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
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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
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. 3.4: Pile Capacity vs Soil Undrained Shear Strength for 12 mm deflection
Fig. 3.5: Pile Capacity vs Soil Undrained Shear Strength for 25 mm deflection
Fig. 3.6: Pile Moment vs Soil Undrained Shear Strength for 6 mm deflection
Fig. 3.7: Pile Moment vs Soil Undrained Shear Strength for 12 mm deflection
Fig. 3.8: Pile Moment vs Soil Undrained Shear Strength for 25 mm deflection
Fig. 3.9: Pile Capacity vs Soil Undrained Shear Strength for 6 mm deflection
Fig. 3.10: Pile Capacity vs Soil Undrained Shear Strength for 12 mm deflection
Fig. 3.11: Pile Capacity vs Soil Undrained Shear Strength for 25 mm deflection
Fig. 3.12: Pile Moment vs Soil Undrained Shear Strength for 6 mm deflection
Fig. 3.13: Pile Moment vs Soil Undrained Shear Strength for 12 mm deflection
Fig. 3.14: Pile Moment vs Soil Undrained Shear Strength for 25 mm deflection
Fig. 3.15: Pile Capacity vs Soil Undrained Shear Strength for 6 mm deflection
Fig. 3.16: Pile Capacity vs Soil Undrained Shear Strength for 12 mm deflection
Fig. 3.17: Pile Capacity vs Soil Undrained Shear Strength for 25 mm deflection
Fig. 3.18: Pile Moment vs Soil Undrained Shear Strength for 6 mm deflection
Fig. 3.19: Pile Moment vs Soil Undrained Shear Strength for 12 mm deflection
Fig. 3.20: Pile Moment vs Soil Undrained Shear Strength for 25 mm deflection
Fig. 3.21: Pile Capacity vs Soil Undrained Shear Strength for 6 mm deflection
Fig. 3.22: Pile Capacity vs Soil Undrained Shear Strength for 12 mm deflection
Fig. 3.23: Pile Capacity vs Soil Undrained Shear Strength for 25 mm deflection
Fig. 3.24: Pile Moment vs Soil Undrained Shear Strength for 6 mm deflection
Fig. 3.25: Pile Moment vs Soil Undrained Shear Strength for 12 mm deflection
Fig. 3.26: Pile Moment vs Soil Undrained Shear Strength for 25 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. 3.28: Pile Capacity vs Depth of soft soil for 12 mm deflection
Fig. 3.29: Pile Capacity vs Depth of soft soil for 25 mm deflection
Fig. 3.30: Pile Moment vs Depth of soft soil for 6 mm deflection
Fig. 3.31: Pile Moment vs Depth of soft soil for 12 mm deflection
Fig. 3.32: Pile Moment vs Depth of soft soil for 25 mm deflection
Fig. 3.33: Pile Capacity vs Depth of soft soil for 6 mm deflection
Fig. 3.34: Pile Capacity vs Depth of soft soil for 12 mm deflection
Fig. 3.35: Pile Capacity vs Depth of soft soil for 25 mm deflection
Fig. 3.36: Pile Moment vs Depth of soft soil for 6 mm deflection
Fig. 3.37: Pile Moment vs Depth of soft soil for 12 mm deflection
Fig. 3.38: Pile Moment vs Depth of soft soil for 25 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
Fig. 3.39: Pile Capacity vs Depth of soft soil for 6 mm deflection
Fig. 3.40: Pile Capacity vs Depth of soft soil for 12 mm deflection
Fig. 3.41: Pile Capacity vs Depth of soft soil for 25 mm deflection
Fig. 3.42: Pile Moment vs Depth of soft soil for 6 mm deflection
Fig. 3.43: Pile Moment vs Depth of soft soil for 12 mm deflection
Fig. 3.44: Pile Moment vs Depth of soft soil for 25 mm deflection
Fig. 3.45: Pile Capacity vs Depth of soft soil for 6 mm deflection
xi
Fig. 3.46: Pile Capacity vs Depth of soft soil for 12 mm deflection
Fig. 3.47: Pile Capacity vs Depth of soft soil for 25 mm deflection
Fig. 3.48: Pile Moment vs Depth of soft soil for 6 mm deflection
Fig. 3.49: Pile Moment vs Depth of soft soil for 12 mm deflection
Fig. 3.50: Pile Moment vs Depth of soft soil for 25 mm deflection
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
Fig. 4.6: Pile lateral capacities with its head Deflection for 25 kpa soil shear
strength
Fig. 4.7: Pile lateral capacities with its head Deflection for 50 kpa soil shear strength
Fig. 4.8: Pile lateral capacities with its head Deflection for 70 kpa soil shear
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
Fig. 4.13: Pile lateral capacities with its head Deflection for 10 kpa soil shear
strength
Fig. 4.14: Pile lateral capacities with its head Deflection for 25 kpa soil shear
strength
Fig. 4.15: Pile lateral capacities with its head Deflection for 50 kpa soil shear
strength
Fig. 4.16: Pile lateral capacities with its head Deflection for 70 kpa soil shear
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
Fig. 5.5: Bore Log of 31
xii
Fig. 5.6: Bore Log of 32
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
Table 3.9: Allowable horizontal load on pile for fixed head condition
Table 3.10: Allowable horizontal load on pile for free head condition neglecting
top 1.5 m soil
Table 3.11: Allowable horizontal load on pile for fixed head condition neglecting
top 1.5 m soil
Table 3.12: Allowable horizontal load on pile for free head condition
Table 3.13: Allowable horizontal load on pile for fixed head condition
Table 3.14: Allowable horizontal load on pile for free head condition neglecting
top 1.5 m soil
Table 3.15: Allowable horizontal load on pile for fixed head condition neglecting
top 1.5 m soil
Table 3.16: Allowable horizontal load on pile for free head condition
Table 3.17: Allowable horizontal load on pile for fixed head condition
Table 3.18: Allowable horizontal load on pile for free head condition neglecting
top 1.5 m soil
Table 3.19: Allowable horizontal load on pile for fixed head condition neglecting
top 1.5 m soil
Table 3.20: Allowable horizontal load on pile for free head condition
xiv
Table 3.21: Allowable horizontal load on pile for fixed head condition
Table 3.22: Allowable horizontal load on pile for free head condition neglecting
top 1.5 m soil
Table 3.23: Allowable horizontal load on pile for fixed head condition neglecting
top 1.5 m soil
Table 3.24: Allowable horizontal load on pile for free head condition
Table 3.25: Allowable horizontal load on pile for fixed head condition
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.
Table 4.5: Lateral capacity of 1 m diameter long pile embedded in soils of
different shear strength with different head deflections.
Table 4.6: Lateral capacity of different diameter of long pile embedded in soils
of shear Strength 10 kpa with different head deflections.
Table 4.7: Lateral capacity and maximum moment of long pile embedded in
soils of different shear strength with different head deflections.
Table 4.8: Lateral capacity and maximum moment of different diameter of long
pile embedded in soils of shear Strength 10 kpa with different head
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
headed piles of diameter 1 m.
Table 4.12: Lateral capacity of 1 m diameter long pile embedded in soils of
different shear strength with different head deflections.
xv
Table 4.13: Lateral capacity of different diameter of long pile embedded in soils
of shear Strength 10 kpa with different head deflections.
Table 4.14: Lateral capacity and maximum moment of long pile embedded in
soils of different shear Strength with different head deflections.
Table 4.15: Lateral capacity and maximum moment of different diameter of long
pile embedded in soils of shear Strength 10 kpa with different head
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.
Table 4.16: Lateral capacity of 1 m diameter long pile embedded in soils of
different shear strength with different head deflections.
Table 4.17: Lateral capacity of different diameter of long pile embedded in soils
of shear Strength 10 kpa with different head deflections.
Table 4.18: Lateral capacity and maximum moment of long pile embedded in
soils of different shear strength with different head deflections.
Table 4.19: Lateral capacity and maximum moment of different diameter of long
pile embedded in soils of shear Strength 10 kpa with different head
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)
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 sub- grade 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:
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.
Figure 3.3: Pile Capacity vs Soil Shear Strength for 6 mm deflection
Figure 3.4: Pile Capacity vs Soil Shear Strength for 12 mm deflection
Figure 3.5: Pile Capacity vs Soil Shear Strength for 25 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
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 (k
ip-ft
)
0
100
200
300
400
500
0 0.5 1 1.5 2
20" Dia Pile24" Dia Pile30" Dia Pile40" Dia Pile
Pile Moment vs Soil Undrained Shear Strength for 0.25" deflection
Soil Undrained Shear Strength (ksf)
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 Capacity vs Soil Shear Strength for 12 mm deflection
Soil Shear Strength (kpa)
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 Capacity vs Soil Shear Strength for 25 mm deflection
Soil Shear Strength (kpa)
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
Figure 3.7: Pile Maximum Moment vs Soil Shear Strength for 12 mm deflection
Figure 3.8: Pile Maximum Moment vs Soil Shear Strength for 25 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 Maximum Moment vs Soil Shear Strength for 12 mm deflection
Soil Shear Strength (kpa)
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 Maximum Moment vs Soil Shear Strength for 25 mm deflection
Soil Shear Strength (kpa)
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 Capacity vs Soil Shear Strength for 6 mm deflection
Soil Shear Strength (kpa)
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 Capacity vs Soil Shear Strength for 12 mm deflection
Soil Shear Strength (kpa)
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 Capacity vs Soil Shear Strength for 25 mm deflection
Soil Shear Strength (kpa)
Pile
C
apac
ity (k
N)
51
Maximum Moment of Pile for Fixed Head Condition
Figure 3.12: Pile Maximum Moment vs Soil Shear Strength for 6 mm deflection
Figure 3.13: Pile Maximum Moment vs Soil Shear Strength for 12 mm deflection
Figure 3.14: Pile Maximum Moment vs Soil Shear Strength for 25 mm deflection
-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
Pile Maximum Moment vs Soil Shear Strength for 6 mm deflection
Soil Shear Strength (kpa)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
Pile Maximum Moment vs Soil Shear Strength for 12 mm deflection
Soil Shear Strength (kpa)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
Pile Maximum Moment vs Soil Shear Strength for 25 mm deflection
Soil Shear Strength (kpa)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)
Figure 3.15: Pile Capacity vs Soil Shear Strength for 6 mm deflection
Figure 3.16: Pile Capacity vs Soil Shear Strength for 12 mm deflection
Figure 3.17: Pile Capacity vs Soil Shear Strength for 25 mm deflection
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 Capacity vs Soil Shear Strength for 6 mm deflection
Soil Shear Strength (kpa)
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 Capacity vs Soil Shear Strength for 12 mm deflection
Soil Shear Strength (kpa)
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 Capacity vs Soil Shear Strength for 25 mm deflection
Soil Shear Strength (kpa)
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
Figure 3.20: Pile Maximum Moment vs Soil Shear Strength for 25 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 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
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 Maximum Moment vs Soil Shear Strength for 6 mm deflection
Soil Shear Strength (kpa)
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 Maximum Moment vs Soil Shear Strength for 6 mm deflection
Soil Shear Strength (kpa)
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)
Figure 3.21: Pile Capacity vs Soil Shear Strength for 25 mm deflection
Figure 3.22: Pile Capacity vs Soil Shear Strength for 12 mm deflection
Figure 3.23: Pile Capacity vs Soil Shear Strength for 25 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 Capacity vs Soil Shear Strength for 6 mm deflection
Soil Shear Strength (kpa)
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 Capacity vs Soil Shear Strength for 12 mm deflection
Soil Shear Strength (kpa)
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 Capacity vs Soil Shear Strength for 25 mm deflection
Soil Shear Strength (kpa)
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
Figure 3.25: Pile Maximum Moment vs Soil Shear Strength for 12 mm deflection
Figure 3.26: 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
Pile Maximum Moment vs Soil Shear Strength for 6 mm deflection
Soil Shear Strength (kpa)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
Pile Maximum Moment vs Soil Shear Strength for 12 mm deflection
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.
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.
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
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)
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
Table 3.12: 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
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
Table 3.13: Allowable horizontal load on pile for fixed head condition
6 mm Deflection. 12 mm Deflection. 25 mm Deflection. Pile (m)
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.
Table 3.14: 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
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
Table 3.15: 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)
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
Table 3.16: 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
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
Table 3.17: Allowable horizontal load on pile for fixed head condition
6 mm Deflection. 12 mm Deflection. 25 mm Deflection. Pile (m)
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
Table 3.18: 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
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
Table 3.19: 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)
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 ) for free head condition. Results are shown in table 3.20
Table 3.20: Allowable horizontal load on pile for free head condition
6 mm Deflection. 12 mm Deflection. 25 mm Deflection. Pile (m) P(kN) Mmax
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 ) for fixed head condition. Results are shown in table 3.21
Table 3.21: Allowable horizontal load on pile for fixed head condition
6 mm Deflection. 12 mm Deflection. 25 mm Deflection. Pile (m)
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
Table 3.22: 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
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
6 mm Deflection. 12 mm Deflection. 25 mm Deflection. Pile (m)
Allowable lateral load, maximum moment and maximum moment location from head of pile for piles embedded in a layered soil having top 1.5 m soft clay ( cu = 10 kpa ) lying over a stiff clay ( cu = 70 kpa ) for free head condition. Results are shown in table 3.24
Table 3.24: 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
Allowable lateral load, maximum moment and maximum moment location from head of pile for piles embedded in a layered soil having top 1.5 m soft clay ( cu = 10 kpa ) lying over a stiff clay ( cu = 70 kpa ) for fixed head condition. Results are shown in table 3.25
Table 3.25: Allowable horizontal load on pile for fixed head condition
6 mm Deflection. 12 mm Deflection. 25 mm Deflection. Pile (m)
0.5 m Dia Pile0.6 m Dia Pile0.75 m Dia Pile1.0 m Dia Pile
Pile Maximum Moment vs Thickness of soft soil for 25 mm deflection
Pile
Max
imum
Mom
ent (
KN
-m)
Thickness of Soft Soil (m)
soft soilcu = 10 kpa
stiff soilcu = 50 kpa
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
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 = 70 kpa
0100200300400500600700800
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 12 mm deflection
Pile
C
apac
ity (K
N)
Thickness of Soft Soil (m)
soft soilcu = 10 kpa
stiff soilcu = 70 kpa
0100200300400500600700800900
100011001200
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 25 mm deflection
Pile
C
apac
ity (K
N)
Thickness of Soft Soil (m)
soft soilcu = 10 kpa
stiff soilcu = 70 kpa
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
0.5 m Dia Pile0.6 m Dia Pile0.75 m Dia Pile1.0 m Dia Pile
Pile Maximum Moment vs Thickness of soft soil for 6 mm deflection
Pile
Max
imum
Mom
ent (
KN
-m)
Thickness of Soft Soil (m)
soft soilcu = 10 kpa
stiff soilcu = 70 kpa
-1250
-1000
-750
-500
-250
0
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 Maximum Moment vs Thickness of soft soil for 12 mm deflection
Pile
Max
imum
Mom
ent (
KN
-m)
Thickness of Soft Soil (m)
soft soilcu = 10 kpa
stiff soilcu = 70 kpa
-2250-2000-1750-1500-1250-1000
-750-500-250
0
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 Maximum Moment vs Thickness of soft soil for 25 mm deflection
Pile
Max
imum
Mom
ent (
KN
-m)
Thickness of Soft Soil (m)
soft soilcu = 10 kpa
stiff soilcu = 70 kpa
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
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 = 70 kpa
0
250
500
750
1000
1250
1500
1750
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 12 mm deflection
Pile
C
apac
ity (K
N)
Thickness of Soft Soil (m)
soft soilcu = 10 kpa
stiff soilcu = 70 kpa
0250500750
1000125015001750200022502500
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 25 mm deflection
Pile
C
apac
ity (K
N)
Thickness of Soft Soil (m)
soft soilcu = 10 kpa
stiff soilcu = 70 kpa
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
0.5 m Dia Pile0.6 m Dia Pile0.75 m Dia Pile1.0 m Dia Pile
Pile Maximum Moment vs Thickness of soft soil for 6 mm deflection
Pile
Max
imum
Mom
ent (
KN
-m)
Thickness of Soft Soil (m)
soft soilcu = 10 kpa
stiff soilcu = 70 kpa
-3500
-3000
-2500
-2000
-1500
-1000
-500
0
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 Maximum Moment vs Thickness of soft soil for 12 mm deflection
0.5 m Dia Pile0.6 m Dia Pile0.75 m Dia Pile1.0 m Dia Pile
Pile Maximum Moment vs Thickness of soft soil for 25 mm deflection
Pile
Max
imum
Mom
ent (
KN
-m)
Thickness of Soft Soil (m)
soft soilcu = 10 kpa
stiff soilcu = 70 kpa
85
Allowable lateral load of pile embedded in layered soil neglecting top 1.5 m soil shear strength for free head condition
Figure 3.39: Pile Capacity vs Depth of soft soil for 6 mm deflection
Figure 3.40: Pile Capacity vs Depth of soft soil for 12 mm deflection
Figure 3.41: Pile Capacity vs Depth of soft soil for 25 mm deflection
0
50
100
150
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 deflectionPi
le
Cap
acity
(KN
)
Thickness of Soft Soil (m)
soft soilcu = 10 kpa
stiff soilcu = 50 kpa
0
50
100
150
200
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 12 mm deflection
Pile
C
apac
ity (K
N)
Thickness of Soft Soil (m)
soft soilcu = 10 kpa
stiff soilcu = 50 kpa
0
50
100
150
200
250
300
350
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 25 mm deflection
Pile
C
apac
ity (K
N)
Thickness of Soft Soil (m)
soft soilcu = 10 kpa
stiff soilcu = 50 kpa
86
Maximum moment of pile embedded in layered soil neglecting top 1.5 m soil shear strength for free head condition
Figure 3.42: Pile Moment vs Depth of soft soil for 6 mm deflection
Figure 3.43: Pile Moment vs Depth of soft soil for 12 mm deflection
Figure 3.44: Pile Moment vs Depth of soft soil for 25 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 Maximum Moment vs Thickness of soft soil for 6 mm deflection
Pile
Max
imum
Mom
ent (
KN
-m)
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
0.5 m Dia Pile0.6 m Dia Pile0.75 m Dia Pile1.0 m Dia Pile
Pile Maximum Moment vs Thickness of soft soil for 12 mm deflection
Pile
Max
imum
Mom
ent (
KN
-m)
Thickness of Soft Soil (m)
soft soilcu = 10 kpa
stiff soilcu = 50 kpa
0100200300400500600700800900
1000110012001300
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 Maximum Moment vs Thickness of soft soil for 25 mm deflection
Pile
Max
imum
Mom
ent (
KN
-m)
Thickness of Soft Soil (m)
soft soilcu = 10 kpa
stiff soilcu = 50 kpa
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
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
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 12 mm deflection
Pile
C
apac
ity (K
N)
Thickness of Soft Soil (m)
soft soilcu = 10 kpa
stiff soilcu = 50 kpa
0100200300400500600700800900
1000
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 25 mm deflection
Pile
C
apac
ity (K
N)
Thickness of Soft Soil (m)
soft soilcu = 10 kpa
stiff soilcu = 50 kpa
88
Maximum moment of pile embedded in layered soil neglecting top 1.5 m soil shear strength for fixed head condition
Figure 3.48: Pile Moment vs Depth of soft soil for 6 mm deflection
Figure 3.49: Pile Moment vs Depth of soft soil for 12 mm deflection
Figure 3.50: Pile Moment vs Depth of soft soil for 25 mm deflection
-1000
-750
-500
-250
0
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 Maximum Moment vs Thickness of soft soil for 6 mm deflection
Pile
Max
imum
Mom
ent (
KN
-m)
Thickness of Soft Soil (m)
soft soilcu = 10 kpa
stiff soilcu = 50 kpa
-2000-1750-1500-1250-1000
-750-500-250
0
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 Maximum Moment vs Thickness of soft soil for 12 mm deflection
0.5 m Dia Pile0.6 m Dia Pile0.75 m Dia Pile1.0 m Dia Pile
Pile Maximum Moment vs Thickness of soft soil for 25 mm deflection
Pile
Max
imum
Mom
ent (
KN
-m)
Thickness of Soft Soil (m)
soft soilcu = 10 kpa
stiff soilcu = 50 kpa
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
For 25 mm deflection
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
For 12 mm deflection
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
0.5 m Dia Pile0.6 m Dia Pile0.75 m Dia Pile1.0 m Dia Pile
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
0.5 m Dia Pile0.6 m Dia Pile0.75 m Dia Pile1.0 m Dia Pile
Pile Capacity vs Pile head deflection
Pile
C
apac
ity (K
N)
Pile head deflection (mm)
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
0.5 m Dia Pile0.6 m Dia Pile0.75 m Dia Pile1.0 m Dia Pile
Pile Capacity vs Pile head deflectionPi
le
Cap
acity
(KN
)
Pile head deflection (mm)
0100200300400500600700800900
10001100
0 2 4 6 8 10
0.5 m Dia Pile0.6 m Dia Pile0.75 m Dia Pile1.0 m Dia Pile
Pile Capacity vs Pile head deflection
Pile
C
apac
ity (K
N)
Pile head deflection (mm)
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
H(kN) M(kN/m) H(kN) M(kN/m) H(kN) M(kN/m)
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
From Table 4.4 it is observed that as the diameter of pile increases the capacity of pile
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
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.
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
Figure 5.5: Bore Log of 31
Light brownish grey very soft CLAY, little fine sand, rarely grit, light-plastic (CH)
9.00
9.
00
132
Figure 5.6: Bore Log of 32
Light brownish grey very soft CLAY, little fine sand, rarely grit, light-plastic (CH)
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.
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.
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
)
Pile head deflection (mm)
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
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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
Thickness of Soft Soil (m)
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)
Thickness of Soft Soil (m)
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
Thickness of Soft Soil (m)
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)
Thickness of Soft Soil (m)
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
Figure A.6: Pile Capacity vs Pile Diameter for 12 mm deflection
Figure A.7: Pile Capacity vs Pile Diameter for 25 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
Cu = 10 kpaCu = 25 kpaCu = 50 kpaCu = 70 kpa
Pile Capacity vs Pile Diameter for 12 mm deflection
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
Cu = 10 kpaCu = 25 kpaCu = 50 kpaCu = 70 kpa
Pile Capacity vs Pile Diameter for 25 mm deflection
Pile Diameter (m)
Pile
C
apac
ity (K
N)
150
Fixed Head Condition
Figure A.8: Pile Capacity vs Pile Diameter for 6 mm deflection
Figure A.9: Pile Capacity vs Pile Diameter for 12 mm deflection
Figure A.10: Pile Capacity vs Pile Diameter for 25 mm deflection
0
400
800
1200
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
400
800
1200
1600
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 12 mm deflection
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
Cu = 10 kpaCu = 25 kpaCu = 50 kpaCu = 70 kpa
Pile Capacity vs Pile Diameter for 25 mm deflection