IMPROVEMENT OF SOFT GROUND USING STONE ...

Tanta University

Faculty of Engineering

Structural Engineering Department

IMPROVEMENT OF SOFT GROUND USING

STONE COLUMNS TECHNIQUE

A THESIS

Submitted for the Degree of Doctor of Philosophy

In Civil Engineering (Structural Engineering)

By Eng. Khaled Abdel Moneim Abdel Hay

Under the Supervision of

Tanta - 2017

Prof. Dr. Mohamed A. Sakr

Professor of Geotechnical Engineering,

Structural Engineering Department,


Tanta University

Assoc. Prof. Dr. Ahmed F. Abdel kader

Associate Professor of Geotechnical Engineering,


Faculty of Engineering,

Tanta University

Prof. Dr. Marawan M. Shahien

Professor of Geotechnical Engineering,



Tanta University

Tanta University

Faculty of Engineering Structural Engineering Department

The Examining Committee

Candidate Name:

KHALED ABD EL-MONEIM ABD EL-HAY

Title of Thesis:

“Improvement of soft ground using stone columns technique”

The Examining Committee:

No. NAME POSITION

1 Prof. Dr. Moustafa Kamel El Ghamrawy Professor of Geotechnical Eng.


Al Azhar University

2 Prof. Dr. Mohamed A. Sakr Professor of Geotechnical Eng.


Tanta University

3 Prof. Dr. Ashraf Kamal Nazir

Professor of Geotechnical Eng.


Tanta University

4 Prof. Dr. Marawan M. Shahien Professor of Geotechnical Eng.


Tanta University

Examining Date: 26 / 4 / 2017

Signatures:

No. NAME SIGNATURE

1 Prof. Dr. Moustafa Kamel El Ghamrawy

2 Prof. Dr. Mohamed A. Sakr

3 Prof. Dr. Ashraf Kamal Nazir

4 Prof. Dr. Marawan M. Shahien

https://www.google.com.eg/url?sa=t&rct=j&q=&esrc=s&source=web&cd=12&cad=rja&uact=8&ved=0ahUKEwidyq3wttXSAhWGtxoKHfrDBdEQtwIIVTAL&url=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DY97XWHgfIf4&usg=AFQjCNFooJVutzS9LOTsMCqOntIYojCo2A&sig2=1yWv3ZjGvdlXVbuWk3OE1Q




سورة ]طه[

(111اآلية )

To

My Parents, Wife and Sons

SUMMARY

i

Summary

This thesis aims to study the application of using stone columns to

strengthen, consolidate the soft clay soil and increase the footing load

capacity. In addition to reduce the expected collapse of the

foundations when constructed on soft soils.

In this research a practical program contains various types of soft clay

soil were prepared in the laboratory. The subgrade soils has been

strengthened by stone columns with different diameters and lengths

and loaded until the failure. The main control parameter of ultimate

load capacity at different cases with corresponding settlement were

recorded and plotted to show the most benefit of such technique in

improving the soft clay below the foundation.

Results demonstrated that the maximum capacity of the load of the

soil reinforced by stone columns depends on the diameter and length

of the stone column. The improvement in the ratio of the carrying

capacity based on a stone column base to about 3.2 times the carrying

capacity of the foundation without stone columns. The study also

included numerical modeling by Geotechnical specialist theoretical

program (Plaxis 2d) for an analysis of the effect of allowing the

drainage of water during loading (Drained conditions) because of the

difficulty of making this technique in the laboratory. The study also

confirmed the theory that the presence of the stone column works to

increase the clay stiffness and significantly improved the coefficient

subgrade modulus which reached to 7.7 times the value of subgrade

soil without soil stone columns.

Keywords:

Stone column, Settlement, Bearing capacity, Soft clay, Undrained shear

strength.

ACKNOWLEDGEMENT

I

ACKNOWLEDGEMENT

First of all, I would like to thank Allah owner of many graces for

enabling me to execute this research and complete this work.

I wish to express his gratitude to Prof. Dr. Mohamed A. Sakr,

professor of Geotechnical Engineering, Faculty of Engineering, Tanta

University, for his constant encouragement, his valuable views and

views and opinions at all step of this study.

I would like to extend special thanks to Prof. Dr. Marawan M.

Shahien, professor of Geotechnical Engineering, Faculty of

Engineering, Tanta University, for his direct supervision, support,

provide me with extremely valuable comments and rational guidance

throughout the research work.

Also, I would like to extend special thanks to A. /Professor Ahmed

Farouk A.E.K Assoc. professor of Geotechnical Engineering,

Faculty of Engineering, Tanta University, for all the effort he paid

during the preparation of this work and encouragement me during all

stages of this research.

I am also grateful to Geotechnical Engineering Laboratory staff

members, Faculty of Engineering, Tanta University for their support

and encouragement during carrying out the numerical work and tests.

This work would not have been possible without the support and love

of my parents nothing to be said is sufficient to reveal my sincere

gratitude.

I owe an expression of special gratitude for my great wife for her

patience and her support at various stages of this work.

ENG. Khaled Abdel Moneim Abdel Hay

ABSTRACT

II

ABSTRACT

Stone columns have been used as an effective technique for improving

the engineering behavior of soft clayey grounds. The soil improvement

via stone columns are achieved from accelerating the consolidation of

weak soil due to shortened drainage path, increasing the load carrying

capacity and settlement reduction due to inclusion of stronger granular

material.

A detailed experimental study on behavior of floating and fully

penetrating single stone column is carried out by varying parameters

like L/D ratio (slenderness ratio) and undrained shear strength of soft

clay. Laboratory tests are carried out on a column of 50 mm, 100 mm,

150 mm and 300 mm in diameter with different length of 100 mm, 200

mm, 300 mm and 400 mm surrounded by soft to medium clay with

different undrained shear strength in the range of 10 to 30 kPa. The

tests are carried out on the entire equivalent area loaded to estimate the

stiffness of the improved ground by the technique.

Finite-element analyses have also been performed using PLAXIS

software aimed at investigating the small scale model that carried out

in the laboratory testing program. The effect of stone column

geometry, undrained shear strength and the effect of drained condition

are also investigated. The load – settlement behaviour responses of the

columns was evaluated of both drained and undrained conditions.

A drained and undrained analysis was carried out using Mohr-

Coulomb’s criterion for soft clay. The modeling of stone columns was

designed by axisymmetric pattern in PLAXIS. The numerical results

from the finite element modeling are compared with the experimental

results which showed good agreement between the results.

III

While the second part of study is related to discuss and develop the

numerical modeling of full scale analysis using most common case

study as stated by Tan et al., 2008.

An Axisymmetric configuration and a Plane strain configuration for

the column are adopted for comparison. The results show that the

axisymmetric configuration shows the best agreement with the case

study results.

Comparison all results from finite element model by examination (Han

and Ye 2001) and (Han and Ye 2002) simplified analytical solution for

the rate of consolidation of stone-column reinforced ground are also

submitted.

Parametric analyses are carried out to study the effect of various

parameters such as the column spacing to diameter ratio and

embankment height. The ratio of modulus of elasticity of the column

to modulus of elasticity of the soft soil on the stress concentration

factor, settlement reduction factors and time reduction factors are also

presented. It helps in increasing efficiency of the stone column

technique. The results of this parametric study are compared with

analytical approaches.

The analysis captured the undrained nature of loading domain in the

loading test. In order to pair the results obtained for undrained

laboratory cases to drained behaviour, a series of finite element

analysis were carried out using drained model for all undrained cases

carried out in the laboratory. The results were performed in the form of

vertical stress versus settlement relationship.

CONTENTS

IV

CONTENTS

Page

ACKNOWLEDGMENT………………...……………………….. I

ABSTRACT ………………………………………………………. III

CONTENTS …………………………………….………………... IV

LIST OF FIGURE ………………….……………………………. X

LIST OF TABLES ……………………..……………………… XXVI

CHAPTER(1) INTRODUCTION

1.1 General…………………………………………………………. 1

1.2 Objectives of the Study…...……………………………............. 2

1.3 Scope of Work…………………………………………………. 3

1.4 Thesis Organization……………………………………………. 3

CHAPTER (2) LITERATURE REVIEW

2.1 Introduction ……………………………………………………. 6

2.1.1 General …………………….………………………………… 6

2.1.2 Definition…………………………………………………….. 7

2.1.3 Historical Review of the Use of Stone Column……………… 7

2.1.4 Characteristics of Ground Improvement Systems …………... 8

2.1.5 Improvement of Soil Characteristics Using Stone Column

Technique ……………………………………………………...…..

9

2.2 Methods of Granular Pile Construction………………………... 10

2.2.1 Vibro – Compaction Method………………………………… 10

2.2.2 Vibro – Replacement Method………………………………... 11

2.2.2.1 Wet Method………………………………………………... 13

2.2.2.2 Dry Method……………........................................................ 14

2.2.2.3 The Dry bottom Feed ……...…………………..…………... 14

V

2.2.4 Vibro – Compozer Method …………………...………….…. 16

2.2.5 Cased– Borehole Method or Rammed Method ………...…… 17

2.3 Engineering Behavior of Composite Ground …………………. 18

2.3.1 Basic Design Parameters..................................…………...…. 18

2.3.1.1 Stone Column Diameter, D ………………….……………. 18

2.3.1.2 Stone Column Pattern………...…......................................... 18

2.3.1.3 Stone Column Spacing…………………………………….. 20

2.3.1.4 Replacement Ratio (as).......................................................... 21

2.3.1.5 Stress Concentration Factor (n)……………………………. 23

2.3.1.6 Back Fill for Stone Columns ………………………...……. 24

2.3.2 Failure Mechanisms................................................................. 24

2.4 Mechanism and Performance of Stone Columns……………… 29

2.5 Experimental Studies ………………………………………….. 29

2.5.1 Field Tests................................................................................ 29

2.5.2 Laboratory Tests....................................................................... 39

2.5.3 Theoretical Studies................................................................... 55

2.5.3.1 Numerical Methods………………………………………... 56

2.6 Ultimate Bearing Capacity of Stone Columns…………………. 58

2.6.1 Isolated, Single Stone Column………………………………. 58

2.6.2 Stone Column Groups………………………………………... 63

2.7 Settlement Analyses……………………………………………. 70

2.7.1 Greenwood Method………………………………………….. 70

2.7.2 Priebe Method…………………………………...…………… 71

2.7.3 Equilibrium Method…………………………………..……… 76

2.7.4 Incremental Method…………………………………………. 78

2.7.5 The Granular Wall Method 80

2.8 Estimation of Rate of Consolidation 81

VI

2.8.1 Consolidation Rate of Improved Ground by Stone Column 81

2.8.2 Stone Columns-Soft Soil Reinforcement System under

Embankment……………………………………………………….. 93

2.9 Smear Zone: Effect on Permeability…………………………… 96

2.10 Scale Effect 101

2.11 Data Base of Stone Column Studies 107

CHAPTER (3) EXPERIMENTAL WORK

3.1 Introduction................................................................................. 113

3.2 Soft Clay preparing…………………………………………. 113

3.2.1 Commercial Kaolinite Clay Type……………………………. 113

3.2.3 Determination of Soil Properties…………………………….. 115

3.2.3.1 Shear strength of Tested Samples …………………………. 116

3.2.3.2 Consistency Limits………………………………………… 117

3.2.3.3 Consolidation tests ………………………………………... 120

3.3 Sand ………………………………………..……………….…. 121

3.4 Columns Materials Properties………………………………….. 124

3.4.1 Stone/ Aggregate ………………..…..………………………. 124

3.5 Test Setup……………………………………………………… 126

3.5.1 Loading Frame………………………………………….......... 126

3.5.1.1 Loading Jack…………………………………………..…… 127

3.5.1.2 Measuring device……………………………………..…… 127

3.5.2 Test Tank…………………………………………………….. 127

3.5.3 Loading plate………………………………………..……….. 127

3.6 Soft clay preparation ……………………………………….….. 127

3.7 Test Procedures…………………………………………………

3.7.1 Column Installation…………………………………………..

3.8 The Experimental Program……………………………………..

128

128

131

VII

CHAPTER (4) EXPERIMENTAL TEST RESULTS

4.1 Introduction……………………………………………………. 133

4.2 Definition of the Failure Load…………………………………. 134

4.3 Effect of Stone Column Diameter ………………...................... 135

4.4 Effect of Stone Column Length…………………………….….. 135

4.5 Improvement Factor, If (%)……………………………….…. 136

4.6 Stone Column Treated Soft Clay Soil in the Case of Undrained

Shear Strength (cu) = 10 kPa……………………………………….

137

4.6.1 Improvement in the Ultimate Load Capacity of the Stone

Column Treated Soft Clay………………………………………….

142



146


Column Treated Soft Clay…………………………………………. 151`



155


Column Treated Soft Clay………………………………………….

160

4.9 Behavior of End Bearing Stone Column …………………….... 163

4.9.1 Bulging Responses of End Bearing Stone Columns…...……. 165

CHAPTER (5) NUMERICAL MODELING

5.1 Introduction …………………………………...……………….. 171

5.2 Finite Element Modeling Program Used in This Research……. 172

5.2.1 Input Program………………………………………………... 172

5.2.1.1 Soil Elements………………………………………………. 172

5.2.1.2 Types of Soil Behavior…………………………………….. 174

5.2.1.3 Boundary Conditions……………………….……………… 175

VIII

5.2.1.4 Mesh Generation …………..……………………………….

5.2.1.5 Initial Conditions…………………………………………...

176

176

5.2.2 Calculation ……………………………….….………………. 177

5.2.2.1 Types of Calculations……………………..……………….. 177

5.2.3 Output …………………………………………..………...…. 178

5.3 The Mohr Coulomb Model……………………………….……. 178

5.3.1 Young’s Modulus……………………………………………. 179

5.3.2 Poisson’s Ratio (υ)…………………………………………… 181

5.3.3 Cohesion (c)…………………………………………….……. 181

5.3.4 Friction Angle

(ϕ )…………...……………………………….. 182

5.3.5 Dilatancy Angle (ψ)……………...…………………..………. 182

5.4 The Hardening Soil Model………………...…………………... 183

5.5 Numerical Model Verification…………………………….…… 183

5.5.1 Validation Using (Ambily and Gandhi, 2007) Results…...….. 183

5.5.2 Validation Using the Results Obtained by (Narasimha Rao et

al., 1992):…………………………………………………………...

189

5.5.3 Verification for Experimental Work of Present Study………. 192

CHAPTER (6) NUMERICAL ANALYSIS

6.1 Introduction …………………………………...…………….…. 200

6.2 Numerical Analysis of Model Testing……………………...….. 200

6.3 Numerical Analysis of Drained Condition ………………….… 215

6.4 Stress – Settlement Curves for End Bearing Stone Column in

drained condition…………………………………………………...

230

6.5 Analysis of Failure Mechanism of Stone Column in Drained

Condition …………………………………………………......……

232

6.6 Comparison Between Drained and Undrained Condition……... 234

IX

6.7 Stress Concentration Ratio at Various Shear Strengths and

Various L/H Ratios for Drained Condition………………………...

263

6.8 Statistical Analysis…………………………………………… 267

CHAPTER (7) COMPARATIVE STUDY

7.1 Scope…………………………………………………………… 270

7.2 Case Study Description ……………..………………………... 270

7.3 Numerical Modeling 2D Finite Element Analyses………...…... 274

7.3.1 Axisymmetric Model………………………………………....

7.3.2 Plane Strain Model Using Equivalent Parameters……………

7.4 Comparison Between the 2D FE Analyses and Field

Measurements………………………………………………………

7.4.1 Settlement………………………………………………….

7.4.2 Excess pore water pressure……………………………….....

276

279

283

283

285

7.5 Examination Method of (Han and Ye 2001 & 2002) ………... 288

7.6 Parametric Study …………..………………………….……… 297

7.6.1 Stress Concentration Factor ………..…………………….… 298

7.6.2 Modular Ratio …..………………………………………..… 298

7.6.3 Settlement Reduction Factor ..……………………………… 298

7.6.4 Time Reduction Factor………………………………………. 298

7.7 Effect of Spacing to the Diameter of Stone Column (S/D)...… 300

7.8 Effect of Stress Level …..…………………………...………... 302

7.9 The Effect of Modular Ratio ……………..………..…………. 305

7.10 Comparative Study…………………………………………… 309

7.10.1 The Stress Concentration Factor …………………...………. 309

7.10.2 The Settlement Reduction Factor …………………...……... 313

6.16.3 The Time Reduction ………………………………….....…. 316

7.11 Comparative study with different investigators on stone 319

X

columns…………………………………………………………......

CHAPTER (8) CONCLUSIONS AND RECOMMENDATIONS

8.1 Introduction…………….……………………..……..…………. 322

8.2 Conclusions Regarding experimental results ………..………… 322

8.3 Conclusions Regarding Numerical Analysis of Laboratory

Model Tests………………………………………………………...

323

8.3.1 Numerical Analysis of Drained Condition (cu = 10 kPa) …… 325

8.4 Conclusions Regarding Comparison Between Drained and

Undrained Condition………………………………………..…...…

327

8.5 Conclusions Regarding Effect of stone column on Subgrade

modulus……………………………………………………………..

328

8.6 Conclusions Regarding Case study and parametric study…….. 329

8.7 Recommendations for Future Studies………………….....……. 330

REFERENCE …………………………………………….…...… 331

PUBLISHED PAPER……………………………………………… 354

ARABIC SUMMARY

LIST OF FIGURES

X Figure Page No.

CHAPTER (2)

2.1 Vibroflot used for vibro-compaction and vibro –replacement

methods (Slocombe et al., 2000)…………………................ 11

2.2 The vibro – compaction process (Bergado et al., 1994)…...… 12

2.3 The vibro – replacement method (Bergado et al., 1994)……. 12

2.4 Range of soils suitable for vibro – compaction and vibro-

replacement (Bergado et al., 1994)…………………………... 13

2.5 Bottom feed of stone column (Slocombe et al., 2000)………. 15

2.6 The vibro composer method (Bergado et al., 1994)…….…… 16

2.7 The cased – borehole method (Bergado et al., 1994)……...… 17

2.8 Equivalent diameter of the tributary soil treated by stone

column (Balaam and Booker, 1981)……………….….….….. 19

2.9 Unit cell idealizations (Barksdale and Bachus 1983)…….….. 21

2.10 Diagram of composite ground (Bergado et al., 1994)...…....... 22

2.11 Area ratios for (i) square grids, (ii) triangular grids and (iii)

pad footing (Bergado et al., 1994) …………………………... 22

2.12 Failure mechanisms of single stone column in homogeneous

soft layer (Barksdale and Bachus. 1983) ……………..…...… 25

2.13 Failure modes of stone column groups (Barksdale and

Bachus. 1983) …………………………………………..…… 26

2.14 Stone column failure mechanisms in nonhomogeneous

cohesive soil (Barksdale and Bachus. 1983) ……...………… 26

2.15

Failure of stone column, (pivarc, 2011)……………...……… 28

XI Figure Page No.

2.16 Comparison of large scale filed loading test results on

untreated soft clay, soft clay reinforced with stone column

and with sand column at Bremerhaven, Germany,

(Greenwood, 1970)……….……………..……………………

31

2.17 Field deformation behaviour of a single column under a

(rigid) plate load test, (Hughes et al., 1976) ………………… 33

2.18 Field load test arrangement (Goughnour and Bayuk, 1979)… 34

2.19 Settlement versus log time at the centre and corners of load

area in field trial (Goughnour and Bayuk, 1979)…..………... 35

2.20 Comparison of load settlement performance of granular

column constructed with different numbers of blows per

compacted layer (Bergado & lam, 1987) …….………..……. 38

2.21 Failure modes of stone columns (Wood et al., 2000)…….….. 42

2.22 Normalized load-settlement results for model footings;

variation of area ratio (short columns) (Wood et al., 2000)..... 43


variation of area ratio (long columns) (Wood et al., 2000)...... 44


variation of column length (short columns) (Wood et al.,

2000)…………………………………………………………. 44


variation of column length (long columns) (Wood et al.,

2000)…………………………………………………………. 45

2.26 Photos of sand column beneath circular footing at

beginning, middle and end of foundation loading process: (a)

150 mm length; (b) 250 mm length (Mckelvey et al.,

2004)………………………………………….……………… 47

2.27 Single column test arrangement (a) column area loading (b)

entire area loading (Ambily and Gandhi., 2007) ……….…… 49

XII Figure Page No.

2.28 Effect of s/d and ϕ on axial capacity of stone

column..……… 50

2.29 Stress settlement behavior under entire area loading (Ambily

and Gandhi, 2007) ……………………………………...….... 51

2.30 Comparison of group column test and single column test

(Ambily and Gandhi, 2007) …………………….........……… 51

2.31 The test setup for single and group column test (Isaac and

Grirish, 2009) ……………………………………..………… 53

2.32 Load –Settlement curve for clay with single column (Isaac

and Grirish, 2009) …………………………………………… 53

2.33 Comparison of stress settlement relation for clay with group

of seven columns (S=2.5D)…………...……………..………. 54

2.34 Comparison of stress settlement relation for clay with with

group of seven columns (S=3D)…………………...………… 54

2.35 Greenwood curves (Greenwood and Kirsch, 1983).….……... 55

2.36 Priebe design curves (Priebe, 1995)…………………………. 56

2.37 Typical test setup examined by (Rao et al., 1992)………….... 62

2.38 Stone column group analysis – firm to stiff cohesive soil

(Barksdale and Bachus, 1983)……………………………….. 64

2.39 Proportional loads on stone columns (Priebe, 1995) …….….. 67

2.40 Settlement for stone column in clay (Greenwood, 1970).…… 71

2.41 Priebe’s settlement improvement factor curves (Priebe,

1995)………………………………………………................. 73

2.42 Additional area ratio curves (Priebe, 1995) …….…………… 75

2.43 Settlement of single footings (Priebe, 1995) ……...………… 75

2.44 Settlement of strip footings (Priebe, 1995)….…………...…... 76

XIII Figure Page No.

2.45 Settlement reduction factor using equilibrium method

(Aboshi et al., 1979)……………………………………….... 78

2.46 Total settlement-time relationship of reinforced soft clay by

Granular piles (Bergado and Long, 1994)…………………... 82

2.47 Total settlement-time relationship of reinforced soft clay by

Vertical drain (Bergado and Long, 1994)…………………… 83

2.48 Definition of terms for modeling (Han and Ye, 2001) …....… 85

2.49 Vertical stress on soil and columns with time, N = 3 and

ns = 5 (Han and Ye, 2001)…………………………………... 87

2.50 Stress concentration ration with time (Han and Ye, 2001)….. 88

2.51 Dissipation of excess pore water pressure, N = 3 and ns = 5

(Han and Ye, 2001)……………….…………………………. 89

2.52 Rate of consolidation of stone column reinforced foundations

(Han and Ye, 2001)…………………………..……………… 90

2.53 Rate of consolidation of stone column reinforced foundations

(Han and Ye, 2001)………………………………………….. 91

2.54 Stress concentration factor. Influence of radial deformation

and plastic strains (Castro and Sagaseta, 2009…………..…... 93

2.55 Suggested variation of horizontal permeability with radius

according to (Onoue et al.,1991)…………………………….. 97

2.56 Section of the test setup showing the smear zone (Indraratna

and Redana, 1998)…………………………………………... 98

2.57 Ratio of horizontal to vertical coefficient of permeability

against the radial distance from the axis of the sand

compaction pile (denoted as drain) (Indraratna and Redana,

1998)………………………………………………………… 99

2.58 Excess pore water pressures during the insertion of the

installation mandrel (Sharma and Xiao, 2000) ………..……. 100

XIV Figure Page No.

2.59 Single column test arrangement dimension (Ambily and

Gandhi, 2007)……………………………………………… 101

2.60

The test setup for single column model test (Isaac and

Grirish, 2009)………………………………………………. 102

2.61

Test arrangement and dimension (Shivashankar et al.,

2011)………………………………………………………… 102

2.62

Schematic view of stone column foundation of (Ali et al.,

2011)…………………………………………………………. 103

2.63

The Schematic diagram of sand column test arrangement

(Tandel et al., 2012)…………………………………………. 104

2.64 Test arrangement (Prasad and Satyanarayana, 2016)………... 104

CHAPTER (3)

3.1 Grain size distribution curve from hydrometer test for the

tested sample………………………………………………… 116

3.2 Classification of soft clay using plasticity chart…………...… 118

3.3 Relation between normal stress and shear strength

(cu =10 kPa)……………………………...…………………... 118


(cu =20 kPa)……………………………...…………………... 119


(cu =30 kPa)……………………………...…………………... 119

3.6 e-log p curve for tested soft clay in odometer……………….. 120

3.7 Sieve analysis curve for used sand…………………………... 122

3.8 Compaction curve for tested sand…………………………... 123

XV Figure Page No.

3.9 Relation between normal stress and shear strength (for tested

sand at maximum dray density)……………………………… 123

3.10 Sieve analysis curve for used stone………………………….. 125

3.11 Relation between normal stress and shear strength for used

stone…………………………………………………………..

125

3.12 Experimental setup.……………..…………………………… 126

3.13 Column Installation………………………………………….. 128

3.14 Lay out of installation steps for the case of floating stone

column………………………………………………………..

129

3.15 Lay out of installation steps for the case of fully penetrate

stone column………………………………………………….

130

3.16 General lay out of the studied parameters. 131

CHAPTER (4)

4.1 Typical load-displacement curves (Hirany and Kulhawy

1989)………………………………………………………… 134

4.2 Variation of the diameter D within the unit cell…………….. 135

4.3 Geometry configurations for model tested stone column ….... 136

4.4 Stress settlement curves for different stone columns L/H

ratios (D = 50 mm, cu = 10 kPa)…… ……………….……… 138


ratios (D = 100 mm, cu = 10 kPa)………………………….… 139


ratios (D = 150 mm, cu = 10 kPa)………………...……….…. 140


ratios (D = 300 mm, cu = 10 kPa)………………..………..… 141

XVI Figure Page No.

4.8 The effect of column length on the improvement factor,

If (%) at different diameters for 25 mm settlement (cu = 10

kPa)…………………………………………………………... 142

4.9 The effect of column diameters on the improvement factor, If

(%) for different lengths at 25 mm settlement (cu = 10 kPa)... 144

4.10

The effect of L/D ratio on the improvement factor,If (%) at

25 mm settlement (cu = 10 kPa)……………………………... 144

4.11

The effect of L/D ratio on the improvement factor, If (%) for

different L/H ratio at 25 mm settlement (cu = 10 kPa)………

145

4.12 The effect of L/H ratio on the improvement factor, If (%)

for different diameters at 25 mm settlement (cu = 10 kPa)…... 145

4. 13 Stress settlement curves for different stone columns L/H

ratios (D = 50 mm, cu = 20 kPa)…………………………..…. 147


ratios (D = 100 mm, cu = 20 kPa)……………………....……. 148


ratios (D = 150 mm, cu = 20 kPa)…………………...………. 149


ratios (D = 300 mm, cu = 20 kPa)……………………….…… 150

4.17 The effect of total column lengths on the percentage of load

increase for different diameters at 25 mm settlement (cu = 20

kPa)…………...……………………………………………… 152

4. 18 The effect of column diameters on the improvement factor, If

(%) for different lengths at 25 mm settlement (cu= 20

kPa)…………………………………………………………...

153

4.19

The effect of L/D ratio on the improvement factor, If (%) at

25 mm settlement (cu = 20 kPa)…………………................... 153

XVII Figure Page No.

4.20 The effect of L/D ratio on the improvement factor, If (%)

for different L/H ratio at 25 mm settlement (cu = 20 kPa)….. 154

4.21 The effect of L/H ratio on the improvement factor, If (%)



ratios (D = 50 mm, cu = 30 kPa)……………….…………….. 156


ratios (D = 100 mm, cu = 30 kPa)…………….………..…….. 157


ratios (D = 150 mm, cu = 30 kPa)……………………………. 158


ratios (D = 300 mm, cu = 30 kPa)……...…………………….. 159

4.26 The effect of column length on the improvement factor, for

different diameters at 25 mm settlement ………. 160

4.27 The effect of column diameter on improvement factor, If (%)

for different lengths at 25 mm settlement..……………...…… 161

4.28

The effect of L/D ratio on the improvement factor, If (%) at

25 mm settlement (cu = 30 kPa)……………………………… 161

4.29

The effect of L/D ratio on the improvement factor, If (%)

for different L/H ratio at 25 mm settlement (cu = 30 kPa) .…. 157

4.30

The effect of L/H ratio on the improvement factor, If (%)


4.31 Stress settlement curves for end bearing stone columns at

different diameters and cu = 10 kPa……………...……...…… 163

4.32 Stress settlement curves for end bearing stone column at

different diameters of and cu = 20 kPa………….....………… 164

XVIII Figure Page No.

4.33 Stress settlement curves for end bearing stone column at

different diameters of and cu = 30 kPa………….…………… 164

4.34 Pouring cement slurry into the stone column to maintain the

shape of the resulting deformation…...……………………… 165

4.35 Separation of stone column from surrounding soil after 24

hours ………………………………………………………… 166

4.36 Shape of stone column after removing it from the

surrounding soil……………………………………………… 166

4. 37 Deformed shape of stone column ……………...……………. 167

4. 38 Stone column shape before and after testing (cu = 10 kPa)..… 167

4.39 Variation of the horizontal displacement for end bearing

loading condition for different undrained shear strength

values, cu (D = 50 mm)………………………...…………….. 168



values, cu (D = 100 mm)……………..….…………………… 169



values, cu (D = 150 mm)………………...…………………… 169



values, cu (D = 300 mm)……………………..…….………… 170

CHAPTER (5)

5.1 Example distribution of nodes and stress points in PlAXIS

finite elements (PlAXIS version 8 manuals)………………… 173

5.2 Mohr’s circle of stress used to drive relation between

undrained shear strength and drained shear parameters

Brinkgreve, 2002)……………………….…………………… 175

XIX Figure Page No.

5.3 Mesh refine in for the proposed model in stability analysis in

2D PLAXIS program………………………………………… 176

5.4 Mohr-Coulomb yield criterion ………………………………. 179

5.5 Definition of E0 and E50 for standard drained triaxial test

results (Brinkgreve, 2002)……..……………………...…....... 180

5.6 Mohr-Coulomb failure envelope with one Mohr failure circle

(Brinkgreve, 2002)…………………………………………... 182

5.7 Finite-element discretization for both cases (Ambily and

Gandhi, 2007) …………………………………..…...……….

185

5.8 Deformed mesh for both cases (Ambily and Gandhi, 2007)… 186

5.9 Verification of are current plaxis results with the load

settlement behavior of loaded stone column alone (Ambily

and Gandhi, 2007)…………………………………………… 187


settlement behavior of entire loaded area (Ambily and

Gandhi, 2007)………………………………………………... 188

5.11 Finite-element discretization of model test (Narasimha Rao et

al., 1992)……………………………………………………... 190


settlement behavior (Narasimha Rao et al., 1992)…………... 186

5.13 The model and the soil mesh for the case of untreated soil….. 192

5.14 Unit cell stone column and unit cell stone column mesh for

the case of treated soil……………………………………….. 193

5.15 Stress settlement response for the two cases of Mohr

Coulomb and hardening soil criteria model, (L = 300 mm &

D = 150 mm)………………………………………………… 194

5.16 Stress settlement behavior of both model test and finite

element at cu = 10 kPa, D = 50 mm and L = 100 mm………. 197

XX Figure Page No.


element at cu = 10 kPa, D = 150 mm and L = 300 mm…….... 197


element at cu = 20 kPa, D = 150 mm and L = 300 mm…….... 198


element at cu = 20 kPa, D = 300 mm and L = 200 mm….…... 198


element at cu = 30 kPa, D = 50 mm and L = 300 mm……….

199

5. 21 Stress settlement behavior of both model test and finite

element at cu = 30 kPa, D = 300 mm and L = 300 mm……... 199

CHAPTER (6)

6.1 Stress – settlement curves for different L/H ratios (D = 50

mm and cu = 10 kPa)………………………………………… 203


mm and cu = 10 kPa)………………………………………… 203


mm and cu = 10 kPa)……………………………………….... 204


mm and cu = 10 kPa)……………………………………….... 204


mm and cu = 20 kPa)………………………………………… 208


mm and cu = 20 kPa)………………………………………… 208


mm and cu = 20 kPa)……………………………………….... 209


mm and cu = 20 kPa)……………………………………….... 209


mm and cu = 30 kPa)………………………………………… 213


mm and cu = 30 kPa)………………………………………… 213

XXI Figure Page No.


mm and cu = 30 kPa)……………………………………….... 214


mm and cu = 30 kPa)………………………………………… 214


mm and cu = 10 kPa)……………………………………........ 218


mm and cu = 10 kPa)………………………………………… 218


mm and cu = 10 kPa)………………………………………… 219


mm and cu = 10 kPa)………………………………………… 219


mm and cu = 20 kPa)…………………………………........... 223


mm and cu = 20 kPa)……………………………………….... 223


mm and cu = 20 kPa)……………………………………….... 224


mm and cu = 20 kPa)……………………………………….... 224


mm and cu = 30 kPa)………………………………………... 228


mm and cu = 30 kPa)………………………………………… 228


mm and cu = 30 kPa)………………………………………… 229


mm and cu = 30 kPa)……………………………………….... 229

6.25 Stress – settlement curves for end bearing stone column,

D = 50 mm at different undrained shear strength …………… 230


D = 100 mm at different undrained shear strength…….….… 231


D = 150 mm at different undrained shear strength….……..… 231


D = 300 mm at different undrained shear strength…………... 232

6.29 Stress – settlement behaviour of floating type stone column

divided into three stages (D= 50 mm, L/H= 0.5)..…………... 233

6.30 Stress - settlement behaviour for the two cases of drained and

undrained conditions (cu = 10 kPa, D = 50 mm)….………… 236

XXII Figure Page No.


undrained conditions (cu = 10 kPa, D = 100 mm)….……… 232










undrained conditions (cu =20 kPa, D = 150 mm)….……… 237









6. 41 Stress - settlement behaviour for the two cases of drained and

undrained conditions (cu = 30 kPa, D = 300 mm)………… 242


undrained conditions (cu = 10 kPa, D = 50 mm)……………. 252


undrained conditions (cu = 10 kPa, D = 100 mm). 252















XXIII Figure Page No.







6.54 The relationship between L/H ratio and increase in the

subgrade modulus for cu = 10 kPa ……..……………………. 259


subgrade modulus for cu = 20 kPa…………………………… 260


subgrade modulus for cu = 30 kPa…………………………… 260

6.57 The relationship between the undrained shear strength cu

(kPa) and the relative subgrade modulus (D = 50 mm)…….. 261


(kPa) and the relative subgrade modulus (D = 100 mm)…... 261


(kPa) and the relative subgrade modulus (D = 150 mm)….. 262


(kPa) and the relative subgrade modulus (D = 300 mm)….. 262

6.61 The relationship between L/H and stress concentration factor

at different shear strength (D = 50 mm).……………….……. 264


at different shear strength (D = 100 mm).……………...……. 265





CHAPTER (7)

7.1 Layout plan of stone column works at New Pantai

expressway………………………………………...………… 272

7.2 Cross section of embankment case history through centerline

of stone columns……………………………..………………

273

XXIV Figure Page No.

7.3 (a) Geometry and boundary conditions for the axisymmetric

model (b) Generated finite element mesh for the

axisymmetric model…………………………………………. 277

7.4 Settlement at SP1 using axisymmetric model………….….… 278

7.5 Excess pore water pressures at point (A) using axisymmetric

model………………………………………………….……... 278

7.6 Geometry and boundary conditions for plane strain with

equivalent parameters finite element model...………...…...... 280

7.7 Generated finite element mesh for plane strain with

equivalent parameters finite element model………………… 280

7.8 Settlements at (SP1) for Plane strain with equivalent

Parameters Finite element model……………………………. 281

7.9 Settlements at (SP2) for Plane strain with equivalent

Parameters Finite element model…………….……………… 281

7.10 Excess pore water pressure at points (A) and (B) for plane

strain with equivalent parameters finite element model…….. 282

7.11 Comparison of settlements at (SP1)…………………………. 284

7.12 Comparison of settlements at (SP2)…………………………. 284

7.13 Comparison of Excess pore water pressure at point (A)…….. 286

7.14 Comparison of Excess pore water pressure at point (B)......… 286

7.15 Variation of stress concentration factor with modular ratio –

linear elastic analysis………………………………………… 290

7.16 Measured and calculated settlement – time curve…………… 296

7.17 Effect of columns spacing on the stress concentration factor.. 300

7.18 Effect of columns spacing on the settlement reduction factor. 301

7.19 Effect of columns spacing on the time reduction factor……... 302

7.20 Effect of stress level on the stress concentration factor …….. 303

7.21 Effect of stress level on the settlement reduction factor……...

304

XXV Figure Page No.

7.22

Effect of stress level on the time reduction factor……………

305

7.23

Effect of Modular ratios on the stress concentration factor….

306

7.24 Effect of Modular ratios on the settlement reduction factor…. 307

7.25 Effect of Modular ratio on the time reduction……………….. 308

7.26 The effect of column spacing on the stress concentration

factor using numerical modeling and theoretical approaches..

310

7.27 The effect of embankment height on the stress concentration

factor using numerical modeling and theoretical ……………

311

7.28 The effect of Modular ratio on the stress concentration factor

using numerical modeling and theoretical approaches……….

313

7.29 The effect of column spacing on the settlement reduction


314

7.30 The effect of embankment height on the settlement reduction


315

7.31 The effect of modular ratio on the settlement reduction factor


316

7.32 The effect of column spacing on the time reduction factor


317

7.33 The effect of embankment height on the time reduction


318

7.34 The effect of modular ratio on the time reduction factor using

numerical modeling and theoretical approaches……………..

319

7.35

Settlement improvement factor against area replacement

ratio for sites with widespread loading ………………...…….

320

LIST OF TABLES

XXVI LIST OF TABLES Page No.

CHAPTER (2)

2.1 Properties of granular columns (Bergado and Lam, 1987)….. 37

2.2 Database of numerical studies on stone columns……………. 108

2.3 Database of laboratory tests on stone columns………………. 110

2.4 Database of field tests on stone columns…………………….. 112

CHAPTER (3)

3.1 Mineralogical composition of the kaolinite used in model

tests (Given by the manufacturer from the Data sheet)…….... 114

3.2 Chemical composition of the kaolinite used in model test

(Given by the manufacturer from the Data sheet)…………… 115

3.3 Properties of used soil………………………………………... 117

3.4 Consolidation properties of tested soft clay………………… 121

3.5 Physical and mechanical properties of tested sand…………. 122

3.6 Experimental program and studied parameters……………… 132

CHAPTER (4)

4.1 The percentage of load increase due to the increase of

columns diameter 50 mm and cu = 10 kpa………………….. 138


columns diameter 100 mm and cu =10 kPa…………………. 139




columns diameter 300 mm and cu =10 kPa………………….. 141


columns diameter 50 mm and cu = 20 kPa…………….......... 147

XXVII LIST OF TABLES Page No.


columns diameter 100 mm and cu =20 kPa………………….. 148


columns diameter 150 mm and cu =20 kpa………………….. 149


columns diameter 300 mm and cu =20 kPa ………………… 150


columns diameter 50 mm and cu = 30 kpa………………… 156



4. 11 The percentage of load increase due to the increase of

columns diameter 150 mm and cu =30 kpa…………………. 158


columns diameter 300 mm and cu =30 kpa………………….

159

CHAPTER (5)

5.1 Details of material properties (Ambily and Gandhi, 2007)….. 184

5.2 Properties of Materials Used for Validation of PLAXIS……. 191

5.3 Mohr Coulomb Parameters for all Materials for the case of

cu = 10,20 and 30 kPa ……...………………………………... 195

5.4 Hardening Soil Parameters for Soft Clay Materials at shear

strength cu = 20 kPa………………………………………… 196

CHAPTER (6)

6. 1 Ratio between stress in undrained condition and drained

condition at 25 mm settlement, (cu =10 kPa)………………... 248

6. 2 Ratio between stress in undrained condition and drained

condition at 25 mm settlement, (cu =20 kPa)……………… 249

XXVIII LIST OF TABLES Page No.

6. 3 Ratio between load in undrained condition and drained

condition at 25 mm settlement, (cu =20 kPa).……..………… 250

6. 4 The values of C1 and C2 for stone column under drained

condition……………………………………………………..

266

CHAPTER (7)

7.1 Material Parameters for Case study……………………….... 274

7.2 Stone columns parameters (equivalent parameters plane

strain model)……………………………………………….… 279

7.3 Comparison between results of settlement at SP1 and SP2…... 285

7.4 Comparison of excess pore water pressure at point (A) and at

point (B)……………………………………………………… 287

7.5 Parametric study……………………………...……………… 299

Chapter (1):

INTRODUCTION

- 1 -

CHAPTER (1)

INTRODUCTION

1.1 General

Soft soil deposits usually exhibit excessive settlement characteristics

and have a low bearing capacity. In order to prevent these problems, it is

necessary to improve the existing soft soil before any construction

activities can be preceded. Many measures have been proposed which

include dewatering, compaction, dynamic compaction, deep mixing,

deep densification, jet grouting, compaction grouting and soil

reinforcement. These methods are regarded as ground improvement

techniques. Among them, stone column (also termed granular pile) has

been generally recognized as a useful technique to improve the weak

ground. This technique requires large size columns of granular material

to be inserted into the ground by means of special vibrators (or other

construction methods) to form a stiffer composite structure with

surrounding soils.

The increases in load bearing capacity, shear resistance, and the

reduction in total settlement together with fast consolidation time are

beneficial effects of stone column in soft soils .Stone columns have been

applied successfully on numerous sites around the world. It gains

reputation by the ability to improve soft ground which allows for safe

and economic construction of road embankment, airfield, residential and

light commercial and industrial structures.

- 2 -

In the present investigation, the technique of stone column is applied to

improve the soft clay deposits. The thesis aims to study the effect of

using such stone columns with different configuration on the ultimate

load capacity of supporting subgrade. The effect of soil stiffness is also

investigated. The thesis contain two part of study, the first one is using

experimental tests to study the problem under investigation. While the

second part aims to study numerically the behaviour of improved soft

ground reinforced with such stone columns.

1.2 Objectives of the study:

The goals of the proposed thesis can be summarized as follows:

- To figure out the previous experimental studies on the performance of

stone column.

- To investigate experimentally the effect of different parameters such

as stone column diameter, length of column and effect undrained shear

strength of soil on the bearing capacity and settlement behavior.

- To study the effect of both drained and undrained condition on the

behavior of composite soil column system.

- To conduct numerical investigation by finite element method to study

the behavior of the stone column distribution inside the soft clay soil in

both drained and undrained conditions.

- To examination (Han and Ye 2001) and (Han and Ye 2002) as a

simplified analytical solution for the rate of consolidation of stone

column reinforced ground.

- 3 -

- To show the effect spacing, stress level and modular ratio on the stress

concentration factor, the reduction of settlement and the reduction in

consolidation time.

1.3 Scope of work

The thesis will study the following subjects:

1- An intensive literature review of the previous studies in the

subjects of behavior of stone column in soft clay.

2- Experimental investigation by means of an intensive

experimental program which contains a number of samples

loaded up to failure and monitors the general behavior.

3- Analytical investigation by using finite element program.

4- To find out the results and the notes for this study.

1.4 Thesis Organization:

This thesis organized in eight chapters, as follows:

Chapter (1):

This chapter presents an introduction to identify the problem, the aim of

Proposed work and dissertation outlines.

Chapter (2):

This chapter includes a literature review about problems associated with

construction on soft clay by using stone columns technique. In addition

to show studies under taken for the problem under investigation.

- 4 -

Chapter (3):

This chapter describes in details the experimental work. Description of

the materials used, preparation of soil specimens, test preparation,

method of installing columns and testing methodology, loading setup

and measuring devices used in the experimental are also presented.

Chapter (4):

The chapter contains analysis and discussion of the experimental results

and the influence of different tests parameters on bearing capacity and

settlement behavior.

Chapter (5):

This chapter presents a brief discussion about finite element method

including analysis sequence and different types of elements that may be

used in the analysis. Also, the finite element analysis program which is

used during this research is briefly discussed. The verification examples

are also presented.

Chapter (6):

This chapter presents the results of numerical models of the problem

under investigation at different studied parameters. It divided into two

parts; the first one is aimed at investigating the numerical analysis of

small scale model that mentioned in laboratory testing program. The

effect of stone column geometry, undrained shear strength and the effect

of drained condition are also investigated. While the second part of

study is related to discuss the numerical modeling of full scale analysis

using most common case study. In this part, the deformation

characteristic of the application of numerical modeling is applied for

large scale embankment of the stone column. In this part, the adopted

- 5 -

case study is used as mentioned by Tan et al., 2008. The settlement

values monitored during and after the construction of the embankment

are introduced. The application of consolidation behavior is also

analyzed. Finally comparison all results from finite element model by

examination (Han and Ye 2001) and (Han and Ye 2002) as a simplified

analytical solution for the rate of consolidation of stone-column

reinforced ground. A parametric study performed to investigate the

effect of different parameters on the performance of stone columns.

Finally, comparison between the results of the numerically performed

parametric study with analytical methods used to estimate the behavior

of the soft soil reinforced by stone columns.

Chapter (7):

This chapter presents a discussion of the numerical modeling of full

scale analysis using most common case study. Also a comparative study

with different researchers is presented with details.

Chapter (8):

This chapter presents the summary and the conclusions of the current

research and recommendations for future studies are presented.

Finally, list of references is given at the end of the thesis.

Chapter (2):

LITERATURE REVIEW

- 6 -

CHAPTER (2)

LITERATURE REVIEW

2.1 Introduction:

2.1.1 General

Because of the ever – increasing value of land, the development of

marginal sites is now often economically feasible. The increased cost

of conventional foundations like concrete piles, and the other several

environmental constraints greatly encouraged the improvement of

weak soils (cohesionless or cohesive soils) by any of these numerous

developed improvement techniques, blasting, soil mixing, tamping,

grouting, nailing, stone and sand piles,…etc.

Stone columns are considered as a versatile, proven and effective

soil improvement and strengthening technique. It has been an

environmentally acceptable and economically viable alternative to

other conventional forms of foundations that can be used for

improving the soft weak cohesive or loose cohesionless soils. The

advantages gained from using this method are the increase in bearing

capacity of foundation soil, reducing total and differential settlement,

and accelerating the consolidation process. It achieved a success in

supporting the structures that tolerates moderate or high differential

settlements, like storage tanks, embankments, and small structures of

moderate to low importance.

- 7 -

2.1.2 Definition

Stone columns are compacted columns of gravel or crushed rock

installed into soft soil. The ground improved by the compacted columns

is sometimes referred to as composite ground. Diameters of these

columns are usually in the range of 0.6 to 1.0 m (Mitchell, 1981).Larger

diameters can be formed by coupling more than one vibrator together.

Column lengths up to 21 m have been installed, and the typical column

spacing is approximately 1.8-2.7 m although smaller spacing is possible,

(Barksdale and Bachus, 1983). Stone column technique is one of the

most commonly used soil reinforcement methods. It is utilized

worldwide to increase the soil‟s bearing capacity, speed up its

consolidation process, and decrease structure settlement.

2.1.3 Historical Review of the Use of Stone Column

In the early nineteenth century, stone columns were first used by

military engineers in France. The columns were 2 m in length and 0.2 m

in diameter. They were constructed in soft estuarine deposits to support

heavy foundations of the artillery bases and to reduce the expected

foundation settlement by a factor of four. Although the method proved

its success, it was almost a century before the technique was used again

(Hughes and Withers, 1974, and Mckelvey and Sivakumar, 2000).

In the 1930‟s, the deep vibrator was developed by the Keller Company

to improve and densify loose cohesionless soils to depths exceeding 30

m. This improvement technique is known as vibro- compaction. Two

decades later, in the 1950‟s, this method was extended to cohesive soils

by introducing granular material through the hole formed by the

- 8 -

vibrator, thus forming a composite ground with higher strength and

lower compressibility. This process is known as vibro-replacement.

Since then, this technique has been widely used in Europe, Asia and the

United States (Mckelvey and Sivakumar, 2000). It has also been

estimated that a total of 50,000,000 meters of columns had been installed

at more than 2000 sites of about 20,000,000m² total area in the period

from 1955 to 1979 (Aboshi et al., 1979).

2.1.4 Characteristics of Ground Improvement Systems

Ground improvement or ground modification engineering is the

collective term for any mechanical, hydrological, physicochemical,

biological methods or any combination of such methods employed to

improve certain properties of natural or man-made soil deposits. The

purposes of the improvement are:-

1-Strengthen ground soil before failure occurs: This type of ground

improvement generally happens where the soil is weak with low bearing

capacity, and groundwater table is high.

2-Strengthen ground soil during soil's useful life period: This type of

ground improvement is generally necessary for proper maintenance or to

repair certain potential failure areas to prolong soil's useful life.

3-Strengthen ground soil after premature or unexpected failure: In many

cases, ground failure is unexpected. However, it is required to examine

the causes of failure before the ground improvement start.

4-Temporary ground improvement systems: This type of ground

improvement system is used in certain conditions and certain locations,

- 9 -

such as underwater repair, or where the permanent structure is under

construction.

2.1.5 Improvement of Soil Characteristics Using Stone

Column Technique

Demand and restrictions on land suitable for construction has in recent

times led to an increasing trend for the construction industry to exploit

sites that were previously considered uneconomical to develop. The use

of these sites for construction requires a coherent and economical

construction technique to be applied. One of these sites is soft clay site

particularly with great depth, which causes troubles during and after

construction due to its low shear strength and high compressibility.

The stone column technique of ground treatment has proven successful

in the following:

(1) Improving slope stability of both embankments and natural slopes.

(2) Increasing bearing capacity.

(3) Reducing total and differential settlements.

(4) Reducing the liquefaction potential of land.

(5) Increasing the time rate of settlement.

(6) Control the deformation and accelerate consolidation.

When loads are applied on soils reinforced with stone columns, a large

portion of the total load is initially resisted by the relatively strong stone

columns which are far more rigid compared to the surrounding cohesive

soil. The remainder of the load is carried by the surrounding soils. As the

consolidation process continues, variations in the sharing of the total

applied load between the stone columns and the soils takes place and the

- 10 -

potion of load transferred from soils to the stone columns, (Mitchell and

Huber (1985); Greenwood (1991))

2.2 Methods of Granular Pile Construction

Various methods have been adopted over the years for the installation of

granular piles. Stone columns being a type of granular piles depending

on their proven applicability and availability of equipment in the

locality. Some of the most common methods are discussed hereinafter:

2.2.1 Vibro – Compaction Method

The vibro – compaction method is used in cohesionless soil to improve

the soil‟s density. The equipment used in this process is called the

vibroflot and is shown in Fig. (2-1).The vibroflot sinks in the ground

under its own weight and with the assistance of water and vibration

(Bergado et al., 1994), until it reaches the required depth. Then, the

vibroflot is withdrawn gradually with subsequent addition of granular

backfill, therefore causing compaction. Fig. (2-2) illustrates the steps of

this process. The range of particle size suitable for vibro – compaction is

shown in Fig. (2-4).

- 11 -

2.2.2 Vibro – Replacement Method

The vibro – replacement method is used to improve cohesive soils with

more than 18% passing No. 200 U.S. standard sieve is shown in Fig. (2-

4).The grain size range of the suitable soils for this treatment is also

shown in Fig. (2-4).The equipment used in drilling a hole in the cohesive

soil is similar to that for vibro – compaction. The methods by which the

granular material is filled into the hole are the wet process (non –

displacement method), dry process (displacement method), and dry

bottom – feed process. A typical vibrator is used in the wet and dry

process. The typical vibrator ranges from 30 to 45 cm in diameter, 2.5m

in length, and is torpedo – shaped as shown in Fig. (2-1) while special

vibrator is used in the dry bottom – feed process.

Fig. (2-1): Vibroflot used for vibro-compaction and vibro -

replacement methods (Slocombe et al., 2000).

- 12 -

Fig. (2-2): The vibro – compaction process (Bergado et al., 1994).

Fig. (2-3): The vibro – replacement method (Bergado et al., 1994).

- 13 -

Fig. (2-4): Range of soils suitable for vibro - compaction and vibro -

replacement (Bergado et al., 1994).

2.2.2.1 Wet Method

In the wet process, a hole is formed in the ground by jetting a vibroflot

down to the desired depth with water. When the vibroflot is withdrawn,

it leaves a borehole of greater diameter than the vibrator. This

cylindrical hole is filled in stages with well – graded 12 to 75 mm size

imported gravel (Bergado et al., 1994) and each stage thoroughly

compacted by reinsertion of the vibrator, pushing the gravel laterally

against the surrounding soil. The wet process is generally suited for

unstable boreholes in case of very soft saturated clay of undrained shear

strength not less than 7 kN/m² and a high ground – water table

(Barksdale and Bachus., 1983). However, in recent years, this method

became restrained to sites with very weak soils only due the

unacceptable environmental effects from the effluent arising from the

water jetting.

- 14 -

2.2.2.2 Dry Method

In the dry process, the vibrator enters the ground under the combined

effect of self-weight, compressed air and vibration. The borehole must

be able to stand open upon the extraction of the vibroflot. Therefore, it

should be applied to stable, insensitive cohesive soils having undrained

shear strength of more than 40 kN/m² and a relatively low ground water

level.

2.2.2.3 The Dry Bottom Feed

In this system the stone is fed to the nose of the vibrator through pipes

attached to the vibrator and extension tubes. This process has the

advantage that it ensures stone reach to the tip point of the vibrator

leading to well compacting and assists in the construction of a high

integrity stone column, Fig. (2-5 a & b) illustrates the bottom feed vibro

replacement process and the equipment used in this method respectively.

(a) The bottom feed vibro replacement process.

- 15 -

(b) Cross section through bottom feed vibratos

Fig. (2-5): Bottom feed of stone columns (Slocombe et al., 2000).

- 16 -

2.2.4 Vibro – Compozer Method

This method is used in Japan to improve soft clays with a high ground –

water level. The resulting column is termed sand compaction pile. The

apparatus and procedure used in the composer system are shown

schematically in Fig. (2-6). The piles are constructed by driving a casing

pipe to the desired depth using a heavy, vertical vibratory hammer

located at the top of the pipe. The casing is filled with sand and the

casing is then withdrawn while compressed air is blown down inside the

casing to hold the sand pile in place and enlarge its diameter. The

process is repeated until the full construction of the compacted granular

pile. The resulting pile is usually 600 to 800 mm in diameter, (Aboshi et

al., 1979).

Fig. (2-6): The vibro composer method (Bergado et al., 1994).

- 17 -

2.2.5 Cased– Borehole Method or Rammed Method

In this method, the piles are constructed by ramming granular materials

into the pre- bored holes in stages using heavy falling weight (usually of

15 to 20 kN) from a height of 1.0 to 1.5m, as shown in Fig. (2-7). It is

distinguished with its low cost, but on the other hand, the disturbance

and subsequent remolding by the ramming operation may limit its

applicability to sensitive soils

Fig. (2-7): The cased – borehole method (Bergado et al., 1994).

- 18 -

2.3 Engineering Behaviour of Composite Ground

2.3.1 Basic Design Parameters

2.3.1.1 Stone Column Diameter, D

Installation of stone columns in soft cohesive soils is basically a

self-compensating process, i.e. the softer the soil, the bigger is the

diameter of the stone column formed. Due to lateral displacement

of stones during vibrations/ramming, the completed diameter of

the hole is always greater than the initial diameter of the probe or

the casing. The column diameter installed by vibroflot (diameter

300-500 mm) varies between 0.6 m in case of stiff clays to 1.1 m

in very soft cohesive soils (Ranjan 1989). The diameter of the

stone column constructed by dry method is less than that of a wet

method (Greenwood and Kirsch 1983).

2.3.1.2 Stone Column Pattern

Stone columns should be installed preferably in an equilateral

triangular pattern which gives the most dense packing although a

square pattern and hexagonal pattern may also be used .A typical

layout in an equilateral triangular pattern, square pattern and

Hexagonal are shown in Fig. (2-8).

- 19 -

Fig. (2-8): Equivalent diameter of the tributary soil treated by

stone column (Balaam and Booker, 1981).

- 20 -

2.3.1.3 Stone Column Spacing

The design of stone columns should be site specific and no precise

guidelines can be given on the maximum and the minimum column

spacing. The spacing of stone columns is generally determined by

settlement tolerances for the loads to be applied and to provide

overlapping zones to cover a wide area of ground (Greenwood, 1970).

Column spacing is also dependent on the degree of improvement

required for providing a satisfactory foundation under the applied design

load. It has been recognized in practice that closer spacing are preferred

under isolated footings than beneath large rafts (Greenwood, 1970).

However, the column spacing may broadly range from 2 to 3 times the

diameter of the column depending upon the site conditions, loading

pattern, column factors, the installation technique, settlement tolerances,

etc... For large projects, it is desirable to carry out field trials to

determine the most optimum spacing of stone columns taking into

consideration the required bearing capacity of the soil and permissible

settlement of the foundation. For purposes of settlement and stability

analysis, it is convenient to associate the tributary area of soil

surrounding each stone column as illustrated in Figs. (2-8 and 2-9). The

tributary area can be closely approximated as an equivalent circle having

the same total area. For an equilateral triangular pattern of stone

columns the equivalent circle has an effective diameter (De) of 1.05S

and for a square grid it is equal to 1.13S and for a hexagonal pattern is

equal to 1.29S where „S‟ is the spacing of stone columns. The resulting

equivalent cylinder of material having a diameter De enclosing the

tributary soil and one stone column is known as the Unit cell.

- 21 -

Fig. (2-9): Unit cell idealizations (Barksdale and Bachus, 1983).

2.3.1.4 Replacement Ratio (as)

The volume of soil replaced by stone columns has an important

effect upon the performance of the improved ground. To quantify

the amount of soil replacement, define the area replacement ratio,

as the ratio of the area of the stone column after compaction (As)

to the total area within the unit cell (A) as illustrate in Fig.( 2-10 )

and (2-11) and expressed as:

as = Ac / (As+Ac) (2.1)

Where:

- 22 -

Ac = Horizontal area of the stone column; and,

As = Horizontal area of the soil surrounding the stone column.

Fig. (2-11): area ratios for (i) square grids, (ii) triangular grids

and (iii) pad footing (Bergado et al., 1994).

Fig. (2-10): Diagram of composite ground (Bergado et al., 1994).

- 23 -

2.3.1.5 Stress Concentration Factor (n)

When the stone column reinforced ground is loaded, concentration of

stress occurs in the stone column, and an accompanying reduction in

stress occurs in the surrounding less stiff soil Fig. (2-9c). The

distribution of vertical stress within a unit cell can be expressed by a

stress concentration factor „n‟ defined as the ratio of the stress in the

stone column (σc) to the stress in the surrounding cohesive soil (σs).

The unit cell can be expresses by a stress concentration factor, n as:

n = σc /σs (2.2)

Where:

σc = Stress in the stone column

σs = Stress in the surrounding soil

The average stress over the unit cell area corresponding to a given area

replacement ratio, as, is expressed as:

σ = σs as+ σc (1- as) (2.3)

The magnitude of stress concentration depends on the relative stiffness

of the stone column and the surrounding soil. The value of n generally

lies between 2 and 6 (Goughnour and Bayuk 1979; Aboshi et al., 1979)

with values of 3-4 usual, at the ground surface. The stress concentration

factor (n) increases with time of consolidation (Han and Ye 1991) and

decreases along the length of the stone column. Higher n value at ground

- 24 -

surface may result if load is applied to the composite ground through a

rigid foundation as compared to the flexible foundation (Barksdale and

Bachus 1983). The stress concentration factor was found to decrease

with the increasing in the applied load (Bergado et al., 1988).

2.3.1.6 Back Fill for Stone Columns

Crushed stone or gravel for the column backfill shall be clean, hard,

unweathered stone free of organics, trash or other deleterious materials

(Barksdale and Bachus, 1983). The criteria for selecting a suitable

backfill material are availability, suitability and economy. Well graded

stones of 75-2 mm size shall be used.

2.3.2 Failure Mechanisms

Stone columns maybe constructed as either end bearing on affirm

stratum underlying soft soil, or as floating columns with its tip

embedded within the soft layer. Consider a single stone column loaded

over just the area of the column as shown in Fig. (2-12). Either end

bearing or floating column greater than about three diameters in length

fail in bulging, Fig. (2-12a). A very short column rested on a firm

stratum will undergo either local or general shear failure, Fig. (2-12b).

Finally, a floating stone column with length less than 2 to 3 diameters

may fail in end bearing in the weak underlying layer, Fig. (2-12c).

- 25 -

In case of stone column groups, the failure may be due to spreading such

as an embankment constructed over stone column improved ground, as

shown in Figs. (2-13a and 2-13b). Also, a group of stone columns

supported on a firm layer may fail in bulging and local shear failure, Fig.

(2-13c). Finally, stone column groups having short stone column can fail

in end bearing as shown in Fig. (2-13d), or perhaps undergo a bearing

capacity failure of individual stone column similar to the failure mode of

short, single stone column.

Fig. (2-12): Failure mechanisms of single stone column in homogeneous

soft layer (Barksdale and Bachus, 1983).

- 26 -

Fig. (2-13): Failure modes of stone column groups (Barksdale and

Bachus, 1983).

Also, the presence of a very weak layer (such as peat) greater than about

one column diameter in thickness can also seriously affect stone column

performance, as depicted in Fig. (2-14).

Fig. (2-14): Stone column failure mechanisms in nonhomogeneous

cohesive soil (Barksdale and Bachus, 1983).

- 27 -

Also, Pivarc (2011) presented the bulging behavior of stone column

results from laboratory tests and comparing the results with Plaxis

model. The laboratory experiments were carried out using stone columns

with diameters of about 60 mm and lengths of 300 mm, 420 mm and 540

mm surrounded by clayey sand, in cylindrical test boxes with a height of

600 mm and with variable inner diameters varying from 125 mm to 253

mm. The cylindrical boxes represent the required area of a unit cell

around a stone column. The stone columns were modeled as a floating

unit in the soil space. The ratios of the length of the stone columns to the

diameter of the stone columns L/d are modeled as 5, 7 and 9. The

bulging of stone column after loading the stone column only and after

loading both the stone column and the surrounding soil are shown in

Figs. (2-15a and 2-15b) respectively. The finite element results and

those obtained from the laboratory experiments appear satisfactory.

Different techniques were used by various researches to examine the

deformation and failure mode of stone column treated ground. X-ray

technique has been used successfully to monitor the deformation of an

isolated granular column and surrounding clay (Hughes and Withers

1974).

- 28 -

(a) Shape of the failed

stone column after the

area of stone column

was loaded

(b) The whole area of

the stone column and

surrounding soil was

loaded

Fig. (2-15): Failure of stone columns, (Pivarc, 2011).

- 29 -

2.4 Mechanism and performance of Stone Columns

The presence of a stone column creates a composite material of lower

overall compressibility and higher shear strength than in-situ soil.

Confinement, and thus stiffness of the stone, is provided by the lateral

stress within the weak soil. When an axial load is applied at the top of a

single stone column, an extension of the column diameter is produced

beneath the surface. This extension in turn, increases the lateral stress

within the clay, which provides an additional confinement for the stone

column. An equilibrium state is eventually reached, resulting in a

reduction in the vertical displacement, when compared with the

untreated ground.

2.5 Experimental Studies

2.5.1 Field Tests

Greenwood, (1970) described the results of trials at Bremerhaven

(Germany) for motorway slip road embankment(s) application. Both

vibro stone columns and sand columns were constructed for comparison

purposes. The stone and sand columns were installed to an average

depth of 6.0 m by the wet top-feed technique through a layer of soft clay

and peat into a fine uniform sand layer).

The stone columns were constructed using gravel of size 30-70 mm with

the sand backfill having a grain size of 0-3 mm. The combined total

thickness of the clay and peat layers was about 3.0 m, with geotechnical

properties summarized in Fig. (2-16).

He reported that the average stone column diameters were 1.2 m, with

columns installed on a 2.3 m triangular grid spacing (Ar = 25%). For the

- 30 -

stone column, sand column and untreated areas, average settlements and

range of settlements after 15 months following. Reduction of settlements

was around 15% where sand columns were installed and 40% where

stone columns where installed, representing settlement improvement

ratios of 1.18 and 1.6 respectively. In addition, closer column spacing

resulted in less settlement.

The field trials demonstrate the importance of using a coarse aggregate

backfill rather than sand in the column construction to lend better

rigidity (stiffness) to the column.

- 31 -

Fig.(2-16): Comparison of large scale field loading test results on

untreated soft clay, soft clay reinforced with stone columns and with

sand columns at Bremerhaven, Germany, (Greenwood, 1970).

- 32 -

Hughes et al. (1975) undertook field scale trials to verify the theory

proposed by Hughes and Withers, 1974 in their laboratory modeling.

A single 730 mm diameter column was installed by the wet top-feed

technique through soft clay strata to the level of a firm stratum at a depth

of 10 m. A rigid 660 mm diameter circular steel plate was used to apply

vertical load to the column as shown in Fig. (2-17).The test was

considered to be undrained since it only took around 30 minutes to

complete. Good agreement was obtained between predicted and

measured load-settlement curves and demonstrated the occurrence of

shear transfer between the column and surrounding clay.

Considering the column as a 'pile', Hughes et al., 1975 defined a critical

length for an isolated column, at which end bearing and friction are

equated. Beyond this length the column was considered not to contribute

extra benefit in terms of enhanced ultimate load, but contributed to

reducing settlements by penetrating to a firm stratum. Based upon the

site specific soil and column parameters the critical depth (zone of

anticipated bulging) translated to about four column diameters, similar

to observations by Hughes and Withers, 1974.

It was observed that the deformed shape was similar to that described by

Hughes and Withers, 1974.

- 33 -

Fig. (2-17): Field deformation behaviour of a single column under a

(rigid) plate load test, (Hughes et al., 1975).

Goughnour and Bayuk (1979) reported the results of a field trial on a

group of columns installed using the wet top-feed technique, through

very soft sensitive silts and clays in Hampton, Virginia (U.S.). As shown

- 34 -

in Fig. (2-18), the columns were installed to an average depth of 6.4 m

and on an approximate 1.8 m grid pattern with a recorded average

diameter of 1.1 m (representing an Ar of 33%).

A vertical load test was undertaken to simulate embankment loading

conditions. Load cells placed on top of stone columns and intervening

clay soil prior to application of load recorded stress concentration ratios

of between 2.6 and 3.0.

Pore pressure measurements indicated that a large stress increase at the

completion of load application occurred at a depth equal to half the

width of the loaded area.

Fig. (2-18): Field load test arrangement (Goughnour and Bayuk, 1979).

- 35 -

Fig. (2-19): Settlement versus log time at the centre and corners of

load area in field trial (Goughnour and Bayuk, 1979).

- 36 -

Munfakh et al, (1984) reported a field study (for a project named

Jordan Road Terminal) on the effectiveness of stone columns in

stabilizing a deep deposit of very soft cohesive soil under a 3.4m height

of embankment load. In situ shear tests showed that a peak internal

frictional angle of 45° is achieved at the surface of an insitu column.

Approximately 40% of settlement reduction was achieved at the end of

the embankment construction period. Significant lateral movements

(maximum value of 60 mm) beneath the embankment were measured

mostly occurring at mid height of the column depth. It was reported that

no significant lateral bulging was observed at the top of the stone

columns. The failure of this testing embankment was accomplished by

adding surcharge and excavation on the supporting side so that the

ultimate failure mode was a combination of general shearing and local

bulging.

Mitchell and Huber, (1985) performed 28 field load tests on individual

stone columns constructed in soft estuarine deposits during the

installation of 6500 stone columns. The stone columns reinforced soft

soil is used to support a large waste water treatment plant. All stone

columns extended completely through the soft soil layer which ranged

from 9 m to 15 m. the diameter of the stone columns ranged from 0.5 m

to 0.75 m. the column spacing ranged from a 1.2 m x 1.5 m pattern to a

2.1 m x 2.1 m pattern.

The results of the load test showed that the existence of the stone column

led to a reduction in settlements to about 30% - 40% compared to the

settlement of the untreated ground.

- 37 -

Bergado and Lam, (1987) reported the results of field trials to

investigate the behavior of granular 'piles' (columns) with different

densities and containing different proportions of sand and gravel,

installed in soft Bangkok clay by the compozer method. Table (2.1)

shows that for the same granular (stone column) materials the ultimate

bearing capacity increases with number of blows per layer during

installation attributed to an increase in density and angle of internal

friction.

Table 2.1 Properties of granular columns (Bergado and Lam, 1987).

The resulting load-settlement curves for the different proportions of

gravel and sand are compared and indicate a higher ultimate capacity for

pure gravel and which equates to the higher reported friction angles in

the literature for compacted gravels compared to those for compacted

sands. The average deformed shape of the granular columns was

described as typically bulging type and it was observed that the

maximum bulge occurred near the top of the column.

- 38 -

The authors indicate that with an initial diameter of 300 mm, the

measurements of bulging recorded were in close agreement with the

field observations of Hughes et al. (1976).

Fig. (2-20) Comparison of load-settlement performance of granular

columns constructed with different numbers of blows per

compacted layer (Bergado and Lam, 1987).

Han and Ye, (1991) presented the results of full scale load tests on

stone columns reinforced soft soil in coastal areas. A total of 16 stone

columns were used in soft soil having a length of 14 m and an average

diameter of 0.85 m arranged in triangular pattern. The treated and

untreated grounds were loaded. It was found that the stone columns

- 39 -

increase the bearing capacity of the treated ground to two times the

untreated ground. Also, it was established that using stone columns to

reinforce soft soil is very effective in decreasing the initial excess pore

water pressure and to keep the foundation stable.

Christoulas et al., (2000) described the results of two instrumented

axial loading tests on large scale model stone columns. Kaolin clay was

used to simulate natural soil conditions. Two columns were constructed

with average diameter of 0.17 m in a cubic pit with 1.5 m edge. The

results of the experimental tests provided support of that the upper part

of the column bulged along a length of about 2.5-3.0 column diameter.

The experimental data of this study suggested that the ultimate load

corresponds to settlements approximately equal to 35 % of the stone

column diameter.

2.5.2 Laboratory Tests

The first laboratory test performed to model stone column reinforced

ground was conducted by Hughes and Withers, (1974). Model columns

were constructed using Leighton Buzzard sand, 150 mm in length, with

diameters ranging from 12.5 to 38 mm; the columns were "floated" in

the surrounding soil.

The soil used in the laboratory scale models was kaolinite consolidated

to unspecified shear strengths. Displacements within the cohesive soil

were cleverly monitored using lead shot placed a priori within the

columns and the surrounding soil; radiographs of the experimental

model revealed the incremental soil movements. Load deformation

- 40 -

results, obtained from stress-controlled tests, were presented in terms of

the ratio of applied stress to undrained shear strength against the percent

of vertical displacement as function of column diameter. Regardless of

the unfortunate omission of the in-situ soil parameters, the test results

plainly show that the ultimate strength of the reinforced ground is a

strong function of the lateral restraint provided by the in-situ soil. These

tests were the first experimental evidence to support the previously

assumed load transfer mechanism.

Narasimha Rao et al., (1992) conducted experimental studies on single

column and continued the work (Rao et al. 1997) on group of columns

comprising 2, 3 and 4 columns in soft clay to study the influence of

moisture content of the soft clay and the effect of slenderness ratio (L/d)

of the stone column. The results showed that the presence of stone

columns increases the support capacity of the soft clay by 2 to 3 times.

The other conclusions drawn were as follows:

- Consistency index plays an important role in load carrying capacity of

the stone column, since the load carrying capacity of stone column

depends on the extent of bulging of column. It was found that the

increase in consistency index increases the capacity under the imposed

load, and the stone column bulges satisfactorily in a soil with

consistency index of 0.5.

- The L/d ratio is an important parameter for the mobilization of skin

friction. The overall length of the column, diameter of the column and

bulging control the skin friction. The ideal L/d ratio of stone columns for

the consistencies tested is in the range between 5 and 10.

- 41 -

- The end bearing values are more in short columns particularly in

column with L/d = 2.5; however the contribution due to end bearing is

less with L/d and is negligible for longer columns (i.e. higher

slenderness ratio). The optimum L/d is 5 to 7, beyond this critical length

there is no significant increase in the load carrying capacity.

- The size of the bearing area has significant effect on the load carrying

capacity of stone columns with lower L/d ratios. At higher values of L/d

of 7 to 9 the increase in bearing area has no influence on capacity.

Also the contribution from the end bearing on limiting axial stress is

very little compared to that due to skin friction.

Wood et al., (2000) performed model tests to determine the mechanisms

of response for beds of clay reinforced with stone columns subjected to

surface footing loads. An exhumation technique was used to discover the

deformed shapes of the stone columns. The laboratory model tests

showed that there was significant interaction between the footing and the

individual stone columns within a group. As a consequence, the load-

settlement relationship for neighboring columns in different locations

was different. Wood et al. reported that it will be more accurate in

design of the stone column reinforced foundation to consider increasing

stiffness towards center of the group. The kinematic constrains that the

rough base of the footings imposes, push the load to greater depths

toward the center of the footing. Based on the study of wood et al.

(2000), the following failure modes of stone columns were proposed as


- 42 -

(a) The bulging failure of a stone column takes place when it is not

prevented from expanding radially by adjacent columns

(b) The bearing capacity failure plan occurs in the head of the column.

(c) Failing by a diagonal shear plane if the stone column has a little

lateral restrains and is subjected to high loads.

(d) Failing by penetration through an underlying soft clay layer if the

stone column is short column.

(e) The compression failure happens when the stone column is long.

(f) A slender stone column can fail by bending if it is laterally loaded.

Fig. (2-21): Failure modes of stone columns (Wood et al., 2000).

Results of the experimental model conducted by Wood et al., (2000) are

illustrated in Figs. (2-22 through 2-25), which give the normalized

footing load versus normalized footing settlement behavior by variable

area ratio values, AS for short and long columns, and column length.

Wood et al., (2000) stated that as the area ratio increases, the stiffness

and thus the strength also increases. Moreover, Wood et al., (2000)

- 43 -

states that there exists a certain point up to which the column length is

relevant and no further advantage is obtained by increasing the column

length beyond that point.

Fig. (2-22): Normalized load-settlement results for model footings;

variation of area ratio (short columns) (Wood et al., 2000).

- 44 -


variation of area ratio (long columns) (Wood et al., 2000).


variation of column length (short columns) (Wood et al., 2000).

- 45 -


variation of column length (long columns) (Wood et al., 2000).

Bae et al., (2002) investigated also the failure mechanism and various

parameters of the behavior of end-bearing single and group stone

columns by laboratory loading tests. Results of the laboratory tests were

verified by finite element model (FEM) analyses. The laboratory tests

and the FEM analyses results showed that the bulging failure mode

appeared in the depth of 1.6 to 2.8 times the column diameter. The major

failure mode of stone columns group is conical failure, the conical

failure angle in short columns was smaller than that in long columns.

The results also showed that the bearing capacity of the stone column is

affected by the undrained shear strength of the surrounding soil, the

spacing distance between columns and the installation of granular mat at

the top of the columns.

- 46 -

Mckelvey et al., (2004) carried out a series of laboratory model tests on

a consolidated clay bed using two different materials:

1. Transparent material with clay like properties prepared by

mixing fumed silica in an oil blend of mineral spirits and crystal

light liquid paraffin.

2. Speswhite Kaolin clay.

The tests on the transparent material permitted visual examination for

the deforming of the stone column during loading. For the Foundation

loading on transparent material samples, three sand columns, 25 mm in

diameter, were installed in a triangular pattern beneath a circular footing,

100 mm in diameter, and also in a row arrangement beneath a strip

footing to depths of 150 mm and 250 mm. For the foundation loading of

Kaolin clay tests, four sand columns, 25 mm in diameter, were installed

in a square pattern beneath a model pad footing, 90 mm x 90 mm, to

depths of 150 mm and 250 mm.

The presence of the granular columns significantly improved the load-

carrying capacity of the soft clay. However, columns with length to

diameter ratio (L/d) more than 6 seem to show further increase in the

load capacity. The results of the tests showed that columns can fail in 3

different ways: bulging, punching and pending. Punching is more

prevalent in short columns whilst bending failure is predominant in

perimeter columns located beyond the center of the footing. Bulging was

more generally common in long columns, as shown in Fig. (2-26).

Beneath the rigid footing, the central column in the stone columns group

- 47 -

deformed or bulged uniformly, while the edge columns bulged away

from the neighboring columns.

(a) 150 mm length (b) 250 mm length

Fig. (2-26): Photos of sand column beneath circular footing at

beginning, middle and end of foundation loading process: (Mckelvey

et al., 2004).

- 48 -

Ambily and Gandhi, (2007) used experimental study to predicate the

behavior of single column and group of seven columns. The test was

carried out by varying parameters like spacing between the columns,

shear strength of soft clay, and loading condition surrounded by soft clay

in cylindrical tanks of 500 mm high and a diameter varying from 210 to

835 mm to represent the required unit cell area of soft clay around each

column assuming triangular pattern of installation of columns. For single

column tests the diameter of the tank was varied from 210 to 420 mm

and for group tests on 7 columns, 835 mm diameter be used. Tests had

been carried out with shear strength of 30, 14, and 7 kPa. The tests are

carried out either with an entire equivalent area loaded to estimate the

stiffness of improved ground or only a column loaded to estimate the

limiting axial capacity, as shown in Fig. (2-27).

During the group experiments, the actual stress on column and clay were

measured by fixing pressure cells in the loading plate. Finite-element

analyses have also been performed using 15-noded triangular elements

with the software package Plaxis. A drained analysis was carried out

using Mohr-Coulomb‟s criterion for soft clay, stones, and sand. The

numerical results from the FEM are compared with the experimental

results which showed good agreement between the results.

- 49 -

Fig. (2-27): Single column test arrangement (Ambily and Gandhi,

2007) (a) column area loading (b) entire area loading.

The following conclusions were drawn based on that study:

1. As spacing increased, axial capacity of the column decreases and

settlement increased up to an s/d of 3, beyond which the change is

negligible.

2. The ratio of limiting axial stress on column to corresponding shear

strength of surrounding clay is found to be constant for any given s /d

and angle of internal friction of stones and it is independent of the shear

strength of the surrounding clay, Fig. (2-28).

- 50 -

Fig. (2-28): Effect of s/d and ϕ on axial capacity of stone column.

(Ambily and Gandhi, 2007).

3. The load settlement behavior of a unit cell with an entire area loaded

is almost linear and it is possible to find the stiffness of improved

ground, Fig. (2-29).

4. Single column tests with an entire unit cell area loaded compare well

with the group test results. Hence the single column behavior with unit

cell concept can simulate the field behavior for an interior column when

large number of columns is simultaneously loaded, Fig. (2-30).

- 51 -

Fig. (2-29): stress settlement behavior under entire area loading

(Ambily and Gandhi, 2007).

Fig. (2-30): Comparison of group column test and single column

test (Ambily and Gandhi, 2007).

- 52 -

Isaac and Grirish, (2009) studied the influence of column material in

the performance of stone column through laboratory experiments on

model stone columns installed in clay. Load tests were carried out on

Kuttanad clay and load deformation curves were plotted for untreated

clay and clay treated with stone column made of five column materials

i.e. quarry dust sea sand, river sand, gravel and stones designated as m1,

m2, m3, m4 and m5 respectively. All experiments were carried out on a

50 mm diameter stone column surrounded by the required soil in a

cylindrical tank of 270mm height and 210mm diameter to represent the

required unit cell area of clay around each column, as shown in Fig. (2-

31). For group of columns, a tank of 270mm height and 520mm

diameter was used.

A finite element analysis using 15-noded triangular elements with the

software package Plaxis was also carried out to compare the load

settlement behavior with the model test, as shown in Fig. (2-32). Load

versus settlement response was determined. Along the periphery of the

tank (interface between the soft clay and the cylindrical surface of the

unit cell), radial deformation was restricted but settlement was allowed.

Along the bottom of the tank both radial deformation and settlement

were restricted. Analysis for a group of seven columns was also carried.

Isaac and Grirish stated that the presence of stone columns considerably

improved the load deformation characteristics of Kuttanad clay. Among

the different stone column materials used, stones were found to be more

effective from single column test and group column test. Also, spacing

of the column played an important role in affecting the load deformation

characteristics, as shown in Figs. (2-33 and 2-34).

- 53 -

Fig. (2-31): The test setup for single and group column test

(Isaac and Grirish, 2009).

Fig. (2-32): Load - Settlement curve for clay with single

Column (Isaac and Grirish, 2009).

- 54 -

Fig. (2-33): Comparison of stress settlement relation for clay

with group of seven columns(S = 2.5D).

Fig. (2-34): Comparison of stress settlement relation for clay

with group of seven columns (S = 3D).

- 55 -

2.5.3 Theoretical Studies

Laboratory research, testing and field studies undertaken over the last

years have led to the development of empirical, analytical and numerical

techniques used to assess column capacity and load-settlement behavior.

In the following sections, a brief description of the design methods used

for assessment of settlement reduction is introduced.

Greenwood, (1970) Introduced design curves to asses settlement

reduction associated with the use of conventional stone columns. The

empirical curves were derived from column groups placed under

widespread loads on uniform soft soil. They represent settlement

reduction as a function of column spacing and the undrained shear

strength of the natural soil (For cu = 20 kPa and 40 kPa). Later,

Greenwood and Kirsch (1983) presented updated curves as a function of

area ratio, as illustrated in Fig. (2-35).

Fig. (2-35) Greenwood curves (Greenwood and Kirsch, 1983).

- 56 -

Priebe, (1976) Proposed a method for assessing settlement reduction

based on the unit cell, elastic theory and Rankine earth pressure theory.

In this model, the stone column was assumed to be incompressible and

surrounded by an elastic material. Soil settlement occurred when lateral

pressure in the column exceeded the confining pressure in the

surrounding soil. Priebe generated a series of design curves where the

basic settlement improvement factor was plotted against the area ratio

for a range of granular materials. The improvement factor is the ratio

between the settlement of the untreated and treated soil. Later Priebe,

1995 presented a revised version which included compressibility,

modular ratio of column and soil, confinement from overburden pressure

and solutions for single and strip footings. An example of these modified

design curves is presented in Fig. (2-36).

Fig. (2-36): Priebe design curves (Priebe, 1995).

2.5.3.1 Numerical Methods

Numerical methods are probably the most theoretically suitable to

modeling stone column treated ground.

Gniel and Bouazza, (2007) reported that Balaam et al., 1977 used finite

element and finite difference methods to explore stone column behavior,

- 57 -

resulting in publication of design curves used to assess settlement

reduction. That work was continued by Balaam and Booker (1981 and

1985) and Balaam and Poulos, 1983.

Recently, sophisticated models have been used to better model soft soil

behavior and its interaction with loaded columns such as the study of

Lee and Pande, 1998 and Tan et al., 2008.

Balaam and Booker, (1985) studied the settlement of a rigid foundation

supported by a layer of clay stabilized with stone columns. The results of

an analytic solution for the settlement, assuming no yield occurs in the

clay or the columns, were presented. Later, this solution was used to

develop an interaction analysis, which considered yielding within the

stone columns. The solutions were obtained from the analysis of a unit

cell. In order to check the validity of these assumptions elastoplastic

FEM analyses were performed and the agreement between the two

methods was very good. The results were plotted as a settlement

correction factor, which is the ratio between actual settlement and elastic

settlement of the foundation. The results showed that the most

significant reduction in settlement occur when the columns are closely

spaced and the column-soil modular ratio is high.

Poorooshasb and Meyerhof, (1997) introduced elastic analyses to

study the settlement reduction of a raft foundation resting on reinforced

soft soil with end bearing stone columns. The results of the analyses

showed that the factors that most severely affect the performance of a

stone column foundation scheme are the spacing and degree of

- 58 -

compaction of the material in the columns which, in turns, control their

strength and stiffness.

Pulko and Majes, (2006) introduced a simple analytical method for the

analysis of stone-column reinforced foundations. The stone-column and

the surrounding soil were modeled as a unit cell, consisting of elastic

soil and rigid plastic column material according to the Mohr-Coulomb

failure law. The dilation of the column material according to the Rowe

stress - dilatancy theory was directly incorporated into the method. The

closed-form solution method was used for the prediction of the effects of

stone-columns on settlement reduction and stresses in the soil and

column. A parametric study was also presented to study the influence of

area replacement ratio and material properties of the granular material

on settlement reduction factor. The study showed the significant effect

of the dilatancy of granular material on the settlement reduction and

stress concentration.

2.6 Ultimate Bearing Capacity of Stone Columns

2.6.1 Isolated, Single Stone Column

The ultimate bearing capacity of stone column in clay depends upon the

internal angle of friction of the column material and the shear strength of

the surrounding clay. For single isolated granular piles, the most

probable failure mechanism is bulging failure. This mechanism develops

whether the tip of the column is floating in the soft soil or resting on a

firm bearing on a firm layer (Barksdale and Bachus 1983). A number of

approaches have been presented by the researchers for predicting the

- 59 -

ultimate capacity of an isolated single stone column surrounded by a soft

soil, which are reviewed in this part.

Greenwood (1970) was one of the first who came up with mechanisms

and explained the load transfer phenomenon in stone columns. He

suggested a method to predict the ultimate bearing capacity of stone

column in c-ϕ soils based on passive pressure approach. The failure of a

single column was assumed to be by bulging of the column up to critical

depth. The ultimate bearing capacity was assumed to be equal to the

ultimate lateral strength of the surrounding soil. Prakash et al. (2000)

reported that, this approach did not take into consideration both of the

passive earth pressure coefficient of stone column material and the

effects of the intervening soil.

Hughes and Withers (1974) indicated that the ultimate column load

depended on the friction angle of the stone used to form the column, the

size of the column, and the restraint of the clay on the uncemented stone.

They considered the bulging type failure of a single stone column to be

similar to a cylindrical cavity expands till reaching the ultimate passive

resistance of the surrounding soil.

Using the elasto-plastic theory, they developed an analytical expression

for the total limiting radial stress as:

(2.7)

Where:

= initial radial effective stress

= initial excess pore water pressure

= undrained cohesion of surrounding soil

- 60 -

If the stone column approached shear failure with an effective angle of

internal friction of ϕ `, then the limiting axial stress in the column was

given by

(

) (2.8)

(

) ) (2.9)

If = 0, drainage into the stone column makes this possible. The value

of σrl or c should be the minimum that would be expected over the

critical length of the column (Lc). If the vertical shear stress developed

along the side of the column was equal to the average shear strength of

the soil when end bearing failure was about to occur, the critical length

can be evaluated by equating the boundary forces on the column;

column load equals the sum of the shaft friction and end bearing force:

(2.10)

Where:

P = ultimate column load

Nc = bearing capacity factor (taken normally as 9 for long

columns).

As1 = surface area of column side.

c and c` = average shaft cohesion and cohesion at the bottom of the

critical length, respectively.

The critical length is the minimum lengths at which both bulging and

end bearing failure occur simultaneously. Hughes et al (1975) carried

- 61 -

out a series of plate loading tests in order to verify the theory proposed

by Hughes and Withers (1974). Excellent agreement was achieved

between the predicted and the measured results.

Narasimha Rao et al., (1992) were conducted Small scale laboratory

tests in (1992) to examine the ultimate bearing capacity of single stone

columns. The influence of the column diameter, length and footing

diameter was investigated by varying the L/d ratio from 3 to 9 and

examining a range of footing diameters, D = 1d–2d, Fig. (2-37). The

tests indicated that the ultimate capacity of stone columns increased with

the L/d ratio, which the authors suggest is the governing factor of

column capacity. A critical L/d ratio appeared to exist between 5 and 7,

beyond which no further increase in ultimate capacity is gained. The

ultimate capacity of stone columns was also observed to increase with

footing size; however, this increase was only noticeable for columns

shorter than 7d.

Fig. (2-37): Typical test setup examined by (Rao et al., 1992).

- 62 -

Bouassida and Hadhri, (1995) determined the extreme load for soils

reinforced by stone columns for the case of isolated column, using the

yield design theory. The plane strain and axisymmetric cases were

studied for the composite ground in order to estimate the value of the

upper and lower bounds of loads. The undrained and drained behaviors

were established for plane strain case, and the undrained condition only

was considered for the axisymmetric case. The influence of gravity was

also studied. It was obvious that the increase in this parameter caused a

considerable increase in the extreme load value in the plane strain

analysis for columns material of high frictional values. But in

axisymmetric case, the influence of gravity was negligible for all values

of the friction angle. Finally, they recommended the use of the upper

bounds determined based on the plane strain assumption for estimating

the bearing capacity of reinforced soil by group of trenches.

2.6.2 Stone Column Groups

Goughnour and Bayuk, (1979) proposed an approach dealing with the

stone column and the surrounding soil as a unit cell to simulate large

group of columns. Stone column material was assumed to be rigid

plastic, surrounding soil to be in the elastic range and the soil at the

boundary of the unit cell to be completely plastic. The assumption of

complete plasticity of soil between unit cells may lead to over

simplification as in case of large groups of columns supporting flexible

footings or in case of embankments where the columns and surrounding

- 63 -

soil are subjected to spreading. The approach is more applicable for

stone columns in soft clays only.

Aboshi et al., (1979) mentioned that the induced stress concentration on

sand piles with increasing settlement was because different deformations

occurred between column and soil. He proposed two equations for

estimating the value of stress concentration factor, n, at yielding of

column material and surrounding soil for undrained and drained

conditions. Then, the relation between the bearing capacity and stress

concentration was postulated in an equation calculating the shear

strength of composite ground based on the circular sliding surface

method.

- 64 -

Barksdale and Bachus, (1983) they proposed a method to estimate the

ultimate bearing capacity of stone column groups of either a square or

infinitely rigid concrete footing resting on the surface of cohesive soil as

depicted in Fig. (2-38). Assuming that foundation was loaded quickly so

that the undrained shear strength is developed in cohesive soil, with the

angle of internal friction bearing negligible, neglecting cohesion in stone

column, and assuming the full mobilization of shear strength of both

stone column and cohesive soil.

Fig. (2-38) Stone column group analysis - firm to stiff cohesive

soil (Barksdale and Bachus, 1983).

- 65 -

For the firm to stiff cohesive soil with undrained strength greater than 30

to 40 kN/m2, the authors approximated the failure surface with two

straight rupture lines as shown in Fig. (2-39).

Assuming the ultimate vertical stress, qult, and the ultimate lateral stress

σ3 to be the principal stresses, then the equilibrium of the wedge

requires:

= σ3 tan2β

` +

tan β

` (2.12)

σ3 = (γcB tan β`/2) +2c (2.13)

Where: (2.14)

tan -1

(µsas tan ) (2.15)

= (1-as) c (2.16)

Where:

γc = saturated or wet unit weight of the cohesive soil

B = foundation width

β` = failure surface inclination

c = undrained shear strength within the undrained

cohesive soil

= angle of internal friction of stone

= composite angle of internal friction on shear

surface

= composite cohesion on the shear surface

- 66 -

For the case of the soft and very soft cohesive soils, the stone column

group capacity was predicated using the capacity of a single, isolated

stone column located within a group, and to be multiplied by the number

of columns. The ultimate bearing capacity for a single, isolated stone

column can be expressed:

qult = C Nc (2.17)

Where:

C = undrained shear strength of cohesive soil

Nc = composite bearing capacity factor for the stone column

Nc ranges from 18 to 20 (Barksdale and Bachus, 1983). For the soft

Bangkok clay, it ranges from 15 to 18, using an initial pile diameter of

25.4 cm with the gravel compacted by a 0.16 ton hammer dropping 0.7m

(Bergado et al., 1994).

Priebe, (1995) presented design chart for determining the portion of the

total load received by the stone column as depicted in Fig. (2-39).The

factor m postulates the increased proportion of the total load carried by

the column. There are two groups of curves, the solid lines present the

value of m based on the value of area replacement ratio, as, and the value

of settlement improvement factor (ratio of settlement of untreated group

to that of treated ground , as determined

(2.18)

- 67 -

Fig. (2-39): proportional loads on stone columns (Priebe, 1995).

The dashed lines give the value of m averaging on the basis of the load

distribution on columns and soil. So, this reduced value of m was

calculated from the following equation:

(2.19)

According to the proportional loads on columns and soil, the shear

resistance from the friction characteristics of the composite ground was

averaged as:

tan ϕ avg = m.tan ϕ c + (1-m`).tan ϕ s (2.20)

The cohesion of the composite ground depends on the area ratio:

cavg = (1-as) .c (2.21)

Due to the damage caused in soil during the process of installation, it

seemed advisable to consider the cohesion proportional to the loads:

cavg = (1- m`) .c (2.22)

- 68 -

The ultimate bearing capacity of a rigid single isolated and strip footings

on the composite ground was estimated by priebe (1991,1995) on the

basis determining a fictitious width b of the footing, which is larger than

the actual width b. In case of ground failure, the failure line of sliding

extending outside the improved area is the same as in case of actual

footing at the actual conditions, but under the footing the rupture surface

would be increased as b' > b.

The value of b' was calculated from:

.

b'=b.e (arc(45 -

avg/2).tan

avg - arc(45-

s/2).tan

s )

(2.23)

Then, this fictitious width is used in determining the bearing capacity by

using the normal bearing capacity factors, the friction angle of the

untreated ground, and the average cohesion according to the proportion

of fictitious width and failure width outside the footing.

Another method was developed by preibe, (1991) for estimating the

bearing value by drawing an approximate failure line for the treated

ground under the footing and the untreated area. The average friction

angle and cohesion values were adopted for the zone of treated ground.

Outside of this zone, parameters of weak soil were used. Then, these

parameters, in addition to the bearing capacity factors, were substituted

the equation of bearing capacity to calculate its value. The

aforementioned two approaches gave results agreed well with that

obtained by Barksdale and Bachus, (1983).

Boussida et al., (1995) studied the improvement of the bearing capacity

of the foundation soil reinforced by columnar inclusions in two stages;

- 69 -

the trixial loading test was simulated on the composite cylindrical cell of

central column surrounded with the weak soil, using the yield design

theory. The second stage, was concerned with estimating the bearing

capacity of a smooth rigid footing resting on the reinforced soil, using

the predetermined solution from the first stage. A quantitative analysis

of the grain of strength due to reinforcement was developed. The bearing

capacity was estimated regardless of the foundation shape or columns

distribution and neglecting the gravitational forces in the analysis.

Bae et al., (2002) studied the failure mechanism and various parameters

influencing the behavior of end bearing stone column groups by

conducting loading tests and unit cell consolidation tests and the results

of model tests are verified through FEM analysis. They found that the

bearing capacity of stone column.

Black et al., (2007) conducted tests on isolated stone column and on a

group of three columns with same area replacement ratio with different

lengths under drained triaxial conditions. They concluded that grouping

of columns can lead to a possible reduction in the stiffness when

compared with a single column at similar area replacement ratio.

- 70 -

2.7 Settlement Analyses

2.7.1Greenwood Method

Greenwood, (1970) presented charts for predicting consolidation

settlements of stone column reinforced clay based on entirely empirical

approach. The total settlement of the composite ground was assumed to

be uniform and was equal to the vertical strain at the top of stone column

plus the compression of soil layer below tip.

Settlement reduction, under widespread loads, is presented as a function

of column spacing and the undrained strength of the clay. The clay

strength considered in the analysis ranged from 20 to 40 kN/ m2 as

shown in Fig. (2-40). Greenwood suggested that these curves be used

with caution within the indicated range (Balaam and Poulos, 1983).

Immediate settlements and shear displacements were neglected,

Greenwood‟s approach compares well with many of the more recent

numerical and theoretical methods of settlement prediction (Mckelevey

and Sivakumar, 2000).

- 71 -

Fig. (2-40): Settlement for stone column in clay (Greenwood, 1970).

2.7.2 Priebe Method

Priebe, (1995) proposed a method for estimating the reduction in

settlement of infinitely loaded foundation supported on ground improved

with stone columns. Depending on his earlier work in 1991. The unit

cell model method was used with area A and a concentric single column

with cross section As. This method was based on some idealized

conditions and assumptions as follows:

The stone column is assumed to be in the plastic equilibrium

state the surrounding soil to behave elastically

The column is resting on a rigid layer.

The column material is incompressible, and the change in

volume within the surrounding soil is directly related to vertical

shortening of the cylindrical column which forms the basis of the

derivation. The radial deformation of the elastic soil was

- 72 -

determined using an infinitely long, elastic hollow cylinder

solution. The elastic cylinder of soil, which had a rigid exterior

boundary coinciding with the boundary of the unit cell, was

subjected to a uniform internal pressure (Barksdale and Bachus,

1983).

Equal vertical settlements of column and soil.

Uniform stresses in the two materials.

Settlement occurred due to bulging of stone column into

surrounding soil. Assuming a constant bulging along the column

length.

The bulk density of column and soil was neglected.

The coefficient of lateral earth pressure was taken equal to Kac

and 1.0 for stone column and surrounding soil, respectively.

According to the aforementioned assumption, Priebe derived the

following equation to calculate the settlement improvement factor,

which equal to the ratio of settlement of original untreated ground

(soil), Sunt, to the settlement of soil treated with stone columns, St, using

poisson‟ s ratio, ν , equal 0.3 .

1 + .

(2.24)

Where:

Kac = coefficient of the active lateral earth pressure of stone column The

relation between the improvement factor, the reciprocal of area

replacement ratio, A/AS , and the angle of internal friction of backfill

A

As

1

)/1.(.4

/5

AAK

AAs

sac

- 73 -

material, ϕ , was illustrated in Fig.(2-41)

Fig. (2-41): Priebe’s settlement improvement factor curves

(Priebe, 1995).

Balaam and poulos (1983) and Barksdale and Bachus (1983) found

that using Fig. (2-42) would over – predict the beneficial effect of stone

columns in reducing settlements when compared with actual field data

and data from other design methods like equilibrium method. As this

method is depending on the elastic theory, it would give a good

agreement with the other non – linear methods at very close column

spacing, but the discrepancy increases as the column spacing increases,

(Balaam and poulos, 1983). Based on the fact that the backfill material is still compressible and also

in the case of A/Ac= 1.0 dose not achieve an infinite value of settlement

improvement factor as determined theoretically for incompressible

material, Priebe had introduced an additional area ratio ∆ (A/Ac) to be

added to the actual value of area ratio. The modified value of area ratio

- 74 -

was used in Fig. (2-42) to get the improvement factor. The additional

area ratio was determined from Fig. (2-42) relating it with the ratio of

column constrained modulus, Ds, to soil constrained modulus, Dc, and

the angle of internal friction of backfill material. The modifications were

extended to introduce the effect of overburden pressure of soil in

increasing the coefficient of the stone column.

As an advanced for his approach, Priebe, (1995) provided design charts

to estimate the settlement of foundation of limited size supported on a

limited number of stone columns as a function of the settlement of

infinite foundation on infinite grid of stone columns, as shown in Fig.

(2-43) and (2-44) for isolated and strip footings, respectively. These

design charts show the relation between the required settlement ratio,

depth of treatment to diameter of stone column ratio d/D, and the

numbers of stone columns under the footing area attributable to a stone

column as well as the foundation pressure were identical in both cases of

foundation of finite size foundation. Also, the load distribution as well as

the lower bearing capacity of the outer columns of the column group

below the footing was taken into consideration.

- 75 -

Fig. (2-42): Additional area ratio curves (Priebe, 1995).

Fig. (2-43): Settlement of single footings (Priebe, 1995).

- 76 -

Fig. (2-44): Settlement of strip footings (Priebe, 1995).

2.7.3 Equilibrium Method

Aboshi et al., (1979) developed the equilibrium method for estimating

the settlement of sand compaction piles in Japan. He assumed an

infinitely loaded area, reinforced with sand piles having a constant

diameter and spacing. The stress concentration factor needed for

calculating the settlement was estimated from the past experience. For

this condition of loading, the assumptions used in this method were:

The unit cell concept assumed to be valid.

The total vertical load applied to the unit cell equals the sum of

the force carried by stone and soil.

The vertical strains at any horizontal level are uniform.

A uniform vertical stress due to external load exists thought the

length of stone column or the compressible layer is divided into

increments.

- 77 -

The settlement Sunt of the untreated soft clayey subsoil under an

average applied stress σ is calculated by the following equation:

Sunt= mv.σ.H (2.25)

Where:

mv = modulus of volume compressibility

H = thickness of clay layer

The settlement St of the treated soil was estimated by the following

equation, taken into account the effect of stress reduction on the soil

surrounding the pile.

St= mv. (µcσ).H (2.26)

Comparing Equation (2.24) with (2.25), settlement reduction ratio β is

the ratio of the settlement of the treated to untreated soil, equals:

β = St / Sunt = µc = 1/ [1+ (n-1) as] (2.27)

A design chart according to Equation (2.27) is shown in Fig. (2-45). it

was reported by Barksdale and Bachus (1983) that this method slightly

overestimated the expected ground improvement and was only useful for

preliminary studies.

- 78 -

Fig. (2-45): Settlement reduction factor using equilibrium method

(Aboshi et al., 1979).

2.7.4 Incremental Method

The method developed by Goughnour and Bayuk, (1979) was an

extension to the work presented by Huges et al. (1975). The unit cell

concept was used considering successive vertical increments, i.e. disc

shaped elements to take into account the increase of the confining

pressure, applied to the stone column by in – situ soil, with depth.

Hence, bulging due to yielding in the column was a function of depth

and occurred initially in the top portion of the column

The stone column material was assumed to be incompressible and all of

the volumetric strain must be accommodated by the surrounding soil, as

it consolidates. Shear stresses were disregarded between stone column

and soil by assuming equal vertical strain in the composite system.

- 79 -

Equations were derived to solve the vertical stain and the average

vertical stress in the in-situ soil surrounding the column for both the

elastic and plastic behavior of the stone. In the plastic analysis, bulging

occurred and column considered in plastic equilibrium state yielding

according to Mohr-coulomb criterion in terms of the angle of internal

friction on effective stress basis. The effect of column installation was

taken into account in the equations by estimating a value for the

coefficient was taken into consideration due to the vertical and lateral

strains. The surrounding soil was assumed behave according to

Terzaghi‟s one dimensional consolidation theory modified to

accommodate both of the vertical and radial consolidation.

For the elastic analysis, the stone and clay were both assumed to behave

as linearly elastic material. In this range, the column would not bulge.

The use of modulus of elasticity in this analysis probably gave higher

values of vertical settlement, as there was some degree of constraint

provided by the boundaries of the unit cell. The actual long – term

settlement was taken from the larger of those computed for the stone

considered as elastic and as plastic material.

Design charts were provided by Goughnour, 1983 to facilitate settlement

calculation instead of using the equations that need iterative procedures

for solution.

- 80 -

2.7.5 The Granular Wall Method

This is a simple way of estimating the improvement of settlement of a

soft cohesive soil reinforced with stone columns reaching a more

resistant stratum. Van Impe and De Beer, (1983) considered two cases

for estimating the improvement of settlement:

1) Under the foundation load, the columns are at the limit equilibrium

and deform at constant volume.

2) Under foundation load, the stone column are deforming elastically.

The stone columns were replaced in the calculation by stone walls with

equivalent area, which is the condition of plane strain. The shear stresses

between column and surrounding soft soil and the own weight of both

the columns and soil were neglected. In addition, the resisting layer

underneath the soft soil was considered undeformable.

The first case of computation was more appropriate than the second one

in calculating the improvement of the settlement. For the first case,

design charts were provided depending on number of parameters, the

pattern of stone columns, their diameter, the angle of shearing strength

of stone material, the odometer modulus of the soft soil and its poisons

ratio. The second case of computation was only valid as long as the

stone column did not reach the plastic condition and the area

replacement ratio was more than 0.7.

This computation method was used in some foundation problems of

large storage tanks on soft soil improved with stone columns, and the

- 81 -

measurements indicated the reliability of this method. However, there

were some shortcomings in this method, as neglecting the shear stresses

transmitted from column to the surrounding soil, which might alter the

column capacity as reported by Huges et al., (1975).

The assumption of uniform bulging along the column was not consistent

with the actual behavior since the bulging was large at smaller depth

than deeper ones due to the effect of confinement of the surrounding soil

to the column.

2.8 Estimation of Rate of Consolidation

2.8.1 Consolidation Rate of Improved Ground by Stone

Column

Field observations showed that stone columns accelerate the

consolidation rate in the soft soil. Field pore water pressure

measurement under an embankment indicated that a homogenous clay

stratum without stone columns area only completed 25% primary

consolidation when that clay with stone columns area completed 100%

primary consolidation, (Munfakh et al., 1984).

Han and Ye, (1992) reported that the rates of settlement of two similar

buildings, one on an unreinforced foundation and the other on stone

columns reinforced foundation in the same site, ached 66 % and 95 %,

respectively in the same time of 480 days. The acceleration of

consolidation rate is accredited to the stone column for providing a

drainage path and relieving excess pore water pressures by transferring

load from the surrounding soft soil to the stone column.

- 82 -

Bergado and Long, (1994) presented the use of the FEM for

embankment simulations. Based on revised Cam clay model for 2-D

consolidation analysis, two test embankments where constructed on soft

Bangkok clay improved by granular piles and vertical drains. The

embankments had 4m height. The soft clay which had 8 m depth is over-

lained by a medium stiff clay layer. In 2-D plane strain model, the

vertical drains and granular piles were converted into continuous walls.

The analysis results showed the granular piles imply more acceleration

of consolidation and more reductions in the total settlement of the soft

clay than vertical drains, as shown in Fig.(2-46) and (2-47).

Fig. (2-46): total settlement-time relationship of reinforced soft clay

by Granular piles (Bergado and Long, 1994).

- 83 -

Fig. (2-47): total settlement-time relationship of reinforced soft clay

by Vertical drain (Bergado and Long, 1994).

Barron, (1947) proposed a known solution which dealt with

consolidation of fine grained soil by vertical drain. The average rate (or

degree) of consolidation in the radial direction is

(2.28)

Where

*

+

(2.29)

- 84 -

( ) Is defined as the diameter ratio which is the ratio between the

diameter of a drain well ( ) and the diameter of its influence zone ( );

( ) is the consolidation time factor for radial flow

The solution of Barron (1947) dealt with the consolidation of fine-

grained soils by vertical drain. Stone columns and vertical drain have

two major differences. First, stone columns have the larger drainage

ability. Barron‟s solution ignored the effect of stiffness difference

between the vertical drain and the surrounding soil on the consolidation

rate. However, the stone columns are much stiffer than vertical drains

and carry a substantial part of the applied load. Second, the stone

columns have a smaller diameter ratio (influence diameter/column

diameter) than drain wells. Typical diameter ratios for stone columns

range from 1.5 to 5. However, the values for well diameter ratios used

by Barron (1947) ranged from 5 to 100.

Han and Ye, (2001) presented a simplified method for computing rate

of the consolidation of the soft soil around stone columns considering

stiffness ratio. Although stone columns and surrounding soil were

assumed linearly elastic in their study, in reality, they have a nonlinear

behavior. Stone columns act as drain wells where vertical and radial

flows are similar to those of Terzaghi 1D solution and the Barron

solution for drain wells in fine grained soils, respectively. The following

relationship is still applicable to calculate time rate and settlement of the

stone column improved ground:

(2.30)

- 85 -

Where,

= degree of consolidation (both radial and vertical direction)

= degree of consolidation (radial direction only)

= degree of consolidation (vertical direction only)

Fig. (2-48): Definition of terms for modeling (Han and Ye, 2001).

- 86 -

An approximate solution can be obtained as follows:

[ ] [ ] (2.31)

Where

, a modified time factor in the radial flow

, a modified time factor in vertical the flow; and H = is the

vertical drainage path.

The modified coefficients of consolidation are as follows:

(

) (2.32)

(

) (2.33)

Where ( ) is the diameter ratio; steady stress concentration ratio ( ) is

the ratio between steady stress in column ( ) and steady stress in soil

( ) at the end of consolidation.

The new solution demonstrates stress transfer from the soil to the stone

columns and dissipation of excess pore water pressure due to the

drainage and vertical stress reduction during consolidation. Ignoring

consolidation due to vertical flow, the calculated average total stress on

the soil and columns for case and are plotted in Fig. (2-

49). This figure, demonstrates that the stress on columns increase with

time, while the stress in soil decreases. This stress transfer from the soil

to the columns is called “stress concentration”.

- 87 -

Fig. (2-49): Vertical stress on soil and columns with time, N = 3 and

ns = 5 (Han and Ye, 2001).

The stress concentration can also be presented in terms of the stress

concentration ratio, as shown in Fig. (2-50). The stress concentration

ratio increases with time and approaches the steady-stress concentration

ratio (ns = 5 in this case). This proposed method indicated the general

trend that the steady-stress concentration ratio increased with the applied

loads .at larger loads than the yield load of the stone columns, the

steady-stress concentration started to decrease.

- 88 -

In the study of Han and Ye (2001), however, no lateral displacement

was assumed in the theoretical development. Therefore, the dissipation

of the excess pore water pressure depends mainly on two factors,

drainage and reduction of vertical stresses. The dissipation of excess

pore water pressure, due to the vertical stress reduction, was about 40%

of the total dissipation for this special case, as shown in Fig. (2-51). The

contribution of vertical stress reduction to the dissipation of excess pore

water pressure explains why stone columns are more effective than drain

wells in accelerating consolidation rate of the soft clays.

Fig. (2-50): Stress concentration ratio with time (Han and Ye, 2001).

- 89 -

Fig. (2-51): Dissipation of excess pore water pressure, N = 3 and

ns = 5 (Han and Ye, 2001).

The comparison between the results of the simplified method and the

numerical study of Balaam and Booker (1981) for all cases indicated

that the computed rate of consolidation by numerical method was greater

than that by the simplified method at the beginning of the consolidation.

However, it is reversed when the rate of consolidation was greater than

approximately 40%. These discrepancies can result from the different

assumptions used in the numerical and simplified methods.

In the numerical study, the lateral displacement was permitted.

However, the lateral displacement was not allowed in the development

of the simplified method. The lateral displacement in the numerical

study tended to reduce the excess pore water pressures at the beginning

ate of consolidation. When more stress is transferred onto the stone

- 90 -

column with time, however, the lateral displacement from the stone

towards the soft soil in the numerical study tends to increase the excess

pore water pressures, so that it slows down the process of consolidation.

The difference between the rate of consolidation from the numerical

analysis and the simplified method is diminished with an increase of the

diameter ratio, N, as shown in Fig. (2-52) and (2-53).

Fig. (2-52): Rate of consolidation of stone column reinforced

foundations (Han and Ye, 2001).

- 91 -

Han and Ye, (2002) developed the following equation to calculate the

rate of consolidation of the stone column reinforced foundation

considering smear zone and well resistance effects:

[ ] (2.34)

(

)

(

) (

)

(

)

(

) (

)

(2.35)

Where:

N , the diameter ratio of the smeared zone to the stone

column

Fig. (2-53): Rate of consolidation of stone column reinforced

foundations (Han and Ye, 2001).

- 92 -

the stone column

Permeability of the smeared soil in the radial direction

= permeability of the undisturbed surrounding soil in the

radial direction

Castro and Sagaseta, (2009) developed equivalent coefficients of

consolidation which account for the lateral movement of the stone

column during the consolidation process. The behaviour of the column

was modeled as an elastic material or as an elasto-plastic dilatant

material with a Mohr-Coulomb failure criterion. Vertical stress increased

in columns with consolidation and column yielding occurred. The

stiffness of columns reduces once yielding occurs, which results in

increased radial deformability of the column. Therefore columns in a

plastic state expand and increase the excess pore water pressure in the

soil. The solution developed by Castro and Sagaseta, (2009) allows the

depth and time of column yielding to be determined. Therefore it is

possible to accurately determine the stresses and strains occurring in

columns at any stage in the loading history. A comparison with Han and

Ye, 2001 of the development of stress concentration ratio with time is


- 93 -

2.8.2 Stone Columns-Soft Soil Reinforcement System

under Embankment

Terzaghi and Peck (1967) stated that the instability of embankment

constructed on soft soil foundations is mainly of two types: a) where the

embankment sinks into the foundation soils and b) failure by spreading.

Hence, stone columns reinforced soils as embankment foundation have

been used as a more effective method to prevent sinking and spreading

failure. Therefore, that technique improves the performance of the

embankment over it by increasing shear strength and bearing capacity as

well as decreasing consolidation settlement and lateral displacement of

the soft foundation soil.

Fig. (2-54): Stress concentration factor. Influence of radial

deformation and plastic strains (Castro and Sagaseta, 2009).

- 94 -

Weber (2006) investigated the behavior of a base reinforced

embankment constructed on a soft clay layer, which was improved with

stone columns. Centrifuge tests were performed in order to gain a deeper

understanding of the interaction problem within the structure. The

centrifuge tests were performed at 50–times gravity. The model

represented a prototype structure of a 7 m clay layer depth with a

compaction pile grid spacing of 1.7 m x 1.7 m and an average pile length

of 5 m with a 0.6 m pile diameter.

The model embankment produced an overburden pressure of about 90

kPa, representing a prototype embankment constructed of sand of about

5 m in height. The test was conducted in a modeling container, which

was divided into 2 sections to permit comparison to be made on the soil

with the same provenance and stress history. In one section, the soft clay

was improved with sand compaction piles, while in the other section, the

clay was not improved.

Due to the ground improvement in this centrifuge test, a factor of

settlement reduction of 2.0 was measured. The acceleration of

consolidation time t90was measured with a factor of 5.0 for the

described test. This showed that the factor of ground improvement a.

Vertical displacement profile b. Horizontal displacement profile at mid

of slope for settlement reduction does not coincide with the factor of

accelerated consolidation time. The reason for that was probably the

floating pile construction and ongoing consolidation in the lowest third

of the clay layer, which was not improved.

- 95 -

Saroglou et al., (2008) presented the ground improvement using stone

columns for the construction of a new high way road from Keratea to

Lavrio, in Attika peninsula, Greece. An embankment of maximum

height of 3 m was constructed on subsoil comprises of soft clays of low

plasticity with intercalations of silty to clayey sands of medium density

with gravel. Using stone columns with a depth of 14 m reduced the total

settlement from 14 cm to 7 cm and accelerated consolidation time from

16 months to a period of 4 months.

Borges et al., (2009) conducted a parametric study to investigate the

influence of several factors on the behavior of soft soils reinforced with

stone columns under embankment loads. Parameters such as

replacement ratio, deformability of the column, thickness of the soft soil,

deformability of the fill and friction angle of the column material were

examined. The confined axisymmetric cylindrical unit cell was used.

The analysis was performed by a finite element program that

incorporates the Biot consolidation theory. The results confirmed that

increasing replacement area ratio or stiffness of the column material

significantly reduces settlements and horizontal displacement and

accelerates the consolidation.

- 96 -

2.9 Smear Zone: Effect on Permeability

The installation of stone columns, or vertical drains, not only influences

the stress level but causes a thin disturbed zone around the inclusion,

which is dependent on the host soil characteristics, and is usually

described as smear zone (e.g. Onoue et al.,(1991); Indraratna and

Redana, (1998); Sharma and Xiao, (2000); Bergado et al., (1991) and

Shin et al., (2009). This zone exhibits a reduced permeability and thus

reduces the drainage performance of the inclusion.

Onoue et al. (1991) conducted small-scale loading tests on sand drains

installed in Boston Blue Clay, while recording the pore water pressures

10 mm under the surface of the clay specimen. Based on their

observations, they suggested dividing the soil surrounding the drains

into three zones:

- Zone I or undisturbed zone, beginning at a distance of 6.5 times the

radius of the drain (rw) from the drain axis;

- Zone II where the installation of the inclusion causes a decrease of the

void ratio and, as a consequence, a decrease of the permeability;

- Zone III or remolded zone where an additional decrease of the

horizontal coefficient of permeability kh is anticipated.

Fig. (2-55) shows the evolution of the normalized horizontal coefficient

of permeability (kho denotes the undisturbed permeability) with the radial

distance from the drain axis.

- 97 -

Fig. (2-55): Suggested variation of horizontal permeability with

radius according to (Onoue et al., 1991).

Indraratna and Redana, (1998) and Indraratna et al., (2001) present

the results of small-scale tests modeling the installation of sand

compaction pile in remolded clay. Indraratna and Redana, 1998

evaluated the extent of the smear zone by determining the

compressibility and permeability parameters at different distances from

the axis of the sand compaction pile. The main conclusions drawn from

these investigations are that the installation effect of the sand

compaction pile on the soil structure is greatest near the boundary of the

sand compaction pile, while the radius of the smear zone rs can be taken

to be equal to 100 mm or 4 to 5 times the radius of the column

(respectively equal in this case to 25 mm and denoted as rw in Fig. (2-

56).

- 98 -

Fig. (2-56): Section of the test setup showing the smear zone

(Indraratna and Redana, 1998).

It could also be observed that the horizontal coefficient of permeability

kh in the smear zone decreased in vicinity of the sand compaction pile,

but that the vertical permeability kv remained almost identical to the

original values in the host soil, even at the column interface. However,

this approach assumes that the smear zone remains homogeneous, which

may lead to some less accurate results than if a difference was made

between smear zone (or remolded zone) and compaction zone (or

disturbed zone), Fig. (2-57).

- 99 -

Fig. (2-57): Ratio of horizontal to vertical coefficient of permeability

against the radial distance from the axis of the sand compaction pile

(denoted as drain) (Indraratna and Redana, 1998).

Sharma and Xiao, 2000 used a large-scale laboratory apparatus to

install vertical sand drains in kaolin samples with different pre-

consolidation pressures. They measured the pore water pressures at

different distances from the drain axis during installation, using 6.4 mm

diameter miniature pore pressure transducers. The experimental setup

allowed for an installation with, and without, smear zone to be

conducted. The mandrel consisted of an open-ended 54 mm diameter

outer tube with a thickness of 2 mm and of a 50 mm diameter inner tube

with a closed bottom end. In the first case, both tubes were fixed

together and pushed into the clay, thus reproducing the common

installation process and causing a smear zone. In the second case, only

the outer tube was pushed into the host soil and subsequently the clay

- 100 -

stuck in the tube was removed carefully with an auger, so that the

installation effects are limited in such a way that they can be neglected

in the analysis.

A comparative study of the response of the soil with and without smear

zone is illustrated in Fig. (2-58), t0 corresponds to the start of the

insertion of the installation mandrel, t1 to the time when the tip of the

mandrel reaches the depth of the transducers and t2 denotes the time

when the mandrel reaches the full penetration depth. The generated

excess pore water pressures are significantly higher in the case with

smear, which is consistent with the expected reduction of horizontal

permeability in the smear zone.

Fig. (2-58) Excess pore water pressures during the insertion of the

installation mandrel (Sharma and Xiao, 2000).

- 101 -

2.10 Scale Effect

There are a variety of researcher has been investigate the model test of

stone column embedded in soft clay soil with studied stone column

dimension relative to tank dimension.

Ambily and Gandhi, (2007) has been investigated the model of stone

column embedded in soft clay with adopted tank diameter in range of

(210mm and 350mm). While the adopted stone column diameter in this

study is constant and equal to 100 mm. This clarify that thickness of the

clay layer a long each side of stone column in rang (x = 0.55D to 1.6D) .

Isaac and Grirish, (2009) used reinforcing columns 50 mm diameter

surrounded by the soil in a cylindrical tank 210mm diameter.This refers

to the width of clay layer along each side of stone column is around (x =

1.6D) of column diameter as shown in Fig. (2-60).

Fig. (2-59): Single column test arrangement dimension (Ambily and Gandhi,

- 102 -

In addition to, Shivashankar, et al., (2011) studied the model of stone

column in soft clay with stone column diameter of 90mm relative to tank

size diameter of 237mm. This indicts that the width of clay layer along

each side of stone column is around ( x = 0.82D) of pile diameter

Fig. (2-60): The test setup for single column model test (Isaac and Grirish, 2009).

Fig. (2-61): Test arrangement and dimension after (Shivashankar, et al., 2011)

- 103 -

Ali, et al., (2011) studied the model of stone column in soft clay with

stone column diameter of 50mm relative to tank size diameter of

300mm, this again shows that the width of clay layer along each side of

stone column is around ( x = 2.5D) of column diameter as shown in Fig.

(2-62).

Tandel, et al., (2012) studied the model of stone column in sand with

stone column diameter of 100mm relative to tank size diameter of

260mm. It can be concluded that the width of clay layer along each side

of stone column is around ( x = 1.6D ) of pile diameter.

Fig. (2-62): Schematic view of stone column foundation of (Ali, et al., 2011).

- 104 -

While Prasad and Satyanarayana, (2016) studied the improvement of

Soft Soil Performance using Stone Columns Improved with Circular

Geogrid Discs. The studied maximum diameter of stone column model

is around 50mm and the diameter of tank is 200mm. Therefore the

thickness of clay layer in each side of stone column in range of 1.5D.

Fig. (2-64): Test arrangement (Prasad and Satyanarayana, 2016)

Fig. (2-63): The Schematic diagram of sand column test arrangement

(Tandel, et al., 2012)

- 105 -

Based on the paper in literature in this thesis about tank size effect, the

adopted minimum and maximum stone column diameter are in rang of

(50, 100, 150, and 300mm) with constant tank diameter of 600mm. This

can be attributed to the width of clay layer along each side of stone

column are found to be (x = 5.5D, 5D, 4.5D and 0.5D). This can

attributed that the adopted stone column and tank size for clay bed are in

rang presented above by the different investigators.

The main essence has been found that the axisymmetric modeling can be

used to study the behavior of foundation. In order to overcome the errors

associated with this modeling, the tank side walls should be built as a

rigid as possible to eliminate the out of plane side movements. The

effect of sidewalls friction can be reduced significantly by using low

friction materials such as glass, polished steel, PVC or greased

membrane.

The small scale model tests can be used to describe a certain

phenomenon. The use of small scale models to investigate the behavior

of full scale foundation is a widely used technique, due to the nature of

soils that has been reported that there are differences between field

behavior and small scale model tests. For interpretation that in case of

shallow foundations, the averages shear strength mobilized along the

slip line under the foundation decreases with the foundation size. It is

clearly shown that the relative compressibility of soils, both with respect

to gravity forces and with respect to the soil strength, increases with the

foundation size ( De Beer, 1963 and Vesic, 1974 )

- 106 -

In summary model footing may be considered as prototype in their

own right. However, and departure from similarity must be identified so

that the applicability of results can be assessed. The general conclusion

drawn from the literature is that there is no scale effect due to the ratio of

the footing size to the particle size provided particle size is small

compared to the footing dimension and stone column. However, scaling

effects due to variations in stress level will occur in 1 g (earth gravity)

modeling. Therefore, it is of limit use in predicting the behavior of a

particular prototype, the use of 1g models can be useful in predicting

general trends of behavior.

- 107 -

2.11 Data Base of Stone Column Studies

The objective of the section is to assemble published results from field,

laboratory, and numerical investigations of stone columns in soft clay in

present research to provide future researchers and designers with easy

access to information and data. The majority of the reviewed papers

include an experimental component that are based on field or laboratory

scale tests conducted on clay specimens reinforced with partially or fully

penetrating that were installed as columns or as groups of stone

columns.

This section aims at summarizing published work on the analysis,

testing, and modeling of soft soils that are reinforced with single stone

columns and stone column groups.

Three subsections are included to demonstrate:

(1) A summary of numerical studies

(2) A summary of laboratory model tests

(3) A summary of field model tests

This can be found in tables (2.2 through 2.4) which show the collected

and investigated approaches by different investigators.

It should be noted that the review incorporates studies that are limited to

applications where stone columns are used to reinforce soft soils (reduce

settlement and increase bearing capacity).

Additional information regarding the test setup, soil and column types

and properties are also included in the table. Detailed information on the

scope and main findings of each paper is presented in the literature

review section and a summary of major findings from the physical,

numerical and analytical models is presented at the end of the Thesis.

- 801 -

Table (2.2) Database of numerical studies on stone columns

Reference Numerical method

(Code) Type of analysis

Constitutive behavior/model

Mesh type External Load

Soil Stone column

Ambiy and Gandhi

(2007) FEM (PLAXIS 2D) Axisymmetric Mohr–Coulomb Mohr–Coulomb 15-noded

triangular Plate Load

Guetif et al. (2007) FEM (PLAXIS 2D) Axisymmetric Mohr–Coulomb Mohr–Coulomb

15-noded

triangular Uniform Pressure

Tan et al. (2008) FEM (PLAXIS 2D)

Axisymmetric &

Equivalent Plane

Strain

Mohr–Coulomb Mohr–Coulomb 15-noded

triangular Embankment

Chen et al. (2009) FDM (FLAC 3D) 3D

Modified Cam-

Clay Mohr–Coulomb Brick and shell Uniform Pressure

Choobbasti et al.

(2011) FEM (PLAXIS 2D) Axisymmetric Mohr–Coulomb Mohr–Coulomb 15-noded

triangular

Footing

Ng and Tan (2012) FEM (PLAXIS 2D) Axisymmetric Mohr–Coulomb Mohr–Coulomb 15-noded

triangular Plate Load

- 801 -

Reference Numerical method

(Code) Type of analysis

Constitutive behavior/model

Mesh type External Load

Soil Stone column

Castro et al. (2013) FEM (PLAXIS 2D) Axisymmetric

Modified Cam-

Clay Hardening Soil

15-noded

triangular Uniform Pressure

Castro et al. (2014) FEM (PLAXIS 2D) Axisymmetric

Modified Cam-

Clay Mohr–Coulomb

15-noded

triangular Embankment

Shahu and Reddy

(2014) FEM (ABAQUS) 3D Modified Cam-

Clay Mohr–Coulomb

20-noded

hexahedral

Footing

Indraratna et al

(2014) Coupled

FDM+DEM

Axisymmetric

Mohr–Coulomb DEM model DEM-FDM grid Column Load

Mohr – Coulomb (MC)

Modified Cam Clay (MCC)

Hardening Soil (HS)

Soft Soil (SS)

Soft Soil Creep (SSC)

The finite element method (FEM)

Finite difference method (FDM)

Discrete element method (DEM)

- 880 -

Table (2.3) Database of laboratory tests on stone columns

Reference

Type of

Experiment

S=single

G=group

Type of

Loading

Foundation

size (cm)

Test

Sample

Size

(cm×cm×

cm)

Column

dimension

(mm)

Area

replacement

ratio %

Soil type Column type Clay cu

(Kpa)

Column

ϕ °

Hughes and

Withers(1974) 1-g (S) C --

22.5×16

×15 D= 12.5-38 -- Kaolin

Lighton

buzzard sand 19 35

Bachus and

Barksdale (1984) 1-g (S/G)

A -- D=10.8,

H=30.5

D=29.3,53.3

L=305 7 and 25

Kaolin Quartz 14.4-19.1 --

F -- 17.3×50.5

×30.5

D=29

L=305 20

Narasimha Rao et

al. (1992) 1-g (S) F 1.5 D

100×80

×100

D=25,50,75

L/D=5,8,12 44.4

Marine

Clay Granite chips

Soft/M.Sti

ff 38

wood et al.

(2000) 1-g (G) F 10 D=30

D=11,17.5

L=300 10-30 Kaolin Quartz 12 --

Mckelvey et

al.(2004) 1-g(G) F 9×9

D=41.3

H=50

D=25

L/D=6,10 24 Kaolin Sand 32 --

Black et al.

(2006) Triaxial (S) F 6

D=30

H=40

D=25

L/D=6and1

0

17 Kaolin Crushed

basalt 35 --

Ambily and

Gandhi (2007) 1-g (S/G) A+C --

D=21,42,8

3 H=45

D=100

L/D=4.5

5.7,10.1,

22.7 CH Stones 7,14,30 43

Isaac and Grirish

(2009) (S/G) C --

single

D=210,

H=270

Group

D=520,H

=270

D=50

L=250 --

Kutt and

Clay

quarry

dust,sea

sand,river

sand,gravel,st

ones

3.1 38,39.5,39

.5,42,43

- 888 -

Type of the study: l-g, triaxial

The column configuration (Single, S or Group, G)

The loading configuration (column loading C, foundation loading F, or area loading A)

Reference

Type of

Experiment

S=single

G=group

Type of

Loading

Foundation

size (cm)

Test

Sample

Size

(cm×cm×

cm)

Column

dimension

(mm)

Area

replacement

ratio %


(Kpa)

Column

ϕ °

Shivashankar

et al. (2010) 1-g (single) C + A --

D = 19–28

H = 72

D = 60–90

mm,

L/D= 6–9,

10–23% ML Silt Aggregate 38

Black et al.

(2011)

Triaxial

(S/G) F 6

D=30

H=40

D=25,32,38

L=125,250,

400

17,28,40 Kaolin Crushed

basalt 35 --

Sivakumar et al.

(2011) Triaxial (S) F 6

D=30

H=40

D=40,50,60

L=400

44.4,69.4,10

0 Kaolin

Crushed

basalt 35 --

Shahu and Reddy

(2011) 1-g (G) F 10

D=30

H=30

D=13,25

L=100,150 10,20,30 Kaolin Barbadur sand 7-9 43.4

- 881 -

Table (2. 4) Database of field tests on stone columns

Reference

Type of

Experiment

S=single

G=group

Type of

Loading

Foundation

size (cm)

Test Sample

Size

(cm×cm×c

m)

Column

dimension

(mm)

Area

replacement

ratio %


(Kpa) Column ϕ °

Hughes et al.

(1975) Field (S) C 66 --

D=0.73m

L=7m -- Grey Silty River Gravel 22 38

Greenwood (1975) Field (S) F 91 -- D=0.58m

L=2.9m 40.6 Boulder Gravel 4.4 --

Bergado and Lam

(1987) Field (S) C -- --

D=0.3m

L=8m -- Bangkok Sand/gravel 20-45 35.6-43.3

Han and Ye (1991) Field (S) C+F 125 -- D=0.85m

L=12m 36and100 Silty Clay Crushed gravel 15 --

White et al. (2007) Field (S/G) C+F 229 -- D=0.76m

L=2.79-5.1m 35 CL Clay

Crushed

Limestone 30 43

Chapter (3):

EXPERIMENTAL WORK

- 113 -

CHAPTER (3)

EXPERIMENTAL WORK

3.1 Introduction

This chapter describes the materials used, mixing procedures and

preparation of the tested soil .The method of installing the stone columns

and testing methodology were illustrated briefly. Loading setup and the

measuring devices that used in the experimental work were also

described. The detailed experimental program was presented in this

chapter. The experimental works were carried out at the Geotechnical

laboratory of Faculty of Engineering, Tanta University.

3.2 Soft Clay Preparing

Obtaining undisturbed soft clay samples from the site is too difficult; so,

the soft clay has been prepared in the laboratory using kaolin according

to Ali, K. et al., (2011). The procedures of preparing of soft clay in the

laboratory were described as following subsections.

3.2.1 Commercial Kaolin Clay Type

Commercially available kaolinite clay type has been used in both

fundamental studies of soil behavior and physical model tests. The

properties of kaolin are somewhat a typical of natural clay soils.

The mineralogical and chemical properties of the kaolinite published by

the manufacturer were presented in Tables (3.1) and (3.2).

White kaolin was used to prepare clay deposits with three different

bearing capacities. In order to reach full saturation and homogeneity, the

- 114 -

clay slurry was mixed at different water content to obtain the desired

density and cohesion. A series of trial mix were done to check the

density by preparing cylinder samples having a diameter of 3.5cm and

height 7cm. The test was carried out at three different samples having

shear strength of 10 kPa, 20 kPa and 30kPa. The corresponding water

contents were found to be 33, 25 and 19% respectively. The clay sultry

mix was prepared using a mechanical mixer operated for 15 minutes

mixing to obtain the final tested form at given water content. The final

mix cohesion was checked by vane shear test which provide a

reasonable fit with direct shear box test results.

Table (3.1): Mineralogical composition of the kaolinite used in the

model tests (After the Data sheet of the manufacturer).

Type of Mineral

Volumetric content

Clay Mineral

90.97

Sodium Feldspar

2.27

Potassium Feldspar

2.31

Free Quartz

4.45

- 115 -

Table (3.2) Chemical composition of the kaolinite used in model tests

(After the Data sheet of the manufacturer).

Element Percentage

SiO2 50 - 56 %

Al2O3 30 - 33 %

Fe2O3 1.0 - 1.3 %

TiO2 1.3 - 1.8 %

MgO 0.05 - 0.10 %

CaO 0.10 - 0.25 %

Na2O 0.07 - 0.15 %

K2O 0.03 - 0.06 %

LOi 11 - 12 %

3.2.3 Determination of Soil Properties

The following tests were performed at three different samples to

determine the properties of the prepared soft clay and to ensure

compliance of the soft clay prepared in the laboratory with properties of

the natural soft clay.

The following tests were conducted on the soft clay such as, water

content, grains, Atterberg limits tests and direct shear box, in addition to

consolidation test.

These tests were performed at the Geotechnical laboratory of Faculty of

Engineering, Tanta University.

- 116 -

In order to obtain the grain size distribution of the kaolinite, first the soil

was wet sieved and then hydrometer test was performed. Grain size

distribution curve of kaolinite is plotted as shown in Figure (3.1).

Fig. (3-1): Grain size distribution curve from hydrometer test for the

tested sample.

It is found that kaolinite is clayey silt which consists of 95% clay and

5% silt size particles.

3.2.3.1 Shear strength of Tested Samples

The shear strength parameters of the tested clay soils were determined

using direct shear box tests and confirmed by laboratory vane shear test.

Soft clay sample in direct shear was collected from the mixed soft. A

normal load is applied to the specimen and the specimen is sheared

across the pre-determined horizontal plane between the two halves of the

0

10

20

30

40

50

60

70

80

90

100

0.00010.0010.010.1

Diameter, mm

Per

cen

tage

of

Pass

ing b

y w

eigh

t %

Fig.1: Grain size distribution curve from hydrometer test for the tested

sample.

- 117 -

shear box with dimensions 6×6×6 cm. Measurements of shear load and

normal displacement are recorded. From the results, the shear strength

parameters of soft clay can be determined as show in Figs. (3-3 through

3-5). The modulus of elasticity (Es) of tested clay soils at different water

content were also calculated from the direct shear box test results as

initial tangent in order to be used in finite element analysis (Table 3.3).

3.2.3.2 Consistency Limits

Consistency limits tests were performed on the soft clay to determine

Liquid limit, Plastic limit, Plasticity index and consistency index of the

soft clay. The results of these tests were presented in Table (3.3). Figure

(3-2) indicated the classification of the soft clay according to united soil

classification system (USCS) as clay with low plasticity (CL).

Table (3.3): Properties of used soil.

Property Soil A Soil B Soil C

Water content 19% 25% 33%

Bulk Density kN/m3 17.8 17.3 16.5

Liquid limit (LL) 41%

Plastic limit (PL) 17%

Plasticity index (Ip) 24%

Consistency index (Ic) 6%

Cohesion (cu) kN/m2 30 20 10

Angle of internal friction (ϕ ) 0 0 0

Modulus of elasticity (Es) kN/m2 6000 4000 2000

- 118 -

Fig. (3-2): Classification of soft clay using plasticity chart.

Fig. (3-3): Relation between normal stress and shear strength

(cu =10 kPa).

0

5

10

15

20

0 20 40 60 80 100 120

Normal stress, kN/m2

Sh

ea

r s

tren

gth

, k

N/m

2

- 119 -


(cu =20 kPa).

0

10

20

30

40

0 20 40 60 80 100 120


Sh

ea

r s

tren

gth

, k

N/m

2

0

20

40

60

0 20 40 60 80 100 120


Sh

ea

r s

tren

gth

, k

N/m

2


(cu =30 kPa).

- 120 -

3.2.3.3 Consolidation tests

After the mixing process, the tested soils ( A, B and C) were prepared to

the desired density and placed in consolidation rings, (75 mm) in

diameter and (19 mm) in height, to be tested by odometer cell. All the

performed tests were done according to (ASTM) specifications, at

different three clay water content and density. The test results of the

odometer tests carried out on the three samples were shown in the Fig.

(3-6). The obtained compressibility parameters were also given in Table

(3.4)

0.1

0.6

1.1

1.6

2.1

2.6

3.1

10 100 1000

Pressure, kPa

Cu = 10 kPa

Cu = 20 kPa

Cu = 30 kPa

Fig. (3-6): e-log p curve for tested soft clay in odometer.

- 121 -

Table (3.4) Consolidation properties of tested soft clay

Property Soil A Soil B Soil C

Saturated density (γsat) kN/ m3 17.8 17.3 16.5

Compression index Cc 0.78 0.65 0.57

Re-Compression index Cr 0.09 0.072 0.064

pc, kN/ m2 70 100 85

3.3 Sand

The sand bed layer was underline the soft clay deposit and consists of

300 mm thickness. Sieve analysis test was performed on a sample of

sand soil; the result is presented in Fig. (3-5). Sand was classified as

poorly graded sand (PS) according to Unified soil classification system

(USCS).

Direct shear test was also performed on samples of sand to get the shear

strength parameters of tested sand at maximum dry density that obtained

from modified proctor test as shown in Fig.(3-6) (dmax = 1.83kN/m3)

and the OMC = 6.7%. While Fig. (3-7) indicates the relation between

normal stress and shear strength for sand samples. From figure cohesion

c = 0.0 and angle of internal friction ϕ =38°. The module of elasticity of

the tested sand (initial tangent modulus for stress strain curve) is found

to be 80000 kN/m2. The main properties of the tested sand are presented

in Table (3.5)

- 122 -

Table (3.5) Physical and mechanical properties of tested sand

Property Value

Specific gravity 2.65

Maximum dry density d max (kN/m3) 18.3

Min dry density - loose case d min (kN/m3) 15.6

Relative density Dr for Max. density 80%

Uniformity coefficient Uc 26

Coefficient of curvature Cc 4.20

Middle size D50% 0.313

Max. shear angle dir 38o

Min. shear angle dir 27o

Modulus of elasticity (kN/m2) 80000

Coefficient of permeability K (cm/sec) 3.2 x 10-2

0

10

20

30

40

50

60

70

80

90

100

0.001 0.01 0.1 1 10 100

Diameter, mm

Percen

t o

f p

ass

ing

%

Silt fraction Sand fraction

Fine Mdium Coarse

Gravel fraction

Fine Medium CoarseClassification

Fig. (3-7): Sieve analysis curve for used sand

sand.

- 123 -

17

17.5

18

18.5

19

19.5

5 5.5 6 6.5 7 7.5 8 8.5 9

(Dry

de

nsi

ty a

s kN

/m3

)

water content as weight percent Wc%

Chart Title

0

20

40

60

80

100

0 20 40 60 80 100 120


Sh

ea

r s

tren

gth

, k

N /

m2

Fig. (3-9): Relation between normal stress and shear strength (for

tested sand at maximum dray density).

Fig. (3-8): Compaction curve for tested sand.

- 124 -

3.4 Columns materials Properties

The materials of column used in the experimental program to improve

the soft clay were stone. The main properties of the adopted aggregate

materials were described in the following sections:

3.4.1 Stone /Aggregate

Sieve analysis test was performed on a sample of adopted stone. The

results were presented in Fig. (3-10). The classification of stone was

poorly graded stone (PS) according to Unified soil classification system

(USCS). The size of grains in range of 2 to 10mm. the uniformity

coefficient and coefficient of curvature are found to be 2.61 and 1.5

respectively.

Direct shear test was also performed on samples of stone to get the shear

strength parameter of the stone at maximum dry density. Where the

obtained maximum dry density from proctor test is (dmax = 1.73kN/m3)

and the OMC = 4.1%.

Fig. (3-11) shows the relation between normal stress and shear strength

for stone samples. It can be concluded that the angle of internal friction

of such tone is 42°.

In general, the main characteristics of the adopted aggregate were agree

with those obtained by Ambily and Gandhi., (2007).

- 125 -

Fig. (3-10): Sieve analysis curve for used stone.

0

10

20

30

40

50

60

70

80

90

100

0.001 0.01 0.1 1 10 100

Diameter, mm

Perc

en

t o

f p

ass

ing

%

Silt fraction Sand fraction

Fine Mdium Coarse

Gravel fraction

Fine Medium CoarseClassification

Chart Title

0

20

40

60

80

100

0 20 40 60 80 100 120


Sh

ea

r s

tren

gth

, k

N /

m2

Fig. (3-11): Relation between normal stress and shear strength for used

stone.

- 126 -

3.5 Test Setup

3.5.1 Loading Frame

Fig. (3-12) shows the experimental set up

Fig. (3-12) Experimental setup.

- 127 -

3.5.1.1 Loading Jack

A hydraulic jack with maximum load capacity of 10 ton was used in all

test

3.5.1.2 Measuring Devices

The following devices were used in testing:

• Calibrated proving ring of 50 kN

• Dial gauge of 0.01mm accuracy and total capacity of 50 mm are used

for settlement measurements

3.5.2 Test Tank

The model tests were carried out in a cylindrical tank manufactured of

steel with dimensions of 600 mm in diameter and 800 mm in height,

made of steel (6 mm in thickness). The test tank is sufficiently rigid and

exhibited no lateral deformation during the tests. The thickness of soil

bed inside the container was 300 mm sand and 400 mm soft clay.

3.5.3 Loading plate

A rigid steel plate with a diameter of 600 mm and a thickness of 12 mm

was used as a loading plate on the entire area including stone column

and the surrounding soil.

3.6 Soft Clay Preparation

Oil is applied to the tank wall to minimize the friction between clay and

tank wall with out figure. The Required quantity of clay is mixed with

the required moisture content. Then the mixture is poured in the tank up

to predetermine depth at studied water content and density. Care was

taken to ensure that no significant air voids are formed in the test bed. At

- 128 -

the center of the prepared clay bed, vane Shear test is carried out to

measure the shear strength of the clay bed.

3.7 Test Procedures

3.7.1 Column Installation

In this part of study the methods of installation and preparation of stone

column model in the laboratory is adopted as follows.

Figures (3-14) and (3-15) show the lay out of installation steps for the

two cases of floating and end bearing stone column respectively.

Same installation procedures are shown in Fig. (3-13)

Fig. (3-13): Column Installation.

(b) Hammer was used to

compact the stone.

(c) The pipe is completely

removed.

(a) The soft clay layer is

placed around the

tube.

- 129 -

(a) (b) (c)

(d) (e) (f)

Fig. (3-14): Lay out of installation steps for the case of floating stone column

(a) Installation of sand bed and soft clay layer below the floating stone column at predetermined

depth.

(b) Installation of a PVC pipe as a floating at the predetermined depth.

(c) Then placing the soft clay layer around the pipe in layers each 50 mm for full depth.

(d) Installation of aggregate in layers each 50 mm to achieve the maximum density using manual

hammer.

(e) After installation of column aggregate, the tube was carefully removed.

(f) Finally, the loading plate was placed and the test load was applied.

- 130 -

(a) (b) (c)

(d) (e)

Fig. (3-15): Lay out of installation steps for the case of fully penetrate stone

column (a) Installation of sand bed and placing the PVC tube at predetermined depth.

(b) Then placing the soft clay layer around the pipe in layers each 50 mm for full depth.

(c) Installation of aggregate in layers each 50 mm to achieve the maximum density using manual

hammer.

(d) After installation of column aggregate, the tube was carefully removed.

(e) Finally, the loading plate was placed and the test load was applied.

- 131 -

3.8 The Experimental Program

The experimental program consists of 51 tests as shown in Table (3.6)

• All the tests were performed using constant circular plate diameter of

600 mm. Fig. (3-16) shows the general lay out of the investigated

parameters.

Diameter of the tank is taken as the diameter of the area of zone of

influence around single stone column. Stone column diameter used for

the test is varied from 50 mm to 300 mm. In the tank, clay is placed for a

height of 400 mm in which the stone column is installed at the center. A

sand layer of 30 mm thick is placed under soft clay layer. Vertical load

is applied either over the entire tank area.

Fig. (3-16): General lay out of the studied parameters.

- 132 -

Table (3.6): Experimental program and studied parameters.

series Studied parameters

1 Without stone column cu = 10, 20 and 30kPa

2

c u =

10 k

Pa

D = 50 mm L/D = 2 ,4 , 6 , 8

L/H = 0.25,0.5,0.75,1.0

D = 100 mm L/D = 1 , 2 , 3 , 4

L/H = 0.25,0.5,0.75,1.0

D = 150 mm L/D = 0.67, 1.33 , 2.0 ,2.67

L/H = 0.25,0.5,0.75,1.0

D = 300 mm L/D = 0.33, 0.67, 1 , 1.33

L/H = 0.25,0.5,0.75,1.0

3

c u =

20 k

Pa

D = 50 mm L/D = 2 ,4 , 6 , 8

L/H = 0.25,0.5,0.75,1.0

D = 100 mm L/D = 1 , 2 , 3 , 4

L/H = 0.25,0.5,0.75,1.0

D = 150 mm L/D = 0.67, 1.33 , 2.0 ,2.67

L/H = 0.25,0.5,0.75,1.0

D = 300 mm L/D = 0.33, 0.67, 1 , 1.33

L/H = 0.25,0.5,0.75,1.0

4

c u =

30 k

Pa

D = 50 mm L/D = 2 ,4 , 6 , 8

L/H = 0.25,0.5,0.75,1.0

D = 100 mm L/D = 1 , 2 , 3 , 4

L/H = 0.25,0.5,0.75,1.0

D = 150 mm L/D = 0.67, 1.33 , 2.0 ,2.67

L/H = 0.25,0.5,0.75,1.0

D = 300 mm L/D = 0.33, 0.67, 1 , 1.33

L/H = 0.25,0.5,0.75,1.0

D is the stone column diameter and L the stone column length.

H is the clay thickness (constant during all tests and equal to 400mm).

Chapter (4):

EXPERIMENTAL TEST RESULTS

- 133 -

CHAPTER (4)

EXPERIMENTAL TEST RESULTS

4.1 Introduction

This chapter concerned with the analysis and discussion of the test

results of the problem under investigation. In this study, experiments

were carried out in the laboratory on scaled down models of single stone

columns formed in soft clay beds. The effects of different factors on the

behaviour of the column were investigated. These factors include the

diameter, length of the column and undrained shear strength of tested

soft clay. Around 12% of the tests in each series were repeated for

verification of results and reproducibility.

The main focus in this chapter is a comparison between behaviour of the

soft clay soil with and without stone column. In order to bring out their

relative performances, single stone columns were formed at the centre of

soft clay beds independently and load tested using circular steel plate as

model footing which resting on total area of column and surrounding

soil. Tests were conducted by varying all these parameters. Tests thus

conducted have shown very consistent results. Results of the tests are

presented and discussed in this chapter. This chapter brings out the

influences of the above mentioned parameters on the improvement of

load carrying capacity of stone columns. The improvement in strength of

columns is correlated with the shear strength of the soil, which is one of

the basic factors for designing the stone column. In addition to the

percentage reduction on settlement for investigated stone columns at

different parameters are discussed in details

- 134 -

4.2 Definition of the Failure Load

In general, load–displacement curves of shallow foundations can exhibit

any one of the three shapes shown in Fig. (4-1) (Hirany and Kulhawy

1989). The peak of curve A and the asymptote of curve C give the

maximum resistance of the foundations for dense sand and stiff clay.

However, load– displacement curves for soft clay and loose sand often

resemble curve B. In this research the load–displacement curves take the

form of curve B in Fig. (4-1) and the ultimate load (Pu) is defined as the

load at 25.0 mm settlement as recommended by Bowels (1996).

Fig. (4-1): Typical load–displacement curves (Hirany and Kulhawy, 1989).

- 135 -

4.3 Effect of Stone Column Diameter

Figure (4-2) shows the horizontal and vertical cross-sectional areas of

the loading configuration with the varying column diameters considered

in this study. The column diameter varied between 50 and 300 mm

within the unit cell, and the column length was varyied from 100 mm to

400 mm.

Fig. (4-2): Variation of the diameter D within the unit cell.

4.4 Effect of Stone Column Length

To study the influence of the variation of column length, floating and

end bearing stone columns were constructed and loaded individually

within the unit cell. All constructed columns had the same diameter.

- 136 -

However, the lengths of columns varied from 100 mm to 400 mm as

shown in Fig. (4-3). All columns were installed in soft clay bed with

undrained shear strength of 10 kPa, 20 kPa and 30 kPa and the

settlements were recorded.

Fig. (4-3): Geometry configurations for model tested stone column.

4.5 Improvement Factor, If (%)

• The percentage of load increase due to the increase of L/D ratio is

expressed as improvement factor, If (%) which can be calculated from

the following Equation:

.

..%

untr

untrtr

P

PPIf

Where:

Ptr. = Stress of treated soil at 25mm

Puntr. = Stress of untreated soil at 25 mm

(4.1)

- 137 -

4.6 Stone Column Treated Soft Clay Soil in the Case of

Undrained Shear Strength (cu) = 10 kPa

Figures (4-4 through 4-7) show the relationships between load (kN) and

settlement (mm), for different diameters of stone column (i.e., 50, 100,

150 and 300 mm), for different length of stone column (i.e., 100, 200,

300 and 400 mm), respectively.

Referring to Figs. (4-4 through 4-7), the following observations may be

drawn:

• At 10 mm settlement and at 25 mm settlement, the stress increases as

the diameter of stone columns increases.

• At 10 mm settlement and at 25 mm settlement, the stress increases as

the length of stone columns increases.

The improvement factor, (If) increases due to the increase of column's

diameters as calculated by Eq. (4.1) and tabulated in tables (4.1 through

4.4)

For all stone columns, the settlement increased gradually with the

increase in the applied stress. However, the rate of increase in settlement

decreased with the increase of the column diameter. This shows that

larger columns with larger diameters can withstand higher loads.

- 138 -

Table (4.1): The percentage of load increase due to the increase of

columns diameter 50 mm and cu = 10 kPa.

Column

Diameter

(mm)

Type of

Column

L/H

L/D

At 10 mm settlement At 25 mm settlement

Load

(kN)

Improvement

factor, If (%)

Load

(kN)

Improvement

factor, If (%)

No column (untreated ) 2.86 - - 5.13 - -

50

Floating 0.25 2.0 4.24 48.15 8.84 72.41

Floating 0.50 4.0 4.77 66.67 9.76 90.34

Floating 0.75 6.0 6.01 89.77 10.9 113.79

End Bearing 1.00 8.0 7.42 109.88 13.4 162.07

0

5

10

15

20

25

30

35

40

0 7 14 21 28 35Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00

Fig. (4-4): Stress settlement curves for different stone columns L/H

ratios (D = 50 mm, cu = 10 kPa).

- 139 -


columns diameter 100 mm and cu =10 kPa.

Column

Diameter

(mm)

Type of

Column

L/H

L/D


Load

(kN)

Improvement

factor, If (%)

Load

(kN)

Improvement

factor, If (%)


100

Floating 0.25 1.0 5.41 88.89 9.90 93.10

Floating 0.50 2.0 5.90 106.17 12.0 134.84

Floating 0.75 3.0 6.89 140.74 12.8 148.97

End Bearing 1.00 4.0 9.40 228.40 16.3 217.24

0

5

10

15

20

25

30

35

40

0 7 14 21 28 35Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00



- 140 -





Column

Diameter

(mm)

Type of

Column

L/H

L/D


Load

(kN)

Improvement

factor, If (%)

Load

(kN)

Improvement

factor, If (%)


150

Floating 0.25 0.15 5.90 106.17 11.2 118.63

Floating 0.50 1.33 6.47 125.93 13.1 155.86

Floating 0.75 2.0 8.02 180.25 14.8 189.66

End Bearing 1.0 2.67 9.72 239.51 17.9 248.28

0

5

10

15

20

25

30

35

40

0 7 14 21 28 35

Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00

- 141 -



Column

Diameter

(mm)

Type of

Column

L/H

L/D


Load

(kN)

Improvement

factor, If (%)

Load

(kN)

Improvement

factor, If (%)


300

Floating 0.25 0.33 7.50 161.73 13.9 171.72

Floating 0.50 0.67 9.72 239.51 5.35 268.97

Floating 0.75 1.0 12.4 332.10 18.9 334.48

End Bearing 1.0 1.33 17.5 511.11 31.6 517.24

0

5

10

15

20

25

30

35

40

0 7 14 21 28 35Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00



- 142 -

4.6.1 Improvement in the Ultimate Load Capacity of the

Stone Column Treated Soft Clay


increase in the applied stress as shown in Figs. (4-4 through 4-7).

However, the rate of increase in settlement decreased with the increase

of the column diameter. This shows that larger columns can withstand

higher compressive loads. The improvement factor for column diameters

of 100 mm, 150 mm and 300 mm to that of the 50 mm column diameter

respectively is graphically shown in Fig. (4-8) It can be inferred that

when the diameter of the stone column in the base soil increases by 2, 3

and 6 times of its initial diameter, its load carrying capacity are

approximately 1.34, 1.53 and 3.2 times higher than the initial strength

respectively.

0

100

200

300

400

500

600

0 100 200 300 400 500

Stone column Length, L(mm)

Im

pro

vem

en

t F

acto

r,

I f (

%)

D = 50 mm

D = 100 mm

D = 150 mm

D = 300 mm

Fig. (4-8): The effect of column length on the improvement factor,

If (%) at different diameters for 25 mm settlement (cu = 10 kPa).

- 143 -

It has been found that the increase of stone column diameter leads to

significant increase on the ultimate capacity of stone column. It is also

found that, at (L = 400 mm), the increase of stone column diameter from

50 to 100 mm increased the ultimate capacity of stone column by

(34.04 %). While for stone column diameter of 300 mm, the ultimate

load capacity is increase by 2.20 times of stone column with diameter 50

mm.

On the other hand, Figs. (4-9 through 4-12) shows the effect of column

diameters on the percentage of load increase, the effect of L/D ratio on

the percentage load increase, the effect of L/D ratio on the improvement

factor, If (%) for different L/H ratio and the effect of L/H ratio on the

improvement factor, If (%) for different diameters at 25 mm settlement

respectively.

- 144 -

Fig. (4-10): The effect of L/D ratio on the improvement factor,If (%)

at 25 mm settlement (cu = 10 kPa).

0

100

200

300

400

500

600

0 100 200 300 400

Stone Column Diameter, D(mm)

Im

pro

vem

ent

Fa

cto

r, I

f (%

)

L = 100 mm

L = 200 mm

L = 300 mm

L = 400 mm

0

100

200

300

400

500

600

0 2 4 6 8 10 L/D

Im

prov

emen

t F

acto

r, I

f (%

)

D=50 mm

D=100 mm

D=150 mm

D=300 mm

Fig. (4-9): The effect of column diameters on the improvement

factor, If (%) for different lengths at 25 mm settlement (cu = 10 kPa).

- 145 -

0

100

200

300

400

500

600

0 2 4 6 8 10 L/D

Im

pro

vem

ent

Fa

cto

r, I

f (%

)

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.0

0

100

200

300

400

500

600

0 0.25 0.5 0.75 1 1.25 L/H

Im

prov

emen

t F

acto

r, I

f (%

)

D=50 mm

D=100 mm

D=150 mm

D=300 mm

Fig. (4-11): The effect of L/D ratio on the improvement factor, If (%)

for different L/H ratio at 25 mm settlement (cu = 10 kPa).

Fig. (4-12): The effect of L/H ratio on the improvement factor, If (%)

for different diameters at 25 mm settlement (cu = 10 kPa).

- 146 -



Figures (4-13 through 4-16) show the relationships between load (kN)

and settlement (mm), for different diameters of stone column (i.e., 50,

100, 150 and 300 mm), for different lengths of stone column (i.e., 100,

200, 300 and 400 mm), respectively.

The percentage of load increase due to the increase of columns

diameters are calculated by Eq. (4.1) and tabulated in table (4.5 through

4.8)


increase in the applied load. However, the rate of increase in settlement

decreased with enlargement of the column size. This shows that columns

with larger diameters can withstand higher loads.

- 147 -



Column

Diameter

(mm)

Type of

Column

L/H

L/D


Load

(kN)

Improvement

factor, If (%)

Load

(kN)

Improvement

factor, If (%)


50

Floating 0.25 2.0 9.19 52.94 18.2 63.17

Floating 0.50 4.0 10.6 76.47 19.8 77.78

Floating 0.75 6.0 11.7 94.12 22.1 98.41

End Bearing 1.00 8.0 15.7 161.76 27.4 146.03

0

5

10

15

20

25

30

35

40

0 14 28 42 56 70Stress, kPa

Sett

lem

en

t, m

m

No column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00



- 148 -





Column

Diameter

(mm)

Type of

Column

L/H

L/D


Load

(kN)

Improvement

factor, If (%)

Load

(kN)

Improvement

factor, If (%)


100

Floating 0.25 1.0 9.83 63.53 19.6 76.19

Floating 0.50 2.0 12.0 100.0 23.4 110.16

Floating 0.75 3.0 14.3 138.24 25.9 133.33

End Bearing 1.00 4.0 18.0 200.0 32 187.30

0

5

10

15

20

25

30

35

40

0 14 28 42 56 70

Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00

- 149 -





Column

Diameter

(mm)

Type of

Column

L/H

L/D


Load

(kN)

Improvemen

t factor, If

(%)

Load

(kN)

Improvement

factor, If (%)


150

Floating 0.25 0.15 11.8 97.06 22.6 103.17

Floating 0.50 1.33 13.3 120.59 26.5 138.10

Floating 0.75 2.0 16.4 173.53 30.2 171.42

End Bearing 1.00 2.67 21.9 264.70 37.65 238.10

0

5

10

15

20

25

30

35

40

0 14 28 42 56 70Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00

- 150 -





Column

Diameter

(mm)

Type of

Column

L/H

L/D


Load

(kN)

Improvement

factor, If (%)

Load

(kN)

Improvement

factor, If (%)


300

Floating 0.25 0.33 15.0 150.0 28.1 152.38

Floating 0.50 0.67 19.1 217.65 37.5 236.50

Floating 0.75 1.0 24.4 305.88 45.3 306.35

End Bearing 1.00 1.33 34.7 477.65 63.1 466.67

0

5

10

15

20

25

30

35

40

0 14 28 42 56 70

Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00

- 151 -



The ratio of the load carrying capacities for column diameters of 100

mm, 150 mm and 300 mm to that of the 50 mm column diameter

respectively is graphically shown in Fig. (4-17) It can be inferred that

when the diameter of the stone column in the base soil increases by 2, 3

and 6 times of its initial diameter, its load carrying capacity are

approximately 1.28, 1.63 and 3.19 times higher than the initial strength

respectively.

It has been found that the increase of stone column diameter leads to

significant increase on the ultimate capacity of stone column. It is also

found that, at (L = 400 mm), the increase of stone column diameter from

50 to 100 mm increased the ultimate capacity of stone column by

(28.08 %). While for stone column diameter of 300 mm, the ultimate

load capacity is increase by 3.19 times of stone column with diameter 50

mm.

- 152 -



the percentage load increase, the effect of L/D ratio on the improvement



respectively.

0

100

200

300

400

500

600

0 100 200 300 400 500

Stone Column Length, L(mm)

I

mp

ro

vem

en

t F

acto

r,

I f (

%)

D = 50 mm

D = 100 mm

D = 150 mm

D = 300 mm

Fig. (4-17): The effect of total column lengths on the improvement

factor, If (%) for different diameters at 25 mm settlement (cu = 20 kPa).

- 153 -

]

0

100

200

300

400

500

600

0 100 200 300 400


Im

pro

vem

en

t F

acto

r,

I f (

%)

L = 100 mm

L = 200 mm

L = 300 mm

L = 400 mm

0

100

200

300

400

500

600

0 2 4 6 8 10L/D

Im

pro

vem

en

t F

acto

r,

I f (

%)

D = 50 mm

D = 100 mm

D = 150 mm

D = 300 mm

Fig. (4-18): The effect of column diameters on the improvement factor,

If (%) for different lengths at 25 mm settlement (cu = 20 kPa).


at 25 mm settlement (cu = 20 kPa).

- 154 -

0

100

200

300

400

500

600

0 2 4 6 8 10L/D

Im

pro

vem

en

t F

acto

r,

I f (

%)

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.0

0

100

200

300

400

500

600

0 0.25 0.5 0.75 1 1.25

L/H

Im

pro

vem

en

t F

acto

r,

I f (

%)

D = 50 mm

D = 100 mm

D = 150 mm

D = 300 mm





- 155 -



Figures (4-22 through 4-25) show the relationships between load (kN)

and settlement (mm), for different diameters of stone column (i.e., 50,

100, 150 and 300 mm), at different lengths of stone column (i.e., 100,

200, 300 and 400 mm), respectively.

The percentage of load increase due to the increase of columns

diameters are calculated by Eq. (4.1) and tabulated in table (4.18 through

4.21)

- 156 -



Table (4-9): The percentage of load increase due to the increase of


Column

Diameter

(mm)

Type of

Column

L/H

L/D


Load

(kN)

Improvement

factor, If (%)

Load

(kN)

Improvement

factor, If (%)


50

Floating 0.25 2.0 13.6 63.83 24.1 50.55

Floating 0.50 4.0 16.1 93.62 30.2 88.74

Floating 0.75 6.0 18.0 117.02 33.6 109.71

End Bearing 1.00 8.0 23.7 185.53 41.7 160.50

0

5

10

15

20

25

30

35

40

0 21 42 63 84 105

Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00

- 157 -





Column

Diameter

(mm)

Type of

Column

L/H

L/D


Load

(kN)

Improvement

factor, If (%)

Load

(kN)

Improvement

factor, If (%)


100

Floating 0.25 1.0 14.8 78.72 29.3 83.22

Floating 0.50 2.0 18.0 117.02 35.2 120.09

Floating 0.75 3.0 20.9 152.34 39.2 145.03

End Bearing 1.00 4.0 27.9 236.60 48.8 204.63

0

5

10

15

20

25

30

35

40

0 21 42 63 84 105Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00

- 158 -





Column

Diameter

(mm)

Type of

Column

L/H

L/D


Load

(kN)

Improvement

factor, If (%)

Load

(kN)

Improvement

factor, If (%)


150

Floating 0.25 0.15 18.0 117.02 34.0 112.36

Floating 0.50 1.33 19.8 138.30 39.6 147.24

Floating 0.75 2.0 24.0 189.36 45.3 182.56

End Bearing 1.00 2.67 32.4 289.79 55.9 248.79

0

5

10

15

20

25

30

35

40

0 21 42 63 84 105

Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00

- 159 -



Column

Diameter

(mm)

Type of

Column

L/H

L/D


Load

(kN)

Improvement

factor, If (%)

Load

(kN)

Improvement

factor, If (%)


300

Floating 0.25 0.33 22.45 170.21 41.47 158.94

Floating 0.50 0.67 28.99 248.40 56.35 251.88

Floating 0.75 1.0 36.77 342.55 68.76 329.36

End Bearing 1.00 1.33 51.79 523.40 93.33 482.78

0

5

10

15

20

25

30

35

40

0 21 42 63 84 105Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00

Fig. (4-25): Stress settlement curves for different stone columns

L/D ratios (D = 300 mm, cu = 30 kPa).

- 160 -





the improvement factor, the effect of L/D ratio on the improvement



respectively.

Fig. (4-26): The effect of column length on the improvement factor,

If (%) for different diameters at 25 mm settlement.

0

100

200

300

400

500

600

0 100 200 300 400 500

Stone Column Length, L(mm)

Imp

rov

emen

t F

act

or,

If

(%)

D = 50 mm

D = 100 mm

D = 150 mm

D = 300 mm

- 161 -

0

100

200

300

400

500

600

0 100 200 300 400


Im

pro

vem

ent

Fa

cto

r, I

f (%

) L = 100 mm

L = 200 mm

L = 300 mm

L = 400 mm

0

100

200

300

400

500

600

0 2 4 6 8 10

L/D

Im

prov

emen

t F

acto

r, I

f (%

)

D = 50 mm

D = 100 mm

D = 150 mm

D = 300 mm

Fig. (4-28): The effect of L/D ratio on the improvement factor, If

(%) at 25 mm settlement (cu = 30 kPa).

Fig. (4-27): The effect of column diameter on the improvement factor,

If (%) for different lengths at 25 mm settlement.

- 162 -

0

100

200

300

400

500

600

0 2 4 6 8 10L/D

Im

pro

vem

ent

Fa

cto

r, I

f (%

)

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.0

0

100

200

300

400

500

600

0 0.25 0.5 0.75 1 1.25

L/H

Im

pro

vem

ent

Fa

cto

r, I

f (%

)

D = 50 mm

D = 100 mm

D = 150 mm

D = 300 mm





- 163 -

4.9 Behavior of end bearing stone column

Figs. (4-31 through 4-33) shows the variations of load settlement curve

for stone column fully penetrate as end bearing case.

It is observed that the increase of undrained shear strength provided a

higher confinement for stone columns as a result the ultimate load

capacity is increased with remarkable reduction in settlement.

Fig. (4-31): Stress settlement curves for end bearing stone columns

at different diameters and cu = 10 kPa.

0

5

10

15

20

25

30

35

40

0 21 42 63 84 105Stress, kPa

Sett

lem

en

t, m

m

No column

D = 50 mm

D = 100 mm

D = 150 mm

D = 300 mm

- 164 -

Fig. (4-32): Stress settlement curves for end bearing stone column at

different diameters of and cu = 20 kPa.

0

5

10

15

20

25

30

35

40

0 21 42 63 84 105Stress, kPa

Sett

lem

en

t, m

m

No column

D = 50 mm

D = 100 mm

D = 150 mm

D = 300 mm

0

5

10

15

20

25

30

35

40

0 21 42 63 84 105Stress, kPa

Sett

lem

en

t, m

m

No Column

D = 50 mm

D = 100 mm

D = 150 mm

D = 300 mm

Fig. (4-33): Stress settlement curves for end bearing stone column at

different diameters of and cu = 30 kPa.

- 165 -

4.9.1 Bulging responses of end bearing stone columns

At the end of each experimental test, the failed stone column was

carefully examined to study the deformed shape by pouring a cement

slurry into the failed stone column, Fig (4-34) and allowing to set for

about 24 hours, Fig (4-35) and the deformed shape was examimed by

scooping the surrounding soil carefully. The resulted shape of the

deformed stone column was observed as shown in Fig. (4-36 & 4-37).

As can be seen in Fig. (4-38) the deformation was more prominent in the

upper part of the column over a length of about 2.5D. The maximum

radial expansion of the column diameter was observed at (1.25-1.5D)

approximately below the top surface of the failed column.

Fig. (4-34): Pouring cement slurry into the stone column to maintain

the shape of the resulting deformation.

- 166 -

Fig. (4-35): Separation of stone column from surrounding soil

after 24 hours

Fig. (4-36): Shape of stone column after removing it from the

surrounding soil.

- 167 -

Fig. (4-37): Deformed shape of stone column.

0

1

2

3

4

0 100 200 300 400 500 600

Diameter, mm

L/D

Before testing

After testing

Fig. (4-38): Stone column shape before and after testing (cu = 10 kPa).

- 168 -

The variations of radial expansion of the four end bearing stone columns

which diameter 50mm, 100mm,150mm and 300mm are shown in Fig.

(4-39 through 4-42). In general, the radial deformation of the columns

increased with depth, reaching its maximum value at a depth of

approximately 1.25D for diameter 50 mm ,100 mm and 150 mm

respectively, while it is found to be 1.5D in case of diameter of 300 mm

. The bulging effect was mainly observed up to an approximate depth of

2.5D. It was evident that the horizontal displacement increased with

applied pressure for all cases since the greater the applied pressure, the

bigger the column bulging. All these findings confirm the observations

made in earlier studies reporting that end bearing fail by bulging.

Fig. (4-39): Variation of the horizontal deformation for end bearing loading

condition for different undrained shear strength values, cu (D = 50 mm).

- 169 -





- 170 -



Chapter (5):

NUMERICAL MODELING

- 171 -

CHAPTER (5)

NUMERICAL MODELING

5.1 Introduction

The Finite Element Method has been applied to Geotechnical

Engineering problems since 1960. It has developed a decade earlier for

applications in Structural Engineering and continuum mechanics. The

name finite element was, however, first coined in a paper by Clough

(1960), in which the technique was presented for plane stress analysis.

Since then, a large amount of research has been devoted to this

technique and a number of research papers and text books have been

published on this subject. The method is now firmly established as an

engineering tool of wide applicability. The main advantage of the

method is that it can be applied to the materials exhibiting non-linear

stress-strain behavior. In the current research the finite element program

of PLAXIS has been used.

Implementation of various constitutive relationships into finite element

method facilitated the study of numerous problems in geotechnical

Engineering. Finite element procedure is a powerful tool that can

analyze problems incorporating non uniform geometry and complicated

boundary conditions. In this chapter, PLAXIS 2D, version 8.2

axisymmetric finite element models were used to compare between

results of experimental work and contain a brief description of the finite

element method for the problem under investigation. The different

constitutive laws in Geomechanics and the utilized material models

formulations are illustrated. Also, the numerical models used in these

- 172 -

studies are discussed in detail. In addition to the experimental analysis

and case studies were verified using the numerical program PLAXIS V

8.2. The parameters that cannot be investigated in the laboratory were

studied by the program.

5.2 Finite Element Modeling Program Used in This

Research

5.2.1 Input Program

In the Input program of the PLAXIS the geometry of the problem is

given by entering different soil layers, structural parts, external loads,

etc. a choice between various available material models, such as Mohr-

Coulomb, Hardening soil, etc., is made at the input for each material.

The material is given relative material properties, such as stiffness and

density, which differs according to the used material model. Appropriate

boundary conditions are then assigned to the whole model. When the

model is complete, a mesh is automatically generated and initial stress

and pore water pressure are initiated before moving to the Calculation

program.

5.2.1.1 Soil Element

During generation of the mesh, soil clusters are divided into triangular

elements. Plaxis provides two types of triangular elements, 6-nodes

elements and 15-nodes elements, as shown in Figure (5-1). During the

finite element calculations, displacements are calculated at those nodes.

On other hand, stress is calculated at individual points called stress

- 173 -

points rather than at the nodes. A 15-nodes triangular element contains

12 stress points while a 6-nodes triangular element contains 3 stress

points. In this research a 15-nodes triangular element was used.

Fig. (5-1): Example distribution of nodes and stress points in

PLAXIS finite elements (PLAXIS version 8 manuals).

- 174 -

5.2.1.2 Types of Soil Behavior

An important feature of the soil is the presence of pore water. Pore water

pressure significantly influences the soil response. To enable

incorporation of the pore water influence in the soil response Plaxis

offers for each model a choice of three types of behavior:

1. Drained behavior where no excess pore water pressure is generated.

This behavior is used for dry soils and also for soil types providing full

drainage due to high permeability, as in sand, or due to low rate of

loading. This option can also be used to model the long-term behavior of

soil without the need to model the precise history of the undrained

loading and consolidation.

2. Undrained behavior in which a full development of excess pore water

pressure is present. This occurs when a soil has low permeability, as in

clay, or under a high rate of loading. The undrained behavior is usually

followed by consolidation in loading phases.

During this research the drained and undrained soil behavior was used in

simulating the soft clay layer. In all models the drained soil behavior

was used in simulating the stone columns and the sand layer as they

have high permeability.

- 175 -

The undrained shear strength of soil is calculated in according to

equation deduced from Fig. (5-2).

( +

(5.1)

5.2.1.3 Boundary Conditions

Boundary conditions are used to describe the fixities for the boundaries

of the problem geometry. In this research the boundary conditions were

set by fixing the vertical boundaries in the horizontal direction only (Ux

= 0) while allowing displacement to take place in the vertical direction;

while a fixation of both vertical and horizontal displacement (Ux = Uy =

0) for the lower horizontal boundary of the problem.

Fig. (5-2): Mohr’s circle of stress used to drive relation between undrained

shear strength and drained shear parameters (Brinkgreve, 2002).

- 176 -

5.2.1.4 Mesh Generation

Plaxis uses unstructured mesh, which is generated automatically with

options for global and local mesh refinement. Plaxis provides several

options of mesh density ranged from very coarse to very fine mesh. In

this research fine mesh size was chosen to model the soil deposit. Mesh

was then refined in zones which stresses and strains are expected to be

high i.e. the soil area surrounding the stone columns, the crust layer and

the embankment body. Fig. (5-3) showed the mesh generation and

geometry of the studied in the (PLAXIS 2D, version 8.2)

Fig. (5-3): Mesh refine in for the proposed model in stability analysis

in 2D PLAXIS program.

5.2.1.5 Initial Conditions

The initial stresses in a soil body are influenced by the weight of the

material and the history of its formation. This stress state is usually

- 177 -

characterized by an initial vertical effective stress (ơ'v). The initial

horizontal effective stress (ơ'h) is related to the initial vertical effective

stress by the coefficient of lateral earth pressure K0.

K0 procedure is a special calculation method available in PLAXIS to

define the initial stresses for the model, taking into account the loading

history of the soil.

In practice, the value of K0 for a normally consolidated soil is often

assumed to be related to the friction angle by Jacky‘s empirical

expression:

(5.3)

When the K0 procedure is adopted, PLAXIS will generate vertical

stresses that are in equilibrium with the self-weight of the soil.

Horizontal stresses are calculated from the specified value of K0

5.2.2 Calculation

After generation of finite element models, calculation can be executed.

Both calculation type and loading type has to be specified in this step.

5.2.2.1 Types of Calculations

Choose between different ways of analysis of the actual problem are

mode in the calculation program. Distinctions of the two types of

calculations were mentioned as follows:

- 178 -

1. Plastic calculation should be selected to carry out an elastic-plastic

deformation analysis in which it is not necessary to take excess pore

water pressure with time into account.

2. Consolidation analysis should be selected when it is necessary to

analyze the development or the dissipation of excess pore water pressure

in water-saturated clay-type soils as a function in time. Plaxis allows for

true elastic-plastic consolidation analyses.

In the current research consolidation analysis was used to be able to

detect the behavior of the stone column-soft soil settlement with time.

5.2.3 Output

When the calculations are completed the results can be viewed in the

output program. A large amount of data can be obtained from finite

element calculation such as stresses, pore water pressure and

displacements.

5.3 The Mohr Coulomb Model

The Mohr Coulomb model is an elastic perfectly plastic model. As

explained before in this chapter, the yield surface of the elastoplastic

model with perfect plasticity is a fixed surface. The yield surface of the

Mohr Coulomb model, as shown in Fig. (5-4), is fully defined by model

parameters and not affected by plastic straining. The Mohr Coulomb

model requires a total of five parameters, which are generally familiar to

most geotechnical engineers and which can be obtained from basic tests

on soil samples. These parameters are Young‘s modulus, E, Poisson‘s

- 179 -

ratio, ν, Friction angle, ϕ , Cohesion, c, and Dilatancy angle, ψ. These

parameters are briefly explained in the following part.

Fig. (5-4): Mohr-Coulomb yield criterion.

5.3.1 Young’s Modulus

Plaxis uses the young‘s modulus (E) as the basic stiffness in the elastic

model and the Mohr Coulomb model. A stiffness modulus has the

dimension of stress. The values of the stiffness parameter adopted in a

calculation require a special attention as many materials show nonlinear

- 180 -

behavior from the beginning of loading. For soils, the initial slope is

usually indicated as ( ), and secant modulus at 50 % strength is

donated ( ), as shown in Fig. (5-5). For materials with a large linear

elastic range it is realistic to use , but for loading of soils is

generally used.

Fig. (5-5): Definition of and for standard drained triaxial test

results (Brinkgreve, 2002).

The studied soft clay soils consist of a homogeneous soil underlain by a

dense sand layer. There are three samples of undrained and drained soft

clay soil types, which were considered in this research.

Bowles, 1996 introduced empirical formulae to calculate stiffness

parameters of clay soil.

- 181 -

A nonlinear analysis was assumed, so that (Es) represent a secant

modulus for low load level.

The Mohr-Coulomb model was considered to model elastic- plastic

behavior of sand soils. These parameters in this model are soil cohesion

(c), angle of internal friction (ϕ ) and soil dilatancy (ψ). Since we

considered sand soils in this study in the drained case, soil cohesion was

set to 1*10-3

kPa to avoid errors.

5.3.2 Poisson’s Ratio (υ)

The selection of a Poisson‘s ratio (υ) is particularly simple when the

elastic model or the Mohr Coulomb model is used for gravity loading.

For this type of loading Plaxis should give realistic ratios of

as both models will give the well-known ratio = υ/(1- υ) . For

one-dimensional compression it is easy to select Poisson‘s ratio that

gives a realistic value of ; hence, υ is evaluated by matching . In

many cases the value of Poisson‘s ratio is ranged between 0.3 and 0.4,

however, it is in the range of 0.5 in the case of undrained behavior.

5.3.3 Cohesion (c)

The cohesive strength has the dimension of stress. Plaxis can handle

cohesion-less soils (c = 0), but some options will not perform well.

Plaxis offers a special option of layers in which the cohesion increases

with depth.

- 182 -

5.3.4 Friction Angle (ϕ) The friction angle, ϕ is entered in degrees. The friction angle largely

determines the shear strength by means of Mohr‘s stress circle, as shown

in Fig. (5-6). The Mohr- Coulomb failure criterion proves to be better

for describing soil behavior than the Druker-Prager approximation, as

the latter failure surface tends to be highly inaccurate for axisymmetric

configurations.

Fig. (5-6): Mohr-Coulomb failure envelope with one Mohr failure

circle (Brinkgreve, 2002).

5.3.5 Dilatancy angle (ψ)

The dilatancy angle, ψ is specified in degrees. Apart from heavily over-

consolidated layers, clay soils tend to show little dilatancy (ψ = 0). The

dilatancy of sand depends on both the density and the friction angle. A

small negative value of ψ is only realistic for extremely loose sands.

- 183 -

5.4 The Hardening Soil Model

The Hardening Soil model is an advanced model used for the simulation

of soil behavior. In this study, the Hardening model was considered to

model elastic- plastic behavior of soft clay soil.

As for the Mohr-Coulomb model, limiting states of stress are described

by means of the friction angle (ϕ ), the cohesion (c) and the dilatancy

angle (ψ). However, soil stiffness is described much more accurately by

using three different input stiffness, such as: Plastic straining due to

primary loading in the standard drained triaxial test,

, the triaxial

unloading stiffness,

and Plastic straining due to primary

compression,

.

5.5 Numerical Model Verification

Two case studies were used for verification of the Finite Element

Models of the (2D PLAXIS, version (8.2) program as presented by

Ambily and Gandhi, (2007) and Narasimha Rao et al., (1992) in order to

confirm the program validity.

5.5.1 Validation Using (Ambily and Gandhi, 2007) Results

The numerical modeling has been validated using results reported by,

Ambily and Gandhi, (2007). In this analysis, soft clay and stone column

is modeled using Mohr-Coulomb criterion (linear elastic). To start with,

the model developed in PLAXIS 2D considering elastic-plastic response

is compared with this similar study.

- 184 -

Model developed by Ambily and Gandhi, 2007studies the behavior of

interior columns among a large group of columns. Here, interior column

was idealized as unit cell as shown in Fig. (5-7). They considered the

following cases.

1) Stone column loaded alone

2) Stone column and surrounding soil loaded together (sand pad is

provided on the top)

The input parameters used in PLAXIS analyses are given in Table (5.1).

The drained behaviour is considered for clay, stone column, and sand.

The simulation of unit cell model is initialized by applying initial

stresses in all materials using K0 procedure. To get equal vertical strain

condition, load is applied as prescribed displacement. Fine meshes

which are generated using 15-noded triangular elements and boundary

conditions for both the cases are shown in Fig. (5-8). Along the lateral

boundaries, radial deformation is restricted but vertical deformation is

allowed. Along the bottom boundary, radial and vertical deformations

are restricted. In this analysis, no interface element is used.

Bulk

density

(kN/m3)

Dry

density

(kN/m3)

Friction

Angle

ϕ

(Degree)

Dilatancy

Ψ

(Degree)

Cohesion

cu

(kN/m2)

Poisson's

ratio

υ

Deformation

Modulus

E

(kN/m2)

Materials

19.45 15.56 _ _ 30

0.42

5500 Soft

Clay

17 16.62 43 10

_

0.3 55000

Stone

16 15.50 30 4 _ 0.3 20000 Sand

Table (5.1): Details of material properties (Ambily and Gandhi, 2007).

- 185 -

Sand layer

Stone

Column

30 mm

450 mm

Soft Clay

100 mm

(a) Case of entire area loaded (b) Case of loaded column alone

Fig. (5-7): Finite-element discretization for both cases (Ambily and Gandhi, 2007).

- 186 -

Figure (5-8) shows deformed mesh at failure for both cases. In the case

of loaded column alone, bulging failure occurs with maximum bulging

at a depth of 0.5 times diameter of granular pile as was noticed in

Ambily and Gandhi‘s study. For the case of entire area loaded, no

bulging is observed and similar behavior reported in their analysis.

(a) Case of loaded column alone (b) Case of entire area loaded

Fig. (5-8): Deformed mesh for both cases (Ambily and Gandhi, 2007).

- 187 -

Based on the axial stress developed at the pile top and settlement

behaviour, for the case of stone column loaded alone, it can be observed

that stone column reaches a failure stage. Settlement behavior of stone

column with respect to axial stress is shown in Fig. (5-8). But for second

case, failure did not take place even for a large settlement of 35 mm and

it is in linear elastic range of loading. Figs. (5-9) and (5-10) show axial

loaded versus settlement behavior from numerical analysis reported by

Ambily and Gandhi, (2007) and PLAXIS analysis. The results from the

present analysis match well with the results obtained by Ambily and

Gandhi, (2007).

Fig. (5-9): Verification of are current plaxis results with the load

settlement behavior of loaded stone column alone (Ambily and

Gandhi, 2007).

0

4

8

12

16

20

24

0 125 250 375 500 625 750

Load, kN

Sett

lem

en

t, m

m

Plaxis result (current study)

Ambily and Gandhi, 2007

- 188 -


settlement behavior of entire loaded area (Ambily and Gandhi,

2007).

0

1

2

3

4

5

6

0 30 60 90 120 150 180

Load, kN

Sett

lem

en

t, m

m

Plaxis result (current study)

Ambily and Gandhi, 2007

- 189 -

5.5.2 Validation Using the Results Obtained by (Narasimha

Rao et al., 1992):

For more confirmation, the model used in this study was validated by

analyzing the load settlement behavior of a single stone column as

discussed by Narasimha Rao et al. (1992).

The test tank used in their experiment is 650 mm diameter and height of

clay bed is 350 mm. A stone column of diameter 25 mm and height 225

mm was made at the center of the clay bed and loaded with a plate of

diameter equal to two times the diameter of the stone column. Properties

of clay and stones are shown in Table 3. An axisymmetric analysis was

carried out using Mohr-Coulomb‘s criterion for clay and stones. The

finite-element discretization using 15-noded triangular elements with

boundary conditions is shown in Fig. (5-11).

Comparing the results obtained from the experimental model test

(Narasimha Rao et al., 1992) and those obtained from PLAXIS analysis,

it was found that both results are matching well and the load

displacement curve has the same trend for the two cases as can be seen

from Fig. (5-12).

- 190 -

(a) Model

(b) Mesh (c) Deformed mesh

Fig. (5-11): Finite-element discretization of model test (Narasimha

Rao et al., 1992).

- 191 -

Table (5.2): Details of material properties (Narasimha Rao et al.,

1992).

Bulk

density

(kN/m3)

Dry

density

(kN/m3)

Friction Angle

ϕ

(Degree)

Dilatancy

Ψ (Degree)

Cohesion

cu (kN/m

2)

Poisson's

ratio

µ

Deformation

Modulus

E

(kN/m2)

Materials

17

16.2

_

_

20

0.45

4000

Soft

Clay

18.9

18.2

38

8

_

0.3

45000

Stones

0

5

10

15

20

25

30

35

0 80 160 240 320 400 480

Load, kN

Sett

lem

en

t, m

m

Plaxis results (current study)

Narasimha Roa et al., 1992


settlement behavior (Narasimha Rao et al., 1992).

- 192 -

5.5.3 Verification for Experimental Work of Present Study

Input parameters that used in the FEM for problem under investigation

were obtained from basic laboratory tests as show in chapter 3.

Plaxis 2D, finite element analysis was carried out for natural clay and for

the same clay modified by single stone column (unit cell) under loading.

The modeling of single stone column is designed by axisymmetric

pattern in Plaxis. The different diameters and length of stone column

were applied for the analysis and the results were compared. The

axisymmetric unit cell was carried out using Mohr–Coulomb‘s and

hardening soil criterion. The studied model dimension was adopted as

shown in the labrtory model test. Figs. (5-13 and 5-14) show the finite

element model for the studied problem.

(a) Untreated soil model (b) Untreated soil mesh

Fig. (5-13): The model and the soil mesh for the case of untreated soil.

- 193 -

The results of finite element analysis for treated clay by single stone

column and untreated clay were compared the load–deformation results

with the laboratory model test results. The input parameters for clay and

stone column material and sand layer (unit weight, cohesion, elastic

modulus, angle of internal friction, Poisson ratio and dilatancy angle) are

given in table (5.3) and Hardening Soil Parameters for Soft Clay table

(5.4).

The numerical analysis were done using both Mohr Coulomb and

hardening soil criteria model. Where Fig. (5-15) shows the load

settlement curve for refer soft clay with stone column for case cu = 20

(a) Treated Soil Model (b) Treated Soil Mesh

Fig. (5-14): Unit cell stone column and unit cell stone column

mesh for the case of treated soil.

- 194 -

kPa , D = 150 mm and L = 300 mm . It has been found that there is

insignificant difference in the numerical result as shown in the relavent

figure for both Mohr Coulomb and Hardening models. It is also found

that the difference is around 5% for both adopted models.

For both Mohr Coulomb and hardening soil it has been found that the

numerical results of both model has the same trend. Therefore the

Mohr Coulomb model was used in the present research due to its

availability for their parameters.

The load settlement behavior of both model test and finite element

analysis at different studied parameters are shown in Figs. (5-16 through

5-21).

0

5

10

15

20

25

30

35

40

0 14 28 42 56 70

Stress, kPa

Sett

lem

en

t, m

m

Mohar-Coulomb

Hardening Soil

Cu = 20 kPa

L/H = 0.75

Fig. (5-15): Stress settlement response for the two cases of Mohr Coulomb

and hardening soil criteria model, (L=300 mm & D = 150 mm).

- 195 -

Table (5.3): Mohr Coulomb parameters for all materials in the cases

of cu = 10, 20 and 30 kPa.

Soil classification Dense sand Stone Soft clay Soft clay Soft clay

Model Used MC MC MC MC MC

Soil behavior Drained Drained Undrained Undrained Undrained

Unit weight

d (kN/m3) 18 18 16 16 16

sat(kN/m3) 19 19 17 17 17

Mohr- Coloumb

failure parameters

Cu, (kPa) - - 10 20 30

38 42 0 0 0

ψ o 8 12 0 0 0

Soil stiffness

Parameters

Mohr column

E (kPa) 80000 100000 2000 4000 6000

υ 0.30 0.35 0.45 0.45 0.45

Rf 0.8 0.8 0.7 0.7 0.7

Permeability

Ky (m/day) 1 10 1e-8 1e

-8 1e-

8

Kx (m/day) 1 10 1e-8 1e-

8 1e-

8

- 196 -

Table (5.4): Hardening soil model parameters for soft clay materials

at shear strength cu = 20 kPa.

Soil classification Soft clay

Model Used Hardening Model

Soil behavior Undrained

Unit weight d (kN/m

3) 16

sat(kN/m3) 17

Hardening soil

failure parameters

Cu, kPa 20

0

ψ, o 0

Soil stiffness

Parameters

Hardening model

4000

6000

8000

ν 0.45

m 0.5

Pref 100

Rf 0.7

Permeability

Ky (m/day) 1e-8

Kx (m/day) 1e-8

- 197 -

Fig. (5-16): Stress settlement behavior of both model test and finite

element at cu = 10 kPa, D = 50 mm and L = 100 mm.

0

5

10

15

20

25

30

35

40

0 7 14 21 28 35Stress, kPa

Sett

lem

en

t, m

m

Experimental

Numerical

0

5

10

15

20

25

30

35

40

0 7 14 21 28 35

Stress, kPa

Sett

lem

en

t, m

m

Experimental

Numerical

Fig. (5-17): Stress settlement behavior of both model test and

finite element at cu = 10 kPa, D = 150 mm and L = 300 mm.

- 198 -



0

5

10

15

20

25

30

35

40

0 14 28 42 56 70Stress, kPa

Sett

lem

en

t, m

m

Experimental

Numerical

0

5

10

15

20

25

30

35

40

0 14 28 42 56 70

Stress, kPa

Sett

lem

en

t, m

m

Experimental

Numerical



- 199 -



0

5

10

15

20

25

30

35

40

0 21 42 63 84 105

Stress, kPa

Sett

lem

en

t, m

m

Experimental

Numerical

0

5

10

15

20

25

30

35

40

0 21 42 63 84 105Stress, kPa

Sett

lem

en

t, m

m

Experimental

Numerical



CHAPTER (6):

NUMERICAL ANALYSIS

- 200 -

CHAPTER (6)

NUMERICAL ANALYSIS AND RESULTS

6.1 Introduction

This chapter presents the results of numerical models of the problem

under investigation at different studied parameters. It is aimed at

investigating the numerical analysis of small scale model that mentioned

in laboratory testing program. The effect of stone column geometry,

untrained shear strength and the effect of drained condition are also

investigated. The main control parameters are stress displacement

response of both drained and untrained conditions. The effect of stone

column on the subgrade stiffness is also submitted.

6.2 Numerical Analysis of Model Testing

Figures (6-1 through 6-4) illustrate the load settlement curves from the

finite element analysis of small scale model for different L/H ratio and

the same shear strength of 10 kPa for different stone column diameters.

The load deformation of numerical results of reinforced subgrade are

compared with untreated soil. Figure (6-1) shows the load carrying

capacity of 50mm diameter stone column. The capacity of 50mm

diameter stone column at 25 mm settlement with L/H ratio of 0.25, 0.50,

0.75 and 1.0 is found to be, 2.42, 2.68, 3.0 and 3.9 kN respectively. The

improvement in the load carrying capacity of stone column is reached to

1.74, 1.92, 2.16 and 2.81 times compared to untreated soil with different

L/H ratio of 0.25, 0.50, 0.75 and 1.0 respectively. The trends obtained

- 201 -

from results show that, by increasing the length of stone column, the

load carrying capacity of stone column increased.

It is noticed that for floating stone column (L/H = 0.25, 0.50, 0.75) the

load settlement response is partially different from the curve of end

bearing case (L/H= 1.0). It can be seen that the same pattern for floating

stone columns with length 100 mm, 200 mm and 300 mm respectively

disagree with the last curve for end bearing stone column with length

400 mm that differentiate from the other curves . One can be concluded

that the failure of stone column for end bearing case is took place due to

bulging failure. While the floating type, the failure is backed to

excessive settlement in the form of punching shear failure as confirmed

by Fig. (6-1). For floating type it can be also indicated that the failure is

obtained due to slippage at interface of stone column.

The capacity of 100mm diameter stone column at 25 mm settlement

with L/H ratio of 0.25, 0.50, 0.75 and 1.0 are 2.56, 3.22, 3.55 and 4.9 kN

respectively as shown in Fig. (6-2). The load carrying capacity of stone

column compared to untreated soft clay with different L/H ratio of 0.25,

0.50, 0.75 and 1.0 are increased by 1.84, 2.32, 2.55 and 3.53 times

respectively. This confirmed again that, increasing the length of stone

column leads to significant increase in the load carrying capacity of

stone column.

It has been found that the stress settlement response for floating stone

column (L/H = 0.25, 0.50, 0.75) is partially different from the curve of

end bearing case (L/H= 1.0). It can be seen that the same pattern for

- 202 -

floating stone columns with length 100 mm, 200 mm and 300 mm

respectively that disagree with the last curve for end bearing stone

column with length 400 mm. This also backed to the bulging failure of

end bearing one. While the large settlement is observed for floating case

due to punching failure.


with L/H ratio of 0.25, 0.50, 0.75 and 1.0 are 3.1, 3.62, 4.05 and 5.35 kN


column compared to untreated soft clay with different L/H ratio 0.25,

0.50, 0.75 and 1.0 is increases up to 2.23, 2.60, 2.91 and 3.85 times

respectively. The trends obtained from results show that, by increasing

the length of stone column, the load carrying capacity of stone column

increases.

While for floating stone column (L/H = 0.25, 0.50, 0.75) it has been

found that the load settlement response is partially different from the

curve of end bearing case (L/H=1.0). It can be seen that the same pattern

for floating stone columns with length 100 mm, 200 mm and 300 mm

respectively are distinctly disagree with the last curve for end bearing

stone column with length 400 mm as shown in Fig. (6-3).

The capacity of 300 mm diameter stone column at 25 mm settlement

with L/H ratio of 0.25, 0.50, 0.75 and 1.0 are 4.05, 5.70, 7.25 and 9.19

kN respectively as shown in Fig. (6-4). The increase in the load carrying

capacity of stone column compared to untreated soft clay with different

L/H ratio 0.25, 0.50, 0.75 and 1.0 are found to be 2.91, 4.10, 5.22 and

6.61 times respectively.

- 203 -

Fig. (6-1): Stress – settlement curves for different L/H ratios

(D = 50 mm and cu = 10 kPa).

0

5

10

15

20

25

30

35

40

0 7 14 21 28 35Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00

0

5

10

15

20

25

30

35

40

0 7 14 21 28 35Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00


(D = 100 mm and cu = 10 kPa).

- 204 -


(D = 150 mm and cu = 10 kPa).

0

5

10

15

20

25

30

35

40

0 7 14 21 28 35Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00

0

5

10

15

20

25

30

35

40

0 7 14 21 28 35

Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00


(D = 300 mm and cu = 10 kPa).

- 205 -

Figures (6-5 through 6-8) illustrate the load settlement curves from finite

element analysis of small scale model for different L/H ratio and the

same shear strength of 20 kPa for different stone column diameter. The

load deformations of numerical results are compared with untreated soil.

Figure (6-5) shows the load carrying capacity of 50mm diameter stone

column. The capacity of 50mm diameter stone column at 25 mm

settlement with L/H ratio 0.25, 0.50, 0.75 and 1.0 are , 4.95, 5.49, 5.97

and 7.55 kN respectively. The load carrying capacity of stone column

compared to untreated soil with different L/H ratio 0.25, 0.50, 0.75 and

1.0 are found to be 1.76, 1.96, 2.13 and 2.97 times respectively. The

trends obtained from results show that by increasing the length of stone

column, the load carrying capacity of stone column is increased.

It can be seen that for floating stone column (L/H = 0.25, 0.50, 0.75), it

has been found that the load settlement response is partially different

from the curve of end bearing case (L/H=1.0). It is found that the same

pattern for floating stone columns with length 100 mm, 200 mm and 300

mm respectively is disagree with the last curve for end bearing stone

column with length 400 mm that differentiate from the other curves. One

can be concluded that the failure of stone column for end bearing case

due to bulging failure. While for the floating type, the failure is backed

to excessive settlement in the form of punching shear failure as

confirmed by Fig. (6-5).


with L/H ratio 0.25, 0.50, 0.75 and 1.0 are 5.35, 6.45, 7.1 and 9.5 kN


- 206 -

column compared to untreated soft clay with different L/H ratio of 0.25,

0.50, 0.75 and 1.0 are found to be 1.91, 2.31, 2.54 and 3.39 times

respectively. The trends obtained from results show that, by increasing

the length of stone column, the load carrying capacity of stone column is

increased.

On the other hand, it is noticed that, for floating stone column (L/H =

0.25, 0.50, 0.75), the load settlement response is partially different from

the case of end bearing (L/H=1.0). It can be seen that the same pattern

for floating stone columns with length 100 mm, 200 mm and 300 mm

respectively are disagree with the curve for end bearing stone column of

length 400 mm that different from the other curves . One can conclude

that the failure of stone column for end bearing case due to bulging

failure. While the floating type, the failure is backed to excessive

settlement in the form of punching shear failure as confirmed by load

settlement response of Fig. (6-6).





0.50, 0.75 and 1.0 are found to be 2.25, 2.68, 2.94 and 3.75 times

respectively. The trends obtained from the results show that, by

increasing the length of stone column, the load carrying capacity of

stone column is increased.

- 207 -

It is noticed that for floating stone column of (L/H = 0.25, 0.50, 0.75), it


from the curve of end bearing case (L/H=1.0). It can be seen that the

same pattern for floating stone columns with length 100 mm, 200 mm

and 300 mm respectively are disagree with the last curve for end bearing

stone column with length 400 mm that different from the other curves .

One can be concluded that the failure of stone column for end bearing

case is obtained due to bulging failure. While for the floating type, the

failure is backed to excessive settlement in the form of punching shear

failure as illustrated in Fig. (6-7).




column compared to untreated soft clay with different L/H ratio of (0.25,

0.50, 0.75 and 1.0) are found to be 2.82, 3.97, 4.86 and 6.54 times

respectively.

- 208 -

0

5

10

15

20

25

30

35

40

0 14 28 42 56 70Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00

0

5

10

15

20

25

30

35

40

0 14 28 42 56 70

Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00


(D = 100 mm and cu = 20 kPa).


(D = 50 mm and cu = 20 kPa).

- 209 -


(D = 150 mm and cu = 20 kPa).

0

5

10

15

20

25

30

35

40

0 14 28 42 56 70

Stress, kPa S

ett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H =1.00

0

5

10

15

20

25

30

35

40

0 14 28 42 56 70Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H =1.00


(D = 300 mm and cu = 20 kPa).

- 210 -

Figures (6-9 through 6-12) illustrate the load settlement curves from

finite element analysis of small scale model for different L/H ratio and

the same shear strength of 30 kPa. The load deformations of numerical

results are compared with untreated soil. Fig. (6-9) shows the load

carrying capacity of 50mm diameter stone column. The capacity of

50mm diameter stone column at 25 mm settlement with L/H ratio of

0.25, 0.50, 0.75 and 1.0 is found to be, 7.7, 8.35, 9.15 and 12.1 kN

respectively. The load carrying capacity of stone column compared to

untreated soil with different L/H ratio 0.25, 0.50, 0.75 and 1.0 are found

to be 1.85, 2.0, 2.20 and 2.91 times respectively. The trends obtained

from the results show that by increasing the length of stone column, the

load carrying capacity of stone column is increased.

It is noticed that for floating stone column (L/H = 0.25, 0.50, 0.75), it




and 300 mm respectively disagree with the last curve for end bearing

stone column with length 400 mm that different from the other curves .


case is due to bulging failure. While the floating type, the failure is

backed to excessive settlement in the form of punching shear failure as



with L/H ratio 0.25, 0.50, 0.75 and 1.0 is 7.9, 10.25, 11.5 and 13.8 kN


- 211 -


0.50, 0.75 and 1.0 is increases 1.90, 2.46, 2.76 and 3.32 times

respectively. The trends obtained from results show that by increasing


increases.

It can be seen that for floating stone column (L/H = 0.25, 0.50, 0.75) it




and 300 mm respectively disagree with the last curve for end bearing

stone column with length 400 mm that differentiate from the other

curves . One can be concluded that the failure of stone column for end

bearing case due to bulging failure. While the floating type, the failure is

backed to excessive settlement in the form of punching shear failure as



with L/H ratio 0.25, 0.50, 0.75 and 1.0 is 9.45, 10.75, 12.2 and 16 kN




respectively. The trends obtained from results show that by increasing


increases.

- 212 -

It is noticed that for floating stone column (L/H = 0.25, 0.50, 0.75) it has

been found that the load settlement response is partially different from

the curve of end bearing case (L/H=1.0). It can be seen that the same

pattern for floating stone columns with length 100 mm, 200 mm and 300

mm respectively disagree with the last curve for end bearing stone

column with length 400 mm that differentiate from the other curves .


case due to bulging failure. While the floating type, the failure is backed

to excessive settlement in the form of punching shear failure as



with L/H ratio 0.25, 0.50, 0.75 and 1.0 is 12.5, 17, 20.3 and 27.1 kN




respectively.

- 213 -


(D = 50 mm and cu = 30 kPa).

0

5

10

15

20

25

30

35

40

0 21 42 63 84 105

Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00

0

5

10

15

20

25

30

35

40

0 21 42 63 84 105

Stress, kPa

Sett

lem

en

t, m

m

No Columnl

L/H =0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00


(D = 100 mm and cu = 30 kPa).

- 214 -

0

5

10

15

20

25

30

35

40

0 21 42 63 84 105

Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H =0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00

0

5

10

15

20

25

30

35

40

0 21 42 63 84 105Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00


(D = 300 mm and cu = 30 kPa).


(D = 150 mm and cu = 30 kPa).

- 215 -

6.3 Numerical Analysis of Drained Condition

This part of study presents the numerical analysis of load displacement

curves of stone column in drained condition for the same proposed

investigated model listed in chapter (3).

Figures (6-13 through 6-16) show the settlement response of stone

column at different L/H ratio and undrained shear strength of (10 kPa).

In case of (D = 50mm) as shown in Fig. (6-13), it has been found that

increasing the L/H ratio significantly improved the load capacity of

stone column until reaching to higher value in end bearing column ( L/H

= 1.0 ).

It is found that the ultimate load capacity of reinforced subgrade by

stone column with (L/H = 0.25 to 0.75) as floating type increased by

around (73 % to 110 %). While at (L/H = 1.0) for end bearing case the

load is increased by 152.5% whereas gradual reduction in settlement can

be achieved by the increase of L/H ratio.

It can be seen that at (L/H = 0.25) the settlement of stone column system

is reduced by 14% of its initial value of system without stone column.

While this reduction is found to be (24%, 30% and 35%) in case of

(L/H = 0.50, 0.75 and 1.0) respectively.

It can be concluded that when the stone column installed in soft clay

under drained condition the settlement is remarkably achieved with

lower improvement in ultimate load capacity.

In case of ( D = 100 mm ) as shown in Fig.(6-14), it has been found that


- 216 -


= 1.0 ).



around (94.3 % to 162.5 %). While at (L/H = 1.0) for end bearing case

the load is increased by 190%, whereas gradual reduction in settlement

can be attained by the increase of L/H ratio.

It can be seen at (L/H = 0.25) the settlement of stone column system is

reduced by 24% of its initial value of system without stone column.

While this reduction is found to be (27%, 31% and 36%) in case of



under drained condition the settlement is remarkably achived with lower

improvement in ultimate load capacity.

On the other hand Fig. (6-15) shows the load displacement curve for

stone column with diameter of (D = 150 mm), it can be noticed that the

increasing of the L/H ratio significantly improved the load capacity of

stone column until reaching to higher value in end bearing column

(L/H = 1.0).



around (121.25 % to 199.38 %). While at (L/H = 1.0) for end bearing

case the load is increased by 231.25% whereas gradual reduction in

settlement can be achieved by the increase of L/H ratio.

- 217 -



While this reduction is found to be (29.4%, 32.5%, 38%) in case of





On the other hand, for maximum stone column diameter, D = 300 mm. It

is observed that the increase of L/H ratio produced a considerable

increase in the ultimate load capacity (Fig. 5-16). It is also found that the

increase of stone column stiffness provides a linear variation in load

displacement curve at L/H = 0.25, 0.50, 0.75 and 1.0. That is backed to

volume of replaced soft clay by stone is remarkably increased by as such

as (50%) case of (L/H =1.0). The improvement in ultimate load capacity

are found to be 173.75, 290, 375, 452.5 % for L/H = 0.25, 0.50, 0.75, 1.0

respectively, while these settlement is reduced by as much as 41% for

end bearing case (L/H = 1.0).

- 218 -


(D = 50 mm and cu = 10 kPa).

0

10

20

30

40

50

60

70

0 7 14 21 28 35Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00

0

10

20

30

40

50

60

70

0 7 14 21 28 35

Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00


(D = 100 mm and cu = 10 kPa).

- 219 -


(D = 150 mm and cu = 10 kPa).

0

10

20

30

40

50

60

70

0 7 14 21 28 35Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00

0

10

20

30

40

50

60

70

0 7 14 21 28 35

Stress, kpa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00


(D = 300 mm and cu = 10 kPa).

- 220 -


column at different L/H ratio and undrained shear strength of (20 kPa).

In case of (D = 50 mm) as shown in Fig. (6-17), it has been found that



= 1.0 ).



around (73.93 % to 110.89 %), while at (L/H = 1.0) for end bearing case

the load is increased by 125.5% whereas gradual reduction in settlement

can be achived by the increase of L/H ratio.



While this reduction is found to be (25%, 31% and 36%) in the cases of








= 1.0 ).




- 221 -

the load is increased by 176.76% whereas gradual reduction in

settlement can be achived by the increase of L/H ratio.



While this reduction is found to be (28%, 32%, 38%) in case of (L/H =

0.50, 0.75 and 1.0) respectively.




Moreover, Fig. (6-19) shows the load displacement curve for stone

column with diameter of (D = 150 mm), it can be noticed that the



= 1.0 ).


stone column with (L/D = 0.25 to 0.75) as floating type increased by

around (109.74 % to 180.52 %). While at (L/H = 1.0) for end bearing

case the load is increased by 209.46% whereas gradual reduction in




While this reduction is found to be (29.4%, 33.5%, 39.5%) in case of


- 222 -

It is worth mentioned that when the stone column installed in soft clay



While for maximum stone column diameter, D = 300 mm. It is observed

that the increase of L/H ratio produced a considerable increase in the

ultimate load capacity (Fig. 5-20). It is also found that the increase of

stone column stiffness provides a linear variation in load displacement

curve at L/H = 0.25 , 0.50 ,0.75 and 1.0 that is backed to volume of

replaced soft clay by stone is remarkably increased by as such as (50%)

in case of (L/H =1.0). The improvement in ultimate load capacity are

found to be 152.44, 261.03, 326.93, 410.03 % for L/H =0.25, 0.50, 0.75,

1.0 respectively, while these settlement is reduced by as much as 43%

for stiff stone column end bearing case (L/H = 1.0).

- 223 -


(D = 50 mm and cu = 20 kPa).

0

10

20

30

40

50

60

70

0 14 28 42 56 70

Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00

0

10

20

30

40

50

60

70

0 4 8 12 16 20

Load, kN

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00


(D = 100 mm and cu = 20 kPa).

- 224 -

0

10

20

30

40

50

60

70

0 14 28 42 56 70Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00

0

10

20

30

40

50

60

70

0 14 28 42 56 70Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00


(D = 300 mm and cu = 20 kPa).


(D = 150 mm and cu = 20 kPa).

- 225 -


column at different L/D ratio and undrained shear strength of (30 kPa).

In case of (D = 50 mm) as shown in Fig. (6-21), it has been found that

increasing the L/D ratio significantly improved the load capacity of


= 1.0 ).



around (72.66 % to 112.24 %), while at (L/H = 1.0) for end bearing case













= 1.0 ).




- 226 -










On the other hand Fig.(6-23) shows the load displacement curve for

stone column with diameter of (D = 150 mm), it can be noticed that the



= 1.0 ).


stone column with (L/D = 0.25 to 0.75) as floating type increased by

around (114.15 % to 184.9 %). While at (L/D = 1.0) for end bearing case





While this reduction is found to be (29.4%, 35%, 40%) in case of (L/H =


- 227 -




While for maximum stone column diameter, D = 300 mm. It is observed

that the increase of L/H ratio produced a considerable increase in the

ultimate load capacity as shown in Fig. (6-24). It is also found that the

increase of stone column stiffness provides a linear variation in load

displacement curve at L/H = 0.25 , 0.50 ,0.75 and 1.0 that is backed to

volume of replaced soft clay by stone is remarkably increased by as such

as (50%) case of (L/H =1.0). The improvement in ultimate load capacity

are found to be 156.21, 263.29, 324.50, 410.52 % for L/H =0.25, 0.50,

0.75, 1.0 respectively, while these settlement is reduced by as much as

45% for stone column of end bearing case (L/D = 1.0).

- 228 -


(D = 50 mm and cu = 30 kPa).

0

10

20

30

40

50

60

70

0 21 42 63 84 105Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00

0

10

20

30

40

50

60

70

0 21 42 63 84 105Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00


(D = 100 mm and cu = 30 kPa).

- 229 -

0

10

20

30

40

50

60

70

0 21 42 63 84 105

Stress, kPa

Sett

lem

en

t, m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00

0

10

20

30

40

50

60

70

0 21 42 63 84 105Stress, kPa

Sett

lem

en

t,m

m

No Column

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00


(D = 300 mm and cu = 30 kPa).


(D = 150 mm and cu = 30 kPa).

- 230 -

6.4 Stress - Settlement Curves for End Bearing Stone

Column in Drained Condition

Figures (6-25 through 6-28) show the stress - settlement response for

end bearing stone column at different undrained shear strength of 10

kPa, 20 kPa and 30 kPa.

Fig. (6-25): Stress – settlement curves for end bearing stone column,

D = 50 mm at different undrained shear strength.

0

5

10

15

20

25

30

35

40

0 21 42 63 84 105Stress, kPa

Sett

lem

en

t, m

m

Cu = 10 kPa

Cu = 20 kPa

Cu = 30 kPa

- 231 -



0

5

10

15

20

25

30

35

40

0 21 42 63 84 105Stress, kPa

Sett

lem

en

t, m

m

Cu = 10 kPa

Cu = 20 kPa

Cu = 30 kPa

0

5

10

15

20

25

30

35

40

0 21 42 63 84 105

Stress, kPa

Sett

lem

en

t, m

m

Cu = 10 kPa

Cu = 20 kPa

Cu = 30 kPa



- 232 -



6.5 Analysis of Failure Mechanism of Stone Column in

Drained Condition

It can be seen that for end bearing stone column, the stone column is

gradually compressed until reaching to bulging failure (general shear

failure) as a result the failure of stone column is a achieved. It can be

noticed that linear relationship is exhibited during all stages of loading

until reaching to failure.

While for partially penetrated stone column or floating types the load

displacement behaviour of stone column divided into three stages.

0

5

10

15

20

25

30

35

40

0 21 42 63 84 105

Stress, kPa

Sett

lem

en

t, m

m

Cu = 10 kPa

Cu = 20 kPa

Cu = 30 kPa

- 233 -

Stage I, at early stage of loading, refers to linear or elastic behaviour.

Stage II, shows plastic behaviour with the increase of loading due to

frictional resistance a long column diameter.

Finally at failure stage III is obtained in the term of punching shear

failure, where at failure the floating stone column is totally moved

downward producing obvious punching shear failure as stated by

(Barksdale and Bachus, 1983).

Fig. (6-29): Stress settlement behaviour of floating type stone

column divided into three stages (D= 50 mm, L/H= 0.5).

- 234 -

6.6 Comparison Between Drained and Undrained

Conditions

This part presents a numerical analysis of the behaviour of the stone

column under both drained and undrained condition. The numerical

results of scaled laboratory model test for drained and undrained

condition are analyzed through the load displacement curves using

axisymmetric model that verified as presented before.

Figures (6-30 through 6-41) shows the load displacement curves of

studied stone column under drained and undrained condition at different

clay shear strength and stone column geometry.

It has been found that the load displacement responses of vertically

loaded stone column under drained condition are totally different from

case of undrained condition. It can be seen that the ultimate load

capacity of stone column in case of no permeation for drainage is higher

than of drained case. Also it was found that the settlement of stone

column soil system is lower than of stone column in drained condition as

confirmed by relevant figures.

It can be concluded that the drained case provided a minor capacity with

high settlement. That is due to the dissipation of pore water pressure,

which can be effectively resisted the additional loads within the stone

column when no permeation allowed for water. Therefore the undrained

case is significantly produced additional resistance for loads.

On the other hand, for floating stone column under undrained case,

linear behavior is achieved for different (L/H) and clay cohesion. While

- 235 -

for end bearing case the nonlinear relationship is achieved at failure.

Because the end bearing stone columns are subjected to vertical

confining pressure that significantly provided additional load resistance.

As a result yielding behavior is observed at failure compared with

floating cases.

The increases of stone column ultimate resistance due to undrained

condition are related to subgrade cohesion and stone column stiffness.

It is observed that the increase in the ultimate load résistance of end

bearing stone columns at (cu = 10 kPa, D = 50 mm) is found to be 12%

as shown in Fig. (6-29d). While at stone columns diameters of (D = 100,

150, 300 mm) for cohesion of cu = 10 kPa, the increase of ultimate

capacity are expected in range of (14%, 17%, 18% and 20%)

respectively. Whereas, the increases of undrained shear strength has also

a great effect on increasing the load capacity under undrained

conditions. It has been found that for stone column diameter of 50 mm,

the increase of load capacity of stone columns were found to be around

24% and 29% at (cu = 20 , 30 kPa) respectively.

In general, it can be concluded that the pore water pressure within the

stone columns can sustain around (12-25%) of ultimate load in drained

case according to stone column geometry and clay cohesion.

- 236 -

0

10

20

30

40

50

60

70

0 7 14 21 28 35Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 7 14 21 28 35Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 7 14 21 28 35Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 7 14 21 28 35Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

(a) L/H = 0.25 (b) L/H = 0.50

(c) L/H = 0.75 (d) L/H = 1.00

Fig. (6-30): Stress - settlement behaviour for the two cases of

drained and undrained conditions (cu = 10 kPa, D = 50 mm).

- 237 -

0

10

20

30

40

50

60

70

0 7 14 21 28 35

Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 7 14 21 28 35

Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 7 14 21 28 35

Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 7 14 21 28 35

Stress, kPa S

ett

lem

en

t, m

m

Drained

Undrained

(a) L/H = 0.25 (b) L/H = 0.50

(c) L/H = 0.75 (d) L/H = 1.00



- 238 -

0

10

20

30

40

50

60

70

0 7 14 21 28 35

Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 7 14 21 28 35

Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 7 14 21 28 35

Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 7 14 21 28 35Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

(a) L/H = 0.25 (b) L/H = 0.50

(c) L/H = 0.75 (d) L/H = 1.00



- 239 -

0

10

20

30

40

50

60

70

0 7 14 21 28 35

Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 7 14 21 28 35

Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 7 14 21 28 35Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 7 14 21 28 35Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

(a) L/H = 0.25 (b) L/H = 0.50

(c) L/H = 0.75 (d) L/H = 1.00



- 240 -

0

10

20

30

40

50

60

70

0 14 28 42 56 70

Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 14 28 42 56 70

Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 14 28 42 56 70

Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 14 28 42 56 70

Stress, kPa S

ett

lem

en

t, m

m

Drained

Undrained

(c) L/H = 0.75 (d) L/H = 1.00



(a) L/H = 0.25 (b) L/H = 0.50

- 241 -

0

10

20

30

40

50

60

70

0 14 28 42 56 70

Stress, kPa

Sett

lem

ent,

mm

Drained

Undrained

0

10

20

30

40

50

60

70

0 14 28 42 56 70

Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 14 28 42 56 70

Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 14 28 42 56 70

Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

(a) L/H = 0.25 (b) L/H = 0.50

(c) L/H = 0.75 (d) L/H = 1.00



- 242 -

0

10

20

30

40

50

60

70

0 14 28 42 56 70Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 14 28 42 56 70Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 14 28 42 56 70Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 14 28 42 56 70Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

(a) L/H = 0.25 (b) L/H = 0.50

(c) L/H = 0.75 (d) L/H = 1.00



- 243 -

0

10

20

30

40

50

60

70

0 14 28 42 56 70Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 14 28 42 56 70

Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 14 28 42 56 70Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 14 28 42 56 70Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

(a) L/H = 0.25 (b) L/H = 0.50

(c) L/H = 0.75 (d) L/H = 1.00



- 244 -

0

10

20

30

40

50

60

70

0 21 42 63 84 105Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 21 42 63 84 105Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 21 42 63 84 105Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 21 42 63 84 105Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

(a) L/H = 0.25 (b) L/H = 0.50

(c) L/H = 0.75 (d) L/H = 1.00



- 245 -

0

10

20

30

40

50

60

70

0 21 42 63 84 105

Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 21 42 63 84 105

Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 21 42 63 84 105

Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 21 42 63 84 105

Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

(a) L/H = 0.25 (b) L/H = 0.50

(c)L/H = 0.75 (d) L/H = 1.00



- 246 -

0

10

20

30

40

50

60

70

0 21 42 63 84 105

Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 21 42 63 84 105

Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 21 42 63 84 105

Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 21 42 63 84 105

Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

(a) L/H = 0.25 (b) L/H = 0.50

(c) L/H = 0.75 (d) L/H = 1.00



- 247 -

0

10

20

30

40

50

60

70

0 21 42 63 84 105Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 21 42 63 84 105

Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 21 42 63 84 105Stress, kPa

Sett

lem

en

t, m

m

Drained

Undrained

0

10

20

30

40

50

60

70

0 21 42 63 84 105Stress, kPa

Sett

lem

en

t, m

m Drained

Undrained

(a) L/H = 0.25 (b) L/H = 0.50

(c) L/H = 0.75 (d) L/H = 1.00



- 248 -

Table (6.1): Ratio between stress in undrained condition and

drained condition at 25 mm settlement, (cu =10 kPa).

Column

diameter

(mm)

Type of

column

Stress in

undrained

condition at

25 mm

settlement

Sund.

Stress in

drained

condition at

25 mm

settlement

Sdr.

Ratio

between

stresses in

two cases

50

Floating 8.60 6.19 0.72

Floating 8.42 6.72 0.80

Floating 10.01 7.96 0.80

End bearing 13.77 11.32 0.82

100

Floating 9.06 6.79 0.75

Floating 11.39 9.13 0.80

Floating 12.67 10.26 0.81

End bearing 17.34 13.31 0.77

150

Floating 11.11 8.42 0.76

Floating 12.95 10.30 0.80

Floating 14.33 11.92 0.83

End bearing 19.00 15.00 0.79

300

Floating 14.61 9.70 0.66

Floating 20.24 14.97 0.74

Floating 25.58 19.07 0.75

End bearing 32.13 25.76 0.80

- 249 -



Column

diameter

(mm)

Type of

column

Stress in

undrained

condition at

25 mm

settlement

Sund.

Stress in

drained

condition at

25 mm

settlement

Sdr.

Ratio

between

stresses in

two cases

50

Floating 17.52 12.10 0.69

Floating 19.50 15.36 0.79

Floating 21.55 18.54 0.86

End bearing 26.72 18.75 0.70

100

Floating 18.83 14.51 0.77

Floating 22.36 17.69 0.79

Floating 25.55 20.95 0.82

End bearing 33.51 28.67 0.83

50

Floating 22.47 16.458 0.73

Floating 26.57 20.88 0.79

Floating 29.62 25.519 0.86

End bearing 38.57 30.79 0.80

300

Floating 28.13 19.75 0.70

Floating 39.99 29.69 0.74

Floating 47.77 36.80 0.77

End bearing 64.57 52.37 0.81

- 250 -



Column

diameter

(mm)

Type of

column

Stress in

undrained

condition at

25 mm

settlement

Sund.

Stress in

drained

condition at

25 mm

settlement

Sdr.

Ratio

between

stresses in

two cases

50

Floating 26.68 21.94 0.82

Floating 29.55 24.49 0.83

Floating 32.55 28.49 0.88

End bearing 42.82 33.79 0.88

100

Floating 28.66 25.12 0.88

Floating 35.92 31.67 0.88

Floating 40.34 36.10 0.89

End bearing 48.83 41.76 0.86

150

Floating 33.79 29.19 0.86

Floating 39.99 33.79 0.85

Floating 44.23 39.99 0.90

End bearing 56.97 45.47 0.80

300

Floating 44.41 30.61 0.69

Floating 60.51 45.47 0.75

Floating 71.13 56.62 0.80

End bearing 96.25 79.79 0.83

- 251 -

In order to show the significant effect of undrained condition in case of

using such stone column within the soft clay layer, Figures (6-42

through 6-53) are illustrated. It is also given for confirmation and

justified the stress behavior of drained cases are lesser than undrained

condition as stated before

It can be seen that the curves of undrained conditions are showed that

the pore water pressure provided a significant additional resistance with

stone columns.

As a results the stress – settlement of undrained cases highly depended

on the pore water pressure and the pore water pressure and stone column

geometry.

- 252 -

0

10

20

30

40

50

60

70

0 7 14 21 28 35Stress, kPa

Sett

lem

en

t, m

m

N

o

C

o

l

u

m

n

L

/

H

=

0

.

2

L

/

H

=

0

.

5

L

/

H

=

0

.

7

L

/

H

=

1

.

0N

o

C

o

l

u

m

n

L

/

H

=

0

.

2

L

/

H

=

0

.

5

L

/

H

=

0

.

7

L

/

H

=

1

.

0

0

10

20

30

40

50

60

70

0 7 14 21 28 35Stress, kPa

Sett

lem

en

t, m

m

Fig. (6-42): Stress - settlement behaviour for the two cases of drained and

undrained conditions (cu = 10 kPa, D = 50 mm).



- 253 -

0

10

20

30

40

50

60

70

0 7 14 21 28 35Stress, kPa

Sett

lem

en

t, m

m

0

10

20

30

40

50

60

70

0 7 14 21 28 35

Stress, kPa

Sett

lem

en

t, m

m





- 254 -

0

10

20

30

40

50

60

70

0 14 28 42 56 70Stress, kPa

Sett

lem

en

t, m

m

0

10

20

30

40

50

60

70

0 14 28 42 56 70

Stress, kPa

Sett

lem

en

t, m

m





- 255 -

0

10

20

30

40

50

60

70

0 14 28 42 56 70

Stress, kPa

Sett

lem

en

t, m

m

0

10

20

30

40

50

60

70

0 14 28 42 56 70Stress, kPa

Sett

lem

en

t, m

m





- 256 -

0

10

20

30

40

50

60

70

0 21 42 63 84 105

Stress, kPa S

ett

lem

en

t, m

m

0

10

20

30

40

50

60

70

0 21 42 63 84 105

Stress, kPa

Sett

lem

en

t, m

m





- 257 -

0

10

20

30

40

50

60

70

0 21 42 63 84 105

Stress, kPa

Sett

lem

en

t, m

m

0

10

20

30

40

50

60

70

0 21 42 63 84 105Stress, kPa

Sett

lem

en

t, m

m





- 258 -

Figure (6-54) shows the relationship between L/H ratio and increase in

the subgrade modulus where subgrade modulus is defined as the ratio

between subgrade modulus of system with stone column to subgrade

modulus without stone column =

It can be seen that the existence of stone column can increase the

subgrade modulus by the increase of stone column diameter.

For drained condition cu = 10 kPa, the improvement on the subgrade

modulus are found to be 1.2, 2.5, 3 and 5.7 time of system without stone

column for column diameter (50,100,150 and 300 mm) respectively.

While in undrained condition these improvements in the subgrade

modulus are found to be 1.9, 2.8, 3.7 and 7.7 time in the same order of

the diameter.

It can concluded that the undrained condition has a great effect on

increasing the subgrade modulus. That is due to the resistance of the

pore water pressure. The induced pore water pressure within the stone

column can increase the resistance of stone against acting loads.

As result the ultimate load capacity is increased by considerable value

compared with drained condition

- 259 -

Fig. (6-54): The relationship between L/H ratio and increase in the

subgrade modulus for cu = 10 kPa.

Figures (6-55 and 6-56) shows the relationship between L/H ratio and

increase in the subgrade modulus for cu = 20 kPa and 30 kPa. Also

Figures (6-57 through 6-60) shows the relationship between cu and

increase in the subgrade modulus for different diameters of stone

column.

0

1

2

3

4

5

6

7

8

0 0.25 0.5 0.75 1 1.25

L/H

Sm

= (

Mw

ith

colu

mn

/ M

wit

hou

t co

lum

n)

D = 50 mm drained

D = 100 mm drained

D = 150 mm drained

D = 300 mm drained

D = 50 mm undrained

D = 100 mm undrained



- 260 -

Fig. (6-55): The relationship between L/H ratio and increase in the

subgrade modulus for cu = 20 kPa.

0

1

2

3

4

5

6

7

8

9

0 0.25 0.5 0.75 1 1.25

L/H

Sm

= (

Mw

ith

colu

mn

/ M

wit

hou

t co

lum

n)

D = 50 mm drained

D = 100 mm drained

D = 150 mm drained

D = 300 mm drained

D = 50 mm undrained




0

1

2

3

4

5

6

7

8

9

0 0.25 0.5 0.75 1 1.25

L/H

Sm

= (

Mw

ith

co

lum

n / M

wit

ho

ut

colu

mn)

D = 50 mm drained

D = 100 mm drained

D = 150 mm drained

D = 300 mm drained

D = 50 mm undrained




Fig. (6-56): The relationship between L/H ratio and increase in

the subgrade modulus for cu = 30 kPa.

- 261 -

Fig. (6-57): The relationship between the undrained shear strength

cu (kPa) and the relative subgrade modulus (D = 50 mm).

0

1

2

3

4

5

6

7

0 5 10 15 20 25 30 35 40 45

cu, kPa

Sm

= (

Mw

ith

colu

mn

/ M

wit

hou

t co

lum

n)

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00

0

1

2

3

4

5

6

7

0 5 10 15 20 25 30 35 40 45

cu, kPa

Sm

= (

Mw

ith

co

lum

n / M

wit

ho

ut

colu

mn)

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00



- 262 -

0

1

2

3

4

5

6

7

0 5 10 15 20 25 30 35 40 45cu, kPa

Sm

= (

Mw

ith

colu

mn

/ M

wit

hou

t co

lum

n)

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00

0

1

2

3

4

5

6

7

0 5 10 15 20 25 30 35 40 45

cu, kPa

Sm

= (

Mw

ith

co

lum

n /

Mw

ith

ou

t co

lum

n)

L/H = 0.25

L/H = 0.50

L/H = 0.75

L/H = 1.00





- 263 -

6.7 Stress Concentration Ratio at Various Shear Strengths

and Various L/H Ratios for Drained Condition

Figures (6-61 through 6.64) show the effect of clay cohesion on

relationship between the stress concentration ratio and L/H ratios at

various diameters for soil treated with single stone column at drained

condition. As mentioned previously the stone columns are constructed in

very soft clays having three shear strengths (cu=10, 20, and 30 kPa) and

four values of L/H ratio. It has been found that the increase of cohesion

leads to significant reduction on stress concentration factor.

At minimum value of stone column diameter (50 mm), it can be seen

that the increase of L/H ratio gradually increase the stress concentration

factor in linear relationship with lower increase in clay cohesion. For

fully penetrated stone column (L/H=1), the stress concentration factor is

found to be increased by 20, 15 and 13% of its initial value of floating

stone column (L/H=0.25) for clay cohesion of (10, 20 and 30kPa)

respectively.

While for maximum stone diameter of 300 mm, these values is found to

be (15.5, 11.5 ad 10.3%) for the same order.

It can be concluded that the lower variation on stress concentration

factor is achived with the increase of (L/H) ratios. The value of stress

concentration factor is found to be within the range of ( 2.3 to 4.3) these

values are agree with the value obtained by (Goughnour and Bayuk

1979; Aboshi et al., 1979).

- 264 -

On the other had the stress concentration factor "n" can be expressed by

the following linear relationship:

n = C1 (L/H) + C2 (6.1)

Where:

C1 and C2 are constants related to (L/H, undrained shear strength and

stone column diameter).

The enclosed proposed equation can be valid for stone column with

diameter equal or less than 300mm

This equation can be used for crude estimation of "n" values for stone

column with different clay cohesion and stone diameter. Table (6.4)

shows the values of C1 and C2.

0

1

2

3

4

5

6

0 0.25 0.5 0.75 1 1.25

L/H

Str

ess

Co

ncen

tra

tio

n F

acto

r,

n

Cu = 10 kPa

Cu = 20 kPa

Cu = 30 kPa

Fig. (6-61): The relationship between L/H and stress concentration

factor at different shear strength (D = 50 mm).

- 265 -

0

1

2

3

4

5

6

0 0.25 0.5 0.75 1 1.25L/H

Str

ess

Co

ncen

tra

tio

n F

acto

r,

n Cu = 10 kPa

Cu = 20 kPa

Cu = 30 kPa

0

1

2

3

4

5

6

0 0.25 0.5 0.75 1 1.25L/H

Str

ess

Co

ncen

tra

tio

n F

acto

r,

n

Cu = 10 kPa

Cu = 20 kPa

Cu = 30 kPa





- 266 -

Table (6.4): The values of C1 and C2 for stone column under drained

condition

Undraied shear

strength (kPa)

Diameter 50 mm

Diameter

100 mm

Diameter

150 mm

Diameter

300 mm

C1 C2 C1 C2 C1 C2 C1 C2

10 0.59 2.86 0.62 2.96 0.6 3.12 0.57 3.71

20 0.52 2.57 0.54 2.67 0.57 2.78 0.52 3.32

30 0.45 2.18 0.46 2.27 0.48 2.37 0.44 2.82

0

1

2

3

4

5

6

0 0.25 0.5 0.75 1 1.25L/H

Str

ess

Co

ncen

tra

tio

n F

acto

r,

n

Cu = 10 kPa

Cu = 20 kPa

Cu = 30 kPa



- 267 -

6.8 Statistical Analysis

The following investigation introduces the verification of the model test

results by the finite element analysis using statistical analysis

procedures. Also, the main nation of this study is to correlate the

relationships of the different experimental variable in the form of

ultimate bearing capacity equations for stone column under

investigation. It also aimed to provide a simple form to crude estimation

of the ultimate bearing capacity of stone column inserted in soft clay at

different analyzed parameters as clay cohesion, stone column geometry

and clay layer thickness.

The obtained results were organized, tabulated and statistically analyzed

using SPSS (statistical program for scientific studies) software statistical

computer package. The 5% level of significance was adopted for

interpretation of test results (P < 5%). The meaning of the (P) value: the

level of in the judgment of significance and the liability of occurrence

the change by chance. T test and Chi square were used in this

investigation and other SPSS application to correlate the tested

parameters or variables.

Statistical enhancements. Perform more in-depth analysis with

additional statistics, including:

New ANOVA procedure with custom models and post-hoc tests. Robust Levene test to compare variance between groups

in the Explore procedure. Harmonic and geometric means in the Means procedure. Interclass correlation in the Reliability procedure

(Professional Statistics option).

- 268 -

One-minus-survival functions in Survival procedures

(Advanced Statistics option). Improved correspondence analysis and multiple

regressions for categorical data (Categories option). The experimental and theoretical results of using different reinforced

techniques were verified by applying unpaired t test and ANOVA testing

difference (comparing differences between two groups or more than two

groups). It has been found that the p value (p < 5%) it was referred that

there was no difference between both experimental and theoretical

results. On the other way, the program was mainly used to provide the

bearing capacity equation or the relationships between studied

parameters in the form of linear equation that correlated the main control

independent parameter qult with other tested parameters. Where the

relationship between ultimate bearing capacity and the tested parameters

(soft clay cohesion cu, stone column stiffness L/D and soft clay

thickness to stone column depth L/H) for stone column on soft clay can

be written respectively by the following equations:

qult = 10.172(L/H) + 0.469Cu – 1.036(L/D) – 4.254 for drained

conditions

qult = 11.558(L/H) + 0.434Cu – 1.0209(L/D) – 4.386 for undrained

conditions

The enclosed proposed expressions are valid for stone column installed

in soft clay layer under the following limits: (or limitation)

i) Compacted dry density of sand under stone column as a

bearing layer (18.3kN /m3) and relative density (80%).

- 269 -

ii) Maximum and minimum grain range of stone column ( 2 to

10 mm)

iii) Stress concentration factor in rage of (n = 2.3 to 4.3)

iv) The stone column depth to clay thickness in range (0.25 to 1)

v) The size effect of test setup adopted in this study are in rage

of (x = 5.5D, 5D, 4.5D and 0.5D). Where x is the spacig from

stone column face to side wall of the adopted tank.

CHAPTER (7):

COMPARATIVE STUDY

- 270 -

CHAPTER (7)

COMPARATIVE STUDY

7.1 Scope

In this chapter a discussion of the numerical modeling of full scale

analysis using most common case study. In this part, the deformation

characteristic of the application of numerical modeling is applied for

large scale embankment of the stone column. In this part, the adopted

case study is used as mentioned by Tan et al., 2008. The soil profile for

the relevant case study and parameters for the different soil layers and

the used stone columns are also explained. The settlement values

monitored during and after the construction of the embankment are

introduced. The application of consolidation behavior is also analyzed.

Finally comparison all results from finite element model 2D by

examination (Han and Ye 2001) and (Han and Ye 2002) as a simplified

analytical solution for the rate of consolidation of stone-column

reinforced ground. Also a comparative study with different researchers

is presented with details.

7.2 Case Study Description The finite element simulation has been applied for the modeling of an

embankment construction for Penchala Toll Plaza project at New Pantai

Expressway, Malaysia, in 2003. A brief description of the project was

given by Tan et al. (2008). The Layout Plan of Stone Column Works

shown in Fig. (7-1). The embankment geometry and the stone column

- 271 -

reinforced soil profile are shown in Fig. (7-2) having a line of symmetry

on the left boundary. The 40 m wide and 1.8 m high embankment is

filled by sandy material. The embankment lies over a 6 m layer of soft

clay underlain by an extended layer of stiff clay. The stone columns,

arranged in a square grid 2.4 m x 2.4 m, extends through the entire soft

clay layer. The upper crust layer is a 1 m thick fill of hard soil, which

was provided as a replacement of soft clay surface to improve ground

for a stable construction platform and to distribute the load on the treated

soil uniformly. The groundwater level is 1 m below the ground surface.

Table (7.1) presents the different parameters for all soil layers, as well

as, the embankment and the used stone columns. The embankment was

constructed over 3 stages, each stage involved a 3 days construction of a

0.6 m height layer of the embankment, and thus the embankment was

built over entire construction duration of 9 days. As the stone columns

extends through the entire soft clay layer and ends at the top of the stiff

clay layer which has a very high elasticity modulus, the stone columns in

this case can be considered as end bearing columns. Also, the columns

can be considered as short columns as there entire length is 6 m only.

- 272 -

Fig. (7-1): Layout plan of stone column works at New Pantai

expressway.

- 273 -

Fig. (7-2): Cross section of embankment case history through

centerline of stone columns.

- 274 -

Table (7.1): Material parameters for case study.

7.3 Numerical Modeling 2D Finite Element Analyses

Because the two dimensional finite element analyses programs are more

commonly used in practice and easily than the three dimensional finite

element analyses program in solving different geotechnical engineering

problems.

An axisymmetric problem involves circular loading where deformations

and stresses are assumed to be identical in any radial direction and a

plane strain problem involves a long body with uniform geometry and

loading in the longitudinal direction. The behavior of stone columns can be examined using the Unit cell

concept (i.e., a cylindrical cell with the stone column at the center and

surrounded by the soft soil within its effective diameter) which can be

Material

Sat.

(kN/m3)

Unsat.

(kN/m3) υ´

E

(kPa)

Kh

(m/s)

Kv

(m/s)

c´

(kPa) ϕ ´

(deg)

Embankment

Fill

20

18

0.3

15000

1.16 x 10-5

1.16 x 10-5

3

33

Crust

18

17

0.3

15000

3.47 x 10-7

1.16 x 10-7

3

28

Soft Clay

15

15

0.3

1100

3.47 x 10-9

1.16 x 10-9

1

20

Stiff Clay

20

18

0.3

40000

3.47 x 10-9

1.16 x 10-9

3

30

Stone Column

20

19

0.3

30000

1.16 x 10-4

1.16 x 10-4

5

40

- 275 -

perfectly simulated using the axisymmetric configuration. However, the

unit cell concept is not suitable to investigate the behavior of the

embankment itself, especially when studying the stability of the

embankment slope; thus, the plan strain configuration is more suitable in

such cases. In the plane strain configuration, the stone columns are

modeled as continuous walls instead of discreet columns, thus, affecting

the results of the entire problem.

Mohr-Coulomb constitutive laws are used to model all different soil

layers as well as the embankment and the stone columns for all the two

dimensional finite element analyses used during this research. The soft

clay and stiff clay layers are modeled in the undrained conditions while

using their effective strength parameters, while, the stone columns,

embankment and the crust layer are modeled in a drained condition.

The horizontal movement is prevented while allowing the vertical

movement for all the vertical boundaries. For the bottom horizontal

boundary both the vertical and horizontal displacements are prevented.

The water flow is prevented through all the vertical and horizontal

boundaries of the models. The stiff clay layer was presented as a layer

with 4 m depth only. The model extends to a distance of 20 m beyond

the embankment width for both configurations of the plane strain

models.

- 276 -

7.3.1 Axisymmetric Model

The axisymmetric model is used to simulate the unit cell concept of the

stone column. Cross section of the model is shown in Fig. (7-3 a).The

radius of the model is determined according to the influence diameter of

the stone column. The influence diameter depends on the columns

arrangement pattern and the distance between the columns. The

influence diameter for a square pattern is 1.13 times the spacing between

the columns. For this case the columns are arranged with spacing of 2.4

m, thus, the radius of the model is 1.36 m. Fig. (7-3 b), shows the

generated finite element mesh of the model. The settlement at (SP1) and

the excess pore water pressure dissipation at point (A) are shown in Figs.

(7-4 and 7-5), respectively.

- 277 -

(a) (b)

Fig. (7-3): (a) Geometry and boundary conditions for the

axisymmetric model (b) Generated finite element mesh for the

axisymmetric model.

Embankment

Stone Column Crust

Soft Clay

Stiff clay

1.36 m

- 278 -

Fig. (7-4): Settlement at SP1 using axisymmetric model.

0

10

20

30

40

50

60

70

80

90

0 10 20 30 40 50 60 70 80 90

Time, day S

ett

lem

en

t, m

m

SP1 Field

SP1 FEM

0

2

4

6

8

10

12

14

16

18

20

0 10 20 30 40 50 60 70 80 90

Time, day

Ex

cess

po

re w

ate

r p

ress

ure ,

kP

a

Fig. (7-5): Excess pore water pressures at point (A) using

axisymmetric model.

- 279 -

7.3.2 Plane Strain Model Using Equivalent Parameters

In this model, the columns are simulated as continuous walls having a

width of 0.8 m which is the same as original diameter of the stone

columns. The parameters of the wall used to simulate the stone column

are replaced by a set of equivalent parameters as shown in table (7.2).

The equivalent parameters are calculated according to equation 6.1

which in cooperates the parameters of the stone column and the soil

according to their areas relative to the area of the wall.

(7.1)

Where:

Xeq. is the equivalent parameter.

Xc is the column parameter.

Xs is the soil parameter.

Ac and As are the column and the in between soil areas respectively.

dc is the stone column diameter.

S is the spacing between columns.

Table (7.2): Stone columns parameters (equivalent parameters

plane strain model).

Material Sat. (kN/m3)

Unsat. (kN/m3)

υ E

(kPa)

Kh

(m/s)

Kv

(m/s)

c

(kPa)

φ

(deg)

Stone

column

16.3

16

0.3

8671

3.04 x 10-5

3.04 x 10-5

2

25

- 280 -

Fig. (7-6): Geometry and boundary conditions for plane strain with

equivalent parameters finite element model.

Fig. (7-7): Generated finite element mesh for plane strain with

equivalent parameters finite element model.

Figures (7-6 and 7-7) show the geometry and boundary conditions of the

used model and the generated finite element mesh, respectively. The

settlement at (SP1) and (SP2), also, the pore water pressure dissipation at

points (A) and (B) are shown in Figs. (7-8 through 7-10), respectively.

Stiff clay

Stiff clay

Soft Clay

Soft Clay

Embankment

Embankment

Stone

Column

Stone

Column

Crust

Crust

- 281 -

Fig. (7-8): Settlements at (SP1) for plane strain with equivalent

Parameters finite element model.

Fig. (7-9): Settlements at (SP2) for plane strain with equivalent

parameters finite element model.

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80 90

Time, day

Sett

lem

en

t, m

m

SP1 Field

SP1 FEM

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80 90

Time, day

Sett

lem

en

t, m

m

SP2 Field

SP2 FEM

- 282 -

Fig. (7-10): Excess pore water pressure at points (A) and (B) for

plane strain with equivalent parameters finite element model.

- 283 -

7.4 Comparison Between the 2D FE Analyses and Field

Measurements

A comparison between the behaviors of the two dimensional analyses of

the case study is introduced. The settlement, the excess pore water

pressure, the development of shear strength with time.

7.4.1 Settlement

Figure (7-11) shows the settlement at (SP1). The plain strain using

equivalent parameters analysis predicts higher values for settlement,

during the construction and early stages after, than all the other

numerical simulations; the settlement value reaches 40 mm at the end of

the construction period of 9 days compared to values of 29 mm, 28 mm

for the three dimensional and Axisymmetric respectively. However, the

plane strain with equivalent parameters analysis gives lower value for

the final settlement (67 mm) when compared to the Axisymmetric 79

The settlement behavior at (SP2) is similar to that at (SP1) as shown in

Fig. (7-12).The equivalent parameters configuration reaches higher

settlement values during the earlier stages (43.5 mm at the end of

construction). However, the settlement values at later stages are lower

for the equivalent parameters configuration (73.5 mm for the final

settlement).

- 284 -

Fig. (7-11): Comparison of settlements at (SP1).

Fig. (7-12): Comparison of settlements at (SP2).

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80 90

Time, day

Sett

lem

en

t, m

m

Field Measurments

Axisymmetric

Plain Strain

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80 90

Time, day

Sett

lem

en

t, m

m

Field Measurments

Axisymmetric

plain strain

- 285 -

Generally, as seen in table (7.3), the axisymmetric analysis gives a very

good agreement with both the 3D analysis and the field measurements

throughout the entire consolidation process.

Case

Settlement at SP1 (mm) Settlement at SP2 (mm)

At time = 9

days (end of

construction)

At time = 90

days (After end

of consolidation)

At time = 9

days (end of

construction)

At time = 90

days (After end

of consolidation)

Field

measurements 27 77 36 79

Axisymmetric 28 79 - -

Plain strain 40 67 43.5 73.5

7.4.2 Excess pore water pressure

The excess pore water pressure readings at points (A) and (B) through a

total period of 90 days are shown in Figs. (7-13) and (7-14) respectively.

The axisymmetric finite element analysis could not be used to

investigate point (B) which is a downside for this configuration type as it

cannot be used to study the behavior of the soft clay layer beyond the

embankment.

Table (7.3): Comparison between results of settlement at SP1 and SP2.

- 286 -

0

2

4

6

8

10

12

14

16

18

20

0 20 40 60 80 100

Time, day

Ex

cess

po

re w

ate

r p

ress

ure,

kP

a Plain Strain

Axisymmetric

0

2

4

6

8

10

12

14

16

18

20

0 15 30 45 60 75 90

Time, day

Ex

cess

po

re w

ate

r p

ress

ure,

kP

a

Point (B)

Fig. (7-13): Comparison of Excess pore water pressure at point (A).

Fig. (7-14): Comparison of Excess pore water pressure at point (B).

- 287 -

At point (A), the axisymmetric gives a higher value of excess pore water

pressure during the construction process and early stages after

construction reaching values of 17 KPa (at the end of construction). The

plane strain with equivalent parameters analysis predicts lower values

for the excess pore water pressure throughout the entire period reaching

a maximum value of 12.7 KPa at the end of construction.

Similarly, At point (B), plane strain with equivalent parameters analysis

simulations gives a value of excess pore water pressure during the

construction process and early stages after construction reaching a

maximum value of 2.9 KPa .

Generally, the axisymmetric shows a relatively good agreement with

field measurements at point (A). However, the plane strain with

equivalent parameters analysis predicts lower values for the excess pore

water pressure at point (A). Another comment is that the plane strain

with equivalent parameters analysis shows a much higher rate for the

consolidation process, as mentioned before, this can be associated to the

fact that the radial flow paths is smaller in this configuration which in

turn speeds up the consolidation process. A summary for the values of

excess pore water pressure for different models is show in table (7.4).

Table (7.4): Comparison of excess pore water pressure at point (A)

and at point (B).

case Maximum Excess pore

water at point (A) (kPa)

Maximum Excess pore

water at point (B) (kPa)

Axisymmetric 17 -

Plain strain 12.7 2.9

- 288 -

7.5 Examination Method of (Han and Ye 2001& 2002)

Area of stone column

effective diameter de = 1.13 S for square pattern

Area of unit cell

The settlement of the natural ground is

(7.2)

Where,

= coefficient of volume compressibility natural soil

= additional vertical stress

= thickness of soil layer

=

= 0.00068 kPa

-1

The settlement of the natural ground is

- 289 -

The settlement of the composite foundation considering the stress

reduction factor

The modular ratio of the columns to the soil

Han and Ye reported The typical elastic modulus ratios of stone column

to soft clay range from 10 to 20

(should be taken in design equal 20)

From Barksdale and Bachus (1983) design chart

The stress concentration ratio

- 290 -

Fig. (7-15): Variation of stress concentration factor with modular

ratio – linear elastic analysis.

Calculation the settlement of natural foundation

The stress reduction factor

- 291 -

where

Formula for the permeability of granular drain with fine contents in

FHWA Highway sub drainage design manual (Moulton, 1980) to

estimate the permeability of granular columns as follows:

Where

Assume = 5 for (20 – 25 % ) clay particles when stone column are installed in clay

- 292 -

Modified coefficients of consolidation of soft soil :

The coefficients of consolidation of soft soil in the vertical and radial

direction are

Modified coefficients of consolidation of soft soil in the vertical and

radial direction are

(

)

(

)

(

)

(

)

- 293 -

The equivalent diameter of the unit cell is

The diameter ratio

Time factors

The time factors in the vertical and radial direction are :

Assume time after one month

Where

Where

- 294 -

Degree of consolidation:

The degree of consolidation due to the vertical flow according to one –

dimensional Terzaghi consolidation theory is :

√

√

(

)

(

) (

)

(

)

( ) (

)

Where , the diameter ratio of the smeared zone to the stone

column

the stone column

Permeability of the smeared soil in the radial direction

If we take according Hansbo, 1987 and Bergado, 1992

- 295 -

(

)

(

)(

)

(

)

(

)(

)

The degree of consolidation due to radial flow is

(

)

The degree of consolidation due to combined vertical and radial flow is

(7.16)

Consolidation settlement at one month after construction:

The consolidation settlement of the composite foundation at one month

after construction

- 296 -

Fig. (7-16): Measured and calculated settlement – time curve

0

10

20

30

40

50

60

70

80

90

0 20 40 60 80 100

Time, day S

ett

lem

en

t, m

m

SP1 Field

Han and Ye, 2002 ( well resistance ), Mr = 27.27

Han and Ye, 2002 ( well resistance ), Mr = 20.0

Han and Ye, 2001( no well resistance)

- 297 -

7.6 Parametric Study

A parametric study has been made to show the effect of various

parameters on different aspects of the behavior of the soft soil clay

reinforced by stone columns.

Parametric studies using the finite-element analysis were performed for

the configuration of stone columns of the case study reported by Tan et

al. (2008).

The axisymmetric model is used to represent this parametric study

because of the axisymmetric model gives the best agreement with the

behavior of the field results.

The most three important factors that control the performance of soil -

stone column system can be identified as different parameters are

studied during this parametric study. These parameters are:

1- Effect spacing to the diameter of stone column ⁄

2- Effect the stress level

3- Effect the modular ratio ⁄

The effect of the last mentioned parameters on the behavior of the

reinforced soft soil is monitored through three following aspects:

1- The stress concentration factor

2- The reduction of settlement

4- The reduction in consolidation time.

Table (7.5) presents all cases which have been analyzed in this study

- 298 -

7.6.1 Stress Concentration Factor

The stress concentration factor ( ) is the ratio of the stress in the stone

column and the stresses to the stress surrounding soil. Equation 6.1

shows the Stress concentration factor definition.

7.6.2 Modular Ratio

The modular ratio ( ) is the ratio between modulus of elasticity of the

stone columns and modulus of elasticity of the surrounding soil.

7.6.3 Settlement Reduction Factor

Settlement reductions factor ( ) is the ratio between the settlement of

the treated soil by stone columns and the settlement of the untreated soil.

7.6.4 Time Reduction Factor

Time reduction factor ( ) is the ratio between the time required to reach

90% of the consolidation process for the soil deposits reinforced using

stone columns and the untreated soil deposits.

- 299 -

Table (7.5): parametric study

Column

diameter,

D

(m)

Column

spacing,

S

(m)

Column

spacing to

diameter

ratio, S/D

Embank-

ment

height, H

(m)

Stress

level

× H

(kN/m2)

Modulus

of

elasticity

of

soft clay,

Ec (kPa)

Modulus of

elasticity of

stone column,

Es (kPa)

Modular

ratio

Es /Ec

0.8

1.6 2

6

32.4

1100

30000

27.27

2.4 3

3.2 4

4.0 5

4.8 6

5.6 7

0.8

2.4

3

1.5 27.00

1100

30000

27.27

2.5 45.00

3.5 63.00

4.5 81.00

5.5 99.00

6.5 117.0

0.8

2.4

3

6

32.4

1100

15000 13.64

25000 22.73

35000 31.82

45000 40.91

55000 50.00

65000 59.10

- 300 -

7.7 Effect of Spacing to the Diameter of Stone

Column ⁄

To study the simultaneous effect of centre to centre spacing (S) and

diameter of stone column (D), six different values; 2, 3, 4, 5, 6 and 7 for

⁄ is investigated. In the case study stone columns is established

with diameter of 0.8 m and spacing of 2.4 m. The effect of changing

value of ⁄ ratio on the stress concentration factor is shown in Fig.

(7-17).

It is found that the stress concentration factor increases from a value of

4.0 to 4.63at spacing to diameter ratio of 2 and 5 respectively. After this

value the stress concentration factor seems be constant until

3.8

4

4.2

4.4

4.6

4.8

5

0 1 2 3 4 5 6 7 8

S /D

Str

ess

co

ncen

tra

tio

n

facto

r (

n)

Fig. (7-17): Effect of columns spacing on the stress concentration factor.

- 301 -

value ⁄ . This can be observed due to load shearing between

columns and surrounding soil as confirmed by arch effect. It has been

found that the optimum spacing is found to be five time of column

diameter (5D) because of the stress concentration factor is remaining

constant. Over this range of spacing inapproachable effect on the stress

concentration factor.

The effect of increasing the column spacing on the reduction in

settlement is shown in Fig. (7-18). The settlement is reduced by as much

as 89% for spacing of 7D, while this reduction is dropped to 36% at S

equal 2D.

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6 7 8

S / D

S

ett

lmen

t red

ucti

on

fa

cto

r

(%)

Fig. (7-18): Effect of columns spacing on the settlement reduction factor.

- 302 -

The effect of increasing the column spacing on the reduction of

consolidation time is shown in Fig. (7-19). The reduction in time of the

consolidation process is gradually increased up to reach the higher value

of 8.4% at (S = 7D) while this value is found to be 2.0% at (S = 2D). It

can be seen that at minimum spacing with the range of S/D < 4, the time

reduction factor is very low.

This shows that the variation of the ⁄ ratio has a much greater

effect on the reduction of settlement when compared to the reduction of

the consolidation time.

7.8 Effect of Stress Level

In this study the height of embankment is varied to evaluate its effects

on the stress level that transferred to stone column system. The

embankment height during this study is taken with the values of 1.5 m,

0

2

4

6

8

10

12

0 1 2 3 4 5 6 7 8

S / D

T

ime r

ed

ucti

on

fa

cto

r

(%)

Fig. (7-19): Effect of columns spacing on the time reduction factor.

- 303 -

2.5 m, 3.5 m, 4.5 m, 5.5 m and 6.5 m, these values agree with stress

levels of 27 kPa, 45 kPa, 63 kPa, 81 kPa, 99 kPa and 117.0 kPa

respectively.

Fig. (7-20) shows that the increases of embankment height lead to

distinctly reduction on the stress concentration factor. It can be observed

that the stress concentration factor is reduced as 3.9 at minimum

embankment height (H =1.5m), while this value is dropped to minimum

level 3.2 at maximum height of the (H = 6.5 m) that is due to, the

considerable increase on the overburden pressure that increased by the

increase of height of the embankment. This can be observed due to the

increase of the stress level affecting on the reinforced soft soil increases

the confinement provided to the stone columns that correspond increases

the columns capacity and the stresses diverting to the columns.

3

3.2

3.4

3.6

3.8

4

0 1 2 3 4 5 6 7 8

Embankment height (m)

S

tress

co

ncen

tra

tio

n f

acto

r

Fig. (7-20): Effect of stress level on the stress concentration factor.

- 304 -

On the other hand, the effect of changing the embankment height on the

reduction in the settlement is shown in Fig. (7-21).The reduction in the

settlement of the reinforced soft soil deposits increases from a value of

55% to 78% when the embankment height varied from 1.5 m to 6.5 m.

This is due to the fact that the stress levels diverting to the soft soil.

Thus, increasing the resulting settlement and in turn decreasing the

reduction in settlement ratio.

The effect of variation the embankment height on the time reduction

factor is shown in Fig. (7-22). It is obvious that the increase in the

embankment height has a relatively minor effect on the time reduction

factor. It is noticed that the time reduction factor is found to be in range

of 2.0 to 2.8% at embankment height of 1.5, 6.5m respectively.

40

50

60

70

80

90

100

0 1 2 3 4 5 6 7 8

Embankment hight (m)

Sett

lem

en

t red

ucti

on

fa

cto

r

(%)

Fig. (7-21): Effect of stress level on the settlement reduction.

- 305 -

Fig. (7-22): Effect of stress level on the time reduction factor.

7.9 The Effect of Modular Ratio

The difference in the modular ratio through this study is done by

increasing the value of the elasticity modulus of the stone columns but

the value of the elasticity modulus for the soft clay is kept at a value

1100 kPa. The modulus of elasticity for the stone columns is taken

15000 kPa, 25000 kPa, 35000 kPa, 45000 kPa, 55000 kPa and 65000

kPa through this parametric study. The effect of the modular ratio on the

stress concentration factor is shown in Fig. (7-23). The stress

concentration factor increase from value of 2.2 to value of 4.0 when

increasing the modular ratio from 13.64 to 59.10. This increase is

explained by the fact that increasing the modular ratio leads to an

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8


Tim

e r

ed

ucti

on

fa

cto

r

(%)

- 306 -

increase in the stone columns stiffness when compared to that of the soft

soil. And therefore higher stresses and more loads are transferred to the

column instead of the soft soil.

The effect of the modular ratio on the settlement reduction factor is

shown in Fig. (7-24). The increase in the modular ratio increases the

relative stiffness of the stone columns which leads to less stresses on the

soft soil. This can explain the decrease in the settlement reduction factor

from 69.5% to 68% as the modular ratio increased from 13.64 to 59.10.

1.8

2.2

2.6

3

3.4

3.8

4.2

4.6

0 10 20 30 40 50 60 70

Modular ratio

S

tress

co

ncen

tra

tio

n f

acto

r

Fig. (7-23): Effect of Modular ratios on the stress concentration.

- 307 -

The effect of the modular ratio on the time reduction factor is shown in

Figures (7-25). A small increase in the value of time reduction factor

from value 1.82% to1.85% as the modular ratio increased from 13.64 to

59.10.

60

65

70

75

80

85

90

0 10 20 30 40 50 60 70

Modular ratio

S

ett

lem

en

t red

ucti

on

fa

cto

r (

%)

Fig. (7-24): Effect of Modular ratios on the settlement reduction factor.

- 308 -

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

0 10 20 30 40 50 60 70

Modular ratio

Tim

e r

ed

ucti

on

fa

cto

r (

%)

Fig. (7-25): Effect of Modular ratio on the time reduction factor.

factor

- 309 -

7.10 Comparative Study

In this section, the results of the parametric study previously performed

using the finite element model are compared to the behavior of the stone

column in soft soil estimated by some of the theoretical approaches as

stated by variety of investigators .

7.10.1 The Stress Concentration Factor

The value of the stress concentration factor generally lies between 2.0

and 6.0 (Goughnour and Bayuk 1979, Aboshi etal. 1979) with values of

3.0 - 4.0 usual, at the ground surface.

A comparison between the stress concentration factor given by the

numerical modeling and that calculated using different theoretical

approaches such as the analytical methods of Pulko and Majes (2006) is

performed.

The effect of the variation of spacing between columns on the stress

concentration factor is illustrated in Fig. (7-26). It is found that the curve

of the behavior predicted by Pulko and Majes (2006) is agreed and has

the same trend to the curve of the present study. It is also found that the

maximum difference between the two cases is found to be around 20%

as clearly shown in the relevant figure. Moreover, at S/D =5, the stress

concentration factor remain constant for both present study and Pulko

and Majs (2006).

- 310 -

Fig. (7-26): The effect of column spacing on the stress concentration

factor using numerical modeling and theoretical approaches.

It can be seen that the concentration factor higher than that estimated

through the numerical modeling. This can be observed due to due to the

assumption that no lateral bulging occurs in the column which in turn

increases the capacity of the column.

When studying the effect of the variation of the embankment height

from 1.5 m to 6.5 this approach gives decrease in the stress

concentration factor from a value of 3.9 to a value of 3.2 for

embankment heights of 1.5m and 6.5m respectively as shown in Fig. (7-

27). .

The analytical approach of Pulko and Majes (2006) gives higher values

for the stress concentration factor than the values estimated by the

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6 7 8

S/D

Str

ess

co

ncen

tra

tio

n f

acto

r

Numerical analyses (Present study)

Pulko and Majes (2006)

- 311 -

numerical analyses as the values of the stress concentration factor lies in

the range between 5 to 6.The difference between the two approaches is

in the 30%. Moreover, the approach by Pulko and Majes (2006) ignore

the effect of the embankment height (i.e. stress level) on the stress

concentration factor as it gives a value of 5.5 for the stress concentration

factor regardless to the stresses applied to the reinforced soil system

which is not accurate according to the numerical study.

On the other hand, the results of variation of the modular ratio in the

numerical study show, the stress concentration factor increase from a

value of 2.2 to a value of 4.0 for modular ratios 13.64 and 59.1

respectively.

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6 7 8

Embankment hight

Str

ess

co

ncen

tra

tio

n f

acto

r

Numerical analyses (Present study)


Fig. (7-27): The effect of embankment height on the stress

concentration factor using numerical modeling and theoretical.

approaches

- 312 -

The relation between the modular ratio and the stress concentration

factor calculated using the analytical approach of Pulko and Majes

(2006) gives higher values for the stress concentration factor than the

values estimated by the numerical analyses as the values of the stress

concentration factor lies in the range between 5 to 6 as shown in Fig. (7-

28). The difference between the two approaches is in the range of 30%

to 65%. Moreover, the approach by Pulko and Majes, (2006) ignores the

effect of the modular ratio on the stress concentration factor as it gives a

value of 5.5 for the stress concentration factor regardless to the modular

ratio to the reinforced soil system which is not accurate according to the

numerical study.

The results of numerical analyses also correspond with the experimental

study conducted by Ambily and Gandhi, (2007) where he showed that

the stress concentration factor (n) increases with the increase in modular

ratio.

- 313 -

Fig. (7-28): The effect of Modular ratio on the stress concentration


7.10.2 The Settlement Reduction Factor

The effect of the column spacing to diameter ratio ⁄ on the

settlement reduction factor show in Fig. (7-29). The settlement reduction

is estimated using numerical analyses as well as theoretical approaches

of Pulko and Majes (2006). It is noticed that the behavior of the

settlement reduction variation with the column spacing by Pulko and

Majes (2006) is similar to that of the parametric study as it increases

from 45% to 92% with the increase of the spacing to diameter ratio from

2 to 6 which corresponds to an increase from 36% to 89% estimated for

the same increase in spacing to diameter ratio using the numerical

analyses.

0

2

4

6

8

10

12

14

16

0 10 20 30 40 50 60 70

Modular ratio

Str

ess

co

ncen

tra

tio

n f

acto

rNumerical analyses (Present study)


- 314 -

The theoretical approach of Pulko and Majes (2006) shows a very good

agreement with the results of the numerical analyses when used to

estimate the settlement reduction factor. The settlement reduction factors

given by both the Pulko and Majes (2006) approach and the numerical

modeling almost coincide with the variation of column spacing.

Fig. (7-29): The effect of column spacing on the settlement reduction


The effect of the embankment height on the settlement reduction factor

show in Fig. (7-30). Pulko and Majes, (2006) approach does not depend

on the applied stress in its calculations and gives a constant value for the

settlement reduction factor with the variation of the embankment height,

the value given by this approach (70%) is almost the average value of

the settlement reduction factor given by the parametric study which

gives a value of 55% at an embankment height of 1.5m and increases to

0

20

40

60

80

100

120

0 1 2 3 4 5 6 7 8

S/D

Sett

lmen

t red

ucti

on

fa

cto

r (

%)

Numerical analyses ( present study )


- 315 -

78% at an embankment height of 6.5m. This can return to the fact that

this approach considers the column lateral bulging as well as its

plasticity.

The effect of the modular ratio on the settlement reduction factor show

in Fig. (7-31). The theoretical approach of Pulko and Majes (2006)

shows a very good agreement with the results of the numerical analyses

when used to estimate the settlement reduction factor. The settlement

reduction factors given by both the Pulko and Majes (2006) approach

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6 7 8


Sett

lmen

t red

ucti

on

fa

cto

r (

%)

Numerical analyses (present study)


Fig. (7-30): The effect of embankment height on the settlement

reduction factor using numerical modeling and theoretical approaches.

- 316 -

and the numerical modeling almost coincide with the variation of the

modular ratio.

Fig. (7-31): The effect of modular ratio on the settlement reduction


7.10.3 The Time Reduction Factor

The analytical method of Han and Ye, (2001) is used comparison

between the time reduction factor given by the parametric study and that

calculated using theoretical approaches. Fig. (7-32) show the variation of

the time reduction factor with spacing between columns.

Spacing between columns as it estimates an increase of the time

reduction factor from 0.15% to 3.2% when increasing the column to

diameter ratio from 2 to 7. This agrees with the findings of the

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80

Modular ratio

Sett

lmen

t red

ucti

on

fa

cto

r (

%)

Numerical analyses ( present study)


- 317 -

numerically performed parametric study, however, the numerical

analyses estimates a higher rate of increase from 0.5% to 4.9% for the

same range of column diameter to spacing ratios.

Fig. (7-33) show the variation of the time reduction factor with

embankment height of the theoretical approach with Han and Ye (2001)

and the parametric study. This approach agreed with the numerical

analyses in the fact that the embankment heights (applied stress level) do

not have a significant effect on the time reduction factor as it gives a

constant value of 0.5% for the time reduction factor for embankment

heights ranging from 1.5m to 6.5m. However, the numerical analysis

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7 8

S/D

Tim

e r

ed

ucti

on

fa

cto

r (

%)

Numerical analyses ( present study )

Han and Ye (2001)

Fig. (7-32): The effect of column spacing on the time reduction


- 318 -

estimates a value of 2% to 2.88% for the embankment heights from

1.5m to 6.5m respectively.

Fig. (7-33): The effect of embankment height on the time reduction


Fig. (7-34) show the variation of the time reduction factor with modular

ratio of the theoretical approach with Han and Ye (2001) and the

parametric study. This approach agreed with the numerical analyses in

the fact that the modular ratio does not have a significant effect on the

time reduction factor as it gives a constant value of 0.4% for the time

reduction factor for modular ratios ranging from 13.64 to 59.1.

However, the numerical analysis estimates an almost constant value of

1.82% for a value of 1.85% for modular ratios from 13.64 to 59.1.

0

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7

Embankment height (m)

Tim

e r

ed

ucti

on

fa

cto

r (

%)

Numerical analyses ( present study)

Han and Ye (2001)

- 319 -

Fig. (7-34): The effect of modular ratio on the time reduction factor

using numerical modeling and theoretical approaches.

7.11 Comparative study with different investigators on

stone columns

In order to show the beneficial effect of stone columns on soft clay as an

improvement tools, a comparative study with different studied stone

columns techniques were carried out.

The values of (n) as presented by (McCabe et.al, 2009), which refers to

settlement performance. It captured in the form of a settlement

improvement factor (n), which defined as:

n = Suntreated /Streated

0

1

2

3

4

5

6

7

8

0 10 20 30 40 50 60 70

Modular ratio

Tim

e r

ed

ucti

on

fa

cto

r (

%)

Numerical analysis ( present study)

Han and Ye (2001)

- 320 -

Where Suntreated is the settlement (of the loaded zone) in the absence of

stone column treatment, and Streated is the corresponding settlement with

stone column treatment.

Fig. (7-35) shows the relationships between (n) versus (A/Ac) area

replacement ratios for different investigated stone column of field study.

The mean curve of (Priebe, 1995) used as a basic improvement factor as

illustrated in the relevant figure. The quantity used by Priebe, 1995

captured the concentration of column array in an infinite grid is referred

to the area replacement ratio, A/Ac where A is the plan area of the ‗unit

cell‘ attributed to a single column, and Ac is the cross-sectional area of

one column.

Also, it can be seen that there is a spread data around the mean curve by

different field tests of mentioned investigators. While for the present

study of small scale test, the value of A/Ac ratio plotted against (n) at

Fig. (7-35): Settlement improvement factor against area replacement

ratio for sites with widespread loading

- 321 -

the same curve for both drained and undrained condition of end bearing

stone columns of (D = 150 mm , 300 mm , cu = 20 kPa)

It has been found that the settlement improved factor n is decreased with

the increase of stone column diameter.

It also has a lower value compared with mean curve of (Priebe, 1995)

and different field data. That is backed to the variation of scale effect

and stress level between the field and small scale test. But the present

data has the same trend. As a result the adopted stone column technique

considered as advanced effective method to increase the soft clay

resistance and control the settlement compared with other investigators.

CHAPTER (8):

CONCLUSIONS AND

RECOMMENDATIONS

- 322 -

CHAPTER (8)

CONCLUSIONS AND RECOMMENDATIONS

8.1 Introduction

A series of small scale laboratory model tests and numerical analysis has

been carried out to investigate the bearing capacity of a circular plate

resting on entire area loading of stone column within soft clay. The

study primary focused on studying the effect of stone column diameter,

length and soft clay shear strength. The drained condition is also

investigated using numerical modeling to compare between drained and

untrained conditions.

8.2 Conclusions Regarding experimental results

The following conclusions can be drawn:

1- The existence of such stone column within the soft clay can

significantly modify the load displacement behaviors.

2- When the stone column in the base soil increased by 2, 3 and 6

times of its initial diameter, the load carrying capacity are

approximately 1.34, 1.53 and 3.2 times of its initial value in case

of (cu = 10 kPa ).

3- In case of stone column installed in soft clay with cohesion 10

kPa with full penetration depth, the increase of stone column

diameter from 50 to 100 mm increased the ultimate capacity by

128%. This increase is found to be 319% for stone column

diameter of 300 mm.

- 323 -

4- The load settlement behaviour of drained condition when entire

area is loaded is almost linear and it is possible to arrive at the

stiffness of the improved ground.

5- The measurements made before and after testing showed that the

ultimate bearing capacity of stone columns increased by about

(1.8 and 5.2) % at L/D = 2, 8 respectively for cu = 10 kPa.

6- The increase of clay cohesion has a relatively minor variation on

the ultimate load capacity of stone columns

7- Stiffness improvement factor is found to be independent on shear

strength of surrounding clay and depends mainly on column

diameter and length.

8- The deformation of end bearing stone column was more

prominent in the upper region over the length of 2.5D. The

maximum lateral deformation (bulging) was found to be at depth

of (1.25-1.5) D below the top surface of the failed column.

9- The failure pattern of floating stone column was observed as a

punching shear failure.

8.3 Conclusions Regarding Numerical Analysis of

Laboratory Model Tests

1- The numerical analysis is helped to understand the failure pattern

of stone column and confirm the model test results.

2- The numerical results using both Mohar column and Hardening

models has the same trend with model test with difference

around 5%.

- 324 -

1- The improvement in the load carrying capacity of stone column

is reached to 1.74, 1.92, 2.16 and 2.81 times compared to

untreated soil with different L/D ratio of 2, 4, 6, and 8

respectively.

2- For floating stone column (L/D = 2, 4, 6) the load settlement

response is partially different from the curve of end bearing case

of (L/D= 8).

3- The capacity of 100mm diameter stone column at 25 mm

settlement with L/D ratio of 1, 2, 3 and 4 are 2.56, 3.22, 3.55 and

4.9 kN respectively. The load carrying capacity of stone column

compared to untreated soft clay with different L/D ratio of 1, 2,

3, and 4 are increased by 1.84, 2.32, 2.55 and 3.53 times

respectively.



5.35 kN respectively. The load carrying capacity of stone column

compared to untreated soft clay with different L/D ratio 1, 2, 3,

and 4 is increases up to 2.23, 2.60, 2.91 and 3.85 times of its

initial value.



9.19 kN respectively. The increase in the load carrying capacity

of stone column compared to untreated soft clay with different

L/D ratio 1, 2, 3, and 4 are found to be 2.91, 4.10, 5.22 and 6.61

times of its initial value.

- 325 -

8.3.1 Numerical Analysis of Drained Condition (cu = 10 kPa)

a) In case of (D = 50 mm),

1- Increasing the L/D ratio significantly improved the load capacity

of stone column until reaching to higher value in end bearing

column (L/D = 4).

2- The ultimate load capacity of reinforced subgrade by stone

column with (L/D = 1 to 3) as floating type increased by around

(73 % to 110 %), while at (L/D = 4) for end bearing case the load

is increased by 152.5%.

3- At (L/D = 1) the settlement of stone column system is reduced by

14% of its initial value of soil without stone column. While this

reduction is found to be (24%, 30% and 35%) in case of (L/D =

2, 3 and 4) respectively.

4- When the stone column installed in soft clay under drained

condition the settlement is remarkably achieved with lower


b) In case of (D = 100 mm),

1- The increase of the L/D ratio significantly improved the load

capacity of stone column until reaching to higher value in end

bearing column (L/D = 4).

2- The ultimate load capacity of reinforced subgrade by stone


(94.3 % to 162.5 %), while at (L/D = 4) for end bearing case the

load is increased by 190%.

3- At (L/D = 1) the settlement of stone column system is reduced by

24% of its initial value of system without stone column. While

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this reduction is found to be (27%, 31% and 36%) in case of

(L/D = 2, 3 and 4) respectively.

c) In case of (D = 150 mm),

1. The ultimate load capacity of reinforced subgrade by stone


(121.25 % to 199.38 %), while at (L/D = 4) for end bearing case

the load is increased by 231.25%.

2. At (L/D = 1) the settlement of stone column system is reduced by

26% of its initial value of system without stone column. While

this reduction is found to be (29.4%, 32.5%, 38%) in case of

(L/D = 2, 3 and 4) respectively.

d) In case of (D = 300 mm),

1. The increase of L/D ratio produced a considerable increase in the

ultimate load capacity. It is also found that the increase of stone

column stiffness provides a linear variation in load displacement

curve at L/D = 0.33, 0.67, 1 and 1.33. The improvement in

ultimate load capacity are found to be 173.75, 290, 375, 452.5 %

for L/D =0.33, 0.67, 1, 1.33 respectively, while the settlement is

reduced by as much as 41% for end bearing case (L/D = 1.33).

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8.4 Conclusions Regarding Comparison Between Drained

and Undrained Condition

2. The load displacement responses of vertically loaded stone

column under drained condition are totally different from case of

undrained condition.

3. The ultimate load capacity of stone column in case of no

permeation for drained is higher than of drained case. Also it was

found that the settlement of stone column soil system is lower

than of stone column in drained condition.

4. The drained case provided a minor capacity with high settlement.

That is due to the dissipation of pore water pressure, which can

be effectively resisted the additional loads within the stone

column when no permeation allowed for water. Therefore the

undrained case is significantly produced additional resistance for

loads.

5. For floating stone column under undrained case, linear behavior

is achieved for different (L/D) and clay cohesion. While for end

bearing case the nonlinear relationship is achieved at failure.

6. The end bearing stone columns are subjected to vertical

confining pressure that significantly provided additional load

resistance. As a result yielding behavior is observed at failure

compared with floating cases.

7. The increases of stone column ultimate resistance due to

undrained condition are related to subgrade cohesion and stone

column stiffness (L/D).

- 328 -

8. At stone columns diameters of (D = 100, 150, 300 mm) for

cohesion of cu = 10 kPa, the increase of ultimate capacity are

expected in range of (14%, 17%, 18% and 20%) respectively.

Whereas, the increases of undrained shear strength has also a

great effect on increasing the load capacity under undrained

conditions. It has been found that for stone column diameter of

50 mm, the increase of load capacity of stone columns were

found to be around 24% and 29% at (cu = 20 , 30 kPa)

respectively.

9. In general, it can be concluded that the pore water pressure

within the stone columns can sustain around (12-25%) of

ultimate load in drained case according to stone column

geometry and clay cohesion.

8.5 Conclusions Regarding Effect of stone column on

Subgrade modulus

1. The existence of stone column can increase the subgrade

modulus by the increase of stone column diameter.

2. For drained condition cu = 10 kPa, the improvement on the

subgrade modulus are found to be 1.2, 2.5, 3 and 5.7 time of soil

without stone column for column diameter of (50,100,150 and

300 mm) respectively. While in the undrained condition these

improvements in the subgrade modulus are found to be 1.9, 2.8,

3.7 and 7.7 time in the same order of the diameter.

3. The undrained condition has a great effect on increasing the

subgrade modulus. That is due to the resistance of the pore water

- 329 -

pressure. The induced pore water pressure within the stone

column can increase the resistance of stone column against

acting loads. As result the ultimate load capacity is increased by

considerable value compared with drained condition.

8.6 Conclusions Regarding Case study and parametric

study

The following conclusions can be drawn:

1. Two dimensional finite element analyses is the most suitable method

for predicting the behavior of stone columns used to improve soft soil

deposits.

2. Increasing the spacing between the stone columns leads to:

- Increase in the stresses transferring to the stone columns to a certain

extent then it becomes insignificant.

- Decrease in the reduction of settlement.

- Decrease in the reduction of consolidation duration.

3. Increasing the stress level on the reinforced soil system leads to:

- Decrease in the stress concentration factor.

- Decrease in the reduction of settlement.

- Almost in significant in the reduction of consolidation duration.

4. Increasing the Modular ratio leads to:

- Increase in the stress concentration factor.

- Slight increase in the settlement reduction.

- Almost in significant in the reduction of consolidation duration.

- 330 -

8.7 Recommendations for Future Studies

1. The application of geogrids or Geosynthetics as an encasement

to increase the confinement and thus the capacity of the

columns.

2. The effect of the cementation of the upper part of the column on

its capacity.

3. The adequacy of different theoretical approaches for different

cases especially long or floating columns needs further study.

4. Study using centrifugal model or large scale tests to provide

more information of loaded stone columns under both drained

and undrained conditions.

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PUBLISHED PAPER

- 354 -

PUBLISHED PAPER Abdel Moneim, K., Farouk, A., Shahein, M. and Sakr, M., (2016):

―Model Study of Stone Columns in Soft Clay‖, the Ninth Alexanria

International Conference on Structural and Geotechnical Engineering

2016, 19 to 21 December.

MODEL STUDY OF STONE COLUMNS IN SOFT CLAY Abdel Moneim, K.

1, Farouk, A.

2, Shahein, M.

3 and Sakr, M.

4

1 Researcher at Structural Engineering Department, Faculty of Engineering, Tanta

University

[email protected] 2Associate Prof., Structural Engineering Department, Faculty of Engineering, Tanta

University

[email protected] 3Prof. of Geotechnical Engineering, Faculty of Engineering, Tanta University, Egypt

[email protected] 4Prof. of Geotechnical Engineering, Faculty of Engineering, Tanta University, Egypt

[email protected]

ABSTRACT Stone columns have been used as an effective technique for improving the engineering

behavior of soft clayey grounds. The soil improvements using stone columns are

achieved via increasing the load carrying capacity and reduction of settlement due to

inclusion of stronger granular material. In this research a detailed experimental study

on the behavior of floating and fully penetrating single stone column model is carried

out. The tested parameters include the stone columns geometry and undrained shear

strength of soft clay. Laboratory tests are carried out on columns of 50 mm, 100 mm,

150 mm and 300 mm in diameter with different lengths of 100 mm, 200 mm, 300 mm

and 400 mm surrounded by a soft to medium clay with different undrained shear

strength in the range of 10 to 30 kPa. The tests are carried out on the entire equivalent

loaded area to estimate the stiffness of the improved ground. The results showed that

the tested stone columns can significantly increase the bearing capacity with a

remarkable reduction of the foundation settlement. It was found also that the ultimate

bearing capacity of a soft clay having a cohesion of 10 kPa increased by about 1.8 (for

partially penetrated stone columns) and keeps increasing as a result of increasing the

column length until reaching a value of 5.2 (for fully penetrated stone column) times

the bearing capacity of the same clay but without the inclusion of a stone column. It

was concluded that, the improvement factor is found to be independent of the shear

strength of the surrounding clay, while it depends mainly on both the column diameter

and length.

Keywords: stone column, Settlement, Bearing capacity, Soft clay, undrained shear

strength.

- 355 -

PUBLISHED PAPER Sakr, M., Shahein, M., Farouk, A. and Abdel Moneim, K., (2017):

―Numerical Modeling of Stone Columns in Soft Clay for Drained and

Undrained Conditions‖, Electronic Journal of Geotechnical Engineering,

Vol.22, PP. 1907-1924.

NUMERICAL MODELING OF STONE COLUMNS IN SOFT

CLAY FOR DRAINED AND UNDRAINED CONDITIONS

SAKR, M.1, SHAHEIN, M.

2, FAROUK, A.

3 and ABDEL MONEIM, K.

4

1 Prof. of Geotechnical Engineering, Faculty of Engineering, Tanta University,

[email protected] 2 Prof. of Geotechnical Engineering, Faculty of Engineering, Tanta University,

[email protected] 3 Assistant Prof. of Structural Engineering Department, Faculty of Engineering, Tanta

University, Egypt,

[email protected] 4 A Researcher at Structural Engineering Department, Faculty of Engineering, Tanta

University, Egypt,

[email protected]

ABSTRACT

During the last three decades, stone columns have been increasingly used worldwide to

improve soft soils by increasing the soil carrying capacity and reducing the settlement.

Stone columns has been successfully applied below foundations of different types of

structures (e.g., oil storage tanks, earthen embankments, raft foundations of high rise

buildings, etc…) where large settlement is highly expected. In this paper, analyses of

stone columns embedded in soft clay soil have been performed using the finite element

numerical program PLAXIS 2D software. Drained and undrained analyses were carried

out using the Mohr-Coulomb‘s model for the soft clay at different shear strength values

(cu). Series of modeled stone columns were simulated at different length to diameter

(L/D) ratios. The results showed that reinforcing soft clay by stone columns having

(L/D) ratios between 2 to 8 increase the load carrying capacity of the clay by nearly

1.74 to 2.81 times the load carrying capacity of the untreated soft clay. In addition, a

comparison between the results of drained and undrained analysis showed that the pore

water pressure within the stone columns in case of undrained condition can sustain

about 12 to 25% of the ultimate load in drained condition depending on dimensions of

the stone column and shear strength of the clay.

Keywords: Stone Columns, PLAXIS 2D, Bearing Capacity, Soft Clay.

ARABIC SUMMARY

ملخص الرسالت

ركاميتاألعمذة التقنيت ستخذامإاللينت بتحسين التربت

١- المقذمت :

ازشثخ ١غذ ثبشئ اغذ٠ذ فمذ ػشفب اإلغب ف اؼظس امذ٠خ اغبثمخ رم٠خا فىشح

زشبسا امذ شذ زا اغبي رمذب عش٠ؼب , ازـج١مبد اخزفخ اؼذ٠ذ عزخذب فا

اعؼب ف وض١ش ازـج١مبد اخزفخ ذعخ اذ١خ خبطخ ف اشآد اغبذح اغذد

. أوزبف اىجبس اغغس اـشق أعبعبد اجب

رؾذ٠ب ػظ١ب شبو از رضثب أ ازشثخ اـ١١خ ا١خ رؼزجش اؽذح ازشثخ راد ا

ا ؼؼف مبخ امض ب از رغؼ لذسح رؾب ػؼ١فظش هذط اذ ر

عزخذا ز ا ب, ف ؽ ابرغ از رؾذس ػمت اجبء ازؾ١ ػ١باج ل١خ ض٠بدح ا٠ؼب

بن اؼذ٠ذ ز ازشثخ وزشثخ رؤع١ظ ؼذ٠ذ اشآد اذ١خ ٠زـت رم١بد خبطخ

عزخذذ زغت ػ شبو زا اع أعزؾذصذ ز فزشاد عبثمخ أازم١بد از لذ

اشأع١خ اظبػ١خ , األػذح ظبسف, ا اغجكازشثخ رؾغ١ خاطب ض ازؾ١

١ عزخذا رم١خ األػذح اؾغش٠خ زؾغاؽذ٠ضب ٠ؼزجش . ....اخاش١خ األػذح اؾغش٠خ

خاص ازشثخ اـ١١خ ا١خ ازم١بد ابخ از رغزعت ػ١ب ازعغ ف دساعزب

وزه ا١زب ف ابرظ جؽا رم١ اإلسرىبص مبخره ذسب اىج١ش ف ص٠بدح

ؾ ظشا غخ رف١زب وب الزظبد٠خ ف ازؼبغ ػ١خ إلرب االص اض ازم١

.رىب١ف اشبئب ثبمبسخ ثبـشق األخش

٢- أهذاف البحث :

ا اغشع زا اجؾش دساعخ أعة رذػ١ ازشث اـ١١ ا١ ثبعزخذا رم١خ

ر رمغ١ اذساع ا عضئ١ : األػذ اؾغش٠ طي ا أذاف اجؾش

خ ؽبالد خزفخ ازشث اـ١١ ٠ؾز ػثاعـخ ثشبظ ػ ػ١ اػذاد دساعخ ر

خزف از ر رذػ١ب ثؤلـبس أؿاي ا١ اغض ؼ١ب ثمببد لض خزف

.ز ازشث١بس الؽظخ عن إلرؾ١ب ؽز اؼد اؾغش ر ا

أصجزذ ازبئظ أ اغؼخ امظ زؾ١ زشث اما ثاعـخ األػذح اؾغش٠خ ٠ؼزذ ػ

لـش اؼد اؾغش ؿ ؽ١ش رظ غجخ ازؾغ ف لذسح رؾ األعبط اشرىض ػ

ثذ أػذح ؽغش٠خ. شح لذسح رؾ األعبط ,٣2ػد ؽغش ا ؽا

أ اإل١بس اؾبدس ؼد اؾغش ف طسح خالي اذساعخ اؼ١خ رالؽق

bulging . ف غبفخ شح ظف لـش اؼد مبعخ عـؼ األسع

ثبـشق اظش٠خ ػ ؿش٠ك اػذاد رط ثاعـخ ثشبظ ظش اشزذ اذساعخ أ٠ؼب

( ؼ رؾ١ زؤص١ش اغبػ ثزظشف ا١ب أصبء ازؾ١ Plaxis 2d) ع١رم زخظض

ا ظؼثخ اعشاء ز ازم١خ ف اؼ دساعخ عن اؼد اؾغش افز ف ازشثخ ظش

اـ١١خ ا١خ ف ز اؾبخ .

أ ؾ اؾ اجؽ ف ؽبخ اغبػ ثزظش٠ف ا١ب ٠م ػ ظ١ش أشبسد اذساعخ

عد ػغؾ ا١ب ف ف اؾبخ اؼبد٠خ ثذ اغبػ زظش٠ف ا١ب , ٠شعغ ره ا رؤص١ش

افشاغبد از رؼ ػ ص٠بدح عؼخ ازؾ١ ؼد اؾغش ػ ػذ اغبػ ١ب

ثبخشط .

رالؽق أ ؾ اؾ اجؽ ٠ؾذس مض ؾف ػ اغبػ ثظشف ا١ب ٠ظ

ثبمبسخ ثبؾبخ اغ١ش زظشفخ. جؽ %٥,% ؾ وزه ٢,ا ؽا

ثبألػذح اؾغش٠خ اغؾخ اـ١١خ ا١ف خاص ازشثخ اؾبدس دساعخ ازـس روزه

ره ػ ؿش٠ك اػذاد رط ثاعـخ زا اجشبظ ازؤوذ دلخ زا غ شس اض

مبسخ زبئغ ثزبئظ ؽم١خ ششع عبثك وب ؼشف ذع١ ارط ره ث

عزخذا اجشاظ اضالص١خ اأ شى ثذلخ ػب١ فب ٠غزعت ػ١ب اغ١رم١١ أ زض١

فزذ امبس ث١األثؼبد ى غذ أ اجشاظ اضبئ١خ األثؼبد األع األوضش ازشبسا

األػبع اضبئ١خ األثؼبد ػغ ازبص اؾس ػغ ازبص اـ زبئظ

رج١ أ ؽ١ش ازبئظ اؾم١خ جشبظاث١ زبئظ مبسخ ؼثبعزخذا خاص ىبفئ

زبئظ اؾم١خ. ػغ ازبص اؾس األلشة

وب أوذد اذساعخ اظش٠خ أ عد اؼد اؾغش ٠ؼ ػ ص٠بدح عغبءح ازشثخ اـ١١خ

ا ٠ؾذس رؾغ ؾف ؼب شخ ازشثخ اذػخ ثبألػذح اؾغش٠خ ثم١خ رظ

شح ل١خ ؼب ازشثخ ثذ أػذح ؽغش٠خ ٧2٧

٣- محتوياث الرسالت :

فظي ٠ى رخ١ظ وب ٠ : صب١خػ اشعبخرؾز

الفصل االول :

ذافب غبي اذساعخ وزه أرشز ػ خض شعبخ ٠ؾز زا افظ ػ مذخ

اغك اؼب ألعضاء اشعبخ رظ١ب . عزؼشاعارؾز ػ

الفصل الثانى :

از عجك ششب ف غبي اجؾش األثؾبس ثؾبسألا٠ؾز ػ شاعؼخ اعزؼشاع

ىبي رغـ١خ اذساعخ اـث اإلعزفبدح ازؼمخ ثبجؾش از ٠ى اإلعزفبدح ب إلعز

. اغبثم١جبؽض١ ب إلعشاء امبسبد اـث ثب

الفصل الثالث :

بر اعشاء اذساع ػ١ اززا افظ ػ طف رفظ١ ذساع اؼ١خ ٠ؾز

ؽ١ش ٠ششػ ثبزفظ١ ازغبسة از ر اعشاءب زؾذ٠ذ اخظبئض اخزفخ اد از ر

ز وزه طف غبص ازؾ١ اغزخذ ششػ ألعضاء اخزف وزه ٠ؾ اعزخذب

خاص ازشثخ از ر اعزخذاب ف اجؾش أ٠ؼب ٠شز ػ ػشع زغبسة ػ

خالي اجشبظ اؼ از ر اعشاإب ػذ ازغ١شاد از ر دساعزباخزف از ر

ػؼ ذساعخ اشىخ.

الفصل الرابع :

ر اعشاء اذساعخ ػ١زا افظ ػ طف رفظ١ جشبظ اظش از ٠ؾز

ؽ١ش ٠ششػ و١ف١خ ػ اجشبظ اغزخذ )ثشبظ اؼبطش اؾذدح( ؼشفخ ل١

اذخالد ف اؾبالد اخزفخ وزه ؿش٠مخ ازؤوذ زبئظ اجشبظ ذ اضمخ ف

اعزخذاخ ػ ؿش٠ك مبسخ زبئظ اجشبظ غ ػذد ازبئظ اشسح اشرجـخ ثزا

ألوضش (Verification) أ (Validation)وب اشز زا افظ ػ ػ اجؾش

شىخ عدح ػ١ب زؾمك ذ دلخ ازبئظ خشعبد اجشبظ ؽز ٠زغ اعزخذا

. اجشبظ ف اشعبخ

الفصل الخامس :

ؼشفخ اؼ١ اذساعخ اغزخشعخ زبئظ ارؾ١ ٠خزض زا افظ ثذساعخ

لذسح رؾ ازشثخ اـ١١خ ا١خ ره ثؼذ ص٠بدح از رئصش ػ اخزف ازغ١شادرؤص١ش

دساعخ ازغ١شاد اخزفخ ث١ب رؤص١شب ػ عن رذػ١ب ثبؼد اؾغش افشد

. اؼد اؾغش خالي سع ػاللبد ث١ب١خ ج١ب ؿج١ؼخ ره اؼاللبد

الفصل السادس :

اذساعخ اظش٠خ ثؤعزخذا اغزخشعخ رؾ١ ازبئظ ٠خزض زا افظ ثذساعخ

ا١ب رظش٠فـبثم جشبظ اؼ ػذ عد ف اؾبخ ا (Plaxis 2d) ثشبظ

رظش٠ف ١ب زشثخ اـ١١خ ا١خ . زشثخ اـ١١خ ا١خ وزه ف ؽبخ عد

الفصل السابع :

ششع عبثك ثبجشبظثبػذاد رط ره ٠خزض زا افظ ثؼ دساعخ مبسخ

ام١بعبد اؾم١خا أللشة ثالوغ١ظ صبئ األثؼبد ل١بعبد ؽم١خ ره ؼشفخ اػغ ا

ظش٠خ وزه ر دساعخ رؤص١ش غبثبد اجؽ فظ اششع ثـشق وزه اعشاء ؽ

از ٠ز اعشاإب زشثخ اـ١١خ ا١خ اذػخ ثبألػذح اؾغش٠خاؼبالد ازظ١١خ

اـجمخ ٠ؼب غز اإلعبدادأاغبفخ ث١ األػذح اؾغش٠خ رؤص١ش ض ف اؼ

اغغش افز وزه اغجخ ث١ ؼب اشخ ؼد اؾغش ا ابرغخ رغ١ش اسرفبع

اـ١١خ ا١خ ػ خظبئظب رؤص١شب ػ ؼب رشو١ض اإلعبداد ؼب اشخ زشثخ

ػ ؼب رخف١غ اجؽ ا٠ؼب ػ ؼب رخف١غ اض االص ؾذس اجؽ

ر از اذساعخ ز زبئظ ث١ مبسخػ رالش ػغؾ ١ب اغب اضائذ, ص ثؼذ ره ر

ازشثخ خاص ف ازؾغ ؾغبة رغزخذ زا األخش اظش٠خ اـشقاؽذ غ ػب

ػ دساعخ مبسخ زبئظ ر , وزهاؾغش٠خ األػذح ثبعزخذا ذػ١بر ب ٠زػذ

اغززغخ اذساعخ اؾب١خ غ اذساعبد اغبثمخ.

الفصل الثامن :

ازط١بد اغززغخ ره ٠ؾز زا افظ ػ ازبئظ اغزخظخ ره اجؾش

:از ٠ى رخ١ظب وبزب اجؾش ألثؾبس اغزمج١خ

المراجع

اخ١شا رز اشعبخ ثمبئخ اشاعغ االثؾبس اغزخذخ ف زا اجؾش.

الملخص العربي

المستخلص

ركاميةاألعمدة التقنية ستخدامإاللينة بالتربة تحسين

ذف زا انبحذ ي دساست اسخخذاو االعذة انحجشت نخقت حذعى انخشبت انطت انهت

انخحكى ف انبط ححس ي قذسة ححها نقايت االحال انحذ ي االاساث

باسطت بشايج عه حخ عه إعذاد دساست حى خقعت نالساساث. ف زا انبحذان

ااع يخخهفت ي انخشب انطت انه انجض يعها بقاياث قص يخخهف انخ حى عه

اس يالحظت إلححها حخ احذعا بأقطاس أطال يخخهف ي انعد انحجش حى

نهخحم نهخشب انقا باسطت األعذة أربخج انخائج أ انسعت انقص .ز انخشبسهك

انحجشت عخذ عه قطش انعد انحجش طن حذ حصم سبت انخحس ف قذسة ححم

يشة قذسة ححم األساط بذ أعذة ,٣2األساط انشحكض عه عد حجش ان حان

عه إعذاد رج باسطت بشايج ظش جحق إشخهج انذساست أضا حجشت.

( نعم ححهم نخأرش انساح بخصشف انا أراء Plaxis 2d) يخخصص

نصعبت إجشاء ز انخقت ف انعم ي اجم ظشا (Drained conditions)انخحم

كا أكذث دساست سهك انعد انحجش انفز ف انخشبت انطت انهت ف ز انحانت .

انذساست انظشت أ جد انعد انحجش عم عه صادة جساءة انخشبت انطت حذد

يشة ٧2٧ححس يهحظ نعايم يشت انخشبت انذعت باألعذة انحجشت بقت حصم ان

.قت يعايم انخشبت بذ أعذة حجشت

ـــاطــعة طنــــــــجـام كــليــــــة الهـــــندسـة

جامعة طنطا - كلية اهلندسة-رسالة علمية مقدمة إىل قسم اهلندسة اإلنشائية

من متطلبات احلصول علىكجزء

الهندسة المدنيه فى درجة دكتور الفلسفة (هندسة االنشاءات)

بعنوان

ركاميةاألعمدة ال تقنية ستخدامبإ تحسين التربة اللينة

إعداد

خالد عبد المنعم عبد الحيم.

جـنة الحكـم والمناقشـةل

الوظيفــــــــــــــة االســــــــــم م

األستاذ بقسم الهندسة اإلنشائية مصطفى كامل الغمراويأ.د. / 1 األزهرجامعة –كلية الهندسة

األستاذ بقسم الهندسة اإلنشائية أ.د. / محمد الغريب صقر 2 جامعة طنطا –كلية الهندسة

األستاذ بقسم الهندسة اإلنشائية أشرف كمال نظيرأ.د. / 3 جامعة طنطا –كلية الهندسة

األستاذ بقسم الهندسة اإلنشائية مروان مغاوري شاهينأ.د. / 4 جامعة طنطا –كلية الهندسة

م 2١1٢/ 4 / ٦٢ تاريخ المناقشة :

توقيعات لجـــنـة الحكــــم والمناقشـــة :

التوقيـــــــــــــع ــماالســــــــ م

مصطفى كامل الغمراويأ.د. / 1

أ.د. / محمد الغريب صقر 2

أشرف كمال نظيرأ.د. / 3

مروان مغاوري شاهينأ.د. / 4

جامعة طنطا كلية اهلندسة

قسم اهلندسة اإلنشائية

رسالة علمية مقدمة إلى جامعة طنطا -كلية الهندسة -قسم الهندسة اإلنشائية

كجزء من متطلبات الحصول على

)هندسة االنشاءات( فى الهندسة المدنيه درجة دكتور الفلسفة

إعداد

خالد عبد المنعم عبد الحيم.

حتت إشراف

٧١٠٢ –طنطا

أ.د محمد الغريب صقراهلندسة اجليوتقنية أستاذ ءاتهندسة اإلنشاقسم

طنطاجامعة -كلية اهلندسة

أ.د مروان مغاوري شاهيهاهلندسة اجليوتقنية أستاذ ءاتهندسة اإلنشاقسم

طنطاجامعة -كلية اهلندسة

أ.م.د أحمد فاروق عبد القادر

مساعد اهلندسة اجليوتقنية أستاذ ءاتهندسة اإلنشاقسم

جامعة طنطا-كلية اهلندسة

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