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ANALYSIS OF LATERALLY LOADED PILE
Norazlin Binti Ahmad
TA Bachelor of Engineering with Honours
775 (Civil Engineering)
N822 2004
2004
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Universiti Malaysia Sarawak Kota Samarahan
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BORANG PENYERAHAN TESIS
Judul: ANALYSIS OF LATERALLY LOADED PILE
SESI PENGAJIAN: 2000 - 2004
Saya NORAZLIN BINTI AHMAD
(HURUF BESAR)
mengaku membenarkan tesis ini disimpan di Pusat Khidmat Maklumat Akademik, Universiti Malaysia Sarawak dengan syarat-syarat kegunaan seperti berikut:
1. Hakmilik kertas projek adalah di bawah nama penulis melainkan penulisan sebagai projek bersama dan dibiayai oleh UNIMAS, hakmiliknya adalah kepunyaan UNIMAS.
2. Naskhah salinan di dalam bentuk kertas atau mikro hanya boleh dibuat dengan kebenaran bertulis daripada penulis.
3. Pusat Khidmat Maklumat Akademik, UNIMAS dibenarkan membuat salinan untuk pengajian mereka.
4. Kertas projek hanya boleh diterbitkan dengan kebenaran penulis. Bayaran royalti adalah mengikut kadar yang dipersetujui kelak.
5. * Saya membenarkan/tidak membenarkan Perpustakaan membuat salinan kertas projek ini sebagai bahan pertukaran di antara institusi pengajian tinggi.
6. ** Sila tandakan (J)
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SULIT (Mengandungi maklumat yang berdarjah keselamatan atau kepentingan Malaysia seperti yang termaktub di dalam AKTA RAHSIA RASMI 1972).
TERHAD (Mengandungi maklumat TERHAD yang telah ditentukan oleh organisasi/
badan di mana penyelidikan dijalankan).
TIDAK TERHAD
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(TANDATANGAN ENULIS) (TANDATANGAN PENYELIA)
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MAHKAMAH SYARIAH MIRJ, 98000 MIRI SARAWAK.
Tarikh:
CATATAN "
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DR. V. A. SAWANT ( Nama Penyelia )
Tarikh: 7-0- %O-'L'
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Potong yang tidak berkenaan.
Jika Kertas Projek ini SULZT atau TERHAD, sila lampirkan surat daripada pihak berkuasa/
organisasi berkenaan dengan menyertakan sekali tempoh kertas projek. Ini perlu dikelaskan sebagai SULZT atau TERHAD.
Pks/2000
Perakuan Penyelia
Laporan Projek Tahun Akhir berikut:
Tajuk : Analysis of Laterally Loaded Pile Nama Penulis : Norazlin Binti Ahmad
No. Matrik : 4867
telah dibaca dan disahkan oleh:
6-
Dr. Vishwas A. Sawant Penyelia
7- Lt - ye2 Lý
Tarikh
O(Dr- ' 1376;?
Pusat Khidrnat MAWrimsrt Akademb trn! N"rZ, .,,. _-,...
ANALYSIS OF LATERALLY LOADED PILE P. KHIDMATMAKLUMATAKADEMK
UNIMAS
IIIuIIIIuIIIIIIII
1000133615IIII
NORAZLIN BINTI AHMAD
This project report is submitted in partial fulfillment of
the requirements for the degree of Bachelor of Engineering with Honours (Civil Engineering)
Faculty of Engineering
UNIVERSITI MALAYSIA SARAWAK 2004
To my parent with love and appreciation.
11
ACKNOWLEDGEMENTS
The author would like to thanks her supervisor Dr. V. A. Sawant for his continuous guidance and help throughout this project work. Dr Sawant took so much of academic interest especially on the application to programming and finite element without which it would not have been possible to carryout this study.
The author would also like to thanks her parents, all her teachers, technicians, and friends for their support, help, advice and encouragement.
ABSTRACT
Generally the lateral load for single pile are analysed as vertical beam support on elastic foundation and the surrounding soil can be modelled by using Winkler's hypothesis which is the soil is replaced by series of infinitely closely spaced independent elastic springs. Usually the solution for laterally loaded pile is based on the subgrade reaction approach concept that provides an efficient solution and the p-y curves are used to present the pile displacement to the nonlinear soil reactions. An analytical study was carried out on laterally loaded pile. The Finite Element Method was used as the analytical tool. Computer programme was developed to study the displacement, shear force, bending moment, rotation and thus the ultimate lateral resistance due to the static load on single piles for cohesive soils. Constant soil modulus and
linearly varying with depth were considered in the analysis. The analysis suggested that the lateral displacement of the pile had a further effect on soil modulus. Thus assumption of constant soil modulus at a particular depth during loading, as suggested by various researcher like Reese (1960), appeared to an over simplification of the reality. However, the ultimate lateral resistance as obtained from the present analysis gave a close approximation to that given by Georgiadis (1992) using the concept of p-y curve and L/d ratio.
iv
ABSTRAK
Pada amnya beban sisi untuk satu cerucuk dikaji sebagai rasuk tegak yang disokong di atas tapak asas anjal dan tanah di sekelilingnya boleh dijadikan sebagai satu model yang menggunakan hipotesis Winkler iaitu tanah akan digantikan dengan satu siri ruang berhampiran yang tidak terhingga bagi spring anjal bebas. Biasanya penyelesaian untuk beban sisi bagi cerucuk adalah berdasarkan konsep `subgrade reaction approach' yang mana memberi penyelesaian yang efisen dan lengkungan p-y digunakan untuk menghasilkan pesongan cerucuk bagi tindak balas tanah bukan linear. Kajian `analytical' telah dikaji untuk cerucuk beban sisi. Kaedah Unsur Tak Terhingga telah digunakan sebagai alat `analytical'.
Program komputer telah dimajukan untuk mengkaji pesongan. `shear force', bending moment,
`rotation' dan juga beban sisi muktamad bergantung kepada beban statik untuk cerucuk individu bagi tanah `cohesive'. Modulus tanah malar dan modulus tanah linear dengan kedalaman diambil kira dalam analisis ini. Kajian ini mencadangkan pesongan sisi suatu cerucuk mempunyai kesan keatas modulus tanah. Dengan itu, andaian terhadap modulus tanah malar pada suatu kedalaman tertentu ketika beban dikenakan seperti yang telah dicadangkan oleh beberapa pengkaji seperti Reese (1960) menunjukkan bahawa simplifikasi terhadap realiti. Walau bagaimanapun beban sisi muktamad seperti yang diperolehi daripada analisis memberi nilai yang hampir seperti yang diberi oleh Georgiadis (1992) menggunakan konsep lengkungan p-y dan nisbah L/d.
V
Fusat Khidmat Makiumat Akademlk VNl VERS1TI MALAYSIA SARAWAIK
943M KMSaanwnlm
LIST OF CONTENTS
Contents
Acknowledgements Abstract
Abstrak
List of tables List of figures List of symbols
Chapter 1 INTRODUCTION 1.1
Chapter 2
1.2 1.3 1.4 1.5 1.6
General
The lateral load
Design criteria of laterally loaded pile Common analysis of single pile
Objectives of analysis Scope of analysis
LITERATURE RIVIEWS 2.1
2.2
2.2.1 2.2.2
Introduction
Subgrade reaction approach Beam on Winkler foundation P-y analysis
Page no
111
iv
V
ix
X
XI
1 1 2 5 6 6
7 7 11 11
V1
2.2.3 p-y analysis background 2.3 Elastic continuum
2.3.1 Elastic continuum background 2.4 Finite element method
2.4.1 Finite element method background
15 18 21 22 23
Chapter 3 METHODOLOGY
3.1 Introduction 26
3.2 Finite element formulation 26
3.2.1 Beam element 27
3.2.2 Spring element 30
3.3 Checking the accuracy of FEM 31
3.4 The effect of soil modulus 33
3.5 L/d ratio effect for the validation of 36 experimental data
Chapter 4 DATA, ANALYSIS AND DISCUSSIONS
4.1 Introduction 38
4.2 Checking the accuracy of FEM 38
4.3 Effect of soil modulus 39
4.3.1 ES constant with depth 40
4.3.2 E, linearly varying with depth 43
4.4 The effect of L/d ratio for the validation of 46 experimental data
Vii
Chapter 5 CONCLUSION References
Appendix A Appendix B Appendix C
50 51 54 63 67
Vlll
LIST OF TABLES
Tables Page no
2.1 The conditions based on pile head for displacement, 12 rotation, shear and moment
4.1 Comparison between displacement, u obtained for FEM 39 and theoretical
4.2 Influence factor for ES constant with depth 40
4.3 Influence factor for ES linearly varying with depth 43 4.4 Ultimate load and non-dimensional load for each case 46
ix
LIST OF FIGURES
Figures Page no
1.1 Load applies on the pile (a) Before bending (b) After 4 bending which are suction on the load side and additional
stress at the far side
1.2 The model of single pile which is lateral load applied at 4 the side
2.1 Distribution of lateral earth pressure in cohesive soil 10 2.2 Winkler assumption (a) Beam on true elastic medium; and 10
(b) Winkler foundation
2.3 The characteristic of single pile (a) The reaction in the 13 single pile (b) Soil pile interaction idealized as
independent spring and (c) The curve diagram at each spring
2.4 Characteristic shapes of the p-y curves in soft clay for 13 static loading
2.5 Floating piles stresses acting on (a) piles, (b) soil adjacent 19 to piles
2.6 The arrangement of element and model for axis symmetry 24 continuum embedded pile in soil
3.1 Beam element 29
3.2 Spring element 29
3.3 Checking the beam element (a) The numbering of each 32 node for beam element, and (b) The vertical beam
idealized as cantilever beam
3.4 Top deflection and rotation for lateral loads on vertical 35 piles for constant kh
3.5 Top deflection and rotation for lateral loads on vertical 35 piles for kh proportional to depth
4.1 Displacement influence factor, IPH for Es constant with 41 depth
4.2 Rotation influence factor, IOH for Es constant with depth 42 4.3 Displacement influence factor, IPH for Es linearly varying 44
with depth
4.4 Rotation influence factor, 19H for Es linearly varying with 45 depth
4.5 Load displacement curve for 25m 47
4.6 Load displacement curve for 40m 48
4.7 Load displacement curve for 50m 49
X
LIST OF SYMBOLS
A parameter for displacement
b pile diameter or width for validation data
B strain displacement transformation matrix (beam element) C, undrained shear strength of the soil
C parameter for small strain stiffness matrix
D pile diameter
Ep pile modulus of elasticity for pile section ES modulus of subgrade reaction
ES; soil modulus at ith node ESj soil modulus at jth node
H horizontal load
H, ý ultimate load
IP moment of inertia for pile section is soil displacement influence factor
IpF displacement influence factor for fixed head pile IpH displacement influence factor for horizontal load IPM displacement influence factor for moment
IeH rotation influence factor for horizontal load IOM rotation influence factor for moment
k parameter of spring element ke beam element stiffness matrix kh horizontal subgrade reaction kL value kh at the pile tip
ks spring element stiffness matrix
kZ stiffness matrix for depth of the soil KR pile flexibility factor
L length of pile
M moment applied at the pile top n the coefficient of soil
N parameter for small strain beam and spring element p lateral forces at the pile
p horizontal displacement
pult ultimate soil resistance pr unit length of pile pX lateral forces for spring element
R parameter for small strain beam element u pile displacement for beam element
y pile displacement
Y5o deflection at one-half of the ultimate soil resistance z depth of the soil
a parameter for defining beam element stiffness factor fore cohesive soil
strain vector for beam element
X1
the strain of one-half the maximum deviator stress vector of nodal displacement
submerged unit weight of soil rotation about y axis
X11
CHAPTER 1
INTRODUCTION
1.1 General
Most of the engineered structure such as multi-storeyed, building, bridges and towers are subjected to lateral pile. Eventually they transmit the load to the ground and the carrying capacity depends on the type of soil. It also depends on the pile configuration. The main components of the pile foundation can be divided into two parts which are the pile cap and the pile itself. Piles are long and slender members which transfer the load to the soil stratum of high bearing capacity avoiding shallow soil of low bearing capacity.
1.2 Lateral loads
Besides of the main purpose which is to transmit a foundation load to a solid ground, the pile foundations also use to resist the lateral load as well as axial and uplift loads. The
1
vertical piles subjected to the lateral loads may be due to wind load, seismic load, or ocean wave forces such as harbour and offshore structures. Lateral forces that act to the pile can be divided into two categories which are active loading and passive loading. The active loading is an external load that applied to the pile which is eventually carried by the soil. The passive loading is a soil movement which is the pile will due to bending stresses.
There are two most important factors that have been developed which the reaction are happened between the soil and pile. The two factors are the distribution of bending moment and deflection along the pile near the ground surface. This reaction occurs because of the complex interaction between the pile and surrounding soil; which are the normal stresses in front of the pile will be increased and will be decreased behind the pile.
1.3 Design criteria of laterally loaded pile
The design parameters for the laterally loaded pile have been studied by many authors.
Some of the important criteria to predict the behaviour of laterally loaded are given by Chen (1999). They are such as degree of fixity, the properties of surrounding soils, stiffness factor, and movement mechanics.
Depending on the degree of fixity piles can be classified as fixed head pile (restrained condition) and free head pile. Both of these degrees of fixity will give a different result for the behaviour of lateral load such as different bending moment and deflection. Depending on the engineering properties of soil, it can be classified as cohesive soil and cohesionless soil.
2
Cohesive soils are such as clays, sandy clay, and silt clays. While cohesionless soil is a soil with high percentage of gravel and sand.
The flexural of stiffness factor will control the behaviour of laterally loaded pile which can be divided into two that are stiffness factor for the cohesive soil and stiffness factor for the cohesionless soil. For movement mechanics can be described as the pile is trying to rotate about a point along its length. When the resistance of applied lateral load are develop, the soil located in front of the vertical pile closed to the ground surface will moves upward. The soil located below the ground surface will moves in a lateral direction to the back side of the pile.
At the same time the soil at the back of the pile below the ground surface will separates from the pile. Thus for the behaviour of lateral pile, the lateral deflections at working load should be limit so it would not damage the pile.
For the pile with small acceptable lateral deflections, the design is determine by lateral deflection at working loads. Therefore the lateral deflections at working loads would be computed according to the concept of coefficient of subgrade reaction. This will be considering for the soil reaction ratio and the equivalent lateral deflections for the constant or linearly varying with depth. For the pile with large acceptable lateral deflections, the design is determined by the ultimate lateral resistance of the pile. The small embedment of ultimate lateral resistance for the pile will be determined by the passive lateral resistance of the surrounding soil.
3
(a)
(b)Figure 1.1: Load applies on the pile (a) Before bending (b) After bending which are suction on the load side and additional stress at the far side
Lateral ---010-
load, P i
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1M, - LJVN, --
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Figure 1.2: The model of single pile which is lateral load applied at the side
4
1.4 Common analysis of single pile
For single pile which is subjected to the lateral load, usually the pile will be analysed as a beam that support on an elastic medium. This method is more preferable because of an efficient solution obtained for the problem involved in laterally loaded pile. Basically there are three common approaches to analyse the behaviour of a single pile subjected to lateral load.
The Winkler Hypothesis or subgrade reaction approach is the most common method that have been use to analyse the lateral load. This approach is using the p-y analysis to analyse the non-linear load deformation behaviour which is described by pile resistance-deflection curves (p-y curve).
The second approach to analyse the pile behaviour is using homogenous elastic continuum or elastic half space. This approach is using the Mindlin's (1936) solution which is employing the analytical point load and considers the distribution of load to the pile and soil.
Finally the more powerful finite element method (FEM) is used to define the behaviour of the pile. In this approach, the beam element and spring element are used to model the pile and the surrounding soil respectively. More accuracy solution for the complex problem can be obtained by this approach.
5
1.5 Objectives of the analysis
The objectives of the analysis of laterally loaded pile are as follow:
i. To find the information on the common approach uses to analyse the lateral load for single pile.
ii. To investigate and collect data for the behaviour of single pile by using three methods.
iii. To analyse and solve the problem of analysis such as the method use and procedure of finite element method (FEM).
iv. To identify the problem involve in the analysis that can be solved using the finite element method.
v. To compare the result obtain with the data develop by the earlier researcher and determined the accuracy of the method use.
1.6 Scope of analysis
This analysis is a parametric study for common approaches use to analyse the behaviour of single pile subjected to the lateral load. This is basically on how its work and the accuracy of the solution can be obtained by using finite element method which are the method will using a beam element and spring element to model the pile and soil respectively. As a result, the analysis will compare the data obtain with the available data establish by previous approach.
6
CHAPTER 2
LITERATURE REVIEW
2.1 Introduction
Basically the capacity of the lateral forces will be smaller than the axial capacity. Thus the soil should not be stressed to its ultimate soil reaction capacity which is the pile's deflection and soil's reactions are depending upon each other. These criteria would be considered to satisfy the behaviour of the lateral load of single pile. Therefore three approaches have been used to analyse the lateral load for single pile which are subgrade reaction approach, elastic continuum and finite element method (FEM).
2.2 Subgrade reaction approach
The subgrade reaction method is more preferable method use by many authors because of its straight forward and easy to apply. Basically this method or also known as beam on an
7
elastic foundation is based on Hetenyi (1946) work. In subgrade reaction theory, the pile is model as an elastic transversely loaded beam while the soil is model based on Winkler's assumptions which the soil idealized as independent spring taken as linearly elastic or non- linear. For the lateral pile loading, the relationship can be defined as:
p= - Eu ... (2.1)
where p is the soil resisting force acting on the pile, u is the displacements of lateral pile and ES is the modulus of soil reaction. The stiffness ES is expressed in unit force per square length.
The negative sign is indicate the direction of the lateral force that acting on the pile which is opposite to the direction of the pile deflection.
Coefficient of horizontal subgrade reaction, kh sometimes used to replace Es, which can be expressed as:
ES = khD (2.2)
where D is the diameter of the pile and the coefficient of horizontal subgrade reaction, kh is in unit force per cubic length. The stiffness kh also taken as linearly varying or constant with depth and not depend upon the pile size. Thus for the kh constant, the variable ß which is subjected to relative stiffness factor for cohesive soil can be expressed as:
I
ß= k4
... (2.3) p
[4E;
Ij
Therefore the behaviour of single pile can be expressed in the form of the governing fourth order differential equation that is:
4
Eplp du+
Esu =O
dz
4(2.4)
8
where Ep is the pile modulus of elasticity for pile section, Ip is the moment of inertia for pile
section, u is the lateral pile defection, z is the depth of soil, and kh is the modulus of subgrade reaction.
The behaviour of lateral pile has been employed for the variation of kh along the pile which is given by Palmer and Thompson (1948). The equation can be expressed as:
kh = k? `L
(2.5)where kL is the value of kh at the pile tip or z=L and n is the coefficient of soil or empirical index that equal to or greater than zero (n >_ 0)
.
According to the equation (2.4) and (2.5) above, hypothesis has been made by making straightforward assumptions. The generally assumption made is for the value n=1 the stiffness kh varies linearly with depth for sand and for the value n=0 the stiffness kh will be constant with depth for clay.
Poulos and Davis (1980) had present the data in tables and charts as a function of depth and non-dimensional coefficients for constant values of ES with depth that can be used to
establish pile displacements, rotations, and distribution of bending moment. Broms (1964a
and 1964b) also presented a theories and rigid method for analysing a lateral load for cohesive and cohesionless soil which is based on Winkler foundation model. His methods basically for computing the ultimate lateral soil resistance with constant modulus of subgrade reaction.
Therefore he defined that kh is linearly increased with depth and compute the lateral soil resistance base on the rankine earth pressure methods.
9
