affect of soil - foundation - structure interaction...
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AFFECT OF SOIL - FOUNDATION - STRUCTURE
INTERACTION ON SEISMIC BEHAVIOUR OF
PILE SUPPORTED FRAME BUILDINGS
Doctoral Thesis submitted by
Sushma Pulikanti (200612001)
in partial fulfillment of the requirement for the degree
of
Doctor of Philosophy in
Civil Engineering
International Institute of Information Technology - Hyderabad
June 2013
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AFFECT OF SOIL - FOUNDATION - STRUCTURE
INTERACTION ON SEISMIC BEHAVIOUR OF
PILE SUPPORTED FRAME BUILDINGS
Doctoral Thesis submitted by
Sushma Pulikanti (200612001)
in partial fulfillment of the requirement for the degree
of
Doctor of Philosophy in
Civil Engineering
(with specialization in Structural Engineering)
International Institute of Information Technology – Hyderabad
June 2013
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Certificate
It is certified that the work contained in this thesis, titled “Affect of Soil – Foundation –
Structure Interaction on Seismic Behaviour of Pile Supported Frame Buildings” by
Ms Sushma Pulikanti, has been carried out under my supervision and to the best of my
knowledge has not been submitted elsewhere for a degree.
Advisor: Ramancharla Pradeep Kumar
Professor of Civil Engineering
Earthquake Engineering Research Centre
International Institute of Information Technology - Hyderabad
June 2013 Hyderabad 500032
India
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Copyright © Sushma Pulikanti, 2013
All Rights Reserved
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Dedicated to my Parents Smt. Pushpa Mohan and Sri. Mohan Reddy, my husband Sri. Ramesh,
my brother Lalith, sister Ramya and my sons Jashvin Reddy and Thanish Reddy whose
continuous support, love and encouragement helped me in fulfilling my dream.
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Abstract The main objective of this research is to contribute to the understanding of the seismic
performance of superstructure considering the complex dynamic interaction between
superstructure, the pile foundation and the soil. As the dynamic response of the structure and the
pile to large extent is inelastic, the primary focus is on studying the behaviour of superstructure
by modeling the nonlinearities of soil, modeling the interface between pile and soil.
To address this problem, a Finite Element Method is used to model soil structure interaction
analysis of pile supported framed structures by programming in MATLAB R2009a using Direct
Method. A parametric study is conducted to understand the pile soil behaviour (Soil Foundation
Interaction (SFI)) by changing various parameters, like pile and soil modulus, pile length, pile
diameter and number of piles of the pile group. In each case the response is converted to
frequency domain to understand the shift in frequency.
Further, an attempt has been made to understand that complex behaviour of Soil Foundation
Structure Interaction (SFSI). For that purpose, a 5 storey pile supported frame structure is
modeled and its nonlinear behaviour under strong earthquake excitations is studied. A
comparison of linear and nonlinear responses and the effect / significance of soil inelasticity on
the structural response are commented.
A SFSI system is modeled by considering the nonlinearity at the interface of the soil and pile.
For that purpose, an interface element is used to model the interface between pile and soil.
Parametric study has been carried out to know the response of pile with and without interface
element and also to know the response of pile supported framed buildings with and without
interface element.
Besides this, the change in response of a high rise structure when a group of adjacent pile
supported structures are present under seismic excitation is also studied (Structure Soil Structure
Interaction (SSSI)). Different case studies are considered, namely 1. the group effect of
structures supported on piles are considered (like group of two identical structures, group of
three identical structures and group of three different structures), 2. the effect of variability in
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structure height is considered (like 5 storey structure, 10 storey structure and 15 storey structure)
and 3. the effect of variability in structure shape is considered. For each case, the SSSI response
is compared with the conventional fixed base response to understand the significance of SSSI.
Few quantitative conclusions as mentioned below are made out of this study by commenting the
significance of each behaviour (free field over SFI, SFSI over fixed base analysis, SSSI over
fixed base analysis).
The presence of soil and foundation in a SSI make a considerable change in response of the
structure with a shift of natural period of the system.
A peculiar behavior in the stress state of pile is observed for both elastic and inelastic soils, this
behavior is because of Soil resistance acting downwards along the pile shaft because of an
applied transient load.
Repeated dynamic contacts of soil and pile is observed for both SFSI and SFI, this is because of
the lateral compression of soil leading to formation of gap between pile and soil. The behavior
on stress state of pile is very much different for the case of analysis with Interface elements.
SSSI effects have been found to be important, when a group of identical structures with same
dynamic characteristics are present,. The middle structures are attracting more displacements
because of trapping of seismic waves. In case of group of structures with variable height, while
considering SSI there is a decrease in response for 15 storey structure when compared to 10
storey structure which is not observed in fixed base system. In case of response of structures of
variable shape the top floors will attract more displacement because of reduced stiffness on top
floors but in conventional fixed base case opposite behavior is observed.
So it has been recognized from this study that a reasonable seismic analysis for high rise
buildings supported on pile foundations is needed to produce a safe and economic design.
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Acknowledgements
First and foremost, I express my sincere gratitude to my advisor Prof. Pradeep Kumar
Ramancharla for the continuous support of my PhD study and research, for his patience,
motivation, enthusiasm, and immense knowledge. His guidance helped me in all the time of
research and writing of this thesis.
I am fortunate enough to get valuable suggestions and advice from my thesis committee
Prof. M. Venkateswarlu, Prof. M R Madhav, Prof. C V R Murty and Dr. Neelima Satyam for their
encouragement, insightful comments, and hard questions.
I am thankful to get constant encouragement, support from all my Research colleagues,
the staff of Earthquake Engineering Research Centre (EERC) and my friends who helped me in
successful completion of my work. Also, I extend my sincere regards to all non teaching staff of
IIIT - H for their timely support.
I express my sincere gratitude to my loving in laws Smt. Revathi and Sri. Damodhar
Reddy for their continuous encouragement and support.
Sushma Pulikanti
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Table of Contents Certificate .................................................................................................................................III
Abstract .................................................................................................................................... VI
Acknowledgements ................................................................................................................ VIII
Table of Contents ..................................................................................................................... IX
List of Figures ......................................................................................................................... XII
List of Tables ......................................................................................................................... XVI
1. Introduction ...........................................................................................................................1
1.1 GENERAL INTRODUCTION ..........................................................................................1
1.1.1 Soil Structure Interaction .............................................................................................1
1.1.2 Pile Foundations ..........................................................................................................6
1.2 CHALLENGES INVOLVED ............................................................................................7
2. Literature Review ................................................................................................................ 13
2.1 SEISMIC BEHAVIOUR OF STRUCTURES SUPPORTED ON PILE FOUNDATIONS .............................................................................................................................................. 13
2.1.1 Summary of Framed Structures supported on pile foundations................................... 18
2.2 SCOPE AND OBJECTIVE ............................................................................................. 20
2.3 SEISMIC BEHAVIOUR OF GROUP OF PILE SUPPORTED STRUCTURES .............. 21
2.4 INTERFACE MODELING.............................................................................................. 22
2.4.1. Thin Layer Elements ................................................................................................ 22
2.4.2. Linkage Elements like discrete springs ..................................................................... 23
2.4.3. Other methods .......................................................................................................... 23
2.5 FINITE ELEMENT METHOD ........................................................................................ 25
2.6 ORGANIZATION OF THE THESIS ............................................................................... 37
3. Method of Analysis Adopted ............................................................................................... 39
3. 1 GENERAL INTRODUCTION ....................................................................................... 39
3.2 VALIDATION OF THE PROGRAM .............................................................................. 40
3.2.1 Geometry and Boundary Condition ........................................................................... 40
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3.2.2 Material Model .......................................................................................................... 43
3.2.3 Loading ..................................................................................................................... 44
3.3 VALIDATION ................................................................................................................ 46
3.3.1 Linear Analysis ......................................................................................................... 46
3.3.2 Nonlinear Analysis .................................................................................................... 48
3.3.2.1 Without Interface element ................................................................................... 49
3.3.2.2 With Interface element ........................................................................................ 49
3.4 RESULTS AND DISCUSSIONS .................................................................................... 51
3.4.1 Without Interface element ......................................................................................... 52
3.4.2 With Interface element .............................................................................................. 52
4. Seismic response of pile in linear soil medium ................................................................... 56
4.1 GENERAL INTRODUCTION ........................................................................................ 56
4.2 METHODOLOGY AND IMPLEMENTATION .............................................................. 56
4.3 PARAMETRIC STUDY .................................................................................................. 58
4.3.1 Modulus of Soil ......................................................................................................... 58
4.3.2 Pile Modulus / Grade of Concrete .............................................................................. 60
4.3.3 Pile length ................................................................................................................. 62
4.3.4 Number of piles in a group ........................................................................................ 62
4.3.5 Effect of different earthquakes ................................................................................... 64
5. Nonlinear Behaviour of Frame Structure with Pile Foundations ..................................... 68
5.1 GENERAL INTRODUCTION ........................................................................................ 68
5.2 METHODOLOGY AND IMPLEMENTATION .............................................................. 69
5.3 PARAMETRIC STUDY ................................................................................................. 71
5.3.1 Only Soil ................................................................................................................... 71
5.3.2 Pile with Linear and Nonlinear Soil ........................................................................... 71
5.3.3 Pile supported framed structure with linear and nonlinear soil ................................... 75
5.4 SIGNIFICANCE OF SOIL FOUNDATION STRUCTURE INTERACTION (SFSI) ...... 81
6. Nonlinear Behaviour of frame with pile foundations with and without Interface Element ................................................................................................................................................. 84
6.1 GENERAL INTRODUCTION ........................................................................................ 84
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6.2 METHODOLOGY AND IMPLEMENTATION .............................................................. 84
6.3 PARAMETRIC STUDY ................................................................................................. 86
6.3.1 Pile with and without interface elements .................................................................... 86
6.3.2 Pile supported frame buildings with and without interface elements .......................... 88
7. Linear Behaviour of Group of Pile Supported Structures ................................................. 90
7.1 GENERAL INTRODUCTION ........................................................................................ 90
7.2 METHODOLOGY AND IMPLEMENTATION .............................................................. 90
7.3 CASE STUDIES TO UNDERSTAND THE GROUP EFFECT OF STRUCTURES RESTING ON PILES ............................................................................................................ 93
8. Summary and Conclusions ............................................................................................... 106
8.1 SUMMARY .................................................................................................................. 106
8.2 CONCLUSIONS ........................................................................................................... 107
8.3 LIMITATIONS OF THE STUDY ................................................................................. 109
8.4 SUGGESTIONS FOR FUTURE WORK ....................................................................... 109
Appendix - A ......................................................................................................................... 111
References.............................................................................................................................. 113
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List of Figures Figure No. Figure Name Page No. Figure. 1.1 Direct Method of Soil-Structure Interaction 3 Figure. 1.2 Substructure Method of Soil Structure Interaction 3
Figure. 1.3 (a) Schematic diagram showing Tower (b) Schematic diagram showing Tower resting on soil 8
Figure. 1.4 (a) Schematic diagram showing Pile supported Jetty (b) Jetty 9
Figure. 1.5 (a) Schematic diagram showing Pile supported framed building (b) Framed Building 9
Figure. 1.6 (a) Schematic diagram showing on ground pipe line (b) Surface Pipe Line 10
Figure. 1.7 Type of Pile Supported Framed Building considered in this study 11
Figure. 2.1 Example of a structure and pile foundation developed using FEM (Cai et al, 2000) 14
Figure. 2.2 Deviation of ground acceleration (Cai et al. 2000). 14
Figure. 2.3 Effect of diameter on displacement for different configurations. (a) and (c) Series arrangement (b) and (d) Parallel arrangement (Chore et al. 2008 a)
16
Figure. 2.4 Typical building frame supported by group of piles (Chore et al. 2010) 17
Figure. 2.5 Different end conditions assumed to prevail at the pile tip (Chore et al. 2010) 18
Figure. 2.6 Schematic diagram showing Structure Soil Structure Interaction of group effect of structures 22
Figure. 2.7 Schematic of Thin Layer (Interface) Element Desai and Zaman et al, 1984 24
Figure. 2.8 Two dimensional Finite Element Model with Gap element in SAP 2000 Nonlinear (Chau et al., 2009) 24
Figure. 2.9 a. Separation or debonding at interface b. Rebonding at interface c. Stiffness envelope at interface.
25
Figure. 2.10 Mohr Coulomb Yield surface in principal stress space 35 Figure. 2.11 Newton Raphson Iteration. 36 Figure. 3.1 3D pile soil system considered for the study (Single Pile) 41 Figure. 3.2 3D pile group soil system considered for the study (Group pile) 41 Figure. 3.3 Eight-node Hexahedral element 42 Figure. 3.4 Stress strain model for soil material 44 Figure. 3.5 Stress strain model for pile material 45
Figure. 3.6 Acceleration Time history and Fourier Amplitude of May18, 1940 Elcentro Earthquake (NS) 46
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Figure. 3.7 Verification of pile head response as cantilever 47 Figure. 3.8 Response of single socketed pile for linear elastic case 49 Figure. 3.9 Response of single socketed pile for plastic soil case 50
Figure. 3.10 Comparison of Response of single socketed pile for elastic soil case with interface element- Present Study and Maheshwari et al., 2004 51
Figure. 3.11 Comparison of Response of single socketed pile for plastic soil case with gap element - Present Study and Maheshwari et al., 2004 52
Figure. 3.12 Response of single socketed pile and pile group for elastic soil case monotonic loading 53
Figure. 3.13 Response of single socketed pile and pile group for plastic soil case monotonic loading 53
Figure. 3.14 Response of single socketed pile for plastic soil case for the case of monotonic loading with and without Gap element 54
Figure. 3.15 Response of Pile group for plastic soil case for the case of monotonic loading with and without Gap element 54
Figure. 4.1 Typical mesh for 3dimensional Finite Element Analysis 57 Figure. 4.2 Acceleration time history of Mar 24, 1995 Chamba Earthquake (NE) 58
Figure. 4.3 Fourier Amplitude spectrum of Mar 24, 1995 Chamba Earthquake (NE) 59
Figure. 4.4 Free field response of different soil strata under Mar 24, 1995 Chamba Earthquake (NE) 60
Figure. 4.5 Fourier Amplitude Spectrum of different soil strata under Mar 24, 1995 Chamba Earthquake (NE) 61
Figure. 4.6 Fourier Amplitude Spectrum of pile and soil for various soil strata under Mar 24, 1995 Chamba Earthquake (NE) 61
Figure. 4.7 Comparison of Fourier Amplitude Spectrum of only soil and pile soil for very soft clay under Mar 24, 1995 Chamba Earthquake (NE) 62
Figure. 4.8 Response of single pile soil for various grades of concrete under Mar 24, 1995 Chamba Earthquake (NE) 63
Figure. 4.9 Response of single pile soil for various pile lengths under Mar 24, 1995 Chamba Earthquake (NE) 63
Figure. 4.10 3D model of different pile groups considered 64
Figure. 4.11 Response of various pile groups under Mar 24, 1995 Chamba Earthquake (NE) 65
Figure. 4.12 Comparison of Fourier Amplitude Spectrum of various earthquakes 66 Figure. 4.13 Fourier Amplitude Spectrum of pile soil for various earthquakes 66
Figure. 4.14 Fourier Amplitude Spectrum of pile soil response of May 18, 1940 Elcentro Earthquake (NS) 67
Figure. 4.15 Pile soil response and Fourier Amplitude Spectrum of May 18, 1940 Elcentro Earthquake (NS) 67
Figure. 5.1 3D Framed structure considered for the analysis 69 Figure. 5.2 3D Pile supported framed structure considered for the analysis 70
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Figure. 5.3 Comparison of dynamic response FEM and SAP under May 18, 1940 Elcentro Earthquake (NS) 71
Figure. 5.4 Comparison of dynamic response of linear and nonlinear analysis only soil under May 18, 1940 Elcentro Earthquake (NS) 72
Figure. 5.5 Comparison of Fourier Transform of linear and nonlinear analysis only soil under May 18, 1940 Elcentro Earthquake (NS) 72
Figure. 5.6 3D Soil Foundation model considered for the analysis 73
Figure. 5.7 Comparison of linear and nonlinear analysis of response of centre of soil when considering soil foundation interaction under May 18, 1940 Elcentro Earthquake (NS)
73
Figure. 5.8 Comparison of Fourier Transform of linear and nonlinear analysis of response of middle of soil when considering soil foundation interaction under May 18, 1940 Elcentro Earthquake (NS)
74
Figure. 5.9 Variation of stress along the length of pile under May 18, 1940 Elcentro Earthquake (NS) (pile 1 under cap 1 (Linear)) 75
Figure. 5.10 Variation of stress along the length of pile under May 18, 1940 Elcentro Earthquake (NS) (pile 2 under cap 1 (Linear)) 76
Figure. 5.11 Variation of stress along the length of pile under May 18, 1940 Elcentro Earthquake (NS) (pile 1 under cap 1 (Nonlinear)) 76
Figure. 5.12 Variation of stress along the length of pile under May 18, 1940 Elcentro Earthquake (NS) (pile 2 under cap 1 (Nonlinear)) 77
Figure. 5.13 Acceleration response of top floor linear and nonlinear analysis under May 18, 1940 Elcentro Earthquake (NS) 77
Figure. 5.14 Fourier transform of top floor linear and nonlinear analysis under May 18, 1940 Elcentro Earthquake (NS) 78
Figure. 5.15 Stress of pile 1 under cap 1for linear analysis considering SFSI under May 18, 1940 Elcentro Earthquake (NS) 78
Figure. 5.16 Stress of pile 1 under cap 1 linear both FI and SFSI at pile head under May 18, 1940 Elcentro Earthquake (NS) 79
Figure. 5.17 Stress of pile 1 under cap 1 nonlinear both FI and SFSI at pile head under May 18, 1940 Elcentro Earthquake (NS) 80
Figure. 5.18 Acceleration response of pile cap and top floor linear analysis considering SFSI under May 18, 1940 Elcentro Earthquake (NS) 80
Figure. 5.19 Acceleration response of pile cap and top floor nonlinear analysis considering SFSI under May 18, 1940 Elcentro Earthquake (NS) 81
Figure. 5.20 Comparison of acceleration response SFSI and FBA systems under May 18, 1940 Elcentro Earthquake (NS) 82
Figure. 5.21 Comparison of Fourier Transform of SFSI and FBA systems under May 18, 1940 Elcentro Earthquake (NS) 83
Figure. 6.1 3D Soil Foundation Interaction Model with Linkage / Gap element 85
Figure. 6.2 Comparison of acceleration response at pile cap with and without link element (FI) under May 18, 1940 Elcentro Earthquake (NS) 86
Figure. 6.3 Comparison of Fourier amplitude spectrum of pile cap with and without link element (FI) under May 18, 1940 Elcentro Earthquake (NS) 87
XV
Figure. 6.4 Stress of pile 1 under cap 1 for FI with link elements under May 18, 1940 Elcentro Earthquake (NS) 87
Figure. 6.5 Comparison of acceleration response of top floor with and without link elements under May 18, 1940 Elcentro Earthquake (NS) 88
Figure. 6.6 Comparison of Fourier amplitude spectrum of top floor with and without link element under May 18, 1940 Elcentro Earthquake (NS) 89
Figure. 7.1 Schematic diagram showing Structure Soil Structure Interaction of group effect of structures 91
Figure. 7.2 Finite model of soil pile frame system 91 Figure. 7.3 Schematic diagram showing variability in structure height 92 Figure. 7.4 Schematic diagram showing variability in structure shape 93 Figure. 7.5 Schematic diagram of fixed base system 94
Figure. 7.6 Response of single building under May 18, 1940 Elcentro Earthquake (NS) (Fixed base system and SSI) 95
Figure. 7.7 Response of two identical buildings under May 18, 1940 Elcentro Earthquake (NS) 95
Figure. 7.8 Fourier Amplitude Spectrum of two identical buildings under May 18, 1940 Elcentro Earthquake (NS) 96
Figure. 7.9 Response of three identical buildings under May 18, 1940 Elcentro Earthquake (NS) 97
Figure. 7.10 Fourier Amplitude Spectrum of three identical buildings under May 18, 1940 Elcentro Earthquake (NS) 98
Figure. 7.11 Response of three different buildings under May 18, 1940 Elcentro Earthquake (NS) 99
Figure. 7.12 Fourier Amplitude Spectrum of three different buildings under May 18, 1940 Elcentro Earthquake (NS) 99
Figure. 7.13 Fundamental mode shapes of Structures of variable 100
Figure. 7.14 Response of Structures of variable height with SSI under May 18, 1940 Elcentro Earthquake (NS) 101
Figure. 7.15 Fourier Amplitude Spectrum of structures of variable height with SSI under May 18, 1940 Elcentro Earthquake (NS) 101
Figure. 7.16 Response of structures of variable height without SSI under May 18, 1940 Elcentro Earthquake (NS) 102
Figure. 7.17 Fourier Amplitude Spectrum of structures of variable height without SSI under May 18, 1940 Elcentro Earthquake (NS) 103
Figure. 7.18 Fundamental mode shapes of structures of variable shape 103
Figure. 7.19 Response of structures of variable shape with SSI under May 18, 1940 Elcentro Earthquake (NS) 104
Figure. 7.20 Response of structures of variable shape without SSI under May 18, 1940 Elcentro Earthquake (NS) 105
Figure. A1 Influence factor IPH for free head Socketed pile in uniform soil b. Yield deflection factor FPF for fixed head pile in uniform soil, Poulos and Davis, 1980
112
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XVII
List of Tables Table No. Table Name Page No.
Table 1.1 Soil Properties 42
Table 4.1 Properties of the Material 58
Table 4.2 Properties of Various Clay 60
Table 7.1 Properties of the Material 93
1
Chapter 1
1. Introduction 1.1 GENERAL INTRODUCTION
After 1994 Niigata earthquake (M 7.5), it was evident that damage to the structure not only
depends on the behavior of super structure but also on the sub-soil below it. Since then, many
researchers have studied the behavior of the soil subjected to the dynamic loading. Investigations
were done experimentally, analytically, numerically and also field observations. From these
investigations, it was understood that the response of soil to dynamic loads plays a major role in
the damage of structures. The behavior of soil becomes much complex and several factors needs
to be considered.
Before starting the actual literature review a brief introduction to Soil Structure Interaction and
Pile Foundations are given in the following sections of this chapter.
1.1.1 Soil Structure Interaction
Since 1960’s, soil-structure interaction (SSI) has been recognized as an important factor that may
significantly affect the relative building response, the motion of base and motion of surrounding
soil (Todorovska and Trifunac, 1990). In general, building-soil interaction consists of two parts;
kinematic and dynamic (or inertial) interaction. The former is a result of wave nature of
excitation and is manifested through the scattering of incident waves from building foundation
and through filtering effect of the foundation that may be stiffer than the soil and therefore may
not follow the higher frequency deformations of soil. This interaction depends on frequency,
angle of incidence and type of incident waves, as well as shape of foundation and on the depth of
embedment. It develops due to presence of stiff foundation elements on or in soil cause
foundation motion to deviate from free-field motions. The later is due to inertia forces of
building and of the foundation which act on soil due to contact area. And it depends on the mass
and height of the building and the mass and depth of foundation, on the relative stiffness of soil
2
compared with the building and on the shape of foundation. It develops in structure due to its
own vibrations which gives rise to base shear and base moment, which in turn cause
displacements of the foundation relative to free field.
Dynamic analysis of soil-structure interaction can be done using
a. Direct Method
b. Substructure Method
a. Direct Method
Direct Method is one in which the soil and structure are modeled together in a single step
accounting for both inertial and kinematic interaction. Inertial interaction develops in structure
due to own vibrations give rise to base shear and base moment, which in turn cause
displacements of the foundation relative to free field. Kinematic interaction develops due to
presence of stiff foundation elements on or in soil cause foundation motion to deviate from free-
field motions. As illustrated in Figure. 1.1, the earthquake ground motions are specified at the
base and the resulting response of the interacting system is computed from the following
equation of motion (Kramer, 2003)
systemtheofonacceleratiandvelocitynt,displacemeare,,and;onAcceleratiGround
put;matricesstiffnessanddamping,massare][,][,][Where
)1.1(
...
..
.....
uuu
u
uuuu
IngsKCM
gsMkcM
b. Sub-Structure method or Multistep Method
Sub-Structure Method is one in which the analysis is broken down into several steps that is the
principal of superposition is used to isolate the two primary causes of soil-structure interaction,
inability of foundation to match the free field deformation and the effect of dynamic response of
structure foundation system on the movement of supporting soil.
3
Kinematic interaction
The deformation due to kinematic interaction alone can be computed by assuming that
foundation has stiffness, but no mass as shown in Figure. 1.2 a. The equation of motion for this
case is (Kramer, 2003)
)2.1(..
*..
gsMukuCM uu soilKIKIKIsoil
Pile Pile
a. Kinematic Interaction analysis b. Inertial interaction analysis
Structure Massless Structure
Structure
Seismic Shaking
Figure. 1.1 Direct Method of Soil-Structure Interaction
u gs
u g s u g s
Figure. 1.2 Substructure method of Soil Structure Interaction
Soil
Soil
Pile
4
Inertial interaction
The structure and foundation (Figure. 1.2 b) do have mass and this mass cause them to respond
dynamically. The deformation due to inertial interaction can be computed from the following
equation of motion (Kramer, 2003)
ninteractioinertialtoduentDisplacemeuand
;onAcceleratiGroundInputgs;systementireofmatrixDampingisc;system
entireofStiffnessis][k;lessmassissoilassumingmatrixmasstheis][
)3.1(
II
..
*
....*
..
ustructure
structureIIIIII
MWhere
gsKIMukucM uuu
The right side of the above equation represents the inertial loading on the structure-foundation
system. This inertial loading depends on the base motion and the foundation input motion, which
reflects the effects of kinematic interaction. In the inertial interaction analysis, the inertial
loading is applied only to the structure; the base of the soil deposit is stationary. The solution to
the entire soil-structure interaction problem is equal to the sum of the solutions of kinematic and
inertial interaction analysis (Zhang and Wolf, 1998).
Generally, in modeling the infinite media problems, two complementary regions can be
distinguished; namely the interior (i.e., a neighborhood of the structure encompassing
heterogeneities, irregularities and nonlinearities) and the exterior (typically a horizontally layered
medium extending to great extent, usually assumed infinite, distance from the structure). Finite
elements have been the most common choice of interior discretization by virtue of their
versatility in dealing with the complexity of this region. On the other hand, the exterior has been
represented by means of a “transmitter” or “absorber” placed on the boundary of the interior.
(Murthy et al. 2004).
In any numerical analysis, results of acceptable accuracy can be obtained by using an
approximate boundary condition. A simple solution to the problem is to move the boundary a
great distance away from the finite structure so that the boundary does not influence results. But,
this violates the concept of computational efficiency. Hence, an artificial boundary condition to
5
simulate a model without any finite boundary is needed. In literature there, are two basic
approaches to this boundary condition, namely (a) create boundary elements with special
properties which allow energy to propagate only from the interior to exterior region that is
transmitting boundaries and (b) create infinite elements.
Transmitting boundary conditions have been introduced since the late 1960s. Most of them are
based on the mathematical representation of plane wave propagation to eliminate the incident
waves at special angle of incident. Lysmer and Kuhlemeyer (1969) proposed the first
transmitting boundary for elastodynamics often referred to as the classical viscous boundary
condition. It absorbs plane waves propagating perpendicularly to the artificial boundary. The
viscous boundary condition can easily be implemented in finite element codes for both frequency
domain and transient analyses. It is algorithmically simple, geometrically universal and
frequency independent. As dashpots have no static stiffness, the viscous boundary condition is
not able to model a static problem as the limiting case of a dynamic problem at low frequency.
Smith (1974) proposed the super position boundary condition to solve both the scalar and elastic
wave propagation problems. The superposition boundary averages the solutions from two sets of
boundary conditions corresponding to symmetry and anti-symmetry, which eliminate the
reflected waves for a single boundary. The formulation is independent of both frequency and
angle of incidence. This boundary condition is unable to eliminate multiple reflections. The
superposition boundary condition was later modified to overcome multiple reflections by
introducing two over lapping narrow boundary neighborhoods in which the reflected waves are
canceled as they occur (Cundall et al. 1978; Kunar and Marti, 1981). Subsequently another
transmitting boundary called the doubly-asymptotic boundary condition for dynamic SSI
(Underwood and Geers, 1981). In this boundary, dashpots and coupled static springs are used
which are asymptotically exact at high and low frequencies for plane waves propagating
perpendicularly to the boundary, respectively. Boundary element method was used to determine
the static-stiffness matrix for the medium leading to fully coupled and non-symmetric
coefficients. The doubly-asymptotic boundary results in errors for modeling the intermediate
frequencies. The approach is temporally local, but spatially global (Bazyar, 2007).
Infinite elements (Bettess and Zienkiewicz, 1977; Astley, 2000) have been developed based on
the finite element technology to absorb outgoing waves to infinity. In this method, decay
6
functions representing the wave propagation towards infinity are used as shape functions of the
displacement. The decay rate and phase velocity must be specified. Most of its developments
have been carried out in the frequency domain. They tend to not performing well in a transient
analysis since the shape of waves is not specified and changing with time.
In the past various damages has been evidenced in the event of major earthquakes, not only
because of structural damage but also due to failure of foundation soil. Few cited examples on
this include the 1985 Mexico earthquake where the damages on 10-12 stories buildings were
observed with partial bearing capacity failure of foundation soil (Mendoza et al, 1988), the 1995
Kobe earthquake where the collapse and overturning of Hanshin expressway is observed because
of sudden increase in natural period with interaction effects, also major collapse of Daikai station
due to poor load transfer mechanisms from soil to structure and interface effects (Montesinos et
al. 2006). In the more recent Haiti earthquake of January 12, 2010, collapse of several buildings
has observed because of deeper rotation failure due to movement of soils (Rathje et al, 2010).
After giving the basic introduction about the topic soil-structure interaction, types of interaction,
methods for solving it, damages that have occurred in the past etc., from next section onwards
we see the details of pile foundations.
1.1.2 Pile Foundations
Pile foundation is a popular method of construction for overcoming the difficulties of foundation
on soft soils. But, until nineteenth century the design was entirely based on experience (Poulos
and Davis, 1980).
It is only too convenient for an engineer to divide the design of major buildings into two
components: the design of the structure and the design of foundations. But in reality, the loads on
foundation determine their movement, but this movement affects the loads imposed by the
structure; inevitably interaction between structure, foundation and soil or rock forming the
founding material together comprise one interacting structural system (Poulos and Davis, 1980).
Significant damage to pile supported structures during major earthquakes (such as 1906 San
Francisco earthquake, 1964 Niigata and Alaska earthquakes) led to an increase in demand to
reliably predict the response of piles. Since then, extensive research have been carried out and
7
several analytical and numerical procedures have been developed to determine the static and
dynamic response of piles subjected to horizontal or vertical loads. Also, full scale experimental
observations on the pile’s behavior and numerous model testing have been carried out. Details of
the same are given in the following sections of this thesis.
Observations of damage to pile foundation of buildings in recent major earthquakes also indicate
substantial instances of the damage at deeper part of the piles. Generally such damages tend to be
common at interfaces of soil layers with prominent stiffness contrast. It is evident that the
damages occurring at deeper part of piles are inherently difficult to detect and practically
impossible to repair. Consequently, adequate provision in the design is indispensable to make
such damages as unlikely as possible.
Reports on the investigation of buildings with pile foundations affected by the Hyogoken-Nambu
earthquake of 1995 indicate reoccurrence of the nature of damage to PHC (Prestressed High
Strength Concrete) piles observed in the Miyagiken-oki earthquake of 1978. In addition, another
distinctive nature of the damage to relatively long piles was observed, where the failure was seen
at deeper parts of relatively long piles and at locations close to distinct soil layer interfaces. Such
failure to piles seem to result due to the existence of lateral stiffness contrast between adjacent
soil layers, including the liquefaction and loss of strength at an intermediate layer (Sugimura et
al, 2001).
A number of approaches have been formulated for the analysis of dynamic soil-pile interaction in
the past years. The research work carried out in the area of seismic soil-pile foundation structure
interaction could be most generally classified into determination of kinematic seismic response
that is determination of pile-head impedance and determination of superstructure seismic
response. Challenges involved in soil-structure interaction are given in the following section.
1.2 CHALLENGES INVOLVED
The seismic excitations experienced by structures is a function of the earthquake source, travel
path effects, local site effects and Soil-structure interaction (SSI) effects. The result of first three
factors is a “free field” ground motion. The structural response to free field motion is influenced
by SSI. In particular, acceleration within the structure is affected by the flexibility of foundation
8
support and variation between foundation and free field motions. Consequently, an accurate
assessment of inertial forces and displacements in structures requires a rational treatment of SSI
effects (Stewart et al, 1999).
SSI analysis procedures are important in various cases of structural and soil conditions. Some of
them are briefly outlined here. Type A structures like Rigid Tower (Figure. 1.3), in which the
supporting soil media will go to nonlinearity and the structure will remain in linear state only.
Type B structures like pile supported Jetties (Figure. 1.4), in which the supporting pile and soil
will go to nonlinearity and the structure will remain in linear state only. Type C structures like
Frame Buildings (Figure. 1.5), in which the pile, soil and structure will go to nonlinear state
under strong seismic shaking. Type D structures like Pipes (Figure. 1.6), in which the supporting
soil media will go to nonlinear state under differential settlement and pipe, will also go to
nonlinear state, etc.,.
Figure. 1.3 Schematic diagram showing Tower
Tower
Layer 1
Layer 2
Layer 3
Figure. 1.3 (a) Schematic diagram showing Tower (b) Tower resting on soil (a)
(b)
9
Layer 1
Layer 2
Layer 3
Figure. 1.5 (a) Schematic diagram showing pile supported framed building (b) Framed Building
Figure. 1.4 (a) Schematic diagram showing Pile supported Jetty (b) Jetty
Jetty
Piles
Frame
Pile
Layer 1
Layer 2
Layer 3
(b)
(a)
(a) (b)
10
In this thesis, Type c structures like pile-supported frame buildings are studied by considering
the material nonlinearity and interface effects. The problem to be addressed is shown in Figure.
1.7. The actual system consisted of a 22m high six floor building called Port and Customs Office
Tower located in Kandla, near The Little Rann of Kachchh on the south eastern coast of the
Kachchh district. The building was founded on 32 short cast in place concrete piles and each pile
was 18m long. The piles were passing through 10m of clayey crust and then terminated in a
sandy soil layer below.
The challenges involved in this analysis are briefly given below.
Generally, a pile can be regarded as a stiff, slender body embedded in a much softer medium
which is soil. When a load is applied to pile, it deforms and interacts with the soil, resulting in
the development of interface pressure along the two media, the distribution of which depends on
applied load and soil-pile properties. So, the study of SSI is important in understanding the
complex behavior of soil and pile. In this thesis, an attempt is made to understand this behavior.
Obtaining appropriate radiation conditions for large-scale engineering problems is the most
challenging part of the dynamic soil-structure interaction. The disturbance travels as a wave in
the ground affecting a very large area, contrary to the static case, where the influence of load is
Figure. 1.6 (a) Schematic diagram showing on ground pipe line (b) Surface Pipe Line
Layer 1
Layer 2
Layer 3
Pipe line Supports
(a) (b)
11
confined to a limited area around the application point of load. In keeping with this point of
view, while performing dynamic analysis, care should be taken in modeling the boundaries.
Various techniques have been used by researchers Viscous boundary, Kelvin element, Infinite
elements, etc., to represent the infinite soil medium. In this research work the boundary has been
modeled by Viscous dampers such that the wave does not come back it attenuates in the ground,
resulting in a loss of energy or radiation damping.
But, what makes dynamic analysis even more difficult is the fact that under large dynamic
loading, the soil in the vicinity of the pile undergoes plastic deformation, thus changing the
response pattern considerably. Also, initial gaps may be developed between pile and soil. The
a. Actual system
20 m
2 m Super Structure
b. System Analyzed
Figure.1.7 Type of Pile Supported Framed Building considered in this study
12
effects of plastic deformation are modeled by considering the material nonlinearity of the soil
and the separation at soil-pile interface has been modeled by considering the
tension/Gap/interface elements. The formulation and detailed discussion on the same has been
given in the subsequent paragraphs.
With the above mentioned difficulties, a comprehensive rigorous solution has been developed
(using Finite Element Method) which could take into account all (nonlinear and interface effects)
aspects of the problem. The detailed discussion on all the issues mentioned above has been
addressed in the following chapters.
13
Chapter 2
2. Literature Review
2.1 SEISMIC BEHAVIOUR OF STRUCTURES SUPPORTED ON PILE
FOUNDATIONS
In this chapter, an attempt is made to bring out the complete state-of-the-art on dynamic analysis
of Framed structures supported on pile foundations. Along with this, a brief introduction about
seismic behaviour of group of pile supported structures and different interface models are given.
It also includes a detailed description about the Finite Element Method.
The work on frame structures supported on pile foundations has been started by Buragohain et al.
in 1977, who evaluated the space frames resting on pile foundation by means of the stiffness
matrix method in order to quantify the effect of soil-structure interaction using simplified
assumptions. In that study, the pile cap was considered to be rigid. The stiffness matrix for the
entire pile group was derived from the principle of superposition using the rigid body
transformation. The foundation stiffness matrix was then combined with the superstructure
matrix to perform the interactive analysis which was carried out in a single step to assess the
effect of soil-structure interaction on the response of structure in terms of change in member
forces and settlements.
After that on the same lines Cai, et al. in 2000 developed a three-dimensional nonlinear Finite
element subsystem methodology to study the seismic soil–pile–structure interaction effects
(Figure. 2.1). In that study the plasticity and work hardening of soil have been considered by
using δ* version of the HiSS modeling. Based on their studies it has been concluded that with the
plasticity-based soil model, the motion of the pile foundation deviated significantly from the
bedrock motion and this departure from the ground motion should not be overlooked in
14
evaluating the seismic kinematic response of pile-supported structures. Also, it has been
observed that the output of the pile head motion revealed an interesting phenomenon: that
although the bedrock input is horizontal, there are some vertical accelerations on the pile heads
(column bases) (Figure. 2.2).
Figure. 2.1 Example of a structure and pile foundation developed using FEM (Cai et al, 2000)
Figure. 2.2 Deviation of ground acceleration (Cai et al. 2000).
15
In Cai et al, work in 2000 the analysis was carried out on fixed boundary conditions and also
damping in the foundation subsystem was neglected. Moreover, the effects of soil nonlinearity
were not analyzed.
Later Yingcai in 2002 studied the seismic behavior of tall building by considering the non-linear
soil-pile interaction, in which a 20-storey building is examined as a typical structure supported
on a pile foundation using DYNAN computer program, leading to the conclusion that the
theoretical prediction for tall buildings fixed on a rigid base without soil-structure interaction
fails to represent the real seismic response, since the stiffness is overestimated and the damping
is underestimated.
Besides, in 2003 Lu et al, studied the dynamic soil-structure interaction of a twelve storey
framed structure supported on raft pile foundations using ANSYS, in which the influence of the
following parameters soil property, rigidity of structure, buried depth, dynamic characteristics on
SSI is studied. It has been observed that effect of SSI on displacement peak value of structure is
greater with increase of structural rigidity.
Ingle and Chore (2007) reviewed the soil-structure interaction (SSI) analysis of framed structures
and the problems related to pile foundations, and underscored the necessity of interactive
analysis to build frames resting on pile foundations by more rational approach and realistic
assumptions. It was suggested that flexible pile caps along with their stiffness should be
considered and the stiffness matrix for the sub-structure should be derived by considering the
effect of all piles in each group. But, the basic problem of the building frame is three
dimensional in nature. Although a complex three-dimensional finite element approach, when
adopted for the analysis, is quite expensive in terms of time and memory, it facilitates realistic
modeling of all the parameters involved. Along these lines, Chore and Ingle (2008 a) presented a
methodology for the comprehensive analysis of building frames supported by pile groups
embedded in soft marine clay using the 3-D finite element method. The effect of various
foundation parameters, such as the configuration of the pile group, spacing and number of piles,
and pile diameter, has been evaluated on the response of the frame. The analysis also considered
the interaction between pile cap and soil. It has been concluded that with the increase in pile
spacing and number of piles in a group, displacement at top of frame decreases. In addition, with
16
the increase in diameter of piles, displacement at top of frame decreases for any spacing owing to
the increased stiffness of pile group at higher diameter as shown in Figure. 2.3. Also the effect of
soil-structure interaction (SSI) is significant on bending moment, i.e. SSI is found to increase the
maximum positive bending moment by 14.01 % and maximum negative bending moment by
27.77 %.
Chore and Ingle (2008 b) reported an interaction analysis on the space frame with pile
foundations using the finite element method, wherein the foundation elements were modeled in
the simplified manner as suggested by Desai et al. (1981). The pile cap was idealized as two
dimensional plate elements, the piles as one dimensional beam elements, and the soil as linearly
elastic independent springs. In this way, the three dimensional pile foundations can be replaced
by an assembly of one dimensional beam elements, two dimensional plate elements and
equivalent springs. The memory requirement is about one tenth of that required by a three
dimensional modeling, making it rather easy to simulate the original complex problem.
Figure. 2.3 Effect of diameter on displacement for different configurations. (a) and (c) Series arrangement (b) and (d) Parallel arrangement (Chore et al. 2008 a)
17
In the studies made by Chore and Ingle (2008 a, b), an uncoupled analysis (sub-structure
approach) of the system of building frame and pile foundation was presented. By this
methodology, a building frame was analyzed separately with the assumption of fixed column
bases. Later, equivalent stiffness was derived for the foundation head and used in the interaction
analysis of the frame to include the SSI effect. More recently, Chore et al. (2009) presented an
interaction analysis for the building frame resting on the pile group using a coupled approach,
i.e., by considering the system of building frame - pile foundation - soil as a single combined
unit. Although such an analysis is computationally uneconomical, fair agreement has been
observed between the results obtained using coupled and uncoupled approaches.
Later Chore et al. in 2010 studied the effect of soil-structure interaction on a single-storey, two-
bay space frame resting on a pile group embedded in the cohesive soil (clay) with flexible cap
(Figure. 2.4). For this purpose a three dimensional Finite Element analysis is carried out
using substructure approach. A parametric study has been conducted to study the effects of pile
spacing, pile configuration, and pile diameter of the pile group on the response of super structure
for different pile tip conditions as shown in Figure. 2.5. The displacement at the top of the frame
is less for fixed base condition and increases by 42 to 103% when the SSI effect is incorporated.
Figure. 2.4 Typical building frame supported by group of piles (Chore et al. 2010).
18
Likewise, with the increase in pile spacing, the top displacement of the frame decreases. The
effect of end conditions at the pile tip is significant as well on the displacement. Though the
displacements obtained for the pinned tip and fixed tip are less than those for the free tip, the end
condition does not have appreciable effect for parallel configuration.
In the work of Chore et al. (2008 a, b, 2010) actual interaction with the soil and foundation has
been neglected by replacing the foundation columns with springs. Similarly, the combined effect
of kinematic and inertial interaction is also neglected by the substructure analysis.
More recently Deepa et al., in 2012 did a Linear static analysis using commercial package NISA
on a four bay frame, from which it has been observed that SSI effects increased the responses in
the frame up to the characteristic depth and decreased when the frame has been treated for twelve
storey RCC frame structure resting on pile foundations full depth.
Vivek et al., in 2012 presented a review on interaction behavior of structure-foundation-soil
system. In which he gave a brief description of research done by various researchers on linear,
nonlinear, elasto-plastic, plastic soil-structure interaction effects under static and dynamic
loading conditions.
2.1.1 Summary of Framed Structures supported on pile foundations
A three-dimensional nonlinear (HiSS) finite element sub-system methodology is used for
studying the seismic soil–pile–structure interaction effects. From the results it has been
Figure. 2.5 Different end conditions assumed to prevail at the pile tip (Chore et al. 2010)
19
concluded that with the plasticity-based soil model, the motion of the pile foundation deviates
significantly from the bedrock motion and this departure from the ground motion should not be
over looked in evaluating the seismic kinematic response of pile-supported structures (Cai et al.
2000).
The effect of soil-structure interaction on a single-storey, two-bay space frame resting on a pile
group embedded in the cohesive soil (clay) with flexible cap is studied using the finite element
analysis by Chore et al. Following conclusions are drawn
1. The effect of SSI on the top displacement of the frame is quite significant. The displacement
is less for fixed base condition and increases by 42 to 103% when the SSI effect is
incorporated.
2. With the increase in pile spacing, the top displacement of the frame decreases. With the
increase in the number of piles in a group under consideration, the displacement decreases.
3. The effect of SSI is significant on bending moment also. The SSI is found to increase the
maximum positive bending moment by 14.98 % and maximum negative bending moment by
27.20 % when compared with the absolute maximum bending moments calculated on the
premise of fixed column bases.
4. The parameters like configuration of pile group, number of piles and diameter of pile, and
end conditions for the pile tip have significant effects on the variation of bending moment in
superstructure columns.
After having a comprehensive literature survey in the previous section, following are the areas
identified which are to be addressed in the “Numerical analysis of pile supported framed
structures”.
1. Soil-structure interaction analysis of pile supported frame structure has not been studied by
considering the heterogeneous soil strata.
2. Soil-pile-structure interaction analysis of a building with infill walls has not been studied.
Under dynamic lateral loading, infill wall imparts considerable lateral stiffness to the
structure, hence the effect of the same must be incorporated in the dynamic analysis.
20
3. Soil-structure interaction analysis of unsymmetrical pile supported frame systems has not
been studied.
4. Under strong earthquake excitation, structure and soil adjacent to foundation work in plastic
range, but most of the present studies are aimed at elastic structural systems with nonlinear
soil models. So effect of interaction by taking nonlinearity of the structure is not studied.
5. A complete three dimensional model representing the soil-pile-frame structure interaction
system with nonlinear soil model and gap separation between pile and soil has not been
studied.
After identifying the areas which are to be addressed in the numerical analysis of pile supported
framed buildings, it has been observed that following are playing a major role in dynamic SSI
analysis 1. The nonlinearity of soil, 2. Contact between pile and soil and 3. Group effect of
neighboring pile supported structures. With the above mentioned problems the main objectives
and scope of this thesis has been given in the following section.
2.2 SCOPE AND OBJECTIVE
A significant number of cases of damage to piles and pile-supported structures during
earthquakes have been observed and from the investigations following them it has been
evidenced that response of soil to dynamic loads is playing a major role in the damage. The
behavior of this becomes much complex when it interacts with the superstructure and the
substructure, making the soil-structure interaction analysis as an important factor in dynamic
analysis. In view of this, there is a great need to understand the complex behavior of the
interaction effect of superstructure, substructure and the sub soil strata.
The main objective of this research is to contribute to the understanding of the seismic
performance of superstructure considering the complex dynamic interaction between
superstructure, the pile foundation and the soil. The Finite Element Method is used to model soil-
structure interaction analysis of pile supported framed structures by programming in
MATLAB R2008a and SAP. A Direct approach is used to model the SSI of five storey frame
building supported on group of piles. The main objectives are
21
1. Studying the dynamic behaviour of super structure by considering the nonlinearity of soil
2. Studying the dynamic behaviour of super structure by modeling the interface between pile
and soil.
3. Studying the dynamic behaviour of group of pile supported structures resting on
homogeneous soil strata.
By keeping in view the above mentioned objectives first a brief description about the Structure
Soil Structure Interaction of Group of Pile supported structures is given followed by methods of
interface modeling and implementation of Finite Element Method in this work (it also includes
the implementation of nonlinearity and interface modeling).
2.3 SEISMIC BEHAVIOUR OF GROUP OF PILE SUPPORTED STRUCTURES
The problem of interaction of adjacent structures through the underlying and surrounding soil
has also been studied in this thesis (Fig. 2.6). A very brief review of it is given in this section.
The study of Structure soil-structure interaction (SSSI) of nearby structures has been started by
the studies of Lee and Wisley in 1970’s, in which they have investigated the seismic response of
several adjacent nuclear reactors using a three dimensional scheme. After this Luco and Contesse
(1973) followed by Wong and Trifunac (1975), studied the problem of interaction between
infinite walls. Later Wang and Schmid (1992) used the finite element and boundary element
coupling models to investigate the dynamic interaction through the under lying or surrounding
soil between three dimensional structures founded on square foundations. Recently Tsogka and
Wirgin (2003) studied the seismic response of group of buildings anchored in soft soil layer
overlying a hard half space. More recently L. A. Padron et al., (2009) studied the dynamic
structure soil-structure interaction of nearby piled buildings under seismic excitation by using
BEM-FEM model. From their study it has been concluded that SSSI effects on group of
structures with similar dynamic characteristics are important.
After having the brief introduction about SSSI, in the following sections various methods of
Interface modeling is given.
22
2.4 INTERFACE MODELING
In any soil structure interaction analysis, relative movement of structure with respect to soil can
occur. The use of continuum elements, with compatibility of displacements, in a finite element
analysis of these situations prohibits relative movement at soil structure interface. Nodal
compatibility of finite element method constrains the adjacent structural and soil elements to
move together. Interface or joint elements as they are sometimes called, can be used to model
the soil structure boundary such as sides of wall or pile, or the underside of footing, etc.,
particular advantages of these type of modeling is the ability to vary the constitutive behavior of
the soil structure interface and to allow differential movement of the soil and structure, that is
stick or no slip, slip, debonding / separation and rebonding. Many methods like use of thin
continuum elements, linkage elements like discrete springs, special interface or joint elements,
etc., are used to model the discontinuous behavior at soil structure interface (David et al., 1999).
2.4.1. Thin Layer Elements
The formulation of thin layer element is based on the assumption that the behavior near the
interface involves a finite thin zone, rather than a zero thickness zone. The four basic modes of
deformation that an interface element undergo are sliding, separation, debonding and rebonding
h 1
d
l 1
u x
u y
Figure. 2.6. Schematic diagram showing Structure Soil Structure Interaction of group effect of structures
h 2
L1
l 2
L2
23
(Figure. 2.7). This behavior is achieved by adopting appropriate constitutive law for the element,
the details and applications of it are given in Desai and Zaman et al, 1984.
2.4.2. Linkage Elements like discrete springs
The linkage elements like discrete springs are characterized by contact stiffness k and gap
separation d (SAP 2000). They can be installed on both sides of the pile as shown in Figure. 2.8.
The nonlinear force deformation relation for the gap element is given by
StiffnessContactkδseperationgapIntialδWhereotherwise
δdifδdkf
;)0(0
)1.2(0)(
In this only two modes of deformation are considered d > 0 for opening mode and d < 0 for
closing mode (Chau et al., 2009).
2.4.3. Other methods
In this formulation, no special elements are used next to the pile but the soil elements adjacent to
pile are used for checking the modes of deformation. The separation / debonding of pile and soil
(as shown in Figure. 2.9 a) along with the rebonding (as shown in Figure. 2.9 b) of pile and soil
has been modeled by checking for the tension in soil elements adjacent to pile. For that purpose
the normal stresses in horizontal direction of all the soil elements adjacent to pile should be
checked for separation or debonding for each and every load step/iteration that is
(2.2)(Tensile)0x σ
In the separation mode, all those elements that are in tension does not impart any stiffness to the
system (as shown in Figure. 2.9c) in horizontal direction, so accordingly the normal stresses are
calculated with changed stiffness and the residual which have dimension of stress, are converted
into loads that are applied to system during iterative corrections, the procedure for convergence
is same as mentioned above for material nonlinearity case. In rebonding state all the elements
regain the stiffness and impart stiffness to the system.
)3.2(εdDσd new
24
Figure. 2.7 Schematic of Thin Layer (Interface) Element Desai and Zaman et al, 1984
Figure. 2.8. Two dimensional Finite Element Model with Gap element in SAP 2000 Nonlinear (Chau et al., 2009)
Load Original position
25
In this Thesis the second method is used that is linkage elements with springs for interface
modeling, the details of how it has been implemented in this work has been given in the
following chapters.
2.5 FINITE ELEMENT METHOD
Finite element analysis is a process in which the structure or continuum is idealized as an
assemblage of elements connected at nodes pertaining to the elements. The externally applied
forces are lumped to these nodes to obtain the equivalent nodal load vectors. The equivalent
nodal loads are equilibrated by the nodal point forces that are equivalent to the element
internal stresses. Compatibility and stress-strain relationships are exactly satisfied, but instead of
force equilibrium at the differential level, only global equilibrium for the complete structure, of
the nodal points and of each element under its nodal point forces is satisfied.
There are generally two approaches associated with the Finite Element Method. These are
1. Force or Flexibility Method, in which the internal forces are unknowns in the problem. In
this method to obtain the governing equations first equilibrium equations are written, then
additional equations are found by introducing compatibility equations. The resulted sets of
algebraic equations are solved for determining redundant or unknown forces.
Body 1
Body 2
Figure. 2.9 a. Separation or debonding at interface b. Rebonding at interface c. Stiffness envelope at interface.
Displacement
Compression
Tension
(a) (c)
Body 1
Body 2
Body 1
(b)
Original position Deformed position Deformed position
26
2. Displacement or Stiffness method, in which the displacements of nodes are unknowns in the
problem. In this the main assumption is the compatibility conditions requiring that the
elements connected at a common node along a common edge, or on a common surface before
loading remain connected at that node, edge or surface after deformation take place. Then
using the equations of equilibrium governing equations is expressed in terms of nodal
displacements and an applicable law relating the forces and displacements are established.
These two approaches results in different unknowns (forces or displacements) in the analysis and
different matrices associated with their formulations (flexibilities or stiffness’s). It has been
shown that for computation purpose displacement approach is more desirable because its
formulation is simpler for most structural analysis problems. So in this thesis, Displacement or
Stiffness method is used to find the solution of the problem (Logan, 2002).
Following is the procedure generally followed in the Finite Element formulation (Displacement
or Stiffness Method) of a problem.
Step 1. Involves dividing the body into equivalent system of finite elements with associated
nodes and choosing the most appropriate element type to model the actual behavior
Step 2. Involves choosing the displacement function within each element. The function is
defined with in using the nodal values of element. Linear, quadratic and cubic polynomials are
frequently used functions because they are simple to work with in finite element formulation. For
a three dimensional element, u, v, w are the displacements associated with the x, y and z
directions. The functions are expressed in terms of nodal unknowns (in the three dimensional
problem, in terms of an x, y and a z component). The same general displacement function is used
repeatedly for each element.
Step 3. Involves deriving the strain/displacement and stress/strain relationships for each finite
element. The stress must be related to strains through the stress/strain law generally called
Constitutive law. The ability to define material behavior accurately is most important in
obtaining acceptable results. The stress strain relation is given by Eq. 2.4.
27
)4.2(
)221
(00000
0)221
(0000
00)221
(000
0001000)1(000)1(
)21()1(a
γγγεεε
υ
υ
υυυυ
υυυυυυ
υυE
τττσσσ
xy
zx
zy
z
y
x
xy
zx
zy
z
y
x
ratiosPoissonυelasticityofModulusEStrainsShearγγγStrainsNormalεεεStressesShearτττStressesNormalσσσWhere
xyzxzy
zyxxyzxzyzyx
';;,,;,,;,,;,,
b)4.2(][
asformimplifiedinwrittenbecanaEq.2.4aboveThe
εDσ
s
For a linear elastic material the [D] matrix takes the above form. Since the problems in
Geotechnical engineering can be expressed either as fully drained problems or fully undrained
behavior. The constitutive behavior for the above cases can be expressed in terms of total
stresses ( σ = σ` + σf ).
straininchangethetopressurefluidporeinchangetherelatingiprelationshveConstituti][
)4.2()][][(
;][;'
''
f
f
ff
DWherecεDDσTherefore
εDσεDσ
For fully drained problems in which there is no change in pore fluid pressure, pf = 0. This
implies that changes in effective and total stresses are same, i.e. { σ ‘ = σf} and that the [D]
matrix contains the effective constitutive behavior. For undrained behavior, the change in pore
fluid pressure is related to the volumetric strain via the bulk compressibility of the pore fluid
(David et al., 1999).
In this thesis work it has been assumed as fully drained behavior so changes in pore fluid
pressure are not considered.
28
Step 4. Involves derivation of element stiffness matrix and equations for three dimensional
elements. The principle of virtual work, the principle of minimum potential energy and
Castiglione’s theorem are frequently used methods for deriving element equations. In this thesis
Principle of virtual work is used to derive the general finite elements equations for a dynamic
system. The principle of virtual work is stated as follows “If a deformable body in equilibrium is
subjected to arbitrary virtual (imaginary) displacements associated with a compatible
deformation of the body, the virtual work of external forces on the body is equal to the virtual
strain energy of the internal stresses.”
Applying the principle to a finite element, we have
elementtheonforcesexternalofworkVirtual;stressesinternaltodueenergystrainVirtualWhere
)5.2()()(
)()(
ee
ee
WδUδWδUδ
The internal virtual strain energy can be expressed using matrix notation as
)6.2()( adVσδεUδV
Te
From above Eq. 2.5 b, we can observe that internal strain energy is due to internal stresses
moving through virtual strains . In turn the external virtual work is due to nodal, surface and
body forces. The external virtual work can be expressed as
matrixvolumeunitperforceBody;matrixareaunitperforceSurfacematrixLoadNodal;occurstractionsurfacewheresurfaceheoveracting
fuctionsntdisplacemevirtualofVector;,,fuctionsntdisplacemevirtualofVector;ntsdisplacemenodalVirtualofVectorWhere
)6.2()()(
XTPt
δψwδvδuδδψdδ
bdVψρXδψdSTδψPdδWδ
s
V
T
S
TS
Te
Substituting Eq. 2.6 a and Eq. 2.6 b in Eq. 2.5, we obtain
)7.2()( V
T
S
TS
T
V
T dVXdSTPddV
The shape functions are independent of time and they are used to relate the displacement
functions to nodal displacements as
29
occursTtractionwheresurfacetheonevaluatedmatrixfunctionShapeNWhere)8.2(
S
dNψanddNψ Ss
Substituting the strain displacement relations, stress strain relations and shape functions into
Eq. 2.7, we obtain
)9.2()( V
TT
S
TS
TT
V
TT dVdNρXNdδdSTNdδPdδdVdBDBdδ
Because d (or dT) is the matrix of nodal displacements, which is independent of spatial
integration, we can write the above equation by taking the dT terms from the integrals to obtain
V
TT
S
TS
TT
V
TT dVdNρXNdδdSTNdδPdδddVBDBdδ )10.2()(
Since Td is an arbitrary virtual nodal displacement vector common to each term in Eq. 2.10, the
following relationship must be true
V V
TT
S
TS
V
T ddVNNρdVXNdSTNPddVBDB )11.2(
We now define
V
Tb
S
TSs
V
T
V
T
dVXNf
dSTNf
dVBDBk
dVNNρm
)15.2(forcesbodytodueloadsnodalEquivalentElement
)14.2(forcessurfacetodueloadsnodalEquivalentElement
)13.2(matrixStiffnessElement
)12.2(matrixMassConsistentElement
Using equations Eq. 2.12 - Eq. 2.15 in Eq. 2.11 and moving the last term of Eq. 2.11 to the left
side, we obtain
)16.2(bs ffPdkdm
30
The above equation (Eq. 2.16) is used for bodies subjected to dynamic (time-dependent) forces.
For static problems, we make dequal to zero in Eq. 2.16 to obtain
)17.2(bs ffPdk
Step 5. Assembling the element equations to obtain the global or total equations and introducing
boundary conditions. The individual element equations generated in Step 4 are now added
together using method of superposition (called Direct Stiffness Method) to obtain the global
equations for the whole structure on the basis of nodal force equilibrium. Implicit in the direct
stiffness method is the concept of continuity or compatibility, which requires that the structure
remain together and that no tears occur anywhere in the structure. The final assembled or global
equation written in matrix form is
ntsdisplacemegeneralizeorfreedomofdegreesnodalstructureunknownandknownofVectord
;matrixstiffnesstotalorglobalStructureK;forcesnodalglobalofVectorFWhere)18.2(dKF
Step 6. Solving for the unknown degrees of freedom or generalized displacements. The above
Eq. 2.18, which has been modified after taking into account boundary conditions, is a set of
simultaneous algebraic equations that can be written in expanded matrix form as
freedomofdegreesnodalunknownofnumbertotalStructurenWhere
)19.2(
.
.......
...
...
.
.
2
1
21
22221
11211
2
1
nnnnn
n
n
n d
dd
KKK
KKKKKK
F
FF
The above equations are solved for d’s by using an Elimination method (such as Gauss Method)
or an iterative method (such as Gauss-Seidel method).
31
Step 7. After finding displacements the important secondary quantities strain and stress (or
moment and shear force) can be obtained by using strain displacement and stress strain relations
(Logan 2002).
Step 8. Dynamic Analysis
In dynamic analysis, the additional fields required to understand the analysis are mass and
damping in addition to the stiffness. These three together resist the applied loads.
The earthquake ground acceleration Űgs is specified at the rigid bedrock layer and the resulting
response of soil structure interaction system is computed from the following equation of motion.
systemtheofonacceleratiandvelocitynt,displacemeare,,;onAccelerati
Ground;matricesstiffnessanddamping,massare][,][,][Where
)20.2(
...
..
.....
uuu
u
uuuu
gsKCM
gsMkcM
Broadly there are two approaches available for solving the above equation (Eq. 2.20) for
transient loads. The first is the method of Duhamel Integrals and the second the method of Direct
Numerical Integration (Madhu, 1993).
The Duhamel Integrals Approach is based on the superposition of the effects of impulses P dτ
from τ = 0 to τ = t. If an impulse I, act on mass m, the instantaneous velocity required by mass is
I/m. Hence, by knowing the solution for an applied initial velocity; we can evaluate the required
superposition. This approach is applicable only for linear problems.
In Direct Numerical Integration Approach, we assume that displacement, velocity and
acceleration are known up to a certain instant t = tn, and the corresponding ones at tn+1 =
tn + ∆t are proposed to be determined. These may be classified into Central Difference Scheme,
Newmark Scheme, Houbolt Scheme, Wilson θ Method etc.,
In this thesis the above Eq. (2.20) is constructed in incremental form using the Direct Numerical
Integration Approach (Newmark average acceleration method which is unconditionally stable for
32
any time step ∆t).
Newmark Scheme is popularly used in practice. This is derived in terms of two parameters β and
γ, which can be adjusted to yield different schemes. Newmark introduced these from a physical
viewpoint to include the effect of acceleration, at the end of interval on displacement and
velocity at the end of the interval. This scheme can be derived by assuming a cubic variation of
displacement within the interval ∆t.
)21.2(32 dcbau
With τ = t – tn, we determine the arbitrary constants in terms of 1,, nnnn uanduuu . These
give,
)22.2(6
16/)( 1 nnn
nnn
ut
tuud
ucubua
Here, nu is the acceleration increment during the time step. Substituting above equations into
Eq. 2.21 and setting τ = ∆t, we obtain
nn
nnn
nnn
nnnn
nnnn
nnnnn
uu
tuγuγutuγuu
tuuuu
tuβuβtuu
tuutuuu
1n1
1
1
1
2
1
21
uWhere
))1(()24.2(
21
)23.2(2
)2)21((
61
21
We obtain 1nu from Eq. 2.23 and using it in Eq. 2.22, we derive the expression for 1nu . These
are as follows
33
)25.2(12
1
12
1111
11
2121
nnnnn
nnnnn
utβγ
uβγ
utβ
γu
tβγ
u
uβ
utβ
utβ
utβ
u
The equation of equilibrium at t = tn+1 ( 1111 nnnn Pukucum ) then gives the following
equation to solve for un+1
)26.2(12
1
121111
2112
nnn
nnnnn
utuut
c
uut
ut
mPukct
mt
From the above equation Eq. 2.26, some observations are made. Firstly, when mass and damping
are absent, a case of static behavior is assumed, ku = P. Secondly, when stiffness and damping
are absent, the solution for the case of mass freely accelerating under the action of the applied
loads has to be obtained. In the similar there are situations of systems with mass and damping
only or stiffness and damping only. Lastly it has been observed that when P is absent, the
solution of free vibrations in terms of u and ů prescribed as initial conditions is obtained. For
average acceleration scheme γ = 1/2 and β=1/6 (Madhu, 1993).
Step 9. The dynamic analysis of structure subjected to dynamic loads is expected to provide a
time history of displacements, stresses and similar quantities of structure response. It also
provides certain dynamic characteristics of structure, such as natural frequencies.
For the linear case, the analysis is carried incrementally as mentioned above, but stiffness and
damping matrices remain constant throughout the analysis and no iterative procedure is required.
Step 10. Nonlinear Analysis
When Nonlinearity is included, matrices K and C do not remain constant but change after each
time step. But in this thesis only the degradation of stiffness (K) is considered.
34
Essentially, nonlinearity of structural problems is of two types. Geometric Nonlinearity and
Material Nonlinearity. The problems of first type arise on account of large displacements, and
those of second type, on account of nonlinear material properties. Generally as the displacements
become large the material response becomes nonlinear. There are also special situations which
render analysis nonlinear. These are special situations such as change in support conditions,
occurrence of contact or impulse conditions between parts of structures and similar situations.
In this thesis Material nonlinearity is considered when the stress strain relationship of the
material is nonlinear, the response of structure is also nonlinear. The main physical feature of
nonlinear material behavior is usually irrecoverability of strain. The simplest stress strain law of
this type that could be implemented in a finite element analysis involves elastic perfectly plastic
material behavior. To take into account complicated process like cyclic loading, transient
loading, yield surface in principal stress space which separates stress states that give rise to
elastic and plastic strains is used.
Algebraically, the surfaces are expressed in terms of a yield or failure function F. This function,
which has units of stress, depends on the material strength and invariant combinations of the
stress components. The function is defined such that it is negative within the yield or failure
surface and zero on the yield or failure surface. Positive values of F imply stresses lying outside
the yield or failure surface which are undefined and which must be redistributed via the iterative
process / increment analysis described as in preceding sections.
Various yield criteria like Tresca Criterion, Von Mises Criterion, Mohr Coulomb Criterion,
Drucker Prager Criterion, etc., are used generally for predicting the failure of different materials.
In this thesis Mohr Coulomb Criterion is used in predicting the failure of both soil and pile, as
this model is suitable for both brittle and ductile failures.
The Mohr Coulomb Yield criterion takes into account the influence of hydrostatic stresses. The
yield function is written in terms of stress states and two material properties the cohesion c and
angle of internal friction φ. For principal stresses in the order σ1 > σ2 > σ3, the Mohr Coulomb
Yield function is (assuming compression as negative)
)27.2(cos2sin)( 3131 cF
35
In principal stress space, the yield surface for Mohr Coulomb criterion has the form of an
irregular hexagonal pyramid as shown in Figure. 2.10. If a material such as concrete is studied
and the strength parameters σc and σt are known then following equations should be used to find
c and φ needed by Mohr Coulomb yield function.
)28.2(tan22
2
1
c
t
t
ctc
Consider that we are incrementing the load from Pn to Pn+1 by applying increment, dPn = Pn+1 –
Pn. The first approximate value is obtained from
)29.2(1)0()0(
nnnn dPPPduK
The first estimate of displacement at load level, Pn+1 is obtained as )0()1(1 nnn duuu . We then
compute Fn+1(1) by substituting the value un+1
(1) for U in calculating internal resistance. Since
un+1(1) is only approximation Fn+1
(1) will not be exactly equal to Pn+1. Hence, the value un+1(1) is
improved by seeking a correction. The requirement to be satisfied is the equation of equilibrium,
)30.2(011 nn FP
Figure. 2.10 Mohr Coulomb Yield surface in principal stress space
36
The initial steps show that Pn+1 – Fn+1(1) is represented by b2b3 and is not equal to zero (Figure.
2.11). The basis of iterative methods of the Newton Raphson type lies in applying corrections
proportional to this difference. First estimate of correction can be found by computing k(1), which
corresponds to slope of the curve at un+1(1). We compute the increment dun
(1) by solving,
)31.2()1(11
)1()1( nnn FPduK
Note : Load is increased from Pn to Pn+1. Increment dun(0) is the initial estimate. The internal
resistance, Fn+1(1) is the first estimate based on displacement, un+1
(1) . b2 b3 is the correction load applied, which determines dun
(1).
Therefore a better estimate of un+1 is obtained as )1(1
)1()2(1 nnn duuu . If we now compute Fn+1
(2)
corresponding to Un+1(2) , we observe that (Pn+1 – Fn+1
(2) ) is smaller than (Pn+1 – Fn+1(1)). In this
manner, we repeat the process until condition (Eq. 2.30) is satisfied to within acceptable
numerical tolerance.
The above iterative method is well known Newton Raphson method. This is expressed in general
terms as follows, with iteration count, I = 1, 2, 3…..
Figure. 2.11 Newton Raphson Iteration.
37
)(1
)()1(1
)(11
)()( )32.2(i
nnii
n
inn
in
i
duuuFPduK
For i=0, we have the initial solution when the load increment is applied
)0(1
)1(1
)0( )33.2(
nnn
nn
duuudPduK
Eqs. (2.32, 2.33) are the standard equations of Newton Raphson iterative method of solving a
nonlinear equation, F (u) = P. Let u be an approximate solution and let du be a correction to be
applied. As incrementing process is continued, the properties of the elements are changed
depending on the extent of plasticity effects (Madhu 1993).
Step 11. Interface Modeling
In this thesis the separation / debonding of pile and soil along with the rebonding of pile and soil
has been modeled by using the Linkage/Gap elements. That is linkage elements with springs for
interface modeling (Linkage elements are kept on either side of the pile as shown in Figure. 5.3).
For the Gap element the force deformation relation as given in Eq. 2.1 is used. To model this
gap element two input parameters has to be specified one the spring constant and d the gap
separation. The spring constant or contact stiffness k should be always 2 times stiffer than
surrounding element.
Step 12. The final goal is to interpret and analyze the results for use in the design/analysis
process. Determination of locations in structure where large deformations and large stress occur
is generally important. The results can be understood in a better way by displaying them in
graphical form.
2.6 ORGANIZATION OF THE THESIS
Chapter 1, presents a brief statement of problem with challenges involved.
Chapter 2, an attempt is made to bring out the complete state of art on dynamic analysis of
framed structures supported on pile foundations. Followed by objectives of the proposed
research. This chapter also covers comprehensively the analysis of Group of pile supported
38
structures, Methods for Interface Modeling and the Method of analysis adopted in this thesis
(Finite Element Method). In the last part, the organization of thesis are explained.
Chapter 3, presents the method of analysis adopted followed by its validation against available
solutions for Bench mark problems in the literature.
Chapter 4, gives Parametric study of seismic pile response in linear soil medium. For that
purpose a dynamic analysis has been carried to study the effect of different parameters on pile
response. The parameters include soil modulus, pile modulus, pile spacing, pile length, pile
diameter, number of piles of the pile group and earthquake characteristics.
Chapter 5, discusses Modeling of frame structure with pile foundation by considering the soil as
both linear and nonlinear. Parametric study has been carried out to know the response of pile
with linear and nonlinear soil and also to know the response of pile supported framed buildings
with linear and nonlinear soil.
Chapter 6, discusses Modeling of frame structure with pile foundations by considering the
nonlinearity of the interface of the soil and pile. An interface element is used to model the
interface between pile and soil. Parametric study has been carried out to know the response of
pile with and without interface element and also to know the response of pile supported framed
buildings with and without interface element.
Chapter 7, compares results of the dynamic soil-structure interaction of a high rise structure in a
visco elastic half space in the presence of nearby pile supported structures. Different case studies
are considered, one in which the group effect of structures supported on piles are considered like
group of two identical structures, group of three identical structures and group of three different
structures, second one in which the effect of variability in structure height is considered like 5
storey structure, 10 storey structure and 15 storey structure and the third one in which the effect
of variability in structure shape is considered.
Chapters 8, summarizes this study, and recalls salient conclusions of this research along with
recommendations for possible future research.
39
Chapter 3
3. Method of Analysis Adopted
3. 1 GENERAL INTRODUCTION
The Review of the Analysis of Pile supported Framed Buildings, indicates that Finite Element
method is widely used for the analysis of pile supported framed buildings. In which the majority
of the work was done by applying an Equivalent static load at the floor level and the study was
limited to the linear analysis of a single storied structure.
Contrary to many similar research efforts, in which the real aim of the seismic analysis is to get
the dynamic response of superstructure, this work is primarily concerned with changes in the
response of superstructure by taking the soil yielding effects and also the interface effects
between the pile and soil into consideration. The study in this Thesis is important as the soil
undergoes to nonlinear state at a very low strain levels and also during dynamic loading a gap is
developed between soil and pile leading to reduction in stiffness of system. As the static analysis
approximate the response to a large extent a detailed dynamic analysis is necessary to understand
the real behavior of the superstructure. So the main aim in this Thesis is to understand the
complex dynamic interaction between the soil, foundation and superstructure with detailed
analysis on soil yielding effects and interface effects on the response of superstructure.
To study this, as discussed in previous sections a three dimensional Finite Element Method is
used for modeling the soil-pile structure interaction using MATLAB R2009a and SAP 2000. In
the following sections of this chapter details about the validation of the program against available
solutions for benchmark problems in the literature is discussed. Validation has been done for
various cases piles embedded in elastic, elasto plastic soils, with and without interface elements.
40
3.2 VALIDATION OF THE PROGRAM
3.2.1 Geometry and Boundary Condition
A three dimensional model as shown in Figure. 3.1 and Figure. 3.2 are used to represent the soil-
pile system in case of single pile and group pile respectively. The soil and pile were modeled
using eight-node hexahedral elements (Figure. 3.3) called brick element. Each node has three
degrees of freedom that is translation u x in x, translation u y in y direction and translation u z in z
direction.
The soil is assumed to be Clay and the piles are made of concrete and have square cross section
with each side 0.5 m. The length of pile 10m with pile slenderness ration of 20. The material
properties of the pile and soil are given in Table 1.1.
Element size
In choosing the element size, aspect ratio (is defined as ratio of longest dimension to the shortest
dimension of a quadrilateral element) of the element plays an important role. In many cases, as
the aspect ratio increases, the inaccuracy of the solution increases. There are exceptions for
which aspect ratio approaching 50 still produce satisfactory results. For example, if stress
gradient is close to zero at some location of actual problem, then large aspect ratios at that
location still produce reasonable results.
In general an element yields best results if its shape is compact and regular, aspect ratio is low,
corner angles of quadrilaterals near 900. The size of mesh mainly depends on loading
conditions (static or dynamic) and geometry of piles. The vertical y direction subdivisions were
kept constant to allow for an even distribution of vertically propagating waves.
For dynamic loading cases the maximum element size should be less than one-fifth to one-eighth
the shortest wavelength (λ) to ensure accuracy (Kramer 2003), i.e.,
HzinfrequencyexcitationtheisfandvelocitywaveshearisVwhichin,Where
)1.3())81()51((
s
max
fVλλE
s
41
Soil
Figure. 3.1 3D pile soil system considered for the study (Single Pile)
Pile 0.5 X 0.5 m
Soil
Figure. 3.2 3D pile group soil system considered for the study (Group pile)
3 Pile Group 0.5 X 0.5m with 2 dia spacing
Bottom face is fixed
15 m 11 m
10 m
Bottom face is fixed
15 m 11 m
10 m
42
Material Properties
Modulus of Elasticity (KN/m2)
Poisson's Ratio
Yield Strain
Clay 11.78 X103 0 0.0002
Concrete 25 X 106 0 0.0035
In this thesis aspect ratio is taken as 1.0 (Logan, 2002) after looking into the constraints on
maximum number of elements with minimum computational time.
Boundary condition
To model the soil-structure interaction problems using the finite-element method the unbounded
domain has to be truncated to a domain of finite size as the size of a finite element is finite. The
boundary condition will be different for static and dynamic analysis.
Figure. 3.3 Eight-node Hexahedral element
Table 1.1. Soil Properties
1
3
4
2
5
6
7
8
X
Y
Z
3i - 1
3i - 2
3i
43
Static Analysis
In a static analysis, an artificial boundary is introduced sufficiently far away from the structure to
truncate a finite region of the unbounded domain. The bounded domain and this finite part of the
unbounded domain form a computational domain to be modeled using finite elements. Because
the displacements decrease with the increasing distance from the structure, simple boundary
conditions such as Dirichlet boundary condition can be enforced on the truncated boundary. This
simple technique of truncating the unbounded domain has been demonstrated to be sufficiently
accurate for statics (Cook et al., 2002).
Dynamic Analysis
But, this simple truncation technique is not applicable to the dynamic analysis of an unbounded
domain. The unboundedness of the domain has an important consequence in wave dynamics:
waves traveling in the unbounded direction are not reflected back to the computational domain.
To define a unique solution for the unbounded soils mathematically, a boundary condition at
infinity has to be defined. The condition of vanishing displacement at infinity is not sufficient
(Wolf, 1985). The boundary condition at infinity should be able to irreversibly transfer energy
from the bounded domain to the unbounded domain and to eliminate the reflection of waves
impinging the boundary. Such a boundary condition is called the radiation condition. Various
techniques have been used by researchers to model this radiation condition like Viscous
boundary (Sushma et al.,(2010)), , Kelvin element, Infinite elements, etc.
For static and dynamic analysis, the bottom edge is fully constrained in all three directions to
model the rigid bed rock. The nodes along the top surface and two lateral surfaces of the mesh
are free to move in all directions.
3.2.2 Material Model
Elastic methods are rather crude for the modeling of the soil, especially when the inertial effects
of the structure are to be taken into account. Hence a nonlinear Bilinear model has been used to
introduce the effect of plasticity. The soil and pile are assumed to behave as elastic perfectly
plastic body. By defining the yield stress of the material and the initial modulus of stress strain
curve, the stress strain behavior is fully defined. Unloading and reloading is assumed to be
44
parallel to the initial loading curve resulting in hysteresis loop as shown in Figure. 3.4 and
Figure. 3.5 for soil and pile respectively.
3.2.3 Loading
The state of stress in the pile–soil system in actual in situ conditions was replicated as an initial
loading condition prior to any additional dynamic or static external load. That is, geostatic
stresses were modeled by applying a global gravitational acceleration, g, to replicate vertically
increasing stress with an increase in depth.
An element of soil in the earth during an earthquake is subjected to time dependent stresses,
displacements and strains that will vary with location and soil type. Nair (1969) classifies three
methods of accounting for earthquake forces.
Monotonic load is the Equivalent static load at surface, taking either this as a certain percentage
of vertical static load, or as base shear utilized in the seismic analysis of structure, or as a force
Figure. 3.4 Stress strain model for soil material
45
based on average ground acceleration (a seismic coefficient times gravitational acceleration). A
monotonic load of 200 kN is given to verify the present study results with the already existing
results from literature.
Earthquakes induce two components of motion in the horizontal and one in the vertical plane, the
amplitude of the later usually being considerably less. Since the two horizontal components are
usually similar, the earthquake motion is usually applied in the form of a prescribed horizontal
acceleration. For the transient motion, the NS component of 1940 Elcentro Earthquake, with
peak ground acceleration equal to 2.93 m/sec2 has been used (Figure. 3.6). A smoothed Fourier
spectrum of acceleration time history has been derived and it was found that the predominant
frequency of excitation is approximately 2.16 Hz.
Figure. 3.5 Stress strain model for pile material
46
3.3 VALIDATION
The static performance of the model was verified against exact available solutions for benchmark
problems including piles in elastic and elasto plastic soils.
In the process of verification incremental steps are followed to ensure that pile, soil and
boundary conditions were separately accounted for to minimize error accumulation. All the
results are compared with the existing studies in literature by applying a monotonically
increasing load at the pile head.
3.3.1 Linear Analysis
In the linear analysis verification process is done in two steps one only for pile and the other one
is when pile is embedded in soil. The details of the same are given below.
0 5 10 15 20 25 30 35-4
-2
0
2
4A
ccel
erat
ion
in m
/sec2
Time in (sec)
0 5 10 15 20 250
1
2
3
Four
ier
Am
plitu
de
Frequency (Hz)
Figure. 3.6 Acceleration Time history and Fourier Amplitude of May18, 1940 Elcentro Earthquake (NS)
47
Pile as a Cantilever
In the linear analysis first the pile mesh was verified by considering the pile as fixed cantilever in
air (no soil). Lateral deflections resulted from a static load for different pile meshes were
compared with those from 1D Beam Flexure Theory as shown in Figure. 3.7. As shown in the
figure the results were converging to the Beam Flexure Theory when mesh is becoming
finer.
0 0.01 0.02 0.03 0.04 0.05 0.06 0.070
50
100
150
200
Displacement in m
Load
in k
N
Mesh 1 (0.67X0.17X0.17)Mesh 2 (0.4X0.17X0.17)Mesh 3 (0.2X0.17X0.17)Mesh 4 (0.1X0.17X0.17)ANSYSBeam Theory
Fixed Face
Figure. 3.7 Verification of pile head response as cantilever
48
Note: Deflection ‘δ’ of the pile head is determined according to Beam Flexure Theory as PL3/
3EpIp, Where P Applied static lateral load, L Length of pile, Ep Young’s Modulus of soil, Ip
Moment of Inertia of Pile (bd3/12). Mesh 1 had 5 horizontal and 20 vertical divisions, Mesh 2
had 5 horizontal and 40 vertical divisions, Mesh 3 had 5 horizontal and 50 vertical divisions,
Mesh 4 had 5 horizontal and 100 vertical divisions.
Pile embedded in Soil - Analytical solution
For the pile embedded in soil case the solution of present analysis is compared with the
analytical solution (See Appendix - A) and previous numerical solutions for available bench
mark problems in literature.
The comparison of the results mentioned above for linear elastic response of single socketed pile
under lateral loading at pile head is shown in Figure. 3.8. Figure shows that results for elastic
case are in good agreement with those obtained by Maheshwari et al., 2004 and ANSYS, but
deflection shown by present model is slightly less that those obtained by Poulos and Davis
(1980). The same variation of results with analytical solution was even observed by Maheshwari
et al., 2004 in their studies. The mesh that yields the closest match that is Mesh 2 of 0.5 X 0.5 m
element size is used in rest of the study.
3.3.2 Nonlinear Analysis
A nonlinear soil model as mentioned above has been used to introduce the effect of plasticity. To
evaluate the effect of soil plasticity on pile response, the soil was modeled as a homogeneous
elastic medium and an elastoplastic using the bilinear model. This model was with zero
strain hardening and therefore progressive yielding was not considered.
In nonlinear analysis, verification is done for two cases that is when interface element is not
present and when interface element is present.
3.3.2.1 Without Interface element
3.3.2.2 With Interface Element
49
3.3.2.1 Without Interface element
In nonlinear analysis without interface element, it is assumed that soil and pile are perfectly
bonded. When interface element is not present verification is done by comparing the results with
Bentley and El Naggar (2000) (Figure. 3.9). The results show that there is a small difference
between the results obtained by present study and those obtained by other approach. This may be
attributed to the use of different model for soil plasticity (Drucker Prager model).
3.3.2.2 With Interface element
When a soil-pile structure model is subjected to seismic excitations, the soil surrounding the pile
may be compressed laterally such that a soil-pile gap separation may develop. These soil-pile
gap separations have been observed in the past both in field and laboratory tests. After 1995
Kobe earthquake the soil-pile gap was observed in reclaimed port Island and also in 1989 Loma
Prieta earthquake, the soil-pile gap developed along the Struve Slough crossing (Chau et al.,
2009).
Figure. 3.8 Response of single socketed pile for linear elastic case.
50
In the present study the separation or gapping is taken into account by checking the tension in
soil elements adjacent to pile. It is assumed that separation occurs in the direction of loading only
and the soil and pile are still in contact in the other direction. At every time step and at every
iteration within the time step, normal stresses in the soil elements are checked against tension for
each Gaussian point. If the normal stress is in tension means separation is assumed. During
separation, the constitutive stiffness matrix is modified by reducing the stiffness of elements
corresponding to that direction to a very small value.
In nonlinear analysis with interface element, the verification is done in two steps that is
elastic soil case with interface element and plastic soil case with interface element by
comparing the results with Maheshwari et al., 2004 (Figure. 3.10 and Figure. 3.11). The
results show that there is a small difference between the results obtained by present study and
those obtained by other study. This may be attributed to the difference in modeling of
initiation of gapping/separation. In the present study, separation is initiated when tension is
Figure. 3.9 Response of single socketed pile for plastic soil case.
51
detected in soil elements adjacent to pile, where as the other approach used a special contact
element at the soil-pile interface.
3.4 RESULTS AND DISCUSSIONS
Single pile and Group piles are analyzed and variations are studied. Single piles are mainly used
for coastal structures such as mooring and berthing piles, but they are usually formed in groups.
But, tall buildings, offshore platforms, quays, viaducts, and bridge piers are generally built on
pile groups. The difference between the behavior of single piles and pile groups is that pile group
response is influenced by the nonlinear pile-soil- pile interaction, the effect of the pile cap, the
spacing of piles, and the arrangement of piles with respect to the direction of applied force
(Charles et al. 2001). The same geometry and mesh are used for soil-pile system for single pile
and group piles (Figure. 3.1 and Figure. 3.2 respectively).
Figure. 3.10 Comparison of Response of single socketed pile for elastic soil case
with interface element- Present Study and Maheshwari et al., 2004
52
3.4.1 Without Interface element
The elastic and nonlinear response of socketed single pile and pile group in the homogeneous
soil stratum has been given below.
For monotonic loading, the elastic and nonlinear responses of single pile and pile group are
shown in Figure. 3.12 and Figure. 3.13 respectively. From the Figure. 3.12 and Figure. 3.13 it
has been observed that the load carrying capacity of single pile is more when compared to the
pile group for the same average load. As the number of piles in the group increases, the over
lapping of stress zones increases, thus, leading to a sharp reduction in the lateral capacity.
3.4.2 With Interface element
The nonlinear response of socketed single pile and pile group in the homogeneous soil stratum
with and without interface element is given under monotonic loading. Figure. 3.14 and Figure.
3.15 show the response of single pile and pile group respectively for monotonic loading with and
without interface element. From the figures it has been observed that when gapping is allowed
Figure. 3.11 Comparison of Response of single socketed pile for plastic soil case with gap element - Present Study and Maheshwari et al., 2004
53
Figure. 3.12 Response of single socketed pile and pile group for elastic soil case monotonic loading
Figure. 3.13 Response of single socketed pile and pile group for plastic soil case monotonic loading
54
Figure. 3.15 Response of Pile group for plastic soil case for the
case of monotonic loading with and without Gap element
Figure. 3.14 Response of single socketed pile for plastic soil case for the case of monotonic loading with and without Gap element
55
along with the soil plasticity, the increase in pile response due to gapping at the soil-pile
interface is not significant. The effect of plasticity in this case over shadows the effect of
gapping. A similar observation in results was made by Maheshwari et al., 2004 in his studies.
56
Chapter 4
4. Seismic response of pile in linear soil medium
4.1 GENERAL INTRODUCTION
In the previous chapter a Finite Element methodology was developed and verified by comparison
with the existing studies in literature. In this chapter the dynamic analysis has been carried to
study the effects of different parameters on pile response, namely the elastic modulus of soil, the
elastic modulus of pile, length of pile, diameter of the pile, number of piles in a pile group, and
the earthquake characteristics. Linear pile and soil response are assumed in all cases and also it
was assumed that a perfect bond is there between pile and soil, so separation of pile and soil is
not considered. The effect of soil yielding and separation of pile and soil will be discussed in
detail in consecutive chapters.
Few quantitative conclusions can be made from this study, because every earthquake is different
and certain general trends can be distinguished. For each case the response will be converted into
frequency domain to understand shift in frequency of the free field system and pile soil system,
thus conclusions are drawn regarding the inclusion of soil foundation interaction in the analysis.
4.2 METHODOLOGY AND IMPLEMENTATION
As discussed in the previous chapters, in this thesis direct approach is used, where the pile, soil
and structure system are modeled together in a single step. For this purpose a three dimensional
Finite Element Method is used for modeling the soil-pile structure interaction using MATLAB
R2009a.
Before starting the actual parametric analysis first model size is fixed. As discussed in Chapter I,
the actual system consisted of a 22m high six floor building called Port and Customs Office
Tower located in Kandla, near The Little Rann of Kachchh on the south eastern coast of the
57
Kachchh district. The building was founded on 32 short cast in place concrete piles and each pile
was 18m long and 0.5 m width. The piles were passing through 10m of clayey crust and then
terminated in a sandy soil layer. So based on these pile dimensions according to Karthigeyan et
al., 2006 (Figure 4.1), the model size for single pile and soil model has been fixed as 20 X 10 X
28. So for all the analysis in this chapter the soil dimensions are taken as 20 X 10 X 28 with pile
length of 16m (there was a problem in meshing so pile dimension is taken as 16m instead of
18m) and pile width 0.5m. The soil and pile are modeled with 8-node brick elements, with
elastic material properties as given in Table 4.1. The base was fixed and four lateral faces have
been modeled as free boundary.
For the transient motion, the N90E component of Mar 24, 1995 Chamba Earthquake, with peak
ground acceleration equal to 1.2309 m/sec2 has been used (Figure. 4.2). A smoothed Fourier
spectrum (Figure. 4.3) of acceleration time history has been derived and it was found that the
predominant frequency of excitation is approximately 2.95 Hz. The response acceleration shown
in all results is that at the pile head. Derived free-field response is also at the same point i.e., at
the location of the pile head, but assumes that there is no pile in the system.
Figure. 4.1 Typical mesh for 3dimensional Finite Element Analysis
58
4.3 PARAMETRIC STUDY
To understand the transient behavior of pile embedded in soil, a parametric study is performed
by varying different parameters.
4.3.1 Modulus of Soil
To understand the difference in transient behavior of pile embedded in the soil and free field
responses, first the free field response of different soils that is very soft clay, soft clay, medium
Component
Modulus of Elasticity
(MPa)
Poisson's
Ratio
Very Soft Clay 15 0 Pile 27390 0
0 2 4 6 8 10 12 14 16 18 20
-1.5
-1
-0.5
0
0.5
1
1.5
Acc
eler
atio
n in
m/s
ec2
Time in seconds
Figure. 4.2 Acceleration time history of Mar 24, 1995 Chamba Earthquake (NE)
Table 4.1 Properties of the Material
59
clay, hard clay are studied and responses are shown in Figure 4.4. From the Figure it has been
observed that the displacement pattern is same for all soils considered except a small
increase in the displacement values of hard, medium and soft clays in increasing order when
compared to very soft clay. So to have a clear understanding on the free field behavior of various
soils, Fourier amplitude of the all responses are plotted and shown in Figure. 4.5. From the figure
it has been observed that the predominant frequency for hard clay is more when compared to
medium, soft and very soft clay in decreasing order.
The Fourier amplitude spectrum of pile soil response of various soils (Table 4.2) has been given
in Figure. 4.6. From the figure it has been observed that the predominant frequency for hard clay
is more when compared to medium, soft and very soft clay in decreasing order. When
Fourier amplitude spectrum of free field response and pile response are compared it has been
observed that the pattern of both are same except a small increase in Fourier amplitude values in
case of free field response when compared to pile soil response (the free field and pile soil
response of soft clay is shown Figure. 4.7). So the conclusion from this is for the parameters
considered in this study there is no change in the predominant frequency value for single pile soil
Figure. 4.3 Fourier Amplitude spectrum of Mar 24, 1995 Chamba Earthquake (NE)
60
and free field cases for various soils. That is presence of single pile embedded in soil does
not make any difference in the increase in predominant frequencies.
4.3.2 Pile Modulus / Grade of Concrete
To understand the effect of pile modulus on the transient behavior of a single pile embedded in
soil, a parametric study has been done for a different grades of concrete (M 30, M 35, M 40,
M 45, M 50) by considering the very soft clay with Chamba Earthquake displacement given at
Component Modulus of Elasticity (MPa)
Very Soft Clay 15 Soft Clay 25
Medium Clay 50 Hard Clay 100
0 2 4 6 8 10 12 14 16 18 20
-30
-20
-10
0
10
20
30
40
50
60
Time in seconds
Dis
plac
emen
t in
mm
Very soft claySoft clayMedium clayHard clay
Figure. 4.4 Free field response of different soil strata under Mar 24, 1995 Chamba Earthquake (NE)
Table 4.2 Properties of Various Clay
61
10-1
100
101
0
10
20
30
40
50
60
70
80
90
Frequency (Hz)
Four
ier
Am
plitu
de in
g
Very soft claySoft clayMedium clayHard clay
10-1
100
101
0
10
20
30
40
50
60
70
80
90
Frequency (Hz)
Four
ier
Am
plitu
de in
g
Pile Very soft clayPile Soft clayPile Medium clayPile Hard clay
Figure. 4.5 Fourier Amplitude Spectrum of different soil strata under Mar 24, 1995 Chamba Earthquake (NE)
Figure. 4.6 Fourier Amplitude Spectrum of pile and soil for various soil strata under Mar 24, 1995 Chamba Earthquake (NE)
62
the bottom face. Figure 4.8 shows the response of single pile and soil for various grades of
concrete. From the figure it has been observed that the effect of soil-pile structure interaction is
independent of grade of concrete for the soil and pile properties considered in this study. That is
there is no change in predominant frequency value for whatever is the grade of concrete
considered (these results are cross checked with SAP).
4.3.3 Pile length
To understand the effect of pile length on the transient behavior of a single pile embedded in soil,
a parametric study has been done for different lengths of piles. The model considered is same as
mentioned above with Chamba Earthquake displacement given at the bottom face. Figure 4.9
4.3.4 Number of piles in a group
To understand the effect of number of piles in a group on the transient behavior of a piles
embedded in soil, a parametric study has been done for a group of two, three and four piles
(Figure. 4.10). The model considered is same as mentioned above with Chamba Earthquake
10
-110
010
10
10
20
30
40
50
60
70
80
90
Frequency (Hz)
Four
ier
Am
plitu
de in
g
Pile & soilSoil
Figure. 4.7 Comparison of Fourier Amplitude Spectrum of only soil and pile soil for very soft clay under Mar 24, 1995 Chamba Earthquake (NE)
63
0 2 4 6 8 10 12 14 16-20
-10
0
10
20
30
40
50
60
Time in seconds
Dis
plac
emen
t in
mm
M 30M 35M 40M 45M 50
0 2 4 6 8 10 12 14 16-20
-10
0
10
20
30
40
50
60
Time in seconds
Dis
plac
emen
t in
mm
L 8L 12L 16L 20L 24
Figure. 4.8 Response of single pile soil for various grades of concrete under Mar 24, 1995 Chamba Earthquake (NE)
Figure. 4.9 Response of single pile soil for various pile lengths under Mar 24, 1995 Chamba Earthquake (NE)
64
displacement given at the bottom face. Figure 4.11 shows the response of pile and soil for
various pile groups. From the figure it has been observed that the soil-pile interaction effect is
independent of number of piles in a group for the soil and pile properties considered in this
study.
4.3.5 Effect of different earthquakes
Each earthquake is unique in itself, to understand how a pile, soil (pile soil interaction) responds
for various earthquakes, a parametric study has been done for various earthquakes. Table 4.2
shows the PGA and predominant frequency range of the earthquakes considered in this study.
Figure. 4.12 shows the Fourier transform all the earthquakes that are considered in this study.
From the figure it has been observed that all the earthquakes have predominant frequency falling
in the broad band frequency range of 1 to 7 Hz. These earthquakes if occurs in the place where
structures fall in this frequency range then there will be a considerable amount of damage.
Figure. 4.10 3D model of different pile groups considered
65
Earthquake Name PGA
(m/sec2) Predominant
Frequency (Hz) May 18, 1940 Elcentro (NS) 2.9272 1.32 - 6.59 Mar 24, 1995 Chamba (NE) 1.24 0.35 - 3.53
Mar 29, 1999 Chamoli (NW ) 1.95 0.85 - 0.95 Mar 29, 1999 Uttarkashi (NW) 2.48 0.92 - 4.24
Figure. 4.13 shows the Fourier amplitude spectrum of pile soil for various earthquakes. From the
figure it has been observed that all the earthquakes which has predominant frequency in broad
band frequency range has been changed to narrow band frequencies of range 0.1 to 1 Hz after the
soil-pile interaction effect. Which means all the low to medium rise structures will have adverse
effects if such kind of earthquakes occurs. So there is a need to perform the dynamic soil-
structure interaction analysis to have a good understanding on the transient behavior. From the
2 4 6 8 10 12 14 16-20
-10
0
10
20
30
40
50
60
Time in seconds
Dis
plac
emen
t in
mm
Two piles with capThree piles with capFour piles with cap
Figure. 4.11 Response of various pile groups under Mar 24, 1995 Chamba Earthquake (NE)
Table 4.2 Details of Earthquakes
66
figures (Figure. 4.12 and Figure. 4.13) we observed a considerable variation in predominant
frequency of the earthquakes and the pile soil interaction. Also there is 10 fold change in the
Fourier amplitude of both (Figure. 4.14). To show this behavior for one earthquake it has been
plotted (Figure 4.15).
10-1
100
101
102
0
0.5
1
1.5
2
2.5
Frequency (Hz)
Four
ier
Am
plitu
de in
g
Elcentro EqChamba EqChamoli EqUttakashi Eq
10-1
100
101
0
50
100
150
200
250
Frequency (Hz)
Four
ier
Am
plitu
de in
g
Elcentro EqUttakashi EqChamoli EqChamba Eq
Figure. 4.12 Comparison of Fourier Amplitude Spectrum of various earthquakes
Figure. 4.13 Fourier Amplitude Spectrum of pile soil for various earthquakes
67
10-1
100
101
1020
10
20
30
40
50
60
70
80
Frequency (Hz)
Four
ier
Am
plitu
de in
g
OutputInput
0 2 4 6 8 10 12 14 16-30
-20
-10
0
10
Acc
eler
atio
n in
m/se
c2
Time in sec
10-1
100
101
0
20
40
60
80
Frequency (Hz)
Four
ier
Am
plitu
de in
g
Figure. 4.15 Pile soil response and Fourier Amplitude Spectrum of May 18, 1940 Elcentro Earthquake (NS)
Figure. 4.14 Fourier Amplitude Spectrum of pile soil response of May 18, 1940 Elcentro Earthquake (NS)
68
Chapter 5
5. Nonlinear Behaviour of Frame Structure with Pile Foundations
5.1 GENERAL INTRODUCTION
In the previous chapter a dynamic analysis has been carried out to understand the effects of
different parameters on pile response, namely the elastic modulus of soil, the elastic modulus of
pile, length of pile, diameter of the pile, number of piles in a pile group, spacing between the
piles and the earthquake characteristics. In this chapter analysis has been done to study the soil-
pile structure interaction effect by modeling the pile supported framed structure on the soil.
Linear structure and pile responses are assumed in all cases with the nonlinear soil yielding
effects. It is assumed that a perfect bond is there between pile and soil, so separation of pile and
soil is not considered (interface modeling). The effect of separation of pile and soil will be
discussed in detail in consecutive chapters.
Few quantitative conclusions can be made from this study by considering the effect of the pile
supported framed building on linear and nonlinear soil models. For each case the response will
be converted into frequency domain to understand shift in frequency of the pile soil system and
pile supported framed building, thus conclusions are drawn regarding the inclusion of soil
foundation interaction effect in the structure analysis.
Before starting the actual analysis first the single bay five storey frame as shown in the Figure.
5.1 have been modeled. Fixed based load analysis has been done for gravity loads using the
commercial package SAP. The loads and moments at the each column base are taken to design
the foundation for the structure using IS 456. From the design, for the structure considered a
2 X 1 pile group with 8 m length pile and a pile cap of 1.5 X 0.3 X 0.3m has to be used under
each column Figure. 5.2.
69
5.2 METHODOLOGY AND IMPLEMENTATION
As discussed in the previous chapters, in this thesis direct approach is used, where the pile, soil
and structure system are modeled together in a single step. For this purpose a three dimensional
Finite Element Method is used for modeling the soil-pile structure interaction using MATLAB
R2009a and SAP 2000. In this chapter only material nonlinearity is considered that is
nonlinearity associated with the inelastic behavior of a component/material.
For the implementation of this nonlinear behavior SAP 2000 is used. To check the applicability
of SAP 2000 to geotechnical problems, the results of SAP 2000 are cross checked with the
results of FEM soil model (Chapter 3) developed in this thesis. The soil has been modeled using
the solid elements available in SAP 2000. The transient response of the SAP 2000 and FEM are
shown in Figure. 5.3. The response shows a good agreement between FEM and SAP results, so
in the later part of the thesis SAP 2000 is used to model the material nonlinearity.
Structures subjected to strong earthquake excitations are often associated with this kind of
nonlinear material behavior that is irrecoverability of strain. The basic requirement to perform
such analysis is the availability of constitutive material model capable of representing the
Figure. 5.1 3D Frame structure considered for the analysis
70
inelastic material behavior. For the materials considered in this study the yield strength in
compression is taken as 25 kN/m2 and yield strength in tension is taken as 10% of yield strength
in compression.
For the transient loads the relationship type which indicates material nonlinearity is the hysteretic
cycle, where the F-D relationship is developed for a system subjected to cyclic loading. Stiffness
and response are evaluated at each time step. Between each displacement step, stiffness may
change due to nonlinear material behavior, in which performance incorporates inelastic response.
The nonlinear equations are solved iteratively in each time step and iterations are carried out
until the solution converges.
Figure. 5.2 3D Pile supported framed structure considered for the analysis
71
5.3 PARAMETRIC STUDY
5.3.1 Only Soil
To study the free field response of soil for linear and nonlinear analysis, the model developed in
chapter 3 is used. The free field transient response of a soil for linear and nonlinear cases is
found by giving NS component Elcentro earthquake as input. Figure. 5.4 and Figure. 5.5 shows
the free field response and Fourier transform of it respectively. From the results it has been
observed that the effect of soil plasticity in case of free field response is not significant for the
soil considered in this analysis.
5.3.2 Pile with Linear and Nonlinear Soil
To study the effect of soil and foundation interaction, the foundation as designed in the previous
section for the framed structure is considered (Figure. 5.6). Figure. 5.7 and Figure. 5.8 show the
response and Fourier Transform of the linear and nonlinear analysis considering the soil
0 5 10 15 20 25 30 35-8
-6
-4
-2
0
2
4
6
8
Time in seconds
Acc
eler
atio
n in
m/se
c2
SAPFEM
Figure. 5.3 Comparison of dynamic response FEM and SAP under May 18, 1940 Elcentro Earthquake (NS)
72
0 5 10 15 20 25 30 35-8
-6
-4
-2
0
2
4
6
Time in seconds
Acc
eler
atio
n in
m/se
c2
NonlinearLinear
10-1
100
101
102
0
2
4
6
8
10
12
Frequency (Hz)
Four
ier
Am
plitu
de
NonlinearLinear
Figure. 5.4 Comparison of dynamic response of linear and nonlinear analysis only soil under May 18, 1940 Elcentro Earthquake (NS)
Figure. 5.5 Comparison of Fourier Transform of linear and nonlinear analysis only soil under May 18, 1940 Elcentro Earthquake (NS)
73
0 2 4 6 8 10 12 14 16 18 20-8
-6
-4
-2
0
2
4
6
Time in seconds
Acc
eler
atio
n in
m/s
ec2
LinearNonlinear
Figure. 5.7 Comparison of linear and nonlinear analysis of response of centre of soil when considering soil foundation interaction under May 18, 1940 Elcentro Earthquake (NS)
Figure. 5.6 3D Soil Foundation model considered for the analysis
2 X 1 Pile Group
Soil
74
foundation interaction (FI). Generally as the displacements become large, the material response
become nonlinear, but for the soil and pile properties considered in this analysis this increase in
displacement is not large, so there is only a marginal increase in response for the nonlinear
analysis. Also it has been observed that Fourier amplitude of nonlinear analysis is very high than
linear analysis with no shift in frequency of the both.
Besides that a peculiar behavior in the stress state of pile is observed as shown in Figure. 5.9.
From the figure it has been observed that stress is maximum at the bottom of the pile that is at
the pile tip, with decreasing order of stresses in the rest of pile. Also at about 1m above the
bottom (pile tip) the stresses are tensile. This behavior may be because of Soil resistance acting
downward along the pile shaft because of an applied transient load. Figure. 5.10 shows the stress
state of pile 2 under pile cap 1, this behavior is little different from the later behavior as here
10-1
100
101
102
0
2
4
6
8
10
12
14
Frequency (Hz)
Four
ier
Am
plitu
de
NonlinearLinear
Figure. 5.8 Comparison of Fourier Transform of linear and nonlinear analysis of response of middle of soil when considering soil foundation interaction under May
18, 1940 Elcentro Earthquake (NS)
75
along with the soil resistance, the group interaction of pile with adjacent piles (piles under cap2)
is also effecting the stress state.
Figure. 5.11 and Figure. 5. 12 show the variation of stress along the length of pile for nonlinear
cases. The behavior of stress state is same as discussed for linear case except the change in
magnitude of stress. This change magnitude for nonlinear case is purely because of the combined
effect of soil plasticity and the kinematic interaction of piles.
5.3.3 Pile supported framed structure with linear and nonlinear soil
A pile supported framed structure as shown in Figure. 5.2 is considered for the soil foundation
structure interaction (SFSI) analysis in this section. The NS component of Elcentro earthquake is
given as input for the transient analysis. Figure. 5.13 and Figure. 5.14 show the response and
Fourier Transform of the linear and nonlinear analysis considering the SFSI. From the response
we can clearly see that there is an increase in response for nonlinear analysis, as under strong
ground excitation, the soil goes to nonlinearity.
0 2 4 6 8 10 12 14 16 18 20-100
-50
0
50
100
150
200
250
300
350
400
Time in seconds
Stre
ss in
kN
/m2
@ Pile Head@ 1m Below@ 2m Below@ 3m Below@ 4 m Below@ Pile Tip
Figure. 5.9 Variation of stress along the length of pile under May 18, 1940 Elcentro Earthquake (NS) (pile 1 under cap 1 (Linear))
76
0 5 10 15 20-200
-100
0
100
200
300
400
500
Time in seconds
Stre
ss in
kN
/m2
@ Pile Head@ 1m Below@ 2m Below@ 3m Below@ 4 m Below@ Pile Tip
0 5 10 15 20-150
-100
-50
0
50
100
150
200
Time in seconds
Stre
ss in
kN
/m2
@ Pile Head@ 1m Below@ 2m Below@ 3m Below@ 4 m Below@ Pile Tip
Figure. 5.10 Variation of stress along the length of pile under May 18, 1940 Elcentro Earthquake (NS) (pile 2 under cap 1 (Linear))
Figure. 5.11 Variation of stress along the length of pile under May 18, 1940 Elcentro Earthquake (NS) (pile 1 under cap 1 (Nonlinear))
77
0 5 10 15 20-150
-100
-50
0
50
100
150
200
250
300
Time in seconds
Stre
ss in
kN
/m2
@ Pile Head@ 1m Below@ 2m Below@ 3m Below@ 4 m Below@ Pile Tip
0 5 10 15 20-20
-15
-10
-5
0
5
10
15
20
Time in seconds
Acc
eler
atio
n in
m/s
ec2
NonlinearLinear
Figure. 5.13 Acceleration response of top floor linear and nonlinear analysis under May 18, 1940 Elcentro Earthquake (NS)
Figure. 5.12 Variation of stress along the length of pile under May 18, 1940 Elcentro Earthquake (NS) (pile 2 under cap 1 (Nonlinear))
78
10-1
100
101
102
0
10
20
30
40
50
60
Frequency (Hz)
Four
ier
Am
plitu
de
NonlinearLinear
0 2 4 6 8 10 12 14 16 18 20-100
0
100
200
300
400
500
Time in seconds
Stre
ss in
kN
/m2
@ Pile Head@ 1m Below@ 2m Below@ 3m Below@ 4 m Below@ Pile Tip
Figure. 5.14 Fourier transform of top floor linear and nonlinear analysis under May 18, 1940 Elcentro Earthquake (NS)
Figure. 5.15 Stress of pile 1 under cap 1for linear analysis considering SFSI under May 18, 1940 Elcentro Earthquake (NS)
79
The behavior on the state of stress, which has been observed in FI section, has been observed
hear also (Figure. 5.15). But while comparing the stress states for FI and SFSI, the stress levels
are more for FI when compared to SFSI in both linear and nonlinear analysis (Figure. 5.16 and
Figure. 5.17). This decrease is because of including the inertial and kinematic interaction effects
in later case.
Figure. 5.18 and Figure 4.19 show the acceleration response of pile cap and structure for both
linear and nonlinear analysis respectively. The spikes observed in the acceleration response of
pile cap specify that impact has occurred between pile and soil (Chau et al., 2009). To make a
better understanding of the spikes enlargement of each of the responses are also given. Because
of the strong ground motion as the input, repeated dynamic contacts of soil and pile cause the
lateral compression of soil leading to formation of gap between pile and soil. To further examine
this phenomenon in the next chapter contact between pile and soil is studied.
0 2 4 6 8 10 12 14 16 18 200
20
40
60
80
100
120
140
Time in seconds
Stre
ss in
kN
/m2
FISFSI
Figure. 5.16 Stress of pile 1 under cap 1 linear both FI and SFSI at pile head under May 18, 1940 Elcentro Earthquake (NS)
80
0 2 4 6 8 10 12 14 16 18 20-20
0
20
40
60
80
100
120
140
Time in seconds
Stre
ss in
kN
/m2
FISFSI
0 2 4 6 8 10 12 14 16 18 20-20
-15
-10
-5
0
5
10
15
20
Time in seconds
Acc
eler
atio
n in
m/s
ec2
Pile CapTop Floor
Figure. 5.17 Stress of pile 1 under cap 1 nonlinear both FI and SFSI at pile head under May 18, 1940 Elcentro Earthquake (NS)
Figure. 5.18 Acceleration response of pile cap and top floor linear analysis considering SFSI under May 18, 1940 Elcentro Earthquake (NS)
81
5.4 SIGNIFICANCE OF SOIL FOUNDATION STRUCTURE INTERACTION (SFSI)
To understand the significance of SFSI over the fixed based analysis (FBA), in this section SFSI
results are compared with fixed based analysis results. For this purpose a pile supported framed
structure as shown in Figure. 5.2 is considered for the soil foundation structure interaction
(SFSI) analysis and a framed structure as shown in Figure. 5.1 is considered for fixed base
analysis. The dynamic analysis is carried out by giving NS component of Elcentro earthquake as
input.
First and foremost, a modal analysis is done for both the cases SFSI and FBA, to know the
period of vibration corresponding to fundamental frequency, called characteristic site period.
This provides a very useful indication of period of vibration at which the most significant
amplification is expected. For FBA system the fundamental period is 0.6528 sec where as for
SFSI system it is 1.238 sec. From this it has been clearly understood that by neglecting the
interaction of soil, foundation and structure in the actual analysis, the fundamental period of the
0 2 4 6 8 10 12 14 16 18 20-20
-15
-10
-5
0
5
10
15
20
Time in seconds
Acc
eler
atio
n in
m/s
ec2
At pile capAt top floor
Figure. 5.19 Acceleration response of pile cap and top floor nonlinear analysis considering SFSI under May 18, 1940 Elcentro Earthquake (NS)
82
system is under estimated and so there will error in finding the significant amplification under
strong ground motion.
Second a dynamic analysis is carried out to find the response of the FBA and SFSI system. In
order to relate the SFSI and FBA effects, the top floor response of FBA and the top floor
response of the frame with SFSI are plotted as shown in Figure. 5.20. From the figure it has been
observed that increase in response for SSI when compared to fixed base is because of accounting
for the kinematic and inertial interactions in later case. That is in this ground acceleration is
getting altered before reaching the surface because of presence of soil that is site effect and also
the presence of stiff foundation elements that is kinematic interaction.
Third, in case of soil foundation structure interaction system the presence of soil and foundation
make a considerable change in response with a shift of natural period of the system as shown in
Figure. 5.21. This shift of period is observed as soil and foundation elements are playing a major
role in the response. At the time of shaking there is a change in dynamic characteristics of the
0 2 4 6 8 10 12 14 16 18 20-20
-15
-10
-5
0
5
10
15
20
Time in seconds
Acc
eler
atio
n in
m/s
ec2
SFSIFBA
Figure. 5. 20 Comparison of acceleration response SFSI and FBA systems under May 18, 1940 Elcentro Earthquake (NS)
83
soil. The stiffness and damping characteristics of soil may change significantly because of the
interaction effect. Also it has been observed that soil between the two piles are more stressed
figure shown in previous sections) which is reason for the increase in the response of structure.
10-1
100
101
1020
5
10
15
20
25
30
35
40
45
50
Frequency (Hz)
Four
ier
Am
plitu
de
SFSIFBA
Figure. 5. 21 Comparison of Fourier Transform of SFSI and FBA systems under May 18, 1940 Elcentro Earthquake (NS)
84
Chapter 6 6. Nonlinear Behaviour of frame with pile foundations with and without Interface Element
6.1 GENERAL INTRODUCTION
In the previous chapter a dynamic soil-pile structure interaction analysis has been carried out on
a pile supported framed structure to understand the effects of nonlinear soil yielding. In this
chapter analysis has been done to study the effect of interaction between pile and soil by
modeling an interface element. Soil-pile structure system (Figure. 5.2) as discussed in chapter 5
is considered. Linear structure and pile responses are assumed in all cases with the nonlinear soil
yielding and interface effects.
Few quantitative conclusions can be made from this study by considering the effect of the pile
supported framed building on linear and nonlinear soil models with and without interface
elements. For each case the response will be converted into frequency domain to understand shift
in frequency of the pile soil system and pile supported framed building, thus conclusions are
drawn regarding the inclusion of soil foundation interaction effect in the structure analysis.
6.2 METHODOLOGY AND IMPLEMENTATION
As discussed in the previous chapters, in this thesis direct approach is used, where the pile, soil
and structure system are modeled together in a single step. For this purpose a three dimensional
Finite Element Method is used for modeling the soil-pile structure interaction using SAP 2000.
In this chapter effect of relative movement of soil and pile that is debonding / separation and
rebonding of pile and soil is considered. To account for the discontinuous behavior at soil-
structure interface many methods like use of thin continuum elements, linkage elements like
discrete springs, special interface or joint elements, etc., are used generally (David et al., 1999).
The details of the interface modeling are discussed in the following sections of the chapter.
85
SAP 2000 is used to model the separation / debonding of the pile, for that the “Gap element” in
Link / Support properties is selected. For the Gap element the force deformation relation as given
in Eq. 2.1 is used. To model this gap element two input parameters has to be specified one the
spring constant and d the gap separation. The spring constant or contact stiffness k should be
always 2 times stiffer than surrounding element, so the value has been taken as 50 kN/m, with
the gap separation of 0.01m.
For the foundation model considered in this analysis, there are 4 pile groups with 2X1 piles for
each group. To understand the interface behavior of pile and soil, the Gap elements are provided
on either side of the pile for all pile groups (Figure. 6.1). To make the analysis simple, the gap
separation is modeled only in the direction of load application, here as the load is applied in x
direction, so Gap elements are also provided in that direction with the same gap for the full depth
of the pile.
Figure. 6.1 3D Soil Foundation Interaction Model with Linkage / Gap element
Pile with link elements
Soil
86
6.3 PARAMETRIC STUDY
In the following section a parametric study has been conducted to understand the interface
behavior of pile and soil by modeling a linkage element between them. The NS component of
Elcentro earthquake is given as input for the transient analysis in the following section.
6.3.1 Pile with and without interface elements
To study the effect of soil and foundation interaction, the foundation as designed in the previous
chapter for the framed structure is considered (Figure. 6.1). Figure. 6.2 and Figure. 6.3 show the
response and Fourier Transform of the soil foundation interaction (FI) system with and without
link elements. From the results it has been observed that there is a minute increase in response
for the analysis with and without link elements for the properties considered in this study.
But there is a drastic difference in the behavior, when the state of stress of soil foundation system
is observed for two cases, with (Figure. 5.9) and without link elements (Figure. 6.4). This may be
Figure. 6.2 Comparison of acceleration response at pile cap with and without
link element (FI) under May 18, 1940 Elcentro Earthquake (NS)
87
0 2 4 6 8 10 12 14 16 18 20
-30
-20
-10
0
10
20
30
Time in seconds
Stre
ss in
kN
/m2
@ Pile Head@ 1m Below@ 2m Below@ 3m Below@ 4 m Below@ Pile Tip
Figure. 6.4 Stress of pile 1 under cap 1 for FI with link elements under May 18, 1940 Elcentro Earthquake (NS)
Figure. 6.3 Comparison of Fourier amplitude spectrum of pile cap with and without link element (FI) under May 18, 1940 Elcentro Earthquake (NS)
88
because of loss of contact between pile and soil. The pile and soil are behaving independently and so there is not much of soil resistance to the piles.
6.3.2 Pile supported frame buildings with and without interface elements
A pile supported framed structure as shown in Figure. 6.1 is considered for the soil foundation
structure interaction (SFSI) analysis in this section. Figure. 6.5 and Figure. 6.6 show the response
and Fourier Transform of the SFSI with and without link elements. From the response we can
clearly see that there is an increase in response for the analysis without link elements. But in
reality due to loss of contact between pile and soil during strong ground motion, there will be
much decrease in response. So by considering all these effects in our analysis makes our
prediction close to reality.
As the contact stiffness and Gap separation assumed in this case is not measured by modeling the
actual stiffness of contact between pile and soil. A detailed analysis of this has to be done to have
a good understanding on this behavior. Also this behavior can be modeled by assuming various
contact stiffness and gap separations along the depth of pile.
Figure. 6.5 Comparison of acceleration response of top floor with and without link elements
under May 18, 1940 Elcentro Earthquake (NS)
89
Figure. 6.6 Comparison of Fourier amplitude spectrum of top floor with and without link element under May 18, 1940 Elcentro Earthquake (NS)
90
Chapter 7
7. Linear Behaviour of Group of Pile Supported Structures
7.1 GENERAL INTRODUCTION
In the previous chapter a dynamic soil-pile structure interaction analysis has been carried out on
a pile supported space framed structure to understand the effects of interaction of pile and soil. In
this chapter analysis has been done to study the dynamic soil-structure interaction of a high rise
structure in a visco elastic half space in the presence of nearby pile supported structures.
Few quantitative conclusions can be made from this by considering different case studies, one in
which the group effect of structures supported on piles are considered like group of two identical
structures, group of three identical structures and group of three different structures, second one
in which the effect of variability in structure height is considered like 5 storey structure, 10
storey structure and 15 storey structure and the third one in which the effect of variability in
structure shape is considered. For each case the effect of structure soil-structure interaction
(SSSI) on seismic response is compared with fixed base response.
In this Chapter a numerical study is carried out by considering the complexities in soil-pile
structure interaction of group of pile supported structures (Figure. 7.1).
7.2 METHODOLOGY AND IMPLEMENTATION
As discussed in the previous chapters, in this thesis direct approach is used, where the group of
pile supported structures is modeled together in a single step. For this purpose a two dimensional
Finite Element Method is used for modeling the structure soil-pile structure interaction using
ANSYS 10. The soil, pile and frame were modeled using 2 d eight nodded quadratic elements
with two degrees of freedom that is translation u x in x and translation u y in y direction.
91
Huge size of the numerical model has been taken to reduce the boundary effect on the results
(Figure. 7.2).
Before starting the actual analysis first we will discuss about the system under consideration
which comprises of several neighboring framed structures of different heights, founded on pile
groups embedded on a visco elastic half space. A plane sketch of problem is given in Figure. 7.1,
with geometric properties of buildings and piles labeled. Pile groups are defined by length l1 and
l2 and sectional diameter d of the piles and L1 and L2 be the width of pile cap. The structural
Pile Soil
Frame
510 m
260 m
u a s
h 1
d
l 1
u x
u y
Figure. 7.2. Finite model of soil-pile frame system
Figure. 7.1 Schematic diagram showing Structure Soil Structure Interaction of group effect of structures
h 2
L1
l 2
L2
92
heights are given by h1 and h2. In studying the effect of change in response due to variability in
structure height, three structures 5, 10 and 15 storied are considered (Figure. 7.3). In studying the
change in response due to variability in structure shape, a Structure b of same height as 15 storey
structure with reduced stiffness on top floors is considered (Figure. 7.4).
The material properties of soil, pile, and frame are given in Table 7.1. It is assumed that pile is
made up of concrete and has a square cross section with each side equal to 0.5 m. Four piles of
length 15m and 10m each are considered for different building configurations with height of
buildings 30m and 15m respectively. The length of the pile cap is taken as 10m and the
distance between the adjacent buildings is also taken as constant for all cases studied. The frame
considered is regular one which is widely used in constructions with one bay 10 stories and one
bay 5 stories with beam size 0.4m, column size 0.4m and storey height equal to 3m and it is
modeled as elastic material. The pile is completely embedded in the soil and it is assumed that
soil and pile are perfectly bonded, so separation between soil and pile is not considered. All
three sides of soil are constrained in both x and y directions. For the dynamic analysis, the NS
component of Elcentro Earthquake record is given as input in all cases.
h 1
d
l 1
u x
u y
h 3
a. 5 Storey Structure
b. 10 Storey Structure
c. 15 Storey Structure
Figure. 7.3. Schematic diagram showing variability in structure height
h 2
L1 L2
l 2 l 3
L3
93
Material Youngs Modulus (kN/m2)
Density (t/m3)
Poisson’s Ratio
Clayey Soil 40 x 103 1.8 0.4
Concrete Pile
19.36 x 106 2.4 0.2
Concrete Frame
25 x 106 2.4 0.2
In the following sections the dynamic behavior of group of structures with same heights and
different heights are studied in order to enhance whether or not the SSSI effects between two
or more adjacent buildings can be of importance. Also the dynamic behavior of structures of
different height and different shape of same height are studied. Note that in all cases distance
between neighboring structures is assumed constant. For each case response of soil-structure
system is compared with fixed base system (Figure. 7.5).
7.3 CASE STUDIES TO UNDERSTAND THE GROUP EFFECT OF STRUCTURES RESTING ON PILES
The influence of SSSI on dynamic response of piled structures is addressed in this section. As a
first case, soil-structure interaction effects on single building is measured by giving NS
component of Elcentro earthquake record as input to the pile soil system shown in Figure. 7.2. In
order to able to relate the SSI effects, the top floor response of fixed base system and the top
l 1 l 1
h 1 h 1
Figure. 7.4. Schematic diagram showing variability in structure shape
L1 L1
Table 7.1 Properties of the Material
94
floor response of the frame with SSI are plotted as shown in Figure. 7.6. From the figure it has
been observed that increase in response for SSI when compared to fixed base is because of
accounting for the kinematic and inertial interactions in later case. That is in this ground
acceleration is getting altered before reaching the surface because of presence of soil that is site
effect and also the presence of stiff foundation elements that is kinematic interaction. Also
in the response of structure with SSI, we see that there is some time for the wave to reach the
structure which is the travel time of the S wave.
Case 1. Group effect of structures resting on piles
a. Group of two identical buildings.
In this group of two identical buildings of same dynamic characteristics (mass, stiffness and
frequency) are modeled as both fixed base system without considering SSI and also as a
whole pile, soil and frame with SSSI. Two buildings of same structural aspect ratios (3)
are kept adjacent to each other and analyzed. Figure. 7.7 shows the dynamic response of
structure soil-structure system together with response of fixed base system under seismic
excitation. In case of structure soil-structure interaction system the presence of neighboring
structure make a considerable change in response with a shift of natural period of the system as
shown in Figure. 7.8. Because of the presence of neighboring structure SSSI period and the fixed
base period differ by a factor of 3. This shift of period is observed as soil and foundation
elements are playing a major role in the response. At the time of shaking there is a change in
h 2
u x u y
L1 L1 L1
Figure. 7.5. Schematic diagram of fixed base system
h 1
h 2
95
0 5 10 15 20-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Time in Sec
Dis
plac
emen
t in
m
With SSIWith out SSI
0 5 10 15 20-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Time in Sec
Dis
plac
emen
t in
m
With SSI left buildingWith SSI right buildingWith out SSI
Figure. 7.6. Response of single building under May 18, 1940 Elcentro Earthquake (NS) (Fixed base system and SSI)
Figure. 7.7. Response of two identical buildings under May 18, 1940 Elcentro Earthquake (NS)
96
dynamic characteristics of the soil. The stiffness and damping characteristics of soil may
change significantly because of the interaction effect. Also it has been observed that soil
between the two piles are more stressed (figure not shown) which is also reason for the
increase in the lateral response of structure. Where as in case of fixed base system the
presence of neighboring structure doesn’t make any difference in the response and both the
frames have same responses at different floor levels and also it has been observed that the
response of the structure in the analysis of group of two identical buildings is same as response
of structure in single building.
b. Group of three identical buildings.
In this group of three identical buildings with same dynamic characteristics (mass, stiffness and
frequency )are modeled as both fixed base system without considering SSI and also as a
whole pile, soil and frame with SSSI. Three buildings of same structural aspect ratios
as 3 are kept adjacent to each other and analyzed. Figure. 7.9 shows the dynamic response of
0 5 10 150
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Frequency
Four
ier A
mpl
itude
With SSIWithout SSI
Figure. 7.8. Fourier Amplitude Spectrum of two identical buildings under May 18, 1940 Elcentro Earthquake (NS)
97
group of three identical buildings. It has been observed that middle building is attracting more
displacements because of trapping of seismic waves at the center due to mutiple
reflection of waves whereas left and right buildings has same response. Same conclusions has
been given by L. A. Padron (2009) in their work that central construction is usually subjected
to strong shaking. The shift of natural period of system is also observed as shown in Figure.
7.10. Because of the presence of neighboring structure SSSI period and the fixed base
period differ by a factor of 4.8. So a reasonable seismic analysis for high rise buildings
supported on pile foundations is needed to produce a safe and economic design which takes
into account this change in period due to group effect.
c. Group of three different buildings.
In this a group of three different buildings with different dynamic characteristics (mass,
stiffness and frequency) are modeled as both fixed base system without considering SSI and
0 5 10 15 20-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Time in Sec
Dis
plac
emen
t in
m
With SSI left buildingWith SSI middle buildingWith SSI right buildingWith out SSI
Figure. 7.9. Response of three identical buildings under May 18, 1940 Elcentro Earthquake (NS)
98
also as a whole pile, soil and frame with SSSI. Three buildings of different
structural aspect ratios as 1.5, 3 and 1.5 are kept adjacent to each other and analyzed.
Figure. 7.11 shows the dynamic response of group of three different buildings adjacent to
each other under seismic excitation. From the figure it has been observed that because
of presence of short period buildings adjacent to long period buildings, the response is changed
significantly as there is a change in dynamic characteristics of soil at the time of shaking. Also
the response of both short buildings is almost same, so only one of the responses is shown in
figure. Whereas for fixed base case the response for both short and long periods buildings are
almost same. To have a safe and economic design it is always preferable to do a detailed
analysis by taking the group effect of buildings. Figure. 7.12 shows the Fourier Amplitude
spectrum, from which we can see that because of presence of neighboring structures with
different dynamic characteristics there is a major shift in SSSI period over fixed based period.
0 5 10 150
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Frequency
Four
ier A
mpl
itude
With SSIWithout SSI
Figure. 7.10. Fourier Amplitude Spectrum of three identical buildings under May 18, 1940 Elcentro Earthquake (NS)
99
0 5 10 15 20-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Time in Sec
Dis
plac
emen
t in
m
With SSI left buildingWith SSI middle buildingWithout SSI left buildingWithout SSI middle building
0 5 10 150
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Frequency
Four
ier A
mpl
itude
With SSI left buildingWith SSI middle buildingWithout SSI left buildingWithout SSI middle building
Figure. 7.11. Response of three different buildings under May 18, 1940 Elcentro Earthquake (NS)
Figure. 7.12. Fourier Amplitude Spectrum of three different buildings under May 18, 1940 Elcentro Earthquake (NS)
100
Case 2. Effect of variability in structure height
In this three different 5 storey, 10 storey and 15 storey framed structures are modeled
individually as both fixed base system without soil-structure interaction and also as a pile soil-
structure system with SSI. Figure. 7. 13 shows the fundamental mode shapes of all the three
structures with their fixed base conditions having fundamental frequency as 2.39 Hz, 1.104 Hz
and 0.68 Hz for 5 storey , 10 storey and 15 storey structures respectively.
Figure. 7. 14 shows the dynamic response of three structures under seismic excitation with
SSI. From the figure it has been observed that after certain height of the building because
of system damping effect there is a decrease in response of the system as we see in case of 15
storey building the response is less compared with 10 storey building. Figure. 7.15
shows the Fourier amplitude spectrum of three structures while considering SSI and all of
them has almost same predominant period with different amplitudes. Figure. 7.16 shows the
dynamic response of the system for fixed base system for all the three structures analyzed.
Figure. 7.13. Fundamental mode shapes of Structures of variable height
5 Storey structure
10 Storey structure
15 Storey structure
101
0 5 10 15 20-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Time in Sec
Dis
plac
emen
t in
m
With SSI 5 storey buildingWith SSI 10 storey buildingWith SSI 15 storey building
0 5 10 150
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Frequency
Four
ier A
mpl
itude
With SSI 5 storeyWith SSI 10 storeyWith SSI 15 storey
Figure. 7.14 Response of Structures of variable height with SSI under May 18, 1940 Elcentro Earthquake (NS)
Figure. 7.15 Fourier Amplitude Spectrum of structures of variable height with SSI under May 18, 1940 Elcentro Earthquake (NS)
102
individually. From the figure it has been observed that for fixed base case the responses are very
less and by considering the whole pile soil system there is an amplification of waves. So while
analyzing any structure consideration of whole system is important because site effect and
the stiff foundation elements are playing a major role in response of system. Figure 7.17 shows
the Fourier amplitude spectrum from which we can see that fixed base predominant period are
different from predominant with SSI, so while analyzing any structure considering it as fixed
base will lead to enormous results.
Case 3. Effect of variability in structure shape
In this two different structures of different dynamic characteristics with different shapes as
shown in Figure. 7.3 are considered. The dynamic analysis is carried out for both fixed base
system without soil-structure interaction and also a pile soil system with SSI. Figure. 7.18
0 5 10 15 20-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
Time in Sec
Dis
plac
emen
t in
m
Without SSI 5 storey buildingWithout SSI 10 storey buildingWithout SSI 15 storey building
Figure. 7.16. Response of structures of variable height without SSI under May 18, 1940 Elcentro Earthquake (NS)
103
0 5 10 150
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Frequency
Four
ier A
mpl
itude
Without SSI 5 storeyWithout SSI 10 storeyWithout SSI 15 storey
Figure. 7.17. Fourier Amplitude Spectrum of structures of variable height without SSI under May 18, 1940 Elcentro Earthquake (NS)
Structure A Structure B
Figure. 7.18 Fundamental mode shapes of structures of variable shape
104
shows the fundamental mode shapes of Structure a and Structure b with their fixed base
conditions having fundamental frequency as 0.68 Hz, 0.76 Hz respectively. Figure. 7.19 shows
the dynamic response of both Structure a and Structure b with SSI. From the figure it has been
observed that for Structure b, the top response is little more compared to response of regular
Structure a, because of sudden change in stiffness of the system, the system is becoming flexible
and it is attracting more seismic forces. Figure. 7. 20 shows the response of two structures for
fixed base condition. From which it has been observed that response of Structure a is more than
the response of Structure b because of neglecting the actual field conditions.
0 5 10 15 20-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
Time in Sec
Dis
plac
emen
t in
m
With SSI 15 storey Structure aWith SSI 15 storey Structure b
Figure. 7.19 Response of structures of variable shape with SSI under May 18, 1940 Elcentro Earthquake (NS)
105
0 5 10 15 20-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Time in Sec
Dis
plac
emen
t in
m
Without SSI 15 storey Structure aWithout SSI 15 storey Structure b
Figure. 7.20 Response of structures of variable shape without SSI under May 18, 1940 Elcentro Earthquake (NS)
106
Chapter 8
8. Summary and Conclusions
8.1 SUMMARY
The post earthquake study of the structures reveals that the interaction of soil and foundation is
playing a major role in the damage/response of structure. In this regard a literature survey has
been done on Frame structures supported on various foundations like isolated footings, mat
foundations, combined footings or pile foundations; Perusal of literature reveals that very few
investigations were done on frame structures supported on pile foundations. So in this thesis, an
attempt is made to bring out the prominent investigations on soil-structure interaction analysis of
framed structures supported on pile foundations.
To address this problem, a Finite Element Method is used to model soil-structure interaction
analysis of pile supported framed structures by programming in MATLAB R2009a using Direct
approach. A parametric study of seismic pile response in linear soil medium is carried out to
understand the effects of modulus of elasticity of pile and soil, pile length, pile diameter, number
of piles of the pile group and effect of different earthquake on the response.
As the dynamic response of the structure and the pile to large extent is inelastic, the primary
focus is on the understanding of the behavior of superstructure by modeling the nonlinearities of
soil, modeling the interface of soil and pile. For this purpose Finite element Program SAP 2000
is used.
Besides this the change in response of a high rise structure when a group of adjacent pile
supported structures are present under seismic excitation is commented and for each case this
SSSI response is compared with the conventional fixed base response. For this purpose Finite
element Program ANSYS is used.
107
The major elements of work undertaken in this study are
1. A numerical model has been developed to understand the dynamic behaviour of pile
supported frame structure using Direct Approach.
2. Behaviour of frame building has been studied by modeling the nonlinearity of soil.
3. Behaviour of frame building has been studied by modeling the interface between pile and
soil.
4. Behaviour of group of pile supported structures has been studied and the responses are
compared with conventional fixed base analysis.
8.2 CONCLUSIONS
The salient conclusions drawn from this study are
1. A Finite Element Method is used to understand the transient behavior of pile supported high
rise structure. From the parametric study of single pile embedded in soil, it has been observed
that for pile and soil properties considered in this study there is not significant variation in the
free field and pile soil response.
2. Also a parametric study is done to understand the effect of various earthquakes on the
response of a single pile embedded in soil. From this a considerable variation in predominant
frequency of the free field soil and the pile soil interaction is observed. So to have a better
understanding on the transient behavior a detailed analysis is required.
3. When the effect of material nonlinearity on a soil foundation interaction of a group of piles
and soil is considered, there is considerable change in response of the two. A peculiar
behavior in the stress state of pile is observed, this behavior is because of Soil resistance
acting downward along the pile shaft because of an applied transient load. So while
designing pile care should be taken in the design of the tip.
4. Also in studying the behavior of the material nonlinearity on soil foundation interaction, the
effect of interaction of pile with adjacent piles on the stress state is clearly seen with a
considerable change in response of the left and right side piles.
108
5. In case of soil foundation structure interaction (SFSI) considering linear and nonlinear
material behavior of the strong ground motion, repeated dynamic contacts of soil and pile
causing the lateral compression of soil leading to formation of gap between pile and soil is
observed. So to have a good understanding on the transient behavior of SFSI, a detailed
analysis has to be done.
6. Also while understanding the significance of SFSI over fixed base analysis, it has been
observed that the presence of soil and foundation make a considerable change in response of
the structure with a shift of natural period of the system, which is an important parameter in
any dynamic analysis.
7. It is important to consider the contact between pile and soil in the dynamic analysis of SFSI
as a drastic change in response is observed. Also the behavior on stress state of pile is very
much different from earlier behavior of not considering link elements between pile and soil.
So neglecting this behavior makes the over estimation in assessing the strength of foundation.
8. Also the change in response of a high rise structure when a group of adjacent pile supported
structures are present is studied for various cases.
9. In case of group of two identical structures with same dynamic characteristics, there is a
significant change in the lateral response because of the presence of adjacent structures and
there is a shift in period by a factor of 3.
10. When group of identical structures with same dynamic characteristics are present, SSSI
effects have been found to be important. The middle structures are attracting more
displacements because of trapping of seismic waves. Also in case of group of structures with
different buildings the change in response is not so significant for fixed base structure
without SSSI.
11. In case of response of structures with variable height, while considering SSI there is a
decrease in response for 15 storey structure when compared to 10 storey structure which is
not observed in fixed base system.
109
12. In case of response of structures of variable shape the top floors will attract more
displacement because of reduced stiffness on top floors but in conventional fixed base case
opposite behavior is observed.
13. The seismic behavior of high rise structures supported on pile foundation is different from
that of rigid base structure. It has been observed from the responses of different cases that the
nonlinearity, contact between pile and soil and group effect of neighboring pile supported
structures are playing a major role in dynamic analysis. So a reasonable seismic analysis for
high rise buildings supported on pile foundations is needed to produce a safe and economic
design.
8.3 LIMITATIONS OF THE STUDY
The following are the limitations of this study.
1. The dynamic loading was applied as 1 dimensional horizontal acceleration and only
horizontal response is measured. Vertical accelerations were ignored because the margin of
safety against static vertical forces usually provided adequate resistance to dynamic forces
induced by vertical accelerations.
2. Although the finite element analysis used in this study includes important features such as
soil nonlinearity and gapping at pile soil interface, it does not account for buildup of pore
pressure due to cyclic/dynamic loading. Thus, neither the potential for liquefaction nor the
dilatational effect of clays and the compaction of loose sands in the vicinity of piles is
accounted for in current analysis.
3. The friction at the soil-pile interface is neglected. At every time step/iteration only separation
and debonding of pile and soil is considered.
4. The presence of steel reinforcement both in structure and piles is not considered.
8.4 SUGGESTIONS FOR FUTURE WORK
The following suggestions are made for future work in this area.
110
1. A detailed SFSI analysis on modeling the layered soil medium, including the effects of water
table.
2. A detailed SFSI analysis on modeling the contact between the pile and soil, taking the effects
of stick or no slip, slip, debonding / separation and rebonding behaviors.
3. SFSI analysis of a building with infill walls can be studied.
4. SFSI analysis of Unsymmetrical pile supported frame systems can be studied.
111
Appendix - A
Analytical Solution for Fixed Head Socketed Pile
The ground line displacement of fixed head socketed pile in uniform soil subjected to horizontal
load H is given by Poulos and Davis (1980)
For reading IPF and FPF from graph (Figure. 2.11) Pile flexibility factor (KR) and L/d values and
Pile flexibility factor (KR) and H/Hu values are needed respectively. (Assumption Applied load H
is very much less than ultimate load Hu)
The Pile Flexibility Factor KR is given by Poulos and Davis (1980)
)11.2(Fig.pileheadfixedforfactorrotationYiledF2.11a) (Fig.pileheadfixedonloadhorizontalforfactorinfluencentDisplacemeIPileofLengthL;LoadHorizontalH;soilofelasticityofModulusE Where
)1(
PF
PF
s
b
FLE
H
IδPF
sPF
pileofInertiaofMomentI;PileofLengthL;pileofelasticityofModulusE;soilofelasticityofModulusEWhere
)2(
P
ps
4LEIE
KS
PPR
112
a
Figure. A1 Influence factor IPH for free head Socketed pile in uniform soil b. Yield deflection factor FPF for fixed head pile in uniform soil, Poulos and Davis, 1980
b
IPH FPF
113
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