WHOLE LIFE GEOTECHNICAL RESPONSE OF TOLERABLY MOBILE SUBSEA INFRASTRUCTURE · principles of critical state soil mechanics in that dissipation of excess pore water pressure generated

WHOLE-LIFE GEOTECHNICAL RESPONSE OF

TOLERABLY MOBILE SUBSEA INFRASTRUCTURE

By

Michael John Cocjin

B.E. (Hons), M.Eng.

This thesis is submitted for the

Degree of Doctor of Philosophy

Centre for Offshore Foundation Systems

School of Civil, Environmental and Mining Engineering

2016

Thesis Declaration

I, Michael John Cocjin, declare that:

The thesis is my own composition, all sources have been acknowledged and my contribution is clearly identified in the thesis. For any work in the thesis that has been co-published with other authors, I have the permission of all co-authors to include this work in my thesis, and there is a declaration to this effect in the front of the thesis, signed by me and also by my supervisor/s and/or co-author/s.

This thesis has been substantially accomplished during enrolment in the degree. This thesis does not contain material which has been accepted for the award of any other degree or diploma in my name, in any university or other tertiary institution.

No part of this work will, in the future, be used in a submission in my name, for any other degree or diploma in any university or other tertiary institution without the prior approval of The University of Western Australia and where applicable, any partner institution responsible for the joint-award of this degree.

The work(s) are not in any way a violation or infringement of any copyright, trademark, patent, or other rights whatsoever of any person.

Date: 30 October 2016

Abstract The motivation of this research is the need to reduce subsea mudmat foundation size and weight, thus easing installation and alleviating costs associated with specialised offshore installation vessels. Subsea mudmat foundation sizes and weights are increasingly exceeding the handling capacity of standard installation vessels as developments move into areas of low strength seabeds, and deeper hotter reservoirs leading to larger thermal design loads increasing the weight of the structure supported by the mudmat foundation.

Offshore oil and gas developments increasingly comprise multiple wells spread across the seabed, connected by a network of in-field flowlines and associated pipeline infrastructure such as pipeline end terminations and in-line structures. It is typical for these subsea pipelines to be laid directly on the seabed, and the supporting mudmat foundations to be installed similarly or lightly embedded. Loads to pipeline infrastructure derive from thermal expansion of the attached pipelines as hot hydrocarbons flow through from the reservoir and are episodic, in synch with start-up and shutdown cycles of field production.

Traditionally, foundations are designed to remain stationary, i.e. they are engineered sufficiently large to resist applied loading without excessive displacement. This study challenges this conventional paradigm and instead explores an emerging design philosophy in which foundations are designed to move tolerably across the seabed in response to applied load, subject to other criteria such as ensuring that the associated settlements do not cause unacceptable secondary loads that may overstress other components of the attached pipeline.

This dissertation advances the understanding of the geotechnical behaviour of tolerably mobile seabed installations in order to provide a robust technical basis for the routine design of such infrastructure. This was achieved by carrying out a whole-life (installation and life of field operation) assessment of the performance of small-scale model tests subjected to typical loading regimes encountered by subsea infrastructures. Comprehensive suites of tests were carried out in a geotechnical centrifuge, enabling the correct simulation of prototype stress conditions and time periods under an enhanced gravitational field.

Initial centrifuge model testing investigated the whole-life response of a tolerably mobile mudmat foundation under episodic cycles of sliding and reconsolidation. A new loading

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apparatus to enable large-amplitude cyclic sliding under constant vertical load, allowing free movement in six degrees of freedom in a centrifuge environment was developed for these tests.

Tests results showed that the operative sliding resistance of the foundation increased with successive cycles of sliding and reconsolidation, reaching a steady state at a minimum density corresponding to the drained strength. Vertical displacement of the foundation correspondingly approached a steady state in line with the reduction in void ratio causing the increase in operative shear strength. The tests results also revealed that under undrained conditions, sliding capacity is dominated by the soil-structure friction resistance while drained shearing resistance of the ploughed soil berm is significant during slow sliding.

These results highlight the significant recovery of soil strength through successive episodes of remoulding and reconsolidation, the underlying mechanism of which follows the principles of critical state soil mechanics in that dissipation of excess pore water pressure generated during remoulding leads to increased effective stress resulting in increased undrained shear strength following reconsolidation.

A theoretical framework based on critical state soil mechanics principles has been developed and validated against the experimental results. The theoretical framework captures the cycle by cycle changes in undrained shear strength, void ratio and corresponding foundation settlement as a function of the critical state soil parameters, the operative foundation weight, and the level of reconsolidation that transpires between cycles of shearing. The framework can be programmed into a spreadsheet or simple calculation code and used as a predictive tool.

Changes in near-surface soil shear strength as a result of periods of remoulding and reconsolidation were further investigated using a conventional flow around T-bar penetrometer and a novel ‘pile penetrometer’, the latter particularly suited to investigating near-surface soil conditions. Cyclic penetrometer tests with and without intervening periods of reconsolidation characterised the softening and hardening characteristics of the soil due to remoulding and reconsolidation. The penetrometer tests with intervening consolidation between cycles of remoulding showed a comparable response to the sliding foundation,

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further demonstrating that the gain in strength from reconsolidation can eclipse the loss of strength caused by remoulding.

The novel pile penetrometer was also used to assess the surficial soil strength profile over a continuous lateral section. This enabled a detailed quantification of strength changes within a continuous cross-section through the foundation footprint, providing insights into strength increase due to episodic shearing and reconsolidation of the soil beneath and surrounding tolerably mobile subsea infrastructure.

The effect of remoulding and reconsolidation of near-surface soft seabed material on the lateral and axial response of a submarine pipeline was also investigated through geotechnical centrifuge modelling. Post-lay consolidation was shown to lead to gains in lateral break out and axial sliding capacity of a pipeline, with post-lay consolidation following dynamic installation (i.e. causing higher excess pore pressure than during static lay) resulting in the greatest resistance.

This study is the first to present a detailed observation and interpretation of the whole-life performance of tolerably mobile subsea foundations that can ultimately provide guidance in the geotechnical design of such infrastructure. Overall, the study has provided insights into improved geotechnical performance of subsea infrastructure through reducing the weight and size of subsea mudmat by enabling tolerable mobility.

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Contents

Thesis Declaration ........................................................................................................ i

Abstract ....................................................................................................................... iii

Contents..................................................................................................................... vii

List of Figures ........................................................................................................... xiii

List of Tables .......................................................................................................... xviii

Notation .................................................................................................................... xix

Acknowledgements ................................................................................................ xxxiii

Authorship Declaration ........................................................................................ xxxvii

Chapter 1. General introduction .............................................................................. 1-1

1.1. Motivation for the research ........................................................................................... 1-1

1.1.1. Operational context of subsea mudmats ............................................................... 1-3

1.1.2. Loading conditions on subsea mudmats ............................................................... 1-4

1.1.3. Redesigning subsea mudmats ................................................................................ 1-5

1.2. Research aims................................................................................................................. 1-8

1.2.1. Observe and quantify the whole-life response of a sliding mudmat foundation through geotechnical centrifuge modelling ..................................................................... 1-8

1.2.2. Quantify the volumetric strains and soil strength changes due to repeated cycles of remoulding and reconsolidation ............................................................................... 1-11

1.2.3. Develop a theoretical model to predict the cycle by cycle whole-life response of a sliding mudmat foundation capturing the effects of repeated shearing, partial remoulding and reconsolidation .................................................................................... 1-12

1.3. Dissertation outline .................................................................................................... 1-12

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Chapter 2. Whole-life response observations ......................................................... 2-15

Prologue .............................................................................................................................. 2-15

Abstract ............................................................................................................................... 2-16

2.1. Background .................................................................................................................. 2-16

2.2. Experimental program ................................................................................................ 2-19

2.2.1. Geotechnical centrifuge facility and equipment ................................................. 2-19

2.2.2. Mudmat foundation model ................................................................................. 2-19

2.2.3. Loading arm ......................................................................................................... 2-20

2.2.4. Instrumentation .................................................................................................... 2-21

2.2.5. Soil sample ............................................................................................................ 2-21

2.2.6. Site characterisation.............................................................................................. 2-22

2.3. Mudmat loading tests ................................................................................................. 2-29

2.3.1. Mudmat installation ............................................................................................. 2-29

2.3.2. Undrained cyclic sliding ....................................................................................... 2-31

2.3.3. Reconsolidation between sliding events.............................................................. 2-31

2.4. Results and discussion ................................................................................................. 2-32

2.4.1. Horizontal resistance ............................................................................................ 2-32

2.4.2. Foundation settlements ........................................................................................ 2-35

2.4.3. Foundation rotation ............................................................................................. 2-37

2.5. Final remarks ............................................................................................................... 2-42

2.6. Acknowledgements ..................................................................................................... 2-44

Chapter 3. Drainage effects .................................................................................... 3-45

Prologue .............................................................................................................................. 3-45

Abstract ............................................................................................................................... 3-46

3.1. Background .................................................................................................................. 3-46

3.2. Foundation tests .......................................................................................................... 3-47

3.2.1. Test set-up ............................................................................................................ 3-47

3.2.2. Soil sample ............................................................................................................ 3-48

3.2.3. Loading program .................................................................................................. 3-49

3.3. Results and discussion ................................................................................................. 3-51

3.3.1. Undrained sliding resistance with consolidation ................................................ 3-51

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3.3.2. Drained sliding resistance ................................................................................... 3-55

3.3.3. Failure envelopes .................................................................................................. 3-55

3.4. Concluding remarks ................................................................................................... 3-57

3.5. Appendix: Bearing capacity ....................................................................................... 3-57

3.6. Acknowledgements .................................................................................................... 3-59

Chapter 4. Whole-life response prediction ............................................................ 4-61

Prologue .............................................................................................................................. 4-61

Abstract............................................................................................................................... 4-62

4.1. Introduction ................................................................................................................ 4-62

4.2. Motivation................................................................................................................... 4-63

4.3. Overview of the framework ....................................................................................... 4-64

4.4. Components of the framework.................................................................................. 4-69

4.4.1. Vertical equilibrium conditions ........................................................................... 4-69

4.4.2. Undrained shear strength .................................................................................... 4-70

4.4.3. Mobilised shear stress .......................................................................................... 4-70

4.4.4. Equivalent cycle number ..................................................................................... 4-71

4.4.5. CSL migration based on shearing cycles ........................................................... 4-71

4.4.6. Generation of excess pore pressure ..................................................................... 4-72

4.4.7. Dissipation of excess pore pressure ..................................................................... 4-73

4.4.8. Change in soil height and surface settlement .................................................... 4-75

4.5. Comparison of theoretical framework and model test data..................................... 4-75

4.5.1. Foundation test .................................................................................................... 4-75

4.5.2. Stress distribution ................................................................................................ 4-76

4.5.3. Calibration and derivation of model parameters ............................................... 4-77

4.5.4. Assessment of the theoretical model .................................................................. 4-85

4.6. Insights into soil response .......................................................................................... 4-90

4.6.1. Void ratio .............................................................................................................. 4-90

4.6.2. Undrained shear strength .................................................................................... 4-93

4.6.3. Stress and state path ............................................................................................ 4-93

4.7. Closing remarks .......................................................................................................... 4-93

4.8. Acknowledgements .................................................................................................... 4-94

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Chapter 5. Seabed strength characterisation .......................................................... 5-95

Prologue .............................................................................................................................. 5-95

Abstract ............................................................................................................................... 5-96

5.1. Introduction ................................................................................................................. 5-96

5.2. Pile penetrometer ........................................................................................................ 5-98

5.3. Laterally loaded pile analysis ...................................................................................... 5-99

5.3.1. 1-way wedge mechanism ..................................................................................... 5-99

5.3.2. 2-way wedge mechanism ................................................................................... 5-100

5.3.3. Full-flow mechanism ......................................................................................... 5-101

5.4. Sample preparation and initial characterisation ...................................................... 5-101

5.5. Pile penetrometer test ............................................................................................... 5-102

5.6. Pile penetrometer analysis ........................................................................................ 5-103

5.7. Measured soil resistance............................................................................................ 5-105

5.8. Example application .................................................................................................. 5-107

5.9. Concluding remarks .................................................................................................. 5-108

5.10. Acknowledgement .................................................................................................. 5-109

Chapter 6. Seabed strength changes..................................................................... 6-111

Prologue ............................................................................................................................ 6-111

Abstract ............................................................................................................................. 6-112

6.1. Introduction ............................................................................................................... 6-112

6.2. Experiments ............................................................................................................... 6-113

6.2.1. Consolidation characteristics ............................................................................. 6-114

6.2.2. Strength characterisation tools .......................................................................... 6-114

6.2.3. Test programme ................................................................................................. 6-115

6.3. Shear strength interpretation through penetrometer tests ..................................... 6-118

6.3.1. T-bar penetrometer ............................................................................................ 6-118

6.3.2. Pile penetrometer ............................................................................................... 6-120

6.4. Part I: Strength assessment in virgin soil ................................................................. 6-122

6.4.1. Intact shear strength ........................................................................................... 6-122

6.4.2. Fully remoulded shear strength ......................................................................... 6-125

6.4.3. Remoulded shear strength with reconsolidation .............................................. 6-126

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6.5. Part II: Strength assessment in foundation footprint ............................................ 6-132

6.5.1. Nonlinear undrained shear strength ................................................................. 6-133

6.5.2. Continuous shear strength profile .................................................................... 6-136

6.6. Final remarks ............................................................................................................ 6-138

6.7. Acknowledgements .................................................................................................. 6-139

Chapter 7. Pipeline installation response observations .........................................7-141

Prologue ............................................................................................................................ 7-141

Abstract............................................................................................................................. 7-142

7.1. Introduction .............................................................................................................. 7-142

7.2. Experimental program ............................................................................................. 7-144

7.2.1. Apparatus ........................................................................................................... 7-144

7.2.2. Soil sample.......................................................................................................... 7-144

7.2.3. Pipe testing programme .................................................................................... 7-148

7.3. Undrained penetration response .............................................................................. 7-150

7.4. Post-lay consolidation response ............................................................................... 7-153

7.5. Axial load-displacement response ........................................................................... 7-157

7.5.1. Post-lay consolidation effects ............................................................................ 7-157

7.5.2. Prediction of undrained axial breakout capacity .............................................. 7-158

7.6. Lateral load-displacement response ........................................................................ 7-158

7.6.1. Installation and post-lay consolidation effects ................................................. 7-158

7.6.2. Comparison with theoretical solutions for unconsolidated, undrained lateral breakout capacity .......................................................................................................... 7-160

7.6.3. Comparison with theoretical solutions for the consolidated, undrained lateral breakout capacity .......................................................................................................... 7-163

7.7. Pipe trajectory ........................................................................................................... 7-165

7.8. Concluding remarks ................................................................................................. 7-168

7.9. Acknowledgements .................................................................................................. 7-169

Chapter 8. Conclusions .........................................................................................8-171

8.1. Introduction .............................................................................................................. 8-171

8.2. Contributions ............................................................................................................ 8-173

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8.2.1. A data set of observations of the whole-life response of a tolerably mobile mudmat from geotechnical centrifuge modelling....................................................... 8-173

8.2.2. An improved understanding of the changing strength of seabed due to repeated cycles of remoulding and reconsolidation ................................................................... 8-175

8.2.3. A theoretical model to predict the cycle by cycle whole-life response of a sliding mudmat foundation capturing the effects of repeated remoulding and reconsolidation 8-176

8.3. Future directions ....................................................................................................... 8-177

References ................................................................................................................ 179

Appendix A. Multi DoF loading in a geotechnical centrifuge ............................ A-193

Prologue ........................................................................................................................... A-193

Abstract ............................................................................................................................ A-194

A.1. Introduction ............................................................................................................. A-194

A.2. Design of the multi-DoF loading system.............................................................. A-195

A.2.1. General arrangement ....................................................................................... A-195

A.2.2. Loading arm description .................................................................................. A-196

A.2.3. System instrumentation ................................................................................... A-198

A.3. Summary of centrifuge test used to illustrate loading system capability ............. A-199

A.3.1. Soil model ......................................................................................................... A-200

A.3.2. Model foundation ............................................................................................ A-200

A.3.3. Loading program .............................................................................................. A-204

A.4. Technical performance of the multi-Dof loading system .................................... A-206

A.5. Example application of the multi-Dof loading system ........................................ A-209

A.6. Closing remarks ...................................................................................................... A-212

A.7. Acknowledgements ................................................................................................. A-214

Appendix B. Interpretation of undrained shear strength presented in the dissertation ............................................................................................................................. B-215

B.1. Summary of corrections applied to undrained shear strength profiles ................. B-215

B.2. Nonlinear districbution of inerital acceleration through the centrifuge model ... B-216

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List of Figures Chapters 1−7

Figure 1.1 Illustration of offshore oil and gas development .................................................. 1-2

Figure 1.2 Illustration of a pipeline-infrastructure system ..................................................... 1-3

Figure 1.3 Idealised mode of operation of a tolerably mobile subsea mudmat .................... 1-4

Figure 1.4 Loads and displacement acting on a mudmat foundation .................................. 1-5

Figure 1.5 Environmental versus thermally-induced pipeline expansion loading ............... 1-6

Figure 1.6 Photos of a deep-water construction vessel with a J-lay tower ........................... 1-7

Figure 1.7 Schematic showing research aims and boundary value problems addressed ...... 1-9

Figure 2.1 Typical layout of pipeline connections with associated infrastructure ............. 2-17

Figure 2.2 Model foundation ............................................................................................... 2-19

Figure 2.3 Test set-up ........................................................................................................... 2-21

Figure 2.4 T-bar penetrometer results ................................................................................. 2-24

Figure 2.5 Piezocone tests results ......................................................................................... 2-26

Figure 2.6 Normalised excess pore pressure under a ‘piezofoundation’ ............................. 2-28

Figure 2.7 Time histories of loading test ............................................................................. 2-30

Figure 2.8 Sliding resistance-displacement response .......................................................... 2-33

Figure 2.9 Horizontal resistance variation factor ................................................................ 2-34

Figure 2.10 Settlement-rotation-sliding resistance responses ............................................ 2-36

Figure 2.11 Cumulative settlements .................................................................................... 2-38

Figure 2.12 Consolidation settlements ................................................................................ 2-38

Figure 2.13 Orientation of the long side of the model foundation .................................... 2-39

Figure 2.14 Formation of soil berm at extremities of the foundation footprint ............... 2-41

Figure 2.15 Foundation rotation during MMUD3 test ..................................................... 2-43

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Figure 3.1 Illustration of sliding foundation concept .......................................................... 3-46

Figure 3.2 Undrained shear strength profile pre- and post-test ......................................... 3-48

Figure 3.3 Displacement sequence during final cycles of test ............................................. 3-50

Figure 3.4 Mobilised soil berm at the foundation leading edge ......................................... 3-50

Figure 3.5 Foundation settlement during sliding cycles ...................................................... 3-52

Figure 3.6 Horizontal load-displacement responses ........................................................... 3-53

Figure 3.7 Increase in mobilised undrained shear strength ................................................. 3-54

Figure 3.8 Failure envelope in vertical-horizontal load space ............................................. 3-56

Figure 4.1 Idealisation of the boundary value problem ....................................................... 4-64

Figure 4.2 A critical state interpretation of a soil element submitted to cyclic surface shearing and reconsolidation .......................................................................................... 4-67

Figure 4.3 Schematic of model framework .......................................................................... 4-68

Figure 4.4 Experimental set-up of the sliding foundation test in the centrifuge .............. 4-76

Figure 4.5 Loading sequence for a sliding foundation test in the centrifuge ..................... 4-77

Figure 4.6 Vertical effective stress, σ′v plotted against void ratio, e .................................... 4-83

Figure 4.7 Change in cycle number ∆Neq with mobilised stress ratio,τ/su ......................... 4-84

Figure 4.8 Residual coefficient of sliding friction ................................................................ 4-85

Figure 4.9 Settlement data and prediction ........................................................................... 4-87

Figure 4.10 Incremental plastic undrained settlements ....................................................... 4-88

Figure 4.11 In situ and sheared/consolidated soil (final) undrained shear strength .......... 4-89

Figure 4.12 Moisture content, mc profile with depth .......................................................... 4-91

Figure 4.13 Cycle by cycle evolution of the current void ratio ............................................ 4-91

Figure 4.14 Cycle by cycle evolution of the current undrained shear strength .................. 4-92

Figure 4.15 State path in vertical effective stress - void ratio space .................................... 4-92

Figure 5.1 Miniature pile penetrometer ............................................................................... 5-97

xiv

Figure 5.2 Failure mechanisms of a pile penetrometer ....................................................... 5-99

Figure 5.3 Undrained shear strength profile from T-bar test .......................................... 5-102

Figure 5.4 Recorded moment loads on the pile penetrometer: ........................................ 5-103

Figure 5.5 Pile penetrometer analysis ................................................................................ 5-104

Figure 5.6 Net lateral force, F; depth of line of action of force F, zLOA ........................... 5-105

Figure 5.7 Pile penetrometer estimates of soil strength .................................................... 5-107

Figure 5.8 Overlay of soil surface image and lateral pile penetrometer resistance .......... 5-109

Figure 6.1 Shallow penetrometers ...................................................................................... 6-115

Figure 6.2 Cyclic loading sequence for penetrometer tests .............................................. 6-116

Figure 6.3 Schematic of foundation footprint ................................................................... 6-119

Figure 6.4 Schematic of pile penetrometer analysis .......................................................... 6-120

Figure 6.5 Penetrometer tests in virgin soil with continuous remoulding cycles ............ 6-123

Figure 6.6 Intact undrained shear strength from T-bar and pile penetrometers ............ 6-123

Figure 6.7 Evolution of soil strength through continuous remoulding cycles ................ 6-125

Figure 6.8 Penetrometer tests in virgin soil with remoulding cycles interspersed with consolidation episodes .................................................................................................. 6-127

Figure 6.9 Evolution of soil strength through continuous remoulding cycles interspersed with consolidation episodes ......................................................................................... 6-128

Figure 6.10 Post-test photos ............................................................................................... 6-130

Figure 6.11 Critical state interpretation of remoulding and reconsolidation cycles ....... 6-131

Figure 6.12 Penetrometer tests in foundation footprint ................................................... 6-134

Figure 6.13 Conversion of net horizontal load, H into soil resistance parameters ......... 6-134

Figure 6.14 Change in elevation on foundation footprint soil ......................................... 6-137

Figure 6.15 Soil strength parameters within foundation footprint .................................. 6-137

Figure 6.16 Contour plots of undrained shear strength ................................................... 6-138

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Figure 7.1 Schematic drawing of model pipe .................................................................... 7-145

Figure 7.2 Characterisation of the soil model using a ball penetrometer......................... 7-147

Figure 7.3 Undrained pipe penetration response showing ................................................ 7-150

Figure 7.4 Variation in pore water pressure along the embedded pipe ............................ 7-152

Figure 7.5 Dissipation-time histories of excess pore pressure at the pipe invert ............. 7-154

Figure 7.6 Effect of consolidation on pipe-soil contact stresses ....................................... 7-156

Figure 7.7 Effect of consolidation on axial pipe resistance ............................................... 7-158

Figure 7.8 Effect of installation and post-lay consolidation on the lateral breakout resistance ........................................................................................................................................ 7-160

Figure 7.9 Unconsolidated lateral breakout responses ...................................................... 7-161

Figure 7.10 Development of soil heave during pipe penetration ...................................... 7-162

Figure 7.11 Consolidated lateral breakout responses ........................................................ 7-164

Figure 7.12 Effect of consolidation on pipe trajectory during axial and lateral loading .. 7-166

Figure 7.13 Effect of pipe weight on the pipe trajectory during lateral breakout ............ 7-166

Figure 7.14 Inclination of displacement paths at lateral breakout compared against existing solutions ......................................................................................................................... 7-167

Figure 8.1 Summary of results ............................................................................................ 8-172

Appendix A

Figure A−1 Schematic of loading arm and actuator system ............................................ A-197

Figure A−2 Positive sign convention for loads and displacements acting on a rectangular foundation .................................................................................................................... A-198

Figure A−3 Undrained shear strength profile with depth ............................................... A-201

Figure A−4 Schematic of model foundation ..................................................................... A-202

Figure A−5 Schematic of the loading arm and model foundation movements ............. A-203

Figure A−6 Centrifuge tests loading program .................................................................. A-205

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Figure A−7 Time-scale plots of the vertical load (V), horizontal displacement (uy), horizontal load (H), vertical displacement (w(laser)), and foundation rotation about the x and y axes (θxx and θyy) ................................................................................................. A-207

Figure A−8 Comparison of foundation movements as measured by the actuator encoders, and independently by lasers ........................................................................................ A-208

Figure A−9 Complete set of test ....................................................................................... A-210

Figure A−10 Post-touchdown and cyclic consolidation settlement ............................... A-211

Figure A−11 Post-touchdown and cyclic consolidation settlement ............................... A-213

Appendix B

Figure B-1 Inertial stresses in a centrifuge model ............................................................. B-217

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List of Tables Chapters 1−7

Table 2.1 Characteristics of kaolin clay ................................................................................ 2-22

Table 2.2 Centrifuge test program ....................................................................................... 2-29

Table 4.1 Framework parameters ......................................................................................... 4-78

Table 4.2 Curve-fitting parameters for plastic strain ratio .................................................. 4-88

Table 6.1 Penetrometer tests programme .......................................................................... 6-117

Table 6.2 Fully remoulded strength properties .................................................................. 6-125

Table 6.3 Foundation test ................................................................................................... 6-131

Table 6.4 Critical state parameters for kaolin clay ............................................................. 6-133

Table 7.1 Pipe tests programme ......................................................................................... 7-149

Appendix B

Table_B-1 Summary of the undrained shear strength profiles ....................................... B-219

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Notation Symbols used and as defined in each chapter

Chapter 1

ω angular rotation of the foundation

θy foundation rotation about the y-axis

θx foundation rotation about the x-axis

w foundation settlement

V vertical load acting on the foundation

uy horizontal displacement of the foundation along the y-axis

ux horizontal displacement of the foundation along the x-axis

T torsional load acting on the foundation

My moment load on the foundation about the y-axis

Mx moment load on the foundation about the x-axis

Hy horizontal load acting along the y-axis of the foundation

Hx horizontal load acting along the x-axis of the foundation

Chapter 2

B foundation breadth

L foundation length

ch horizontal coefficient of consolidation

cref operative coefficient of consolidation

cv vertical coefficient of consolidation

D piezofoundation diameter

H horizontal load

Hres,cyc residual resistance during sliding cycles

Hres,N=0.5 residual resistance during the first slide

Ir rigidity index of the soil

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k gradient of undrained shear strength with depth

kB/sum non-dimensional shear strength heterogeneity index

N cycle number

Ncv bearing capacity factor

qop operative vertical bearing pressure

qT-bar T-bar resistance

qu ultimate vertical bearing capacity

R piezocone radius

St soil sensitivity

su undrained shear strength

su,cyc undrained shear strength measured during cycles of penetration and extraction

su/σ′vo normally consolidated strength ratio

sum mudline shear strength

T non-dimensional time for dissipation (creft/B2)

t dissipation time

T* non-dimensional time for interpretation of piezocone results (cht/R2Ir0.5)

T50 non-dimensional time for 50 % pore pressure dissipation

Top non-dimensional time for accumulated operational duration (creftop/B2)

top accumulated operational duration

trecon reconsolidation period

Trecon non-dimensional time for reconsolidation period (creftrecon/B2)

tslide sliding duration

Tslide non-dimensional time for sliding duration (creftslide/B2)

u horizontal displacement of foundation

V vertical load

v sliding rate

xx

w vertical displacement of foundation

z depth

zCPTu depth of piezocone tests

dθL incremental rotation of the foundation about the short axis

∆µ horizontal resistance variation factor (Hres,cyc/Hres,N=0.5)

∆N cycle number increment

∆su strength variation factor (su,cyc/su)

du incremental horizontal displacement of foundation

∆ue excess pore pressure

∆ue,i initial excess pore pressure

γ′ average effective unit weight of the soil

ϕ′ internal angle of friction

µ mobilised coefficient of sliding friction

µres residual coefficient of sliding friction (Hres,cyc/V)

θL rotation of the foundation about the short axis

σ′v0 in situ effective vertical stress

Chapter 3


L foundation length

Abase basal area of the model foundation

Aberm area of soil berm


f non-dimensional factor determining drained horizontal load capacity

h height of soil berm

Hdr,base drained sliding resistance mobilised by the foundation base

Hdr,berm drained sliding resistance mobilised by the ploughed soil berm

xxi

Hun undrained sliding resistance

Hun,base undrained sliding resistance mobilised by the foundation base

Hun,berm undrained sliding resistance mobilised by the ploughed soil berm

kin-situ in situ gradient of undrained shear strength with depth

N cycle number (undrained loading)

Nγ bearing capacity factor for soil surcharge

N50 cycle number when 50 % of drained sliding resistance has been reached through undrained sliding cycles

Ncv bearing capacity factor for a rectangular surface mat

NT-bar T-bar factor

sγ bearing capacity factor for foundation shape effects

St soil sensitivity

su,in-situ in situ undrained shear strength

su,mob mobilised undrained shear strength (Hun/Abase)

su,rem remoulded undrained shear strength (su,in-situ/St)

su,ϕ' mobilised drained shear strength

su/σʹvc normally consolidated undrained strength ratio

sum,f mudline shear strength measured at the foundation footprint

sum,in-situ in situ undrained shear strength at the mudline

t dissipation (consolidation) time

T non-dimensional time for dissipation (consolidation)

T50 time factor when 50 % of drained sliding resistance has been reached through undrained sliding cycles

u horizontal displacement of foundation

v sliding rate of foundation

Vdr unconsolidated, drained vertical load capacity

Vo uniaxial vertical bearing capacity

Vop operative vertical load

Vun unconsolidated, undrained vertical load capacity

xxii

Vun(cons) consolidated, undrained vertical load capacity

w vertical displacement of foundation

wplough depth of ploughed soil

z depth

∆sum change in undrained shear strength

∆tdr one-way drained slide duration

∆tun one-way undrained slide duration


ϕ′ internal angle of friction

κ strength heterogeneity index

θ inclination of foundation ‘ski’ from the horizontal (soil surface)

Chapter 4


L foundation length

(su/σ′v0)NCL normally consolidated strength ratio

a void ratio - permeability relationship parameter

b void ratio - permeability relationship parameter

bNCL compression destructuring index, where 0 < bNCL < ∞


d drainage length

e void ratio

eeqm void ratio at the state of equilibrium

Gs specific particle density

Iσ influence factor for vertical stress

Iτ influence factor for shear stress

k coefficient of soil permeability

M slope of CSL in vertical effective stress - shear stress (σ′v - τ) plane

xxiii

m consolidation constant

mc moisture content of the soil

N number of loading cycles

Neq(95) number of cycles required for 95 % of the migration of the current CSL to the final location

OCR over-consolidation ratio

p′ mean principal effective stress

q deviatoric stress

R spacing ratio

R0 initial spacing ratio

Rf final spacing ratio

St soil sensitivity


su,f final undrained shear strength

t reconsolidation period

T dimensionless time factor

T50 dimensionless time factor for 50 % of the consolidation settlement to occur

U degree of consolidation based on settlement

v0 curve-fitting parameters for plastic strain ratio


Vu,cons consolidated, undrained vertical load capacity

w settlement of the soil surface

wp undrained shearing settlement

z soil depth

α factor to account for the anisotropic dissipation of pore water pressure during consolidation

β excess pore pressure parameter defining the curvature of the σ′v - τ effective stress path

xxiv

χ remoulding parameter

∆ei additional void ratio at σ′v = σ′v,i, where virgin yielding begins

∆Neq equivalent number of cycles

du sliding movement

∆ue,dis dissipated excess pore water pressure

∆ue,gen generated excess pore water pressure

dwp plastic undrained settlement

Γ void ratio intercept at σ′v = 1 kPa of the critical state line (CSL) in the e – lnσ'v plane

Γ0 void ratio intercept at σ′v = 1 kPa of the initial critical state line (CSL) in the e – lnσ′v plane

γ'av average effective unit weight of the soil

γw unit weight of water

κ slope of unload-reload line

Λ curve-fitting parameters for plastic strain ratio

l slope of normal compression line (NCL) in the e – lnσ′v plane

N void ratio intercept at σ′v = 1 kPa of the Normal Compression Line (NCL) in the e – lnσ′v plane

σ′v vertical effective stress

σop vertical stress applied at the mudline

σ′v,CSL vertical effective stress on the critical state line (CSL)

σ′v,eqm vertical effective stress at equilibrium state

σ′v,i vertical effective stress where virgin yielding begins

σ′v,max maximum vertical effective stress experienced by the soil

σ′v0 in situ soil self-weight vertical effective stress

τop horizontal shear stress

xxv

Chapter 5

Ae,pile projected area of the embedded pile penetrometer

Di inner pile penetrometer diameter

Do outer pile penetrometer diameter

∆u rate of lateral translation

F net lateral force

k strength gradient determined from T-bar

k1 gradient of resistance determined from pile penetrometer

Mn bending moments

Ndeep bearing factor corresponding to deep failure mechanisms

Nh lateral bearing capacity factor

Nshallow bearing factor at the soil surface

NT-bar T-bar factor

qh lateral resistance

qh1 lateral soil resistance at the pile toe

qho lateral resistance at mudline

su undrained shear strength of the soil

sum strength at mudline

u lateral translation

z depth below the soil surface

zcrit depth where the transition from wedge to full-flow occurs

ze pile penetrometer embedment

zLOA line of action of net lateral force

α ratio of the strength at mudline to the strength gradient and outer pile diameter

β ratio of the strength at mudline to the strength gradient

xxvi

Chapter 6


ch horizontal coefficient of consolidation


D pile penetrometer diameter

dH horizontal load due to additional volume of soil ahead of the pile penetrometer

e void ratio

H net horizontal load on pile penetrometer

K gradient of resistance on virgin soil

k gradient of strength on virgin soil

Kcons gradient of resistance within the zone of influence

kcons gradient of strength within the zone of influence

M critical state friction constant

M1, M2, M3, M4 recorded moment loads at strain gauges 1 to 4

N loading cycle number

Npile horizontal bearing capacity factor

NT-bar T-bar bearing factor

qhm mudline resistance of pile penetrometer on virgin soil

qT-bar T-bar resistance

su undrained shear strength of the soil

su,op intact undrained shear strength on virgin soil

su,T-bar undrained shear strength through T-bar

(su/σ′v)NC normally consolidated strength ratio

su0,pile(peak) undrained shear strength through pile penetrometer representing peak horizontal load condition

su0,pile(res) undrained shear strength through pile penetrometer representing residual horizontal load condition

sum undrained shear strength of the soil at the mudline level

xxvii

T non-dimensional time factor

t consolidation (or dissipation) time

U degree of consolidation

umax maximum generated excess pore water pressure

V vertical load on the T-bar

z depth from free soil surface

zcons depth of influence

ze embedment depth of pile penetrometer

zf elevation of footprint mudline relative to original virgin soil surface

zLOA depth of line of action of horizontal load, H

zmax maximum vertical length of the drainage path from the cycled zone

∆ef total change in void ratio

∆su ratio of the cyclic to intact soil strengths, or final to intact soil strengths

drem fully remoulded strength variation factor

dz change in elevation of footprint mudline

κ slope of the reconsolidation line

l slope of the normally consolidated and critical state lines

σ′v effective vertical stress

Chapter 7

D pipe diameter

L pipe length

(su/σ′v)NC normally consolidated strength ratio

(V/Dsu0)UU normalised unconsolidated undrained vertical pipe resistance mobilised at the effective embedment

As/AP ratio of the shaft to the projected area of the ball penetrometer


D′ effective contact width of the pipe

xxviii

fb soil buoyance enhancement factor

Fbuoy soil buoyancy force on the ball penetrometer

fσ stress factor

fsu strength factor

H/Dsu0 normalised lateral resistance

H/V lateral friction factor

Hax axial horizontal load

Hax/Dsu0 normalised axial breakout resistance

Hax/V axial friction factor

k undrained shear strength gradient

m constant

N′ effective normal force around the pipe-soil contact

N95 number of cycles required to achieve 95 % of fully remoulded strength from the intact strength

Nb self-weight factor

Nball ball penetrometer factor

Nc soil bearing factor reflecting the soil resistance component

p pipe-soil contact perimeter

qball penetration resistance measured by the ball penetrometer

qm net penetration resistance of the ball penetrometer


Su,cyc cyclic/remoulded undrained shear strength

su0 intact, in situ, undrained shear strength

sum mudline undrained shear strength

T non-dimensional time factor

t time

T50 time factor when 50 % of the increase in total contact enhancement factor, ζ has occurred

u pore pressure

xxix

u0 hydrostatic pressure

uinv pore pressure at the pipe invert (averaged)

uside pore pressure at the side pore pressure transducers (averaged)

V/D pipe vertical bearing pressure per unit length

V/Dsu0 normalised vertical penetration resistance

Vmax vertical load at a penetration of w/D = 0.5


Vop/Vmax unloading ratio

Vult,CU consolidated undrained ultimate vertical load capacity

Vult,UU unconsolidated undrained ultimate vertical load capacity

w pipe penetration at the invert level

x lateral displacement

x/D normalised lateral displacement

y axial displacement

y/D normalised axial displacement

z depth

α net area ratio of the load cell core to the shaft area

d pipe-soil friction angle

drem final remoulded strength of the soil

∆su increase in the undrained shear strength due to consolidation

∆u excess pore pressure around the pipe

∆u̅ sum of excess pore pressure around the pipe (averaged)

∆uinv excess pore pressure at the pipe invert (averaged)

∆urear excess pore pressure at the rear side of the pipe (averaged)

∆uside excess pore pressure at the side pore pressure transducers (averaged)

∆wheave effective increase in embedment due to soil heave


θ inclination from the vertical of the vertical load acting on the pipe

xxx

θ′ half of the central angle formed by the effective contact width of the pipe

θPPT central angle of side-to-side pore pressure transducers

σr total radial stress

σv0 in situ total overburden stress

ζ total contact enhancement factor/fully consolidated undrained effective contact enhancement factor

ζ′ effective contact enhancement factor

ζUU unconsolidated undrained effective contact enhancement factor

Appendix A

A foundation basal area


L foundation length

H horizontal load

N loading cycles


uy horizontal displacement

uy(encoder) displacement of the actuator’s horizontal axis

uy(laser) laser displacement sensor measurement

V vertical load (submerged weight of the foundation)


w vertical displacement

w(encoder) displacement of the actuator’s vertical axis

wcons consolidation settlement

(su/σ′v0)NC normally consolidated strength ratio

µ coefficient of sliding friction (H/V)

γ′avg average effective unit weight of the soil

xxxi

ϕ′ internal angle of soil friction

θxx rotation about the x axis

θyy rotation about the y axis

Appendix B

g Earth’s gravity

n scaling factor

r radial distance from the fixed axis of rotation

Re effective centrifuge radius

Rt radial distance from the axis of rotation to the top of the soil model

zm depth of the soil model from the top surface

ω angular rotational speed of the centrifuge

xxxii

Acknowledgements

My sincere thanks to my mentors Prof. Susan Gourvenec, Prof. David White and Prof. Mark Randolph for their superb supervision, guidance, and patience throughout the completion of this work − to Susie for paving the way for me to work on a research project that has challenged, inspired and given me every opportunity to develop and hone my skills and for always looking out for my best interests throughout these years; to Dave for constantly inspiring me to always think creatively and for his very hands-on mentorship and astute attention to details that has (hopefully) rubbed off on me over the years; and to Mark for his insightful and always helpful suggestions and guidance to bring the best out of my PhD work. Not many are given the chance to work with and be mentored by the bests in the field, and for that I am eternally grateful for the remarkable and awesome experience and honour to be under the tutelage of these three and for the extraordinary, and lasting influence and inspiration they have imparted to my (not-so-young) life.

Special thanks are also given to Dr. Conleth O’loughlin for his valuable contributions to this work, particularly in the development of the experimental equipment used in the study; to the skillful staff in the Centre for Offshore Foundation Systems – to Manuel Palacios, Kelvin Leong, and David Jones for their assistance and technical expertise in the conduct of experiments; to Monica Mackman, Dana Mammone, Ivan Kenny, Monika Mathyssek-Kilburn, and Lisa Melvin for all the assistance they have extended during my stay at the Centre; and to Dr. Shiaohuey Chow, Dr. Nathalie Boukpeti, Dr. Christina Vulpe, and Dr. Xiaowei Feng for always welcoming my need for technical discourse from time to time.

Appreciation is also given to Prof. Mark Cassidy for allowing and providing me the financial assistance I needed to complete this work during the last three months.

Thanks are also given to Prof. Yuxia Hu for giving me the opportunity to teach young Australians as a tutor to her classes, an experience which I have immensely enjoyed.

My PhD experience was substantially enriched by all the good friends and acquaintances I have met in and outside the University throughout the course of this work, and where my heartfelt gratitude is due:

xxxiii

To Leyton Greener and Craig Whittaker for being the most wonderful friends, for their constant provision of means to enjoy the Australian life, and for the generous amount of time and friendship they have given me while I was completing this study.

To John Morton and Jaya Matthews for all the fun and the ups-and-downs shared at the Nicholson, and Raffaele Ragni and Deidre Collins for welcoming me in Leederville as I finish this work.

To my first friends in the University Beverly Oh, Joyce Ong, and Luciana Ferreira for all those years of hunting good food around Perth.

To Cathal Colreavy for the endless banter and laughter – the honour was mine for being seated next to the best geotechnics PhD student in the world (top that Cotsy!).

To the founding fathers of the Lunch Club (circa summer of 2013) Colm O’Beirne, Simon Leckie, Yusuke Suzuki, Pauline Truong, and Anthony Blake (and partners) for the great comradeship over the years, and for sharing with me this great academic adventure.

To the many great friends I have met during my time at the Centre particularly Adriano Castelo, Chao Han, Xiaojun Li, Hongliang Ma, Henning Mohr, Yining Teng, Joe Tom, Neyamat Ullah, and Dimitra Zografou.

To my Tokyo Tech friends Andra Mijares, Eden Mariquit, Paul Jason Co, Weemer Wee and Chris Pangilinan for the great fun and company during my time in Japan, and whose friendship I have constantly missed.

To my badminton friends both at the University and at Wesley College for being my ultimate source of relaxation when not behind my desk.

To Joane “Crazy” Timones for trailblazing my way down under.

To my grade school friends Leah Gorospe, Des Poticar-Biboso, Daryl Jamero, Aden Fajanilbo and Rhyan Sabio who have always kept me grounded to never lose sight of chasing a childhood dream.

Finally, I am thanking my mother for her never-ending love and support all throughout my postgraduate studies in foreign shores, when all she has always wished for was for me to be home.

***

xxxiv

I am thankful for the International Postgraduate Research Scholarship and Lloyds Register Foundation Scholarship for the financial support I have received while completing this study.

Thanks are also given to the American Society of Mechanical Engineers for partially funding my attendance to the 2014 Outreach for Engineers Specialty forum in San Francisco.

This project was made possible by an Australian Research Council grant (DP140100684), and is acknowledged.

Maraming salamat

ありがとう

Thank you

Michael

Perth, October 2016

xxxv

Authorship Declaration This thesis is presented as a series of papers that have been published, accepted for publication or submitted for publication but not yet accepted. The contributions of the candidate for the papers comprising Chapters 2 to 7 and Appendix A and the bibliographical details of the work are outlined below.

Paper 1 presented in Chapter 2 is authored by the candidate, Prof. Susan Gourvenec, Prof. David White and Prof. Mark Randolph. The candidate designed and carried out the programme of in situ and foundation tests in the centrifuge under the guidance of the co-authors. The candidate analysed and interpreted the tests results reported in this paper. The candidate prepared the first draft of the paper and all authors reviewed and contributed to the final draft.

Paper 1 bibliographical details:

Cocjin, M., Gourvenec, S., White, D., & Randolph, M. (2014). Tolerably mobile subsea foundations – observations of performance. Géotechnique 64(11), 895–909, http://dx.doi.org/10.1680/geot.14.P.098

Paper 2 presented in Chapter 3 is authored by the candidate, Prof. Susan Gourvenec, Prof. David White and Prof. Mark Randolph. The candidate designed and carried out the programme of in situ and foundation tests in the centrifuge under the guidance of the co-authors. The candidate analysed and interpreted the tests results reported in this paper. The candidate prepared the first draft of the paper and all authors reviewed and contributed to the final draft.


Cocjin, M., Gourvenec, S., White, D., & Randolph, M. (2015). Effects of drainage on the response of a sliding subsea foundation. In Proc. 3rd Int. Sym. On Frontiers in Offshore Geot. 2015, Oslo (ed V. Meyer), Vol. 2, pp. 777 – 782. Rotterdam, the Netherlands: Balkema

xxxvii

http://dx.doi.org/10.1680/geot.14.P.098

Paper 3 presented in Chapter 4 is authored by the candidate, Prof. Susan Gourvenec, Prof. David White and Prof. Mark Randolph. The candidate developed the analytical framework presented in this chapter, with the guidance of the co-authors. The coding, calibration and implementation of the framework were carried out by the candidate, with inputs from all the co-authors. The candidate prepared the first draft of the paper. All authors reviewed and contributed to the final draft.


Cocjin, M., Gourvenec, S., White, D., & Randolph, M. (2017). Theoretical framework for predicting the response of tolerably mobile subsea installations. Géotechnique, http://dx.doi.org/10.1680/jgeot.16.P.137

Paper 4 presented in Chapter 5 is authored by the candidate, Prof. David White, and Prof. Susan Gourvenec. The candidate designed and carried out the programme of in situ tests in the centrifuge under the guidance of the co-authors. The candidate analysed and interpreted the tests results reported in this paper. The candidate prepared the first draft of the paper and all authors reviewed and contributed to the final draft. The candidate also prepared and presented the work in the conference where the paper was submitted to.


Cocjin, M., White, D., & Gourvenec, S. (2014). Continuous characterisation of near-surface soil strength. In Proc. 33rd Int. Conf. on Ocean, Offshore and Arctic Eng’g, San Francisco, Vol. 3, pp. V003T10A010. American Society of Mechanical Engineers (ASME).

Paper 5 presented in Chapter 6 is authored by the candidate, Prof. David White, and Prof. Susan Gourvenec. The candidate designed and carried out the programme of in situ tests in the centrifuge under the guidance of the co-authors. The candidate analysed and interpreted the tests results reported in this paper. The candidate prepared the first draft of the paper and all authors reviewed and contributed to the final draft.

xxxviii

http://dx.doi.org/10.1680/jgeot.16.P.137


Cocjin, M., White, D., & Gourvenec, S. (2017). Shear strength changes of surficial soil under cyclic loading. Submitted to ASCE Journal of Geotechnical and Geoenvironmental Engineering on October 2016.

Paper 6 presented in Chapter 7 is authored by the candidate, Prof. Susan Gourvenec, and Prof. David White. The candidate analysed and interpreted the tests results reported in this chapter, under the guidance of the co-authors. The candidate prepared the first draft of the paper. All authors reviewed and contributed to the final draft.


Cocjin, M., Gourvenec, S., & White, D. (2017). Softening and consolidation around seabed pipelines: Centrifuge modelling. Géotechnique, http://dx.doi.org/10.1680/geot./16-P-280

Paper 7 presented in Appendix A is co-authored by the candidate with Dr. Conleth O’Loughlin and Prof. Susan Gourvenec. The candidate designed and carried out the programme of in situ and foundation tests in the centrifuge under the guidance of the second co-author. The candidate analysed and interpreted all the tests results reported in this paper, with inputs from all the co-authors. The candidate prepared the first draft of the paper. All authors reviewed and contributed to the final draft.


O’Loughlin, C., Cocjin, M., & Gourvenec, S. (2017) A new apparatus for multi-planar loading of a subsea foundation in the centrifuge. Submitted to International Journal for Physical Modelling in Geotechnics on June 2016.

Prepared by:

Michael Cocjin 30-10-16

xxxix

http://dx.doi.org/10.1680/geot./16-P-280

The candidate’s statements regarding his contribution to each of the works listed above are correct.

xl

Chapter 1. General introduction

1.1. Motivation for the research

Offshore oil and gas developments are increasingly adopting subsea architecture as illustrated in Figure 1.1. Hydrocarbons are extracted from multiple wells and transported through a network of in-field production flowlines, to a central processing facility. The processing facility can be found either offshore to a fixed platform (e.g. a jacket structure), or a floating facility (e.g. a tension leg platform or floating production storage and offloading vessel), or onshore. Infrastructure to support subsea developments includes pipeline end manifolds, pipeline end terminations (PLEM and PLET) and in-line structures, which are often supported on shallow mat foundations or ‘mudmats’.

Offshore developments are increasingly sited in areas with low strength seabeds requiring large foundations to mobilise adequate geotechnical resistance, producing from deeper reservoirs. This leads to higher thermal expansion loads, and requires more functions from the subsea infrastructure, thus increasing the weight of the structure supported by subsea mudmats. Accommodation of softer seabeds and higher loads in conjunction with traditional design methods often results in mudmats exceeding the size or weight that can be installed with standard installation vessels.

1-1

1-2 |Whole-life geotechnical response of tolerably mobile subsea infrastructure

Figure 1.1 Illustration of offshore oil and gas development options showing subsea infrastructure and tie backs to various processing facilities

Fixe

d pl

atfo

rmTe

nsio

n le

g pl

atfo

rmFl

oatin

g pr

oduc

tion

stor

age

and

offlo

adin

g (F

PSO

)

Sate

llite

fiel

d

PLEM

/PLE

T

Tieb

ack

to o

ther

sate

llite

fie

lds

Wel

l

Stee

l cat

enar

y ris

ers (

SCRs

)

Anch

orin

g sy

stem

s

Prod

uctio

n ris

erSt

eel p

ipe

tend

ons

Subs

ea d

istrib

utio

n un

it

Prod

uctio

n flo

wlin

es

To o

nsho

re in

stal

latio

n

Man

ifold

In-fi

eld

flow

line

Wel

l

General introduction | 1-3

Figure 1.2 Illustration of a pipeline-infrastructure system

The present research responds to the need to reduce subsea mudmat foundation size and weight, thus easing installation and reducing project costs. The study challenges the traditional paradigm that foundations should remain stationary and explores the potential tolerable mobility of subsea mudmats as a method of reducing required mudmat size and weight.

1.1.1. Operational context of subsea mudmats

Figure 1.2 illustrates a section of a subsea development showing mudmats supporting subsea pipeline infrastructure. In service, pipelines expand as hot oil or gas passes through during a production startup and contract during cooling due to a shutdown (Figure 1.3). During cycles of thermal expansion and contraction, the pipeline and foundations supporting pipeline infrastructure are subjected to episodic loading. Operational periods between scheduled shutdowns may last several weeks or months with shutdown periods typically lasting as short a time as possible (Rong et al. (2009), Carr et al. (2006)).

Shutdown cycles

Subsea production equipment

PLET

Start up cycles

Shutdown cycles

Start up cycles

Cyclic mudmat movement

Cyclic pipeline movement


Figure 1.3 Idealised mode of operation of a tolerably mobile subsea mudmat

1.1.2. Loading conditions on subsea mudmats

Episodic loading of a foundation from pipeline thermal expansion and contraction is transmitted to the underlying seabed resulting in generation of excess pore water pressures, which dissipate during the operational or shutdown periods when the load is constant. Dissipation of the excess pore pressure leads to reconsolidation beneath the foundation, causing a reduction in void ratio and increase in undrained shear strength.

Figure 1.4 shows the multi-directional loading and displacements that subsea mudmats can experience due to thermal expansion and contraction of a pipeline. Thermally induced axial and lateral displacements of the pipeline during operation give rise to horizontal loading (Hx, Hy) and displacement (ux, uy) of the attached foundation, submitting the supporting soil to shear stress reversal during loading cycles (Cathie et al. (2008), Bruton et al. (2008)). Installation loads due to connection misalignment or spool expansion loads acting at vertical and horizontal eccentricities to the centroid of the foundation may also induce significant moment (Mx, My) and rotation (θx, θy) (pitch and roll), as well as torsional load (T) and angular rotation (ω) on the mudmat. In contrast, the vertical load (V) is quasi static and typically small in comparison with the bearing capacity. Settlements (w) due to the weight of the structure may often not be a significant design issue so long as the settlement occurs before tie-in. However, repeated lateral loading and periods of intervening consolidation can lead to significant settlements that will potentially impact attached infrastructure.

Pipeline expansion loads imparted to the supporting mudmat foundation depend on many factors including but not limited to (1) the pipeline and transported product properties (e.g.


heat transfer properties of the pipeline and the level of temperature/pressure and flow direction of transient hydrocarbon, see Carr et al. (2006)), (2) pipeline design (e.g. buckle design strategy, see Bruton et al. (2010) and Perinet and Frazer (2006)) and (3) geotechnical considerations (e.g. axial and lateral pipe ‘friction factors’, see Cathie et al. (2005), White and Randolph (2007)).

1.1.3. Redesigning subsea mudmats

Foundations are conventionally engineered sufficiently large to resist all the applied loading with minimal displacement – and this increasingly leads to very large and heavy subsea mudmats. The basis of this research is to challenge the paradigm that a foundation should remain stationary and instead investigate the feasibility of tolerable mobility of subsea foundations, i.e. to slide across the seabed in response to the pipeline thermal expansion and contraction loads (Figure 1.3). Tolerable mobility is well suited to foundations for pipeline infrastructure as pipeline expansion loads are displacement sensitive such that displacement of the foundation relieves the load (in contrast to environmental loading where displacement of the structure does not result in a reduction of the load felt by the structure) (Figure 1.5).

Figure 1.4 Loads and displacement acting on a mudmat foundationsupporting a pipeline

Vertical load, V (self-weight)

Roll

Axial pipe movement

z

x

yPitch

Lateral pipe buckling ux, Hx

θxx, Mxx

uy, Hy

θyy, Myyω, T

Settlement, w


Figure 1.5 Environmental versus thermally-induced pipeline expansion loading

Designing for tolerable mobility of a subsea mudmat supporting a pipeline would result in the reduction of the size and therefore weight of the mudmat (Randolph et al. (2011); Cathie et al. (2008)), without the need to provide the foundation with, for example, corner pin piles (e.g. Gaudin et al. (2012), Dimmock et al. (2013)) and alleviates the need for internal shear keys (e.g. Mana et al. (2012), Feng et al. (2014a)). As a result, tolerably mobile foundations offer the opportunity of smaller and lighter foundations that are easier to fabricate and install in-line with the pipeline, using existing pipeline laying vessels (Figure

1.6).

The design challenge for tolerably mobile subsea mudmats is to engineer a foundation that can undergo controlled and limited sliding across the seabed to relieve some of the applied operational loads, subject to other criteria such as ensuring that the associated settlements during sliding or rotations do not cause unacceptable secondary loads that may overstress other components of the attached pipeline system (Fisher and Cathie (2008)).

Tolerable mobility of subsea mudmats is a novel concept but is not entirely radical as it is a natural progression of the now widely-accepted practice of allowing seabed pipelines to move in a controlled manner to accommodate operational loading (Bruton et al. (2010), White and Cathie (2011)). Indeed, the first industry application of a sliding mudmat, for a pipeline end termination (PLET), was recently included as part of Chevron’s Wheatstone project off the north-west of Australia (Deeks et al. (2014)).

Foundation displacement

Exte

rnal

load

s tra

nsm

itted

to th

e fo

unda

tion

Thermal expansion load

Environmental load (e.g. hydrodynamics)


Figure 1.6 Photos of a deep-water construction vessel with a J-lay tower (inset: installation of pipeline and in-line mudmat) (Wolbers et al. (2003)).

Mudmat

Pipeline


1.2. Research aims

The overarching goal of this research project was to advance the understanding of the geotechnical behaviour of tolerably mobile subsea mudmats, allowing reduction of foundation size and weight, facilitating installation and reducing costs associated with specialised heavy lift installation vessels. This goal was achieved through three main aims:

Aim 1: Observe and quantify the whole-life response of a sliding mudmat foundation through geotechnical centrifuge modelling

Aim 2: Quantify the volumetric strains and soil strength changes due to repeated cycles of remoulding and reconsolidation

Aim 3: Develop a theoretical model to predict the cycle by cycle whole-life response of a sliding mudmat foundation capturing the effects of repeated shearing, partial remoulding and reconsolidation

The concepts of remoulding and reconsolidation governing the response of tolerably mobile subsea mudmats were also applied to the interpretation of the lateral break out and axial response of a subsea pipeline as part of this research project.

Figure 1.7 illustrates these study aims alongside a schematic of the boundary value problems addressed in this dissertation. The following subsections detail how these aims were achieved.

1.2.1. Observe and quantify the whole-life response of a sliding mudmat foundation through geotechnical centrifuge modelling

The first aim of this research project was to provide realistic observations of the life cycle performance of a subsea mudmat foundation and pipeline, given the lack of existing relevant experimental work (Cathie et al. (2008)). This aim was achieved through geotechnical centrifuge modelling of a mudmat foundation submitted to episodic large amplitude lateral displacements associated with thermal expansion and contraction of an attached pipeline, at prototype stress levels and durations.


Figure 1.7 Schematic showing research aims and boundary value problems addressed

Seabed

Sliding cycles, N

Shea

r str

engt

h, s

u Reconsolidation effects

Remoulding effects

Aim 2

Aim 3

Quantification of the changes in soil strength and their influence on the performance of sliding

foundation and pipeline

Development of an analytical framework for predicting the whole life response of a sliding


Pipe laying

Lateral breakout

Changing soil strength around a pipeline

Changing soil strength beneath a cyclically sliding foundation

Cycles of foundation sliding, N

Realistic observation of the whole life response of a sliding


Settlement

Horizontal translation

Pitch/rollAim 1

zx y

Soil element

Submerged weight

Brea

kout

res

istan

ce

Consolidated failure envelope

Unconsolidated failure envelope

Effective vertical stress, s′v

Void

ratio

, e

Undrained remoulding cycles

Undrained remouldingcycles with intervening

reconsolidation

Drained remoulding

NCL

CSL

Changing geometry of the soil surface around

a pipeline


Geotechnical centrifuge modelling is a well-established method of reliably replicating soil response in small scale geotechnical models (Schofield (1980), Taylor (1995), Muir Wood (2004)). With this technique, self-weight stress and gravity dependent processes are correctly reproduced and observations from small-scale models can be related to the full-scale prototype situation using well-established scaling laws (Garnier et al. (2007)). In the centrifuge, a small-scale model is subjected to an acceleration that is n times the gravity of the Earth. The ratio n is the scaling factor required to convert dimensions in a centrifuge model to the dimensions of the corresponding field-scale situation.

Processes of extended duration such as consolidation can be modelled in a practical timeframe in the centrifuge. Centrifugal acceleration of a saturated soil sample results in hydraulic gradients n times steeper and drainage paths n times shorter than at prototype scale, resulting in consolidation times being reduced by a factor n2. This allows for in situ soil strength profiles from self-weight consolidation to be replicated and long-term events such as the whole-life cyclic loading of a subsea field to be observed within a practical test period.

A suite of geotechnical centrifuge tests was carried out to model a tolerably mobile subsea mudmat. The test program was designed to investigate the effects of operational vertical load (self-weight), and duration of reconsolidation in between loading cycles on the long-term performance of the mudmat foundation. The tests examined key operational performance indicators including the sliding resistance of the foundation, both during the breakout movement and the sliding cycles, and the accumulation of cycle by cycle foundation displacements (settlement and rotation) over the simulated whole-life of the field.

A rough interface for the underside of the foundation was modelled to effect the greatest pore pressure increase and therefore gain in sliding resistance and foundation settlements in order to better illustrate the governing mechanisms. A smoother interface would be expected to lead to reduced shear stresses and shear induced excess pore pressure in the underlying soil, effecting less gain in resistance and settlement.

The simulation of the loading conditions on a tolerably mobile mudmat foundation was achieved through a new loading apparatus, designed and built in-house, that enables large-amplitude cyclic sliding under constant vertical load and allows movement in six degrees of freedom. Using this new loading apparatus, accurate observations of the model foundation


behaviour, in particular the changing modes of movements and evolution of sliding resistance of the mudmat foundation, could be identified. The loading arm applied vertical and horizontal load with minimal moment. It is acknowledged that moment can be significant in some scenarios for subsea foundations but further investigation of the effect of moment was beyond the scope of this research project.

1.2.2. Quantify the volumetric strains and soil strength changes due to repeated cycles of remoulding and reconsolidation

The second aim of this research project was to quantify the strength changes in the soil undergoing cycles of remoulding and reconsolidation. Recent studies have shown that the recovery of soil strength through reconsolidation can eclipse the reduction in strength due to remoulding if consolidation is permitted between loading cycles (White and Hodder (2010), Hodder et al. (2013), Gourvenec et al. (2014), Yan et al. (2014)).

To achieve the second aim, a series of cyclic penetrometer tests were carried out in the centrifuge samples, with the tests focusing on assessing the strength of near-surface soil that interacts with the subsea infrastructure. In addition to a conventional full-flow T-bar penetrometer, a novel ‘pile’ penetrometer was used. The pile penetrometer is a vertically oriented cylindrical section that is translated laterally through the soil sample (Sahdi et al. (2015)). The penetrometer programme included tests that mirrored the loading regime prescribed in the mudmat foundation tests, i.e. modelling remoulding with intervening periods of consolidation, enabling a direct comparison of the soil softening and hardening between the independent observations.

The change in soil strength within the foundation footprint after cycles of sliding and reconsolidation due to start-up and shutdown operations was also assessed using the shallow penetrometers. The purpose of these tests was to directly quantify the final distribution of the undrained shear strength of the soil in comparison with the in situ profile, after the soil has experienced cycles of excess pore water pressure generation and dissipation, in response to the large amplitude lateral displacements of the model foundation.

A series of dissipation tests were carried out to determine the consolidation characteristics of the sample.


1.2.3. Develop a theoretical model to predict the cycle by cycle whole-life response of a sliding mudmat foundation capturing the effects of repeated shearing, partial remoulding and reconsolidation

The third aim of this research project was to develop a predictive framework for the whole-life response of tolerably mobile subsea mudmats on soft seabeds. This was achieved by developing a theoretical model based on critical state soil mechanics that is appropriate for normally consolidated or lightly over-consolidated soil. The model relates the macro-behaviour of the foundation to the change in soil strength at the elemental level. The model enables prediction of the changes in sliding resistance and settlement throughout the life cycle of a tolerably mobile subsea mudmat. The model is programmable in a spreadsheet or simple calculation tool enabling easy adoption.

1.3. Dissertation outline

The body of this dissertation is presented as a collection of published papers or submitted for publication with each chapter representing a single paper, presenting a specific topic that contributes to the achievement of the aims of this research project, as set out in Section 1.2.

Each chapter begins with a prologue to provide necessary context. The body of each chapter is formed from the published or submitted paper and as such includes an abstract, introduction and concluding remarks specific to the topic. A conclusions chapter is presented at the end of the dissertation to encapsulate the main findings and contributions of the dissertation, including potential research themes for future work.

Below is an outline of each chapter included in this dissertation.

Chapter 2 presents results of three tolerably mobile mudmat centrifuge tests in which the mudmat was subjected to undrained large amplitude lateral displacement with intervening consolidation. The results are the first to report a whole-life observation of the response of a subsea mudmat spanning up to 60 years of simulated field operation. Essential aspects of foundation design and operational conditions that affect the long-term performance of a tolerably mobile subsea mudmat are identified in this chapter. Chapter 2 contributes to achieving Aim 1 of the research project. This chapter also briefly reports on the results of the dissipation tests carried out to provide a proper assessment of the consolidation behaviour of soft normally consolidated clay. A procedure for estimating the degree of consolidation in the soil beneath a foundation is presented, contributing to Aim 2 of the


research project. Details of the loading apparatus developed to actuate the large amplitude lateral displacements at constant operational vertical load with multi-degree of freedom movement are presented in Appendix A at the end of the dissertation.

Chapter 3 compares the response of a tolerably mobile subsea mudmat to undrained and drained sliding, assessing the effects of drainage on the performance of the sliding foundation. A comparison of the mobilised resistance of a monotonically sliding mudmat foundation with undrained (fast) and drained (slow) loading rates is presented. The contribution to the sliding resistance of axial friction between the mudmat foundation and the sheared soil, and the berm formation ahead of the sliding foundation is quantified in this chapter. This chapter further contributes to the understanding of sliding foundation behaviour, contributing to Aim 1.

Chapter 4 presents a theoretical model to predict soil-structure interaction during episodes of horizontal surface shearing and reconsolidation. The model is based on critical state soil mechanics, and provides an iterative procedure to calculate the cycle by cycle changes in undrained shear strength, void ratio and corresponding mudmat settlement as a function of critical state soil parameters, the operative infrastructure weight, and the level of reconsolidation between cycles of shearing. The model is validated against the centrifuge test results presented in Chapter 2. This chapter achieves Aim 3.

Chapter 5 introduces the pile penetrometer as a tool to assess near-surface seabed shear strength and presents an evaluation of the appropriate lateral bearing capacity factors for the interpretation. The chapter outlines a simple process for deriving the undrained shear strength through established pile foundation analysis. This chapter contributes to achieving Aim 2 of the research project.

Chapter 6 presents the results of cyclic penetrometer tests carried out to investigate the softening and hardening of near-surface soil strength as a result of remoulding and reconsolidation. This chapter quantifies the degradation of soil strength due to continuous soil remoulding, and the gain in soil strength due to reconsolidation occurring between cycles of soil remoulding. The spatial extent and magnitude of soil strength recovery due to cycles of shearing and reconsolidation experienced by the soil within and around the footprint of the sliding mudmat foundation (reported in Chapter 2) are presented. This chapter contributes to Aim 2 of the research project.


Chapter 7 presents the results of a suite of geotechnical centrifuge tests on a section of model pipeline. This chapter demonstrates the influence of pipe installation conditions (causing remoulding), pipe weight, and post-lay consolidation on the lateral breakout capacity and axial response of submarine pipelines. Recommendations for the accurate use of existing analytical and numerical solutions to better predict the pipeline breakout capacity are given in this chapter. This chapter draws on the same concepts of remoulding and reconsolidation that govern the response of tolerably mobile subsea mudmats.

Chapter 8 encapsulates the main findings derived from this study. Research themes that could potentially be pursued following the present dissertation are also outlined.

Appendix A details the new loading apparatus designed and fabricated in-house for the centrifuge tests of the tolerably mobile subsea mudmats. The apparatus can model large-amplitude cyclic loading of a foundation with unconstrained movement in six degrees of freedom and is equipped with monitoring devices to record loads and displacements in the vertical and horizontal planes and rotations about both orthogonal axes. The advantages and technical capacity of the apparatus are described, and a validation of the system performance is presented.

Appendix B summarises the derived undrained shear strength profiles presented in the dissertation.

Chapter 2. Whole-life response observations

Prologue

Chapter 2, which was published in Géotechnique under the title “Tolerably mobile subsea foundations − observations of performance” in 2014 (Cocjin et al. (2014a)), serves as the backbone of this dissertation.

The chapter presents a programme of geotechnical centrifuge tests to investigate tolerable mobility of subsea mudmats. It sets out the details of the model mudmat foundation tests and presents results and interpretation from the observations on the whole-life performance of a model mudmat foundation submitted to typical field loading conditions encountered by an in-field pipeline. The results in Chapter 2 also formed the basis of developing the theoretical framework presented in Chapter 4.

Chapter 2 also describes the different in situ tests employed to characterise the normally consolidated soil sample, results of which were carried through in the interpretation presented in subsequent chapters of the dissertation. These include the dissipation tests, from which a consolidation model for the soil was derived, and moisture content core samples from which relevant critical state parameters were inferred. Results of penetrometer tests using a standard T-bar are also reported in this chapter, establishing the in situ undrained shear strength of the soil, a parameter critical in the correct interpretation of the foundation behaviour and the overall soil response. Results of these in situ tests became the basis for calibrating the theoretical model presented in Chapter 4, and further substantiated the discussion on near-surface soil strength changes in Chapter 6.

The loading apparatus employed in the foundation tests described in this chapter is described in detail in Appendix A.

2-15

2-16 | Whole-life geotechnical response of tolerably mobile subsea infrastructure

Abstract

Increasing demands for oil and gas exploration in deep water with soft seabed conditions are resulting in the size and weight of subsea shallow foundations stretching the capabilities of installation technologies. One innovation to reduce foundation footprints involves designing foundations to move in a tolerable manner to absorb applied loads rather than being engineered to resist these loads and remain stationary. Critical design considerations are the evolution of foundation capacity and the mode of foundation displacement. The foundation should be designed to slide with acceptable settlement and rotation to prevent overstressing the joints with connected pipelines. This chapter presents observations from centrifuge model tests of a mat foundation designed to slide under applied loading. The foundation is subjected to a simulated lifetime of operation, with many cycles of sliding and intervening periods of consolidation. The results provide insights to assist design, including a remarkable rise in the lateral foundation resistance over the sliding events, through repeated episodes of shearing and reconsolidation, and quantification of the accumulated settlements and rotations. The foundation is shown to translate with minimal rotation. The settlement between sliding events is more significant. This is due to the tendency for soft clay to contract on shearing, as excess pore pressures generated during sliding subsequently dissipate. The sliding-induced consolidation settlements control the tolerability of the performance of the mobile foundation.

2.1. Background

Offshore oil and gas developments are increasingly adopting subsea architecture with multiple wells connected by a network of in-field flowlines and associated pipeline infrastructure such as manifolds, end terminations and in-line structures. Pipeline infrastructure is typically supported on shallow foundations or ‘mudmats’ that range from 3 m to over 30 m in edge length (Figure 2.1).

Whole-life response observations | 2-17

Figure 2.1 Typical layout of pipeline connections with associated infrastructure

Subsea pipelines experience periodic cycles of thermal expansion and contraction due to start up and shutdown operations over the life cycle of a field. The thermal expansion of a pipeline causes horizontal loads, moments and in some cases torsion to be transferred to the mudmats supporting the pipeline infrastructure.

Conventionally, mudmats are designed to resist these operational loads and remain stationary. The size of mudmats is increasing to suit heavier subsea infrastructure and to spread load across sufficient area on very soft soils found in deeper water. Mudmats are ideally installed by the same vessel that lays the pipeline, which imposes limitations on the size and weight of mudmats that can be handled, while a second vessel on site for installation of the mudmats may be financially prohibitive. This impasse provides the motivation to optimise design solutions.

Various approaches have been proposed for reducing subsea mudmat size and weight, including optimisation of mudmat configuration through the provision of corner pin piles and internal shear keys (Gaudin et al. (2012), Dimmock et al. (2013), Mana et al. (2012), Feng et al. (2014a)), reducing conservatism in design methodology (Feng et al. (2014b)), and reliance on enhanced shear strength due to consolidation between set down and operation (Gourvenec et al. (2014)).

The study presented in this chapter addresses the potential of tolerable foundation mobility to reduce foundation footprints – i.e. foundations that are designed to move within acceptable serviceability limits to relieve some of the applied loads, rather than being


engineered sufficiently large to resist all loading. Foundation mobility is a radical, but a logical progression of the now widely accepted practice of allowing deep water submarine pipelines to move axially and buckle laterally in response to thermal expansion as an alternative to providing expensive restraints against movement. A contrast exists between onshore and offshore practice in terms of tolerable mobility. In typical onshore applications, the ultimate limit load is reached at displacements much larger than those considered serviceably tolerable. In the subsea mudmat case, tolerable displacements exceed by far the displacement needed to mobilise the limiting resistance (although the tolerable rotations may still be small and comparable to onshore cases).

The design challenge is to engineer a foundation that can undergo controlled and limited sliding across the seabed to relieve some of the applied operational (pipeline) loads, while not damaging pipeline connection points through unwanted rotation or excessive settlement. The notion of foundation mobility has been proposed in the past (Cathie et al. (2008)) and methods to address some aspects of geotechnical design have been suggested (Bretelle and Wallerand (2013), Deeks et al. (2014)). However, no data on the performance of mobile foundations is available in the public domain on which to base or assess the proposed methods.

This chapter presents results from centrifuge model tests of a mudmat foundation on soft clay. The foundation was set down under an operative vertical load and subjected to periodic undrained translation, unconstrained against rotation about either the long or short axis, with intervening periods of consolidation. Conditions representative of the field were modelled. The translation of the foundation with intervening periods of rest represented the response to thermal expansion and contraction of a connected pipeline during cycles of start-up and shutdown operations.

Changes in sliding resistance, settlements and rotation of the foundation during sliding cycles and intervening periods of rests are presented. Observed changes in topography and strength of underlying soil exposed to periodic remoulding due to foundation sliding and intervening periods of reconsolidation are also presented.


Figure 2.2 Model foundation: (a) long side, (b) short side, and (c) positive sense for loads and displacements (after Butterfield et al. (1997)) (units: millimetres in model scale)

2.2. Experimental program

2.2.1. Geotechnical centrifuge facility and equipment

The tests were conducted at the University of Western Australia – Centre for Offshore Foundation Systems (UWA-COFS) fixed beam centrifuge which has a nominal radius of 1.8 m (Randolph et al. (1991)). The tests reported in this chapter were carried out at an acceleration level of 100g. The soil sample was set-up in a rectangular strong box with internal dimensions 390 mm by 650 mm by 300 mm high. A loading actuator with vertical and horizontal axes of motion (De Catania et al. (2010)) was employed. Data acquisition used a high-speed Ethernet-based system with data streaming in real-time to a remote desktop (Gaudin et al. (2009)).

2.2.2. Mudmat foundation model

A rectangular mudmat foundation with breadth to length aspect ratio B/L = 0.5 was used in this study. The model mudmat foundation, as illustrated in Figure 2.2, designed to act as a rigid slab, was fabricated with underside base plate dimensions B = 50 mm and L = 100 mm (5 m by 10 m prototype scale), and height 5 mm (0.5 m prototype scale). An edge ‘ski’ was inclined at 30° giving plan dimensions of 67.3 mm by 117.3 mm (6.7 m by 11.7 m

25.0

30°30°

Roller

Rotation about the long axis

(b)

5.0

30°30°50.050.0

10.0

20.0

25.0 (DIA)

Hinge

Rotation about the short axisLaser target

Base plate

Loading arm

(a)

Ski Ski

SkiSki

Loading direction

w

u

V

H

θ

Reference position

Current position

(c)

25.0

RP

RP

RP


prototype scale) at the top surface (Figure 2.2). The purpose of the ‘ski’ is to reduce foundation tipping (overturning) and encourage sliding.

The rectangular mat was fabricated from acetal (polyoxymethylene or POM) with density of 1,410 kg/m3. The low density allows the self-weight bearing pressure of the model foundation to match load levels of mudmats employed in the field (which in practice are made of heavier material but are not solid in cross section). The Young’s modulus and Poisson ratio of acetal are Eacetal = 3.1 GPa, and νacetal = 0.39, respectively, sufficiently stiff to be considered as rigid relative to the considerably less stiff soil.

Fine silica sand was glued to the base plate to provide a rough foundation-soil interface while faces of the edge ‘ski’ had a smooth finish. A rough condition represents an extreme interface condition, with a smoother interface leading to reduced shear stresses and shear-induced excess pore pressure in the underlying soil. However, the same trends and principles of behaviour described here would still be applicable. Many types of seabed material would lead to scouring, and gradual roughening, of any coating applied to the underside of the mudmat.

The midpoint of the underside base plate was taken as the reference point (RP) where the loads and displacements are defined. The positive sign convention for the loads and displacements is illustrated in Figure 2.2(c), following Butterfield et al. (1997).

2.2.3. Loading arm

The model mudmat foundation was attached to a specially designed loading arm that enabled free rotation of the foundation about two axes and control of vertical load, as shown in Figure 2.3. The arm was connected to the foundation through a hinged joint 10 mm above the top of the base plate (Figure 2.2(a)). The hinge enables rotation about the short axis of the foundation, while a roller bearing within the loading arm (Figure 2.3) enables rotation about the long axis (Figure 2.2(b)).

A vertically-oriented load cell was connected directly above the RP through a padeye to measure the operative vertical foundation-seabed load (relative to the equilibrium state under the self-weight of the foundation and loading arm), while an S-shaped axial load cell was positioned in-line with the loading arm between the roller bearing and the hinge at the end of the loading arm to measure the applied horizontal load (Figure 2.3).


Figure 2.3 Test set-up on loading arm

2.2.4. Instrumentation

Vertical displacement at the four corners of the acetal mudmat foundation were measured by four Keyence® laser displacement sensors (Model LB-70-11) mounted on a steel plate fixed to the actuator. The sensors track the circular disk targets installed at each corner of the foundation (Figure 2.2, and Figure 2.3), giving vertical displacements at these locations. The average of the four laser measurements was taken to provide the vertical displacement of the mudmat foundation. Rotation about the reference point (RP – at centre of base of mudmat) was determined from the difference between pairs of vertical laser readings while the horizontal travel of the model foundation was measured using the horizontal displacement transducer of the actuator.

2.2.5. Soil sample

Kaolin slurry with water content twice the liquid limit (120 %) was normally consolidated in the centrifuge at 100g for 3.5 days. Geotechnical properties of kaolin clay as determined

Loading arm

Model foundation

HingeBase plate

Actuator attachment

Horizontal load cell

Vertical load cell

Roller

Laser targets Laser targets

Hinge


from laboratory element tests are given in Table 2.1 (Stewart (1992), Acosta-Martinez and Gourvenec (2006)).

Two-way drainage for consolidation was provided by means of a 50 mm thick silica sand layer at the bottom of the strongbox. After consolidation was essentially complete, a thin layer of soil (~ 0 – 5 mm or 0 – 0.5 m prototype scale, depending on the location in the box) was scraped from the top of the sample to provide a smooth and level surface. After re-equilibration and swelling, the final height of the soil sample was 130 mm, equivalent to 13 m depth at 100g.

Table 2.1 Characteristics of kaolin clay (after Stewart (1992), and Acosta-Martinez and Gourvenec (2006))

Property Value

Liquid Limit, LL 61%

Plastic Limit, PL 27%

Soil particle density, Gs 2.6

Plasticity Index, Ip 34

Critical state friction constant, M 0.92

Void ratio at p' = 1 kPa on CSL, ecs 2.14

Slope of normal consolidation line, l 0.205

Slope of swelling line, κ 0.044

Poisson's ratio, ν 0.3

Angle of internal friction, ϕ' = sin-1(3M/6+M) 23°

2.2.6. Site characterisation

Intact and remoulded shear strength profiles and consolidation characteristics of the soil sample were determined using miniature in situ characterisation tools. The in situ effective vertical stress profile was determined from the profile of saturated unit weight which was obtained from moisture content measurements following the testing programme.

2.2.6.1. Undrained shear strength characteristics

T-bar tests (Stewart and Randolph (1991), Stewart and Randolph (1994)) were conducted on the soil sample to determine the undrained shear strength, su. A standard miniature T-bar with a projected penetrating area of 100 mm2 was used. The tests were carried out at a penetration rate of 1 mm/s to ensure undrained conditions (Randolph and Hope (2004)).


Figure 2.4(a) plots the T-bar resistance, qT-bar with depth, z where su = qT-bar/NT-bar was interpreted assuming a constant T-bar factor of 10.5 (Stewart and Randolph (1994)). The in situ, intact shear strength of the soil was taken from the first penetration resistance (marked by a thicker line in Figure 2.4(a)), and was approximated to vary linearly with depth as:

kzss umu += 2.1

where sum = 0.53 kPa is the mudline shear strength and k = 0.86 kPa/m is the gradient of strength with depth. The T-bar extraction was halted at a depth of 40 mm below the mudline and ten cycles of penetration and extraction were carried out over the model depth range of 40 – 60 mm before the full extraction of the T-bar (Figure 2.4(b)). The cyclic sequence to achieve fully remoulded conditions is used to define an accurate zero reference for the resistance data, and to measure the remoulded strength of the soil sample. The strength variation factor, ∆su = su,cyc/su indicates the change in strength during T-bar cycles, where su,cyc is the strength measured during cycles of penetration and extraction, and is plotted against cycle number in Figure 2.4(b). The reduction in strength during cyclic penetration and extraction observed in Figure 2.4(b) is conventionally described as a remoulding process (e.g. Randolph (2004)), and is predominantly due to the generation of positive excess pore pressure, but may also reflect a change in the mobilised strength ratio or a degradation of the soil structure (as discussed by Randolph et al. (2007), White and Hodder (2010), Hodder et al. (2013)). After a few passes, a steady and reduced T-bar resistance is mobilised, indicative of the remoulded strength of the soil. The final value of ∆su ~ 0.4 indicates a sensitivity, St ~ 2.4 where St is defined as the ratio of the intact to remoulded strength as measured via cyclic penetrometer tests (Randolph (2004), White and Hodder (2010)).


Figure 2.4 T-bar penetrometer results: (a) T-bar resistance, qT-bar for T-bar 1 test and effective vertical stress, σ'vo profiles with prototype depth, z; (b) strength variation factor, ∆su = su,cyc/su against cycle number for T-bar 1 test, showing load-displacement path of cyclic loading (inset); (c) T-bar resistance, qT-bar profile with prototype depth, z for T-bar 2 test; and (d) strength variation factor, ∆su against cycle number for T-bar 2 test

A second T-bar test involved cycles of penetration and full extraction with a rest period of 780 sec (representing 0.25 years in prototype scale), with the T-bar held above the mudline for the periods of rest. A total of 60 cycles were conducted. The measured profiles of qT-bar with depth, z are presented in Figure 2.4(c). This test was designed to investigate the regain in soil strength during 0.25 years of reconsolidation following undrained failure (with an associated generation of excess pore pressure). The strength variation factor, ∆su inferred at penetration depth of 4.0 m is presented in Figure 2.4(d) and indicates an increase in


undrained shear strength with increasing loading cycles, to a final strength of ~ 3.0 times the in situ value. This ratio is similar to the relative penetration resistance during the first penetration of T-bar tests performed at drained and undrained rates in kaolin (House et al. (2001)).

This contrasting behaviour between the two T-bar tests indicates that the gain in strength from reconsolidation can eclipse the loss of strength caused by remoulding. This behaviour is consistent with a critical state framework, in which undrained failure of contractile material around the T-bar generates positive pore pressure, which dissipates during the reconsolidation period causing a reduction in moisture content and a gain in undrained strength (see White and Hodder (2010)). The reduction in moisture content is evident in the local settlement of the soil surface, which causes the touchdown point when T-bar resistance is first recorded to become deeper with each cycle (Figure 2.4(c)). The mechanism of soil strength regain due to remoulding and reconsolidation is shown later to be relevant to the sliding foundation response.

2.2.6.2. Moisture content determination

Figure 2.4(a) shows the profile of in situ effective vertical stress, σ′v0 with depth as derived from moisture content data obtained from core soil samples taken at different locations in the box. The average effective unit weight over the depth of the sample (~ 2B) is γ′ = 5.7 kN/m3 leading to a ratio of T-bar undrained shear strength to in situ effective vertical stress of su/σ′vo ~ 0.15 over the depth investigated.

2.2.6.3. Consolidation characteristics

The operative coefficient of consolidation that governs the consolidation processes during the mudmat foundation tests was determined as follows:

2.2.6.3.1. Determination of horizontal coefficient of consolidation, ch

The horizontal coefficient of consolidation, ch of the soil sample was determined through a series of in-flight miniature piezocone penetrometer (CPTu) dissipation tests, where the pore water flow is primarily radial, but also different zones of soil experience plastic or unloading effective stress paths, at model depths below the mudline, zCPTu = 40, 70 and 90 mm (correspondingly zCPTu/B = 0.8, 1.4 and 1.8). Results from these tests are presented in


Figure 2.5(a) where change in excess pore pressure as a ratio of the initial excess pore pressure, ∆ue/∆ue,i is plotted against a time factor, T* given by:

5.02*

r

h

IRtc

T =

2.2

with R being the piezocone radius = 5 mm. Dissipation curves presented in Figure 2.5(a) correspond to a rigidity index, Ir of 88 following the method proposed by Mayne (2001), and after a correction made for the initial value of excess pore pressure as suggested by Sully et al. (1999).

Figure 2.5 Piezocone tests results showing: (a) dissipation of excess pore pressure at the level of filter u2 expressed as a ratio of excess pore pressure over initial value, ∆ue/∆ue,i plotted against time factor, T* = cht/R2Ir

0.5, and (b) coefficient of consolidation against effective vertical stress, σ'v

Values of the horizontal coefficient of consolidation, ch were extrapolated from these dissipation curves using a correlation with a theoretical solution based on T50, the time for dissipation of 50 % of the initial excess pore pressure (Teh and Houlsby (1991)). Values range from 7.7 < ch (m2/yr) < 13.0, and are plotted in Figure 2.5(b) against effective vertical stress, σ′v as given in Figure 2.4(a) corresponding to the level of zCPTu. The plot also includes recent results obtained by Chow et al. (2014) and Colreavy’s unpublished data (2013) from in-flight piezocone tests on UWA kaolin clay with ch values at higher levels of σ′v.


2.2.6.3.2. Determination of vertical coefficient of consolidation, cv

A variation of the vertical coefficient of consolidation, cv with effective vertical stress, σ′v for σ′v < 500 kPa is obtained from one-dimensional Rowe cell consolidation tests on UWA kaolin clay reported in House et al. (2001), and can be expressed as:

( ) 47.0'16.03.0 vvc σ⋅+= 2.3

with cv and σ′v being in m2/yr and kPa, respectively. From this expression, the average ratio of the horizontal to vertical coefficient of consolidation, ch/cv for the range of stress level relevant to the tests (i.e. σ′v < 120 kPa) was obtained as 4.4. This is consistent with, although slightly greater than, the ratio of 3.5 for normally consolidated kaolin argued theoretically by Mahmoodzadeh et al. (2014).

2.2.6.3.3. Determination of representative coefficient of consolidation for foundation response, cref

To provide additional information on the rate of consolidation beneath the model mudmat foundation, a series of load-controlled dissipation tests using a ‘piezofoundation’ was carried out. These tests are akin to a plate loading test, but with pore pressure measurement. A rigid circular foundation (diameter = 40 mm model scale) instrumented with a pore pressure sensor at the centre of its base plate, and a load cell to measure an operative vertical bearing pressure, qop (which is held constant during a dissipation phase) was used. During the tests, the piezofoundation was placed on the soil surface and loaded to the desired qop of 10.5 kPa (PF 1) and 20.5 kPa (PF 2).

Results from these tests are presented in Figure 2.6 showing the change in excess pore pressure as a ratio of the initial excess pore pressure, ∆ue/∆ue,i against a time factor, T given by:

2D

tcT ref=

2.4

where t is dissipation time, and D is foundation diameter. cref is an operative coefficient of consolidation representative of the rate of consolidation underneath a foundation carrying a steady vertical bearing pressure of qop with cref being cv < cref < ch.


Values of cref were determined by fitting the measured dissipation curves to solutions based on elastic isotropic finite-element analysis of a rough, circular foundation (Gourvenec and Randolph (2010)) and on elasto-plastic finite-element analysis of a rectangular foundation with B/L = 0.5 (Feng & Gourvenec (unpublished data, 2014)). A value of cref = 2.7·cv was obtained with cv given by Equation 2.3 assuming σ′v = qop. Values of cref projected for the range of bearing pressures relevant to the study are shown in Figure 2.5(b).

Figure 2.6 Normalised excess pore pressure under a ‘piezofoundation’, ∆ue/∆ue,i plotted against time factor, T = creft/D2

The excess pore pressure time histories observed with the piezofoundation and captured by the finite-element analysis (Gourvenec and Randolph (2010); Feng & Gourvenec (unpublished data, 2014)) exhibit the characteristic Mandel-Cryer effect (Mandel (1950); Cryer (1963)), with excess pore pressure increasing above the initial value of stress change during the early stage of consolidation. The Mandel-Cryer effect is a stress transfer effect significant in three-dimensional consolidation. It results from the more rapid dissipation of excess pore pressure in soil near the edges of the foundation than near the centre. The resulting (greater) compression of the soil at the edges leads to a temporary (initial) transfer of total stress, and hence increase in excess pore pressure, in the central part of the foundation.


2.3. Mudmat loading tests

The sliding tests with the model mudmat foundation involved three elements: (a) touchdown of the foundation, followed by consolidation under self-weight, (b) sliding events, performed at a rate to achieve an undrained soil response, and (c) periods of reconsolidation between the sliding cycles. A time history of the applied vertical load and horizontal displacement during the tests is illustrated in Figure 2.7 and is summarised in Table 2.2.

Table 2.2 Centrifuge test program

Parameters Units in prototype scale

MMUD1 MMUD2 MMUD3

Ultimate vertical bearing pressure, qu = Ncvsum kPa 6.18 6.18 6.18

Target operational vertical bearing pressure ratio, qop/qu - 0.3 0.5 0.3

Normalised horizontal displacement, u/B - 0.5 0.5 0.5

Reconsolidation period, trecon years 0.25 0.25 1.5

Total number of slides - 80 80 80

2.3.1. Mudmat installation

Touchdown of the mudmat foundation was achieved by driving the vertical axis of the loading actuator at a slow rate of 0.01 mm/sec until the required (compressive) vertical load was recorded on the load cell. The vertical axis of the actuator was locked to load-control mode after touchdown and achievement of the required vertical load in order to ensure that a constant operative vertical bearing pressure, qop was imposed on the seabed throughout the test (Figure 2.7(a)).

Values of qop, which represent the self-weight of the fully submerged foundation and the equipment that the mudmat supports, were determined as a percentage of the predicted ultimate vertical bearing capacity, qu = Ncv·sum of the model foundation, where Ncv is the bearing capacity factor relevant to the non-dimensional shear strength heterogeneity index, kB/sum, with k being the gradient of undrained shear strength with depth. An Ncv of 11.66 was used based on results of finite-element analysis of the bearing capacity of a rough based surface foundation with B/L = 0.5 (Feng et al. (2014b)). Two different values of qop were


considered, corresponding to ratios of operational to ultimate bearing capacity, qop/qu of 0.3 (MMUD1 and MMUD3) and 0.5 (MMUD2). These ratios are typical of field conditions, and are within a range that would be expected to cause a pure sliding mechanism in response to horizontal loading under undrained conditions (Green (1954), Gourvenec and Randolph (2003), Cathie et al. (2008)).

A consolidation period of 4.5 prototype years was allowed after touchdown of the mudmat (Figure 2.7(a)). This period is equivalent to a time factor of T ~ 0.4, which, based on Figure

2.6, would have been sufficient for ~ 95% of excess pore pressures directly beneath the model foundation to have dissipated, bringing the soil beneath the foundation close to a fully consolidated state before the operational loading (sliding) began.

Figure 2.7 Time histories of loading test (in prototype scale): (a) operative vertical bearing pressure, qop and ratio of operative to ultimate vertical bearing capacity, qop/qu; and (b) normalised horizontal displacement, u/B during loading cycles


2.3.2. Undrained cyclic sliding

The cycles of undrained foundation sliding commenced after the initial self-weight consolidation period. As illustrated in Figure 2.7(b), one cycle of sliding constitutes a pair of sliding movements of u = 0.5·B (2.5 m prototype scale). A single slide represents a cycle number increment of ∆N = 0.5, so the first forward and backward slides are denoted by N = 0.5 and N = 1.0 respectively. A total of N = 40 cycles was carried out during each mudmat test. Sliding was conducted at a rate of v = 1 mm/sec. This loading rate corresponds to a one-way sliding duration of tslide = 25 sec (3 days in prototype scale), equivalent to an elapsed time factor, Tslide = creftslide/B2 ~ 0.001. This duration is sufficiently short that negligible dissipation of excess pore water occurs in the soil beneath the foundation during sliding (based on dissipation curve for vertical loading of a foundation shown in Figure 2.6).

2.3.3. Reconsolidation between sliding events

A reconsolidation period, trecon = 780 sec in model scale (0.25 years in prototype scale, Trecon = creftrecon/B2 of 0.02) was prescribed after each forward slide before the subsequent backward slide during tests MMUD1 and MMUD2, while a longer intervening period of reconsolidation, trecon = 4,680 sec (1.5 years in prototype scale, Trecon = creftrecon/B2 of 0.13) was prescribed in test MMUD3. The selected durations reflect a range of periods that a pipeline may remain in operation between scheduled shutdowns and thus the foundation will remain at the forward position, represented by the 0.5·B movement from the original position (Figure 2.7). The degree of consolidation taking place during the operational period, Trecon can be closely approximated by the dissipation curve in Figure 2.6 (where trecon of 0.25 and 1.5 years results to ~ 10 % and ~ 70 % pore pressure dissipation, respectively). A pause of 8 sec in model scale (1 day in prototype scale) was included after each backward slide prior to the next forward slide (Figure 2.7(b)), representing a brief shutdown period when the pipe cools and contracts and the foundation returns to its original position. During the waiting periods, the foundation was prevented from moving horizontally, but was free to settle under the applied qop.


2.4. Results and discussion

2.4.1. Horizontal resistance

Horizontal resistance mobilised during sliding is expressed in terms of a mobilised coefficient of sliding friction, µ given by Equation 2.5:

VH

=µ

2.5

where H and V are the horizontal and vertical loads between the foundation and the underlying soil. The variation of µ with normalised horizontal footing displacement, u/B highlighting selected cycles for MMUD1, is shown in Figure 2.8(a), with the recorded horizontal load, H in Figure 2.8(b). The resistance, µ for the first movement (N = 0.5) for all three tests is shown in Figure 2.8(c). The mobilised horizontal resistance reaches a peak at the extremities of a slide but has a steady residual value over the majority of the sliding movement. The steady residual value increases with loading cycles.

The peak resistances are identified in Figure 2.8(a) by the labels A – C. Peak A reflects an increased sliding resistance due to consolidation of the underlying soil after a period of consolidation – at the start of the forward slide in the first cycle following set down and at the start of the reverse slide in each cycle. Peaks B and C are due to the interaction of the mudmat ski with the soil berms that build up at the limits of the movement.

2.4.1.1. Mobilised resistance during first slide

The residual resistance during the first slide of each test (Figure 2.8(c)), expressed as an equivalent friction coefficient, was approximately within Hres,N=0.5/V of 0.11–0.14, which is comparable to the normally consolidated strength ratio of 0.15 for the soil sample, interpreted from the T-bar and moisture content tests. It is perhaps surprising that the T-bar strength ratio su/σ′vo and Hres,N=0.5/V are so similar, given the high sliding distance and therefore shear strain beneath the foundation, but it appears that the two mechanisms generated comparable levels of excess pore pressure. On the other hand, the initial peak gave approximately double the resistance, but was extremely brittle.


Figure 2.8 Sliding resistance-displacement response: (a) mobilised coefficient of sliding friction, µ = H/V plotted against normalised horizontal footing displacement, u/B for all loading cycles during MMUD1 test; (b) mobilised horizontal loads, H plotted against normalised horizontal footing displacement, u/B during MMUD1 test; and (c) mobilised coefficient of sliding friction, µ = H/V during first slide of MMUD1, MMUD2, and MMUD3 tests

2.4.1.2. Mobilised resistance in cycles of sliding

To quantify the variation in sliding resistance with continued cycles of sliding, the steady residual value, Hres,cyc, at u/B = 0.25 is used. The horizontal resistance variation factor, ∆µ = Hres,cyc/Hres,N=0.5 and equivalent friction coefficient, µres = Hres,cyc/V are plotted against cycle number, N and time factor, Top = creftop/B2 in Figure 2.9(a-d) where top is the accumulated operational time which includes all undrained sliding, and reconsolidation events.

The trend of increasing ∆µ with N or Top = creftop/B2 indicates that the loss of strength during the shearing process (sliding) is surpassed by the regain in strength of the soil beneath the mudmat foundation during the intervening reconsolidation periods. In all tests, the residual sliding resistance rises by a factor of 3– 4 with continued cycles of shearing and reconsolidation (Figure 2.9(a–b)). The long term sliding resistance approaches a drained value, which can be estimated as tanϕ' = 0.42 where ϕ' = 23.5° is the internal angle of friction (Figure 2.9(c–d)). This represents the state at which the soil beneath the foundation


has undergone sufficient cycles of sliding, pore pressure generation and reconsolidation to reach the critical state and eliminate any tendency for contraction and further excess pore pressure generation. Depending on the duration of each cycle, this evolution may occur in a single cycle or progressively through multiple episodes of sliding and consolidation as similarly observed on pipe-soil interaction reported in White et al. (2012), Randolph et al. (2012), and Yan et al. (2014).

Figure 2.9 Horizontal resistance variation factor, ∆µ = Hres,cyc/Hres,N=0.5 plotted against: (a) cycle number, N and (b) accumulated time factor, Top = creftop/B2; and residual coefficient of sliding friction, µres = Hres,cyc/V plotted against: (c) cycle number, N and (d) accumulated time factor, Top = creftop/B

There is remarkable similarity between the cyclic hardening from the episodic T-bar (∆su from Figure 2.4(d), which is also shown on Figure 2.9(a)), and the mudmat tests. The


underlying behaviour is the same – successive cycles of undrained failure, either through remoulding (T-bar) or shearing (mudmat), followed by pore pressure dissipation under a total stress level that is approximately constant after each cycle (overburden stress in the T-bar test, and qop in the mudmat tests). In both cases, the soil begins in a normally-consolidated state and approaches the critical state for that controlling stress. A simple theoretical estimation of this rise in strength, considering a single soil element and original Cam clay, would be exp(1–κ/l) ∼ 2.2. This is slightly lower than the observed rise, probably because the high strain shearing process generates greater excess pore pressure than implied by the original Cam clay spacing ratio (e = 2.8) (White and Hodder (2010)).

The drained or critical state is reached in fewer cycles when a longer reconsolidation time is adopted. The time factor normalisation (Equation 2.4) provides closer alignment of the results from all three tests (Figure 2.9(b,d)). The drained limit of µres ∼ tanϕ' is reached within a time factor of Top ∼ 1. This is more rapid dissipation compared to purely vertical loading (for which T90 ∼ 2 in Booker and Small (1986)) which can be attributed to the smaller zone of shearing, therefore the shorter drainage length during sliding failure compared to vertical loading.

During the final stage of test MMUD3, the residual sliding resistance began to fall. This transition is attributed to a changing distribution of contact between the mudmat and the seabed, and is discussed later.

2.4.2. Foundation settlements

The cumulative foundation settlements at the RP normalised by footing breadth are presented in Figure 2.10(a–b). These values are taken at the mid-point of each sweep, u/B = 0.25, and are compared against the mobilised sliding friction, µres = Hres,cyc/V. The full RP settlement history of each test is plotted against the normalised horizontal displacement of the foundation, u/B in Figure 2.11. The incurred settlements are greater for the heavier mudmat (Figure 2.10(a), Figure 2.11(b)), as would be expected.

A more subtle observation is that the prolonged intervening reconsolidation period reduces the incurred settlements for a given number of cycles (Figure 2.11(c)). This shows that the gain in strength due to consolidation causes the undrained settlement within each sliding movement to be reduced (Figure 2.10(b)). Therefore, although the extended rest period


between cycles allows a greater level of consolidation settlement, the undrained settlements incurred during each sliding movement are reduced.

Figure 2.10 Settlement-rotation-sliding resistance responses: (a–b) Cumulative settlements normalised by footing breadth, w/B, and (c–d) cumulative rotation about the short axis, θL observed half-way of the total sliding distance (i.e. at u/B = 0.25) plotted against residual coefficient of sliding friction, µres = Hres,cyc/V

The mudmat movement and consolidation periods create a settlement bowl that slopes downwards towards the operating position, as shown in Figure 2.11. The slope forms during the early cycles due to the soil surface geometry caused by the initial ploughing action. The asymmetry is sustained by the greater consolidation settlement that accumulates at the ‘operating’ limit compared to the ‘shutdown’ limit. The inclination of the mudmat movement during sliding reaches 0.5°–0.85° by the end of the tests, which is relatively small


compared to common design tolerances. However, the cumulative settlement is approximately 10 % of the foundation breadth, which is very significant and likely to be more onerous on connection integrity than the rotation.

The foundation settlement during the reconsolidation periods (i.e. the ‘operating’ periods) of cycles 1, 10 and 40 is shown in Figure 2.12. The 0.25 years reconsolidation period is insufficient to reach the full consolidation settlement during cycle 1, with approximately 60 % additional settlement projected to be mobilised after the 1.5 years reconsolidation period. By the 10th and 40th cycles, all three cases show a stiffer response, with a reduced level of incremental consolidation settlement. The rate of settlement increases during these later cycles, reflecting a rise in cref due to the changing stiffness, with 0.25 years rest period being sufficient for the consolidation settlement to stabilise.

2.4.3. Foundation rotation

The settlements of the foundation viewed perpendicular to the sliding direction are presented in Figure 2.13 at the ‘shutdown’ and ‘operating’ positions (u/B = 0 and 0.5 respectively) for selected sliding cycles of the three tests. This portrayal of the settlement data shows the rotation of the foundation about the short axis, θL, which is plotted against µres for values at u/B = 0.25 in Figure 2.10(c–d). In general, the cumulative rotation incurred in any of the tests is very small, with maximum values of θL < 0.4° in tests MMUD1 and MMUD2 (Figure 2.10(c)), and < 1.5° in MMUD3 (Figure 2.10(d)).

Figure 2.13 shows that the leading edge of the foundation tipped down at an angle of θL ~ 0.2° as the foundation translated for the first time to a weaker patch of soil (N = 0.5). This resulted in ploughing of soil ahead of the foundation, establishing berms as evidenced in Figure 2.14.


Figure 2.11 Cumulative settlements observed during episodes of sliding and intervening rest periods normalised by footing breadth plotted against normalised horizontal displacement, u/B for tests (a) MMUD1, (b) MMUD2, and (c) MMUD3

Figure 2.12 Consolidation settlements incurred during intervening rest periods at ‘operating’ position normalised by foundation breadth, B plotted against time (prototype scale) for loading cycles N = 1, 10, and 40


Figure 2.13 Orientation of the long side of the model foundation at the ‘shutdown’ and ‘operating’ positions at selected sliding cycles during (a) MMUD1, (b) MMUD2, and (c) MMUD3 tests


The rotation θL occurs concurrently with undrained settlements during the sliding movements of the foundation. During the reconsolidation periods, minimal further rotation occurs. A subtle observation in Figure 2.13 is that the rotation incurred during early cycles of sliding is reduced during the following reconsolidation period. The trailing end of the foundation in the operating position, which can be considered to be sitting on the ‘free’ soil surface, settled at a faster rate compared to at the leading edge, which is ‘buried’ at some depth. This differential rate in consolidation along the long-axis of the foundation is possibly due to the difference in drainage path length for excess pore water dissipation at the opposite edges of the foundation. Build-up of soil berms next to the leading edge of the foundation at the operating position (Figure 2.14) would have led to locally increased length of drainage path, resulting in slower consolidation and settlement at that side. A consequence of this is the levelling of the differential settlements during the ‘operating’ period, which mitigated the accumulation of rotation.

The first few episodes of reconsolidation incurred large consolidation settlements particularly for the extended reconsolidation period (MMUD3 in Figure 2.12). As a result, soil berms also formed at the ‘free’ side of the foundation (peripheries of side C in Figure

2.13) during the early cycles of reconsolidation. The foundation is seen to override this soil berm as it translated back to its original position during shutdown after the second reconsolidation episode in MMUD3 as evidenced by a steep increase in rotation of dθL ~ 0.5° during N = 2.0 (Figure 2.13(c)).

The foundation footprint in the operating position (i.e. after the forward slide) continued to deepen with increasing settlements during the reconsolidation periods, exacerbating the cumulative rotation with ensuing sliding cycles (Figure 2.10(d), Figure 2.13(c)). As the foundation translates from the ‘shutdown’ to the ‘operating’ position, the leading edge of the foundation tips down to the deepened soil. Over time, and through repetitive cycles of reconsolidation, the soil at the ‘operating’ position strengthened and eventually the rate of sinkage lessened and the rotation stabilised.

In test MMUD3 the cumulative rotation reached a peak value of θL ~ 1.5° at the end of the 20th loading cycle, corresponding to Top = 2.5, and decreased afterwards. This achievement of peak θL triggered the decline of the sliding resistance with time during Top > 2.5 (Figure

2.9(b)). To understand the foundation behaviour during this time, foundation settlements at different increments of normalised horizontal displacement, du/B, and incurred


incremental rotation, dθL during N = 29.5 are presented in Figure 2.15(a) and Figure

2.15(b), respectively.

During the sliding movement in later cycles, the leading edge of the foundation settled at a higher rate than the opposite (trailing) edge, as shown in Figure 2.15(a) for N = 29.5. The figure confirms that at different stages of du/B, a portion of foundation base slightly lifted off from the soil footprint: at the trailing side during 0 < du/B < 0.4 (positive dθL in Figure

2.15(b)), and at the leading side during 0.4 < du/B < 0.5 when the foundation skis impacted against the berms at the terminating end of the slide (negative dθL in Figure 2.15(b)).

The partial loss of basal contact during the sliding movements in test MMUD3 for N > 20 resulted in load being concentrated on only part of the foundation underside, including on the skis. This concentration of load raises the contact stress and therefore creates new excess pore pressure. As a result, the stable sliding resistance corresponding to the drained value is no longer attained, resulting in the decline of the sliding resistance during this time (Figure

2.9).

Figure 2.14 Formation of soil berm at extremities of the foundation footprint

Sliding direction

Sliding direction

~70 - 75 mm

B = 50 mm 67.32

MMUD 2

8.66 mm

~30

MMUD 1

MMUD 3

Soil berm at ‘operating’ side


Sliding distance : 25 mm



2.5. Final remarks

The potential of a tolerably mobile mudmat foundation to support subsea pipeline infrastructure was investigated. A rectangular mat foundation provided with sloping sides, or ‘skis’, to encourage sliding, was translated laterally over the surface of soft clay relevant to many deep water seabed soils. During translation, the foundation was unconstrained against settlement or rotation in any orientation. Undrained sliding cycles replicating the dynamics associated with thermal expansion and contraction of the attached subsea pipelines were modelled at correct prototype stress levels and over typical durations. Results presented highlighted changes in sliding resistance, settlements and rotation of the foundation during sliding cycles and intervening periods of reconsolidation between loading cycles.

Sliding resistance was observed to increase with increasing cycles of sliding and reconsolidation. This increase is primarily due to the regain in soil strength achieved during periods of rest between successive pipe operations, during which time dissipation of excess pore pressure results in a reduction in the moisture content and consequential increase in the undrained shear strength of the soil in the vicinity of the foundation. Current results showed that this regain in undrained shear strength during reconsolidation surpassed the loss of strength associated with soil shearing and reduction of effective stress during undrained sliding cycles.

The regain in undrained shear strength is controlled by the operative vertical bearing pressure carried by the foundation, and the duration of the reconsolidation period between sliding cycles. Increase in foundation bearing pressure, and extended rest periods between sliding cycles resulted in a greater increase in sliding resistance over time. Long term sliding resistance approached a drained value, which can be estimated by an equivalent mobilised coefficient of sliding friction given by the internal soil friction angle at critical state.

Undrained settlements associated with sliding were found to increase with increase in foundation bearing pressure. Extended rest periods between operational cycles resulted in a decrease in undrained settlements incurred during sliding.

Foundation rotation was incurred simultaneously with mobilisation of undrained settlements, but was seen to be small compared to common design tolerances for pipeline connections.


Figure 2.15 Foundation rotation during MMUD3 test: (a) Orientation of long side of foundation, and (b) incremental rotation, θL during slide N = 29.5


Foundation sliding displaced soil towards each end of the sliding footprint creating berms. The formation of the berms significantly affected the foundation movements during sliding as a physical barrier and by increasing the drainage path length to one edge of the foundation.

Over time, extended rest periods caused a progressive sloping of the foundation footprint. A partial loss of contact between the foundation and the soil was instigated when the relative difference between the slope of the footprint at the ‘shutdown’ and ‘operating’ positions became sufficiently large. This loss of contact resulted in a decline of sliding resistance with time. The presence of the foundation skis was seen to constrain the rotation of foundation during sliding as it impacted on the soil berms that were deposited around the foundation footprint.

The reported study has identified key aspects of foundation design and operational conditions that affect the response of a sliding foundation. Significantly, the study has demonstrated that settlement between sliding events is more significant than foundation rotation, such that excess pore pressure generated during sliding and subsequent dissipation during reconsolidation controls the tolerability of performance of the mobile foundation. The results demonstrate the potential for tolerably mobile foundations to support subsea pipeline infrastructure for offshore oil and gas development.

2.6. Acknowledgements

This work forms part of the activities of the Centre for Offshore Foundation Systems (COFS), currently supported as a node of the Australian Research Council Centre of Excellence for Geotechnical Science and Engineering and as a Centre of Excellence by the Lloyd’s Register Foundation (LRF). The LRF helps to protect life and property by supporting engineering-related education, public engagement and the application of research. The work presented in this chapter is supported through ARC grant (DP140100684) and this support is gratefully acknowledged.

Chapter 3. Drainage effects

Prologue

Continuing on the general observations on the whole-life response of the sliding mudmat foundation presented in Chapter 2, Chapter 3 explores on the effects of drainage (or sliding rate) on the foundation performance.

In Chapter 2, the undrained sliding resistance is mobilised by the axial friction at the soil-foundation interface. In Chapter 3, it is demonstrated that in addition to the soil-foundation friction, the resistance offered by the soil berm ploughed ahead of the sliding foundation becomes an important component once the sliding rate allows for drainage in the soil during sliding.

The paper that forms this chapter was published in the proceedings of the 3rd International Symposium on Offshore Geotechnics, Oslo in 2015, under the title “Effects of drainage on the response of a sliding subsea foundation” (Cocjin et al. (2015)).

3-45


Abstract

This chapter investigates the effects of drainage on the performance of a sliding foundation as support to subsea pipeline infrastructure. A centrifuge test involving a sliding foundation on soft clay submitted to cycles of periodic monotonic undrained and drained sliding is presented. The results highlight the rise in sliding resistance under undrained conditions through cycles of sliding and intervening consolidation. The undrained resistance converges towards the drained value. Slow drained cycles encounter additional shearing resistance mobilised by ploughing of a drained soil berm ahead of the foundation.

3.1. Background

The potential of sliding foundations as a solution to support pipeline end terminations has recently been advocated with quantitative observations (Chapter 2, Deeks et al. (2014)) building on previous qualitative guidance (Cathie et al. (2008)).

Sliding foundations, as illustrated in Figure 3.1, are designed to move across the seabed within acceptable serviceability limits to accommodate pipeline movements associated with operational start-ups and shutdowns. They offer the potential for a reduced foundation size and less costly fabrication and installation.

Figure 3.1 Illustration of sliding foundation concept

Drainage effects | 3-47

Pipeline expansions must be resisted or absorbed by the associated infrastructure such as manifolds, end terminations (PLEMs/PLETs) and in-line structures. The rate of movement of the pipeline, and hence of the connected sliding foundation, can vary by several orders of magnitude during thermal expansions, depending on the operating conditions and the pipeline structural response. Due to this variation in the rates of loading and displacement, the governing drainage condition during the foundation movement can span from fully drained (zero build-up of excess pore pressures) to fully undrained (zero dissipation of excess pore pressures). Also, drainage and consolidation will occur during the intervals between movements. In order to predict the foundation behaviour, it is necessary to assess the variation in mobilised soil strength and geotechnical resistance brought about by the drainage during sliding and the intervening consolidation.

For a sliding foundation (or a seabed pipeline), the relative magnitude of the undrained and drained resistance depends on the tendency of the surrounding soil to generate positive or negative pore pressures when sheared. Once sliding is initiated, failing the soil at the foundation-soil interface, any excess pore pressure will begin to dissipate, and the density and therefore the undrained strength of the soil will change. The undrained strength at the interface will evolve towards a value equal to the drained resistance associated with a critical state condition, i.e. zero potential for further volume change. Depending on the duration of each cycle, this evolution may occur in a single cycle or progressively through multiple episodes of sliding and consolidation (Randolph et al. (2012), Chapter 2, Yan et al. (2014)). Soil below the large strain interface will not reach failure and hence will not reach the same critical state equilibrium void ratio as an element just beneath the foundation.

In this chapter, the variation in sliding resistance from undrained to drained conditions is demonstrated through results from a centrifuge model test of a sliding foundation. Sliding is performed at an undrained rate with intervening consolidation, and at a drained rate.

3.2. Foundation tests

3.2.1. Test set-up

The tests were conducted in the University of Western Australia fixed beam centrifuge at an acceleration level of 100g. The rectangular mudmat foundation had a rough base plate, with dimensions of B = 50 mm, L = 100 mm giving prototype dimensions of B = 5 m, L = 10 m, and height 5 mm (0.5 m prototype scale). The foundation had an edge ‘ski’ inclined


at θ = 30° up from the horizontal, giving plan dimensions of 67.3 mm by 117.3 mm (6.7 m by 11.7 m prototype scale) at the upper face.

The purpose of the ski is to encourage sliding and reduce foundation overturning. A specially-designed loading arm enables the vertical foundation-seabed load and the applied horizontal load on the model foundation to be measured independently, while leaving the foundation unconstrained against rotation in the plane of, and perpendicular to, sliding.

3.2.2. Soil sample

A normally consolidated kaolin clay sample was prepared in-flight wherein slurry with water content of 120 % was consolidated under its self-weight in the centrifuge at 100g for 3.5 days. A thin layer of soil was then scraped from the top of the sample to provide a smooth and level surface, and to set a small non-zero strength intercept at the mudline.

T-bar penetrometer tests (Stewart and Randolph (1994)) were carried out to determine profiles of in situ undrained shear strength, su,in-situ. The T-bar was penetrated at a rate of 1 mm/s which is sufficient to ensure undrained conditions in kaolin clay. The resulting in situ shear strength profile with depth, z is presented in Figure 3.2, where su,in-situ was interpreted assuming a constant T-bar factor, NT-bar = 10.5 (Stewart and Randolph (1994)). The profile is fitted by a linear relationship given by:

)(86.053.0,, kPazzkss situinsituinumsituinu +=+= −−− 3.1

Figure 3.2 Undrained shear strength profile pre- and post-test


Cycles of T-bar penetration and extraction were carried out over a depth range of 4 - 6 m (prototype scale) before full extraction to provide the remoulded shear strength. A sensitivity, St = 2.4 was obtained as the ratio between the initial and fully remoulded penetration resistance (Chapter 2).

3.2.3. Loading program

The foundation tests involved three phases: (1) consolidation after foundation installation; (2) sliding cycles at an undrained displacement rate with intervening periods of consolidation, and; (3) a final sliding cycle at a drained displacement rate.

3.2.3.1. Post-installation consolidation

A consolidation period of t = 4.5 years (prototype scale) was allowed after touchdown of the model foundation. This consolidation period corresponds to a time factor, T = creft/B2 ~ 0.38 using a coefficient of consolidation, cref = 2.1 m2/yr obtained from pore pressure dissipation data measured in a separate ‘piezofoundation’ test (Chapter 2). This period is sufficient for almost full consolidation beneath the foundation before the operational sliding began. Consolidation took place under a constant operative vertical load, Vop = 92.5 kN, which is 30 % of the theoretical unconsolidated, undrained vertical load capacity, Vun (see Section 3.5). This ratio of Vop/Vun represents typical field conditions and is in the range that leads to a pure sliding mechanism under horizontal loading in undrained conditions (Gourvenec and Randolph (2003)).

3.2.3.2. Undrained sliding with consolidation intervals

Following post-installation consolidation, the foundation was translated back and forth horizontally over a distance of u = 2.5 m (u = 0.5·B) at a displacement rate v = 1 mm/s (model scale). This rate corresponds to a one-way slide duration of ∆tun ~ 3 days (25 s in model scale), equivalent to an elapsed time factor, ∆T = cref∆tun/B2 ~ 0.001. This duration is sufficiently short that negligible dissipation of excess pore water occurs in the soil beneath the foundation (based on the dissipation curve for vertical loading of a foundation on an elastic medium from Gourvenec and Randolph (2010)).

A total of N = 40 undrained sliding cycles were carried out where a single cycle (∆N = 1) comprised a forward slide, a rest period of 780 s (0.25 years in prototype scale) in the outward, ‘operational’ position, and a reverse slide to the ‘shutdown’ position. A rest period


of 9 s (1 day prototype scale) was prescribed between cycles to represent the duration of a shutdown. Figure 3.3 presents the time history of foundation displacement (in prototype scale) for the last 2 cycles of undrained sliding and the subsequent drained cycle.

During each operational (reconsolidation) period following undrained sliding, the foundation was prevented from moving horizontally but was free to settle under the applied Vop. Pore pressure dissipation occurred beneath the foundation during this time.

Figure 3.3 Displacement sequence during final cycles of test

Figure 3.4 Mobilised soil berm at the foundation leading edge


3.2.3.3. Drained sliding

After the 40th undrained sliding cycle (after a total elapsed time of Σtun ~ 16 years (Figure

3.3)), a drained cycle was performed with the model foundation translating at a displacement rate of v = 0.01 mm/s (model scale). At this rate, a one-way slide is equivalent to an elapsed time factor, ∆T = cref∆tdr/B2 ~ 0.07 where ∆tdr ~ 290 days (2500 s in model scale). This duration would permit significant dissipation of excess pore water during sliding.

3.3. Results and discussion

Sliding capacity is comprised of base sliding resistance at the foundation-soil interface, and the shearing resistance beneath the soil berm being ploughed ahead of the foundation (Figure 3.4). It is assumed that the soil berm at the leading edge of the foundation takes the form of an isosceles triangle with opposite angles conforming to the angle made by the foundation skis on the soil surface, θ. The soil berm has an average effective unit weight of γ', and an area, Aberm, that increases as the integrated product of the displacement (u) and the depth, wplough of soil being ploughed (Figure 3.5), giving berm height:

θtanbermAh =

3.2

where the incremental height increase, dh due to an increment of forward motion, du, is

duh

wdh plough

2tanθ=

3.3

3.3.1. Undrained sliding resistance with consolidation

The mobilised sliding resistance during the first (N = 0.5) and last (N = 39.5) forward undrained slides is plotted against the horizontal displacement of the foundation in Figure

3.6. The resistance has a steady residual value over the majority of the slide. The rise in resistance observed towards the end of the forward slide (u > 1.85 m) is due to the front of the foundation impacting on a collapsed portion of the berm. The sliding resistance at remoulded state during undrained sliding cycles, Hun can be estimated as:

bermunbaseunun HHH ,, += 3.4


where Hun,base is the base sliding resistance and Hun,berm is the undrained shearing resistance of the ploughed soil berm. The berm term can be estimated by assuming that the sliding plane at the base of the soil berm at the leading edge of the foundation mobilises a shear stress equal to the initial remoulded shear strength, su,rem = su,in-situ/St at the level of the current mudline:

=

θtan2

,,BhsH remubermun

3.5

The reducing settlement rate of the foundation with cycles, and therefore decreasing wplough,, leads to a decreasing height, h of the triangular soil wedge and decreasing contribution to Hun,berm. Undrained shearing of the berm contributes only a minor proportion of the total undrained sliding resistance. Even for the largest incremental settlement, during N = 0.5, Hun,berm represents < 10 % of the sliding resistance (Figure 3.6).

Figure 3.5 Foundation settlement during sliding cycles


Figure 3.6 Horizontal load-displacement responses

The steady state (remoulded) sliding resistance mid-way through each slide (i.e. at u = 0.25·B) can therefore be expressed as the mobilised undrained strength at the foundation underside, su,mob = Hun/Abase. In the first sliding event (N = 0.5), this strength is the consolidated undrained strength of the soil, corresponding to large interface shearing, since the soil beneath the foundation was brought close to a fully consolidated state prior to sliding (see Chapter 2). su,mob is plotted against the elapsed time factor since the first slide, T = cref Σtun/B2 and cycle number, N in Figure 3.7. The increase of su,mob with T or N demonstrates that the regain in soil strength beneath the foundation during the operational periods (i.e. the dissipation and reconsolidation phases) eclipses the initial loss of strength associated with remoulding and generation of excess pore water pressures during the first slide (Figure 3.6). During reconsolidation, the dissipation of pore pressure in the foundation footprint results in a reduction of the void ratio, leading to an increase in the strength during a subsequent slide.

With repeated cycles of sliding and reconsolidation, the sheared soil reaches a critical state – a state characterised by no further generation of excess pore water pressure during the shearing process or void ratio reduction during reconsolidation. The tendency of the soil beneath the foundation to contract diminishes as the critical state is approached, as evidenced by the decreasing incremental settlement, wplough with increasing sliding cycles


shown in Figure 3.5. The mobilised undrained shear strength su,mob at the critical state is equivalent to a drained value, su,ϕ′ given by the applied foundation-soil stress and internal soil friction at critical state , ϕ′ = 23.5°:

base

op

base

basedru A

VA

Hs

'tan,',

ϕϕ == 3.6

Figure 3.7 Increase in mobilised undrained shear strength as a function of time factor, T = cref Σtun/B2 and cycle number, N

The rise in sliding resistance and su,mob towards su,φ is approximately exponential with time or cycles – as seen by Yan et al. (2014) for pipelines – and can be expressed as a function of the time factor, T, as:

( )

−−==

50',, 8.0exp1

TTms

AHTs u

base

unmobu ϕ

3.7

where m = 1 – (su,mob(N=0.5)/su,φ). 50 % of the increase in mobilised shearing resistance was reached after an overall elapsed time of T50 ~ 0.17. The value of T50 is specific to the


adopted duration of reconsolidation between sliding movements, which controls the frequency with which each packet of excess pore pressure is generated (and therefore the overall consolidation rate). In this test, the duration of a single cycle, ∆N = 1 was ∆T = 0.02, so Equation 3.7 can be expressed in terms of cycle number, N as:

( )

−−==

50',, 8.0exp1

NNms

AHNs u

base

unmobu ϕ

3.8

with N50 ~ 9 corresponding to T50. Yan et al. (2014) also showed that this hardening rate (given by N50) depends on the ratio between the plastic and elastic volumetric compressibility of the soil.

3.3.2. Drained sliding resistance

The horizontal resistance mobilised during drained sliding is plotted against horizontal displacement of the foundation in Figure 3.6, and can be estimated as:

bermdrbasedrdr HHH ,, +=

3.9

where Hdr,base is the drained base sliding resistance given by Equation 3.6. The progressive increase in Hdr with foundation sliding is due to mobilisation of the drained resistance of the ploughed soil berm, Hdr,berm which can be estimated as:

'tantan

' 2, ϕ

θγ

=

BhH bermdr

3.10

The drained ploughing resistance is derived from the shear stress mobilised by the triangular wedge of soil due to its self-weight (taking an average stress of γ′h/2 – Figure 3.4). Drained shearing of the berm contributes a significant proportion of the total drained sliding resistance, in contrast to the undrained case.

3.3.3. Failure envelopes

Figure 3.8 shows the load path of the mobilised foundation resistance in vertical-horizontal load space, corresponding to the load-displacement response shown in Figure 3.6. Failure envelopes for consolidated undrained, and drained loading are derived in Section 3.5 and superimposed.


The sliding and reconsolidation cycles enlarge the consolidated undrained failure envelope. The increase in the horizontal load apex of the envelope is proportional to the increase in mobilised shear strength, su,mob with T or N (Equations 3.7 – 3.8), and causes the consolidated undrained and drained envelopes to intersect at the sliding load path of the foundation. The mobilised ploughing resistance, Hdr,berm during drained sliding pushes the load state outside the drained failure envelope, which relates only to basal sliding. The increase in the vertical load apex of the failure envelope is not in the same proportion as the horizontal apex because the vertical capacity is governed by the shear strength in a greater depth of soil beneath the foundation (see Section 3.5). The trajectory of plastic footing displacements du/dw is illustrated in the inset to Figure 3.8 confirming an associated flow rule governing the undrained sliding failure. The trajectory of plastic footing displacements during the drained sliding also exhibits predominantly sliding movement with little incremental settlement (thus du >> dw) (see also Figure 3.5).

Figure 3.8 Failure envelope in vertical-horizontal load space, showing load paths of sliding cycles


3.4. Concluding remarks

The effects of loading rate and cumulative cycles of sliding on the response of a mobile subsea foundation have been investigated in a centrifuge model test. Foundation sliding, representing the response to thermal expansion and contraction of the attached pipelines, was modelled at prototype stress level and over the duration of a facility life-cycle. The interpretation of the results has shown that:

Sliding capacity is comprised of the base resistance mobilised at the soil-foundation interface, and shearing resistance mobilised by the ploughed soil berm. Under undrained conditions, the sliding capacity was found to be dominated by the base resistance. In contrast, the drained shearing resistance of the ploughed soil berm was found to be significant.

Reconsolidation between cycles of undrained sliding enhanced the base resistance under undrained conditions. Undrained base resistance approached the drained value after several cycles of sliding and reconsolidation. The sheared soil beneath the foundation reached a critical state wherein further shearing due to foundation sliding resulted in no further generation of excess pore pressures or void ratio reduction. The drained resistance depends on the foundation-soil friction angle at a critical state, reached at large sliding displacements.

These results demonstrate the importance of changes in soil strength in response to the failure inherent in the concept of a sliding foundation. Changes in soil strength are evident from the foundation sliding resistance and from post-test penetrometer measurements in the foundation footprint. The long-term soil strength and the transitional process follow critical state concepts. In the final state, the soil beneath the foundation no longer generates positive pore pressure when sheared, and the basal sliding is equal to the drained value regardless of the rate and duration of sliding. These observations contribute to the understanding of sliding foundations, assisting their design. The rising resistance of a sliding foundation also affects the force transmitted back to the connected pipeline, and potentially the pipeline structural response.

3.5. Appendix: Bearing capacity

The unconsolidated, undrained vertical load capacity, Vun is expressed as:


basesituinumcvun AsNV −= , 3.11

where Ncv is the bearing capacity factor for a rectangular surface mat for the dimensionless strength heterogeneity index, κ = kin-situB/sum,in-situ. For the conditions in this study, Ncv = 11.6 (Feng et al. (2014b)). The consolidated, undrained vertical load capacity, Vun(cons), following set-down of the foundation and full primary consolidation under self-weight prior to sliding can be estimated by the approach set out by Gourvenec et al. (2014)

unsituinum

umconsun V

ss

V ⋅

∆+=

−,)( 1 3.12

where ∆sum is the change in strength due to preload, which is equivalent to the product of the applied load and the normally consolidated undrained strength ratio, su/σʹvc (Gourvenec et al. (2014)). At the end of the test, the shear strength beneath the foundation was essentially uniform over the relevant depth range (Figure 3.2), i.e. κ = 0. For this case, Ncv(κ =

0) = 5.7 (Gourvenec et al. (2006)), giving the final undrained vertical capacity as

basef,um)(cvf,un AsNV 0== κ 3.13

sum,f = 2.1 kPa within the foundation footprint, measured after all the sliding events (Figure

3.2).

The unconsolidated undrained horizontal sliding capacity (at steady state) is given as the product of the initial remoulded shear strength at the mudline intercept, sum,in-situ/St, and the basal area. The consolidated undrained horizontal sliding capacity is determined from the mobilised undrained shear strength given by Equation 3.7 or Equation 3.8.

The undrained vertical-horizontal failure envelope is defined as:

;0.1=unH

H for 4.0≤unVV , 3.14

;25311

4.02

−−=

unun VV

HH for 4.0>unVV 3.15


The shape of the undrained unconsolidated normalised V-H failure envelope is assumed to hold for the consolidated undrained cases (Bransby (2002)).

The drained V-H failure envelope is given by Gottardi et al. (1999) as:

−

=

oobasedr VV

VV

HH 14

, 3.16

where Vo is the uniaxial vertical bearing capacity, forming the apex of this parabolic envelope, and corresponds to Vdr given by:

( ) basedr AsBNV ⋅= γγγ '5.0 3.17

Nγ and sγ are the bearing capacity and shape factors that depend on ϕ′ and B/L respectively. Estimates of Nγ and sγ as proposed by Meyerhof (1963) were used to determine the failure envelope in Figure 3.8.

The drained horizontal load capacity is defined by a non-dimensional factor,

dr

basedr

VH

f ,= 3.18

where a factor f = 0.12 (Gottardi et al. (1999)) was used. For low levels of V relevant to the test, f = 0.12 closely approximates to f = tanϕ′ given by Equation 3.6.


This work forms part of the activities of the Centre for Offshore Foundation Systems (COFS), currently supported as a node of the Australian Research Council Centre of Excellence for Geotechnical Science and Engineering and as a Centre of Excellence by the Lloyd's Register Foundation (LRF). The LRF helps to protect life and property by supporting engineering-related education, public engagement and the application of research. The work presented in this chapter is supported through ARC grant DP140100684. The third author is supported by Shell Australia. Special thanks are given to Mr Manuel Palacios and Mr Kelvin Leong, Senior Centrifuge Technicians and to Dr. Xiaowei Feng for their valuable help during this study.

Chapter 4. Whole-life response prediction

Prologue

An understanding of the whole-life response of a mudmat foundation supporting a pipeline has been established through the physical modelling observations presented in the preceding chapters. In summary, it has been shown that the undrained sliding resistance of the mudmat foundation increased with increasing cycles of sliding and intervening reconsolidation by way of the cumulative hardening of the soil beneath the foundation during reconsolidation. The long-term sliding foundation response as observed from the centrifuge results, was seen to follow the critical state behaviour of the soil. This formed the basis of the development of the theoretical framework presented in this chapter.

The theoretical framework presented in Chapter 4 considers a one-dimensional column of soil elements beneath a sliding subsea installation (which could be either a sliding foundation or a pipeline), with each element responding via a simple form of critical state model that relates the cyclic change in void ratio with the change in effective stress (excess pore pressure), associating these changes to the changes in soil surface settlement and changes in the undrained shear strength at each soil element.

The framework relies on the basic critical state parameters of the soil sample. These model parameters were calibrated using the interpreted results of the in situ tests described in Chapter 2. The model was implemented, and predictions of the resistance and settlement of a seabed mudmat foundation during episodes of horizontal movement and intervening periods of consolidation were compared against one of the centrifuge test results reported in Chapter 2.

This chapter was published in Géotechnique under the title “Theoretical framework for predicting the response of tolerably mobile subsea installations” (Cocjin et al. (2017b)).

4-61


Abstract

Tolerable mobility of subsea foundations and pipelines supporting offshore oil and gas developments has recently become an accepted design concept. It enables a smaller foundation footprint and so is a potential cost-saving alternative to conventionally engineered ‘fixed’ seabed foundations. Dominant sources of loading on subsea infrastructure arise from connection misalignment or thermal and pressure-induced expansion, and these are reduced if the structure is permitted to displace while ensuring that additional loading is not induced by excessive settlements. A sound prediction of the resulting sliding response will provide a robust design basis for mobile subsea infrastructure. This paper presents a theoretical model based on critical state soil mechanics to predict the performance of a subsea installation that is founded on soft, normally consolidated or lightly overconsolidated soil, and subjected to intermittent horizontal sliding movements. The framework is validated against centrifuge test results and is shown to capture the essential elements of the soil–structure interaction, which include: (a) the changing soil strength from cycles of sliding and pore pressure generation; (b) the regain in strength due to dissipation of excess pore pressure (consolidation); and (c) the soil contraction and consequent settlement of the foundation caused by the consolidation process.

4.1. Introduction

Subsea facilities to support oil and gas developments include pipelines and associated structures that experience significant loads from thermal and pressure-induced expansions, as well as connector misalignment. These loads are relieved if the infrastructure can move, so the conventional design approach of aiming to eliminate plastic movements or to resist factored maximum loads can be inefficient. Instead, an emerging design philosophy is to allow foundations and pipelines to move back and forth in response to such loads, subject to other criteria such as ensuring that the associated settlements do not cause unacceptable secondary loads (Fisher and Cathie (2008), Chapter 2, Deeks et al. (2014)).

For robust design of such tolerably mobile seabed infrastructure, it is necessary to predict the changing seabed resistance through cycles of infrastructure movement, and also the accumulating settlements. The framework presented in this chapter provides these predictions by applying a methodology based on critical state soil mechanics that is appropriate for soft normally-consolidated or lightly-overconsolidated soil. The framework

Whole-life response prediction | 4-63

is validated against centrifuge test results of a tolerably mobile sliding subsea foundation but is equally applicable to other boundary value problems that involve horizontal shearing at the mudline, such as axial walking of seabed pipelines.

4.2. Motivation

To predict the resistance and settlement of a seabed installation during episodes of horizontal movement and intervening periods of consolidation, three key elements are required: (i) the undrained strength associated with large strains that cause remoulding, and the associated pore pressure generation, (ii) the changes in strength due to dissipation of the excess pore pressure (consolidation), and (iii) the contraction and consequent settlement caused by the consolidation process.

Previous research on shallow foundations under cyclic loading has mainly focused on events that are fully undrained, such as for conditions beneath a typical gravity-based platform during a design storm event (e.g. Andersen (1976), Andersen (2009)), Xiao et al. (2016)). Some studies have investigated the subsequent change in soil strength due to reconsolidation (e.g. France and Sangrey (1977)), but the timescales are such that this has limited practical relevance for fixed surface-piercing offshore platforms founded on clay. Subsea infrastructure is supported on foundations of smaller dimension than for a gravity based or jacket platform and the governing load cases are typically caused by thermal expansion or operating pressures in pipelines, which have a much longer cyclic period – typically days or weeks – so significant consolidation can occur between load cycles.

The combined effects on soil strength and infrastructure settlement of cycles of loading and consolidation can be captured via an effective stress framework based on critical state concepts. Such a framework has been proposed previously to analyse the cyclic remoulding and reconsolidation processes during penetration of a cylinder into the seabed, such as a T-bar penetrometer or a pipeline element (Hodder et al. (2013), White and Hodder (2010)). In this analysis, the degradation of soil strength comes from the gross remoulding of the soil around the pipe due to cyclic vertical movement.

In the case of an installation moving horizontally at the soil surface, the shearing process is concentrated close to the surface, as illustrated by analyses of a pipeline sliding over soft clay presented by Yan et al. (2014). In this case the associated generation of excess pore pressure varies with depth according to the distribution of mobilised shear stress. Through cycles of


sliding and reconsolidation, the surrounding soil gains strength from episodes of undrained failure followed by pore pressure dissipation and contraction.

In the present study, this behaviour is idealised as one-dimensional – in an extension of the widely-used oedometer method for foundation settlement (Skempton and Bjerrum (1957)) – and both the settlement and the evolving sliding resistance are calculated on a cycle by cycle basis. This methodology provides a practical tool to support the design of tolerably mobile subsea installations.

Figure 4.1 Idealisation of the boundary value problem showing distributed loads on the surface of a semi-infinite mass

4.3. Overview of the framework

The problem addressed in this study is illustrated in Figure 4.1. An infinite half space is considered with a constant vertical stress applied at the mudline, σop, representing the submerged self-weight of the subsea facility. Cycles of horizontal shear stress, τop, in alternating directions are applied at the mudline to represent the effect of the sliding movement, du, of the infrastructure. Sliding is assumed to take place at a rate that causes an

σv

τop

σop

z

It

Is

Mudlinedu

Soil element at depth, zτ


undrained soil response, with intervening periods of consolidation between each shear stress reversal. The half-space is idealised as a one-dimensional column of soil elements, each subject to a vertical total stress and cycles of horizontal shear stress, and responding according to a simple form of critical state model. The framework can be applied in a cycle by cycle manner, solving for the response at each soil element to determine the cumulative change in void ratio and the variation in shear stress and settlement at the soil surface. Key elements of the framework include:

(i) Profiles of vertical stress and horizontal shear stress with depth, proportional to σop and τop

(ii) A critical state model for undrained shear strength, su, defined in the volumetric plane in terms of void ratio, e, and vertical effective stress, σ′v, and in the stress plane in terms of su and σ′v, which defines the current undrained strength and the excess pore pressure generated during shearing to failure. A critical state line (CSL) is defined in the usual way and is reached when the soil is first sheared to failure. However, the CSL is not fixed in the volumetric plane but instead migrates towards a limiting lower void ratio as a result of on-going cycles of shearing

(iii) Simple scaling rules for cycles of shear stress that do not cause failure of the soil element, to determine the generated excess pore pressure in pre-failure cycles and the equivalent fraction of a full cycle of shearing, to determine the CSL migration

The imposed soil stresses during shearing cycles on a soil element located at a depth, z below the surface, are the total vertical stress, σv and shear stress, τ. These are defined as proportions of the surface values by influence factors Iσ and Iτ that scale the distribution of vertical and shear stresses with depth (Iσ = Iτ = 1 at z = 0 and Iσ = Iτ → 0 for z → ∞) (with the geostatic vertical stress superimposed). Solutions for stress profiles with depth are presented by Poulos and Davis (1974) for different surface loading configurations on an elastic half space.

The critical state framework is defined in terms of the vertical stress and horizontal shear stress acting in the ground (Figure 4.1), since these are more convenient inputs than the mean principal effective stress, p', and the deviatoric stress, q, for the boundary conditions


being considered. This simplification is similar to the approach adopted by White and Hodder (2010) and Hodder et al. (2013) for cyclic penetrometer resistance.

Figure 4.2 illustrates a critical state interpretation of the problem, in terms of the state and stress paths in (a) σ′v – e, and (b) σ′v – τ planes, respectively.

An initially normally consolidated, (point A in Figure 4.2(a)) or lightly over consolidated soil (point B) is considered. During undrained shearing, for instance from sliding of a surface foundation or pipeline, positive excess pore pressure is generated, ∆ue,gen > 0, resulting in a decrease of the effective vertical stress, σ′v. The stress state moves towards the CSL at constant void ratio, e. Unless the ratio of applied shear stress to shear strength at a greater depth is lower than that at the surface, the soil element at the mudline level will fail, so the stress state reaches the CSL (B to C in Figure 4.2(a)). Elements of soil at depth will move towards, but not reach the critical state line (B to C'), at least during the initial cycle. At the critical state, the current undrained shear strength is mobilised (C in Figure 4.2(b)).

During the subsequent period of consolidation, the excess pore pressures dissipate (∆ue,dis through C – D in Figure 4.2, or with partial consolidation terminating at D') and the effective vertical stress returns towards the initial condition, i.e. σv = σ′v. The increase in σ′v follows the unload-reload line (URL), defined by slope κ, causing a decrease in the void ratio (∆e), and an accumulation of settlement at the soil surface. The shear stress could be sustained during this period, or could decay (if the infrastructure is held at a fixed position, for example), but for simplicity the framework does not distinguish between these cases.

During subsequent shearing cycles the soil element will fail at a higher vertical effective stress, σ′v (D – E, Figure 4.2(a)) and consequentially mobilise a larger shear stress at failure (E in Figure 4.2(b)).


Figure 4.2 A critical state interpretation of a soil element submitted to cyclic surface shearing and reconsolidation, presented in the (a) volumetric (inset: migration and decay of critical state line), and (b) stress planes

Slope: l

NCL at low σ′v

∆eNCL at high σ′v

Final CSL

Cyclic CSL migration to final CSL:

Cyclic decay of ∆e

σ′v (log scale)

Void

ratio

, e

(a)

(b)

∆ue

-∆ue, σv, σ′v

Hor

izont

al sh

earin

g st

ress

, τ

B

CE

Total Stress Path (TSP): (σv ,τ)

D

Slope: M

Effective Stress Path (ESP): (σ′v ,τ),

β > 1

ESP: β = 1

Void

ratio

, e

NCL

CSL

(∆ue,gen > 0 )

σ′v = 1.0 kPa

l

B

D

κ

C

E

A

κ

∆e

N

G

-∆ue, σ′v (log scale)

URL

σop

C′

z = 0z > 0

D′

Nth CSL


Figure 4.3 Schematic of model framework

z

τ

σop

duf (su(min), Iτ)

dh

f (∆e)

σ′v

e

Rf

R = f (∆Neq)

R0

(a) Current effective vertical stress

(c) Mobilised shear stress in a cycle

(d) Cycle number

(e) Current critical state line

(g) Pore pressure dissipation and void ratio reduction in a cycle

(h) Change in soil layer height and surface settlement in a cycle

f (Iσ , σop) : Equilibrium stateσ′v

In-situ

σop

f (σ′v) : Nth cycle

z

z

Neq

f (τ/su)

Inc. χ

∆Neq(z=0)

z

(f) Maximum potential excess pore pressure in a cycle

e

σ′v

Current CSL

∆ue,max

σ′v,CSL

Equilibrium stress state

e

σ′v

su = f (M, N)

(b) Current undrained shear strength

τop

e

σ′v, -∆ue

∆ue,dis

σ′v(N-1) - ∆ue,gen

κ∆ee

σ′v(N-1)

∆ue,gen

∆eU=1

σ′v

− Eq. (4-1)

− Eq. (4-5)

− Eq. (4-7)

− Eq. (4-8)

− Eq. (4-9)

− Eq. (4-11)

− Eq. (4-13)

− Eq. (4-19)

Eq. (4-18)

− Eq. (4-20)

− Eq. (4-4)


4.4. Components of the framework

Figure 4.3 presents the components of the framework in the order that they are required to perform a cycle by cycle calculation. The components are introduced in the same sequence below.

4.4.1. Vertical equilibrium conditions

The framework first considers vertical equilibrium of the soil mass under the applied vertical stress at the surface and the soil self-weight stresses (Figure 4.3(a)). The equilibrium vertical effective stress at depth z is:

σσσσ Iopveqmv ⋅+= 0, '' 4.1

where σ′v0 is the in situ soil self-weight vertical effective stress, equivalent to γ′av·z with γ′av being the average effective unit weight of the overlying soil, σop is the applied vertical stress at the surface, due to the submerged self-weight of the infrastructure, and Iσ is the influence factor defining the distribution of applied vertical stress with depth.

The void ratio at the state of equilibrium, eeqm, is defined as:

( ) ( )NCLb

eqmv

ivieqmveqm OCR

eOCROCRe

⋅∆++⋅−N=

,

,, '

'ln'ln

σσ

κσl 4.2

where N and l are state parameters defining the void ratio at σ′v = 1 kPa and the slope of the normal compression line (NCL) at high levels of σ′v, respectively. The over-consolidation ratio, OCR is defined as the ratio of the maximum vertical effective stress experienced by the soil, σ′v,max, over the equilibrium vertical effective stress, σ′v,eqm where σ′v,max is the sum of the in situ self-weight vertical effective stress and additional soil surcharge pressure (σ′v,max = σ′v0 + σ′v,sur).

A curved NCL is considered (Figure 4.2(a)) which accounts for the additional void ratio at low levels of vertical stress. This feature is required to match the experimental data shown later, and follows the model defined by Liu and Carter (2003). The additional void ratio at low levels of σ'v is represented by the last term on the right-hand side of Equation 4.2, where ∆ei is the additional void ratio at σ′v = σ′v,i where virgin yielding begins at effective stress, σ′v,i. Power bNCL quantifies the rate of increase of void ratio with decreasing σ′v.


The initial CSL in e - ln(σ′v) space (Figure 4.2(a)) is a curved line parallel to the NCL, defined by the initial spacing ratio, R0, given by the ratio of vertical stresses on the NCL and the initial CSL in e - ln(σ′v) space:

−

Γ−N=

κl0

0 expR 4.3

At any void ratio, e, the corresponding vertical effective stress on the CSL, σ′v,CSL can be calculated from Equation 4.4:

( ) ( )NCLb

CSLv

iviRCSLv R

eke

∆−+−Γ=

,

,, '

'1'ln

σσ

σl 4.4

The spacing ratio, R and parameter kR in Equation 4.4 concurrently increase with cycles of shearing, which causes the CSL to migrate to a lower void ratio with increasing cycles to represent cyclic densification, as introduced later in Section 4.4.5.

4.4.2. Undrained shear strength

The undrained shear strength, su, of a soil element is mobilised when the stress state reaches the CSL, and is calculated from the vertical effective stress at failure via a strength parameter, M (Figure 4.2(b), Figure 4.3(b)):

vu Ms '5.0 σ= 4.5

The distribution of the current shear strength with depth can therefore be derived from the current void ratio through:

−Γ

=l

eMsu exp5.0 4.6

4.4.3. Mobilised shear stress

Cycles of surface shearing mobilise a shear stress, τop at the soil surface, with magnitude diminishing with depth (Figure 4.3(c)). The mobilised shear stress will be controlled by the weakest ‘slice’ of soil in the one-dimensional column, with both su and τ varying with depth.


For most practical soil strength profiles which have su increasing with depth, failure will occur at the soil surface, but strictly τop is controlled by:

=

ττ

Isu

op min 4.7

between z = 0 and ∞.

The mobilised shear stress at depth z can then be determined as τ = Iττop where Iτ is the influence factor defining the distribution of shear stress with depth.

4.4.4. Equivalent cycle number

For a soil element that fails during each cycle of shear stress, the cycle number is simply equal to the number of shear stress reversals. However, for soil elements that mobilise only a fraction of the undrained strength during a cycle, an equivalent number of cycles is defined, ∆Neq, to allow these ‘partial’ cycles to be accumulated (Figure 4.3(d)):

χτ

=∆

ueq s

N 4.8

Since ∆Neq varies with depth, each soil layer possesses a different total of equivalent cycles, which reduces with increasing depth.

The power χ controls the nonlinearity of equivalent cycle number with the stress ratio, τ/su, and is expected to be greater than unity, implying an escalating rate of ‘damage’ the closer the shear stress is to the soil strength. Selection of an appropriate value for χ is presented in the section on calibration and derivation of model parameters.

4.4.5. CSL migration based on shearing cycles

A limitation of the basic critical state models such as Original and Modified Cam Clay is that the progressive densification that results from multiple cycles of shearing to the critical state is not captured. In the present study, to overcome this limitation, the critical state line migrates to a lower void ratio as a function of the number of equivalent cycles experienced. This concept is achieved by defining a progressive increase in the spacing ratio, R, with cycles of shearing (Figure 4.3(e)). The spacing ratio is assumed to increase from the initial value of R0 towards a limiting value, Rf, according to:


( ) Rf kRRRR ⋅−+= 00 4.9

where R0 is calculated from the critical state parameters and the in situ stresses in the virgin soil (defined later in Equation 4.27)) and Rf is determined from the initial spacing ratio and soil sensitivity defined by a cyclic T-bar test (Equation 4.28). The parameter kR depends on the number of cycles (or equivalent cycles – Equation 4.8) of failure previously imposed on the soil element:

∆−−= ∑

)95(3exp1

eq

eqR N

Nk 4.10

where ∑∆Neq provides the current equivalent cycle number and Neq(95) is a parameter controlling the rate of migration of the CSL, equal to the number of cycles required for 95 % of the migration of the current CSL to the final location. The selection of a value of Neq(95) is presented later, with the case study for the sliding foundation.

4.4.6. Generation of excess pore pressure

The excess pore pressure mobilised when a soil element is sheared to failure (Figure 4.3(f)) is given by:

CSLvveu ,max, '' σσ −=∆ 4.11

where σ′v is the current (pre-shearing) vertical effective stress. During the first shearing cycle, σ′v = σ′v,eqm (Equation 4.1), while during subsequent shearing cycle, σ′v is calculated as:

genediseNvv uu ,,)1('' ∆−∆+= −σσ 4.12

where σ′v(N-1) is the (pre-shearing) vertical effective stress of the preceding cycle, and ∆ue,dis is the dissipated excess pore pressure during the current reconsolidation cycle (to be defined later).


The generated excess pore pressure, ∆ue,gen is given by:

βτ

⋅∆=∆

uegene s

uu max,, 4.13

The parameter β represents the curvature of the σ′v - τ effective stress path created by the generated excess pore pressure, ∆ue,gen. For β = 1 the stress path is linear, but β > 1 is more typical, reflecting the shape of the stress path derived from Cam clay-type models, as shown schematically in Figure 4.2(b).

4.4.7. Dissipation of excess pore pressure

The degree of consolidation, U (based on settlement, rather than pore pressure dissipation), after shearing during a reconsolidation period can be estimated through a normalised time-settlement response of the form:

m

TT

U−

+

=

501

1

4.14

In the present analysis, U is inferred from a solution based on elasto-plastic finite element analysis of a boundary value problem (e.g. Gourvenec and Randolph (2010), Gourvenec et al. (2014), Feng and Gourvenec (2015), (Feng and Gourvenec, 2016) for shallow foundations, or Chatterjee et al. (2012c) and Chatterjee et al. (2013) for pipelines). It is assumed that the global dissipation rates identified in these previous studies provide adequate approximations of the pore pressure dissipation at element level within the one-dimensional model used in the present study.

In Equation 4.14 the parameter T50 refers to the dimensionless time factor for 50 % of the consolidation settlement, w to occur (i.e. U = ∆e/∆eU=1 = 0.5 where ∆e is the change in void ratio within a consolidation cycle, and ∆eU=1 is the reduction in current void ratio when full consolidation takes place within a cycle such that when t → ∞, U = 1 as defined below), and m is a constant. The dimensionless time, T is expressed as:


2d

tcT ref= 4.15

where t is the reconsolidation period, and d is drainage length (depending on the dimension of the infrastructure, typically taken as the foundation breadth, B or pipe diameter, D). The current operative coefficient of consolidation, cref can be obtained as:

( )

+=

w

vref ekc

lγσ

α'

1 4.16

where α is a factor to account for the anisotropic dissipation of pore water pressure during consolidation (Chapter 2), and k is the coefficient of soil permeability which can be expressed as a function of void ratio as:

+=

eeak

b

1 4.17

with a and b being fitting parameters to estimate the permeability-void ratio relationship of the soil (Sahdi (2013)).

The reduction in the current void ratio during a reconsolidation cycle for an equivalent degree of consolidation, U (Figure 4.3(g)) is equivalent to ∆e = ∆eU=1·U, where ∆eU=1 can be obtained as:

∆−=∆ =

geneeqmv

eqmvU u

e,,

,1 '

'ln

σσ

κ 4.18

where Δue is the current excess pore water pressure. During reconsolidation, the vertical effective stress increases by an amount equivalent to the dissipated excess pore pressure, which is given by (Figure 4.3(g)):

( )eeqmvdise ueu ∆−

−

∆

=∆ ,, '1exp σκ

4.19

This completes the calculations for a given cycle of shearing and reconsolidation, and the current void ratio, e is updated by ∆e through Equation 4.18, leading to a revised undrained strength, su, (Equation 4.6) to be used for the next cycle computation.


4.4.8. Change in soil height and surface settlement

As the cycles progress, accumulating change in void ratio allows the change in height of each soil element with height, dz (Figure 4.3(h)) to be determined as:

dzeeh

01+∆

=d 4.20

Equation 4.20 is integrated over the whole depth of the soil column to obtain the incremental settlement of the soil surface within a cycle of reconsolidation,

∫∞

=

=0z

hdzw dd 4.21

where the current settlement of the soil surface, w, is obtained by summing dw for the current number of cycles N,

∑=N

ww1

d 4.22

4.5. Comparison of theoretical framework and model test data

The proposed framework has been applied to centrifuge test results reported in Chapter 2. The sliding resistance and settlement of a rectangular mat foundation on normally-consolidated clay is analysed, as well as changes in the strength of the underlying soil. Pertinent details of the centrifuge model testing and calibration of the framework parameters are outlined below.

4.5.1. Foundation test

The centrifuge test was conducted in the University of Western Australia – Centre for Offshore Foundation Systems (UWA – COFS) fixed beam centrifuge at an acceleration level of 100g.

The rectangular model foundation (Figure 4.4) (with dimensions B = 5 m and L = 10 m at prototype scale) was set down on the surface of a bed of normally consolidated kaolin clay and subjected to cycles of undrained sliding with periods of intervening consolidation. An operative vertical stress σop = 1.85 kPa (equivalent to an operative vertical load, Vop = 92.7


kN) was imposed by the model foundation throughout the test. The soil was allowed to consolidate fully under this stress prior to the cycles of sliding and consolidation. The loading sequence prescribed in the centrifuge test is illustrated in Figure 4.5. The foundation was translated horizontally a distance du = 0.5B at a rate of 1 mm/s, which was sufficiently rapid to maintain undrained conditions during the slide. A single slide (which occurred only once at the start of the sliding cycles), or a double slide (reverse and forward without intervening consolidation) is defined as a single cycle. The consolidation period after each movement lasted t = 1.5 years at prototype scale, during which the foundation was prevented from moving horizontally but was free to settle under the applied σop.

The foundation sliding resistance and settlements were recorded over cycles of horizontal sliding and intervening periods of consolidation, totalling more than 60 years (prototype scale) of foundation response.

4.5.2. Stress distribution

The influence factors for the vertical stress, Iσ and shear stress, Iτ distribution beneath the centreline of a rectangular, uniformly loaded area on the surface of a semi-infinite mass (Holl (1940)) were adopted, given by:

Figure 4.4 Experimental set-up of the sliding foundation test in the centrifuge

Outline of top surface

Model foundation

Sliding direction

Loading arm attached to actuator

B L


Figure 4.5 Loading sequence for a sliding foundation test in the centrifuge

4.23

4.24

where l = 0.5L and b = 0.5B with L > B. The parameters r1, r2, and r3 are given as follows:

( )( )( ) 5.0222

3

5.0222

5.0221

zblr

zbr

zlr

++=

+=

+=

4.25

4.5.3. Calibration and derivation of model parameters

Appropriate parameter values for the application of the theoretical framework were drawn from auxiliary tests carried out during the sliding foundation tests in the centrifuge as reported in Chapter 2. Table 4.1 provides a list of these model parameters and corresponding calibrated values used in the application of the theoretical model.

Double reversing slideSingle slide

Time (years)1.5

Nor

mal

ised

horiz

onta

l di

spla

cem

ent,

du/B

0.5

Neq(z=0) = 1.0… Nth → 40

0

Reconsolidation cycle

4.5

Installation consolidation

In-situconditions Equilibrium

Conditions (initial)

∆Neq(z=0) = 0.5

∆Neq(z = 0) = 0.5

∆Neq(z=0) = 0.5

+

+

= −

2

2

2

133

1 11tan2rrr

lbzzrlbI

πσ

−

= −

32

13

1tan2rr

lbzzrlbI

πτ


Table 4.1 Framework parameters (a of d)

Not

es o

n ca

libra

tion

or so

urce

of s

elec

ted

valu

e

Test

par

amet

er

Test

par

amet

er

Test

par

amet

er

Obt

aine

d fr

om m

oist

ure

cont

ent d

ata

of so

il co

re sa

mpl

es

Obt

aine

d fr

om m

oist

ure

cont

ent d

ata

of so

il co

re sa

mpl

es, a

nd in

situ

und

rain

ed sh

ear

stre

ngth

of t

he so

il sam

ple

as a

sses

sed

from

a

T-ba

r pen

etro

met

er

Ratio

of i

ntac

t to

fully

rem

ould

ed sh

ear

stre

ngth

obt

aine

d fr

om c

yclic

T-b

ar

pene

trom

eter

test

Valu

e

5 m

10 m

1.85

kPa

5.9

kN/m

3

0.15

2.4

Desc

riptio

n

Foun

datio

n br

eadt

h

Foun

datio

n le

ngth

Ope

rativ

e ve

rtica

l bea

ring

pres

sure

Uni

t wei

ght o

f the

soil (

aver

age)

Nor

mal

ly c

onso

lidat

ed st

reng

th ra

tio

Soil s

ensit

ivity

Dim

ensio

n

L L

m/L

T2

m/T

2 L2

[-]

[-]

Para

met

er

B L σ op

γ ′ av

[su/

σ′v0

] NCL

S t

Fram

ewor

k co

mpo

nent

s

Boun

dary

con

ditio

ns

Soil s

ampl

e ch

arac

teris

tics


Table 4.1 Framework parameters(b of d)

Not

es o

n ca

libra

tion

or so

urce

of s

elec

ted

valu

e

Calib

rate

d fr

om m

oist

ure

cont

ent

data

of s

oil c

ore

sam

ples

Criti

cal s

tate

par

amet

er fr

om S

tew

art (

1992

), Ch

apte

r 2

Valu

e

2.44

7

1.2

1.5

kPa

1 0.1

2.16

3

0.26

1

0.92

Desc

riptio

n

Void

ratio

inte

rcep

t at σ′ v

= 1

kPa

of th

e N

orm

al C

ompr

essio

n Lin

e (N

CL) i

n th

e e

– ln

σ′v p

lane

Addi

tiona

l voi

d ra

tio a

t σ′ v

= σ′

v,i, w

here

vi

rgin

yie

ldin

g be

gins

Initi

al v

ertic

al y

ield

stre

ss

Com

pres

sion

dest

ruct

urin

g in

dex,

whe

re 0

<

b NCL

< ∞

Slop

e of

swel

ling

line

Void

ratio

inte

rcep

t at σ′ v

= 1

kPa

of th

e in

itial

crit

ical s

tate

line

(CSL

) in

the

void

ra

tio -n

atur

al lo

garit

hm o

f ver

tical

ef

fect

ive

stre

ss (e

– ln

σ′v)

plan

e

Slop

e of

NCL

in th

e e

– ln

σ′v p

lane

Slop

e of

CSL

in v

ertic

al e

ffect

ive

stre

ss -

sh

ear s

tres

s (σ′

v - τ)

pla

ne

Dim

ensio

n

[-]

[-]

m/L

T2

[-]

[-]

[-]

[-]

[-]

Para

met

er

N

∆ei

σ'vi

b NCL

κ Γ 0

l M

Fram

ewor

k co

mpo

nent

s

Void

ra

tio

- ve

rtica

l ef

fect

ive

stre

ss re

latio

nshi

p

Shea

r str

ess -

ver

tical

effe

ctiv

e st

ress

rela

tions

hip


Table 4.1 Framework parameters(c of d)

Not

es o

n ca

libra

tion

or so

urce

of s

elec

ted

valu

e

Calib

rate

d fr

om m

oist

ure

cont

ent d

ata

of so

il co

re sa

mpl

es a

nd in

situ

und

rain

ed sh

ear

stre

ngth

of t

he so

il sam

ple

as a

sses

sed

from

a

T-ba

r pen

etro

met

er

Cycle

num

ber r

equi

red

for t

he c

urre

nt sp

acin

g ra

tio, R

to b

e eq

uiva

lent

to 9

5% o

f the

val

ue o

f th

e fin

al sp

acin

g ra

tio, R

f. Fitt

ed b

ased

on

mod

el te

st o

bser

vatio

ns.

Equi

vale

nt to

the

prod

uct o

f the

initi

al sp

acin

g ra

tio a

nd so

il se

nsiti

vity

, i.e

. R0S

t, ca

libra

ted

as

in R

0

A pa

rabo

lic c

urva

ture

of t

he e

ffect

ive

stre

ss

path

in th

e st

ress

pla

ne w

as se

lect

ed

Sele

cted

to m

imic

a pa

rabo

lic c

urva

ture

of t

he

effe

ctiv

e st

ress

pat

h in

the

stre

ss p

lane

, and

co

nsist

ent w

ith e

xper

imen

tal o

bser

vatio

ns

Valu

e

7.97

8

40

19.1

48

2 2.5

Desc

riptio

n

Initi

al sp

acin

g ra

tio

CSL

mig

ratio

n pa

ram

eter

Fina

l spa

cing

ratio

Exce

ss p

ore

pres

sure

par

amet

er,

repr

esen

ts th

e cu

rvat

ure

of th

e σ′

v - τ

effe

ctiv

e st

ress

pat

h cr

eate

d by

the

gene

rate

d ex

cess

por

e pr

essu

re,

Rem

ould

ing

para

met

er, c

ontr

ols t

he

fract

ion

of th

e fu

ll por

e pr

essu

re th

at is

ge

nera

ted

durin

g sh

earin

g w

ithou

t fai

lure

Dim

ensio

n

[-]

[-]

[-]

[-]

[-]

Para

met

er

R 0

Neq

(95)

R f β χ

Fram

ewor

k co

mpo

nent

s

CSL

mig

ratio

n/de

cay

Rem

ould

ing


Table 4.1 Framework parameters (d of d)

Not

es o

n ca

libra

tion

or so

urce

of s

elec

ted

valu

e

Obt

aine

d fr

om a

fini

te-e

lem

ent a

naly

sis o

f a

rect

angu

lar s

lidin

g m

udm

at (s

ee F

eng

and

Gour

vene

c (20

15))

Obt

aine

d fr

om R

owe

cell t

ests

on

kaol

in c

lay

(see

Sah

di (2

013 )

)

Obt

aine

d fr

om th

e di

ssip

atio

n re

spon

se o

f a

‘pie

zofo

unda

tion’

repo

rted

in C

hapt

er 2

Obt

aine

d fr

om R

owe

cell t

ests

on

kaol

in c

lay

(see

Sah

di (2

013)

)

Obt

aine

d fr

om a

fini

te-e

lem

ent a

naly

sis o

f a

rect

angu

lar s

lidin

g m

udm

at (s

ee F

eng

and

Gour

vene

c (20

15)

Uni

vers

al c

onst

ant

Valu

e

0.04

3

0.27

7 m

/yea

r

2.7

3.5

1.05

9.81

Desc

riptio

n

Dim

ensio

nles

s tim

e fa

ctor

for 5

0 %

of t

he

cons

olid

atio

n se

ttle

men

t to

occu

r

Void

ratio

- pe

rmea

bilit

y re

latio

nshi

p pa

ram

eter

Ratio

of v

ertic

al to

ope

rativ

e co

effic

ient

co

effic

ient

Void

ratio

- pe

rmea

bilit

y re

latio

nshi

p pa

ram

eter

Cons

tant

Uni

t wei

ght o

f wat

er

Dim

ensio

n

[-]

L/T [-]

[-]

[-]

m/T

2 L2

Para

met

er

T 50 a α b m

γ w

Fram

ewor

k co

mpo

nent

s

Cons

olid

atio

n pa

ram

eter

s

Oth

ers


4.5.3.1. Critical state parameters

The critical state parameters l, κ and N were calibrated from the moisture content profile of the centrifuge model soil sample.

The moisture content, mc at different depths was obtained from vertical core samples taken from undisturbed sites of the centrifuge soil sample. This was used to calculate the effective unit weight of the soil as γ′av = γw(Gs–1)/(1–e0) where e0 = mcGs is the in situ void ratio, and γw is the unit weight of water. The specific particle density, Gs = 2.6 (Stewart (1992)) yielded an average effective unit of γ′av = 6.0 kN/m3 over the range 0.4 < z (m) < 11.5.

The in situ void ratio, i.e. in the virgin soil prior to placement or loading of the foundation, e0, and the natural logarithm of the vertical effective stress, σ′v0 = γ′av·z representing undisturbed soil are presented in Figure 4.6. The measured data show higher in situ void ratios at low stress levels (σ′v0 < 10 kPa) than predicted by critical state parameters derived from one-dimensional compression tests at higher stresses (Stewart (1992)). This reflects the high compressibility of clays with high initial water contents (Boukpeti et al. (2012)) and justifies our use of a modified shape of NCL and CSL, following Liu and Carter (2003).

By minimising the residuals between the measured and predicted void ratio from Equation

4.2, best-fit values for the slopes, l and κ, and void ratio intercept at σ′v = 1 kPa, N, and additional void ratio parameters ∆ei, σ′v,i and bNCL, were obtained (Table 4.1).

The value of the void ratio intercept at σ′v = 1 kPa of the initial CSL in the ln(σ′v) – e plane, Γ0 was obtained by equating the ratio of the in situ undrained shear strength (Equation 4.6) and the effective vertical stress at the NCL (Equation 4.2), with the normally consolidated strength ratio of the soil, (su/σ′v0)NC such that

N+

=Γ

NCv

usM 0

0 '2ln

σl 4.26

4.5.3.2. Spacing ratio

The initial spacing ratio, R0, is expressed as a function of the normally consolidated strength ratio by substituting Equation 4.26 into Equation 4.3:


−=

NCv

usM

R0

0 '2lnexp

σlκl 4.27

wherein the obtained R0 (Table 4.1) is derived from an (su/σ′v0)NC ~ 0.15 reported in Chapter 2 from T-bar penetrometer tests, assuming M = 0.92 following Stewart (1992).

The final spacing ratio, Rf, which defines the limiting position of the CSL in the volumetric plane, was obtained from the measured soil sensitivity through cyclic T-bar penetrometer tests, St ∼ 2.4 (Chapter 2) as:

tf SRR 0= 4.28

Figure 4.6 Vertical effective stress, σ′v plotted against void ratio, e showing measured data on in situ and sheared/consolidated soil (final), with linear models of the normal compression line (NCL) based on curve fits using state parameters obtained from the centrifuge, and one-dimensional compression tests (x axis in natural logarithm scale)


Figure 4.7 Change in cycle number ∆Neq with mobilised stress ratio,τ/sufor different values of χ

4.5.3.3. Remoulding parameter

The variation of the change in equivalent cycle number ∆Neq caused by the mobilised stress ratio,τ/su is illustrated in Figure 4.7 for different values of χ. The parameter χ controls the level of ‘damage’ for non-failing soil elements as quantified in Equation 4.8. A choice of χ > 1 reflects a realistic assumption regarding the level of ‘damage’ for non-failing soil elements as a function of the mobilised stress ratio,τ/su. A very large χ would limit significant ‘damage’ only to a soil element that has reached the critical state failure, whereas a linear variation of the level of ‘damage’ with τ/su is implied by χ = 1. As χ controls the fraction of the full pore pressure that is generated during shearing without failure, the τ/su versus ∆Neq representation (as shown in Figure 4.7) might be expected to resemble a mirror image of the effective stress path in (σ′v, τ) space. For soft clays this path bends to the left, and is approximately elliptical (e.g. as in Modified Cam Clay). The adopted value of χ = 2.5 approximates this well, and might therefore be expected to apply more generally, as well as fitting the present experimental data.


Figure 4.8 Residual coefficient of sliding friction, µ = τop/σop mobilised at every loading cycle, measured from sliding foundation test in the centrifuge, and the prediction by the theoretical model

Similarly, by using β = 2 in Equation 4.13, a parabolic form is adopted for the curvature tracked by the generated excess pore pressure, ∆ue,gen in (σ′v - τ) space (Figure 4.2(b)). A value of Neq(95) = 40 provided a good match with the observed data.

4.5.4. Assessment of the theoretical model

This section compares the results from the framework with observations from the centrifuge model test reported in Chapter 2.

4.5.4.1. Foundation sliding resistance

Figure 4.8 compares the horizontal sliding resistance calculated by the framework (via Equation 4.7) and measured in the centrifuge test. The model captures well the general trend and magnitude of increasing sliding resistance due to increasing soil strength following cycles of shearing and reconsolidation. A residual coefficient of sliding friction, µ = τop/σop is calculated at every sliding cycle where τop obtained from the centrifuge test refers to the residual, steady state, shear stress mobilised at a horizontal foundation displacement of du/B = 0.25. The test results showed a declining sliding resistance during the later cycles (N > 30) which was not included in Figure 4.8. This occurred because contact between the


edge of the mudmat and the seabed was not maintained as the mudmat moved in to and out of the depression created by the consolidation process and onto the adjacent berm (see Chapter 2). Further work would be required to introduce this three dimensional behaviour into a theoretical model.

4.5.4.2. Foundation settlement

Figure 4.9(a) compares the calculated and measured accumulation of foundation consolidation settlement. The measured consolidation settlement in the early cycles is slightly greater than the calculations while the settlement in the later cycles and the final consolidation settlement are very well matched.

The final consolidation settlement was obtained from the measured initial and final void ratio profiles (Figure 4.6) by summing the changes in soil height with depth. The settlement derived from the changes in void ratio is identical to the final cyclic consolidation settlement measured directly from the foundation test, providing confidence in the two independently calculated values (Figure 4.9(a)).

The settlement of the foundation accumulates over a larger number of cycles than the rise in sliding resistance, which is virtually complete after 20 cycles (Figure 4.8). This is due to continued pore pressure generation due to pre-failure shearing in the deeper soil, which leads to settlement but no change in the sliding resistance, which is controlled by the shallow soil. The framework correctly captures these different rates of resistance and settlement build-up with sliding cycles.

The sliding movement of the foundation also contributes plastic vertical displacement to the overall settlement, as evidenced from the centrifuge data in Figure 4.9(b), which shows the overall cumulative foundation settlement against the horizontal sliding displacement, du. The undrained shearing settlement, wp is deducted from the overall cumulative foundation settlement in Figure 4.9(b) and plotted against cycle number in Figure 4.9(a). This settlement is due to the ploughing of the sheared soil during sliding (Chapter 3), and is presented in Figure 4.10 as a plastic strain ratio, dwp/du plotted against the normalised vertical load v = Vop/Vu,cons where Vu,cons is the consolidated, undrained vertical load capacity calculated from the updated soil strength following Gourvenec et al. (2014).


Figure 4.9 Settlement data and prediction showing (a) accumulation of foundation settlement with increasing loading cycles, measured from sliding foundation test in the centrifuge, and the prediction by the theoretical model; and (b) overall foundation settlements measured in the centrifuge test


Figure 4.10 Incremental plastic undrained settlements

Table 4.2 Curve-fitting parameters for plastic strain ratio

Parameter Value

Λ 0.008

v0 0.27

ξ 0.5

An associated flow rule was considered for prediction of the plastic settlement, but the actual response is non-associated, with higher settlement observed than predicted using normality combined with the failure envelopes for rectangular surface foundations by Feng et al. (2014b) and the classical solution for a strip foundation by Green (1954). This is consistent with previous model test observations reported by Martin and Houlsby (2001), who applied an ad hoc scaling to the flow rule to capture non-associativity in their model tests of foundations on clay. In the present case, a simple relationship between the plastic strain direction and the normalised vertical load derived from the centrifuge data in Figure

4.10 is given as:


( )ξ

dd

0vvu

wp −Λ= for v > v0, 4.29

and

0=u

wp

dd

for v ≤v0 4.30

where Λ and ξ are fitting parameters (see Table 4.2), and v0 is the lowest vertical load ratio with non-zero plastic strain. The cut-off of v0 = 0.27 is lower than the theoretical value derived from failure envelopes (0.4 and 0.5 in Feng et al. (2014b) and Green (1954), respectively).

4.5.4.3. Undrained shear strength profiles

Figure 4.11 shows a good correlation between the in situ undrained shear strength in the virgin soil, su,0 profile measured in the centrifuge sample with a miniature T-bar test (Stewart and Randolph (1991)) and calculated by the framework through Equation 4.6.

Figure 4.11 In situ and sheared/consolidated soil (final) undrained shear strength profiles with depth measured from the centrifuge test soil sample, and prediction by the theoretical model


A T-bar test was also carried out in the foundation footprint, after removal of the foundation at the end of the test, to assess the final undrained shear strength, su,f of the sheared and consolidated soil. The profile of su,f, measured from the surface of the foundation footprint is compared with the calculations from the theoretical framework in Figure 4.11 and also shows good agreement (noting that the T-bar diameter corresponds to 0.5 m at prototype scale, so detection of the hardened zone is challenging).

4.5.4.4. Moisture content profiles

Figure 4.12 compares the in situ and final moisture content profiles with depth from the framework and measured in the centrifuge test sample. The framework result was derived from the cycle by cycle void ratio profile, where moisture content was obtained as mc = e/Gs

for the first and last cycle. The framework provides a good estimate of the in situ moisture content profile of the centrifuge test sample, and a reasonable estimate of the lower post-test moisture content at shallow depth.

4.6. Insights into soil response

The analysis framework has been shown to provide good predictions of the foundation resistance to sliding and settlement with cycles of shearing and consolidation, as well as capturing the changing undrained shear strength and moisture content of the underlying soil. The framework can also provide insights into the cycle by cycle elemental soil response as described below.

4.6.1. Void ratio

Figure 4.13 shows the cycle by cycle evolution of the profile of void ratio, e as a function of depth for 40 loading cycles. The general behaviour shows that during the early cycles, the greatest contraction is at the soil surface. However, as this zone hardens, the shear stress and pore pressure generation in the deeper soil increase, leading to a greater change in void ratio. This effect propagates deeper but diminishes as the mobilised shear stress becomes a smaller proportion of the in situ shear strength.


Figure 4.12 Moisture content, mc profile with depth measured from the centrifuge test soil sample, and the prediction by the theoretical model

Figure 4.13 Cycle by cycle evolution of the current void ratio, e as a function of depth reflecting the degradation of the mudline level


Figure 4.14 Cycle by cycle evolution of the current undrained shear strength, su as a function of depth reflecting the degradation of the mudline level

Figure 4.15 State path in vertical effective stress - void ratio space of a soil element at shearing interface, i.e. at z = 0


4.6.2. Undrained shear strength

Figure 4.11 is replotted in Figure 4.14 to show the cycle by cycle evolution of undrained shear strength, su (Equation 4.6) as a function of depth showing the general increase in soil strength, over the depth of influence of pore pressure generation, with increasing cycles of surface shearing and reconsolidation. The undrained shear strength close to the surface reaches a limiting value after some cycles, while the zone of strength gain propagates deeper. This stabilisation of the strength reflects the final critical state being reached and the end of the CSL migration, leading to no further excess pore pressure.

4.6.3. Stress and state path

State paths during cycles of surface shearing and reconsolidation for a soil element at the shearing interface (z = 0) is presented in e - ln(σ′v) space for 40 loading cycles in Figure 4.15. This figure shows the progressive reduction of vertical effective stress at constant void ratio within a surface shearing cycle, and the recovery of effective stress and associated reduction in void ratio during each reconsolidation period. The decay and migration of the CSL in e – ln(σ′v) space becomes less pronounced with increasing cycles of shearing and reconsolidation. The effect of partial consolidation is also seen by the decreasing value of σ′v from σ′v,eqm with increasing loading cycle.

4.7. Closing remarks

The analytical framework set out in this study is an extension of the widely-used oedometer method for estimating foundation settlement. It provides a basis to predict the changing seabed resistance and accumulating settlements of surface installations that experience cycles of horizontal sliding movements.

The framework considers a one-dimensional column of soil elements beneath a foundation, with each element subject to a vertical total stress and cycles of horizontal shear stress, and responding via a simple form of critical state model. The framework is presented in a cycle by cycle manner, solving for the response at each soil element to determine the cumulative change in void ratio, defining changes in soil shear strength and surface settlement.

The change in undrained shear strength is quantified in terms of the generation and dissipation of excess pore water pressure. The model incorporates the effects of partial dissipation of excess pore water pressure during cycles of reconsolidation. Soil contraction


due to void ratio reduction during cycles of reconsolidation allows for the estimation of soil surface settlement.

The framework was shown to simulate well the behaviour of a tolerably mobile subsea foundation tested at prototype stress levels in the centrifuge. The model captures the increasing foundation sliding resistance due to increasing soil strength, the overall settlement of the foundation following cycles of shearing and reconsolidation, as well as the different build-up rates of resistance and settlement. The theoretical model also provided an accurate estimate of the spatial variation with depth of the undrained shear strength and the moisture content of the soil within the foundation footprint.

This framework provides a simple yet effective means to analyse a soil-structure interaction process that involves episodes of horizontal surface shearing and reconsolidation. It is a simple tool that is convenient for foundation design purposes – validated for specific conditions, if necessary, via more complex model tests or numerical analysis. It also provides a simple method to integrate the foundation behaviour into a structural model that includes the connected equipment such as pipelines, without requiring the full soil domain to be modelled explicitly. It offers a useful addition to the toolbox of methods that can be used to design and optimise subsea installations.


This work forms part of the activities of the Centre for Offshore Foundation Systems (COFS), currently supported as a node of the Australian Research Council’s Centre of Excellence for Geotechnical Science and Engineering, and through the Fugro Chair in Geotechnics, the Lloyd’s Register Foundation Chair and Centre of Excellence in Offshore Foundations and the Shell EMI Chair in Offshore Engineering. The work presented in this chapter is supported through ARC grant DP140100684.

Chapter 5. Seabed strength characterisation

Prologue

The previous chapters have demonstrated that a sound understanding of the strength of the seabed interacting with the subsea infrastructures is crucial in the understanding of the response of the infrastructure and the accurate prediction of the operational response. The importance of near-surface soil strength is recognised and investigated in the next two chapters, Chapter 5 and Chapter 6, where a novel penetrometer designed to assess the undrained shear strength of surficial soil is presented. The tool is a shallowly embedded pile, dragged laterally across the seabed, aptly named the “pile penetrometer”.

In this chapter, a simple process for deriving the undrained shear strength using the pile penetrometer through established pile foundation analysis is presented. The derived shear strength from the pile penetrometer was compared against existing solutions for a laterally loaded pile, and against the shear strength as assessed by a T-bar penetrometer.

It is noted that the profiles of undrained shear strength with depth reported in this chapter, derived from both the T-bar and the pile penetrometers were uncorrected for the slight nonlinear distribution of inertial acceleration through the centrifuge model. Details of this correction are presented in Appendix B, which is applied in the derivation of the undrained shear strength profiles reported in all the other chapters. The slight difference in the derived shear strength profile presented in this chapter, resulting from neglecting the variation in gravity field correction, has no impact on the accuracy or relevance of the method of interpretation for the pile penetrometer presented.

Chapter 5 has first appeared in the proceedings of the 33rd International Conference on Ocean, Offshore and Arctic Engineering, San Francisco under the title “Continuous characterisation of near-surface soil strength” (Cocjin et al. (2014b)).

5-95


Abstract

A sound understanding of near-surface soil strength is essential for the accurate prediction of the response of structures laid on or shallowly embedded in the seabed. However, characterisation of the uppermost region of the seabed, which is typically very soft and at a low-stress state, is extremely challenging. This chapter demonstrates a novel technique for characterising the in situ undrained shear strength of near-surface soils using a newly-developed pile penetrometer. The pile penetrometer is vertically embedded into the near-surface soil and is driven laterally. A simple calculation of the resistance mobilised over the embedded depth of the pile penetrometer is presented along with its application to the continuous measurement of spatial variation in near-surface strength in virgin and disturbed regions of soil.

5.1. Introduction

Deepwater sites typically consist of normally consolidated fine-grained sediments (either clay, or carbonate muds and silts) and are characterised by extremely soft near-surface material. In situ testing using full-flow penetrometers, such as the T-bar or ball have increasingly been employed to characterise these soil types (Randolph et al. (2011)). A drawback of conventional penetrometers is the uncertainty in the assessed shear strength at very shallow penetrations (White et al. (2010)). To properly interpret the soil shear strength at shallow depths by conventional full-flow penetrometers, corrections must be made to the measured penetration resistance to account for near-surface effects brought about by soil buoyancy and the changing failure mechanism mobilised prior to the full flow of soil around the penetrating bar (White et al. (2010)). These corrections are further complicated by the entrainment and mixing of water into the sediment as the penetrometer enters and exits the seabed during cyclic tests. Also, conventional penetrometer tests, whether using the traditional cone or full flow penetrometers, are conducted at discrete locations to provide a shear strength profile with depth. They do not provide a continuous lateral profile of strength.

Seabed strength characterisation | 5-97

Figure 5.1 Miniature pile penetrometer

To provide an alternative tool that overcomes some of these limitations, a novel penetrometer was developed at the University of Western Australia (UWA) (Sahdi (2013)) to: (1) directly assess the shear strength of shallow soils without necessitating progressively changing corrections to relieve near-surface effects, and (2) increase efficiency in obtaining lateral variations in soil strength. The tool is primarily targeted at assisting small scale model testing, such as centrifuge studies at UWA, but it is potentially applicable in the field at larger scale.

Figure 5.1 shows a miniature model of this newly-developed penetrometer. This device is a short rigid cylinder, and works by being dragged laterally through soil while the bending moment is measured at multiple locations above the soil surface. The penetrometer operates in a mode similar to a laterally loaded pile, thus is aptly called a pile penetrometer. The strength profile of the soil can be assessed by evaluating the lateral resistance, qh, along the embedded depth, and the line of action of the resultant force (Sahdi (2013)).

The pile penetrometer assists in prediction of near-surface seabed strength properties, which currently remains very challenging. Characterisation of near-surface seabed sediments is particularly important for the design of as-laid or shallowly embedded offshore


structures such as pipelines, mudmats and steel catenary risers, where only the upper one or two metres are of interest (Randolph and White (2008a)).

This chapter presents an evaluation of appropriate lateral bearing capacity factors for the pile penetrometer. The derived lateral bearing capacity factor was validated by comparison with shear strength profiles measured with a full-flow T-bar penetrometer. An assessment of the lateral variation in near-surface soil strength is demonstrated through test data of disturbed soil beneath a sliding foundation.

5.2. Pile penetrometer

The prototype pile penetrometer shown in Figure 5.1 was designed to resemble an open-ended pile with a hollow, cylindrical cross section having outer and inner diameters of Do = 4.72 and Di = 2.90 mm, respectively. The hollow shaft minimizes the soil disturbance when inserting the penetrometer into the soil.

The pile penetrometer was fabricated from 6061 T6-grade Aluminum with a total length of 130 mm. A 25 mm long threaded section with a diameter of 7 mm enables the pile penetrometer to be bolted and fixed vertically to a horizontally-driven actuator.

A pair of strain gauges was fixed on opposite sides of the pile cylinder at 4 levels below the threaded section as shown in Figure 5.1. These strain gauges provide a record of the bending moment at levels A, B, C and D, located at 55 mm, 70 mm, 85 mm and 100 mm respectively from the free-end of the pile penetrometer. They were attached on the pile penetrometer using Vishay® AE-10 adhesive kit, and were coated with a layer of epoxy resin to protect against moisture.

During the test, the pile penetrometer was laterally translated at a constant rate of u = 1 mm/s to maintain an undrained loading condition (Finnie and Randolph (1994)). The pile penetrometer was translated maintaining at a constant tip embedment of ze = 30 mm (3 m in prototype scale). Ten cycles of displacement were carried out with a travel distance of about 10·Do.


Figure 5.2 Failure mechanisms of a pile penetrometer in lateral translation without rotation: (a) 2-way wedge; (b) 1-way wedge; (c) full-flow

5.3. Laterally loaded pile analysis

5.3.1. 1-way wedge mechanism

The pile penetrometer acts as a cantilever beam when displaced laterally through the soil, held fixed at the threaded section (Figure 5.1). There is no rotation and the soil along the embedded depth, ze, imparts a distributed lateral resistance, qh along the pile shaft as illustrated in Figure 5.1. The different forms of failure mechanism expected for a laterally loaded pile are shown schematically in Figure 5.2.

A general form to express the resistance on a laterally loaded pile, qh is given by Equation

5.1 as (Murff and Hamilton (1993)):

zsNq uhh γ+= 5.1

where Nh is the lateral bearing capacity factor that varies with depth, su is the undrained shear strength of the soil and γz is the soil surcharge (which is applicable only for a one-way wedge failure mechanism). Based on theoretical upper bound plasticity calculations considering different linear strength profiles and a pile free to rotate, Murff and Hamilton (1993) proposed an empirical expression for Nh as:

zcrit

ze

2-way wedges 1-way wedge Full-flow

∆u ∆u ∆u

Gap

Fixed

Pile penetrometer

qh

(a) (b) (c)

Mudline


( )

−

⋅−−= oDz

shallowdeepdeeph eNNNNβ

5.2

where Nshallow is the bearing factor at the soil surface and Ndeep is the bearing factor corresponding to the deep failure mechanism. For a one-way wedge failure mechanism in which the pile can rotate, β depends on the ratio of the strength at mudline, sum, to the strength gradient, k times the pile diameter Do:

6;05.025.0 <+= ααβ if 5.3

and

6;55.0 <= αβ if 5.4

where α = sum/kDo. Murff and Hamilton (1993) recommended values of 2 and 9 for Nshallow and Ndeep. Experimental validation by Sahdi (2013) using miniature pile penetrometers indicated values of 2 and 10.5 respectively.

5.3.2. 2-way wedge mechanism

A 2-way wedge mechanism governs close to the surface if tension can be sustained on the trailing face of the pile, or if the soil strength to self-weight ratio is sufficiently low that the soil behind the pile cannot support its own weight. The 2-way mechanism leads to an approximate doubling of the bearing factor, Nh, but the surcharge term in Equation 5.1 is now not applicable (Murff and Hamilton (1993)). The resulting lateral soil resistance, qh cannot exceed that corresponding to the deep failure mechanism determined by the bearing capacity factor at depth, Ndeep so that Equation 5.1 is rewritten as:

udeepuhh sNsNq ≤= 2 5.5

where Nh can be estimated from Equation 5.2. The factor 2 in Equation 5.5 reflects the symmetry of the active and passive wedges, although the actual bearing factor for the combined failure will generally exceed twice the single wedge bearing factor since rotation is prevented – see, for example, Randolph et al. (1998).


5.3.3. Full-flow mechanism

In very soft soil, a plane strain flow-around mechanism occurs over virtually the full embedded pile depth, as illustrated in Figure 5.2(c). For this mechanism the lateral resistance can be calculated as (Randolph and Houlsby (1984)):

udeeph sNq = 5.6

Rigorous lower and upper bound solutions for the case of a full-flow mechanism below the wedge mechanism presented by Randolph and Houlsby (1984) showed that the bearing factor, Ndeep varies between 9.14 (fully smooth) to 11.94 (fully rough).

5.4. Sample preparation and initial characterisation

A normally consolidated soil sample was prepared in a centrifuge strong box to represent a model seabed. A slurry made from commercially available kaolin clay with moisture content twice the liquid limit (120%) was normally consolidated in the UWA beam centrifuge at 100g for 3.5 days. The variation in shear strength su with depth z was then determined through a miniature cyclic T-bar test. The result is shown in Figure 5.3. The first penetration resistance (marked by a thicker line) can be expressed as:

kzss umu += 5.7

where the shear strength at mudline, sum = 0.54 kPa, with a gradient of increasing strength with depth of k = 0.59 kPa/m. The undrained shear strength was interpreted assuming a constant T-bar factor, NT-bar = 10.5 (Stewart and Randolph (1994)).

The T-bar was penetrated up to a prototype depth of 10 m below the soil surface at a penetration rate of 1 mm/s which is sufficient to ensure undrained loading conditions in this soil (Finnie and Randolph (1994)). Ten cycles of penetration and extraction between prototype depths of 4 – 6 m were carried out primarily to benchmark an accurate zero reference for the T-bar resistance data.


Figure 5.3 Undrained shear strength profile from T-bar test

5.5. Pile penetrometer test

Figure 5.4 presents the measured bending moment loads (M1, M2, M3 and M4, corresponding to level A, B, C and D strain gauges respectively) during a pile penetrometer test in the soil sample. The embedded depth was 30 mm and the lateral cycles of translation were 40 mm in each direction performed at 1 mm/s velocity; equivalent to 3 m and 4m in prototype scale, respectively.

Figure 5.4(a) shows the moment resistance for all the loading cycles at level A strain gauge (closest to the mudline) while Figure 5.4(b) shows the moment resistance during the first forward translation at all four levels of strain gauge.

A peak in resistance was mobilised during the first translation immediately after the pile penetrometer was displaced, and a steady state and lower resistance was achieved after a translation of ~2·Do (Figure 5.4(b)). The initial peak resistance is due to consolidation around the pile following the installation process, whereas the steady state resistance gives an indication of the shear strength based on intact material subjected to the same disturbance as caused by the T-bar.


Figure 5.4 Recorded moment loads on the pile penetrometer: (a) at level A (M1), showing all cycles, and (b) at levels A to D, showing only the first forward translation

5.6. Pile penetrometer analysis

The pile penetrometer can be simplified into a cantilever beam subjected to a net lateral force due to the soil resistance, F acting at some depth, zLOA (Figure 5.5). The magnitude of the net lateral force, F is equal to the slope of the moment curve along the pile penetrometer shaft:


( )dz

zdMF = 5.8

The bending moment distribution along the pile penetrometer shaft can be projected from any pair of recorded moment loads, M1 to M4. As there is no lateral load above the soil, the bending moment distribution is linear.

A least squares method was employed to calculate the best-fit line representing the recorded moment loads along the pile shaft. The slope of the best-fit line gives the net lateral force, F (Equation 5.8), and the zero bending moment-intercept is the location of the line of action, zLOA of the force, F.

Figure 5.6 plots the net lateral force, F and location of its line of action, zLOA against the lateral translation of the pile penetrometer normalised by its outer diameter, u/Do. A steady-state load, F ~ 1.5 N, acting about zLOA ~ 20 mm (equivalent to 2 m in prototype scale) below the mudline can be observed for pile penetrometer displacements of u > 5·Do. In the same figure, the mean deviation of the recorded bending moments from the best-fit line is shown to be close to zero.

Figure 5.5 Pile penetrometer analysis

k1

qh0

Fixed

∆u

Embedded depth, ze

z

Net lateral force, F

( )dz

zdM

Depth of line of action, zLOA

qh(z)

M(z)

Pile penetrometer

Strain gaugesM2

M1

M3

M4

qh1


Figure 5.6 Net lateral force, F; depth of line of action of force F, zLOA and error in linear fit to moment load data, Merror plotted against normalised lateral displacement, u/Do of the pile penetrometer

5.7. Measured soil resistance

The lateral soil resistance, qh can be obtained from the net lateral force, F by assuming a linearly increasing qh from the mudline to the pile toe as illustrated in Figure 5.5. This approach is justified by the near-constant value of Nh applicable along the pile length. The calculations set out in Equations 5.1 – 5.6 indicate that the lateral resistance, qh, from the 1-way and 2-way wedge mechanisms exceeds the flow around resistance (Ndeepsu) beyond 7.5 mm depth. This is likely to over-estimate the critical depth since the Murff & Hamilton solution for Nh is based on a pile head that is free to rotate. Constraint of the rotation will raise the bearing factor close to Ndeep at the surface for a 2-way wedge (Randolph et al. (1998)).

The distribution of qh along the embedded depth is given by the gradient of resistance, k1 in kPa/m where the intercept of qh at the soil surface is qh0 = 5.67 kPa based on the T-bar strength at mudline (qh0 = Ndeepsum). The lateral soil resistance at the pile toe, qh1 was calculated from the average lateral pressure exerted by the net lateral force, F over the embedded depth,


hopilee

h qAFq −=

,1 5.0

5.9

where Ae,pile is the projected area of the embedded pile penetrometer. The gradient of resistance, k1 is thus obtained as:

e

hoh

zqqk −

= 11 5.10

Figure 5.7(a) plots the back-calculated lateral resistance qh0 and qh1, and the slope of lateral resistance with depth, k1 against normalised lateral penetrometer translation, u/Do. In the same figure, a resistance gradient scaled directly from the T-bar strength gradient, k is shown to closely approximate the slope of lateral resistance with depth, k1 at steady state resistance.

On the other hand, the back-calculated distribution of lateral soil resistance, qh over the embedded depth at different stages of penetrometer translation is plotted in Figure 5.7(b). The corresponding profile of qh based on the linear strength profile derived from the T-bar predicts significantly lower qh compared to the back-analysis for ∆u < 5·Do.

However, the mobilised lateral resistance decreases with increasing lateral translation and a unique resistance distribution can be obtained after a lateral translation of 5 pile diameters, signifying that a steady state resistance has been reached. This steady state lateral resistance measured from the pile penetrometer, qh, shows good agreement directly with the T-bar penetration resistance, qT-bar. This indicates that a constant bearing factor along the entire length is a reasonable assumption for back-analysis as shown by the good correspondence in Figure 5.7(b) of Equation 5.6 (Ndeep = 10.5).


Figure 5.7 Pile penetrometer estimates of soil strength , showing: (a) lateral resistance qh0 and qh1, and slope of lateral resistance, k1 plotted against normalised lateral translation, u/Do of the pile penetrometer, and (b) measured and predicted profile of soil resistance, qh with depth

The good agreement between the resistance measured from the pile penetrometer and the estimate assuming a full flow mechanism is consistent with the visual observations of flow around the pile penetrometer at the surface, rather than failure by lifting and heaving soil ahead and to the side.

5.8. Example application

The miniature pile penetrometer developed for use in centrifuge testing could be scaled up for use in the field to characterise the near-surface seabed shear strength and assess the lateral heterogeneity of the seabed. The pile penetrometer represents an alternative tool for


particular applications, notably where near-surface strength and lateral heterogeneity is of interest.

The near-surface strength of the seabed may exhibit considerable spatial variability due to surface disturbance, remoulding and reconsolidation. These processes can occur near foundations and are often present where pipelines interact with the seabed.

Figure 5.8 demonstrates the use of the pile penetrometer in characterising the lateral heterogeneity in the strength of near-surface soils. In this example the soil disturbance was a result of repeated shearing due to cyclic sliding of a surface foundation with intervening periods of reconsolidation. The net lateral force, F is compared for pile penetrometer tests carried out with the same embedment, ze, on the disturbed patches of soil in the foundation footprint, with a separate test in adjacent virgin soil also being shown. The net lateral force, F within the foundation footprint is higher than on the virgin soil (Figure 5.8) indicating the strengthening of the soil due to soil reconsolidation beneath the footing.

A sudden increase in lateral force was measured when the pile penetrometer passed through the soil berm which was deposited during the foundation sliding. In addition, the line of action rose higher. A lower and decreasing net lateral force, F is observed at the end of the drag test indicating that the pile penetrometer returned to a patch of virgin soil beyond the zone of influence of the foundation (u > 28·Do in Figure 5.8).

These measurements show the continuous lateral variation in soil strength, and illustrate the sensitivity of the pile penetrometer to these changes.


A novel ‘pile penetrometer’ that operates in a mode similar to a laterally loaded pile has been developed to provide a method of continuous lateral profiling of near-surface seabed shear strength. A simple process of assessing the near-surface soil resistance using the pile penetrometer is presented and is validated through experimental results. A steady state resistance occurring after the pile penetrometer has laterally translated by 5 pile diameter distance is identified to provide a good measure of the in situ shear strength of the soil.

In normally-consolidated soil the steady state lateral soil resistance measured through the pile penetrometer compares well with existing solutions for a laterally loaded pile assuming a full-flow mechanism at all depths. Similarly, this steady state resistance agrees closely with


the vertical penetration resistance measured by the T-bar. The application of the pile penetrometer has been demonstrated by assessing the near-surface soil strength across zones of virgin and disturbed soil. Changes in soil strength in near-surface soil due to soil remoulding and reconsolidation as well as soil berming are captured through continuous profiling of soil resistance using the pile penetrometer.

5.10. Acknowledgement

This work forms part of the activities of the Centre for Offshore Foundation Systems (COFS), currently supported as a node of the Australian Research Council Centre of Excellence for Geotechnical Science and Engineering and as a Centre of Excellence by the Lloyd's Register Foundation. Lloyd’s Register Foundation invests in science, engineering and technology for public benefit, worldwide.

Figure 5.8 Overlay of soil surface image and lateral pile penetrometer resistance around a foundation footprint with disturbed, remoulded and reconsolidated soil

Chapter 6. Seabed strength changes

Prologue

In this chapter, the pile penetrometer introduced in Chapter 5 is employed to directly investigate the softening and hardening behaviour of near-surface soil strength as a result of remoulding and reconsolidation. The results were compared with companion T-bar tests, carried out in the same sample, reported in Chapter 2. Similitude of penetrometer responses with model foundation test results described in Chapter 2 and Chapter 3 are also presented in this chapter, citing on the increasing soil strength with increasing cycles of remoulding and reconsolidation.

This chapter also presents a direct assessment of the soil strength in the footprint left by one of the model foundation tests reported in Chapter 2, with the T-bar providing the final profile at a single location within the footprint, and the pile penetrometer mapping a continuous shear strength profile across the foundation footprint.

This chapter has been submitted for publication to the Journal of Geotechnical and Geoenvironmental Engineering, ASCE with the working title “Shear strength changes of surficial soil under cyclic loading” (Cocjin et al. (2016)).

6-111


Abstract

Deepwater subsea infrastructure for offshore oil and gas developments are often supported on shallow foundations that interact only with a shallow zone of the seabed. Some of these structures submit the underlying soil to episodic cycles of loading that can lead to significant changes in near-surface soil strength. This chapter describes results from a centrifuge modelling program involving a shallow subsea foundation that slides intermittently across the seabed. It investigates the influence of this repetitive shearing and episodic consolidation on the changes in strength of soft fine-grained soil. A new type of soil characterisation tool, the pile penetrometer, was used, which allows assessment of the strength of a soft seabed over a continuous lateral profile. The results show detailed cross-sections of strength that give agreement at specific vertical profiles with a conventional T-bar penetrometer test. Finally, the paper shows the influence of episodic cycles of shearing and consolidation on the soil strength beneath shallow foundations and highlights the novelty of the pile penetrometer in mapping these effects.

6.1. Introduction

Assessment of the mechanical behaviour of near-surface seabed sediments is increasingly important with the trend of offshore oil and gas developments to adopt subsea architecture, which is generally founded on or in the upper few metres of the seabed. Interest is driven by the large capital investment in subsea infrastructure whose size is strongly affected by the surficial soil strength, and the inherent difficulty in characterising this strength.

Subsea infrastructure such as manifolds and pipeline end termination structures often only penetrate into the upper 1 or 2 m of the seabed, which in soft fine-grained sediments possess very low undrained strength (< 5 kPa).

A consideration for subsea foundation design is the episodic nature of the loading over the field life that leads to changes in the operative shear strength. For instance, operational loads on as laid subsea pipelines and subsea foundations involve periodic cyclic shearing due to start-up and shutdown operations over the life cycle of a field and can lead to significant changes in near-surface soil strength (Yan et al. (2014), Chapter 2). This strength increase brought about by the repetitive remoulding and reconsolidation of the seabed can potentially be utilised for efficiencies in subsea foundation and pipeline design.

Seabed strength changes | 6-113

A second consideration in subsea foundation design is the local heterogeneity of the seabed strength. It is common design practice to combine strength profiles from in situ tests across a soil zone extending many kilometres across the field location, and perform statistical analysis on those many profiles to determine the design soil strength profiles for any single location, regardless of whether a specific penetrometer test was performed at that point (e.g. Lloret-Cabot et al. (2012), Bransby et al. (2015), Liu et al. (2015), Li et al. (2015)). This combination of zonal data is considered necessary to account for lateral heterogeneity in strength, even over the length scale of a typical foundation footprint. Measurement of seabed properties over a continuous lateral section can assist in better capturing a true picture, or reducing uncertainty, of the local heterogeneity of the seabed. A novel concept for continuous undrained strength measurement across a lateral section is a vertically orientated penetrometer (Sahdi et al. (2015), Chapter 5), a miniature instrumented pile that is translated through the soil. Measured bending moments along the shaft can be transformed into estimates of the soil strength over the embedded length. Such a device offers the potential to determine lateral heterogeneity via tests performed over distances relevant to the length scale of a foundation.

This chapter describes results from a suite of centrifuge tests involving the vertically orientated penetrometer, called ‘pile penetrometer’ in this study, to assess the strength of near-surface soil, in a virgin condition and in the footprint of a shallow foundation. The foundation underwent cyclic episodes of sliding and intervening rest periods, leading to changes in undrained strength of the underlying and surrounding soil. The chapter has two parts: (I) assessment of soil strength on virgin soil to determine its intact and fully remoulded shear strength and to quantify the change in strength during remoulding and reconsolidation cycles, and (II) assessment of the strength profile on a full cross-section beneath a foundation that has undergone cycles of shearing and reconsolidation.

6.2. Experiments

All experiments were conducted in the University of Western Australia geotechnical beam centrifuge at an acceleration level of 100g, as part of the program introduced in Chapter 2. Results are presented in model scale dimensions, unless stated otherwise.

A normally-consolidated kaolin clay sample was prepared by consolidation under self-weight from a clay slurry with water content twice the liquid limit (120 %) at 100g for 3.5


days. After consolidation was complete, a thin layer of soil was scraped from the top of the sample to provide a smooth, level surface, and to provide a small non-zero intact mudline strength. After re-equilibration and swelling, the final height of the soil sample was 130 mm (13 m prototype depth). A water level at 15 mm above the soil surface was maintained throughout the tests to prevent the soil surface from drying.

6.2.1. Consolidation characteristics

Piezocone penetrometer tests performed in flight in the same sample were used to estimate the coefficient of consolidation profile. The horizontal coefficient of consolidation, ch was obtained as 4.4·cv where the vertical coefficient of consolidation, cv was estimated to vary with the effective vertical stress, σ′v < 500 kPa as (Chapter 2):

( ) 47.0'16.03.0 vvc σ+= 6.1

with cv and σ′v being in m2/year and kPa, respectively.

6.2.2. Strength characterisation tools

The soil sample was characterised with a miniature T-bar penetrometer (Stewart and Randolph (1991), Figure 6.1(a)) and a novel pile penetrometer (Chapter 5, Sahdi et al. (2015), Figure 6.1(b)). The miniature T-bar penetrometer was used to determine the in situ strength over the full depth of the sample.

The miniature pile penetrometer shown in Figure 6.1(b) resembles an open-ended pile with an outer diameter of D = 4.72 mm (0.472 m, prototype scale). It is fabricated from aluminium with a total length of 130 mm, and is fixed vertically to a horizontally-driven actuator (De Catania et al. (2010)). Pairs of strain gauges are fixed on opposite sides of the device as shown in Figure 6.1(b), and are oriented to face the directions of motion. Connected via a bridge circuit, they record the bending moments, M1 to M4 at the specified elevations.


Figure 6.1 Shallow penetrometers: (a) T-bar, and (b) pile

6.2.3. Test programme

Table 6.1 provides a summary of the penetrometer tests presented in this chapter. Three pile penetrometer tests and three T-bar tests were carried out, four of which on virgin soil and two within the footprint of a sliding foundation.

The penetrometer tests on virgin soil were carried out following the displacement sequence illustrated in Figure 6.2. In tests Pile1 and T-bar1, the penetrometers were cycled in the soil without interruption (Figure 6.2(a)), while an intervening pause between displacement cycles was observed in tests Pile2 and T-bar2 (Figure 6.2(b)). The intervening pause allows excess pore pressures generated during displacement cycles to dissipate, i.e. ‘reconsolidation’ of the sheared soil. The duration of this intervening reconsolidation period was 780 sec (0.25 years, prototype scale).


Figure 6.2 Cyclic loading sequence for penetrometer tests: (a) continuous remoulding cycles, and (b) remoulding cycles interspersed with consolidation episodes

Tim

e (s

ec)

780

Sweeping distance (pile penetrometer)

Penetration depth (T-bar penetrometer)

Max

. 0N

thre

cons

olid

atio

n cy

cle

Tim

e (s

ec)

Sweeping distance (pile penetrometer)

Penetration depth (T-bar penetrometer)

Max

. 0

Nth

cycl

e

Inst

alla

tion

cons

olid

atio

n:

500

–Pi

le p

enet

rom

eter

0 –

T-ba

r pen

etro

met

er

(b)(a)

Inst

alla

tion

cons

olid

atio

n:

500

–Pi

le p

enet

rom

eter

0 –

T-ba

r pen

etro

met

er

780

Nth

cycl

e


Table 6.1 Penetrometer tests programme

Tests Pile3 and T-bar3 were carried out within the soil footprint left following a sliding foundation model test (test MMUD1 in Chapter 2), after the foundation was carefully lifted away. The displacement sequence illustrated in Figure 6.2(a) was followed during these tests. Figure 6.3 shows the foundation footprint and locations of tests Pile3 and T-bar3. The foundation footprint has a total length of 125 mm (along the y axis) and 50 mm

Test

na

me

Soil

loca

tion

Cons

olid

atio

n du

ratio

n be

twee

n cy

cles,

sec

(yea

rs,

prot

otyp

e sc

ale)

Num

ber o

f cy

cles,

N

Disp

lace

men

t rat

e (m

m/s

)

Horiz

onta

l sw

eep

dist

ance

of p

ile

pene

trom

eter

or p

enet

ratio

n de

pth

of T

-bar

,

mm

(m, p

roto

type

scal

e)

Pile

1 Vi

rgin

0

(0)

10

1.0

40 (4

)

Pile

2 Vi

rgin

78

0 (0

.25)

60

60

(6, p

ile p

enet

rom

eter

hel

d in

in

sert

ion

loca

tion)

Pile

3 Fo

otpr

int

0 (0

) 3

168

(16.

8)

T-ba

r1

Virg

in

0 (0

) 10

1.0

100

(10)

; cyc

lic ra

nge:

20

(2)

T-ba

r2

Virg

in

780

(0.2

5)

60

45 (4

.5, T

-bar

with

draw

n fr

om so

il du

ring

cons

olid

atio

n)

T-ba

r3

Foot

prin

t 0

(0)

10

80 (8

)


width made by the foundation base (composed of 100 mm foundation length, and 25 mm extent of sliding excursion). Inclined ‘skis’ around the perimeter extend the maximum plan dimensions to 142.3 mm by 67.3 mm.

The level of the foundation footprint, zf relative to the original virgin soil surface was also determined post-foundation test. A topographical laser scan of the soil footprint was carried out and the elevation profile of a cross-section located 20 mm away from the footprint centreline, parallel to the Pile3 route is shown in Figure 6.3.

In all tests, the pile penetrometer was inserted into the soil with the pile toe set at a depth of ze = 30 mm (3 m prototype scale) from the free soil surface. After insertion, the vertical axis of the actuator was locked to maintain this pile embedment level and the penetrometer was held at the insertion location for 500 sec (0.17 years, prototype scale) to allow dissipation of excess pore pressure generated during insertion.

6.3. Shear strength interpretation through penetrometer tests

6.3.1. T-bar penetrometer

The undrained shear strength of the soil, su is derived from the T-bar penetrometer tests following a plasticity solution for the limiting pressure acting on a cylinder embedded in cohesive soil (Martin and Randolph (2006)) as:

barT

barTbarTu N

qs−

−− =, 6.2

where qT-bar is the measured T-bar resistance, and NT-bar is the T-bar bearing factor, assumed equivalent to 10.5.


Figure 6.3 Schematic of foundation footprint showing locations of T-bar3 and Pile3 tests

Test

T-b

ar3

2525

125

Exte

nt o

f fou

ndat

ion

base

foot

prin

t

Test

Pile

3 in

serti

on p

oint

Foun

datio

n ba

se lo

catio

n du

ring

inte

rven

ing

reco

nsol

idat

ion

Exte

nt o

f fou

ndat

ion

‘ski

’ foo

tprin

t

8.6

Test

Pile

3 en

d po

int

Exte

nt o

f soi

l ber

m

~30

9.5

8.6

25

8.6

8.6

15 5

Slid

ing

excu

rsio

n

27.5

15

Cro

ss-s

ectio

n of

topo

grap

hica

l sca

n re

pres

entin

g z f

y10

2030

4050

6070

8090

100

110

120

130

140

150

160

170

0

Virg

in s

oil

Foun

datio

n ba

seFo

unda

tion

ski

Test

Pile

3 ro

ute

-5 0 5zf: mm


Figure 6.4 Schematic of pile penetrometer analysis showing: (a) conversion of measured bending moment to a net horizontal load, H with line of action at depth, zLOA from soil surface, and (b) derivation of horizontal soil resistance, qh from H and zLOA

6.3.2. Pile penetrometer

Figure 6.4 illustrates the conversion of the bending moment measurements on the pile penetrometer to an idealised profile of net pressure, qh, acting on the pile. Soil strength is then derived by considering the failure mechanism of a pile under pure horizontal

Fixe

d

du

Line

of a

ctio

n of

ho

rizon

tal l

oad,

zLO

A

Stra

in g

auge

s

M

M2 M

1

M3

M4

z pile

H

pile

dzdMH

=-d

z

Embe

dded

de

pth,

ze

q hm

K

zDdH d

q h

Fixe

d

z

du

(a)

(b)


translation without rotation, where the undrained shear strength can be derived as (Chapter 5, Sahdi et al. (2015)):

pile

hpileu N

qs =, 6.3

The horizontal bearing capacity factor, Npile is assumed equivalent to the T-bar bearing factor, NT-bar = 10.5 over the embedded depth of the pile penetrometer, consistent with the use of a constant NT-bar in the interpretation of su through the T-bar (Equation 6.2). Neglect of the near-surface variation in Npile and NT-bar has minimal influence in this soft soil.

The pile penetrometer translating horizontally in the soil is assumed to act as a cantilever beam subjected to a distributed horizontal soil resistance. The bending moment profile in the strain gauges can be represented by an equivalent net horizontal load, H acting at a point along the pile at a depth, zLOA from the soil mudline (Figure 6.4(a)). The magnitude of H is equal to the slope of the moment profile above the soil, dM(z)/dz, and zLOA is the depth where the bending moment distribution projected from the recorded moment loads M1 to M4 reaches zero. A least square method is employed to calculate H and zLOA from the best-fit line representing the four measured moment loads.

H and zLOA are then used to calculate the distribution of net pressure, qh, where this profile can be defined by two unknown parameters (e.g. a mudline value and a linear increase with depth). H is equivalent to the total net pressure, qh acting along the embedded depth (ze) of the pile penetrometer (Figure 6.4):

dzqdzqDH

zh

z

h

e

∫∫−

−=0

0 d

6.4

The second term on the right hand side of Equation 6.4 is the additional horizontal resistance mobilised when the soil elevation encountered by the pile penetrometer changes relative to the soil elevation at the location of pile insertion by dz (Figure 6.4(b)).

zLOA can be expressed as the ratio of the total moment about the mudline level and the net horizontal load arising from the soil resistance on the embedded portion of the pile penetrometer as:


dzq

zdzq

ze

e

z

h

z

h

LOA

∫

∫=

0

0 6.5

6.4. Part I: Strength assessment in virgin soil

This section presents the results of the penetrometer tests carried out on virgin soil with the aim to quantify the shear strength properties of the soil. Soil strength is assessed under two conditions: (1) continuous cyclic remoulding (Pile1 and T-bar1 tests), and (2) cyclic remoulding with intervening reconsolidation (Pile2 and T-bar2 tests).

6.4.1. Intact shear strength

Vertical load, V and net horizontal load, H acting on the T-bar and pile penetrometers are plotted against the penetrometer displacements for cyclic tests with continuous remoulding cycles on virgin soil in Figure 6.5(a) and Figure 6.5(b), respectively. Figure 6.5(b) also includes a plot of the depth for the line of action, zLOA of the horizontal load. The load-displacement response during the first penetration of the T-bar and the first sweep of the pile penetrometer is marked by thicker black lines in the said figures. The first sweep of the pile penetrometer is characterised by an initial peak value of H which is due to the effect of consolidation following insertion of the pile penetrometer, followed by a steady residual value after a horizontal pile translation of about 20 mm (~ 4·D). Cyclic penetration and extraction of the T-bar was carried out over the depth range 40–60 mm after a full penetration to 85 mm, while cyclic sweep of the pile penetrometer was carried over the full length of the first sweep (40 mm). Vertical and horizontal loads on the T-bar and pile penetrometers were seen to degrade during the cyclic tests.

Figure 6.6(a) shows the estimates of the intact undrained shear strength, su0 within the upper 30 mm of virgin soil (equal to ze), obtained from the first penetration and the first sweep responses (i.e. N = 0.5) of the T-bar and pile penetrometers, respectively.


Figure 6.5 Penetrometer tests in virgin soil with continuous remoulding cycles showing: (a) vertical load measured by the T-bar, V plotted against penetration depth, z, and (b) horizontal load, H and corresponding depth for the line of action, zLOA derived from the pile penetrometer plotted against horizontal pile translation, y

Figure 6.6 Intact undrained shear strength from T-bar and pile penetrometers: (a) undrained shear strength profiles, and (b) ratio of pile to T-bar undrained shear strengths, su0,pile(peak)/su0,T-bar


The intact undrained shear strength as assessed through the T-bar (Equation 6.2) was found to increase linearly with depth. A linear fit to this variation of strength with depth within z < ze is given by:

kzss umbarTu +=−,0 6.6

where sum = 0.66 kPa is the virgin soil mudline shear strength, and k = 0.073 kPa/mm (0.73 kPa/m in prototype scale) is the strength gradient.

To derive the intact undrained shear strength through the pile penetrometer (Equation 6.3), a linear profile of qh with depth was assumed to concur with the shape of the strength profile inferred from the T-bar on virgin soil. The assumed qh increases linearly with depth at a rate of K from a net pressure of qhm at the mudline level (Figure 6.4(b)). qhm and K can be obtained by simultaneously solving for Equation 6.4 and Equation 6.5 with H and zLOA being known variables (Figure 6.5(b)). On virgin soil, a minimal change in soil surface elevation within the pile route was observed during the first sweep (dz = 0), effectively eliminating the second term on the right hand side of Equation 6.4.

Figure 6.6(a) shows the undrained shear strength profiles derived from the pile penetrometer on virgin soil representing the initial peak in horizontal load (su0,pile(peak)) and the steady residual horizontal load (su0,pile(res)) (see Figure 6.5(b)). T-bar estimate of the intact shear strength falls between these two pile penetrometer estimates, where for a given depth, su0,pile(peak) and su0,pile(res) were found greater and lesser than su0,T-bar, respectively. This observation is consistent with the findings reported by Sahdi et al. (2015) who compared the same set of penetrometers.

As mentioned above, su0,pile(peak) reflects a raised undrained shear strength following consolidation of the soil around the pile penetrometer after installation. This can be estimated analytically using cavity expansion theory as presented in Randolph et al. (1979). The analytical solution predicts a ~ 35 % increase from intact unconsolidated value (given by su0,T-bar) after an elapsed time factor of T = cht/D2 of 5.1, where t is the time between installation and first sweep of the pile penetrometer (Figure 6.2(b)), and ch is the horizontal (radial) coefficient of consolidation chosen at the mid-level of the pile embedment following Equation 6.1. The obtained ratio of su0,pile(peak) over su0,T-bar with depth is plotted in Figure 6.6(b) and close to the analytical solution.


6.4.2. Fully remoulded shear strength

The evolution of soil strength through continuous remoulding cycles in virgin soil is presented in Figure 6.7. Cyclic undrained shear strength profiles as derived from the T-bar (during penetration) and pile penetrometer (residual horizontal load condition during forward sweeps) are shown in Figure 6.7(a), indicating a reduction in soil strength from the intact value with increasing loading cycles.

A strength variation factor, ∆su defined as the ratio of the cyclic to intact soil strengths, is presented in Figure 6.7(b) as a function of cycle number, N. The remoulded strength (su during N > 0.5) is inferred at different depths of the cycled soil where the fully remoulded variation factor, drem and the rate of strength degradation with loading cycles were found similar for different depth locations in the T-bar test. The obtained drem (Table 6.2) was reached after N = 5 cycles. This value is consistent with other published results in normally consolidated kaolin (Hodder et al. (2010), Zhang et al. (2011), Sahdi et al. (2015)).

Figure 6.7 Evolution of soil strength through continuous remoulding cycles in virgin soil: (a) cycle by cycle undrained shear strength profiles (penetration in T-bar and forward sweeps in pile penetrometer), and (b) strength variation factor, ∆su with cycle number, N

Table 6.2 Fully remoulded strength propertiesas assessed by T-bar and pile penetrometers

Property T-bar Pile penetrometer

Fully remoulded degradation factor, drem 0.36 0.42

Cycle number required to achieve 95% degradation from the initial strength, N95

3 2


In contrast, the pile penetrometer inferred different values of drem at different depths, where Figure 6.7(b) shows a regain in strength near the pile toe the last part of the test, a behaviour consistent with data reported in Sahdi et al. (2015). The time delay between consecutive penetrometer passes allowed for reconsolidation of the remoulded soil. This reconsolidation had more effect on the pile penetrometer response than on the T-bar because the amplitude of the cyclic movement of pile penetrometer is greater, resulting in a greater consolidation duration. The pile penetrometer also affects a zone of soil closer to a drainage boundary (i.e. free soil surface), allowing a faster rate of dissipation. By comparing the dimensionless dissipation time, T = cvt/zmax2 (where cv is inferred at the level of zmax, with zmax being the maximum vertical length of the drainage path from the cycled zone), it is found that the cyclic pile penetrometer test has an accumulated dissipation time 5 times longer than the T-bar test at the end of N = 10.

The change in remoulded strength assessed through the pile penetrometer (on average over ze) and from the T-bar test follow the commonly-used exponential degradation curve pattern (Einav and Randolph (2005)) given by:

( )[ ]( )

95

5.03

1 NN

remremu es−−

−+=∆ dd 6.7

where N95 is the number of cycles required to achieve 95 % of drem from the intact strength.

Table 6.2 tabulates the values of drem and N95 that provided best-fit to the T-bar and pile penetrometers responses in Figure 6.7(b).

6.4.3. Remoulded shear strength with reconsolidation

Results for tests T-bar2 and Pile2 in which the penetrometers were cycled in virgin soil with intervening periods of reconsolidation (780 sec, 0.25 years, prototype scale) between each remoulding cycle are presented in this subsection (see Table 6.1 or Figure 6.2(b)).

The load responses are shown in Figure 6.8(a) and Figure 6.8(b), respectively. The derived cyclically-evolving undrained shear strength profiles are shown in Figure 6.9(a). The strength profiles from the pile penetrometer are inferred from horizontal loads at horizontal pile translation of y = D (Figure 6.8(b)). These results indicate an increasing soil strength with increasing cycles of remoulding and reconsolidation within the cycled zone.


In the T-bar test, the gain in soil strength due to consolidation is most apparent at depths greater than 40 mm below the original soil surface. At shallow positions, the gain in strength is masked by the reduction in the soil depth at that same vertical position, due to settlement of the surface. This settlement at the location of T-bar2 test after completion of the test is visible in Figure 6.10(a).

Figure 6.8 Penetrometer tests in virgin soil with remoulding cycles interspersed with consolidation episodes showing (a) vertical load measured by the T-bar, V plotted against penetration depth, z; (b) horizontal load, H and corresponding depth for the line of action, zLOA derived from the pile penetrometer plotted against horizontal pile translation, y


Figure 6.9 Evolution of soil strength through continuous remoulding cycles interspersed with consolidation episodes in virgin soil: (a) cycle by cycle undrained shear strength profiles (penetration in T-bar and forward sweeps in pile penetrometer), and (b) strength variation factor, ∆su with cycle number, N

After completing the test cycles in T-bar2, the T-bar was penetrated to a depth of 95 mm before finally extracted (Figure 6.8(a)). This post-cycle test revealed an even greater degree of soil hardening beneath the cycled zone, reflecting a maximum 7.5 fold increase in soil strength in a zone of soil 1.5 T-bar diameters beneath the deepest location reached by the invert of the T-bar penetrometer. In this zone the soil must still experience some shearing


as the T-bar approaches then retreats, but to a lower strain level and with only one event per cycle (rather than two, one during each direction of penetrometer movement). The observed strength gain suggests that at this location, the ‘benefit’ of pore pressure generation and dissipation still prevails, but the loss of strength from remoulding is less, due to the lower disturbance.

Similar reconsolidation effects are apparent in the pile penetrometer results. In Figure

6.8(b), a peak in horizontal load is observed in the load-displacement response during forward sweeps following a period of consolidation when the pile was held fixed at y = 0. This peak load increases with increasing loading cycles (inset figure in Figure 6.8(b)). The residual horizontal load (H at y > 4·D) also increases with increasing cycles for N < 10. For N > 10, this load reduces when the volume of soil mobilised ahead of the pile during horizontal translation diminishes due to local settlement of the soil surface, as evidenced by the post-test photograph in Figure 6.10(b). The depth for the line of action of load H is also plotted in Figure 6.8(b), and shows that this depth is unaffected by the changing magnitude of the horizontal load and remained near-constant at zLOA ~ 0.6·ze during the loading cycles.

The change in soil strength (∆su) for cyclic penetrometer tests with intervening consolidation periods is shown in Figure 6.9(b). ∆su from the T-bar is derived from z = 40 mm, whereas this factor is derived from su at y = D, averaged over the 30 mm embedment of the pile penetrometer. Also included in this figure is the evolution of the sliding resistance of a sliding foundation with intervening consolidation of similar duration to the penetrometer tests (see MMUD1 test in Chapter 2, and Table 6.3). In all cases the reduction in strength during undrained soil failure (either through cyclic remoulding in T-bar and pile penetrometers, or shearing to failure of soil beneath a sliding foundation) is overridden by the gain in strength from reconsolidation (White and Hodder (2010), Chapter 2, Chapter 3, Chapter 4). The cyclic penetrometer tests match the sliding foundation response in terms of the rate of strength increase with loading cycles, and the final cyclic to intact soil strength ratio. In all cases, cyclic to intact soil strength ratio plateaued at ~ 3 after 20-25 loading cycles.

The rise in soil strength resulting from periodic remoulding and intervening consolidation can be captured by an analytical model based on critical state soil mechanics (e.g. White and Hodder (2010); Chapter 4) which relates the gain in soil strength, ∆su with the reduction in void ratio per consolidation cycle, ∆e as:


∆

=∆lesu exp 6.8

l is the slope of the normally consolidated and critical state lines (NCL, CSL) in effective stress-void ratio (σ′v - e) space (Table 6.4, Figure 6.11). e decreases with increasing cycle concurrent to the decrease in excess pore pressure generated and dissipated during successive remoulding and consolidation cycles, respectively.

The ratio of cyclic reduction in void ratio and the total change in void ratio, ∆ef is given by:

−=

∆∆ ∑

=

−

1

1

1N

N

fee

lκ

lκ 6.9

where κ is the slope of the reconsolidation line (RCL) in σ′v - e space (Table 6.4, Figure

6.11). The total change in void ratio, ∆ef is simply given by the vertical distance between the NCL and CSL, which can be shown as a function of the normally consolidated strength ratio (su/σ′v)NC (~ 0.15 in present tests, see Chapter 2) by:

−=∆

NCv

uf

sM

e'

2lnσ

l 6.10

where M is the critical state friction constant (Table 6.4).

Figure 6.10 Post-test photos: (a) T-bar2, and (b) Pile2

(a) (b)

Pile location during

consolidation


Table 6.3 Foundation test

Property Unit Value

Operational vertical bearing pressure ratio, qop/qu [-] 0.3

Sliding distance mm (m, prototype scale) 25 (2.5)

Displacement rate mm/s 1

Intervening consolidation duration per displacement cycle sec (years, prototype scale) 780 (0.25)

Number of cycles, N [-] 40

Figure 6.11 Critical state interpretation of remoulding and reconsolidation cycles showing the state path in vertical effective stress, σ′v and void ratio, e space of a soil element undergoing (a) full, and (b) partial consolidation between remoulding cycles


Above framework considers full consolidation of soil in between remoulding cycles (Figure

6.11(a)). The effect of partial consolidation can be incorporated in above analysis using consolidation settlement or excess pore pressure dissipation models to deduce the degree of consolidation or percentage of excess pore water pressure generated/dissipated, U per loading cycle (Figure 6.11(b)).

Figure 6.11(a−b) shows the cycle by cycle change in void ratio and effective vertical stress representing a soil element within the penetrometer route undergoing undrained failure with full and partial consolidation occurring between remoulding cycles, respectively. In this analysis, the state path starts on the NCL (point A), and moves to the CSL (point B) during remoulding, generating an excess pore water pressure of umax. During consolidation, the state path moves from points B to C, with the increase in σ′v equivalent to the dissipated excess pore pressure, umax for full consolidation or umax·U for partial consolidation (alternatively, ∆e·U when using consolidation settlement models). This process repeats with increasing loading cycles until the soil undergoes sufficient cycles of failure, pore pressure generation and reconsolidation to reach a final critical void ratio (F), thereby eliminating any tendency for contraction and further excess pore pressure generation. The analytical prediction of strength increase through Equations 6.8−6.10 is shown to accurately capture the observed evolution of soil strength from cyclic penetrometer tests with intervening periods of consolidation in Figure 6.9(b).

6.5. Part II: Strength assessment in foundation footprint

This section presents the results of penetrometer tests Pile3 and T-bar3 carried out within the footprint of a sliding foundation (see Figure 6.3). The aim is to assess the nonlinear undrained shear strength profile at a discrete location within the footprint through a T-bar test and compare with a strength profile from the pile penetrometer. Subsequently a continuous soil strength ‘map’ across the footprint is derived from the pile penetrometer results to demonstrate the determination of a continuous (lateral) record of soil strength.

Detailed results of the sliding foundation test can be found in Chapter 2 and pertinent information about the test is summarised in Table 6.3. In Figure 6.9(b), the sliding resistance measured during the foundation tests (expressed as the ratio of the cyclic sliding resistance and the sliding resistance during the first cycle) was seen to increase with loading cycle N. The increase in sliding resistance is due to dissipation of shear induced excess pore


pressure in the soil underneath the foundation (Chapter 2, Chapter 4). The corresponding undrained shear strength gain is assessed in this section.

6.5.1. Nonlinear undrained shear strength

Figure 6.12(a) compares the intact undrained shear strength profile in virgin soil (T-bar1 test), and within the foundation footprint (T-bar3 test). The strength increase in the footprint soil is quantified in Figure 6.12(b) through the strength variation factor, ∆su, which in this case is given by the ratio of the shear strengths in the footprint over the virgin soil. The increase in undrained shear strength affected a depth of influence, zcons ~ 15 mm, or about 30 % of the foundation breadth, B = 50 mm. The gain in strength is greatest near the mudline, more than doubling at that depth. This high strain shearing zone generates maximum excess pore pressure during foundation sliding that consequently translates to greater gains in strength following the dissipation of excess pore pressure during consolidation.

Table 6.4 Critical state parameters for kaolin clay (after Stewart (1992))

Property Value

Critical state friction constant, M 0.92

Slope of normal consolidation line, l 0.205

Slope of swelling line, κ 0.044


Figure 6.12 Penetrometer tests in foundation footprint soil showing: (a) undrained shear strength profile in a sliding foundation footprint compared against intact shear strength in virgin soil, and (b) strength variation factor, ∆su profile in a sliding foundation footprint compare between T-bar and pile penetrometers estimates

Figure 6.13 Conversion of net horizontal load, H into soil resistance parameters for a pile penetrometer translating through soil with nonlinear strength profile

ze

Fixed

du

qhm,pile

Kpile

q

zLOA

H + dH

Kcons

qcons

zcons


As shown by the T-bar test result in Figure 6.12, the strength increase near the soil surface of the sliding foundation footprint resulted in a nonlinear variation of undrained shear strength with depth. To concur with this shape, interpretation of the pile penetrometer assumes a bi-linear profile of qh as illustrated in Figure 6.13. Within zcons, qh decreases linearly with depth at a rate of Kcons from a net pressure of qcons at the footprint mudline level. Below the zone of influence, qh matches the virgin soil condition. The two unknowns that define the bi-linear qh profile in Figure 6.13, zcons and Kcons, are determined by simultaneously solving for Equation 6.5 and Equation 6.11:

( ) dzqD

dHH ez

h∫=+

0

6.11

where (H + dH) is the effective horizontal load acting on the pile, with dH being the additional horizontal load mobilised due to the changing elevation of the footprint, dz. dH is derived by solving for the second term on the right hand side of Equation 6.4, assuming a linear profile for qh in this case (Figure 6.4(b)). The change in soil elevation, dz used in the limits of integration in Equation 6.4 is inferred from the elevation profile of the foundation footprint, zf shown in Figure 6.3. The deduced dz is plotted against horizontal pile translation, y in Figure 6.14(a) alongside the depth for the line of action, zLOA of the net horizontal load, H. Change in zLOA with y matches the change in the profile elevation of the footprint where zLOA is seen to shift upward when the pile penetrometer encounters a negative change in elevation (a higher soil surface, e.g. when the pile penetrometer moves out of the basal footprint and encounters the slope made by the foundation ski). Within the basal footprint, zLOA/ze ~ 0.55, a ratio lower than observed in virgin soil (Figure 6.5(b)) which suggests that the geometric centre of a trapezoidal resistance profile moved closer to the surface, consistent with increased resistance near the footprint mudline.

The derived additional horizontal load dH, net horizontal load H, and effective horizontal load (H + dH) acting on the pile penetrometer are plotted against the horizontal pile translation, y in Figure 6.14(b).

The change in mudline shear strength, dsum = (qcons – qhm,pile)/Npile, the strength gradient within the depth of influence, kcons = Kcons/Npile and the location of zcons within the Pile3 test route as inferred following above procedure are shown in Figure 6.15(a-c). Using these


values, the undrained shear strength profile through the foundation footprint can be determined by:

>+

<<−+=

conspilepileum

consfconsumpileumfu

zzzks

zzzzksss

if

if

,

,,

d 6.12

The strength variation factor, ∆su with depth obtained through Equation 6.12 from the Pile3 test matches that obtained from T-bar3 test as shown in Figure 6.12(b). The factor representing the pile penetrometer estimate was derived at the footprint location, y = 35.5 mm (Figure 6.3, Figure 6.15), which is equidistant from the location of the T-bar3 test to the foundation centreline during installation, along y axis.

6.5.2. Continuous shear strength profile

A continuous shear strength profile along the route of the pile penetrometer was generated using Equation 6.12.

Figure 6.16(a−b) presents the soil strength maps on virgin soil, showing good agreement between the Pile1 test and from the Pile3 test when the penetrometer is outside the foundation footprint and soil berm during the last 30 mm of the test (see Figure 6.3). This similarity is further demonstrated in Figure 6.16(c) which shows discrete su profiles obtained within the penetrometer routes presented in Figure 6.16(a−b).

Figure 6.16(d−e) shows the generated maps of soil strength, su and strength variation factor, ∆su (ratio of footprint over virgin soil su) for the Pile3 test. These maps reveal a varying and localised soil strength increase due to consolidation of the soil beneath the foundation. The strength gain within the basal footprint is highest at, and decreases away from, the centre (also shown in Figure 6.15(a)). At the centre of the basal footprint, the strength is more than twice the value of the intact virgin shear strength at that corresponding depth, corroborating the T-bar3 test result shown in Figure 6.12(a).

The pile penetrometer result also revealed a strength increase within the soil berm formation next to the foundation footprint, and showed that positive gain in soil strength can extend up to a lateral distance of 0.8·B from the edge of the foundation base.


Figure 6.14 Change in elevation on foundation footprint soil showing (a) local change in mudline level dz, and depth for line of action, zLOA of the horizontal load H, and (b) additional horizontal load dH, net horizontal load H, and effective horizontal load (H + dH) acting on the pile penetrometer plotted against the horizontal pile translation, y

Figure 6.15 Soil strength parameters within foundation footprint: (a) change in mudline shear strength, dsum, (b) strength gradient within depth of influence, kcons, and (c) depth of influence, zcons


Figure 6.16 Contour plots of undrained shear strength in (a) virgin soil in free field location, (b) virgin soil adjacent to foundation footprint, (c) discrete locations within the pile penetrometer route, (d) foundation footprint, and (e) strength variation factor, ∆su in foundation footprint

6.6. Final remarks

This chapter investigated the strength changes occurring near-surface soil during cyclic remoulding, taking into account the effects of intervening reconsolidation. A simple process of assessing and interpreting near-surface soil resistance using a novel pile penetrometer was presented, and was validated through a suite of centrifuge tests, with comparison to the conventional T-bar penetrometer.

Results show the pile penetrometer produces shear strength estimates comparable to T-bar penetrometer data.

Soil strength recovery occurs even during continuous remoulding cycles and this is evident in an increase in soil strength evident in the latter part of the pile penetrometer tests. This


highlights the importance of recognising that reconsolidation may cause the apparent remoulded strength observed in this type of test to exceed the true remoulded strength.

Cyclic penetrometer tests that included deliberate periods of intervening reconsolidation between cycles showed the same rate of increase in strength with loading cycles as a periodically sliding foundation, enabling their potential use as predictive tools.

Finally, the study demonstrated the novelty of the new pile penetrometer in providing a detailed mapping of soil strength profile over a continuous lateral distance, which is an improvement from the conventional vertically-penetrating penetrometers which can only provide data at discrete, spaced out locations.

This chapter advances the understanding of the behaviour of near-surface soil relevant to the conditions in offshore soft clays, particularly when subjected to long term cyclic loading. It illustrates the use of a novel in situ soil characterisation device adapted for the particular purpose of assessing shallow and low-strength fine-grained sediments, over a continuous lateral extent.


This work forms part of the activities of the Centre for Offshore Foundation Systems (COFS), currently supported as a node of the Australian Research Council’s Centre of Excellence for Geotechnical Science and Engineering, and through the Fugro Chair in Geotechnics, the Lloyd’s Register Foundation Chair and Centre of Excellence in Offshore Foundations and the Shell EMI Chair in Offshore Engineering. The work presented in this chapter is supported through ARC grant DP140100684.

Chapter 7. Pipeline installation response observations

Prologue

The preceding chapters have established the general concepts of remoulding and reconsolidation of seabed deposits through the whole-life response of a subsea mudmat foundation supporting a pipeline, and of the changes in soil strength interacting with this infrastructure, enabling a correct prediction of the long-term overall response. The recurring theme in the earlier chapters is the significant influence of remoulding and reconsolidation on the operational performance of infrastructure laid on the seabed. Drawing on this theme further, Chapter 7 presents results of centrifuge tests involving a model pipeline with a loading programme designed to investigate the influence of the level of soil remoulding during installation, and the degree of post-lay consolidation on the subsequent axial and lateral breakout resistance of the pipeline.

The centrifuge tests presented in Chapter 7 were carried out in a separate strongbox of clay to that presented in the chapters regarding the foundation tests, but again on a normally consolidated kaolin clay as in the preceding chapters.

Chapter 7 has been accepted for publication in Géotechnique under the title “Softening and consolidation around seabed pipelines: Centrifuge modelling”(Cocjin et al. (2017a)).

7-141


Abstract

Solutions for lateral breakout and axial response of submarine pipelines are well established if the undrained shear strength conditions of the soil are known and defined simply (such as uniform or increasing proportionally with depth). In reality, the geometry of the free surface and the distribution of undrained shear strength around a submarine pipeline post-lay are affected by the lay process. This is because of soil berms that form adjacent to the pipe, and remoulding and subsequent reconsolidation of the seabed. The effect of post-lay consolidation on the subsequent lateral and axial response of submarine pipelines has not been previously investigated through physical model testing.

This paper presents results from centrifuge model tests describing lateral breakout behaviour of a pipe on soft clay as a function of (i) pipe installation conditions, (ii) post-lay pipe weight and (iii) consolidation prior to break out. In addition, the effect of post-lay consolidation on axial pipe response is studied. The experimental results are compared with available numerical and analytical predictions.

The results quantify the influence of the installation process, pipe weight and post-installation consolidation on the lateral break out resistance and trajectory of the pipe and also the axial pipe response, and show how existing prediction methods can capture these effects.

7.1. Introduction

Networks of in-field pipelines are a central component of offshore subsea developments, creating an increasing need to better understand pipeline behaviour during installation and operation to improve design outcomes.

Offshore in-field pipelines are generally laid directly on the seabed, and left unburied. The pipe partially embeds into the seabed during the laying process due to its self-weight and dynamic lay effects. The lay process submits the soil to disturbance and remoulding, resulting in softening of the seabed deposit surrounding the newly installed pipe. However, after laying, the vertical load on the seabed is reduced to the static pipe weight, and the soil around the pipe consolidates under that load. For the soft, normally consolidated soils typically found offshore, this consolidation process leads to an increase in the strength of the seabed deposit surrounding the pipeline.

Pipeline installation response observations | 7-143

The dominant operational forces on deepwater in-field pipelines are from internal temperature and pressure, rather than external hydrodynamic loading. High pipeline temperature causes longitudinal expansion, which is opposed by axial resistance between the pipe and the seabed (Bruton et al. (2008)). Excessive compressive forces arising from thermal expansion or high internal pressure lead to buckling of the pipeline in the lateral direction, with the buckling response depending critically on the soil resistance. Many subsea developments adopt the practice of controlled lateral buckling where a pipeline is allowed to buckle tolerably at designated locations to relieve the thermal and pressure-induced loading (Sinclair et al. (2009)). Lateral buckles along the pipeline can significantly influence the global response of the flowline including the attached infrastructure such as the pipeline end termination or manifolds (PLET/PLEMs).

In recent years, axial and lateral pipe–soil interactions have been studied extensively by researchers, with a particular focus on the undrained conditions that generally prevail during lateral pipe movements on fine-grained soils. Solutions for penetration, axial and lateral responses using analytical approaches (Randolph and Houlsby (1984), Murff et al. (1989), Martin and Randolph (2006), Randolph and White (2008b), Martin and White (2012), Randolph et al. (2012)) and finite element analysis (FEA) both through small-strain (Aubeny et al. (2005), Merifield et al. (2008), Merifield et al. (2009), Krost et al. (2011), Chatterjee et al. (2014)) and large-deformation approaches (Wang et al. (2010), Chatterjee et al. (2012c), Chatterjee et al. (2012a), Chatterjee et al. (2012b), Chatterjee et al. (2013)) are plenty, and can provide a prediction of pipe axial or lateral breakout capacity if the undrained shear strength conditions of the soil are known and defined simply (such as uniform or increasing linearly with depth). Experimental investigations into pipeline behaviour have also been performed at large scale and at reduced scale in a centrifuge, as reported by Bruton et al. (2006), Bruton et al. (2008), Cheuk et al. (2007), Dingle et al. (2008) and Cardoso and Silveira (2010). These studies have led to empirical expressions for the unconsolidated lateral breakout resistance and the subsequent steady residual resistance, simulating a model pipe that breaks out immediately after installation.

In reality, the geometry of the free surface and the distribution of the undrained shear strength around a pipeline post-lay can be significantly affected by the remoulding process during the pipe laying. The axial and lateral resistance subsequently available between the pipeline and the soil is influenced by consolidation of the soil around the pipeline that takes


place between the laying process and when the pipeline operation starts. The resulting changes in soil strength and pipe-soil resistance are the subject of this chapter. Results of a suite of geotechnical centrifuge tests designed to explore the changes in axial and lateral breakout resistances resulting from installation disturbance and reconsolidation in soft clay are reported and interpreted.

7.2. Experimental program

7.2.1. Apparatus

7.2.1.1. Centrifuge and actuation

The tests were carried out in the 1.8 m radius beam centrifuge at the Centre for Offshore Foundation Systems at the University of Western Australia (Randolph et al. (1991)). The platform of the rotating arm holds a strongbox with dimensions 650 mm by 390 mm in plan and 325 m deep with a maximum payload of 200 kg at 200g. Box-mounted actuators control vertical and horizontal loads or displacements of the model through an instrumented loading arm. In-house software is used for control and data acquisition during tests (Gaudin et al. (2009), De Catania et al. (2010)). The tests reported in this chapter were carried out at 25g.

7.2.1.2. Model pipe

A schematic drawing of the model pipe is shown in Figure 7.1(a-b). The model pipe has a diameter of 30 mm, 150 mm long, representing a diameter of D = 0.75 m and a length of L = 3.75 m at prototype scale. The pipe was fabricated from a solid piece of aluminium with sand glued to the bottom half to provide a rough pipe-soil interface.

The pipe section was instrumented with 6 pore pressure transducers (PPTs) located along the length of the underside of the pipe at the invert and at the sides between the pipe axis and invert. The arc length between the invert and side PPTs is 15.7 mm (0.39 m, prototype

scale), forming a central angle of θPPT = 60°.

7.2.2. Soil sample

To make the model seabed, kaolin clay slurry with water content of 120 % (or twice its liquid limit) was mixed for 2 days in a vacuum. The slurry was poured into the strongbox over a sand drainage layer covered with a geotextile. The sample was consolidated in-flight,


continuously for 65 hours at the test acceleration of 25g to achieve a normally consolidated deposit. Full consolidation was verified via a linearly increasing shear strength profile with depth obtained from ball penetrometer tests. The top of the sample was then scraped to provide a flat and smooth working surface, removing 2-3 mm of clay in the process, leading to a nominal non-zero mudline strength.

Figure 7.1 Schematic drawing of model pipe: in (a) transverse and (b) plan view; and (c) idealisation of loads acting on the pipe


A miniature ball penetrometer (Chung and Randolph (2004), Low et al. (2007), Colreavy et al. (2016)) with diameter of 15 mm (0.375 m, prototype scale) was used to measure the shear strength profile of the soil sample. The ball penetrometer was penetrated into the soil sample at a rate of 1 mm/s to ensure undrained conditions (Randolph and Hope (2004)). The first penetration was carried out up to a depth of 88 mm (2.2 m prototype scale), after which 10 cycles of penetration and extraction were carried out between depths 24 mm (0.6 m) and 70 mm (1.75 m) before the penetrometer was completely extracted.

The penetration resistance measured by the ball penetrometer, qball was corrected for unequal pore pressure and overburden pressure following the expression defined by Chung and Randolph (2004):

( )[ ][ ]psvballm AAuqq /100 ασ −−−= 7.1

where qm is the net penetration resistance, σv0 is the in situ total overburden stress, u0 is the hydrostatic pressure, As/AP is the ratio of the shaft to the projected area of the ball penetrometer, and parameter α is the net area ratio of the load cell core to the shaft area (equivalent to 0.85 for the tests considered here).

The undrained shear strength, su, is back calculated from the net penetration resistance, qm as:

−=

p

buoym

ballu A

Fq

Ns 1 7.2

where Fbuoy is the soil buoyancy force on the ball penetrometer and Nball is the constant ball penetrometer factor, assumed equivalent to 10.5, typical for penetrometer penetration tests (Low et al. (2007), Colreavy et al. (2016)).

The in situ and remoulded shear strength profiles derived from the cyclic ball penetrometer test are shown in Figure 7.2(a) and Figure 7.2(b), respectively. The shear strength profile was calculated by adopting a constant value for Nball over the entire sample depth, which introduces minimal near-surface error for a normally consolidated soil (Colreavy et al. (2010); Low et al. (2010)). The resulting intact, in situ, undrained shear strength, su0 was approximated to increase linearly with depth, z within 0 < z (mm) < 40 (1 m depth in prototype scale) as:


Figure 7.2 Characterisation of the soil model using a ball penetrometer showing: (a) undrained shear strength, su with depth, z (prototype scale), and (b) degradation of soil strength during cyclic penetrometer test plotted in terms of remoulded strength ratio, drem,cyc = su,cyc/su0 against cycle number, N

kzss umu +=0 7.3

with mudline strength of sum = 0.1 kPa, and strength gradient of k = 0.7 kPa/m. Degradation in shear strength due to remoulding during the cyclic phase of the ball penetrometer test shows a final remoulded strength of the soil, drem = 0.47 (Figure 7.2(b)), where drem is defined as the ratio of the remoulded to intact strength as measured halfway of the cycled route (z = 47 mm, or 1.175 m in prototype scale). The evolution of the remoulded shear strength with loading cycle shown in Figure 7.2(b) can be captured by the


commonly-used exponential degradation curve pattern (Einav and Randolph (2005)) given by:

( )[ ]( )

95

5.03

0

, 1 NN

remremu

cycu es

s −−

−+= dd 7.4

where su,cyc is the strength measured during the cyclic phase of the ball penetrometer test, and N95 = 2.5 is the number of cycles required to achieve 95 % of drem from the intact strength.

The moisture content profile of the soil model was also determined from core samples taken after all the tests, where an average effective unit weight, γ′ = 5.7 kN/m3 over the depth of the soil model was obtained.

7.2.3. Pipe testing programme

A series of pipe tests was carried out, as summarised in Table 7.1. Each test involved initial penetration of the pipe to a depth equal to half the diameter (w/D = 0.5) to simulate the installation or pipe ‘laying’ process. The pipe was then unloaded to an operative vertical load, Vop, defined as a proportion of the load, Vmax achieved at a penetration of w/D = 0.5, where Vop represents the pipe weight. Unloading ratios, Vop/Vmax = 1, 0.5, 0.25, 0.125 were considered as detailed in Table 7.1.

Following installation, axial or lateral breakout of the pipe was simulated immediately, or after a period of consolidation that allowed essentially full dissipation of the excess pore pressures developed during installation. The pipe was translated axially (dy in Figure 7.1(b)) and laterally (dx in Figure 7.1(b)) under constant vertical load, Vop allowing the pipe to rise or fall to maintain this load, to assess the breakout resistance.

Two alternative ‘laying’ methods were considered: undrained monotonic vertical penetration and undrained cyclic installation, simulated by a specified pattern of oscillations, thus remoulding the surrounding soil. The adopted pattern of lateral displacement during the cyclic penetration mimics the disturbance and remoulding associated with a real lay process.


Table 7.1 Pipe tests programme

Load

ing

cond

ition

s

§ † § § † † † † ‡

Deta

iled

test

pro

cedu

re

§ - M

onot

onic

pene

trat

ion

to w

/D (V

max

) → U

nloa

d to

Vop

/Vm

ax →

Bre

akou

t

† - M

onot

onic

pene

trat

ion

to w

/D (V

max

) → U

nloa

d to

Vop

/Vm

ax →

Cons

olid

ate

→ B

reak

out

‡ - C

yclic

pen

etra

tion

to w

/D (V

max

) → U

nloa

d to

Vop

/Vm

ax →

Cons

olid

ate

→ B

reak

out

Cons

olid

atio

n pr

ior t

o br

eak-

out

No

Yes N

o

No

Yes

Yes

Yes

Yes

Yes

Vert

ical in

stal

latio

n

Mon

oton

ic

Mon

oton

ic

Cycli

c w

ith o

scilla

tions

in

x di

rect

ion

Vert

ical lo

ad ra

tio, V

op/V

max

du

ring

post

-lay

cons

olid

atio

n

0.25

0.25

0.

25

0.12

5

1 0.5

0.25

0.12

5

0.25

Reco

rded

max

. pe

netr

atio

n re

sista

nce,

V m

ax: k

N/m

2.8

2.4 2.9

2.7

2.7

2.6

2.6

2.9

1.9

Initi

al

pene

trat

ion,

w

/D

0.5

0.5

Test

nam

e

Axia

l bre

akou

t

R4U

U_A

X

R4CU

_AX

Late

ral b

reak

out

R4U

U

R8U

U

R1CU

R2CU

R4CU

R8CU

Rem

R4CU


7.3. Undrained penetration response

The influence of installation or pipe ‘laying’ method on the pipe penetration response is presented in Figure 7.3.

Figure 7.3 Undrained pipe penetration response showing: (a) buoyancy resistance, Nbγ′w and vertical bearing pressure per unit length, V/D; (b) normalised vertical penetration resistance, V/Dsu0; and (c) excess pore water pressure at the pipe invert normalised by vertical bearing pressure per unit length, ∆uinv/(V/D), plotted against the normalised pipe embedment at the invert level, w/D, during penetration (inset in (a): pipe displacement in lateral and vertical directions (x/D – w/D) during monotonic and cyclic penetration)


The pipe penetration resistance is expressed in terms of the pipe vertical bearing pressure per unit length, V/D, and normalised vertical penetration resistance, V/Dsu0. Profiles with pipe invert embedment, w/D for different tests are shown in Figure 7.3(a) and Figure 7.3(b), respectively. An inset figure in Figure 7.3(a) shows the pipe displacements during penetration, indicating the trajectory of the monotonically and cyclically penetrated pipe cases.

The monotonic penetration response is highly repeatable as shown in Figure 7.3(a–b). A linear increase in V/D with depth is observed in these cases, with the response dominated by the linear variation of the undrained shear strength with depth (Equation 7.3). The increase in V/Dsu0 with depth on monotonic cases is compared against existing numerical solutions (Aubeny et al. (2005) and Chatterjee et al. (2012a), based on small-strain and large deformation finite element analyses, respectively) as shown in Figure 7.3(b). At w/D = 0.5, a normalised vertical penetration resistance of Vmax/Dsu0 ~ 10.5 is recorded in the centrifuge tests close to the value derived by Aubeny et al. (2005). The numerical solutions presented in Figure 7.3(b) considers V/Dsu0 as a sum of the soil resistance and a component due to buoyancy as the pipe becomes embedded within the soil, expressed as:

+=

00

'

ubc

u swNN

DsV γ

7.5

where the soil bearing factor, Nc reflects the component of the soil resistance, typically expressed in terms of a power law function of the penetration depth (Aubeny et al. (2005)). The pipe buoyancy resistance, Nbγ′w increases with depth as shown in Figure 7.3(a), where Nb is the self-weight factor given by:

DwAfN s

bb = 7.6

Nb is proportional to the potential energy needed to lift the displaced soil with a nominal weight of Asγ′ to the top of the pre-existing heave next to the pipe, with As being the cross-sectional area of the embedded pipe. When the displaced soil forms heave mounds and alters the geometry of the soil next to the pipe, the soil buoyancy is enhanced through the factor fb where an fb = 1 corresponds to no heave, following Archimedes’ principle (buoyancy force being equal to the weight of the displaced fluid). The effects of buoyancy and the changes in soil geometry and development of soil heave during penetration are not


considered in the upper bound plasticity solution presented by Randolph and White (2008b) which assumes a flat seabed surface, resulting in lower V/Dsu0 estimates compared to the values observed in the current centrifuge tests (Figure 7.3(b)).

Figure 7.4 Variation in pore water pressure along the embedded pipe in test R2CU, showing: (a) pore water pressure, u measured at different pore pressure transducers (PPTs), and penetration resistance V/D, during the whole test, plotted against time, t in prototype scale; (b) hydrostatic pore water pressure, u0 , and pipe invert record of pore water pressure, uinv, and excess pore water pressure, ∆uinv, plotted against normalised pipe embedment at the invert level, w/D during penetration


Existing solutions do not capture the more complicated penetration response exhibited by a cyclically penetrated pipe (Figure 7.3(b)). The cyclic penetration of the pipe mobilised a lower V/D and V/Dsu0 compared to monotonically penetrated pipes. The decrease in penetration resistance during the oscillating movements of the pipe is reflected by the elevated pore water pressure in the surrounding soil shown in Figure 7.3(c) which plots the excess pore water pressure at the pipe invert as a ratio of the pipe vertical bearing pressure per unit length, ∆uinv/(V/D).

7.4. Post-lay consolidation response

Figure 7.4(a) presents the variation with time, t (prototype scale) of the pore water pressure, u, relative to a datum of zero prior to penetration of the pipe, for each of the PPTs installed in the model pipe during penetration, post-lay consolidation, and lateral loading in test R2CU. The average pore pressure recorded by the invert and side PPTs are denoted as uinv and uside, respectively. In general, pore pressure around the pipe increases when the soil is loaded, as V/D increases, and when remoulded via the simulated dynamic lay process. However, pore pressure reduces at constant V/D during post-lay consolidation, during which time the excess pore water pressure at the pipe invert, ∆uinv which is equivalent to the difference between u0 and the invert pore water pressure, uinv as shown in Figure 7.4(b), dissipates.

The change in excess pore pressure at the pipe invert level, normalised by the maximum value recorded under the maximum vertical load, is shown in Figure 7.5(a) for various tests, with the time axis zeroed at the moment when the reduction in vertical load is complete. The subsequent unloading from Vmax to Vop is evident in a concurrent drop in excess pore pressure at the invert level.

The influence of pipe weight on the post-lay dissipation behaviour of the invert excess pore pressure is shown more clearly in Figure 7.5(b) which plots ∆uinv relative to V/D against time factor, T = cvt/D2 with cv being the vertical coefficient of consolidation. At the start of consolidation, the excess pore pressure is higher relative to the applied stress for increasing unloading ratio, Vmax/Vop. The additional excess pore water pressure generated by the cyclic penetration of the pipe is also evident in this figure (compare RemR4CU against R4CU in Figure 7.5(b)).


Figure 7.5(c) shows that the post-lay dissipation behaviour in pipe cases with Vop >0.5·Vmax (R1CU and R2CU) is close to the solutions derived from elasto-plastic (Chatterjee et al. (2012c)), and elastic (Krost et al. (2011)) small-strain FEA models. For pipes at a higher overloading ratio and with remoulding during installation, the additional excess pore pressure created by these effects initially leads to normalised excess pore pressures at the invert > 1. However, with dissipation, all responses converge towards the theoretical solution. The only exception is R8CU, which is an outlier. For this high overloading ratio, only small level of remnant excess pore pressure is needed at the invert to cause a high value of (∆u/∆uini)inv.

Figure 7.5 Dissipation-time histories of excess pore pressure at the pipe invert, ∆uinv during consolidation: (a) normalised by initial excess pore pressure at maximum vertical load, ∆uinv (max) plotted against time, t in prototype scale; (b) normalised by penetration resistance, V/D plotted against time factor, T = cvt/D2 and (c) normalised by initial excess pore pressure under operative consolidation load, (∆uini)inv plotted against time factor, T = cvt/D2, where t = 0 at the moment when the reduction in vertical load is complete


The dissipation of excess pore pressure during post-lay consolidation results in an increase in effective stress in the soil around the pipe. The effective stress increase can be illustrated by defining an effective contact enhancement factor, ζ′ given by the ratio of the effective normal force, N′ acting around the pipe-soil contact and the pipeline submerged weight per unit length, V (White and Randolph (2007), Krost et al. (2011)) as:

VN ''=ζ

7.7

At full consolidation (when the excess pore pressure is completely dissipated), the effective stress is equal to the total stress around the pipe. A total force, N can be obtained by summing the normal contact stresses over the pipe-soil contact perimeter, p and this force exceeds the pipeline submerged weight per unit length, V due to a ‘wedging’ effect around the curved pipe surface. The ratio ζ = N/V was derived by White and Randolph (2007) following the elastic solution for a line load acting on a half-space, assuming that the normal stress on the pipe wall varies with cosθ, where θ is the inclination from the vertical. ζ = N/V can then be obtained as:

θθθθζcossin

sin2+

==VN

7.8

where cosθ = 1 – 2(w/D). Through Equation 7.8, the total force, N acting on the pipe with embedment of w = 0.5D is 1.27V.

The effective force, N′ in Equation 7.7 is determined following the principle of effective stress as:

upNN ∆−=' 7.9

where ∆u̅ is the average excess pore pressure around the pipe, obtained in this case by linearly interpolating the recorded excess pore pressures at the pipe invert (∆uinv), the side PPTs (∆uside), and the zero pore pressure at the edge of the pipe and soil surface.

The distribution of the total radial stress, σr and the interpolated ∆u during consolidation, normalised by the prescribed vertical bearing pressure, V/D is shown in Figure 7.6(a) and Figure 7.6(b) for tests R4CU_AX and RemR4CU, respectively. Figure 7.6(a) also includes


the distribution of ∆u around the pipe in test R4UU_AX just before the pipe was displaced axially. These results are converted to the effective contact enhancement factor, ζ′ (Equation

7.7), varying with time factor, T = cvt/D2 in Figure 7.6(c) where the vertical coefficient of

consolidation, cv (m2/year) was assumed to vary with stress (in kPa), via the increase in mean effective stress at the pipe-soil contact, N′/p through the form cv = (0.3+0.16N′/p) 0.47 (Chapter 2).

Figure 7.6 Effect of consolidation on pipe-soil contact stresses showing distribution of the total radial stress, σr and the interpolated excess pore pressure, ∆u normalised by the prescribed vertical bearing pressure, V/D during tests (a) R4CU_AX, and R4UU_AX (before axial loading) and (b) RemR4CU, and (c) increase in effective contact enhancement factor, ζ′ with time expressed as time factor, T = cvt/D

2

Figure 7.6(c) shows that the elastic small-strain FEA solution by Krost et al. (2011) matches the increase in ζ′ with time for the case without vertical unloading (R1CU). In this case, the average excess pore pressure and the effective stress have equal contribution to the total stress immediately after vertical unloading, with the effective stress eventually increasing to total stress with the dissipation of the excess pore pressure. The increase in ζ′ with time can be expressed in form given by Equation 7.10 as:


( )

+

−+= m

UU

TT 501' ζζζζ 7.10

where ζ (Equation 7.8) and ζUU are the fully consolidated (T ∞) and unconsolidated (T ~ 0) undrained effective contact enhancement factors.

In Equation 7.10, T50 is the time factor when 50 % of the increase in ζ has occurred and m is a constant. Equation 7.10 is plotted in Figure 7.6(c) using m = 1.05, and T50 = 0.135 suggested for rough pipe with embedment of w = 0.5D (Chatterjee et al. (2012c)), and matches well the measured trends.

The unconsolidated undrained effective contact enhancement factor, ζUU reduces with increasing overload ratio, and is reduced further for the case with remoulding during pipe penetration (case RemR4CU). This is because the overloading and remoulding processes both create additional excess pore pressure, meaning that initially a lower portion of the pipe weight is carried by effective stress. After full dissipation, however, the effective contact enhancement factor returns to the total stress value (ζ′ = ζ), which for w/D = 0.5 is estimated as ζ = 1.27. An important consequence of this effect is that there is a lower axial friction initially available, as discussed in the following section, and Equation 7.10 combined with the observed values of ζUU provides a basis to estimate the time period over which this evolves.

7.5. Axial load-displacement response

7.5.1. Post-lay consolidation effects

The axial friction factor, Hax/V and normalised axial breakout resistance, Hax/Dsu0 are plotted against the normalised axial displacement, y/D for test with and without post-lay consolidation (R4CU_AX and R4UU_AX) in Figure 7.7(a) and Figure 7.7(b), respectively. Consolidation prior to axial breakout results in higher steady-state (‘residual’) axial resistance, and also a pronounced peak exhibited initially. The peak and residual resistances during axial displacement after post-lay consolidation, when expressed as a friction factor, are 3.5 and 1.6 times greater than the residual resistance with breakout immediately after installation.


Figure 7.7 Effect of consolidation on axial pipe resistance showing: (a) axial friction factor, Hax/V and (b) normalised axial breakout resistance, Hax/Dsu0, plotted against normalised axial displacement, y/D

7.5.2. Prediction of undrained axial breakout capacity

The increase in axial breakout resistance due to consolidation is directly linked to the effective contact enhancement factor, ζ′ (Equation 7.7) where the axial friction factor, Hax/V can be expressed as:

dζ tan'=V

Hax 7.11

where d is the pipe-soil friction angle. Using the excess pore pressure prior to axial loading, Equation 7.11 provides a good prediction to the observed axial residual resistance on both the consolidated and unconsolidated cases, assuming a pipe-soil friction angle of d = 27.5°, which is typical for kaolin at low stresses (Hill et al. (2012)).

7.6. Lateral load-displacement response

7.6.1. Installation and post-lay consolidation effects

The effect of post-lay consolidation and pipe ‘laying’ method on the lateral load-displacement response is shown in Figure 7.8(a) and Figure 7.8(b) which plots the normalised lateral resistance, H/Dsu0 and lateral friction factor, H/V against the normalised lateral displacement, x/D for tests with Vop/Vmax = 0.25 (R4 series). V/Dsu0 and w/D during the lateral displacement of the pipe are correspondingly provided in Figure 7.8(c) and Figure

7.8(d). Although the tests took place with a constant simulated pipe weight, V/Dsu0


increases as the pipe rises, reflecting the reduction in in situ soil strength at the pipe invert level.

The lateral response after post-lay consolidation exhibited higher resistance than the case without post-lay consolidation (compare R4CU and R4UU in Figure 7.8(a–b)). An immediate peak was recorded during lateral breakout following consolidation, similar to the observations made on the axial breakout response shown in Figure 7.7(a–b). An improvement in lateral resistance due to consolidation is observed within ~ 0.6D lateral distance from the as-laid location (Figure 7.8(a–b)). The breakout resistance is 1.8 times greater with post-lay consolidation than without, after which the lateral resistance (H/Dsu0 and H/V) on both the consolidated and unconsolidated cases converge to a similar value as the pipe moves further away from the as-laid position, encountering soil unaffected by the post-lay consolidation. The gain in lateral resistance due to post-lay consolidation is also higher for the pipe that was cyclically installed than in the pipe that followed monotonic penetration (compare R4CU against RemR4CU in Figure 7.8(a–b)). Cyclic remoulding of soil during pipe laying also created a wider zone of strengthened soil, where enhancement of resistance can be observed up to 0.75D lateral distance from the installation location (although the test was terminated shortly afterwards). Cyclic remoulding of soil during pipe laying led to elevated levels of excess pore pressure (Figure 7.3(c)) that consequently resulted in a greater reduction in moisture content and therefore strengthening after dissipation.

The observed differences in breakout resistance are consistent with the excess pore pressure recorded at the PPT on the rear side of the pipe, ∆urear shown in Figure 7.8(e). Higher negative pore pressure is observed for the higher breakout resistance, but in all cases the excess pore pressure is lost after approximately 0.5 diameters of movement, when a gap at the rear of the pipe causes pore pressures at the PPT location to become hydrostatic. The outcome – which is initially counter-intuitive – arises as more softening during pipe laying results in more net hardening after consolidation.


Figure 7.8 Effect of installation and post-lay consolidation on the lateral breakout resistance, showing (a) lateral resistance normalised by the in situ, undrained shear strength at the level of the pipe invert, H/Dsu0 (su0 not constant), (b) lateral friction factor, H/V, (c) normalised vertical resistance, V/Dsu0, (d) normalised pipe invert elevation, w/D, and (e) excess pore pressure at the rear face of the pipe, ∆urear normalised by the vertical bearing pressure per unit length, V/D, plotted against normalised lateral displacement, x/D for tests with operative vertical load ratios, Vop/Vmax = 0.25 (R4 series)

7.6.2. Comparison with theoretical solutions for unconsolidated, undrained lateral breakout capacity

The effect of pipe weight on the lateral breakout resistance for cases without post-lay consolidation is assessed through failure envelopes defining the combination of vertical and lateral loads in Figure 7.9. The unconsolidated undrained lateral breakout capacity,


indicated by the individual data markers, is defined as the maximum resistance recorded during the lateral displacement of the pipe, and occurred after x ~ 0.3D. Unconsolidated undrained failure envelopes in V/Dsu0 – H/Dsu0 and H/V – V/Vult,UU load spaces are shown on Figure 7.9(a) and Figure 7.9(b), respectively. These are based on the upper bound plasticity solution by Randolph and White (2008b) for weightless soil, and numerical limit analysis by Martin and White (2012) for weighty soil. In both cases the pipe is assumed to be fully rough, wished-in-place and at an embedment of w/D = 0.5 in a soil with strength proportional to depth. Both solutions underestimate the unconsolidated undrained lateral breakout capacity observed in the present set of centrifuge test results, which is attributed to the neglect of heave and soil berms as earlier demonstrated in Figure 7.3(b), noting that this penetration resistance would determine the size of the failure envelope in the lateral load dimension.

Figure 7.9 Unconsolidated lateral breakout responses, showing: (a) normalised lateral resistance, H/Dsu0, and (b) lateral friction factor, H/V responses, relative to theoretical failure envelopes


Figure 7.10 Development of soil heave during pipe penetration, shown by a sequence of test photos in the following order: (a) before penetration, (b) during penetration, and (c) at maximum penetration


The formation of soil heave beside the pipe during penetration is shown in Figure 7.10 through a sequence of underwater photographs taken during a pipe test. This heave results in an additional embedment, and provides additional resistance during lateral breakout as the pipe mobilises a greater volume of soil. The effect of the heave can be estimated by considering the volume of the soil displaced by the pipe during penetration. Dingle et al. (2008), through observations of the changes in soil surface profiles during pipe penetration using image analyses, estimated the effective increase in embedment, ∆wheave as:

( )

−−

=

∆ −2

1 '1''sin'8.08

1DD

DD

DD

DD

Dwheave 7.12

where D′ = 2D[(w/D) – (w/D)2]0.5. An effective embedment of ~ 0.7D for a pipe penetrated to w = 0.5D is derived through Equation 7.12. The unconsolidated undrained failure envelope corresponding to this effective embedment using the limit analysis solution by Martin and White (2012) predicts well the lateral breakout capacity observed in the present set of centrifuge test results shown in Figure 7.9.

7.6.3. Comparison with theoretical solutions for the consolidated, undrained lateral breakout capacity

The effect of pipe weight on the lateral breakout resistance for cases with post-lay consolidation is assessed through failure envelopes in Figure 7.11.

The consolidated undrained lateral breakout capacity, indicated by individual data markers, is defined as the peak resistance recorded during the immediate lateral displacement of the pipe, and occurred during x ~ 0.01D, which is a smaller displacement than for the unconsolidated cases.

The consolidated undrained failure envelope is derived by scaling the unconsolidated undrained envelope as a function of the increase in the undrained shear strength due to consolidation, ∆su using an approach set out by Gourvenec et al. (2014) for shallow foundations. The mobilised soil below the pipe is lumped as a single element for which the operative increment in consolidation stress due to the preload can be estimated for initially normally consolidated conditions as:

=∆

DNfc σσ '

7.13


Figure 7.11 Consolidated lateral breakout responses, showing: (a) normalised lateral resistance, H/Dsu0, and (b) lateral friction factor, H/V responses, relative to theoretical failure envelopes

where N is the enhanced normal force that takes into account the wedging effect around the pipe as defined by Equation 7.8 (Chatterjee et al. (2014)), while the factor fσ takes into account the non-uniform distribution of the stress in the affected zone of soil. The resulting increase in strength of the soil affected by consolidation is then calculated as:

NCv

ucsuu

sfs

∆=∆

''

σσ

7.14

where the shear strength factor fsu scales the gain in strength of the ‘lumped’ soil to that mobilised during subsequent failure, and (su/σ′v)NC is the normally consolidated strength ratio of the soil, equivalent to 0.15 in the present test conditions.

The consolidated undrained vertical and lateral breakout capacities are assumed to scale with the increase in the undrained shear strength in the form:


( )UUuNCv

uVsu

u

u

UUult

CUult

DsVsff

ss

VV

+=

∆+=

00,

,

'11

σσ 7.15

( )UUuNCv

uHsu

u

u

UUult

CUult

DsVsff

ss

HH

+=

∆+=

00,

,

'11

σσ

7.16

where (V/Dsu0)UU is the normalised unconsolidated undrained vertical pipe resistance mobilised at the effective embedment. Separate scaling factors, fσ and fsu in Equations 7.15 -

7.16 allow the response in the overconsolidated conditions to be captured, but in the present normally consolidated conditions, there is effectively a single scaling parameter, fσfsu for a particular load path. The increase in the vertical and lateral breakout capacities through consolidation as observed in the present set of centrifuge test results is predicted well through Equations 7.15 - 7.16 using the scaling parameters fσ fsu(V) = 0.439 derived in FEA studies carried out by Chatterjee et al. (2014) for pipe, and fσ fsu(H) = 0.919 derived by Feng and Gourvenec (2015) as shown in Figure 7.11. The results demonstrate that the expansion of the failure envelopes through consolidation is captured well by the theoretical framework outlined by Gourvenec et al. (2014), where the increase in operative soil strength is linked to the pipe weight. The observed increase in lateral breakout capacity, Hult, due to consolidation is higher than the predicted gain in vertical pipe capacity, Vult, consistent with analysis of mudmat foundations (Feng and Gourvenec (2015)). For the load levels used in the model test cases, the theoretical envelope and the experimental results show gains in lateral breakout capacity of 20% - 50%

7.7. Pipe trajectory

The effect of post-lay consolidation and installation or pipe ‘laying’ method on the pipe trajectory during subsequent axial and lateral loading is summarised in Figure 7.12. The figure plots the normalised pipe embedment at the invert level, w/D against the normalised axial displacement, y/D and normalised lateral displacement, x/D for tests with Vop/Vmax = 0.25 (R4 series). Overall, the trajectory is approximately the same with the pipe moving upwards as expected for the pipe weight relative to the vertical bearing capacity, at a slope of ~ 1° and ~ 10° during axial and lateral displacements, respectively. When the pipe is loaded axially or laterally immediately after the installation, larger upward displacements were recorded than during the movement of pipe after a period of post-lay consolidation.


Figure 7.12 Effect of consolidation on pipe trajectory during axial and lateral loading shown in three-dimensional normalised (x/D, y/D, w/D) space

Figure 7.13 Effect of pipe weight on the pipe trajectory during lateral breakout


The effect of pipe weight on the pipe trajectory during lateral loading is shown in Figure

7.13. The present centrifuge response is compared against large-deformation finite-element analysis (LDFEA) results reported in Wang et al. (2010), where the general behaviour between two set of results is similar with lighter pipes (Vop < 0.5Vmax) rising from breakout embedment during lateral displacement, and heavier pipes moving downward penetrating deeper into the soil with increasing lateral displacement, x/D.

The direction of pipe displacement during lateral breakout at failure, dw/dx, for varying Vop/Vmax can be directly assessed by assuming an associated flow rule (or normality), where dw/du at failure can be assumed normal to the failure envelope defined in the V-H load space. Recorded dw/dx for a given Vop/Vmax obtained in the centrifuge tests are compared against existing solutions in Figure 7.14(a) and Figure 7.14(b) for cases without and with post-lay consolidation.

In general, dw/dx observed in the centrifuge tests for Vop < 0.5·Vmax of a pipe with and without post-lay consolidation agrees closely with existing solutions based on LDFEA estimates (Wang et al. (2010)), and based on limit analysis (Martin and White (2012)) after accounting for the effective embedment as discussed above. However, both solutions slightly over predict dw/dx for Vop > 0.5·Vmax.

Figure 7.14 Inclination of displacement paths at lateral breakout compared against existing solutions , shown for: (a) cases without post-lay consolidation, and (b) cases with post-lay consolidation



This chapter has presented results of a centrifuge test programme that investigated the influence of installation or laying method, and post-lay consolidation on the axial and lateral breakout response of a pipeline section on a normally consolidated soil.

Different initial conditions involving varying levels of generation and dissipation of excess pore pressure during pipe installation, and operative vertical loads (representing a range of pipe weight) were explored. Axial and lateral breakout response of the pipe was assessed under undrained loading conditions immediately after installation, or after a period of consolidation to allow essentially full dissipation of the excess pore pressures developed during installation.

The results showed a strong installation effect. This effect results from post-laying consolidation, and is enhanced if the lay process involves remoulding. Four key conclusions emerge following the observations made:

1. After pipeline installation, the strength of the surrounding soil can be significantly enhanced due to consolidation under the pipe self-weight.

2. Cyclic pipe movements or oscillations during installation create additional excess pore pressure in the soil surrounding the pipeline. Although this remoulding weakens the soil in the short term, the subsequent strength gain during consolidation is greater than following monotonic installation.

3. The axial and lateral breakout resistance is significantly enhanced by these changes in strength – by 20% - 50% for the cases in this study. The relevant operative strength should be used with existing solutions to estimate breakout resistance. A theoretical framework and numerically derived scaling factors were presented for the pipeline conditions considered in this study.

4. The penetration of the pipe results in additional embedment due to the development of soil heave next to the embedded pipe. This additional effective embedment results in additional breakout resistance, and existing numerical and analytical solutions based on wished-in-place (no heave) conditions should be modified using the effective embedment. When the solutions are applied in this way, in combination with the in situ soil strength, the response is predicted well.


These results illustrate how the installation process and post-installation consolidation effects combine to alter the soil strength around a seabed pipeline, and show how existing prediction methods can capture these effects.


The work described here forms part of the activities of the Centre for Offshore Foundation Systems, currently supported as a node of the Australian Research Council Centre of Excellence for Geotechnical Science and Engineering. This support is gratefully acknowledged. The technical support provided by beam centrifuge technician, Mr. Manuel Palacios is also gratefully acknowledged. The third author acknowledges the support of the Shell EMI Chair in Offshore Engineering, at UWA.

Chapter 8. Conclusions

8.1. Introduction

This study has advanced the understanding of the whole-life geotechnical behaviour of tolerably mobile subsea mudmats, and has fulfilled the research aims presented in Chapter 1. The main contributions of the study, in response to the three major aims of the research project set out in Section 1.2, include:

Contribution 1: A data set of observations of the whole-life response of a tolerably mobile mudmat from geotechnical centrifuge modelling (Chapter 2, Chapter 3, and Appendix A)

Contribution 2: An improved understanding of the changing strength of seabed due to repeated cycles of remoulding and reconsolidation (Chapter 5 and Chapter 6)

Contribution 3: A theoretical model to predict the cycle by cycle whole-life response of a sliding mudmat foundation capturing the effects of repeated shearing and reconsolidation (Chapter 4)

The study has also applied the key theme of changing strength of the seabed through remoulding and reconsolidation to the interpretation of the effect of pipeline installation and self-weight on axial and lateral breakout response (Chapter 7).

The results and interpretation presented in this dissertation study provide a basis for geotechnical design of tolerably mobile subsea mudmats enabling a reduction in size and weight and easing existing installation challenges.

8-171


Figure 8.1 Summary of results

Conclusions | 8-173

8.2. Contributions

Figure 8.1 illustrates the key contributions of this study alongside the schematic of the boundary value problems addressed. Key findings are summarised in the following subsections.

8.2.1. A data set of observations of the whole-life response of a tolerably mobile mudmat from geotechnical centrifuge modelling

The study has contributed to the understanding of the whole-life geotechnical response of a subsea infrastructure through a benchmark observation on the long-term behaviour of a sliding subsea mudmat foundation, fulfilling Aim 1 of the research study set out in Chapter 1.

The study is the first published scientific work (Chapter 2, Chapter 3) that captured an observation and analysis of a whole-life response of a subsea infrastructure. The time scale prescribed to mimic a whole-life operation of the subsea mudmat foundation in the centrifuge is the longest reported simulation to date, providing information spanning up to 60 years of equivalent field observation essential to the complete understanding of such typically long term responses encountered offshore. The result is a set of high-quality data on this increasingly topical and important subject in offshore geotechnics.

Figure 8.1 under Contribution 1 encapsulates the main findings and observations of the whole-life response of a tolerably mobile mudmat submitted to periodic loading cycles associated with the thermal expansion and contraction of an attached subsea pipeline. Salient results including the evolution of sliding capacity (in terms of Hres and Hres/V), settlement (w/B) and rotation (θL) of the foundation during the imposed loading cycles, N are summarised in Figure 8.1.

In general, the performance of the tolerably mobile mudmat is controlled by the excess pore pressure generated and dissipated in the underlain soil, occurring in line with production start-up (foundation slides in response to thermal loading, shearing the soil) and operation (foundation remains static under the operative weight during pipeline operation, reconsolidating the soil).

The undrained sliding capacity of the mudmat increased progressively with increasing cycles of undrained shearing and reconsolidation of the underlain soil.


The increase in undrained sliding capacity is a consequence of the regain in the undrained shear strength of the soil during reconsolidation when the excess pore pressure dissipates and the effective vertical stress increases under a constant total vertical stress (operative weight). This strength increase was observed to surpass the loss of strength associated with soil shearing and reduction of effective stress during undrained sliding cycles.

Extending the duration of intervening reconsolidation between consecutive shearing cycles, and increasing the operative weight of the infrastructure (provided that the weight is within the limit that results in a pure sliding mechanism in response to horizontal loading under undrained conditions) enhanced the long term undrained sliding capacity of the mudmat foundation.

The long term undrained sliding capacity attains a drained value, given by the internal soil friction at critical state (tanϕ′), when the soil, after sufficient cycles of excess pore pressure generation and dissipation, densifies and reaches a critical state.

The critical state – characterised by no further contraction of the soil due to undrained shearing (i.e. minimal settlement during sliding), can be achieved through slow drained cyclic shearing, or progressively through multiple cycles of successive undrained shearing and reconsolidation cycles, depending on the timescale prescribed for the period of reconsolidation following a cycle of shearing or soil remoulding.

The overall long term settlement of the sliding mudmat foundation (incurred during undrained shearing, and intervening reconsolidation) is more significant than the accumulated foundation rotation. The maximum long term settlement was recorded at ~10 % of the foundation breadth, B at the end of a 15-year operation with production shutdown and start-up cycles occurring every third month. On the other hand, the maximum overall

rotation was recorded at ~1.5°, small compared to common design tolerances or pipeline connections. The accumulated overall settlements decreased with extended duration of intervening reconsolidation, and increase with increased operative weight of the infrastructure.

The soil-foundation base shear resistance and the resistance offered by the soil berm ploughed ahead of the foundation comprise the sliding capacity of the mudmat foundation. Soil-foundation base shear resistance governs during fast, undrained sliding while the ploughing resistance becomes significant during slow, drained sliding.

Conclusions | 8-175

All these observations contribute to the understanding of the whole-life geotechnical behaviour of a tolerably mobile mudmat, providing essential information to inform geotechnical design.

Apart from the geotechnical observations, the study has also advanced the technology needed to replicate more realistically the complicated loading conditions of tolerably mobile subsea mudmats through development of a loading actuation system configured to allow multi-planar loading and multi degree of freedom movement in a geotechnical centrifuge environment (Appendix A).

8.2.2. An improved understanding of the changing strength of seabed due to repeated cycles of remoulding and reconsolidation

The study has contributed to the understanding of the changing strength of the seabed, relating the development and dissipation of excess pore pressure in the soil surrounding subsea infrastructure to the observed performance of the infrastructure. This contribution achieves Aim 2 of the research study presented in Chapter 1.

Figure 8.1 presents the key results under Contribution 2 that capture the changing seabed strength including the increase in undrained shear strength (∆su) through cycles of soil remoulding and reconsolidation as assessed by the T-bar and pile penetrometers, replicating the increase in the undrained sliding capacity of the mudmat foundation. Also presented is the enhanced undrained shear strength within the foundation footprint imparted by cycles of shearing and reconsolidation during the foundation loading, as mapped out by the T-bar and pile penetrometers. Positive effects on pipe-soil resistance and stability following the enhancement of soil strength around the pipe due to soil remoulding and post-lay consolidation during pipe installation are also shown.

The results demonstrate that the conventional T-bar and the novel pile penetrometers were able to capture at the elemental level the evolution of the response exhibited at the macro level by the subsea infrastructure given a similar prescribed degree of consolidation (Chapter 5, Chapter 6). The reduction in strength during undrained shearing which resulted in the development of excess pore pressure in the soil, either through cyclic remoulding in T-bar and pile penetrometers, or shearing to failure of the soil beneath a mudmat under large amplitude sliding, was shown to be overridden by the gain in strength from reconsolidation when the pore pressure dissipated. In all cases, the rate of increase of the soil strength with


loading cycles is the same, reflecting a ~3 times increase in the in situ (intact) value after 20-25 loading cycles, with each cycle representing 0.25 years of reconsolidation period between successive soil remoulding episodes. These results demonstrate that a time scaled response obtained from the penetrometer can be applied to enable a convenient prediction of the long-term macro-responses of a subsea infrastructure.

The study has also successfully demonstrated the pile penetrometer in providing a detailed mapping of soil strength profile over a continuous lateral distance, which is an improvement from conventional vertically-penetrating penetrometers which can only provide data at discrete intervals. The pile penetrometer enabled a direct assessment of the variation and localisation of soil strength increase due to consolidation of the soil beneath the foundation.

The rise in soil strength resulting from periodic remoulding and intervening consolidation, as demonstrated in the penetrometer tests and corroborating the response of the tolerably mobile mudmat, follows critical state concepts where progressive soil hardening reflecting the gain in soil strength can be related to the reduction in void ratio per consolidation cycle.

The study has also shown that soil remoulding and reconsolidation, which occurs during the laying of a pipeline, has significant benefits on subsequent pipe-soil resistance (Chapter 7). Gains in strength of the surrounding soil due to post-lay consolidation resulted in increased axial and lateral breakout capacities, and a more stable trajectory during the breakout movement of the pipe. The gain in soil strength due to consolidation was enhanced by dynamic pipe lay effects leading to higher excess pore pressure in the soil.

8.2.3. A theoretical model to predict the cycle by cycle whole-life response of a sliding mudmat foundation capturing the effects of repeated remoulding and reconsolidation

The study has established a simple yet effective predictive model to analyse a soil-structure interaction process that involves episodes of horizontal surface shearing and reconsolidation. As summarised in Figure 8.1, the model provides a prediction of the cycle by cycle evolution of the seabed resistance determining the operational capacity (presented as Hres/V) of the overlying infrastructure undergoing cycles of horizontal sliding movements, as well as the cycle by cycle accumulation of void ratio reduction in the soil following cyclic consolidation determining the settlements of the seabed infrastructure (w/B), fulfilling Aim 3 of the study defined in Chapter 1.

Conclusions | 8-177

The predictive model considered a one-dimensional column of soil elements beneath a seabed installation, with each element subjected to a vertical total stress and cycles of horizontal shear stress, and responding via a critical state model. The current effective stress (σ′v) and void ratio (e) of each soil element was calculated in a cycle by cycle manner, evolving in terms of the generation and dissipation of excess pore water pressure. The effects of partial dissipation of excess pore water pressure during cycles of reconsolidation were incorporated and the void ratio reduction incurred during these cycles was calculated to represent the soil surface settlement.

The model was validated against centrifuge test results of the tolerably mobile mudmat, where the model prediction was seen to capture well the observed whole-life foundation response including the increasing foundation sliding resistance due to increasing soil strength, the overall settlement of the foundation following cycles of shearing and reconsolidation, and the different build-up rates of resistance and settlement. The model also provided good prediction of the measured profiles for the undrained shear strength and moisture content of the soil with depth within the foundation footprint representing the final state after a whole-life cycle of shearing and reconsolidation.

The model is easily programmable into a spreadsheet or simple calculation code and needs only standard critical state soil parameters.

8.3. Future directions

Further research to complement the research findings set out in this dissertation includes extension of the centrifuge model tests and theoretical framework to natural seabed deposits and development of in situ testing tools for use offshore to reliably measure seabed strength in the upper few metres. Investigation into the effect of the constraint provided by the attached pipelines on the response of a tolerably mobile mudmat (such as the presence of large in-plane or out-of-plane moment loads), the influence of soil-foundation interface roughness, and the effects of the displacement sensitive nature of pipeline loading on mudmat displacements would also be of value in advancing the geotechnical design basis for tolerably mobile subsea mudmats.

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Appendix A. Multi DoF loading in a geotechnical centrifuge

Prologue

This appendix provides the design configuration and specifications of the new loading apparatus employed in the model mudmat foundation tests reported in Chapter 2.

Appendix A has been submitted for publication in the International Journal for Physical Modelling in Geotechnics with a working title “A new apparatus for multi-planar loading of a subsea foundation in the centrifuge”(O’Loughlin et al. (2016)).

A-193

A-194 | Whole-life geotechnical response of tolerably mobile subsea infrastructure

Abstract

This study considers an alternative approach for multi-planar loading and multi degree of freedom movement in geotechnical centrifuge model tests. The multi degree of freedom loading system allows for vertical load control on the vertical axis, and either displacement or load control on the two horizontal axes, while allowing rotation about these axes. The system is described in detail and the system performance is validated through results from a centrifuge test comparing observed results with analytical and numerical solutions. The validation of the system considers a mudmat foundation under large amplitude lateral displacement, where two displacement degrees of freedom and two rotational degrees of freedom were of interest. However, the apparatus is versatile and can be used for testing other foundation types or pipelines, with up to six degrees of freedom.

A.1. Introduction

Offshore structures are typically subjected to multi-directional loading and respond with displacement in multiple degrees of freedom. Foundations of fixed-base structures, oil and gas platforms or wind turbines, experience a combination of vertical load from the self-weight of the structure, horizontal loads from the action of wind, waves and currents, and moment loading from the height offset between the action of the horizontal loads and the foundation; foundations of subsea structures can experience complex multi-directional loading from multiple pipeline and spool expansion loads acting at vertical and horizontal eccentricities to the centroid of the foundation (Randolph (2012), Feng et al. (2014b)); offshore pipelines are subject to vertical self-weight loads, multi-directional installation loads and thermally induced axial and lateral loads during operation and respond with settlement/burial, axial walking and lateral buckling.

Independent control of loading and acquisition of displacement, or vice versa, in all six degrees of freedom poses quite an experimental challenge for actuation systems. This is more achievable at 1g than in a centrifuge as the space requirements for the actuation and position measurement systems can be more easily accommodated on the laboratory floor than within the constrained space available on a centrifuge package (Byrne (2013)). Centrifuge actuators typically have two or three displacement degrees of freedom (DoF) along the horizontal and vertical planes, although actuation systems that add a rotational DoF have also been developed (Dean et al. (1997), Punrattanasin et al. (2003), Cocjin and

Multi DoF loading in a geotechnical centrifuge | A-195

Kusakabe (2013), Kong (2011), Zhang et al. (2013), Gaudicheau et al. (2013)). To the authors’ knowledge a six DoF actuation system has not yet been developed for use in a geotechnical centrifuge.

Independent control of loads or displacement in all degrees of freedom is not a necessity for many practical applications involving multi-directional loading and resulting displacements. A practical approach to multi DoF actuation in a geotechnical centrifuge may, in many cases, be to use existing actuators to control displacements or loads along the principal axes, while permitting rotational degrees of freedom about the same axes. This Appendix describes such an approach, firstly describing a new multi-DoF loading system, before assessing the system performance as measured in a centrifuge mudmat test on normally consolidated kaolin clay.

A.2. Design of the multi-DoF loading system

A.2.1. General arrangement

The general arrangement of the new multi-DoF loading system, actuator and model is illustrated in Figure A−1.

The multi-DOF loading system (item [1] in Figure A−1) enables movement in four DoF under vertical load control and with either horizontal load or displacement control. As shown by Figure A−1(a-b), it is designed to be operated in conjunction with an actuator[2] that provides motion in the vertical and horizontal directions. The actuator is mounted on top of a strongbox containing the soil model. The main part of the multi-DoF loading system is a “C-shaped loading arm” (described in detail in the following section) that connects to the actuator by way of a solid aluminium shaft secured at the collar connection[6] of the actuator’s vertical axis. Two rotational DoF are allowed for within the C-shaped loading arm, which together with the two translational DoF provided by the horizontal and vertical axes of the actuator, comprise the four DoF allowed on the model infrastructure. This is shown by Figure A−2, which also defines the positive sign convention for the loads and displacements, and the reference point (RP) where the loads and displacements are defined on a rectangular foundation.

The multi-DoF loading system was developed for and trialled on a model pipeline end termination mudmat, where displacement along the longitudinal and vertical axes, and rotation about the two orthogonal horizontal axes were of interest (i.e. four DoF). However,


the use of an actuator with a second horizontal axis and an additional rotational degree of freedom within the C-shaped arm would enable load or displacement control in three DoF and movement in all six DoF (without control in the rotational DoF).

The multi-DoF loading system can be operated in either load or displacement control on the horizontal axis and on load control on the vertical axis. Motion along these actuator axes is provided by DC servo-motors that drive vertical and horizontal lead screws[7,8] (Figure

A−1(b)). The actuator axes are controlled by the UWA Package Actuator Control System (PACS) (De Catania et al. (2010)), an in-house software written in Labview. This software runs on an in-flight computer mounted on the centrifuge and acts as a slave to a master computer in the centrifuge control room, with communication via an Ethernet link across an optical slip ring. The control software is operated via a remote desktop linked to the in-flight computer.

Load- or displacement-controlled operation of the actuator can be achieved with a software feedback loop using the outputs of a load cell[11,12] or a displacement transducer[4,5]. The software can also automate loading or displacement sequences through its waveform generator. The waveform can be generated for monotonic loading or displacement sequences using a ramp function, or cyclic loading or displacement sequences using a sine, square, triangle or sawtooth function (De Catania et al. (2010)).

A.2.2. Loading arm description

As described above, the C-shaped loading arm provides the rotational DoF. Details of the loading arm are provided in Figure A−1(c-d). The upper C section is fabricated from aluminium and is 235 mm long along the y axis, with provision for a bolted connection to the aluminium shaft attached to the actuator.


Figure A−1 Schematic of loading arm and actuator system highlighting: (a) movement in the vertical direction, (b) movement in the horizontal direction, (c) loading arm profile view in the y-z plane, and (d) loading arm profile view in the x-z plane

(a)

y

z

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Components of the loading arm:(11) Vertically-suspended load cell(12) Horizontal load cell(13) Loading arm hinge(14) Roller bearing(15) Free-end hinge(16) Lower eyelet(17) Upper eyelet(18) Horizontal laser target

Main components:(1) Loading arm(2) Loading actuator(3) Model infrastructure(4) Keyence® laser displacement sensors

(vertically-orientated) with casing(5) Keyence® laser displacement sensors

(horizontally-orientated) with casing

(12)(13)(15)

(14)

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Middle C

Upper C

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Top of strong box

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Components of the loading actuator:(6) Collars for vertical shaft connection(7) Vertical DC servo-motor with encoder(8) Horizontal DC servo motor with encoder (9) Vertical lead screw(10) Horizontal lead screw, with parallel LVDT

(7)

(8)

(9)

(10)(10)


Figure A−2 Positive sign convention for loads and displacements acting on a rectangular foundation

An eyelet[17] is provided at the free end of the upper C section to append the vertically-suspended load cell[11], while the other end is bolted to a vertical shaft forming the middle C section. The shaft for the middle C section is fabricated from stainless steel, 105 mm long with 25 mm diameter, and is attached to the lower C section by a hinge. The lower C section is comprised of an S-shaped load cell[12], an in-line stainless steel cylindrical roller bearing[14] and a 100 mm long aluminium section with a hinge[15] at its free end. The roller bearing provides the rotational DoF about the y axis, whereas the hinge at the end of the aluminium section provides the connection to the foundation model and the rotational DoF about the x axis. An eyelet[16], located directly above this hinge, connects to the vertically-suspended load cell[11] via wire cable and polyethylene line (to eliminate rigidity), completing the connection between the upper and lower C sections. The height of the hinge[15] from the base of the attached model foundation is adjustable depending on the test requirements.

A.2.3. System instrumentation

A vertically-suspended load cell[11] with a measurement range of 1.4 kN is suspended in-line between the eyelets[17,16] on the upper and lower C sections. The load cell was connected to the upper eyelet[17] using steel cable, but to the lower eyelet[16] using the polyethylene line, to ensure that the link between the two eyelets could only be in tension. This was a design requirement as this load cell measures the combined self-weight of the lower C section and the attached model foundation when not in contact with the soil surface. The submerged weight of the foundation, V, and hence the on-bottom pressure applied to the soil, can then

y

z

xθxx, Mxx = 0

θyy, Myy = 0w, V

uy, Hyux = 0, Hx = 0

BL

ω = 0, T = 0

RP


be controlled by operating the vertical axis of the actuator under load control using the analogue feedback from the vertical load cell. The S-shaped axial load cell[12] on the lower C section has a measurement range of 150 N and measures the horizontal load, H, along the y axis.

Displacements along the y and z axes are measured using the optical encoders located on the vertical and horizontal axes of the actuator. A laser displacement sensor[5] (Keyence®, model LB-70-11) with a measurement range of 80 mm is located on a bracket connected to the actuator and oriented towards a target[18] at the junction of the middle and lower C sections of the loading arm (Figure A−1(c)). This provides an additional measurement of the foundation displacement along the y axis, independent of that determined from the optical encoder on the actuator’s horizontal axis.

Four additional laser displacement sensors[4] with a measurement range of 80 mm measure the vertical displacement at each corner of the foundation, although these measurement locations can be adjusted if required. These displacement sensors are mounted directly above the model foundation on a steel plate that is fixed to the actuator, such that the sensors move horizontally in unison with the actuator and hence the model foundation (Figure A−1(b)). Independent measurement of these corner vertical displacements allows the rotation about the x and y axes – θxx and θyy respectively – to be determined.

A.3. Summary of centrifuge test used to illustrate loading system capability

System performance of the multi-DoF loading system is assessed in the next section using the results from a centrifuge test that was conducted to investigate the load and displacement response of a pipeline end termination mudmat foundation on normally consolidated clay when subjected to cycles of large-amplitude lateral movements under low vertical load, simulating the expansion associated with start-up and shut-down operations of an offshore pipeline. Testing was conducted in the UWA beam centrifuge. A complete description of this centrifuge, as commissioned in 1989, is provided by Randolph et al. (1991). A full description of the testing arrangement, programme of testing from which this test was drawn, and interpretation of results are presented in Chapter 2. The test reported here corresponds to Test MMUD1 reported in Chapter 2. Selected testing details are repeated here for completeness. Results are reported in model scale, unless stated otherwise, in order to demonstrate the accuracy of the new loading system.


A.3.1. Soil model

A normally consolidated kaolin clay sample was prepared from slurry at twice the liquid limit and consolidated under self-weight in the centrifuge at 100g for 3.5 days. After consolidation was essentially complete, the centrifuge was stopped and a minimum amount of clay was scraped from the sample to create a level surface. The final sample dimensions were 650 mm by 390 mm in plan with a height of 130 mm. A miniature T-bar penetrometer (Stewart and Randolph (1991)) with a projected (penetrating) area of 100 mm2 was used to determine the depth profile of undrained shear strength, su. The T-bar was penetrated into the soil at a rate of 1 mm/s to ensure undrained conditions (Randolph and Hope (2004)) and su was determined from the measured penetration resistance using a constant T-bar factor of 10.5 (Stewart and Randolph (1994)). Figure A−3 shows the su profile with depth, which can be well described by su = 0.53 + 0.86z (kPa), where z is the penetration depth in prototype scale (m). The average effective unit weight of the soil, γ′avg = 5.7 kN/m3 was assessed from moisture content measurements made on a core sample taken after testing, giving a normally consolidated strength ratio of (su/σ′v)NC ~ 0.15, similar to that determined from other recent centrifuge studies on UWA kaolin (Chow et al. (2014), Hu et al. (2014), Morton et al. (2014)).

A.3.2. Model foundation

A rectangular mudmat foundation, with aspect ratio B/L = 0.5, was used in the centrifuge test. Figure A−4 shows a schematic of this model foundation attached to the loading arm, showing profile views in (a) y-z, and (b) x-z planes. The foundation has underside base plate dimensions, B = 50 mm and L = 100 mm (giving a basal area of A = 5000 mm2), and a height of 5 mm (equivalent to prototype plan dimensions of 5 m by 10 m and height of 0.5 m). The model foundation was fabricated with an edge ‘ski’ (inclined at 30°) along each side. The purpose of the ski was to reduce foundation tipping (overturning) and encourage sliding.

The mudmat was fabricated from acetal (polyoxymethylene (POM)) that has a density of 1410 kg/m3, which is sufficiently low to allow a model mudmat of solid section to replicate the self-weight of a field mudmat, typically manufactured from steel but not solid in section. With the current modelling approach, as described earlier, adjustment to a targeted


submerged on-bottom weight is achieved using load control on the vertical axis of the actuator. This capability means that scaling of the submerged weight of the prototype foundation is not a modelling requirement, although was achieved in this case. Acetal has a Young’s modulus and Poisson ratio of 3.1 GPa and 0.39 respectively, sufficiently stiff to be considered as rigid relative to the soft clay. Fine silica sand was glued to the base plate as a rough foundation–soil interface was of interest for these tests. The faces of the edge ‘ski’ retained a smooth finish.

Figure A−3 Undrained shear strength profile with depth of soil model derived from a T-bar penetrometer test


Figure A−4 Schematic of model foundation: (a) along the long side (y-z plane), and (b) along the short side (x-z plane)

B=

50.0

30°

30°

Rolle

rRota

tion

abou

t y- a

xis

(b)

5.0

30°

30°

L = 1

00.0

10.0

20.0

25.0

(DIA

)

Hing

e

Rota

tion

abou

t x-a

xis

Lase

r tar

get

Base

plat

e

Load

ing

arm

(a)

Ski

RP

z

y

z

x

15.0

Wat

er

surfa

ce

Soil s

urfa

ce

RP

Ski

Ski

Ski


Figure A−5 Schematic of the loading arm and model foundation movements through: (a) vertical motion of the loading actuator, (b) horizontal motion of the loading actuator, (c) rotation about x-axis of the foundation at the foundation hinge, and (d) rotation about y-axis of the foundation through the horizontal roller bearing

Circular discs propped on slender posts were located at each corner of the model foundation to serve as targets for the vertically-orientated laser displacement sensors. The height of the

wu y

θ xx

θ yy

(a)

(b)

(c)

(d)

Hin

ge

Rolle

r bea

ring

z

y

z

y

z

x

z

y


posts can be adjusted to keep the circular discs above the water surface during the test to avoid refraction of the laser beam in the water.

Figure A−5 shows the DoF for the model foundation with the currently configured loading system and the two-directional actuator. Vertical displacement of the model foundation along the z axis is quantified either through the displacement of the actuator’s vertical axis, w(encoder) or through the average of the corner vertical laser displacements, w(laser) (Figure

A−5(a)). Horizontal displacement of the model foundation along the y axis may be taken either as the displacement of the actuator’s horizontal axis, uy(encoder) or from the independent laser displacement sensor measurement, uy(laser) (Figure A−5(b)). Rotation of the model foundation about the x and y axes – θxx and θyy respectively – may be quantified from the difference of corner vertical laser displacement measurements (Figure A−5(c-d)). While the current system configuration enables foundation displacement in four DoF, displacement-control is limited to horizontal y axis.

A.3.3. Loading program

As described earlier, the four DoF loading system is operated with the vertical axis of the actuator under load control and the horizontal axis of the actuator under either displacement or load control. The test presented here to illustrate the performance of the apparatus employed displacement control for the horizontal axis. The time history of imposed loads and displacements are shown in Figure A−6: vertical load, V (Figure A−6(a)) and horizontal displacement, uy (Figure A−6(b)).

Phase 1 of the test involved foundation touchdown and consolidation under the operative vertical load, Vop. Foundation touchdown can be performed under either displacement or load control. In this test, displacement control was used with the vertical axis of the actuator displaced positively – initially at a velocity of 0.1 mm/s, reducing to 0.01 mm/s as the foundation approached the mudline – until about one third of the targeted load was observed, at which point the vertical axis of the actuator was switched into load-control mode and a target load of Vop specified. This process was automated using the PACS software, with manual fine adjustment of the load control as required. A consolidation period of approximately 4 hours (4.5 years in prototype scale) was allowed after touchdown of the mudmat to bring the soil beneath the foundation sufficiently close to a fully consolidated state at the end of the installation phase. During Phase 1 (including the


consolidation stage), settlement along the z axis, and rotation about the x and y axes were permitted, but horizontal displacement along the y axis was not allowed.

Figure A−6 Centrifuge tests loading program showing time-scales of the (a) vertical load, V and (b) horizontal displacement, uy imposed on the mudmat foundation

Phase 2 involved undrained large amplitude cyclic sliding of the mudmat foundation. As in Phase 1, the actuator motion was automated using the waveform generator in the PACS software. The sliding cycles are as defined in Figure A−6(b) and comprise a forward slide equal to half the breadth of the foundation uy(max) = 0.5·B, a long interim pause during which Δuy = 0, a backward slide until uy = 0, and finally a short interim pause during which Δuy = 0. The horizontal displacement was carried out at a velocity of 1 mm/s. This gives a one-way sliding duration of 25 s (< 3 days in prototype scale), sufficiently short for any significant dissipation of excess pore water in the soil beneath the foundation to occur during sliding (Chapter 2). The test involved N = 40 loading cycles, with each loading cycle comprising a forward slide, long period of consolidation, backward slide and short period of consolidation. The long interim pause permitted after each forward slide represents the

Time

Time

Vert

ical

load

, VH

oriz

onta

l disp

lace

men

t al

ong

y-ax

is, u

y

Phase 1 Phase 2

Reconsolidation episodes

uy(max)

Post-touchdown

consolidation

Waveform starts

Vop

(a)

(b)

1Cycle number, N 2 40…


period when a pipeline is in operation between scheduled shutdowns, with shutdowns typically occurring a few times a year. As such the reconsolidation episode at uy = uy(max) was 13 minutes, equivalent to 3 months in prototype scale. The short interim pause permitted after each backward slide simulates the brief shutdown period after the pipe cools and contracts and the foundation has returned to its installation position, uy = 0. Shutdowns are typically less than a day, modelled in the centrifuge test as 8 s. During Phase 2, settlement along the z axis, and rotation about the x and y axes were permitted, with horizontal displacement along the y axis allowed only during the forward and backward slides but locked during the interim pauses.

An operative vertical load, Vop corresponding to ~ 30% of the unconsolidated, undrained vertical capacity of the mudmat foundation, was selected as a realistic field value, and to allow for a pure sliding mechanism in response to horizontal loading under undrained conditions (Green (1954);Gourvenec and Randolph (2003); Cathie et al. (2008)).

A.4. Technical performance of the multi-Dof loading system

The technical performance of the multi DoF loading system is examined in this section by considering the load and displacement response of the model foundation during the test. Figure A−7 shows a time history of the vertical load, V; horizontal displacement, uy(encoder) (i.e. taken as the horizontal displacement of the actuator); horizontal load, H; vertical displacement, w(laser) (i.e. taken as the average of the vertical displacements at the foundation corners ); and foundation rotation about the x and y axes – θxx and θyy respectively. The data are provided in Figure A−7(a) through to Figure A−7(e) for vertical touchdown of the foundation, Figure A−7(f) through to Figure A−7(j) for post-installation consolidation and the first 15 undrained sliding cycles, and Figure A−7(k) through to Figure A−7(o) for the first sliding and re-consolidation cycle.


Figure A−7 Time-scale plots of the vertical load (V), horizontal displacement (uy), horizontal load (H), vertical displacement (w(laser)), and foundation rotation about the x and y axes (θxx and θyy) during: (a-e) touchdown of the foundation into the soil surface, (f-j) post-installation consolidation and undrained sliding cycles, and (k-o) first sliding and reconsolidation cycle

It is clear from Figure A−7 that the system is capable of enabling and measuring required foundation movements in four DoF; displacements develop along the y and z axes, and rotations develop about the x and y axes. Displacement along the z axis, w(laser), is continuous


during the test as this axis is operated in load control, whereas displacement only occurs along the y axis, uy(encoder) during the forward and backward slides. The change in z axis displacement, i.e. settlement, Δw, is positive during the post-touchdown consolidation, cycles of re-consolidation and during forward slides, but negative during backward slides. As the foundation is free to rotate about the x and y axes, θxx and θyy are non-zero throughout the test, and change most rapidly during the undrained sliding cycles.

Figure A−8 Comparison of foundation movements as measured by the actuator encoders, and independently by lasersin (a) vertical, and (b) horizontal direction

Vertical load develops from time, t = -240 s to t = 0 as the foundation is gradually lowered to the soil surface under displacement control, initially at a displacement rate of 0.1 mm/s (to t = -167 s) and then 0.01 mm/s. From t = 0 the vertical axis was under load control, with the achieved load in the range Vop = 10 ± 0.35 N during the consolidation phase when ∆uy =


0, and Vop = 10 ± 1.5 N during the undrained sliding cycles when ∆uy ≠ 0. The higher variation in the achieved load reflects the difficulty in selecting PID (proportional–integral–derivative) controller parameters that work effectively during static and non-static conditions. However, it is worth noting that the maximum variation corresponds to 0.1 % of the measurement range of the load cell (1.4 kN) and that the variation would reduce if a load cell with a lower measurement range were used. The horizontal load, H is essentially zero during foundation touchdown and post-touchdown consolidation, which is to be expected as uy = 0 during this time. During the undrained sliding cycles, H is positive during forward slides and negative during backward slides. H also increases with increasing loading cycles, reflecting the higher seabed strength brought about by the consolidation periods between sliding events.

Figure A−8 compares the foundation displacements as assessed from the actuator motion with the independent laser displacement sensor measurements in: (a) vertical and (b) horizontal directions. The vertical displacement of the actuator, w(encoder), is typically no more than 0.2 mm lower than that determined from the average of the laser displacement sensors, w(laser), equivalent to less than 4% difference in the actual displacement. The horizontal displacement of the actuator uy(encoder) is initially close to the value measured by the horizontal laser displacement sensor, uy(laser). However, as the cycles progress, the difference between uy(encoder) and uy(laser) increases to a maximum deviation of 1.5 mm (6 %) due to a progressive increase in system compliance brought about by the increasing horizontal load, H, reflecting the strength increases in the clay. This reduced slide displacement was negligible for the current test, involving slide distances of 0.5·B. In other scenarios it may be more appropriate to use the independent displacement measurement rather than the encoder as the displacement feedback for the actuator’s horizontal axis.

A.5. Example application of the multi-Dof loading system

The load and displacement response from the sliding mudmat foundation test is presented in Figure A−9. Figure A−9(a) shows (imposed) horizontal displacement against (observed) settlement over the 40 cycles of the test, and Figure A−9(b) shows the cycle by cycle increase in horizontal sliding resistance against the (imposed) horizontal displacement. Figure A−9(c-

d) represent the measured displacement and load respectively, midway through the slide, i.e. at uy/B = 0.125. Foundation rotations, θxx and θyy are provided in Figure A−9(e), showing that rotations are minimal.


Figure A−9 Complete set of test showing: (a) foundation settlement (laser), w(laser) and (b) horizontal load, H plotted against horizontal displacement (encoder), uy(encoder), and mid-slide values of (c) foundation settlement (laser), w(laser), (d) horizontal load, H, and (e) rotation about the x and y axes, θxx and θyy plotted against cycle number, N

An independent quantification of the foundation consolidation settlement was made by considering the difference in void ratio profiles with depth obtained within the foundation footprint and in free-field soil (e0) from vertical core soil samples taken after the test (inset


Figure A−10(a)). The final consolidation settlement is calculated from the measured change in void ratio by

∫∑∞→

=+∆

=z

zfcons dz

eew

0 0, 1

A 1

and is seen to agree well with the final value of consolidation settlement Σwcons determined from the laser displacement sensors as shown in Figure A−10(a).

Figure A−10 Post-touchdown and cyclic consolidation settlement plotted against cycle number, N (inset: void ratio profile with depth obtained at a free-field soil (virgin), e0 and within foundation footprint soil), and (b) overview photograph of foundation footprint after the test, showing peripheral berm formation


The difference between the total observed settlement, Σw and the accumulated consolidated settlement, Σwcons is a measure of the amount of soil that accumulates as berms on either side of the foundation during the sliding cycles, shown in Figure A−10(b).

The measured horizontal resistance, H, expressed as a coefficient of sliding friction, µ = H/V, during the first slide and during the loading cycles is plotted against normalised foundation displacement, uy/B in Figure A−11(a−b), respectively. During the first slide, a peak resistance at low horizontal displacement is observed which then reduces with foundation displacement, reaching a steady state of µ = 0.15 at uy/B ≈ 0.15. The steady state coefficient of sliding friction derived from the test observation agrees well with analytical and numerical predictions based on critical state soil mechanics (Chapter 4; Feng and Gourvenec (2016)).

Figure A−11(c), which plots the mid-slide values of coefficient of sliding friction, µ against cycle number, N shows that a long term sliding resistance given by tanϕ′ where ϕ′ = 23.5° is the internal angle of soil friction, is eventually achieved when the soil has undergone sufficient cycles of sliding (and hence shearing), pore pressure generation and reconsolidation to reach critical state conditions, resulting in no further contraction and excess pore pressure generation (Chapter 2−Chapter 4, Feng and Gourvenec (2016)).

A.6. Closing remarks

Multi degree of freedom loading in a geotechnical centrifuge environment is challenging, but necessary to understand the behaviour of geotechnical structures that experience combined loading. This study has simplified the challenge somewhat by proposing a multi DoF loading system that uses a conventional two or three dimensional actuator to actuate along the principal axes, while using roller bearings to allow rotation about the same axes. While the system does not permit for independent control of the rotational DoF, the simplicity and flexibility of the system is appealing and sufficient for simulating various boundary value problems involving multi-directional loading and freedom of movement. This has been demonstrated in this study by simulating the whole-life cycle of a pipeline end termination mudmat under large amplitude lateral displacement. The loading arm apparatus could also be used to investigate the performance of other foundation systems or pipelines under selected modes of multi-directional loading.


Figure A−11 Post-touchdown and cyclic consolidation settlement plotted against cycle number, N (inset: void ratio profile with depth obtained at a free-field soil (virgin), e0 and within foundation footprint soil), and (b) overview photograph of foundation footprint after the test, showing peripheral berm formation


A.7. Acknowledgements

This work forms part of the activities of the Centre for Offshore Foundation Systems (COFS), currently supported as a node of the Australian Research Council’s Centre of Excellence for Geotechnical Science and Engineering, and through the Fugro Chair in Geotechnics, the Lloyd’s Register Foundation Chair and Centre of Excellence in Offshore Foundations and the Shell EMI Chair in Offshore Engineering. The work presented in Appendix A is supported through ARC grant DP140100684. Development of the multi DoF loading system was supported through a contract with Fugro AG.

Appendix B. Interpretation of undrained shear strength presented in the dissertation

B.1. Summary of corrections applied to undrained shear strength profiles

Undrained shear strength profiles with depth were derived from the measured resistance from T-bar (Chapter 2 to Chapter 6, Appendix A), pile (Chapter 5 to Chapter 6) and ball (Chapter 7) penetrometers. Corrections were made to the measured data to account for (1) variation in the g-field throughout the depth of the centrifuge soil sample and (2) buoyancy effects. Table_B-1 provides a summary of all the strength profiles presented in each chapter of the dissertation.

The first correction was applied to the measured T-bar resistance with the corrected profile presented in Chapter 2 to Chapter 4, Chapter 6, and Appendix A. The correction for the variation in the g-field throughout the depth of the centrifuge soil sample, as applied, resulted in a slight increase in the gradient of resistance with depth, and has more effect on the whole-depth profile than on the profile derived near the soil surface. Thus, the correction was not applied to the pile penetrometer data (Chapter 5 to Chapter 6) which inquired the near-surface soil strength. The undrained shear strength profile inferred from the T-bar as presented in Chapter 5 was also not corrected for the variation in gravity field as this was an early interpretation of the data. However, the neglect of this correction which resulted in the slight difference in the derived shear strength profile presented in Chapter 5 from the profiles presented in the other chapters of the dissertation, had no impact on the accuracy or relevance of the method of interpretation for the undrained shear strength of the soil sample as presented in Chapter 5.

The correction was also not applied on the ball data obtained on the soil sample where the model pipe tests were carried out because the depth of interest for these tests was only limited within the upper 15 mm of the soil sample (0.375 m in prototype scale, under 25g).

The procedure for the correction for the variation in the g-field throughout the depth of the centrifuge soil sample is presented in the subsequent section.

The second correction related to buoyancy effects was applied to the ball data to account for these effects in the analysis of the model pipe data, allowing a direct and parallel interpretation between the ball-derived soil resistance and the pipe penetration response.

B-216 | Whole-life geotechnical response of tolerably mobile subsea infrastructure

Buoyancy effect becomes significant when the model penetrates the soil, which is not the case for the foundation test and the pile penetrometers (Chapter 2 to Chapter 6, Appendix A), and thus was not accounted for in these cases. The correction for buoyancy effects on the ball data is provided in detail in Chapter 7.

The soil samples established in the model mudmat (Chapter 2 to Chapter 6, Appendix A) and pipe (Chapter 7) tests were characterised by an in situ undrained shear strength that linearly increased with depth, confirming the normally consolidated soil conditions attained in both samples. The in situ shear strength profile with depth is defined by the mudline intercept of the shear strength, and the gradient of strength increase with depth. In Chapter 2 to Chapter 5, Chapter 7 and Appendix A, the fitted line was correlated for the whole depth of penetrometer penetration, whereas this line was represented only for the upper portion of the soil in Chapter 6.

B.2. Nonlinear districbution of inerital acceleration through the centrifuge model

The measured resistance from the conventional full flow T-bar penetrometer test was corrected for the nonlinear distribution of the intertial acceleration through the centrifuge model following the procedure proposed by Taylor (1995).

The correction takes into account the slight variation in acceleration through the soil model because of the varying angular rotational speed of the centrifuge, ω at different radial distance, r from the fixed axis of rotation as shown in Figure B-1(a). In prototype conditions, i.e. in the field, the gravity stress varies linearly with depth (Figure B-1(b)). In comparison, the variation in acceleration through the soil model in an accelerated field would result in a slightly nonlinear variation of inertial stress, shown exaggerated in Figure B-1(c) for clarity.

Based on Taylor’s recommendation, the effective centrifuge radius, Re is set at one-third of the depth of the soil model from the axis of rotation of the centrifuge:

3m

tehRR += B 1

where Rt is the radial distance from the axis of rotation to the top of the soil model.

Interpretation of undrained shear strength in the dissertation | B-217

Figure B-1 Inertial stresses in a centrifuge model induced by rotation about a fixed axis in comparison with the gravitational stresses in the corresponding prototype (after Taylor (1995))

The angular rotational speed of the centrifuge, ω was then deduced by assuming a one-to-one correspondence between the prescribed level of gravity (product of the scaling factor, n and the Earth’s gravity, g) and that felt by the soil at the level of the effective centrifuge radius:

5.0

=

eRngϖ B 2

The angular acceleration imposed on a soil element at a radial distance, r from the fixed axis of rotation is then given by:

r2ϖ=Θ B 3

with r expressed as:

Model

Depth, zm

Inertia stress

hm

ω

Prototype

Gravity stress

hp

g

ω2r

Axis of rotation

Stress

Depth

Rt

h

2h/3

h/3

Depth, zp

(a) (b) (c)

Rt

B-218 | Whole-life geotechnical response of tolerably mobile subsea infrastructure

mt zRr d+= B 4

and zm being the depth of the soil model from the top surface.

Finally, the scaling factor that accounts for the varying acceleration level through the soil model is given by:

gn Θ

=ϖ B 5

Interpretation of undrained shear strength in the dissertation | B-219

Table_B-1 Summary of the undrained shear strength profiles presented in each chapter

Shea

r str

engt

h gr

adie

nt: k

Pa/m

0.86

0.86

0.86

0.59

-

0.73

-

0.71

0.86

Mud

line

shea

r st

reng

th: k

Pa

0.53

0.53

0.53

0.54

-

0.66

-

0.09

0.53

Max

imum

dep

th n

orm

alise

d by

pe

netr

omet

er d

iam

eter

whe

re lin

ear

fit w

as e

stim

ated

15 (w

hole

dep

th)

15 (w

hole

dep

th)

15 (w

hole

dep

th)

15 (w

hole

dep

th)

6 (n

ear-

surf

ace)

6 (n

ear-

surf

ace)

6 (n

ear-

surf

ace)

13 (w

hole

dep

th)

15 (w

hole

dep

th)

Corr

ectio

n fo

r bu

oyan

cy

effe

cts

No

No

No

No

No

No

No

Yes

No

Corr

ectio

n fo

r no

nlin

ear

acce

lera

tion

Yes

Yes

Yes

No

No

Yes

No

No

Yes

Box

Mud

mat

Mud

mat

Mud

mat

Mud

mat

Mud

mat

Mud

mat

Mud

mat

Pipe

line

Mud

mat

Pene

trom

eter

ty

pe

T-ba

r

T-ba

r

T-ba

r

T-ba

r

Pile

T-ba

r

Pile

Ball

T-ba

r

Chap

ter

Chap

ter 2

Chap

ter 3

Chap

ter 4

Chap

ter 5

Chap

ter 6

Chap

ter 7

Appe

ndix

A

Documents

WHOLE LIFE GEOTECHNICAL RESPONSE OF TOLERABLY MOBILE SUBSEA INFRASTRUCTURE · principles of critical state soil mechanics in that dissipation of excess pore water pressure generated