3,/(62,/,17(5$&7,2 1%

PILE SOIL INTERACTION BY FINITE

ELEMENT METHOD IN ABAQUS

Submitted in partial fulfilment of the requirements

of the degree of Bachelor of civil engineering

by

Mr. Ansari Azhar Niyaz 13CES07 Mr. Ansari Junaid Ahmed Shafeeque Ah. 13CES08 Mr. Barudgar Mohd Atique Sadique 13CES11 Mr. Khan Abid Noor 13CES20

Supervisor(s):

Prof. Dada.S.Patil

Department of Civil engineering School of Engineering and Technology

Anjuman-I-Islam’s Kalsekar Technical Campus Plot No. 2 & 3, Sector-16, Near Thana Naka, Khandagaon

New Panvel, New Mumbai 410206, 2016-2017

ii

CERTIFICATE

This is to certify that Mr. Ansari Azhar Niyaz (13CES07), Mr. Ansari Junaid Ahmed

Shafeeque Ah. (13CEs08), Mr. Barudgar Mohd Atique Sadique (13CEs11) and Mr. Khan Abid

Noor (13CEs20) are the students of Semester-VIII of B.E. Civil has satisfactorily completed

and delivered a special topic, seminar report on “Soil-Pile Interaction by Finite Element

Method in Abaqus” in partial fulfilment for the completion of the B.E. in Civil Engineering

course conducted by the University of Mumbai in Anjuman-I-Islam’s Kalsekar Technical

Campus, New Panvel, Navi Mumbai, during the academic year 2016-2017

Prof. Dada.S.Patil

(Guide)

Dr. R. B. Magar Dr. Abdul Razak Hunnutagi

(HOD) (Director)

iii

PROJECT REPORT APPROVAL FOR B. E

This B. E. Project Part-A entitled “Pile Soil Interaction by FEM in Abaqus” Mr.

Ansari Azhar Niyaz (13CES07), Mr. Ansari Junaid Ahmed Shafeeque Ah.

(13CES8), Mr. Barudgar Mohd Atique Sadique (13CES11), Mr. Khan Abid Noor

(13CES20) by Dada.S.Patil is approved for the degree of Bachelor of Engineering

in Civil Engineering.

Examiners

1. …………………………

2. …………………………

Supervisors:

1. …….…………………….

2. …………………………

Chairman

………………………………

Date: 5-May-2017

Place: Panvel

iv

DECLARATION

We Mr. Ansari Azhar Niyaz (13CES07), Mr. Ansari Junaid Ahmed Shafeeque Ah.

(13CES8), Mr. Barudgar Mohd Atique Sadique (13CES11), Mr. Khan Abid Noor

(13CES20) Civil engineering student of Anjuman Islam Kalsekar Technical Campus,

hereby declare that I have completed the project titled Soil-Pile Interaction by Finite Element

Method in Abaqus during the academic year 2016-2017. I declare that this written submission

represents my ideas in my own words and where others' ideas or words have been included, I

have adequately cited and referenced the original sources. I also declare that I have adhered to

all principles of academic honesty and integrity and have not misrepresented or fabricated or

falsified any idea/data/fact/source in my submission. I understand that any violation of the

above will be cause for disciplinary action by the Institute and can also evoke penal action from

the sources which have thus not been properly cited or from whom proper permission has not

been taken when needed.

Mr. Ansari Azhar Niyaz(13CES07) Mr. Ansari Junaid Ahmed Shafeeque Ah(13CES8)

Mr. Barudgar Mohd Atique Sadique(13CES11)

Mr. Khan Abid Noor(13CES20)

v

ACKNOWLEDGEMENT

It is to express our sincerest regards to our project Guide, Prof. Dada.S.Patil for their valuable

inputs, valuable, guidance, encouragement, whole-hearted cooperation throughout the duration

of our project.

We deeply express our sincere thanks to our Head of Department Dr. R. B. Magar and our

Director Dr. Abdul Razak Hunnutagi for encouraging and allowing us to present the project

on the topic “Pile Soil Interaction by Finite Element Method in Abaqus” in partial

fulfilment of the requirements leading to the award of Bachelor of Civil Engineering degree.

We take this opportunity to thank all our Professors and non-teaching staff who have directly

or indirectly helped our project, especially Prof. Shaikh Wasim. We pay our respects and love

to our parents and all other family members and friends for their love and encouragement

throughout our career.

Mr. Ansari Azhar Niyaz

Mr. Ansari Junaid Ahmed Shafeeque Ah.

Mr. Barudgar Mohd Atique Sadique

Mr. Khan Abid Noor

(Semester- VII &VIII, B.E. Civil)

AIKTC- New Panvel

Navi Mumbai.

vi

ABSTRACT

Soil is a complex, heterogeneous material, having a strongly nonlinear response under action

of external load. Due to this the constitutive laws associated to various soil types (cohesive,

non-cohesive, saturated or unsaturated etc.) are continuously developed and improved. Analysis

of soil had been and still a very challenging task for geotechnical engineers throughout the

world. This is due to the non-linear behavior of soil and inability of constitutive relations in

predicting exact behavior of soil. To overcome these difficulties in analysis, there is various

material models has been developed with more complex constitutive relationship. Material

models such as Mohr-Coulomb model uses very complex constitutive relationship. Solution of

this complex partial differential equation is tedious and time consuming process, hence Finite

Element Method is used to solve these equations.

Present study focuses on the settlement analysis of pile foundation in a cohesive soil by using

Mohr- Coulomb model. In addition to settlement analysis, this study also incorporates soil-

structure interaction between pile and soil. The results obtain after the analysis shall be

compared with analysis without soil-structure interaction and conclude the suitability of using

Soil-Structure interaction in pile settlement analysis.

KEY WORDS: Constitutive relationship, Mohr-Coulomb Model, Finite Element Method,

Soil-Structure Interaction

vii

CONTENTS

1

Project Report Approval for B. E iii

Declaration iv

Acknowledgement v

Abstract vi

Contents vii

List of figures ix

List of tables x

Abbreviation Notation and Nomenclature xi

Chapter 1 Introduction 1

1.1 Abaqus 2 1.2 Finite element method (F.E.M) 2

1.2.1 Historical Background 3 1.2.2 Basic Steps 5 1.2.3 Advantages of the finite element method over other numerical methods 6 1.2.4 Constitutive model: theory and implementation 7

1.3 Objective of project 18 1.4 Scope of project 19

Chapter 2 Literature Review 20

Chapter 3 Methodology 30

3.1 Finite element modelling 31 3.1.1 Mesh and boundary conditions 31 3.1.2 Constitutive modelling 32

Chapter 4 Validation to Software 33

4.1 General 33 4.2 Module 34

4.2.1 The part module 34 4.2.2 The Property module 34 4.2.3 The Assembly module 35 4.2.4 The Step module: 35 4.2.5 The Load module: 35 4.2.6 The Mesh module: 36 4.2.7 The Job module: 39 4.2.8 The Sketch module: 39

4.3 Contours 40 4.4 X–Y data 40 4.5 Result 41

Chapter 5 Analysis and results 43

5.1 Analysis on pile 43

viii

5.1.1 Effect of different size of mesh of pile 43 5.1.2 Effect of the diameter of the pile 46

Chapter 6 Conclusion 48

References 50

ix

LIST OF FIGURES

Figure 1:1 Transverse Isotropy coordinate axes convention .................................................... 10

Figure 1:2 Mohr-Coulomb failure criteria ................................................................................ 14

Figure 1:3 Domain used in the definition of the flow rule ....................................................... 15

Figure 3:1 (i)Typical finite element mesh (ii)Pile soil interface modelling (a) no slip (b) slip

(c) Coulomb’s frictional law............................................................................................. 32

Figure 4:1 Part module ............................................................................................................. 34

Figure 4:2 Property Module ..................................................................................................... 35

Figure 4:3 Boundary condition ................................................................................................. 36

Figure 4:4 Mesh ........................................................................................................................ 37

Figure 4:5 Slave mesh .............................................................................................................. 38

Figure 4:6 Master mesh ............................................................................................................ 38

Figure 4:7 Deformed shape ...................................................................................................... 40

Figure 4:8 Displacement v/s Load ............................................................................................ 41

Figure 4:9 Stress blub ............................................................................................................... 42

Figure 4:10 Terzaghi’s shear failure zones............................................................................... 42

Figure 3:2 Load vs Settlement curve of the pile (for different mesh size) ............................... 45

Figure 3:3 Settlement of pile model ......................................................................................... 45

Figure 3:4 Settlement of the Pile (cross section) ...................................................................... 46

Figure 3:5 Load vs Settlement curve (Increase in Diameter) ................................................... 47

x

LIST OF TABLES

Table 3:1 Properties of Materials 30

Table 3:2 Loading analysis with different mesh size 44

xi

ABBREVIATION NOTATION AND NOMENCLATURE

FEM - Finite Element Method

FEA - Finite Element Analysis

FDM - Finite Difference Method

1

Chapter 1 Introduction

When piles are subjected to various type of loadings like static, dynamic, or inclined, lateral

loads it undergoes settlement which imparts or tends soil to undergo change in its properties

like change in dilation angle or changes in stress in dominated part which in recent years

analyzed by usual methodologies and by constitutive partial differential equations.

Relative movements between bodies in contact are described either by a local high velocity

gradient or by a kinematic discontinuity. In both cases, the development of a nonlinear behavior

within contact, inducing a very slow rate of convergence of the global solution except for

models of thin layers. Two major kinds of constitutive equations are used for modelling the

soil-structure interface behavior, often associated with the Finite Element method. The first

one considers the soil-structure interface as a thin continuum (Desai, 1981; Ghaboussi et al.,

1973), thus the thickness of the interface elements should then be specified. In the second

approach, the interface zone is replaced by a two-dimensional continuum (Boulonand

Jarzebowski,1991; Genset al.,1989) subjected to kinematic discontinuities and exhibiting

tangential as well as normal displacement jumps. Most interface models were employed

in Elastic–plastic form by Boulon, Gens, Desaian Ghaboussi his paper aims at investigating

pile–soil interaction through changing pile–soil interface coefficient and studying this

phenomenon for the settlement of pile, shear stress and forces in the pile. The numerical

PILE SOIL INTERACTION BY FINITE ELEMENT METHOD IN ABAQUS

2

modelling is going to be carried out by means of the Finite Element method as it allows for

modelling complicated nonlinear soil behavior and various interface conditions, with different

geometries and soil properties.

1. Excess pore pressure: Ability to deal with excess pore-pressure phenomena. Excess pore

pressures are computed during plastic calculations in undrained soil.

2. Soil-pile interaction: Interfaces can be used to simulate intensely shearing zone in contact

with the pile, with values of friction angle and adhesion different to the friction angle and

cohesion of the soil.

3. Better insight into soil-structure interaction.

4. Soil model: It can reproduce advanced constitutive soil models for simulation of non-linear

behavior.

1.1 Abaqus

Abaqus/CAE is a complete Abaqus environment that provides a simple, consistent interface for

creating, submitting, monitoring, and evaluating results from Abaqus/Standard and

Abaqus/Explicit simulations. Abaqus/CAE is divided into modules, where each module defines

a logical aspect of the modelling process; for example, defining the geometry, defining material

properties, and generating a mesh. As you move from module to module, you build the model

from which Abaqus/CAE generates an input file that you submit to the Abaqus/Standard or

Abaqus/Explicit analysis product. The analysis product performs the analysis, sends

information to Abaqus/CAE to allow you to monitor the progress of the job, and generates an

output database. Finally, you use the Visualization module of Abaqus/CAE (also licensed

separately as Abaqus/Viewer) to read the output database and view the results of your analysis.

1.2 Finite element method (F.E.M)

A finite element method (abbreviated as FEM) is a numerical technique to obtain

an approximate solution to a class of problems governed by elliptic partial differential

equations. Such problems are called as boundary value problems as they consist of a partial

differential equation and the boundary conditions. The finite element method converts the


3

elliptic partial differential equation into a set of algebraic equations which are easy to solve.

The initial value problems which consist of a parabolic or hyperbolic differential equation and

the initial conditions (besides the boundary conditions) cannot be completely solved by the

finite element method. The parabolic or hyperbolic differential equations contain the time as

one of the independent variables. To convert the time or temporal derivatives into algebraic

expressions, another numerical technique like the finite difference method (FDM) is required.

Thus, to solve an initial value problem, one needs both the finite element method as well as the

finite difference method where the spatial derivatives are converted into algebraic expressions

by FEM and the temporal derivatives are converted into algebraic equations by FDM.

1.2.1 Historical Background

The words "finite element method" were first used by Clough in his paper in the Proceedings

of 2nd ASCE (American Society of Civil Engineering) conference on Electronic Computation

in 1960. Clough extended the matrix method of structural analysis, used essentially for frame-

like structures, to two-dimensional continuum domains by dividing the domain into triangular

elements and obtaining the stiffness matrices of these elements from the strain energy

expressions by assuming a linear variation for the displacements over the element. Clough

called this method as the finite element method because the domain was divided into elements

of finite size. (An element of infinitesimal size is used when a physical statement of some

balance law needs to be converted into a mathematical equation, usually a differential equation).

Argyris, around the same time, developed similar technique in Germany. But, the idea of

dividing the domain into a number of finite elements for the purpose of structural analysis is

older. It was first used by Courant in 1943 while solving the problem of the torsion of non-

circular shafts. Courant used the integral form of the balance law, namely the expression for the

total potential energy instead of the differential form (i.e., the equilibrium equation). He divided

the shaft cross-section into triangular elements and assumed a linear variation for the primary

variable (i.e., the stress function) over the domain. The unknown constants in the linear

variation were obtained by minimizing the total potential energy expression. The Courant's


4

technique is called as applied mathematician's version of FEM where as that of Clough and

Argyris is called as engineer's version of FEM.

From 1960 to 1975, the FEM was developed in the following directions:

(1) FEM was extended from a static, small deformation, elastic problems to

dynamic (i.e., vibration and transient) problems,

small deformation fracture, contact and elastic -plastic problems,

non-structural problems like fluid flow and heat transfer problems.

(2) In structural problems, the integral form of the balance law namely the total potential energy

expression is used to develop the finite element equations. For solving non-structural problems

like the fluid flow and heat transfer problems, the integral form of the balance law was

developed using the weighted residual method.

(3) FEM packages like NASTRAN, ANSYS, and ABAQUS etc. were developed.

The large deformation (i.e., geometrically non-linear) structural problems, where the domain

changes significantly, were solved by FEM only around 1976 using the updated Lagrangian

formulation. This technique was soon extended to other problems containing geometric non-

linearity:

dynamic problems,

fracture problems,

contact problems,

elastic-plastic (i.e., materially non-linear) problems.

Some new FEM packages for analyzing large deformation problems like LS-DYNA, DEFORM

etc. were developed around this time. Further, the module for analyzing large deformation

problems was incorporated in existing FEM packages like NASTRAN, ANSYS, ABAQUS etc.


5

1.2.2 Basic Steps

The finite element method involves the following steps.

First step, the governing differential equation of the problem is converted into an integral form.

These are two techniques to achieve this:(i) Variational Technique and (ii) Weighted Residual

Technique. In variational technique, the calculus of variation is used to obtain the integral form

corresponding to the given differential equation. This integral needs to be minimized to obtain

the solution of the problem. For structural mechanic’s problems, the integral form turns out to

be the expression for the total potential energy of the structure. In weighted residual technique,

the integral form is constructed as a weighted integral of the governing differential equation

where the weight functions are known and arbitrary except that they satisfy certain boundary

conditions. To reduce the continuity requirement of the solution, this integral form is often

modified using the divergence theorem. This integral form is set to zero to obtain the solution

of the problem. For structural mechanics’ problems, if the weight function is considered as the

virtual displacement, then the integral form becomes the expression of the virtual work of the

structure.

In the second step, the domain of the problem is divided into a number of parts, called as

elements. For one-dimensional (1-D) problems, the elements are nothing but line segments

having only length and no shape. For problems of higher dimensions, the elements have both

the shape and size. For two-dimensional (2D) or axis-symmetric problems, the elements used

are triangles, rectangles and quadrilateral having straight or curved boundaries. Curved sided

elements are good choice when the domain boundary is curved. For three-dimensional (3-D)

problems, the shapes used are tetrahedron and parallelepiped having straight or curved surfaces.

Division of the domain into elements is called a mesh.

In third step, over a typical element, a suitable approximation is chosen for the primary variable

of the problem using interpolation functions (also called as shape functions) and the unknown

values of the primary variable at some pre-selected points of the element, called as the nodes.

Usually polynomials are chosen as the shape functions. For 1-D elements, there are at least 2

nodes placed at the end-points. Additional nodes are placed in the interior of the element. For

2-D and 3-D elements, the nodes are placed at the vertices (minimum 3 nodes for triangles,

minimum 4 nodes for rectangles, quadrilaterals and tetrahedral and minimum 8 nodes for

parallelepiped shaped elements). Additional nodes are placed either on the boundaries or in the

interior. The values of the primary variable at the nodes are called as the degrees of freedom.


6

To get the exact solution, the expression for the primary variable must contain a complete set

of polynomials (i.e., infinite terms) or if it contains only the finite number of terms, then the

number of elements must be infinite. In either case, it results into an infinite set of algebraic

equations. To make the problem tractable, only a finite number of elements and an expression

with only finite number of terms are used. Then, we get only an approximate solution.

(Therefore, the expression for the primary variable chosen to obtain an approximate solution is

called an approximation). The accuracy of the approximate solution, however, can be improved

either by increasing the number of terms in the approximation or the number of elements.

In the fourth step, the approximation for the primary variable is substituted into the integral

form. If the integral form is of variational type, it is minimized to get the algebraic equations

for the unknown nodal values of the primary variable. If the integral form is of the weighted

residual type, it is set to zero to obtain the algebraic equations. In each case, the algebraic

equations are obtained element wise first (called as the element equations) and then they are

assembled over all the elements to obtain the algebraic equations for the whole domain (called

as the global equations).

In this step, the algebraic equations are modified to take care of the boundary conditions on the

primary variable. The modified algebraic equations are solved to find the nodal values of the

primary variable.

In the last step, the post-processing of the solution is done. That is, first the secondary variables

of the problem are calculated from the solution. Then, the nodal values of the primary and

secondary variables are used to construct their graphical variation over the domain either in the

form of graphs (for 1-D problems) or 2-D/3-D contours as the case may be.

1.2.3 Advantages of the finite element method over other numerical

methods

The method can be used for any irregular-shaped domain and all types of boundary

conditions.

Domains consisting of more than one material can be easily analyzed.


7

Accuracy of the solution can be improved either by proper refinement of the mesh or by

choosing approximation of higher degree polynomials.

The algebraic equations can be easily generated and solved on a computer. In fact, a

general purpose code can be developed for the analysis of a large class of problems.

FEM is best method for analysis of complex geometry structure for better and high accuracy

analysis by method of discretization and meshing. FEM is applicable to 1D, 2D as well as 3D

model analysis. Modelling of complex geometries and shape is easy. Boundary conditions can

be easily incorporated in FEM. It is easy to control the accuracy by refining the mesh or using

higher order elements. FEM is commonly introduced as a special case of Galerkin method. The

process, in mathematical language, is to construct an integral of the inner product of the residual

and the weight functions and set the integral to zero. In simple terms, it is a procedure that

minimizes the error of approximation by fitting trial functions into the PDE. The residual is the

error caused by the trial functions, and the weight functions are polynomial approximation

functions that project the residual. The process eliminates all the spatial derivatives from the

PDE, thus approximating the PDE locally with

A set of algebraic equations for steady state problems,

A set of ordinary differential equations for transient problems.

FEA is a good choice for analyzing problems over complicated domains (like piles, raft

footings), when the domain changes (as during a solid state reaction with static boundary), when

the desired precision varies over the entire domain, or when the solution lacks smoothness. For

instance, in a pile settlement simulation it is possible to increase prediction accuracy in

"important" areas like the top portion of pile as it is subjected to loadings and reduce it in its

middle portion (thus reducing cost of the simulation) and thereby again increasing prediction

accuracy at bottom of pile.

1.2.4 Constitutive model: theory and implementation

There are eleven basic constitutive models provided in FLAC Version 5.0, arranged into null,

elastic and plastic model groups:


8

Null model group

null model

A null material model is used to represent material that is removed.

The stresses within a null zone are set to zero; no body forces (e.g., gravity) act on these zones.

The null material may be changed to a different material model at a later stage of the simulation.

In this way, backfilling an excavation, for example, can be simulated.

Elastic model group

The models in this group are characterized by reversible deformations upon unloading; the

stress strain laws are linear and path-independent.

Elastic, Isotropic model

The elastic, isotropic model provides the simplest representation of material behavior. This

model is valid for homogeneous, isotropic, continuous materials that exhibit linear stress-strain

behavior with no hysteresis on unloading.

In this model, the relation of stress to strain in incremental form is expressed by Hooke’s law

in plane strain as:

∆σ11 = α1 ∆e11 +α2 ∆e22

∆σ22 = α2 ∆e11 +α1 ∆e22

∆σ12 = 2G ∆e12 (∆σ21 = ∆σ12)

∆σ33 = α2 (∆e11 +∆e22)

where α1 = K +(4/3) G;

α2 = K −(2/3) G;

K = bulk modulus; and

G = shear modulus.

∆eij = (1/2*(∂ui/∂xj + ∂uj/∂xi) ∆t

∆eij = the incremental strain tensor;

ui = the displacement rate;

∆t = time step;

In plane stress, these equations become;

∆σ11 = β1 ∆e11 +β2 ∆e22

∆σ22 = β2 ∆e11 +β1 ∆e22

∆σ12 = 2G ∆e12 (∆σ21 = ∆σ12)

∆σ33 = 0

where β1 = α1 −(α22/α1); and


9

β2 = α2 −(α2 2/α1).

For axisymmetric geometry:

∆σ11 = α1 ∆e11 +α2 (∆e22 +∆e33)

∆σ22 = α1 ∆e22 +α2 (∆e11 +∆e33)

∆σ12 = 2G ∆e12 (∆σ21 = ∆σ12)

∆σ33 = α1 ∆e33 +α2 (∆e11 +∆e22)

Elastic, Transversely isotropic model

The elastic, transversely isotropic model gives the ability to simulate layered elastic media in

which there are distinctly different elastic moduli in directions normal and parallel to the layers.

The elastic moduli are defined as follows:

E1 (or Ex) - modulus of elasticity in plane of isotropy

E2 (or Ey) - modulus of elasticity in plane perpendicular to plane of isotropy

G12 (or Gxy) - cross-shear modulus between plane of isotropy and perpendicular plane (i.e., xy-

or yz-plane)

G13 (or Gxz) - shear modulus in plane of isotropy

ν21 (or νyx) - Poisson’s ratio for the normal strain in the x-direction in plane of isotropy related

to the normal strain in the y-direction in the perpendicular plane due to uniaxial stress in the y-

direction

ν31 (or νzx) - Poisson’s ratio for the normal strain in the x-direction in the plane of isotropy

related to the normal strain in the z-direction due to uniaxial stress in the z-direction

A transversely isotropic elastic material is characterized by five independent constants (or

moduli).

For a transversely isotropic body whose plane of isotropy lies within the xz-plane, the following

relations apply:

E3 = E1 (or Ez = Ex)

ν31 = ν13 (or νzx = νxz)

ν23 = ν21 (or νyz = νyx)

G23 = G12 (or Gyz = Gxy)

G13 = E1/2(1 + v31) (or Gxz = Ex/2(1 + vzx)

V12 = v21 E1/E2 (or vxy = vyx Ex/Ey)


10

Figure 1:1 Transverse Isotropy coordinate axes convention

(xz-direction is plane of isotropy)

There are limitations on the variations in elastic properties (Amadei 1982). The

following restrictions apply:

Ex > 0

Ey > 0

Gxy > 0

νxy2 ≤ 1

νxz2 ≤ 1

(1−νxz) − (2Ex νyx2) /Ey ≥ 0

For a general orthotropic elastic body, the stress-strain equations are given by Lekhnitskii

(1981, p. 34):

∆e11 = S11 ∆σ11 +S12 ∆σ22 +S13 ∆σ33 + S16 ∆σ12

∆e22 = S12 ∆σ11 +S22 ∆σ22 +S23 ∆σ33 + S26 ∆σ12

∆e33 = S13 ∆σ11 +S23 ∆σ22 +S33 ∆σ33 + S36 ∆σ12 …. (1)

∆e23 =1/2[(S44 ∆σ23) + (S45 ∆σ13)]

∆e13 =1/2[(S45 ∆σ23) + (S55 ∆σ13)]

∆e12 =1/2[(S16 ∆σ11) + (S26 ∆σ22) + (S36 ∆σ33) + (S66 ∆σ12)]

A state of plane stress with respect to the xy-plane is obtained by setting

∆σ33 = ∆σ13 = ∆σ23 = 0


11

In equation (1) This gives:

∆e11 = S11 ∆σ11 +S12 ∆σ22 +S16 ∆σ12

∆e22 = S12 ∆σ11 +S22 ∆σ22 +S26 ∆σ12

∆e12 =1/2 (S16 ∆σ11 +S26 ∆σ22 +S66 ∆σ12)

Which can be written as:

The stress-strain relations can easily be found by inverting the matrix.

A state of plane strain in the xy-plane is obtained from Eq (1) by setting

∆e33 = ∆e13= ∆e23 = 0

This results in:

∆e11 = 11∆σ11 +S12∆σ22 +S13∆σ33 +S16∆σ12

∆e22 = S12∆σ11 +S22∆σ22 +S23∆σ33 +S26∆σ12

0 = S13∆σ11 +S23∆σ22 +S33∆σ33 +S36∆σ12

0 = S44∆σ23 +S45∆σ13

0 = S55∆σ13 +S45∆σ23

∆e12 =1/2(S16∆σ11 +S26∆σ22 +S36∆σ33 +S66∆σ12)

which can be written

The stress-strain relations can be obtained by inverting the matrix.

Plastic model group

All plastic models potentially involve some degree of permanent, path-dependent deformations

(failure); a consequence of the nonlinearity of the stress-strain relations. The different models

in FLAC are characterized by their yield function, hardening/softening functions and flow rule.

The yield functions for each model define the stress combination for which plastic flow takes

place. These functions or criteria are represented by one or more limiting surfaces in a

generalized stress space with points below or on the surface being characterized by an

incremental elastic or plastic behavior, respectively. The plastic flow formulation in FLAC rests


12

on basic assumptions from plasticity theory that the total strain increment may be decomposed

into elastic and plastic parts, with only the elastic part contributing to the stress increment by

means of an elastic law. In addition, both plastic and elastic strain increments are taken to be

coaxial with the current principal axes of the stresses (only valid if elastic strains are small

compared to plastic strains during plastic flow). The flow rule specifies the direction of the

plastic strain increment vector as that normal to the potential surface; it is called associated if

the potential and yield functions coincide, and non-associated otherwise. See Vermeer and

deBorst (1984) for a more detailed discussion on the theory of plasticity.

For the Drucker-Prager, Mohr-Coulomb, ubiquitous-joint, strain-softening and bilinear-

softening ubiquitous models, a shear yield function and a non-associated shear flow rule are

used. For the double-yield model, shear and volumetric yield functions, non-associated shear

flow and associated volumetric flow rules are included. In addition, the failure envelope for

each of these models is characterized by a tensile yield function with associated flow rule. The

modified Cam-clay model formulation rests on a combined shear and volumetric yield function

and associated flow rule. The Hoek-Brown model uses a nonlinear shear yield function and a

plasticity flow rule that varies as a function of the stress level.

In FLAC, the out-of-plane stress is taken into consideration in the formulation that is expressed

in three-dimensional terms. All models are based on plane-strain conditions, with the exception

of the strain-softening model, which is also available in a plane-stress option. Note also that all

plasticity models are formulated in terms of effective stresses, not total stresses.

Drucker-Prager model

The Drucker-Prager plasticity model may be useful to model soft clays with low friction angles;

however, this model is not generally recommended for application to geologic materials. It is

included here mainly to perform it comparison with other numerical program results.

The failure envelope for this model consists of a Drucker-Prager criterion with tension cutoff.

The shear flow rule is non-associated and the tensile flow rule is associated. For a detailed

description of the model see, for example, Chen and Han (1988).


13

Mohr-Coulomb model

The Mohr-Coulomb model is the conventional model used to represent shear failure in soils

and rocks. Vermeer and deBorst (1984), for example, report laboratory test results for sand and

concrete that match well with the Mohr Coulomb criterion.

The failure envelope for this model corresponds to a Mohr-Coulomb criterion (shear yield

function) with tension cutoff (tensile yield function). The shear flow rule is non-associated and

the tensile flow rule is associated.

In the FLAC implementation of this model, principal stresses σ1, σ2, σ3 are used, the out-of-

plane stress, σz, being recognized as one of these. The principal stresses and principal directions

are evaluated from the stress tensor components and ordered so that (recall that compressive

stresses are negative)

σ1 ≤ σ2 ≤ σ3 …. (1)

The corresponding principal strain increments ∆e1, ∆e2, ∆e3 are decomposed as follows

∆ei = ∆eie + ∆ei

P i = 1,3 …. (2)

where the superscripts e and p refer to elastic and plastic parts, respectively, and the plastic

components are nonzero only during plastic flow. The incremental expression of Hooke’s law

in terms of principal stress and strain has the form

∆σ1 = α1∆e1e +α2(∆e1 +∆e3

e)

∆σ2 = α1∆e2e +α2(∆e1 +∆e3

e) (3)

∆σ3 = α1∆e3e +α2(∆e1

e +∆e2e)

where α1 = K +4G/3 and α2 = K −2G/3.

Yield and Potential Functions

With the ordering convention of Eq. (1), the failure criterion may be represented in the plane

(σ1, σ3) as illustrated in Figure below.


14

Figure 1:2 Mohr-Coulomb failure criteria

The failure envelope is defined from point A to point B by the Mohr-Coulomb yield function

fs = σ1 − σ3Nφ +2c√Nφ

and from B to C by a tension yield function of the form

ft = σt –σ3

where φ is the friction angle, c, the cohesion, σt, the tensile strength and

Nφ = (1+sin φ) / (1−sin φ)

Note that only the major and minor principal stresses are active in the shear yield formulation;

the intermediate principal stress has no effect. For a material with friction, φ = 0 and the tensile

strength of the material cannot exceed the value σtmax given by

σtmax =c/tan φ

The shear potential function gs corresponds to a non-associated flow rule and has the form

gs = σ1 −σ3 Nψ

where ψ is the dilation angle and

Nψ = (1+sin ψ) / (1−sin ψ)

The associated flow rule for tensile failure is derived from the potential function gt, with

gt = − σ3

The flow rules for this model are given a unique definition in the vicinity of an edge of the

composite yield function in three-dimensional stress space by application of a technique,

illustrated below, for the case of a shear-tension edge. A function h (σ1, σ3) = 0 is defined which

is represented by the diagonal between the representation of f s = 0 and f t = 0 in the (σ1, σ3)

plane (see Figure 2.8). This function has the form

h = σ3 –σt +αp (σ1 –σp)

where αP and σP are constants defined as


15

αP =√1 + Nφ2 + Nφ

and

σP = σt Nφ −2c√Nφ

Figure 1:3 Domain used in the definition of the flow rule

ubiquitous-joint model

The ubiquitous-joint model is an anisotropic plasticity model that includes weak planes of

specific orientation embedded in a Mohr-Coulomb solid.

In this model, which accounts for the presence of an orientation of weakness (weak plane) in a

FLAC Mohr-Coulomb model, yield may occur in either the solid or along the weak plane, or

both, depending on the stress state, the orientation of the weak plane and the material properties

of the solid and weak plane.

In the FLAC implementation, use is made of a technique by which general failure is first

detected and relevant plastic corrections are applied as indicated in the FLAC Mohr-Coulomb

model description. The new stresses are then analyzed for failure on the weak plane and updated

accordingly. The criterion for failure on the plane consists in a local form of the Mohr-Coulomb

yield condition with tension cutoff, the local shear flow rule is non-associated, and the local

tension flow rule is associated. The FLAC Mohr-Coulomb model was addressed above;

developments related to plastic flow on the weak plane are outlined in this section.

strain-hardening/softening model

The strain-hardening/softening model allows representation of nonlinear material softening and

hardening behavior based on prescribed variations of the Mohr-Coulomb model properties

(cohesion, friction, dilation, tensile strength) as functions of the deviatoric plastic strain.


16

This model is based on the FLAC Mohr-Coulomb model with non-associated shear and

associated tension flow rules, as described earlier. The difference, however, lies in the

possibility that the cohesion, friction, dilation and tensile strength may harden or soften after

the onset of plastic yield. In the Mohr-Coulomb model, those properties are assumed to remain

constant. Here, the user can define the cohesion, friction and dilation as piecewise-linear

functions of a hardening parameter measuring the plastic shear strain. A piecewise-linear

softening law for the tensile strength can also be prescribed in terms of another hardening

parameter measuring the plastic tensile strain. The code measures the total plastic shear and

tensile strains by incrementing the hardening parameters at each time step and causes the model

properties to conform to the user-defined functions.

bilinear strain-hardening/softening ubiquitous-joint model

The strain-hardening/softening ubiquitous-joint model allows representation

ofmaterialsofteningandhardeningbehaviorforthematrixandtheweakplane based on prescribed

variations of the ubiquitous-joint model properties (cohesion, friction, dilation, tensile strength)

as functions of deviatoric and tensile plastic strain. The variation of material strength properties

with mean stress canal so be taken into account by using the bilinear option.

Thebilinearstrain-hardening/softeningubiquitous-

jointmodelisageneralizationoftheubiquitousjoint model described in above model. In the

bilinear model, the failure envelopes for the matrix and joint are the composite of two Mohr-

Coulomb criteria with a tension cutoff that can harden or soften according to specified laws. A

non-associated flow rule is used for shear-plastic flow and an associated flow rule for tensile-

plastic flow.

The softening behaviors for the matrix and the joint are specified in tables in terms of four

independent hardening parameters, two for the matrix and two for the joint, which measure the

amount of plastic shear and tensile strain, respectively. In this numerical model, general failure

is first detected for the step and relevant plastic corrections are applied. The new stresses are

then analyzed for failure on the weak plane and updated accordingly. The hardening parameters

are incremented if plastic flow has taken place and the parameters of cohesion, friction, dilation

and tensile strength are adjusted for the matrix and the joint using the tables.


17

double-yield model

The double-yield model is intended to represent materials in which there may be significant

irreversible compaction in addition to shear yielding, such as hydraulically-placed backfill or

lightly-cemented granular material.

modified Cam-clay model

The modified Cam-clay model may be used to represent materials when the influence of volume

change on bulk property and resistance to shear need to be taken into consideration, such as soft

clay.

The modified Cam-clay model is an incremental hardening/softening elastoplastic model. Its

features include a particular form of nonlinear elasticity and a hardening/softening behavior

governed by volumetric plastic strain (“density” driven). The failure envelopes are self-similar

in shape and correspond to ellipsoids of rotation about the mean stress axis in the principal

stress space. The shear flow rule is associated; no resistance to tensile mean stress is offered in

this model. See Roscoe and Burland (1968) and Wood (1990) for a detailed discussion on the

modified Cam-clay model. (For convenience, we drop the qualifier “modified” in the following

discussion. Recall that all models are expressed in terms of effective stresses. In particular, all

pressures referred to in this section are effective pressures.)

Hoek-Brown model

The Hoek-Brown failure criterion characterizes the stress conditions that lead to failure in intact

rock and rock masses. The failure surface is nonlinear and is based on the relation between the

major and minor principal stresses. The model incorporates a plasticity flow rule that varies as

a function of the confining stress level.

There are also six time-dependent (creep) material models available in the creep model option

for FLAC (see Section 2 in Optional Features), and two pore-pressure generation models

available in the dynamic analysis option (see Section 3 in Optional Features).

Input parameters to all of these built-in models can be controlled via FISH to modify the

behavior of the models. For example, a nonlinear, elastic model can be created by making the

elastic modulus a function of confining stress (see Section 3.7.8 in the User’s Guide).

Duplicates of several of the built-in elastic and plastic models are provided as FISH functions;

these are described in Section 3 in the FISH volume and contained in the “\FISH” directory.

Users may modify these files as they see fit, or use them as a basis for creating their own


18

constitutive models (see Section 2.8 in the FISH volume). See “HYP.FIS” in Section 3 in the

FISH volume for an example FISH constitutive function of a nonlinear elastic, hyperbolic

model.

The stresses within a null zone are set to zero; no body forces (e.g., gravity) act on these zones.

The null material may be changed to a different material model at a later stage of the simulation.

In this way, backfilling an excavation, for example, can be simulated.

2.3 Elastic Model Group

The models in this group are characterized by reversible deformations upon unloading; the

stress strain laws are linear and path-independent.

2.3.1 Elastic, Isotropic Model

In this model, the relation of stress to strain in incremental form is expressed by Hooke’s law

in plane strain as:

1.3 Objective of project

a) To create material model for cohesive soil by using Mohr-Coulomb model in ABAQUS-

2016

b) To validate the material model and FEM method results by using Terzaghi’s failure theory

and principle stress concept.

c) To carry settlement analysis of group pile in cohesive soil by considering Soil-Pile

interaction.

d) To carry settlement analysis of group pile in cohesive soil without considering Soil-Pile

interaction.

d) To compare results of analysis with and without Soil-Pile interaction.

e) To conclude the suitability of using Soil-Pile interaction in settlement analysis of Piles.


19

1.4 Scope of project

a) The analysis of piles will be done in only in cohesive soil with uniform stratification

b) Mohr-Coulomb model is used for settlement analysis and validation purpose. This model

uses a linear plastic stress-strain curve; in reality the stress strain behavior is non-linear plastic

in case of cohesive soil.

c) Finite Element method will be employed for analysis with static loading conditions.

d) This study does not include the effect for drainage condition in settlement analysis.

e) The friction parameters used for Soil-Pile interaction are assumed to constant and Pile Load

Vs pile settlement curve is assumed to be linear.


20

Chapter 2 Literature Review

Kazimierz Józefiaka

Year of publication-2015

The objective of this paper is to model a soil-pile system using FEM implemented in Abaqus

software. The numerical results of pile bearing capacity and pile settlement were compared with

static load test results of CFA piles carried out during construction of Lazienkowska tract

flyover in Warsawand with engineering analytical calculations according to Euro code 7and

Polish Standard Code.

Finite element model was used to perform bearing capacity calculations. The problem was run

in 2 steps. During the first step geostatic equilibrium was achieved. In step 2, coupled analysis

was invoked and the pile displacement was applied using the vertical speed boundary condition

to force the top surface to move 0.01m/min.

The finite element analysis with simple constitutive models and parameters’ estimation shows

quite good agreement with the field test settlements for the loading part. Significant difference


21

is seen for the unloading. Comparing curves for µ=∞ and tied nodes, one can see that the “elastic

slip” related to contact formulation has some impact on results. For FEM analysis involving

pile settlement the proper identification of the pile shaft-soil interface is of great importance.

However, the real interface behavior is complicated and not fully understood. Elimination of

the “elastic slip” for friction formulation involves using Lagrange multiplayers. It is not

computationally efficient and the results presented herein show that it does not necessarily

improve agreement with test data. The FEA provides very safe estimation of bearing capacity.

Often bearing capacity of piles is achieved at a displacement which is destructive for an

engineering structure. Because of that, experience is needed in order to reduce bearing capacity

values calculated assuming full mobilization of shaft friction.

Ahmed Abdel


In this paper a lateral displacement of 2 cm was applied to the top of the pile while maintaining

a zero slope in a guided fixation. A combined lateral and axial load of 300 kN was also studied.

The paper compared between the bending moments and lateral displacements along the depth

of the pile obtained from the FD solutions and FE analyses. A parametric study was conducted

to study the effect of crucial design parameters such as the modulus of elasticity of soil and the

number of nonlinear soil springs that can be used to model the soil. A good agreement between

the results obtained by the FE models and the FD solution was observed. Also, the FE models

were capable of predicting the pile–soil interaction for all types of soft soil

Mohammed Mahdi jalali


The impact of loading on the pile displacement was explored applying Mohr Coulomb as well

as Hard-soil behaviour laws. The measurements based on the Mohr-Coulomb Behaviour Law

are much more accurate compared to those performed through Hard soil Behaviour Law

(Graphs 1 to 4), when the appropriate interface is taken into consideration. However, the results


22

of Graphs 4 to 7 shows that hard soil Behaviour Law is more accurate and precise compared to

Mohr-Coulomb Behaviour law, when the interface is less effective.

In Mohr-Coulomb Behaviour Law, the shear stress is measured more accurately when the

appropriate interface coefficient is taken into consideration (Figures 4 to 7). While the interface

coefficient is less effective, the Hard soil Behaviour Law measures the shear stress more

accurately.

By Mounir E. Mabsout


Results from the computational driving of a concrete pile below a prebored hole (referred to as

a "prebored" pile for convenience) in an undrained, normally consolidated clayey soil are

presented. The analysis uses a nonlinear, finite-element model that simulates the penetration of

the pile into the soil. The response of the pile-soil system is examined at various preboring

levels. A comparison between the responses of normally consolidated clays with various

strengths is discussed. The influence of pile-soil friction and tip bearing on the response is also

investigated.

R.P. Cunha


A semi analytical procedure is presented and used herein to compute the settlement and the

normal force distribution of axially loaded concrete bored piles. These piles were constructed

in the tropical soil of the city of Brasília, which is a typical lateraled and collapsible clayey

material of the Brazilian Central Plateau. They were constructed under differing construction

procedures, which have influenced in their final behaviour, in terms of load x settlement curves.

The paper demonstrates that with the use of well-established soil parameters for this

geotechnical material, with a sound theoretical model & numerical tool, it is possible to simulate

reasonably well the in situ behavior of the bored piles.


23

K. Johnson, P. Lemckea et. al


In this paperwork, 3D finite element modelling was used to explore the effect of pile shape,

sand properties, pile length and loading conditions on the capacity of a pile. Using trends

discovered by these simulations design charts were developed to aid consultants when

determining the bearing capacity for oblique interaction for square piles. It was found through

a carefully planned sensitivity analysis that sand properties and pile shape can influence the

capacity of a pile extensively.

C. J Lee and Charles W. W Ng

Year of publication- 2004

The investigation of down drag has attracted far less attention than the study of drag load over

the years. In this paper, several series of two-dimensional axisymmetric and three-dimensional

numerical parametric analyses were conducted to study the behaviour of single piles and piles

in 333 and 535 pile groups in consolidating soil. Both elastic no-slip and elasto-plastic slip at

the pile–soil interface were considered. For a single pile, the down drag computed from the no-

slip elastic analysis and from the analytical elastic solution was about 8–14 times larger than

that computed from the elasto-plastic slip analysis. The softer the consolidating clay, the greater

the difference between the no-slip elastic and the elasto-plastic slip analyses. For the 535 pile

group at 2.5 diameter spacing, the maximum down drag of the center, inner, and corner piles

was, respectively, 63, 68, and 79% of the maximum down drag of the single pile. The reduction

of downdrag inside the pile group is attributed to the shielding effects on the inner piles by the

outer piles. The relative reduction in downdrag (Wr) in the 535 pile group increases with an

increase in the relative bearing stiffness ratio (Eb /Ec), depending on the pile location in the

group.

R. L. Raper


One numerical technique that could be used to predict soil compaction is the finite element

method (FEM). linear elastic parameters for each element in the model. Incremental leading


24

was used by the finite element model to gradually load the soil so that these linear parameters

could be varied many times ever the loading period. The finite element model was compared

with data obtained from soil bin research. Results showed that a flat disc load was modelled

well but a spherical disc load was not.

Suleyman Kocak


A simple three-dimensional soil structure interaction (SSI) model is proposed. First, a model is

developed for a layered soil medium. In that model, the layered soil medium is divided into thin

layers and each thin layer is represented by a parametric model. The parameters of this model

are determined, in terms of the thickness and elastic properties of the sublayer, by matching, in

frequency wave number space, the actual dynamic stiffness matrices of the sublayer when the

sublayer is thin and subjected to plane strain and out-of-plane deformations with those predicted

by the parametric model developed in this study. Then, by adding the structure to soil model a

three-dimensional finite element model is established for the soil structure system. For the

floors and footings of the structure, rigid diaphragm model is employed. Based on the proposed

model, a general computer software is developed. Though the model accommodates both the

static and dynamic interaction effects, the program is developed presently for static case only

and will be extended to dynamic case in a future study. To assess the proposed SSI model, the

model is applied to four examples, which are chosen to be static so that they can be analyzed

by the developed program. The results are compared with those obtained by other methods.

B. Pallavi Ravishankar

Year of Publication – 2013

Tall asymmetric buildings experience more risk during the earthquakes (Ming, 2010). This

happens mainly due to attenuation of earthquake waves and local site response which get

transferred to the structure and vice versa. This can be well explained by the Dynamic Soil

Structure Interaction (DSSI) analysis. In this research paper 150 m tall asymmetrical building


25

with two different foundation systems like raft and pile is considered for analysis and assuming

homogeneous sandy soil strata results are studied for input of Bhuj ground motion (2001, M=

7.7). The response of structure in terms of SSI parameters under dynamic loading for a given

foundation system has been studied and compared to understand the soil structure interaction

for the tall structures. It has been clearly identified that the displacement at top is more than that

at bottom of the building and stresses are more at immediate soil layer under foundation than

the below layers.

Abdoullah Namdar


The soil mechanic laboratory results help in accurate soil foundation design and enhancement

failure mitigation. The mixing soil design has been used in many geotechnical engineering for

soil improvement. In this paper, several types of soil foundations have been made from mixed

soil. The bearing capacity of soil foundations by using mixed soil parameters and change

footing dimensions have been calculated. 180 footings, placed on 15 soil foundation types have

been designed. It is assumed the underground water has not effect to bearing capacity of soil

foundation. The results of numerical analysis and mixed soils technique have been combined.

The numerical analysis has supported mixed soil design, and introduced an appropriate result

for soil foundation design. The effects of mixed soil on depth and width of footing have been

compared. The mixed soil design influenced numerical analysis result, and economically, soil

foundation design helps to select the appropriate dimensions of footings. The result of

numerical analysis supports geotechnical and structural engineering codes, predicts structural

stability with different age, natural hazard and prevention as well as it is useful in understanding

safe bearing capacity of soil foundation behavior.

To accurate understanding failure mitigation of soil foundation, the numerical analyses of

several soil foundations and results of mixed soil technique have been employed. 180 footings

have been designed placing them on 15 soils foundation types. It has been observed that the

mixed soil technique has the ability to predict soil foundation behavior. The results show soil

parameters control footing dimensions. The effect of mixed soil on footing depth and width

have been compared. The soil mineralogy and morphology govern safe bearing capacity of soil

foundation and size of concrete foundation. The result of numerical analysis supports


26

geotechnical and structural engineering codes, natural hazard prediction, prevention and

understanding soil foundation behavior, predicts structural stability with different age.,. The

methodology in this research work supports the application of mixed soil in designing soil

foundation. To extent this research work, the role of mixed soil design in stress path can be

investigated.

Thevaneyan K. David


This paper presents background information relevant to the modelling of soil-structure

interaction. The interaction between the structural element (i.e. pile foundation or abutments)

and the soil medium is believed to have the potential to alter considerably the actual behaviour

of any structure. Modelling of the structural element is rather simple and straightforward when

compared to modelling the structure in interaction with soil. It is known that the structural

analysis simplifies soil behaviour, while geotechnical analysis simplifies structural behaviour.

The choice of an appropriate soil constitutive model may have significant influence on the

accuracy of soil-structure interaction analyses. A 2D finite element analysis on a pile-cap-pile-

soil model replicating actual field work was performed in this paper using OASYS SAFE to

further substantiate the choice of an appropriate soil constitutive model for the purpose of soil-

structure interaction modelling.

However, studies revealed that the hyperbolic stress-strain relationships, developed, provide a

simple model which encompasses the most important characteristics of soil stress-strain

behaviour, using data from conventional laboratory tests. Due to its simplicity, applicability to

drained and undrained

problems, and the availability of a database of hyperbolic stress-strain parameters, the

hyperbolic model is frequently used in soil-structure interaction problems. The model has been

successfully applied to a variety of soil-structure interaction problems. It is also recognized that

whatever constitutive model is chosen for the soil, the best confirmation of its predictive

capacity comes from the comparison with measurements taken from real structures, since the

more complex a constitutive law is, the larger is the set of parameters involved in its definition.


27

Anuj chandiwala

Year of Publication-2013

In recent years, there have been an increasing number of structures using piled rafts as the

foundation to reduce the overall and differential settlements. For cases where a piled raft is

subjected to a non-uniform loading, the use of piles with different sizes can improve the

performance of the foundation. Extensive research work has been performed in the past to

examine the behavior of piled rafts. However, most of the research was focused on piled rafts

supported by identical piles, and the use of non-identical piles has not received much attention.

In this paper, the behavior of piled raft is examined by the use of a computer program MIDAS

GTS based on the finite layer and finite element methods. The finite layer method is used for

the analysis of the layered soil system. The finite element method is used for the analysis of the

raft and piles. Full interaction between raft, piles and soil which is of major importance in the

behavior of piled rafts is considered in the analysis. Among the four different types of

interaction present in the piled raft foundation. The interaction between piles plays an important

role. Two dimensional (2D) finite element analysis of un-piled and piled raft foundations with

sandy soil. For the un-piled raft, the normalized settlement parameter (IR) for the raft sizes of

8mx8m and 15mx15m ranged as 1.03-1.17mm and 0.66- 0.83mm respectively. In the case of

the piled raft with raft thickness of 0.25, 0.40, 0.80, 1.50, 3.0m, the corresponding maximum

settlements are 66, 64, 63.7, 63mm. The results of these analyses are summarized into a series

of design charts, which can be used in engineering practice.

Further, it can be concluded that the foregoing simple example demonstrates the following

important points for practical design:

• The raft thickness affects differential settlement and bending moments, but has little effect

on load sharing or maximum settlement.

• Piles spacing plays an important role on the performance of piled raft foundation. It affects

greatly the maximum settlement, the differential settlement, the bending moment in the raft,

and the load shared by the piles.

• To reduce the maximum settlement of piled raft foundation, optimum performance is likely

to be achieved by increasing the length of the piles involved. While the differential settlement,

the maximum bending moment and the load sharing are not affected much by increasing the

pile lengths.


28

Dr. Hussein A. Shaina


Pile foundations are commonly used to resist vertical and lateral loads applied to structures.

Usually, these kinds of loads will act together to form a combination of loads, such as oblique

forces that have a component of vertical and lateral forces. Predicting the behavior of piles

subjected to oblique loads still remains a challenging task to geotechnical engineers. In this

paper, results of numerical simulation of vior of piles as embedded in cohesion less soil under

oblique loads are presented by using ABAQUS. For the cohesion less soil, the Mohr-Coloumb

constitutive law has been used to simulate the surrounding soil while the linear elastic model is

used for modelling of the pile. The interactions between the pile and the surrounding soil are

modelled thoroughly using contact elements based on slave-master concept. The results are

shown in terms of load/displacement curves for the components of vertical and the lateral

loading portions in different inclination angles. Finally, conclusions and recommendations are

given concerning the design of piles under oblique loads.

The finite element models used in this paper allowed the investigation into the response of the

pile under oblique loads. A 3D numerical model is developed with ABAQUS software is used

to in this investigation. This study provides a comparison of common techniques for analysis

of single piles subjected to oblique loads in different inclination angle. The piles were subjected

to variously inclined loads (α=30o, 45o, 60o), with α measured from the horizontal direction.

The following conclusions are drawn from the present investigation:

1. The stiffness of pile is almost affected on the behavior of pile subjected to combine

vertical and lateral loading (oblique loads).

2. The vertical and horizontal loads level itself strongly depends on the load inclination angle

(α).

3. The ultimate vertical pile capacity of the pile is decreased by additional horizontal loading.

Dr Omar-al-Farouk


The piled raft is a geotechnical composite construction consisting of three elements: piles,


29

raft and soil. It is suitable as a foundation for large buildings. This paper presents an analysis

of piled raft foundation, included material nonlinearity and soil structure interaction. An

efficient computer program in FORTRAN 90is developed for this analysis. A 20 node

isoperimetric brick element has been used to model pile, raft, soil and interface materials. Thin

layer interface element has been used to model the contact zone between the pile and soil, and

between raft and soil. The behavior of the piled raft material is simulated by using a linear

elastic model. However, the behavior of soil and interface materials is simulated by an elasto-

plastic model by the use of Mohr-Coulomb failure criterion. Some of the variables of piled-raft

system, related to settlement and differential settlement in sandy soil, have been studied, where

the length of piles and distance between piles an effective role in reducing both settlement and

differential settlement of foundation system. Also increasing the thickness of raft foundation

reduces the effectiveness of additional piles for the purpose of reducing differential settlement.

1. The computer code developed is found to be very useful and can be used for wide range of

applications in many soil and soil-structure interaction problems.

2. The three-dimensional nonlinear and linear finite element model, which was adopted in the

present work, is suitable for predicting the behavior of a soil-pile-raft system. The numerical

results were in good agreement with available experimental load-settlement results throughout

the entire range of behaviour.

3. From numerical investigations, the main effective factors on the behavior of a piled-raft

foundation were, pile length, pile spacing, pile diameter, number of piles, total piles area, and

raft thickness.

4. Pile length has a significant influence in reducing both central and differential settlements. It

is observed that it is possible to reduce the settlement more than (40%) with pile length equals

to (80%) of soil layer depth.

5. Piles/Raft area ratio has a significant effect on reducing settlement, (75%) of settlement

reduction can be obtained with a Piles/Raft area ratio in the range of (0.15-0.2).

6. Increasing of raft thickness reduces the effect of adding piles for controlling differential

settlement. Raft thickness has a very small effect on reducing settlement ratio for the central

settlement


30

Chapter 3 Methodology

A methodology for analyzing pile-soil interaction under static load has been discussed. Three

dimensional mathematical modelling of pile-soil system has been carried out in finite element

analysis package Abaqus considering surface to surface interactions at the interface. Soil and

Pile both have been modelled using 8-noded brick elements (C3D8R). Soil strata have been

idealized with elastic-plastic Mohr-Coulomb model whereas piles have been idealized to

behave linearly elastic. Some important modelling techniques and analysis sequences have been

suggested for better numerical convergence for this nonlinear solid to solid contact problem.

Vertical load settlement behavior of single pile is obtained from analysis and compared with

published field test result, showing a reasonable agreement. Load displacement behavior of

another field test comprising of single pile and pile-group subjected to lateral loads is modelled

and compared with test results.

Table 3:1 Properties of Materials

r E

(MPa)

µ γ

kN/m³

C

(kPa)

Φ

(degree)

Soil 200 0.3 19 100 0

Pile 25000 0.2 24 - -


31

Problem Statement

Types of soil: Clay

Angle of internal friction: 0°

Effective cohesion: 100 N/mm²

Seepage condition: undrained condition

Material model: Mohr-coulomb model

Method of analysis: Finite element analysis

Type of pile: Friction pile

Pile material: Concrete (M30)

No of Pile: 9

Size of pile: Length-10m & Diameter-30mm

Arrangement of pile in group: square type

Loading condition: static

3.1 Finite element modelling

3.1.1 Mesh and boundary conditions

The behavior of the Pile-Soil was investigated by carrying out 3D numerical analysis. Six-node

triangular elements were used to represent piled elements. Fig. (1) shows a typical finite element

mesh used in this numerical study. The parameters for a series of the static finite element

analyses are pile sizes and number of piles. Material properties of pile and undrained soil

parameters are tabulated in table below.


32

3.1.2 Constitutive modelling

The material behavior of the soil was modelled with a Mohr-Coulomb model, and to simplify

the analysis process, average values of material parameters (as mentioned above) were adopted

for the soil layer. Since the piles have great Young’s modulus in comparison with the soil, they

remain in elastic range. Due to the aforementioned reason, they were modelled with a non-

porous linear elastic model. The modelling techniques used for the pile-soil interface were

generally divided into two types: thin layer element and slip element. The former was used by

Jeong et al. (2004) and Lee et al. (2010), in which the slip behavior between the adjacent

surfaces could be considered. The latter was used by Reul and Randolph (2004) and a middle

layer is used to model the interface using the behavior of the soil. In this case when a slide

occurs, the shear stress (τ) will be created in the interface and the relationship between shear

force and normal pressure P’ is governed by a modified Coulomb’s friction theory. In this paper,

the pile-soil interface was modelled by slip elements. The schematic diagram of pile-soil

interface elements with undrained parameters is shown in Fig. (2).

Figure 3:1 (i)Typical finite element mesh (ii)Pile soil interface modelling (a) no slip (b)

slip (c) Coulomb’s frictional law


33

Chapter 4 Validation to Software

4.1 General

Abaqus is a complete environment that provides a simple, consistent interface for creating,

submitting, monitoring, and evaluating results from Abaqus/Standard and Abaqus/Explicit

simulations which works on Finite element method. Abaqus is divided into modules, where

each module defines a logical aspect of the modelling process; for example, defining the

geometry, defining material properties, and generating a mesh which constitute to form a Finite

element model. We move from module to module, we build the model from which Abaqus

generates an input file that we submit to the Abaqus/Standard or Abaqus/Explicit analysis

product. The analysis product performs the analysis using FEM, sends information to Abaqus

to allow us to monitor the progress of the job, and generates an output database with more

precision and accuracy.

Problem statement:

Types of soil: Clay

Angle of internal friction: 0°

Effective cohesion: 100 N/mm²

Bearing capacity of soil: 160 N/mm²

Seepage condition: undrained condition

Material model: Mohr-coulomb model


34

Method of analysis: Finite element analysis

Dilation angle: 0°

Poisson ratio: 0.33 N/mm²

Modelling of software:

4.2 Module

4.2.1 The part module

Parts are the building blocks of an Abaqus/CAE model. We use the Part module to create each

part, and we use the Assembly module to assemble instances of the parts.

Figure 4:1 Part module

4.2.2 The Property module

We use the Property module to define materials, define beam section profiles, define sections

and assign sections.


35

Figure 4:2 Property Module

4.2.3 The Assembly module

We use the Assembly module to create and modify the assembly. A model contains one main

assembly, which is composed of instances of parts from the model as well as instances of other

models.

4.2.4 The Step module:

We use the Step module to create analysis steps, specify output requests, specify adaptive

meshing, and specify analysis controls.

4.2.5 The Load module:

We use the Load module to define and manage the following prescribed conditions:


36

Loads

Boundary conditions

Figure 4:3 Boundary condition

4.2.6 The Mesh module:

The Mesh module contains tools that allow us to generate meshes on parts and assemblies

created within Abaqus/CAE. In addition, the Mesh module contains functions that verify an

existing mesh.

4.2.6.1 Understanding the role of the Mesh module

The Mesh module use to generate meshes on parts and assemblies created within Abaqus/CAE.

Various levels of automation and control are available so that we can create a mesh that meets

the needs of analysis. As with creating parts and assemblies, the process of assigning mesh

attributes to the model—such as seeds, mesh techniques, and element types—is feature based.

As a result, we can modify the parameters that define a part or an assembly, and the mesh

attributes that we specified within the Mesh module are regenerated automatically.

The Mesh module provides the following features:


37

Tools for prescribing mesh density at local and global levels.

Model colouring that indicates the meshing technique assigned to each region in the

model.

A variety of mesh controls, such as:

Element shape

Meshing technique

Meshing algorithm

Figure 4:4 Mesh


38

Figure 4:5 Slave mesh

Figure 4:6 Master mesh


39

4.2.7 The Job module:

We use the Job module to create and manage analysis jobs and to view a basic plot of the

analysis results. We can also use the Job module to create and manage adaptivity analyses and

co-executions.

4.2.7.1 Understanding the role of the Job module

Once we have finished all of the tasks involved in defining a model (such as defining the

geometry of the model, assigning section properties, and defining contact), we can use the Job

module to analyse model. The Job module allows we to create a job, to submit it for analysis,

and to monitor its progress. If desired, we create multiple models and jobs and run and monitor

the jobs simultaneously.

4.2.8 The Sketch module:

Sketches are two-dimensional profiles that are used to help form the geometry defining an

Abaqus/CAE native part. We use the Sketch module to create a sketch that defines a planar

part, a beam, or a partition or to create a sketch that might be extruded, swept, or revolved to

form a three-dimensional part. This chapter explains how we use the tools within the Sketch

module to create, modify, and manage sketches.

We use the Visualization module to view model and the results of analysis.

we use the Sketch module to create and manage two-dimensional profiles that are not associated

with a feature; these profiles are known as stand-alone sketches. Stand-alone sketches can be

incorporated in the current sketch, and they will overlay any existing geometry.

Undeformed shape

An undeformed shape plot displays the initial shape or the base state of model.

Deformed shape


40

A deformed shape plot displays the shape of model according to the values of a nodal variable

such as displacement.

Figure 4:7 Deformed shape

4.3 Contours

For an output database, a contour plot displays the values of an analysis variable such as stress

or strain at a specified step and frame of analysis. For a model in the current model database, a

contour plot displays the value of a load, a predefined field, or an interaction at a selected step

of model. The Visualization module represents the values as customized coloured lines,

coloured bands, or coloured faces on model.

4.4 X–Y data

An X–Y plot is a two-dimensional graph of one variable versus another.


41

4.5 Result

The Visualization module provides graphical display of finite element models and results. It

obtains model information from the current model database or model and result information

from an output database.

1) By using this software, we find the displacement force with respect to time in the form of

graph as shown below.

Figure 4:8 Displacement v/s Load


42

2) Stress bulb also getting by this software with stress readings database as shown as in figure.

Figure 4:9 Stress blub

3)Terzaghi’s shear failure zones also be formed by software as show below.

Figure 4:10 Terzaghi’s shear failure zones

Looking at these three results, we can conclude that the material model works properly.


43

Chapter 5 Analysis and results

5.1 Analysis on pile

5.1.1 Effect of different size of mesh of pile

The pile soil model has been prepared in ABAQUS as show in figure and load has been

applied in the form of pressure of the top of the pile cap as shown in figure

In order to get the most accurate results mesh sensitivity analysis has to be done to find out right

size of mesh. Following sizes has been made and analysed and load vs settlement curves has

been plotted.


44

Table 5:1 Loading analysis with different mesh size

Loads condition and modelling is kept as per the modelling and analysis is done. load is

increased at rate of 50kN.In addition to that a conversion study is done by taking various

mesh size i.e. 20 mm 25 mm and 30 mm mesh size. From observation it can be concluded

that, the load vs settlement comes close to experimental results at mesh size 25 mm. hence

here after modelling of soil is done by using 25 mm mesh size.

Load

(kN)

Load for 30

mm mesh

size (m)

Load for 25

mm mesh

size (m)

Load for 20

mm mesh

size (m)

0 0 0 0

50 0.005 0.008 0.009

100 0.018 0.010 0.014

150 0.016 0.014 0.021

200 0.020 0.018 0.026

250 0.025 0.022 0.031

300 0.032 0.027 0.034

350 0.032 0.036 0.038


45

Figure 5:1 Load vs Settlement curve of the pile (for different mesh size)

.

Figure 5:2 Settlement of pile model

0

50

100

150

200

250

300

350

400

450

0 10 20 30 40 50 60

30 mm mesh size 20 mm experimental results 25 mm mesh size


46

Also from the graph it can be seen that the settlement is linear with respect to the load. This

indicates the behaviour of the Mohr-Coulomb model is valid, Because Mohr-Coulomb shows

linearity in any settlement and deflection analysis.

Figure 5:3 Settlement of the Pile (cross section)

5.1.2 Effect of the diameter of the pile

In order to study the effect of diameter on pile settlement, diameter of the pile has been

increased by 10 % and analysis has been done. Following graph shows decrease in the

settlement due to increase in the diameter.


47

Figure 5:4 Load vs Settlement curve (Increase in Diameter)

The above graph shows the decrease in the settlement due to increase in the pile diameter.

The decrease in the settlement is about 15% with increase in diameter of 10 %.

0

5

10

15

20

25

30

35

40

45

0 1 2 3 4 5 6 7 8


48

Chapter 6 Conclusion

The pile soil model is very complex and difficult to simulate; it requires very high

degree of accuracy in defining the soil structure interaction behaviour.

One of the best way to define the Soil Structure Interaction Fem based model is to

create a friction surface model on pile and soil by using interaction module in

ABAQUS.

The interaction behaviour depends upon the coefficient of friction between soil and

pile and has a very high value in case of sandy granular soil.

The Fem analysis is subjected to mesh sensitivity and proper mesh sensitivity study

has to be done in order to validate the results.

Usually finer mesh giver more accurate results as show in the above analysis but

results keep on distorting after an optimum value of mesh density.

The settlement behaviour of pile depends upon type of soil, length of pile and diameter

of the pile.

Incense in the diameter of the pile decrease the settlement. And vis versa.


49

Future Scopes

All the analysis is the thesis work has been done by using Mohr-Coulomb Model,

other models can also be used to check their validity in determining the pile

settlement.

Pour water pressure has not been considered while doing the analysis, for better results

pour water pressure can be simulated in FEM.

Also for this thesis effect of length of the has not been considered, it, may be shown

that with increase in the length there is a subsequent decrease in the pile settlement.


50

REFERENCES

1. Dr. hussein.A.shaia, Dr. Sarmad A. Abbas (2015), Three dimensional analysis response of

pile subjected to oblique loads.

2. Johnson, K. et al. (2006). Modelling the load–deformation response of deep foundations

under oblique loading.

3. Kazimierz Józefiak et. al(2015), Numerical modelling and bearing capacity analysis of pile

foundation

4. Mohammad Mahdi Jalali et. al(2012), Using Finite Element method for Pile-Soil Interface

(through PLAXIS and ANSYS) .

5. Thevaneyan K. David et. al.(2015), Finite Element Modelling of Soil-Structure Interaction

6. Dr desai, notes on Application of Finite Element and Constitutive Models.

7. R. L. Raper et. al(2010), Prediction of soil stresses using the finite element method

8. Ioannis ANASTASOPOULOS et. al.(2012), Non-linear soil-foundation interaction:

numerical analysis

9. http://cedb.asce.org

10.Abdoullah Namdar, Xiong feng(2009), Evaluation of safe bearing capacity of soil

foundation by using numerical analysis method.

3,/(62,/,17(5$&7,2 1%

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