i

NUMERICAL SIMULATION OF BEARING CAPACITY FOR RIGID FOOTING

ON COHESIVE SOIL

ZARINA BINTI YUSOF

A project report submitted in partial fulfillment of the

requirements for the award of the degree of

Master of Engineering (Civil – Geotechnics)

Faculty of Civil Engineering Universiti Teknologi Malaysia

JUNE 2013

iii

Especially dedicated to:

My parents

Yusof bin Abdullah & Esah@Azizah binti Ali

Who give motivation and loves...

My beloved supervisor, Dr. Nazri bin Ali

Who give the guidance with continuously in finishing this thesis...

All my friends

For their helping and loyalty of this friendship...

iv

ACKNOWLEDGEMENT

Assalamualaikum w.b.t.

In the name of Allah, the most gracious, the most compassionate. I am

grateful that is preparing this project report, I was given the opportunity to be in

contact with many people, researchers and practitioners. They have contributed

towards my feeling and thoughts. In particular, I would like to express my greatest

gratitude to my supervisor, Dr. Nazri bin Ali for encouragement, guidance and critics.

Without the continuous support, this project would not be as it is present here.

I would also like to take this opportunity to express my sincere appreciation

my beloved friend Tuan Nor Hazwani, Khairun Nissa, Farah Nadiah and Norizaidah

for spending such a valuable time with me. I really enjoyed and have a great time

doing my final year project with the presence of you all.

Last but not least, I would like to thanks my parents, sisters and brothers for

continuously supporting me and give me strength to face everything I have been

through. I will always remember what you all have done to me.

.

v

ABSTRACT

Foundation is one of the main component structures in civil engineering

construction. It is crucial to make sure that the load distribution on the soil is

adequate to prevent soil failure.. Foundation transfers the loads from superstructure

to substructure or soil. A foundation plays an important role as an interface between

the load carrying components of a structure to the ground. Foundations can be

classified into two categories. Those are shallow foundations and deep foundation.

To make sure that the load distribution is sufficient, the size and type of foundation

should be well determined. The increases size of footing which compared with the

column supports gives and increased contact area between the footing and the soil.

Besides that the increasing of friction angle will increase the value of bearing

capacity factor. So, the increasing of bearing capacity factor will increase the

ultimate bearing capacity and automatically increasing the value of allowable or safe

loading to the footing. In this study have two methods to analysis the value of

bearing capacity which is Terzaghi’s equation and Meyerhof / Hansen’s equation.

Therefore, a computer programming is to be developed using Visual Basic 6.0 which

is able to analyze and design the foundation or footing such as strip, square, circular

and rectangular footing. Plaxis 2D will validate the computer programming to make

sure the computer programming can be used. The comparison between both

computer programming is discussed in this study. The computer programming is

expected to reduce time and its nature is easy to use and understand.

vi

ABSTRAK

Penapak adalah salah satu struktur komponen utama dalam pembinaan

kejuruteraan awam. Ia adalah penting untuk memastikan bahawa pengagihan beban

pada tanah adalah mencukupi untuk mencegah kegagalan tanah. Penapak

memindahkan beban dari struktur untuk substruktur atau tanah. Asas memainkan

peranan penting sebagai antara muka di antara beban dibawa komponen struktur ke

tanah. Asas boleh diklasifikasikan kepada dua kategori. Kategori itu adalah asas

cetek dan asas dalam. Untuk memastikan bahawa pengagihan beban yang

mencukupi, saiz dan jenis asas perlu juga ditentukan. Saiz kenaikan kedudukan yang

berbanding dengan ruang menyokong memberikan dan meningkatkan kawasan

sentuhan antara asas dan tanah. Selain itu peningkatan sudut geseran akan

meningkatkan nilai yang mengandungi faktor kapasiti. Jadi, peningkatan faktor

keupayaan galas akan meningkatkan keupayaan galas muktamad dan secara

automatik meningkatkan nilai beban dibenarkan atau selamat untuk kedudukan itu.

Dalam kajian ini mempunyai dua kaedah untuk analisis nilai keupayaan galas iaitu

persamaan Terzaghi dan persamaan Meyerhof / Hansen. Oleh itu, pengaturcaraan

komputer akan dibangunkan dengan menggunakan Visual Basic 6.0 yang mampu

untuk menganalisis dan mereka bentuk asas atau asas seperti jalur, persegi,

kedudukan bulat dan segi empat tepat. Plaxis 2D akan mengesahkan pengaturcaraan

komputer untuk memastikan pengaturcaraan komputer itu boleh digunakan.

Perbandingan antara kedua-dua pengaturcaraan komputer dibincangkan dalam kajian

ini. Pengaturcaraan komputer dijangka akan mengurangkan masa dan sifat adalah

mudah untuk digunakan dan difahami.

vii

TABLE OF CONTENT

CHAPTER TITLE PAGE

DECLARATION ii

DEDICATION iii

ADKNOWLEDGEMENT iv

ABSTRACT v

ABSTRAK vi

TABLE OF CONTENTS vii

LIST OF TABLES xi

LIST OF FIGURES xii

LIST OF SYMBOLS xiv

LIST OF APPENDICES xv

1 INTRODUCTION

1.1 Background of the Study 1

1.2 Statement of the Problem 3

1.3 Objective of the Study 3

1.4 Scope of Study 4

1.5 Significant of Study 4

2 LITERATURE REVIEW

2.1 Introduction 5

2.2 Ultimate Bearing Capacity 7

2.3 Types of Footing 11

2.4 Terzaghi’s Theory 14

2.5 Meyerhof/ Hansen’s Theory 20

viii

2.5.1 Shape Factor 23

2.5.2 Depth Factor 23

2.5.3 Inclination Factor 24

2.6 Cohesive Soil 25

2.7 Microsoft Visual Basic 27

2.8 Plaxis 2D 28

3 METHODOLOGY

3.1 Introduction 30

3.2 Theoretical Background 32

3.3 Case study 34

3.4 Computer Programming (Visual Basic) 34

3.4.1 Characteristic of Visual Basic 35

3.4.2 Environment of Visual Basic 35

3.4.2.1 Toolbar 37

3.4.2.2 Toolbox 37

3.4.2.3 Form 38

3.4.2.4 Project Explorer 38

3.4.2.5 Properties Window 39

3.4.2.6 Form Layout 39

3.5 Flowchart of Visual Basic 40

3.6 Plaxis Software 42

3.6.1 Plaxis Use 43

3.7 Expected Result 44

4 COMPUTER PROGRAMMING DEVELOPMENT

4.1 Introduction 45

4.2 Parameters 45

4.3 Flowchart of Computer Programming 48

4.4 Computer Programming 48

4.4.1 Main Menu 49

4.4.2 Option Menu 50

4.4.3 Analysis Menu 51

ix

4.4.4 Terzaghi’s Equation 51

4.4.4.1 Analysis Menu – Step 1 52

4.4.4.2 Analysis Menu – Step 2 53

4.4.5 Meyerhof/Hansen’s Equation 54

4.4.5.1 Analysis Menu – Step 1 55

4.4.5.1 Analysis Menu – Step 2 56

4.4.6 Ground Water Table 58

4.4.7 Coding 58

4.4.8 Summary 59

4.5 Analysis using Plaxis 59

5 RESULTS AND DISCUSSION

5.1 Introduction 66

5.2 Example of Manual Calculation Based on Case

Study 1 67

5.2.1 Result Comparison 70

5.2.2 Summary 72

5.3 Validation using Visual Basic with Plaxis Based

on Case Study 2 72

5.3.1 Calculation using Visual Basic 72

5.3.2 Analysis using Plaxis 73

5.3.3 Comparison Result 74

5.4 Sensitivity Analysis for the Parameter Cohesion

Soil 75

5.4.1 Terzaghi’s Equation 75

5.4.2 Meyerhof / Hansen’s Equation 75

5.5 Conclusion 76

6 CONCULSION AND RECOMMENDATION

6.1 Introduction 77

6.2 Recommendations 78

6.3 Conclusion 79

REFERENCES 80

x

APPENDIX A 82

APPENDIX B 83

APPENDIX C 84

APPENDIX D 85

APPENDIX E 86

xi

LIST OF TABLES

TABLE NO. TITLE PAGE

2.1 Terzaghi;s bearing capacity factors Nc, Nq and Nγ 17

2.2 Terzaghi’s bearing capacity factors N’c, N’q and N’γ 19

2.3 Meyerhof/Hansen’s bearing capacity factors Nc, Nq

and Nγ 22

4.1 Parameter in Terzaghi’s equation 46

4.2 Parameter in Meyerhof / Hansen’s equation 46

4.3 Parameter in case study 1 46

4.4 Parameter in case study 2 47

4.5 The output 47

5.1 Parameter for calculation 67

5.2 Summary or comparison between manual calculation

and using computer programming 71

5.3 Comparison bearing capacity factor 74

xii

LIST OF FIGURES

FIGURE NO. TITLE PAGE

1.1 Individual footing 2

2.1 Sketches of bearing capacity failures in soil 6

2.2 Bearing capacity theories of Prandtl and Terzaghi 7

2.3 General shear failure surface is approximated by

Terzaghi 15

2.4 Eason and Shield kinematical and static solution 27

2.5 Typical mesh and boundary conditions for footing

Simulations 29

3.1 Flowchart of methodology 31

3.2 New project form 36

3.3 New interface 36

3.4 Toolbar 37

3.5 Toolbox 37

3.6 Form 38

3.7 Project Explorer 38

3.8 Properties Window 39

3.9 Form Layout 39

3.10 Flowchart of Visual Basic 40

3.11 Flowchart of Plaxis procedures 43

4.1 Modelling 45

4.2 Flowchart of programme 48

4.3 Welcome Screen 49

4.4 Main Menu 49

xiii

4.5 Information of footing design interface 50

4.6 Method 51

4.7 Types of footing 52

4.8 Analysis Menu – step 1 53

4.9 Analysis Menu – Step 2 54

4.10 Eccentricity Menu 54

4.11 Display result 1 56

4.12 Display Result 2 57

4.13 The ground water effect 58

4.14 Coding of computer programming 59

4.15 Geometry model 60

4.16 General setting 61

4.17 Dimension 61

4.18 General soil data 62

4.19 Soil data parameters 62

4.20 Meshing shape 63

4.21 Calculation process 63

4.22 Deformed mesh 64

4.23 Continue calculation process 64

4.24 Analysis result 65

5.1 Example of Meyerhof/Hansen’s question 67

5.2 Results from computer programming 71

5.3 Calculation by Visual Basic 73

5.4 Graph of settlement and the ratio of the resistance force

to the value of distributed load 74

5.5 Sensitivity analyses for c using Terzaghi’s Equation 75

5.6 Sensitivity analysis for c using Meyerhof/Hansen’s

Equation 76

xiv

LIST OF SYMBOLS

B - Width of footing

c - Cohesion of soil

Df - Depth of footing

Fcd, Fqd, Fγd - Depth factor

Fcs, Fqs, Fγs - Shape factor

Fci, Fqi, Fγi - Inclination factor

L - Length of footing

Nc, Nq, Nγ - Bearing capacity factor

q - Overburden at the base leveled footing

qu - Ultimate bearing capacity qnett - Nett bearing capacity qall - Allowable bearing capacity qsafe - Suitable or safe loading ɸ - Friction angle γ - Unit weight of soil

xv

LIST OF APPENDICES

APPENDIX TITLE PAGE

A Meyerhof’s λ factors for a rectangular footing 82

B Effect of the location of groundwater table on the

Bearing capacity of soils 83

C Case study information 84

D Graph Terzaghi;s bearing capacity factors Nc, Nq and Nγ 85

E Graph Meyerhof/Hansen’s bearing capacity factors Nc 86

1

CHAPTER 1

INTRODUCTION

1.1 Background of the study

The lowest part of a structure that transmits its weight to the underlying soil

or rock is the foundation. Foundation transfers the loads from superstructure to

substructure or soil. A foundation plays an important role as an interface between

the load carrying components of a structure to the ground. Foundations can be

classified into two categories. Those are shallow foundations and deep foundation.

A shallow foundation is a type of foundation which transfers building loads to the

earth very near the surface. The shallow foundation is rather than to a subsurface

layer or a range of depths as does a deep foundation. Meanwhile a deep foundation

is a type of foundation that is distinguished from shallow foundation by the depth

that is embedded into the ground. The reasons use the deep foundations that are

because very large design loads a poor soil at shallow depth or site constraints.

There are different terms used to describe different types of deep foundations

including piles, drilled shafts, caissons and piers. The function foundations are if the

soil of sufficient bearing capacity lies immediately below the structure then the load

2

can be spread by footimg. Footing are range from isolated pads supporting

individual columns through strips supporting walls or closely space columns to raft

footing supporting the whole structure. However, if the soil has insufficient bearing

capacity then it is necessary to use deep foundations such as piles to transmit the load

to deeper firmer strata.

The increases size of footing which compared with the column supports gives

and increased contact area between the footing and the soil. The increased area

serves to reduce pressure on the soil to an allowable amount, thereby preventing

excessive settlement or bearing failure of the foundation. The footing are has four

different type of shape. Those are strip footing, square footing, circular footing and

rectangular footing. This is when use Terzaghi’s equation. Meyerhof / Hansen’s

method only has a general equation for bearing capacity. Figure 1.1 show the

example of individual footing.

Figure 1.1 Individual footing

3

1.2 Statement of the Problem

There are two methods to calculate the ultimate bearing capacity. Those are

using Terzaghi’s equation and Meyerhof / Hansen’s equation. Terzaghi’s equation

has four different equations for four different shapes of footing that are strip footing,

square footing, circular footing and rectangular footing and for Meyerhof / Hansen’s

only have a general equation to find the ultimate bearing capacity.

The ultimate bearing capacity, qu is the maximum bearing pressure that the

soil can withstand. Besides that, the ultimate bearing capacity also is the load per

unit area that will cause a shear failure of the soil immediately below foundation.

The values are established from the principles of soil mechanics on the basics of load

tests and other experimental determinations. The factors that influencing the bearing

capacity are unit weight of the soil, shear strength of soil, soil deformation,

characteristic of the soil, size of the footing, shape of the footing, depth of footing

and the ground water table. Nowadays many design process of the footing are using

the computer programming to make the design easy and faster with all factor needed.

1.3 Objectives of the Study

The aims of this study are:-

a) To determine the value of the ultimate bearing capacity using

computer programming.

b) To analyzed the appropriate design with all variables involve using

computer programming

c) To verify the design calculation using Visual Basic with Plaxis.

4

1.4 Scope of the Study

The study is to calculate or to determine the size of footing design by

considering the type of soil that is cohesive soil, shape, depth, and inclination factor

of the footing and the ultimate bearing capacity. The analysis and the result obtained

by using computer programming that are Visual Basic with Plaxis and the parameters

required will obtained from the case study.

1.5 Significance of study

The significance of study about the bearing capacity of rigid footing on

cohesive soil using the computer programming are want to know or to calculate the

result more quickly and easy. It is because before this we calculate or determine the

design of the footing using manual. So, it will take much time to finish it.

80

REFERENCES

Arash Alimardani Lavasan and Mahmoud Ghazavi. (2012). Behavior of Closely

Spaced Square and Circular Footings on Reinforced Sand. Vol. 52. 160 – 167

Boussida, M. and Porbaha, A. (2004). Ultimate Bearing Capacity of Soft Clays

Reinforced by a Group of Columns-Application to a Deep Mixing Technique.

Soils and Foundations, Vol. 44, No. 3, 91-101.

Braja M. Das. (2007), Theoretical Foundation Engineering, 1st Edition, Henderson,

Nevaja, J. Ross Publishing.

Braja M. Das (2009). Shallow Foundations, Bearing Capacity snd Settlement, 2nd

Edition, Taylor & Francais Group.

Christopher M. Frenz. (2002). Visual Basic and Visual Basic.NET for Scientist and

Engineers Barkeley, Apress.

Chungsik Yoo. (2001). Laboratory Investigation of Bearing Capacity Behavior of

Strip Footing on Geogrid-reinforced Sand Slope. 279 – 298.

D. Loukidis, R. Salgado. (2009) Bearing Capacity of Strip Footings in Sand Using

Finite Elements.36: 871 -879.

D. V. Griffiths, M.ASCE; Gordon A. Fenton, M.ASCE; and N. Manoharan,

Aff.ASCE. 2002.

H. A. Taiebat and J. P. Carter. (2002) Bearing Capacity of Strip and Circular

FOundations on Undrained Clay Subjected to Eccentric Loads. 32: No, 1, 61 –

64.

H. A. Taiebat and J. P. Carter. (2000) Numerical Studies of the Bearing Capacity of

Shallow Foundations on Cohesive Soil Subjected to Combined Loading. 50: 409 –

418

Islam, M. S. and Hashim, R. (2009). Bearing Capacity of Stabilised Tropical Peat by

Deep Mixing Method. Australian Journal of Basic and Applied Sciences, 3(2),

682-688.

Jean Salcon.(2002). Confining Effect on the Bearing Capacity of Circular Footings

on a Purely Cohesive Soil. 330: 521 – 525

81

Jellali, B., Boussida, M., and de Buhan P. (2005). A Homogenization Method for

Estimating the Bearing Capacity of Soils Reinforced by Columns. International

Journal for Numerical and Analytical Method in Geomechanics, Vol. 29, 989-

1004.

Junhwan Lee, Rodrigo Salgado, Sooil Kim. (2005) . Bearing Capacity of Circular

Footings Under Surcharge Using State-Dependent Finite Element Analysis. 32:

445 – 457

Jun Otani, Hidetoshi Ochiaai, Kentaro Yamamoto. (1998). Bearing capacity analysis

of reinforced foundations on cohesive soil.. 16: 195 – 206

Kitazume, M., Ikeda, T., Miyajima, S. and Karastanev, D. (1996). Bearing Capacity

of Improved Ground With Column Type DMM. Proc. of the 2nd International

Conference on Ground Improvement Geosystems. Vol. 1, 503-508.

L. Zhao, J. H. Wang. (2008) Vertical Bearing Capacity for Ring Footings. 35: 292 –

304

M. Hjiaj, A. V. Lyamin and S. W. Sloan. (2005). Numerical Limit Analysis Solutions

for the Bearing Capacity factor Nγ. Vol. 52. 1681 – 1704.

Mohammed Hjiaj, Andrei V. Lyamin, Scott W. Sloan. (2004). Bearing Capacity of a

Cohesive –Frictional Soil Under Non-eccentric Inclined Loading. 31: 491 – 516

Mostafa A. El. Sawwaf. (2007). Behavior of Strip Footing on Geogrid – Reinforced

Sand Over a Soft Clay Slope. Vol. 25. 50 – 60.

N. Manoharan and S. P. Dasgupta. (1995). Bearing Capacity of Surface Footings by Finite Elements. Vol. 54. 563 – 586.

N. S. V. Kameswara Rao. (2011) Foundation Design, Theory and Practice, John

Wiley 7 Sons (Asia) Pte Ltd.

Radoslaw L. Michalowski , Liangzhi You. (1998). Effective Width Rule in

Calculations of Bearing Capacity of Shallow Footings. 23: 237 – 253

S. Benmebarek, M. S. Remadna, N. Benmebarek and L. Belounar. (2012). Numerical

Evaluation of the Bearing Capacity Factor N’γ of Ring Footings. 132 – 138.

Y. L. Kuo, M. B. Jaksa, A. V. Lyamin, Kaggwa. (2009). ANN-Based Model for

Predicting the Bearing Capacity of Strip Footing on Multi-Layered Cohesive Soil.

36: 503 – 516