DISS. ETH NO. 22107 INFLUENCE OF SMEAR AND COMPACTION ...

Research Collection

Doctoral Thesis

Influence of smear and compaction zones on the performance ofstone columns in lacustrine clay

Author(s): Gautray, Jean N.F.

Publication Date: 2014

Permanent Link: https://doi.org/10.3929/ethz-a-010247610

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DISS. ETH NO. 22107

INFLUENCE OF SMEAR AND COMPACTION ZONES ON THE PERFORMANCE

OF STONE COLUMNS IN LACUSTRINE CLAY

A thesis submitted to attain the degree of

DOCTOR OF SCIENCES of ETH ZURICH

(Dr. sc. ETH Zürich)

presented by

Jean Nicolas François-Xavier Gautray

MSc ETH Civil Eng.

born on 29.08.1987

citizen of France

accepted on the recommendation of

Prof. Dr. Sarah M. Springman

Dr. Jan Laue

Prof. Dr. Helmut Schweiger

2014

À et grâce à mon père

Acknowledgements

I

Acknowledgements

Many people in my personal and professional environment have helped me over numerous

years to become the person I am today, to reach my goals and to achieve this work.

A very special thanks goes of course to my deceased father François Gautray, who was my

dad, my best friend and my confident for twenty six years and whose heart decided to let go

last fall. He always put me back on track when troubles appeared, gave me everything he

could so I got to achieve my goals and not a single word of this thesis would have been

written without his help. His inspiration, his advice and his personality shall accompany and

help me forever.

My step-mother Catherine Rodier could find the words to teach me how to write properly, to

help me learn foreign languages and to bear me when I was a rather complicated kid. She

helped me to become a grown-up and has been a true mother at my side at any time for the

past seventeen years.

Julia Selberherr has been bringing me sunshine and warmth, this even in the darkest and

coldest moments. She has helped me to find new perspectives, has enlightened my world

with her smile, and will hopefully continue to do so. My thanks also go to her family, who

welcomed me with open arms and offered me a second home.

A requirement for the conduction of a PhD thesis is of course not only a favourable personal

situation but also an adequate professional environment.

This is why I would like to thank my supervisor Prof. Dr. Sarah Springman for taking the

decision to give me a position in her group and for giving me the opportunity to conduct this

research. The benefits from this position over the past four years will surely be helpful in the

future.

Dr. Jan Laue was supportive in his role as a co-supervisor by being available and excited

about news ideas and suggestions.

The assistance of my second co-supervisor, Prof. Dr. Helmut Schweiger, was decisive in the

conduction of the numerical modelling. His availableness during my stays in Graz, Austria

was remarkable and his advice of great value. The help from his assistants Dr. Franz

Tschuchnigg and Dr. Bert Schädlich was also very deeply appreciated.

Dr. Michael Plötze was always very helpful and his expertise in the domain of clay

mineralogy and of Mercury Intrusion Porosimetry was much esteemed. The expertise of

Gabriela Peschke was also of great help in order to obtain high quality Environmental

Scanning Electron Microscopy results.

Acknowledgements

II

A central part of this work is the modelling of boundary value problems under enhanced

gravity using the geotechnical drum centrifuge at the ETH Zürich. Such modelling activities

are unthinkable without a highly competent technical staff.

Markus Iten provided his expertise for the management of the geotechnical centrifuge and

his good mood, even when having to pop up at 4 o’clock in the morning. None of the tests

would have been possible without him.

The help Heinz Buschor and Andreas Kieper was also absolutely essential for the production

of the new centrifuge tools coming out of Dr Jan Laue’s and/or of my imagination. Their

ability to deliver very high quality products within short time periods was crucial and always

deeply appreciated.

Modern techniques always involve more complicated technologies which make the help of an

electrical engineering technician of immense value. Ernst Bleiker was always available to

help me out with the numerous electrical issues I had during the conduction of my thesis and

his ability to think “out of the box” to find imaginative and effective solutions in order to solve

complicated problems within very tight time periods was of invaluable support.

My thanks also go to Dr. Pierre Mayor for his valuable support and good advice.

Eventually, I would like to thank Ralf Herzog, Dr. André Arnold, Frank Fischli, and Dr. Ferney

Morales for their good company and nice conversations over the past years, and the other

members of the Institute for Geotechnical Engineering, whom I worked with, for their help

with professional matters.

Contents

III

Contents

Acknowledgements ................................................................................................................ I

Contents ................................................................................................................................III

List of figures ........................................................................................................................ XI

List of tables .................................................................................................................... XXXI

Abstract .......................................................................................................................... XXXV

Kurzfassung ................................................................................................................. XXXVII

1 Introduction .................................................................................................................... 1

1.1 Motivation .............................................................................................................. 1

1.2 Thesis layout .......................................................................................................... 2

2 State of the art of ground improvement with stone columns ........................................... 5

2.1 General considerations about ground improvement ............................................... 5

2.2 Objectives of ground improvement of soft soils with stone columns ....................... 7

2.3 Construction techniques ......................................................................................... 8

2.4 Bearing behaviour of stone columns submitted to vertical loading ........................10

2.4.1 Bearing behaviour ...........................................................................................10

2.4.2 Stress concentration on stone columns ...........................................................12

2.4.3 Ultimate Limit State response to vertical load ..................................................18

2.5 Design of stone columns .......................................................................................22

2.5.1 Bearing capacity ..............................................................................................22

2.5.1.1 Bulging failure ..........................................................................................22

2.5.1.2 Shear failure .............................................................................................24

2.5.1.3 Penetration of short columns ....................................................................29

2.5.2 Settlement calculation .....................................................................................30

2.5.2.1 Settlement calculations based on equilibrium considerations ...................31

2.5.2.2 Settlement calculations based on empirical methods ...............................35

2.5.3 Comparison of the design procedures .............................................................44

2.6 Load-transfer behaviour of stone columns ............................................................46

2.7 Load-transfer behaviour in inclusion-supported embankments ..............................53

2.8 Effect of stone columns on the consolidation time .................................................57

2.9 Analytical considerations about the installation of inclusions in soil .......................59

2.9.1 Cavity expansion theory ..................................................................................60

Contents

IV

2.9.2 Strain Path Method and Shallow Strain Path Method ......................................63

2.10 Observations concerning the installation effects of piles and stone columns on the

soil .............................................................................................................................66

2.10.1 Pile installation ................................................................................................66

2.10.2 Changes of host soil properties due to the installation of stone columns .........68

2.10.2.1 Effect on soil resistance and stress levels ................................................69

2.10.2.2 Smear and compaction zones: effect on permeability ..............................74

2.10.3 Radial drainage around stone columns ...........................................................85

2.11 Summary of the state of the art of ground improvement with stone columns .........88

3 Centrifuge modelling .....................................................................................................91

3.1 Historical background ...........................................................................................91

3.2 Principles of centrifuge modelling ..........................................................................92

3.2.1 Scaling factors.................................................................................................94

3.2.2 Advantages and disadvantages of physical modelling under enhanced gravity ..

........................................................................................................................94

3.3 Centrifuge modelling of ground improvement measures .......................................96

3.4 Techniques adopted ........................................................................................... 109

3.4.1 ETH Zürich geotechnical drum centrifuge and equipment ............................. 109

3.4.2 Pore pressure transducers (PPTs) ................................................................ 110

3.4.3 Load cells ...................................................................................................... 110

3.4.4 T-Bar penetrometer ....................................................................................... 111

3.4.5 Electrical impedance needle .......................................................................... 113

3.5 Model soils .......................................................................................................... 116

3.5.1 Birmensdorf clay ........................................................................................... 116

3.5.2 Quartz sand .................................................................................................. 117

3.5.3 Perth sand ..................................................................................................... 118

3.6 Soil model ........................................................................................................... 118

3.6.1 Preparation of Birmensdorf clay .................................................................... 119

3.6.2 Preparation of a soil model in a cylindrical strongbox .................................... 119

3.6.3 Preparation of a soil model in an oedometer container .................................. 121

3.6.4 Preparation of a soil model in an adapted oedometer container .................... 124

3.6.5 Installation of the PPTs ................................................................................. 124

3.6.5.1 Installation of the PPTs into a cylindrical strongbox and an adapted

oedometer container ............................................................................................... 125

Contents

V

3.6.5.2 Installation of the PPTs into a model consolidated in an oedometer

container and installed in the 400 mm diameter strongbox ..................................... 126

3.6.6 Identification of the locations of the stone columns ........................................ 127

3.7 Centrifuge tests ................................................................................................... 128

3.7.1 Overview ....................................................................................................... 128

3.7.2 Groundwater level ......................................................................................... 130

3.7.3 Tests conducted with specimens prepared in a cylindrical strongbox ............ 131

3.7.3.1 Loading of a single stone column (JG_v2, JG_v3 and JG_v6) ............... 131

3.7.3.2 Loading of a stone column group (JG_v8, JG_v10) ................................ 133

3.7.4 Tests conducted with specimens prepared in an oedometer container (JG_v1,

JG_v4, JG_v5) ............................................................................................................ 137

3.7.5 Tests conducted with specimens prepared in an adapted oedometer container

(JG_v7, JG_v9) .......................................................................................................... 141

4 Results from the centrifuge tests................................................................................. 143

4.1 Undrained shear strength .................................................................................... 143

4.1.1 Theoretical prediction .................................................................................... 143

4.1.2 Shear strength profile for pre-consolidation up to σ’v = 100 kPa .................... 145

4.1.3 Shear strength profile for pre-consolidation up to σ’v = 200 kPa .................... 147

4.1.4 Summary of the back-calculated values of the shear strength parameters a and

b ...................................................................................................................... 148

4.2 Pore pressure measurements conducted during the installation of stone columns ...

........................................................................................................................... 150

4.2.1 Measurements conducted during the installation of a single stone column .... 150

4.2.2 Measurements conducted during the installation of a stone column group .... 154

4.3 Measurements conducted during the footing loading of a single stone column

installed in a specimen prepared in a full cylindrical strongbox ....................................... 156

4.4 Measurements conducted during the footing loading of a single stone column

installed in a specimen prepared in an (adapted) oedometer container .......................... 159

4.4.1 Measurements conducted in a specimen consolidated up to σ’v = 100 kPa .. 159

4.4.2 Measurements conducted in a specimen consolidated up to σ’v = 200 kPa .. 163

4.4.3 Comparison of the results ............................................................................. 166

4.4.4 Load transfer around a single stone column .................................................. 168

4.5 Measurements conducted during the footing load of a stone column group ........ 176

4.5.1 Test JG_v8 (a / dsc = 2 [-]) ............................................................................. 176

4.5.2 Test JG_v10 (a / dsc = 2 [-]) ........................................................................... 179

Contents

VI

4.6 Comparison of the measurements around a single stone column and inside a stone

column group .................................................................................................................. 185

4.7 Electrical impedance measurements ................................................................... 188

4.7.1 Measurements around a single stone column ............................................... 188

4.7.1.1 Measurements conducted in specimens consolidated up to σ’v = 100 kPa

(test JG_v5) ............................................................................................................ 189

4.7.1.2 Measurements conducted in a specimen consolidated up to σ’v = 200 kPa

(test JG_v5) ............................................................................................................ 191

4.7.2 Measurements around a stone column group (test JG_v8) ........................... 193

4.8 Summary of the conducted modelling under enhanced gravity ........................... 196

5 Complementary investigations .................................................................................... 197

5.1 Oedometer tests conducted on samples extracted from the soil model used for the

centrifuge test JG_v9 ...................................................................................................... 197

5.2 Oedometer tests conducted on samples extracted from soil models after

consolidation .................................................................................................................. 203

5.3 Electrical impedance measurement under 1 g .................................................... 207

5.4 Microscopic investigations .................................................................................. 210

5.4.1 Description of the Scanning Electron Microscope .......................................... 210

5.4.2 Description of the Environmental Scanning Electron Microscope .................. 212

5.4.3 Results obtained ........................................................................................... 213

5.5 Mercury Intrusion Porosimetry (MIP) ................................................................... 215

5.5.1 General principle ........................................................................................... 215

5.5.2 Sample preparation ....................................................................................... 216

5.5.3 Apparatus used ............................................................................................. 216

5.5.4 Results obtained ........................................................................................... 217

6 Numerical modelling ................................................................................................... 219

6.1 Principles of numerical modelling of ground improvement ................................... 219

6.1.1 Improvement through compaction (embankment loading with installation of

vertical drains) ............................................................................................................ 219

6.1.2 Discrete modelling of improvement through material addition with displacement

...................................................................................................................... 221

6.2 Literature review of numerical modelling of ground improvement through stone

columns and prefabricated vertical drains ....................................................................... 224

6.2.1 Numerical modelling of ground improvement with stone columns and

prefabricated vertical drains ........................................................................................ 224

Contents

VII

6.2.2 Analogy to installation of rigid inclusions ....................................................... 234

6.3 Constitutive models ............................................................................................. 237

6.3.1 Mohr-Coulomb model .................................................................................... 237

6.3.1.1 Description ............................................................................................. 237

6.3.1.2 Limitations of the Mohr-Coulomb model ................................................. 239

6.3.1.3 Input parameters of the Mohr-Coulomb model ....................................... 239

6.3.2 Hardening Soil Model .................................................................................... 239

6.3.2.1 Stiffness moduli ...................................................................................... 240

6.3.2.2 Yield surfaces ........................................................................................ 241

6.3.2.3 Shear strain hardening ........................................................................... 242

6.3.2.4 Volumetric hardening ............................................................................. 243

6.3.2.5 Limitations of the Hardening Soil Model ................................................. 244

6.3.2.6 Input parameters of the Hardening Soil Model ....................................... 245

6.4 Axisymmetric numerical modelling ...................................................................... 246

6.4.1 Options discarded ......................................................................................... 246

6.4.2 Model ............................................................................................................ 248

6.4.3 Results .......................................................................................................... 251

6.5 3D numerical modelling ....................................................................................... 266

6.5.1 Model ............................................................................................................ 266

6.5.2 Results .......................................................................................................... 269

6.6 Summary of numerical modelling ........................................................................ 276

7 Summary .................................................................................................................... 279

7.1 General considerations ....................................................................................... 279

7.2 Findings from centrifuge modelling and complementary investigations ............... 279

7.3 Numerical modelling ........................................................................................... 282

7.4 Outlook ............................................................................................................... 287

8 Appendices ................................................................................................................. 289

8.1 Pore pressure and load measurements conducted during loading with a footing on

a single stone column installed in a specimen prepared in an oedometer container (test

JG_v1) ........................................................................................................................... 290

8.2 Pore pressure and load measurements conducted during loading a single stone

column installed in a specimen prepared in an oedometer container (test JG_v5) with a

circular footing ................................................................................................................ 292

Contents

VIII

8.3 Pore pressure and load measurements conducted during loading a single stone

column installed in a specimen prepared in a full cylindrical stongbox (test JG_v6) with a

circular footing ................................................................................................................ 293

8.4 Values of the J4 factor according to Grasshoff (1978) ......................................... 294

8.5 Comparison of the analytical and measured excess pore water pressure around a

single stone column when the maximum load is applied (P = 80 kPa, test JG_v1) ......... 294

8.6 Electrical impedance measurements conducted during the test JG_v9 ............... 295

8.7 Electrical impedance measurements conducted under 1 g ................................. 298

8.8 Vertical strain increments computed numerically for test JG_v7 .......................... 301

8.9 Shear strain increments computed numerically for test JG_v7 ............................ 303

8.10 Development of plastic points (test JG_v7) ......................................................... 306

8.11 Deformed mesh (test JG_v9) .............................................................................. 309

8.12 Total stress distribution computed numerically for test JG_v9 ............................. 310

8.13 Vertical strain increments computed numerically for test JG_v9 .......................... 311

8.14 Shear strain increments computed numerically for test JG_v9 ............................ 314

8.15 Excess pore water pressures computed numerically for test JG_v9 .................... 317

8.16 Development of plastic points (test JG_v9) ......................................................... 318

8.17 Total vertical stress distribution as a function of the radial distance at depths of 0

m, 2 m, 4 m and 6 m (test JG_v7) .................................................................................. 321

8.18 Total vertical stress distribution as a function of the radial distance at depths of 0

m, 2 m, 4 m and 6 m (test JG_v9) .................................................................................. 322

8.19 Comparison of the measured and modelled excess pore water pressures for the

test JG_v7 ...................................................................................................................... 323


test JG_v9 ...................................................................................................................... 324

8.21 Distribution of the total vertical stresses for footing settlements of 100 mm and of

400 mm (test JG_v10) .................................................................................................... 326

8.22 Total vertical stress distribution below the footing for a settlement of 100 mm (test

JG_v10) .......................................................................................................................... 329


JG_v10) .......................................................................................................................... 332


JG_v10) .......................................................................................................................... 335


test JG_v10 .................................................................................................................... 337

8.26 Development of plastic points (test JG_v10) ....................................................... 338

Contents

IX

9 List of subscripts and symbols .................................................................................... 343

10 References ................................................................................................................. 353

Contents

X

List of figures

XI

List of figures

Figure 1.1: Installation effects around a stone column at a model depth of 40 mm @ 50 g

(Weber, 2008). ...................................................................................................................... 2

Figure 2.1: Dry replacement technique: (a) filling the supply hopper, (b) penetration, (c)

compaction by step-wise withdrawal and reinsertion (d) finishing (Keller Grundbau, 2013). . 9

Figure 2.2: Wet top feed technique: (a) penetration, (b) filling, (c) compacting, (d) finishing

(International Construction Equipment Holland, 2013). .......................................................... 9

Figure 2.3: Ramming installation technique: (a) inserting granular plug, (b) driving up to the

desired depth, (c) filling with granular soil, (d) compacting and withdrawing casing, (e)

finishing (Van Impe et al., 1997b). ........................................................................................10

Figure 2.4: Interactions at stake under a footing (after Kirsch, 2004). ...................................11

Figure 2.5: Loading situations of stone columns (Kirsch, 2004). ...........................................12

Figure 2.6: Total vertical stress distribution of a uniform vertical stress σ (a) plan view

showing respective areas of stone columns (Asc) and soft soil (As), (b) cross-section showing

stress distribution onto the column (σsc) and the host soil (σs) (after Aboshi et al., 1991). .....13

Figure 2.7: Measured stress concentration factors at (a) St. Helens and (b) Canvey Island

(Greenwood, 1991). .............................................................................................................15

Figure 2.8: Cross-section of the test site at Humber Bridge (after Greenwood, 1991). .........16

Figure 2.9: Measured stress concentration factors at Humber Bridge (Greenwood, 1991). ..16

Figure 2.10: Stress concentration factors in 1 g small-scale model and field tests (Muir Wood

et al., 2000). .........................................................................................................................17

Figure 2.11: Failure mechanisms for a single stone column (a) bulging (b) bearing failure (c)

shear failure (d) penetration of short columns (e) shortening of long columns (f) deflection of

slender columns (Muir Wood et al., 2000) based on Waterton & Foulsham (1984). ..............18

Figure 2.12: Failure mechanisms for groups of stone columns (a) bulging failure and loss of

horizontal support (b) shearing failure (c) block failure and column penetration (Kirsch, 2004).

.............................................................................................................................................19

Figure 2.13: Deformed sand columns at the end of the footing penetration (Muir Wood et al.,

2000). ...................................................................................................................................20

Figure 2.14: Zone of influence of a footing on the underlying soil (a) “rigid” cone beneath

footing (b) variation of angle β with area replacement ratio (Muir Wood et al., 2000). ..........21

Figure 2.15: Deformed stone columns at the end of the footing penetration (McKelvey et al.,

2004). ...................................................................................................................................21

Figure 2.16: Shear failure of a stone column (after Muir Wood et al., 2000). ........................24

Figure 2.17: Truncated conical failure mechanism according to Brauns (1978a) (a) cross-

section, (b) plan view and (c) forces acting on volume A. .....................................................25

Figure 2.18: Stone column group analysis – firm to stiff fine-grained soil (Barksdale &

Bachus, 1983). .....................................................................................................................27

Figure 2.19: Clay and columns represented (a) discretely and (b) as an equivalent plane wall

(Springman et al., 2014). ......................................................................................................28

List of figures

XII

Figure 2.20: Stability considerations on a slip circle passing through soft soil and the

equivalent plane walls (numbers 1 to 11 show the sequence of the slices) (Springman et al.,

2014). ...................................................................................................................................29

Figure 2.21: Various stone column arrangements with the domain of influence of each

column (Balaam & Poulos, 1983). ........................................................................................30

Figure 2.22: Stress distribution on a rigid footing. .................................................................31

Figure 2.23: Evaluation of the stress distribution parameter depending on the different kinds

of mixture (Omine & Ohno, 1997). ........................................................................................33

Figure 2.24: Settlement diagram for stone columns installed in uniform soft clay (Greenwood,

1970). ...................................................................................................................................36

Figure 2.25: Values of the ground improvement factor n0 depending on the area replacement

ratio, for a Poisson’s ratio of 1/3 (after Priebe, 1995). ...........................................................37

Figure 2.26: Values of an additional component of the area replacement ratio to account for

column compressibility, for a Poisson’s ratio of 1/3 (after Priebe, 1995). ..............................38

Figure 2.27: Determination of an influence factor y for the calculation of a depth coefficient fd

for a Poisson’s ratio of 1/3 (γs: unit weight of the host soil; d: improvement depth; p: footing

load) (after Priebe, 1995). .....................................................................................................39

Figure 2.28: Priebe method best-fit line, with data sorted based on the site soil conditions

(Douglas & Schaefer, 2012). ................................................................................................40

Figure 2.29: Static system for the settlement calculation of groups of floating stone columns,

according to Priebe (2003) (Kirsch, 2004). ...........................................................................41

Figure 2.30: (a) Rheological modelling of the behaviour of stone columns, (b) Calculation

approach in plane-strain (Van Impe et al., 1997b). ...............................................................42

Figure 2.31: Graphical determination of the settlement reduction factor β (Van Impe & De

Beer, 1983). .........................................................................................................................43

Figure 2.32: Comparison of the ultimate bearing capacities as a function of the angle of

friction calculated using different procedures (after Greenwood & Kirsch, 1983). .................45

Figure 2.33: Comparison of results obtained from empirical models and elastic theories with

field observations (after Greenwood & Kirsch, 1983). ...........................................................46

Figure 2.34: Experimental setup for a single stone column loaded vertically through a rigid

footing (Sivakumar et al., 2011). ...........................................................................................47

Figure 2.35: Pressure distribution with depth during footing loading of a 60 mm diameter

stone column for different settlements (Sivakumar et al., 2011). ...........................................48

Figure 2.36: Representative borehole and selected soil properties from Red River research

site in Winnipeg, Canada. w: natural water content (horizontal bars display Atterberg limits);

γwet: unit weight of saturated soil; σ: stress; σ’pc: preconsolidation pressure; σ’v0: initial vertical

effective stress; u0: initial pore water pressure (Thiessen et al., 2011). .................................49

Figure 2.37: Red River test site in Winnipeg, Canada: stabilisation of river bank using a

combination of void and rockfill columns (a) cross-section and (b) plan view of the research

site (Thiessen et al., 2011). Elevations and distances in metres. ..........................................50

Figure 2.38: Red River test site in Winnipeg, Canada: pore water response to loading

(Thiessen et al., 2011). .........................................................................................................51

List of figures

XIII

Figure 2.39: Red River test site in Winnipeg, Canada: instrumentation layout (Thiessen et al.,

2011). ...................................................................................................................................51

Figure 2.40: Measured deformations along A axis (in downslope direction) at Red River test

site in Winnipeg, Canada: (a) SI-1 at crest of slope; (b) SI-4 in between columns along upper

row; (c) SI-7 in a column in upper row; (d) SI-10 downslope of columns (Thiessen et al.,

2011). ...................................................................................................................................53

Figure 2.41: Soil arching in stone column-supported embankment (after Deb, 2010). ..........54

Figure 2.42: Proposed foundation model for soft soil reinforced with stiffer inclusions (after

Deb, 2010). ..........................................................................................................................55

Figure 2.43: Effect of (a) ultimate bearing capacity of the soft soil and (b) the shear modulus

of the embankment soil on the arching ratio (Deb, 2010). .....................................................56

Figure 2.44: Arching effect in the embankment (Indraratna et al., 2013). ..............................57

Figure 2.45: Consolidation process for (a) a single stone column and (b) a group of stone

columns (after Black et al., 2007). ........................................................................................58

Figure 2.46: Comparison of the excess pore water pressure dissipation for displacement

piles and stone columns (McCabe et al., 2009). ...................................................................59

Figure 2.47: Geometric representation of cylindrical cavity expansion in either two or three

(spherical) dimensions (Vesic, 1972). ...................................................................................60

Figure 2.48: Deformation paths during penetration of a cone into clay calculated using the

SPM (Baligh, 1985). .............................................................................................................64

Figure 2.49: (a) Radial and (b) vertical deformation profiles after the installation of a simple

pile obtained with the SSPM analysis (Sagaseta & Whittle, 2001). .......................................65

Figure 2.50: Deformation and density changes during the penetration of a pile in dense sand

(after Linder, 1977). ..............................................................................................................67

Figure 2.51: (a) Half-cone inserted in sand (b) test set up (Davidson et al., 1981). ...............68

Figure 2.52: Displacements (in mm) and volumetric strains (in %) for jacking a half-CPT cone

into (a) loose sand (relative density = 25 %) (b) dense sand (relative density = 115 %)

(Davidson et al., 1981). ........................................................................................................68

Figure 2.53: Evolution of the undrained shear strength ratio (normalised to pre-installation

values) over time after the installation of stone columns (Aboshi et al., 1979). .....................69

Figure 2.54: Evolution of the unconfined compressive strength of clay over time (Asaoka et

al., 1994). .............................................................................................................................70

Figure 2.55: Profile of the host soil treated by SCP installation at the Bothkennar test site, as

investigated by Watts et al. (2000). ......................................................................................71

Figure 2.56: Lateral stress changes measured by earth pressure cells following poker

penetration and retraction during stone column compaction at the Bothkennar test site (Watts

et al., 2000). .........................................................................................................................72

Figure 2.57: Dynamic probing of the radial densification of the fill around a stone column at

the Bothkennar test site (Watts et al., 2000). ........................................................................72

Figure 2.58: Illustration of the different stress zones around the pier (rf = 1.9 m) in the

Memphis, USA case history (Handy et al., 2002). .................................................................73

Figure 2.59: Response of pore pressure transducers installed 2 m, resp. 4 m, below the

ground surface to column loading at the Raploch test site (Egan et al., 2009). .....................74

List of figures

XIV

Figure 2.60: Suggested variation of horizontal permeability with radius according to Onoue et

al. (1991) (after Saye, 2001). ................................................................................................75

Figure 2.61: Section of the test setup showing the smear zone (after Indraratna & Redana,

1998). ...................................................................................................................................75

Figure 2.62: Ratio of horizontal to vertical coefficient of permeability against the radial

distance from the axis of the SCP (denoted as drain) (Indraratna & Redana, 1998). ...........76

Figure 2.63: Excess pore water pressures during the insertion of the installation mandrel

(Sharma & Xiao, 2000). ........................................................................................................77

Figure 2.64: Variation of the horizontal permeability with radial distance to the drain for an

installation that causes a smear zone (Sharma & Xiao, 2000). .............................................77

Figure 2.65: Back-calculated sets of coefficients of relative horizontal permeability in the

undisturbed host soil (kh) and in the smear zone (k’h) and horizontal coefficient of

consolidation ch values, assuming ds = 2 dm (Bergado et al., 1991). .....................................79

Figure 2.66: Directions of the horizontal penetration tests (Shin et al., 2009). ......................80

Figure 2.67: Electrical resistivity and estimated outer boundary of the smear zone (Shin et

al., 2009). .............................................................................................................................81

Figure 2.68: Dimensions of the smear zone derived from the electrical resistance probe. All

dimensions in millimetres (Shin et al., 2009). ........................................................................81

Figure 2.69: Variation of the porosity as a function of the distance from the stone column axis

(Weber et al., 2010). .............................................................................................................83

Figure 2.70: Variation of the dry bulk density as a function of the distance from the stone

column axis (Weber et al., 2010). .........................................................................................83

Figure 2.71: Compression and smear zone around sand compaction piles (Juneja et al.,

2013). ...................................................................................................................................84

Figure 2.72: Scanning Electron Microscopy images of kaolin clay specimen adjacent to the

stone column installed and sheared (CIU) at 50 kPa (a) without smear and (b) with smear

(Juneja et al., 2013). .............................................................................................................84

Figure 2.73: Radial drainage within a unit cell (after Barron, 1948). ......................................85

Figure 3.1: Acceleration acting on a body rotating with angular velocity ω (Springman, 2004).

.............................................................................................................................................92

Figure 3.2: Principle of centrifuge modelling (after Schofield, 1980). ....................................93

Figure 3.3: Comparison of the stress profiles (a) in a prototype, (b) in a small-scale model

and (c) in a centrifuge model (after Laue, 1996). ..................................................................93

Figure 3.4: Distribution of the vertical stress with depth in a prototype situation and in the

centrifuge (zs denotes the depth of the sample) (after Taylor, 1995). ....................................95

Figure 3.5: (a) Cross-section of the centrifuge model of a clay sample reinforced by wick

drains and basal reinforcement loaded by an embankment and (b) influence of the drains on

the dissipation of excess pore water pressures during and after embankment construction

(Sharma & Bolton, 2001). .....................................................................................................96

Figure 3.6: Comparison between settlement improvement ratios obtained with the solution of

Priebe (1995) solution and from centrifuge tests (Al-Khafaji & Craig, 2000). .........................97

Figure 3.7: Pile lateral pressure as a function of the lateral displacement y normalised by the

pile radius d (Dyson & Randolph, 1998). ..............................................................................98

List of figures

XV

Figure 3.8: Sand compaction pile installation tool used at the National University of

Singapore. All dimensions are in mm (Ng et al., 1998). ........................................................99

Figure 3.9: Embankment constructed on soft clay (U2) and when improved by SCPs installed

at 1g (R1_20) or at 50 g (D50_20) (a) deformation grid lines in clay improved with SCPs built

in-flight (b) maximum lateral displacement (in mm) of the grid line L2 with g-level (Lee et al.,

2001). ................................................................................................................................. 100

Figure 3.10: Layout of SCPs and transducers for the installation of SCPs in test T7, D 20 mm

(D: SCP diameter) (Lee et al., 2004). ................................................................................. 100

Figure 3.11: Layout of SCPs and transducers for tests: (a) T1, D 18 mm; (b) T2, D 20 mm;

(c) T3, D 16 mm; (d) T4, D 17 mm; (e) T5, D 20 mm; (f) T6, D 20 mm (D SCP diameter) (Lee

et al., 2004). ....................................................................................................................... 101

Figure 3.12: (a) Total horizontal stress at 60 mm depth and (b) pore pressures at 80 mm

depth during SCP installation in clay. Line 1: time at which the casing tip reaches the depth

of the transducers. Line 2: time at which the casing tip reaches the full penetration and

withdrawal starts. Line 3: time at which the casing tip reaches the depth of the transducers

during withdrawal. Line 4: end of the SCP installation (Lee et al., 2004). ............................ 102

Figure 3.13: Ratios of measured to calculated horizontal stresses and pore pressures plotted

against (a) dt / D and (b) rt / D (Lee et al., 2004). ................................................................ 103


against the ratio of the depth of the transducers dt to the radial distance of the transducers rt

(Lee et al., 2004). ............................................................................................................... 103

Figure 3.15: Layout of sand compaction piles (P1 to P4) and location of the T-Bar test

(denoted as s) for pile group tests featuring either a) 2 piles or b) 4 piles (all dimensions in

mm) (Yi et al., 2013). .......................................................................................................... 104

Figure 3.16: Undrained shear strengths measured in the centrifuge for different tests (Yi et

al., 2013). ........................................................................................................................... 105

Figure 3.17: Experimental setup for the in-flight installation of stone columns (Weber et al.,

2005). ................................................................................................................................. 106

Figure 3.18: Detailed view of the stone column installation tool developed by Weber (2004).

........................................................................................................................................... 107

Figure 3.19: Settlements measured with and without stone columns at the toe of the

embankment (1), and on top of the embankment (2) (after Weber 2008). .......................... 107

Figure 3.20: Evolution of the pore water pressure after embankment construction in the

improved ground within the sand pile grid (---) in comparison with unimproved ground (––) at

three depths in the model with a groundwater table located at the surface of the model in the

middle of the container: P1 = 120 mm, P2 = 70 mm, P3 = 25 mm equivalent to prototype

depths of 6 m, 3.5 m and 1.25 m respectively (after Weber, 2008). .................................... 108


(Weber, 2008). ................................................................................................................... 108

Figure 3.22: Cross-section of the ETH Zürich geotechnical drum centrifuge (Springman et al.,

2001). ................................................................................................................................. 109

Figure 3.23: Cross-section of the transducer DRUCK PDCR 81 (König et al., 1994). ......... 110

Figure 3.24: Load cell produced by Hottinger Baldwin Messtechnik GmbH (Arnold, 2011). 111

List of figures

XVI

Figure 3.25: T-Bar penetrometer (a) front view and (b) side view. ...................................... 112

Figure 3.26: T-Bar penetrometer (after Weber, 2008). ........................................................ 112

Figure 3.27: T-Bar penetrometer mounted on the working arm of the tool platform in the

centrifuge (after Weber, 2008). ........................................................................................... 112

Figure 3.28: T-Bar calibration setup (after Weber, 2008). ................................................... 113

Figure 3.29: Electrical impedance needle (a) side view and (b) tilted view of the tip (outer

diameter 1 mm). ................................................................................................................. 114

Figure 3.30: Schematic views of the electrical impedance needle (a) covered, (b) with the

cover retracted and (c) cross-section A-A (Gautray et al., 2014). ....................................... 115

Figure 3.31: Ultrasonic bath Emmi 4, produced by EMAG AG (Gautray et al., 2014). ........ 115

Figure 3.32: Vacuum mixer. ............................................................................................... 119

Figure 3.33: General view (a) cylindrical strongbox used for the consolidation of Birmensdorf

clay under the hydraulic press, (b) view of the channels filled with Perth sand and (c) filling

with clay suspension. ......................................................................................................... 120

Figure 3.34: Hydraulic press used for the consolidation of clay. ......................................... 121

Figure 3.35: Preparation of the clay model (a) slurry inside the oedometer container (b) under

consolidation in the oedometer container. .......................................................................... 122

Figure 3.36: Schematic representation (a) of the possible cylindrical rupture zones when

extracting the clay sample from the container and (b) of the use of the plastic sheet in order

to prevent the adhesion between clay and oedometer container. ....................................... 122

Figure 3.37: (a) Removal of the oedometer container from the sample (b) view of the model

with clay sample surrounded by Perth sand. ...................................................................... 123

Figure 3.38: Ports for the installation of PPTs into the soil model prepared in 250 mm

diameter containers ............................................................................................................ 124

Figure 3.39: PPT installation tool. ....................................................................................... 125

Figure 3.40: Installation of the PPTs in the cylindrical strongbox (a) introduction of the PPTs

through the dedicated ports into the pre-drilled hole (b) filling of the pre-drilled hole with slurry

(Weber, 2008). ................................................................................................................... 125

Figure 3.41: PPT installation setup for a specimen consolidated in an oedometer container.

........................................................................................................................................... 126

Figure 3.42: Insertion of the PPT installation tool into the clay specimen using the installation

device. ................................................................................................................................ 127

Figure 3.43: Pin used to mark the positions of the stone columns to be installed (a) plan view

and (b) side view. ............................................................................................................... 128

Figure 3.44: Tilted view of the pin used to mark the positions of the stone columns to be

constructed with the stone column installation tool. ............................................................ 128

Figure 3.45: Vertical cross-section of the experimental setup in the centrifuge for the

specimens prepared in a cylindrical strongbox (Section 3.6.2), in an oedometer container and

in an adapted oedometer container (Section 3.6.4) (after Weber, 2008). ............................ 129

Figure 3.46: Position of the water level in the soil and in the standpipe for specimens

prepared in a cylindrical strongbox (tests JG_v2, JG_v3, JG_v6, JG_v8 and JG_v10). ...... 130


prepared in an oedometer container (tests JG_v1 and JG_v5). .......................................... 131

List of figures

XVII


prepared in an adapted oedometer container (tests JG_v7 and JG_v9). ............................ 131

Figure 3.49: Specimens prepared in a cylindrical strongbox: (a) plan view and (b) cross-

section of the soil model with positions of the PPTs and of the stone columns. .................. 133

Figure 3.50: Specimens prepared in a cylindrical strongbox: cross-section of the soil model,

with positions of the PPTs and of the stone columns (a / dsc = 2 [-]). .................................. 134

Figure 3.51: Specimens prepared in a cylindrical strongbox: plan view of the soil model with

positions of the PPTs and of the stone columns (a / dsc = 2 [-]). .......................................... 135

Figure 3.52: Specimens prepared in a cylindrical strongbox: insertion points of the electrical

impedance needle: positions of the reference points RP1 and RP2 and the points A2 to J2 (a

/ dsc = 2 [-]). ........................................................................................................................ 136

Figure 3.53: Specimens prepared in an oedometer container and surrounded by Perth sand:

(a) plan view and (b) cross-section of the soil model with positions of the PPTs and of the

stone column. ..................................................................................................................... 138

Figure 3.54: Comparison of the lateral stresses acting on the clay sample for specimens

prepared in an oedometer container and surrounded by Perth sand (σ’h Perth sand, calculated

based on the silo theory) and for specimens prepared in a rigid container (cylindrical

strongbox or adapted oedometer) with a pre-consolidation of σ’v = 100 kPa (σ’h clay, 100 kPa) or

of σ’v = 200 kPa (σ’h clay, 200 kPa). ........................................................................................... 140


insertion points of the electrical impedance needle and positions of the reference points RP1

and RP2 and the points A to F. ........................................................................................... 141

Figure 3.56: Specimens prepared in an adapted oedometer: (a) plan view and (b) cross-

section of the soil model with positions of the PPTs and of the stone column. .................... 142

Figure 4.1: Profile of the vertical effective stress in the centrifuge (σ’v,centrifuge) and under the

press (σ’v,press) for a pre-consolidation of 100 kPa. .............................................................. 144


press (σ’v,press) for a pre-consolidation of 200 kPa. .............................................................. 144

Figure 4.3: Profiles of the over-consolidation ratio for pre-consolidation stresses of 100 kPa

and 200 kPa. ...................................................................................................................... 145

Figure 4.4: Profiles of the undrained shear strength obtained with the T-Bar during tests

JG_v2 (su,JG_v2), JG_v8 (su,JG,v8) and JG_v10 (su,JGv10,A and su,JG,v10,B) compared with

theoretical predications based on Trausch-Giudici (2003, su,TG) and Küng (2003, su,K) and

with the back-calculated values of the parameters a and b (su,JG). ...................................... 146

Figure 4.5: Profiles of the undrained shear strength obtained with the T-Bar during test

JG_v9 (su,JG_v9,A and su,JG_v9_B) compared with theoretical predictions based on Trausch-

Giudici (2003, su,TG) and on Küng (2003, su,K), and with the back-calculated values of the

parameters a and b (su,JG). ................................................................................................. 146


JG_v1 (su,JG_v1) and JG_v5 in the specimen consolidated up to 200 kPa (su,JG_v5) compared

with the profile obtained with back-calculated values of the parameters of a and b (su,JG). .. 147

Figure 4.7: Profiles of the undrained shear strength obtained with the T-Bar during test

JG_v7 (su, JG_v7,A and su, JG_v7_B) compared with theoretical predictions based on Trausch-

List of figures

XVIII

Giudici (2003, su,TG) and on Küng (2003, su,K) and with the back-calculated values of the

parameters a and b (su,JG). ................................................................................................. 148

Figure 4.8: Profiles of the back-calculated undrained shear strength for a specimen prepared

in a full cylindrical strongbox (su,JG,1) and in adapted oedometers (su,JG,2 and su,JG,3). .......... 149

Figure 4.9: Installation of a compacted column in a specimen pre-consolidated up to 200 kPa

(test JG_v7) (a) pore water pressures (b) depth of the tip of the installation tool with time. . 151

Figure 4.10: Insertion of the stone column installation tool in a specimen pre-consolidated up

to 200 kPa (tests JG_v7) (a) excess pore water pressures (b) depth of the tip of the

installation tool with time. .................................................................................................... 152


to 200 kPa (test JG_v7): excess pore water pressures. ...................................................... 153


to 100 kPa (test JG_v9) (a) excess pore water pressures (b) depth of the tip of the

installation tool with time. .................................................................................................... 154

Figure 4.13: Insertion of the stone column installation tool in a specimen consolidated up to

100 kPa (test JG_v10) (a) excess pore water pressures (b) location of the stone columns

installed. ............................................................................................................................. 155


100 kPa (test JG_v10): excess pore water pressures. ........................................................ 156

Figure 4.15: Loading of a single stone column in a specimen pre-consolidated up to 100 kPa

(test JG_v2) (a) excess pore water pressures (b) evolution of the footing load (c)

deformation controlled footing settlement. .......................................................................... 158


(test JG_v9) (a) excess pore water pressures (b) evolution of the footing load (c) deformation

controlled footing settlement. .............................................................................................. 160


(test JG_v9), dissipation with time of the excess pore water pressures at a depth of 48 mm

around the stone column (a) from 0 s to 2000 s and (b) from 3000 s to 9000 s after reaching

the peak footing load (which corresponds to t = 0 s). .......................................................... 161


(test JG_v9): dissipation of the excess pore water pressures at a depth of 96 mm with time


the peak footing load (which corresponds to t = 0 s). ......................................................... 162


(test JG_v9): rate of dissipation of excess pore water pressures with time after reaching the

peak footing load (which corresponds to t = 0 s). ................................................................ 163


(JG_v7) (a) excess pore water pressures (b) evolution of the footing load (c) deformation


Figure 4.21: Distribution of the excess pore water pressure with increasing radial distance to

the axis of the stone column at a depth of 48 mm as a percentage of the applied footing load

P. ....................................................................................................................................... 167

List of figures

XIX


the axis of the stone column at a depth of 96 mm as a percentage of the applied footing load

P. ....................................................................................................................................... 168

Figure 4.23: Isobars of vertical stress increments under a vertically loaded quadratic plate

(Lang et al., 2007). ............................................................................................................. 169

Figure 4.24: Isobars of peak values of excess pore pressures measured in the centrifuge

under a vertically loaded circular footing resting on top of a stone column. ......................... 174

Figure 4.25: Isobars of vertical stress increments under a vertically loaded circular footing

(after Grasshoff, 1978). ...................................................................................................... 174

Figure 4.26: Distribution of the total vertical stress increase as a function of the radial

distance from the stone column at 96 mm depth as a percentage of the applied footing load

P, and in comparison with the depth factor J4 according to Grasshoff (1978). .................... 175

Figure 4.27: Excess sand shown on top of columns B, D and E within the footprint of the

footing on the surface of the clay model after test JG_v8. .................................................. 177

Figure 4.28: Loading of a stone column group in a specimen pre-consolidated up to 100 kPa

(JG_v8) (a) excess pore water pressures (b) evolution of the footing load (c) deformation


Figure 4.29: Position of the footing used for the loading phase during test JG_v10 (a = 24

mm). ................................................................................................................................... 180

Figure 4.30: Test JG_v10: (a) excess pore water pressures (b) evolution of the footing load

(c) footing settlement during the loading phase of a stone column group. .......................... 181


the axis of the centre stone column at depths of 30 mm and of 80 mm as a percentage of the

applied footing load P (test JG_v10). .................................................................................. 182












Figure 4.35: Excess pore water pressures during the footing load test on a single stone

column (test JG_v9). .......................................................................................................... 186

Figure 4.36: Excess pore water pressures during the footing load test on a stone column

group (test JG_v10). The maximum load was reached at 1000 s. ...................................... 186




List of figures

XX





(Weber, 2008). ................................................................................................................... 188

Figure 4.40: Positions of the needle insertion points around a single stone column, and

extent of the zones 2 and 3 according to Weber (2008)...................................................... 188

Figure 4.41: Impedance recorded at reference points RP1 and RP2 during test JG_v5. .... 189

Figure 4.42: Impedance recorded at the points A, B and C during test JG_v5. ................... 190

Figure 4.43: Impedance recorded at the points D, E and F during the test JG_v5. ............. 190

Figure 4.44: Impedance recorded at the reference points RP1 and RP2 during test JG_v5.

........................................................................................................................................... 191

Figure 4.45: Impedance recorded at the points A, B and C during test JG_v5. ................... 192

Figure 4.46: Impedance recorded at the points D, E and F during test JG_v5. ................... 193

Figure 4.47: Positions of the needle insertion points around a stone column group (test

JG_v8, a / dsc = 2 [-]. .......................................................................................................... 194


........................................................................................................................................... 194

Figure 4.49: Impedance recorded at the points A2, B2 and C2 during test JG_v8. ............. 195

Figure 4.50: Impedance recorded at the points D2, E2 and F2 during test JG_v8. ............. 195

Figure 4.51: Impedance recorded at the points G2, H2, I2 and J2 during test JG_v8. ........ 196

Figure 5.1: Plan view of the extraction positions of the specimens for oedometer tests (test

JG_v9). .............................................................................................................................. 197

Figure 5.2: Cross-section of the extraction positions of the specimens for oedometer tests

(test JG_v9). ....................................................................................................................... 198

Figure 5.3: Distribution of the over-consolidation ratio of the specimens used for the

oedometer tests during the centrifuge test. ......................................................................... 198

Figure 5.4: Evolution of the void ratio with one dimensional loading in an oedometer. ........ 199

Figure 5.5: Distribution of the confined stiffness moduli as a function of the vertical effective

stress. ................................................................................................................................ 200

Figure 5.6: Distribution of the mean vertical (ME, v, average) and horizontal (ME, h, average) confined

stiffness moduli as a function of the vertical effective stress. .............................................. 202

Figure 5.7: Distribution of the mean settlements for the samples extracted in the vertical and

horizontal directions with one-dimensional loading in an oedometer. .................................. 202

Figure 5.8: Definition of Eoedref from oedometer test results (after Brinkgreve & Broere, 2008).

........................................................................................................................................... 203

Figure 5.9: Evolution of the permeability with one dimensional loading in an oedometer. ... 203

Figure 5.10: Extraction positions of the samples for oedometer tests (test JG_v10). .......... 204

Figure 5.11: Distribution of the over-consolidation ratio in the horizontal direction of the

specimens used for the oedometer tests. ........................................................................... 204

Figure 5.12: Evolution of the void ratio with one dimensional loading in an oedometer. ...... 205

Figure 5.13: Distribution of the horizontal confined stiffness moduli as a function of the

vertical stress. .................................................................................................................... 206

List of figures

XXI

Figure 5.14: Evolution of the coefficient of permeability with one dimensional loading in an

oedometer. ......................................................................................................................... 207

Figure 5.15: Setup for the insertion of the electrical impedance needle under 1 g in the

laboratory (a) schematic view (b) picture. ........................................................................... 208

Figure 5.16: Positions of the insertion points of the electrical impedance needle under 1 g. All

dimensions in mm. ............................................................................................................. 209

Figure 5.17: Impedance recorded under 1 g after completion of the first consolidation stage.

........................................................................................................................................... 209

Figure 5.18: Impedance recorded under 1 g after completion of the fifth consolidation stage.

........................................................................................................................................... 210

Figure 5.19: Illustration of the contact between the electron beam and the surface of the

sample (Peschke, 2013). .................................................................................................... 211

Figure 5.20: Electron interaction volume within a sample (after Science Education Resource

Center, 2013). .................................................................................................................... 211

Figure 5.21: Types of interaction between electrons and a sample (Science Education

Resource Center, 2013). .................................................................................................... 212

Figure 5.22: Schematic of an ESEM illustrating the different pressures zones (Donald, 2003).

........................................................................................................................................... 213

Figure 5.23: ESEM picture of zone 2, located a radial distance of 1 mm from the edge of the

column and at a depth of 40 mm below the surface, with the radial axis horizontal (Weber,

2008). ................................................................................................................................. 214

Figure 5.24: ESEM picture of the zone 3 located at a radial distance of 5 mm from the edge

of the column and at a depth of 20 mm below the surface, with the radial axis horizontal. .. 214

Figure 5.25: ESEM pictures of the zone 3 at a radial distance of 5 mm from the edge of the

column and at (a) 60 mm depth and (b) 100 mm depth, with the radial axis horizontal. ...... 215

Figure 5.26: Vacuum pump. ............................................................................................... 216

Figure 5.27: Dilatometer (a) containing the soil specimen before and (b) containing mercury

after the investigation using the macro pore unit Pascal 140. ............................................. 217

Figure 5.28: Porosity as a function of the radial distance from the axis of the stone column at

a depth of (a) 20 mm (b) 60 mm (c) 100 mm. ..................................................................... 218

Figure 6.1: Conversion of axisymmetric unit cell into plane-strain for drains (a) axisymmetric

radial flow (b) plane-strain (Indraratna & Redana, 1997). ................................................... 220

Figure 6.2: Cross-sections of the stone column (a) unit-cell; and plane-strain conversions

according to (b) method 1 and (c) method 2 (Tan et al., 2008). .......................................... 222

Figure 6.3: Plan view of 2D stone columns strips (a) width of an equivalent strip (b) strip

spacing (Chan & Poon, 2012). ............................................................................................ 224

Figure 6.4: Soil profile and properties at Tianjin Port in Beijing, China (Rujikiatkamjorn et al.,

2007). ................................................................................................................................. 225

Figure 6.5: Case study at Tianjin Port in Beijing, China: embankment and vacuum loading on

soft soil stabilised by drains (a) loading history and (b) comparison of the predicted (FEM)

and measured (Field) consolidation settlements (Rujikiatkamjorn et al., 2007). .................. 226

List of figures

XXII

Figure 6.6: Embankment pre-loading at Tianjin Port in Beijing, China (a) loading history (b)

comparison of the results obtained via 2D and 3D modelling with field observations

(Indraratna et al., 2009). ..................................................................................................... 227

Figure 6.7: Development of settlement at the crest of an embankment constructed in-flight on

remoulded Birmensdorf clay reinforced with stone columns – comparison between numerical

model and centrifuge results (Weber et al., 2009). ............................................................. 228

Figure 6.8: Numerical and experimental study of PVDs installed in clay (a) plan view with

dimensions of the smear and transition zones in terms of mandrel size (b) comparison of

settlement obtained with results by Indraratna & Redana (1998) (Basu et al., 2010). ......... 229

Figure 6.9: Model geometry and axisymmetric finite element mesh with applied radial

deformation of the stone column wall (Castro & Karstunen, 2010). .................................... 230

Figure 6.10: Normalised excess pore pressures generated by the stone column installation

(Castro & Karstunen, 2010). ............................................................................................... 230

Figure 6.11: Decrease of the undrained shear strength after column or pile installation

(Castro & Karstunen, 2010). ............................................................................................... 231

Figure 6.12: Unit cell (a) typical stone column–reinforced soft clay deposit supporting an

embankment; (b) unit cell idealisation; (c) cross-section (Indraratna et al., 2013). .............. 233

Figure 6.13: Influence of clogging on the normalised average excess pore water pressure

and on the normalised average ground settlement (Indraratna et al., 2013). ...................... 234

Figure 6.14: Boundary conditions for (a) the fixed pile approach (b) the moving pile approach

(Dijkstra et al., 2011). ......................................................................................................... 235

Figure 6.15: Comparison of calculated and measured stress response at the tip of the pile

during installation for the fixed pile approach (after Dijkstra et al., 2011). ........................... 236


during installation for the moving pile approach (after Dijkstra et al., 2011). ....................... 236

Figure 6.17: Modelling technique for the simulation of the pile insertion (after Grabe &

Pucker, 2012). .................................................................................................................... 237

Figure 6.18: Elastic perfectly plastic model. ........................................................................ 238

Figure 6.19: Impact of the effective cohesion on the failure line in a – σ’ diagram. ........... 238

Figure 6.20: Effective stress paths followed real soil and FEM prediction using the Mohr-

Coulomb model. ................................................................................................................. 239

Figure 6.21: Hyperbolic stress-strain relation in primary loading and unloading-reloading in a

CDC triaxial test (Schanz et al., 1999). ............................................................................... 240

Figure 6.22: Successive yield loci for shear strain hardening for various values of the plastic

shear strain γp and failure surface for m = 0.5 [-] (Brinkgreve & Broere, 2008).................... 241

Figure 6.23: Cap yield surface of the HSM for volumetric hardening in the - plane (after

Brinkgreve & Broere, 2008). ............................................................................................... 242

Figure 6.24: Representation of yield contours of the HSM in effective principal stress space

(Schanz et al., 1999). ......................................................................................................... 244

Figure 6.25: Representation of the associated flow rule in triaxial space. ........................... 245

Figure 6.26: Modelling of the insertion of the stone column installation tool by means of

application of prescribed displacements on the wall of an initial cavity (Weber, 2008). ....... 246

List of figures

XXIII

Figure 6.27: 2D axisymmetric numerical model for a unit cell including a single stone column.

........................................................................................................................................... 251

Figure 6.28: Comparison of the experimental and numerical load-settlement curves for tests

JG_v7 and JG_v9. .............................................................................................................. 252

Figure 6.29: Deformed mesh obtained for test JG_v7 for a settlement of 850 mm and a

footing load of 145.44 kPa. ................................................................................................. 253

Figure 6.30: Vertical strain increment computed numerically for test JG_v7 for a settlement of

850 mm and a footing load of 145.44 kPa. ......................................................................... 253

Figure 6.31: Total vertical stress distribution computed numerically for test JG_v7 for a

settlement of 850 mm and a footing load of 145.44 kPa. .................................................... 254

Figure 6.32: Development of plastic points during the loading phase for test JG_v7 (a) for a

settlement of 100 mm (P = 85 kPa), (b) for a settlement of 400 mm (P = 115.2 kPa) and (c)

for a settlement of 850 mm (P = 145.44 kPa). .................................................................... 255

Figure 6.33: Vertical stress distribution from a line load below a rigid strip footing (a) for the

self-weight of the footing and for a global safety factor equal to (b) 3.0, (c) 2.0, (d) 1.5 and (e)

1.0 (Jessberger, 1995). ...................................................................................................... 256

Figure 6.34: Pressure distribution under the footing for a settlement of 100 mm at prototype

scale (2 mm under 50 g) for (a) test JG_v7 (P = 55.6 kPa) and (b) test JG_v9 (P = 46.1

kPa). ................................................................................................................................... 257


scale (8 mm under 50 g) for (a) test JG_v7 (P = 110.1 kPa) and (b) test JG_v9 (P = 90.1

kPa). ................................................................................................................................... 257


scale (16 mm under 50 g) for test JG_v9 (P = 118.1 kPa). ................................................. 258

Figure 6.37: Total vertical stress distribution under the footing, as a function of the radial

distance, for settlements of 100 mm, 400 mm and 850 mm for test JG_v7 (σc = 200 kPa).

........................................................................................................................................... 259


distance, for settlements of 100 mm, 400 mm and 850 mm for test JG_v9 (σc = 100 kPa).

........................................................................................................................................... 259

Figure 6.39: Total vertical stress distribution, as a function of the radial distance, under the

footing (z = 100 mm) and at depths of 2 m, 4 m and 6 m for a footing settlement of 100 mm

during the footing loading for test JG_v7 (P = 85 kPa). ....................................................... 260



during the footing loading for test JG_v9 (P = 70.8 kPa). .................................................... 260

Figure 6.41: Distribution of the stress concentration factor m over depth for footing

settlements of 100 mm, 400 mm and 850 mm for test JG_v7 (σc = 200 kPa). .................... 261


settlements of 100 mm, 400 mm and 850 mm for test JG_v9 (σc = 100 kPa). .................... 261

Figure 6.43: Distribution of the normalised stress concentration factor m over depth for

footing settlements of 100 mm, 400 mm and 850 mm for test JG_v7 (σc = 200 kPa). ........ 262

List of figures

XXIV


footing settlements of 100 mm, 400 mm and 850 mm for test JG_v9 (σc = 100 kPa). ......... 263

Figure 6.45: Direction of the total principal stress at the end of the loading phase for test

JG_v7 (P = 141.90 kPa). .................................................................................................... 263

Figure 6.46: Distribution of the excess pore water pressures computed numerically for test

JG_v7 for a footing settlement of 850 mm and a footing load of 141.90 kPa. ..................... 264

Figure 6.47: Comparison of the values of the excess pore water pressures measured during

test JG_v7 with the values obtained numerically with Plaxis 2D (P1 till P3). ....................... 265

Figure 6.48: Comparison of the experimental load-settlement curves for test JG_v7 (σc = 200

kPa) with the numerical simulations, with and without installation effects. .......................... 266


kPa) with the numerical simulations, with and without installation effects. .......................... 266

Figure 6.50: General view of the 3D mesh (groundwater table 0.5 m below the surface). ... 267

Figure 6.51: Plan on the stone column group. .................................................................... 267

Figure 6.52: Side view of the stone columns and zones created to represent the installation

effects (the base of the box is located 1 m below the toe of the compaction zone), in which

clay and compaction zone (left hand side), respectively clay, compaction zone and smear

zone (right hand side), were hidden in order to expose the smear zone, respectively the

stone column. ..................................................................................................................... 268

Figure 6.53: Plan on the stone column group with position of the square footing, as applied in

the centrifuge test JG_v10. ................................................................................................. 268

Figure 6.54: Comparison of the experimental and numerical load-settlement curves for the

test JG_v10. ....................................................................................................................... 269

Figure 6.55: Pressure distribution under the square footing for a settlement of 100 mm at

prototype scale (2 mm under 50g) for test JG_v10. ............................................................ 270

Figure 6.56: Distribution of the total vertical stresses for test JG_v10 (σc = 100 kPa) for a

settlement of 850 mm and a footing load of 138.66 kPa (section 1-1, Figure 6.51). The

dimensions are given in Figure 6.51 and Figure 6.52. ........................................................ 270




Figure 6.58: Total vertical stress distribution under the footing for a settlement of 850 mm for

test JG_v10 (σc = 100 kPa, P = 138.66 kPa). Negative stresses denote compression. The

dimensions are shown in Figure 6.51 and Figure 6.53........................................................ 272

Figure 6.59: Total vertical stress distribution at a depth of 6 m for a settlement of 850 mm for




test JG_v10, with the values obtained numerically with Plaxis 3D (P1 till P3). .................... 273


JG_v10 (σc = 100 kPa) for a settlement of 850 mm and a footing load of 138.66 kPa (section

1-1, Figure 6.51). ................................................................................................................ 274

List of figures

XXV


JG_v10 (σc = 100 kPa) for a settlement of 850 mm and a footing load of 138.66 kPa (section

2-2, Figure 6.51). ................................................................................................................ 274

Figure 6.63: Deformed columns A, C and D for test JG_v10, for a settlement of 850 mm and

a footing load of 138.66 kPa, in which clay, compaction zone and smear zone were hidden in

order to expose the deformation of the stone columns. ...................................................... 275

Figure 6.64: Comparison of the experimental load-settlement curves for test JG_v10 with the

numerical simulations, with and without, installation effects. ............................................... 276

Figure 7.1: Distribution of the vertical stress increase as a function of the radial distance from

the stone column at 96 mm depth as a percentage of the applied footing load P and

comparison with the depth factor J4 according to Grasshoff (1978). ................................... 280


diameter 1 mm). ................................................................................................................. 280

Figure 7.3: ESEM picture of zone 3, located at a radial distance of 5 mm from the edge of the

column and at a depth of 20 mm below the surface, with the radial axis horizontal. ........... 281

Figure 7.4: Porosity as a function of the radial distance from the axis of the stone column at a

depth of (a) 20 mm (b) 60 mm (c) 100 mm. ........................................................................ 282













JG_v7 for a footing settlement of 850 mm and a footing load of 141.90 kPa. ..................... 286


under a vertically loaded circular footing resting on top of a stone column. ......................... 286


(test JG_v1): (a) excess pore water pressures (b) evolution of the footing load (c) footing

settlement. .......................................................................................................................... 291


(test JG_v5): (a) excess pore water pressures (b) evolution of the footing load (c) footing

settlement. .......................................................................................................................... 292


(test JG_v6): (a) Excess pore water pressures (b) evolution of the footing load (c) footing

settlement. .......................................................................................................................... 293

Figure 8.4: Impedance recorded at the reference points RP1 and RP2 during test JG_v9

(Container A). ..................................................................................................................... 295

List of figures

XXVI


(Container B). ..................................................................................................................... 295

Figure 8.6: Impedance recorded at the points A, B and C during test JG_v9 (Container A).

........................................................................................................................................... 296

Figure 8.7: Impedance recorded at the points D, E and F during test JG_v9 (Container A).

........................................................................................................................................... 296

Figure 8.8: Impedance recorded at the points A, B and C during test JG_v9 (Container B).

........................................................................................................................................... 297

Figure 8.9: Impedance recorded at the points D, E and F during test JG_v9 (Container B).

........................................................................................................................................... 297


dimensions in mm. ............................................................................................................. 298

Figure 8.11: Impedance recorded under 1 g after completion of the second consolidation

stage. ................................................................................................................................. 299

Figure 8.12: Impedance recorded under 1 g after completion of the third consolidation stage.

........................................................................................................................................... 299

Figure 8.13: Impedance recorded under 1 g after completion of the fourth consolidation

stage. ................................................................................................................................. 300

Figure 8.14: Vertical strain increments computed numerically for test JG_v7 for a settlement

of 100 mm and a footing load of 85 kPa. ............................................................................ 301


of 400 mm and a footing load of 115.2 kPa ........................................................................ 302

Figure 8.16: Shear strain increments computed numerically for test JG_v7 for a settlement of

100 mm and a footing load of 85 kPa. ................................................................................ 303


400 mm and a footing load of 115.2 kPa. ........................................................................... 304


850 mm and a footing load of 145 kPa. .............................................................................. 305

Figure 8.19: Development of plastic points during the loading phase for test JG_v7 for a

settlement of 100 mm (P = 85 kPa). ................................................................................... 306


settlement of 400 mm (P = 115.2 kPa). .............................................................................. 307


settlement of 850 mm (P = 145.44 kPa). ............................................................................ 308


footing load of 115.11 kPa. ................................................................................................. 309




100 mm and a footing load of 70.8 kPa. ............................................................................. 311



List of figures

XXVII



Figure 8.27: Shear strain increment computed numerically for test JG_v9 for a settlement of







JG_v9 for a footing settlement of 850 mm and a footing load of 115.11 kPa ...................... 317


settlement of 100 mm (P = 70.8 kPa). ................................................................................ 318


settlement of 400 mm (P = 94.3 kPa). ................................................................................ 319


settlement of 850 mm (P = 119.67 kPa). ............................................................................ 320

Figure 8.34: Total vertical stress distribution as a function of the radial distance under the


during the footing loading for test JG_v7 (P = 115.2 kPa). .................................................. 321


footing (z = 850 m) and at depths of 2 m, 4 m and 6 m for a footing settlement of 850 mm

during the footing loading for test JG_v7 (P = 145.44 kPa). ................................................ 321



during the footing loading for test JG_v9 (P = 94.3 kPa). .................................................... 322



during the footing loading for test JG_v9 (P = 119.67 kPa). ................................................ 322




test JG_v7 with the values obtained numerically with Plaxis 2D (P7). ................................. 323






test JG_v9 with the values obtained numerically with Plaxis 2D (P7). ................................. 325

Figure 8.43: Distribution of the total vertical stresses for test JG_v10 for a settlement of 100

mm and a footing load of 76 kPa (section 1-1, Figure 6.51). The dimensions are given in

Figure 6.51 and Figure 6.52. .............................................................................................. 326

List of figures

XXVIII


mm and a footing load of 76 kPa (section 2-2, Figure 6.51). The dimensions are given in



mm and a footing load of 108.60 kPa (section 1-1, Figure 6.51). The dimensions are given in



mm and a footing load of 108.60 kPa (section 2-2, Figure 6.51). The dimensions are given in

































test JG_v10 with the values obtained numerically with Plaxis 3D (P4 till P6). ..................... 337


test JG_v10 with the values obtained numerically with Plaxis 3D (P7). ............................... 337

List of figures

XXIX

Figure 8.59: Development of plastic points during the loading phase for test JG_v10 (section

1-1, Figure 6.51) for a settlement of 100 mm (P = 76 kPa). ................................................ 338


1-1, Figure 6.51) for a settlement of 400 mm (P = 108.60 kPa). ......................................... 339




2-2, Figure 6.51) for a settlement of 100 mm (P = 76 kPa). ................................................ 340





List of figures

XXX

List of tables

XXXI

List of tables

Table 2.1: Classification of ground improvement methods (after Chu et al., 2009). ............... 5

Table 2.2: Classification of ground improvement methods (after Chu et al., 2009). ............... 6

Table 2.3: Suggested values of the stress concentration ratio m for specific combinations of

area replacement ratio as and effective friction angle of the stone column material for

compacted sand columns after Ichimoto & Suematsu (1981). ..............................................14

Table 2.4: Summary of 1 g small-scale model tests (σc: pre-consolidation stress; su:

undrained shear strength; rsc: radius of the stone columns; L: length of the stone columns; a:

spacing of the stone columns; as: area replacement ratio) (after Muir Wood et al., 2000). ....18

Table 2.5 Summary of inclinometer and piezometer installations at Red River test site in

Winnipeg, Canada: (SI: slope inclinometer; PZ: piezometer; VW: vibrating wire) (after

Thiessen et al., 2011). ..........................................................................................................52

Table 2.6: Geotechnical properties of Busan clay (Shin et al., 2009). ...................................80

Table 3.1: Summary of the main scaling factors (after Schofield, 1980). ..............................94

Table 3.2: Classification and selected mechanical properties of Birmensdorf clay (after

Weber, 2008). .................................................................................................................... 116

Table 3.3: Selected properties of Birmensdorf clay, determined from oedometer tests. ...... 117

Table 3.4: Parameters for the quartz sand used as stone column material (Weber, 2008). 117

Table 3.5: Selected properties of Perth Sand (Nater, 2005). .............................................. 118

Table 3.6: Summary of the containers used for the preparation of soil models for centrifuge

tests. .................................................................................................................................. 118

Table 3.7: Summary of the main system parameters. ......................................................... 129

Table 3.8: Overview of the experimental setup used for the different tests. ........................ 130

Table 3.9: Testing procedure for tests conducted using the full cylindrical strongbox (loading

of a single stone column, tests JG_v2, JG_v3 and JG_v6). ................................................ 132

Table 3.10: Overview of the experimental setups used for the different tests. .................... 134


of a stone column group, tests JG_v8 and JG_v10). .......................................................... 137

Table 3.12: Testing procedure for tests conducted using the specimens prepared in an

oedometer or in an adapted oedometer (tests JG_v1, JG_v4, JG_v5, JG_v7 and JG_v9). 140

Table 4.1: Values of a and b obtained by Trausch-Giudici (2003) and Küng (2003). .......... 144

Table 4.2: Comparison of the back-calculated values of the parameters a and b with those

proposed by Trausch-Giudici (2003) and Küng (2003). ...................................................... 149

Table 4.3: Response of the PPT to the applied footing load on a single stone column during

test JG_v2. ......................................................................................................................... 157


the test JG_v6. ................................................................................................................... 157


the test JG_v9. ................................................................................................................... 159


test JG_v7 (adapted oedometer). ....................................................................................... 164

List of tables

XXXII


test JG_v1 (cylindrical strongbox with clay surrounded by sand). ....................................... 164


test JG_v5 (cylindrical strongbox with clay surrounded by sand). ....................................... 166

Table 4.9: Calculation of the over-consolidation ratio at the installation depths of the PPTs

depending on the pre-consolidation stress σc. .................................................................... 170

Table 4.10: Coefficients of earth pressure at rest of the over-consolidated Birmensdorf clay

with depth. .......................................................................................................................... 170

Table 4.11: Values of the pore pressure parameter A depending on the type of clay

(Skempton, 1954). .............................................................................................................. 171

Table 4.12: Comparison of the peak analytical and measured excess pore water pressure at

end of the loading phase of a single stone column (test JG_v9, σc = 100 kPa, P = 119.67

kPa). ................................................................................................................................... 172



kPa). ................................................................................................................................... 172



kPa). ................................................................................................................................... 172

Table 4.15: Back-calculated values of the vertical stress increases at the locations of the

PPTs P4, P5, P6 and P7 for tests JG_v1, JG_v5, JG_v7 and JG_v9. ................................ 175

Table 4.16: Response of the PPT to the applied footing load on a stone column group during

test JG_v8. ......................................................................................................................... 179


test JG_v10. ....................................................................................................................... 180

Table 5.1: Compression indexes CC obtained from the oedometer tests. ........................... 199

Table 5.2: Compression indexes CS obtained from the oedometer tests. ............................ 200

Table 5.3: Vertical (ME,v) and horizontal (ME,h) confined stiffness moduli obtained from the

oedometer tests and values of the over-consolidation ratios for samples extracted vertically

(OCRv) and horizontally (OCRh). ........................................................................................ 201

Table 5.4: Compression indexes CC obtained from the oedometer tests. ........................... 205

Table 5.5: Compression indexes CS obtained from the oedometer tests. ............................ 206

Table 5.6: Overview of the consolidation stages for the implementation of the electrical

impedance needle under 1 g. ............................................................................................. 208

Table 6.1: Input parameters for the Mohr-Coulomb model. ................................................. 239

Table 6.2: Stiffness moduli used in the HSM. ..................................................................... 240

Table 6.3: Input parameters for the soil stiffness in the HSM. ............................................. 245

Table 6.4: Description of the calculation phases used in the axisymmetric model. ............. 247

Table 6.5: Summary of the Hardening Soil parameters for the clay. ................................... 248

Table 6.6: Mohr-Coulomb parameters for the stone column material. ................................. 249

Table 6.7: Summary of the Hardening Soil parameters for the smear zone. ....................... 249

Table 6.8: Summary of the Hardening Soil parameters for the compaction zone. ............... 250

List of tables

XXXIII

Table 6.9: Comparison of the experimental and numerical values of the maximum footing

loads. ................................................................................................................................. 251

Table 6.10: Comparison of the values of the maximum footing loads obtained numerically

with (Pmax, Plaxis) and without (Pmax, Plaxis, no smear) installation effects for a settlement of 850 mm.

........................................................................................................................................... 265


loads for a footing settlement of 850 mm. ........................................................................... 269


with (Pmax, Plaxis) and without (Pmax, Plaxis, no smear) installation effects. ....................................... 275

Table 8.1: Values of the factor J4 in ‰ (Lang et al., 2007) (z: depth of the point considered;

R: radius of the circular footing; a: radial distance of the point considered from the centre of

the footing). ........................................................................................................................ 294

Table 8.2: Comparison of the analytical and measured excess pore water pressure during

the loading phase of a single stone column (test JG_v1, σc = 200 kPa, P = 80 kPa). ......... 294

Table 8.3: Overview of the consolidation stages conducted for the insertion of the electrical

impedance needle under 1 g. ............................................................................................. 298

List of tables

XXXIV

Abstract

XXXV

Abstract

Switzerland’s main infrastructures and industrial installations are located in the so-called

Mittelland, the plain between Jura and the Alps, where the flat areas are mostly formed of

soft lacustrine deposits which are the residual products of the last glaciations. Such soil

conditions cause challenges for constructions in terms of the Ultimate Limit State (ULS) as

their bearing capacity may be insufficient. Moreover, the Serviceability Limit State (SLS) may

become problematic, as the low permeability of lacustrine deposits cause consolidation times

of several years, which leads to continuous settlements of the structures over this period.

Stone columns have proven to be an efficient ground improvement method in soft soils, as

they increase the stiffness and strength of the subsoil, as well as reducing the consolidation

time through shorter (radial) drainage paths. This allows higher loads to be carried, with

lower post-construction settlements.

However, installation effects, identified e.g. by Weber (2008) impair the performance of stone

columns in terms of drainage capacity. The spatial distribution of these effects long remained

unclear, which represented a gap of knowledge that this research aimed to fill.

The load-settlement behaviour of composite foundations with stone columns was

investigated in the geotechnical drum centrifuge at the ETH Zürich. The use of a centrifuge

enables a reproduction of the in-situ stress states and thus an accurate reproduction of the

mechanisms developing during the installation and subsequent loading of granular

inclusions. Stone columns were installed in-flight in a geotechnical drum centrifuge and

subsequently loaded with rigid footings while monitoring the footing load and the pore water

pressures in the clay specimen. The findings of the physical modelling under enhanced

gravity gave an insight into the load-transfer behaviour with depth around a stone column.

The insertion of an electrical needle measuring the impedance in the host soil surrounding

the inclusions also gave valuable information about the extent of the micromechanical

reorganisation of the clay particles caused by the installation and loading of a stone column.

Samples were extracted from the soft soil bed around the piles after the centrifuge tests in

order to conduct complementary investigations, namely oedometer tests, Mercury Intrusion

Porosimetry (MIP) and Environmental Scanning Electron Microscopy (ESEM). The MIP

investigations showed that the extent of the macromechanical installation effects remains

constant with depth and reaches 2.5 times the radius of the stone column from the centre of

the inclusions. The ESEM observations confirmed the interpretation of the measurements

made with the electrical needle, according to which a progressive reorganisation of the clay

particles occurs up to a distance corresponding to 5 times the radius of the inclusions from

the axis of the stone column.

The outcomes of the physical modelling under enhanced gravity as well as those of the

subsequent micromechanical investigations were used for the construction of a numerical

model aiming to reproduce the centrifuge tests.

Abstract

XXXVI

The numerical model developed in the course of this research allows the installation effects

to be considered in a simplified form as it does not require modelling the installation phase of

the inclusions. A good prediction of the load-settlement behaviour of composite foundations

using stone columns in soft clays has been reached. Interesting insights into the variation of

the stress concentration with depth were obtained, as it was shown that the stress

concentration factor reaches values ranging from 1.0 to 1.5 in the lower third of the stone

column. This could open up the way for a more economical design of granular inclusions, as

the diameter and thus the quantity of material needed, could be reduced in zones where the

stress concentration is low. This should be confirmed by further research, taking the

influence of varying soil characteristics and stress history as well as of different types of

loading, into account.

Kurzfassung

XXXVII

Kurzfassung

Die wichtigsten Infrastrukturen der Schweiz befinden sich in dem sogenannten Mittelland,

der Ebene zwischen Jura und den Alpen, mit flachen Zonen aus weichem Seebodenlehm,

die Restprodukte von den letzten Vereisungen darstellen. Derartige Bodenverhältnisse

stellen eine Herausforderung für bauliche Anlagen in Bezug auf den Grenzzustand der

Tragsicherheit (ULS) dar, da deren Tragfähigkeit unzureichend sein kann. Auch der

Grenzzustand der Gebrauchstauglichkeit (SLS) kann sich problematisch erweisen, da die

niedrige Durchlässigkeit von Seebodenlehmen zu Konsolidationszeiten von mehreren Jahren

bis hin zu Jahrzehnten führt, was kontinuierliche Setzungen der Anlagen über diese

Zeitperiode zur Folge hat.

Kiessäulen stellen eine effiziente Methode der Baugrundverbesserung dar. Auf der einen

Seite steigern sie durch die Verdichtung des umgebenden Bodens und die Zuführung von

tragfähigem Material die Steifigkeit des Baugrundes. Auf der anderen Seite werden die

Drainagewege verkürzt, was eine Reduktion der Konsolidierungszeit bewirkt. Allerdings

beeinträchtigen Effekte, die sich aus der Herstellung der Säulen ergeben, vor allem die

Wirkung der Drainage durch das Entstehen von Schmierzonen wie auch durch die

Verdichtung, die eine Reduktion der Durchlässigkeit im weichen Boden bewirkt. Die

Verteilung dieser Zonen in radialer wie auch vertikaler Richtung ist dabei nicht abschliessend

geklärt.

Das Last-Setzungsverhalten von starren Fundamenten auf Kiessäulen wurde in der

geotechnischen Trommelzentrifuge der ETH Zürich untersucht. Mittels einer Zentrifuge

können die in-situ Spannungszustände im Boden simuliert werden. Damit stellen sich

realitätsnahe Mechanismen während der Installation und der darauf folgenden Belastung von

Kiessäulen ein. Dabei wurden Kiessäulen im Flug in einer geotechnischen

Trommelzentrifuge installiert und anschliessend mit starren Fundamenten unter

Überwachung der Fundamentbelastung und der Porenwasserdrücke im Tonmodell belastet.

Die Ergebnisse der physikalisen Modellierung unter den Bedingungen eines erhöhten

Schwerfeldes gaben einen Einblick in das Lastabtragungsverhalten einer Kiessäule über die

Tiefe. Die Einbringung einer elektrischen Nadel zur Messung der Impedanz des Bodens um

die Inklusionen lieferte wertvolle Informationen über den Umfang der durch die

Kiessäuleninstallation und -belastung verursachten mikromechanischen Reorganisation der

Tonpartikel.

Im Anschluss an die Zentrifugenversuche wurden Proben aus dem weichen Bodenmodell

um die Säulen entnommen, um ergänzende Untersuchungen, nämlich Oedometerversuche,

Quecksilberporosimetrie und Environmental Scanning Electron Microscopy (ESEM)

durchzuführen. Die Quecksilberporosimetrie-Untersuchungen haben gezeigt, dass der

Umfang der makromechanischen Installationseffekte über die Tiefe konstant bleibt und sich,

gemessen ab der Säulenachse, über einen Bereich bis zum 2.5-fachen Radius der Kiessäule

erstreckt. Die ESEM-Beobachtungen haben die Interpretation der Messungen mit der

elektrischen Nadel bestätigt, der zufolge eine progressive Reorganisation der Tonpartikel in

einem Bereich mit dem fünffachen Radius der Kiessäulen, gemessen ab deren Achse,

stattfindet.

Kurzfassung

XXXVIII

Basierend auf den Ergebnissen der physikalischen Modellierungen unter den Bedingungen

eines erhöhten Schwerefeldes sowie der nachfolgenden mikromechanischen

Untersuchungen wurde ein numerisches Modell zur Reproduktion der Zentrifugentests

entwickelt.

Dieses numerische Modell ermöglicht eine vereinfachte Berücksichtigung der

Installationseffekte, da es auf die Modellierung der Installationsphase im numerischen Modell

verzichtet. Die gefundenen Zonen wurden mit veränderten Parametern als Makromodell

vorgegeben. Es wurde eine gute Prognose des Last-Setzungsverhaltens von

Verbundfundationen mit Kiessäulen erreicht. Dies lieferte interessante Einblicke in die

Variation der Spannungskonzentration über die Tiefe, da gezeigt wurde, dass der

Spannungskonzentrationsfaktor Werte zwischen 1,0 und 1,5 in dem tieferen Drittel der

Kiessäulen erreicht. Dies könnte den Weg zu einer wirtschaftlicheren Bemessung von

Kiessäulen weisen, da der Durchmesser und damit die benötigten Rohstoffmengen in den

Zonen mit niedriger Spannungskonzentration reduziert werden könnten. Dies sollte durch

weitere Forschung bestätigt werden, indem der Einfluss von wechselnden

Bodeneigenschaften, der Spannungsgeschichte sowie verschiedener Belastungstypen,

berücksichtigt wird.

1 Introduction

1

1 Introduction

1.1 Motivation

The Swiss Mittelland is a zone of vital importance for the country, where key infrastructure,

and lifelines industrial complexes and numerous buildings of national relevance are to be

found and where the demand for land suitable for construction is still growing. However, the

ground in the flat areas is mostly constituted of soft normally or slightly over-consolidated

lacustrine deposits that were formed after the last glaciations.

Building on soft soils presents challenges concerning design in respect of both the Ultimate

Limit State (ULS) and the Serviceability Limit State (SLS). Normally or slightly over-

consolidated lacustrine soils may not provide sufficient bearing capacity to support the

planned infrastructure. In addition, the low permeability will lead to consolidation times that

may last years or decades, and which will lead to on-going settlements during this period.

Numerous methods are available in foundation engineering to reduce settlements or

circumvent low bearing capacities by increasing the load transfer capacity, such as

preloading, grouting, deep mixing or support piling (Fleming et al., 1992). Drains, sometimes

combined with preloading or vacuum techniques, are used to accelerate the consolidation

process. An amalgamation of these two effects can be achieved by implementing stone

columns as a ground improvement measure. These elements are usually less costly and

more environmentally friendly than deep foundations, as no manmade substances are

introduced into the soil. The host soil will also react in a stiffer way as the ratio of area

improved by stone columns is increased, while the main direction of dissipation of excess

pore water pressure will change from vertical to radial in the horizontal plane. The soil

structure in varved lacustrine soils aids this process since the horizontal permeability is often

one to two orders of magnitude higher than the vertical permeability, leading to acceleration

of the consolidation process by several orders of magnitude.

However, the installation of stone columns disturbs the soil microstructure around the

inclusion, causing the appearance of smear and compaction zones, as shown in Figure 1.1

(Weber, 2008). The mixed zone (zone 1) can be considered to be part of the stone column

and contains a mix of host soil and column material. The smear zone (zone 2), located

directly at the boundary of the stone column, exhibits an alignment of the clay minerals along

a residual shear surface, which will counteract the improving effect of the inclusions both in

load transfer and in blocking seepage flow. The compaction zone (zone 3) is located in an

annulus around the smear zone and is associated with increased density and reduced pore

space, which likewise impedes radial drainage. The fourth zone can be considered as a free-

field zone, where no significant installation effects can be identified.

1.2 Thesis layout

2


(Weber, 2008).

Although numerous scientific projects have been conducted on this topic, the spatial

distribution of these installation effects, namely zones 2 and 3, remained unclear. This

represents a gap in knowledge, which has significant relevance for optimising design.

In order to fill this gap, tests under enhanced gravity were conducted in the ETH Zürich

geotechnical drum centrifuge (Springman et al., 2001), during which stone columns were

installed into a soft soil specimen in-flight. Some of the inclusions were loaded using a stiff

foundation and the distribution of the density of the host soil around the stone columns was

investigated using an electrical impedance needle. Some samples were extracted from the

specimen used for the centrifuge investigations for further investigations in the laboratory.

These included oedometer tests, microscopic investigations and Mercury Intrusion

Porosimetry to determine the spatial distribution of the installation effects with depth and

radial distance to the inclusions.

The findings from the centrifuge tests and subsequent complementary investigations were

validated by a numerical model.

1.2 Thesis layout

This thesis is divided into six chapters:

- Chapter 1 introduces the motivation of the research and the methodology adopted,

- Chapter 2 consists of a literature review of research on stone columns in terms of

objectives, construction techniques, bearing behaviour, design, load-transfer

behaviour, effect on the consolidation time and impact onto the host soil,

- Chapter 3 presents the basic physics of centrifuge modelling before a literature

review of how centrifuge modelling has been used to develop process understanding

of various forms of ground improvement. The methods adopted in this thesis, as well

as the materials used, the preparation techniques for the soil specimens and the

centrifuge tests conducted are described subsequently,

- Chapter 4 shows the results of the centrifuge tests in terms of undrained shear

strength, pore pressure measurements during the installation of the stone columns,

1 Introduction

3

measurements conducted while loading the stone columns and electrical impedance

measurements,

- Chapter 5 displays the complementary investigations conducted using specimens

extracted from soft soil specimens used for the centrifuge tests. These investigations

included oedometer tests, electrical impedance measurements under Earth’s gravity

and microscopic and Mercury Intrusion Porosimetry investigations,

- Chapter 6 presents the basic principles and a literature review of numerical modelling

of ground improvement methods, focussing particularly on columnar inclusions and

drains. Subsequently, the numerical models used in this thesis and the results

obtained in the axisymmetric and three-dimensional numerical modelling are

presented.

- Chapter 7 synthesises the outcomes of the thesis.

1.2 Thesis layout

4

2 State of the art of ground improvement with stone columns

5


2.1 General considerations about ground improvement

Ground improvement aims to enhance the engineering properties of a soil in terms of bearing

capacity and / or stiffness in order to make it suitable for construction. Chu et al. (2009)

present an overview of the different ground improvement methods and suggest a subdivision

into five categories: ground improvement without admixtures in coarse-grained soils, ground

improvement without admixtures in fine-grained soils, ground improvement with admixtures,

ground improvement with grouting type admixtures, and earth reinforcement (Table 2.1 and

Table 2.2).

Table 2.1: Classification of ground improvement methods (after Chu et al., 2009).

A. Ground

improvement

without

admixtures in

coarse-grained

soils

A1. Dynamic compaction Densification of granular soil by dropping a heavy

weight from air onto ground

A2. Vibro compaction Densification of granular soil using a vibratory probe

inserted into ground

A3. Explosive compaction Shock waves and vibrations are generated by blasting

to cause granular soil to settle through liquefaction or

compaction

A4. Electric pulse compaction Densification of granular soil using the shock waves and

energy generated by electric pulse under high voltage

A5. Surface compaction (including

rapid impact compaction)

Compaction of fill or ground at the surface or shallow

depth using a variety of compaction machines

B. Ground

improvement

without

admixtures in

fine-grained

soils

B1. Replacement / displacement

(including load reduction using

lightweight materials)

Remove poor quality soil by excavation or displacement

and replace it by good quality soil or rocks. Some

lightweight materials may be used as backfill to reduce

the load or earth pressure

B2. Preloading using fill (including

the use of vertical drains)

Fill is applied to pre-consolidate compressible soil so

that its compressibility will be considerably reduced

when future loads are applied, and removed

subsequently

B3. Preloading using vacuum

(including fill and vacuum)

Vacuum pressure of up to 90 kPa is used to pre-

consolidate compressible soil so that its compressibility

will be much reduced when future loads are applied

B4. Consolidation with enhanced

drainage (including the use of

vacuum)

Similar to dynamic compaction except vertical or

horizontal drains (or possibly together with a vacuum)

are used to dissipate pore pressures generated in soil

during compaction

B5. Electro-osmosis or electro-

kinetic consolidation

DC current causes water in soil or solutions to flow from

anodes to cathodes which are installed in soils

B6. Thermal stabilisation using

heating or freezing

Change the physical or mechanical properties of soil

permanently or temporarily by heating or freezing the

soil

B7. Hydro-blasting compaction Collapsible soil (loess) is compacted by a combined

action of wetting and deep explosion along a borehole

2.1 General considerations about ground improvement

6

Table 2.2: Classification of ground improvement methods (after Chu et al., 2009).

C. Ground

improvement

with

admixtures or

inclusions

C1. Vibro replacement or stone

columns

Hole jetted into soft, fine-grained soil and back filled with

densely compacted gravel or sand to form columns

C2. Dynamic replacement Aggregates are driven into soil by high energy dynamic

impact to form columns. The backfill can be either sand,

gravel, stone or demolition debris

C3. Sand compaction piles Sand is fed into ground through a casing pipe and

compacted by either vibration, dynamic impact, or static

excitation to form columns when the casing has been

removed

C4. Geotextile confined columns Sand is fed into a closed bottom geotextile lined

cylindrical hole to form a column

C5. Rigid inclusions (or composite

foundation)

Use of piles, rigid or semi-rigid bodies or columns which

are either premade or formed in-situ to strengthen soft

ground

C6. Geosynthetic reinforced

column or pile supported

embankment

Use of piles, rigid or semi-rigid columns / inclusions and

geosynthetic grids to enhance the stability and reduce

the settlement of embankments

C7. Microbial methods Use of microbial materials to modify soil to increase its

strength and stiffness or reduce its permeability

C8. Other methods Unconventional methods, such as formation of sand

piles using blasting and the use of bamboo, timber and

other natural products

D. Ground

improvement

with grouting

admixtures

D1. Particulate grouting Grouting granular soil or cavities or fissures in soil or

rock by injecting cement or other particulate grouts

either to increase the strength or reduce the

permeability of soil or ground

D2. Chemical grouting Solutions of two or more chemicals react in soil pores to

form a gel or a solid precipitate either to increase the

strength or reduce the permeability of soil or ground

D3. Mixing methods (including

premixing or deep mixing)

Treating the weak soil by mixing it with cement, lime, or

other binders in-situ using a mixing machine or before

placement

D4. Jet grouting High speed jets at depth erode the soil and inject grout

to form columns or panels

D5. Compaction grouting Very stiff, mortar-like grout is injected into discrete soil

zones and remains in a homogeneous mass so as to

densify loose soil or lift settled ground

D6. Compensation grouting Medium to high viscosity particulate suspensions are

injected into the ground between a subsurface

excavation and a structure in order to negate or reduce

settlement of the structure due to ongoing excavation

E. Earth

reinforcement

E1. Geosynthetics or

mechanically stabilised earth

Use of the tensile strength of various steel or

geosynthetic material to enhance the shear strength of

soil and stability of roads, foundations, embankments,

slopes, or retaining walls

E2. Ground anchors or soil nails Use of tensile strength of embedded nails or anchors to

enhance the stability of slopes or retaining walls

E3. Biological methods using

vegetation

Reinforcing and stabilising slopes using roots of

vegetation


7

Table 2.1 and Table 2.2 show the wide range of possibilities available in the field of ground

improvement. The aim of this dissertation is the investigation of the behaviour of stone

columns installed in clay, which is why the categories C1 and C3 (Table 2.2) will be

considered into more detail, while the other possibilities will not be considered further.

Stone columns are installed using a vibrating poker, creating a cavity in the ground, which is

subsequently filled with coarse-grained material (gravel or sand). The advantage of this

replacement technique is the flexibility of its application, as it can be used over a wide range

of possible host soil grain sizes. This work is focused on fine-grained lacustrine soils for

which this technique offers a very cost effective solution to improve the relevant properties.

2.2 Objectives of ground improvement of soft soils with stone

columns

The objectives of ground improvement in soft soils by means of granular inclusions can be

divided into two categories:

- the increase of stiffness and shear strength of the host soil, which can prove to be

very valuable e.g. underneath an embankment, to prevent the formation of a slip

circle or under foundations to reduce settlements and

- the amelioration of the drainage conditions through a reduction of the length of the

drainage path. This usually also takes advantage of the structural anisotropy, which is

often to be found in soft soils and which results in a significantly higher permeability in

the horizontal than in the vertical direction. The improved drainage conditions lead to

a reduction of the consolidation times and a quicker increase in stiffness and

strength.

Detailed considerations concerning ground improvement can be found, among others, in

Greenwood & Kirsch (1983), Barksdale & Bachus (1983), Van Impe (1989), Bergado et al.

(1994), Ou & Woo (1995), Van Impe et al. (1997b, 1997a, 1997c) and Chu el al. (2009).

Granular inclusions, also called stone columns, stone compaction piles, sand columns or

sand compaction piles, refer to the same type of construction. The differences in

denomination are due to variations of the material fed in, or to the construction technique.

None of the columns contain binding material (such as cement or lime). As a consequence,

they need to be supported by the surrounding material, which makes them flexible. This is a

major difference to rigid inclusions such as concrete piles, which rely on tip bearing and shaft

friction.

A limiting factor for the implementation of granular inclusions in soft soils is the capacity of

the host soil to provide lateral support to the inclusions. A range of values can be found in the

literature for the minimal acceptable undrained shear strength. Older studies suggested

values ranging from su = 7.5 kPa (Greenwood, 1970) to su = 15 kPa (Greenwood & Kirsch,

1983), while the German authorities (Forschungsgesellschaft für das Strassenwesen, 1979)

advised values of su from 15 kPa to 25 kPa. However, further research (Raju, 1997; Priebe,

2.3 Construction techniques

8

2003; Wehr & Maihold, 2012) showed that these values were significantly too conservative

and that the construction of granular inclusions was possible in soils exhibiting undrained

shear strengths as low as 5 kPa.

A geotextile encasement can also be installed if the undrained shear strength of the soil is

too low to provide the necessary horizontal support (Raithel et al., 2005). A geotextile “sock”

with a tensile strength of 200 kPa to 400 kPa is therefore inserted into the installation

mandrel and filled with sand or gravel. The mandrel is subsequently extracted from the host

soil and the geotextile “sock” provides lateral support to the inclusion. The bearing

mechanisms of encased stone columns remain the same as for non-encased inclusions.

Typical dimensions of granular inclusions in soft soils range from 6 to 20 m in length and,

with a diameter between 0.6 and 1.2 m. It is possible to achieve depths up to 30 m,

depending on the construction technique and host soil (Keller Grundbau, 2013).

2.3 Construction techniques

There are many different techniques that are applied to construct granular inclusions,

although all exhibit two steps. Firstly, the coarse soil (gravel or sand) is introduced into the

subsoil without contamination from the surrounding weak soil. Subsequently, the granular

soil is compacted, either by means of vibration or tamping.

The installation of stone columns is mainly achieved by using the dry bottom feed process

(Figure 2.1). After the vibrator has been filled with gravel featuring grain sizes ranging from

10 to 40 mm (Greenwood & Kirsch, 1983), it is introduced into the subsoil aided by

compressed air. Once the desired depth is reached (Figure 2.1 b), the vibrator is pulled up

(typically 0.3 m to 1.0 m), which causes the gravel to fill the cavity created. The compaction

is then achieved through re-penetration of the vibrator (typically 0.2 m to 0.8 m, Figure 2.1 c).

The compaction steps are repeated until the surface is reached. Surface compaction is

subsequently necessary to achieve a flat plane. This technique is most appropriate for

penetration depths of less than 20 m (Kirsch & Kirsch, 2010).

The wet top feed technique is an alternative to the dry bottom feed technique (Figure 2.2), in

which the penetration of the vibrator is assisted by water under high pressure, which loosens

the soft soil and supports the cavity created. The gravel is then fed from the surface through

the cavity, while the vibrator is pulled up (typically 0.5 m). Compaction is achieved by the re-

penetration of the vibrator (typically 0.4 m). An advantage of this technique, compared to the

dry bottom feed technique, is that it is possible to reach greater depths (in the range of 30

m). However, the negative influence of the added water on the soil behaviour has to be taken

into account. Moreover, flushing water charged with fine particles is produced, which has to

be recycled or cleaned before being returned to nature.


9

(a) (b) (c) (d)

Figure 2.1: Dry replacement technique: (a) filling the supply hopper, (b) penetration,

(c) compaction by step-wise withdrawal and reinsertion (d) finishing

(Keller Grundbau, 2013).

(a) (b) (c) (d)

Figure 2.2: Wet top feed technique: (a) penetration, (b) filling, (c) compacting, (d) finishing

(International Construction Equipment Holland, 2013).

It is also possible to install the column by ramming rather than using vibration techniques.

Figure 2.3 illustrates this process, which was originally proposed by Franki (Franke, 1997).

Granular material is fed into a casing, which is then driven into the soil up to the desired

depth, with the help of an internal pile hammer, to form a stone column. The casing is then

Water

Flushing

waterFlushing

water

2.4 Bearing behaviour of stone columns submitted to vertical loading

10

filled with granular material through the top of the installation tube and the compaction is

carried out with the internal pile hammer, while the installation tube is withdrawn gradually

while ensuring that no gaps are able to form between the casing, the ground and the

granular pile. Information about the host soil can be gained based on the number of blows of

the pile hammer (Van Impe et al., 1997b) to reach a certain depth.

Figure 2.3: Ramming installation technique: (a) inserting granular plug, (b) driving up to the

desired depth, (c) filling with granular soil, (d) compacting and withdrawing

casing, (e) finishing (Van Impe et al., 1997b).

2.4 Bearing behaviour of stone columns submitted to vertical

loading

2.4.1 Bearing behaviour

The basic response of stone columns to vertical loading consists of:

- internal deformations (shear and volumetric),

- the mobilisation of a shaft friction at the cylindrical interface between columns and

host soil, and

- the mobilisation of a tip resistance.


11

The mechanisms of the mobilisation of shaft friction and tip resistance are similar to the case

of long, slender piles (Fleming et al., 1992), particularly in respect of the load transfer

between the shaft and the pile base as a function of the load.

The bearing behaviour of stone columns is governed by a complicated set of interaction

mechanisms between stone column and the ground, column and column in a group, column

and any form of footing and finally the footing with the ground (Figure 2.4, Kirsch, 2004).

Figure 2.4: Interactions at stake under a footing (after Kirsch, 2004).

Some typical loading situations of stone columns are summarised in Figure 2.5, which

represent a first insight into the behaviour of stone columns under normally vertical loading.

The first difference is of course whether the ground improvement concerns a single column

or a column group. The type of loading also plays a role, in terms of the general behaviour of

stone columns:

- a conventional vertical load applied directly to the top of a stone column (Figure

2.5 a) leads to settlement at the surface and lateral squeeze into the host soil, due

to lateral deformation of the column,

- a vertical load acting on a rigid footing built on top of a stone column (Figure 2.5

b) applies a constant settlement over the length of the footing and hence volume

loss occurs in the soft ground. The load causes a lateral deformation of the

column,

- loads applied onto stone column groups (Figure 2.5 c and d) trigger a similar

response to the case of single stone columns (Figure 2.5 a and b), with the

addition of the interaction between the columns. Figure 2.5 (d) shows the

response of a group of stone columns to an inclined load (in this case

embankment loading). This specific case shows similar mechanisms to those

observed with a rigid footing, however in a different geometric arrangement.

Loading

Flexural rigidity EI

Interaction:

Footing – column

Footing – soil

Column – soil

Column – column


12

A fact common to all loading situations is that the undrained response of the host soil causes

the column to deform laterally or “bulge”, which in turn loads the subsoil laterally. This leads

to further settlements of the footing. However, these settlements increase the vertical loading

of the host soil, which cause a rise of the horizontal stresses supporting the stone column.

(a) (b) (c) (d)

Single

column

Single column loading by

a rigid footing

Column group loaded

by a rigid footing

Column group with

flexible loading, e.g.

dam

Figure 2.5: Loading situations of stone columns (Kirsch, 2004).

2.4.2 Stress concentration on stone columns

The load applied is transmitted to both host soil and compacted granular inclusions.

However, a stress concentration will occur above the stiff stone columns and the stress

repartition between subsoil and stone column needs to be accounted for. Equilibrium has to

be satisfied, which Aboshi et al. (1991) formulated for a unit cell in a quadratic organisation

(Figure 2.6) as follows:

( ) 2.1

2.2

with a distance between the axis of the stone columns in a quadratic grid

Asc stone column cross-section

As soft soil cross-section in the unit cell (As = a2 – Asc)

σ total stress acting on the unit cell

σsc total stress acting on the stone column

σs total stress acting on the soft soil surface


13

(a) (b)

Figure 2.6: Total vertical stress distribution of a uniform vertical stress σ (a) plan view

showing respective areas of stone columns (Asc) and soft soil (As), (b) cross-

section showing stress distribution onto the column (σsc) and the host soil (σs)

(after Aboshi et al., 1991).

The determining geometrical factor is the area replacement ratio as, which is the ratio

between the column cross-section and the total cross-section of the unit cell:

( ) 2.3

The total vertical stress distribution can be described by means of a stress concentration

factor m, defined as the ratio between the stress acting on the stone column and the stress

acting on the host soil:

2.4

These two values then enable the vertical stresses acting on the stone column and on the

subsoil to be calculated:

( ) 2.5

( ) 2.6

The total vertical stress acting on the stone column depends strongly on the geometric

boundary conditions, namely the diameter and distance from axis to axis of the columns.

Barksdale & Takefumi (1991) show that the stress concentration factor m decreases with an

increasing replacement ratio as, while Ichimoto & Suematsu (1981) suggest values of m for

design depending on the area replacement ration as and on the angle of friction of the

column material φ’sc (Table 2.3).

Asc

As

a

a

a

a

sstσs

σsc

σ

a


14

Table 2.3: Suggested values of the stress concentration ratio m for specific combinations of

area replacement ratio as and effective friction angle of the stone column

material for compacted sand columns after Ichimoto & Suematsu (1981).

as [%] φ’sc m [-]

0 – 30 30 3

30 – 70 30 2

> 70 35 1

The values after Ichimoto & Suematsu (1981) should only be considered for a first evaluation

of the stress concentration on top of sand columns, as they do not account either for group

effects or variations of the properties of the host soil and only consider a certain range of

possible effective angles of friction of the stone column material. Although these limitations

are present, the values proposed by Ichimoto & Suematsu (1981) have been partially verified

by various field measurements. Gruber (1995) measured the load carried by some of the

stone columns constructed in soft ground under an embankment by means of load cells.

Stress concentrations of between 2.5 and 3.5 could be measured at the surface for area

replacement ratios between 4% and 11%. Kirsch (2004) conducted diverse tests in which he

installed load cells under footings built on groups of stone columns with area replacement

ratios varying from 10 % to 70 %, and recorded stress concentrations of 1.5 to 2.5. The

column located in the middle of the group was less loaded than those on the borders, which

is also known from investigations into the response of pile groups to axial load.

Greenwood (1991) shows that, besides the geometric parameters, the type and magnitude of

loading also plays a role in the distribution and magnitude of the stress concentration.

Greenwood (1991) conducted three different loading tests at three different locations in the

United Kingdom and in three different sets of ground conditions. In the first case (located in

St Helens), a stiff footing was used to load stone columns (φ’sc = 42°) constructed in sandy

silt (φ’s = 30°). The area replacement ratio was of about 45 %.The stress concentration was

approximately equal to 3.5 for a load of 40 kPa and decreased to about 2.0 for the failure

load of 200 kPa (Figure 2.7 a). The stress concentration factor decreased slightly with

increasing cycles of loading.


15

(a) (b)

Figure 2.7: Measured stress concentration factors at (a) St. Helens and (b) Canvey Island

(Greenwood, 1991).

The second test was conducted on Canvey Island, where a group of stone columns

(featuring a diameter of 750 mm and reaching a depth of 10 m) was constructed in silty clay

and loaded with a 36 m diameter oil storage tank, which is assumed to be a flexible loading

scenario (Figure 2.7 b). The columns were installed in a triangular pattern with a spacing of

1.5 m (as 45 %) and the pressure cells were placed close to the centre of the tank. The

tank was subsequently filled slowly with water over 100 days up to a failure load of 130 kPa.

Again, the stress concentration was found to decrease with increasing loads. However, the

values were significantly higher, as they started from 25 to reach 5 at high loads. Greenwood

(1991) explains that this is due to the low strength of the subsoil on Canvey Island (su = 20

kPa), which supported very little charge at the beginning of the loading, before starting to

consolidate, which led to a redistribution of the stress at the surface and to a decrease in the

stress concentration factor. This shows that the stress concentration is not only controlled by

geometrical parameters, as assumed by Ichimoto & Suematsu (1981) as the stress

concentrations factors measured by Greenwood (1991) on Canvey Island show significant

higher values of up to 25 in comparison with the maximum value of 3 suggested by Ichimoto

& Suematsu (1981) (Table 2.3).

The third and last test was performed at Humber Bridge, where stone columns installed in

silty clays (su ranging from 11 to 121 kPa, denoted as cu in Figure 2.8) were loaded by an 8

m high embankment built with compacted chalk fill to a unit weight of 20.8 kN/m3. The stone

columns had a diameter of 775 mm, reached a depth of 9 m and were installed in a triangular

pattern with a spacing of 2.25 m.

Average ground pressure [kN/m2]

040 80 120 160 200S

tre

ss c

on

ce

ntr

atio

nfa

cto

rm

[-]

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

1st cycle loading

2nd cycle loading

3rd cycle loading

Surcharge [kN/m2]0 20 40 60 80 100 120

0

5

10

15

20

25

Str

ess c

once

ntr

ation

facto

rm

[-]


16

Figure 2.8: Cross-section of the test site at Humber Bridge (after Greenwood, 1991).

The trend of the measured stress concentrations was found to be contrary to the two other

sites in this case. Greenwood (1991) explains why it rose with increasing loading (Figure 2.9)

by the significant initial compaction of the host soil: the initial stiffness of the subsoil was

comparable to that of the granular inclusions at low stresses, thus leading to a stress

concentration factor lower than one for the initial phase of the embankment loading (up to

about 1.5 m embankment height).

Figure 2.9: Measured stress concentration factors at Humber Bridge (Greenwood, 1991).

The results presented by Greenwood (1991) show the difficulty in assessing the stress

concentration factor m. This factor does not only depend on geometrical parameters, as

suggested by Ichimoto & Suematsu (1981), but also on the parameters of the host soil, as

Applied stress [kN/m2]0 40 80 120 160 200

Applied stress [kN/m2]

Str

ess c

once

ntr

ation

facto

rm

[-]

1

2

3

4

5

6


17

demonstrated by the results of the test conducted on Canvey Island (Figure 2.7 b). The

measured stress concentrations at Humber Bridge (Figure 2.9) also show that the difference

between the properties of the host soil and those of the stone column material can play a

decisive role in the development of stress concentrations. As a consequence, reliable

predictions of the stress concentration factor m can only be achieved by considering the

geometrical parameters of the boundary value problem, the parameters of the host soil as

well as by comparing these to those of the stone column material.

Muir Wood et al. (2000) conducted small scale loading tests on a rigid footing placed on

groups of stone columns with varying lengths and spacing (Table 2.4) and installed in kaolin

which was consolidated up to 120 kPa and unloaded to 30 kPa. The unscaled data (denoted

as Model test in Figure 2.10) from tests with an area replacement ratio of 24 % were then

compared with the field data obtained by Greenwood (1991) at the Humber Bridge (denoted

as Field data in Figure 2.10). The trends observed are very similar, although the replacement

ratios (denoted as As in Figure 2.10) were not equal.

Although a good agreement between test data and field observations was reached in terms

of stress concentration in this case, questions can be raised regarding the limitations of

small-scale tests in terms of reproduction of the in-situ stress states within the host soil in a

full-scale boundary value problem. This leads to a higher influence of dilatancy on the

loading behaviour of the composite foundation, thus affecting the determination of the

Serviceability Limit State (SLS).

Figure 2.10: Stress concentration factors in 1 g small-scale model and field tests (Muir Wood

et al., 2000).

Str

ess c

on

ce

ntr

atio

n fa

cto

r m

[-]

Ratio of applied pressure to initial undrained shear

strength of the host soil [-]

Field data: As = 21% (Humber Bridge, afterModel test: As = 24%

Field data: As = 21% (Humber Bridge,

after Greenwood, 1991)


18

Table 2.4: Summary of 1 g small-scale model tests (σc: pre-consolidation stress; su:

undrained shear strength; rsc: radius of the stone columns; L: length of the stone

columns; a: spacing of the stone columns; as: area replacement ratio) (after Muir

Wood et al., 2000).

Test σc

[kPa]

su

[kPa]

rsc

[mm]

L

[mm]

a

[mm] L / rsc

as

[%]

TS02 180 23 5.5 100 25.3 18.2 15

TS03 110 5 5.5 100 30.8 18.2 10

TS04 160 16.5 5.5 150 19.8 27.2 24

TS05 120 10.5 5.5 100 17.6 18.2 30

TS07 120 8 5.5 150 30.8 27.2 10

TS08 120 15 5.5 100 19.8 18.2 24

TS09 120 11.5 8.75 160 31.5 18.2 24

TS10 120 11.5 8.75 100 28 11.4 30

TS16 120 11.5 5.5 100 30.8 18.2 10

TS17 120 14 5.5 160 19.8 29 24

TS19 120 10 5.5 160 19.8 18.2 24

TS21 120 10 5.5 100 19.8 18.2 24

TL02 120 17 8.75 160 31.5 18.2 24

TS20 120 14 5.5 100 19.8 18.2 24

TS11 120 14 - - - - -

TS20/2 120 14 - - - - -

2.4.3 Ultimate Limit State response to vertical load

Stone columns exhibit different Ultimate Limit State (ULS) responses to vertical loading,

depending on the boundary conditions. Figure 2.11 shows a summary of the different

possible failure mechanisms that were presented in Muir Wood et al. (2000): bulging, surficial

bearing failure, shear failure, penetration of short columns, shortening of long columns and

deflection of slender columns.

(a) (b) (c) (d) (e) (f)

Figure 2.11: Failure mechanisms for a single stone column (a) bulging (b) bearing failure (c)

shear failure (d) penetration of short columns (e) shortening of long columns (f)

deflection of slender columns (Muir Wood et al., 2000) based on Waterton &

Foulsham (1984).

σ’v,max

3-4 d

d

σ’vmax


19

Hughes & Withers (1974) suggest that the most likely failure mechanism is bulging failure

(Figure 2.11 a), even though it is relatively difficult to make a clear difference between

deformation and failure. Lateral deformation is necessary to activate the support of the

surrounding host soil and thus the resistance. Shear failure can occur either near to the

surface in the form of a bearing failure (Figure 2.11 b) or deeper as a shear surface develops

in the column (Figure 2.11 c). Datye (1982) describes the penetration of short columns

(Figure 2.11 d), which is due to inadequate dimensions (diameter and length of the column)

with respect to the load and the undrained shear strength in the ground. Muir Wood & Hu

(1997) and Muir Wood et al. (2000) describe the last two possible failure mechanisms

illustrated in Figure 2.11 (e & f), namely the shortening of long columns and the deflection of

slender columns. The last case is caused by uneven application or inclined of load and

insufficient lateral support of the host soil.

Groups of stone columns encounter similar failure mechanisms to those faced by single

columns. Kirsch (2004) illustrates some of the different possible failures for a group of stone

columns (Figure 2.12), which are governed by complex interactions (Figure 2.4): bulging

failure and loss of horizontal support, shearing failure, block failure and column penetration.

(a) (b) (c)

Figure 2.12: Failure mechanisms for groups of stone columns (a) bulging failure and loss of

horizontal support (b) shearing failure (c) block failure and column penetration

(Kirsch, 2004).

These theoretical considerations could also be observed in small scale model tests

conducted using clay specimens (Muir Wood et al., 2000). The sand used to model the

inclusions had an effective angle of friction of 30°. The penetration of short columns can

clearly be observed in Figure 2.13 (a). The shape of the deformed columns was obtained by

removing the sand from the inclusions after the footing loading and by pouring in a plaster in

order to represent the deformed shape. The excavation of the clay then allowed for a clear

identification to be obtained of the features of the response of stone columns to loading. The

horizontal arrows at the sides of the pictures show the original depth of the columns. Bulging

(marked with the letter A in Figure 2.13 a and b) occurs when the radial expansion of the

column is not prevented by adjacent soil. Shear planes (marked with the letter B in Figure

2.13 a and b) may appear through the column when the inclusion is subjected to high shear

stresses with limited lateral restraint.


20

(a) (b)

Figure 2.13: Deformed sand columns at the end of the footing penetration (Muir Wood et al.,

2000).

Muir Wood et al. (2000) suggest using the deformation observed in the plastered small-scale

model stone columns to estimate the zone of influence of the footing on the underlying

improved soil. This zone of influence may be assumed to be conical, as shown in Figure

2.14, while the angle β increases with an increasing area replacement ratio (denoted as Area

ratio in Figure 2.14). The angle β can be used to determine the average mobilised angle of

friction of the improved ground with the following formula (Muir Wood et al., 2000):

2.7

The experimental results show that the average mobilised angle of friction of the improved

ground is about 41° for an area replacement ratio as of 30%, which is close to the angle of

friction for pure sand at the stress levels in a small scale model during the test. The value of

falls to approximately 23° for area replacement ratios of 24% and 10%, which is close to

the value of the drained angle of friction of pure clay (Figure 2.14 a).

However, the tests were conducted at small-scale and hence low stress states within the

host soil. Moreover, Muir Wood et al. (2000) noted that there was dilatancy of the sand,

although the column material was medium dense. These issues raise some concern about

the possibility to extrapolate the mechanical results correctly in terms of effective angle of

friction to a full-scale boundary value problem. This is especially the case for high area

replacement ratios (30 %), for which is close to the effective angle of friction of sand.

However, this should only have a limited impact for area replacement ratios in the range of

10 %, as is then close to the effective angle of friction of clay.


21

(a) (b)

Figure 2.14: Zone of influence of a footing on the underlying soil (a) “rigid” cone beneath

footing (b) variation of angle β with area replacement ratio (Muir Wood et al.,

2000).

McKelvey et al. (2004) conducted loading tests of groups of stone columns installed in a

saturated transparent soil, which allowed the deformation mechanisms to be observed

directly. The rigid footing was circular with a diameter of 100 mm while the stone columns

featured a diameter of 25 mm and a length of 150 mm (area replacement ratio of 23 %).

Sand with an effective angle of friction of 34 ° was used to build the columns. McKelvey et al.

(2004) noted that the columns deformed into a barrel shape (Figure 2.15), the depth of which

was shown to depend on the length of the columns. The vertical oval lighter zones in Figure

2.15 however tend to indicate that boundary effects occurred in this case as the columns

were installed near to the edges of the strongbox. Although this does not impact strongly on

qualitative aspects of the deformations mechanisms, quantitative conclusions should be

handled with care.

Figure 2.15: Deformed stone columns at the end of the footing penetration (McKelvey et al.,

2004).

β

2.5 Design of stone columns

22


A number of different methods are available to design stone columns, as well as to anticipate

their behaviour, both for Serviceability Limit State (SLS) and Ultimate Limit State (ULS).

The ULS embraces situations in which safety is involved, i.e. collapse of a structure or where

a risk for human lives, or severe economic loss, is present (Orr & Farrell, 1999). In the case

of stone columns, the verification of the ULS is based on the calculation of the bearing

capacity of single inclusions, as well as that of the whole group of stone columns. The

bearing capacity of the inclusions is dependent on the properties of the host soil and on the

boundary conditions. The host soil provides lateral support to the column, while complex

interactions (Figure 2.4) will develop in case of groups of stone columns depending on

relative effects of geometry and strength, which in turn will also have an influence on the

bearing capacity of the system.

The SLS corresponds to situations in which the requirements of a structure are no longer met

to guarantee serviceability (Orr & Farrell, 1999). In the case of stone columns, the verification

of the SLS is based on the comparison of the calculated value of the expected settlements

with the acceptable value.

Summaries of the most common design methods can be found e.g. in Soyez (1987),

Bergado et al. (1994), Gruber (1995), Daramalinggam (2003) and Kirsch (2004).

2.5.1 Bearing capacity

The three most common failure mechanisms: bulging failure, shear failure and penetration of

short columns (Figure 2.11 a, c and d) are investigated here. The calculation of the bearing

capacity of a single column is usually conducted based on the solutions for a single pile.

However, models developed in order to calculate the bearing capacity of groups of stone

columns for bulging failure (Madhav & Viktar, 1978), as well as for shear failure when loaded

by a footing (Barksdale & Bachus, 1983) and by an embankment (Springman et al., 2014)

are also presented.

2.5.1.1 Bulging failure

Bergado et al. (1994) propose a design procedure based on Greenwood (1970) to determine

the bulging failure load of a stone column. The fundamental idea is that the bulging failure

load is reached when the horizontal load of the column exceeds the passive resistance of the

host soil, mixing drained and undrained behaviour. The bulging failure load can be expressed

as follows:

( √ )

2.8

with qsc, bulging bulging failure load of a single stone column

unit weight of the host soil

z depth from surface of composite foundation


23

Kp, s coefficient of passive earth pressure of the host soil

su undrained shear strength of the host soil

φ’sc effective angle of friction of the stone column material

Vesic (1972) and Datye (1982) propose a procedure based on the cavity expansion theory.

The ultimate bearing capacity for bulging is then formulated as:

(

)

2.9

with F’c cavity expansion parameter

F’q cavity expansion parameter

q0 overburden pressure at the depth where the bulging occurs

The two cavity expansion parameters can be determined, assuming fully undrained

behaviour so that the volumetric strain in the plastic region is equal to zero:

(

) ( )

2.10

2.11

with Ir stiffness index

φ’s effective angle of friction of the host soil

The stiffness index Ir is defined as:

( )

2.12

with Es Young’s modulus of the host soil

u undrained Poisson’s ratio ( )

G shear modulus

Hughes & Withers (1974) also suggest a design procedure based on cavity expansion theory

and formulate the ultimate bearing capacity as:

( )

2.13

Stuedlein & Holtz (2012) proposed the following modification of Equation 2.13, based on the

analysis of load tests:

( ( ) )

2.14

with σr0 ultimate total in-situ lateral stress at the depth where the bulging occurs


24

Madhav & Viktar (1978) extend the solution recommended by Hughes & Withers (1974) to

the plane-strain case in order to be able to consider groups of stone columns and propose

the following formulation:

( ) (

)

[ (

)

] 2.15

with φ’sc effective angle of friction of the stone column material


γs unit weight of the host soil

z depth from surface of composite foundation

K0 coefficient of earth pressure at rest

qs bearing capacity of the host soil expressed as ( ⁄ )

Nc dimensionless bearing capacity parameter according to Terzaghi (1943)

W width of equivalent granular pile strip

B width of loaded area

2.5.1.2 Shear failure

Bergado et al. (1994) present an overview of different possible design procedures in order to

assess the ultimate load acting on a stone column that would cause a shear failure (Figure

2.16), which, in reality, would only occur after significant bulging would have taken place.

Figure 2.16: Shear failure of a stone column (after Muir Wood et al., 2000).

Barksdale & Bachus (1983) point out that Greenwood (1970) and Wong (1975) assume that

the lateral resistance developed by the surrounding soil is equal to the passive resistance

mobilized behind a retaining wall. This is a synonym of plane-strain loading and does not

take the three-dimensional aspects of a stone column into account. Barksdale & Bachus

(1983) however admit that the design procedure proposed by Wong (1975) appears to


25

correlate well with field measurements. Bergado et al. (1994) formulate the procedure

suggested by Wong (1975) in the following manner:

( √ )

[ (

)] 2.16

with qsc, shear shear failure load of a single stone column

As soft soil cross-section in the unit cell (Equation 2.2)

Kp,s coefficient of passive earth pressure of the host soil

q0 over-burden pressure at the depth where the shear failure occurs


Ka, sc coefficient of active earth pressure of the column material

dsc stone column diameter

L length of stone column

Brauns (1978a, 1980) suggests a design procedure based on a truncated conical failure

mechanism, illustrated in Figure 2.17. The assumptions made in this case are that the

volume of the stone column remains constant and that the shear stress around the columns

(shaft) as well as the tangential stress along the failure mechanism may be neglected. The

resulting bearing capacity is formulated as:

(

( )) (

) ( )

2.17

2.18

with q surcharge at the surface

δ inclination of the failure mechanism within the host soil

δsc inclination of the failure surface within the stone column

(a) (b) (c)

Figure 2.17: Truncated conical failure mechanism according to Brauns (1978a) (a) cross-

section, (b) plan view and (c) forces acting on volume A.

Barksdale & Bachus (1983) propose a formulation of the ultimate shear failure load of stone

column groups. They therefore consider the situation of a square or an infinitely long footing

suc

c

su fksu fk

suc

c

su fksu fk

suc

c

su fksu fk

A A


26

located at the surface of a soft soil reinforced with stone columns (Figure 2.18). Several

assumptions are made in this model:

- the speed of loading is high enough in order to ensure that undrained behaviour may

be assumed in the soft soil,

- the full shear strength of the soft soil and of the stone column is mobilised,

- the failure surface can be approximated by two straight lines,

- the soil immediately beneath the foundation reaches failure along a straight rupture

surface, triggering the shear resistance of a triangular block (Figure 2.18).

According to Barksdale & Bachus (1983), the shear failure load can be calculated from the

following set of equations:

2.19

2.20

2.21

(

) 2.22

( ) 2.23

( ) 2.24

with σ3 average lateral confining pressure

β inclination of the failure surface

su, avg composite undrained shear strength

B foundation width



φ’avg composite angle of friction between host soil and stone columns

as area replacement ratio

μsc stress concentration factor for the stone column

μs stress concentration factor for the host soil


27

Figure 2.18: Stone column group analysis – firm to stiff fine-grained soil (Barksdale &

Bachus, 1983).

Springman et al. (2014) present solution taking the influence of the stone columns on the

external bearing capacity of an embankment with base reinforcement into account. They

therefore first consider the series of stone columns and host soil (Figure 2.19 a) as being

replaced by an equivalent plane wall (Figure 2.19 b).

The shear strength of the i-th element in an equivalent plane wall can be formulated as:

⁄

⁄

2.25

( ) 2.26

(

⁄

)

⁄

2.27


28

with qsc,shear,PW,i shear strength of the i-th equivalent plane wall

su undrained shear strength

dsc stone column diameter (denoted as d in Figure 2.19 and Figure 2.20)

a spacing between stone columns

σ’n,PW,i normal effective stress acting on the shear plane in the i-th equivalent

plane wall element (Figure 2.20)



γeq equivalent unit weight of the composite plane wall

zi depth of the i-th slice below the surface

σ’sc,i normal effective stress applied to the shear plane in the i-th stone

column

αi inclination angle of the shear plane in the i-th slice

ui pore water pressure acting on the slip surface for the i-th slice

γsc unit weight of the stone column material

(a) (b)

Figure 2.19: Clay and columns represented (a) discretely and (b) as an equivalent plane wall

(Springman et al., 2014).

The external ultimate resistance should be checked based on a slip-circle analysis according

to Bishop (1955) and taking the influence of the base reinforcement (denoted as ZRd in Figure

2.20) into account (Figure 2.20), in which the system is divided into slices in order to

calculate the stability. σ’n,PW,d and σ’c,d denote the design values of the effective normal stress

acting on the slip surface in the plane walls and in the clay slices, respectively. The

difference between the stresses acting on top of the stone columns may be ignored, which is

on the safe side, or the suggestions made by Aboshi et al. (1991) may be used to assess the

stress distribution between granular inclusions and soft soil. The ratio between the resisting

moment and the moment triggered by the actions is the safety factor for a slip surface.

Although this approach is widely used in practice, it has limitations, as it assumes that the

geometry of the boundary value problem may be modelled by plane wall, which is not always

the case.


29

Figure 2.20: Stability considerations on a slip circle passing through soft soil and the

equivalent plane walls (numbers 1 to 11 show the sequence of the slices)

(Springman et al., 2014).

2.5.1.3 Penetration of short columns

The failure mechanism of penetration is limited to short columns, which are assumed to

behave like piles and to be subjected to tip resistance and friction, under the assumption that

the lateral support of the host soil is high enough to mobilise the frictional resistance qf. The

failure load can then be assessed as:

2.28

with qt tip resistance

qf frictional resistance around the shaft

As this mechanism develops only when there are inadequate geometrical dimensions

(diameter and length) of the stone column, Brauns (1978a) proposes an upper and a lower

bound for the length of the column, under the assumption that the self-weight of the column

may be ignored and that the tip resistance is equal to (Scott, 1963). The upper

bound, above which a verification of the penetration may be regarded as superfluous, is:

2.29

with rsc radius of the stone column


su undrained shear strength of the host soil at the base of the stone column


30

The minimal length of the stone column in order to prevent a punch-through failure can be

estimated as:

(

) 2.30

with rsc radius of the stone column


su undrained shear strength of the host soil at the base of the stone column

These proofs are simplistic in the sense that they assume a constant value of the undrained

shear strength throughout the depth of the soft soil. However, as long as the failure

mechanism of penetration only occurs for short inclusions, this simplification can be

considered to be valid for practical cases.

2.5.2 Settlement calculation

The settlement calculation is normally conducted under the assumption that the situation at

hand can be modelled in plane-strain. Each column and its surrounding area will respond in

the same manner and that a unit cell approach can be applied. Three possible arrangements

of the columns are shown in Figure 2.21: a hexagonal, a square or a triangular pattern

(Balaam & Poulos, 1983).

(a) (b) (c)

Figure 2.21: Various stone column arrangements with the domain of influence of each

column (Balaam & Poulos, 1983).

Depending on the pattern, the domain of influence D of the column can be estimated as:

- (

)

for a hexagonal pattern,

- (

)

for a square pattern, and

- (

)

for a triangular pattern,

with a spacing between the axis of the stone columns.

A ground improvement factor n0 is used to assess the settlement of the improved ground,

whereby the factor n0 is commonly defined as the ratio between the settlements of the virgin


31

host soil over the settlements of the improved ground. The settlement reduction factor

represents the inverse of n0.

2.31

with n0 ground improvement factor

s0 settlement of the host soil

si settlement of the improved layer

β settlement reduction factor

Three main types of settlement calculation may be identified, namely based on equilibrium

considerations (Section 2.5.2.1), empirical methods (Section 2.5.2.2) and numerical

modelling. A detailed description of the development of numerical modelling of stone

columns using finite elements can be found in Chapter 6 of this thesis.

2.5.2.1 Settlement calculations based on equilibrium considerations

Models proposed by Baumann & Bauer (1974), Aboshi et al. (1979), Omine & Ohno (1997)

and Goughnour (1983) for the calculation of settlements are presented in this section.

Baumann & Bauer (1974) consider the situation of a stone column loaded by a rigid footing,

assuming a constant Young’s Modulus of the stone column material with regard to depth and

horizontal extent. Similar to Equation 2.1, the equilibrium condition can be defined as:

2.32

with σ0 average load intensity on the footing

A footing area

σs total stress acting on the host soil

As soft soil cross-section in the unit cell


Asc stone column cross-section

Figure 2.22: Stress distribution on a rigid footing.

sstσs

σsc

σ0

dsc

zsc

ssc ss

a


32

Due to the rigidity of the footing, the settlements of the stone column (ssc) and of the subsoil

(ss) have to be equal and can be calculated as:

( )

(

)

2.33

2.34

with ssc settlement of the stone column

Esc Young’s modulus of the stone column material

zc depth to which the column has been compacted

a √ ⁄

A footing area

rsc radius of the stone column


σs total stress acting on the soft soil surface

ss settlement of the host soil

Es Young’s modulus of the host soil

The Young’s moduli of the stone column material and of the host soil should be determined

for the equivalent effective stress levels, based on laboratory or field tests. The radial

deformation of the column can be assessed as:

(

)

2.35

Equations 2.33, 2.34 and 2.35 can be rearranged and expressed as:

[

(

)]

[

(

)] 2.36

with Ks coefficient of earth pressure of the host soil

Ksc coefficient of earth pressure of the column material

The value of Ks lies between the at-rest and the passive coefficient in order to take the lateral

loading of the host soil by the stone column triggered by the bulging deformation of the

inclusion into account. Ksc varies between the at-rest and the active coefficient, so that the

influence of the deformation caused by the loading is considered.

Hughes et al. (1975) proposed to divide the subsoil into different layers, based on the

assumption of constant volume, triggering a radial expansion of the column, while settlement

occurred. This approach enables to avoid assuming that the stiffness parameters are

constant over the whole depth of the inclusion and thus enables a more precise assumption


33

of the settlements. The following formulation for the evaluation of the settlement of a stone

column is used:

∑

2.37

with Hi thickness of the i-th layer

δri / r radial strain of the i-th layer, obtained from pressuremeter tests

Aboshi et al. (1979) and Omino & Ohno (1997) propose simple solutions, which can be

implemented as a first approximation. Aboshi et al. (1979) formulate the settlement sv of a

composite foundation under a stiff footing load as follows:

( )

2.38

( ) 2.39

with sv settlement of the composite foundation

P footing load

H thickness of the layer


m stress concentration ratio


Omine & Ohno (1997) also present a simple procedure based on the two-phase mixture

model (Omine et al., 1993). A two-phase mixture consists of a basic material (the matrix) and

another material (the inclusion). A summary of the different possible situations, which can be

encountered for the determination of the stress distribution parameter, is given in Figure

2.23.

Horizontal laminate Vertical laminate

Mixture with

inclusions distributed

at random

Mixture with rod

shaped inclusions

Constant stress Constant strain Constant strain

energy

Approximation based

on Finite Element

Method

Figure 2.23: Evaluation of the stress distribution parameter depending on the different kinds

of mixture (Omine & Ohno, 1997).


34

Due to the geometrical organisation of granular inclusions, the case of a group of stone

column may be assumed to be represented by a “Mixture with rod shaped inclusions” (Figure

2.23), for which the parameter evaluating the stress distribution can be assessed as:

2.40

The homogenised Young’s modulus for the two-phase mixture, which can be implemented in

a settlement calculation, is expressed as:

( )

( )

2.41

with fsc volume content of the stone column

Goughnour (1983) conducted a one-dimensional elastic-plastic analysis of the settlement of

a vertically loaded stone column for stiff loads (thus assuming that the stone column and the

surrounding soil have deformed equally at the top). The stone column response was taken

as rigid-plastic and incompressible in the plastic phase. As in the solution proposed by

Hughes et al. (1975), the subsoil is subdivided into layers. In this case however, this

calculation is used to assess the stress increments at different depths. The set of equations

for the evaluation of the settlement is:

( )

[

( )

( ) ] 2.42

( )

[ (

)] 2.43

( )

( ) ( ) ( ) (

⁄ )

(

⁄ )

( )

2.44

(√

)

√

√

2.45

(

) ( )

[(

)(

)

]

2.46


35

(

) ( )

[

(

)(

⁄

)

]

2.47

with εv vertical strain (same for stone column and host soil)

as replacement ratio

Cc compression index of the host soil

e0 initial void ratio of the host soil

(P0)V, s initial effective vertical stress in the host soil

ΔP footing load increment


(ΔP)*V, s effective vertical stress increase in the host soil averaged over the

horizontal projected area of host soil

(ΔP)*V effective vertical stress increase averaged over horizontal projected

area of the unit cell

(P0)V, sc initial effective vertical stress in the stone column


K coefficient of earth pressure

F parameter depending on K0 and as

This is an iterative solution, which can be used to carry out parametric studies to investigate

the interaction between various factors.

2.5.2.2 Settlement calculations based on empirical methods

Empirical models introduced by Greenwood (1970), Priebe (1976), Priebe (1995), Priebe

(2003) and Van Impe & De Beer (1983) are presented in this section.

Greenwood (1970) proposes the design diagram shown in Figure 2.24, based on field

measurements, in order to assess the settlement of a composite foundation. Two important

assumptions are made in this case:

- the curves do not take the immediate settlement and shear displacement into

consideration,

- the stone columns rest on firm clay, sand or harder ground.

Although this approach presents an opportunity to determine the settlement of a composite

foundation based on the undrained shear strength of the host soil and on the spacing

between the columns, the degree of uncertainty leads Greenwood (1970) to point out that

these curves are to be used with caution.


36

Figure 2.24: Settlement diagram for stone columns installed in uniform soft clay (Greenwood,

1970).

Priebe (1976) presented his first design procedure in order to calculate the settlements of

composite foundations, which he then developed over subsequent years (Priebe, 1988,

1995). The basic approach adopted by Priebe (1976) is based on that of the cavity

expansion theory presented in Gibson (1961). This application leads to the calculation of the

ground improvement factor n0 (graphically illustrated in Figure 2.25 for different values of the

angle of friction of the column material, denoted in this formula as ), formulated as follows:

[

⁄ ( )

( )

] 2.48

( ) ( ) ( )

2.49

(

⁄ )

2.50

with n0 ground improvement factor


Ka, sc coefficient of active earth pressure of the stone column material

’ Poisson’s ratio of the host soil


In his original approach, Priebe (1976) assumes that the stone columns rest on a hard soil

layer, that the host soil is isotropic, that the self-weight of the stone columns and of the soil

may be neglected and that the stone columns are incompressible and reach internal shear

failure. Neglecting the self-weight means that the pressure difference between the stone

columns and the surrounding soil only depends on the loading applied on top of the inclusion

and its repartition over depth. This assumption was found to be very conservative when

comparing the predictions obtained with field measurements (Ulrichs & Wernick, 1986).


37

Figure 2.25: Values of the ground improvement factor n0 depending on the area replacement

ratio, for a Poisson’s ratio of 1/3 (after Priebe, 1995).

Two of the assumptions made earlier in the settlement calculations proposed by Priebe

(1976) can be avoided, as shown in Priebe (1995).

Firstly, the influence of the compressibility of the stone columns can be taken into account

using an additional ground improvement factor n1, which is also shown in Figure 2.26, where

denotes the angle of friction of the stone column material:

[

⁄ ( )

( )

] 2.51

⁄ ( ⁄ )

2.52

( ⁄ )

( ) 2.53

( ) ( )

( )

√[

( )

]

( )

2.54

2.55

with n1 ground improvement factor for column compressibility


Ka, sc coefficient of active earth pressure of the stone column material

n0 ground improvement factor (Equation 2.48)

ME, s confined stiffness modulus of the host soil

ME, sc confined stiffness modulus of the stone column material

Area ratio 1 / as [-]

Impro

vem

ent

facto

rn

0[-

]

⁄


38

Figure 2.26: Values of an additional component of the area replacement ratio to account for

column compressibility, for a Poisson’s ratio of 1/3 (after Priebe, 1995).

Secondly, the effect of the overburden pressure and of the self-weight of the stone column

and soft soil can be considered using a depth coefficient fd (Figure 2.27) and the resulting

improvement factor n2. Due to the fact that n2 is dependent on the depth, Priebe (1995)

suggests that the subsoil should be subdivided into layers of thickness Δt, so that the

settlement calculations can be carried out:

with n2 depth-dependent ground improvement factor

n1 ground improvement factor for compressibility (Equation 2.51)

fd depth coefficient

K0,sc coefficient of earth pressure at rest of the stone column material

Δt layer thickness



Figure 2.27 shows curves allowing for a graphical determination of the factor fd. It assumed

that the host soil and the stone column material exhibit the same unit weight. This is not

conservative, and so it is recommended that Equations 2.56 and 2.57 are used for the

determination of n2, in order to be on the safe side.

Confined stiffness modulus ratio ME,sc / ME,s [-]

Additio

n t

oth

eA

rea R

atio

Δ(1

/ a

s)

[-]

⁄

2.56

∑( )

2.57


39

Figure 2.27: Determination of an influence factor y for the calculation of a depth coefficient fd

for a Poisson’s ratio of 1/3 (γs: unit weight of the host soil; d: improvement depth;

p: footing load) (after Priebe, 1995).

The total settlement for homogeneous conditions can be estimated on the basis of these

parameters as:

2.58

with P vertical footing load

H thickness of the layer of soft soil

ME, s confined stiffness modulus of the host soil

n2 depth-dependent ground improvement factor (Equation 2.56)

The approaches proposed by Priebe (1976) and Priebe (1995) can now be compared. The

overburden pressure and the self-weight of the stone column reduce the improvement factor

when the compressibility of the stone column material is taken into account.

Priebe’s (1995) method is widely used in practice for the calculation of settlements for soft

layers reinforced with stone columns, although Ellouze et al. (2010) note some

inconsistencies in this process as Priebe (1995) uses the same unit cell model for two

different situations:

- firstly, it is assumed that no vertical deformation takes place during the cavity

expansion, so a solution based on plane-strain conditions can be found,

- secondly, the solution obtained is used to model the application of a uniform

vertical load, which would cause uniform settlement throughout the cell.

Area ratio 1 / as [-]

Influence

facto

ry

[-]

⁄


40

Douglas & Schaefer (2012) investigate the reliability of Priebe’s (1995) method based on

case studies with a maximum measurement of settlement of 8 cm. They conclude that the

settlements calculated have an 89 % probability of being larger than the measured values,

which means that the results obtained from Priebe (1995) are conservative (Figure 2.28).

They also note that the site conditions only have a minor influence on the results of the

calculations.

As a conclusion, it can be said that the simplicity of Priebe’s (1995) approach, as well as its

strong tendency to deliver an overestimation of the settlements, has assured its success

among practising engineers over the years, although it is bound by some restrictive

assumptions.

Figure 2.28: Priebe method best-fit line, with data sorted based on the site soil conditions

(Douglas & Schaefer, 2012).

Priebe (2003) also develops a design procedure in order to be able to consider the case of

floating stone columns (Figure 2.29). This avoids the necessity of assuming that the columns

rest on a hard soil layer. The total settlement can be calculated as:

2.59

with si calculated settlement of the improved layer

sc calculated settlement of the untreated layer

reduced settlement due to the stress concentration at the tip of the stone

column =

( )⁄

se settlement due to the stress concentration at the tip of the stone column

s0 settlement of the treated layer without ground improvement


41

Improved layer Untreated layer Stress concentration

Figure 2.29: Static system for the settlement calculation of groups of floating stone columns,

according to Priebe (2003) (Kirsch, 2004).

psc,0 and pc,0 denote the load acting on top of the stone column and on top of the host soil,

respectively, evaluated with the stress concentration factor m. psc,u and pc,u refer to the

stresses present at the depth of the tip of the column and in the host soil, respectively.

The settlements se can be calculated based on the stress concentration psc, u at the base of

the stone columns and on the resulting force Pe, illustrated in Figure 2.29.

( ) 2.60

with psc, u stress acting within the column at the depth of the tip of the column

P footing loading

A footing area

m stress concentration factor


The correction of the settlements se should allow for a reduction of the error due to the stress

concentration in the stone columns.

Tre

ate

dla

ye

rU

ntr

ea

ted

laye

r

sisi sc se

psc,0psc,0

psc,0

pc,0

psc,upsc,u

psc,u

pc,u

s = 0

teσc

σe

pepe

Pe

2 rsc

P

P


42

(a)

(b)

Figure 2.30: (a) Rheological modelling of the behaviour of stone columns, (b) Calculation

approach in plane-strain (Van Impe et al., 1997b).

Van Impe & De Beer (1983) propose an approach based on a model of a stone column

resting on an undeformable bearing layer in plane-strain (Figure 2.30 b). It is further

assumed that the stone column material mobilises its plastic peak resistance while the host

soil remains elastic, which is considered using the rheological model shown in Figure 2.30

(a). The calculation aims at the determination of the settlement reduction factor , as defined

in Equation 2.31 and calculated here resolving a system of non-linear equations. The

fundamental behaviour difference between host soil and columns (elastic versus plastic) may

however raise some questions concerning the validity of the model to solve practical

P

Soil

Column

H

L

L

sv

Rigid base


43

boundary value problems, given that the soft soil would be more likely than the columns to

reach a plastic state.

2.61

( ) (

)

2.62

(

) 2.63

with s total settlement

β settlement reduction factor

s0 settlement of the treated layer without ground improvement

H thickness of the treated layer

effective Poisson’s ratio

P footing load


Figure 2.31: Graphical determination of the settlement reduction factor β (Van Impe & De

Beer, 1983).

L, sr and in Figure 2.30 (b) denote the spacing between the stone column, the radial

deformation of the inclusions and the radial stress acting on the columns, respectively.

0 0.2 0.4 0.6 0.8 1.0

0

20

40

60

80

100

as


44

The settlement reduction factor β can be determined graphically depending on the angle of

friction of the stone column material, denoted as ϕ1 in Figure 2.31. p0 denotes the footing

load and Es the Young’s modulus of the host soil.

2.5.3 Comparison of the design procedures

The overview of the design procedures gives a summary of the main calculations and an

indication of the possibilities available. It is not surprising to note a relatively large variation of

the results obtained due to the different assumptions, models, methods and simplifications

used for the determination of the bearing capacity and settlements of soft ground reinforced

with stone columns. This is shown, for example, in Greenwood & Kirsch (1983) (Figure 2.32,

Figure 2.33).

The results obtained for the ultimate bearing capacity with a solution based on the cavity

expansion theory (Vesic, 1972) are the highest (Figure 2.32), which can be assumed to be

due to the high compaction of the host soil triggered by the installation process. This is

confirmed by the proximity of the results obtained by the method proposed by Brauns

(1978a, 1978b), which assumes the mobilisation of a passive earth pressure in the host soil

surrounding the inclusion. The lowest values are obtained assuming a bulging failure of the

stone column (Hughes & Withers, 1974). The results obtained by Bell (1915) do not consider

granular inclusions, and are based on the horizontal pressures and can therefore be

considered to be a reference value in order to quantify the reinforcing effect of stone

columns.

The results of field experiments presented in Hughes et al. (1975) and Appendino &

Comastri (1970) all lie between the results obtained considering a bulging failure and based

on the cavity expansion theory, which can be considered to be lower and upper bounds,

respectively.

Figure 2.33 shows a comparison of the results obtained from different approaches with field

observations. The model proposed by Priebe (1976) represents a compromise between the

other approaches and enable reasonable predictions of the behaviour observed in the field.

The solution presented by Baumann & Bauer (1974), based on equilibrium considerations

(Section 2.5.2.1), overestimates the improvement effect of the granular inclusions regarding

the settlements compared to the great majority of the field observations. This is also the case

of the approach presented by Greenwood (1970), which is to be handled with care, as

already described in Section 2.5.2.2.

The results obtained using the approach presented by Balaam (1978) highlight the impact of

the ratio between the stiffness of the column (denoted as Ec in Figure 2.33) and of the host

soil (denoted as Es in Figure 2.33). This has a greater influence on the ground improvement

factor than the type of loading (flexible / rigid footing).


45

Figure 2.32: Comparison of the ultimate bearing capacities as a function of the angle of

friction calculated using different procedures (after Greenwood & Kirsch, 1983).

The significant variation in the results obtained from the different procedures, as well as the

large spread in the field data, makes it difficult to draw definitive conclusions. However, the

assumptions made by the different models have to be kept in mind when implementing them

in design calculations.

Terzaghi’s (1936) wise advice should not be forgotten either: “Whoever expects from soil

mechanics a set of simple, hard and fast rules for settlement computation will be deeply

disappointed… The nature of the problem strictly precludes such rules.”

’

2.6 Load-transfer behaviour of stone columns

46

Figure 2.33: Comparison of results obtained from empirical models and elastic theories with

field observations (after Greenwood & Kirsch, 1983).


Although a large amount of research on the ultimate limit state and serviceability limit state of

stone columns has been carried out, the actual mechanisms through which the load applied

on a stone column is transferred within the inclusion and to the surrounding host soil have

received little attention. Sivakumar et al. (2011) investigated the load transfer between a

stone column (the diameter of which varied from 40 mm to 60 mm) that expanded throughout

the depth of the sample and the surrounding clay during consolidation and subsequent

foundation loading means of small-scale experiments. Clay samples of 400 mm in height and

300 mm in diameter were used for the experimental setup (Figure 2.34), while the lateral

movements were blocked at the boundary by rigid walls. The stone columns were installed

by pouring basalt (particle sizes ranging from 2.5 mm to 3 mm) into a pre-bored hole and

compacting it manually. Pressure cells were installed in the stone column to record the

stresses measured in the inclusion. Once the installation of the stone column in the clay

specimen was complete, the sample was consolidated up to 300 kPa. A footing loading was

subsequently applied to the column only at a rate of 1 kPa / h.

1/as


47

Figure 2.34: Experimental setup for a single stone column loaded vertically through a rigid

footing (Sivakumar et al., 2011).

Figure 2.35 shows the vertical pressure distribution with depth during the footing for different

footing settlements. The minimum increase of vertical pressure is observed at a depth about

300 mm, corresponding to a distance of 5 times the diameter of the column from the surface.

Sivakumar et al. (2011) report that the minimal increase of vertical pressure during the

loading of a 40 mm diameter column was observed at 200 mm, there again corresponding to

a distance of 5 times the diameter of the inclusion. The rise of the recorded vertical

pressures below a depth of 300 mm is thought to be due to the fact that the compression of

the host soil at higher depths due to the bulging of the stone column is not as marked as

near the surface. This leads to the stiffness of the host soil being lower and thus a higher

stress concentration within the stone column. Although this is qualitatively plausible, the

reproduction of the in-situ stresses is impossible with small-scale laboratory experiments. As

a consequence, the validity of a quantitative extrapolation to a full-scale boundary value

problem is not granted. Moreover, the influence of the interaction between pressure cells and


48

stone column material is not discussed, which may raise some questions about the

quantitative results shown in Figure 2.35.

Figure 2.35: Pressure distribution with depth during footing loading of a 60 mm diameter

stone column for different settlements (Sivakumar et al., 2011).

Full-scale investigations are relatively rare, but Thiessen et al. (2011) considered the

behaviour of rockfill (maximum grain size of 150 mm) columns used to stabilise riverbanks.

The installation procedure used in this case differed from the commonly used vibro-

replacement or vibro-compaction techniques (Figure 2.1). The columns were pre-bored using

a rotary rig, filled from the surface and compacted with a vibro-lance.

Site characterisation was conducted prior to installing the columns. The results can be seen

in Figure 2.36. No significant difference between the mechanical properties of the clays and

silt were found. Values of c’ = 5 kPa for the effective cohesion and φ’ = 19° for the effective

angle of friction, both for large strains, were determined by means of consolidated undrained

triaxial tests with pore pressure measurement (CIU).

The columns were installed in a triangular pattern, with a diameter of 2.13 m, a centre-to-

centre spacing of 3.1 m and an average length of 6.9 m, reaching about 1 m into the till

(Figure 2.37 a). Void columns were excavated with a diameter of 0.48 m and to a depth just

above an elevation of 219 m (Figure 2.37 a and b). They were left empty during the duration

of the loading in order to provide a vertical plain around the edge of the research area to

concentrate shear strains and thereby to reduce undesired deformation outside the test

zone. This setup also allowed for plane-strain assumptions to be made for the analysis of the

experimental results.

Vertical pressure: kPa

Depth

: m

0 200 400 600 800 1000 1200

0

200

100

300

400

0

1 mm

2 mm

8 mm

16 mm


49

Figure 2.36: Representative borehole and selected soil properties from Red River research

site in Winnipeg, Canada. w: natural water content (horizontal bars display

Atterberg limits); γwet: unit weight of saturated soil; σ: stress; σ’pc:

preconsolidation pressure; σ’v0: initial vertical effective stress; u0: initial pore

water pressure (Thiessen et al., 2011).

An embankment was built at the test area over a period of 9 days on the ground surface with

fill material compacted a dry unit weight of 15.6 kN/m3 (Figure 2.37 a and Figure 2.38). The

load was maintained constant after completion of the embankment construction.

The response of the soil to the loading was monitored by means of slope inclinometers

(denoted as SI in Figure 2.37 b, Figure 2.38 and Figure 2.39) and piezometers (denoted as

VW in Figure 2.38 and Figure 2.39). Table 2.5 gives details above a summary of the

installation depths of the inclinometers (denoted as SI) and piezometers (denoted as PZ and

VW).


50

(a)

(b)

Figure 2.37: Red River test site in Winnipeg, Canada: stabilisation of river bank using a

combination of void and rockfill columns (a) cross-section and (b) plan view of

the research site (Thiessen et al., 2011). Elevations and distances in metres.


51

Figure 2.38: Red River test site in Winnipeg, Canada: pore water response to loading

(Thiessen et al., 2011).

Figure 2.39: Red River test site in Winnipeg, Canada: instrumentation layout (Thiessen et al.,

2011).

Time (days)

To

tal h

ea

d(m

)

Pla

ce

dfill

(t)

0 1 2 3 4 5 6 7 8 9

220

221

222

223

224

225

226

0

500

1000

1500

2000

1000

1500

VW-A (z = 11 m)

VW-B (z = 7.3 m)

VW-D (z = 5.8 m)

VW-E (z = 6.1 m)Loading


52

Table 2.5 Summary of inclinometer and piezometer installations at Red River test site in

Winnipeg, Canada: (SI: slope inclinometer; PZ: piezometer; VW: vibrating wire)

(after Thiessen et al., 2011).

Installation Ground [m] Bottom

reading [m] Installation Ground [m]

Bottom

reading [m]

SI-1 232.01 215.30 PZ-2 215.40 229.46

SI-2 229.46 215.27 VW-A 218.65 229.62

SI-4 225.65 211.95 VW-B 222.29 229.62

SI-5 231.86 212.16 VW-C 226.56 229.62

SI-6 - 218.30 PZ-7 Well 225.52

SI-7 225.52 216.69 VW-D 219.61 225.40

SI-8 225.40 214.28 VW-E 219.70 225.79

SI-9 - 217.61 VW-F 222.16 225.81

SI-10 223.47 213.87

SI-11 225.38 215.32

SI-12 225.57 212.86

It was observed that the pore water response to loading (Figure 2.38) changed with time and

as the footprint of the loading evolved. The response of the piezometers A and B, located

underneath the crest of the embankment (at depths of 11 m and 7.3 m below the ground

surface, respectively), increased with time as the loading was placed directly over the

piezometers. However, the response of the piezometer B to loading was stronger than that of

the piezometer A and the excess pore water pressures were dissipated faster as well. This

can be explained by the greater measurement depth of the piezometer A compared to that

of the piezometer B. The relatively low response of the piezometer D (located at a depth of

5.8 m below the ground surface) to loading was explained to be due to its vicinity to the void

columns. Inversely, the response of the piezometer E, located at mid-distance between the

crest and the toe of the embankment (at a depth of 6.1 m below the ground surface),

diminished with time. Thiessen et al. (2011) do not give any explanation for the slower

reaction to loading of the piezometer E. The rate of dissipation of the excess pore water

pressures is however similar to that measured by the piezometer B, which is consistent with

the similar installation depths.

The investigation of the deformations triggered by the loading of the test area delivered some

interesting information regarding the load transfer of the inclusions. Inclinometer SI-7 was

located at the toe of the embankment and shows a bending behaviour over the length of the

column, which would suggest that shear stresses developed in the column over the whole

depth of the clay and dissipated in the silt.

The measurements recorded by the inclinometers SI-4 and SI-10 cannot be regarded

as trustworthy due to some issues during the installation of the nearby rockfill columns.


53

SI-1, located under the crest of the embankment, did not record significant bending over the

length of the columns.

A local shear surface can be identified in each case at the top of the inclusions (SI-4, SI-7,

and SI-10) or at the crest of the embankment (SI-1).

Figure 2.40: Measured deformations along A axis (in downslope direction) at Red River test site in Winnipeg, Canada: (a) SI-1 at crest of slope; (b) SI-4 in between columns along upper row; (c) SI-7 in a column in upper row; (d) SI-10 downslope of columns (Thiessen et al., 2011).

2.7 Load-transfer behaviour in inclusion-supported embankments

The load-transfer behaviour of embankments supported by rigid inclusions has been

described in detail over the past decades (e.g. Hewlett & Randolph (1988); Fleming et al.

(1992); Han & Gabr (2002); Aslam & Ellis (2010); Baudouin et al. (2010)). These studies

highlighted the development of soil arching within the embankment between the inclusions

due to differential stiffness between the stiffer inclusions and the softer soil in-situ (Figure

2.41).

0

0(a) 0 0 0(b) (c) (d)

SI-1 SI-4 SI-7 SI-10

10 20 0 20 0 10 20A axis deflection (mm)

10 20 0

A axis deflection (mm)

10212

214

216

218

226

228

230

232

Ele

vation (

m)

220

222

224

Ele

vation (

m)

Clay

till

Top of

columns

ClayDay 3.3Day 6.5Day 11Day 18

Clay

till

Silt

till


54

Soil arching can be quantified using a soil arching ratio ρ. This ratio is equal to zero when the

formation of an arch between the inclusions is complete and defined as:

2.64

with ρ soil arching ratio (ρ = 0 represents complete soil arching and ρ = 1 represents

no soil arching)

σs stress acting on the soft soil midway between two inclusions

γe unit weight of fill

He embankment height

σ0 load acting on the top of the embankment

Recent studies (e.g. Deb, 2010 and Indraratna et al., 2013) showed that arching also occurs

when stone column-supported embankments are constructed with a geosynthetic base

reinforcement (σt in Figure 2.41 denotes the average pressure acting onto the base

reinforcement) as the soil between the stone columns settles more than the inclusions due to

the embankment load. This settlement (denoted as ΔS in Figure 2.41) is however reduced by

the shear resistance of the embankment soil (denoted as in Figure 2.41). As a

consequence, the load acting on top of the inclusions (denoted as σc in Figure 2.41)

increases whereas the loading of the soft soil (denoted as σs in Figure 2.41) decreases.

Figure 2.41: Soil arching in stone column-supported embankment (after Deb, 2010).

Top of embankment

Shear

planeGeosynthetic

reinforcement

Stone

columns

Soft soil

σs

σc

σt

σt

ΔΔS

Granular

Granular

layer

He

Top of embankment

σ0


55

The stiffness of the base reinforcement and the embankment height play a role in the

development of soil arching:

- as the stiffness of the base reinforcement increases, less differential settlements

occur and the arching is reduced,

- the shear strength of the embankment material is too low for arching to occur if

the embankment height is not large enough. An increase of the embankment

beyond the minimum height necessary to fully mobilise arching effects does not

have any consequence on arching.

Deb (2010) develops a mathematical model based on plane-strain considerations to

investigate the behaviour of stone column-supported embankments. The soft soil is modelled

using spring-dashpots and the columns are simulated using stiffer nonlinear springs (Figure

2.42). He highlights that soil arching is more marked with decreasing bearing capacity of the

soft soil (Figure 2.43 a), as well as with increasing shear modulus of the embankment soil

(Figure 2.43 b).

Figure 2.42: Proposed foundation model for soft soil reinforced with stiffer inclusions (after

Deb, 2010).

Although this model presents the advantage to enable a simulation of the soil with elements

featuring clear parameters, some drawbacks are present as well. First, the interaction

between granular inclusions and host soil as well as the bulging deformations cannot be

taken into account. Second, Deb (2010) does not give any indication either about the method

used to determine the spring constants implemented in this specific case or about the values

of the constants used, which may raise some questions about the validity of the results as

the spring constant for the spring with dashpot ks0 plays a major role in the outcomes

(Figure 2.43), many of the parameters used being normalised by ks0B2 (B being the half width

of the embankment).

2B

Rough elastic membrane

(geosynthetic layer)

Pasternak shear

layer (granular

layer)

Spring-dashpot

(soft soil)

Stiffer non-linear

springs (stone

column)

Firm soil or bedrock

Embankment modelled by

Pasternak shear layerTTT T


56

(a) (b)

ks0: spring constant per unit area for the spring with dashpot (Figure 2.42)

B: half width of the embankment

Ge*: shear modulus of the embankment soil normalised by ks0B2

Gr*: shear modulus of the granular layer (Figure 2.41) normalised by ks0B2

Ec: Young’s modulus of the stone column material

Es: Young’s modulus of the soft soil

U: degree of consolidation of the soft soil

: ultimate shear resistance of the embankment soil normalised by ks0B

2

: ultimate shear resistance of the granular layer normalised by ks0B

2

s: spacing between the columns

bw: width of the stone columns

qus*: bearing capacity of the host soil normalised by ks0B.

Figure 2.43: Effect of (a) ultimate bearing capacity of the soft soil and (b) the shear modulus

of the embankment soil on the arching ratio (Deb, 2010).

Indraratna et al. (2013) consider arching effects in a numerical analysis of a stone column-

supported embankment and formulate an expression for the normal stress within the

embankment along the radial R-direction σr (Figure 2.44):

( )

2.65

with σr normal stress in soil element along R-direction

R global radial coordinate

Kp, e coefficient of passive earth pressure of the embankment

γe unit weight of fill

qs in Figure 2.44 denotes the surcharge load intensity applied onto the surface of the

embankment, rc the radius of a stone column, re the radius of influence of a stone column, H

the thickness of the soft soil deposit and He the height of the embankment.


57

Figure 2.44: Arching effect in the embankment (Indraratna et al., 2013).

Soil arching causes an increase of the load applied onto the inclusions supporting the

embankment and a reduction of the load applied onto the soft soil. This can be an

explanation for the rising stress concentration observed by Greenwood (1991) at Humber

Bridge (Figure 2.9): once soil arching is complete, the additional load applied onto the

embankment is transmitted to the inclusions, triggering an increase of the stress

concentration factor.

2.8 Effect of stone columns on the consolidation time

Stone columns do not only increase the bearing capacity and improve the performance of the

subsoil by reducing deformations but they might also cause a significant reduction of the

consolidation time due to an inversion of the main drainage direction from vertical to

horizontal assuming one-dimensional consolidation conditions, through a reduction of the

drainage length. This often takes advantage of the natural anisotropy of most soft soils,

which exhibit a strikingly higher permeability in the horizontal direction than in the vertical

one. The reduction of the length of the drainage path d plays the most important role for the

reduction of the consolidation time, because the consolidation time is proportional to d2:

2.66

with t consolidation time

Tv dimensionless time factor

d length of the drainage path

γw unit weight of water

k coefficient of permeability

ME confined stiffness modulus

2.8 Effect of stone columns on the consolidation time

58

Sivakumar et al. (2004) conducted triaxial tests on sand columns installed in clay specimens

and show a significant reduction of the consolidation time for the specimens with stone

column.

Black et al. (2007) investigate the performance of single stone columns and of groups of

stone columns using small-scale laboratory experiments under 1 g (triaxial setup). They

show a considerable acceleration of the consolidation process with increasing length of the

inclusion (denoted as Hc in Figure 2.45) over the height of the layer to be treated (denoted as

Hs in Figure 2.45).

(a) (b)

Figure 2.45: Consolidation process for (a) a single stone column and (b) a group of stone

columns (after Black et al., 2007).

McCabe et al. (2009) present results from field tests enlightening the positive influence of

stone columns on the consolidation time compared to displacement piles (Figure 2.46). A

significant acceleration of the consolidation process can be noted when stone columns are

installed instead of piles. The dimensionless time factor for a radial flow Th is defined as:

2.67

2.68

with Th dimensionless time factor for radial flow

ch horizontal coefficient of consolidation (Equation 2.69)

t consolidation time

r radius of stone column or pile

req equivalent radius of a square pile

Square root time (min0.5) Square root time (min0.5)

20 40 60 800

20

40

Degre

eofconsolid

atio

n, U

(%

)

60

80

100

0

20

40

Degre

eofconsolid

atio

n, U

(%

)60

80

100

20 40 60 80

(a) (b)

100 mm

32 mm


59

The horizontal coefficient of consolidation ch can be formulated as:

2.69

with kh coefficient of horizontal permeability

ME, h horizontal confined stiffness modulus


Figure 2.46: Comparison of the excess pore water pressure dissipation for displacement

piles and stone columns (McCabe et al., 2009).

However, although the beneficial effect of stone columns on the consolidation time is not to

be doubted, the insertion of the mandrel causes some installation effects that can be

detrimental to the drainage efficiency of stone columns. These effects have an influence

on the stress levels in the host soil surrounding the column and trigger the development of a

so-called smear zone.

2.9 Analytical considerations about the installation of inclusions in

soil

Due to the similarity of the physical mechanisms encountered during the construction of piles

and stone columns, the studies conducted on the installation effects of rigid inclusions are

considered here as well. The influence of the construction of piles on the pore pressures, and

on the total stress distribution in the surrounding soil, plays an important role in the

determination of the shaft resistance and in the tip bearing load.

Time factor, Th = cht/4r2 or cht/4r2eq

0.01 0.1 1 10 100

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

De

gre

eo

fco

nso

lida

tio

n, U

Driven five-pile group, r/R>5

(Belfast clay )40

Jacked single pile, r/R=1

(Bothkennar clay )51

Jacked single pile, r/R=1

(Belfast clay )52

Stone column, r/R=5

(Keller GE Contract B)

2.9 Analytical considerations about the installation of inclusions in soil

60

2.9.1 Cavity expansion theory

The installation of a driven pile or of a stone column can be modelled by a stress expansion

theory approach at the tip and by a cavity expansion theory approach along the shaft. This

section deals with the cavity expansion approach.

Vesic (1972) proposes a theoretical approach to calculate the total stress changes as well as

the excess pore water pressures generated by the expansion of a cavity in plane-strain

conditions.

The system considered by Vesic (1972) is that of a spherical cavity or of a cylindrical cavity

with an initial radius Ri expanded by a pressure p. The application of the pressure will trigger

the formation firstly of an elastic and then of a plastic zone around the cavity, the radius of

which will increase until the pressure reaches pu. The cavity will then exhibit a radius Ru and

the plastic zone will have expanded to Rp. The soil mass beyond Rp remains in an elastic

state.

Figure 2.47: Geometric representation of cylindrical cavity expansion in either two or three

(spherical) dimensions (Vesic, 1972).

Rp

Ru

Ripu

sq

sq

sr

sp

up

plastische Zone

elastische ZonePlastic zone

Elastic zone


61

A cylindrical cavity is considered here since it is more applicable to the installation of the

stone column, even more than for rigid piles, through the radial compaction applied. The

radius of the plastic zone can be estimated as:

√

(

⁄ )

√

2.70

with Rp radius of the plastic zone

Ru final cavity radius

Ir stiffness index of soil (Equation 2.12)

I’rr reduced stiffness index for cylindrical cavity

Δ volumetric strain in the plastic zone

φ’s effective angle of friction of the host soil

The theory developed by Vesic (1972) relies on a total stress approach. Undrained behaviour

( = 0 [-]) is simulated by setting the effective angle of friction of the host soil equal to 0,

which does not represent reality. Equation 2.70 can be simplified to:

√ 2.71

The ultimate cavity pressure pu can be computed as:

2.72

(

) 2.73

(

) (

)

(

)⁄

2.74

with su undrained shear strength of the host soil

φ’s effective angle of friction of the soil

F’c cavity expansion parameter

F’q cavity expansion parameter

For undrained behaviour, Fc’ can be simplified to:

2.75

The radial stress in the plastic zone can then be formulated as:

(

) 2.76

with pu ultimate cavity pressure (Equation 2.72)

r distance from centreline


62

When considering a cavity expansion under undrained conditions, the excess pore water

pressures generated are also to be determined. Within the plastic zone, the excess pore

water pressures can be formulated as:

[ ( )

] 2.77

2.78

with A pressure parameter according to Skempton (1954)

Rp radius of the plastic zone

q0 over-burden pressure


The formulation of the excess pore water pressures outside the plastic zone is:

(

)

2.79

with α Henkel’s (1959) pore pressure parameter for the particular stress level

( )

Henkel’s (1959) pore pressure parameter can be expressed as a function of the pressure

parameter A (Equation 2.78) according to Skempton (1954):

√ (

) 2.80

Randolph & Wroth (1979) consider the pile installation process as the expansion of a cavity

from zero radius to r0 (r0 being the radius of the pile) and formulate the generated excess

pore water pressure at a radius r within the plastic zone based on equations proposed by

Gibson & Anderson (1961) and Hill (1950). They assume that the mean effective stress

remains constant under undrained conditions:

( ) [ (

) (

)] 2.81

with δσr radial total stress change

δσθ circumferential total stress change

The radial and circumferential total stress changes are then estimated as:

[ (

) (

)] 2.82

[ (

) (

)] 2.83


63

This allows a determination of the undrained shear strength at failure:

( ) 2.84

2.9.2 Strain Path Method and Shallow Strain Path Method

Besides the stress changes induced by the installation of inclusions in the subsoil, the

deformation field generated is also of interest. Baligh (1985) first presented the Strain Path

Method (SPM) in order to predict the soil disturbances caused by the insertion of objects in

the subsoil. Whereas the SPM can be compared to the Stress Path Method, it replaces

stress-control with strain-control, which is relevant for many events that are dictated by rate

of displacement.

The main elements of the SPM are:

- the velocity fields.

The SPM assumes that the deformations of the subsoil during penetration can be

decoupled from the constitutive relationships of the soil, which simplifies the

problem considerably. It is recommended to integrate the deformations from the

velocity fields.

- the constitutive relationships.

The effective stress path can be determined along a strain path by using either an

effective stress model, or a total stress approach in which the deviatoric stresses

as well as the pore pressures are considered.

- equilibrium.

As long as strains are not completely decoupled from stresses, the solutions

based on approximate strain fields may not be considered totally exact and the

computed stress may not always satisfy all equilibrium requirements. Two

approaches can be used to solve this inconsistency. The first one is to solve a

series of Poisson equations to calculate the pore pressures until the requirements

are fulfilled. The second, more engineering-oriented approach is to apply

corrective total stresses on the element considered to satisfy equilibrium and

boundary conditions.

Baligh (1985) uses the SPM to assess the soil deformations during penetration of a cone into

the soil (Figure 2.48). Besides the expected outwards radial displacement of soil elements,

two interesting observations can be made. First, the elements retrieve their original elevation

once the penetration is achieved, with the exception of the point located on the surface of the

cone. Second, the circular shape of the deformation paths can be of interest when

investigating clayey soils, as it might indicate a reorganisation of the direction of the clay

platelets up to a distance of 5 times the radius of the installed cone. Although the final state

seems similar to that obtained with pure cavity expansion, the values of the strains of the

elements are different.


64

Figure 2.48: Deformation paths during penetration of a cone into clay calculated using the

SPM (Baligh, 1985).

The SPM is restricted to conditions of steady, deep penetrations. This is fine in order to

predict the soil movements near the tip but might lead to problems for the prediction of

movements in the far-field, where the surface may influence the deformations. Based on

Sagaseta (1987), Sagaseta & Whittle (2001) propose the Shallow Strain Path Method

(SSPM) in order to address these disadvantages of the SPM by integrating the boundary

conditions of the stress-free ground surface.


65

(a) (b)

Figure 2.49: (a) Radial and (b) vertical deformation profiles after the installation of a simple

pile obtained with the SSPM analysis (Sagaseta & Whittle, 2001).

The stress state of the ground surface is modelled by the incorporation of corrective shear

tractions. Large strains are taken into account by formulating the velocities of the soil

elements instead of their displacements. However, the consideration of large strains is only

partial, as long as the deformations induced by the corrective shear tractions are assessed

with small-strain elastic solutions.

The small-strain solutions (denoted here with the subscript ss) for surface displacements due

to the installation of a pile featuring a radius r0 and a length L at a distance r from the

centreline are:

( )

√ 2.85

( )

(

√ ) 2.86

2.10 Observations concerning the installation effects of piles and stone columns on the soil

66

with r distance from centreline

r0 pile radius

L pile length

Figure 2.49 shows the predicted vertical and radial displacements obtained using the SSPM

for a pile with an embedment depth of L/R = 10 which has been driven into the soil from the

surface (R denotes the radius of the pile). Only a tear-shaped zone, located in front of the tip,

undergoes downward displacements, while the rest of the mass exhibits upwards

movements. The size of this zone was found not to be related to the pile radius. The biggest

heave is observed in the immediate vicinity of the pile shaft. However, the extent of the

significant soil movements (5 times the pile radius) is comparable to those observed with

calculations made using the SPM (Figure 2.48). Although these results are very interesting,

the conditions applied at the interface between pile and soil are not specified, thus making

any generalisation of the outcomes difficult.

2.10 Observations concerning the installation effects of piles and

stone columns on the soil

2.10.1 Pile installation

Randolph et al. (1979) conducted numerical investigations based on the cavity expansion

theory presented by Ladanyi (1963) and Vesic (1972). The main emphasis was the

determination of the effective and total stresses around a pile during installation and

subsequent consolidation relative to the shaft resistance. A first finding was that the over-

consolidation ratio (OCR) does not have a major influence on the stress changes. Second, it

was observed that the sensitivity of clay does play an important role on the development of

shaft friction around driven piles in clay. The authors further show that the installation of a

pile causes excess pore pressure which can be evaluated within the plastic zone (that is for

, with r0 the radius of the pile and Rp the radius of the plastic zone) as:

2.87

√

2.88

with Δu excess pore pressure


Rp radius of the plastic zone


r0 pile radius

G shear modulus of the soil

The effect of pile installation on sand may also be regarded as interesting. Linder (1977)

conducted laboratory tests during which he installed piles in sand specimen by ramming the

inclusions into the host soil. He could identify different zones around a pile tip in sand,


67

depending on the depth of the pile, as illustrated in Figure 2.50. Densified and loosened

zones could be observed. A major difference can be noted in comparison with the analytical

predictions in clay (Figure 2.49) as no surface heave was detected in this case. This shows

that although tests conducted with sand specimens can deliver some interesting information

about the stress expansion at the tip of the pile, the consequences of the cavity expansion

along the shaft can be very different from those in clay.

Figure 2.50: Deformation and density changes during the penetration of a pile in dense sand

(after Linder, 1977).

The effect of the driving stiff inclusions into sand seems to depend strongly on the density of

the subsoil. Davidson et al. (1981) conduct model tests of the introduction of a CPT cone

adjacent to a glass wall fixed in the container with inside dimensions of length 1.0 m, width of

1.0 m and height 0.65 m (Figure 2.51 a) and follow the resulting displacements using a set of

two cameras (Figure 2.51 b). Several tests were conducted with sands prepared to different

densities.

A similar displacement pattern, as found by Linder (1977), could be observed in the case of a

loose sand (relative density of 25 %, Figure 2.52 a). No movements at the surface could be

observed beyond a distance of 3 times the cone radius from the cone centre. A similar

pattern to that predicted by Sagaseta & Whittle (2001) for clay was detected for a dense

sand (relative density of 115 %, Figure 2.52 b) as heave could be observed up to 8.5 times

the cone radius from the cone centre. This shows the impact of the soil density on the

Displacement

zone

Initial depth

Core

Compaction

zone

Shear and loosening zone

“Filling up” of the

loosening zone

(post-compaction)

~ 1.30 m

~ 3.30 m


68

measured results as Linder (1977) did not measure heave, although he described his sample

as being dense (no measure of the relative density was given).

(a) (b)

Figure 2.51: (a) Half-cone inserted in sand (b) test set up (Davidson et al., 1981).

(a) (b)

Figure 2.52: Displacements (in mm) and volumetric strains (in %) for jacking a half-CPT cone

into (a) loose sand (relative density = 25 %) (b) dense sand (relative density =

115 %) (Davidson et al., 1981).

2.10.2 Changes of host soil properties due to the installation of stone columns

The changes in subsoil caused by the installation of stone columns are theoretically

comparable to those observed during the penetration of piles. However, the bearing

mechanisms of rigid piles and stone columns are significantly different. The influence of

excess pore water pressures and of their dissipation on the bearing capacity of piles can be

of importance, as they affect the shaft as well as the tip resistances. In the case of stone

columns, the major issue is the lateral support of the granular material by the host soil and

not the shaft resistance.

Sand

Half-cone Half-cone

Sand

Glass wall

Camera

Jack


69

2.10.2.1 Effect on soil resistance and stress levels

Aboshi et al. (1979) examine data from field tests where stone columns were installed in

clay. They observe a short-term reduction of the undrained shear strength due to the

disturbance of the clay structure by the penetration of the installation tool. However, the ratio

of the measured undrained shear strength after the installation (denoted as c in Figure 2.53)

to the undrained shear strength measured before the construction process (denoted as c0 in

Figure 2.53) reaches unity at least after a month. The increase of the ratio c/c0 up to values

of 1.7 can be explained by an increase of the effective stresses in the host soil. These

observations show that the installation process of stone columns has only a short-term effect

in terms of the bearing capacity of a composite foundation. However, the authors do not

specify the method used to determine the undrained shear strength, do not give the

distances from the location of the measurements to the stone columns and do not state the

sort of clay and their stress history. This lack of information does not allow a detailed

interpretation of the results.

Figure 2.53: Evolution of the undrained shear strength ratio (normalised to pre-installation

values) over time after the installation of stone columns (Aboshi et al., 1979).

Asaoka et al. (1994) conducted in-situ loading tests with composite foundations on sand

compaction piles (SCP) with a relatively low replacement ratio (as = 25%) in Maizuru, Kyoto,

Japan. The soil at the test site is composed of clayey alluvial deposits. The SCP construction

phase lasted approximately 200 days. The loading was then conducted in two phases. First,

a sand mat and an empty concrete caisson were placed on the surface of the composite soil

after SCP installation. This phase was maintained for about 10 months. The caisson was

subsequently filled with sand and a steel tank was positioned on top of the caisson in order

to apply additional load by filling the tank with water. The second loading phase lasted for

9 days and the last 43 % of the load was applied within less than 2.5 hours. Figure 2.54


70

shows the profiles of the axial compressive strength before the installation of the SCP and

after the first loading phase. The measured unconfined compressive strength of the host soil

exhibits a significant increase at every depth after the SCP installation. Although the results

seem interesting, the authors do not give detailed information about the characteristics of the

host soil. They also do not specify how the unconfined compressive strength was determined

and do not mention the distances from the locations where the measurements were

conducted to the stone columns. As for Aboshi et al. (1991), this lack of information does not

allow any definitive conclusions to be drawn.

Figure 2.54: Evolution of the unconfined compressive strength of clay over time (Asaoka et

al., 1994).

The increase in horizontal stresses due to SCP installation was investigated based on field

tests, e.g. Gruber (1995) and Watts et al. (2000). Watts et al. (2000) conducted tests at the

Bothkennar test site in Scotland, where a soft clayey layer rests on a firm clayey or silty layer

(Figure 2.55).

Figure 2.56 shows the lateral stress changes during the penetration of the 0.3 m diameter

poker (- - -) and the subsequent compaction of the column, which generally exhibited a

radius of about 0.35 m. The continuous lines show the change in stress during the

compaction of the inclusion. The results obtained with the earth pressure cell G4 (installed at

a depth of 2.5 m from the surface at a distance of 0.9 m from the centre of the column) are

represented by black squares ( ) and those obtained with the earth pressure cell G1

(installed at a depth of 2.5 m and a distance of 1.5 m from the centre of the column) are

illustrated by black circles ( ). Compaction was achieved by extraction and reinsertion of the

poker.

An increase of the stress level could first be detected when the poker tip reached the depth

of the cells and the effect diminished with increasing distance from the column axis. A

significant increase of the lateral stresses could be observed during the penetration as well

as retraction and re-insertion of the poker during the compaction phases. The increases in

lateral earth pressures disappeared immediately after the extraction of the poker from the


71

host soil. This would indicate that the installation of stone columns does not change the

stress state of the host soil, although it causes an increase of the undrained shear strength

(e.g. Aboshi et al., 1991; and Asaoka et al., 1994) and of the density of the soft soil bed

around the inclusions.

The results of dynamic probing using a Standard Penetration Test (SPT) at increasing

distance from the column axis shown in Figure 2.57 indicate more significant compaction

close to the edge of the column than 0.6 m away from the centre of the inclusion. The

highest compaction is reached in the granular fill, but an increase in blow counts can also be

noted in the so-called “cohesive” fill.

Figure 2.55: Profile of the host soil treated by SCP installation at the Bothkennar test site,

as investigated by Watts et al. (2000).


72

Figure 2.56: Lateral stress changes measured by earth pressure cells following poker

penetration and retraction during stone column compaction at the Bothkennar

test site (Watts et al., 2000).

Figure 2.57: Dynamic probing of the radial densification of the fill around a stone column at

the Bothkennar test site (Watts et al., 2000).

0 10 20 30 40 50 60

Increase in horizontal earth pressure at depth of cell: kN/m2

0

4.0

De

pth

ofp

oke

rtip

belo

wo

rig

ina

l g

rou

nd

leve

ld

urin

gtr

ea

tmen

t: m

0.5

1.0

1.5

2.0

2.5

3.0

3.5De

pth

ofp

oke

rtip

belo

wo

rig

ina

l g

rou

nd

leve

ld

urin

gtr

ea

tmen

t: m

Depth of cells

Cells G4 G1

0.9 1.5Distance from

column centre: m

Change in stress:

poker penetration

Change in stress:

column conpaction


73

Handy & White (2006) summarised field tests featuring the construction of rammed

aggregate piers at different sites. A site was located at Memphis, USA, where the subsoil

was over-consolidated low-plasticity clay featuring an effective angle of friction of 25° and a

unit weight of 19.6 kN/m3. The results obtained in Memphis, USA show different stress zones

appearing around the pier during the installation. A plastic zone forms in the vicinity of the

pier, while the subsoil further away from the inclusion remains in an elastic state. The

appearance of a passive zone, leading to the creation of radial cracks near the surface was

also noted (Figure 2.58).

Figure 2.58: Illustration of the different stress zones around the pier (rf = 1.9 m) in the

Memphis, USA case history (Handy et al., 2002).

Egan et al. (2009) conducted instrumented field tests in order to assess the response of pore

water pressure to loading (Figure 2.59). Three rows of five columns with dimensions of

550 mm diameter and 5.5 m length were therefore installed in normal-consolidated Carse

clay in Raploch, Scotland. Oedometer tests conducted on Carse clay indicated that the

vertical coefficient of consolidation cv was comprised between 0.6 and 1.7 m2 / year while the

horizontal coefficient of consolidation ch was determined in-situ to have values ranging from

1.3 to 7.0 m2 / year. The peak, denoted as Column construction in Figure 2.59, actually

corresponds to the behaviour just after completion of the installation of the inclusion, as the

pore pressure transducers (PPT) were removed during the construction phase, in order to

prevent any damage. Interestingly, the installation depth of the transducers does not seem to

play a major role in terms of the measured excess pore water pressures. It can, however, be

argued that the variation in installation depth of the PPT is minute as it varies from 2 m to

4 m underneath the ground surface, which does not allow for an analysis to be conducted of

the influence of this factor on the response. However, a good correlation between the

formulation of the excess pore pressures generated by the installation of a pile formulated by

Randolph et al. (1979, Equation 2.87) and the recorded values could be observed. Although


74

these results seem very interesting, the authors do not indicate the load applied on the

footing, which limits the interpretation of the results to a qualitative domain.

Figure 2.59: Response of pore pressure transducers installed 2 m, resp. 4 m, below the

ground surface to column loading at the Raploch test site (Egan et al., 2009).

2.10.2.2 Smear and compaction zones: effect on permeability

The installation of stone columns, or of 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 &

Redana, 1998; Sharma & 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 remoulded zone where an additional decrease of the horizontal

coefficient of permeability kh is anticipated.

Figure 2.60 shows the evolution of the normalised horizontal coefficient of permeability (kho

denotes the undisturbed permeability) with the radial distance from the drain axis.

Date

Pre

ssur

e[k

Pa]


75

Figure 2.60: Suggested variation of horizontal permeability with radius according to Onoue et

al. (1991) (after Saye, 2001).

Indraratna & Redana (1998) and Indraratna et al. (2001) present the results of small-scale

tests modelling the installation of SCP in remoulded clay. Indraratna & Redana (1998)

evaluated the extent of the smear zone by determining the compressibility and permeability

parameters at different distances from the axis of the SCP. The main conclusions drawn from

these investigations are that the installation effect of the SCP on the soil structure is greatest

near the boundary of the SCP, while the radius of the smear zone (denoted as rs in Figure

2.61) 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 Figure 2.61).

Figure 2.61: Section of the test setup showing the smear zone (after Indraratna & Redana,

1998).

SandSand

SCP Sand Sand

Impermeable

l = 950 mm

Sand

D = 450 mm

Sand

Sand

Sa

nd

Sand

Sand

Smear zone

Sand

SandSa

nd

Sand Sand

rwrs

Remoulded

clay

Smear zone

Rigid

boundary


76

It could also be observed that the horizontal coefficient of permeability k’h in the smear zone

decreased in vicinity of the SCP, but that the vertical permeability k’v remained almost

identical to the original values in the host soil, even at the column interface (Figure 2.62).

However, this approach assumes that the smear zone remains homogeneous, which may

lead to some less accurate results than if a difference is made between smear zone (or

remoulded zone, Figure 2.60) and compaction zone (or disturbed zone, Figure 2.60).

Figure 2.62: Ratio of horizontal to vertical coefficient of permeability against the radial

distance from the axis of the SCP (denoted as drain)

(Indraratna & Redana, 1998).

Sharma & 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 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

Figure 2.63. 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


77

pressures are significantly higher in the case with smear, which is consistent with the

expected reduction of horizontal permeability in the smear zone.

Figure 2.63: Excess pore water pressures during the insertion of the installation mandrel

(Sharma & Xiao, 2000).

Figure 2.64: Variation of the horizontal permeability with radial distance to the drain for an

installation that causes a smear zone (Sharma & Xiao, 2000).


78

The horizontal permeability was determined from oedometer tests conducted on samples

extracted from the model after the installation of the sand drain (Figure 2.64). The results of

these investigations indicate that the coefficient of horizontal permeability decreased by a

factor of 1.3 in the smear zone compared to the intact zone. It was also observed that the

effect of the reconsolidation due the insertion of the mandrel was of higher significance than

the remoulding of the host soil. A comparable subdivision is proposed, as suggested by

Onoue et al. (1991), with a remoulded zone next to the drain surrounded by a reconsolidation

zone. The extents differ, as the remoulded zone is limited to a small extent in the immediate

vicinity to the drain, while the ratio of the radius of the reconsolidated zone rs to the radius of

the drain rw is set equal to s = rs / rw = 4 [-].

Bergado et al. (1991) conducted field tests as well as laboratory investigations, in order

to assess the extent and properties of the smear zone around vertical drains. Assuming that

the diameter of the smear zone (ds) is twice the diameter of the mandrel (dm),

Bergado et al. (1991) detected an influence of the size of the mandrel on the zone of

disturbance in field tests. The back-calculated value of the horizontal coefficient of

consolidation ch, by means of oedometer tests, is smaller for a large mandrel than for a small

mandrel (Figure 2.65), and the rate of increase of kh / kh’ was greater as a function of ch for

the large mandrel.

The laboratory experiments conducted could also confirm the suggestion made by

Hansbo (1987) that the horizontal coefficient of permeability within the smear zone k’h can be

considered equal to the vertical coefficient of permeability in the undisturbed zone kv. In

addition, the coefficient of horizontal permeability of the smear zone was found to be 1.75

times smaller (on average) than the coefficient of horizontal permeability in the undisturbed

zone.


79

Figure 2.65: Back-calculated sets of coefficients of relative horizontal permeability in the

undisturbed host soil (kh) and in the smear zone (k’h) and horizontal coefficient of

consolidation ch values, assuming ds = 2 dm (Bergado et al., 1991).

Chai & Miura (1999) also report that laboratory tests generally tend to underestimate the

values of the hydraulic conductivity of the natural deposits, as a consequence of the sample

disturbance and sample size effects. They therefore suggest a correction factor Cf:

(

)

2.78

with kh coefficient of horizontal permeability of the undisturbed host soil

k’h coefficient of horizontal permeability in the smear zone

Cf conversion factor between coefficients of permeability obtained in the

laboratory and in the field

l laboratory

Shin et al. (2009) conducted small-scale tests under 1 g using a micro-cone penetrometer

(denoted as MCP in Figure 2.66) with a diameter of 5 mm and an electrical resistance probe

(denoted as ERP in Figure 2.66) to identify the extent of the smear zone around rectangular-

shaped drains. Figure 2.66 shows the experimental setup used. The soil used was Busan

clay, the properties of which are given in Table 2.6. The specimen has a diameter of 700 mm

and a height of 1000 mm, while the mandrel has dimensions of 50 x 25 mm.


80

Table 2.6: Geotechnical properties of Busan clay (Shin et al., 2009).

Soil properties Values

Water content [%] 56

Liquid limit [%] 46.4

Plastic limit [%] 24.1

Plasticity index [%] 22.3

Specific density [g / cm3] 2.64

The electrical resistance probe consists of a needle with an outer diameter of 2.108 mm and

an inner diameter of 0.254 mm, in which a cable is installed and glued. The electrical

resistance R of the soil is measured at the tip of the tool, and the electrical resistivity can be

obtained as:

2.79

with α electrode shape factor, determined through calibration

ρ electrical resistivity

Figure 2.66: Directions of the horizontal penetration tests (Shin et al., 2009).


81

The smear zone was assumed to have been reached once the resistivity deviated from the

plateau reached within the undisturbed zone. The point of deviance is marked by the arrow

SR in Figure 2.67. Due to the rectangular form of the drain, the smear zone has an elliptical

form (Figure 2.68), the extent of which is about 4 times the equivalent mandrel radius in the

longer axis of the mandrel and 3.3 times the equivalent mandrel radius in the shorter axis of

the mandrel.

Figure 2.67: Electrical resistivity and estimated outer boundary of the smear zone (Shin et

al., 2009).

Figure 2.68: Dimensions of the smear zone derived from the electrical resistance probe. All

dimensions in millimetres (Shin et al., 2009).

aa


82

Weber et al. (2010) present the results of micro-mechanical investigations using Mercury

Intrusion Porosimetry (MIP) that were conducted in order to determine the extent of the

compacted zone around stone columns, using samples extracted after centrifuge model

tests. The MIP technique was first presented by Winslow & Shapiro (1959) and proposes to

determine the pore diameter by measuring the intrusion of mercury into a sample under a

specific pressure. The diameter is inversely related to the insertion pressure by the equation

proposed by Washburn (1921):

2.80

with σ surface tension

θ wetting angle for mercury, assumed to be equal to 130° for clay minerals at

room temperature (Diamond, 1970)

p mercury pressure

The measurements show an increase of the dry bulk density of the host soil as well as a

decrease of the porosity up to a distance of about three times the radius of the column from

the column axis (Figure 2.69 and Figure 2.70). A similar distribution of the porosity to that

suggested by Onoue et al. (1991) can be observed, which indicates that the assumption

made by Indraratna & Redana (1998) that the smear zone remains homogeneous may be

simplistic. However, the radial extent of the installation effects is less important in this case

than measured by Onoue et al. (1991) in small-scale laboratory experiments. This would

tend to indicate that this extent depends on the stress, which would speak for the physical

modelling under enhanced gravity, as it can reproduce the in-situ stress states, which small-

scale laboratory experiments cannot. However, the fact that Weber et al. (2010) do not

indicate the depth from which the samples used for the MIP investigations have been

extracted is a problem here, as it could be argued that the different radial extents measured

are due to different measurement depths.


83

Figure 2.69: Variation of the porosity as a function of the distance from the stone column axis

(Weber et al., 2010).

Figure 2.70: Variation of the dry bulk density as a function of the distance from the stone

column axis (Weber et al., 2010).

Juneja et al. (2013) make a distinction between a smear zone, where the clay is disturbed

and remoulded, and a compression zone, where the clay is laterally compressed due to

the installation of the inclusion (Figure 2.71), in a similar manner to Onoue et al. (1991),

Weber (2008) and Weber et al. (2010). The experimental process consisted of isotropic

consolidated undrained triaxial shear (CIU) tests conducted on clay samples in which sand


84

compaction piles (SCP) were installed. The surface of the cylindrical casing used to install

the SCP was varied from smooth (in order to limit the appearance of the smear zone to a

minimum) to gritty (in order to cause the appearance of a smear zone). Figure 2.72 shows

that a significant microstructural remoulding of clay occurs within the smear zone,

thus leading to a reduction of the pores and of the permeability. However, as in

Weber et al. (2010), no indication of the depth at which these measurements were conducted

is given, thus raising some questions about the effect of depth onto the development of

smear around stone columns.

Figure 2.71: Compression and smear zone around sand compaction piles (Juneja et al.,

2013).

(a) (b)

Figure 2.72: Scanning Electron Microscopy images of kaolin clay specimen adjacent to the

stone column installed and sheared (CIU) at 50 kPa (a) without smear and

(b) with smear (Juneja et al., 2013).


85

2.10.3 Radial drainage around stone columns

The analysis of the consolidation of a grid is usually conducted based on the drainage

conditions of a unit cell (Figure 2.73). The radius R of such a unit cell can be determined

based on the grid arrangement, as shown in Figure 2.21.

Figure 2.73: Radial drainage within a unit cell (after Barron, 1948).

The theory of radial drainage, considering the influence of a disturbed zone, was first

developed by Barron (1948), with the following assumptions:

- all vertical loads are initially carried by excess pore water pressure,

- all displacements within the soil mass occur in a vertical direction,

- a triangular pattern of drains is most economical,

- the zone of influence of a drain is circular,

- the load is uniformly distributed.

In case of equal vertical strain and of a radial flow to a central drain, the excess pore water

pressure due to radial flow can be formulated at a location r from the axis of the inclusion

as:

[ (

)

(

) ( )]

2.89

[

(

)

(

) ( )] 2.90

2.91

Störzone mit verminderterDurchlässigkeit

R

rw

rs

r

Drain

Disturbed zone with reduced

permeability


86

2.92

2.93

2.94

with Δur excess pore water pressure due to radial flow

r average excess pore water pressure due to radial flow

rs radius of the smear zone


kh coefficient of horizontal permeability in the undisturbed host soil

kh’ coefficient of horizontal permeability of the disturbed host soil

n radius ratio of the unit cell to the drain (Equation 2.93)

s radius ratio of the smear zone to the drain

Δu0 initial uniform excess pore water pressure

base of natural logarithms

Th dimensionless time factor for radial flow

R radius of the unit cell considered

rw radius of the drain

The time factor Th for a radial flow can be estimated at a certain time t as:

2.95

with ch horizontal coefficient of consolidation (Equation 2.69)

Alternatively, Th can also be determined based on the assumption of an average degree of

consolidation for a radial flow as:

(

) 2.96

Th in Equation 2.96 does not only depend on the average degree of consolidation but also on

the parameter (Equation 2.90), that is on the geometrical dimensions of the unit cell and on

the extent of the remoulded zone. Further research has been conducted based on the work

of Barron’s (1948), e.g. Hansbo et al. (1981), Han & Ye (2001) and Han & Ye (2002).

Hansbo et al. (1981) reformulated the factor (Equation 2.96), in order to take the influence

of depth on the radial flow, as:

(

)

( )

2.97


87

with z depth of soil

l half-length of drain

qw discharge capacity of the drain

The analytical solutions proposed by Barron (1948) and Hansbo et al. (1981) have to be

used with care when applied to stone columns, as they have been developed for vertical

drains and neglect the difference between the stiffnesses of the stone column and of the host

soil, as pointed out e.g. by Han & Ye (2002). Moreover, the radius of influence of stone

columns is usually smaller than the radius of influence of vertical drains. Han & Ye (2001)

suggest that a modified time factor is adopted for radial flow Thm (Equation 2.99), based on a

modified horizontal coefficient of consolidation chm (Equation 2.100), in order to assess the

average degree of consolidation for a radial flow taking these two aspects into account:

2.98

2.99

( )

⁄

⁄

( )

⁄

2.100

with average degree of consolidation for a radial flow

Thm modified dimensionless time factor for radial flow

factor defined in Equation 2.90

chm modified horizontal coefficient of consolidation

de diameter of the unit cell considered

ME, sc confined stiffness modulus of the stone column material

ME, s confined stiffness modulus of the undisturbed host soil




Han & Ye (2002) propose to take the influence of the characteristics of composite

foundations reinforced by stone columns into account by formulating the average degree of

consolidation for a radial flow :

2.101

2.102

2.11 Summary of the state of the art of ground improvement with stone columns

88

(

)

2.103

( (

)

)

(

) (

)

(

)

2.104

with average degree of consolidation for a radial flow

t consolidation time

chm modified horizontal coefficient of consolidation

de diameter of the unit cell considered

ks coefficient of permeability of the undisturbed host soil

ks’ coefficient of permeability of the soil in the smear zone

H height of the unit cell considered

dsc diameter of the stone column

n radius ratio of the unit cell to the drain (Equation 2.93)

s radius ratio of the smear zone to the drain (Equation 2.94)

The solutions proposed by Barron (1948), Hansbo et al. (1981) and Han & Ye (2001, 2002)

all assume an instantaneous and uniform loading of the unit cell.

Wang (2009) formulates a solution using an expression for the degree of consolidation, and

thus taking the time-dependency of the loading into account, based on similar assumptions:

( )

∫ ( ( ) )

∫

2.105

with U average degree of consolidation

average final settlement

s(t) average settlement at time t

q(t) average applied loading at time t

average pore pressure throughout the soil-stone column cylinder

q0 ultimate loading

2.11 Summary of the state of the art of ground improvement with

stone columns

Ground improvement with stone columns has experienced massive development over the

past decades, which has largely been led by industry innovation and enabled by the

development of progressively computerised machinery. Stone columns increase the stiffness

and strength of the host soil and decrease the consolidation time by taking advantage of the

natural anisotropy of permeability in the ground and reducing the (radial) drainage paths. The

increase in stiffness and strength allows higher loads to be carried, with lower post-

construction settlements.


89

The bearing behaviour of stone columns is based on complex interactions between host soil,

inclusions and supported structure. These interactions are governed by the difference of the

characteristics of the host soil and of the stone column material and are further influenced by

installation effects.

The installation of stone columns changes the structure of the host soil, which influences

both the bearing behaviour and the drainage performance of the columns themselves. In

soils with low sensitivity, the insertion of the installation mandrel causes radial compaction of

the host soil around the column, through a cyclic increase in the horizontal stresses.

However, installation effects, mostly described as smear zone in the literature, also appear

around the inclusions, which have a negative influence on the reduction of the consolidation

time as they cause a reduction of the permeability. Some researchers (e.g. Indraratna &

Redana, 1998) assume that the installation of stone columns cause a so-called “smear

zone”, which they assume to be homogeneous over its whole extent. Others (e.g.

Onoue et al., 1991; Weber et al., 2010) however show that the permeability and the porosity

are not constant over the whole radial extent of the installation effects and suggest making a

distinction between smear and compaction zones. The vertical distribution of the installation

effects remains unknown, and is the main theme of this research.

In addition, geometrical aspects such as the spacing of the columns and their diameter play

a key role in the bearing behaviour of stone columns, which differs from that of rigid

inclusions such as piles. Inner deformation is necessary to mobilise the bearing mechanisms

of stone columns. Applying a load usually causes radial lateral spreading bulging of the

column in its upper part. The surrounding host soil provides the necessary lateral support to

the column material.

The vertical loading of a composite foundation provokes a re-distribution of the stress under

the foundation as stone columns exhibit a significantly higher stiffness than the host soil. The

ratio of the observed stresses at the top of stone columns to the stresses measured at the

surface of the host soil (stress concentration ratio m) usually ranges from 2 to 6 but can

reach peaks as high as 25. The evolution of this ratio shows different trends with increasing

loading of the composite foundation. A direct comparison is difficult, as the values of this ratio

depend on the type of loading (flexible / stiff), as well as on the stress history and

characteristics of the host soil. Deeper knowledge of the installation effects might help to

clarify the reasons for the differences in stress concentration factor m.

2.11 Summary of the state of the art of ground improvement with stone columns

90

3 Centrifuge modelling

91


3.1 Historical background

Craig (2002) gives an historical overview of centrifuge modelling over the last 150 years by

presenting seven scientists and engineers considered to have or have had an influence on

the development of this technique.

The first person known to have proposed physical modelling under enhanced gravity is

Edouard Phillips. He was born in 1821 and published on this topic from 1845 until his death

in 1889. Phillips used the rotation and related acceleration to conduct model tests on the

understanding of various forms of failure of railway bridges or parts thereof.

Bucky (1931) made use of centrifuge modelling in order to investigate mine roof stability at

Columbia University (USA). He was also reported to have been engaged in military

applications.

In the former USSR, two people (Davidenkov, 1933; Pokrovsky, 1933) seem to have worked

independently on the development of physical modelling using centrifugal acceleration. The

use of this modelling technique was restricted mainly to military purposes, and was aimed at

simulating the effect of explosives on various forms of buried infrastructure.

Karl Terzaghi is widely acknowledged as being the father of soil mechanics. Although he was

not keen on using physical models, he was aware of the activity of Bucky, having been

offered a position at Columbia University in the early 1930s and he corresponded with Peter

Rowe in the 1950s.

Peter Rowe conducted the first centrifuge studies using large models in the 1970s, which

was contemporary to the development of the oil and gas offshore industry in the UK. He

demonstrated the advantages of using physical modelling under enhanced gravity through

programmes aiming at simulating the effect of cyclic loading due to waves and wind on

offshore platforms and piles and jack-up structures on a range of natural and laboratory soils.

Andrew Schofield covered a wide range of subjects in his research, but most of interest here

are the summary and extension of scaling laws (Schofield, 1980), without which the correct

conduction and interpretation of centrifuge modelling is not possible. He expended a

considerable effort in the context of modelling soft ground behaviour, thus developing the

Critical State Soil Mechanics framework (Schofield & Wroth, 1968).

Eventually, Sarah Springman, former student of Andrew Schofield’s in Cambridge, can be

considered as one of the leading current researchers in the field of centrifuge modelling.

After bringing centrifuge technology to the ETH Zürich (Springman et al., 2001), she has lead

a number of studies aimed at resolving problems investigated elsewhere by means of small-

scale physical or numerical models, such as natural hazards (Chikatamarla, 2005; Imre,

2010), ground improvement in soft soils (Weber, 2008) or soil-structure interaction (Nater,

2005; Arnold, 2011).

3.2 Principles of centrifuge modelling

92


A main challenge of physical modelling is the reproduction of the stress state present in a soil

mass. Due to the range of dimensions in civil engineering, full-scale tests are not often

conducted and small-scale tests under 1 g cannot reproduce the stress fields active in reality

(Figure 3.3). The use of centrifuge modelling allows the stress states acting in soil mass in

reality to be reproduced while using small-scale models, by taking advantage of the

acceleration acting on a rotating body. A body rotating around an axis is submitted to a radial

(centripetal) and tangential acceleration, as shown in Figure 3.1.

Figure 3.1: Acceleration acting on a body rotating with angular velocity ω (Springman, 2004).

Centrifuge modelling takes advantage of the action of the centripetal acceleration a, which

depends on the angular velocity ω and on the radius r. The centripetal acceleration can be

formulated as:

3.1

Equation 3.1 can, in case of a constant radius, be reduced to

3.2

The centripetal acceleration causes a field of increased gravity to act on the rotating body,

which allows the scaling factors to be derived:

3.3

with n factor of increase of the Earth’s gravity

g Earth’s gravity


93

Figure 3.2: Principle of centrifuge modelling (after Schofield, 1980).

Due to the field of increased gravity generated by the rotational movement, a centrifuge

model can be subjected to the same stress state and distribution as a prototype model

(Figure 3.3), although its dimensions are divided by the factor of increase of the Earth’s

gravity n (Laue, 1996, 2002).

Figure 3.3: Comparison of the stress profiles (a) in a prototype, (b) in a small-scale model

and (c) in a centrifuge model (after Laue, 1996).

The dimensions of the model built under 1 g can be reduced by the factor n, as they are then

exposed to an acceleration increased by the same factor under n times the Earth’s gravity.

The gradient of the increase of stress with depth is significantly higher in the centrifuge than

in reality, which can play an important role when modelling shallow boundary value

problems. It also should be noted that the increase in acceleration field is not linear (Taylor,

1995).

PrototypeSmall-scale model

Small-scale model

CentrifugeCentrifuge model

n – Factor of increase of Earth’s

gravity

σ’v – Effective vertical stress

γ – Specific unit weight

zm – Depth in model

zp – Depth in prototype

(a)

(b)

(c)


94

3.2.1 Scaling factors

The lengths of a model built under 1 g are scaled with a factor n when submitted to n times

the Earth’s gravity. The scaling factors are derived from these and from the stress

equivalence between model and prototype. A summary of the main scaling factors is given in

Table 3.1.

Table 3.1: Summary of the main scaling factors (after Schofield, 1980).

Parameter Scale

(model / prototype)

Acceleration [m/s2] n

Linear dimension [m] 1/n

Stress [kPa] 1

Strain [-] 1

Unit weight [N/m3] n

Force [N] 1/n2

Time (diffusion) [s] n2

3.2.2 Advantages and disadvantages of physical modelling under enhanced

gravity

Mayne et al. (2009) give an overview of the advantages and limitations of physical modelling

under enhanced gravity. The main advantages are listed here:

- the stress levels present in reality can be reproduced using models with smaller

dimensions,

- key mechanisms of the behaviour of soil may be revealed,

- the model build-up and the loading systems allow for knowledge of the

characteristics of the subsoil and for the possibility to validate predictions,

- the testing time is reduced significantly (see Table 3.1), which is of particular

interest when modelling diffusion processes in low permeability soils,

- the costs are relatively low, especially when compared to full-scale tests,

- the user is able to witness the deformation and failure mechanisms while these

are taking place.


95

Some issues however remain, which should not be forgotten when using centrifuge

modelling for the investigation of static boundary value problems (dynamic situations are not

considered here):

- the factor of increase of the Earth’s gravity n is not constant with depth, so that the

vertical stresses vary with the depth of the sample (Figure 3.4). The reference

radius, at which the nominal acceleration acts, is usually set at two thirds of the

depth of the sample. The vertical stresses in the centrifuge are underestimated

above the reference radius and overestimated underneath the reference radius

(see Figure 3.4),

- the use of reconstituted soils is more appropriate for this testing procedure. The

use of natural soils is possible, however, it does not make much sense as the

features are scaled up by a factor n and the stress history is inconsistent. This

limits the possibility to investigate the effect of fabric on the behaviour of natural

clays,

- the influence of the Coriolis effect on falling particles in the centrifuge must be

accounted for planning the test and analysing the data,

- the dimensions of shear surfaces may not be scaled correctly,

- boundary effects might appear if sufficient care has not been taken when

determining the boundary conditions,

- the size of any instrumentation (sensors or embedded) may be excessive and

cause the outcome of the test to be affected,

- the stress history of the soil may not be equal to that encountered in in-situ

situations,

- the construction methods usually differ from those imposed in the field.

Figure 3.4: Distribution of the vertical stress with depth in a prototype situation and in the

centrifuge (zs denotes the depth of the sample) (after Taylor, 1995).

3.3 Centrifuge modelling of ground improvement measures

96


Numerous studies dealing with the modelling of ground improvement measures under

enhanced gravity, using drains and granular inclusions, can be found in the literature.

Sharma & Bolton (2001) present the results of centrifuge tests modelling embankments

constructed on soft clay (Figure 3.5 a) and show the positive influence of wick drains

installed in the host soil on the dissipation of excess pore water pressures (Figure 3.5 b), as

the time needed for 90 % of the excess pore water pressures to dissipate is reduced by

about 50 %.

(a) (b)

Figure 3.5: (a) Cross-section of the centrifuge model of a clay sample reinforced by wick

drains and basal reinforcement loaded by an embankment and (b) influence of

the drains on the dissipation of excess pore water pressures during and after

embankment construction (Sharma & Bolton, 2001).

Other studies focus on the self-weight consolidation of clay layers improved by vertical

inclusions. Kitazume et al. (1993) investigate the behaviour of soft clay improved with so-

called fabri-packed sand drains (sand drains coated with a plastic material) for the needs of a

land reclamation project in Haneda, Japan. Studies considering the influence of uncoated

stone and sand columns in soft soils are presented now.

Almeida et al. (1985) investigate the behaviour of embankments constructed on normally

consolidated kaolin clay, with and without reinforcement by stone columns. The installation of

stone columns in this case is again performed outside the centrifuge under 1 g by pouring

sand into bored holes. A decrease of the settlements by a factor 2 was observed while the

excess pore water pressures triggered by the embankment loading were significantly lower

with stone columns, than without.

Al-Khafaji & Craig (2000) studied the behaviour of a tank foundation on soft clay reinforced

by sand columns installed under 1 g by pouring and vibrating sand in pre-bored holes with

area replacement ratios varying from 10% to 40%. The container used was a rigid strongbox


97

560 mm square and 460 mm deep while the clay specimen had a thickness of 200 mm. The

clay was loaded by a 325 mm diameter tank with a flexible base. Figure 3.6 shows a

comparison of the settlement improvement ratios obtained by using the analytical solution

presented in Priebe (1995) with measurements from centrifuge tests. A replacement ratio

smaller than 25% does not seem to have a major influence on the settlement performance of

the composite foundation. This comparison suggests that the angle of friction of the

compacted columns (denoted as Φc in Figure 3.6) is only 30°. However, no direct

measurement of the sand density or angle of friction has been performed during these tests,

which makes any definitive conclusion difficult. The ratios of the stiffness of the stone column

(denoted as Ec in Figure 3.6) to the stiffness of the untreated host soil (denoted as Es in

Figure 3.6) seem to be realistic.

Figure 3.6: Comparison between settlement improvement ratios obtained with the solution of

Priebe (1995) solution and from centrifuge tests (Al-Khafaji & Craig, 2000).

Zwanenburg et al. (2002) conducted centrifuge tests of loading of sand piles and sand walls

installed in clay under 1 g by pouring dry sand into pre-drilled holes. The length of the

inclusions is varied, so that both floating and end-bearing columns are investigated. The

results of these tests show a strong influence of the length of the inclusions, as end-bearing

columns are much more effective than floating columns in achieving significant settlement

reduction (41.5 % opposed to 6.1 %). The outcomes of the centrifuge investigations are used

to back-calibrate a numerical model.

Numerous other references can be found in the literature. The behaviour of soft soils

improved by stone columns installed by pouring and compacting sand into pre-bored

holes under 1 g was investigated by e.g. Terashi et al. (1991), Stewart & Fahey (1993),

and Jung et al. (1998). Another method was adopted by Huat & Craig (1994),

Priebe (1995), φc = 30°, Ec/Es = 7

Priebe (1995), φc = 35°, Ec/Es = 7

Priebe (1995), φc = 40°, Ec/Es = 7

Centrifuge results, Ec/Es = 7


98

Kitazume et al. (1998), Rahman et al. (2000) and Lee et al. (2006), who installed granular

columns by inserting a frozen sand cylinder into the soft soil bed under 1 g, and

subsequently loaded the composite foundation under enhanced gravity.

The major issue in the research on centrifuge modelling of ground improvement mentioned

above is, however, the fact that the construction of the inclusions is conducted under the

Earth’s natural gravity field, which means that the stress states are actually at a prototype

scale. The consequences of the displacement induced by the insertion of the mandrel can

not to be modelled by installing a stone column under 1 g by drilling a hole in the soft soil bed

and filling it with coarse grained material due to the fact that the actual stress state present

in-situ is not modelled correctly. The influence of the installation technique of the inclusion on

the loading behaviour can be highlighted by consideration of a similar boundary value

problem, e.g. by Dyson & Randolph (1998), who compared the behaviour under lateral

loading of piles installed by different techniques: pre-installed, jacked at 1 g, jacked at 160 g

and driven at 160 g (Figure 3.7). The influence of the installation technique can be seen as

the installation in-flight leads to significantly stiffer behaviour under loading.

Figure 3.7: Pile lateral pressure as a function of the lateral displacement y normalised by the

pile radius d (Dyson & Randolph, 1998).

A major step forward to solve the issue of constructing stone columns in flight was made by

Ng et al. (1998), who presented a setup developed for the beam centrifuge at the National

University of Singapore (Figure 3.8). The installation tool is pushed into the soft soil while

sand is fed through an Archimedes’ screw driven by a hydraulic motor. The SCP is

constructed during the withdrawal of the tool and its diameter can be varied by adjusting the

speed at which the installer is withdrawn from the model. The transport through the

Archimedes’ screw tends to crush the SCP material, which might be a concern, as

uncontrolled modification of the physical properties of the inclusion occurs. The rapid delivery

Normalised lateral displacement y / d

0 0.05 0.1 0.15 0.2

0

0.1

0.2

0.3

0.4

Pile

la

tera

l p

ressu

rep

[M

Pa

]

Driven

Jacked at 160 g

Jacked at 1 g

Pre-installed

asd

asd

asd

asd


99

of sand in-flight through the screw results in the development of significant heat, which leads

to the necessity to immerse the clay bed under a thin layer of water prior to the column

installation, in order to prevent the clay model from losing moisture and cracking.

Figure 3.8: Sand compaction pile installation tool used at the National University of

Singapore. All dimensions are in mm (Ng et al., 1998).

Lee et al. (2001) investigate the influence of constructing stone columns in flight by

conducting centrifuge tests modelling the behaviour of an embankment constructed on a soft

clay bed. Unimproved ground (denoted as U2 in Figure 3.9 b) is compared with a host soil

improved by inserting frozen SCPs under 1 g (denoted as R1_20 in Figure 3.9 b) and by

installing SCPs in-flight using the installation process described in Ng et al. (1998) (denoted

as D50_20 in Figure 3.9 b). Several observations could be made:

- the heave of the surface was significantly more important in the case of SCPs

built in-flight than when installing frozen sand samples under 1 g,

- the negative consequences of the thawing process of the frozen SCPs on the

clayey host soil could be avoided by the in-flight installation,

- the SCPs installed in-flight behave in a stiffer manner (Figure 3.9 c). This was to

be expected due to the compaction taking place during the insertion of the

installation tool.

(1)(1)

(1) Hydraulic cylinder

(2) Hydraulic motor

(3) Storage hopper

(4) XY table

(5) Soil sample

(6) Strongbox

(2)(2)

(2)(3)

(2)(4)

(5)

(2)(6)

640

560

430


100

(a) (b)

Figure 3.9: Embankment constructed on soft clay (U2) and when improved by SCPs installed

at 1g (R1_20) or at 50 g (D50_20) (a) deformation grid lines in clay improved

with SCPs built in-flight (b) maximum lateral displacement (in mm) of the grid

line L2 with g-level (Lee et al., 2001).

Again, using the in-flight installation setup presented in Ng et al. (1998), Lee et al. (2004)

conducted centrifuge tests to model the installation of SCPs in clay while recording pore

pressures and total stresses by means of pore pressure transducers and total stress

transducers, respectively (Figure 3.12). The goal was to investigate the impact of the

installation of SCPs on the host soil in terms of increase of pore water pressure and stresses.

Figure 3.10 and Figure 3.11 show the layout of the experimental set-ups used.

Figure 3.10: Layout of SCPs and transducers for the installation of SCPs in test T7, D 20 mm

(D: SCP diameter) (Lee et al., 2004).

G-level

Ma

xim

um

la

tera

l d

isp

lace

me

nt

U2

R1_20

D50_20

40.0

20.0

0.0

0 50 100 150


101

(a) (b) ©

(d) (e) (f)

Figure 3.11: Layout of SCPs and transducers for tests: (a) T1, D 18 mm; (b) T2, D 20 mm;

(c) T3, D 16 mm; (d) T4, D 17 mm; (e) T5, D 20 mm; (f) T6, D 20 mm (D SCP

diameter) (Lee et al., 2004).


102

The strongest reaction of the subsoil at a given depth occurs when the tip of the casing

reaches that depth and only very little excess pore pressure dissipation occurs during the

withdrawal of the mandrel (Figure 3.12). This is consistent with the low coefficient of

consolidation of 1 m2/year measured in the host soil used. It can also be seen that, other

than reported in Watts et al. (2000) from field tests (Figure 2.56), the total stress level does

not return to its original state immediately upon extraction of the poker. This might also be

due to the low coefficient of consolidation of the clay sample.

(a)

(b)

Figure 3.12: (a) Total horizontal stress at 60 mm depth and (b) pore pressures at 80 mm

depth during SCP installation in clay. Line 1: time at which the casing tip

reaches the depth of the transducers. Line 2: time at which the casing tip

reaches the full penetration and withdrawal starts. Line 3: time at which the

casing tip reaches the depth of the transducers during withdrawal. Line 4: end of

the SCP installation (Lee et al., 2004).

Figure 3.13 shows ratios of measured (Δσ, respectively Δu) to calculated ( , respectively

) total stresses and pore pressures plotted as function of the depth of the transducers dt

(Figure 3.13 a) and of the radial distance rt of the transducers from the axis of the SCP

(Figure 3.13 b), each normalised with the SCP diameter D. The calculated stresses and pore


103

pressures were computed here with a modified formulation of the cavity expansion theory

according to Vesic (1972).

Figure 3.13 (a) shows that the ratios ⁄ and ⁄ increase with increasing depth of the

transducers, although a significant scatter of the measurements is noted. This is not

surprising as plane-strain conditions in cavity expansion problems are approached when

depth increases. The measurements presented also support the suggestion formulated by

Randolph & Wroth (1979) that plane-strain conditions are reached for a ratio ⁄ equal to 5.

Figure 3.13 (b) shows that the ratios ⁄ and ⁄ increase with decreasing distance to

the column axis. Finally, the ratios ⁄ and ⁄ rise towards a steady value of 1 when

the ratio dt / rt increases (Figure 3.14).

(a) (b)


against (a) dt / D and (b) rt / D (Lee et al., 2004).


against the ratio of the depth of the transducers dt to the radial distance of the

transducers rt (Lee et al., 2004).

dt / D rt / D

,

,

,

dt / rt


104

Yi et al. (2013) present the results of investigations conducted using the Archimedes’ screw

(Ng et al., 1998) in order to assess the effect of the construction of sand compaction piles on

the undrained shear strength of soft soils. The T-Bar (Yi et al., 2010) was used to investigate

groups of 2 and 4 columns (Figure 3.15 a and b), built either in rapid succession (denoted as

I2 in Figure 3.16) or in a time interval allowing for the excess pore water pressures generated

by the installation to dissipate before the installation of the consecutive inclusion (denoted as

I 45 in Figure 3.16).

(a) (b)

Figure 3.15: Layout of sand compaction piles (P1 to P4) and location of the T-Bar test

(denoted as s) for pile group tests featuring either a) 2 piles or b) 4 piles (all

dimensions in mm) (Yi et al., 2013).

It was observed that the installation of a second pile in quick succession (denoted as 2P-I2 in

Figure 3.16) did not add any strength to the soil compared to the situation in which a single

pile was installed. An increase in the measured shear strength was observed after the

installation of a column group, which is thought to be due to the inevitable dissipation of the

excess pore water pressures taking place during the time necessitated for the repositioning

of the SCP installation tool.

However, the dissipation of the excess pore water pressure between the installation of the

SCPs has a strong influence on the measured undrained shear strength (Figure 3.16). A

substantial increase (about 50 %) compared to the single pile situation, and to the situation in

which the SCPs were installed in quick succession could be observed both in the case

featuring 2 piles (denoted as 2P-I45 in Figure 3.16) and in the case featuring 4 piles (denoted

as 4P-I45 in Figure 3.16).

This shows that the strength increase triggered by sand piles is not cumulative if the piles are

installed in a quick succession. If sufficient time is allowed for the dissipation between the

different installation phases, the increases can be added, by considering the increased

undrained shear strength after each pile has been constructed.


105

Figure 3.16: Undrained shear strengths measured in the centrifuge for different tests

(Yi et al., 2013).

Although the installation technique developed by Ng et al. (1998) represents an extremely

valuable improvement in modelling in the centrifuge, compared to the installation of granular

inclusions under 1 g, the two drawbacks brought up earlier through the Archimedes’ screw:

particle crushing and heat creation might influence the results, especially due to the need to

submerge the model below water.

These two issues were solved by Weber (2004) by developing a stone column installation

tool for the ETH Zürich geotechnical drum centrifuge (Springman et al., 2001) in order to

model the bottom feed construction technique. This tool consists of an open-ended filling

tube attached to the working arm of the centrifuge and which is driven into the clay model

(Figure 3.17). A drawing pin is pushed into the surface of the clay bed in order to seal the tip

of the tube in order to prevent the filling tube from clogging, and remains in the soil model

after the installation of the granular inclusion (denoted as Lost tip in Figure 3.17). In the case

this has not been effective, the rotations of the drum and of the tool platform can be

decoupled, allowing the tool platform to be stopped in order to unclog the filling tube without

disturbing the stress history of the soil sample in the drum.

In situ

1 pile, post-installation

long-term strength

1 pile, post-installation,

long-term strength

2 piles, 2 min interval,

long-term strength


long-term strength


long-term strength


long-term strength

1P-LT

2P-I2

2P-I45

4P-I2

4P-I45

Undrained shear strength su [kPa]

0 5 10 15 20 25

Depth

[m]

0

1

2

3

4

5


106

The granular column material is fed from outside the centrifuge through a flexible sand feed

pipe once the desired installation depth is reached, and the filling tube can either be

withdrawn in one extraction, thus creating an uncompacted stone column, or a compaction

regime can be applied by withdrawing the tube by a certain distance before pushing it into

the model again. The compaction process causes the stone column diameter to increase

from 10 mm (outer diameter of the installation tool) to about 12 mm.

Figure 3.17: Experimental setup for the in-flight installation of stone columns (Weber et al.,

2005).

Figure 3.18 presents a detailed view of the installation tool. The flexible sand feed pipe (3)

has an inner diameter of 28 mm, the transition unit (5) an inner diameter of 7.5 mm and the

filling tube an inner diameter of 8.4 mm.

This method solves the issue of grain crushing that was encountered by Ng et al. (1998),

however there are some limitations in terms of the range of grain sizes that can be used

without clogging the filling tube. Moreover, no heat is created by pushing a tube into the host

soil, which means that the height of the groundwater table can be varied to suit the

requirements of the test.

There are two main differences between the bottom feed construction technique used in situ

and the experimental setup proposed by Weber (2004). Compressed air is used in the field

to prevent the tip of the installation mandrel from clogging, as opposed to a lost tip in the

centrifuge. Also, no vibratory movements can be achieved in the centrifuge, as opposed to

the field situation.

Chair for Geotechnics

Construction of sand compaction pile in soft soils

Dr. Jan Laue Construction Processes in Geotechnical Engineering

Axis

r

z

w

q

Pore pressuretransducers

Flexible sandfeed pipe

r-z-working

arm

Tool platform

Filling tube

Soil model

Lost tip

Laser distancegauge

Transition

unit


107

Figure 3.18: Detailed view of the stone column installation tool developed by Weber (2004).

Using his setup, Weber (2008) conducted centrifuge tests to model the behaviour of

embankments built on soft clay, with and without stone columns. Improving the ground

reduced the settlements observed on top of the embankment (Figure 3.19), as well as

accelerating dissipation of the excess pore water pressures generated by the installation of

the embankment, by a factor of four, for an area replacement ratio as of 10 % (Figure 3.20).

Figure 3.19: Settlements measured with and without stone columns at the toe of the

embankment (1), and on top of the embankment (2) (after Weber 2008).

1

2

3

45

6

7

1 Working arm

2 Tool clamp

3 Flexible sand feed pipe

4 Inlet unit

5 Transition unit

6 Filling tube

7 Laser distance gauge

(1)(2)

(1)

(2)

0 200 400 600 800 1000 1200

Time [min]

8

7

6

5

4

3

2

1

0

-1

Sett

lem

ents

[m

m]

Time [min]unimproved

improved


108

Figure 3.20: Evolution of the pore water pressure after embankment construction in the

improved ground within the sand pile grid (---) in comparison with unimproved

ground (––) at three depths in the model with a groundwater table located at the

surface of the model in the middle of the container: P1 = 120 mm, P2 = 70 mm,

P3 = 25 mm equivalent to prototype depths of 6 m, 3.5 m and 1.25 m

respectively (after Weber, 2008).

Moreover, due to the effective reproduction of the construction process, Weber (2008) could

also investigate the installation effects of stone columns in soft soils in more detail at

micromechanical scale. The development of different zones around the granular inclusions

could be observed (Figure 3.21):

- zone 1, where the coarse grains and clay are mixed,

- zone 2, where a clear reorganisation of the clay platelets parallel to the column

axis can be seen,

- zone 3, where a reduction of the void ratio and of the porosity could be measured

(Figure 2.69), and

- zone 4, where no clear installation effects can be noted.


(Weber, 2008).

0 200 400 600 800 1000 1200 1400

P1

P2

P3

Time [min]

0

20

40

60

80

100

120

140

Pore

wate

rpre

ssure

[kP

a]

P1

P2

P3


109

3.4 Techniques adopted

3.4.1 ETH Zürich geotechnical drum centrifuge and equipment

The ETH Zürich geotechnical drum centrifuge (Springman et al., 2001) has a diameter of 2.2

m and can achieve a maximal acceleration of 440 g, while the maximal weight of the model

in the drum is 2 tons. The axis of rotation of the drum is vertical, which means that the

centripetal acceleration acts in a horizontal plane and that the models have to be mounted on

a vertical plane. Figure 3.22 shows a cross-section of the machine.

The equipment implemented comprised:

- the stone column installation tool: the in-flight stone column installation is

performed using the experimental setup described in Weber (2004), Weber et al.

(2005) and Weber (2008), as well as in Section 3.3,

- aluminium footings: a 28-mm radius circular stiff aluminium footing was used in

order to load a single stone column and a 56 x 56 mm square stiff aluminium plate

was used to load a stone column group.

Figure 3.22: Cross-section of the ETH Zürich geotechnical drum centrifuge (Springman et al.,

2001).


110

3.4.2 Pore pressure transducers (PPTs)

The pore water pressures are recorded in the centrifuge using DRUCK PDCR 81 (König et

al., 1994) transducers. These sensors measure the pressure difference between the

atmospheric air pressure and the fluid pressure acting through the porous stone on the

silicon diaphragm (Figure 3.23). Transducers are produced for different operational pressure

ranging from 75 mbar up to 35 bar, and can all measure positive and negative pore water

pressure. The sensors used here have a maximal operational pressure of 7 bar and can

measure suction up to 1 bar. The saturation of the ceramic filter fitted to the PPTs is

extremely important in order to obtain reliable measurements. This saturation is obtained

using a pressure chamber with de-aired water under varying cycles of vacuum and pressure.

The pressure chamber is also used to conduct the calibration (R2 ranging from 0.99992 to

0.99999).

The form of the PPTs causes a sensitivity of the measurements to the orientation of the filter

(Figure 3.23). Thus good care during the installation of the PPTs in the soil model is

therefore necessary in order to obtain reliable results.

Figure 3.23: Cross-section of the transducer DRUCK PDCR 81 (König et al., 1994).

3.4.3 Load cells

Load cells manufactured by the company Hottinger Baldwin Messtechnik GmbH

(Figure 3.24) were used in this research. The maximum capacity of the load cells was 2 kN,

respectively 10 kN. The producer predicts a linear deviation of the results of 0.011 % for a

2 kN load cell and of 0.061 % for a 10 kN load cell. The maximum loads recorded during the

footing loadings conducted during the centrifuge tests were of about 350 N, which

corresponds to an error of 0.0385 N for a 2 kN load cell and of 0.2135 N for a 10 kN load cell.

This error was considered irrelevant in the present research, and was discarded for the

interpretation of the results.

The calibration was conducted in the same manner as for the T-Bar penetrometer

(Section 3.4.4) and load cells were mounted on the arm supporting the aluminium footing


111

and on the stone column installation tool. This measured the footing load as well as the

vertical load applied during the construction and compaction of the stone column.

Figure 3.24: Load cell produced by Hottinger Baldwin Messtechnik GmbH (Arnold, 2011).

3.4.4 T-Bar penetrometer

A T-Bar penetrometer is used to measure the undrained shear strength of the soil. The

penetrometer used in the centrifuge at ETH Zürich (Figure 3.26) is based on the tool

presented in Stewart & Randolph (1991) and in Stewart & Randolph (1994).

Stewart and Randolph (1994) formulate the undrained shear strength as:

3.4

with P force per unit length acting on the T-Bar

d diameter of the T-Bar

Nb T-Bar factor

The T-Bar factor Nb is dependent on the surface roughness of the material. Its analytical

value (Stewart & Randolph, 1991) varies from 9.0 (smooth surface) to 12.0 (fully rough

surface). Adhesion factors of 0 and 1 are extremely unlikely to be reached, therefore

intermediate values of Nb are used and must be combined with the effect of smooth ends of

the circular bar, which is not infinitely long. Randolph & Houlsby (1984) suggest that a value

of 10.5 is implemented for general use. This value was used for the assessment of the

undrained shear strength with the T-bar penetrometer, thus neglecting the effects of the

smooth ends of the tool (Figure 3.25) and the influence of the penetrometer shaft on the flow

mechanism around the T-Bar.

Figure 3.25 shows the dimensions of the penetrometer used in this test series (Figure 3.26

and Figure 3.27). The force P (Equation 3.4) is measured using four strain gauges installed

on a round cylinder at the end of the penetrometer shaft (Figure 3.25).

The calibration is conducted using the setup shown in Figure 3.28 (a). The penetrometer is

inverted and clamped vertically, and loaded in compression through a saddle placed on the


112

bar, which is connected by a rigid string to single weights placed on a horizontal plate

hanging beneath the device. The values measured by the strain gauges are recorded (Figure

3.28 b).

(a) (b)

Figure 3.25: T-Bar penetrometer (a) front view and (b) side view.

Figure 3.26: T-Bar penetrometer (after Weber, 2008).

Figure 3.27: T-Bar penetrometer mounted on the working arm of the tool platform in the

centrifuge (after Weber, 2008).

Strain gauges Shaft

Shaft

Strain gauges


113

Figure 3.28: T-Bar calibration setup (after Weber, 2008).

3.4.5 Electrical impedance needle

This tool was presented in Gautray et al. (2014). An assessment of the density changes

within a soil mass can be achieved by means of measuring resistance. Such methods can be

divided in measurements of the thermal resistance of the soil (Shublaq, 1992) and

measurements of the electrical resistance (Cho et al., 2004; Shin et al., 2009; Dijkstra et al.,

2012).

As shown e.g. by Weber (2008), the installation of stone columns in soft clay compacts the

host soil around the inclusion (Figure 3.21). In order to assess the spatial distribution of the

zone affected, an electrical impedance needle was developed at ETH Zürich,

which measures the impedance (electrical resistivity) of the soft soil in-flight

(Gautray et al., 2014), under the assumption that an increased density of the host soil

increases the electrical impedance recorded. Such measurements enable an insight to be

obtained into the variations of density around granular inclusions. This represents a step

forward compared to 1 g tests, presented e.g. in Shin et al. (2009), due to the more accurate

reproduction of the stress field, which is particularly important in terms of the resistance to

radial compaction (Section 3.2).

The design of the electrical impedance needle used in this research was inspired by Cho et

al. (2004), who inserted such a tool into the host soil, while measuring the electrical resistivity

at the tip. Cho et al. (2004) used 3 needles with diameters of 2.108 mm, 1.270 mm and 2.159

mm respectively. However, due to the scaling of the dimensions in the centrifuge, the

diameter of the impedance needle had to be reduced to 1 mm, in order to keep the difference

between diameter of the impedance needle and medium grain size at prototype scale within

acceptable limits.

Vesic (1977) highlighted the problems encountered during the insertion of an inclusion with a

flat tip into the soil, namely the formation of a dense plug, which then moves with the tip.

However, practical considerations prevailed for the choice of the tip shape, which was set to

be flat (Figure 3.29).

Halterung

Waagschale mit Gewichten

T-Bar Penetrometer

Messwerterfassung

Support

Value recording Weighting scale

T-Bar Penetrometer

T-Bar Penetrometer

Weight


114

(a) (b)


diameter 1 mm).

Although a wedged tip shape seems more adequate at first glance, its implementation in the

centrifuge may not be straightforward. The main challenge is the construction of such a

wedged form for the small diameter (1 mm). Geometrical imperfections at model scale will

also be strongly amplified at prototype scale due to the scaling factors. This might drastically

reduce the quality of the results, mainly due to any uncontrollable changes of direction of

penetration, which could be caused by an imperfect wedge.

Figure 3.30 shows a schematic view of the needle, which is made of a 1 mm diameter

stainless steel tube (inner diameter 0.8 mm) in which an electrical cable was incorporated

and glued. The electrical impedance (Z) is measured at the tip of the cable. A cover had to

be developed to make sure that the wind induced by the rotational movement of the

centrifuge would not trigger vibrations of the needle, which might provoke a distortion of the

actual location of the measurement performed, or even breakage of the needle. Due to the

centripetal acceleration, this cover is maintained over the needle (Figure 3.30 a) until the soil

surface is reached and then remains at the surface while the needle is pushed into the host

soil (Figure 3.30 b).

The development of the electrical impedance needle was an iterative process. The use of the

tool and the implementation process are presented in Section 4.7. This tool was first inserted

with a velocity of 3 mm /s into a soil specimen during the centrifuge test JG_v1, where

clogging of the tip prevented accurate measurement of the impedance. A water container

was built into the model used for a subsequent centrifuge test in order to clean up the tip in-

flight, but this procedure was not successful.

The tip of the needle was cleaned most efficiently using an ultrasonic bath (model Emmi 4,

produced by EMAG AG, Figure 3.31), which was mounted in the centrifuge drum and

subsequently filled with water. Such a bath generates ultrasound waves in order to clean

delicate items. The needle was immersed in the basin of the ultrasonic bath in flight, which

enabled the clay obstructing the tip of the tool to be removed, as the ultrasonic waves

destroyed the bonds that had formed between the clay particles and the electrical impedance

needle. The results of the measurements conducted with the electrical impedance needle

can be found in Section 4.7 and Appendices 8.6 and 8.7.


115

(a)

(b)

(c)

Figure 3.30: Schematic views of the electrical impedance needle (a) covered, (b) with the

cover retracted and (c) cross-section A-A (Gautray et al., 2014).

Figure 3.31: Ultrasonic bath Emmi 4, produced by EMAG AG (Gautray et al., 2014).

200 mm

90 mm

165 mm

50 mm

3.5 Model soils

116

3.5 Model soils

3.5.1 Birmensdorf clay

Three and a half tons of natural clay were extracted in 1999 during the construction of the

Birmensdorf traffic interchange near Zürich, Switzerland. This material has been stored since

then at ETH Zürich as a laboratory material and was used in several research projects

(Trausch-Giudici, 2003; Nater, 2005; Messerklinger, 2006; Weber, 2008). Many researchers

have investigated a range of properties, based on intact and remoulded specimens

(Fauchère, 2000; Fleischer, 2000; Panduri, 2000; Züst, 2000; Basler, 2002; Küng, 2003;

Messerklinger et al., 2003; Plötze et al., 2003; Trausch-Giudici, 2003; Nater, 2005;

Messerklinger, 2006). A summary of the mineralogical composition of Birmensdorf clay can

be found in Plötze et al. (2003).

This clay was also used as a soft soil bed for the centrifuge tests conducted in this research.

Applications of remoulded clays as soil models, including the effect of stress history, have

been discussed in Springman (2014), with specific reference to remoulded Birmensdorf clay.

A summary of these investigations is given in Table 3.2.

The soil models for the centrifuge tests are prepared using a clay suspension featuring a

water content higher than 100 %, which is then consolidated under a hydraulically loaded

piston in an oedometer (Section 3.6). This enables, in addition to the preparation of the

sample, the determination of different soil mechanical properties, some of which are

presented in Table 3.3.

Table 3.2: Classification and selected mechanical properties of Birmensdorf clay (after Weber, 2008).

USCS classification CH

Clay particle content from

sedimentation analysis < 2μm [%] 42

Liquid limit wl [%] 58

Plastic limit wp [%] 19

Plasticity index Ip [%] 39

Critical state effective angle of friction

φ’cv [°] 24.5

Effective cohesion c’ [kPa] 0


117

Table 3.3: Selected properties of Birmensdorf clay, determined from oedometer tests.

Specific density of the saturated soil ρg – normally

consolidated under σ’v = 100 kPa [g/cm3] 1.85

Specific density of the saturated soil ρg – normally

consolidated under σ’v = 200 kPa [g/cm3] 2.01

Void ratio e under σ’v = 100 kPa [-] 1.06

Void ratio e under σ’v = 200 kPa [-] 0.73

Vertical permeability k under σ’v = 100 kPa [m/s] 2.1 10-9

Vertical permeability k under σ’v = 200 kPa [m/s] 6.25 10-10

Vertical coefficient of consolidation cv for a load

increment from 50 kPa to 100 kPa [m2/s] 2.5 10-7

Confined stiffness modulus ME for a load increment

from 50 kPa to 100 kPa [kPa] 1410

Vertical coefficient of consolidation cv for a load

increment from 100 kPa to 200 kPa [m2/s] 1.5 10-7

Confined stiffness modulus ME for a load increment

from 100 kPa to 200 kPa [kPa] 2230

3.5.2 Quartz sand

The quartz sand used to construct the columns in this research is exactly the same as that

used by Weber (2008). Properties of this soil were investigated by Weber (2008) and are


Table 3.4: Parameters for the quartz sand used as stone column material (Weber, 2008).

USCS classification SP

Grain shape Semi-angular slightly rounded

Coefficient of uniformity [-] 1.4

Coefficient of gradation [-] 1.0

Specific density ρs [g/cm3] 2.65

Maximum bulk density ρd,max [g/cm3] 1.62

Minimum bulk density ρd,min [g/cm3] 1.50

Critical state effective angle of friction φ’cv [°] 37

Compression index Cc [-] 0.088

Swelling index Cs [-] 0.007

Coefficient of permeability k [m/s] 2 10-3

3.6 Soil model

118

3.5.3 Perth sand

The same Perth sand as used by Weber (2008) was used as a drainage bed and filling

material depending on the experimental setup (Section 3.6). Selected properties of this

material are listed in Table 3.5.

Table 3.5: Selected properties of Perth Sand (Nater, 2005).

USCS classification SP

Grain size d10 [mm] 0.14

Coefficient of uniformity [-] 2.2

Coefficient of gradation [-] 1.0

Specific density ρs [g/cm3] 2.65

Maximum bulk density ρd,max [g/cm3] 1.60

Minimum bulk density ρd,min [g/cm3] 1.50

Critical state effective angle of friction φ’cv [°] 30

Void ratio e [-] 0.5 – 0.7

Coefficient of permeability k under σ’v = 200 kPa [m/s] 2 – 4 10-5

The coefficient of permeability is significantly higher than that of Birmensdorf clay. Even

though the filter criteria according to Terzaghi (1925) are not fulfilled, there did not appear to

be any infiltration of the clay suspension into the sand. It could be observed that the drainage

function was maintained during the entire consolidation phase, and during the duration of the

centrifuge tests.

3.6 Soil model

Table 3.6 gives a summary of the containers used for the preparation of the soil models used

for centrifuge tests.

Table 3.6: Summary of the containers used for the preparation of soil models for centrifuge

tests.

Consolidation

stress Preparation container

Number of specimens

tested

100 Cylindrical strongbox (Ø 400 mm) 6

100 Oedometer container (Ø 250 mm) 1

100 Adapted oedometer container (Ø 250 mm) 2

200 Oedometer container (Ø 250 mm) 2

200 Adapted oedometer container (Ø 250 mm) 2


119

3.6.1 Preparation of Birmensdorf clay

The first step of the preparation of the models used in this work is homogenisation of the

clayey material stored in transport containers. Clay with a water content ranging from 100 %

to 120 % is placed into a vacuum mixer (Figure 3.32). Once a homogeneous suspension is

obtained, the vacuum is activated for a period of 12 hours to remove any air bubbles.

Figure 3.32: Vacuum mixer.

3.6.2 Preparation of a soil model in a cylindrical strongbox

Centrifuge tests were conducted using a 400 mm diameter cylindrical strongbox. The

advantage of this method is that the model can be prepared outside the centrifuge while the

instrumentation for the specimen can be inserted relatively easily.

The base plates of all containers are equipped with channels (Figure 3.33 a), which are then

filled with Perth sand (Figure 3.33 b) to prevent the drainage channels from clogging during

the filling of the strongbox with the clay suspension (Figure 3.33 c). This permits the model to

drain in both vertical directions, reducing the consolidation time under the press and the

testing time in the centrifuge. The channels also allow water to be fed into the base of the

model during the test under enhanced gravity. Once the mixing process is over

(Section 3.6.1), the clay suspension obtained is poured into the container directly from the

vacuum mixer (Figure 3.33 c).

3.6 Soil model

120

(a) (b)

(c)

Figure 3.33: General view (a) cylindrical strongbox used for the consolidation of Birmensdorf

clay under the hydraulic press, (b) view of the channels filled with Perth sand

and (c) filling with clay suspension.

A hydraulic press (Figure 3.34) is used in order to consolidate the sample under oedometric

conditions. The consolidation takes place with progressive vertical loading steps of 6, 12, 25,

50, and 100 kPa. The preloading of the sample under the press then determines the OCR of

the model in-flight, which is presented in detail for each test in the subsequent sections.

Once the consolidation under a load of 100 kPa is achieved, the model height is manually

reduced to 160 mm using a cutting blade, the specimen is unloaded, the water valves are

closed, the PPTs are installed (Section 3.6.5.1), the model is mounted into the centrifuge and

the water supply is connected to the plate of the container.


121

Figure 3.34: Hydraulic press used for the consolidation of clay.

3.6.3 Preparation of a soil model in an oedometer container

Clay specimens for centrifuge tests were also prepared in smaller oedometer containers

(250 mm diameter, Figure 3.35 a). The motivation for the use of such containers was the

opportunity to install instrumentation very close to the inclusion.

The drainage occurs in the model container both at the surface and at the bottom of the soil

model. As the containers were not equipped with a riled plate similar to the cylindrical

centrifuge strongbox mentioned above, a filter plate, covered with filter paper to prevent

clogging, was installed at the bottom of the specimen in order to ensure there would be

drainage capacity at the bottom of the sample.

The container is filled with slurry up to a height of 360 mm and the consolidation is conducted

using a different oedometer press (Figure 3.35 a) with similar progressive loading steps of 6,

12, 25, 50, 100 kPa and 200 kPa, respectively. One of the two samples used for the test

JG_v5 was only consolidated up to 100 kPa.

As the 250 mm diameter oedometer container was originally not equipped with ports on the

side walls so that PPTs can be installed in the clay, the sample had to be removed from the

container before this was possible. Cylindrical rupture zones would be possible during the

extraction of the soil model from the oedometer container due to the adhesion of clay to the

container (Figure 3.36 a). Therefore a plastic sheet was installed around the circumference

of the oedometer container (Figure 3.35 a, Figure 3.36 b) in order to avoid adhesion between

container and sample. This allows for the consolidated sample to be removed, using the

crane at disposal in the laboratory next to the ETH Zürich drum centrifuge (Figure 3.37 a).

The container is lifted vertically at a constant rate (approximately 4 cm/min) and the clay

sample does not experience any lateral movement during this phase, thus reducing the

disturbance of the sample during the removal of the sample from the container to a minimum.

3.6 Soil model

122

(a) (b)

Figure 3.35: Preparation of the clay model (a) slurry inside the oedometer container (b) under

consolidation in the oedometer container.

(a) (b)

Figure 3.36: Schematic representation (a) of the possible cylindrical rupture zones when

extracting the clay sample from the container and (b) of the use of the plastic

sheet in order to prevent the adhesion between clay and oedometer container.

Once the sample has been extracted, the PPTs are then installed (Section 3.6.5.2), the clay

sample is put into the 400 mm diameter strongbox and the gap between sample

and strongbox is filled with Perth sand by means of dry pluviation with compaction

(Figure 3.37 b). A density index ID of approximately 70 % was reached.

Plastic sheet


123

(a) (b)

Figure 3.37: (a) Removal of the oedometer container from the sample (b) view of the model

with clay sample surrounded by Perth sand.

This preparation procedure causes additional disturbance to the specimen as a manual

manipulation of the sample is necessary to install it into the 400 mm diameter strongbox after

the installation of the PPTs, the effect of which is extremely difficult to quantify. Moreover, the

removal of the lateral support from the container affects the stress history. The coefficient of

earth pressure at rest K0 of Birmensdorf clay is:

3.5

with K0 coefficient of earth pressure at rest

φ’ effective angle of friction of Birmensdorf clay (Table 3.2)

Thus, for a principal vertical stress σ1’ of 200 kPa acting on the soil specimen in the

oedometer container, the horizontal principal stress σ3’ is equal to 116 kPa. The removal of

the soil model from the oedometer container causes a dissipation of the horizontal principal

stress, which is subsequently equal to 0 kPa. Thus the model can not only swell vertically,

but also horizontally. The filling of the gap between soil model and container wall with Perth

sand provided a lateral support to the clay sample, although it is not rigid. Thus the horizontal

principal stress σ3’ will be smaller than in an oedometer container. However, no stress

measurements were conducted within the soil, making a quantitative interpretation of the

changes of the horizontal principal stress impossible. A quantitative comparison of the lateral

stresses acting on the clay sample for specimens prepared in an oedometer container and

surrounded by sand and for specimens prepared in a rigid container (cylindrical strongbox or

adapted oedometer) is given in Section 3.7.4.

ClayPerth sand

Cables from PPTs

3.6 Soil model

124

These considerations led to the adaptation of the 250 mm oedometer containers so that they

could be mounted directly into the centrifuge, avoiding the need to remove the sample from

the stiff container (Figure 3.37 a) and the subsequent filling of the gap with compacted sand

(Figure 3.37 b). This avoided the soil model from being disturbed and the stress history from

being affected beyond the planned stress paths.

3.6.4 Preparation of a soil model in an adapted oedometer container

Adapted oedometer containers were used for centrifuge tests. Holes were drilled in the walls

of the containers presented in Section 3.6.3, so that PPTs could be installed in the

clay samples (Figure 3.38). Base plates were constructed similar to those used in the

strongbox (Section 3.6.2). The filling procedure is exactly the same as described in

Section 3.6.2: Perth sand is used as drainage bed at the bottom of the sample

(Figure 3.33 b) and the clay suspension is filled into the container directly from the vacuum

mixer (Figure 3.33 c) up to a height of 360 mm.

Figure 3.38: Ports for the installation of PPTs into the soil model prepared in 250 mm

diameter containers

After the consolidation phase, the height of the model is manually reduced to 160 mm using

a cutting blade, the PPTs are installed through the dedicated connections (Section 3.6.5.1),

the model is mounted into the centrifuge and the water supply is connected to the base plate

of the container.

3.6.5 Installation of the PPTs

The PPTs are installed into the consolidated clay models using a technique described in

König et al. (1994). Firstly holes (diameter 7 mm) are pre-drilled in the clay. These holes

need to be a few millimetres shorter than the intended penetration length of the PPTs in

order to ensure that the filters of the transducers (Figure 3.23) can be slightly pressed into

the host soil, guaranteeing a good connection in the planned location.

Base

plate

Ports for installation of the PPTs


125

The PPTs are then inserted into the pre-drilled hole using the installation tool shown in

Figure 3.39, which has a rill against which the PPT can be held while pushing it into the soil.

Once the desired penetration is reached, the tool is pulled back out of the model and the

transducer remains in the clay. A slight counter pressure applied on the cable of the PPT

is usually sufficient to separate the transducer from the installation tool. The pre-drilled

hole is sealed with a clay paste of the same origin as the host soil by using a syringe

(Figure 3.40 b).

Figure 3.39: PPT installation tool.

3.6.5.1 Installation of the PPTs into a cylindrical strongbox and an

adapted oedometer container

Insertion of the transducers into the models consolidated in the cylindrical strongbox and in

the adapted oedometer containers is conducted in the same manner. The installation tool

(Figure 3.39) is held horizontally and lateral movements are also prevented when passing it

through the port (Figure 3.40 a). The penetration length is marked on the installation tool,

taking the thickness of the container walls, as well as the length of the connections into

account.

(a) (b)

Figure 3.40: Installation of the PPTs in the cylindrical strongbox (a) introduction of the PPTs

through the dedicated ports into the pre-drilled hole (b) filling of the pre-drilled

hole with slurry (Weber, 2008).

Rill

3.6 Soil model

126

3.6.5.2 Installation of the PPTs into a model consolidated in an oedometer

container and installed in the 400 mm diameter strongbox

A special installation setup had to be developed (Figure 3.41) to install the pore pressure

transducers into a model that had been consolidated in an oedometer container. It consists

of a circular plate which is positioned at the upper surface of the cylindrical clay sample after

the oedometer ring had been removed and held in place by aluminium cylinders penetrating

slightly into the clay sample. Holes were drilled at the edge of the circular plate to achieve a

precise and stable positioning of the installation device, which is fixed to 2 vertical cylinders

and can be moved up and down depending on the depth at which the transducers have to be

installed.

Figure 3.41: PPT installation setup for a specimen consolidated in an oedometer container.

The installation tool (Figure 3.39) can then be positioned on the installation device, ensuring

that the tool is oriented horizontally, while preventing lateral movement (Figure 3.42).

The PPTs are then pushed into pre-drilled holes in a similar manner to that used for

installation in the cylindrical strongbox. The holes are sealed with a slurry of Birmensdorf clay

using a syringe.

Aluminium cylinders

holding the plate

in place

Installation

device

Holes used to

position the

installation

device

Consolidated

clay sample


127

Figure 3.42: Insertion of the PPT installation tool into the clay specimen using the installation

device.

3.6.6 Identification of the locations of the stone columns

The positions of the stone columns to be installed have to be marked before the start of the

centrifuge test. Drawing pins are used to seal the tip of the stone column installation tool and

are pushed into the planned locations on the surface of the clay model.

A difference was made between the models prepared in the cylindrical strongbox (Section

3.6.2), where four stone columns were installed and those consolidated using the oedometer

containers (Sections 3.6.3 and 3.6.4), where a single column was built. In the first case, the

model was installed in the centrifuge and the stone column installation tool, mounted on the

working arm of the tool platform, was used to mark the locations of the four inclusions to be

built. A pin was then positioned correspondingly at each location.

In the second case, it was of extreme importance to install the pin precisely in the middle of

the sample as PPTs are then installed very near to the column (Figure 3.53 and Figure 3.56)

and any error in the positioning of the pin can have important negative consequences (the

stone column installation tool could hit and destroy some of the transducers). One of the

aluminium cylinders holding the plate in place at the upper surface of the clay sample (Figure

3.41) was therefore positioned exactly in the middle of the plate, thus delivering a precise

location of where to install the pin.

The type of the drawing pins used in this research differ from the original industrial drawing

pins used by Weber (2008). There was only a very small margin of error in the positioning of

the stone column installation tool, otherwise the tip would clog. The pins used in this project

have a circular base and a conical cross-section (Figure 3.43 and Figure 3.44). This provided

a significantly higher degree of safety against clogging.

3.7 Centrifuge tests

128

(a) (b)

Figure 3.43: Pin used to mark the positions of the stone columns to be installed (a) plan view

and (b) side view.

Figure 3.44: Tilted view of the pin used to mark the positions of the stone columns to be

constructed with the stone column installation tool.


3.7.1 Overview

Although different experimental setups were used, the main system parameters for the

centrifuge tests such as acceleration, height of the model and drainage conditions, were the

same for all the tests conducted, and are summarised in Table 3.7. The reference radius

(radius at which the nominal acceleration acts) is set at 2/3rds of the model height, as

suggested by Schofield (1980).

Vertical cross-sections of the different experimental setups used are shown in Figure 3.45

(detailed representations at scale are presented in Sections 3.7.2, 3.7.4 and 3.7.5). A

standpipe (9) was installed in order to control the position of the groundwater level. Table 3.8

gives an overview of the experimental setups (Sections 3.7.2, 3.7.4 and 3.7.5) used for the

test series.

7.2 mm

5 m

m

11

mm

1 m

m

2.5 mm

2 mm

Stone column installation tool

Pin


129

Table 3.7: Summary of the main system parameters.

Model height [mm] 160

Stone column length [mm] 120

Nominal acceleration [g] 50

Reference radius 2/3rds of the model height

Drainage conditions Double-sided

Insertion depth of the T-Bar [mm] 140

Insertion depth of the electrical

impedance needle [mm] 115

Full cylindrical

strongbox

Specimen prepared in an

oedometer container

Adapted oedometer

container

1 Water supply 6 Drainage bed

2 Drum 7 Standpipe

3 Strongbox with base plate 8 Water escape valve

4 Groundwater level 9 Adjustment base

5 Soil model 10 Perth Sand

Figure 3.45: Vertical cross-section of the experimental setup in the centrifuge for the

specimens prepared in a cylindrical strongbox (Section 3.6.2), in an oedometer

container and in an adapted oedometer container (Section 3.6.4) (after Weber,

2008).


130

Table 3.8: Overview of the experimental setup used for the different tests.

Test Full cylindrical

strongbox

Specimen

prepared in an

oedometer

container

Adapted

oedometer

container

Pre-

consolidation

stress σc [kPa]

JG_v1 X (1 container) 200



JG_v5 X (2 containers) 100 / 200


JG_v7 X (2 containers) 200




3.7.2 Groundwater level

The position of the groundwater level is a key parameter for the tests conducted. The

saturation of the clay model has to be guaranteed during the whole duration of the centrifuge

tests, i.e. about 36 hours. Water is therefore supplied from the bottom of the model, as

shown in Figure 3.45, and the position of the groundwater level in the model is controlled by

a standpipe.

The surface of the clay model is vertical in the drum while the groundwater level is curved

due to the acceleration field in the centrifuge. The position of the water level in the soil and

in the standpipe is shown for the different setups used in Figure 3.46, Figure 3.47 and

Figure 3.48.


prepared in a cylindrical strongbox (tests JG_v2, JG_v3, JG_v6, JG_v8 and

JG_v10).


131


prepared in an oedometer container (tests JG_v1 and JG_v5).


prepared in an adapted oedometer container (tests JG_v7 and JG_v9).

3.7.3 Tests conducted with specimens prepared in a cylindrical strongbox

3.7.3.1 Loading of a single stone column (JG_v2, JG_v3 and JG_v6)

This setup was used for the tests JG_v2, JG_v3 and JG_v6. The boundary conditions can be

attributed to those of an oedometer, as the radial strains are restricted on the sides. Seven

PPTs, the locations of which can be seen in Figure 3.49 (a) and (b), were installed in the soil

model. A goal of these tests was to determine whether the main part of the installation effects

appeared during the insertion of the mandrel, during its removal or during the compaction of

the granular inclusion.

To this means, four columns (Figure 3.49 a) were installed in the following sequence:

- column A was built without compaction,

- columns B and C were installed with a compaction regime of 15/10,

- column D was left unfilled. The stone column installation tool was inserted, the

centrifuge was stopped and the installation tool was pulled out.


132

Although the installation tool was pulled out of column D, the fact that this was done under 1

g and not under enhanced gravity limited the impact of the removal of the mandrel in terms of

radial relaxation of the host soil. The length of the stone columns installed in the centrifuge is

linked to the length of the sand feed pipe of the filling tube, which has to be stretched in order

to prevent the filling material from clogging in the feed pipe (Weber, 2008). As a

consequence, the sand feed pipe had to be changed after the installation of the columns A

and B.

A compaction regime of 15/10 means that once the tip of the stone column installation tool

has reached the desired depth of 120 mm, the tool is pulled out 15 mm before being inserted

by 10 mm again. This process is iterative until the tip of the tool reaches the surface of the

soil model. The stone column diameter increases from 10 mm (outer diameter of the

installation tool) to 12 mm during the compaction.

A T-Bar test, the location of which can be seen in Figure 3.49 (a) was conducted in order to

determine the undrained shear strength of the host soil. The compacted column B was

subjected to a displacement-controlled loading (v = 0.02 mm/s up to a depth of 17 mm) using

a stiff circular aluminium footing (diameter 56 mm). Table 3.9 contains a summary of the

testing procedure.


of a single stone column, tests JG_v2, JG_v3 and JG_v6).

Step Nr. Activity Duration

1 Start of the centrifuge and consolidation of

the model under its self-weight under

increased gravity

10 h

2 Installation of columns A and B 2 h

3 Dissipation of the excess pore water

pressures triggered by the installation of the

stone columns

3.5 h

4 Displacement-controlled loading of column

B

40 min


pressures triggered by the footing load

10 h

6 Installation of column C 1 h

7 T-Bar test 1 h

8 Installation of column D 1 h

9 Centrifuge stopped -


133

(a)

(b)

Figure 3.49: Specimens prepared in a cylindrical strongbox: (a) plan view and (b) cross-

section of the soil model with positions of the PPTs and of the stone columns.

3.7.3.2 Loading of a stone column group (JG_v8, JG_v10)

This setup was used for the tests JG_v8 and JG_v10. Seven PPTs, the locations of which

can be seen in Figure 3.51 and Figure 3.50, were installed in the soil model. Five compacted

stone columns (compaction regime 15/10) were built over a time frame of 1 hour and the

A


134

stone column group was then subjected to a displacement-controlled loading (v = 0.02 mm/s

up to a depth of 17 mm) with a square footing (56 mm x 56 mm).

Figure 3.50: Specimens prepared in a cylindrical strongbox: cross-section of the soil model,

with positions of the PPTs and of the stone columns (a / dsc = 2 [-]).

Table 3.10: Overview of the experimental setups used for the different tests.

Test Stone column diameter

dsc [mm]

Distance a between the

axis of the columns

[mm]

Ratio a / dsc [-]

JG_v8 12 24 2

JG_v10 12 24 2

JG_v10 12 30 2.5


135

Figure 3.51: Specimens prepared in a cylindrical strongbox: plan view of the soil model with

positions of the PPTs and of the stone columns (a / dsc = 2 [-]).

The electrical impedance needle (Section 3.4.5) was used between the installation of the

columns and the footing load. Two measurements were first conducted at reference points 1

and 2 (RP1 and RP2 in Figure 3.52), located 100 mm away from the axis of the stone

column A, both laterally and vertically. The needle was then inserted at decreasing distances

towards the axis of the stone column A (points A2 to J2 in Figure 3.52).


136

Figure 3.52: Specimens prepared in a cylindrical strongbox: insertion points of the electrical

impedance needle: positions of the reference points RP1 and RP2 and the

points A2 to J2 (a / dsc = 2 [-]).

Figure 3.52 illustrates a situation with a ratio a / dsc equal to 2, as used during the test JG_v8.

Although this ratio was modified during the test JG_v10, the distances of the needle points to

the axis of the column A were kept unchanged. The distance a between the axis of the

columns was varied from twice to 2.5 times the diameter of the column, as described in

Table 3.10. Table 3.11 shows a summary of the testing procedure.


137


of a stone column group, tests JG_v8 and JG_v10).


1 Start of the centrifuge and consolidation of

the model under its self-weight under

increased gravity

10 h

2 Installation of the stone columns in rapid

sequence

1 h


pressures caused by the installation of the

stone columns, T-Bar test and

implementation of the electrical impedance

needle

4 h

4 Displacement-controlled loading of the

stone column group

40 min


pressures triggered by the footing load

7 h


3.7.4 Tests conducted with specimens prepared in an oedometer container

(JG_v1, JG_v4, JG_v5)

This setup was used for the tests JG_v1, JG_v4 and JG_v5. One single sample, pre-

consolidated up to 200 kPa, was examined in tests JG_v1 and JG_v4. Two specimens were

installed symmetrically in the centrifuge for JG_v5, one of which was pre-consolidated up to

100 kPa and the other up to 200 kPa. Although Perth sand used to fill the gap between the

clay specimen and the container wall was compacted (Section 3.6.3), the boundary

conditions were not equivalent to those of an oedometer, as the clay / sand interface is not

rigid.

Seven PPTs, the locations of which can be seen in Figure 3.53, were installed in the soil

model. A compacted stone column was installed in the middle of the model (Figure 3.53).

The compaction regime was again 15/10.


138

(a)

(b)


(a) plan view and (b) cross-section of the soil model with positions of the PPTs

and of the stone column.

The tool used for compacting Perth sand around the clay sample had a length of 40 mm and

a width of 10 mm. Assuming a depth of influence of the compaction of 20 mm, the profile of

the horizontal stresses acting on the clay sample at the interface with Perth sand can be

A

A


139

calculated (with the effective angle of friction of Perth sand equal to 30°) using the increased

coefficient of earth pressure at rest:

3.6

with increased coefficient of earth pressure at rest


φ’ effective angle of friction

The profile of the lateral stresses acting on clay specimens prepared in a rigid container

(cylindrical strongbox or adapted oedometer) can be assessed using the coefficient of earth

pressure at rest of an over-consolidated soil:

( )

3.7

with K0OC coefficient of earth pressure at rest of an over-consolidated soil

K0NC coefficient of earth pressure at rest of a normally consolidated soil

OCR over-consolidation ratio


The profiles of the over-consolidation ratios used for the calculation of the horizontal stresses

are shown in Figure 4.3. Figure 3.54 shows a comparison of the lateral stresses acting on

the clay sample for specimens prepared in an oedometer container and surrounded by Perth

sand (denoted as σ’h Perth sand) and for specimens prepared in a rigid container with a pre-

consolidation of σ’v = 100 kPa (denoted as σ’h,clay, 100 kPa) or of σ’v = 200 kPa (denoted as

σ’h,clay, 200 kPa).

The lateral support by Perth sand is calculated based on the silo theory. Perth sand offers an

approximately similar support of the sample to the rigid container (for a pre-consolidation of

σ’v = 100 kPa) up to 20 mm (Figure 3.54), which corresponds to the assumed influence depth

of the compaction. However, below the depth of influence of the compaction, the horizontal

stress acting on the clay sample at the sand/clay boundary remains constant at 32 kPa, while

the horizontal stress acting on specimens prepared in rigid containers would rise up to 93

kPa (for a pre-consolidation of σ’v = 100 kPa) and to 137 kPa for a pre-consolidation of σ’v =

200 kPa) at a depth of 160 mm.

A T-Bar test, the location of which is given in Figure 3.53 (a) was conducted in order to

determine the undrained shear strength of the host soil. Seven PPTs (Figure 3.53 a and b)

were installed in the soil model. The column was then subjected to a displacement-controlled

loading (v = 0.02 mm/s up to a depth of 17 mm) using a stiff aluminium footing (diameter

56 mm).


140

Figure 3.54: Comparison of the lateral stresses acting on the clay sample for specimens

prepared in an oedometer container and surrounded by Perth sand (σ’h Perth sand,

calculated based on the silo theory) and for specimens prepared in a rigid

container (cylindrical strongbox or adapted oedometer) with a pre-consolidation

of σ’v = 100 kPa (σ’h clay, 100 kPa) or of σ’v = 200 kPa (σ’h clay, 200 kPa).

The last step of the tests consisted of measurements using the electrical impedance needle

(Section 3.4.5). Two measurements were first conducted in the far field, namely at the

reference points 1 and 2 (RP1 and RP2 in Figure 3.55), located 62.5 mm away from the axis

of the stone columns both laterally and vertically. The needle was then inserted at

decreasing spacing towards the stone column axis (points A to F in Figure 3.55). A summary

of the testing procedure is shown in Table 3.12.

Table 3.12: Testing procedure for tests conducted using the specimens prepared in an

oedometer or in an adapted oedometer (tests JG_v1, JG_v4, JG_v5, JG_v7 and

JG_v9).


1 Start of the centrifuge and consolidation of the

model under its self-weight under increased gravity

7 h

2 Installation of the stone column 1 h

3 Dissipation of the excess pore water pressures

caused by the installation of the stone column

3.5 h

4 Displacement-controlled loading of the column 40 min

5 Dissipation of the excess pore water pressures

caused by the footing load

10 h

6 T-Bar test 1 h

7 Insertion of the electrical impedance needle 5 h


0

20

40

60

80

100

120

140

160

0 20 40 60 80 100 120 140

De

pth

[m

m]

σ'h [kPa]

σh' sand σh' 100 kPa σh' 200 kPaσ'h Perth sand [kPa] σ'h clay, 100 kPa [kPa] σ'h clay, 200 kPa [kPa]


141


insertion points of the electrical impedance needle and positions of the reference

points RP1 and RP2 and the points A to F.

3.7.5 Tests conducted with specimens prepared in an adapted oedometer

container (JG_v7, JG_v9)

The experimental setup using specimens prepared in an adapted oedometer container is

similar to that using specimens prepared in an oedometer container. However, the boundary

conditions are, in this case, oedometric.


142

Such a setup was used for the tests JG_v7 and JG_v9. A plan view and a cross-section of

the model can be seen in Figure 3.56. Seven PPTs, the locations of which can be seen in

Figure 3.56 were installed in the soil model.

The steps of the tests (column installation, footing load, T-Bar test and implementation of the

electrical impedance needle) are similar to those given in Table 3.12. The electrical

impedance needle was inserted at the same positions as those shown in Figure 3.55.

(a)

(b)

Figure 3.56: Specimens prepared in an adapted oedometer: (a) plan view and (b) cross-

section of the soil model with positions of the PPTs and of the stone column.

4 Results from the centrifuge tests

143


The following chapter presents the results obtained from 8 centrifuge tests, during which a

total of 12 specimens were investigated. All tests were conducted under 50 g. Although the

nominal acceleration actually acts at a depth of 2/3rds of the model height, it is assumed that

the whole specimen is subjected to 50 times the Earth’s gravity. This limits the error, as the

g-level will be under-estimated above and overestimated below 2/3rds of the height.

Due to mechanical issues with the centrifuge, the specimen used for test JG_v3 was left

under the consolidation press for about 5 months, which led to aging effects. The results

from this test could not be exploited in the end.

4.1 Undrained shear strength

The clay slurry was consolidated up to vertical effective stresses of either 100 kPa or 200

kPa depending on the experimental setup used. The pre-consolidation determines the OCR

and the theoretical profile of the undrained shear strength with depth. A theoretical prediction

of the undrained shear strength was compared with the results obtained experimentally in-

flight using the T-Bar penetrometer (Section 3.4.4).

4.1.1 Theoretical prediction

Ladd et al. (1977) propose the following expression for the calculation of the undrained shear

strength su:

4.1

(

)

4.2

4.3

with su undrained shear strength

σ’v vertical effective stress


a, b undrained shear strength parameters

nc normally consolidated

σ’v,max maximum vertical effective stress

Ladd et al. (1977) suggest values of b ranging between 0.75 and 0.85. Trausch-Giudici

(2003) and Küng (2003) conducted triaxial tests in order to propose the values of a and b for

the Birmensdorf clay used in this research (Table 4.1).

The over-consolidation ratio OCR was determined based on the pre-consolidation stress

applied during the preparation of the specimens (σ’v,max = σ’v,Press) and the vertical stress

profile obtained under a nominal constant acceleration of 50 g (σ’v, = σ’v,Centrifuge). Figure 4.1

and Figure 4.2 show the profiles of the effective vertical stresses under the press (σ’v,Press)


144

and in-flight under 50g (σ’v,Centrifuge) for pre-consolidation stresses of 100 kPa and 200 kPa,

respectively. Figure 4.3 represents the corresponding profiles of the over-consolidation ratio.

Table 4.1: Values of a and b obtained by Trausch-Giudici (2003) and Küng (2003).

Trausch-Giudici Küng

a [-] 0.26 0.34

b [-] 0.73 0.73

Ip [%] 26-56 26-56


press (σ’v,press) for a pre-consolidation of 100 kPa.


press (σ’v,press) for a pre-consolidation of 200 kPa.

0

20

40

60

80

100

120

140

0 20 40 60 80 100 120

De

pth

[m

m]

σ'v [kPa]

σ' press σ' centrifugeσ'v,Press σ'v,Centrifuge

0

20

40

60

80

100

120

140

0 50 100 150 200 250

De

pth

[m

m]

σ'v [kPa]

σ' press σ' centrifuge

σ'v,Press

σ'v,Centrifuge


145

Figure 4.3: Profiles of the over-consolidation ratio for pre-consolidation stresses of 100 kPa

and 200 kPa.

4.1.2 Shear strength profile for pre-consolidation up to σ’v = 100 kPa

Figure 4.4 shows the shear strength profiles obtained for specimens pre-consolidated up to

100 kPa. The profiles calculated using the predictions according to Trausch-Giudici (2003)

and Küng (2003) are denoted as su,TG and su,K, respectively. The profile measured in a full

cylindrical strongbox is represented by su,JG_v2 while the profiles measured in specimens

prepared in adapted oedometers are denoted as su,JG_v8, su,JG_v10,A and su,JG_v10,B, respectively.

An error in the software controlling the movement of the tool platform prevented steps 6 to 8

from being conducted (installation of column C, T-bar test, installation of column D,

Table 3.9) for test JG_v6. The undrained shear strength profiles obtained during the tests

JG_v2, JG_v8 and JG_v10 are presented in Figure 4.4. The steep increase of the undrained

shear strength near the surface measured in container B during test JG_v9 (denoted as

su,JG_v10,B in Figure 4.4) is due to the presence of clay on the T-bar after testing in container A,

which increased the values measured at the beginning of the penetration. This effect was

noted for all second T-bar measurements (denoted as e.g. su,JG_v9,A in Figure 4.5).

The results obtained with the values of a and b proposed by Trausch-Giudici (2003) and

Küng (2003) (denoted as su,TG and su,K, respectively, in Figure 4.4) overestimate the

undrained shear strength in this case. This might be due to the fact that Trausch-Giudici

(2003) and Küng (2003) investigated specimens with plasticity indexes Ip ranging from 26 %

to 56 % and back-calculated the parameters a and b in order to obtain the best fit of the

results, which might not correspond to the Ip of 39 % of the soil used in this research. The

results from the T-Bar were well fitted with a = 0.22 [-] and b = 0.65 [-] (curve denoted as su,JG

in Figure 4.4). This value of b is significantly lower than the suggestion made by Ladd et al.

(1977), which is entirely feasible and would indicate a small over-consolidation of the model

at the surface.

0

20

40

60

80

100

120

140

160

0 10 20 30 40 50

De

pth

[m

m]

OCR [-]

Series1 Series2σ'v= 100 kPa σ'v = 200 kPa


146


JG_v2 (su,JG_v2), JG_v8 (su,JG,v8) and JG_v10 (su,JGv10,A and su,JG,v10,B) compared

with theoretical predications based on Trausch-Giudici (2003, su,TG) and

Küng (2003, su,K) and with the back-calculated values of the parameters a and b

(su,JG).

Figure 4.5: Profiles of the undrained shear strength obtained with the T-Bar during

test JG_v9 (su,JG_v9,A and su,JG_v9_B) compared with theoretical predictions based

on Trausch-Giudici (2003, su,TG) and on Küng (2003, su,K), and with the back-

calculated values of the parameters a and b (su,JG).

The two specimens (A and B) used for test JG_v9 were consolidated up to 100 kPa and the

boundary conditions are clearly defined, as the lateral movements at the boundary were

restricted by the stiff container (adapted oedometer). Figure 4.5 shows a comparison

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

De

pth

[m

m]

su [kPa]

su, K su, TG su,JG_v2 su,JG_v8

su,JG_v10,A su,JG_v10,B su,JG

su,K su,TG su,JG_v2 su,JG_v8

su,JG_v10,A su,JG_v10,B su,JG

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

De

pth

[m

m]

su [kPa]

su2, K su1, TG su,A su,B su,JGsu,K su,TG su,JG_v9,A su,JG_v9,B su,JG


147

between the measured values of the undrained shear strength (denoted as su,JG_v9,A and

su,JG_v9,B) with the theoretical predictions.

The values of a and b proposed by Trausch-Giudici (2003) and Küng (2003) (denoted as

su,TG and su,K, respectively, in Figure 4.5) tend to overestimate the undrained shear strength.

The results obtained from the T-Bar were well fitted with a = 0.22 [-] and b = 0.79 [-] (curve

denoted as su,JG in Figure 4.5). The back-calculated value of b lies between 0.75 and 0.85,

as suggested by Ladd et al. (1977), and is also close to the values suggested by

Trausch-Giudici (2003) and Küng (2003) (b = 0.73 [-]).

4.1.3 Shear strength profile for pre-consolidation up to σ’v = 200 kPa

Figure 4.6 shows a comparison of the shear strength profiles obtained during the tests

conducted with specimens prepared in oedometer containers and subsequently transferred

into the cylindrical strongbox. Tests JG_v1 (denoted as su,JG_v1) and JG_v5 for the specimen

consolidated up to 200 kPa (denoted as su,JG_v5), are reported with the profile obtained using

the back-calculated values of a and b for the specimen prepared in an adapted oedometer

container and pre-consolidated up to 100 kPa (Section 4.1.2).


JG_v1 (su,JG_v1) and JG_v5 in the specimen consolidated up to 200 kPa (su,JG_v5)

compared with the profile obtained with back-calculated values of the

parameters of a and b (su,JG).

Test JG_v1 was the first test conducted using the experimental setup with a specimen

consolidated in an oedometer and manually transferred into the centrifuge strongbox. It is

therefore assumed that the lower undrained shear strength measured during test JG_v1 is

due to a greater disturbance of the specimen during the transfer than during test JG_v5

It is interesting that the profile of the undrained shear strength recorded during test JG_v5 is

very close to the back-calculated profile of test JG_v9. This indicates that the strengthening

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

De

pth

[m

m]

su [kPa]

su,JG_v1 su_JG_v5 su,JGsu,JG_v5su,JG,v1 su,JG,v5 su,JG


148

effect of the higher over-consolidation of the specimen (200 kPa for test JG_v5 opposed to

100 kPa for test JG_v9) on the undrained shear strength is opposed by the loss of constraint

of the flexible boundary conditions (interface sand / clay opposed to clay / steel) and by the

disturbance caused by the manual transfer of the specimen from the oedometer container to

the strongbox.

Figure 4.7 shows a comparison of the shear strength profiles obtained during test JG_v7

(denoted as su,JG_v7_A and su,JG_v7_B), conducted using a specimen prepared in an adapted

oedometer container, with the theoretical predictions according to Trausch-Giudici (2003)

and Küng (2003) (denoted as su,TG and su,K, respectively). The experimental results (denoted

as su,JG in Figure 4.7) are fitted reasonably well with a = 0.17 [-] and b = 0.79 [-].

Figure 4.7: Profiles of the undrained shear strength obtained with the T-Bar during

test JG_v7 (su, JG_v7,A and su, JG_v7_B) compared with theoretical predictions based

on Trausch-Giudici (2003, su,TG) and on Küng (2003, su,K) and with the back-

calculated values of the parameters a and b (su,JG).

4.1.4 Summary of the back-calculated values of the shear strength parameters

a and b

Figure 4.8 shows the profiles of the back-calculated undrained shear strength for specimens

prepared in a full cylindrical strongbox (su,JG,1, σc = 100 kPa) and in adapted oedometers

(su,JG,2, σc = 100 kPa and su,JG,3, σc = 200 kPa). Table 4.2 shows a comparison of the back-

calculated values of the parameters a and b with those proposed by Trausch-Giudici (2003)

and Küng (2003).

The influence of the pre-consolidation on the undrained shear strength is clear as peak

values of about 27 kPa are reached for a pre-consolidation stress of 200 kPa, as opposed to

about 20 kPa for a pre-consolidation stress of 100 kPa.

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60

De

pth

[m

m]

su [kPa]

su2, K su1, TG su,A su,B su,Gsu,K su,TG su,JG_v7,A su,JG_v7,B su,JG


149

The impact of the vicinity of the rigid boundary to the location of the penetration of the T-Bar

is not as marked as that of the pre-consolidation stress but it can be noted as well, with an

increase in su of about 4 kPa from a specimen prepared in a full cylindrical strongbox to a

specimen prepared in an adapted oedometer. This can be explained by the fact that the

adapted oedometer has a smaller diameter (250 mm) than the strongbox (400 mm), inducing

a slightly higher constraint to the specimen. Although the over-consolidation of the soil is

taken into account by Equation 4.1, the pre-consolidation stress does seem to have an

influence on the value of factor a (Table 4.2).

Figure 4.8: Profiles of the back-calculated undrained shear strength for a specimen prepared

in a full cylindrical strongbox (su,JG,1) and in adapted oedometers (su,JG,2 and

su,JG,3).

Table 4.2: Comparison of the back-calculated values of the parameters a and b with those

proposed by Trausch-Giudici (2003) and Küng (2003).

a [-] b [-]

This work (σc = 100 kPa,

full cylindrical strongbox) 0.22 0.65


adapted oedometer) 0.22 0.79


adapted oedometer) 0.17 0.79

Trausch-Giudici (2003) 0.26 0.73

Küng (2003) 0.34 0.73

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

De

pth

[m

m]

su [kPa]

su,JG su,JG su,Gsu,JG,1 su,JG,2 su,JG,3

4.2 Pore pressure measurements conducted during the installation of stone columns

150

4.2 Pore pressure measurements conducted during the installation

of stone columns

4.2.1 Measurements conducted during the installation of a single stone

column

The PPTs from which the data discussed in the upcoming section were obtained were

located as follows:

- P1, P2 and P3 at a depth of 48 mm below the surface of the soft soil and at a

radial distance of 12 mm, 18 mm and 30 mm, from the axis of the column,

respectively,


radial distance of 12 mm, 18 mm and 30 mm, from the axis of the column,

respectively, and

- P7 at a depth of 140 mm below the surface of the soft soil and aligned with the

axis of the stone column.

The pore water pressures were measured continuously during the installation of stone

columns into the soft soil model. Both compacted and non-compacted columns were

installed, while pore pressure measurements were recorded at different radial distances to

the axis of the columns, depending on whether the test was conducted using a full cylindrical

strongbox or a specimen prepared in an oedometer container. The PPTs installed in

specimens prepared in (adapted) oedometers are significantly closer to the column than

those installed in the full cylindrical strongbox. Their reaction to the installation process is

therefore greater. Figure 4.9 presents the results from the installation of a compacted column

during test JG_v7 (specimen pre-consolidated up to 200 kPa in an adapted oedometer).

The transducers exhibit the greatest reaction during the installation phase when the tip of the

installation tool reaches the depth where they are installed (Figure 4.9 a, arrows 1 till 3). The

greatest reaction during the compaction phase occurs when the tip of the installation tool is

approximately 30 mm above the depth of the transducers (Figure 4.9 a, arrows 4 and 5). The

pore water pressures decrease rapidly once the tool is extracted from the model (Figure 4.9

a, arrow 6), as the load applied by the installation tool disappears.

Transducer P6 reacted slowly, which is the reason why no peak can be noted in Figure 4.9

(a). The arrows (7) till (9) in Figure 4.9 (b) mark the most important phases of the installation

process:

- the start of tool insertion into the model (arrow 7),

- the start of the compaction process (arrow 8),

- the removal of the tool from the model (arrow 9).


151

1,2,3: tip of

the installation

tool at the

depth of the

PPTs

4,5: tip of the

intsallation

tool about 30

mm above the

PPTs

6: extraction of

the installation

tool

(a)

7: start of the

insertion of the

installation

tool

8: start of the

compaction

phase

9: extraction of

the installation

tool

(b)

Figure 4.9: Installation of a compacted column in a specimen pre-consolidated up to 200 kPa

(test JG_v7) (a) pore water pressures (b) depth of the tip of the installation tool

with time.

The influence of the radial distance to the axis of the columns, as well as of the depth, can be

noted when considering the insertion phase (t = 0 s to t = 80 s in Figure 4.9) only

(Figure 4.10):

- the time needed for the transducers to react to column construction is longer with

increasing distance to the axis of the column. Figure 4.10 a (arrow 1) shows the

consecutive peak values of the excess pore water pressures measured by the

transducers P1, P2 and P3, marked with vertical dashed lines. This tendency is

more prone with increasing depth (arrow 2 for P4 and P5),

- the excess pore pressures caused by the installation of the stone column increase

with depth (Figure 4.10 a).

0

20

40

60

80

100

120

140

160

0 100 200 300 400 500

Po

re w

ate

r p

res

su

res

[k

Pa

]

Time [s]

P1 P2 P3 P4 P5 P6 P7

-140

-120

-100

-80

-60

-40

-20

0

0 100 200 300 400 500

De

pth

[m

m]

Time [s]

Depth P4 -P6

Depth P1 -P3

(1)

(2)

(3)

(4) (5)

(6)

(8)

(7) (9)


152

1: tip of the

installation

tool reaches

the depth of

P1

2: tip of the

installation

tool reaches

the depth of

P4

(a)

(b)


to 200 kPa (tests JG_v7) (a) excess pore water pressures (b) depth of the tip of

the installation tool with time.

Figure 4.11 shows the dissipation with time of the excess pore water pressures caused

by the installation of a stone column in a specimen pre-consolidated up to 200 kPa

(test JG_v7). The excess pore water pressures are dissipated after about 1500 s, which

shows the impact of the stone column on the consolidation time of the specimen. The time

needed for consolidation of a clay specimen, without a stone column, in-flight under 50 g can

be calculated as:

4.4

with t90 time needed to reach a consolidation of 90 %

Tv dimensionless time factor (equal to 0.848)

d length of the drainage path (80 mm at model scale, corresponding to 4 m at

prototype scale in this case)

cv coefficient of consolidation (equal to 2.5 . 10-7 m2/s, Table 3.3)

0

10

20

30

40

50

60

0 20 40 60 80

Ex

ce

ss

po

re w

ate

r p

res

su

res

[k

Pa

]

Time [s]

P1 P2 P3 P4 P5 P6 P7

-140

-120

-100

-80

-60

-40

-20

0

0 20 40 60 80

De

pth

[m

m]

Time [s]

Depth P4 -P6

Depth P1 -P3

(1)

(2)


153

The stone column causes a reduction of the consolidation time by a factor of about 15, which

is consistent with the reduction of the drainage path from 80 mm to 6 mm for the PPTs

closest to the column and to 24 mm for the PPTs furthest away from the column.


to 200 kPa (test JG_v7): excess pore water pressures.

The pre-consolidation stress plays a role regarding the magnitude of excess pore pressure

caused during the installation of the stone columns (Figure 4.10 a and Figure 4.12 a).

Figure 4.12 (a) shows that the general trend remains the same as for specimens with higher

OCRs. The time needed for the transducers to react is longer with increasing distance to the

axis of the column (arrows 1 and 2) and the time difference between the reactions of the

different sensors is more marked with increasing depth (arrows 1 and 2). The recorded peak

values by P4, P5 and P6 vary quite significantly even though the sequence of the reactions is

logical. This variation might be due to a lower stiffness of the back-fill of the cavity made for

the installation of the PPT in comparison with the host soil. The intensity of the excess pore

water pressures generated decreases with decreasing consolidation stress σc.

0

20

40

60

80

100

120

140

160

0 1000 2000 3000 4000 5000

Po

re w

ate

r p

res

su

res

[k

Pa

]

Time [s]

P1 P2 P3 P4 P5 P6 P7


154

1: tip of the

installation

tool reaches

the depth of

P1

2: tip of the

installation

tool reaches

the depth of

P4

(a)

(b)


to 100 kPa (test JG_v9) (a) excess pore water pressures (b) depth of the tip of

the installation tool with time.

4.2.2 Measurements conducted during the installation of a stone column

group


located as follows:


radial distance of 12 mm, 18 mm and 30 mm, from the axis of the centre column,

respectively,



respectively, and

0

10

20

30

40

50

60

0 20 40 60 80

Ex

ce

ss

po

re w

ate

r p

res

su

res

[k

Pa

]

Time [s]

P1 P2 P3 P4 P5 P6 P7

-140

-120

-100

-80

-60

-40

-20

0

0 20 40 60 80

De

pth

[m

m]

Time [s]

Depth P4 -P6

Depth P1 -P3

(1)

(2)


155

- P7 at a depth of 65 mm below the surface of the soft soil and at a radial distance

of 18 mm from the axis of the centre column.

1: Installation

of column A

2: Installation

of column B

3: Installation

of column C

4: Installation

of column D

5: Installation

of column E

(a)

(b)


100 kPa (test JG_v10) (a) excess pore water pressures (b) location of the stone

columns installed.

Figure 4.13 shows the evolution of the excess pore water pressures over time during the

installation of a stone column group (test JG_v10). The reason for the development of

negative excess pore pressures at the location of P5 during the installation of the column D

is unknown, but might be due to movement of the columns A and C caused by the

compaction process of column D.

0

20

40

60

80

100

0 500 1000 1500 2000 2500 3000 3500

Po

re w

ate

r p

res

su

res

[k

Pa

]

Time [s]

P1 P2 P3 P4 P5 P6

aaa

aaa

(1) (2) (3) (4) (5)

4.3 Measurements conducted during the footing loading of a single stone column installed in

a specimen prepared in a full cylindrical strongbox

156

The transducers show a greater reaction to the installation of column A, which is due to the

vicinity of this inclusion and to the orientation of the filter plate of the PPTs towards the centre

of the specimen. The reaction of the PPTs to the installation of the subsequent columns,

as well as the rate of dissipation of the excess pore water pressures after the installation

(Figure 4.13 a), is similar for columns B, C, D and E. The excess pore water pressures

caused by the installation of the stone column group are dissipated after about 1000 s

(Figure 4.14), which is faster than in the case of a single stone column and shows the

increased drainage performance of a stone column group, compared to a single stone

column.


100 kPa (test JG_v10): excess pore water pressures.

4.3 Measurements conducted during the footing loading of a single

stone column installed in a specimen prepared in a full

cylindrical strongbox

The measurements presented here were performed in specimens prepared in the full

cylindrical strongbox (400 mm diameter). The PPTs from which the data discussed in the

upcoming section were obtained were located as follows:

- P1, P2 and P3 at radial distance of 262 mm from the loaded column and a depth

of 60 mm, 85 mm and 110 mm from the surface of the soft soil specimen,

respectively,

- P4 and P6 at a radial distance of 56 mm from the loaded column and a depth of

85 mm from the surface of the soft soil specimen,

- P5 and P7 at radial distance of 56 mm from the loaded column and a depth of

60 mm and 110 mm from the surface of the soft soil specimen, respectively.

0

20

40

60

80

100

0 1000 2000 3000 4000 5000 6000 7000

Po

re w

ate

r p

res

su

res

[k

Pa

]

Time [s]

P1 P2 P3 P4 P5 P6


157

The values recorded by transducers P1, P2 and P3 are not discussed here due to the

distance of the PPTs from the footing. Figure 4.15 (a), (b) and (c) show the recordings of the

PPTs P4 to P7, the load-settlement curve and the settlement-time curve recorded during test

JG_v2. The data obtained during test JG_v6 are presented graphically in Appendix 8.3. The

quantitative values are shown in Table 4.3 and Table 4.4.

The ratios of the peak value of the recorded excess pore pressure to the peak value of the

applied footing load (Δumax / Pmax) recorded by the transducers P6 and P7 remain remarkably

constant between test JG_v2 and test JG_v6 (12.52 % and 13.47 % for P6 and 6.17 % and

6.42 % for P7).


test JG_v2.

PPT

Maximal excess

pore water pressure

Δumax [kPa]

Maximal load

applied on the

footing Pmax [kPa]

Δumax / Pmax [%]

P4 (z = 85 mm) 7.64 94.72 8.07

P5 (z = 60 mm) 6.02 94.72 6.36

P6 (z = 85 mm) 11.86 94.72 12.52

P7 (z = 110 mm) 5.84 94.72 6.17


the test JG_v6.

PPT

Maximal excess

pore water pressure

Δumax [kPa]

Maximal load

applied on the

footing Pmax [kPa]

Δumax / Pmax [%]

P4 (z = 85 mm) 16.59 115.22 14.40

P5 (z = 60 mm) 3.50 115.22 3.04

P6 (z = 85 mm) 15.52 115.22 13.47

P7 (z = 110 mm) 7.40 115.22 6.42


a specimen prepared in a full cylindrical strongbox

158

(a)

(b)

(c)


(test JG_v2) (a) excess pore water pressures (b) evolution of the footing load

(c) deformation controlled footing settlement.

0

2

4

6

8

10

12

14

0 200 400 600 800 1000

Ex

ce

ss

po

re w

ate

r p

res

su

re

[kP

a]

Time [s]

P4 P5 P6 P7

0

10

20

30

40

50

60

70

80

90

100

0 200 400 600 800 1000

Fo

oti

ng

lo

ad

ing

[k

Pa

]

Time [s]

-20

-15

-10

-5

0

0 200 400 600 800 1000

Fo

oti

ng

se

ttle

me

nt

[mm

]

Time [s]


159

4.4 Measurements conducted during the footing loading of a single

stone column installed in a specimen prepared in an (adapted)

oedometer container


located at the same positions as presented in Section 4.2.

4.4.1 Measurements conducted in a specimen consolidated up to

σ’v = 100 kPa

Figure 4.16 and Table 4.5 present the results of the measurements conducted during the

loading of a single column installed in a clay specimen that has been consolidated up to

100 kPa in an adapted oedometer (test JG_v9). The influence of the installation depth can be

noted as a decrease of the measured excess pore water pressures ranging from 40 % to

55 % can be observed between the PPTs installed at 48 mm depth (P1, P2 and P3) and

those installed at a depth of 96 mm (P4, P5 and P6).

More interesting is the influence of the radial distance to the axis of the column. P1 and P2

show a similar response to the applied load (0.35 Pmax and 0.37 Pmax, respectively) while P3

displays a significantly smaller reaction (0.27 Pmax). The same trend can qualitatively be

observed at a greater depth, although the quantitative reactions are less pronounced, as P4

and P5 record a peak excess pore pressure of about 0.24 Pmax and P6 only of 0.20 Pmax.

P7, installed directly below the column at a depth of 140 mm, records a peak excess pore

pressure of 0.11 Pmax. However, the influence of the lost tip of the stone column onto the

drainage is very difficult to quantify.


the test JG_v9.

PPT

Maximal excess

pore water pressure

Δumax [kPa]

Maximal load

applied on the

footing Pmax [kPa]

Δumax / Pmax [%]

P1 (z = 48 mm) 42.23 119.67 35.28

P2 (z = 48 mm) 44.41 119.67 37.11

P3 (z = 48 mm) 33.33 119.67 27.85

P4 (z = 96 mm) 29.21 119.67 24.41

P5 (z = 96 mm) 28.67 119.67 23.96

P6 (z = 96 mm) 23.80 119.67 19.89

P7 (z = 140 mm) 13.46 119.67 11.25


a specimen prepared in an (adapted) oedometer container

160

(a)

(b)

(c)


(test JG_v9) (a) excess pore water pressures (b) evolution of the footing load (c)

deformation controlled footing settlement.

0

10

20

30

40

50

0 500 1000 1500 2000 2500

Ex

ce

ss

po

re w

ate

r p

res

su

re

[kP

a]

Time [s]

P1 P2 P3 P4 P5 P6 P7

0

20

40

60

80

100

120

140

0 500 1000 1500 2000 2500

Fo

oti

ng

lo

ad

ing

[k

Pa

]

Time [s]

-20

-15

-10

-5

0

0 500 1000 1500 2000 2500

Fo

oti

ng

se

ttle

me

nt

[mm

]

Time [s]


161

Figure 4.17 and Figure 4.18 show the dissipation with time of the excess pore water

pressures after reaching the peak footing load at depths of 48 mm and 96 mm, respectively.

In both cases, an accelerated dissipation can be noted 250 s after reaching the peak footing

load (which corresponds to t = 0 s). The influence of the stone column on the drainage length

is visible in the magnitude of the dissipation of the excess pore water pressure: a diminution

of approximately 17 kPa is measured, at a depth of 48 mm, 6 mm and 12 mm from the edge

of the stone column, while this reduction is only about 11 kPa, when measured 24 mm away

from the edge of the column.

(a)

(b)


(test JG_v9), dissipation with time of the excess pore water pressures at a depth

of 48 mm around the stone column (a) from 0 s to 2000 s and (b) from 3000 s to

9000 s after reaching the peak footing load (which corresponds to t = 0 s).

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40Ex

ce

ss

po

re w

ate

r p

res

su

res

[k

Pa

]

Radial distance [mm]

t = 0 s t = 250 s t = 500 s t = 750 st = 1000 s t = 1500 s t = 2000 s

Edge of the stone column

0

1

2

3

4

5

6

7

8

9

10

0 10 20 30 40Ex

ce

ss

po

re w

ate

r p

res

su

res

[k

Pa

]


t = 3000 s t = 4000 s t = 5000 s t = 6000 st = 7000 s t = 8000 s t = 9000s




162

A similar observation can be made at a depth of 96 mm as a reduction of approximately

8.5 kPa is measured 6 mm and 12 mm from the edge of the column while this is only 7.5 kPa

at a location of 24 mm from the edge of the column. A pseudo-constant rate of dissipation is

reached 2000 s after the peak footing load has been applied.

(a)

(b)


(test JG_v9): dissipation of the excess pore water pressures at a depth of

96 mm with time around the stone column (a) from 0 s to 2000 s and (b) from

3000 s to 9000 s after reaching the peak footing load (which corresponds to

t = 0 s).

These observations are confirmed by consideration of the evolution of the rate of dissipation

of excess pore water pressures over time after the peak footing load has been applied

(Figure 4.19): the rate drops from approximately 0.07 kPa /s (transducers P1 and P2), 0.045

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40Ex

ce

ss

po

re w

ate

r p

res

su

res

[k

Pa

]


t = 0 s t = 250 s t = 500 s t = 750 st = 1000 s t = 1500 s t = 2000 s


0

1

2

3

4

5

6

7

8

9

10

0 10 20 30 40Ex

ce

ss

po

re w

ate

r p

res

su

res

[k

Pa

]


t = 3000 s t = 4000 s t = 5000 s t = 6000 st = 7000 s t = 8000 s t = 9000s



163

kPa /s (transducer P3) and 0.03 kPa /s (transducers P4, P5 and P6) immediately after the

peak footing has been reached (t = 0 s) to values of approximately 0.01 kPa / s at t = 1000 s.

The rate of dissipation reaches a pseudo-constant state at about t = 2000 s after the peak

footing load was applied.


(test JG_v9): rate of dissipation of excess pore water pressures with time after

reaching the peak footing load (which corresponds to t = 0 s).

4.4.2 Measurements conducted in a specimen consolidated up to

σ’v = 200 kPa

Table 4.6 and Figure 4.20 present the results of the measurements conducted during the

loading of a single column installed in a clay specimen consolidated up to 200 kPa in an

adapted oedometer (250 mm in diameter, test JG_v7).

Similar loadings were conducted during tests JG_v1 and JG_v5, in which specimens were

pre-consolidated up to 200 kPa in an oedometer (250 mm in diameter) and subsequently

transferred into a cylindrical strongbox (400 mm in diameter). The gap was filled with

compacted sand. The results of the tests JG_v1 and JG_v5 are presented graphically in

Appendices 8.1 and 8.2. Quantitative results are summarised in Table 4.7 and Table 4.8.

The relative difficulty in assessing the influence of the manual steps of the preparation of the

specimen consolidated in an oedometer and installed in the cylindrical strongbox, as well as

of the boundary conditions on the loading behaviour, has to be kept in mind when

considering the results of tests JG_v1 and JG_v5.

Figure 4.20 (a) shows that the installation depth of the transducers and the radial distance to

the axis of the column have a great influence on the recorded excess pore water pressure

due to the footing load as the drop of the values of the excess pore water pressures caused

by the footing loading ranges from 20 % to 45 % between 48 mm and 96 mm. This drop is

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Δu

/ Δ

t [k

Pa

/s]

Time [s]

P1 P2 P3 P4 P5 P6



164

less important than in the case of a specimen pre-consolidated up to 100 kPa, which

indicates a higher load transfer into depth with increasing pre-consolidation stress. This can

be explained by the higher stiffness of the host soil. However, as for the case of the loading

on a single stone column, installed in a specimen pre-consolidated up to 100 kPa, the radial

distance to the axis of the column plays an important role in the measurements, as the

excess pore water pressures are significantly higher near the edge of the stone column than

further off (Table 4.6).

The increase of pre-consolidation stress from 100 kPa (test JG_v9) to 200 kPa (test JG_v7)

causes a jump of the maximal applied load of 21.5 %. The observations made during the

loading of a stone column installed in a specimen consolidated up to 100 kPa are also valid

here. The ratios Δumax / Pmax are remarkably similar (Table 4.5 and Table 4.6), independently

of the over-consolidation of the specimen and of the load applied at the surface.


test JG_v7 (adapted oedometer).

PPT

Maximal excess

pore water pressure

Δumax [kPa]

Maximal load

applied on the

footing Pmax [kPa]

Δumax / Pmax [%]

P1 (z = 48 mm) 51.31 145.44 35.28

P2 (z = 48 mm) 50.86 145.44 34.97

P3 (z = 48 mm) 35.62 145.44 24.49

P4 (z = 96 mm) 36.57 145.44 25.14

P5 (z = 96 mm) 35.24 145.44 24.23

P6 (z = 96 mm) 29.66 145.44 20.39

P7 (z = 140 mm) 24.00 145.44 16.50


test JG_v1 (cylindrical strongbox with clay surrounded by sand).

PPT

Maximal excess

pore water pressure

Δumax [kPa]

Maximal load applied

on the footing Pmax

[kPa]

Δumax / Pmax [%]

P1 (z = 48 mm) 21.66 80.00 27.08

P2 (z = 48 mm) 16.72 80.00 20.90

P3 (z = 48 mm) 11.33 80.00 14.16

P4 (z = 96 mm) 18.41 80.00 23.01

P5 (z = 96 mm) 13.92 80.00 17.40

P6 (z = 96 mm) 17.67 80.00 22.09

P7 (z = 140 mm) 11.77 80.00 14.71


165

(a)

(b)

(c)


(JG_v7) (a) excess pore water pressures (b) evolution of the footing load (c)

deformation controlled footing settlement.

0

10

20

30

40

50

60

0 500 1000 1500 2000 2500

Ex

ce

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ate

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res

su

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[kP

a]

Time [s]

P1 P2 P3 P4 P5 P6 P7

-20

0

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100

120

140

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0 500 1000 1500 2000 2500

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m]

Time [s]



166


test JG_v5 (cylindrical strongbox with clay surrounded by sand).

PPT

Maximal excess

pore water pressure

Δumax [kPa]

Maximal load applied

on the footing Pmax

[kPa]

Δumax / Pmax [%]

P1 (z = 48 mm) 42.24 120.14 35.16

P2 (z = 48 mm) 35.05 120.14 29.17

P3 (z = 48 mm) 17.22 120.14 14.33

P4 (z = 96 mm) 23.46 120.14 19.53

P5 (z = 96 mm) 22.40 120.14 18.65

P6 (z = 96 mm) 19.67 120.14 16.37

P7 (z = 140 mm) 15.33 120.14 12.76

The difference between the applied footing loads is due to specimen disturbance during the

preparation. Test JG_v1 was the first to be conducted using specimens prepared in

oedometer containers and then transferred to the cylindrical centrifuge strongbox. Thus the

results need to be treated with caution. The specimen preparation procedure was not

completely controlled, which complicates any quantitative conclusion about the loading

behaviour during this test.

This disturbance was reduced to a minimum for test JG_v5. The ratios of the maximal

excess pore water pressures to the applied footing load for this test show a good agreement

with the results from test JG_v7. The peak load reaches values close to those obtained

during test JG_v9 (Pmax = 119.67 kPa), conducted with a specimen prepared in an adapted

oedometer and pre-consolidated up to 100 kPa.

The rigid, oedometric, lateral boundary conditions in test JG_v7 lead to an increase of the

maximal footing load applied by 21 %, compared to equivalent results from test JG_v5.

4.4.3 Comparison of the results

Similarities and differences appear when comparing the distribution of the excess pore water

pressure during footing loading for the tests JG_v1, JG_v5, JG_v7 and JG_v9. The influence

of the specimen disturbance on the results of test JG_v1 is significant when considering the

results obtained at a depth of 48 mm (Table 4.7), as the ratios of excess pore water pressure

to footing load are significantly lower than for the other tests at a radial distance of 12 mm

and 18 mm from the axis of the stone column. Although these ratios are close to those

measured during the other tests at higher depths, the quantitative influence of the specimen

disturbance is unclear and the results of test JG_v1 will not be discussed in greater detail.

The influence of the different drainage conditions is also noticeable. The ratio of excess pore

water pressure to footing load is similar for the tests JG_v5, JG_v7 and JG_v9 at a distance

of 12 mm from the axis of the stone column. This confirms the limited disturbance of the

specimen caused by the installation of the specimen from the oedometer container into the


167

strongbox for the preparation of test JG_v5. However, the ratios of excess pore water

pressure to applied load tend to remain constant between 12 mm and 18 mm from the axis

of the column for the cases of rigid and impermeable boundaries of the clay specimen

(tests JG_v7 and JG_v9), while this ratio drops significantly in case of non-rigid and

permeable boundaries (interface clay / sand for test JG_v5).

The impact of the over-consolidation on the ratio of excess pore water pressure to footing

load is, on the contrary very limited, as the difference between the results of tests JG_v7

(σc = 200 kPa) and JG_v9 (σc = 100 kPa) are very similar.


the axis of the stone column at a depth of 48 mm as a percentage of the applied

footing load P.

Figure 4.22 shows the distribution of the excess pore water pressure around the stone

column at a depth of 96 mm. The outcomes of tests JG_v7 (σc = 200 kPa) and JG_v9 (σc =

100 kPa) can be considered to be equal at this location as the difference in the ratios of

excess pore water pressure to applied footing load at a given radial distance from the axis of

the column does not exceed 5%, which confirms that the impact of the over-consolidation

ratio on the distribution of the excess pore water pressure is very limited. However, the

impact of the drainage conditions is clear as the normalised values recorded during

test JG_v5 lie about 5 % below those recorded during tests JG_7 and JG_v9.

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30

No

rma

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% P

]


JG_v5 JG_v7 JG_v9




168


the axis of the stone column at a depth of 96 mm as a percentage of the applied

footing load P.

4.4.4 Load transfer around a single stone column

The load transfer around a single stone column can be investigated based on data collected

during the centrifuge tests. The first step is a comparison of the excess pore water pressures

recorded with the values obtained theoretically, for the case of a vertical footing load applied

on a homogeneous and isotropic host soil, in order to assess the influence of the granular

inclusion on the load spreading. A second step consists of a back-calculation of the vertical

total stress increments based on the pore water pressure measurements.

Grasshoff (1978) proposed a model to assess the distribution of the vertical stresses in soil

under a loaded circular plate. This model relies on the assumption that the soil behaviour

remains elastic throughout loading, that means the stresses are proportional to the strains,

and that the soil is homogeneous and isotropic. Grasshoff (1978) suggests that the vertical

stress increment can be calculated using a factor J4 (a table of the values of this factor is

given in Appendix 8.4), as follows:

4.5

with Δσz vertical stress increase

J4 depth factor according to Grasshoff (1978)

P footing load

The excess pore water pressures recorded during the centrifuge tests can be compared with

a back-calculation of the excess pore water pressures caused by a vertical load on a

homogeneous and isotropic host soil.

0

5

10

15

20

25

30

0 5 10 15 20 25 30No

rma

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]


JG_v5 JG_v7 JG_v9



169

Figure 4.23: Isobars of vertical stress increments under a vertically loaded quadratic plate

(Lang et al., 2007).

Skempton (1954) formulates the following expression for the assessment of the excess pore

water pressures in a known stress field:

( ) 4.6

with Δu excess pore water pressure

A, B pore pressure parameters according to Skempton (1954)

σr radial stress

σa axial stress

It is assumed that the radial stress σr is equal to the horizontal stress σh and that the axial

stress σa is equal to the vertical stress σv. Equation 4.6 can thus be formulated as:

( ) 4.7

with Δσh horizontal stress increment

Δσv vertical stress increment

The coefficient of earth pressure at rest K0 needs to be assessed in order to calculate the

horizontal stress increase Δσh. Mayne & Kulhawy (1982) suggest the following formula in

order to take the over-consolidation into account for the determination of K0:

4.8







170

It is necessary to determine the over-consolidation ratio OCR to calculate the excess pore

water pressure at the installation depths of the PPTs. The values obtained are summarised

in Table 4.9, although they do not take the additional consolidation due to the installation of

the stone column into account. A linear distribution of stress over depth in the specimen is

assumed.

Table 4.9: Calculation of the over-consolidation ratio at the installation depths of the PPTs

depending on the pre-consolidation stress σc.

Depth

[mm]

Unit weight of saturated

host soil γg [kN/m3]

Vertical stress under

enhanced gravity

σ’z,centrifuge[kPa]

OCR [-]

σc = σ’v.max =

100 kPa

σc = σ’v.max =

200 kPa

σc = σ’v.max =

100 kPa

σc = σ’v.max =

200 kPa

σc = σ’v.max =

100 kPa

σc = σ’v.max =

200 kPa

48 18.5 20.1 20.4 24.24 4.90 8.25

96 18.5 20.1 40.8 48.48 2.45 4.13

140 18.5 20.1 59.5 70.70 1.68 2.83

The effective angle of friction of the Birmensdorf clay is =24.5° (Table 3.2) and K0NC = 1 -

sin . The values of K0OC are summarised in Table 4.10.

Table 4.10: Coefficients of earth pressure at rest of the over-consolidated Birmensdorf clay

with depth.

Depth

[mm]

OCR [-] K0

NC [-] K0

OC [-]

σc = 100 kPa σc = 200 kPa σc = 100 kPa σc = 200 kPa

48 4.90 8.25 0.585 1.13 1.40

96 2.45 4.13 0.585 0.848 1.05

140 1.68 2.83 0.585 0.725 0.901

With Δσh = K0OC Δσv’ + Δu, Equation 4.6 can be rewritten as:

[

( )

] 4.9

Equation 4.9 can be reformulated as:

(

( ))

4.10

Skempton (1954) suggests a value of B equal to 1 for fully saturated soils submitted to fully

undrained loading. The parameter B defines the portion of the total surcharge converted into

excess pore water pressure. The value of the parameter A should ideally be determined

experimentally. Good approximations are summarised in Table 4.11, depending on the type

of clay. The values of A used in Table 4.12, Table 4.13 and Table 4.14 were set in order to

take the influence of the variation of the over-consolidation ratio with depth into account.


171

Table 4.11: Values of the pore pressure parameter A depending on the type of clay

(Skempton, 1954).

Type of clay A

Clays of high sensitivity 0.75 – 1.5

Normally consolidated clays 0.5 – 1

Compacted sandy clays 0.25 – 0.75

Lightly over-consolidated clays 0 – 0.5

Compacted clay-gravels -0.5 – 0.25

Heavily over-consolidated clay -0.5 – 0

Equation 4.10 can thus be reformulated, using Equation 4.5 as:

( ) (

( ))

4.11

Reformulating Equation 4.11 gives an expression of the excess pore water pressure Δu:

(

( ))

( (

) ) 4.12

This formulation allows the excess pore water pressure caused by a vertical load applied at

the surface of a homogeneous isotropic host soil to be calculated. The results are presented

in Table 4.12, Table 4.13, Table 4.14 and Table 8.2. The parameter B was set equal to 0.8 in

order to take the partial dissipation of excess pore water pressures during the loading phase

into account. The parameter A was varied in order to take the variation of over-consolidation

with depth into account. The peak values of the excess pore water pressures estimated with

Equation 4.11 are denoted as ΔuSkempton, while the peak values measured during the

centrifuge tests are denoted as Δucentrifuge.

The manual manipulation necessary for the insertion of the PPTs and the installation of the

specimen into the strongbox during test JG_v1 was relatively cumbersome, which led to

significant disturbance of the specimen. The results are summarised in Appendix 8.5, but will

not be investigated in further detail in this section.

The influence of the stone column on the load distribution with depth can clearly be noted as

the ratio increases from values close to one at a depth of 48 mm, to values between 2 and 3

at a depth of 96 mm. A significantly higher part of the load is transmitted at depths of 96 mm

and 140 mm in the presence of the granular inclusion, compared to the case where a vertical

load is applied at the surface of a homogeneous isotropic fine-grained host soil.



172


end of the loading phase of a single stone column (test JG_v9, σc = 100 kPa,

P = 119.67 kPa).

PPT J4 [%]

Δσa = Δσz

= J4 P

[kPa]

A [-] ΔuSkempton [kPa] Δucentrifuge [kPa] Δucentrifuge /

ΔuSkempton [-]

P1 32.30 38.65 0.3 38.65 42.23 1.09

P2 29.13 34.86 0.3 34.86 44.41 1.27

P3 21.45 25.67 0.3 25.67 33.33 1.30

P4 11.45 13.70 0.4 13.70 29.21 2.13

P5 11.03 13.20 0.4 13.20 28.67 2.17

P6 9.73 11.64 0.4 11.64 23.80 2.04

P7 5.70 6.82 0.4 6.82 13.46 1.97



P = 145.44 kPa).

PPT J4 [%]

Δσa = Δσz

= J4 P

[kPa]


ΔuSkempton [-]

P1 32.30 46.98 0.1 39.68 51.31 1.29

P2 29.13 42.37 0.1 35.79 50.86 1.42

P3 21.45 31.20 0.1 26.36 35.62 1.35

P4 11.45 16.65 0.2 13.42 36.57 2.73

P5 11.03 16.04 0.2 12.93 35.24 2.73

P6 9.73 14.15 0.2 11.41 29.66 2.60

P7 5.70 8.29 0.2 6.52 24.00 3.68



P = 120.14 kPa).

PPT J4 [%]

Δσa = Δσz

= J4 P

[kPa]


ΔuSkempton [-]

P1 32.30 38.81 0.1 32.78 42.24 1.29

P2 29.13 35.00 0.1 29.57 35.05 1.19

P3 21.45 25.77 0.1 21.77 17.22 0.79

P4 11.45 13.76 0.2 11.09 23.46 2.12

P5 11.03 13.25 0.2 10.68 22.40 2.10

P6 9.73 11.69 0.2 9.42 19.67 2.09

P7 5.70 6.85 0.2 5.39 15.33 2.84


173

An influence of the over-consolidation ratio on the response of the composite foundation to

vertical loading can be detected. The ratios Δucentrifuge / ΔuSkempton range from 1.29 to 1.42 at a

depth of 48 mm for a specimen consolidated up to 200 kPa (test JG_v7, Table 4.13), while

they only reach values ranging from 1.09 and 1.30 at the same depth for a specimen

consolidated up to 100 kPa (test JG_v9, Table 4.12). This shows that the higher stiffness of

the host soil caused by the higher pre-consolidation of the specimen reduces the stress

concentration on top of the column and causes a higher load of the host soil. This effect

remains present with increasing depth as the ratios Δucentrifuge / ΔuSkempton range from 2.60 to

2.73 at a depth of 96 mm for a specimen consolidated up to 200 kPa (test JG_v7,

Table 4.13) while they only reach values comprised between 2.04 and 2.17 for a specimen

consolidated up to 100 kPa (test JG_v9, Table 4.12).

Although assumptions had to be made, these results provide a first insight into the load

distribution under a vertically loaded footing placed on stone column in comparison with a

uniform load applied on an isotropic soil. Back-calculation of the total vertical stress increase

based on the recorded excess pore water pressures was conducted to circumvent this issue.

Figure 4.24 shows isobars of the recorded peak excess pore water pressures during

application of the footing load onto the composite foundation, as percentage of the applied

footing load P. The isobars were evaluated as an average of the measurements recorded

during the centrifuge tests JG_v5, JG_v7 and JG_v9. Due to irregularities in the construction

of the columns, a direct evaluation of the percentage of load transmitted to the column and to

the host soil is not possible. A good example of the reasons for this can be seen in Figure

4.27:

- an excess of sand was poured in columns B, D and E, which could not be

compacted and remained on the clay surface as a heap of dry sand, which was

subsequently pushed into the host soil by the footing during loading,

- column C was not filled up to the surface, causing a closure of the unfilled cavity

during the loading phase.

As a consequence, no ideal case, in which the top of the column coincides with the surface

of the soft soil specimen, could be reached.

Although the stress distribution directly underneath the footing could not be accurately

measured, the impact of the stone column on the load distribution with depth can be

identified by comparing the isobars of the peak values of the excess pore water pressures

measured under a vertically loaded circular footing (Figure 4.24) with the distribution of the

vertical stress increments caused by loading a circular footing of same dimensions and

resting on a homogeneous soil (Figure 4.25). The stone column causes a transfer of the load

applied on the surface into greater depths compared to a homogeneous soil.



174


under a vertically loaded circular footing resting on top of a stone column.

Figure 4.25: Isobars of vertical stress increments under a vertically loaded circular footing

(after Grasshoff, 1978).

The distribution of the total vertical stress increment can be reformulated, using Equation

4.12, as a function of the excess pore water pressure recorded with depth:

[ (

( ) )]

[ (

) ] 4.13

with Δσz vertical stress increase

A, B pore pressure parameters according to Skempton (1954)

Δu recorded excess pore water pressure during the centrifuge tests

K0OC coefficient of earth pressure at rest of an over-consolidated soil


175


The results obtained are presented in Table 4.15, both as absolute values and relative to the

applied footing load P. The values of the parameter A assumed are shown in Table 4.12 and

Table 4.13, and those of K0OC in Table 4.10. B was set to 0.8, as before.

Due to the influence of the lateral loading applied through the lateral deformation of the stone

column at the depth of the transducers P1 to P3, the back-calculation was limited to the

deeper PPTs (P4 to P6, installed at a depth of 96 mm below the surface). The radial

deformation of the granular inclusion due to the footing load may be assumed to be

negligible at that depth, so that the coefficient of earth pressure K0OC may be used, although

transducer P4 is within the compaction zone.

Table 4.15: Back-calculated values of the vertical stress increases at the locations of the

PPTs P4, P5, P6 and P7 for tests JG_v1, JG_v5, JG_v7 and JG_v9.

PPT

Δσa = Δσz

Test JG_v1

(P = 80 kPa)

Test JG_v5

(P = 120.14 kPa)

Test JG_v7

(P = 145.44 kPa)

Test JG_v9

(P =119.67 kPa)

[kPa] [% P] [kPa] [% P] [kPa] [% P] [kPa] [% P]

P4 22.83 28.54 29.10 24.22 45.36 31.19 37.38 31.24

P5 17.26 21.58 27.78 23.13 43.71 30.05 36.69 30.66

P6 21.92 27.40 24.40 20.31 36.79 25.30 30.46 25.45

P7 14.97 18.71 19.49 16.22 30.51 20.98 17.63 14.73

Figure 4.26: Distribution of the total vertical stress increase as a function of the radial

distance from the stone column at 96 mm depth as a percentage of the applied

footing load P, and in comparison with the depth factor J4 according to Grasshoff

(1978).

0

5

10

15

20

25

30

35

0 5 10 15 20 25 30

Δσ

z[%

P]


JG_v5 JG_v7 JG_v9 J4 J4J4


4.5 Measurements conducted during the footing load of a stone column group

176

Figure 4.26 shows a graphical representation of the values obtained. The qualitative stress

distribution caused by the footing load (Figure 4.26) is similar in all cases and indicates the

transmission of load by the stone column into deeper areas of the host soil (Figure 4.26).

The load transfer behaviour becomes even more visible by comparing the coefficients J4 for

the locations of transducers P4, P5, P6 and P7 with the back-calculated values of the vertical

stresses (Figure 4.26). The load transmitted increases by a factor of almost 3 due

to the stone column when the boundary conditions of the specimen are rigid (tests JG_v7

and JG_v9). Comparing the results obtained from tests JG_v7 (σc = 200 kPa) and

JG_v9 (σc = 100 kPa) shows that the OCR does not affect the percentage of the load applied

on the surface which is transmitted into depth.

4.5 Measurements conducted during the footing load of a stone

column group

Three tests have been conducted with groups of stone columns: tests JG_v8 (1 container)

and JG_v10 (2 containers). However, some issues occurred:

- an uneven sand layer formed between the surface of the soft soil specimen and

the footing during construction of the stone columns in test JG_v8 (Figure 4.27,

Section 4.5.1). Thus, the quantitative results of this test should be considered with

care, as the exact stress distribution directly under the footing is not clear,

- the stone column installation tool clogged in one specimen during test JG_v10

(a / dsc = 2.5) during the installation of the first two columns of the group (columns

A and B, Figure 3.51). The installation of the rest of the inclusions was abandoned

and no loading phase was conducted. The specimen was solely used to conduct

site investigation using a T-Bar (curve denoted as su,JG_v10,B in Figure 4.4).


located as follows:



respectively,



respectively, and

- P7 at a depth of 55 mm below the surface of the soft soil and at a radial distance

of 18 mm from the axis of the centre column.

4.5.1 Test JG_v8 (a / dsc = 2 [-])

The results of the measurements conducted, while the stone column group (a / dsc = 2 [-])

was loaded during test JG_v8, are presented in Figure 4.28 and in Table 4.16. Transducer


177

P4 was located 150 mm away from the axis of the centre column in test JG_v8, as opposed

to 12 mm from the axis of the centre column during test JG_v10.

The load-settlement behaviour (Figure 4.28 b) turns out to be pseudo-linear. This can be

explained by the fact that too much sand was poured into the installation tool for columns B,

D and E (Figure 4.27), which meant that the excess that could not be compacted into the

cylindrical hole in the host soil remained on the surface as a heap of dry sand on top of these

three columns. These heaps were pressed into the clay by the footing, thus forming a sand

layer between the footing and the clay. On the contrary, not enough sand was poured in for

the construction of column C, which caused an empty cavity between top of the column and

surface of the soft soil specimen.

Figure 4.27: Excess sand shown on top of columns B, D and E within the footprint of the

footing on the surface of the clay model after test JG_v8.

The installation depth of the transducers influences the response time of their reaction to

loading. P1, P2 and P3 exhibit the fastest reaction, while the time needed for P5 and P6 to

react is significantly longer. The response time of P7 is between that of P2 and that of P5,

which makes sense given the fact that P2 is installed 30 mm, P7 55 mm and P5 80 mm

under the surface of the clay specimen.

Column B Column C

Column DColumn E

Column A


178

(a)

(b)

(c)


(JG_v8) (a) excess pore water pressures (b) evolution of the footing load

(c) deformation controlled footing settlement.

0

10

20

30

40

50

0 500 1000 1500Ex

ce

ss

po

re w

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r p

res

su

re

[kP

a]

Time [s]

P1 P2 P3 P4 P5 P6 P7

0

20

40

60

80

100

120

140

0 500 1000 1500

Fo

oti

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lo

ad

ing

[k

Pa

]

Time [s]

-20

-15

-10

-5

0

0 500 1000 1500

Fo

oti

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ttle

me

nt

[mm

]

Time [s]


179


test JG_v8.

PPT

Maximal excess

pore water pressure

Δumax [kPa]

Maximal load

applied on the

footing Pmax [kPa]

Δumax / Pmax [-]

P1 (z = 30 mm) 43.52 124.01 35.09

P2 (z = 30 mm) 31.44 124.01 25.35

P3 (z = 30 mm) 34.14 124.01 27.53

P4 (z = 80 mm) 5.39 124.01 4.35

P5 (z = 80 mm) 27.98 124.01 22.56

P6 (z = 80 mm) 27.22 124.01 21.95

P7 (z = 55 mm) 33.05 124.01 26.65

Table 4.16 shows that the differences in magnitude of excess pore water pressure generated

by the footing load are less distinct with depth than when loading a single stone column

(Section 4.4). The ratio Δumax / Pmax drops in this case solely by 15 % to 25 % between

a depth of 30 mm and 80 mm, as opposed to a drop of about 40 to 55 % from a depth of

48 mm to 96 mm for a single stone column (Table 4.5). This would suggest a different load

transfer mechanism for a single stone column compared with a group of stone columns as a

larger part of the load applied to the surface is transferred to depth in this particular group of

stone columns. Due to the issues encountered during the installation of the stone columns

during this test, however, the interpretation will be conducted based on the results from

test JG_v10.

4.5.2 Test JG_v10 (a / dsc = 2 [-])

The results of the measurements conducted during the loading phase of the stone column

group (a / dsc = 2 [-]) for test JG_v10 are presented in Figure 4.30 and in Table 4.17. The

testing procedure (Table 3.11) was slightly amended, as the centrifuge was stopped after the

installation of the stone columns in order to remove the sand particles from the surface of the

clay so that the surface would be level and the stress distribution could be measured.

Unfortunately, the tool platform was positioned incorrectly with respect to the drum, which

caused the footing used for the loading phase not to be in the position planned (Figure 4.29).

The results shown in Table 4.17 indicate that the load transfer behaviour with depth in case

of a stone column group is similar to the case of a single stone column. The ratio Δumax / Pmax

drops by 80 to 95% for an increase of depth of 50 mm (from 30 mm to 80 mm below the

surface of the clay specimen)as opposed to test JG_v8. This would indicate that a lower part

of the load applied on the surface is transmitted into depth. However, the increased drainage

capacity of the stone column group compared to the case of a single stone column causes

an accelerated rate of dissipation of the excess pore water pressures (Figure 4.34). This

complicates significantly an accurate estimation of the stress levels based on the recorded


180

excess pore water pressures as it is not possible to assess which part of the excess pore

water pressure was already dissipated when the peak footing load was reached.

Figure 4.29: Position of the footing used for the loading phase during test JG_v10 (a = 24

mm).


test JG_v10.

PPT

Maximal excess

pore water pressure

Δumax [kPa]

Maximal load

applied on the

footing Pmax [kPa]

Δumax / Pmax [%]

P1 (z = 30 mm) 44.82 142.01 31.56

P2 (z = 30 mm) 35.65 142.01 25.10

P3 (z = 30 mm) 23.30 142.01 16.41

P4 (z = 80 mm) 22.36 142.01 15.75

P5 (z = 80 mm) 19.86 142.01 13.98

P6 (z = 80 mm) 25.64 142.01 18.06

P7 (z = 55 mm) 29.35 142.01 20.67

The drainage effect of the stone column group can be observed as the magnitude of the

ratios Δumax / Pmax is significantly lower in case of the stone column group (Figure 4.31) than

in case of a single stone column (Figure 4.21 and Figure 4.22). The effect of the incorrect

positioning of the platform can be noted when considering the drop of normalised excess

pore water pressure from P2 to P3 (Figure 4.31). The reason why the measurements made

by transducer P6 are higher than those made by transducer P3 is unknown.


181

(a)

(b)

(c)

Figure 4.30: Test JG_v10: (a) excess pore water pressures (b) evolution of the footing load

(c) footing settlement during the loading phase of a stone column group.

0

10

20

30

40

50

0 500 1000 1500Ex

ce

ss

po

re w

ate

r p

res

su

re

[kP

a]

Time [s]

P1 P2 P3 P4 P5 P6 P7

0

20

40

60

80

100

120

140

160

0 500 1000 1500

Fo

oti

ng

lo

ad

ing

[k

Pa

]

Time [s]

-20

-15

-10

-5

0

0 500 1000 1500

Fo

oti

ng

se

ttle

me

nt

[mm

]

Time [s]


182


the axis of the centre stone column at depths of 30 mm and of 80 mm as a

percentage of the applied footing load P (test JG_v10).

Figure 4.32 and Figure 4.33 show the dissipation with time of the excess pore water

pressures after the peak footing load at depths of 30 mm and 80 mm, respectively. In both

cases, an accelerated dissipation can be noted 250 s after the peak footing load has been

reached (which corresponds to t = 0 s). The influence of the stone column group on the

drainage length is visible in the magnitude of the dissipation of the excess pore water

pressure at a depth of 30 mm as a diminution of approximately 23 kPa is measured 6 mm

away from the edge of the centre column, while this drop is only of 17 kPa and 12 kPa when

measured 12 mm and 24 mm away from the edge of the centre column, respectively.

A similar observation to that made at a depth of 96 mm around a single stone column can be

made at a depth of 80 mm at distances of 6 mm and 12 mm from the edge of the centre

column: the excess pore water pressure dissipation remains constant up to a distance of

12 mm from the edge of the column and reaches approximately 8 kPa. The uncertainty about

the measurements made by transducer P6 prevents a quantitative analysis of the results

from being carried out.

0

5

10

15

20

25

30

35

0 5 10 15 20 25 30

No

rma

lis

ed

ex

ce

ss

po

re w

ate

r p

res

su

re [

% P

]


z = 30 mm z = 80 mm


P2

P1

P3

P4P5

P6


183

(a)

(b)


(test JG_v10), dissipation with time of the excess pore water pressures at a

depth of 30 mm around the stone column (a) from 0 s to 2000 s and (b) from


t = 0 s).

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40Ex

ce

ss

po

re w

ate

r p

res

su

res

[k

Pa

]


t = 0 s t = 250 s t = 500 s t = 750 st = 1000 s t = 1500 s t = 2000 s


0

1

2

3

4

5

6

7

8

9

10

0 10 20 30 40Ex

ce

ss

po

re w

ate

r p

res

su

res

[k

Pa

]


t = 3000 s t = 4000 s t = 5000 s t = 6000 s t = 7000 s



184

(a)

(b)


(test JG_v10), dissipation with time of the excess pore water pressures at a

depth of 80 mm around the stone column (a) from 0 s to 2000 s and (b) from


t = 0 s).

The increased drainage performance of a stone column group compared to a single stone

column can be noted by comparing the rates of dissipation of the excess pore water

pressures with time. The values reached in case of a stone column group are significantly

higher as they range from 0.045 kPa / s to 0.09 kPa / s at a depth of 30 mm and reach

approximately 0.035 kPa / s at a depth of 80 mm. Moreover, a pseudo-constant rate of

dissipation is reached at t = 1500 s after the peak footing load has been applied, opposed to

t = 2000 s in case of a single stone column.

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40Ex

ce

ss

po

re w

ate

r p

res

su

res

[k

Pa

]


t = 0 s t = 250 s t = 500 s t = 750 st = 1000 s t = 1500 s t = 2000 s


0

1

2

3

4

5

6

7

8

9

10

0 10 20 30 40Ex

ce

ss

po

re w

ate

r p

res

su

res

[k

Pa

]


t = 3000 s t = 4000 s t = 5000 s t = 6000 s t = 7000 s



185




4.6 Comparison of the measurements around a single stone

column and inside a stone column group

Although the transducers have not been installed at similar locations for all of the

investigations, a comparison between the behaviour under loading of a single stone column

and of a group of stone columns reveals some interesting insights. Figure 4.35 and

Figure 4.36 show the evolution of the excess pore water pressures during the loading

of a single stone column (on the example of JG_v9) and of a stone column group

(test JG_v10), respectively.

For clarity, the installation depths of the different transducers are recalled:

- in case of a single stone column (test JG_v9):

o P1, P2 and P3 at a depth of 48 mm under the surface of the clay

specimen,

o P4, P5 and P6 at a depth of 96 mm,

o P7 at a depth of 140 mm directly under the column,

- in case of a stone column group (test JG_v10):

o P1, P2 and P3 at a depth of 30 mm under the surface of the clay

specimen,

o P4, P5 and P6 at a depth of 80 mm,

o P7 at a depth of 55 mm.

The magnitudes of the excess pore water pressures recorded by transducers P1, P2 and P3

are very similar in both cases, although the installation depths and the applied footing load

(119.67 kPa for test JG_v9 and 142.01 kPa for test JG_v10) are different. This shows the

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0 1000 2000 3000 4000 5000 6000 7000

Δu

/ Δ

t [k

Pa

/ s

]

Time [s]

P1 P2 P3 P4 P5 P6

4.6 Comparison of the measurements around a single stone column and inside a stone

column group

186

efficiency of a stone column group in terms of dissipation of excess pore water pressures.

The shallower installation depth of the transducers, coupled with the higher footing load

acting on the stone column group should otherwise have led to the appearance of higher

excess pore water pressure than in the test featuring a single stone column.

Figure 4.35: Excess pore water pressures during the footing load test on a single stone

column (test JG_v9).

Figure 4.36: Excess pore water pressures during the footing load test on a stone column

group (test JG_v10). The maximum load was reached at 1000 s.

The drainage performance of a stone column group is highlighted by a comparison of the

rates of dissipation of the excess pore water pressures for a single inclusion (Figure 4.39)

and for a group of inclusions (Figure 4.38). These rates are significantly higher in the case of

a stone column group as they reach values of up to 0.09 kPa / s immediately after the peak

footing load has been applied, while the maximal rate of dissipation around a stone column is

0

10

20

30

40

50

0 1000 2000 3000 4000 5000 6000 7000 8000

Ex

ce

ss

po

re w

ate

r p

res

su

re

[kP

a]

Time [s]

P1 P2 P3 P4 P5 P6 P7

0

10

20

30

40

50

0 1000 2000 3000 4000 5000 6000 7000 8000Ex

ce

ss

po

re w

ate

r p

res

su

re

[kP

a]

Time [s]

P1 P2 P3 P4 P5 P6 P7


187

only approximately 0.07 kPa / s in case of a single stone column, which corresponds to a

29 % higher performance of the stone column group. Moreover, a pseudo-constant value of

the rate of dissipation is reached after 1500 s in the case of a group, as opposed to 2000 s

for a single inclusion.







0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0 1000 2000 3000 4000 5000 6000 7000

Δu

/ Δ

t [k

Pa

/s]

Time [s]

P1 P2 P3 P4 P5 P6

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0 1000 2000 3000 4000 5000 6000 7000

Δu

/ Δ

t [k

Pa

/ s

]

Time [s]

P1 P2 P3 P4 P5 P6

4.7 Electrical impedance measurements

188


Electrical impedance measurements were conducted to determine the distribution of the

installation effects around stone columns with depth. The electrical impedance needle was

inserted at a speed of 3 mm /s. The measurements were conducted using a frequency of 200

kHz. Other frequencies were tried as well (50 kHz and 100 kHz), but the precision of the

measurements was best for a frequency of 200 kHz. The voltage was 1 V. The different

zones identified by Weber (2008) are already described in Section 3.3, but Figure 4.39 is

included here to recall the distribution of the 4 zones detected.


(Weber, 2008).

4.7.1 Measurements around a single stone column

The first successful implementation of the needle for electrical impedance measurements

occurred during test JG_v5. The results obtained are presented in the following section,

while those from test JG_v9 can be found in Appendix 8.6.

Figure 4.40: Positions of the needle insertion points around a single stone column, and

extent of the zones 2 and 3 according to Weber (2008).

Figure 4.40 shows the positions of the points where the electrical impedance needle was

inserted around a single stone column, together with the extent of zones 2 and 3, according


189

to Weber (2008). Figure 3.55 shows the positions of the Reference Points (denoted as RP1

and RP2 in Figure 4.41 and Figure 4.44). The PPTs were installed in the upper half of the

specimen (Figure 3.53) and have thus no influence on the measurements conducted with the

electrical impedance needle. The order in which the measurements were conducted was the

same for all tests: the needle was first inserted at reference points RP1 and RP2 and

subsequently at points A, B, C, D, E and F in this order. The tip of the needle was immersed

for 5 minutes in the ultrasonic bath (Section 3.4.5) after each insertion. Due to the scatter of

the results, a moving average (interval of 6 measurements with 4 measurements per

seconds) was calculated in order to improve the readability of the graphs.

4.7.1.1 Measurements conducted in specimens consolidated up to

σ’v = 100 kPa (test JG_v5)

The needle was inserted after the installation of the stone column and subsequent

consolidation of the specimen in this case. Figure 4.41 shows the measurements at the two

reference points RP1 and RP2, located 88 mm away from the axis of the stone column. No

significant differences could be found in the two profiles.

Figure 4.41: Impedance recorded at reference points RP1 and RP2 during test JG_v5.

Figure 4.42 shows the impedance values measured at points A, B and C. No significant

difference between the recorded values at these three points can be noted. Unlike the profile

obtained at the Reference Points, the slight decrease of the measured impedance between

10 mm and 40 mm depth (denoted as A in Figure 4.41) cannot be seen. It is rather surprising

that the measurements conducted at the three points A, B and C show similar values and

distribution, as point C is located only 15 mm away from the axis of the column. This location

would be expected to be on the borderline of the compaction zone (zone 3 according to

Weber (2008), Figure 4.39). Thus the impedance would be expected to rise in accordance

with a higher density in the host soil.

0

20

40

60

80

100

120

0 0.002 0.004 0.006 0.008 0.01

De

pth

[m

m]

Impedance [Ohm]

RP1 RP2

A


190

Figure 4.42: Impedance recorded at the points A, B and C during test JG_v5.

Figure 4.43 shows the impedance values measured at point D, E and F. A significant

increase in the impedance can be noted in the upper third of the zones 2 and 3 around the

stone column. This indicates that compaction of the host soil was greater near to the surface

due to the installation of the stone column. The recorded values also diminish below about

40 mm at point F, which is in zone 2 closest to the stone column. This might indicate a

stronger vertical reorganisation of the clay particles.

Figure 4.43: Impedance recorded at the points D, E and F during the test JG_v5.

The analytical solutions proposed by the Strain Path Method (Baligh, 1985) and the Shallow

Strain Path Method (Sagaseta & Whittle, 2001) (Section 2.9.2) suggest that a reorganisation

of the clay platelets could occur up to a distance of 6 times the radius of the inclusion. The

impedance measured at point F (Figure 4.43) is significantly lower than at the other points

investigated. Located 7 mm away from the axis of the stone column, point F is within zone 2

0

20

40

60

80

100

120

0 0.002 0.004 0.006 0.008 0.01

De

pth

[m

m]

Impedance [Ohm]

Point A Point B Point C

0

20

40

60

80

100

120

0 0.002 0.004 0.006 0.008 0.01

De

pth

[m

m]

Impedance [Ohm]

Point D Point E Point F


191

(Figure 4.39), whereas Weber (2008) showed a clear reorganisation of the clay platelets

parallel to the axis of the inclusion. The absence of any obvious increase in the recorded

impedance at point C is also thought to be due to a vertical reorganisation of the clay

particles. The results show that the impedance measured with the electrical impedance

needle is obviously sensitive to the organisation of the particles.

4.7.1.2 Measurements conducted in a specimen consolidated up to

σ’v = 200 kPa (test JG_v5)

The results obtained from the insertion of the electrical impedance needle during test JG_v5,

in the specimen consolidated up to 200 kPa, are presented in this section. In this case, a

footing load of 120.14 kPa was applied after the installation of the stone column. The needle

was inserted after the footing loading phase and subsequent dissipation of the excess pore

water pressures.

Figure 4.44 shows the measurements taken at the two reference points RP1 and RP2,

located 88 mm away from the axis of the stone column. No significant variation of the

measured impedance, either over the depth or between the two points, can be noted.

The values are higher than in the specimen consolidated up to 100 kPa (Figure 4.41),

which is consistent with the assumption that the impedance increases in denser soils

(Cho et al., 2004).


Figure 4.45 and Figure 4.46 show the results of the impedance measurements conducted at

points A, B, C, D, E and F. These points, with the exception of point A, are located within the

imprint area of the footing (Figure 4.40). Therefore the measured profiles start at a depth of

17 mm, as the electrical impedance needle was inserted after the footing loading (Table

3.12).

0

20

40

60

80

100

120

0 0.002 0.004 0.006 0.008 0.01

De

pth

[m

m]

Impedance [Ohm]

RP1 RP2


192

No significant difference can be noted between the measurements conducted at points A, B

and C (Figure 4.45). The reason for the drop in measured impedance at point C at a depth of

60 mm (Figure 4.45) could be a local reorganisation of the clay platelets. The explanation of

the lack of increase in the impedance at points B and C is the same as in Section 4.7.1.1,

which is a vertical reorganisation of the clay platelets as suggested by Baligh (1985) and

Sagaseta & Whittle (2001). However, no influence of the footing load can be seen either.

This tends to indicate that the measured impedance is more sensitive to the micro-

mechanical reorganisation of the clay platelets than to the macro-mechanical increase of

density. Points B and C are located within the area where a footing load was applied, which

caused compaction of the host soil. However, point B is located 18 mm, and point C 15 mm

away from the axis of the column. This implies that the effect of bulging of the stone column

on the density of the host soil is not as extreme as at point D, E and F (Figure 4.46) and the

vertical reorganisation of the clay platelets has a higher influence on the measured

impedance than the increase in density due to the vertical loading. This interpretation could

be confirmed by Environmental Scanning Electron Microscope (ESEM) observations

(Section 5.4).

Figure 4.45: Impedance recorded at the points A, B and C during test JG_v5.

A clear influence of the footing load can be noted at a distance of 12 mm from the axis of the

stone column (Figure 4.46, point D). The depth of the increase of the recorded values of the

impedance is significantly higher than in the case of an unloaded inclusion (Section 4.7.1.1).

Even though the footing loading has not been carried out up to failure, the load will have

caused lateral deformation of the column. This leads to a further compression of the host soil

and to an increase in the measured impedance.

The measured impedance at point F below a depth of 90 mm is remarkably constant, and

is significantly lower than the values measured at the reference points RP1 and RP2

(Figure 4.44). As point F is located within zone 2 according to Weber (2008), where a vertical

reorganisation of the clay platelets is observed, this tends to indicate that the bulging of the

0

20

40

60

80

100

120

0 0.002 0.004 0.006 0.008 0.01

De

pth

[m

m]

Impedance [Ohm]



193

stone column due to vertical loading caused a reorganisation of the clay platelets up to a

depth of 90 mm, and that the particles are vertical below that depth.

Figure 4.46: Impedance recorded at the points D, E and F during test JG_v5.

4.7.2 Measurements around a stone column group (test JG_v8)

In addition to the measurements around single stone columns, impedance measurements

were also conducted around a stone column group (test JG_v8) after installation of the stone

columns and dissipation of the excess pore water pressures and prior to the footing loading.

The needle was first inserted at reference points RP1 and RP2 and subsequently at points

A2, B2, C2, D2, E2, F2, G2, H2 and I2 (Figure 3.52), in that order. The tip of the needle was

immersed for 5 minutes in the ultrasonic bath (Section 3.4.5) after each insertion. All

investigations were conducted in specimens that had been pre-consolidated up to σ’v = 100

kPa.

Figure 4.48 shows the impedance recorded at the reference points RP1 and RP2, located

100 mm away from the axis of the column (Figure 3.52), during tests JG_v8. No clear pattern

can be identified in the results. This is thought to be due to the fact that the needle was not

inserted into the soft soil vertically, but at an angle of 7°. As a consequence, the sensitivity of

the measurements to the micro-mechanical organisation of the clay platelets had a high

impact on the measured results.

0

20

40

60

80

100

120

0 0.002 0.004 0.006 0.008 0.01

De

pth

[m

m]

Impedance [Ohm]



194

Figure 4.47: Positions of the needle insertion points around a stone column group

(test JG_v8, a / dsc = 2 [-].


The impedance recorded at points A2, B2 and C2, located outside the imprint area of the

footing are presented in Figure 4.49. The impedance measured at point A2 is higher than at

the other two points below 40 mm. The recordings at point C2 are closer to those at point B2,

and the values of the impedance at point B2 are comparable with those obtained at points A,

B and C for the investigations around a single stone column (Figure 4.45). The tip of the

needle clogged partially, although the tool was routinely cleaned in the ultrasonic bath, for

the test at point B2, which may explain the smaller impedance values. The light decrease of

the impedance recorded between points A2 and C2 below 20 mm is thought to be due to a

0

20

40

60

80

100

120

0 0.005 0.01 0.015 0.02

De

pth

[m

m]

Impedance [Ohm]

RP1 RP2


195

vertical reorganisation of the clay platelets caused by the installation of the stone column

group.

Figure 4.49: Impedance recorded at the points A2, B2 and C2 during test JG_v8.

The results of the impedance measurements conducted at points D2, E2 and F2 are

presented in Figure 4.50. The measurements at point D2 (25 mm away from the axis of the

column A) are similar to the values obtained at point E for the investigations around a single

stone column (9 mm away from the axis of the column, Section 4.7), with impedance values

of about 0.006 Ohm. This indicates a significantly wider extent of the reorganisation of the

clay platelets in the case of a stone column group.

Figure 4.50: Impedance recorded at the points D2, E2 and F2 during test JG_v8.

The wide spatial extent of particle reorganisation is confirmed by the impedance values

recorded at points E2, F2, G2, H2, I2 and J2 (Figure 4.50 and Figure 4.51). These are similar

0

20

40

60

80

100

120

0 0.005 0.01 0.015 0.02

De

pth

[m

m]

Impedance [Ohm]

Point A2 Point B2 Point C2

0

20

40

60

80

100

120

0 0.002 0.004 0.006 0.008 0.01

De

pth

[m

m]

Impedance [Ohm]

Point D2 Point E2 Point F2

4.8 Summary of the conducted modelling under enhanced gravity

196

in magnitude and variation to the recordings conducted at point F around a single stone

column (Figure 4.46), located in zone 2 (Figure 4.39), where Weber (2008) found the clay

platelets to be organised parallel to the stone column axis.

Figure 4.51: Impedance recorded at the points G2, H2, I2 and J2 during test JG_v8.

4.8 Summary of the conducted modelling under enhanced gravity

Centrifuge tests were carried out in order to model boundary value problems with stone

columns and represent a central part of this work. This section presents a short summary of

the insights gained about the influence of the OCR, on the load transfer behaviour of stone

columns, and on the microscopic phenomena caused by the installation of granular

inclusions.

It has been shown that the over-consolidation ratio of the soft soil plays a role in the

magnitude of the excess pore water pressures generated during the installation phase of the

inclusions, as a greater OCR leads to higher excess pore water pressures. The depth under

the surface of the soft soil also plays a role, as the deeper the elements the higher the

excess pore water pressures.

The interpretation of the results obtained from the footing loads showed that there was load

transfer to depth in the presence of a stone column, as the back-calculated vertical load

increased at a depth of 96 mm under the surface of the clay to a factor of about three times

greater with a granular inclusion, than without (Figure 4.26).

A consistent trend between a wide range of measurements with the electrical impedance

needle indicates that the clay particles underwent microscopic reorganisation up to a

distance of 30 mm from the axis of a stone column (corresponding to 5 times the radius of

the inclusion). The extent of the macroscopic mechanical installation effects will be

investigated in more detail in the following chapter.

0

20

40

60

80

100

120

0 0.002 0.004 0.006 0.008 0.01

De

pth

[m

m]

Impedance [Ohm]

Point G2 Point H2 Point I2 Point J2

5 Complementary investigations

197


5.1 Oedometer tests conducted on samples extracted from the soil

model used for the centrifuge test JG_v9

Four samples were extracted from the soft soil bed, two each in a horizontal and a vertical

direction, after test JG_v9 (σc = 100 kPa), in order to conduct oedometer tests and

to investigate the anisotropy of the host soil. The oedometer cells have a diameter of

56.419 mm and a height of 20 mm.

The extraction positions are shown in a plan view in Figure 5.1. The specimens

JG_v9 – Oedo 1 and JG_v9 – Oedo 3 were extracted vertically from a maximum depth of

120 mm (denoted as [1] in Figure 5.2) while the samples JG_v9 – Oedo 2 and JG_v9 – Oedo

4 were extracted horizontally from a maximum depth of 90 mm (denoted as [2] in Figure 5.2).

The specimens were extracted from such locations so that they were not influenced by the

installation or by the loading of the stone column (Figure 5.2). Metallic sampling cylinders

were therefore pushed into the clay sample approximately 2 hours after the end of the

centrifuge test, and the soil around the pots was cut using a thin metallic wire so that the

specimens were almost undisturbed. The sampling cylinders were subsequently directly

mounted into an oedometer cell.

Figure 5.1: Plan view of the extraction positions of the specimens for oedometer tests (test

JG_v9).


centrifuge test JG_v9

198

Figure 5.2: Cross-section of the extraction positions of the specimens for oedometer tests

(test JG_v9).

Figure 5.3: Distribution of the over-consolidation ratio of the specimens used

for the oedometer tests during the centrifuge test.

Figure 5.3 shows the profiles of the over-consolidation ratios in the vertical and horizontal

directions (denoted as OCR (vertical) and OCR (horizontal), respectively) during the

centrifuge test. A constant g level throughout the specimen was assumed for the calculation

of the OCR. A maximal vertical effective stress σ’v,max of 100 kPa was used in the vertical

case and K0 conditions were assumed. With a K0 value of 0.585 (Table 4.10), a maximal

horizontal vertical stress σ’h,max of 58.5 kPa is obtained. The over-consolidation ratio of the

specimens extracted vertically ranged from 2.4 to 2 (denoted as V in Figure 5.3) of that of the

specimens extracted horizontally from 4.0 to 1.5 (denoted as H in Figure 5.3). The extraction

procedure caused relatively small disturbance of the specimens, and thus it was hoped that

the stress history would be conserved in the best possible manner. The specimens were

0

20

40

60

80

100

120

140

160

0 5 10 15 20

De

pth

[m

m]

OCR [-]

OCR (vertical) OCR (horizontal)

HH

V


199

loaded up subsequently to σ’v = 200 kPa in the oedometer, before undergoing two unloading-

reloading cycles from σ’v = 200 kPa to σ’v = 50 kPa and back to σ’v = 200 kPa.

The evolution of the void ratio under one dimensional vertical loading is shown in Figure 5.4.

The quantitative difference in void ratio between the two samples extracted in the vertical

direction (denoted as JG_v9 – Oedo 1 and JG_v9 – Oedo 3 in Figure 5.4) remains more or

less constant throughout the loading steps, and is only about 7 %. This may be due to the

higher g level acting during the centrifuge test at the extraction position of the specimen

JG_v9 – Oedo 1, due to the greater radial distance from the centre of the centrifuge. The

results from the two samples extracted in the horizontal direction almost superpose in both

figures.

Figure 5.4: Evolution of the void ratio with one dimensional loading in an oedometer.

As long as the specimens were pre-consolidated vertically up to 100 kPa (which corresponds

to a horizontal load of 58 kPa assuming K0 conditions), the compression index CC is to be

calculated for the load step ranging from 100 kPa to 200 kPa. The values obtained are


Table 5.1: Compression indexes CC obtained from the oedometer tests.

Load

interval

[kPa]

CC, vertical [-] CC, horizontal [-]

OCR [-] JG_v9 –

Oedo 1

JG_v9 –

Oedo 3

JG_v9 –

Oedo 2

JG_v9 -

Oedo 4

100 - 200

(loading) 0.045 0.044 0.043 0.045 1.0

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1 10 100 1000

e [

-]

Vertical effective stress [kPa]

JG_v9 - Oedo 1 (Vertical) JG_v9 - Oedo 2 (Horizontal)


σ'v,max

σ'h,max



200

The swelling index for the unloading-reloading path CS can be calculated for the two

unloading-reloading cycles for 200 kPa to 50 kPa and back to 200 kPa. The results obtained

are presented in Table 5.2. The values of the compression indexes CC and CS are

remarkably similar for all tests. The impact of the over-consolidation ratio on the loading

behaviour can be noted as the compression indexes CS of the samples extracted horizontally

are lower than those of the samples extracted vertically, which is due to the higher over-

consolidation of the specimens (Figure 5.3).

Table 5.2: Compression indexes CS obtained from the oedometer tests.

Load

interval

[kPa]

CS, vertical [-] CS, horizontal [-]

OCR [-] JG_v9 –

Oedo 1

JG_v9 –

Oedo 3

JG_v9 –

Oedo 2

JG_v9 -

Oedo 4

200 - 50

(unloading) 0.012 0.012 0.011 0.011 4.0

50 - 200

(reloading) 0.015 0.014 0.013 0.013 1.0

200 - 50

(unloading) 0.012 0.012 0.011 0.011 4.0

50 - 200

(reloading) 0.016 0.015 0.014 0.014 1.0

Figure 5.5: Distribution of the confined stiffness moduli as a function of the vertical effective

stress.

The values obtained of the confined stiffness moduli ME, for the different load intervals, are

presented in Table 5.3. The vertical and horizontal confined stiffness moduli are denoted as

ME, v and ME,h, respectively.

0

500

1000

1500

2000

2500

3000

0 50 100 150 200

ME

[kP

a]

Vertical effective stress σ'v [kPa]



σ'v,maxσ'h,max


201

The calculated stiffnesses in the horizontal direction tend to be higher than the values

calculated in the vertical direction. As stated earlier, this is due to the greater over-

consolidation of the samples extracted horizontally (Figure 5.3) compared to those extracted

vertically. However, this difference is only about 10 % and may be considered irrelevant for

engineering purposes (Figure 5.5 and Figure 5.6).

Table 5.3: Vertical (ME,v) and horizontal (ME,h) confined stiffness moduli obtained from the

oedometer tests and values of the over-consolidation ratios for samples

extracted vertically (OCRv) and horizontally (OCRh).

Load

interval

[kPa]

ME, v [kPa] OCRv

[-]

ME, h [kPa] OCRh

[-] JG_v9 –

Oedo 1

JG_v9 –

Oedo 3 Average

JG_v9 –

Oedo 2

JG_v9 -

Oedo 4 Average

0 - 12.5

(loading) 982.7 755.6 869.1 8.0 1082.8 1164.4 1123.6 4.64

12.5 - 25

(loading) 774 871.1 822.5 4.0 841.8 892.9 867.3 2.32

25 - 50

(loading) 1057.1 1073.0 1065.0 2.0 1037.3 1077.6 1057.5 1.16

50 - 100

(loading) 1490.3 1652.9 1571.6 1.0 1432.7 1567.4 1500.0 1.0

100 - 200

(loading) 2430.1 2164.5 2297.3 1.0 2433.1 2472.2 2452.6 1.0

200 - 50

(unloading) 12448.1 12345.7 12396.9 4.0 14018.7 13157.9 13643.6 4.0

50 - 200

(reloading) 10416.7 10380.6 10398.6 1.0 11673.2 11278.2 11475.7 1.0

200 - 50

(unloading) 12244.9 12244.9 12244.9 4.0 13953.5 13333.3 13643.4 4.0

50 - 200

(reloading) 9460.7 9434.0 9448.8 1.0 10526.3 10238.9 10382.6 1.0

The tangent stiffness for primary oedometer loading for a reference effective stress of

100 kPa is of particular interest for the numerical modelling using the Hardening Soil Model

(Section 6.3.2.6). Figure 5.7 shows the distribution of the mean vertical strain with increasing

vertical loading. The definition of the tangent stiffness for primary oedometer loading Eoedref is

displayed in Figure 5.8. The slopes of the tangents to the load-strain curve were determined

to be 1900 kPa in both vertical and horizontal cases, for a vertical effective stress of 100 kPa

(Figure 5.7). Another important parameter for the numerical modelling is the unloading-

reloading stiffness Eurref, which is set to an average value of 13000 kPa (Table 5.3).



202

Figure 5.6: Distribution of the mean vertical (ME, v, average) and horizontal (ME, h, average) confined

stiffness moduli as a function of the vertical effective stress.

Figure 5.7: Distribution of the mean settlements for the samples extracted in the vertical and

horizontal directions with one-dimensional loading in an oedometer.

The calculated values of the coefficient of permeability k, computed based on the time-

settlement curve of each load step (as suggested by Lang et al., 2007), are displayed in

Figure 5.9. The distribution of the permeability (Figure 5.9) has a similar form in the

horizontal and vertical directions. No significant difference could be measured in terms of

coefficient of permeability between the horizontal and the vertical directions. The first point

obtained for specimen JG_v9 – Oedo 4 may be regarded as an outlier, inherent to the

uncertainty of laboratory investigations.

These investigations lead to the conclusion that although some anisotropy could be detected

in terms of stiffness, no significant influence of the fabric on the void ratio distribution, or on

the values of the coefficient of permeability, could be ascertained.

0

500

1000

1500

2000

2500

3000

0 50 100 150 200

ME

[kP

a]


ME vertical ME horizontalME, v, averageME, h, average

σ'v,maxσ'h,max

0

2

4

6

8

10

12

14

0 50 100 150 200

Ve

rtic

al s

tra

in Δ

h /

h0

[%]


Settlement (vertical) Settlement (horizontal)


203

Figure 5.8: Definition of Eoedref from oedometer test results (after Brinkgreve & Broere, 2008).

Figure 5.9: Evolution of the permeability with one dimensional loading in an oedometer.

5.2 Oedometer tests conducted on samples extracted from soil

models after consolidation

Due to problems encountered during the installation of the PPTs, the first attempt to conduct

the centrifuge test JG_v10 failed, which gave the opportunity to extract samples from the soil

models prepared in cylindrical strongboxes (σc = 100 kPa) without being exposed to

enhanced gravity. Four samples were withdrawn, 15 days after the removal of the

consolidation load, in the horizontal direction at two different depths and were submitted to a

vertical load up to 200 kPa, and to unloading – reloading cycles.

The specimens JG_v10_Oedo 1 and JG_v10_Oedo 3 were extracted from a depth of up to

75 mm, while the samples JG_v10_Oedo 2 and JG_v10_Oedo 4 were extracted from up to

σ’v

pref

Δh/h0

4E-10

6E-10

8E-10

1E-09

1.2E-09

1.4E-09

1.6E-09

1.8E-09

2E-09

0 50 100 150 200

k [

m/s

]




5.2 Oedometer tests conducted on samples extracted from soil models after consolidation

204

120 mm below the surface (Figure 5.10). The oedometer cells and the extraction procedure

used are the same as those described in the previous section.

Figure 5.10: Extraction positions of the samples for oedometer tests (test JG_v10).

Figure 5.11 shows the distribution of the over-consolidation ratio in the horizontal direction

(σ’h,max = 58.5 kPa) with depth for the sample from which the specimen used for the

oedometer tests were extracted. The OCR ranges from 50 to 28 for specimens extracted

from a depth up to 120 mm (denoted as 120 mm in Figure 5.11) and from 170 to 40 for

specimens extracted from a depth up to 75 mm (denoted as 75 mm in Figure 5.11).

Figure 5.11: Distribution of the over-consolidation ratio in the horizontal direction of the

specimens used for the oedometer tests.

The evolution of the void ratio with one-dimensional vertical loading is shown in Figure 5.12.

The results of the samples extracted from 75 mm (denoted as JG_v10 - Oedo 1 - z = 75 mm

and JG_v10 - Oedo 3 - z = 75 mm) and 120 mm (denoted as JG_v10 - Oedo 2 - z = 120 mm

and JG_v10 - Oedo 4 - z = 120 mm) are remarkably close (Figure 5.12).

0

20

40

60

80

100

120

140

160

0 50 100 150 200 250 300

Dep

th [

mm

]

OCR [-]

75 mm

120 mm


205

Figure 5.12: Evolution of the void ratio with one dimensional loading in an oedometer.

As long as the specimens were pre-consolidated vertically up to 100 kPa (which corresponds

to a horizontal load of 58 kPa assuming K0 conditions), the compression index CC is to be

calculated for the load step ranging from 100 kPa to 200 kPa. The obtained values are

presented in Table 5.4. No significant variation of the results can be noted between the two

extraction depths.

Table 5.4: Compression indexes CC obtained from the oedometer tests.

Load

interval

[kPa]

CC, z = 75 mm [-] CC, z = 120 mm [-]

OCR [-] JG_v10 -

Oedo 1 - z

= 75 mm

JG_v10 -

Oedo 3 - z

= 75 mm

JG_v10 -

Oedo 2 - z

= 120 mm

JG_v10 -

Oedo 4 - z

= 120 mm

100 - 200

(loading) 0.048 0.043 0.046 0.047 1.0

The calculated values of the compression index CS for the unloading-reloading cycles are

presented in Table 5.5. No significant impact of the over-consolidation can be noted as the

values of CS for samples extracted up to a depth of 75 mm and those for samples extracted

up to a depth of 120 mm are very similar (Table 5.5). The higher values of the compression

index CS for the bigger load steps (marked with an asterisk * in Table 5.5) can be explained

by the accumulation of plastic deformation during cycling loading, or ratcheting, as shown

e.g. in Alonso-Marroquin et al. (2008).

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1 10 100 1000

e [

-]


JG_v10 - Oedo 1 - z = 75 mm JG_v10 - Oedo 2 - z = 120 mm


σ'v,maxσ'h,max

5.2 Oedometer tests conducted on samples extracted from soil models after consolidation

206

Table 5.5: Compression indexes CS obtained from the oedometer tests.

Load interval [kPa]

CS, z = 75 mm [-] CS, z = 120 mm [-]

OCR

[-]

JG_v10 -

Oedo 1 - z

= 75 mm

JG_v10 -

Oedo 3 - z

= 75 mm

JG_v10 -

Oedo 2 - z

= 120 mm

JG_v10 -

Oedo 4 - z

= 120 mm

200 – 100 (unloading) 0.005 0.003 0.004 0.004 2.0

100 – 200 (reloading) 0.007 0.005 0.005 0.006 1.0

200 - 50 (unloading) * 0.013 0.009 0.010 0.011 4.0

50 – 100 (reloading) 0.006 0.004 0.004 0.005 2.0

100 – 50 (unloading) 0.005 0.003 0.003 0.004 4.0

50 - 200 (reloading) * 0.015 0.011 0.012 0.013 1.0

200 – 100 (unloading) 0.005 0.003 0.003 0.003 2.0

100 – 200 (reloading) 0.007 0.005 0.005 0.005 1.0

Figure 5.13 shows the distribution of the horizontal confined stiffness moduli obtained from

the oedometer tests as a function of the applied vertical stress. No significant variation of the

stiffness with depth can be noted. Figure 5.14 shows that no significant variation of the

permeability of the sample with depth could be measured.

Figure 5.13: Distribution of the horizontal confined stiffness moduli as a function of the

vertical stress.

0

500

1000

1500

2000

2500

3000

0 50 100 150 200

ME

, h

[kP

a]




σ'h,max σ'v,max


207

Figure 5.14: Evolution of the coefficient of permeability with one dimensional loading in an

oedometer.

5.3 Electrical impedance measurement under 1 g

In order to assess the accuracy of the electrical impedance to density changes, it was

decided to test the tool developed for the centrifuge (Figure 3.30) under 1 g conditions in the

laboratory. A soil model was prepared in the same way as for a centrifuge test using an

oedometer container (Sections 3.6.3 and 3.6.4) and the electrical impedance needle was

inserted up to a depth of 115 mm using the setup shown in Figure 5.15 at three different

points (Figure 5.16) after the completion of each consolidation step (Table 5.6). The model

was therefore unloaded, the top plate was removed and the needle was inserted manually

into the specimen. This operation took approximately 5 minutes, which allows fully undrained

behaviour to be assumed for the soil specimen. The needle was guided vertically in order to

prevent any corruption of the results through an unanticipated change of direction. The

position of the setup was changed for two subsequent consolidation stages: the insertion

points at the end of the consolidation stages 1, 3 and 5, respectively 2 and 4, are located at

the same positions.

0

5E-10

1E-09

1.5E-09

2E-09

2.5E-09

3E-09

0 50 100 150 200

k [

m/s

]




5.3 Electrical impedance measurement under 1 g

208

(a) (b)

Figure 5.15: Setup for the insertion of the electrical impedance needle under 1 g in the

laboratory (a) schematic view (b) picture.

Table 5.6 shows an overview of the load steps and of the density and void ratio of the clay at

the end of the corresponding consolidation stages. Figure 5.17 and Figure 5.18 show the

results of the investigation conducted after the first and after the fifth consolidation stage. The

other outcomes are shown in Appendix 8.7.

Table 5.6: Overview of the consolidation stages for the implementation of the electrical

impedance needle under 1 g.

Consolidation stage Consolidation effective

stress [kPa] Density [kN/m3] Void ratio [-]

1 12.5 16.8 1.53

2 25 17.4 1.30

3 50 18.1 1.20

4 100 18.7 1.06

5 200 20.4 0.73

20

0 m

m

115 mm Clay

Container

Needle


209


dimensions in mm.

Figure 5.17: Impedance recorded under 1 g after completion of the first consolidation stage.

The density changes do not significantly affect the measured impedance values under 1 g.

However, the values obtained are one order of magnitude higher at 1 g than under 50g,

which is unexpected as the unit weight of the soil (kN/m3) should be n times higher under

enhanced gravity than under Earth’s gravity (n being the factor of increase of the Earth’s

gravity in the centrifuge), triggering higher impedance values. These observations confirm

that the electrical impedance needle should be used in-flight as a tool for complementary

qualitative investigations rather than to obtain quantitative results.

Clay

Insertion

points

1 2

3

0

20

40

60

80

100

120

0.043 0.044 0.045 0.046 0.047

De

pth

[m

m]

Impedance [Ohm]

Point 1 (Stage 1) Point 2 (Stage 1) Point 3 (Stage 1)

5.4 Microscopic investigations

210

Figure 5.18: Impedance recorded under 1 g after completion of the fifth consolidation stage.


In order to investigate the spatial distribution of the compaction zone, samples were taken at

a radial distance of 11 mm from the axis of the compacted column C that was installed during

test JG_v2 at different depths: 20 mm, 60 mm and 100 mm at model scale. Even though an

optical microscope is a useful tool in many research areas, the maximum resolution is

500 nm (5.10-7 m), which means that the clay particles (grain size < 2.10-6 m) can hardly be

detected. This is the reason why it was decided to conduct only investigations using an

Environmental Scanning Electron Microscope.

5.4.1 Description of the Scanning Electron Microscope

A Scanning Electron Microscope (SEM) circumvents the issue of the resolution, as it can

reach resolutions of 3 nm (3.10-9 m). The major difference between optical microscopes and

SEMs is that the sample is illuminated by electrons rather than a light beam (i.e. photons).

The maximal resolution of SEMs depends on diverse factors, the most important being the

spot diameter of the electron beam on the surface of the sample: an SEM cannot detect

elements smaller than the “spot diameter” (Figure 5.19). An SEM, in contrast to an optical

microscope, does not deliver a real picture of the sample but generates a virtual illustration.

The electron beam illuminates a point of the sample, creating a pixel of the virtual illustration,

before being displaced. The combination of the pixels obtained forms the illustration of the

sample.

An SEM illustration is generated by the signals produced by the interaction between the

incident electron beam and the sample, which is recorded by detectors mounted in the

sample chamber. The interaction volume between sample and electron beam (Figure 5.20)

depends on the velocity of the primary electrons within the beam – the higher the speed the

0

20

40

60

80

100

120

0.043 0.044 0.045 0.046 0.047

De

pth

[m

m]

Impedance [Ohm]



211

bigger the interaction volume – and on the spot diameter (Figure 5.19). The different

products generated within the electron interaction volume are illustrated in Figure 5.21.

Figure 5.19: Illustration of the contact between the electron beam and the surface of the

sample (Peschke, 2013).

Figure 5.20: Electron interaction volume within a sample

(after Science Education Resource Center, 2013).

Although SEMs are a major step forward in terms of resolution, compared to optical

microscopes, they still suffer from two major limitations:

- the electrical conductibility of the sample.

If electrical non-conductive samples are investigated, the interaction between the

electron beam and the surface of the sample triggers a significant electrical

charge within the sample, which disturbs the signal coming from the electron-

sample interaction and produces bright surfaces in the illustration.

sample surface

Auger electrons

secondary electrons

characteristics X-rays

back-scattered electrons

Bremsstrahlung X-rays

secondary fluorescence

Spot diameter


212

- the need for vacuum.

A high quality electron beam can only be achieved under a very high vacuum of

10-6 to 10-7 torr (Donald, 2003). As a consequence, vacuum-incompatible

specimens, such as humid or outgassing samples, cannot be investigated using

an SEM.

These two limitations reduce the field of application of SEMs to electrical conductive, vacuum

compatible samples.

Figure 5.21: Types of interaction between electrons and a sample

(Science Education Resource Center, 2013).

5.4.2 Description of the Environmental Scanning Electron Microscope

Environmental Scanning Electron Microscopes (ESEM) sidestep these two problems by

enabling the presence of gas (mostly water vapour) in the sample chamber, while

maintaining the high resolution of the SEMs. If electrical non-conductive samples are

investigated, the gas interacts with the sample surface in order to dissipate the negative

charge.

The limitation concerning the high vacuum is circumvented by using differential pumps along

the column by means of a series of different pressure zones with increasing pressure

towards the sample chamber. The high vacuum needed for the generation of a high quality

electron beam can be conserved in this way, while pressures up to 10 torr can be reached in

proximity to the sample (Figure 5.22). This way, hydrated samples can be investigated in the

original state, if water vapour is used as a gas in the specimen chamber. The specific ESEM

model used for the investigations conducted here was a Quanta 600 produced by FEI.

characteristic X-rays

Bremsstrahlung X-rays

visible light (cathodoluminescence)

heat

diffracted electrons

transmitted electrons

sample surface

Auger

electrons

secondary

electrons

back-scattered

electrons

incident electron beam


213

Figure 5.22: Schematic of an ESEM illustrating the different pressures zones (Donald, 2003).

5.4.3 Results obtained

Figure 5.23 shows the results of the ESEM investigation conducted by Weber (2008) in

zone 2 (magnification 800 times), in which the clay particles have been reorganised

vertically, parallel to the axis of the stone column.

The investigations using the electrical impedance needle (Section 4.7) showed that the

distribution of zone 2 is homogeneous over the whole depth of the column. The spatial

distribution of zone 2 was therefore not investigated further at the microscopic scale.

Figure 5.24 shows the result of the ESEM investigation of zone 3 (specimen located at a

radial distance of 5 mm from the edge of the column) at a depth of 20 mm (magnification

1500 times). A start of the vertical reorganisation of the clay particles can be observed as the

organisation of the longer particles has a vertical trend, although most of the clay platelets

are still organised randomly.

Figure 5.25 shows the results of the ESEM investigation into zone 3 (specimen located at a

radial distance of 5 mm from the edge of the column, as illustrated in Figure 5.24) at depths

of 60 mm and 100 mm (magnification 1500 times). The same mechanisms, as at a depth of

20 mm, can be observed here as the longer particles are organised with a vertical trend.


214

These observations confirm the interpretation of the results of the investigations conducted

with the electrical impedance needle according to which the reduction of the measured

impedance is due to a vertical reorganisation of the clay particles. This reorganisation is a

progressive mechanism starting in zone 3, in which the longer clay particles start to exhibit a

vertical trend and ending in zone 2, in which both the longer particles and the clay platelets

are reorganised vertically.

Figure 5.23: ESEM picture of zone 2, located a radial distance of 1 mm from the edge of the

column and at a depth of 40 mm below the surface, with the radial axis

horizontal (Weber, 2008).

Figure 5.24: ESEM picture of the zone 3 located at a radial distance of 5 mm from the edge

of the column and at a depth of 20 mm below the surface, with the radial axis

horizontal.

50 μm

30 μm

Longer

particles

5 mm

Sto

ne

co

lum

n


215

(a) (b)

Figure 5.25: ESEM pictures of the zone 3 at a radial distance of 5 mm from the edge of the

column and at (a) 60 mm depth and (b) 100 mm depth, with the radial axis

horizontal.

5.5 Mercury Intrusion Porosimetry (MIP)

MIP investigations were conducted to investigate the distribution of the density changes

caused by the installation of the stone columns with depth.

5.5.1 General principle

As mentioned in Section 2.10.2.2, the Mercury Intrusion Porosimetry was developed to

assess the pore diameter in a non-destructive manner. The pore diameter is inversely related

to the mercury insertion pressure by the equation proposed by Washburn (1921):

2.80

with σ surface tension

θ wetting angle for mercury, assumed to be equal to 130° for clay minerals at

room temperature (Diamond, 1970)

p mercury pressure

The porosity is obtained by dividing the total pore volume calculated, based on the pore

diameter, by the total volume of the sample investigated.

20 μm 20 μm

Longer particles


216

5.5.2 Sample preparation

42 undisturbed samples were extracted from the soft clay bed at depths of 20 mm, 60 mm

and 100 mm (model scale) at distances of 7 mm, 13 mm, 18 mm, 23 mm, 31 mm and 36 mm

from the axis of the stone column after the centrifuge tests had been carried out. The

samples were then freeze-dried before applying vacuum by means of a vacuum pump

(Figure 5.26).

Figure 5.26: Vacuum pump.

5.5.3 Apparatus used

The apparatuses used were the models Pascal 140 and Pascal 440, produced by

CE Instruments Ltd (2014), to measure pore diameters ranging from 1.8 nm to 58 μm. The

specimens were first placed in a volume calibrated glass vessel (dilatometer, Figure 5.27 a)

and evacuated to approximately 0.03 kPa using the Pascal 140. The dilatometer was then

filled with mercury up to a given level (Figure 5.27 b) and the pressure was raised

continuously from vacuum to 375 kPa in the macro pore unit. Once this pressure was

reached, the dilatometer containing the specimen was transferred to the Pascal 440 and the

pressure was raised stepwise up to 400 MPa. The measurement of the electrical capacity

along the capillary tube of the dilatometer allows the penetration of the mercury into the

pores of the specimen to be determined.


217

(a) (b)

Figure 5.27: Dilatometer (a) containing the soil specimen before and (b) containing mercury

after the investigation using the macro pore unit Pascal 140.

5.5.4 Results obtained

The first observation is that the edge of the zone in which the host soil becomes denser

through the installation of the stone column remains constant with depth (Figure 5.28). This

compaction zone reaches 13 mm from the axis of the inclusion, corresponding to about twice

the radius of the column, which confirms the observations made by Weber (2008), who

identified that zone 3 extended to 15 mm from the axis of the stone column (Figure 3.21,

Figure 5.28).

The impact of the over-consolidation on the porosity can be noted as the porosity of the host

soil outside the compaction zones rises from approximately 33 % at a depth of 20 mm

(OCR = 11.8 [-]) to 34 % at depths of 60 mm and 100 mm (OCR = 3.9 [-] and OCR = 2.4 [-],

respectively).

The influence on the porosity of the greater number of extraction-reinsertion cycles that the

host soil undergoes near the surface is highlighted by comparing the results of the

measurements at the edge between the smear and compaction zones. A value of 29 % was

obtained at a depth of 20 mm (Figure 5.28 a), while values of 30 % and of 31 % are reached

at depths of 60 mm, respectively 100 mm (Figure 5.28 a and b).

The MIP investigations indicate that the extent of installation effects of stone columns

probably remains constant with depth while the compaction of the inclusion causes a more

significant reduction of porosity at the zone 2-3 boundary at shallower depths than at the tip

of the column.

Soil

specimen

Mercury


218

(a)

(b)

(c)

Legend:

Figure 5.28: Porosity as a function of the radial distance from the axis of the stone column at

a depth of (a) 20 mm (b) 60 mm (c) 100 mm.

26

28

30

32

34

36

38

40

0 5 10 15 20 25 30 35 40

Po

ros

ity [

%]

Distance from stone column axis [mm]

Stone

column

Edge of densification OCR = 11.8 [-]

26

28

30

32

34

36

38

40

0 5 10 15 20 25 30 35 40

Po

ros

ity [

%]


Edge of densificationStone

column

OCR = 3.9 [-]

26

28

30

32

34

36

38

40

0 5 10 15 20 25 30 35 40

Po

ros

ity [

%]


Measured data

Hyperbolic trend function


column

Smear zone (zone 2 in Weber, 2008)

Zone 3 (Weber, 2008)

OCR = 2.4 [-]

Compaction zone

Measured data


26

28

30

32

34

36

38

40

0 5 10 15 20 25 30 35 40

Po

ros

ity [

%]


Measured data

Average


column



OCR = 2.4 [-]

Compaction zone

6 Numerical modelling

219


The rapid development of computer science and increase of computing power over the past

decades have led to an extended use of numerical modelling, in order to solve engineering

problems in general, and geotechnical issues in particular. These numerical analyses are

conducted using the Finite Element Method (FEM), the principles of which are presented e.g.

in Zienkiewicz (1977) and Bathe (1996). The calculations conducted herein are performed

with the commercial code Plaxis (2D Version 2012.2 and 3D Version 2013.1).

6.1 Principles of numerical modelling of ground improvement

Schweiger & Schuller (2005) present an overview of the principles of numerical modelling for

ground improvement. These methods can be divided into improvement through compaction

(e.g. dynamic compaction or embankment preloading with vertical drains), through material

addition without displacement (e.g. mixed-in-place and injections), through material addition

with displacement (e.g. stone columns) and through structural elements (e.g. cemented

columns). Only cases of improvement through compaction, and through material addition

with displacement, are considered here due to the focus of this research. These techniques

can be implemented in the modelling of improved soft soil loaded by an embankment or a

foundation. Different approaches are available to convert an axisymmetric unit cell into a

plane-strain boundary value problem, which are presented in this section.

6.1.1 Improvement through compaction (embankment loading with installation

of vertical drains)

A combination of embankment loading and vertical drains is often used in order to preload

and consolidate soft soils. These boundary value problems can be modelled with software

that couples mechanical and hydraulic behaviour. This work focuses on stone columns, thus

the modelling of drains only will be treated in this review. The permeability properties of the

host soil have to be modified correspondingly, in order to take the installation effects of the

drains into effect.

Indraratna & Redana (1997) propose a conversion from an axisymmetric unit cell to a plane-

strain unit (Figure 6.1). The width bw of a drain, as well as the width bs of the smear zone

under plane-strain conditions, can be assessed for a square pattern as:

6.1

6.2

and for a triangular pattern as:

6.3


220

6.4

with bw width of the drain in plane-strain conditions

bs width of the smear zone in plane-strain conditions



S spacing (axis to axis) between two adjacent drains

(a) (b)

Figure 6.1: Conversion of axisymmetric unit cell into plane-strain for drains (a) axisymmetric

radial flow (b) plane-strain (Indraratna & Redana, 1997).

Unlike Onoue et al. (1991) and Weber (2008), Indraratna & Redana (1997) assume that the

smear zone is homogeneous across the shear and radial compaction zones. The decrease

of the horizontal permeability of the undisturbed host soil in plane-strain conditions kh,p,

neglecting the smear effect, can be formulated as:

( ) 6.5

6.6

with kh,p coefficient of horizontal permeability of the undisturbed host soil in plane strain

conditions

kh horizontal permeability of the undisturbed host soil

R radius of the axisymmetric unit cell


n radius ratio of the unit cell to the drain well


221

Under the assumption that the radius of the axisymmetric unit cell R and the width of the

corresponding zone in plane-strain B (Figure 6.1) are equal, the decreased horizontal

permeability within the smear zone in plane-strain conditions k’h,p can be expressed as:

( )

( )

6.7

6.8

6.9

6.10

with k’h coefficient of horizontal permeability in the smear zone

kh horizontal permeability of the undisturbed host soil

k’h,p coefficient of horizontal permeability in the smear zone in plane-strain

conditions



s radius ratio of the smear zone to the drain well


B width of the zone of influence in plane-strain conditions

Indraratna et al. (2005) refine the formulation proposed by Indraratna & Redana (1997) in

order to circumvent the assumption that the radius of the unit cell R is equal to the width of

the corresponding zone in plane-strain B. While the formulation of the horizontal permeability

of the host soil in plane-strain kh,p is still expressed as in Equation 6.5, the equivalent

horizontal permeability within the smear zone k’h,p is defined as (with n and s according to

Equation 6.6 and Equation 6.8, respectively):

[ (

)

]

6.11

( )

( ) 6.12

( )

( ) [ ( )

( )] 6.13

6.1.2 Discrete modelling of improvement through material addition with

displacement

The soil-structure interaction can be modelled efficiently by using the unit cell approach while

the load transfer underneath composite foundations can also be replicated accurately. A


222

practical advantage of this approach is the limited time needed for a calculation, which

simplifies investigations with parametric studies.

The actual geometry of the foundation can be modelled more accurately using a three-

dimensional (3D) approach, while constitutive models for stone columns and host soil can be

differentiated, as required. Stress paths, (differential) settlements and the different

interactions that develop underneath a loaded composite foundation, as shown e.g. in Figure

2.4, can be reproduced more accurately.

Two-dimensional (2D) modelling of stone columns remains, however, very common and can

be conducted either by converting the mechanical and permeability properties of the soil

(Section 6.1.1), or by adapting the geometry of the boundary value problem. Tan et al. (2008)

present two methods to convert the axisymmetric model to an equivalent plane-strain model.

The effect of smear is neglected in this basic approach.

(a) (b) (c)

Figure 6.2: Cross-sections of the stone column (a) unit-cell; and plane-strain conversions

according to (b) method 1 and (c) method 2 (Tan et al., 2008).

Method 1 adapts the stiffness and permeability parameters of the unit-cell (Figure 6.2 a) to fit

the plane-strain conditions (Figure 6.2 b). The validity of the approach according to Method 1

was confirmed by comparison with results obtained from field testing (Ng & Tan, 2012). The

width of the plane-strain column (denoted as bc in Figure 6.2) is equal to the radius of the

unit-cell stone column (denoted as rc in Figure 6.2) and the width B of the zone considered in

plane-strain is also equal to the radius R of the unit-cell.

The plane-strain permeability is adjusted according to the following set of equations:

( )

( )

[

( )

⁄

( )

⁄

⁄

]

[ ( )

⁄

⁄

( )

⁄

]

6.14

( ) (

)

6.15

for axisymmetric conditions 6.16

R

Legend:

Flow path

Rrc

2B 2B

BB

bc bc

R

Legend:

Flow path

Rrc

2B 2B

BB

bc bc

R

Legend:

Flow path

Rrc

2B 2B

BB

bc bc


223

in plane-strain conditions 6.17

with Esc Young’s modulus of the stone column material



kh, p coefficient of horizontal permeability of the undisturbed host soil in plane-strain

conditions

kh coefficient of horizontal permeability of the undisturbed host soil

B width of the zone of influence in plane-strain conditions

p plane-strain conditions

R radius of the unit cell


Method 2 converts the unit-cell geometry (Figure 6.2 a) to plane-strain conditions (Figure 6.2

c). This approach assumes that the drainage capacity of the column and the replacement

ratio remain constant in plane-strain and axisymmetric conditions. The width of the stone

column in plane-strain conditions is given by:

6.18

Under the assumption that the total area for a square pattern of column is equivalent (Barron,

1948), the relationship between R (Figure 6.2 a) and B (Figure 6.2 c) can be expressed as:

6.19

Chan & Poon (2012) suggest that the mechanical properties of the composite foundation

should be adapted. They consider strips each featuring a width equal to an equivalent square

for the cross-sectional area (Figure 6.3 a) and a depth equal to that of the inclusions. Under

the assumption that the spacing between the strips is equal to the spacing b between the

discrete columns for a square pattern and to √ b/2 for a triangular pattern (Figure 6.3 b) they

formulate an equivalent Young’s modulus Eeq and cohesion c’eq as well as an equivalent

angle of friction ’eq for the strips, while the calculation of the equivalent angle of friction

requires an assumption of the stress concentration on top of the inclusions, which is

summarised by the parameter m (Equation 6.22):

6.20

6.21

6.22

with Eeq equivalent Young’s modulus

c’eq equivalent cohesion

’eq equivalent angle of friction

6.2 Literature review of numerical modelling of ground improvement through stone columns

and prefabricated vertical drains

224

c’s effective cohesion of the host soil

c’sc effective cohesion of the stone column material

’s effective angle of friction of the host soil

’sc effective angle of friction of the stone column material


(a) (b)

Figure 6.3: Plan view of 2D stone columns strips (a) width of an equivalent strip (b) strip

spacing (Chan & Poon, 2012).

Two-dimensional modelling in plane-strain enables a good approximation to be made of the

serviceability limit state provided that the stiffness chosen for the host soil and stone column

material are appropriate for the loading cases considered. However, parameter conversion

from 3D to 2D geometry leads to an alteration of the stress path within the inclusions. This

can cause challenges for the estimation of the ultimate limit state (Schweiger & Schuller,

2005).

6.2 Literature review of numerical modelling of ground

improvement through stone columns and prefabricated vertical

drains

6.2.1 Numerical modelling of ground improvement with stone columns and

prefabricated vertical drains

Rujikiatkamjorn et al. (2007) present the results of the finite element analysis of a case study

at Tianjin Port in Bejing, China, of an embankment stabilised by vertical drains combined with

vacuum loading to accelerate dissipation of excess pore pressure. Figure 6.4 shows the soil

profile and properties at the location of the case study. A vacuum pressure of 80 kPa was

applied and a 3 m high embankment was built in order to reach a loading of 120 kPa (Figure

6.5 a). The settlements were monitored with settlement gauges installed below the top of the

embankment and were measured at depths of 3.5 m, 7.0 m, 10.5 m and 14.5 m below the

surface of the host soil.

d = diameter of

stone column

a = width of equivalent

strip in 2D FEA

b cos30°

2D strip

Asoil

Acolumn b


225

Figure 6.4: Soil profile and properties at Tianjin Port in Beijing, China

(Rujikiatkamjorn et al., 2007).

The conversion presented in Indraratna & Redana (1997) was implemented to conduct a

plane-strain calculation and the modified Cam-Clay theory (Roscoe & Burland, 1968). Figure

6.5 shows that the results of the numerical analysis are in good agreement with the

observations in the field. However, various assumptions had to be made to calibrate the

numerical model, such as the ratio of the horizontal permeability of the undisturbed host soil

kh to the permeability within the smear zone k’h. This ratio was assumed to be equal to 3. The

settlements were slightly over-estimated by the numerical model up to a depth of 7.0 m

below the ground surface, and slightly underestimated at a depth 10.5 m. However, the

overall match was very good.

Atterberg limits [%]Vane shear strength

[kPa] Void ratio [-] Description

of soil

Silty clay(dredged from sea bed)

Muddy clay

Soft silty clay

Stiff silty clay

Depth

[m]

Plastic limit

Water content

Liquid limit



226

Figure 6.5: Case study at Tianjin Port in Beijing, China: embankment and vacuum loading on

soft soil stabilised by drains (a) loading history and (b) comparison of the

predicted (FEM) and measured (Field) consolidation settlements

(Rujikiatkamjorn et al., 2007).

Indraratna et al. (2009) conducted both two- and three-dimensional analyses of the Tianjin

Port in Beijing, China, using the modified Cam-Clay theory (Roscoe & Burland, 1968). The

soil properties determined at the test site are presented in Figure 6.4. A vacuum pressure of

80 kPa was applied before a 3 m high embankment was built in order to reach a load of

120 kPa. The settlements were monitored with settlement gauges installed below the top of

(a)

(b)

Vacuum pressure under membrane

Pre

load

pre

ssure

[kP

a]

Surface (Field)

3.5 m (Field)

7.0 m (Field)

10.5 m (Field)

14.5 m (Field)

Surface (FEM)

3.5 m (FEM)

7.0 m (FEM)

10.5 m (FEM)

14.5 m (FEM)

0 40 80Time [days]

120Time [days]

160 200

1.6

0

40

80

120

160

Settle

ment [m

m]

1.2

0.8

0.4

Settle

ment [m

m]

Pre

load

pre

ssure

[kP

a]

a aVacuum plus preloading


227

the embankment and were measured at depths of 1.0 m and 5.0 m below the surface of the

host soil. The plane-strain study was conducted by implementing the permeability conversion

presented in Indraratna (2005), which leads to good agreement between the two-dimensional

modelling with field data, as well as with the three-dimensional analysis (Figure 6.6).

Figure 6.6: Embankment pre-loading at Tianjin Port in Beijing, China (a) loading history (b)

comparison of the results obtained via 2D and 3D modelling with field

observations (Indraratna et al., 2009).

Weber et al. (2009) present a numerical back-calculation of the centrifuge tests conducted by

Weber (2008) on 1.85 m high embankments placed in-flight (using balls of lead shot) on

over-consolidated remoulded Birmensdorf clay, reinforced with stone columns that had been

constructed in-flight. Birmensdorf clay was modelled using the Hardening Soil Model (Schanz

et al., 1999), stone column material with the Mohr-Coulomb model and the installation

process is modelled by the application of outwards and downwards prescribed

displacements on the edge of an initial cavity. The settlements computed with this procedure

showed a good agreement with the observations made during centrifuge tests (Figure 6.7).

Vacuum pressure under membrane

Vacuum plus preloading

5 m

1 m

120400

Time [days]80

Time [days]

(a)

(b)

0.8

0

Tim

e [

da

ys]

Tim

e [

da

ys]

Pre

loa

dp

ressu

re[k

Pa

]

0.6

0.4

0.2

Se

ttle

me

nt

[mm

]

40

80

120

160

Field

3D

2D



228

Figure 6.7: Development of settlement at the crest of an embankment constructed in-flight on

remoulded Birmensdorf clay reinforced with stone columns – comparison

between numerical model and centrifuge results (Weber et al., 2009).

Basu et al. (2010) make a distinction between a smear and a transition zone, in a similar way

to Onoue et al. (1991) (Figure 2.60) and investigate the effect of soil disturbance around

Prefabricated Vertical Drains (PVD). In this case, the drains have a rectangular cross-section

(a x d), thus the extent of the disturbed zone cannot be expressed in terms of equivalent

mandrel diameter. The decrease of horizontal permeability within the transition zone (i.e. for

⁄⁄ , Figure 6.8 a). is expressed as a function of the permeability of the

undisturbed soil and of the smear zone:

( )

(

) lx/2 2x tx/2 6.23

with kht(x) horizontal permeability within the transition zone for a horizontal flow in the x

direction.

A similar expression is obtained for the variation of kht in the y direction by substituting x with

y in Equation 6.23. The results obtained from an experimental study with small-scale model

tests conducted by Indraratna & Redana (1998) (Figure 2.61 and Figure 2.62) and the

numerical analysis correlate well with results obtained by Basu et al. (2010) using the

modified Cam-Clay theory (Figure 6.8 b). It is surprising, however, that the settlement

calculated without transition zone become significantly higher than those obtained with a

smear zone when the load is increased from 100 kPa to 200 kPa. This could be due to an

over-estimation of the excess pore pressure dissipation caused by the absence of smear

zone with reduced permeability around the drain, which would cause an over-estimation of

the settlements at the beginning of the loading phase. However, the experiment was stopped

10 days after the increase of the load, thus preventing the analysis of the long-term

behaviour of the improved ground under loading. It would also be interesting to confront the

0 50 100 150 200 250 300 350 400 450 500

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Zeit [d]

Se

tzu

ng

en

[m

]

Numerische Berechnung

ZentrifugenversuchFEMFEM

Centrifuge

Settle

ment

[m

m]

Time [d]

(2)

(2)


229

model with field measurements or data from centrifuge modelling in order to overcome the

limitations of small-scale tests concerning the reproduction of the stress levels at prototype

scale (Section 3.2).

(a) (b)

Figure 6.8: Numerical and experimental study of PVDs installed in clay (a) plan view with

dimensions of the smear and transition zones in terms of mandrel size (b)

comparison of settlement obtained with results by Indraratna & Redana (1998)

(Basu et al., 2010).

Castro & Karstunen (2010) investigate the installation effects around stone columns installed

in over-consolidated Bothkennar Clay. The boundary conditions are such that the excess

pore water pressures can only dissipate towards the column and the surface. The column

material is not modelled and the cavity is maintained as a hole with infinite permeability

throughout the consolidation process. This does not allow for the interaction between column

material and surrounding soil to be taken into account. The authors assume that the

permeability of the column material is high enough compared to that of the surrounding soil

to be considered infinite and that the displacement of the soil-column interface after

installation only has minor consequences on the soil properties.

The constitutive models S-CLAY1 (Wheeler et al., 2003) and S-CLAY1S (Karstunen et al.,

2005) were used and the results were compared with those obtained using the modified

Cam-Clay model (denoted as MCC in Figure 6.10). Good agreement of the excess pore

water pressures generated by the column installation normalised by the undrained shear

strength (denoted as cu in Figure 6.10) can be observed between the models at all depths.

The normalisation enables a direct comparison to be made between data obtained from

different depths, soil models and field measurements.

mandrel

transition zone

boundary

Smear Zone: 2 p 3

Transition Zone: 6 p 12

transition

transitsmear zone

boundary

Time [days]

Settle

ments

[m

m]

Str

ess [kP

a]

0 10 20 30 40 50

200

100

0

40

80

120

160

Measured (Indraratna & Redana 1998)

Present Analysis

(Smear Zone = 2d, Transition zone

= 5d, khs/kh0 = 0.2)

Analysis Without Transition Zone

(Smear Zone = 2d, khs/kh0 = 0.2)



230

Figure 6.9: Model geometry and axisymmetric finite element mesh with applied radial

deformation of the stone column wall (Castro & Karstunen, 2010).

Figure 6.10: Normalised excess pore pressures generated by the stone column installation

(Castro & Karstunen, 2010).

Impermeable boundary


231

Figure 6.11: Decrease of the undrained shear strength after column or pile installation

(Castro & Karstunen, 2010).

The variation of the undrained shear strength (denoted as cu in Figure 6.11) obtained

numerically was compared with the data obtained by Roy et al. (1981) for the installation of

piles in field tests. Good agreement between the field observations and the outcomes of the

calculations using the constitutive model S-CLAY1S can be observed for the estimation of

the reduction of the undrained shear strength (normalised with the initial undisturbed shear

strength, denoted as cu0 in Figure 6.11). The results are consistent with the observations

made by Roy et al. (1981), who determined that the radial extent of destructuration of the

host soil was smaller than the radius of influence of the excess pore water pressures. Roy et

al. (1981) however conducted field tests in sensitive clay with a water content noticeably

higher than the liquid limit. Thus, the results may not be generalised.

Indraratna et al. (2013) propose a numerical model using the finite-difference method and

based on a unit cell approach for the boundary value problem of soft soil reinforced by stone

columns, and loaded uniformly by an embankment (Figure 6.12 a and b). The cross-section

of the unit cell is subdivided into 4 different zones: the unclogged column zone (denoted as

rc’), the clogged column zone (denoted as rc), the smear zone (denoted as rs) and the

undisturbed zone (denoted as re).

A soft clay layer with a thickness H overlays an impervious rigid boundary and is improved by

a group of stone columns resting on the rigid boundary. The constitutive model used has

been presented by Indraratna et al. (2013). A range of assumptions were made in this model:

- Darcy’s law is valid and no vertical water flow occurs within the soil mass. No flow

occurs through the cylindrical boundary and the base of the unit cell,

- the flow remains at steady state,

- all compressive strains are vertical,



232

- the elastic part of the settlement may be neglected compared to the plastic

consolidation settlement,

- the degree of saturation of the soil mass is 1 and the water is incompressible,

- the coefficients of permeability and compressibility of the soil mass remain

constant throughout the consolidation process.

Limited information is available in the literature for the determination of the value of the

clogging parameters α and of αk. Mays (2010) suggests values ranging for 0 (representing

total clogging of the column) to 1 (representing a totally unclogged column). The effective

radius r’sc of the column with clogging is expressed as:

6.24

with r’sc effective radius of the stone column (denoted as r’c in Figure 6.12)

rsc radius of the stone column (denoted as rc in Figure 6.12)

α non-dimensional factor ranging for 0 to 1 ( representing fresh and totally

unclogged columns)

The coefficient of horizontal permeability in the clogged column zone may be written as:

6.25

with kh,cl coefficient of horizontal permeability in the clogged zone

k’h coefficient of horizontal permeability in the smear zone

αk ratio of horizontal permeability of the clogged column zone to that of the

smear zone

This approach allows Indraratna et al. (2013) to investigate the influence of clogging on the

dissipation velocity of the generated excess pore water pressures (Figure 6.13). The

clogging reduces the settlements for Tr < 1 and delays the dissipation of excess pore water

pressure. However, as the stress distribution remains the same, the same total settlements

occur.

Although this model opens up some interesting perspectives, it also features some

limitations. Vertical flow is neglected although it can influence the performance of the

improved foundation system. This can be exacerbated when there is a sand bed underneath

the clay layer or for short stone columns. The loading is also assumed to be steady and

uniform, which means that the model is not able to cope with cyclic or time-dependent

loadings.


233

Figure 6.12: Unit cell (a) typical stone column–reinforced soft clay deposit supporting an

embankment; (b) unit cell idealisation; (c) cross-section (Indraratna et al., 2013).



234

Figure 6.13: Influence of clogging on the normalised average excess pore water pressure

and on the normalised average ground settlement (Indraratna et al., 2013).

6.2.2 Analogy to installation of rigid inclusions

The similarity between the installation processes for piles and stone columns has already

been mentioned (Section 2.8). Dijkstra et al. (2011) propose to simulate the installation

phase in axisymmetric conditions using a fixed pile and a moving pile approach (Figure 6.14)

with a hypoplastic constitutive model. The soil moves around the inclusions in the first case

(Figure 6.14 a) while the pile is inserted into the ground in the second (Figure 6.14 b). Due to

the immobility of the pile in the first approach (Figure 6.14 a), the initial stiffness response

during the insertion depends on the location in the mesh where the displacements are

plotted. This issue is solved by the second approach (Figure 6.14 b).

a

a

Time factor Tr

10.80.60.40.20

0

0.03

0.06

0.09

0.12

0.15

0.18

No

rma

lize

da

ve

rag

eg

rou

nd

se

ttle

me

nt

No

rma

lize

da

ve

rag

ee

xce

ss

po

rep

ressu

re

0.0

0.2

0.4

0.6

0.8

No clogging

α = 0.75; αk = 1.0

α = 0.75; αk = 0.5

α = 0.5; αk = 1.0

α = 0.5; αk = 0.5

No clogging

α = 0.75; αk = 1.0

α = 0.75; αk = 0.5

α = 0.5; αk = 1.0

α = 0.5; αk = 0.5


235

(a) (b)

Figure 6.14: Boundary conditions for (a) the fixed pile approach (b) the moving pile approach

(Dijkstra et al., 2011).

The fixed pile and moving pile approaches are used to simulate centrifuge tests during which

piles were installed in sand. The measured effective stress in the centrifuge (denoted as

meas. in Figure 6.15 and Figure 6.16) is compared with the stress at the pile base calculated

with the fixed pile approach (denoted as FP in Figure 6.15) and with the moving pile

approach (denoted as MP in Figure 6.16) for different values of the initial porosity n0 of the

host soil. Loose conditions are modelled with n0 = 0.439 [-], medium dense conditions with

n0 = 0.415 [-] and dense conditions with n0 = 0.389 [-]. The fixed pile approach tends to

overestimate the stress response while the moving pile approach tends to underestimate the

response, in comparison with the measured tip resistance.

q

pile

L

R

soil

H

inflow of material with prescribed velocity

W

geometry lineinfluence radius of

geometry line == pile radius

node in pile, v = vpile

node in soil

v not prescribed



236


during installation for the fixed pile approach (after Dijkstra et al., 2011).


during installation for the moving pile approach (after Dijkstra et al., 2011).

-14000 -12000 -10000 -8000 -6000 -4000 -2000 00

-16000

5

4.5

4

3.5

3

2.5

2

1.5

1

0.5

0

σyy;base [kPa]

Pile

dis

pla

ce

me

nt[m

]

0

FP; n0=0.439

FP; n0=0.415

FP; n0=0.389

meas.; n0=0.389

meas.; n0=0.439

meas.; n0=0.415

FP; n0=0.439

FP; n0=0.415

FP; n0=0.389

meas.; n0=0.389

meas.; n0=0.415

meas.; n0=0.415

-14000 -12000 -10000 -8000 -6000 -4000 -2000 00

-16000

5

4.5

4

3.5

3

2.5

2

1.5

1

0.5

0

σyy;base [kPa]

Pile

dis

pla

cem

ent[m

] 0

MP; n0=0.439

MP; n0=0.415

MP; n0=0.389

meas.; n0=0.389

meas.; n0=0.439

meas.; n0=0.415

meas.; n0=0.389

MP; n0=0.439

MP; n0=0.415

MP; n0=0.389

meas.; n0=0.439

meas.; n0=0.415


237

Grabe & Pucker (2012) modelled the construction of displacement piles using finite

elements. They built construction aids (denoted as Pipe in Figure 6.17) into the mesh and

inserted the piles into the soil continuum along the aids. Although this way of modelling the

insertion of an inclusion into the soil is interesting, the results presented by Grabe & Pucker

(2012) are specifically related to the most relevant mechanisms for piles. This study focuses

on the influence of the rotating speed of the mandrel, as well as its form.

Figure 6.17: Modelling technique for the simulation of the pile insertion

(after Grabe & Pucker, 2012).

6.3 Constitutive models

The granular inclusions were modelled using the Mohr-Coulomb (MC) model, while the soft

soil was idealised with the Hardening Soil Model (HSM) in Plaxis

(Brinkgreve & Broere, 2008).

6.3.1 Mohr-Coulomb model

6.3.1.1 Description

The MC model is a linear elastic perfectly plastic model in which the strains are decomposed

into an elastic and a plastic part (εe and εp respectively, Figure 6.18). Plasticity is associated

with the development of irreversible strains. A yield function f is used to assess whether

plasticity occurs in a calculation: plastic yielding is associated with the condition f = 0.

Pile

Pipe,

R=1 mm

Soil continuumSoil continuum


238

Figure 6.18: Elastic perfectly plastic model.

The two parameters controlling the yield surface are the effective cohesion c’ and the

effective angle of friction . The effective cohesion can be used to model approximately the

effect of suction or cementation on the intersection of the failure line with the vertical axis in a

– σ’ diagram (Figure 6.19).

Figure 6.19: Impact of the effective cohesion on the failure line in a – σ’ diagram.

Special attention should be given to the definition of the Young’s modulus E, as this

parameter controls the development of strains. The initial stiffness modulus Ei (Figure 6.21)

can be used for soils with a large elastic compression domain. It is more common to use the

secant stiffness in a consolidated drained triaxial test E50 (Figure 6.21) to represent the

loading of soils. In case of unloading and reloading, e.g. for applications in tunnelling, the

stiffness for unloading – reloading (Figure 6.21) should be used. Unlike the Hardening Soil

Model (HSM, Section 6.3.2), the stiffness moduli used in the Mohr-Coulomb model are not

stress-dependent.

f = 0

’

0

c’

τ [kPa]

Failure line

σ’ [kPa]

’


239

The tangent stiffness for primary oedometer loading Eoed can be calculated as:

( )

( ) ( ) 6.26

with Eoed tangent stiffness for primary oedometer loading

E Young’s modulus

Poisson’s ratio

6.3.1.2 Limitations of the Mohr-Coulomb model

Although Mohr-Coulomb is a well-proven failure criterion, it exhibits some limitations, two of

which are exposed here. First, a linear elastic stiffness behaviour is assumed up to the failure

surface, which limits the ability of the model to predict deformations before yielding. Second,

the use of effective strength parameters in undrained analysis leads to an overestimation of

the undrained shear strength by Δsu due to the different stress paths followed in reality and

by the FEM model (Figure 6.20).

Figure 6.20: Effective stress paths followed real soil and FEM prediction using the

Mohr-Coulomb model.

6.3.1.3 Input parameters of the Mohr-Coulomb model

The Mohr-Coulomb model requires five parameters, as summarised in Table 6.1.

Table 6.1: Input parameters for the Mohr-Coulomb model.

E Young’s modulus [kPa]

’ Poisson’s ratio [-]

c’ Cohesion [kPa]

Effective angle of friction [°]

Angle of dilatancy [°]

6.3.2 Hardening Soil Model

The Hardening Soil Model (HSM) is an elasto-plastic model, formulated in 3D, which differs

from the Mohr-Coulomb model as the soil behaviour before failure can be better modelled

q

p’

FEM prediction with

Mohr-Coulomb

Real soil behaviour

Δsu

φ’


240

using three input stiffness moduli (Figure 6.21). The HSM is based on the Mohr-Coulomb

failure criterion, but the shear strain hardening (Figure 6.22) caused by deviatoric loading,

and the volumetric hardening (Figure 6.23) induced by volumetric strains, are both accounted

for. Schanz et al. (1999) present a detailed description of the HSM.

6.3.2.1 Stiffness moduli

The HSM uses stiffness moduli determined in two-dimensional, axisymmetric, triaxial

compression tests. Three stiffness moduli are used in order to describe the loading

behaviour of the soil. Ei is the initial tangent stiffness modulus and E50 is the secant stiffness,

both for primary axial loading and Eur is the stress-dependent stiffness for unloading-

reloading paths. All stiffnesses are those obtained from a consolidated drained triaxial test in

axial compression (CIDC or CADC). While the differentiation between isotropic and

anisotropic consolidation is not often made in practice, both kinds of triaxial tests will be

denoted from here on as CDC. The different stiffness moduli (Figure 6.21) used in the HSM

are listed in Table 6.2.

Table 6.2: Stiffness moduli used in the HSM.

Ei Initial tangent stiffness modulus

E50 Secant stiffness for primary loading in a CDC triaxial test

Eur Stress-dependent stiffness for unloading – reloading in a CDC triaxial test

Figure 6.21: Hyperbolic stress-strain relation in primary loading and unloading-reloading in a

CDC triaxial test (Schanz et al., 1999).

E50 is obtained from a CDC triaxial test for a mobilisation of 50 % of the failure shear strength

qf (Figure 6.21). It is preferred as stiffness for initial loading to the initial stiffness modulus Ei,

Asymptote

E50

1Ei

1

Eur

1

qf

qa

q

ε1


241

which is more difficult to determine experimentally, and gives a good approximation of the

initial behaviour of the soil. E50 is defined as:

(

)

6.27

with E50 secant stiffness for primary loading in a CDC triaxial test

E50ref secant stiffness for primary loading in a CDC triaxial test corresponding to the

reference stress pref

pref reference stress, usually set equal to 100 kPa

σ’3 principal effective stress

c’ effective cohesion


m power for stress-level dependency of stiffness. This factor should be equal to

1.0 in the case of soft clays [-] (Schanz et al., 1999).

The unloading – reloading path (for OCR > 1) is purely non-linear elastic and Eur is

formulated as:

(

)

6.28

with Eur unloading / reloading stiffness

Eurref unloading / reloading stiffness corresponding to the reference stress pref

6.3.2.2 Yield surfaces

The two yield surfaces considered by the HSM are shown in Figure 6.22 (shear strain

hardening) and Figure 6.23 (volumetric hardening). The shear strain hardening corresponds

to the rotation of the yield loci with increasing plastic shear strain γp, while the volumetric

hardening denotes the expansion of the cap yield surface with growing volumetric strains.

Figure 6.22: Successive yield loci for shear strain hardening for various values of the plastic

shear strain γp and failure surface for m = 0.5 [-] (Brinkgreve & Broere, 2008).

Deviatoric stress q [kPa]

Mean effective stress p’ [kPa]

Mohr-Coulomb failureMohr-Coulomb failure line


242

Figure 6.23: Cap yield surface of the HSM for volumetric hardening in the - plane

(after Brinkgreve & Broere, 2008).

6.3.2.3 Shear strain hardening

Shear strain hardening (Figure 6.22) is controlled by two yield functions, f12 and f13

(Equations 6.29 and 6.30), which are defined as:

(

)

⁄ (

)

(

)

6.29

(

)

⁄ (

)

(

)

6.30

(

) 6.31

6.32

⁄

6.33

with f12, f13 yield surfaces in σ1, σ2 and σ1, σ3 planes, respectively [-]

E50 secant stiffness for primary loading in a CDC triaxial test

σ’1, σ’2, σ’3 principal effective stresses

Eur unloading / reloading stiffness in a CDC triaxial test

γp plastic shear strain [-]

Rf failure ratio, usually set equal to 0.9 [-]

c’ effective cohesion


ε1p, ε2

p principal plastic strains [-]

εvp plastic volumetric strain [-]

Ei initial stiffness modulus in a CDC triaxial test

q deviatoric stress

qf deviatoric stress at failure

‘

Cap yield surface

p’

pp’c’ cotφ’

α pp’


243

Schanz et al. (1999) assume that the approximation made in Equation 6.32 is valid under the

assumption that the plastic volumetric strains are equal to zero. Although this is never

precisely the case, Schanz et al. (1999) declare that the plastic volumes changes in “hard”

soils tend to be small compared to the axial strain, which they contend makes this

approximation acceptable. This is discussed in Section 6.3.2.5.

The yield loci can be visualised in a p’-q plane (Figure 6.22) for a given constant value of the

plastic shear strain γp. Plotting such loci, which satisfy the condition f12 = f13 = 0, implies using

Equations 6.27, 6.28, 6.29 and 6.30. The shape of the curves depends on the value selected

for m. Straight lines are obtained for m = 1.0 (as for example for the Mohr-Coulomb failure

line, Figure 6.22), and curves for lower values of this parameter (Figure 6.22). The failure

criterion is given by the MC-failure condition.

6.3.2.4 Volumetric hardening

The volumetric hardening corresponds to the expansion of the cap yield surface with

increasing volumetric strains (Figure 6.23). The formulation of a cap yield surface is

necessary for a model with independent input of E50ref

, mainly controlling the shear yield

surface and the plastic strains related to it, and of Eoedref, controlling the cap yield surface and

the plastic strains originating from it. The cap yield surface can be expressed as:

6.34

6.35

( )

6.36

6.37

with fc cap yield surface [-]

special stress measure for deviatoric stresses

p’ mean effective stress

σ’1, σ’2, σ’3 principal effective stresses


α cap parameter relating to K0NC [-]

pp pre-consolidation stress

δ parameter depending on the effective angle of friction [-]

is a 3D generalisation of the formulation of the deviatoric stress q for a triaxial compression

stress state (q = σ1’ – σ3’), which allows for the principal effective stress σ’2 to be considered

by using a factor δ. is equal to q for a triaxial compression (σ’2 = σ’3). A 3D formulation of

the deviatoric stress is necessary in order to obtain yield contours in effective principal stress

space (Figure 6.24).


244

Figure 6.24: Representation of yield contours of the HSM in effective principal stress space

(Schanz et al., 1999).

The magnitude of the yield cap is mainly controlled by the pre-consolidation stress pp

(Equation 6.34). The hardening function relating pp to the volumetric cap strain εvpc is:

(

)

6.38

with εvpc volumetric cap strain [-]

cap parameter relating to Eoedref [-]

m power for stress-level dependency of stiffness [-]

pp pre-consolidation stress

pref reference stress

The cap parameters α and β are not direct input parameters, but their magnitude can be

defined by the values of K0NC and Eoed

ref (Brinkgreve & Broere, 2008). Figure 6.23 shows the

yield surfaces of the HSM model in - space, taking the effect of any effective cohesion c’

into account, and displaying the location of the cap yield surface.

6.3.2.5 Limitations of the Hardening Soil Model

The assumption made by Schanz et al. (1999) is only valid for “hard” soils, i.e. rocks, and

could be assumed to be representative in the highly over-consolidated zones of the clay

samples used in this research (OCR > 20, Figure 4.3), that is up to a depth of 15 mm (σc =

100 kPa), respectively 20 mm (σc = 200 kPa). This assumption is however violated in both

fine grained and coarse grained soils and in the lower part of the soil samples used in this

research, where OCR < 20.

In p’-q space, neglecting the volumetric part of the plastic strain εvp causes a rotation of the

incremental plastic strain d εp, which becomes vertical (Figure 6.25) instead of being normal

to the critical state line (associated flow rule). This rotation results in a state that violates the

σ’2

σ’3

σ’1


245

consistency condition during plastic loading, according to which the stress states before and

after plastic loading have to be on the failure surface, which can be expressed as:

6.39

with F failure surface

p’ mean effective stress

q deviatoric stress

This challenges the theoretical evolution of the distribution of the yield loci during shear strain

hardening (Figure 6.22).

Figure 6.25: Representation of the associated flow rule in triaxial space.

6.3.2.6 Input parameters of the Hardening Soil Model

Some of the parameters of the HSM (the failure parameters , c’ and ) coincide with those

of the Mohr-Coulomb model (Table 6.1). The required input parameters for the soil stiffness

are summarised in Table 6.3.

Table 6.3: Input parameters for the soil stiffness in the HSM.

E50ref

Secant stiffness for primary loading in a CDC triaxial test

corresponding to the reference stress pref [kPa]

Eoedref

Tangent stiffness for primary oedometer loading corresponding to

the reference stress pref [kPa]

Eurref

Unloading / reloading stiffness in a CDC triaxial test corresponding

to the reference stress pref [kPa]

m Power for stress-level dependency of stiffness [-]

’ur Poisson’s ratio for unloading - reloading [-]

pref Reference stress [kPa]

K0NC Coefficient of earth pressure at rest of a normally consolidated soil [-]

Rf Failure ratio, usually set equal to 0.9 [-]

0

q, dεsp

p’, dεvp

1

M

dεvp

dεsp

dεp

Critical state line

dεp (dεvp=0)

6.4 Axisymmetric numerical modelling

246


The numerical modelling was first conducted using an axisymmetric 2D model and

subsequently in 3D. This section presents the ideas and options discarded (Section 6.4.1)

that led to the model used (Section 6.4.2), as well as the results obtained (Section 6.4.3) with

the axisymmetric numerical modelling.

2-dimensional axisymmetric numerical modelling of the centrifuge tests has been conducted

using specimens prepared in adapted oedometer containers (Section 3.7.5), namely tests

JG_v7 (pre-consolidation up to 200 kPa) and JG_v9 (pre-consolidation up to 100 kPa). The

modelling was carried out using the code Plaxis 2D Version 2012.2, with an axisymmetric

model and 15-noded elements.

6.4.1 Options discarded

Modelling the installation phase of inclusions into soil is cumbersome. A relatively elegant

solution using the commercially available code Abaqus is the method proposed by Grabe &

Pucker (2012), which was presented in the previous section. However, the use of Plaxis 2D

restricts the possibilities of modelling the installation phase to the application of radially

outwards and vertically downwards prescribed displacements applied on the vertical limits of

an initial cavity (Weber, 2008; Figure 6.26).

Figure 6.26: Modelling of the insertion of the stone column installation tool by means of

application of prescribed displacements on the wall of an initial cavity (Weber,

2008).

The modelling of the installation phase in a 2D axisymmetric model conducted by Weber

(2008) delivered some results in good agreement with the results obtained from centrifuge

tests, in respect of the stress paths and excess pore pressures. However, the stiffness of the


247

soft clay bed had to be adapted in the numerical analysis to achieve a good fit to the load-

settlement behaviour during embankment loading.

Moreover, the modelling of the installation phase is very cumbersome in practical cases,

which has stimulated the research towards the development of a simple and realistic

numerical modelling approach by taking the installation effects into account. The goal is to

develop an approach that a practical engineer might be willing and able to use. This has led

to the decision to adopt a “wished-in-place” approach, in order to model both the inclusions

and any installation effects.

The influence of the over-consolidation of the soft soil can be taken into account by defining

a Pre-Overburben-Pressure (POP) in the numerical parameters describing the soil

properties, when calculating the initial stress field. The Plaxis code (Brinkgreve & Broere,

2008) recalculates the coefficient of earth pressure at rest K0, taking the pre-consolidation

into account by using the following formula:

( )

| |

6.40




ur Poisson’s ratio for the unloading-reloading

POP Pre-Overburden-Pressure

| | absolute value of the vertical total stress

Although this approach looks tempting, it leads to an overestimation of the horizontal stress

near the surface due to the very high values reached in predicting the OCR, and thus to an

unrealistic failure state because of the generation of the stresses during the initial phase.

The initial stress state was calculated by modelling the consolidation under 1 g. This was

done by implementing a soil featuring the properties of the slurry used in the preparation of

the soil models (Section 3.6) and loading it by 100 kPa or 200 kPa, depending on the

centrifuge test modelled. The calculation phases are listed in Table 6.4.

Table 6.4: Description of the calculation phases used in the axisymmetric model.

Phase Action

Initial

phase Generation of an initial stress state with the slurry (clay with reduced unit weight)

1 Loading of the slurry

2 Unloading of the slurry

3 Replacement of the slurry by clay with properties determined in the laboratory

4 Activation of the clusters corresponding to the stone columns and to the

installation effects

5 Loading of the stone columns using prescribed displacements

6 Dissipation of the excess pore water pressures generated


248

6.4.2 Model

The numerical modelling was conducted at prototype scale. The mesh for the axisymmetric

model (Figure 6.27) is 6.25 m wide and 8 m high, corresponding to the prototype dimensions

of the adapted oedometer containers (Sections 3.6.3 and 3.7.5). The stone column is

modelled by a cluster featuring a width of 0.3 m and a height of 6 m. The water table is

located 0.5 m below the surface of the model.

The Hardening Soil parameters used to model the clay are listed in Table 6.5. The soil

properties implemented in the numerical model were determined in laboratory experiments

(Sections 3.5.1 and 5.1). The unloading / reloading stiffness had to be amended

in order to improve the match between recorded and modelled load-settlement curves

(Figure 6.28), but the difference between the value used in the numerical model and the

value determined in the laboratory is acceptable (15000 kPa instead of 13000 kPa).

A value of 50 kPa was assigned to represent cohesion in the 0.2 m thick layer at the top of

the model, in order to prevent the appearance of very large unrealistic soil movements at the

surface during loading. The displacement-controlled footing loading was modelled by

applying prescribed displacements at the surface of the model. A displacement of 850 mm

(17 mm @ 50 g) was applied over a time of 2.125.106 s (850 s @ 50 g).

Table 6.5: Summary of the Hardening Soil parameters for the clay.

Parameter σc [kPa] Value

Unit weight γsat [kN/m3] 100 18.50

200 20.10

Coefficient of horizontal permeability kx [m/s] 100 1.10-9

200 5.10-10

Coefficient of vertical permeability ky [m/s] 100 5.10-10

200 2.5.10-10

Secant stiffness for primary loading in CDC triaxial test E50ref

[kPa] 100 / 200 2362

Tangent stiffness for primary oedometer loading Eoedref [kPa] 100 / 200 1900

Unloading / reloading stiffness Eurref [kPa] 100 / 200 15000

Reference stress for stiffness pref [kPa] 100 / 200 100

Poisson´s ratio for unloading / reloading ur [-] 100 / 200 0.2

Power for stress-level dependency of stiffness m [-] 100 / 200 1

Effective cohesion c’ [kPa] 100 / 200 1

Effective angle of internal friction φ’cv [°] 100 / 200 24.5

Angle of dilatancy y [°] 100 / 200 0


249

The Mohr-Coulomb parameters used for the stone column material are summarised in

Table 6.6.

Table 6.6: Mohr-Coulomb parameters for the stone column material.

Parameter Value

Unsaturated unit weight γunsat [kN/m3] 15.00

Saturated unit weight γsat [kN/m3] 20.00

Isotropic coefficient of permeability [m/s] 1.10-5

Young´s modulus E [kPa] 20000

Poisson’s ratio [-] 0.3

Effective cohesion c’ [kPa] 1

Effective angle of internal friction φ’ [°] 37.00

Angle of dilatancy y [°] 10.00

The influence of the installation effects is taken into account by means of a wished-in-place

procedure. The dimensions of the corresponding zones must be defined. Weber (2008)

showed the appearance of a smear zone, in which the clay platelets display a vertical

reorganisation. This zone is 2 mm wide at model scale under 50 g, i.e. 0.1 m at prototype

scale (Figure 3.21). This was modelled numerically by a cluster extending radially outwards

and vertically downwards 0.1 m from the edge of the stone column (Figure 6.27). The

extensive destructuring undergone by the clay within the smear zone is taken into account by

a reduction of the stiffness by a factor of 0.8 (Table 6.7).

Table 6.7: Summary of the Hardening Soil parameters for the smear zone.



200 20.10

Coefficient of horizontal permeability kx [m/s] 100 / 200 1.10-10

Coefficient of vertical permeability ky [m/s] 100 / 200 1.10-10


[kPa] 100 / 200 1889





250

Onoue et al. (1991) identified a reduction of the horizontal permeability by a factor of about

0.8 in the so-called disturbed zone (Figure 2.60). Such an approach was implemented here,

while the extent of this zone is different to that suggested by Onoue et al. (1991).The radial

extent of this zone is 2.5 times the radius of the stone column, which takes Weber’s (2008)

findings, as well as the results of the investigations conducted with the electrical impedance

needle (Section 4.7), into account. Its vertical extent from the toe of the stone column is 1.5

times the diameter of the inclusion (Figure 6.27), which is in good agreement with the

observations made by Linder (1977) for inclusions installed in dense sand (Figure 2.50). This

annular zone will be described from now on as the compaction zone. The permeability of the

compaction zone was reduced by a factor of 0.8, compared to that of the surrounding soft

clay, while the stiffness was increased by a factor of 1.2 in order to take the strength increase

caused by the stone column installation into account (Table 6.8).

Table 6.8: Summary of the Hardening Soil parameters for the compaction zone.



200 24.10

Coefficient of horizontal permeability kx [m/s] 100 8.10-10

200 4.10-10

Coefficient of vertical permeability ky [m/s] 100 4.10-10

200 2.10-10


[kPa] 100 / 200 2834





251

Figure 6.27: 2D axisymmetric numerical model for a unit cell including a single stone column.

6.4.3 Results

Figure 6.28 shows a comparison of the load-settlement curves for tests JG_v7

(σc = 200 kPa) and JG_v9 (σc = 100 kPa) obtained experimentally in the centrifuge (denoted

as JG_v7 and JG_v9, respectively) and numerically (denoted as

JG_v7 – Plaxis and JG_v9 – Plaxis, respectively). The settlement of the footing in the

centrifuge was scaled up to prototype scale. The maximum values of the footing load can be

modelled with satisfying precision (Table 6.9).


loads.

Test Pmax, Centrifuge

[kPa]

Pmax, Plaxis

[kPa]

Difference

[%]

JG_v7 (σc = 200 kPa) 145.44 141.90 2.49

JG_v9 (σc = 100 kPa) 119.67 115.11 3.96

Stone column

Smear zone

Compaction zone

8 m

6m

6.1

m

7m

Clay

0.3 m

0.4 m

0.75 m

0.2 m

6.25 m

1.4 m

Prescribed displacements

x

y


252

Figure 6.28: Comparison of the experimental and numerical load-settlement curves for tests

JG_v7 and JG_v9.

Figure 6.29 and Appendix 8.11 show the deformed mesh obtained after modelling the footing

loading during tests JG_v7 and JG_v9, respectively. The differences are minimal and tend to

indicate that the depth of the bulging deformation of the columns is independent of the pre-

consolidation stress. The deformation of the inclusion is concentrated in both cases near the

surface, while the displacements of the toe are negligible. This is confirmed by the

distribution of the vertical strain increments computed numerically for test JG_v7, for a

footing settlement of 850 mm (Figure 6.30). The vertical and shear strain increment

computed for tests JG_v7 and JG_v9 are presented in Appendices 8.8 and 8.9, and

Appendices 8.13 and 8.14, respectively. Both vertical and shear strain increments are

concentrated near the surface up to a depth of 2.0 m. The deformations below that depth are

negligible and the total vertical stress increase at the toe of the inclusion is minimal

(Figure 6.31). The sudden vertical stress increase within the stone column at a depth of

approximately 3 m cannot be explained either by any physical mechanisms or by the

distribution of the vertical strain increments (Figure 6.30) and is thus assumed to be due to a

local numerical instability.

0

20

40

60

80

100

120

140

160

0 100 200 300 400 500 600 700 800 900

Fo

oti

ng

lo

ad

ing

[k

Pa

]

Footing settlement [mm]

JG_v7 JG_v7 - Plaxis JG_v9 JG_v9 - Plaxis


253


footing load of 145.44 kPa.


850 mm and a footing load of 145.44 kPa.

Stone column

Smear zone

Compaction zone

8 m

6m

6.1

m

7m

Clay

0.3 m

0.4 m

0.75 m

0.2 m

6.25 m

1.4 m

0.8

5 m

x

y


254


settlement of 850 mm and a footing load of 145.44 kPa.

The development of plastic points during the loading phase is presented in Figure 6.32.

Failure points denote elements that are located on the Mohr-Coulomb failure line

(Figure 6.19, respectively Figure 6.22), while Cap points and Hardening points refer to

elements undergoing plastic shear strain hardening (Figure 6.22, Section 6.3.2.3) and plastic

volumetric hardening (Figure 6.23, Section 6.3.2.4), respectively. Tension cut-off points

denote elements which would be in tension if the value of cohesion was positive. The depth,

up to that elements undergo plastic shear hardening, ranges from 3.2 m for a settlement of

100 mm (P = 85 kPa) to 4.0 m for a settlement of 850 mm (P = 145.4 kPa), as illustrated in

Figure 8.19 to Figure 8.21. Failure points reach a depth of 2.0 m within the stone column for

a settlement of 100 mm (Figure 8.19) and of approximately 2.5 m for settlements of 400 mm

(Figure 8.20) and 850 mm (Figure 8.21). These points are present up to a depth of 1.5 m

within the host soil for a settlement of 400 mm (Figure 8.20) and up to a depth of 2.0 m for a

settlement of 850 mm (Figure 8.21), which corresponds to the zone where the excess pore

water pressures are the highest (Figure 6.46).


255

(a) (b) (c)

Figure 6.32: Development of plastic points during the loading phase for test JG_v7 (a) for a

settlement of 100 mm (P = 85 kPa), (b) for a settlement of 400 mm

(P = 115.2 kPa) and (c) for a settlement of 850 mm (P = 145.44 kPa).

Figure 6.28 shows that the initial stiffness in the load-settlement curve obtained in the

numerical model is noticeably higher than that measured in the physical model. Three

explanations can be proposed:

- the clay sample used for the centrifuge test was thicker than 160 mm after

consolidation under the press. The height of the sample was reduced manually,

which is thought to have caused a disturbed layer with reduced stiffness near the

surface of the sample,

- the assumption made for the numerical modelling is that of a full contact between

footing and soil specimen. However, the surface onto which the load was applied

during the centrifuge tests was not perfectly smooth,

- in combination with the development of the stress distribution under a rigid footing

(Nater, 2005), the actual stress distribution differs from the theoretical stress

distribution expected under a rigid footing (Figure 6.33), which causes a less stiff

response than was computed numerically. The latter can also be seen when

comparing field measurements with results from numerical modelling

(Arnold, 2011).

The first explanation is not easy to prove numerically. The attempts to model the disturbance

of the soil near the surface were not conclusive. However, the implementation of pressure

pads between the footing and the surface of the subsoil has given an insight into


256

the pressure distribution under the footing during loading for tests JG_v7 and JG_v9

(Figure 6.34, one pixel corresponds to a surface of approximately 1 mm2). The blue surfaces

in Figure 6.34 represent, for a footing settlement of 100 mm at prototype scale, the zones in

which a load is actually applied onto the soil, while the white areas correspond to the

unloaded zones. The location of the stone column is, in both cases, marked by a yellow

circle. However, the quantity of sand that was poured into the feed pipe during the installation

of the stone column was not sufficient for the top of the column to reach the surface of the

soft soil. This created a cavity, which can be seen in Figure 6.34 (a), as no load was applied

at the location of the stone column. This cavity was closed during loading as clay collapsed

into it (Figure 6.34 b). Thus the loading was actually applied on a clay surface, which covered

the stone column, and no significant pressure difference could be measured (Figure 6.34 b).

(a) (b) (c) (d) (e)

Figure 6.33: Vertical stress distribution from a line load below a rigid strip footing (a) for the

self-weight of the footing and for a global safety factor equal to (b) 3.0, (c) 2.0,

(d) 1.5 and (e) 1.0 (Jessberger, 1995).

The representation of the pressure distribution shows that the surface onto which a load is

actually applied is significantly smaller than in an ideal case. As the load is brought onto the

footing in a displacement-controlled manner, it builds up noticeably lower than as calculated

numerically.

Figure 6.35 shows the distribution of the loaded zones under the footing for a settlement of

400 mm at prototype scale for the tests JG_v7 and JG_v9. The location of the stone column

is, in both cases, that indicated in Figure 6.34. No significant pressure difference could be

measured as the load was actually applied on a clay surface, which covered the stone

column. The white vertical stripes on the right hand side are due to local failure of the row of

sensors in the pressure pads. Figure 6.35 (a) shows, without doubt, that full contact has

been reached between footing and clay surface during test JG_v7, for a settlement of 400

mm at prototype scale. Such an assessment is not as straightforward in the case of

test JG_v9. In addition to the white stripes on the right hand side, the white zones in the

bottom right corner indicate an unloaded zone.


257

(a) (b)

0 kPa 100 – 140 kPa 140 – 180 kPa


scale (2 mm under 50 g) for (a) test JG_v7 (P = 55.6 kPa) and (b) test JG_v9 (P

= 46.1 kPa).

(a) (b)

0 kPa 100 – 140 kPa 140 – 180 kPa 180 – 220 kPa


scale (8 mm under 50 g) for (a) test JG_v7 (P = 110.1 kPa) and (b) test JG_v9

(P = 90.1 kPa).

However, the fact that most of these apparently unloaded zones are still present for a

settlement of 800 mm at prototype scale (Figure 6.36), indicates that there might be a local

measurement issue of the pressure pads. As a consequence, full contact between footing

and clay surface may be assumed for a settlement of 400 mm at prototype scale during

test JG_v9.

Stone

column

Stone

column

56 m

m

56 m

m


258

0 kPa 100 – 140 kPa 140 – 180 kPa 180 – 220 kPa


scale (16 mm under 50 g) for test JG_v9 (P = 118.1 kPa).

These observations confirm the second explanation for the initial difference between

centrifuge and numerical modelling of the load-settlement behaviour. They also show that the

results obtained with the proposed numerical model are in good agreement with the

measurements conducted in the centrifuge when full contact between the footing and the

clay surface is attained in the centrifuge.

Figure 6.37 and Figure 6.38 show the stress distribution under the footing, as computed

numerically for footing settlements of 100 mm, 400 mm and 850 mm for tests JG_v7 and

JG_v9, respectively. The differences between the measurements obtained with the pressure

pads (Figure 6.34, Figure 6.35 and Figure 6.36) and the stress distributions computed

numerically are significant as a strong stress concentration on top of the stone column is

obtained numerically, which was not the case during centrifuge tests due to the issues

encountered with the filling of the inclusion. However, the stress peaks that were measured

by the pressure pads around the edge of the footing, once full contact between footing and

clay was reached, were also observed in the numerical modelling.

The stress concentration factor m at the top of the stone column computed numerically

reaches a value of approximately 3 in both tests JG_v7 and JG_v9 for a footing settlement of

100 mm and decreases to approximately 2.6, for a footing settlement of 400 mm

and 2 (test JG_v7), respectively 2.3 (test JG_v9) for a footing settlement of 850 mm

(Figure 6.41 and Figure 6.42). This confirms the dependency of the stress concentration

factor on the load applied on the composite foundation and is consistent with the

measurements obtained by Greenwood (1991) at St. Helens (Figure 2.7).

The influence of the varying stiffnesses of the smear and compaction zones and of the host

soil can be noted when comparing the stress distribution under the footing. The compaction

zone, which has the highest stiffness (Table 6.8), attracts more load than the surrounding

host soil, the stiffness of which is lower (Table 6.5). The surrounding host soil is also carrying

56

mm


259

more load than the smear zone, which has the lowest stiffness (Table 6.7). The differences

between the three zones are less with decreasing pre-consolidation of the sample, which can

be noted when comparing the distribution computed for tests JG_v7

(σc = 200 kPa, Figure 6.37) and JG_v9 (σc = 100 kPa, Figure 6.38).


distance, for settlements of 100 mm, 400 mm and 850 mm for test JG_v7

(σc = 200 kPa).


distance, for settlements of 100 mm, 400 mm and 850 mm for test JG_v9

(σc = 100 kPa).

Figure 6.39 and Figure 6.40 present the distribution of the total vertical stress computed

numerically for tests JG_v7 and JG_v9, respectively, as a function of the radial distance from

0

50

100

150

200

250

300

350

400

450

0 0.5 1 1.5

To

tal ve

rtic

al s

tre

ss

σv

[kP

a]

Radial distance [m]

100 mm (P = 85 kPa) 400 mm (P = 115.2 kPa)850 mm (P = 145.44 kPa)

Edge of stone column

Sm

ear

zon

e

Compactionzone

Edge of footing

0

50

100

150

200

250

300

350

400

450

0 0.5 1 1.5

To

tal ve

rtic

al s

tre

ss

σv

[kP

a]

Radial distance [m]

100 mm (P = 70.8 kPa) 400 mm (P = 94.3 kPa)850 mm (P = 119.67 kPa)


Sm

ear

zon

e

Compactionzone

Edge of footing


260

the axis of the stone column at depths of 0 m, 2 m, 4 m and 6 m and for a footing settlement

of 100 mm. A dissipation of the stress peak measured at the edge of the footing with depth is

observed. The load transferred to the stone column does not vary significantly between 0 m

and 2 m and between 4 m and 6 m depth. The decrease of load transferred to the column

between depths of 2 m and 4 m can be explained by the increase of the load transferred to

the surrounding host soil. The differences between loads transferred to smear and

compaction zones and host soil become less marked with increasing depth.


footing (z = 100 mm) and at depths of 2 m, 4 m and 6 m for a footing settlement

of 100 mm during the footing loading for test JG_v7 (P = 85 kPa).



of 100 mm during the footing loading for test JG_v9 (P = 70.8 kPa).

0

50

100

150

200

250

300

0 0.5 1 1.5

To

tal ve

rtic

al s

tre

ss

σv

[kP

a]

Radial distance [m]

z = 100 mm z = 2 m z = 4 m z = 6 m


Sm

ear

zon

e

Compactionzone

Edge of footing

0

50

100

150

200

250

300

0 0.5 1 1.5

To

tal ve

rtic

al s

tre

ss

σv

[kP

a]

Radial distance [m]

z = 100 mm z = 2 m z = 4 m z = 6 m


Sm

ear

zon

e

Compactionzone Edge of

footing


261

Figure 6.41 and Figure 6.42 show the distribution with depth of the stress concentration

factor m for footing settlements of 100 mm, 400 mm and 850 mm for tests JG_v7 and JG_v9,

respectively. A decrease of the stress concentration at the top of the stone column (z = 0 m)

with increasing load can be noted. The stress concentration decreases with depth to reach a

value of approximately 1 at the toe of the stone column. However, a greater decrease of the

stress concentration factor with depth is observed for lower loads than for higher loads, as

shown in Figure 6.43 and Figure 6.44, in which the values of the factor m are normed with

the initial value.


settlements of 100 mm, 400 mm and 850 mm for test JG_v7 (σc = 200 kPa).


settlements of 100 mm, 400 mm and 850 mm for test JG_v9 (σc = 100 kPa).

The low values of the stress concentration in the lower third of the stone column (values

ranging from 1 to 1.5 for depths between 4 m and 6 m) could open up the way to a more

sustainable use of the stone column material as the diameter of the inclusions could be

reduced in the deeper zones, where its impact is less significant, and augmented near the

0

1

2

3

4

5

6

0 0.5 1 1.5 2 2.5 3

Dep

th [

m]

m [-]

s = 100 mm (P = 85 kPa) s = 400 mm (P = 115.2 kPa)s = 850 mm (P = 141.9 kPa)

0

1

2

3

4

5

6

0 0.5 1 1.5 2 2.5 3

De

pth

[m

]

m [-]



262

surface, where its influence is greater. This hypothesis should, however, be confirmed by

further numerical and physical modelling, and the influence of a variation of the stone column

diameter on the load transfer and on the drainage performance would need to be

investigated in detail.

Figure 6.43 and Figure 6.44 present the distribution of the normalised stress concentration

factor with depth. The decrease of the values is greater for lower loads. This can be

explained by the transmission of the normal loading in the stone column over depth by the

activation of skin friction around the stone column with increasing loading. This causes a

rotation of the direction of the principal stresses, as σ1 tilts from an angle of 90° to an angle of

approximately 45° (Figure 6.45), which causes an additional load to act on the surrounding

host soil.


footing settlements of 100 mm, 400 mm and 850 mm for test JG_v7

(σc = 200 kPa).

0

1

2

3

4

5

6

0 0.5 1 1.5

De

pth

[m

]

m / m0 [-]



263


footing settlements of 100 mm, 400 mm and 850 mm for test JG_v9 (σc = 100

kPa).

Figure 6.45: Direction of the total principal stress at the end of the loading phase for

test JG_v7 (P = 141.90 kPa).

0

1

2

3

4

5

6

0 0.5 1 1.5

De

pth

[m

]

m / m0 [-]


Stone column

Smear zone

Compaction zone

Clay

6 m

1.4 m


264

Figure 6.46 and Appendix 8.15 show the distribution of the excess pore water pressures

computed numerically for tests JG_v7 and JG_v9, respectively. Significant differences

between the measurements from centrifuge tests (Figure 4.24) and the results of the

numerical modelling can be noted, as the excess pore water pressures computed

numerically are concentrated in a zone extending from 0.8 m to 2.0 m depth, while the

outcomes from physical modelling under enhanced gravity indicate a distribution of the

excess pore water pressures along the stone column down to its toe.

A comparison of the excess pore water pressures measured in the centrifuge during

tests JG_v7 and JG_v9 from the PPTs inserted into the soil model, with the values obtained

numerically, is shown in Figure 6.48 and Appendices 8.19 and 8.20, respectively. The

difference between the values of the excess pore water pressures recorded during the tests,

and those modelled numerically, is significant. However, the pore water pressures are often

difficult to reproduce due to the insufficiencies of the constitutive models

(Brinkgreve & Broere, 2008). Therefore load-settlement curves were given higher priority and

the efforts to try and match the values of the excess pore water pressures were not pursued.


JG_v7 for a footing settlement of 850 mm and a footing load of 141.90 kPa.


265


test JG_v7 with the values obtained numerically with Plaxis 2D (P1 till P3).

An investigation of the influence of the installation effects on the load-settlement behaviour is

made possible by assigning the material Clay to the clusters Compaction zone and Smear

zone (Figure 6.27) in order to neglect the impact of the installation phase of the stone column

onto the host soil. Figure 6.48 and Figure 6.49 show comparisons of the load-settlement

curves obtained from the physical modelling and from the numerical modelling with, and

without, installation effects for tests JG_v7 and JG_v9, respectively. Table 6.10 summarises

the maximum values of the footing load. The percentage differences of the maximum footing

loads remain in both cases under 10 %. It is interesting that this difference rises with

increasing pre-consolidation stress (200 kPa for test JG_v7, 100 kPa for test JG_v9). This is

consistent with the greater differences between the smear and compaction zones and clay

observed in stress distribution under the footing with increasing pre-consolidation stress

(Figure 6.37 and Figure 6.38).


with (Pmax, Plaxis) and without (Pmax, Plaxis, no smear) installation effects for a settlement

of 850 mm.

Test Pmax, Plaxis

[kPa]

Pmax, Plaxis, no smear

[kPa]

Difference

[%]

JG_v7 (σc = 200 kPa) 141.90 130.72 8.55

JG_v9 (σc = 100 kPa) 115.11 110.90 3.80

0

10

20

30

40

50

60

0 500000 1000000 1500000 2000000 2500000

Ex

ce

ss

po

re w

ate

r p

res

su

re

[kP

a]

Time [s]

P1 P2 P3 P1 - Plaxis P2 - Plaxis P3 - Plaxis

6.5 3D numerical modelling

266


kPa) with the numerical simulations, with and without installation effects.


kPa) with the numerical simulations, with and without installation effects.


6.5.1 Model

The modelling was conducted using the Plaxis 3D code Version 2013.1 with 15-noded

elements. Figure 6.50 shows a general view of the mesh used to model test JG_v10. The

model has a rectangular shape, the width of which was set equal to the diameter of the

strongbox at prototype scale. The groundwater table was located 0.5 m below the surface of

the model.

0

20

40

60

80

100

120

140

160

0 100 200 300 400 500 600 700 800 900

Fo

oti

ng

lo

ad

ing

[k

Pa

]


JG_v7 JG_v7 - Plaxis JG_v7 - Plaxis (no smear)

0

20

40

60

80

100

120

140

0 100 200 300 400 500 600 700 800 900

Fo

oti

ng

lo

ad

ing

[k

Pa

]




267

Figure 6.50: General view of the 3D mesh (groundwater table 0.5 m below the surface).

The experience of the 2D axisymmetric modelling was transferred into the three-dimensional

model and the dimensions of the stone columns, smear zones and compaction zones were

implemented accordingly (Figure 6.51 and Figure 6.52). The red points in Figure 6.51 are of

graphical nature and do not have any physical meaning. Figure 6.52 shows a side view of

the stone column group (Figure 6.51), in which clay and compaction zone (left hand side),

respectively clay, compaction zone and smear zone (right hand side), were hidden in order to

expose the smear zone, respectively the stone column. A value of 50 kPa was assigned to

model cohesion in the 0.2 m thick layer at the top of the model, in order to prevent the

appearance of very large unrealistic soil movements at the surface during loading. The

calculation phases (Table 6.4) and the materials properties used (Table 6.5, Table 6.6, Table

6.7, Table 6.8) are the same as for the axisymmetric modelling.

Figure 6.51: Plan on the stone column group.

8 m

20 m

Clay

0.2 m

y

x

z

Clay

Stone

column

Smear

zone

Compaction

zone

0.6 m

0.8 m1.5 m

0.85 mA

B C

DF

x

y

1

1

2 2


268

Figure 6.52: Side view of the stone columns and zones created to represent the installation

effects (the base of the box is located 1 m below the toe of the compaction

zone), in which clay and compaction zone (left hand side), respectively clay,

compaction zone and smear zone (right hand side), were hidden in order to

expose the smear zone, respectively the stone column.

Figure 6.53: Plan on the stone column group with position of the square footing, as applied in

the centrifuge test JG_v10.

The actual position of the footing during the loading phase in the centrifuge (Figure 4.29) was

modelled numerically at a similar position by shifting the centre of the footing laterally 0.4 m

(corresponding to 8 mm under 50 g, Figure 4.29) and vertically 0.05 m (corresponding to

6 m6.1 m

7 m

0.2 m

Stone column

Smear zone Compaction zone

0.6 m0.8 m1.5 m

Clay

Stone

column

Smear

zone

Compaction

zone

2.8 m

2.8 m

Footing

0.4 m

0.05 m

x

y


269

1 mm under 50 g, Figure 4.29). Figure 6.53 shows a plan view of the stone column group

with the position of the square footing.

6.5.2 Results

Figure 6.54 shows a comparison between the load-settlement curves obtained

experimentally in the centrifuge (denoted as JG_v10) and numerically (denoted as

JG_v10 – Plaxis) for test JG_v10. As for the 2D numerical modelling, the final part of the

load-settlement curves measured during the centrifuge test and obtained through numerical

modelling matched quite well (Table 6.11). The reason for the initial difference between the

measured and computed load-settlement curves is the same as in the axisymmetric case

(Figure 6.55), although the centrifuge has been stopped after the stone column installation in

order to remove the sand particles from the clay surface, and to obtain as smooth a sample

surface as possible.


loads for a footing settlement of 850 mm.

Test Pmax, Centrifuge

[kPa]

Pmax, Plaxis

[kPa]

Difference

[%]

JG_v10 (σc = 100 kPa) 142.01 138.66 2.42

Figure 6.54: Comparison of the experimental and numerical load-settlement curves for the

test JG_v10.

Figure 6.56 and Figure 6.57 show the distribution of the total vertical stresses with depth. A

similar mechanism to that observed in the 2D case (Figure 6.31) can be observed as the

load transfer to the toe of the inclusions is minimal. The distributions of the vertical stresses

for footing settlement of 100 mm, and 400 mm, are shown in Appendix 8.21.

0

20

40

60

80

100

120

140

160

0 100 200 300 400 500 600 700 800 900

Fo

oti

ng

lo

ad

ing

[k

Pa

]


JG_v10 JG_v10 - Plaxis


270

0 kPa 100 – 140 kPa 140 – 180 kPa

Figure 6.55: Pressure distribution under the square footing for a settlement of 100 mm at

prototype scale (2 mm under 50g) for test JG_v10.


settlement of 850 mm and a footing load of 138.66 kPa (section 1-1, Figure

6.51). The dimensions are given in Figure 6.51 and Figure 6.52.

56

mm

56

mm

AB D


271


settlement of 850 mm and a footing load of 138.66 kPa (section 2-2, Figure

6.51). The dimensions are given in Figure 6.51 and Figure 6.52.

The development of plastic points during footing loading for test JG_v10 is shown in

Appendix 8.26. A similar extent of the plastic (hardening) points is noted for section 1-1

(Figure 6.51), while the effect of the stone column group can be noted in section 2-2

(Figure 6.51), as the plastic points reach higher depths (approximately 4 m) than in the

axisymmetric case, for which plastic points were computed up to a depth of approximately

2 m under the surface of the host soil. The impact of this distribution can be noted by the

distribution of the excess pore water pressures (Figure 6.61), which are significantly less

concentrated outside the group than in the axisymmetric case (Figure 6.46). A similar

distribution of the excess pore water pressures is observed within the stone column group

(Figure 6.62) and around a single stone column (Figure 6.46).

Figure 6.58 and Figure 6.59 show the stress distribution under the footing, and at a depth of

6 m, respectively, for a settlement of 850 mm. The stress distributions below the footing at

depths of 2 m and 4 m under the surface of the model are shown in Appendix 8.24. A similar

overall development of the values of the stress concentration factor can be observed, as in

the axisymmetric modelling. For a footing settlement of 850 mm, the factor m for the whole

group has a value of approximately 2.5 directly under the footing Figure 6.58) and decreases

to approximately 1 at a depth of 6 m (Figure 6.59). Similar values are obtained for footing

settlements of 100 mm (Appendix 8.22), and of 400 mm (Appendix 8.23). The stone column

group can thus be considered as an equivalent pier at its toe.

The average stress acting on top of column A is of approximately 300 kPa to 325 kPa, while

that acting on top of columns C and D is of 225 to 250 kPa and that on columns B and E

of 125 kPa to 175 kPa. The variation between the total vertical stress acting on top of


272

columns C and D, and columns B and E, respectively, is due to the non-centred position of

the footing during the centrifuge test (Figure 6.53).

The lower installation depths of the PPTs P1, P2 and P3 (30 mm at model scale, i.e. 1.5 m at

prototype scale) shows that an acceptable match of the excess pore water pressures caused

by the footing load can be achieved near the surface of the sample during the loading phase

with the numerical model presented (Figure 6.60). This appears to be random, as the PPTs

are located in the zone where the excess pore water pressures computed numerically, and

shown in Figure 6.61 and Figure 6.62, have been concentrated. The asymmetric distribution

of the excess pore water pressures is due to the position of the footing (Figure 6.53). A

comparison of the excess pore water pressures measured in the centrifuge with those

computed numerically is presented in Appendix 8.25.


test JG_v10 (σc = 100 kPa, P = 138.66 kPa). Negative stresses denote

compression. The dimensions are shown in Figure 6.51 and Figure 6.53.

A

B C

DE


273





test JG_v10, with the values obtained numerically with Plaxis 3D (P1 till P3).

A

B C

DE

0

5

10

15

20

25

30

35

40

45

50

0 500000 1000000 1500000 2000000 2500000

Ex

ce

ss

po

re w

ate

r p

res

su

re

[kP

a]

Time [s]



274

Figure 6.61: Distribution of the excess pore water pressures computed numerically for

test JG_v10 (σc = 100 kPa) for a settlement of 850 mm and a footing load of

138.66 kPa (section 1-1, Figure 6.51).


test JG_v10 (σc = 100 kPa) for a settlement of 850 mm and a footing load of

138.66 kPa (section 2-2, Figure 6.51).

Figure 6.63 shows the deformation of the columns A, C and D (Figure 6.51) caused by the

footing load of 138.66 kPa. Figure 6.63 is a side view of the model (similar to Figure 6.52), in

which clay, compaction zone and smear zone were hidden in order to expose the

deformation of the stone columns. The outer columns (C and D) deform laterally, while the

B A D


275

radial deformation of the centre column is marginal. As in the axisymmetric case, the

deformations do not extend to the bottom of the inclusions. The fact that the bulging

deformation of the columns C and D is is directed towards the outside of the group is due to

the compaction of the host soil caused by the installation of column A.

Figure 6.63: Deformed columns A, C and D for test JG_v10, for a settlement of 850 mm and

a footing load of 138.66 kPa, in which clay, compaction zone and smear zone

were hidden in order to expose the deformation of the stone columns.

The influence of the installation effects on the load-settlement behaviour was investigated by

assigning the material Clay to the clusters Compaction zone and Smear zone (Figure 6.51

and Figure 6.52). Figure 6.64 shows a comparison of the load-settlement curves obtained

from the physical modelling and from the numerical modelling with, and without, installation

effects for the tests. The installation effects do not influence the load-settlement curve at the

beginning of the loading, but cause a slight offset of the curve after the initial loading phase.

Table 6.12 summarises the maximum values of the footing load. The difference in the

maximum loads, with and without a smear and a compaction zone, is in the same order of

magnitude as in the axisymmetric case for a pre-consolidation stress σc = 100 kPa.


with (Pmax, Plaxis) and without (Pmax, Plaxis, no smear) installation effects.

Test Pmax, Plaxis

[kPa]

Pmax, Plaxis, no smear

[kPa]

Difference

[%]

JG_v10 (σc = 100 kPa) 138.66 135.10 2.64

0.85 m

6 m Stone column A

Stone column C

Stone column D

6.6 Summary of numerical modelling

276

Figure 6.64: Comparison of the experimental load-settlement curves for test JG_v10 with the

numerical simulations, with and without, installation effects.


The numerical modelling performed aimed at simulating the tests conducted under enhanced

gravity. A wished-in-place approach was adopted in order to avoid modelling the entire

installation phase of the stone columns, and thus to obtain a numerical model that a practical

engineer might be willing to use. Weber’s (2008) findings about the extent of smear and

compaction zones were successfully implemented, which confirms that an approach

considering a homogeneous smear zone (e.g. Indraratna & Redana, 1997) is rather

simplistic, although it may deliver good results in some cases.

The model adopted for the numerical approach takes the installation effects into account, as

well as proposes simple conversion factors for the soil properties in the smear and

compaction zones, based on the properties of the host soil. The results obtained provide a

good match to the load-settlement behaviour in the centrifuge model and allow some insights

into the load-transfer behaviour of single stone columns and of stone column groups to be

gained. A significant decrease of the stress concentration factor with depth is observed in

both cases, as this factor reaches values ranging from 1.0 to 1.5 in the lower third of the

stone column. This could open up the way to a more economical and sustainable design of

granular inclusions as their diameter could be reduced in zones where the stress

concentration is low.

The outcomes of the numerical modelling show a very small load transfer to the toe of the

stone columns and thus a very little mobilisation of the tip resistance. This might also be a

possibility to achieve a more economical design as the length of the inclusions could be

reduced without losing lead bearing performance, if the drainage function is of secondary

importance.

0

20

40

60

80

100

120

140

160

0 100 200 300 400 500 600 700 800 900

Fo

oti

ng

lo

ad

ing

[k

Pa

]




277

However, the values of the excess pore water pressures computed numerically do not

correspond well, and underestimate those measured during the centrifuge tests. Although

this is an issue for scientific work, it is of less relevance compared to the correct modelling of

the load-settlement behaviour in practical cases.

As a conclusion, the model proposed allows insights into the stress paths, although the

constitutive model used for the modelling of clay (HSM) assumes a fully elastic behaviour

within the yield surface, which is not fully realistic. The model also reaches its goal of

providing a practically applicable way of taking the installation effects of stone columns into

account and delivers a good prediction of the load-settlement behaviour of the composite

foundation. From a scientific point of view, improvements can still be reached in the

computation of excess pore water pressures.


278

7 Summary

279

7 Summary

7.1 General considerations

Ground improvement aims to enhance the engineering properties of a soil in terms of bearing

capacity and / or stiffness in order to make it suitable for construction. The continuous

technological innovation of the past decades has enabled the development of machinery to

build stone columns efficiently. These granular inclusions both stiffen the soil and allow for

higher loads to be carried while reducing post-construction settlements. The consolidation

time is also shorter because the length of the drainage paths is decreased as well.

The bearing behaviour of stone columns differs from that of rigid inclusions, such as piles, as

the host soil plays a decisive role in providing lateral support to the stone column material.

The interactions between host soil, inclusions and supported structure are governed by the

difference between the characteristics of the host soil and influenced by the installation

effects, especially in clay. Although the development of installation effects is acknowledged,

different approaches exist to take them into account.

The installation effects are the cause of a decrease in the drainage performance of the stone

columns, as they cause radial compaction of the host soil. A reorientation of the clay platelets

reduces the permeability as well. Some researchers (e.g. Indraratna & Redana, 1998)

assume that the soil properties are constant over the whole extent of the installation effects;

the so-called smear zone. Others, such as Onoue et al. (1991) and Weber et al. (2010),

identify variation in the values of the permeability and porosity in the host soil around stone

columns and therefore subdivide the installation effects into smear and compaction zones.

Although the latter approach delivers more accurate results than the former one, the vertical

distribution of the two zones remains unknown.

The bearing behaviour of stone columns is further influenced by geometrical aspects such as

the spacing between the inclusions and their diameter. A re-distribution of the stresses under

a foundation is noted during footing loading, due to the significantly higher stiffness of the

stone columns compared with that of the host soil. The stress concentration ratio m

quantifies this effect and usually ranges from 2 to 6. The values are influenced by the

intensity and type of loading (flexible / stiff), and by the stress history and characteristics of

the host soil. A better knowledge of the installation effects might help understanding some of

the differences in stress concentration, which is the main focus of this study.

7.2 Findings from centrifuge modelling and complementary

investigations

The installation of stone columns into a clay specimen in-flight, in a geotechnical centrifuge,

enabled insights to be gained into the factors influencing the installation effects and into the

bearing behaviour of composite foundations with measurements of pore pressures, load-

settlement behaviour and electrical impedance measurements. It also offered the chance to

7.2 Findings from centrifuge modelling and complementary investigations

280

study the micro-mechanical impact of the installation on the host soil, with complementary

investigations conducted after the centrifuge tests.

The magnitude of the excess pore water pressures caused by the insertion of the installation

mandrel into the host soil is mostly governed by the over-consolidation ratio OCR, as it

becomes greater with an increasing OCR. A transfer of the load applied on the surface into

the host soil could be measured as the load-increase at a depth of 96 mm under the surface

(at 50 g) was shown to be 3 times higher with a stone column than without (Figure 7.1). This

could not be reproduced in the numerical modelling of the centrifuge test, but important

insights were gained about the stress distribution with depth, which are summarised in

Sections 7.3 and 7.4.

Figure 7.1: Distribution of the vertical stress increase as a function of the radial distance from

the stone column at 96 mm depth as a percentage of the applied footing load P

and comparison with the depth factor J4 according to Grasshoff (1978).

An electrical impedance needle (Figure 7.2) was developed in order to measure the electrical

impedance in the host soil surrounding the stone columns, to determine the extent of the

installation effects. A consistent trend observed during the investigations conducted with the

electrical impedance needle indicated a microscopic reorganisation of the clay particles up to

a distance of 5 times the radius of the stone column from the axis of the inclusion. The

outcomes also indicated a constant extent of the smear zone with depth, as long as no

significant bulging deformation occurs.

(a) (b)


diameter 1 mm).

0

5

10

15

20

25

30

35

0 5 10 15 20 25 30

Δσ

z[%

P]


JG_v5 JG_v7 JG_v9 J4 J4J4


7 Summary

281

The interpretation of the impedance measurements was confirmed by observations using

Environmental Scanning Electron Microscopy (ESEM), which identified a progressive vertical

reorganisation of longer particles in the compaction zone with decreasing distance from the

edge of the stone column (Figure 7.3). Weber (2008) observed a reorganisation of all clay

platelets within the smear zone (ranging from the edge of the stone column to a radial

distance of 2 mm from the interface stone column / clay).

Figure 7.3: ESEM picture of zone 3, located at a radial distance of 5 mm from the edge of the

column and at a depth of 20 mm below the surface, with the radial axis

horizontal.

Complementary investigations to study the extent of the compaction zone around a stone

column were conducted using Mercury Intrusion Porosimetry (MIP) on samples extracted

from clay specimens used for the modelling under enhanced gravity at depths of 20 mm, 60

mm and 100 mm below the surface of the model. These investigations showed that the

macroscopic effects on the porosity of the host soil could only be detected up to a distance of

about twice the radius of the inclusions from its axis, which confirmed Weber’s (2008)

findings. The extent of the compaction zone was shown to remain constant over the depth of

the stone column (Figure 7.4). An effect of the compaction cycles on the porosity of the

surrounding host soil near the surface was identified: the porosity at the interface between

the smear zone and the compaction zone drops from 31 % at a depth of 100 mm below the

surface to 29 % at a depth of 20 mm. These findings were transferred into the numerical

model used in this research in order to achieve a usable model for design.

30 μm

Longer

particles

5 mm

Sto

ne

co

lum

n

7.3 Numerical modelling

282

(a)

(b)

(c)

Legend:

Figure 7.4: Porosity as a function of the radial distance from the axis of the stone column at a

depth of (a) 20 mm (b) 60 mm (c) 100 mm.


The aim of the numerical modelling conducted was to achieve a numerical model, which a

practical engineer may be willing to use, and which takes the installation effects of stone

columns into account. Such a model, using a “wished-in-place” approach, was developed

26

28

30

32

34

36

38

40

0 5 10 15 20 25 30 35 40

Po

ros

ity [

%]


Stone

column

Edge of densification OCR = 11.8 [-]

26

28

30

32

34

36

38

40

0 5 10 15 20 25 30 35 40

Po

ros

ity [

%]



column

OCR = 3.9 [-]

26

28

30

32

34

36

38

40

0 5 10 15 20 25 30 35 40

Po

ros

ity [

%]


Measured data



column



OCR = 2.4 [-]

Compaction zone

Measured data


26

28

30

32

34

36

38

40

0 5 10 15 20 25 30 35 40

Po

ros

ity [

%]


Measured data

Average


column



OCR = 2.4 [-]

Compaction zone

7 Summary

283

based on the findings from the centrifuge tests and from the complementary investigations

conducted.

A good prediction of the load-settlement behaviour was achieved, although the initial

response of the composite foundation computed numerically was significantly stiffer than that

measured during centrifuge tests. This was found to be due to a difference between the

stress distribution under the footing computed numerically and that measured in the

centrifuge. Such differences in the initial phase of loading could also be observed by Arnold

(2011), when comparing field measurements and results from centrifuge tests.

A significant decrease of the load transfer onto the stone columns could be measured below

4 m depth, as the stress concentration factor reached values close to unity. This could open

up new perspectives for a more sustainable construction of stone columns as the radius of

the inclusions could be increased near the surface, where the stress concentration factor

ranges between 2.5 and 3 (Figure 7.5), and reduced in zones where the concentration factor

is of 1.0 to 1.5 (Figure 7.6). This could allow for a reduction of the material needed and thus

for a lower impact on the environment and economy. Although the distribution of the

installation effects was successfully modelled, the influence of the diameter variation of the

stone column on the load transfer, and on the drainage performance, would have to be

investigated in detail before it can be implemented in practice.

The investigation of the total vertical stress distribution in 2D and 3D (Figure 7.7 and

Figure 7.8) shows clearly that there is very little load transfer to the toe of the stone column.

Thus, if tip resistance is needed, shorter columns would be more sensible than longer

inclusions. This should however be done taking the drainage performance needed into

account, which is of course smaller for shorter columns. A new design philosophy could be

achieved, implementing stone columns depending on the local needs: shorter inclusions with

constant diameter could be built in cases where tip resistance needs to be mobilised and

where the drainage performance is of less importance, while longer stone columns could be

reserved to the cases where a high drainage efficiency needs to be reached in order to

reduce consolidation time, while the diameter of the inclusions could be reduced in the lower

third, where the stress concentration is low.

The distribution of the computed values of the excess pore water pressures caused by the

footing loading (Figure 7.9) is significantly different from those measured in-flight

(Figure 7.10). However, the modelling of pore water pressures is a delicate subject, as the

constitutive models available still have some insufficiencies in that domain.


284







A

B C

DE

A

B C

DE

7 Summary

285




settlement of 850 mm and a footing load of 138.66 kPa (section 1-1,

Figure 6.51). The dimensions are given in Figure 6.51 and Figure 6.52.

AB D


286


test JG_v7 for a footing settlement of 850 mm and a footing load of 141.90 kPa.


under a vertically loaded circular footing resting on top of a stone column.

7 Summary

287

7.4 Outlook

This research has reached its aim to identify the spatial distribution of installation effects

around stone columns. The findings of the centrifuge modelling and subsequent

complementary investigations were successfully implemented in a numerical model. The

model proposed opens new perspectives in the consideration of installation effects around

stone columns in practical cases, as it shows that a practical, simplified modelling of granular

inclusions with installation effects is possible.

The variation of the values measured with the electrical impedance needle under Earth’s

gravity and under 50 g might be due to a scaling effect of the electrical waves under

enhanced gravity. An investigation of this scaling effect could open up new perspectives for

the implementation of the electrical impedance needle in a wider range of boundary value

problems, including in-situ tests.

This numerical model was developed based on tests and investigations conducted with one

type of host soil and a specific stone column material. A validation or optimisation ought to be

conducted considering other types of clays (and varying pre-consolidation stress) and a

variation of the granular material used for the stone column construction.

The literature review has shown that the stress concentration on top of stone columns

depends on the interaction between type of loading (flexible / stiff) and load intensity, on the

stress history, and on the characteristics of the host soil. A sensitivity analysis could

therefore be conducted in order to quantify the impact of these different factors (type of

loading, stress history and host soil) on the dissipation of the stress concentration with depth

observed in the numerical modelling.

Another interesting point for further research would be the conduction of full-scale

experiments in order to investigate the effect of the differences between the bottom field

installation technique used in practice and that used in the centrifuge. This could enable a

further optimisation of the numerical model to be achieved, which would allow for a wider use

of the numerical model in practice.

A topic of interest from a scientific point of view will be the development of numerical

constitutive models allowing for an accurate reproduction of the excess pore water pressures

in the host soil. The implementation of a bubble model (Stallebrass & Taylor, 1997) could

solve the issue of the unrealistic fully elastic behaviour of clay within the yield surface

observed with the HSM.

The implementation of interface elements between the zones representing the installation

effects in the numerical modelling could be investigated when using another numerical code

than Plaxis. The use of such elements with the numerical code Plaxis is not sensible in this

specific case as it would suppose that the zones are very clearly separated and thus not take

the progressive evolution of the soil characteristics with radial distance to the axis of the

inclusion into account.

7.4 Outlook

288

Finally, the influence of a diameter variation should be investigated in order to validate the

outcomes of the numerical model in terms of reduction of the stress concentration factor in

the lower third of the inclusions.

8 Appendices

289

8 Appendices

Appendices 8.1, 8.2 and 8.3 present the measurements (pore water pressure, footing load

and footing settlement) recorded during the loading phase of tests JG_v1, JG_v5 and JG_v6

respectively. Appendix 8.4 presents the values of the J4 factor according to Grasshoff (1978)

and Appendix 8.5 shows a comparison between the measured values of the excess pore

water pressure during the loading phase of test JG_v1 with back-calculated values (Section

4.4.4).

Appendices 8.6 and 8.7 show the electrical impedance measurements conducted in-flight

during test JG_v9 and under 1 g on soil prepared in the laboratory at successive phases to

achieve the same stress history, hence with varying soil densities (Section 5.3), respectively.

Appendices 8.8, 8.9 and 8.10 show the distribution of vertical strain increments, the

distribution of shear strain increments and the development of plastic points computed

numerically for test JG_v7.

Appendices 8.11 and 8.12 present the deformed mesh and the distribution of total vertical

stresses obtained at the end of the loading phase for the numerical modelling of test JG_v9,

respectively.

Appendices 8.13, 8.14 and 8.16 the distribution of vertical strain increments, the distribution

of shear strain increments and the development of plastic points computed numerically for

test JG_v9.

Appendix 8.15 presents the distribution of the excess pore water pressures computed

numerically for test JG_v9.

Appendices 8.17 and 8.18 show the distribution with depth of the total vertical stress

computed numerically with depth for footing settlements of 400 mm and 850 mm for

tests JG_v7 and JG_v9, respectively.

Appendices 8.19 and 8.20 present comparisons of the values of the excess pore water

pressure measured in the centrifuge with the values obtained from numerical modelling for

tests JG_v7 and JG_v9, respectively.

Appendix 8.21 presents the total vertical stress distribution for test JG_v10 for footing

settlements of100 mm and 400 mm.

Appendices 8.22, 8.23 and 8.24 show the distribution of the total vertical stress below the

footing with depth, for test JG_v10, for footing settlements of 100 mm, 400 mm and 850 mm.

Appendix 8.25 presents a comparison of the values of the excess pore water pressure

measured in the centrifuge with the values obtained from numerical modelling for

test JG_v10. Appendix 8.26 shows the development of plastic points during footing loading

for test JG_v10.

8.1 Pore pressure and load measurements conducted during loading with a footing on a

single stone column installed in a specimen prepared in an oedometer container (test JG_v1)

290

8.1 Pore pressure and load measurements conducted during

loading with a footing on a single stone column installed in a

specimen prepared in an oedometer container (test JG_v1)

A connection problem between the computers mounted on the tool platform and the

computer in the control room led to a false evaluation of the position of the footing relative to

the surface of the model during test JG_v1. As a consequence, the stone column underwent

preloading and the pore pressure measurements of the footing load could not be exploited

fully.

Figure 8.1 shows the measurements conducted during test JG_v1. The increase in pore

water pressures at approximately 500 s (Figure 8.1 a) is due to a manipulation of the

actuator arm, which caused an unintended load to be applied to the granular inclusion.

The applied load was not recorded and could not be visually controlled by the operative

personal due to a loss of the connection between the computers installed on the tool platform

of the centrifuge and those in the control room. Nevertheless, the data are given here for

reference and potential further analysis.

8 Appendices

291

(a)

(b)

(c)


(test JG_v1): (a) excess pore water pressures (b) evolution of the footing load

(c) footing settlement.

0

5

10

15

20

25

30

35

0 500 1000 1500 2000 2500 3000Ex

ce

ss

po

re w

ate

r p

res

su

re

[kP

a]

Time [s]

P1 P2 P3 P4 P5 P6 P7

-40

-20

0

20

40

60

80

100

0 500 1000 1500 2000 2500 3000

Fo

oti

ng

lo

ad

ing

[k

Pa

]

Time [s]

-18

-13

-8

-30 500 1000 1500 2000 2500 3000

Fo

oti

ng

se

ttle

me

nt

[mm

]

Time [s]

8.2 Pore pressure and load measurements conducted during loading a single stone column

installed in a specimen prepared in an oedometer container (test JG_v5) with a circular

footing

292


loading a single stone column installed in a specimen prepared

in an oedometer container (test JG_v5) with a circular footing

(a)

(b)

(c)


(test JG_v5): (a) excess pore water pressures (b) evolution of the footing load


0

5

10

15

20

25

30

35

40

45

50

0 500 1000 1500 2000 2500

Ex

ce

ss

po

re w

ate

r p

res

su

re

[kP

a]

Time [s]

P1 P2 P3 P4 P5 P6 P7

-20

0

20

40

60

80

100

120

0 500 1000 1500 2000 2500Fo

oti

ng

lo

ad

ing

[k

Pa

]

Time [s]

-20

-15

-10

-5

0

0 500 1000 1500 2000 2500

Fo

oti

ng

se

ttle

me

nt

[mm

]

Time [s]

8 Appendices

293


loading a single stone column installed in a specimen prepared

in a full cylindrical stongbox (test JG_v6) with a circular footing

(a)

(b)

(c)


(test JG_v6): (a) Excess pore water pressures (b) evolution of the footing load


0

2

4

6

8

10

12

14

16

18

0 500 1000 1500 2000

Ex

ce

ss

po

re w

ate

r p

res

su

re

[kP

a]

Time [s]

P4 P5 P6 P7

0

10

20

30

40

50

60

70

80

90

100

110

120

0 500 1000 1500 2000

Fo

oti

ng

lo

ad

ing

[k

Pa

]

Time [s]

-20

-15

-10

-5

0

0 500 1000 1500 2000

Fo

oti

ng

se

ttle

me

nt

[mm

]

Time [s]

8.4 Values of the J4 factor according to Grasshoff (1978)

294

8.4 Values of the J4 factor according to Grasshoff (1978)

Table 8.1: Values of the factor J4 in ‰ (Lang et al., 2007) (z: depth of the point considered;

R: radius of the circular footing; a: radial distance of the point considered from

the centre of the footing).

8.5 Comparison of the analytical and measured excess pore water

pressure around a single stone column when the maximum

load is applied (P = 80 kPa, test JG_v1)

Table 8.2 shows a comparison of the analytical and measured excess pore water pressure

during the footing loading phase for test JG_v1, as a complement to the data presented in

Section 4.4.4 about load transfer around a single stone column.

Table 8.2: Comparison of the analytical and measured excess pore water pressure during

the loading phase of a single stone column (test JG_v1, σc = 200 kPa, P = 80

kPa).

PPT J4 [%]

Δσa = Δσz

= J4 P

[kPa]


ΔuSkempton [-]

P1 32.30 25.84 0.1 21.83 21.66 0.99

P2 29.13 23.30 0.1 19.68 16.72 0.85

P3 21.45 17.16 0.1 14.50 11.33 0.78

P4 11.45 9.16 0.2 7.38 18.41 2.49

P5 11.03 8.82 0.2 7.11 13.92 1.96

P6 9.73 7.78 0.2 6.27 17.67 2.82

P7 5.70 4.56 0.2 3.59 11.77 3.28

8 Appendices

295

8.6 Electrical impedance measurements conducted during the test

JG_v9

The results of the investigations conducted with the electrical impedance needle during test

JG_v9 are presented here. Both container A and container B were pre-consolidated up to

100 kPa. The column installed in container A was loaded using a 56 mm diameter stiff

circular footing.


(Container A).


(Container B).

0

20

40

60

80

100

120

0 0.002 0.004 0.006 0.008 0.01

De

pth

[m

m]

Impedance [Ohm]

RP 1 RP 2

0

20

40

60

80

100

120

0 0.002 0.004 0.006 0.008 0.01

De

pth

[m

m]

Impedance [Ohm]

RP 1 RP 2

8.6 Electrical impedance measurements conducted during the test JG_v9

296

Figure 8.6: Impedance recorded at the points A, B and C during test JG_v9 (Container A).

Figure 8.7: Impedance recorded at the points D, E and F during test JG_v9 (Container A).

0

20

40

60

80

100

120

0 0.002 0.004 0.006 0.008 0.01

De

pth

[m

m]

Impedance [Ohm]


0

20

40

60

80

100

120

0 0.002 0.004 0.006 0.008 0.01

De

pth

[m

m]

Impedance [Ohm]


8 Appendices

297

Figure 8.8: Impedance recorded at the points A, B and C during test JG_v9 (Container B).

Figure 8.9: Impedance recorded at the points D, E and F during test JG_v9 (Container B).

0

20

40

60

80

100

120

0 0.002 0.004 0.006 0.008 0.01

De

pth

[m

m]

Impedance [Ohm]


0

20

40

60

80

100

120

0 0.002 0.004 0.006 0.008 0.01

De

pth

[m

m]

Impedance [Ohm]


8.7 Electrical impedance measurements conducted under 1 g

298


The results of the insertion of the electrical impedance needle under 1 g (Section 5.3) are

presented here. For clarity, the different consolidation stages conducted, as well as the

location of the insertion points, are given in Table 8.3 and Figure 8.10, respectively.

Table 8.3: Overview of the consolidation stages conducted for the insertion of the electrical

impedance needle under 1 g.

Consolidation stage Consolidation effective

stress [kPa] Density [kN/m3] Void ratio [-]

1 12.5 16.8 1.53

2 25 17.4 1.30

3 50 18.1 1.20

4 100 18.7 1.06

5 200 20.4 0.73


dimensions in mm.

Clay

Insertion

points

1 2

3

8 Appendices

299

Figure 8.11: Impedance recorded under 1 g after completion of the second consolidation

stage.

Figure 8.12: Impedance recorded under 1 g after completion of the third consolidation stage.

0

20

40

60

80

100

120

0.043 0.044 0.045 0.046 0.047

De

pth

[m

m]

Impedance [Ohm]


0

20

40

60

80

100

120

0.043 0.044 0.045 0.046 0.047

De

pth

[m

m]

Impedance [Ohm]



300

Figure 8.13: Impedance recorded under 1 g after completion of the fourth consolidation

stage.

0

20

40

60

80

100

120

0.043 0.044 0.045 0.046 0.047

De

pth

[m

m]

Impedance [Ohm]


8 Appendices

301

8.8 Vertical strain increments computed numerically for test

JG_v7

The distribution of the vertical strain increments computed numerically for test JG_v7 using

an axisymmetric model is presented in this section.


of 100 mm and a footing load of 85 kPa.

8.8 Vertical strain increments computed numerically for test JG_v7

302


of 400 mm and a footing load of 115.2 kPa

8 Appendices

303

8.9 Shear strain increments computed numerically for test JG_v7

The distribution of the shear strain increments computed numerically for test JG_v7 using an

axisymmetric model is presented in this section.


100 mm and a footing load of 85 kPa.


304



8 Appendices

305


850 mm and a footing load of 145 kPa.

8.10 Development of plastic points (test JG_v7)

306


The development of plastic points during footing loading of a single stone column for test

JG_v7 obtained numerically using an axisymmetric model is presented in this section. The

development of plastic points during the loading phase is presented in Figure 6.32. Failure

points denote elements that are located on the Mohr-Coulomb failure line (Figure 6.19,

respectively Figure 6.22), while Cap points and Hardening points refer to element undergoing

plastic shear strain hardening (Figure 6.22, Section 6.3.2.3) and plastic volumetric hardening

(Figure 6.23, Section 6.3.2.4), respectively. Tension cut-off points denote elements which

would undergo tension if the value of cohesion was positive.


settlement of 100 mm (P = 85 kPa).

8 Appendices

307


settlement of 400 mm (P = 115.2 kPa).


308



8 Appendices

309

8.11 Deformed mesh (test JG_v9)

Figure 8.22 shows the deformed mesh at the end of the modelling of the footing load during

test JG_v9. The applied load was 115.11 kPa and the settlement reached 850 mm.


footing load of 115.11 kPa.

Stone column

Smear zone

Compaction zone8

m

6m

6.1

m

7m

Clay

0.3 m

0.4 m

0.75 m

0.2 m

6.25 m

1.4 m

0.8

5 m

x

y

8.12 Total stress distribution computed numerically for test JG_v9

310

8.12 Total stress distribution computed numerically for test JG_v9

Figure 8.23 presents the distribution of total vertical stresses computed numerically for test

JG_v9 for a settlement of 850 mm and a footing load of 119.67 kPa.



8 Appendices

311


The distribution of the vertical strain increments computed numerically for test JG_v9 using

an axisymmetric model is presented in this section.




312



8 Appendices

313




314


The distribution of the shear strain increments computed numerically for test JG_v7 using an

axisymmetric model is presented in this section.



8 Appendices

315




316



8 Appendices

317

8.15 Excess pore water pressures computed numerically for test

JG_v9

The distribution of the excess pore water pressures computed numerically for test JG_v9

using an axisymmetric model is presented in Figure 8.30.


test JG_v9 for a footing settlement of 850 mm and a footing load of 115.11 kPa


318



JG_v9 obtained numerically using an axisymmetric model is presented in this section. Failure

points denote elements that are located on the Mohr-Coulomb failure line (Figure 6.19,

respectively Figure 6.22), while Cap points and Hardening points refer to element undergoing

plastic shear strain hardening (Figure 6.22, Section 6.3.2.3) and plastic volumetric hardening

(Figure 6.23, Section 6.3.2.4), respectively. Tension cut-off points denote elements which

would undergo tension if the value of cohesion was positive.



8 Appendices

319




320



8 Appendices

321

8.17 Total vertical stress distribution as a function of the radial

distance at depths of 0 m, 2 m, 4 m and 6 m (test JG_v7)


numerically for test JG_v7 as a function of the radial distance from the axis of the stone

column under the footing and at depths of 2 m, 4 m and 6 m and for footing settlements of

400 mm and 850 mm, respectively.



of 400 mm during the footing loading for test JG_v7 (P = 115.2 kPa).


footing (z = 850 m) and at depths of 2 m, 4 m and 6 m for a footing settlement of

850 mm during the footing loading for test JG_v7 (P = 145.44 kPa).

0

50

100

150

200

250

300

350

400

0 0.5 1 1.5

To

tal ve

rtic

al s

tre

ss

σv

[kP

a]

Radial distance [m]

z = 400 mm z = 2 m z = 4 m z = 6 m


Sm

ear

zon

e

Compactionzone

Edge of footing

0

50

100

150

200

250

300

350

400

0 0.5 1 1.5

To

tal ve

rtic

al s

tre

ss

σv

[kP

a]

Radial distance [m]

z = 850 mm z = 2 m z = 4 m z = 6 m


Sm

ear

zon

e

Compactionzone

Edge of footing

8.18 Total vertical stress distribution as a function of the radial distance at depths of 0 m, 2

m, 4 m and 6 m (test JG_v9)

322

8.18 Total vertical stress distribution as a function of the radial

distance at depths of 0 m, 2 m, 4 m and 6 m (test JG_v9)


numerically for test JG_v9 as a function of the radial distance from the axis of the stone

column at depths of 0 m, 2 m, 4 m and 6 m and for footing settlements of 400 mm and 850

mm, respectively.







0

50

100

150

200

250

300

0 0.5 1 1.5

To

tal ve

rtic

al s

tre

ss

σv

[kP

a]

Radial distance [m]

z = 400 mm z = 2 m z = 4 m z = 6 m


Sm

ear

zon

e

Compactionzone Edge of

footing

0

50

100

150

200

250

300

350

0 0.5 1 1.5

To

tal ve

rtic

al s

tre

ss

σv

[kP

a]

Radial distance [m]

z = 850 mm z = 2 m z = 4 m z = 6 m


Sm

ear

zon

e

Compactionzone

Edge of footing

8 Appendices

323

8.19 Comparison of the measured and modelled excess pore water

pressures for the test JG_v7

Figure 8.38 and Figure 8.39 present a comparison of the excess pore water pressures

measured in the centrifuge with those computed numerically for test JG_v7 using an

axisymmetric model.




test JG_v7 with the values obtained numerically with Plaxis 2D (P7).

0

10

20

30

40

0 500000 1000000 1500000 2000000 2500000

Ex

ce

ss

po

re w

ate

r p

res

su

re

[kP

a]

Time [s]


0

5

10

15

20

25

30

0 500000 1000000 1500000 2000000 2500000

Ex

ce

ss

po

re w

ate

r p

res

su

re

[kP

a]

Time [s]

P7 P7 - Plaxis

8.20 Comparison of the measured and modelled excess pore water pressures for the test

JG_v9

324



Figure 8.40, Figure 8.41 and Figure 8.42 present a comparison of the excess pore water

pressures measured in the centrifuge with those computed numerically for test JG_v9 using

an axisymmetric model.





0

5

10

15

20

25

30

35

40

45

50

0 500000 1000000 1500000 2000000 2500000

Ex

ce

ss

po

re w

ate

r p

res

su

re

[kP

a]

Time [s]


0

5

10

15

20

25

30

35

0 500000 1000000 1500000 2000000 2500000

Ex

ce

ss

po

re w

ate

r p

res

su

re

[kP

a]

Time [s]


8 Appendices

325



0

2

4

6

8

10

12

14

16

0 500000 1000000 1500000 2000000 2500000

Ex

ce

ss

po

re w

ate

r p

res

su

re

[kP

a]

Time [s]

P7 P7 - Plaxis

8.21 Distribution of the total vertical stresses for footing settlements of 100 mm and of 400

mm (test JG_v10)

326

8.21 Distribution of the total vertical stresses for footing settlements

of 100 mm and of 400 mm (test JG_v10)

Figure 8.43, Figure 8.44, Figure 8.45 and Figure 8.46 present the distribution of the total

vertical stresses for test JG_v10 for settlements of 100 mm and 400 mm.

Figure 8.43: Distribution of the total vertical stresses for test JG_v10 for a settlement of

100 mm and a footing load of 76 kPa (section 1-1, Figure 6.51). The dimensions

are given in Figure 6.51 and Figure 6.52.

8 Appendices

327


100 mm and a footing load of 76 kPa (section 2-2, Figure 6.51). The dimensions

are given in Figure 6.51 and Figure 6.52.


400 mm and a footing load of 108.60 kPa (section 1-1, Figure 6.51). The

dimensions are given in Figure 6.51 and Figure 6.52.

8.21 Distribution of the total vertical stresses for footing settlements of 100 mm and of 400

mm (test JG_v10)

328


400 mm and a footing load of 108.60 kPa (section 2-2, Figure 6.51). The

dimensions are given in Figure 6.51 and Figure 6.52.

8 Appendices

329

8.22 Total vertical stress distribution below the footing for a

settlement of 100 mm (test JG_v10)

Figure 8.47, Figure 8.48, Figure 8.49 and Figure 8.50 present the total vertical stress

distribution below the footing for a settlement of 100 mm under the footing and at depths of 2

m, 4 m and 6 m below the surface, respectively.




A

BC

DE


JG_v10)

330







A

B C

DE

A

B C

DE

8 Appendices

331




A

B C

DE


JG_v10)

332



Figure 8.51, Figure 8.52, Figure 8.53 and Figure 8.54 present the total vertical stress

distribution below the footing for a settlement of 100 mm under the footing and at depths of 2

m, 4 m and 6 m below the surface, respectively.




A

B C

DE

8 Appendices

333







A

B C

DE

A

B C

DE


JG_v10)

334




A

B C

DE

8 Appendices

335



Figure 8.55 and Figure 8.56 present the total vertical stress distribution below the footing for

a settlement of 850 mm at depths of 2 m and 4 m below the surface, respectively.




A

B C

DE


JG_v10)

336




A

B C

DE

8 Appendices

337



Figure 8.57 and Figure 8.58 present a comparison of the excess pore water pressures

measured in the centrifuge with those computed numerically for test JG_v10 using a 3D-

model.





0

5

10

15

20

25

30

0 500000 1000000 1500000 2000000 2500000

Ex

ce

ss

po

re w

ate

r p

res

su

re

[kP

a]

Time [s]


0

5

10

15

20

25

30

35

0 500000 1000000 1500000 2000000 2500000

Ex

ce

ss

po

re w

ate

r p

res

su

re

[kP

a]

Time [s]

P7 P7 - Plaxis


338



JG_10 obtained numerically using an axisymmetric model is presented in this section.

Failure points denote elements that are located on the Mohr-Coulomb failure line (Figure

6.19, respectively Figure 6.22), while Cap points and Hardening points refer to elements

undergoing plastic shear strain hardening (Figure 6.22, Section 6.3.2.3) and plastic

volumetric hardening (Figure 6.23, Section 6.3.2.4), respectively. Tension cut-off points

denote elements that would undergo tension, if the value of cohesion was positive.


1-1, Figure 6.51) for a settlement of 100 mm (P = 76 kPa).

8 Appendices

339


1-1, Figure 6.51) for a settlement of 400 mm (P = 108.60 kPa).




340


2-2, Figure 6.51) for a settlement of 100 mm (P = 76 kPa).



8 Appendices

341




342

9 List of subscripts and symbols

343


Subscripts Description Unit

c Clay [-]

s Host soil [-]

sc Stone column [-]

p Plane-strain conditions [-]

Symbol Description Unit

2D Two-dimensional [-]

3D Three-dimensional [-]

a Centripetal acceleration [m/s2]

a Distance between the axis of the stone columns [m]

as Replacement ratio [-]

a √ ⁄ [-]

a Undrained shear strength parameter [-]

as, p Replacement ratio in plane-strain conditions [-]

A Footing area [m2]

A Pore pressure parameter according to Skempton (1954) [-]

Asc Stone column cross-section [m2]

As Soft soil cross-section in the unit cell (As = a2 – Asc) [m2]

b Undrained shear strength parameter [-]

bc Width of the equivalent plane-strain column [m]

bs Width of the smear zone in plane-strain conditions [m]

bsc Width of the stone-column in plane-strain conditions [m]

bw Width of a drain in plane-strain conditions [m]

B Width of loaded area [m]

B Foundation width [m]

B Width of the zone of influence in plane-strain conditions [m]

B Pore pressure parameter according to Skempton (1954) [-]

c’ Effective cohesion [kPa]

c’eq Equivalent effective cohesion [kPa]

ch Horizontal coefficient of consolidation [m2/year]

chm Modified horizontal coefficient of consolidation [m2/year]

c’s Effective cohesion of the host soil [kPa]

c’sc Effective cohesion of the stone column material [kPa]

cv Coefficient of consolidation [m2/s]

Cc Compression index [-]

Cf Conversion factor between coefficients of permeability

obtained in the laboratory and in the field - according to Chai &

Miura (1999)

[-]


344

Cs Swelling index [-]

CPT Cone Penetration Test [-]

d Length of the drainage path [m]

d Diameter of the T-Bar [m]

d Pore diameter [m]

de Diameter of the unit cell considered [m]

dsc Stone column diameter [m]

dεed Elastic deviatoric volumetric strain increment [-]

dεev Elastic volumetric strain increment [-]

dεpd Plastic deviatoric strain increment [-]

dεpv Plastic volumetric strain increment [-]

D Diameter of the zone of influence of a stone column [m]

e Void ratio [-]

e Base of natural logarithms [-]

e0 Initial void ratio [-]

es Void ratio of the host soil [-]

esc Void ratio of the stone column material [-]

E Young’s modulus [kPa]

Eeq Equivalent Young’s modulus [kPa]

Ei Initial stiffness modulus [kPa]

Eoed Tangent stiffness for primary oedometer loading [kPa]

Eoedref Tangent stiffness for primary oedometer loading corresponding

to the reference stress pref (Hardening Soil Model)

[kPa]

Es Young’s modulus of the host soil [kPa]

Es, p Young’s modulus of the host soil in plane-strain conditions [kPa]

Esc Young’s modulus of the stone column material [kPa]

Esc, p Young’s modulus of the stone column material in plane strain

conditions

[kPa]

Eu Elasticity modulus of the undrained soil [kPa]

Eur Unloading / reloading stiffness in a CDC triaxial test [kPa]

Eurref Unloading / reloading stiffness in a CDC triaxial test

corresponding to the reference stress pref (Hardening Soil

Model)

[kPa]

E50 Secant stiffness for primary loading in a CDC triaxial test [kPa]

E50ref Secant stiffness for primary loading in a CDC triaxial test

corresponding to the reference stress pref (Hardening Soil

Model)

[kPa]

ESEM Environmental Scanning Electron Microscope [-]

f Yield function [-]

F Failure surface [-]

fsc Volume content of the stone column [m3]

f12, f13 Yield surfaces yield surfaces in σ1, σ2 and σ1, σ3 planes, [-]


345

respectively (Hardening Soil Model)

F’c Cavity expansion parameter [-]

F’q Cavity expansion parameter [-]

FEM Finite Element Method [-]

g Earth’s gravity ( ) [m/s2]

G Shear modulus of the soil [kPa]

H Height of the unit cell considered [m]

H Thickness of the layer [m]

He Embankment height [m]

HSM Hardening Soil Model [-]

Ip Plasticity index [%]

Ir Stiffness index [-]

I’rr Reduced stiffness index for cylindrical cavity [-]

J4 Depth factor according to Grasshoff (1978) [-]

k Coefficient of permeability [m/s]

kh Coefficient of horizontal permeability of the undisturbed host

soil

[m/s]

kh, cl Coefficient of horizontal permeability in the clogged zone [m/s]

kh,p Coefficient of horizontal permeability of the undisturbed host

soil in plane-strain conditions

[m/s]

k’h Coefficient of horizontal permeability in the smear zone [m/s]

k’h,p Coefficient of horizontal permeability in the smear zone in

plane-strain conditions

[m/s]

kht Coefficient of horizontal permeability in the transition zone [m/s]

ks Coefficient of permeability of the undisturbed host soil [m/s]

ks’ Coefficient of permeability of the soil in the smear zone [m/s]

kv Coefficient of vertical permeability [m/s]

K Coefficient of earth pressure [-]

K0 Coefficient of earth pressure at rest [-]

Increased coefficient of earth pressure at rest [-]

K0,sc Coefficient of earth pressure at rest of the stone column

material

[-]

K0NC Coefficient of earth pressure at rest of a normally consolidated

soil

[-]

K0OC Coefficient of earth pressure at rest of an over-consolidated

soil

[-]

Ka Coefficient of active earth pressure [-]

Ka, sc Coefficient of active earth pressure of the stone column

material

[-]

Ks Coefficient of earth pressure of the host soil [-]

Ksc Coefficient of earth pressure of the stone column material [-]

Kp Coefficient of passive earth pressure [-]


346

Kp, e Coefficient of passive earth pressure of the embankment [-]

l Half-length of drain [m]

ID Density index [%]

L Pile length [m]

L Length of stone column [m]

m Stress concentration ratio [-]

m Power for stress-level dependency of stiffness. This factor

should be equal to 1.0 in the case of soft clays (Hardening Soil

Model)

[-]

M Slope of critical state line (Cam Clay) [-]

ME Confined stiffness modulus [kPa]

ME, h Horizontal confined stiffness modulus [kPa]

ME, s Confined stiffness modulus of the undisturbed host soil [kPa]

ME, sc Confined stiffness modulus of the stone column material [kPa]

ME, v Vertical confined stiffness modulus [kPa]

MC Mohr-Coulomb [-]

MCC Modified Cam-Clay [-]

MIP Mercury Intrusion Porosimetry [-]

n Factor of increase of the Earth’s gravity in the centrifuge [-]

n Radius ratio of the unit cell to the drain well [-]

n0 Initial porosity of the host soil [-]

n0 Ground improvement factor [-]

n1 Ground improvement factor for compressibility [-]

n2 Depth-dependent ground improvement factor [-]

Nb T-Bar factor [-]

Nc, Nγ, Nq Dimensionless bearing capacity parameters [-]

OCR Over-consolidation ratio [-]

p’ Mean effective stress [kPa]

p Mercury pressure [kPa]

psc,u Stress acting within the column at the depth of the tip of the

column

[kPa]

pp Pre-consolidation stress [kPa]

pu Ultimate cavity pressure [kPa]

pref Reference stress (Hardening Soil Model) [kPa]

P Footing load [kPa]

P Force per unit length acting on the T-Bar [kN/m]

POP Pre-Overburden-Pressure [kPa]

PPT Pore pressure transducer [-]

PVD Prefabricated vertical drain [-]

(P0)V,s Initial effective vertical stress in the host soil [kPa]

(P0)V,SC Initial effective vertical stress in the stone column [kPa]


347

(ΔP)*V Effective vertical stress increase averaged over horizontal

projected area of the unit cell

[kPa]

(ΔP)*V,s Effective vertical stress increase in the clay averaged over the

horizontal projected area of host soil

[kPa]

q Surcharge at the surface [kPa]

q Deviatoric stress [kPa]

Special stress measure for deviatoric stresses [kPa]

q(t) Average applied loading at time t [kPa]

q0 Overburden pressure [kPa]

q0 Ultimate loading [kPa]

qf Frictional resistance [kPa]

qf Deviatoric stress at failure [kPa]

qs Bearing capacity of the host soil [kPa]

qsc Bearing capacity of a stone column [kPa]

qsc, bulging Bulging failure load of a stone column [kPa]

qsc, shear Shear failure load of a single stone column [kPa]

qsc, shear, PW,i Shear strength of the i-th equivalent plane wall [kPa]

qt Tip resistance [kPa]

qw Discharge capacity of the drain [m3/year]

r Radius [m]

r Radius of stone column or pile [m]

r Distance from centreline [m]

r0 Pile radius [m]

rsc Radius of the stone column [m]

r’sc Effective radius of the stone column [m]

rs Radius of the smear zone [m]

rs Radius of the remoulded zone [m]

rw Radius of the drain [m]

R Radius of the unit cell considered [m]

R Electrical resistance [Ω]

R Global radial coordinate [m]

Req Equivalent radius of square pile [m]

Rf Failure ratio, usually set equal to 0.9 (Hardening Soil Model) [-]

Ri Initial radius of the cavity [m]

Rp Radius of the plastic zone [m]

Rs Radius of the smear zone [m]

Ru Final cavity radius [m]

s Total settlement [m]

s Radius ratio of the smear zone to the drain well [-]

s Distance between the axis

S Spacing (axis to axis) between two adjacent drains [m]


348

ss Settlement of the host soil [m]

ssc Settlement of the stone column [m]

sc Settlement of the layer [m]

se Settlement due to the stress concentration at the tip of the

stone column

[m]

se’ Reduced settlement due to the stress concentration at the tip

of the stone column

[m]

si Settlement of the improved layer [m]

s(t) Average settlement at time t [m]

sr Radial deformation [m]

su Undrained shear strength of the host soil [kPa]

sv Vertical settlement [m]

sv Settlement of the composite foundation [m]

su, avg Composite undrained shear strength [kPa]

s0 Settlement of the treated layer without ground improvement [m]

Average final settlement [m]

S Spacing (axis to axis) between two adjacent drains [m]

SCP Sand Compaction Pile [-]

SEM Scanning Electron Microscope [-]

SLS Serviceability Limit State [-]

SPM Strain Path Method [-]

SPT Standard Penetration Test [-]

SSPM Shallow Strain Path Method [-]

t Consolidation time [s]

t90 Time needed to reach a consolidation of 90 % [s]

Th Dimensionless time factor for radial flow [-]

Thm Modified dimensionless time factor for radial flow [-]

Tv Dimensionless time factor [-]

TST Total stress transducer [-]

u Pore water pressure [kPa]

ui Pore water pressure at the slip surface for the i-th slice [kPa]

Average pore pressure throughout the soil-stone column

cylinder

[kPa]

U Overall average degree of consolidation [-]

Average degree of consolidation for a radial flow [-]

ULS Ultimate Limit State [-]

wl Liquid limit [%]

wp Plastic limit [%]

W Width of equivalent pile strip [m]

z Depth [m]

zc Depth to which the column has been compacted [m]

zf Depth of foundation [m]


349

zi Depth of the i-th slice below the surface [m]

Z Electrical impedance [Ω]

α Electrode shape factor [1/cm]

α Henkel’s (1959) pore pressure parameter for the particular

stress level

[-]

α Non-dimensional factor for the consideration of the clogging of

a stone column

[-]

α Cap parameter relating to K0NC (Hardening Soil Model) [-]

αf Pressure parameter according to Skempton (1954) [-]

αi Inclination angle of the lower side of the i-th slice [°]

αk Ratio of horizontal permeability of the clogged column zone to

that of the smear zone

[-]

αvs Coefficient of compressibility of the host soil [m2/kN]

αvsc Coefficient of compressibility of the stone column material [m2/kN]

β Inclination of the failure surface [°]

β Settlement reduction factor [-]

β Cap parameter relating to (Hardening Soil Model) [-]

δ Inclination of the failure mechanism [°]

δri / r Radial strain [-]

δσr Radial total stress change [kPa]

δσθ Circumferential total stress change [kPa]

Δ Volumetric strain in the plastic zone [-]

ΔP Footing load increment [kPa]

Δt Layer thickness [m]

Δu0 Initial uniform excess pore water pressure [kPa]

Δumax Maximal excess pore water pressure [kPa]

Δur Excess pore water pressure due to radial flow [kPa]

Average excess pore water pressure due to radial flow [kPa]

Δσ Pressure difference on a footing [kPa]

Δσa Axial stress increase

Δσz Vertical stress increase [kPa]

εr Radial strain [-]

εv Vertical strain [-]

εrp Plastic volumetric strain [-]

εe Elastic strain [-]

εp Plastic strain [-]

εvpc Volumetric cap strain (Hardening Soil Model) [-]

ε1p, ε2

p Principal plastic strains [-]

φ’ Effective angle of friction [°]

Average mobilised effective angle of friction of the improved

ground [°]


350

φ’cv Critical state effective angle of friction [°]

φ’eq Equivalent effective angle of friction [°]

φ’s Effective angle of friction of the host soil [°]

φ’sc Effective angle of friction of the stone column material [°]

γc Unit weight of clay [kN/m3]

γe Unit weight of fill [kN/m3]

γeq Equivalent unit weight of the plane wall [kN/m3]

γq Unit weight of saturated soil [kN/m3]

γs Unit weight of the host soil [kN/m3]

γsc Unit weight of the stone column material [kN/m3]

γw Unit weight of water [kN/m3]

γp Plastic shear strain [-]

Effective Poisson’s ratio [-]

u Undrained Poisson’s ratio (

u = 0.5 [-]) [-]

ur Poisson’s ratio for unloading - reloading [-]

Poisson’s ratio [-]

Slope of swelling line (Cam Clay) [-]

Slope of normal consolidation line (Cam Clay) [-]

μsc Stress concentration factor for the stone column [-]

Wetting angle for mercury [°]

ρ Electrical resistivity [Ω.m]

ρ Soil arching ratio [-]

ρd,max Maximum bulk density [g/cm3]

ρd,min Minimum bulk density [g/cm3]

ρg Specific density of the saturated soil [g/cm3]

ρs Specific density [g/cm3]

σ Surface tension (MIP) [N/m]

σ Total stress acting on the unit cell [kPa]

σa Axial stress [kPa]

σc Pre-consolidation stress [kPa]

σh Horizontal stress [kPa]

σ’n,PW,i Normal stress applied on the i-th equivalent plane wall [kPa]

σr Radial stress [kPa]

σr Normal stress in soil element along R-direction [kPa]

σr0 Ultimate total in-situ lateral stress [kPa]

σs Total stress acting on the soft soil surface [kPa]

σsc Total stress acting on the stone column [kPa]

σsc,i Normal stress acting on the i-th stone column [kPa]

σ*v Tip resistance [kPa]

σv Vertical total stress [kPa]

σ’v Vertical effective stress [kPa]


351

σ’v,max Maximum vertical effective stress [kPa]

σ0 Average load intensity on a footing [kPa]

σ0 Load acting on the top of the embankment [kPa]

σ’1, σ’2, σ’3, Principal effective stresses [kPa]

σ1, σ2, σ3, Principal total stresses [kPa]

σ3 Average lateral confining pressure [kPa]

σθ Tangential total stress [kPa]

Angular velocity [rad/s]

Angle of dilatancy [°]


352

10 References

353

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