presented

work on laterally loaded piles in layered soils. It is noted that there are limited

literature reporting on pile behavior under lateral loading in layered soil.

To determine the lateral pile capacity the full scale lateral pile load test may be

conducted in the field or it can be evaluated from the various methods proposed by

various authors.

Conventional statically approach was proposed by Brinch Hansen and Broms. The

ultimate laterally resistance of free headed rigid piles based essentially on earth-

pressure theory has been given by Brinch Hansen who also considered the variation of

soil resistance with a depth along the pile. The theory developed by Broms is

essentially the same as Brinch Hansens theory except that simplification are made to

the ultimate soil-resistance and distribution along the pile and consideration given to

fixed-head and free head piles.

3

The subgrade-reaction model of soil behavior, which was originally proposed by

Winkler in 1867, characterizes the soil as a series of unconnected linear-elastic

springs, so that deformation occurs only where loading exists. The subgrade-reaction

approach has been widely employed in foundation practice because it provides a

relative simple means of analysis and enables factors such as nonlinearity, variation of

soil stiffness with depth, and layering of the soil profile to be taken into account

readily.

The linear spring model may be adopted in case where soil strains are small. Under

extreme pile loading condition it is important to make use of a non-linear soil spring

model referred as ‘p-y’ curve by Matlock and Reese. Considerable effort has been put

into the refinement of p-y curve formulations on the basis of measurement of the

behavior of laterally loaded piles. As a result such formulations are widely accepted

as being reliable and they are quoted in documents such as the American Petroleum

Institute Code.

1.3 Objectives of the Study

Objectives of the study of laterally loaded piles embedded in layered soil are as

follows:

I. To develop load displacement relationship of laterally loaded piles

embedded in layered soil.

II. To calculate the bending moment and shear force of laterally loaded piles

embedded in layered soil.

III. To compare field load test results with analytical findings.

IV. To prepare charts and figures for analysis and design of laterally loaded pile

embedded in layered and homogeneous soil.

1.4 Methodology

To develop load displacement relationship for laterally loaded piles embedded in

layered and homogeneous soil analytically, methodologies which are taken are as

follows:

I. Modeling the pile as a beam supported by discrete springs to represent

the soil resistance and analyzing FEM software package (SAP).

II. Determining the displacement, bending moment and shear force of free

4

headed and fixed headed piles of different diameter and length subjected

to lateral load considering the springs as linear and non-linear.

III. Comparing the analytical results with field load test results.

1.5 Organization of the Thesis

The thesis is arranged into six chapters and one appendix. In Chapter One,

background and objectives of the research is described. Chapter Two contains the

literature review where history, use and researches on evaluation of the pile lateral

capacity as well as the Winkler method and the concept of p-y curves of soil are

presented. It also contains the evaluation of modulus of subgrade reaction of various

type of soil.

Chapter Three contains detail analysis and results of laterally loaded pile embedded in

homogeneous and layered soil using FEM software package (SAP). It also contains

required charts & graphs. Chapter Four contains discussion on the results which are

listed at chapter three. Piles embedded in layered and homogeneous soil are discussed

separately. Chapter Five contains a case study of pile lateral test performed at Kuril

Fly over project, at Khilkhet, Dhaka. Chapter Six contains conclusion and

recommendations for future research.

5

CHAPTER 2

LITERATURE REVIEW

2.1 General

The report documents the development of analysis of laterally loaded piles in uniform

soil as well as in the layered soil profile. The Pressure - Displacement (p - y) approach

has been widely used to design piles subjected to lateral loading. Based on the

Winkler foundation theory, the method models the lateral soil structure interaction

with empirically derived nonlinear spring. The advancement of computer technology

has made it possible to study this problem using more rigorous Finite Element

Method (FEM). In this study the layering effect of the soil has been incorporated. In

practical the soil exists with various layer of soil like clay with sand, sand with silt,

clay, sand, clay layer or various pattern. Analysis of this type of soil profile is really

very important as well as complicated compared with the uniform soil profile.

Overall, Pile foundations are frequently used to support various structures built on

sand/clay soils, where shallow foundations would undergo excessive settlements or

bearing capacity failure. These piles are used to support vertical loads, lateral loads

and combinations of vertical and lateral loads. The methods of analysis commonly

used in predicting the behavior of piles under pure axial loads could be categorized

into: (i) subgrade reaction method (Coyle and Reese 1966, Kraft et al.1981; Zhu and

Chang 2002 ) (ii) elastic continuum approaches (Poulos 1968; Xu and Poulos2000 ),

and (iii) finite element methods (Desai 1974; Trochanis et al. 1991; Wang and Sitar

2004). Similarly, the methods to study the behavior of piles and pile groups under

pure lateral loads could be categorized into; (i) limit state method (Broms 1964); (ii)

subgrade reaction method (Matlock and Reese 1960); (iii) elastic continuum approach

(Poulos 1971; Banerjee and Davis 1978); (iv) p-y method (Reese et al. 1974) and (v)

finite element methods (Muqtadir and Desai 1986; Brown and Shie 1991; Trochanis

et al. 1991; Kimura et al. 1995; Yang and Jeremic 2002 and 2005). ( K.Rajagopal and

S.Karthigeyan, 2008).

The behavior of piles under lateral loads on homogeneous clay soil and soil layered

system of soft clay lying above a stiff clay soil are studied here and draw, compared

6

pressure – displacement (p-y) curves, bending moment, shear force, lateral pressure

and displacement of the pile head along the depth of pile.

This study, provides a general overview of laterally loaded piles. Explain why lateral

loads act on piles and how piles interact with the surrounding ground as a result of

those lateral loads. Present the available methods of analysis of laterally loaded piles,

discuss where improvements are necessary and point out scope of this work.

Here some analysis using FEM software for various type of soil in respect of depth,

diameter of the pile, various type of combination of soil profile and finding out the

behavior of the pile with the bending moment, deflection & soil response are given.

2.2 Structures subjected to lateral loads

Piles are relatively long, slender members that transmit foundation loads through soil

strata of low bearing capacity to deeper soil or rock strata having a high bearing

capacity. They are used when for economic, constructional or soil condition

considerations it is desirable to transmit loads to strata beyond the practical reach of

shallow foundations. Piles are also used to anchor structures against uplift forces and

to assist structures in resisting lateral and overturning forces.

After selecting materials for the pile foundation to make sure of durability, the

designer begins with the components of loading on the single pile or the group. With

the axial load, lateral load, and overturning moment, the engineer must ensure that the

single pile, or the critical pile in the group, is safe against collapse and does not

exceed movements set by serviceability. High rise structures whose foundations are

supported by piles need analysis of lateral loading effect for earthquake, wind or

similar type natural disasters.

Piles are frequently subjected to lateral forces and moments: for example, in quay and

harbor structures, where horizontal forces are caused by the impact of ships during

berthing and wave action; in offshore structures subjected to wind and wave action; in

pile supported structures; in lock structures; in transmission-tower foundations, where

high wind forces may act; and in structures constructed in earthquake areas.

7

In the above examples, there are some cases in which the external horizontal loads act

at the pile head (i.e., at the top section of the pile). Such loading is called active

loading (Fleming et al. 1992, Reese and Van Impe 2001). Common examples are

lateral loads (and moments) transmitted to the pile from superstructures like buildings,

bridges and offshore platforms. Sometimes the applied horizontal load acts in a

distributed way over a part of the pile shaft; such a loading is called passive loading.

Examples of passive loading are loads acting on piles due to movement of slopes or

on piles supporting open excavations. There are cases in which external horizontal

loads are minimal or absent; even then external moments often exist because of load

eccentricities caused by construction defects, e.g., out-of-plumb constructions. Thus,

piles in most cases are subjected to lateral loads. Consequently, proper analysis of

laterally loaded piles is very important to the geotechnical and civil engineering

profession.

In the design of pile foundations against lateral loading, two criteria must be satisfied:

1. The pile must have an adequate factor of safety against the maximum lateral

loading that might be applied to it, and

2. The deflection that occurs due to a working load must be in an acceptable

range that superstructure can withstand (Poulos and Davis,1980).

2.3 Load Transfer Mechanisms and Failure Modes of Laterally Loaded Piles

A proper understanding of the load transfer mechanisms for piles is necessary for

analysis and design. Piles transfer axial and lateral loads through different

mechanisms. In the case of axial (vertical) loads, piles may be looked upon as axially

loaded columns; they transfer loads to the ground by shaft friction and base resistance

(Figure 2-1) (Salgado 2008). As a pile is loaded axially, it slightly settles and the

surrounding soil mass offers resistance to the downward movement. Because soil is a

frictional material, frictional forces develop at the interface of the pile shaft and the

surrounding soil that oppose the downward pile movement. The frictional forces

acting all along the pile shaft partly resist the applied axial load and are referred to as

shaft resistance, shaft friction or skin friction. A part of the axial load is transferred to

the ground through the bottom of the pile (commonly referred to as the pile base). As

a pile tries to move down, the soil mass below the pile base offers compressive

8

resistance to the movement. This mechanism is called base resistance or end-bearing

resistance. The total resistance (shaft friction plus end-bearing resistance) keeps a pile

in equilibrium with the applied load. Piles that transfer most of the axial load through

the base are called end-bearing piles, while those that transfer most of the load

through shaft friction are called friction piles. For end-bearing piles, it is necessary to

have the pile base inserted into a strong layer of soil (e.g., dense sand, stiff clay or

rock). Typically, engineers would prefer to design end-bearing piles because the base

resistance is more reliable than shaft friction. However, if no such strong layer is

available at a site, then engineers have to rely only on shaft friction; in such a case the

pile is called a floating pile.

Figure 2.1: Load Transfer Mechanism of Axially Loaded Piles

In the case of lateral loads, piles behave as transversely loaded beams. They transfer

lateral load to the surrounding soil mass by using the lateral resistance of soil (Figure

2.2).When a pile is loaded laterally, a part or whole of the pile tries to shift

horizontally in the direction of the applied load, causing bending, rotation or

translation of the pile (Fleming et al.1992, Salgado 2008). The pile presses against the

soil in front of it (i.e., the soil mass lying in the direction of the applied load),

generating compressive and shear stresses and strains in the soil that offers resistance

to the pile movement. This is the primary mechanism of load transfer for lateral loads.

The total soil resistance acting over the entire pile shaft balances the external

Applied Axial force

Ground Surface

Pile Shaft Resistance

Base Resistance

9

horizontal forces. The soil resistance also allows satisfaction of moment equilibrium

of the pile.

Figure 2.2: Load Transfer Mechanism of Laterally Loaded Piles

Often, the load acting on a superstructure is larger than the capacity of a single pile.

When that happenes, piles are grouped under each column to resist the total force

acting at the column base. The piles in a group no longer behave as isolated units but

interact with each other and resist the external load in an integrated manner.

Consequently, the response of a single pile differs from that of a pile placed within a

pile group (Prakash and Sharma 1990, McVay 1998., Ilyas et al. 2004, Bogard and

Matlock 1983, Ashour et al. 2004). Each pile in a group, whether loaded axially or

laterally, generates a displacement field of its own around itself. The displacement

field of each pile interferes and overlaps with those of the adjacent piles; this results

in the interaction between piles. Similarly to single piles, pile groups have two

resistance mechanisms against vertical loads: friction along the sides and base

resistance.

However, compared with the behavior of an isolated pile, the response of a pile within

a group differs due to the interaction of the adjacent piles. The difference in response

is more pronounced for pile groups that resist vertical loads primarily by side friction

(Figure 2.3). Additional forces are induced along the pile shafts due to the settlement

10

of adjacent piles. Thus, the piles resist not only the vertical column load but also the

interaction forces along the pile shafts. For end bearing piles, however, a larger

fraction of the applied load is supported by the compressive resistance of the ground

below the pile base because of which the interaction along the pile shafts is minimal.

Consequently, the response of each pile within a group is closer to that of a single

isolated pile.

Figure 2.3: Load transfer mechanism for vertically loaded pile group

Interaction between piles occurs in the case of laterally loaded pile groups as well. In

a laterally loaded pile group, each pile pushes the soil in front of it (i.e., in the

direction of the applied force). Movement of the piles placed in the first (leading) row

in the direction of the applied force is resisted by the soil in front of it. In contrast, the

piles in the rows behind the first row (i.e., the piles in the trailing rows) push on the

soil which in turn pushed on the piles in the rows in front of them (Figure 2-4). The

resistive forces acting on the trailing-row piles are in general less than the resistive

forces acting on the leading row (Prakash and Sharma 1990,Salgado 2008, Ilyas et al.

2004, Ashour et al. 2004).

11

Figure 2.4: Illustration of overlapping zones creating additional load on piles

within a group

The kinematics of axially loaded piles is simple: the pile moves vertically downward

under the acting load and, if the resistive forces (i.e., shaft and base resistances)

exceed the limit values, then the pile suffers excessive vertical deflection (plunging)

leading to collapse. The kinematics and failure mechanisms of laterally loaded piles

are more complex and vary depending on the type of pile.

Since laterally loaded piles are transversely loaded, the pile may rotate, bend or

translate (Fleming et al. 1992, Salgado 2008). As the pile moves in the direction of the

applied force, a gap may also open up between the back of the pile and the soil over

the top few meters. If the pile is short and stubby, it will not bend much but will rotate

or even translate (Figure 2-5). Such piles are called rigid piles. If the pile is long and

slender, then it bends because of the applied load (Figure 2-6). These piles are called

flexible piles. In most practical situations, piles are long enough to behave as flexible

piles. For flexible piles, the laterally loaded pile problem is one of soil-structure

interaction; i.e., the lateral deflection of the pile depends on the soil resistance, and the

resistance of the soil, in turn, depends on the pile deflection.

12

Figure 2.5: Kinematics of Rigid Piles

Figure 2.6: Kinematics of Flexible Piles

The kinematics of a vertically loaded pile group is similar to that of an axially loaded

pile. A vertically loaded pile group moves down under the applied load. However, the

difference in the response of a pile in a group and a similarly loaded isolated pile is

that the pile in a group undergoes more settlement due to the additional downward

forces acting on it due to the interaction of the adjacent piles (Figure 2-7) (Fleming

and Randolph 1985, Salgado 2008).

13

Figure 2.7: Kinematics of a vertically loaded pile group

The kinematics of a laterally loaded pile group is such that the piles in a group may

have vertical movement in addition to lateral movement, rotation and bending. If, due

to the externally applied force and moment, the pile cap rotates, then the piles in the

rows in front of the pile-cap center undergo downward movement while those behind

undergo uplift (Figure 2-8) (Fleming and Randolph 1985, Salgado 2008). However, if

the rotation of the pile cap is not large, then the piles can be assumed to move only in

the horizontal direction.

Failure is a term that engineers define for their convenience. For a structure or a

foundation there is some preset criteria that has to be satisfy for their structural

stability and equilibrium. If one or more of those criteria are not satisfied, then the

structure or the foundation can be said that it has failed. In general, two classes of

criteria: (1) ultimate limit states and (2) serviceability limit states (Salgado

2008).Ultimate limit states are associated with dangerous outcomes, such as partial or

total collapse of a structure. Serviceability limit states are used as measures to

maintain the serviceability of a structure. In general, serviceability limit states refer to

tolerable settlements or deflections. For design, all the possible ultimate and

serviceability limit states associated with a particular structural or foundation element

are identified and then it is designed so that all the limit states are satisfied.

14

Figure 2.8: Kinematics of a laterally loaded pile group

One ultimate limit state for laterally loaded piles is reached if the resistive stresses in

the soil attain the limit (yield) value over a substantial portion of the pile length so

that plastic flow occurs within the soil mass resulting in large lateral deflections,

translation or rotation of the pile (e.g., inflexible piles, with possible yield or breakage

of the pile at one or more cross sections). This ultimate limit state may lead to

collapse of the superstructure. For flexible piles, the mechanism consists of a plastic

wedge of soil that forms in front of the pile, leading to excessive lateral deflection and

bending. If the bending moment is excessive, plastic hinges may form, leading

possibly to collapse. Much before this pile-centered ultimate limit state is reached,

other ultimate limit states or serviceability limit states may occur as the pile head

deflection exceeds the tolerable head deflection. Hence, it is the restriction of the

horizontal pile deflection that determines the limits of pile performance and designs in

most cases. In fact, in most cases, piles are first designed against ultimate limit states

corresponding to axial loads (i.e., against the limit vertical load carrying capacity) and

then checked against serviceability limit states corresponding to axial and lateral loads

(i.e., against vertical and lateral deflections).

In the case of laterally loaded pile groups, a serviceability limit state restricting the

lateral deflection would govern the design in most cases. However, checks against

ultimate limit states resulting from the yielding of soil in front of pile rows (as well as

the limit states due to formation of plastic hinges in the piles) may also be required.

15

Additionally, checks might be necessary against the limit states arising due to the

rotation of the pile cap and the associated vertical movement of the piles.

2.4 Analysis Methods

Having assessed the statics, kinematics and the possible failure modes of laterally

loaded piles, the methods available for analyzing them so that safe designs can be

produced are discussed here. Piles with active loading are discussed here. Most of the

analyses available in the literature are developed for active loading, although most of

the methods can be extended to passive loading as well. Research on analysis of

laterally loaded piles started more than five decades ago. As a consequence of such

sustained research, a number of analysis methods that can be used for design (an

account of the salient analysis methods available can be obtained from Poulos and

Davis 1980, Scott 1981, Fleming et al. 1992, Reese and Van Impe 2001, Reese et al.

2006). Broadly, the methods of analysis can be classified into following approaches:

2.4.1 Broms Method (1964a and 1964b)

The Broms method is an approximate approach which is subject to significant

limitations relative to the more sophisticated p-y models that are recommended and

available using computer software. The Broms method is a simplified limit

equilibrium solution that is suitable for simple analyses of relatively short, stiff piles

subject to lateral shear and overturning moments. The moment distribution along the

length of pile cannot be analyzed from Broms method. Examples of structures which

might be analyzed using the Broms method include sign or sound wall foundations in

uniform or relatively simple soil profiles.

In order to perform an analysis using this method, a simple soil passive pressure

diagram is assumed and a limit equilibrium solution can be obtained through

derivation of equations of static equilibrium of shear and moment in the shaft.

Although the original paper proposed a method for analysis of piles with full moment

connection to a cap which is “fixed” against rotation, it is recommended that the use

of the method is limited to these simple applications in which shear and overturning

are applied at the top of a shaft which is free to rotate. The method is most suited to

analysis of strength limit states. Analysis of deformations (serviceability) in the

original papers was based on a simplified subgrade reaction model for an elastic pile

16

that is not considered to be very reliable. For analysis of geotechnical strength limit

state of a pile using the Broms method, a resistance factor of 0.4 is recommended.

This recommendation is provided based on the judgment of the authors,

considering the fact that:

the method uses a bearing capacity type analysis based on a limit

equilibrium solution, similar to a bearing capacity analysis of a shallow

foundation

the method is recommended only for non-critical structures such as

signs, light poles, or sound walls, and not for bridges or retaining walls

the geotechnical information at specific foundation locations in the

aforementioned type of applications is often sparse, based on crude sampling

from borings at widely spaced locations

the current AASHTO code does not provide guidance for the

evaluation of geotechnical strength of piles using the Broms method.

Broms Method for Cohesive Soils

The maximum soil resistance per unit length of shaft in cohesive soils is taken as 9

times the cohesion (undrained shear strength) times the shaft diameter, with an

exclusion zone in the top 1.5 shaft diameters as illustrated on Figure 2.9.

In order to achieve horizontal force and moment equilibrium, the portion of the earth

pressure in the upper portion of the shaft will oppose the applied shear force, and the

portion of the earth pressure at the base of the diagram will act as shown in

order to restrain the shaft toe. The resulting earth pressure, shear, and moment

diagrams would be as shown on Figure 2.10.

17

Figure 2-9: Broms Earth Pressures for Cohesive Soils

Figure 2-10: Broms Pressure, Shear, Moment Diagrams for Cohesive Soils

The point of zero shear, and thus the point of maximum moment, occurs at a depth, f,

below the top of the uppermost earth pressure diagram as shown on Figure 2-10. In

order to satisfy horizontal force equilibrium about that point, the earth pressures

below the point of zero shear must sum to zero, and therefore the earth pressures on

each side of the shaft over the region labeled “g” must be equally divided on each

side of the shaft. The crossover pressures result in the triangular shape of the shear

diagram over this region with the peak at g/2 as shown. Note that this simplified

diagram inherently assumes that the shaft rotates about the point at g/2 where the

earth pressures cross the shaft axis, and that the full earth pressure is mobilized

immediately above and below this point even though the displacement must be

extremely small near the point of rotation. In order to satisfy moment equilibrium, the

18

resultant moment due to the earth pressures acting on the region g below the point of

zero shear must equal the maximum moment, which is the moment due to the forces

and earth pressures above the point of zero shear.

From the diagrams shown on Figure 2-10, the following equations are obtained:

Pt = 9suBbf 2-1 Therefore: f = Pt/9suBb 2-2 Maximum moment: Mmax = Mt + Pt (f + 1.5Bb) – (9suBbf2/2) 2-3 Determine g from Mmax: Mmax = 4.5suBbg2/2 2-4 Therefore: g = [2 Mmax / 4.5suBb]1/2 2-5 and the minimum length of the shaft is then: L ≥ 1.5Bb + f + g 2-6

Broms Method for Cohesionless Soils

The maximum soil resistance per unit length of shaft in cohesionless soils is assumed

to be three times the Rankine passive earth pressure times the shaft diameter. Thus, at

a depth, z, below the ground surface the soil resistance per unit length of shaft, pz, can

be obtained as follows:

pz = 3Bbσ' Kp 2-7 Kp = tan2(45+φ/2) 2-8 Where, σ' = Effective vertical stress at depth z, = γz γ = Unit weight of soil Kp = Rankine coefficient of passive earth pressure φ = Angle of internal friction of soil

19

The earth pressure diagram used for design is illustrated on Figure 2.11. The passive

earth pressure should actually cross the vertical axis at the point of rotation, and the

pressures below the point of rotation should act in the same direction as the load.

However, as a simplification, the pressure diagram is taken as shown and the portion

on the left hand side is replaced by a concentrated force at the bottom of the shaft

(in a manner similar to the simplified earth support method used for walls). With

uniform soil of weight γ, the vertical stress σ’ at the base of the shaft at depth L will

be γL and the passive earth pressure at the base of the triangular pressure diagram will

be 3BbγLKp.

Requirements of overall moment equilibrium are applied in order to determine the

minimum length of the shaft, Lmin, to satisfy geotechnical strength requirements.

At the base of the shaft:

Figure 2.11: Broms Pressure, Shear, Moment Diagrams for Cohesionless Soils

ΣMb = 0 = Mt + PtLmin - 3BbγLminKp(Lmin/2)(Lmin/3) 2-9 The solution of the cubic Equation 2-9 provides Lmin.

The point of zero shear, and thus the point of maximum moment, occurs at a depth, f,

at which point the passive pressure is 3Bbγf Kp, so:

Pt = 3Bbγf Kp (f2/2) = 1.5Bbγ (f2) Kp 2-10

f = [Pt/ (1.5Bbγ Kp)]½ 2-11

Maximum moment:

Mmax = ΣMf = Mt + Pt (f) – (½Bbγf/3 Kp) 2-12

20

Figure 2.12 and 2.13 are provided by Broms for graphical estimate of pile ultimate

lateral load capacity for cohesive soil of short rigid pile and long flexible pile

respectively.

Figure 2.14 provides the lateral deflection calculation both short and long pile

embedded in cohesive soil

Figure 2.12: Ultimate lateral resistance of short pile in cohesive soil

21

Figure 2.13: Ultimate lateral resistance of long pile in cohesive soil

Figure 2.14: Charts for calculation of lateral deflection at ground

surface of horizontally loaded pile in cohesive soil (after Broms 1964)

22

2.4.2 Beam-on-Elastic Foundation

Hetenyi (1946) originally presented beam-on-elastic-foundation solutions (also

known as the subgrade reaction method) in the form of the governing fourth-order

differential equation:

��

= � 2-13

with p = -Esy and where E and I are the pile modulus of elasticity and moment of

inertia, y is the pile deflection, x is the depth below the soil surface, Es is the modulus

of subgrade reaction, and p is the reaction of soil on the pile. As is the case with the

elastic continuum method, analytical solutions are not available for arbitrary

distributions of soil or pile stiffness. This method has mainly been applied to static

lateral pile loading problems, and is therefore used for the determination of pile head

stiffness analyses.

Matlock and Reese (1960) presented a generalized iterative solution method for rigid

and flexible laterally loaded piles embedded in soils with two forms of varying

modulus with depth. Davisson and Gill (1963) investigated the case of a laterally

loaded pile embedded in a layered soil system with a constant (but different) modulus

of subgrade reaction in each layer. They concluded that the near surface modulus was

the controlling factor for the pile response, and that soil investigations and

characterization should be focused in this zone. In classic companion papers, Broms

(1964a, b) described a method for analyzing lateral pile response in cohesive and

cohesionless soils. His method for computing ground surface deflections of rigid and

flexible fixed and free head piles was based on a modulus of subgrade reaction using

values suggested by Terzaghi (1955). For undrained loading, he designated that a

constant subgrade modulus be used with a value of 9su for the ultimate lateral soil

resistance. For drained loading cases, a subgrade modulus linearly increasing with

depth was specified and a Rankine earth pressure-based method was used for

computing an ultimate resistance assumed equal to 3KpDp γ'h.

Jamilokowski and Garassino (1977) provided a state-of-the-art discussion on soil

modulus and ultimate soil resistance for laterally loaded piles. Randolph and Houlsby

(1984) used classical plasticity theory to derive lower and upper bound values of the

23

limiting pressure on an undrained laterally loaded pile that ranged from approximately

9 to 12 su as a function of pile roughness. Hansbro (1995) revisited Brom’s

computation of drained ultimate lateral resistance, and based on results of centrifuge

tests conducted by Barton (1982) suggested that a drained ultimate lateral resistance

of Kp2Dpγ'h is more appropriate for cohesionless soils. Kulhawy and Chen (1995)

applied Brom’s concepts to drilled shafts, recognizing the components of resistance to

lateral loading unique to drilled shafts, and noted the importance of conducting

appropriate laboratory tests for laterally loaded pile and drilled shaft analysis.

2.4.3 Beam-on-Winkler Foundation

By accepting Winkler’s foundation assumption (1876) that each layer of soil responds

independently to adjacent layers, a beam and discrete spring system may be adopted

to model pile lateral loading. Although this assumption ignores the shear transfer

between layers of soil, it has proven to be a popular and effective method for static

and dynamic lateral pile response analyses. In this method, the soil-pile contact is

discretized to a number of points where combinations of springs and dashpots

represent the soil-pile stiffness and damping at each particular layer. These soil-pile

springs may be linear elastic or nonlinear; p-y curves typically used to model

nonlinear soil-pile stiffness have been empirically derived from field tests, and have

the advantage of implicitly including pile installation effects on the surrounding soil,

unlike other methods. In advanced applications, capabilities for soil-pile gapping,

cyclic degradation, and rate dependency are also provided. A singular disadvantage of

a beam-on-Winkler-foundation model is the two-dimensional simplification of the

soil-pile contact, which ignores the radial and three dimensional components of

interaction. For dynamic loadings, “free-field” soil acceleration time histories are

usually computed in a separate site response analysis, double integrated to

displacement time histories, and then externally applied to the soil-pile springs. The

multi-step uncoupled approach has the disadvantage of potentially introducing

numerical errors in the integration step, and artificially separates the overall soil-pile

system response. Recently, investigators have begun to develop fully-coupled

analyses wherein both soil and soil-pile superstructure response can be simultaneously

evaluated (Lok, 1999). McClelland and Focht (1958) can be said to be the originators

of the p-y method of laterally loaded pile analysis. They proposed a procedure for

24

correlating triaxial stress strain data to a pile load-deflection curve at discrete depths,

and estimating the modulus of subgrade reaction at each layer. Of particular interest is

the ensuing discussion provided by Peck, Matlock, and others to their paper, wherein

Reese first presented his concept of a near surface wedge (Figure 2.15) and deep

plasticity flow failure models, with an ultimate undrained resistance of 12 su.

Figure 2.15: Lateral Loading Near Surface Passive Wedge Geometry and Soil-Pile

Forces (after Reese, 1958)

2.4.4 Elastic Continuum Approach

The elastic continuum analytical method is based on Mindlin’s (1936) closed form

solution for the application of point loads to a semi-infinite mass. The accuracy of

these solutions is directly related to the evaluation of the Young’s modulus and the

other elastic parameters of the soil. This approach is limited in the sense that

nonlinear soil-pile behavior is difficult to incorporate (the equivalent linear method is

available), and it is more appropriately applied for small strain, steady state vibration

problems. In addition, layered soil profiles cannot be accommodated, and only

solutions for constant, linearly increasing, and parabolically increasing soil modulus

with depth have been derived. True continuum models do have the advantage of

intrinsically modeling the effects of radiation damping, whereas discrete models must

artificially simulate this energy dissipation mode.

25

Tajimi (1966) was the first to describe a dynamic soil-pile interaction solution based

on elastic continuum theory. He used a linear Kelvin-Voigt visco-elastic stratum to

model the soil and ignored the vertical components of response. His basic method has

been modified and extended by Tazoh et al. (1988) and other researchers to include

superstructure inertial effects. Poulos has been a major progenitor of elastic solutions

for soil and rock mechanics, and has worked extensively on all aspects of pile

foundation response to axial and lateral loads. In Poulos (1971a, b) he first published

elastic continuum solutions for laterally loaded single piles and groups under static

loading. Poulos and Davis (1980) presented a comprehensive set of analysis and

design methods for pile foundations based on elastic continuum theory.

Poulos (1982) described a procedure for degradation of soil pile resistance under

cyclic lateral loading and compared it to several case studies. In a different approach,

Swane and Poulos (1984) proposed a subgrade reaction method that provided for

progressive soil-pile gapping with bilinear elasto-plastic springs and friction slider

blocks. In the 29th Rankine Lecture, Poulos (1989) presented a compendium of his

work on axial pile loading.

2.5 Mechanics concerning response of soil to lateral loading

2.5.1 General

The mechanics concerning response of piles to lateral loading embedded in soil is to

establish a relationship between the soil stiffness and the stiffness of the pile materials

itself.

The Winkler method, or sometimes known as the subgrade reaction method, currently

appears to be the most widely used in a design of laterally loaded piles. The method

was first introduced by Winkler (1867) to analyze the response of beams on an elastic

subgrade by characterizing the soil as a series of independent linearly-elastic soil

springs. Since then, this concept has been extensively employed for the laterally

loaded pile problem. One of the great advantages of this method over the elastic

continuum method is that the idea is easy to program in the finite difference or finite

element methods and that the soil nonlinearity and multiple soil layers can be easily

26

taken into account. The concept can be easily implemented in dynamic analysis. In

addition, the computational cost is significantly less than the finite element method.

However, the obvious disadvantage of this method is the lack of continuity; real soil

is at least to some extent continuous.

2.5.2 Modulus of Subgrade Reaction

Foundation-ground interaction has been one of the challenging problems in

geotechnical engineering since late nineteenth century. Because of the complexity of

soil behavior, subgrade in soil-foundation interaction problems is replaced by a much

simpler system called subgrade model. One of the most common and simple models

in this context is Winkler hypothesis. Winkler idealization represents the soil medium

as a system of identical but mutually independent, closely spaced, discrete and

linearly elastic springs and ratio between contact pressure, P, at any given point and

settlement, y, produced by it at that point, is given by the coefficient of subgrade

reaction, ks (Dutta and Roy 2002).

At first, this concept was introduced to use in analysis of rigid plates, but during the

following decades the theory was expanded to include the computation of stresses in

flexible foundations (Terzaghi 1955). In the area of soil-foundation interaction, lots of

investigators have utilized this model, such as Biot (1937), Terzaghi (1955), Vesic

(1961), Horvath (1989), Daloglu and Vallabhan (2000) and so on. Since 1920, the

theory of subgrade reaction has also been used for computing stresses in piles and

sheet piles, which are acted on by horizontal forces above the ground surface. In this

case, the ratio between contact pressure and displacement of pile referred to as the

coefficient of horizontal subgrade reaction, kh (Terzaghi 1955). However, the methods

to calculate the modulus of subgrade reaction of soil for the analysis of piles lateral

capacity calculations the term of subgrade reaction indicates the pressure, P, per unit

area of the surface of the contact between a loaded beam or slab and the subgrade on

which it rests and on to which it transfers the loads. The coefficient of subgrade

reaction, k, is the ratio between the soil pressure, P, at any given point of the surface

of contact and the displacement, y, produced by the load application at that point:

27

�= �� 2.14

To implement this concept for a laterally loaded pile, the above equation (2.14) has

been modified frequently (e.g. Reese and Matlock, 1956; and Davisson and Gill,

1963) as

�= ��

2.15

where k is the modulus of subgrade reaction (F/L2) and p is the soil reaction per unit

length of the pile (F/L). It should be noted that the dimensions of each variable are

given in parentheses.

With the subgrade reaction concept, the lateral pile response can be obtained by

solving the forth order differential equation as:

��

+ ��= 0 2.16

where Ep is the modulus of elasticity of the pile, Ip is the moment of inertia of the pile,

and z is depth.

Solutions of Eq. (2.16) can be obtained either analytically or numerically.

Analytical solutions are only available in the case of constant modulus of subgrade

reaction with depth. For other subgrade reaction distribution, the solutions are

conveniently solved by using the finite difference method.

Hetenyi (1946) provided solutions for a variety of infinite beams on an elastic

Winkler subgrade by solving analytically the governing equations. The solutions can

be applied to analyze the response of a laterally loaded pile with a constant subgrade

reaction. Barber (1953) provided the solutions to determine the deflections and

rotation at the ground surface using the convenient plots for cases of constant soil

modulus of subgrade reaction, as well as the linearly increasing soil modulus of

subgrade reaction with depth. Several functions of distribution of modulus of

28

subgrade reaction with depth (i.e., polynomial function and power function) have

been considered by Matlock and Reese (1960). Matlock and Reese give the solutions

for a special case soil profile where the modulus of subgrade reaction has some finite

value at the ground surface and continues to increase linearly with depth.

Davisson and Gill (1963) extended the subgrade reaction theory to analyze the

behavior of laterally loaded piles in a two-layer soil system for both free and fixed

head conditions and provided the results in non-dimensional forms.

The values of modulus of subgrade reaction can be obtained using the in-situ testing,

such as the plate loading test. For practical purposes, Terzaghi (1955) recommended

the rough estimate values of coefficient of subgrade reaction for stiff clay and sand

to be used for analyzing pile response using subgrade theory. He stated that the linear

relationship between the soil pressure and displacement was valid for values of the

soil pressure that were smaller than about one-half of the bearing stress.

Another method in estimating the modulus of subgrade reaction is the use of the

equation proposed by Vesic (1961). Vesic provided a relationship between the

modulus of subgrade reaction, k, used in the Winkler spring problem and the material

properties in the elastic continuum problem as

�= �.�� (��)

��

��/��

2.17

Where,

Es = soil modulus of elasticity,

μs = Poisson’s ratio of the soil,

D = pile diameter, and

EpIp = flexural rigidity of the pile.

By knowing the soil modulus of elasticity from the laboratory or field testing, as well

as the pile property, the modulus of subgrade reaction can be estimated.

29

2.5.3 Subgrade modulus related to piles under lateral loading

The concept to the subgrade modulus has been presented in technical literature from

early days and values have been tabulated in textbooks and other documents.

Engineers performing analyses of piles under lateral loading, prior to developments

reported herein, sometimes relied on tabulated values of the subgrade modulus in

getting the soil resistance. Numerical values of the subgrade modulus are certainly

related to values of Es and to Epy in some ways; therefore, an explanation of the term

subgrade modulus by way of a simple experiment is desirable.

Figure 2.16a shows a plan view of the plate with m and n indicating the lengths of the

sides. If a concentrated vertical load is applied to the plate at the central point, the

resulting settlement is shown by Section A-A in Figure 2.16b, along with an assumed

uniform distributed load. If increasingly larger loads are applied, a unit load-

settlement curve is subsequently developed, as shown by the typical curve in Figure

2.16c. The figure indicates that the magnitude of the unit load reached a point where

settlement continued without any increase in load.

Several lines are drawn in Figure 2.16c from the origin of the curve to points on the

curve. The slopes of these lines with units of F/L are defined as the subgrade

modulus, and are a measure of the stiffness of the soil under the particular loading.

As shown, the maximum value is for a line drawn through the initial portion of the

curve, with the other lines giving lower values.

If a plate with dimensions larger or smaller than given by m and n is employed in the

same soil, one could expect a different result. Further, the stiffness of the plate itself

can affect the results, because the plate would deform in a horizontal plane, depending

on the method of loading. Also, soils with a friction angle will exhibit an increased

stiffness with depth. As can be understood, except in some special cases, values of

such type of subgrade moduli are of limited value in the solution of a problem of

soil-structure interaction but are only useful in merely differentiating the stiffness of

various soils (and rocks) such as soft clay, stiff clay, loose sand, dense sand, sound

limestone, or weathered limestone.

30

Figure 2.16: Description of experiment loading to definition of subgrade modulus.

More recent in situ testing research revealed the possibility to estimate for example

the lateral subgrade modulus from Menard pressuremeter tests (Y. Ikeda et al. 1998,

Imai T. 1970) and from Marchetti dilatometer tests.

From the work of Baldi et al. (1986) and Robertson et al. (1989), one could in this

respect at least for displacement piles, go out from flat dilatometer tests (DMT) in

order to estimate directly the Epy at a given depth from the dilatometer modulus EDMT

= 34.7 (P1 — P0); P1 & Po are DMT readings (Fig.2.8d). In our proposal, we would

implement a simplified relation for the case of lateral loading of displacement piles:

Epy (at the DMT testing depth) = F. EDMT 2.18

with: F = 2 for N.C. sands; F = 5 for O.C. dense sands; F = 10 for N.C. clays.

2.5.4 Theoretical solution by Skempton for subgrade modulus of soil

Skempton (1951) wrote that ‘simple theoretical considerations’ were employed to

develop a prediction for load-settlement curves. Even a limited solution, for saturated

clays, is useful to reflect the practical application of theory. The theory has some

relevance to p-y curves because the resistance to the deflection of a loaded area is

common to both a horizontal plate and a pile under lateral loading.

31

As noted earlier, the mean settlement of a foundation, sm of width b on the surface of a

semi-infinite solid, based on the theory of elasticity is given by Equation 2.19

�� = ��

�� 2.19

Where, q = foundation pressure; ��= influence coefficient; υ= Poisson’s ratio of the

solid; and Es = Young’s modulus of the solid.

In Equation 2.19, Poisson’s ratio can assumed to be 1/2 for saturated clays if there is

no change in water content. For a rigid circular footing on the ground surface Ip can

be taken as π/4 and the failure stress qf be taken as equal 6.8cu, where cu is the

undrained shear strength. Making the substitutions indicated and setting Sm = Sm1 for

the particular case

�� = �

��

��

2.20

Skempton noted that the influence value Ir decreases with depth below the surface but

the bearing capacity factor increases; therefore, as a first approximation Equation 2.20

is valid for any depth.

In an undrained compression test, the axial strain is given by the following equation.

�= ��

= ∆�� 2.21

where E = Young’s modulus at the stress (σ1-σ3) level.

For saturated clays with no water content change, Equation 2.21 may be rewritten as

follows.

�= ��

(�� )(�� )�

2.22

Where, (σ1- σ3)f = failure stress.

Equations 2.21 and 2.22 show that, for the same ratio of applied stress to ultimate

stress, the strain in the footing test (or pile under lateral loading) is related to the strain

in the laboratory compression test by the following equation.

32

�� = 2� 2.23

Skempton’s arguments based on the theory of elasticity and also on the actual

behavior of full-scale foundations led to the following conclusion:

Thus, to a degree of approximation (20%) comparable with the accuracy of the

assumptions, it may be taken that Equation 2.23 applies to a circular or square

footing.

As may be seen in the analyses shown above, Skempton allowed the Young’s

modulus of the soil, Es to be nonlinear and to assume values from Esmax to much lower

values when the soil was at failure. The assumption of a nonlinear value of Es is

remarkable because of varying state of stress of elements below the footing.

Skempton pointed out that the value of Ir for a footing with a length to width ratio of

10 was reported by Terzaghi (1943) and Timoshenko (1934) to be 1.26. If the bearing

capacity factor is taken as 5.3cu, Equation 2.23 can be written as follows.

�� = 2.5� 2.24

Skempton stated that the failure stress for a footing reaches a maximum value of 9cu.

A curve of resistance as a function of deflection could be obtained for a long strip

footing, then, by taking points from a laboratory stress-strain curve and using

Equation 2.24 to obtain deflection and 4.5∆� to obtain soil resistance.

2.5.5 Empirical Equations for Estimating ks

Bowles (1997) suggested an equation for estimating ks using the allowable bearing

pressure qa which is shown in Eq. 2.25 as follows:

��= �� ,� × �� × �� × �� + �� ,� × �� 2.25

Where, �� ,� = 1.3 to 1.7 and �� ,� = 2 to 4.4 for rounded pile

SF = safety factor used to obtain qa (usually 3 for clay; 2 for cohesionless soil)

Nq = Bearing capacity factor

n = 0.4 to 0.6 so ks does not increase too much with depth

C = 12 for Fps unit

33

Cm = �

2.0, �� = � ≤ 0.457 �

1.0 + � ��,� �

��.��

≥ 1.5, �� = � > 0.457 �1.25, �� = � > 1200 � �

If qa = qu (unconfined compression test) and omit the Nq term in Eq. 2.25

the value of ks in Fps units for a pile of unknown B is

ks = Cm x 12 x SF x qu = 2 x 3 x 12 x qu = 72 qu

Davisson and Robinson (1965) suggested a value of ks 10525 su, KN/m3

Using the standard penetration test data [see Yoshida and Yoshinaka (1972)]

to obtain

Es = 650N kPa 2.26

From this value ks can be found from the equation proposed by Pyke and

Beikae (1983):

��= �.��

2.27

2.5.6 Concept of p-y Curves

All of the solutions based on subgrade reaction theory mentioned in the previous

sections are valid only for a case of linear soil properties. In reality, the relationship

between soil pressure per unit pile length p and deflection y is nonlinear. Taking the

nonlinearity of soil into account, the linear soil springs are replaced with a series of

nonlinear soil springs, which represent the soil resistance-deflection curve so called,

“p-y” curve. The p-y curves of the soil have been developed based on the back

analysis of the full scale lateral pile load test. This concept was first developed by

McClelland and Focht (1958).

The concept of a p-y curve can be defined graphically as shown in Figure 2.18. It was

assumed that the pile was perfectly straight prior to driving and there was no bending

of the pile during driving. The soil pressure acting against the pile prior to loading can

be reasonably assumed to be uniform (Figure 2.18a). The resultant pressure for this

34

condition is zero. If the pile is loaded with a given lateral deflection as shown in

Figure 2.18b, a net soil reaction will be obtained by the integration of the soil

pressures around the pile giving the unbalanced force per unit length of the pile. This

process can be repeated in concept for a series of deflections resulting in a series of

forces per unit length of pile which may combine to form a p-y curve. In a similar

manner, the sets of p-y curves along the pile as shown in Figure 2.19 can be obtained.

If such a set of curves can be predicted, the yield pile deflection, pile rotation, bending

moment, shear, and soil reaction for any load capable of being sustained by the pile

can be obtained by solving the beam equation.

The series of p-y curves greatly depends upon the soil type. The p-y curves can be

obtained experimentally by conducting the full scale testing of instrumented piles in

the type of soil deposit interested. Figure 2.19 presents the methodology in developing

the p-y curves. The bending moment diagram along the pile can generally be

computed by the product of pile curvatures, which are computed from the measured

strain along the pile, with the known pile stiffness. Double differentiation of the

bending moment diagram produces the soil reaction curve. The deflection along the

pile can be obtained by double integration of the curvature diagram. Therefore, the

soil reaction versus the deflection of the pile, p-y curve, at a given depth can be

obtained.

Though the Winkler method neglects soil continuity, a disadvantage to a considerable

extent, it has been overcome through calibrating p-y curves to full-scale test results.

However, many factors which influence the behavior of laterally loaded piles have

been lumped into the characteristic shape of the p-y curves and difficult to separate

due to the limit number of the full-scale testing. Some of the parameters which may

have a significant effect on the pile response have not been investigated

systematically such as the pile diameter effect, the effect of soil gapping, and the

validity of using these p-y curves for a rigid pile case. Further research on these issues

needs to be investigated in order to improve the existing p-y curves for the wider

range of application.

Several researchers have proposed methods to construct p-y curves for various soil

types based upon back-computation from full-scale test results. The following

paragraphs presents the brief description of each p-y curves currently available in the

35

industry. Most of these p-y curves have been incorporated in the commercial

programs in analyzing behavior of laterally loaded pile, such as COM624P (Wang

and Reese, 1993), LPILE (Reese et al., 2000), and FLPIER (University of Florida,

1996). of Constant Soil Modulus (after Poulos, 1971)

Figure 2.17: Implementation of Winkler Spring Concept for Laterally Loaded Pile

Problem

Figure 2.18: Definition of p-y Concept with a) Pile at Rest; b) Pile after Load

Applied (after Dunnavant, 1986)

36

Figure 2.19: Typical Family of p-y Curves Response to Lateral Loading (after

Dunnavant, 1986)

Figure 2.20: Deflections, slopes, bending moments, shearing forces, and soil reactions for elastic conditions (after Reese and Matlock).

37

Figure 2.21: Characteristic Shape of p-y Curve for Soft Clay (after Matlock, 1970)

In Matlock (1970) method the p-y curve is initially parabolic in shape and after pu

point it becomes parallel to the deflection axis. Federal Highway Authority (US

department of transportation) proposed in their document (FHWA-IP-84-11, JULY

1984) that the initial portion of p-y curve may be used straight line (constant ks) whose

results are almost same as proposed p-y method of Matlock.

2.5.7 p-y curves for clay soil

Matlock (1970) conducted full-scale lateral load tests on a 0.3 m diameter

instrumented steel pipe pile embedded in soft clay deposit at Lake Austin, Texas.

The methodology to develop the p-y curves was proposed based on the back

computed p-y curves from the test results. Figure 2.21a presents the characteristic

shape of the soft clay p-y curves for static loading case which can be represented by

using cubic parabola relationship as:

2.28

where: pu = ultimate soil resistance which is related to the undrained shear strength of

the soil as well as a function of depth, and y50 = the soil displacement at one-half of

ultimate soil resistance.

38

A summary of procedure in developing the soft clay p-y curves is given in Table 2.1

Table 2.1 Summary of Procedure in Developing p-y curves for clay soil

(Matlock, 1970)

39

CHAPTER 3

ANALYSIS AND RESULTS OF LATERALLY LOADED PILES

3.1 INTRODUCTION

In this chapter detail analysis and results of piles embedded in homogeneous &

layered soil are presented. The analysis procedure and results has been shown in table

& various graphical forms. Various diameters of piles of length 23 m have been

analyzed in various soil types having soft to stiff clay of various top deflections. From

the structural strength & serviceability point of view BNBC & other building code

permits maximum 25 mm pile top deflection due to lateral load.

3.2 METHODOLOGY OF ANALYSIS

The analysis has been done using the p-y methods of soil & the Finite Element

Software SAP. Soil has defined series of soil spring which gives lateral support of pile

embedded in soil during the lateral load applied on the pile top. The spring values

evaluated from Robinson’s (1978) modulus of subgrade reaction equation presented

in chapter 2.

Selection of pile diameter and length

In this analysis 500 mm, 600 mm, 750 mm & 1 m diameter pile of length of

23 m have considered.

Soil type

Cohesive soil of undrained shear strength 10 kpa, 25 kpa, 50 kpa & 70 kpa are

taken. Pile diameter and soil type are shown in table 3.1.

Pile head deflection

In this analysis maximum lateral load capacity & bending moment are

analyzed for 6 mm, 12 mm & 25 mm top deflection.

Determination of spring constant for pile model

The first step is to determine whether the pile will behave as a short rigid unit

or as an infinitely long flexible member. This is done by calculating the

stiffness factor T for the particular combination of pile and soil. The stiffness

factors are governed by the stiffness (EI value) of the pile and the

40

compressibility of the soil. The latter is expressed in terms of a ‘soil modulus’,

which is not constant for any soil type but depends on the width of the pile B

and the depth of the particular loaded area of soil being considered. For most

normally consolidated clays and for granular soils the soil modulus is assumed

to increase linearly with depth, for which

stiffness factor, T = � ��

� (in units of length) Reese (3.1)

Values of nh are as follows: Soft normally-consolidated clays: 350 to 700 kN/m3

Having calculated the stiffness factor T, the criteria for behaviour as a short rigid pile or as a long elastic pile are related to the embedded length L as follows:

Short Rigid Pile (free head) L ≤ 2T Elastic Long Pile (free head) L ≥ 4T

Considering 500 mm & 1 m diameter pile of length 23 m and soft soil of cu = 10 kpa

for 500 mm diameter pile E = 20x106 kN/m2

I = 3.26 x 10-3 m4

nh = 500 kN/m3

L = 4 * 2.64 = 10.6 m < 23 m, so pile is long pile. 1 m diameter pile

E = 20x106 kN/m2 I = 52.21 x 10-3 m4

nh = 500 kN/m3 L = 4 * 4.61 = 18.5 m < 23 m, so pile is long pile.


�

T = �� ∗ �.��

��

� = 2.64 m


�

T = �20 x 106 ∗ 52.21 x 10−3

500

� = 4.61 m

41

Table 3.1 Pile analysis data for homogeneous soil

Pile Diameter (mm) Soil Shear Strength (kpa) Length of Pile (m)

500 10,25,50,70 23

600 10,25,50,70 23

750 10,25,50,70 23

1000 10,25,50,70 23

It is assumed that the soil is homogeneous & isotropic in full depth & the water table

at the ground level. Two types of mode may be analyzed for lateral loads are

1. Considering full depth of soil is effective (Fig 3.1 a)

2. Neglecting top 1.5 m soil shear strength (Fig 3.1 b) (Broms 1964)

(a) (b)

Figure 3.1: Location of spring (a) Considering full depth of soil effective, (b)

Neglecting top 1.5 m soil shear strength

23 m

Ground Level

1.5 m

Pile

P

300 m

m

23 m

Ground Level

Pile

P 300 m

m

42

3.3 STEPS FOR ANALYSIS OF PILES EMBEDDED IN SOIL

Step 1: Determination of spring constant

Spring constant, k = 67 * Cu* 2 * b = 67 * 0.2 * 2 * 20/12 = 60.8 kN/m.

(Davisson & Robinson, 1965)

Figure 3.2: Load vs deflection graph showing spring constant & pult

Step 2: Determination of pult

pult = 11* cu * b = 11 * 0.2 * 20/12 = 16.3 kN (Matlock & Reese, 1956)

it is the maximum value of pult , the initial some spring pult values are calculated as per

the soil passive resistance, after that this value is dominating.

According to Broms method, the initial some spring can withstand only 3 times the

soil passive resistance. In this example it is 2 instead of 3 because some writers

suggested that this value should not exceed 2 (AASHTO Design Manual for Drilled

Shaft).

For 0.5 m pile

Passive resistance of soil = (1/2 * kp * * h2 + 2 * c *�� )

(Rankine’s theory)

For first spring the value will be = (1/2*1* 0.06 * 12 + 0.4)*2*20/12 = 4.9 kN

2nd spring value will be = 7.5 kN

3rd spring value will be = 9.9 kN

4th spring value will be = 12.9 kN

5th spring value will be = 16.9 kN which is larger than 16.3 kN (maximum value of

pult) so the value of pult of 5th and so on springs are taken = 16.3 kN.

Deflection, y

Load

, p

pult

Spring constant, k

43

The values of spring constant, pult for computer analysis are shown in table 3.2

Table 3.2 Values of spring constant & pult of different Clay soils.

From computer analysis the results are shown in th article 3.4

Value 500 mm dia pile 600 mm dia pile 750 mm dia pile 1000 mm dia pile

cu (kpa)

Depth (m)

Spring Constant

kN/m pult

(kN)

Spring Constant

kN/m pult

(kN)

Spring Constant kN/m

pult (kN)

Spring Constant

kN/m pult

(kN) 10 0.3 61 4 79 9 95 9 122 9 0.6 131 9 158 13 190 13 245 13 0.9 131 13 158 18 190 18 245 18 1.2 131 18 158 22 190 22 245 27 23.0 131 18 158 22 190 22 245 31

25 0.3 152 9 177 18 201 18 316 18 0.6 305 18 354 31 403 31 631 31 0.9 305 31 354 40 403 40 631 49 1.2 305 40 354 49 403 49 631 67 1.5 305 40 354 49 403 58 631 80 1.8 305 40 354 49 403 58 631 107 2.1 305 40 354 49 403 58 631 133 23.0 305 40 354 49 403 58 631 160

50 0.3 316 9 347 18 381 18 617 18 0.6 359 18 694 31 762 31 1235 36 0.9 359 31 694 40 762 40 1235 53 1.2 359 40 694 49 762 49 1235 62 1.5 359 49 694 80 762 67 1235 80 1.8 359 67 694 93 762 80 1235 107 2.1 359 80 694 93 762 93 1235 133 2.4 359 80 694 93 762 120 1235 160 23.0 359 80 694 18 762 120 1235 160

70 0.3 454 18 533 31 617 18 911 18 0.6 909 31 1066 40 1235 31 1822 36 0.9 909 40 1066 49 1235 40 1822 53 1.2 909 49 1066 67 1235 49 1822 62 1.5 909 67 1066 80 1235 67 1822 80 1.8 909 80 1066 93 1235 89 1822 107 2.1 909 93 1066 107 1235 120 1822 133 2.4 909 120 1066 120 1235 160 1822 160 2.7 909 120 1066 133 1235 182 1822 187 3.0 909 120 1066 147 1235 182 1822 205 23.0 909 120 1066 147 1235 182 1822 222

44

3.4 Allowable lateral load for piles embedded in homogeneous soil

Allowable loads for long pile, maximum moment and its location from head of the

pile for free head conditions are shown in table 3.3.

Table 3.3: Allowable horizontal loads on pile for free head condition

6 mm deflection 12 mm deflection 25 mm deflection Pile cu

(kpa) P

(kN) Mmax

(kN/m) L (m)

Location of max moment from top of pile

P (kN)

Mmax (kN/m)

L (m) Location of max moment from top of pile

P (kN)

Mmax (kN/m)

L (m) Location of max moment from top of pile

0.5

10 40 38 2.4 71 76 2.4 116 151 2.4

24 80 63 1.8 133 121 1.8 214 234 2.1

48 107 83 1.5 169 161 1.5 267 324 1.8

72 151 103 1.5 222 193 1.5 325 359 1.8

0.6

10 62 67 2.7 111 124 2.7 169 238 2.7

24 111 95 2.1 205 193 2.1 311 367 2.4

48 165 132 1.8 254 250 1.8 387 483 2.1

72 196 163 1.8 267 295 1.8 400 506 2.1

0.75

10 80 103 3.0 147 214 3.0 231 396 3.4

24 156 161 2.4 280 331 2.4 445 666 2.7

48 231 231 2.1 356 435 2.1 534 816 2.4

72 267 272 2.1 400 505 2.1 623 986 2.4

1.0

10 142 227 4.0 249 449 4.0 378 836 4.3

24 267 354 3.0 467 666 3.0 756 1340 3.4

48 378 476 2.7 601 909 2.7 956 1768 3.0

72 445 571 2.4 667 1034 2.4 1023 1931 2.7

Ground Level

Pile

P

Clay Soil

Cu= 10 kpa25 kpa

50 kpa70 kpa 23

m

45

Allowable loads for long pile, maximum moment and its location from the top of the

pile for fixed head condition are shown in table 3.4.

Table 3.4: Allowable horizontal load on pile for fixed head condition 6 mm deflection 12 mm deflection 25 mmdeflection

Pile cu (kpa)

P (kN)

Mmax (kN/m) L (m)

P (kN)

Mmax (kN/m) L (m)

P (kN)

Mmax (kN/m) L (m)

0.5

10 76 -113 23 5 142 -226 48 5 222 -423 102 5

25 156 -186 39 4 276 -362 78 4 423 -662 163 4

50 222 -249 53 3 356 -456 106 3 534 -779 204 3

70 311 -318 71 3 445 -518 124 3 689 -945 258 3

0.6

10 111 -185 38 5 222 -381 79 5 311 -646 156 6

25 222 -295 61 4 414 -590 132 4 601 -1020 245 4

50 329 -399 84 4 534 -748 169 4 801 -1295 326 4

70 400 -481 106 3 601 -831 201 3 890 -1444 400 4

0.75

10 156 -313 65 6 298 -630 131 6 445 -1119 265 7

25 311 -496 102 5 556 -966 204 5 845 -1768 428 5

50 467 -691 147 4 756 -1274 291 4 1157 -2258 578 5

70 556 -804 178 4 890 -1472 360 4 1423 -2720 748 4

1.0

10 289 -715 150 8 512 -1360 286 8 712 -2244 537 8

25 534 -1074 223 6 934 -2020 426 6 1601 -3838 843 6

50 756 -1387 286 5 1290 -2656 592 5 2224 -4736 1178 6

70 934 -1673 367 5 1512 -3087 734 5 2446 -5127 1360 5

Ground Level

Pile

P

Clay Soil

Cu=

23 m

10 kpa25 kpa

50 kpa70 kpa

46

3.5 Allowable lateral load for piles embedded in homogeneous soil neglecting

head 1.5 m soil shear strength


pile for free head condition are shown in table 3.5

Table 3.5: Allowable horizontal load on pile for free head condition neglecting top 1.5 m soil shear strength

6 mm deflection 12 mm deflection 25 mm deflection Pile cu

(kpa) P

(kN) Mmax

(kN/m) L

(m) P

(kN) Mmax

(kN/m) L (m) P

(kN) Mmax

(kN/m) L

(m) 0.5

10 13 33 3 31 67 3 53 122 3 25 25 48 2 49 97 2 89 192 3 50 33 61 2 58 116 2 98 212 2 70 45 79 2 80 152 2 125 258 2

0.6

10 25 54 3 49 109 3 89 204 3 25 40 82 3 76 154 3 142 307 3 50 53 102 2 98 196 2 165 365 3 70 62 116 2 111 226 2 187 426 2

0.75

10 40 95 4 76 184 4 133 354 4 25 62 136 3 125 272 3 222 539 3 50 89 182 3 160 354 3 276 694 3 70 107 218 3 178 400 3 289 734 3

1.0

10 76 204 4 156 394 4 267 816 4 25 133 320 3 236 594 3 400 1102 4 50 178 408 3 311 782 3 512 1360 3 70 209 476 3 343 870 3 578 1681 3

Ground Level

Pile

P

Clay Soil

Cu=

23 m

1.5 m

10 kpa25 kpa

50 kpa70 kpa

47


pile for fixed head condition are shown in table 3.6.

Table 3.6: Allowable horizontal load on pile for fixed head condition neglecting top

1.5 m soil shear strength 6 mm deflection 12 mm deflection 25 mm deflection

Pile cu (kpa)

P (kN)

Mmax (kN/m)

L (m)

P (kN)

Mmax (kN/m) L (m)

P (kN)

Mmax (kN/m) L (m)

0.5

10 45 -101 25 5 80 -185 48 5 142 -354 95 5

25 76 -146 38 4 133 -268 75 4 231 -494 147 4

50 98 -178 53 3 169 -326 102 3 276 -577 196 4

70 125 -208 64 3 209 -370 124 3 334 -658 231 3

0.6

10 67 -163 38 6 133 -326 78 6 222 -598 161 6

25 116 -242 61 4 222 -476 122 4 378 -872 245 5

50 160 -306 83 4 276 -564 163 4 445 -993 313 4

70 187 -340 101 3 298 -598 188 3 489 -1088 374 4

0.75

10 102 -283 65 6 200 -569 133 6 334 -1043 268 7

25 178 -422 102 5 334 -816 204 5 578 -1550 422 6

50 254 -544 143 4 432 -1006 286 4 703 -1768 544 5

70 289 -607 170 4 489 -1125 347 4 801 -2018 680 4

1.0

10 200 -646 144 8 356 -1197 272 8 556 -2069 524 8

25 334 -918 211 6 623 -1795 435 6 1068 -3293 843 6

50 467 -1185 294 6 801 -2190 585 6 1379 -4134 1210 6

70 556 -1374 367 5 912 -2421 707 5 1468 -4314 1360 5

Ground Level

Pile

P

Clay Soil

Cu=

23 m

1.5 m

10 kpa25 kpa

50 kpa70 kpa

48

3.6 GRAPHICAL FORM OF PILES IN HOMOHENEOUS SOIL

Allowable Lateral Capacity for Free Headed Piles

Figure 3.3: Pile Capacity vs Soil Shear Strength for 6 mm deflection



0200400600800

1000120014001600

0 0.5 1 1.5 2

20" Dia Pile24" Dia Pile30" Dia Pile40" Dia Pile

Pile MOMENT vs Soil Undrained Shear Strength for 0.5" deflection

Soil Undrained Shear Strength (ksf)

Pile

M

omen

t (ki

p-ft

)

0100200300400500600700800

0 0.5 1 1.5 2


Pile MOMENT vs Soil Undrained Shear Strength for 0.5" deflection


Pile

M

omen

t (k

ip-ft

)

0

100

200

300

400

500

0 0.5 1 1.5 2


Pile Moment vs Soil Undrained Shear Strength for 0.25" deflection


Pile

M

omen

t (k

ip-ft

)

0

200

400

600

0 20 40 60 80

0.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile

Pile Capacity vs Soil Shear Strength for 6 mm deflection

Soil Shear Strength (kpa)

Pile

C

apac

ity (k

N)

0

200

400

600

800

0 20 40 60 80

0.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile



Pile

C

apac

ity (k

N)

0

200

400

600

800

1000

1200

0 20 40 60 80

0.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile



Pile

C

apac

ity (k

N)

49

Maximum Moment for Free Headed Piles

Figure 3.6: Pile Maximum Moment vs Soil Shear Strength for 6 mm deflection



0

200

400

600

800

0 20 40 60 80

0.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile

Pile Maximum Moment vs Soil Shear Strength for 6 mm deflection

Soil Shear Strength (kpa)Pile

Max

imum

Mom

ent(

kN-m

)

0

200

400

600

800

0 20 40 60 80

0.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile



Pile

Max

imum

Mom

ent(

kN-m

)

0

200

400

600

800

1000

1200

0 20 40 60 80

0.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile



Pile

Max

imum

Mom

ent(

kN-m

)

50

Allowable Lateral Load for Fixed Head Condition

Figure 3.9: Pile Capacity vs Soil Shear Strength for 6 mm deflection Figure 3.10: Pile Capacity vs Soil Shear Strength for 12 mm deflection Figure 3.11: Pile Capacity vs Soil Shear Strength for 25 mm deflection

0

400

800

1200

0 20 40 60 80

0.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile



Pile

C

apac

ity (k

N)

0

400

800

1200

1600

0 20 40 60 80

0.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile



Pile

C

apac

ity (k

N)

0

400

800

1200

1600

2000

2400

0 20 40 60 80

0.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile



Pile

C

apac

ity (k

N)

51

Maximum Moment of Pile for Fixed Head Condition




-2400

-1600

-800

0

0 20 40 60 800.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile



Max

imum

Mom

ent(

kN-m

)

-4000

-3200

-2400

-1600

-800

0

0 20 40 60 800.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile



Max

imum

Mom

ent(

kN-m

)

-5600

-4800

-4000

-3200

-2400

-1600

-800

0

0 20 40 60 800.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile



Max

imum

Mom

ent(

kN-m

)

52

Allowable Lateral Load of Pile for Neglecting Top 1.5 m Soil Shear Strength (Free Head Condition)




0

100

200

300

0 20 40 60 80

0.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile



Pile

C

apac

ity (k

N)

0

100

200

300

400

0 20 40 60 80

0.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile



Pile

C

apac

ity (k

N)

Pile

C

apac

ity (k

N)

0100200300400500600700

0 20 40 60 80

0.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile



Pile

C

apac

ity (k

N)

53

Maximum Moment of Pile for Neglecting Top 1.5 m Soil Shear Strength Figure 3.18: Pile Maximum Moment vs Soil Shear Strength for 6 mm deflection Figure 3.19: Pile Maximum Moment vs Soil Shear Strength for 12 mm deflection


0

200

400

600

0 20 40 60 80

0.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile



Pile

Max

imum

Mom

ent(

kN-m

)

0

200

400

600

800

1000

0 20 40 60 80

0.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile



Pile

Max

imum

Mom

ent(

kN-m

)

0200400600800

100012001400160018002000

0 20 40 60 80

0.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile



Pile

Max

imum

Mom

ent(

kN-m

)

54

Allowable Lateral Load of Pile for Neglecting Top 1.5 m Soil Shear Strength (Fixed Head Condition)




0

200

400

600

0 20 40 60 80

0.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile



Pile

C

apac

ity (k

N)

0200400600800

100012001400

0 20 40 60 80

0.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile



Pile

C

apac

ity (k

N)

0200400600800

1000120014001600

0 20 40 60 80

0.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile



Pile

C

apac

ity (k

N)

55

Maximum Moment of Pile for Neglecting Top 1.5 m Soil Shear Strength Figure 3.24: Pile Maximum Moment vs Soil Shear Strength for 25 mm deflection



-1600

-1200

-800

-400

0

0 20 40 60 800.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile



Max

imum

Mom

ent(

kN-m

)

-2800-2400-2000-1600-1200

-800-400

0

0 20 40 60 800.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile



Max

imum

Mom

ent(

kN-m

)

-4800-4400-4000-3600-3200-2800-2400-2000-1600-1200

-800-400

0

0 20 40 60 800.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile



Max

imum

Mom

ent(

kN-m

)

56

Pile Maximum Moment Location from Head of Pile (Free Head Condition)

Figure 3.26a: Pile Maximum Moment Location vs Soil Shear Strength for 6 mm deflection

Figure 3.26b: Pile Maximum Moment Location vs Soil Shear Strength for 12 mm deflection

Figure 3.26c: Pile Maximum Moment Location vs Soil Shear Strength for 25 mm deflection

0

10

20

30

40

50

0 20 40 60 80

0.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile

Location of Maximum Moment vs Soil Shear Strength for 6 mm deflection


Loca

tion

of M

axim

um

Mom

ent(m

)

0

10

20

30

40

50

0 20 40 60 80

0.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile



Loca

tion

of M

axim

um M

omen

t(m)

0

10

20

30

40

50

0 20 40 60 80

0.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile



Loca

tion

of M

axim

um M

omen

t(m)

57

Pile Maximum Moment Location from Head of Pile Neglecting top 1.5 m Soil Shear Strength (Free Head Condition)

Figure 3.26d: Pile Maximum Moment Location vs Soil Shear Strength for 6 mm deflection

Figure 3.26e: Pile Maximum Moment Location vs Soil Shear Strength for 12 mm deflection

Figure 3.26f: Pile Maximum Moment Location vs Soil Shear Strength for 25 mm deflection

0

10

20

30

40

50

0 20 40 60 80

0.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile



Loca

tion

of M

axim

um

Mom

ent(m

)

0

10

20

30

40

50

0 20 40 60 80

0.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile



Loca

tion

of M

axim

um M

omen

t(m)

0

10

20

30

40

50

0 20 40 60 80

0.5 m Dia Pile

0.6 m Dia Pile

0.75 m Dia Pile

1.0 m Dia Pile



Loca

tion

of M

axim

um

Mom

ent(m

)

58

3.7 RESULTS OF PILES EMBEDED IN LAYERED SOIL

Soil layering effect on pile lateral loading has been discussed with two types soil. One

soft soil laying over a stiff soil has been analyzed in the same procedure discussed

previously for homogeneous soil. Top soft soil of shear strength 10 kpa of different

depth of 3 m to 12.1 m, laying over 50 kpa stiff soil.

Table 3.7: Values of spring constant & pult for analysis of different layer of soil.

500 mm dia pile

600 mm dia pile 750 mm dia pile 1000 mm dia

pile

Depth m

cu kpa

spring constant (kN/m)

pult (kN)


pult (kN)


pult (kN)


pult (kN)

0.3 10 61 4 73 9 93 9 122 9 0.6 10 122 9 147 18 184 18 245 18 0.9 10 122 18 147 22 184 22 245 27 1.2 10 122 18 147 22 184 27 245 31 1.5 10 122 18 147 22 184 27 245 31 1.8 10 122 18 147 22 184 27 245 31 2.1 10 122 18 147 22 184 27 245 31 2.4 10 122 18 147 22 184 27 245 31 2.7 10 122 18 147 22 184 27 245 31 3.0 10 122 18 147 22 184 27 245 31 6.1 50 365 45 438 53 547 58 730 89 6.4 50 607 67 728 85 911 89 1216 133 6.7 50 607 80 728 98 911 111 1216 160 7.0 50 607 85 728 98 911 120 1216 160 7.3 50 607 85 728 98 911 120 1216 160 7.6 50 607 85 728 98 911 120 1216 160 7.9 50 607 85 728 98 911 120 1216 160 8.2 50 607 85 728 98 911 120 1216 160 8.5 50 607 85 728 98 911 120 1216 160

23.0 50 607 85 728 98 911 120 1216 160

59

Allowable lateral load, maximum moment and maximum moment location from head of pile for piles embedded in a layered soil having top 3 m soft clay ( cu = 10 kpa ) lying over a stiff clay ( cu = 50 kpa ) for free head condition. Results are shown in table 3.8

Table 3.8: Allowable horizontal load on pile for free head condition 6 mm Deflection. 12 mm Deflection. 25 mm Deflection.

Pile (m) P(kN) Mmax L (m) P(kN) Mmax

L (m) P(kN) Mmax L (m)

0.5 42 142 3 76 289 3 125 583 3 0.6 58 200 3 111 405 3 169 778 3 0.75 93 498 3 182 1023 3 311 2046 3 1.0 182 1183 4 334 2313 4 578 4604 4

Ground Level

Pile

P

Soft Clay

Cu= 10 kpa

20 m

3 m

Stiff Clay

Cu= 50 kpa

60

Allowable lateral load, maximum moment and maximum moment location from head of pile for piles embedded in a layered soil having top 3 m soft clay ( cu = 10 kpa ) lying over a stiff clay ( cu = 50 kpa ) for fixed head condition. Results are shown in table 3.9

Table 3.9: Allowable horizontal load on pile for fixed head condition 6 mm Deflection. 12 mm Deflection. 25 mm Deflection.

Pile (m)

P (kN)

Mmax L (m)

P (kN)

Mmax L (m)

P (kN)

Mmax L (m)

0.5 93 -485 147 4 174 -930 285 4 285 -1739 583 4 0.6 116 -627 129 5 222 -1250 258 5 334 -2282 543 5 0.75 222 -1503 427 6 423 -2985 890 6 712 -5524 1708 6 1.0 445 -3558 947 6 845 -6992 1868 6 1512 -13976 4003 6

Ground Level

Pile

P

Soft Clay

Cu= 10 kpa

20 m

3 m

Stiff Clay

Cu= 50 kpa

61

Allowable lateral load, maximum moment and maximum moment location from head of pile for piles embedded in a layered soil having top 3 m soft clay ( cu = 10 kpa ) lying over a stiff clay ( cu = 50 kpa ) neglecting top 1.5 m soil shear strength for free head condition. Results are shown in table 3.10

Table 3.10: Allowable horizontal load on pile for free head condition neglecting top 1.5 m soil

6 mm Deflection. 12 mm Deflection. 25 mm Deflection. Pile (m) P(kN) Mmax L (m) P(kN) Mmax


0.5 16 107 3 31 218 3 58 440 3 0.6 29 218 3 58 436 3 107 863 4 0.75 45 374 4 89 756 4 156 1441 4 1.0 98 979 5 160 1935 5 334 3719 5

Ground Level

Pile

P

Soft Clay

Cu= 10 kpa

20 m

3 m

Stiff Clay

Cu= 50 kpa

1.5 m

62

Allowable lateral load, maximum moment and maximum moment location from head of pile for piles embedded in a layered soil having top 3 m soft clay ( cu = 10 kpa ) lying over a stiff clay ( cu = 50 kpa ) neglecting top 1.5 m soil shear strength for fixed head condition. Results are shown in table 3.11

Table 3.11: Allowable horizontal load on pile for fixed head condition neglecting top 1.5 m soil

6 mm Deflection. 12 mm Deflection. 25 mm Deflection. Pile (m)

P (kN)

Mmax L (m)

P (kN)

Mmax L (m)

P (kN)

Mmax L (m)

0.5 49 -360 116 5 89 -676 222 5 156 -1250 445 5 0.6 76 -605 200 5 151 -1214 405 5 267 -2295 823 5 0.75 120 -1099 365 6 240 -2228 756 6 445 -4404 1584 6 1.0 267 -2771 867 6 480 -5560 1779 6 934 -10435 3469 6

Ground Level

Pile

P

Soft Clay

Cu= 10 kpa

20 m

3 m

Stiff Clay

Cu= 50 kpa

1.5 m

63

Allowable lateral load, maximum moment and maximum moment location from head of pile for piles embedded in a layered soil having top 6 m soft clay ( cu = 10 kpa ) lying over a stiff clay ( cu = 50 kpa ) for free head condition. Results are shown in table 3.12


6 mm Deflection. 12 mm Deflection. 25 mm Deflection. Pile (m) P (kN) Mmax L (m) P(kN) Mmax


0.5 42 129 3 76 267 3 125 560 3 0.6 58 205 3 111 405 3 169 778 3 0.75 80 343 3 151 689 3 245 1406 3 1.0 142 770 4 258 1521 4 400 2918 4

Ground Level

Pile

P

Soft Clay

Cu= 10 kpa

17 m

6 m

Stiff Clay

Cu= 50 kpa

64

Allowable lateral load, maximum moment and maximum moment location from head of pile for piles embedded in a layered soil having top 6 m soft clay ( cu = 10 kpa ) lying over a stiff clay ( cu = 50 kpa ) for fixed head condition. Results are shown in table 3.13



P (kN)

Mmax L (m)

P (kN)

Mmax L (m)

P (kN)

Mmax L (m)

0.5 80 -383 85 5 151 -778 169 5 222 -1370 356 5 0.6 120 -658 156 6 222 -1259 303 6 320 -2193 623 6 0.75 165 -1112 311 6 311 -2197 623 6 480 -3977 1268 6 1.0 311 -2615 778 7 578 -5129 1539 7 890 -9247 3114 7

Ground Level

Pile

P

Soft Clay

Cu= 10 kpa

17 m

6 m

Stiff Clay

Cu= 50 kpa

65

Allowable lateral load, maximum moment and maximum moment location from head of pile for piles embedded in a layered soil having top 6 m soft clay ( cu = 10 kpa ) lying over a stiff clay ( cu = 50 kpa ) neglecting to 1.5 m soil shear strength for free head condition. Results are shown in table 3.14.


top 1.5 m soil



0.5 16 107 6 31 218 3 56 418 3 0.6 25 178 3 49 356 3 89 676 3 0.75 45 356 4 85 712 4 142 1232 4 1.0 80 712 4 160 1477 4 231 2825 4

Ground Level

Pile

P

Soft Clay

Cu= 10 kpa

17 m

6 m

Stiff Clay

Cu= 50 kpa

1.5 m

66

Allowable lateral load, maximum moment and maximum moment location from head of pile for piles embedded in a layered soil having top 6 m soft clay ( cu = 10 kpa ) lying over a stiff clay ( cu = 50 kpa ) neglecting to 1.5 m soil shear strength for fixed head condition. Results are shown in table 3.15


top 1.5 m soil


P (kN)

Mmax L (m)

P (kN)

Mmax L (m)

P (kN)

Mmax L (m)

0.5 45 -320 80 5 85 -632 165 5 147 -1183 334 5 0.6 67 -534 133 5 133 -1059 262 5 231 -2051 569 5 0.75 107 -974 249 7 205 -1899 498 7 356 -3674 1103 7 1.0 205 -2193 636 8 387 -4270 1272 8 667 -8256 2802 8

Ground Level

Pile

P

Soft Clay

Cu= 10 kpa

17 m

6 m

Stiff Clay

Cu= 50 kpa

1.5 m

67

Allowable lateral load, maximum moment and maximum moment location from head of pile for piles embedded in a layered soil having top 9.1 m soft clay ( cu = 10 kpa ) lying over a stiff clay ( cu = 50 kpa ) for free head condition. Results are shown in table 3.16




0.5 42 133 2 71 245 2 116 494 2 0.6 58 200 3 111 409 3 178 783 3 0.75 80 338 3 151 689 3 245 1401 3 1.0 142 743 4 258 1477 4 400 2882 4

Ground Level

Pile

P

Soft Clay

Cu= 10 kpa

14 m

9 m

Stiff Clay

Cu= 50 kpa

68

Allowable lateral load, maximum moment and maximum moment location from head of pile for piles embedded in a layered soil having top 9.1 m soft clay ( cu = 10 kpa ) lying over a stiff clay ( cu = 50 kpa ) for fixed head condition. Results are shown in table 3.17



P (kN)

Mmax L (m)

P (kN)

Mmax L (m)

P (kN)

Mmax L (m)

0.5 80 -383 80 5 151 -778 165 5 222 -1370 338 5 0.6 116 -627 133 5 222 -1245 267 5 356 -2357 560 5 0.75 156 -1076 231 6 303 -2073 445 6 445 -3612 890 6 1.0 289 -2340 534 8 534 -4599 1068 8 756 -7829 2180 8

Ground Level

Pile

P

Soft Clay

Cu= 10 kpa

14 m

9 m

Stiff Clay

Cu= 50 kpa

69

Allowable lateral load, maximum moment and maximum moment location from head of pile for piles embedded in a layered soil having top 9.1 m soft clay ( cu = 10 kpa ) lying over a stiff clay ( cu = 50 kpa ) neglecting top 1.5 m soil shear strength for free head condition. Results are shown in table 3.18


top 1.5 m soil



0.5 16 107 3 31 214 3 53 396 3 0.6 27 191 3 53 387 3 98 756 3 0.75 40 320 4 80 636 4 142 1232 4 1.0 80 712 4 156 1423 4 267 2691 4

Ground Level

Pile

P

Soft Clay

Cu= 10 kpa

14 m

9 m

Stiff Clay

Cu= 50 kpa

1.5 m

70

Allowable lateral load, maximum moment and maximum moment location from head of pile for piles embedded in a layered soil having top 9.1 m soft clay ( cu = 10 kpa ) lying over a stiff clay ( cu = 50 kpa ) neglecting top 1.5 m soil shear strength for fixed head condition. Results are shown in table 3.19


top 1.5 m soil


P (kN)

Mmax L (m)

P (kN)

Mmax L (m)

P (kN)

Mmax L (m)

0.5 45 -325 80 5 80 -601 156 5 147 -1188 329 5 0.6 71 -565 133 5 133 -1059 258 5 245 -2113 565 5 0.75 107 -961 227 6 200 -1837 445 6 334 -3381 890 6 1.0 200 -2104 489 8 378 -4114 979 8 578 -6983 1837 8

Ground Level

Pile

P

Soft Clay

Cu= 10 kpa

14 m

9 m

Stiff Clay

Cu= 50 kpa

1.5 m

71



6 mm Deflection. 12 mm Deflection. 25 mm Deflection. Pile (m) P(kN) Mmax

L (m) P(kN) Mmax


0.5 40 125 2 71 245 2 116 489 2 0.6 58 200 3 111 405 3 178 783 3 0.75 80 338 3 151 689 3 231 1272 3 1.0 142 743 4 258 1477 4 391 2771 4

Ground Level

Pile

P

Soft Clay

Cu= 10 kpa

11 m

12 m

Stiff Clay

Cu= 50 kpa

72




P (kN)

Mmax L (m)

P (kN)

Mmax L (m)

P (kN)

Mmax L (m)

0.5 80 -383 80 5 147 -752 156 5 218 -1334 316 5 0.6 111 -627 133 5 222 -1245 262 5 356 -2366 556 5 0.75 160 -1045 222 6 298 -2046 445 6 445 -3607 867 6 1.0 280 -2224 476 8 512 -4319 925 8 756 -7864 1984 8

Ground Level

Pile

P

Soft Clay

Cu= 10 kpa

11 m

12 m

Stiff Clay

Cu= 50 kpa

73

Allowable lateral load, maximum moment and maximum moment location from head of pile for piles embedded in a layered soil having top 12.1 m soft clay ( cu = 10 kpa ) lying over a stiff clay ( cu = 50 kpa ) neglecting top 1.5 m soil shear strength for free head condition. Results are shown in table 3.22


top 1.5 m soil

6 mm Deflection. 12 mm Deflection. 25 mm Deflection. Pile (m) P(kN) Mmax

L (m) P(kN) Mmax


0.5 16 107 3 31 214 3 53 396 3 0.6 25 178 3 49 356 3 89 672 3 0.75 40 316 4 76 596 4 142 1232 4 1.0 80 712 4 151 1379 4 267 2691 4

Ground Level

Pile

P

Soft Clay

Cu= 10 kpa

11 m

12 m

Stiff Clay

Cu= 50 kpa

1.5 m

74

Allowable lateral load, maximum moment and maximum moment location from head of pile for piles embedded in a layered soil having top 12.1 m soft clay ( cu = 10 kpa ) lying over a stiff clay ( cu = 50 kpa ) neglecting top 1.5 m soil shear strength for fixed head condition. Results are shown in table 3.23

Table 3.23: Allowable horizontal load on pile for fixed head condition neglecting top 1.5 m soil


P (kN)

Mmax L (m)

P (kN)

Mmax L (m)

P (kN)

Mmax L (m)

0.5 45 -325 80 5 85 -636 160 5 142 -1143 311 5 0.6 67 -534 125 5 133 -1068 254 5 231 -1975 512 5 0.75 111 -1005 236 6 200 -1842 436 6 334 -3381 890 6 1.0 200 -2100 480 8 378 -4097 961 8 601 -7384 1957 8

Ground Level

Pile

P

Soft Clay

Cu= 10 kpa

11 m

12 m

Stiff Clay

Cu= 50 kpa

1.5 m

75




L (m) P(kN) Mmax

L (m)

0.5 53 200 3 98 400 3 178 801 3 0.6 80 329 3 156 654 3 267 1290 3 0.75 125 578 3 222 1201 3 423 2357 3 1.0 222 1245 4 423 2446 4 756 4893 4

Ground Level

Pile

P

Soft ClayCu= 10 kpa

21 m

1.5 m

Stiff Clay

Cu= 70 kpa

76




P (kN)

Mmax L (m)

P (kN)

Mmax L (m)

P (kN)

Mmax L (m)

0.5 133 -632 156 4 245 -1201 298 4 423 -2224 592 4 0.6 200 -1050 245 5 378 -2002 489 5 667 -4003 1023 5 0.75 311 -1868 427 6 578 -3558 823 6 1023 -6983 1708 6 1.0 534 -3852 845 6 1023 -7562 1690 6 1868 -13344 3514 6

Ground Level

Pile

P

Soft ClayCu= 10 kpa

21 m

1.5 m

Stiff Clay

Cu= 70 kpa

77

3.8 GRAPHICAL FORM OF PILES IN LAYERED SOIL

Figure 3.27: Pile Capacity vs Depth of soft soil for 6 mm deflection



0

100

200

300

400

0 2 4 6 8 10 12 14

0.5 m Dia Pile0.6 m Dia Pile0.75 m Dia Pile1.0 m Dia Pile

Pile Capacity vs Thickness of soft soil for 6 mm deflection

Pile

C

apac

ity (K

N)

Thickness of Soft Soil (m)

soft soilcu = 10 kpa

stiff soilcu = 50 kpa

0

100

200

300

400

500

600

700

0 2 4 6 8 10 12 14



Pile

C

apac

ity (K

N)




0100200300400500600700800900

10001100

0 2 4 6 8 10 12 14



Pile

C

apac

ity (K

N)




78

Maximum moment of pile embedded in layered soil for free head condition

Figure 3.30: Pile Moment vs Depth of soft soil for 6 mm deflection Figure 3.31: Pile Moment vs Depth of soft soil for 12 mm deflection

Figure 3.32: Pile Moment vs Depth of soft soil for 25 mm deflection

0

200

400

600

0 2 4 6 8 10 12 14


Pile Maximum Moment vs Thickness of soft soil for 6 mm deflection

Pile

Max

imum

Mom

ent (

KN

-m)




0

200

400

600

800

1000

0 2 4 6 8 10 12 14



Pile

Max

imum

Mom

ent (

KN

-m)




0200400600800

100012001400160018002000

0 2 4 6 8 10 12 14



Pile

Max

imum

Mom

ent (

KN

-m)




79

Allowable lateral load of pile embedded in layered soil for fixed head condition




0

250

500

750

1000

0 2 4 6 8 10 12 14



Pile

C

apac

ity (K

N)




0

250

500

750

1000

1250

1500

0 2 4 6 8 10 12 14



Pile

C

apac

ity (K

N)




0250500750

1000125015001750200022502500

0 2 4 6 8 10 12 14



Pile

C

apac

ity (K

N)




80

Maximum moment of pile embedded in layered soil for fixed head condition




-2000

-1500

-1000

-500

0

0 2 4 6 8 10 12 14



Pile

Max

imum

Mom

ent (

KN

-m)




-3000

-2500

-2000

-1500

-1000

-500

0

0 2 4 6 8 10 12 14



Pile

Max

imum

Mom

ent (

KN

-m)




-5500-5000-4500-4000-3500-3000-2500-2000-1500-1000

-5000

0 2 4 6 8 10 12 14



Pile

Max

imum

Mom

ent (

KN

-m)




81

Allowable lateral load of pile embedded in layered soil for free head condition Figure 3.38a: Pile Capacity vs Depth of soft soil for 6 mm deflection

Figure 3.38b: Pile Capacity vs Depth of soft soil for 12 mm deflection Figure 3.38c: Pile Capacity vs Depth of soft soil for 25 mm deflection

0

100

200

300

400

500

0 2 4 6 8 10 12 14



Pile

C

apac

ity (K

N)




0100200300400500600700800

0 2 4 6 8 10 12 14



Pile

C

apac

ity (K

N)




0100200300400500600700800900

100011001200

0 2 4 6 8 10 12 14



Pile

C

apac

ity (K

N)




82

Maximum moment of pile embedded in layered soil for free head condition Figure 3.38d: Pile Moment vs Depth of soft soil for 6 mm deflection Figure 3.38e: Pile Moment vs Depth of soft soil for 12 mm deflection Figure 3.38f: Pile Moment vs Depth of soft soil for 25 mm deflection

-750

-500

-250

0

0 2 4 6 8 10 12 14



Pile

Max

imum

Mom

ent (

KN

-m)




-1250

-1000

-750

-500

-250

0

0 2 4 6 8 10 12 14



Pile

Max

imum

Mom

ent (

KN

-m)




-2250-2000-1750-1500-1250-1000

-750-500-250

0

0 2 4 6 8 10 12 14



Pile

Max

imum

Mom

ent (

KN

-m)




83

Allowable lateral load of pile embedded in layered soil for fixed head condition

Figure 3.38g: Pile Capacity vs Depth of soft soil for 6 mm deflection

Figure 3.38h: Pile Capacity vs Depth of soft soil for 12 mm deflection

Figure 3.38i: Pile Capacity vs Depth of soft soil for 25 mm deflection

0

250

500

750

1000

0 2 4 6 8 10 12 14



Pile

C

apac

ity (K

N)




0

250

500

750

1000

1250

1500

1750

0 2 4 6 8 10 12 14



Pile

C

apac

ity (K

N)




0250500750

1000125015001750200022502500

0 2 4 6 8 10 12 14



Pile

C

apac

ity (K

N)




84

Maximum moment of pile embedded in layered soil for fixed head condition

Figure 3.38j: Pile Moment vs Depth of soft soil for 6 mm deflection

Figure 3.38k: Pile Moment vs Depth of soft soil for 12 mm deflection

Figure 3.38l: Pile Moment vs Depth of soft soil for 25 mm deflection

-2000

-1500

-1000

-500

0

0 2 4 6 8 10 12 14



Pile

Max

imum

Mom

ent (

KN

-m)




-3500

-3000

-2500

-2000

-1500

-1000

-500

0

0 2 4 6 8 10 12 14



Pile

Max

imum

Mom

ent (

KN

-m)




-6000-5500-5000-4500-4000-3500-3000-2500-2000-1500-1000

-5000

0 2 4 6 8 10 12 14



Pile

Max

imum

Mom

ent (

KN

-m)




85

Allowable lateral load of pile embedded in layered soil neglecting top 1.5 m soil shear strength for free head condition




0

50

100

150

0 2 4 6 8 10 12 14


Pile Capacity vs Thickness of soft soil for 6 mm deflectionPi

le

Cap

acity

(KN

)




0

50

100

150

200

0 2 4 6 8 10 12 14



Pile

C

apac

ity (K

N)




0

50

100

150

200

250

300

350

0 2 4 6 8 10 12 14



Pile

C

apac

ity (K

N)




86

Maximum moment of pile embedded in layered soil neglecting top 1.5 m soil shear strength for free head condition




0

100

200

300

400

0 2 4 6 8 10 12 14



Pile

Max

imum

Mom

ent (

KN

-m)




0

100

200

300

400

500

600

700

0 2 4 6 8 10 12 14



Pile

Max

imum

Mom

ent (

KN

-m)




0100200300400500600700800900

1000110012001300

0 2 4 6 8 10 12 14



Pile

Max

imum

Mom

ent (

KN

-m)




87

Allowable lateral load of pile embedded in layered soil neglecting top 1.5 m soil shear strength for fixed head condition

Figure 3.45: Pile Capacity vs Depth of soft soil for 6 mm deflection Figure 3.46: Pile Capacity vs Depth of soft soil for 12 mm deflection Figure 3.47: Pile Capacity vs Depth of soft soil for 25 mm deflection

0

100

200

300

0 2 4 6 8 10 12 14



Pile

C

apac

ity (K

N)




0

100

200

300

400

500

600

0 2 4 6 8 10 12 14



Pile

C

apac

ity (K

N)




0100200300400500600700800900

1000

0 2 4 6 8 10 12 14



Pile

C

apac

ity (K

N)




88

Maximum moment of pile embedded in layered soil neglecting top 1.5 m soil shear strength for fixed head condition




-1000

-750

-500

-250

0

0 2 4 6 8 10 12 14



Pile

Max

imum

Mom

ent (

KN

-m)




-2000-1750-1500-1250-1000

-750-500-250

0

0 2 4 6 8 10 12 14



Pile

Max

imum

Mom

ent (

KN

-m)




-3750-3500-3250-3000-2750-2500-2250-2000-1750-1500-1250-1000

-750-500-250

0

0 2 4 6 8 10 12 14



Pile

Max

imum

Mom

ent (

KN

-m)




89

3.9 LATERAL CAPACITY OF PILES USING BROMS METHOD

Broms method provides solution for both short and long pile installed in cohesive and

cohesionless soil respectively. Brom considered pile fixed or free to rotate at the head.

Lateral deflection at the working load has been calculated using concept of subgrade

reaction.

For cohesive soil,

β = � ��

�

EI = Stiffness of pile section

k = Coefficient of Soil horizontal subgrade reaction

d = Diameter of pile.

When, β L ≤ 2.5 Pile is considered as short rigid pile

β L ≥ 2.5 Pile is considered as long flexible pile

Homogeneous soil of undrain shear strength cu = 10 kpa, has used by the help of

charts suggested by Brom of figures 2.14 given in chapter 2.

Concrete pile having diameter of 500 mm and length 23 m. Pile length is checked

whether it is short rigid pile or long flexible pile.

β = � ��

� = � ��.� ∗�.�

�∗�� × ��∗�.�� × ��

= 0.08 m

β L = 1.95 ≥ 2.5, so the pile is long flexible pile.

From figure 2.17

��

�� = 10 => pt =

��

�� =

�.��/��∗��.�∗��∗��

�� = 36 KN

So for 12 mm and 25 mm deflection, pt = 71 KN and 142 KN.

90

CHAPTER 4

DISCUSSION

4.1 General

Piles embedded in homogeneous soil of different soil shear strength having different

pile diameter and head deflection are analyzed. Piles embedded in layered soil like

soft soil lying over stiff soil are analyzed.

4.2 Piles embedded in homogeneous soil

In this article the analysis & results of piles embedded in homogeneous soil are

discussed. All the piles having total length of 23 m (long pile). Diameter of the piles

considered 500 mm, 600 mm, 750 mm and 1 m. The soils shear strength considered

10 kpa, 25 kpa, 50 kpa and 70 kpa. The cohesive soil considered very soft having

shear strength of 10 kpa and 25 kpa and stiff soil of shear strength 50 kpa and 70 kpa.

The discussion is done on the basis of analysis & results which are presented in

chapter 3.

The analysis has been done using the p-y methods of soil and the Finite Element

Software SAP. The surrounding soil is defined series of spring which gives lateral

support to the pile. Springs are defined 1ft centre to centre to the pile and lateral load

applied on the head of pile. The spring values evaluated from Robinson’s (1978)

modulus of subgrade reaction equation.

4.2.1 Free headed piles

Free headed piles are free to rotate and may translate in the direction of application of

load at their head. A reinforced concrete pile of 1 m diameter embedded in soft

(cu = 10 kpa) cohesive soil with 267 kN horizontal load is shown in figure 4.1. In

figure 4.2, 4.3 and 4. 4 deflected shapes of pile, soil reactions and bending moment

diagrams are shown respectively.

Figure 4.2 shows pile deflection diagram with respect to pile length. It is seen from

the figure that pile maximum deflection occurs at the pile head. From figure 4.2 it can

observed that maximum deflection occurs at head of pile in the direction of

91

application of load. At some depth below pile deflection is opposite to the application

of load occurs, this results are well agreed with the diagram proposed by Broms.

Figure 4.3 soil reaction diagrams with respect to pile length are shown. It is seen from

the figure that soil reaction reaches maximum value at the below of pile head. At

depth about 1.5 m below pile head (ground level) the soil reaction is maximum. This

is because in this area soil passive resistance is fully mobilized due to large deflection.

Below 1.5 m the passive resistance of soil is not fully mobilized. It is partially

mobilized due to small deflection of the pile.

Figure 4.4 pile bending moment diagram with respect to pile length is shown. It is

seen from the figure that maximum moment occurs at some depth below from pile

head which is around 4.5 m from pile head. At greater depth the moment diagram is

slightly negative.

92

Typical Diagrams for 1 m pile embedded in homogeneous soil of shear strength 10 kpa of depth 23 m. Free headed piles are shown.

H=267 kN

23 m

c =10 kpa

Pile Diameter = 1 mR.C.C Pile

23 m

Soil

Figure: 4.1: Pile Embedded in Homogeneous soil Figure: 4. 2: Deflected shape of pile

Figure: 4. 4: Pile Bending Moment Diagram

Figure: 4.3: Soil Reaction Diagram

Deflection

Dep

th o

f pile

(ft)

Dep

th o

f pile

Dep

th o

f pile

Soil Reaction Bending Moment

93

Relationship between pile capacity and soil shear strength

In figure 3.3 to 3.5 pile lateral capacities with soil shear strength are shown for

different diameter and pile head deflections. It can be observed from figure 3.3, 3.4

and 3.5 for a given head deflection the capacity of lateral loaded pile increases with

the increase of soil shear strength. But the increase is not linear. The rate of increase

of lateral capacity decrease with the increase of shear strength of the soil. In table 4.1

pile lateral load capacity for 1 m diameter pile embedded in different soil shear

strength of different head deflections are shown.

Table 4.1: Lateral capacity of 1 m diameter long pile embedded in soils of different

shear strength with different head deflections.

cu kpa

H (Lateral load) kN

For 6 mm deflection

H (Lateral load) kN

For 12 mm deflection

H (Lateral load) kN


10 133 249 356

30 303 489 801

50 387 601 979

From table 4.1 it can be observed that the lateral capacity of pile increases with the

increases of allowable pile head deflection. If the allowable deflection of pile head

increases 4 times (6 mm to 25 mm) the lateral capacity of pile increases 2.5 times

(387 kN to 979 kN) for pile embedded in a soil having shear strength cu = 50 kpa.

However the increase is not linear. This is because for smaller deflections soil passive

resistance does not reach the ultimate capacity so it gives larger resistance to the pile

resulting larger lateral capacity of the pile. For large deflections large portion of soil

passive resistance reaches the ultimate value which gives comparatively less

resistance to the pile resulting less lateral capacity of the pile.

It is also seen that as the soil shear strength increases 5 times (9.5 kpa to 50 kpa) the

pile lateral capacity increases 3 times (133 kN to 387 kN).

94

Relationship of pile lateral capacity with its diameter

It can be observed from figure 4.5, 4.6, 4.7 and 4.8 for a given head deflection the

capacity of lateral load of pile increases with the increase of pile diameter. But the

increase is not linear. In table 4.2 pile lateral load capacity for 50 kpa shear strength of

different pile diameter with different head deflections are shown.

Table 4.2: Lateral capacity of different diameter of long pile embedded in soils having

shear strength 10 kpa with different head deflections.

Diameter

of pile (m)

H (Lateral load) kN

For 6 mm deflection

H (Lateral load) kN


H (Lateral load) kN

For 25 mm

deflection

0.5 40 71 116

0.6 62 111 169

0.75 80 147 231

1.0 142 249 378

From Table 4.2 it is observed that as the diameter of pile increases the capacity of pile

lateral load is also increases. Considering 6 mm deflection, diameter (Cross sectional

area) increase 4 times (0.5 m to 1 m) corresponding pile lateral capacity increases

around 3.5 times (40 kN to 142 kN).

Relationship between pile head deflection and diameter with maximum moment

and soil shear strength

Pile lateral capacity and maximum moment vary with the increase of soil shear

strength, pile diameter as well as pile head deflection. From analysis of chapter 3 the

results are shown in figures 3.3 to 3.8 for free headed piles are discussed here.

In table 4.3 pile lateral load capacity and maximum moment for 1 m diameter with its

soil shear strength of different head deflections are shown.

95

Allowable pile lateral capacity for a given pile head deflection for free headed piles

embedded in a soil of shear strength cu = 10 kpa

Figure 4.5: Pile lateral capacities with Pile head Deflection for 10 kpa soil shear strength Allowable pile lateral capacity for a given pile head deflection for free headed piles embedded in a soil of shear strength cu = 25 kpa Figure 4.6: Pile lateral capacities with Pile head Deflection for 25 kpa soil shear strength

0

100

200

300

400

0 5 10 15 20 25 30


Pile Capacity vs Pile head deflectionPi

le

Cap

acity

(KN

)

Pile head deflection (mm)

0

100

200

300

400

500

600

700

800

0 2 4 6 8 10


Pile Capacity vs Pile head deflection

Pile

C

apac

ity (K

N)


96

Allowable pile lateral capacity for a given pile head deflection for free headed piles embedded in a soil of shear strength cu = 50 kpa

Figure 4.7: Pile lateral capacities with Pile head Deflection for 50 kpa soil shear strength

Allowable pile lateral capacity for a given pile head deflection for free headed piles embedded in a soil of shear strength cu = 75 kpa

Figure 4.8: Pile lateral capacities with Pile head Deflection for 75 kpa soil shear strength

0100200300400500600700800900

10001100

0 2 4 6 8 10



le

Cap

acity

(KN

)


0100200300400500600700800900

10001100

0 2 4 6 8 10



Pile

C

apac

ity (K

N)


97

Table 4.3: Lateral capacity and maximum moment of long pile embedded in soils of

different shear Strength with different head deflections for 1.0 m diameter pile.

cu (kpa) 6 mm deflection 12 mm deflection 25 mm deflection

H(kN) M(kN/m) H(kN) M(kN/m) H(kN) M(kN/m)

10 142 227 249 449 378 836

30 303 381 489 700 801 1387

50 378 476 601 925 956 1768

From table 4.3 it is observed that pile moment increases as the soil strength increase.

It is seen that as the soil shear strength increases 5 times (9.5 kpa to 50 kpa) the

corresponding pile lateral capacity increases 2.65 times (142 kN to 378 kN) and

moment increases 2.0 times (224 kN/m to 476 kN/m).

As pile head deflection increases 4.0 times (6 mm to 25 mm) corresponding pile

lateral capacity increases 2.65 times where as the moment increases 3.68 times (227

kN/m to 836 kN/m). In table 4.4 pile lateral load capacity and moment for 10 kpa

shear strength of different pile diameter with different head deflections are shown.

Table 4.4: Lateral capacity and maximum moment of different diameter of long pile

embedded in soils of shear Strength 10 kpa with different head deflections.

Pile diameter

(m)

6 mm deflection 12 mm deflection 25 mm deflection


0.5 40 38 71 76 116 151

0.6 62 67 111 124 169 238

0.75 80 103 147 214 231 396

1.0 142 227 249 449 378 836


lateral load also increases. Considering 6 mm deflection, diameter (cross sectional

area) increase 4 times (0.5 m to 1 m) corresponding pile lateral capacity increases

around 3.5 times (40 kN to 142 kN) where as the moment increases 6 times (38 kN/m

to 227 kN/m).

98

4.2.2 Fixed Headed piles

Fixed headed piles are free to translation but rotation is restrained at their head.

In figure 4.9 a pile of 1 m diameter embedded in homogeneous soil of shear strength

cu = 10 kpa is shown for analysis of lateral loading. In figure 4.10, 4.11 and 4.12 soil

reactions, deflected shape of pile and corresponding bending moment diagrams are

shown respectively.

Figure 4.10 soil reaction diagrams with respect to pile length are shown. It is seen

from the figure that soil reaction reaches maximum value at the below of pile head,

this is because the head soil passive resistance is quite lower than the soil of greater

depth. Figure 4.11 pile head deflection diagram with respect to pile length is shown. It

is seen from the figure that pile maximum deflection occurs at the head.

Figure 4.12 pile bending moment diagram with respect to pile length is shown. It is

seen from the figure that maximum negative moment occurs at the head of the pile

and maximum positive moment occurs at some depth below from pile head which is

around 8 m below from pile head.

Typical Diagrams of fixed headed pile of 1 m diameter embedded in homogeneous

soil of shear strength 10 kpa and depth 23 m are shown here.

99

H = 556 kN

23 m

23 m

c =10 kpa

Pile Diameter = 1 mR.C.C Pile

Soil

Figure: 4.9: Pile Embedded in Homogeneous soil Figure: 4.10: Deflected Shape of Pile

Figure: 4.12: Pile Bending Moment Diagram Figure: 4.11: Soil Reaction Diagram

Deflection

Dep

th o

f pile

D

epth

of p

ile

Dep

th o

f pile

Soil Reaction Bending Moment

100

Results of pile which are rotationally restrained at their head are discussed here with

the help of figures 3.9, 3.10 and 3.11. Pile lateral capacity with soil undrained shear

strength for different head deflections of 6 mm, 12 mm and 25 mm are shown in the

figures. In all cases the pile length is 23 m and diameter of piles are 0.5 m, 0.6 m,

0.75 m and 1 m respectively. The results are plotted to evaluate the pile lateral

capacity during various soil shear strength of different diameter and different head

deflections. As the head deflection increases the pile lateral capacity increases. For

smaller diameter of piles the increase rate is linear up to 25 kpa of soil strength and

after that it becomes constant. For larger diameter of piles like 1 m the increases rate

is linear up to 50 kpa of soil shear strength after that it become constant. The

relationships are also shown in graphical form in figure 4.13 to 4.16.

Relationship between pile capacity with soil shear strength

For given diameter of pile for a given head deflection the lateral load capacity

increases as the soil shear strength increase. But the increase is not linear. The rates of

increase of horizontal capacity decrease with the increase of shear strength of the soil.



cu kpa

H (Lateral load) kN

For 6 mm deflection

H (Lateral load) kN


H (Lateral load) kN

For 25 mm

deflection

10 289 512 689

30 623 1068 1744

50 756 1299 2002

From table 4.5 it can be observed that the lateral capacity of pile increases with the

increases of allowable pile head deflection. However the increase is not linear. It is

also seen that as the soil shear strength increases 5 times the corresponding pile lateral

capacity increases 2.6 times.

If the allowable deflection of pile head increases the lateral capacity of pile also

increases for the given soil shear strength. The lateral capacity of a given pile

decreases with the decrease of soil shear strength.

101


It can be observed from figure 3.9 to 3.10 that for a given head deflection the capacity

of lateral load of pile increases with the increase of pile diameter. But the increase is

not linear. The results are shown in table 4.6.

Table 4.6: Lateral capacity of different diameter of long pile embedded in soils of


Diameter

of pile (m)

H (Lateral load) kN

For 6 mm deflection

H (Lateral load) kN

For 12 mm

deflection

H (Lateral load) kN

For 25 mm

deflection

0.5 67 156 200

0.6 111 214 289

0.75 156 267 423

1.0 280 512 712


lateral load also increases. For 500 mm diameter pile of 6 mm deflection capacity is

67 kN whereas for 1 m diameter pile capacity is 180 kN. This is around 4.2 times

greater. It is also seen that as the pile head deflection increases the pile lateral load

capacity also increases.



Pile lateral capacity and maximum moment vary with the increase of soil shear

strength, pile diameter as well as pile head deflection. From analysis of chapter 3 the

results are shown in figures 3.9 to 3.14. Fixed headed piles are discussed here. The

results are shown in table 4.7 and 4.8.

102



cu

(kpa)



10 289 163 -715 512 313 -1360 689 571 -2244

30 623 231 -1115 1068 453 -2040 1744 884 -4080

50 756 286 -1387 1299 592 -2656 2002 1178 -4736


pile embedded in soils of shear strength 10 kpa with different head deflections.

From table 4.7 and 4.7 it is observed that pile moment increases as the soil strength,

pile head deflection and pile diameter increase. The increase is not linear. But the rate

of increase decreases as the soil strength increases.

It is also seen that as the soil shear strength increases 5 times pile lateral load capacity

increases 3 times, moment increases 2 times. As the pile head deflection increases the

pile lateral capacity increases 2.5 times, moment increases 3.5 times.

On the other hand as the pile diameter increases, the pile lateral load capacity

increases 3.5 times whereas its moment increases 6 times. It also seen that as the pile

head deflection increases pile lateral load capacity increases 2.5 times, moment

increases 3.5 times.

Pile

diameter

(m)



0.5 67 53 -249 156 106 -456 200 204 -779

0.6 111 84 -399 214 169 -748 289 326 -1295

0.75 156 147 -691 267 291 -1274 423 578 -2258

1.0 280 286 -1387 512 592 -2656 712 1178 -4736

103

Allowable pile lateral capacity for a given pile head deflection for fixed headed piles embedded in a soil of shear strength cu = 10 kpa

Figure 4.13: Pile lateral capacities with pile head deflection for 10 kpa soil shear strength


Figure 4.14 Pile lateral capacities with pile head deflection for 20 kpa soil shear strength

0

200

400

600

800

0 5 10 15 20 25 30



le

Cap

acity

(KN

)


0200400600800

10001200140016001800

0 2 4 6 8 10



Pile

C

apac

ity (K

N)


104





0200400600800

1000120014001600180020002200

0 2 4 6 8 10



Pile

C

apac

ity (K

N)


0200400600800

10001200140016001800200022002400

0 2 4 6 8 10



Pile

C

apac

ity (K

N)


105

4.2.3 Comparisons between free headed and fixed headed piles

From the results of pile analysis of homogeneous soil it is seen from the figures of 3.1

to 3.14 as the soil shear strength increases the lateral pile capacity also increases both

in the cases of free and fixed headed conditions but the increase is more in fixed head

condition than free headed. The capacity also increases as the pile diameter increases

as well as the deflection increases.

Relationship between free headed and fixed headed pile capacity with respect to

its soil shear strength and pile head deflections

Results for free headed and fixed headed piles embedded in homogeneous soil which

are shown in chapter 3 are discussed here. Free headed piles are free to rotate whereas

fixed headed piles are restrained at their head for rotate. Fixed headed piles are fixed

at their head to restrain the rotations.

In table 4.9 pile lateral load capacity of 1 m diameter pile with shear strength of

different head deflections are shown.

Table 4.9: Relationship between lateral capacities of free headed and fixed headed

piles of diameter 1 m.

cu

kpa 6 mm deflection 12 mm deflection 25 mm deflection

H (kN) H (kN) H (kN)

Free Fixed Free Fixed Free Fixed

10 133 289 249 512 356 689

30 303 623 489 1068 801 1566

50 387 756 601 1299 979 2002

From table 4.9 it is seen that the pile lateral capacity is greater in fixed headed piles

from free headed piles. For 6 mm deflection of 50 kpa soil shear strength pile capacity

is 387 kN for free headed condition whereas it is 756 kN for fixed headed condition

which is almost 2 times.

As the pile head deflection increases 6 mm to 25 mm for 50 kpa soil shear strength

for free headed piles the increase is 387 kN to 979 kN and for fixed headed condition

it is 756 kN to 2001 kN. The increase is around 2.5 times. So for free headed and

106

fixed headed piles, as the pile head deflection increases the pile lateral capacity

increase is almost same.

Table 4.10: Relationship between lateral capacities of free headed and fixed headed

piles of different diameter.

Pile diameter

(m)


H (kN) H (kN) H (kN)

Free Fixed Free Fixed Free Fixed

0.5 40 67 76 156 111 200

0.6 58 111 107 214 178 289

0.75 80 156 142 267 222 423

1.0 147 280 254 512 356 712

From table 4.10 it is seen that for 500 mm pile of 6 mm deflection pile lateral capacity

is 40 kN for free head condition whereas for fixed headed piles it is 67 kN on the

other hand for 1 m pile it is 147 kN and 280 kN respectively. So the increase is

around 2.0 times. For the increase of pile head deflection from 6 mm to 25 mm pile

lateral load increases 180 kN to 712 kN for fixed headed condition whereas it is

147 kN to 356 kN for free headed condition respectively. So the increase is almost 2.5

times for both the cases.

Relationship of free headed and fixed headed piles with respect to maximum

moment

Results for free headed and fixed headed piles embedded in homogeneous soil which

are shown in chapter 3 are discussed here in respect of their moment. Free headed

piles have only positive moments whereas fixed headed piles have positive as well as

negative moment at their head.

107

Table 4.11: Relationship between maximum moments of free headed and fixed


cu

(kpa)

Deflection 6 mm Deflection 12 mm

Free Headed Fixed Headed Free Headed Fixed Headed

H

(kN)

+M

(kN/m)

H

(kN)

+M

(kN/m)

-M

(kN/m)

H

(kN)

+M

(kN/m)

H

(kN)

+M

(kN/m)

-M

(kN/m)

10 133 224 289 163 -715 249 449 512 313 -1360

30 303 381 623 231 -1115 489 700 1068 453 -2040

50 387 476 756 286 -1387 601 925 1299 592 -2656

From table 4.11 it is seen that pile maximum moment for free headed condition the

negative moment is higher with same head deflection and the positive moment are

less than free headed piles. The maximum negative moment for fixed headed

condition it occurs at the connection point of pile and pile cap where as for free

headed pile the maximum positive moment occurs below from application of load.

For 6 mm deflection of 50 kpa soil shear strength for free headed condition its

moment is 476 kN/m whereas for fixed headed condition it is 286 and -1387 kN/m.

The moment is almost 3.0 times higher in the case of fixed headed condition because

its lateral capacity is also very high which are 387 kN and 756 kN respectively. It is

also noted that pile lateral capacity increases 2.0 times whereas moment increases

around 3.0 times.

4.2.4 Free headed piles neglecting head 1.5 m soil shear strength

In some cases head 1.5 m of soil neglected for the analysis of pile lateral load due to

the scouring effect, excavation for pile cap construction, tension cracks developed in

clay soil or new construction adjacent to the structure. Broms method for lateral

loaded pile analysis is done neglecting head 1.5 m soil shear strength. In these

connection head 5 feet neglected analysis and its results are discussed here.

Results of piles having diameter 500 mm, 600 mm, 750 mm and 1 m embedded in

uniform soil with soil shear strength of 10 kpa, 25 kpa. 50 kpa and 70 kpa for head

deflection 6 mm, 12 mm and 25 mm which are shown in figure 3.15 to 3.26

respectively. In all conditions pile length was 23 m long pile.

108

Relationship between pile capacity and soil shear strength

It can be observed from figure 3.15, 3.16 and 3.17 for 1 m diameter of pile for a given

head deflection (6 mm) the capacity of lateral load of pile increases with the soil

strength. But the increase is not linear. The rates of increase of horizontal capacity

decrease with the increase of shear strength of the soil.



cu kpa

H (Lateral load) kN

For 6 mm deflection

H (Lateral load) kN

For 12 mm

deflection

H (Lateral load) kN


10 76 156 267

30 142 254 423

50 178 311 512

From table 4.12 it can be also observed that the lateral capacity of pile increases with

the increases of allowable pile head deflection. However the increase is not linear. It

is also seen that as the soil shear strength increases 5 times the corresponding pile

lateral capacity increases 2.35 times.

As deflection increases 4 times (6 mm to 25 mm) corresponding lateral capacity for

10 kpa soil shear strength increases 3.5 times (76 kN to 267 kN).

Comparing these results with the results which are shown in table 4.1 of considering

full depth soil shear strength the values are 76 kN and 133 kN for 6 mm deflection of

10 kpa soil shear strength and 178 kN and 387 kN for 50 kpa soil shear strength. It is

seen that if head 1.5 m soil shear strength is neglected then the pile capacity becomes

half of full depth soil shear strength.


It can be observed from figure 3.15, 3.16 and 3.17 for a given head deflection the

capacity of lateral load of pile increases with the increase of pile diameter. But the

increase is not linear. The results are shown in table 4.13.

109



Diameter of pile (m)

H (Lateral load) kN For 6 mm deflection



0.5 13 31 53

0.6 25 49 89

0.75 40 76 133

1.0 76 156 267

From Table 4.13 it is observed that as the diameter of pile increases the capacity of

pile lateral load also increases. For 500 mm diameter pile of 6 mm deflection capacity

is 13 kN whereas for 1 m diameter pile capacity is 76 kN. This is around 5.66 times

greater. It is also seen that as the pile head deflection increases the pile lateral load

capacity also increases.


full depth soil shear strength the values are 40 kN and 13 kN for 6 mm deflection for

500 mm diameter pile and 142 kN and 76 kN for for 1 m diameter pile respectively. It

is seen that if head 1.5 m soil shear strength is neglected then the pile capacity

decreases.



From figure 3.15 to 3.20 the pile lateral capacity and maximum moment are shown

for different soil shear strength, pile diameter. The results are shown in table 4.14.



cu (kpa) 6 mm deflection 12 mm deflection 25 mm deflection


10 76 204 156 401 267 816

30 142 340 254 639 423 1115

50 178 408 311 796 512 1360

110

From table 4.14 it is observed that pile moment increases as the soil strength, pile

head deflections increase. It is also seen that as the soil shear strength increases 5

times pile lateral load capacity increases 3 times (76 kN to 178 kN) whereas pile

moment increases 2 times (204 kN/m to 408 kN/m). As the pile head deflection

increases 4 times (6 mm to 25 mm) pile lateral capacity increases 3.5 times (76 kN to

267 kN) whereas the moment increases 3.5 times 408 kN/m to 1360 kN/m).


embedded in soils of shear Strength 10 kpa with different head deflections.

Pile

diameter



0.5 13 33 31 67 53 122

0.6 25 54 49 109 89 204

0.75 40 95 76 184 133 354

1.0 76 204 156 394 267 816

From table 4.15 it is observed that pile moment increases as the pile diameter

increases. It is seen that as the pile diameter increases 4 times (0.5 m to 1 m) pile

lateral capacity increases 5.5 times (13 kN to 76 kN) whereas the moment increases

6.6 times (122 kN/m to 816 kN/m).

Comparing these results with the results which are shown in table 4.3 and 4.4

considering full depth soil shear strength the values are shown in the table 4.15a.

Considering free headed piles both the cases of 1 m diameter piles.

In table 4.15a pile lateral capacity and moment for 1 m diameter pile with soil shear

strength of different pile head deflection for considering full depth soil shear strength

and neglecting head 1.5 m soil strength are shown.

111

Table 4.15a: Relationship of lateral load capacity and maximum moment of free

headed plies considering full depth and neglecting head 1.5 m of soil.

cu

(kpa)


H0 H1.5 m M0 M1.5 m H0 H1.5 m M0 M1.5 m H0 H1.5 m M0 M1.5 m

0.2 30 17 165 150 56 34 330 295 80 60 605 600

0.6 68 32 280 250 110 57 515 480 180 90 1020 850

1.0 87 40 350 300 135 70 680 580 220 115 1300 1000

From this table it can be seen that pile lateral capacity is almost half if neglecting pile

head 1.5 m soil strength but the moment remains almost same.

4.2.5 Fixed headed piles neglecting head 1.5 m soil shear strength

Piles that are fixed at their head neglecting head 1.5 m soil shear strength are

discussed here. Results of piles analysis having diameter 500 mm, 600 mm, 750 mm

and 1 m embedded in uniform soil with soil shear strength of 10 kpa, 25 kpa. 50 kpa

and 70 kpa for head deflection 6 mm, 12 mm and 25 mm which shown are in figure

3.21 to 3.26 respectively. In all conditions pile length was 23 m.

Relationship of pile lateral capacity with soil shear strength

For given diameter of pile for a given head deflection (6 mm) the lateral load capacity

increases as the soil shear strength increases. But the increase is not linear. The rate of

increase of horizontal capacity decreases with the increase of shear strength of the

soil.

In table 4.16 pile lateral load capacity for 1 m diameter with its soil shear strength of

different head deflections are shown.

112



cu

kpa

H (Lateral load) kN

For 6 mm deflection

H (Lateral load) kN


H (Lateral load) kN


10 200 289 556

30 378 667 1134

50 467 778 1401

From table 4.16 it can be found that as the soil shear strength increases pile lateral

load capacity also increases. As the soil shear strength increases 5 times the

corresponding pile lateral capacity increases 2.35 times. It can be also observed that

the lateral capacity of pile increases with the increases of allowable pile head

deflection. As deflection increases 4 times (6 mm to 12 mm) corresponding lateral

capacity for 10 kpa soil shear strength increases 2.75 times (200 kN to 556 kN).


full depth soil shear strength the values are 76 kN and 44 kN for 6 mm deflection for

500 mm diameter pile and 289 kN and 200 kN for 1 m diameter pile respectively. It is

seen that if head 1.5 m soil shear strength is neglected then the pile capacity becomes

1.5 times less than the capacity of considering full depth soil shear strength.


It can be observed from figure 3.21, 3.22 and 3.23 for a given head deflection (6 mm)

the capacity of lateral load of pile increases with the increase of pile diameter. But the

increase is not linear. The results are elaborately shown in table 4.17.

In table 4.17 pile lateral load capacity for 10 kpa shear strength of different pile

diameter with different head deflections are shown.

113



Diameter

of pile (m)

H (Lateral load) kN

For 6 mm deflection

H (Lateral load) kN


H (Lateral load) kN


0.5 45 67 133

0.6 67 111 222

0.75 98 156 334

1.0 200 334 556

From Table 4.17 it is observed that as the diameter of pile increases the capacity of

pile lateral load also increases. For 500 mm diameter pile of 6 mm deflection capacity

is 44 kN whereas for 1 m diameter pile capacity is 200 kN. This is around 4.5 times

greater.

Relationship between pile head deflection and diameter with moment and soil

shear strength

From figure 3.21 to 3.26 the pile lateral capacity and maximum moment are shown

for different soil shear strength, pile diameter. The results are shown in table 4.18.



Su

(kpa)



10 200 144 -646 289 272 -1197 556 524 -2069

30 378 224 -938 667 462 -1836 1134 884 -3332

50 467 294 -1185 778 585 -2190 1401 1210 -4134


It is seen that as the soil shear strength increases 5 times pile lateral load capacity

increases 2.33 times (200 kN to 467 kN) whereas pile moment increases 2 times (144

kN/m to 294 kN). As the pile head deflection increases 4 times (6 mm to 25 mm) pile

lateral capacity increases 3.0 times (200 kN to 556 kN) where as the moment

increases 3.2 times (-646 kN/m to -2069 kN/m).

114


embedded in soils of shear strength 10 kpa with different head deflections.

Pile diameter

(m)



0.5 45 25 -101 67 48 -185 133 95 -354

0.6 67 38 -163 111 78 -326 222 161 -598

0.75 98 65 -283 156 133 -569 334 268 -1043

1.0 200 144 -646 356 272 -1197 556 524 -2069


It is seen that as the pile diameter increases 4 times pile lateral load capacity increases

4 times (44 kN to 200 kN) whereas pile moment increases 5.5 times (24 kN/m to 144

kN/m). Comparing these results with the results which are shown in table 4.7 and 4.8

of considering full depth soil shear strength. The values are shown in the table 4.19a.

Considering fixed headed piles both the cases of 1 m diameter piles. In table 4.19a

pile lateral capacity and moment for 1 m diameter pile with soil shear strength of

different pile head deflection for considering full depth soil shear strength and

neglecting head 1.5 m soil strength are shown.

Table 4.19a: Lateral load capacity and maximum moment of fixed headed plies for

considering full depth and neglecting head 1.5 m of soil.

cu

(kpa)


H0 H1.5 m M0 M1.5 m H0 H1.5 m M0 M1.5 m H0 H1.5 m M0 M1.5 m

10 65 45 -526 -475 115 65 -1000 -880 155 125 -1650 -1521

30 140 85 -820 -690 240 150 -1500 -1350 392 255 -3000 -2450

50 170 105 -1020 -871 292 175 -1953 -1610 450 315 -3482 -3040

From table 4.19a it can be seen that pile lateral capacity is almost 1.5 times (289 kN

to 200 kN) less than considering full depth soil strength for neglecting head 1.5 m soil

strength but the moment is almost same for lower head deflections (-715 kN/m to

-646 kN/m). As the soil shear strength increases 5 times moment increases almost 2

times (-646 kN/m to -1185 kN/m).

115

Relationship between location of pile maximum moment with soil shear strength,

head deflection and diameter

In table 4.19b pile maximum moment location from pile head are shown with respect

to pile diameter and soil undrained shear strength for considering full depth of soil

shear strength.

Table 4.19b: Location of pile maximum moment from head of pile for considering

full depth.

From table 4.19b it is seen that as the soil shear strength increase 7.5 times (9.5 kpa to

70 kpa) location of maximum moment point decreases 1.6 times (2.4 m to 1.5 m).

It is also seen that as the pile diameter increases 4 times (0.5 m to 1 m) location of

maximum moment point increases 1.6 times (2.4 m to 4 m).

In table 4.19c pile maximum moment location from pile head are shown with respect

to pile diameter and soil undrained shear strength for neglecting head 1.5 m soil shear

strength.

Pile diameter (m)

Undrain Shear Strength (kpa) 10 24 48 72

0.5 383 287 239 239 0.6 431 335 287 287 0.75 479 383 335 335 1.0 622 479 431 383

116

Table 4.19c: Location of pile maximum moment from head of pile for neglecting head

1.5 m of soil.

From table 4.19c it is seen that as the soil shear strength increases 7.5 times (9.5 kpa

to 70 kpa) location of maximum moment point decreases 1.4 times (3 m to 2.1 m).

It is also seen that as the pile diameter increases 4 times (0.5 m to 1 m) location of

maximum moment point increases 1.4 times (3 m to 4.2 m).

Comparing table 4.19b and 4.19c it is found that as the head 1.5 m soil is neglected

the pile maximum moment location decreases as soil shear strength increases and

location increases as pile diameter increases.

Pile

diameter (m)

Undrain Shear Strength (kpa)

10 24 48 72

0.5 479 383 335 335 0.6 527 431 383 383 0.75 575 479 431 431 1.0 670 527 479 479

117

4.3 PILES EMBEDDED IN LAYERED SOIL

Piles embedded in layered soil are discussed here. Pile foundations are designed in

soft soil that shallow foundation may not take the load of a structure. There might be

possibility of a stiff soil layer below the soft layer. The effect of the stiff layer to the

lateral load carrying capacity of a pile is discussed here. The different shear strength

in different layer of soil thickness are discussed with the help of results of article 3.6

of chapter 3. The pile which are analyzed having total length of 23 m and the upper

soft soil layer shear strength is 10 kpa and lower stiff layer having shear strength47.8

kpa and 70 kpa. The soft soil layer thicknesses are 1.5, 3, 6, 9 and 12 m. Diameters of

piles are 500 mm, 600 mm, 750 mm and 1 m.

4.3.1 Free headed and fixed headed piles

In figures 3.27 to 3.38 pile capacities with depth of soft soil for different head

deflections are shown. The head deflection varies from 6 mm to 25 mm. The layer of

soft soil is taken from the ground level. The layer thicknesses of soft soil are 1.5, 3, 6,

9 and 12 m. The soft soil consists of shear strength 10 kpa. The stiff soil layer below

soft layer having shear strength 50 kpa. Figure 3.38a to 3.38l are for layer of stiff soil

of shear strength 70 kpa. Figure 3.39 to 3.50 presents pile lateral capacity and

maximum moment for pile of neglecting top 1.5 m soil shear strength. Figure 3.51 to

3.52 for 500 mm diameter pile lateral capacity for both free and fixed head conditions.

Figure 3.53 to 3.54 for 1 m diameter pile lateral capacity for both free and fixed head

conditions. Figure 3.55 to 3.60 for pile lateral capacity with pile diameter are shown

for both free and fixed head conditions.

Relationship between pile lateral capacity and thickness of soft soil (cu = 10 kpa )

laying over a stiff soil (cu = 50 kpa )

Pile lateral capacity varies with the thickness of top soft soil layer and the shear

strength of stiff soil layer beneath the soft soil. For layered soil top soil shear strength

taken very soft clay of shear strength 10 kpa and below stiff soil having shear strength

50 kpa. Analysis was performed for various thicknesses of soft and stiff soil layers

and of different diameter of pile. As the layer thickness of soft soil increases the pile

lateral capacity changes which is shown in table 4.20.

118

Table 4.20: Pile lateral load with thickness of soft soil for free head condition (6 mm

top deflection).(soft soil, cu = 10 kpa and stiff soil, cu = 50 kpa)

Thickness of soft layer (m) 0 2 3 6 9 12

Pile lateral capacity(kN)

0.5 m dia pile

98 67 45 45 45 45

pile lateral capacity(kN)

1.0 m dia pile

378 245 182 147 142 142

From table 4.20 it is seen that as the layer thickness of soft soil increases, pile lateral

load capacity decreases. From table 4.20 for 500 mm diameter pile if the soft soil

layer thickness goes to 1.5 m to 3 m (stiff layer at 3 m from 1.5 m level) the pile

lateral capacity is 44 kN then 67 kN. If the stiff soil exists at 3 m or greater than 3 m

of soil then the lateral capacity of pile remains constant (44 kN). For 1 m diameter

pile of same condition if the stiff soil exists at 6 m or greater than 6 m of soft soil then

the lateral capacity of pile remains constant (142 kN). So the presence of stiff soil

below 6 m top soft soil the benefit to lateral capacity of stiff soil is negligible .

Presence of stiff layer below soft layer after 1.5 m will reduce the pile lateral capacity

1.5 times (378 kN to 245 kN for 1 m diameter pile).

Figure 3.33 to 3.35 are for fixed headed pile lateral capacity for different pile head

deflections are plotted with respect to thickness of top soft soil. The results are shown

in table 4.21.

Table 4.21: Pile lateral load with thickness of soft soil for fixed head condition (top 6

mm deflection). (soft soil cu = 10 kpa and stiff soil cu = 50 kpa)



0.5 m dia pile

222 125 89 80 80 80


1.0 m dia pile

756 601 445 311 289 289

From table 4.21 it is seen that as the layer thickness of soft soil increases, pile lateral

load capacity decreases. From table 4.21 for 500 mm diameter pile if the soft soil

119

layer thickness goes to 1.5 m to 3 m (stiff layer at 3 m from 1.5 m level) the pile

lateral capacity is 89 kN then 125 kN. If the stiff soil exists at 6 m or greater than 3 m

of soil then the lateral capacity of pile remains constant (80 kN). For 1 m diameter

pile of same condition if the stiff soil exists at 6 m or greater than 9.1 m of soft soil

then the lateral capacity of pile remains constant (289 kN). So the presence of stiff

soil below 9 m top soft soil the benefit to lateral capacity of stiff soil is negligible.

Presence of stiff layer below soft layer after 1.5 m will reduce the pile lateral capacity

1.25 times (756 kN to 600 kN) for 1 m diameter pile.

4.3.2 Comparison between pile lateral capacity for free head and fixed head

condition

From table 4.20 and 4.21 it is seen that fixed head pile lateral capacities are higher

than the free headed piles embedded in layered soil. If the piles are fixed at their top

then the stiff soil layer contributes more over the free headed piles. For 1 m diameter

pile if the stiff soil exists 6 m or greater than 6 m of soft soil then its lateral capacity

remains constant whereas for fixed headed piles it is after 9 m of soft soil above stiff

soil.

Relationship between pile maximum moment and depth of soft soil

In figure 3.30 to 3.32 pile maximum moments with depth of soft soil has been plotted

of different diameter and different head deflections for free head conditions.

Considering full depth of stiff soil having shear strength 50 kpa and top 1.5 m, 3 m, 6

m, 9 m, 12 m of soft soil having shear strength of 10 kpa. The results are shown in

table 4.22.

120

Table 4.22: Pile maximum moment with depth of soft soil for free head condition and

top deflection 6 mm. (soft soil cu = 10 kpa and stiff soil cu = 50 kpa)

From table 4.22 for 500 mm diameter pile if the soft soil layer thickness goes to 1.5 m

to 3 m (stiff layer at 3 m from 1.5 m level) the pile lateral capacity decreases 1.5 times

(67 kN to 44 kN) and its maximum moment decreases 1.67 times (61 kN/m to 37

kN/m). If the stiff soil exists at 6 m or greater than 6 m of soft soil then the lateral

capacity of pile remains constant (44 kN) and pile maximum moment also remains

constant 34 kN/m. For 1 m diameter pile of same condition if the stiff soil exists at

6 m or greater than 6 m of soft soil then the lateral capacity of pile remains constant

(142 kN) and its maximum moment is 231 kN/m. So the presence of stiff soil below 9

m top soft soil the benefit to lateral capacity of stiff soil is negligible. Presence of stiff

layer below soft layer after 1.5 m will reduce the pile lateral capacity 1.34 times (245

kN to 182 kN) and maximum moment 1.2 times ( 394 kN/m to 326 kN/m) for 1 m

diameter pile. Presence of stiff layer below a soft layer shows that the rate of decrease

of moment is lower than the rate of lateral capacity of pile.

In figure 3.36 to 3.38 pile maximum moments with depth of soft soil has been plotted




table 4.23.

Thickness of

soft layer (m)

0.0 1.5 3.0 6.1 9.1 12.2

H M H M H M H M H M H M

Pile lateral

capacity(kN)

and moment

(kN/m) for

0.5 m dia pile

98 267 67 200 45 120 45 111 45 111 45 111

Pile lateral

capacity(kN)

and moment

(kN/m) for 1

m dia pile

378 1557 245 1290 182 1068 147 778 142 756 142 756

121

Table 4.23: Pile maximum moment (Negative Moment) with respect to depth of soft

soil for fixed head condition.(soft soil cu = 10 kpa and stiff soil cu = 50 kpa)



(125 kN to 89 kN) and its maximum moment decreases 1.15 times (156 kN/m to 136



constant 129 kN/m. For 1 m diameter pile of same condition if the stiff soil exists at

6 m or greater than 6 m of soft soil then the lateral capacity of pile remains constant

(289 kN) and maximum moment is 680 kN/m. So the presence of stiff soil below 9 m

top soft soil the benefit to lateral capacity of stiff soil is negligible. Presence of stiff

layer below soft layer after 1.5 m will reduces the pile lateral capacity 1.35 times (600

kN to 445 kN) and maximum moment 1.12 times (1224 kN/m to 1088 kN/m) for 1 m



4.3.3 Comparison between pile maximum moment for free head and fixed head

condition

From table 4.22 and 4.23 it is seen that pile maximum moment is 3.0 times (1387

kN/m to 476 kN/m) for fixed head condition over free head condition where lateral

capacity increases 2 times (378 kN to 756 kN). If the stiff soil exists below 1.5 m of

Thickness of

soft layer (m)

0.0 1.5 3.0 6.1 9.1 12.2


Pile lateral

capacity(kN)

and moment

(kN/m) for 0.5

m dia pile

222 890 125 512 89 445 80 423 80 423 80 423

Pile lateral

capacity(kN)

and moment

(kN/m) for 1 m

dia pile

756 4537 601 4003 445 3558 311 2669 289 2357 289 2224

122

soft soil then the maximum moment for free head condition decreases 1.2 times (476

kN/m to 394 kN/m) whereas for fixed head condition it is 1.13 times (1387 kN/m to

1224 kN/m). So it is seen that in fixed head condition pile maximum moment does not

decrease as much as free headed condition as the depth of stiff layer below soft layer

increases.

Relationship between pile lateral capacity and thickness of soft soil (cu = 10 kpa )

laying over a stiff soil (cu = 70 kpa )

In figure 3.38a to 3.38c pile capacity with depth of soft soil has been plotted of

different diameter and different head deflections for free head conditions. Considering

full depth of stiff soil having shear strength 70 kpa and top 1.5 m, 3 m, 6 m, 9 m, 12 m

of soft soil having shear strength of 10 kpa. The results are shown in table 4.24.

Table 4.24: Pile lateral load with depth of soft soil for free head condition (6 mm top

deflection). (soft soil cu = 10 kpa and stiff soil cu = 70 kpa)



0.5 m dia pile

156 53 40 36 31 31


1.0 m dia pile

445 222 156 133 111 111


to 3 m (stiff layer at 3 m from 1.5 m level) the pile lateral capacity is 40 kN than 53

kN. If the stiff soil exists at 3 m or greater than 3 m of soil then the lateral capacity of

pile remains constant (31 kN). For 1 m diameter pile of same condition if the stiff soil

exists at 6 m or greater than 6 m of soft soil then the lateral capacity of pile remains

constant (111 kN). So the presence of stiff soil below 6 m top soft soil the benefit to

lateral capacity of stiff soil is negligible. Presence of stiff layer below soft layer after

1.5 m will reduce the pile lateral capacity 2.0 times (445 kN to 222 kN) for 1 m

diameter pile.

In figure 3.38d to 3.38f pile capacity with depth of soft soil has been plotted of

different diameter and different head deflections for fixed head conditions.


123


table 4.25.

Table 4.25: Pile lateral load with depth of soft soil for fixed head condition (6 mm top

deflection). (soft soil cu = 10 kpa and stiff soil cu = 70 kpa)



0.5 m dia pile

289 133 89 76 71 71


1.0 m dia pile

934 534 400 311 267 267


to 3 m (stiff layer at 3 m from 1.5 m level) the pile lateral capacity is 89 kN then 133

kN. If the stiff soil exists at 3 m or greater than 3 m of soil then the lateral capacity of

pile remains constant (71 kN). For 1 m diameter pile of same condition if the stiff soil

exists at 6 m or greater than 6 m of soft soil then the lateral capacity of pile remains

constant (267 kN). So the presence of stiff soil below 6 m top soft soil the benefit to

lateral capacity of stiff soil is negligible. Presence of stiff layer below soft layer after

1.5 m will reduce the pile lateral capacity 2.0 times (934 kN to 534 kN) for 1 m

diameter pile.

4.3.4 Comparison between pile lateral capacity for free head and fixed head

condition for stiff soil of 70 kpa laying below soft soil

From table 4.24 and 4.25 it is seen that for 500 mm diameter pile lateral capacity is

2.0 times (289 kN to 156 kN) for fixed head condition over free head condition. As

the depth of soft soil is 1.5 m then the lateral capacity for free head condition for 1 m

pile decreases 2.0 times (445 kN to 222 kN) whereas for fixed head condition it is

1.75 times (934 kN to 534 kN).

Relationship between pile maximum moment and depth of soft soil for stiff soil

of shear strength 70 kpa

In figure 3.38g to 3.38i pile maximum moment with depth of soft soil has been

plotted of different diameter and different head deflections for free head conditions.

124



table 4.26.

Table 4.26: Pile maximum moment with depth of soft soil for free head condition &

6 mm head deflection. (soft soil cu = 10 kpa and stiff soil cu = 70 kpa)


to 3 m (stiff layer at 3 m from 1.5 m level) the pile lateral capacity decreases 1.33

times (53 kN to 40 kN) and its maximum moment decreases 1.45 times (200 kN/m to

138 kN/m). If the stiff soil exists at 6 m or greater than 6 m of soft soil then the lateral


constant 31 kN/m. For 1 m diameter pile of same condition if the stiff soil exists at 6

m or greater than 6 m of soft soil then the lateral capacity of pile remains constant

(111 kN) and maximum moment is 204 kN/m. So the presence of stiff soil below 9 m

top soft soil the benefit to lateral capacity of stiff soil is negligible. Presence of stiff





Thickness of

soft layer (m)

0.0 1.5 3.0 6.1 9.1 12.2


Pile lateral

capacity(kN)

and moment

(kN/m) for

500 mm dia

pile

156 356 53 200 40 138 36 111 31 102 31 102

Pile lateral

capacity(kN)

and moment

(kN/m) for 1

m dia pile

445 1868 222 1245 156 979 133 712 111 667 111 667

125

In figure 3.38j to 3.38l pile maximum moment with depth of soft soil has been plotted




table 4.27.

Table 4.27: Pile maximum moment (Negative Moment) with depth of soft soil for

fixed head condition & 6 mm head deflection.(soft soil cu = 10 kpa and stiff soil cu =

70 kpa)



(30 kip to 20 kip) and its maximum moment decreases 1.42 times (193 kN/m to 136



constant 102 kN/m. For 1 m diameter pile of same condition if the stiff soil exists at 6

m or greater than 6 m of soft soil then the lateral capacity of pile remains constant

(267 kN/m) and maximum moment is 775 kN/m. So the presence of stiff soil below 9

m top soft soil the benefit to lateral capacity of stiff soil is negligible. Presence of stiff



Thickness of

soft layer (m)

0.0 1.5 3.0 6.1 9.1 12.2


Pile lateral

capacity(kN)

and moment

(kN/m) for 0.5

m dia pile

289 979 133 632 89 445 76 356 71 334 71 334

Pile lateral

capacity(kN)

and moment

(kN/m) for 1 m

dia pile

934 5560 534 3852 400 3260 311 2602 267 2535 267 2535

126



4.3.5 Comparison between pile maximum moment for free head and fixed head

condition

From table 4.26 and 4.27 it is seen that pile maximum moment is 3.0 times (1700

kN/m to 571 kN/m) for fixed head condition over free head condition where lateral

capacity increases 2 times (934 kN to 445 kN). As the depth of soft soil is 1.5 m then

the maximum moment for free head condition decreases 1.5 times (571 kN/m to 381

kN/m) where as for fixed head condition it is 1.44 times (1700 kN/m to 1178 kN/m).

4.3.6 Comparison between pile capacity of stiff soil of 50 kpa and 70 kpa below

soft soil.(ration 1.0/0.2 = 5 and 1.5/0.2 = 7.5)

For free head condition of 1.5 m soft soil and 50 kpa stiff soil the rate of decrease of

pile lateral capacity is 1.5 times (378 kN to 245 kN) whereas for 70 kpa stiff soil it is

2.0 times (445 kN to 222 kN). Maximum moment is 1.2 times (476 kN/m to 394

kN/m) whereas for 70 kpa stiff soil it is 1.5 times (571 kN/m to 381 kN/m).

For fixed head condition of 1.5 m soft soil and 50 kpa stiff soil the rate of decrease of

pile lateral capacity is 1.25 times (934 kN to 756 kN) whereas for 70 kpa stiff soil it is

1.75 times (934 kN to 534 kN). Maximum moment is 1.13 times (1387 kN/m to 1224

kN/m) whereas for 70 kpa stiff soil it is 1.44 times (1700 kN/m to 1178 kN/m).

It is also seen that as the diameter increases pile lateral capacity increases 3.86 times

(98 kN to 378 kN) whereas pile moment increases 6 times (82 kN/m to 476 kN/m).

It is also seen that as the soil shear strength is higher in below soft soil then the pile

lateral capacity increases. For lower diameter pile i.e. 500 mm diameter pile the

capacity decreases 3 times (156 kN to 53 kN) for 1.5 m soft soil whereas for larger

diameter pile i.e. 1 m diameter pile the capacity decreases 2 times (445 kN to 222

kN). For taking the benefit of stiff soil lateral capacity below the soft soil larger

diameter pile will be more appropriate rather than lower diameter pile.

127

CHAPTER 5

CASE STUDY: LATERAL PILE LOAD TEST OF KURIL FLYOVER

PROJECT AT DHAKA

5.1 INTRODUCTION

In this chapter a pile lateral load test performed at Kuril fly over project under direct

supervision of Dr. Syed Fakhrul Ameen (Professor BUET) is presented. In this test

two 1m dia pile (reaction pile) of length 40m has been used to apply incremental

lateral load & corresponding deflection have been recorded.

5.2 OVERVIEW OF THE PROJECT

The project is located at Kuril intersection in the city. The length of the project is 3.1-

kilometre with 6.7-9.2 metre width. There are four loops, while the height of the

flyover is 14.5 metre. There is single level unidirectional traffic movement and there

is 20 traffic directions. The project is completed in April 2012.

The piers are founded on piles having diameter of 1m of length of around 40m from

existing ground level. The 1m diameter piles are designed for around 200 ton service

loads. Most of piers are founded on 4 pile groups.

Figure 5.1: Perspective view of Kuril Fly Over

128

5.3 LOCATION OF THE PILE LATERAL LOAD TEST AREA

The location where the pile load test has been performed is shown in figure 5.2 &

corresponding soil test bore-log are also shown here.

Figure 5.2: Location of lateral load test

Location of Pile Lateral Load test

129

Figure 5.3: Location of soil test bore hole

From this picture it is found that for lateral load test data the bore hole number of 9,

31 & 32 will be best fit and the bore log are shown below.

Location of Pile Lateral Load test

130

Figure 5.4: Bore Log of 19

Light brownish grey very soft CLAY, little fine sand, rarely grit, light-plastic (CH)

9.00

9.

00

131



9.00

9.

00

132



9.00

9.

00

133

5.4 Test Equipment and Instruments

The test equipment and instruments consist mainly of the load application

arrangement and the movement measuring instruments. These are presented

separately.

5.4.1 Test Equipment for load Application:

A typical load application and measurement system consists of hydraulic cylinder,

hydraulic jacks, pressure gauge, bearing plate. The lateral load applied by hydraulic

cylinder is measured by a calibrated pressure gauge. The complete jacking system

including the hydraulic cylinder, valves, pump and pressure gauges should be

calibrated as a single unit.

5.4.2 Test Equipment for measurement:

Reference Beam: The reference beams to which the dial gauges are attached should

be rigid and stable. A light lattice girder with high stiffness in the vertical direction is

recommended. This is better than heavy steel sections of lower rigidity. To minimize

disturbance to the reference beams, the supports should be firmly embedded in the

ground away from the influence of the loading system. All reference beams are

independently supported with supports firmly embedded in the ground at a clear

distance of 3 m from the test pile.

Dial Gauges: Dial gauges have 75 mm travel with 0.25 mm precision. 50 x 50 mm

Glass square is installed perpendicular to the direction of gage-stem travel. All dial

gauges; scale and reference point are clearly marked with a reference number to assist

in recording data accurately. Gauges attached to the test pile are mounted to prevent

movement relative during the test.

Wire, Mirror and Scale System: This consists of mounting a mirror and a scale on

the top center of the test pile. A wire is then stretched perpendicular to the line of load

application and passing over the face of the scale. The sale should have 0.25 mm

sensitivity. The mirror and the scale move with the pile and the wire is stationary. The

difference of the final and the initial reading on the scale gives pile movement.

134

Some pictures of the test setup at the Kuril fly-over project are shown below.

Figure 5.7: Excavated & piles are open for test setup

Figure 5.8: Setup systems for testing the piles

135

Figure 5.9: Hydraulic jack setup for application of lateral load on piles

Figure 5.10: Dial gauge reading are recorded

136

5.5 Test Procedures

1. Two free head piles simultaneously pushed apart by applying self-balancing

compressive lateral load

2. Figure 1 show the general arrangement for this test.

Figure 5.11: Instrument set-up for applying lateral load to the pile

3. The test area within a radius of 3 m from the test pile shall be excavated. Before

applying the test load, any annular space around the upper portion of the test piles

should be filled with sand or other suitable material and the same material and back

filling methods should be used for all production piles. Lateral test load shall be

applied at approximately pile cut off elevation.

E.G.L

TEST PILE

Load Cell

Dial Guage

Hydraulic Jack

Supporting Frame

1 m 1 m

3 m

137

4. Maximum test load= 135 KN (15 ton) (150 percent of design load 10 ton).

5. Apply the total load in 10 steps to 150 percent of design load (e.g., 25 percent, 50

percent, 75 percent, 100 percent, 125 percent, 150 percent). The 25 percent and 50

percent of design load increments are applied for 10 min each and the 75 percent load

increment is maintained for 15 min. Other load increments are maintained for 20 min

each.

6. After maintaining 150 percent design load for 60 min. unload the pile in steps of 50

percent of the design load (e.g., to 150 percent, 100 percent, 50 percent and 0 percent,

maintaining each load decrement for 10 min). So the loading and unloading sequence

of the test shall be according with the following table, unless the maximum tip

deflection becomes 10 mm earlier, in which the loading shall not increase any further.

7. The lateral movement of the test pile will be measured to accuracy 0.01 mm using

dial gauges and wire, mirror and scale system. The deflection of two piles shall be

measured separately against independent references. Result of both piles shall be

compiled and submitted. This will constitute the result of a single test.

8. No additional load in excess of the loading specified above is necessary.

138

Table 5.1 Shows load and corresponding deflection values which are obtain from the lateral load test

From the table 5.1 it can be found that at 133 KN load the deflection is around 1.95 mm which is very small as per BNBC of allowable deflection may be up to 25mm.

5.6 Computer analysis using soil spring

Using the Finite Element Software Package “SAP” we can generate a model of the

same pile with the soil spring values giving all the boundary conditions and after

analyzing we get the results as below.

From chapter 3 the calculation of the soil spring values, pult and passive resistance can

be done from the soil test report data which are shown in figure 5.5.

Table 5.2 Shows soil spring values and pult for corresponding soil layer.

Load (KN)

Deflection (mm)

0 0 13 0.19 27 0.29 40 0.5 53 0.67 67 0.8 80 0.97 91 1.14 96 1.23 101 1.33 107 1.43 133 1.95

107 1.94 80 1.93 53 1.82 27 1.39 0 0.39

Table 5.1: Load and deflection from lateral pile load test

139

Depth m Spring No Spring values, kN/m

Soil pult (kN)

15 1st 151 18

16 2nd 303 53

17 3rd 506 76

18 4th 506 93

19 5th 506 111

20 6th 506 129

21 7th 506 151

22 8th 506 174

23 9th 506 209

24 to 75 10th and above 506 245

From this data, using the computer analysis by SAP the following results are found which are shown in table 5.3.

Using the values found from lateral load test results shown in table 5.1 and from computer analysis results shown in table 5.3 the following graph has been plotted.

Load (KN)

Deflection (mm)

0 0 13 0.21 27 0.42 40 0.63 54 0.84 67 1.04 81 1.25 95 1.46

108 1.67 122 1.88 135 2.1

Table 5.2: Spring value and ultimate soil resistance for computer analysis

Table 5.3: Load and deflection results from computer analysis

140

Figure 5.12 shows the load vs Pile head deflection diagram for both load test results and computer analysis results.

5.7 Comments

It can be observed that the pile load test results are well agreed with the results obtained from computer analysis using soil spring values. Spring constant are taken from Davisson & Robinson’s (1965) equation.

Figure 5.12 Load vs Pile head Deflection graph (load test and computer analysis)

0

20

40

60

80

100

120

140

160

0 0.5 1 1.5 2 2.5

Load Teat

Computer Analysis

Load vs Pile head deflection

Load

(KN

)


141

CHAPTER 6

CONCLUSION

1 CONCLUSIONS

6.1 General

Piles are frequently subjected to lateral forces acting on its head. An adequate factor

of safety against ultimate resistance and an acceptable deflection at service load

criteria must be satisfied in the design of such pile foundations. Frequently the pile is

embedded in layered soil which consist soft clay over stiff clay. In this paper piles

having different diameter embedded completely in homogeneous soil and in layered

soil are analyzed using Winkler spring model. In this model soil has defined series of

non linear elastic spring so that deformation occurs only where loading exists.

In layered soil, two layer of soil having different thickness of upper soft soil and stiff

soil lying below the soft soil are analyzed. Piles are long pile of diameter 500 mm,

600 mm, 750 mm and 1000 mm.

6.2 Conclusion

In this study behavior of piles embedded in homogeneous soil of different soil shear

strength having different pile diameter and head deflection are analyzed. Piles

embedded in layered soil with soft soil over lying stiff soil are analyzed.

From this study following conclusions are drawn:

i. For piles embedded in homogeneous soil for a given pile head deflection the lateral capacity increases as the soil shear strength increases. If the pile diameter increases the lateral capacity also increases. Lateral capacity also increases if the allowable pile head deflection increases.

ii. For larger diameter piles the lateral capacity increases more rapidly than smaller diameter piles.

iii. When top 1.5 m soil shear strength is neglected then the lateral capacity of pile becomes half for a given pile head deflection compared with taking full depth soil.

iv. In layered soil if the top soft soil thickness increases then the pile lateral capacity decreases for a given pile head deflection. For a given thickness of soft layer laying above a stiff layer the effect of lateral capacity is higher in larger diameter pile than the small diameter pile.

142

vi. If there is a stiff soil below a soft soil, large diameter pile have greater advantages for lateral loads.

6.3 Recommendations for Future Study

From the present study, the recommendations for future study may be summarized as follows:

i. In some cases clay soil may exist below sandy soil or sandy soil below clay soil. In this case the analysis can be done to find out the behavior of pile to lateral loads. Pile lateral load behavior in multi layered soil may be study.

ii. Different soil shear strength can be taken to evaluate the lateral behavior of piles embedded in the soil.

iii. Clay soil has taken in the study, for sandy soil the analysis should be done to evaluate lateral behavior of pile.

iv. In p-y curve the initial curve is taken straight line to simplify the analysis. To account real behavior of pile embedded in soil the initial parabolic curve to estimate the spring value may be done.

v. In this study single pile has analyzed for lateral loading, in practical case there is seldom use of single pile in foundation of a structure. They are usually remains in a group. Lateral behavior of group piles in lateral loading may be study for practical purposes

vi. In this study, piles are analyzed for static loading only. Further study can be done using cyclic conditions.

143

REFERENCES

American Petroleum Institute, (1984). Recommended Practice for Planning,

Designing, and Constructing fixed offshore Platforms, Code RP2A (15th), Dallas,

Texas

Anderson, Townsend. (2002) “A Laterally Loaded Pile Database”. Deep

Foundations 2002: An International Perspective on Theory, Design,

Construction, and Performance pp. 262-273

Anderson, J.B., Townsend, F.B., and Grajales, B. (2003). “Case History Evaluation

of Laterally Loaded Piles,” Journal of Geotechnical and Geoenvironmental

Engineering, ASCE, Vol. 129, No. 3, pp. 187-196.

Ashour, M., Norris, G., and Pilling, P. (1998). “Lateral Loading of a Pile in Layered

Soil Using the Strain Wedge Model,” Journal of Geotechnical and Geoenvironmental

Engineering, ASCE, Vol. 124, No. 4, pp. 303-315.

Banerjee, P. K., & Davies, T. G. (1978). The Behavior of Axially and Laterally

Loaded Single Piles Embedded in Non-Homogeneous Soils. Geot., vol.28, no. 3;

309-326

Bowles (1997). “Foundation Analysis and Design 5th Edition” MacGraw-Hill

Companies

Brown, D. (2007). “Rapid Lateral Load Testing of Deep Foundations.” Journal of the

Deep FoundationsInstitute, Vol. 1, No. 1, pp. 54- 62.

Brinch Hansen, J. (1961). The ultimate resistance of rigid piles against transverse

forces, Danish Geotechnical Institute Bulletin No. 12, p. 5-9.

Broms,B.B (1964). Lateral Resistance of Piles in Cohesive

Soil.J.S.M.F.D.,ASCE,vol.90, SM2:27-63

144

Broms, B.B (1964). Lateral Resistance of Piles in Cohesionless Soil. J.S.M.F.D.,

ASCE, vol.90, SM2: 123-156

Davisson, M. T. & Gill, H. L. Laterally Loaded piles in Layered Soil System.

J.S.M.F.D., ASCE, vol.89, SM3: 63-94 (1963).

Matlock, Reese, (1960). Generalized Solutions for laterally Loaded Piles,

Journal of the Soil Mechanics and Foundations Division, ASCE, Vol.86, No SM5,

Proc.Paper 2626, pp.63-91

Matlock, H. (1970). "Correlation for Design of Laterally Loaded Piles in Soft Clay,"

in Proceedings, Second Offshore Technology Conference, Dallas, Texas, pp. 577 -

594.

Poulos, H. G. (1975). Lateral Load-Deflection Prediction for Pile Groups. Jnl. Geot.

Eng. Div., ASCE, vol.101, no. GT1:19-34

Reese, L. C., Cox, W, R., and Koop, F. D. (1975). "Field Testing and Analysis of

Laterally Loaded Piles in Stiff Clay," in Proceedings, Seventh Offshore Technology

Conference, Vol. 2, Dallas, Texas, pp. 672-690.

Reese, L.C. & Van Impe, W.F. (2001), Single Piles & Groups under Lateral Loading,

A.A.Balkema, UK.

Rollins, K. M., Peterson, K. T., and Weaver, T. J. (1998). Lateral load behavior

of full-scale pile group in clay, J. of Geotech. and Geoenviron. Engrg., ASCE,

124(6), 468–478

Rollins, K., Bowles, S., Brown, D., Ashford, S, (2007). Lateral load testing of large

drilled shafts after blast-induced liquefaction. Procs. 4th Intl. Conf. on Earthquake

Geotechnical Engrg., Springer, Paper 1141

145

Smith, T.D., Slyh, R. (1986) "Side Friction Mobilization Rates for Laterally

Loaded Piles from the Pressuremeter, “ Proceedings of the Second

International Symposium, The Pressuremeter and its Marine Application”,

Texas A&M, May ASTM STP 950, pp. 478-491

Tomlinson, M.J. (1994). “Pile Design and Construction Practices”, Fourth Edition,

Taylor & Francis.

Welch, R. C., and Reese, L. C. (1972). "Laterally Loaded Behavior of Drilled

Shafts," Research Report No. 89-10, Center for Highway Research, The University

of Texas at Austin, May.

146

Appendix A:

GRAPHS FOR FREE HEADED AND FIXED HEADED PILE CAPACITY

AND MOMENT

147

0.5 m Pile Capacity vs Thickness of Soft Soil (Free & Fixed Head Conditions)

Figure A.1: 0.5 m Pile Capacity vs Depth of soft soil (Free Head & Fixed Head) 0.5 m Pile Maximum Moment vs Thickness of Soft Soil (Free & Fixed Head Conditions)

Figure A.2: 0.5 m Pile Moment vs Depth of soft soil (Free Head & Fixed Head)

0

100

200

300

0 2 4 6 8 10 12 14

6 mm deflection (Free Head)6 mm deflection (Fixed)12 mm deflection (Free Head)12 mm deflection (Fixed)25 mm deflection (Free Head)

0.5 m diameter Pile Capacity vs Thickness of soft soil


Pile

C

apac

ity (K

N)

-600

-500

-400

-300

-200

-100

0

100

200

300

0 2 4 6 8 10 12 14

6 mm deflection (Free Head)6 mm deflection (Fixed)12 mm deflection ( Free Head)12 mm deflection (Fixed)25 mm deflection (Free Head)


Pile

Mom

ent (

KN

-m)

0.5 m diameter Pile Maximum Moment vs Thickness of soft soil

148

1.0 m Diameter Pile Capacity vs Depth of Soft Soil (Free & Fixed Head Conditions)

Figure A.3: 1.0 m Pile Capacity vs Depth of soft soil (Free Head & Fixed Head) 1.0 m Pile Moment vs Depth of Soft Soil (Free & Fixed Head Conditions)

Figure A.4: 1.0 m Pile Moment vs Depth of soft soil (Free Head & Fixed Head)

0

500

1000

0 2 4 6 8 10 12 14

6 mm deflection (Free Head)6 mm deflection (Fixed)12 mm deflection (Free Head)12 mm deflection (Fixed)25 mm deflection (Free Head)

1.0 m diameter Pile Capacity vs Thickness of soft soil


Pile

C

apac

ity (K

N)

-4000-3500-3000-2500-2000-1500-1000

-5000

50010001500

0 5 10 15

6 mm deflection (Free Head)6 mm deflection (Fixed)12 mm deflection (Free Head)12 mm deflection (Fixed)


Pile

Mom

ent (

KN

-m)

1.0 m diameter Pile Maximum Moment vs Thickness of soft soil

149

Pile Capacity vs Diameter of Pile for Free head Condition

Figure A.5: Pile Capacity vs Pile Diameter for 6 mm deflection



0

200

400

600

0 0.2 0.4 0.6 0.8 1 1.2

Cu = 10 kpaCu = 25 kpaCu = 50 kpaCu = 70 kpa

Pile Capacity vs Pile Diameter for 6 mm deflection

Pile Diameter (m)

Pile

C

apac

ity (K

N)

0

200

400

600

800

0 0.2 0.4 0.6 0.8 1 1.2



Pile Diameter (m)

Pile

C

apac

ity (K

N)

0

200

400

600

800

1000

1200

0 0.2 0.4 0.6 0.8 1 1.2



Pile Diameter (m)

Pile

C

apac

ity (K

N)

150

Fixed Head Condition




0

400

800

1200

0 0.2 0.4 0.6 0.8 1 1.2



Pile Diameter (m)

Pile

C

apac

ity (K

N)

0

400

800

1200

1600

0 0.2 0.4 0.6 0.8 1 1.2



Pile Diameter (m)

Pile

C

apac

ity (K

N)

0

400

800

1200

1600

2000

2400

0 0.2 0.4 0.6 0.8 1 1.2



Pile Diameter (m)

Pile

C

apac

ity (K

N)

Documents

BEHAVIOUR OF LATERALLY LOADED PILES IN LAYERED SOIL · 2019-04-28 · 2.4.1 Broms method 15 2.4.2 Beam-on-elastic foundation approach 22 2.4.3 Beam-on-winkler foundation 23 2.4.4