geotechnical analysis of oﬀshore pipelines and steel ...geotechnical analysis of oﬀshore...

Geotechnical analysis of offshore pipelines

and steel catenary risers

by

Matthew Steven Hodder

B.Eng.

School of Civil and Resource Engineering

Faculty of Engineering, Computing and Mathematics

This thesis is presented for the degree of

Doctor of Philosophy

at The University of Western Australia

December 2009

Abstract

As hydrocarbon developments move further offshore into deeper water, the pipelines and

risers used in the transportation of oil and gas form an increasingly significant compo-

nent of the development infrastructure. Offshore pipelines and risers must be designed to

withstand exposure to a range of loading conditions throughout their lifetime. On-bottom

pipelines laid directly on the seabed must be shown to be stable and not become over-

stressed when subjected to environmental and operational loads. Similarly, risers, which

transport hydrocarbon products between deep water floating platforms and the seabed,

are subjected to various cyclic loadings and must be shown to not suffer from fatigue

damage. The interaction of the pipeline or riser with the seabed serves as boundary con-

ditions in a structural analysis of the system. Therefore, an accurate representation of

the geotechnical behaviour in a pipe-soil interaction model is critical to the assessment of

structural response.

This thesis investigates the interaction of cylindrical objects with soil, and its appli-

cation to the analysis and design of offshore pipelines and risers. The behaviour observed

during experimental investigations performed to assess the effect of various loading con-

ditions on pipe-soil interaction response is used to develop analytical models which are

appropriate for use in an integrated soil-structure interaction assessment of the pipe-soil

system. The combined vertical-lateral behaviour of on-bottom pipelines is explored. An

interaction model is presented which is applicable to the prediction of pipeline response

when subjected to combined vertical and lateral loading on a soft clay seabed in undrained

conditions. The effects of various vertical cyclic loading regimes on pipe-soil interaction

in soft clay are investigated experimentally. Results from a suite of tests exploring a

wide range of vertical cyclic loading conditions in the touchdown zone of a steel catenary

riser are presented. Pipe-soil interaction stiffness is observed to vary widely according

to operative seabed strength variation from initial in situ strength conditions. Analyti-

cal frameworks are presented which describe the variability of operative undrained shear

strength due to the effects of soil remoulding along with subsequent reconsolidation. The

overall behaviour of the lower section of a steel catenary riser is explored experimentally.

iii

Geotechnical analysis of offshore pipelines and steel catenary risers

Details of an instrumented pipeline which was developed to investigate three-dimensional

riser-seabed response are presented. The apparatus and analysis methodology developed

allows for comparison of behaviour observed during experiments performed using a short

‘element’ of pipeline assuming two-dimensional plane-strain conditions and the validation

of pipe-soil interaction models developed from element tests.

This thesis progresses the understanding of geotechnical aspects of offshore pipeline

and riser behaviour. It advances the predictive capabilities of pipe-soil interaction models,

enabling more accurate response assessment and efficient design.

iv

Contents

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

Table of contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

Thesis format and authorship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

Chapter 1 General Introduction

1.1. Introduction to Offshore Pipelines and Steel Catenary Risers . . . . . . . . 1-1

1.2. Aim of Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2

1.2.1. Combined loading response of pipelines . . . . . . . . . . . . . . . . 1-3

1.2.2. The effects of cyclic loading on pipe-soil interaction . . . . . . . . . . 1-5

1.2.3. Physical modelling of the touchdown zone of a steel catenary riser . 1-5

1.3. Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-7

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-11

Chapter 2 A Plasticity Model for Predicting the Vertical and Lateral

Behaviour of Pipelines in Clay Soils

2.1. Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1

2.2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1

2.3. Experimental Developments . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3

2.3.1. Equipment developed . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3

v


2.3.2. Sample preparation and site characterisation . . . . . . . . . . . . . 2-3

2.3.3. Experimental strategy and summary . . . . . . . . . . . . . . . . . . 2-6

2.4. Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-11

2.4.1. Hardening law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-11

2.4.2. Yield surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-14

2.4.3. Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-21

2.4.4. Flow rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-23

2.5. Retrospective Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-24

2.5.1. Swipe tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-25

2.5.2. Inclined penetration tests . . . . . . . . . . . . . . . . . . . . . . . . 2-25

2.5.3. Summary of retrospective simulations . . . . . . . . . . . . . . . . . 2-26

2.6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-31

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-33

Chapter 3 Undrained Response of Shallow Pipelines Subjected to

Combined Loading

3.1. Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1

3.2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1

3.3. Experimental Programme . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3

3.4. Numerical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-6

3.4.1. Yield surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-6

3.4.2. Flow rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-7

3.5. Retrospective Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-9

3.5.1. Swipe tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-10

3.5.2. Probe tests (constant vertical load) . . . . . . . . . . . . . . . . . . . 3-10

3.5.3. Constant load path test . . . . . . . . . . . . . . . . . . . . . . . . . 3-12

3.6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-16

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-19

vi

Chapter 4 Centrifuge Modelling of Riser-Soil Stiffness Degradation in

the Touchdown Zone of a Steel Catenary Riser

4.1. Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1

4.2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2

4.3. Experimental Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-3

4.4. Sample Preparation and Characterisation . . . . . . . . . . . . . . . . . . . 4-5

4.5. Cyclic Riser Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-7

4.5.1. Cyclic total resistance . . . . . . . . . . . . . . . . . . . . . . . . . . 4-7

4.5.2. Buoyancy effect: modified Archimedes’ principle . . . . . . . . . . . 4-9

4.5.3. Back-calculation of buoyancy effect . . . . . . . . . . . . . . . . . . . 4-11

4.5.4. Back-calculation of cyclic soil strength response . . . . . . . . . . . . 4-13

4.6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-15

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-17

Chapter 5 An Analysis of Soil Strength Degradation During Episodes

of Cyclic Loading, Illustrated by the T-bar Penetration Test

5.1. Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-1

5.2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-1

5.3. Model Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-2

5.4. Cumulative Damage Number Interpretation . . . . . . . . . . . . . . . . . . 5-5

5.5. Strength Degradation and Accumulation of Damage . . . . . . . . . . . . . 5-6

5.6. Operative Shear Strength Calculation . . . . . . . . . . . . . . . . . . . . . 5-8

5.7. Mobilisation of Operative Shear Strength . . . . . . . . . . . . . . . . . . . 5-8

5.8. Example Application of Framework . . . . . . . . . . . . . . . . . . . . . . . 5-9

5.8.1. Derivation of framework parameters . . . . . . . . . . . . . . . . . . 5-9

5.8.2. Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-14

5.9. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-16

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-17

vii


Chapter 6 Effect of Remoulding and Reconsolidation on the

Touchdown Stiffness of a Steel Catenary Riser:

Observations from Centrifuge Modelling

6.1. Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-1

6.2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-2

6.3. Experimental Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-4

6.4. Sample Preparation and Site Characterisation . . . . . . . . . . . . . . . . . 6-6

6.5. Test Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-8

6.6. Interpretation of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-8

6.6.1. Buoyancy adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . 6-10

6.6.2. Displacement controlled tests . . . . . . . . . . . . . . . . . . . . . . 6-13

6.6.3. Comparison with hyperbolic model . . . . . . . . . . . . . . . . . . . 6-17

6.6.4. Effect of reconsolidation periods on response . . . . . . . . . . . . . 6-19

6.6.5. Comparison to T-bar site investigation . . . . . . . . . . . . . . . . . 6-19

6.6.6. Load controlled tests . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-22

6.7. Summary of Observed Seabed Stiffness . . . . . . . . . . . . . . . . . . . . . 6-26

6.8. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-31

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-33

Chapter 7 An Effective Stress Framework for the Variation in

Penetration Resistance Due to Episodes of Remoulding

and Reconsolidation

7.1. Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-1

7.2. Introduction and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-2

7.2.1. Geotechnical design of steel catenary risers . . . . . . . . . . . . . . 7-2

7.2.2. Remoulding and reconsolidation of soft soils . . . . . . . . . . . . . . 7-3

7.2.3. Analysis procedure for remoulding and reconsolidation . . . . . . . . 7-3

7.3. Observed Effects of Remoulding and Reconsolidation . . . . . . . . . . . . . 7-4

7.3.1. Effect on vertical pipe-soil stiffness . . . . . . . . . . . . . . . . . . . 7-4

7.3.2. Effect on T-bar penetration resistance . . . . . . . . . . . . . . . . . 7-7

viii

7.3.3. Comparison of pipe-soil and T-bar behaviour . . . . . . . . . . . . . 7-7

7.4. Model Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-9

7.4.1. Framework overview . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-9

7.4.2. Accumulation of excess pore pressure . . . . . . . . . . . . . . . . . 7-12

7.4.3. Calculation of operative undrained shear strength . . . . . . . . . . 7-14

7.4.4. Excess pore pressure dissipation . . . . . . . . . . . . . . . . . . . . 7-15

7.5. Calibration of Framework Parameters . . . . . . . . . . . . . . . . . . . . . 7-18

7.5.1. Initial specific volume profile . . . . . . . . . . . . . . . . . . . . . . 7-18

7.5.2. Initial remoulded stress profile . . . . . . . . . . . . . . . . . . . . . 7-20

7.5.3. Lumped strength parameter . . . . . . . . . . . . . . . . . . . . . . . 7-20

7.6. Example Simulation Using Framework . . . . . . . . . . . . . . . . . . . . . 7-26

7.6.1. Discussion of simulation results . . . . . . . . . . . . . . . . . . . . . 7-26

7.6.2. Possible refinements of framework . . . . . . . . . . . . . . . . . . . 7-30

7.7. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-30

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-33

Chapter 8 3D Experiments Investigating the Interaction of a Model

SCR with the Seabed

8.1. Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-1

8.2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-2

8.3. Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-3

8.4. Experimental Set-Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-5

8.4.1. Flume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-5

8.4.2. Actuator and pipe connection . . . . . . . . . . . . . . . . . . . . . . 8-6

8.4.3. Pipe and instrumentation . . . . . . . . . . . . . . . . . . . . . . . . 8-6

8.4.4. Instrument calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 8-10

8.5. Numerical Analysis of Physical Model . . . . . . . . . . . . . . . . . . . . . 8-10

8.6. Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-14

8.6.1. Monotonic test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-15

8.6.2. Cyclic test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-16

ix


8.7. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-26

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-27

8.A. Appendix A – Analysis of the Experimental Data . . . . . . . . . . . . . . . 8-29

Chapter 9 Concluding Remarks

9.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-1

9.2. Original Contributions and Main Findings . . . . . . . . . . . . . . . . . . . 9-1

9.2.1. Combined loading response of pipelines . . . . . . . . . . . . . . . . 9-1

9.2.2. The effects of cyclic loading on pipe-soil interaction . . . . . . . . . . 9-2

9.2.3. Physical modelling of the touchdown zone of a steel catenary riser . 9-4

9.2.4. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-5

9.3. Recommendations for Future Work . . . . . . . . . . . . . . . . . . . . . . . 9-7

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-9

x

Acknowledgements

I am grateful for the continual guidance and support made available throughout my studies

by my supervisor, Professor Mark Cassidy. Furthermore, I must express my gratitude to-

wards Professor David White, who effectively became a second supervisor to me, providing

much guidance and advice.

I appreciate the support offered by Dr Byron Byrne at the University of Oxford, and

for providing me with the opportunity of spending part of my PhD in Oxford. It was an

enjoyable and enriching experience.

The assistance provided by the beam and drum centrifuge technicians, Don Herley

and Bart Thompson, along with the workshop and electronics technicians is gratefully

acknowledged. Further thanks also go to the technical staff at Oxford.

I must also thank my partner, Didie, for her love and support. I would also like to

thank my parents for their ceaseless encouragement.

The financial support provided by the Western Australian Energy Research Alliance

postgraduate top-up scholarship, the University of Western Australia Convocation Post-

graduate Research Travel Award and the departmental Ad Hoc top-up scholarships is

gratefully acknowledged.

xi

Thesis format and authorship

In accordance with regulations of the University of Western Australia, this thesis is sub-

mitted as a series of papers. Chapters 2, 3, 4, 5, 6 and 8 are papers which have been

published, while Chapter 7 has been accepted for publication. The contributions of the

candidate and co-authors for the papers comprising Chapters 2–8 are as follows:

Paper 1

The first paper is presented as Chapter 2 and is authored by the candidate and Professor

Mark J. Cassidy. The paper is published as:

Hodder, M. S., and Cassidy, M. J. (2010). A plasticity model for predicting the vertical andlateral behaviour of pipelines in clay soils. Geotechnique, 60(4):247–263.

The candidate:

• planned the experimental testing programme in consultation with Professor Cassidy;

• performed the experiments in the drum centrifuge using an instrumented loading

arm designed by the candidate;

• analysed the data obtained from the experiments and calibrated the force-resultant

model components under the guidance of Professor Cassidy;

• using a purpose built FORTRAN program for the application of a pipe on calcareous

sand provided by Professor Cassidy, re-coded several subroutines of the program to

reflect the updated force-resultant model parameters for the application of a pipe on

soft clay;

• conducted retrospective numerical simulations of several experiments performed by

the candidate using the revised FORTRAN program;

• wrote the majority of the paper in collaboration with Professor Cassidy.

xiii


Paper 2

The second paper is presented as Chapter 3 and is authored by the candidate, Professor

Mark J. Cassidy and David Barrett. The paper is published as:

Hodder, M. S., Cassidy, M. J., and Barrett, D. (2008). Undrained response of shallow pipelinessubjected to combined loading. In Proc. 2nd British Geotechnical Association International Con-ference on Foundations, Dundee, Scotland.

The candidate:

• calibrated the component parameters of the force-resultant model developed in

Chapter 2 necessary for the application of zero pipe uplift capacity using experi-

mental data obtained from testing performed by Barrett;

• re-coded several subroutines of the FORTRAN program used in Chapter 2 to reflect

the updated force-resultant model parameters for the application of a pipe on soft

clay with zero pipe uplift capacity;

• conducted retrospective numerical simulations of several experiments performed by

Barrett using the revised FORTRAN program;

• wrote the majority of the paper in collaboration with Professor Cassidy.

Paper 3

The third paper is presented as Chapter 4 and is authored by the candidate, Professor

David J. White and Professor Mark J. Cassidy. The paper is published as:

Hodder, M. S., White, D. J., and Cassidy, M. J. (2008). Centrifuge modelling of riser-soilstiffness degradation in the touchdown zone of a steel catenary riser. In Proc. InternationalConference on Offshore Mechanics and Arctic Engineering, Estoril, Portugal.

The candidate:

• planned the experimental testing programme in consultation with Professor White

and Professor Cassidy;

• performed the experiments in the beam centrifuge;

• analysed the data obtained from the experiments under the guidance of Professor

White and Professor Cassidy;

• wrote the majority of the paper in collaboration with Professor White and Professor

Cassidy.

xiv

Paper 4

The fourth paper is presented as Chapter 5 and is authored by the candidate, Professor


Hodder, M. S., White, D. J., and Cassidy, M. J. (2010). An analysis of soil strength degradationduring episodes of cyclic loading, illustrated by the T-bar penetration test. International Journalof Geomechanics, 10(3):117–123.

The candidate:

• developed the analytical framework in consultation with Professor White and Pro-

fessor Cassidy;

• calibrated the framework components using experimental data obtained from testing

conducted by the candidate under the guidance of Professor White and Professor

Cassidy;

• coded the framework algorithm in a MATLAB program;

• conducted a retrospective numerical simulation of a cyclic T-bar experiment using

the MATLAB program;


Cassidy.

Paper 5

The fifth paper is presented as Chapter 6 and is authored by the candidate, Professor


Hodder, M. S., White, D. J., and Cassidy, M. J. (2009). Effect of remolding and reconsolidationon the touchdown stiffness of a steel catenary riser: observations from centrifuge modeling. In Proc.41st Offshore Technology Conference, Houston, USA.

The candidate:

• planned the experimental testing programme in consultation with Professor White

and Professor Cassidy;

• performed the experiments in the beam centrifuge;

• analysed the data obtained from the experiments under the guidance of Professor

White and Professor Cassidy;


Cassidy.

xv


Paper 6

The sixth paper is presented as Chapter 7 and is authored by the candidate, Professor

David J. White and Professor Mark J. Cassidy. The paper has been accepted for publica-

tion as:

Hodder, M. S., White, D. J., and Cassidy, M. J. (2010). An effective stress frameworkfor the variation in penetration resistance due to episodes of remoulding and reconsolidation.Geotechnique, accepted for publication.

The candidate:

• developed the analytical framework in consultation with Professor White and Pro-

fessor Cassidy;

• calibrated the framework components using experimental data obtained from testing

conducted by the candidate under the guidance of Professor White and Professor

Cassidy;

• coded the framework algorithm in a MATLAB program;

• conducted a retrospective numerical simulation of an episodic cyclic T-bar experi-

ment with intervening pause periods using the MATLAB program;


Cassidy.

Paper 7

The seventh paper is presented as Chapter 8 and is authored by the candidate and Dr. By-

ron W. Byrne as a collaboration between the University of Western Australia and the

University of Oxford. The paper is published as:

Hodder, M. S., and Byrne, B. W. (2010). 3D experiments investigating the interaction of amodel SCR with the seabed. Applied Ocean Research, 32(2):146–157.

The candidate:

• planned the experimental testing programme in consultation with Dr. Byrne;

• designed the instrumented pipe and pipe-actuator connection in consultation with

Dr. Byrne;

• performed the experiments;

• analysed the data obtained from the experiments;

• wrote the majority of the paper in collaboration with Dr. Byrne.

xvi

The experiments were performed using a pipeline testing facility incorporating a flume,

computer-controlled actuation device and soil sample preparation system previously de-

veloped by D.Phil candidate Jens Schupp and Dr. Byrne.

I certify that, except where specific reference is made in the text to the work of others, the

contents of this thesis are original and have not been submitted to any other university.

xvii

1General Introduction

1.1 Introduction to Offshore Pipelines and Steel Catenary

Risers

The continuing depletion of fossil fuel reserves in shallow water require oil and gas extrac-

tion to take place in environments of ever increasing water depth. As the developments

move further offshore, the pipelines and risers used in the transportation of hydrocar-

bon products form an increasingly important component of the deep water development

infrastructure. During the design process, it must be shown that the pipeline or riser

will not suffer overstressing when subjected to the various loading regimes throughout its

lifetime — with a failure having obvious environmental and economic consequences. The

interaction with the seabed is an essential component of the analysis undertaken in the

design process. This thesis investigates various geotechnical aspects of the interaction of

pipelines and risers with the seabed.

It is common to bury or trench offshore pipelines during their installation in shallow

water in order to provide protection and restraint against lateral loads. In deep water,

however, burial or trenching is uneconomical and pipelines are generally laid directly on

the seabed. On-bottom pipelines are subjected to various combined vertical and horizontal

loading conditions (Figure 1.1) ranging from those induced from external environmental

effects to cycles of operational temperature fluctuation which can cause the pipeline to

buckle laterally. The designer must quantify the response of the pipeline when subjected

to these loads to assess the pipeline stability and ensure stress levels are acceptable. For

meaningful assessments to be made, it is essential to model the pipe-soil interaction accu-

rately. The guidance provided in traditional design codes such as those published by AGA

(1993) and DNV (2007) regarding the interaction of the pipeline and seabed becomes

limited as designers utilise more sophisticated analysis methods such as an integrated

fluid-soil-structure approach or are required to limit and predict pipeline displacements as

part of the design criteria.

A typical deep water offshore development consists of a floating vessel or platform,

a mooring system and risers used to transport the hydrocarbon product between the

1-1


seabed

Vertical load

Horizontal load

Figure 1.1: On-bottom pipeline subjected to combined loading

platform and the seabed. Steel catenary risers (SCRs) can be a more cost effective option

than traditional vertical or flexible risers and consist of a steel pipe, typically of 200-

500 mm diameter, suspended in the form of a catenary from the vessel to the seabed

(Figure 1.2). The region where the SCR lands on the seabed is known as the ‘touchdown

zone’. Throughout the lifetime of the facility, the movement of the floating platform

caused by wind and waves will induce many cycles of loading on the riser pipe at the

touchdown zone. At this location, analysis shows that a fatigue ‘hot spot’ forms as a

result of the repetitive cyclic load application on the riser. The pipe-soil interaction in

the touchdown zone is complex and the assumed seabed stiffness can heavily influence

the fatigue life prediction of the riser (Bridge et al., 2004; Bridge, 2005; Clukey et al.,

2007). With fatigue life assessments a critical design issue, an accurate representation of

the pipe-soil interaction in the touchdown zone is an essential component to meaningful

analysis results.

1.2 Aim of Research

The overarching aim of this thesis is to advance the understanding of pipe-soil load-

displacement response through the analysis of data obtained via physical modelling and

the development of interaction models which can function as boundary condition elements

between the soil and pipe in a structural analysis. The areas of research of the thesis are

illustrated in Figure 1.3. Various aspects of pipe-soil interaction are explored; however, the

relationship between pipe-soil load and displacement serves as the fundamental underlying

concept which is common across the research areas.

The detail of the specific areas of research with associated aims are described in the

following subsections.

1-2

General Introduction

seabed

touchdown zone

riser

mooringsystem

floating vessel or platformfloating vesselor platform

mooringsystem

seabed

steel catenary riser

touchdown zone

Figure 1.2: Schematic of a typical deep water offshore development showing steel catenaryriser and touchdown zone

1.2.1 Combined loading response of pipelines

As illustrated in Figures 1.1 and 1.3a, on-bottom pipelines are subjected to combined ver-

tical and horizontal loadings which arise from external environmental effects and/or opera-

tional temperature fluctuation. The combined loading response of on-bottom pipelines has

been typically assessed using a ‘friction factor’ approach — where the horizontal capacity

of the pipe-soil system is related to the vertical load on the pipe — or as a two-component

model where the effects of friction are combined with the additional horizontal capacity

provided by the soil beside the pipe, as described by Cathie et al. (2005), for example.

It is usual to include various empirical factors in the capacity calculations to account for

different soil types and site variability. The reliance on empirical factors can obscure an

understanding of the underlying mechanics that dictate the response of the pipe-soil sys-

tem, which can make projection of a method to conditions outside past experience and

observations difficult. In addition, the relative magnitudes of displacement components

as the pipe is loaded and possibly fails the soil are not able to be captured when us-

ing traditional two-component models which only quantify the ultimate capacity of the

system.

There exists a need to develop interaction models which have the ability to predict

the combined loading pipe-soil response using more fundamental concepts that reduce the

dependence on empiricism. A ‘force-resultant’ model links the forces on a soil-structure

element to associated displacements in a framework similar to a material constitutive

model which links stresses and associated strains. These models are based on strain-

hardening plasticity theory and have been used successfully in the past to predict the

behaviour of a range of shallow foundation types on various soil conditions (as examples,

1-3


(a)

(b)(c)

On-bottom pipeline

Steel catenary riser

Aim 1:

combined loading

response of pipelines

[Chapters 2–3]

Aim 2:

effects of cyclic loading

on pipe-soil interaction

[Chapters 4–7]

Aim 3:

physical modelling of lower section of

steel catenary riser in the touchdown zone

[Chapter 8]

seabed

pipe element

pipe element

Figure 1.3: Schematic of research aims

1-4


see, Tan, 1990; Martin, 1994; Gottardi et al., 1999; Zhang, 2001). They can be ‘attached’

directly to structural elements in numerical analyses, incorporating complex geotechnical

behaviour within the interaction model without having to represent the surrounding soil

as a semi-infinite medium.

To this end, the first objective of this thesis is:

• to develop a force-resultant model which can be used to predict the response of a

pipeline subjected to combined vertical and horizontal loading.

1.2.2 The effects of cyclic loading on pipe-soil interaction

A steel catenary riser will be subjected to many cycles of loading throughout its lifetime,

as illustrated in Figure 1.3b. The contact between the riser pipe and the seabed in the

touchdown zone of a steel catenary riser is typically represented using a series of closely

spaced pipe-soil interaction models which link the vertical pipe-soil contact force and the

vertical displacement of the pipe as shown in Figure 1.4. It is common to idealise the

interaction using linear springs with stiffness proportional to the strength of the soil,

however, some models include the non-linearity of the pipe-soil response (Bridge et al.,

2004; Aubeny and Biscontin, 2008; Randolph and Quiggin, 2009).

The seabed soils found where SCRs operate are typically soft clays and the rate at

which the riser pipe displaces induces an undrained response in the surrounding seabed

soil. The cyclic loading conditions the riser will be subjected to throughout its lifetime

can cause changes in the operative strength of the seabed soil. Robust cyclic loading can

soften the surrounding soil which can be exacerbated due to the entrainment of water into

the soil if the riser pipe is lifted clear above the seabed surface before being repenetrated.

The dissipation of excess pore pressure generated during the undrained response of the

soil can induce further changes in the operative strength. Soil strength variation directly

influences the pipe-soil interaction stiffness. Therefore, the quantification of operative

seabed strength change from the in situ value is essential for an accurate fatigue life

prediction to be made for the SCR.

The second objective of this thesis is:

• to investigate the effects of cycles of vertical motion on pipe-soil interaction along

with the development of analytical frameworks to quantify operative soil strength

variation — incorporating phenomena such as softening due to soil remoulding and

the effects of reconsolidation.

1.2.3 Physical modelling of the touchdown zone of a steel catenary riser

It is common for the pipe-soil interaction models used in the analysis of SCRs to be devel-

oped using behaviour observed during experimental testing conducted with a short section

of model riser pipe. Using an ‘element’ of model pipe, the interaction is somewhat sim-

plified and two-dimensional, plane strain conditions can be assumed. The data obtained

1-5


Pipeseabed

Vertical pipe-soil load

Ver

tica

lpip

edispla

cem

ent

2D pipe-soil interactionmodel linking vertical loadand displacement

series of pipe-soilinteraction models

seabed

SCR

Figure 1.4: Schematic of pipe-soil interaction model in the touchdown zone of a steelcatenary riser

1-6


in this style of testing provides invaluable insight regarding the pipe-soil response and can

be used to directly calibrate interaction models such as those presented by Bridge et al.

(2004), Aubeny and Biscontin (2008) and Randolph and Quiggin (2009). However, it is

important to validate the interaction models developed using two-dimensional assumptions

against experimental data gathered from a more realistic modelling of the field behaviour

(as illustrated in Figure 1.3c) to determine the influence of effects not able to be captured

in two-dimensional testing.

The third and final objective of this thesis is:

• to develop a laboratory apparatus which represents a more realistic modelling of field

behaviour and perform experiments supported by an appropriate analysis methodol-

ogy to supplement the observations gained through two-dimensional element testing.

1.3 Thesis Outline

The body of this thesis is presented as a collection of technical papers with each chapter

comprising a different paper. Each chapter begins with an introduction and review of

current practices and literature relevant to the particular topic. These introductory sec-

tions overlap somewhat across the various chapters as a result of this style of thesis. Each

chapter closes with concluding remarks specific to the topic of the chapter. Conclusions

relevant to the entire thesis are presented along with recommendations for future work in

a final chapter (Chapter 9). Chapters 2–8 form the thesis body and address the research

aims as follows.

1. The combined vertical and horizontal loading behaviour of pipelines

• Chapter 2 presents a force-resultant model applicable to predicting the com-

bined loading response of a pipeline on soft clay. The model is derived using

experimental data along with theoretical and numerical techniques. A purpose

written FORTRAN program is used to numerically retrospectively simulate

several combined loading experiments. The model’s predictive capability is

demonstrated through comparison of the numerical and experimental response.

• Chapter 3 outlines modifications to the components of the model described in

Chapter 2 required for an application of zero pipe uplift capacity with a focus

on the behaviour at shallow pipe embedments. The original model presented

in Chapter 2 includes an uplift capacity that was observed in the experimental

testing from which the model was derived. This uplift capacity requires tensile

stress to be sustained at the pipe-soil interface and certain conditions or conser-

vatism may warrant its exclusion — particularly at shallow embedments. The

components of the modified model for an application of zero uplift capacity are

validated via numerical retrospective simulation of several combined loading

experiments of a shallowly embedded pipe including conditions of vertical load

control and realistic combined loading paths.

1-7


2. The effects of vertical cyclic loading on pipe-soil interaction

• Chapter 4 presents the results of an experiment conducted to explore the ef-

fects of soil strength degradation caused by vertical cycling in soft clay. During

the test, large-amplitude vertical cycling was imposed between fixed displace-

ment limits — representative of a storm condition. The pipe was lifted clear

above the model seabed surface, allowing the entrainment of water into the

soil. The dominance of soil buoyancy on the pipe-soil response in very soft, re-

moulded soil is identified and the enhanced strength degradation due to water

entrainment is quantified by comparison to the soil sensitivity calculated from

a site investigation conducted in the same soil sample.

• Chapter 5 continues the strength degradation theme of Chapter 4 and presents

an analytical framework applicable to the prediction of the degraded operative

undrained shear strength experienced by a cylinder subjected to cycles of gen-

eral vertical displacement. The soil strength is assumed to drop from the in situ

value to a remoulded state using degradation parameters that can be obtained

via site investigation data. The framework is demonstrated by numerically sim-

ulating a test in which a cylindrical site investigation tool is cycled in a soft

clay sample.

• Chapter 6 presents the results of a suite of tests performed to investigate the

effects of a wide range of cyclic loading conditions on the pipe-soil interaction

stiffness. Large and small-amplitude cycling under both load and displacement

control were conducted with some tests involving intervening pause periods, al-

lowing the effects of reconsolidation on the response to be explored. The results

are presented as a ‘secant stiffness ratio’ for adoption within a linear idealisation

of the unload-reload response. The effects of remoulding and reconsolidation

on the pipe-soil interaction stiffness are quantified and are compared against

the softening and subsequent recovery of strength after pause periods observed

in a site investigation style test which was conducted in the same soil sample.

• Chapter 7 extends the analytical framework presented in Chapter 5 to include

the recovery of soil strength through reconsolidation after periods of inactivity

observed in Chapter 6. The undrained shear strength degradation in Chapter 5

due the accumulation of ‘damage’ is replaced by a reduction in operative effec-

tive stress via an increase of excess pore pressure generated during undrained

loading. By linking the excess pore pressure to a dissipation model, recon-

solidation effects can be included in the framework. The analytical model is

demonstrated by numerically simulating a test in which a cylindrical site in-

vestigation tool is cycled in a soft clay sample with intervening pause periods

between cyclic episodes.

1-8


3. Physical modelling of the touchdown zone of a steel catenary riser

• Chapter 8 describes the details of a novel experimental apparatus developed

for the investigation of the response of the lower section of a steel catenary

riser in the touchdown zone. Data gathered from monotonic and cyclic exper-

iments are presented. A simple analysis methodology is outlined for the back

calculation of the distribution of vertical reaction throughout the touchdown

zone, facilitating the comparison of pipe-soil bearing stress experienced by an

‘element’ of pipe against results obtained from two-dimensional experiments.

1-9


References

AGA (1993). Submarine pipeline on-bottom stability. Vol. 1: Analysis and design guide-lines. Technical report, American Gas Association (AGA).

Aubeny, C. P. and Biscontin, G. (2008). Interaction model for steel compliant riser onsoft seabed. In Proc. 40th Offshore Technology Conference, Houston, USA.

Bridge, C. D. (2005). Effects of seabed interaction on steel catenary risers. PhD thesis,School of Engineering, The University of Surrey.

Bridge, C. D., Laver, K., Clukey, E. C., and Evans, T. R. (2004). Steel catenary risertouchdown point vertical interaction model. In Proc. 36th Offshore Technology Confer-ence, Houston, USA.

Cathie, D. N., Jaeck, C., Ballard, J. C., and Wintgens, J. F. (2005). Pipeline geotechnics —state-of-the-art. In Proc. International Symposium on Frontiers in Offshore Geotechnics,pages 95–114, Perth, Australia.

Clukey, E. C., Ghosh, R., Mokarala, P., and Dixon, M. (2007). Steel catenary riser(SCR) design issues at touch down area. In Proc. 17th International Offshore and PolarEngineering Conference, pages 814–819, Lisbon, Portugal.

DNV (2007). Recommended practice RP-F-109: On-bottom stability design of submarinepipelines. Technical report, Det Norske Veritas (DNV).

Gottardi, G., Houlsby, G. T., and Butterfield, R. (1999). Plastic response of circularfootings on sand under general planar loading. Geotechnique, 49(4):453–469.

Martin, C. M. (1994). Physical and numerical modeling of offshore foundations undercombined loads. DPhil. thesis, The University of Oxford.

Randolph, M. F. and Quiggin, P. (2009). Non-linear hysteretic seabed model for catenarypipeline contact. In Proc. International Conference on Ocean, Offshore and ArcticEngineering, Honolulu, USA.

Tan, F. S. C. (1990). Centrifuge and theoretical modeling of conical footings on sand. PhDthesis, The University of Cambridge.

Zhang, J. (2001). Geotechnical stability of offshore pipelines in calcareous sand. PhDthesis, School of Civil and Resource Engineering, The University of Western Australia.

1-11

2A Plasticity Model for Predicting the Vertical and Lateral

Behaviour of Pipelines in Clay Soils

2.1 Abstract

A complete theoretical model for predicting the undrained behaviour of a rigid pipe in clay

soils when subjected to combined vertical and horizontal loading is described. Physical

modelling of a pipe on soft, lightly overconsolidated kaolin clay was conducted, with the

experimental test programme specifically designed to establish the model parameters. The

testing was conducted within the University of Western Australia’s geotechnical drum cen-

trifuge using an element of pipe 10 mm in diameter, 50 mm in length and at an acceleration

50 times the Earth’s gravity. The model presented is expressed by the force resultants

on the pipe and the corresponding displacements and allows predictions of response to be

made for various vertical and horizontal load or displacement combinations. However, it

is limited to monotonic loading and does not account for the influence of berms created

by repetitive large lateral displacements. The model is verified in this paper by retrospec-

tively simulating a selection of combined loading tests and comparing the output with the

experimentally recorded results.

2.2 Introduction

Pipelines laid directly on the seabed are a critical link between major offshore oil and gas

developments and the mainland. With any failure or disruption having obvious economic

and environmental consequences, offshore pipelines must be stable under the loading condi-

tions experienced during their design life. Environmental loading from waves and currents

or even axial stresses induced by high operational temperatures and pressures can apply a

combined vertical, V , and lateral load, H, on the pipe. Engineers using standard industry

guidelines (such as AGA, 1993; DNV, 2007) have typically designed pipelines based on

capacity predictions using empirical approaches calibrated against experimental testing

data (though arguably for a limited range of soil conditions, Zhang and Erbrich, 2005).

These traditional approaches have considered the lateral resistance of pipelines as a sin-

2-1


gle friction factor, with resistance directly proportional to the pipeline’s submerged unit

weight, or as a ‘two component’ model that consists of a sliding and passive resistance

component (Cathie et al., 2005). The predictive capability of these traditional approaches

becomes limited as pipeline engineers utilise more sophisticated design approaches and

assessment criteria, such as integrated hydrodynamic and structural modelling and limit-

ing pipeline movements. The use of numerous ad hoc empirical factors (such as Wagner

et al., 1987; AGA, 1993; Verley and Lund, 1995) limits implementation in any integrated

hydrodynamic, structural and geotechnical assessment.

The use of force-resultant plasticity models are proving an effective alternative in

modelling soil-structure interaction of shallow foundations. When applied to pipe-soil

response, they provide a more fundamental understanding of the mechanisms involved and

can be incorporated directly within sophisticated pipeline analysis programs (Cathie et al.,

2005; Zhang and Erbrich, 2005; White and Randolph, 2007). Zhang et al. (1999, 2002)

outlined such a model for predicting the drained behaviour of vertically and laterally loaded

pipes on calcareous sands. Also using sand, Calvetti et al. (2004) performed experimental

and numerical investigations regarding the combined loading behaviour of pipelines but

with a focus on the impact of a landslide on the pipeline. Similarly, di Prisco et al. (2004)

presented a model derived using analytical methods applicable to capturing the response

in a cohesive soil, also with a landslide-impact focus. Utilising the same framework, this

paper describes a plasticity model for pipes on clay soils under undrained conditions. The

model expresses the pipeline behaviour purely in terms of the vertical and lateral loads

on the pipeline and the corresponding displacements, with the sign convention adopted

shown in Figure 2.1. The advantage of this formulation is that the geotechnical behaviour

can be incorporated directly into structural finite element programs, without any need for

special transition or interface elements between the structure and soil.

The model is based on displacement hardening plasticity theory and has four compo-

nents:

1. A yield surface in combined loading space that describes the boundary of elastic and

plastic states;

2. A hardening law relating the evolution of yield surface size with plastic displacement;

3. A description of elastic response; and

4. A flow rule that determines the ratio between plastic displacement components dur-

ing a plastic loading step.

The use of the consistency condition allows numerical formulation of a model that can

predict the load-displacement response. However, this is limited to monotonic loading and

relatively small movements. The lateral response of pipes in soft clays is affected by the

building up of berms and trenches around the pipe side. Large deformation movement

can be controlled by these berms and the model does not incorporate this response.

2-2

A Plasticity Model for Predicting the Vertical and Lateral Behaviour of Pipelines in Clay Soils

w

u

D

V

H

Figure 2.1: Sign convention of load and displacement

As consistent with pipeline analysis all horizontal, H, and vertical, V , loads in the

model are per unit length of pipe. Experimental, theoretical and numerical techniques

have been used to derive the model components. An introduction to the experiments

conducted is initially presented, before the plasticity model is described. Finally, the

application of the model is shown by retrospective numerical simulation of a selection of

the pipe-soil experiments.

2.3 Experimental Developments

2.3.1 Equipment developed

The tests were conducted in the drum centrifuge facility at the University of Western

Australia (Stewart et al., 1998). The drum centrifuge at UWA has an outer diameter of

1200 mm, a channel height of 300 mm and a radial depth of 200 mm. Tests were performed

at an acceleration of 50 times that of Earth’s gravity (referred to as 50 g), using a model

pipe element of 10 mm diameter and 50 mm length (0.5 m and 2.5 m respectively at pro-

totype scale). The length to diameter ratio of the pipe was such that end effects were

believed to be negligible and 2D plane strain conditions are assumed. The pipe element

was attached to the end of a loading arm as shown in Figure 2.2. The loading arm was

strain gauged to record axial and bending loads from which the vertical and horizontal

forces on the pipe element due to soil reaction were derived. An adjustment for the chang-

ing effective weight of the model pipe and loading arm with radial position within the

centrifuge was made to the vertical loads.

2.3.2 Sample preparation and site characterisation

All tests were conducted using saturated kaolin clay with properties set out in Table 2.1.

Kaolin powder was combined with water to produce a slurry with a moisture content

of approximately 105 %. This was mixed in a barrel mixer for five hours with a vacuum

applied for the final two hours in order to remove any air from the slurry. A sand drain was

created at the base of the sample by spraying a 10 mm thick sand layer into the centrifuge

2-3


10mm

50mm

Bending strain gauging

Axial load cell

Figure 2.2: Pipe element attached to loading arm

Table 2.1: Kaolin clay properties (after Stewart, 1992)

Property Symbol Value

Liquid Limit LL 61 %Plastic Limit PL 27 %

Plasticity Index Ip 34 %Soil Particle Density Gs 2.6

Angle of Internal Friction (triaxial compression) φ′ 23◦

Critical State Frictional Constant M 0.92Voids Ratio @ p′ = 1kPa on C.S.L. ecs 2.14

Critical State Parameter Γ = 1 + ees 3.14Slope of N.C.L. (loading) λ 0.205

Slope of S.L. (O.C. line, unloading) κ 0.044Plastic Volumetric Strain Ratio Λ = (λ − κ) /λ 0.785

Coefficient of Consolidation (mean) cv ≈ 2m2/yearCompression Index Cc 0.48

Swelling Index Cs 0.092

2-4


channel. The slurry was then slowly pumped into the channel under a layer of water to

avoid any air entrainment. The channel was filled with the slurry and the acceleration

increased to 50 g. The sample was left to partially consolidate overnight. The following day

the channel was topped up with additional slurry. The sample was then left for two days to

consolidate by which time the pore pressures had stabilised and the sample was normally

consolidated. To increase the sample strength near the surface to allow for loads to be

reliably measured at small pipe embedments, the sample was lightly overconsolidated. To

achieve this, a sand layer of 45 mm thickness was sprayed onto the surface of the sample.

The sample was left to consolidate until the pore pressures stabilised. This required an

additional two days. The centrifuge was then stopped and the sand layer removed. The

sample was approximately 125 mm deep (6.25 m at prototype scale).

To determine the strength profile a 5 mm diameter T-bar penetrometer (Stewart and

Randolph, 1991, 1994; Watson, 1999) was used. Over the course of testing 26 T-bar

tests were conducted. The tests were performed at penetration rates between 0.5 and

2 mm/s corresponding to non-dimensional velocities vDT−bar/cv (where v is the penetration

velocity, DT−bar is the diameter of the T-bar and cv is the coefficient of consolidation)

between 40 and 160 indicating undrained conditions (Finnie, 1993). The undrained shear

strength, su, was estimated based on the relationship:

su =V

NcA(2.1)

where V is the vertical load recorded by the T-bar load cell, Nc an assumed bearing

capacity factor and A the projected area of the T-bar. A single Nc value of 10.5 has been

widely used in interpreting T-bar data (as examples see Randolph et al., 1998; Watson,

1999; House et al., 2001; Cassidy et al., 2004; Chung and Randolph, 2004). However,

as the soil strength near the surface was critical in interpreting the experimental results,

depth dependent bearing capacity factors derived by Barbosa-Cruz and Randolph (2005)

were used. These factors were calculated by rigorous large deformation analyses of a

rigid cylinder penetrated from a very small embedment to a depth of five diameters, with

the Remeshing and Interpolation Technique with Small Strains (RITSS) utilised in the

solution routine (Hu and Randolph, 1998). The penetration of a smooth and rough pipe

into homogeneous and non-homogeneous soil was analysed. The non-homogeneous soil

had a linearly increasing shear strength with depth profile and a ρDT−bar/sum ratio equal

to 0.3, where ρ is the shear strength gradient and sum is the undrained shear strength at

the soil surface. The relationship:

Nc = φNNc,deep (2.2)

provides a simple formulation that can be used to fit their data, where Nc,deep is the

maximum value of Nc and is applicable to deep behaviour at several pipe diameters embed-

ment. φN is a transition factor in the form of a general ellipse that captures the variation

2-5


of Nc with depth:

(

1 −z

zN,deep

)AN

+ φBNN = 1 (2.3)

where z = z/DT−bar is the depth of the T-bar into the sample normalised by the

diameter of the T-bar, zN,deep is the normalised depth at which Nc,deep occurs and AN,

BN are parameters controlling the abruptness of the transition at zN,deep and the initial

steepness of the relationship respectively. The transition factor can be written directly as:

φN =

[

1 −

(

1 − min

(

1,z

zN,deep

))AN]1/BN

(2.4)

Table 2.2 shows the parameters for use in Equation 2.4 for the cases presented by

Barbosa-Cruz and Randolph along with parameters for average pipe interface roughness

and soil homogeneity. While Barbosa-Cruz and Randolph back calculated Nc values using

the undrained shear strength at the point of maximum contact width of the pipe, the

parameters in Table 2.2 are derived from and relative to the undrained shear strength at

the pipe invert and the full pipe diameter, without any correction made for the change in

contact width for depths less than 0.5 diameters.

The strength profile obtained using a depth dependant Nc relationship with parameters

for average pipe interface roughness and soil homogeneity (Nc,deep = 9.87 and zN,deep, AN,

BN = 4.63, 1.26, 3.24 respectively) is compared to that derived using a constant Nc of 10.5

in Figure 2.3. The profiles are an average of the 26 T-bar penetration tests. A linear

fit to the shear strength profile to a depth of 2.5m is also shown. This was the region

where the majority of testing occurred and could be approximated as having an undrained

shear strength of 3.5 kPa at the soil surface and an increasing shear strength gradient of

0.7 kPa/m (at prototype scale).

The resulting ρD/sum ratio for the sample is equal to 0.1, which lies between the two

Barbosa-Cruz and Randolph cases. Furthermore, if a submerged unit weight of 6 kN/m3

is assumed, which is typical for soft kaolin clay, a su/γ′z ratio of 1.3 is obtained at an

embedment of one model pipe diameter. This also lies between the Barbosa-Cruz and

Randolph values of 1.5 and 1.1 for the homogeneous and non-homogeneous cases respec-

tively. This ratio is a critical parameter influencing the embedment at which backflow

occurs and therefore, effects the vertical penetration response. Because the sample values

for these two ratios lie between the cases presented by Barbosa-Cruz and Randolph, the

application of the presented Nc formulation is justified.

2.3.3 Experimental strategy and summary

Experiments were performed to establish the V : H force-resultant model parameters for

the application of a pipe on clay soil, subjected to undrained conditions. While particular

attention was given to the calibration of the yield surface and flow rule parameters for

2-6


Undrained shear strength, su [kPa]

Equiv

alen

tpro

toty

pe

dep

th,z

[m]

z/D

T−

bar[-]

su = 3.5 + 0.7z kPa

(z in m)

Shear strength

profile using

constant Nc = 10.5

Shear strength profile

using depth dependant

Nc formulation

(Equations 2.2 and 2.4

0 2 4 60

2

4

6

8

10

0

0.5

1

1.5

2

2.5

Figure 2.3: Sample shear strength profile

shallow pipe embedments more typically encountered in practice, a wide range of pipe

penetrations was explored to allow for a thorough investigation of the variation of vertical

and horizontal capacities with embedment and to identify the transition of these model

components to a deep mechanism. The following tests were conducted:

• four vertical penetration (load-unload-reload) tests to calibrate the hardening law,

uplift capacity and provide an estimate of vertical elastic stiffness;

• 15 swipe tests at depths ranging from 0.2 to 5 diameters to investigate the yield

surface shape variation with embedment; and

• six inclined penetration tests to investigate the flow rule; three tests from the soil

surface at angles of 22.5◦, 45◦ and 67.5◦ to the horizontal and an additional three

from an initial embedment of one diameter at equivalent penetration angles.

Further details of these tests are provided in Tables 2.3–2.6 and in the proceeding

discussion on the model.

2-7

Geote

chnic

alanaly

sisofoffsh

ore

pip

elin

es

and

steelcate

nary

risers

Table 2.2: Bearing capacity factor parameters

Case Roughness Homogeneity Nc,deep zN,deep AN BN Source of data for parameter fitting

1 Smooth Homogeneous 9.35 3.65 1.23 2.88 Barbosa-Cruz and Randolph (2005)2 Rough Homogeneous 12.11 5.00 1.11 2.60 Barbosa-Cruz and Randolph (2005)3 Smooth Non-Homogeneous 8.39 3.14 1.17 3.14 Barbosa-Cruz and Randolph (2005)4 Rough Non-Homogeneous 10.06 4.64 1.18 3.58 Barbosa-Cruz and Randolph (2005)5 Average Homogeneous 10.73 5.00 1.12 3.11 Average of cases 1 and 26 Average Non-Homogeneous 9.18 4.04 1.26 3.40 Average of cases 3 and 47 Smooth Average 8.71 3.15 1.17 3.01 Average of cases 1 and 38 Rough Average 11.16 5.00 1.08 3.10 Average of cases 2 and 49 Average Average 9.87 4.63 1.26 3.24 Average of cases 1–4

Table 2.3: Summary of vertical penetration tests

Test Number Description Figure

1.201.1 Penetrate to 8D with unload-reload loops at ∼ 1D, 3D, 5D, 7D 2.5, 2.6, 2.111.202 Penetrate to 8D with unload-reload loops at ∼ 1D, 3D, 5D, 7D 2.5, 2.6, 2.111.203 Penetrate to 8D with unload-reload loops at ∼ 2D, 4D, 6D 2.5, 2.6, 2.111.204 Penetrate to 8D with unload-reload loops at ∼ 2D, 4D, 6D 2.5, 2.6, 2.11

2-8


Table 2.4: Summary of normally loaded swipe tests

Test NumberDescription Results

Figurew/D

at Hmax

V/V0 Hmax/V0 u/D

1.302.1 0.2 0.438 0.274 0.065 2.8, 2.9, 2.10a1.303 0.3 0.384 0.334 0.056 2.8, 2.91.304 0.4 0.465 0.385 0.066 2.8, 2.9

1.305.2(a) 0.5 0.410 0.343 0.075 2.7a, 2.8, 2.9, 2.10b, 2.131.306 0.75 0.374 0.384 0.105 2.8, 2.9

1.302.1 1.5 0.252 0.611 0.236 2.8, 2.9, 2.10c1.303 2 0.256 0.621 0.262 2.8, 2.91.304 3 0.068 0.786 0.550 2.8, 2.9

1.305.2(b) 4 0.070 0.768 0.515 2.8, 2.91.306 5 0.059 0.834 0.584 2.8, 2.9, 2.10d

Table 2.5: Summary of overloaded swipe tests

Test NumberDescription Results

Figurew/D unload at Hmax

initial during swipe V/V0 V/V0 Hmax/V0 u/D

1.311 0.2 0.17 -0.324 0.266 0.220 0.087 2.8, 2.10a, 2.141.309 0.5 0.43 -0.345 0.291 0.305 0.148 2.7b, 2.8, 2.10b1.316 0.75 0.59 -0.458 0.273 0.288 0.125 2.81.315 3 2.83 -0.466 0.203 0.531 0.764 2.81.309 4 3.87 -0.447 0.177 0.704 0.951 2.8

Table 2.6: Summary of inclined penetration tests

Test NumberDescription

Figurew/D angle to

initial final horizontal [◦]

1.402 0 2 22.5 2.121.401 0 2 45 2.12, 2.151.403 0 2 67.5 2.12

1.404.1 1 3 22.5 2.12, 2.161.405 1 3 45 2.121.406 1 3 67.5 2.12

2-9

Geote

chnic

alanaly

sisofoffsh

ore

pip

elin

es

and

steelcate

nary

risers

Table 2.7: Summary of model parameters

Model Component Parameter Dimension Description Parameter Value Notes

Geometry D L External pipe diameter user definedExternal pipe diameter used in theexperiments was 0.5 m (at prototypescale)

Soil strengthsum

ρF/L2

F/L3 Undrained shear strength at soil surface user defined

Used to define the undrained shearstrength at the pipe invert, su0, ac-cording to Equation 2.6. The soilsample used in the experiments hadan sum = 3.5 kPa and ρ = 0.7 kPa/m

Hardening law

Nc,deep

zN,deep

AN

BN

----

Vertical bearing capacity factor at deep embedmentNormalised pipe invert embedment at Nc,deep

Curve fitting parameterCurve fitting parameter

see Table 2.2

Used to define the vertical bearing ca-pacity factor, Nc, according to Equa-tions 2.2 and 2.4, substituting z withw. The undrained vertical bearing ca-pacity per unit length of pipe, V0, iscalculated according to Equation 2.5

Uplift capacity

(Vt/V0)deep

wuplift,deep

Auplift

Buplift

----

Normalised uplift capacity at deep embedmentNormalised pipe invert embedment at (Vt/V0)deep


-0.754

1.163.35

Used to define the normalised upliftcapacity, Vt/V0, according to Equa-tions 2.7 and 2.8

Yield surface

h0,surface

h0,deep

wh,deep

Ah

Bh

β1

β2

-----

--

Normalised horizontal capacity at surfaceNormalised horizontal capacity at deep embedment

Normalised pipe invert embedment at h0,deep


Yield surface curvature parameter for low (V/V0)Yield surface curvature parameter for high (V/V0)

0.1470.83.51.291.59

0.750.75

aUsed to define the normalised hori-zontal capacity, h0 = Hmax/V0, ac-cording to Equations 2.11 and 2.12b

cd

Elasticity Kv - Vertical elastic stiffness constant 200Used to define the vertical and hor-izontal elastic stiffnesses as kve =Kvsu0 and khe = 0.925kve

Flow ruleβ3

β4

--

Plastic potential curvature parameter for low (V/V0)Plastic potential curvature parameter for high (V/V0)

0.650.65

2-1

0


2.4 Model

The sign conventions and nomenclature used in the model are shown in Figure 2.1. All of

the parameters describing the model, as well as typical parameter values, are set out in

Table 2.7.

2.4.1 Hardening law

The premise of the force-resultant plasticity model is that the yield surface can be described

by the current plastic vertical displacement of the pipe. Therefore, an accurate description

for the purely vertical loading of a pipe is required. It is usual to define the vertical capacity

of a pipe penetrating undrained soil as:

V0 = Ncsu0D (2.5)

where Nc is a bearing capacity factor and su0 the undrained shear strength of the soil

at the pipe invert. In most applications this is approximated as:

su0 = sum + ρwp (2.6)

The vertical capacity per unit length has been written as V0, a value that will also be

used to define the positive apex point of the yield surface. The pipe invert embedments

in Equations 2.5 and 2.6 which define the hardening law refer to the plastic component,

wp, of the total pipe invert embedment, w.

Bearing capacity factors applicable to the penetration of cylinders into undrained soil

have been presented by, amongst others, Murff et al. (1989), Aubeny et al. (2005), Barbosa-

Cruz and Randolph (2005) and Merifield et al. (2008). The differences between various

Nc relationships is not the focus of this paper, and the approach described in Section 2.3.2

(for undrained shear strength interpretation of T-bar data) is again assumed in defining

the model’s hardening law. In the context of the model, however, the normalised sample

depth, z, in Equation 2.4 is replaced with the normalised pipe invert embedment, w. Using

average pipe interface roughness and soil homogeneity parameters (case 9 in Table 2.2),

Figure 2.4 shows a comparison of the Nc formulation in Equation 2.2 against various

other relationships found in the literature. For embedments up to 0.5D, the relationship

derived from Barbosa-Cruz and Randolph displays general agreement against the other

relationships. For deeper embedments, Equation 2.2 results in a significantly higher value

of Nc compared to Aubeny et al. (2005), which is expected because they deliberately

modelled an open trench.

This hardening law formulation was confirmed experimentally by conducting vertical

penetration tests. These tests also involved unload-reload loops and extraction to inves-

tigate elastic stiffness and uplift capacity respectively. The results from all four vertical

penetration tests and a theoretical solution using the linear shear strength profile derived

2-11


Pipe invert embedment, w/D [-]

Bea

ring

capac

ity

fact

or,N

c[-]


Bea

ring

capac

ity

fact

or,N

c[-]

Equations 2.2 and 2.4Murff et al. (1989) - roughMurff et al. (1989) - smoothAubeny et al. (2005) - roughAubeny et al. (2005) - smoothMerifield et al. (2008) - roughMerifield et al. (2008) - smooth

Equations 2.2 and 2.4Aubeny et al. (2005) - roughAubeny et al. (2005) - smooth

(a)

(b)

0 1 2 3 4 5

0 0.1 0.2 0.3 0.4 0.5

0

1

2

3

4

5

6

7

8

9

10

0

1

2

3

4

5

6

Figure 2.4: Bearing capacity factor comparison

2-12


V/D [kPa]

Pip

ein

vert

embed

men

t,w

/D[-] Theoretical

-80 -40 0 40 800

2

4

6

8

Figure 2.5: Results of vertical penetration tests

from the T-bar tests and an Nc relationship using average pipe roughness and soil ho-

mogeneity parameters in Equation 2.4 are shown in Figure 2.5. The theoretical solution

is plotted against the total vertical pipe invert embedment, w, calculating the elastic

component, we, using the vertical elastic stiffness to be discussed in Section 2.4.3.

2.4.1.1 Possible uplift capacity

The unload-reload curves displayed an uplift capacity of the pipe. At shallow embedment

this is due to negative pore pressures in the soil below the pipe and suction at the pipe-soil

interface. At deeper embedments backfill was observed to occur over the top of the pipe,

enhancing the negative vertical load capacity, Vt. Figure 2.6 shows the variation in uplift

capacity with embedment that occurred in the tests. A peak of these values could be fitted

by scaling the uplift capacity relative to a limiting value, (Vt/V0)deep, as:

Vt

V0

= φuplift

(

Vt

V0

)

deep

(2.7)

where φuplift is a transition factor and is defined as:

φuplift =

[

1 −

(

1 − min

(

1,w

wuplift,deep

))Auplift]1/Buplift

(2.8)

where wuplift,deep is the normalised pipe embedment at which (Vt/V0)deep occurs and is

equal to 4 and Auplift, Buplift are fitting parameters equal to 1.16 and 3.35 respectively.

The proportion of uplift capacity against the initial installation capacity is shown to

change from around −0.3 at shallow embedment before maintaining a constant ratio of

2-13



Uplift

capac

ity,

−V

t/V

0[-]

Equation 2.7

Experimental observation

0 2 4 6 80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Figure 2.6: Variation in uplift capacity

(Vt/V0)deep = −0.75.

This uplift capacity was recorded immediately after the initial embedment. Equa-

tions 2.7 and 2.8 therefore effectively represent the loss of capacity due to remoulding by

half a cycle of pipe penetration. In application of the model, factors such as the degree of

consolidation, rate of extraction and any previous cyclic motion should also be considered.

If sustained uplift was expected, for instance, assuming even small levels of uplift capacity

would be considerably unconservative.

No uplift capacity was assumed in the combined load yield surfaces derived by the

numerical formulation of White and Randolph (2007) and Merifield et al. (2008). However,

in this paper Equations 2.5 and 2.7 will be used to define the apex of the yield surface for

compressive and tensile vertical load respectively, and the yield surface shape parameters

derived for those extremes. For applications when no tensile capacity is to be assumed,

alternative shape parameters of the yield surface are provided in White and Randolph

(2007), Hodder et al. (2008) and Merifield et al. (2008).

2.4.2 Yield surface

2.4.2.1 Definition

The yield surface is a boundary in vertical and horizontal load space that separates elastic

and elasto-plastic states. The basis of the model espoused here is that the yield surface

size is a direct function of the plastic vertical penetration. Therefore, the size and shape

of the yield surface was investigated experimentally by conducting ‘swipe’ tests at many

different pipe embedments. In the swipe tests, the pipe was initially penetrated to the

2-14


desired depth before being displaced horizontally whilst the vertical displacement was

held constant. The combined horizontal-vertical load path recorded during the swipe is

assumed to track the yield surface at the investigated embedment, provided that the ratio

of the vertical elastic stiffness to vertical plastic stiffness is large. This was originally

suggested by Tan (1990) before being used successfully by, amongst others and for a range

of shallow foundation types, Martin (1994), Gottardi et al. (1999), Martin and Houlsby

(2000), Zhang (2001) and Cassidy et al. (2004).

2.4.2.2 Experimental swipe tests

Ten normally loaded swipe tests at depths ranging from 0.2 to 5 diameters and five over-

loaded swipe tests at depths ranging from 0.2 to 4 diameters were conducted (see Table 2.4

and 2.5 respectively). Using the terminology adopted by Zhang (2001), a ‘normally’ loaded

swipe is a test in which the pipe is driven horizontally immediately after penetration to the

required depth. The result is a swipe load path that starts at the pure vertical capacity

V0. Figure 2.7a shows a typical result from a normally loaded swipe (test 1.305.2(a) in

Table 2.4).

In order to investigate the yield surface shape at the apex associated with low or

negative vertical loads, ‘overloaded’ swipes were performed. In this test the pipe was

penetrated to the required depth, unloaded to a vertical load less than V0 by pulling up

slightly on the pipe element using displacement control, and then swiped horizontally while

the vertical displacement was held constant. All of the overloaded swipes in this series

of tests investigated the yield surface shape in negative vertical load space, as described

in Table 2.5. Several overloaded swipes were performed at each embedment in order to

achieve a tensile force as close as possible to the uplift capacity Vt. An example overloaded

swipe is shown in Figure 2.7b (test 1.309 in Table 2.5).

It can be seen in Figure 2.7 that non-zero horizontal load was recorded during the

vertical penetration phase of the swipe tests. A likely source of this is slight lateral

asymmetry in the bearing failure mechanism as the pipe penetrated into the soil which

would cause a small horizontal load to be exerted on the pipe.

For embedments greater than one diameter an adjustment to remove the passive pres-

sure on the loading arm during the swipe was made to the recorded horizontal load.

Throughout the swipe, the portion of the loading arm embedded in the soil can be as-

sumed to act as a laterally loaded pile. A trapezoidal pressure distribution was adopted

which resulted in a load correction of φNcDarm (w − D) [sum + 0.5ρ (w − D)], where Darm

is the diameter of the loading arm, (w − D) is the length of the loading arm in the soil

and sum + 0.5ρ (w − D) the average shear strength along that length. φ is a remoulding

factor used to account for the reduction in strength of the soil due to the initial penetra-

tion of the pipe element. It was assumed to be equivalent to that observed in the vertical

unload-reload tests and a value of 0.75 was used. Nc is a bearing capacity factor equal to

10.5 (Randolph and Houlsby, 1984; Martin and Randolph, 2006) which is applicable to a

2-15


V/D [kPa]

H/D

[kPa]

V/D [kPa]

H/D

[kPa]

Horizontal swipe

at constant w

Penetration

Penetration

Horizontal swipe

at constant w

Unload

(a) (b)

-10 0 10 200 4 8 12 16-1

0

1

2

3

4

5

6

7

-1

0

1

2

3

4

5

6

7

Figure 2.7: Typical load paths during (a) normally loaded swipe and (b) overloaded swipe

Normalised vertical load, V/V0 [-]

Nor

mal

ised

hor

izon

tallo

ad,H

/V0

[-]

Swipes at

w/D > 1

Swipes at

w/D < 1

-0.5 -0.25 0 0.25 0.5 0.75 1-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 2.8: Normalised results from all swipe tests. Values of h0 and V/V0 at Hmax can befound in Tables 2.4 and 2.5

2-16


deeply buried cylinder — or in this case a laterally loaded pile. The load correction was

applied at a rate proportional to the increase in horizontal load throughout the swipe test.

Figure 2.8 shows the results of all of the normally loaded and overloaded swipes. To

allow comparison between the various swipe tests, the recorded loads have been normalised

by V0, the peak vertical load recorded during the initial penetration phase of the swipe

test. For clarity, data from the initial penetration phases of the tests has been omitted.

Test details and summary results are also provided in Tables 2.4 and 2.5.

2.4.2.3 Yield surface equation

A yield surface proposed by Martin (1994) and Martin and Houlsby (2000) for the ap-

plication of spudcan foundations on clay is espoused in this paper to generally fit the

experimental data well. In order to achieve this, however, their yield surface expression,

f , requires adjustment to include negative vertical loads. It now takes the form:

f =H

h0V0

− βfac

(

V

V0

−Vt

V0

)β1(

1 −V

V0

)β2

= 0 (2.9)

where h0 = Hmax/V0 defines the ratio of peak horizontal to vertical load, with Hmax

the peak horizontal load capacity. The ratio Vt/V0 is defined by Equation 2.7. The fitting

parameters β1 and β2 define the curvature of the surface. By defining the value of βfac as:

βfac =(β1 + β2)

(β1+β2)

ββ11 ββ2

2

(

1 −Vt

V0

)(β1+β2)(2.10)

the size of the surface in horizontal load space is maintained solely through definition

of h0.

Figure 2.9 shows the increase in h0 with embedment that was observed in the swipe

tests. Also shown are the results from tests conducted on the laboratory floor by Barrett

(2005) using overconsolidated kaolin clay. These tests concentrated on pipe behaviour at

shallow embedments and therefore data from swipe tests at 0.05, 0.1 and 0.25 diameters

were combined with the centrifuge data to provide information on horizontal capacity over

a wider range of embedment depths.

The following expression relating the horizontal capacity and the vertical penetration

was fitted to the data:

h0 = h0,surface + φh (h0,deep − h0,surface) (2.11)

where h0,surface is the value of h0 at zero embedment, h0,deep is the limiting value of h0

and describes the horizontal capacity at several diameters embedment (when h0 becomes

2-17



Pea

khor

izon

talca

pac

ity,

h0

=H

max/V

0[-]


Pea

khor

izon

talca

pac

ity,

h0

=H

max/V

0[-]

Centrifuge

Laboratory floor

- Barrett (2005)

Equation 2.11

Merifield et al. (2008)

- rough

Merifield et al. (2008)

- smooth

Centrifuge

Laboratory floor

- Barrett (2005)

Equation 2.11

(a) (b)

0 1 2 3 4 50 0.25 0.5 0.75 1

0.6

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0

0.1

0.2

0.3

0.4

0.5

Figure 2.9: Variation in horizontal capacity

independent of embedment) and φh is a transition factor defined as:

φh =

[

1 −

(

1 − min

(

1,w

wh,deep

))Ah]1/Bh

(2.12)

2.4.2.4 Deriving yield surface size parameters

Theoretically, the contact between the pipe and the soil approaches a line at the surface,

though for a very small penetration it effectively acts as a thin strip footing. With full

contact on the back of the pipe, an appropriate value for h0,surface could be1

2 + π≈

0.194, the theoretical value for a strip footing on homogeneous soil, or half this value

if assuming zero tensile capacity at the pipe-soil interface on the back of the pipe. It

is of course impossible to confirm this theoretical concept experimentally and a best fit

of the experimental data was found to limit towards a value of h0,surface = 0.147, which

is approximately halfway between the assumptions of full contact and breakaway on the

back of the pipe.

A value of h0,deep = 0.8 was observed to occur after an embedment of wh,deep = 3.5 in

the experimental results. For a deeply buried pipe, wished into place and in uniform soil,

the horizontal and vertical capacity would be of the same magnitude. In the experiments,

however, the shear strength increased with depth and there existed a zone of remoulded

soil more concentrated at the side of and above the pipe. For these reasons a value of

h0,deep less than one is expected and the value of 0.8 is reasonable. Values of Ah and Bh

equal to 1.29 and 1.59 respectively provide the best fit to the shape between h0,surface and

h0,deep.

2-18


Similarly, as seen in Tables 2.4 and 2.5, the normalised horizontal displacement at which

the maximum horizontal load occurred also increased with embedment. This reflects the

larger loads and amount of surrounding soil requiring mobilisation at deeper embedments.

However, as was observed in the increase in h0 with depth, u/D at Hmax becomes relatively

consistent after approximately 3 diameters embedment.

Also shown on Figure 2.9 are values of h0 presented by Merifield et al. (2008) for smooth

and rough pipes. These relationships were derived from FE and upper bound analyses for

a pipe wished into place (pre-embedded) with a zero tension pipe-soil interface, allowing

breakaway of the soil from the pipe when under tensile stress. The experimental data shows

a horizontal capacity approximately 35% and 10% higher than proposed by Merifield et al.

for pipe embedments equal to 0.1D and 0.5D respectively. This difference is likely due

to the additional horizontal capacity provided by the heave of soil caused by the initial

penetration process and lateral motion of the swipe, which was not included in the FE

and upper bound analyses. Bransby et al. (2008) investigated combined loading capacity

using FE analysis for both wished into place pipes and pipes penetrated from the surface.

While they did not propose a formulation relating horizontal capacity and embedment,

the horizontal capacity appeared slightly higher in the case of a pipe penetrated from the

surface than for the equivalent wished into place.

2.4.2.5 Deriving yield surface shape parameters

With the yield surface size with embedment established through Equation 2.11, consid-

eration is now given to its shape. The experimental data shows the peak horizontal load

occurring at progressively smaller values of V/V0 with increasing embedment (Tables 2.4

and 2.5), an observation also provided by Bransby et al. (2008). Although this peak posi-

tion changes, a reasonable fit of the swipe tests is achieved using values of β1 = β2 = 0.75

consistently for all embedments. The change in shape is accounted for by the increase in

Vt/V0 described in Equation 2.7. This is observed in Figure 2.10 where the experimental

swipes and numerical yield surfaces are compared for embedments of 0.2, 0.5, 1.5 and 5 di-

ameters. The yield surface expression generally fits the experimental data of the shallower

swipes well (Figures 2.10a, b, c) but provides only a moderate fit to the deep swipe at five

diameters (Figure 2.10d). For this reason, more emphasis has been placed on fitting the

yield surface curvature parameters β1 and β2 at embedments up to 1.5 diameters. These

embedments are also more typically expected in pipeline applications.

Also shown in Figures 2.10a and 2.10b are yield surfaces proposed by Merifield et al.

(2008). For high V/V0 the yield surface shapes are similar, although the zero uplift capacity

assumption of Merifield et al. leads to significant differences in the horizontal capacity at

low V/V0. The location of the surface peak (i.e. value of V/V0 at Hmax) is lower than in the

Merifield et al. formulation, although the resulting surface peak using Equations 2.9–2.11

better reflects the experimental results. A similar result was also reported by Bransby

et al. (2008). For an embedment of 0.167 diameters, Bransby et al. state a V/V0 of

2-19



Nor

mal

ised

hor

izon

tallo

ad,H

/V0

[-]


Nor

mal

ised

hor

izon

tallo

ad,H

/V0

[-]


Nor

mal

ised

hor

izon

tallo

ad,H

/V0

[-]


Nor

mal

ised

hor

izon

tallo

ad,H

/V0

[-]

Equations 2.9–2.11

Merifield et al. (2008) - rough

Merifield et al. (2008) - smooth

Equations 2.9–2.11

Merifield et al. (2008) - rough

Merifield et al. (2008) - smooth

Equations 2.9–2.11 Equations 2.9–2.11

Overloaded

experimental swipe

Normally loaded

experimental swipe

Overloaded

experimental swipe

Normally loaded

experimental swipe

Normally loaded

experimental swipe

Normally loaded

experimental swipe

w/D = 0.2 w/D = 0.5

w/D = 1.5 w/D = 5

(a) (b)

(c) (d)

0.9

-1 -0.5 0 0.5 1-1 -0.5 0 0.5 1

-0.5 0 0.5 1-0.5 0 0.5 1

0

0.25

0.5

0.75

1

0

0.25

0.5

0.75

1

0

0.25

0.5

0.75

0

0.25

0.5

0.75

Figure 2.10: Yield surface at pipe invert embedments of (a) 0.2D, (b) 0.5D, (c) 1.5D and(d) 5D

2-20


0.3 to 0.4 at the peak Hmax. This agrees well with the value of 0.34 that results from

the equations given here. At low, but still positive V/V0 the model results in a similar

horizontal capacity to that reported by Bransby et al..

2.4.3 Elasticity

A definition of elasticity is required for the model to describe the response of load combi-

nations inside the yield surface. The elastic relationship is defined as:

{

δV

δH

}

=

[

kve 0

0 khe

]{

δwe

δue

}

(2.13)

where δ denotes an increment and kve and khe represent the elastic stiffness of vertical

and horizontal loading respectively. we and ue are the elastic vertical and horizontal

displacements.

2.4.3.1 Vertical elastic stiffness

The vertical elastic stiffness, kve = Kvsu0, is assumed to be proportional to the undrained

shear strength and was derived from the experimental data by calculating the vertical

elastic stiffness factor, Kv = ∆V/∆wsu0, throughout the unload loops performed in the

vertical penetration tests (noting that ∆V and ∆w are relative to the load and displace-

ment at the point of unload). Figure 2.11a shows that when viewed on a log-log scale, Kv

varies approximately linearly with the level of normalised displacement. Also indicated on

the figure are three levels of ∆w/D which represent an unload to V/Vt = 1, 0.5 and 0 (i.e.

to peak uplift capacity, half of the peak capacity and to zero vertical load respectively). As

an average description of the variable unload stiffness observed in the experiments, a single

value of Kv = 200 is used in the model. This corresponds to an unload to V/Vt = 0.5.

Alternatively, by dividing Kv by Nc, a parameter typically referred to as the ‘stiffness

ratio’ or ‘normalised secant stiffness’, Ksec, is obtained. It is generally discussed in the

context of steel catenary risers (SCRs) and can be used to predict the response of SCRs

by defining the seabed as a bed of linear springs with stiffness, ksec, which is scaled relative

to the ultimate bearing pressure as ksec = KsecNcsu0. Figure 2.11b shows the variation in

Ksec with normalised displacement, using the depth dependent Nc formulation outlined in

Section 2.3.2. Dividing Kv by Nc produces a more unique relationship against normalised

displacement with less spread of the experimental data, indicating there may be some

depth dependency in the parameter Kv.

Bridge et al. (2004) proposed that normalised uplifts, ∆w/D, of around 0.025 and

0.1 are required to mobilise unloads to V/Vt = 0 and 1 respectively. This corresponds

to Ksec values of 40 and 20, if assuming equivalent uplift and penetration resistances.

The experimental data presented in this paper displays slightly different behaviour, with

normalised uplifts of 0.015 and 0.3 required to unload to V/Vt = 0 and 1. However, the

normalised secant stiffness, Ksec, values at ∆w/D equal to 0.025 and 0.1 are similar to

2-21


Change in pipe invert embedment throughout uplift, ∆w/D [-]

Ver

tica

lel

asti

cst

iffnes

sfa

ctor

,K

v=

∆V

/∆w

s u0

[-]

Change in pipe invert embedment throughout uplift, ∆w/D [-] Unlo

adse

cant

stiff

nes

sra

tio,

Ksec=

∆V

/∆w

s u0N

c[-]

(a)

(b)

V = 0.5VtV = 0 V = Vt

V = 0 V = 0.5Vt V = Vt

V = 0

V = 0.5Vt

V = Vt

V = 0

V = 0.5Vt

V = Vt

Average unload secant stiffness ratio at:

Average vertical elastic stiffness factor at:

Average pipe

displacement at:

Average pipe

displacement at:

Hyperbolic relationship -

Aubeny et al. (2008)

10−3 10−2 10−1 100

10−3 10−2 10−1 100

100

101

102

103

100

101

102

103

104

Figure 2.11: Response throughout uplift

2-22


those proposed by Bridge et al. (2004), with values of 45 and 14 respectively.

The variation of Ksec can be described by a hyperbolic relationship (Audibert et al.,

1984; Bridge et al., 2004; Aubeny et al., 2008; Aubeny and Biscontin, 2008). Shown on

Figure 2.11b is the variation in Ksec using a formulation presented by Aubeny et al. (2008)

for describing the unload-reload behaviour observed during cyclic pipe tests conducted in

soft kaolin clay on the laboratory floor. The hyperbolic relationship shows good agreement

with the centrifuge experimental data presented in this paper.

2.4.3.2 Horizontal elastic stiffness

The horizontal elastic stiffness, khe, was not directly investigated and was simply scaled

relative to the vertical elastic stiffness. The vertical and horizontal elastic solutions pre-

sented in Gazetas et al. (1985) and Gazetas and Tassoulas (1987) for a surface strip footing

have been used to calculate the ratio khe/kve. The model presented here uses a value of

khe/kve = 0.925 which was obtained using a Poisson’s ratio, ν = 0.49.

2.4.4 Flow rule

A flow rule is required in the model to determine the relative horizontal and vertical dis-

placement magnitudes when a load combination reaches the yield surface causing further

plastic penetration and expansion of the yield surface. Inclined penetration (or radial dis-

placement) experiments were conducted from the surface and from an initial embedment

of one diameter to investigate the form of an appropriate flow rule. Figure 2.12 shows the

load paths traced during the inclined penetration tests normalised by su0D.

Normality (or flow associated with the yield surface) was tested by comparing the

plastic penetration ratio during the experiment,∆up

∆wp, with the theoretical prediction,

∂f/∂H

∂f/∂V. Averaged over the six inclined penetration tests, the experimental and theoretical

results were not equal and slight non-association was predicted. Better agreement was

found between the experimental displacement ratio and that predicted by the model by

defining a plastic potential, g, of similar form to the yield surface but with its curvature

modified to:

g =H

h0V ′

0

− β′

fac

(

V

V ′

0

−Vt

V0

)β3(

1 −V

V ′

0

)β4

= 0 (2.14)

where V ′

0 is a dummy parameter defining the intersection of the plastic potential surface

that passes through the current load point with the vertical load axis, β3 and β4 are the

modified curvature parameters and β′

fac is defined by Equation 2.10, but substituting β3

and β4 in place of β1 and β2. While investigating optimum values of β3 and β4, the ratio of

the plastic potential curvature parameters, β3/β4, was constrained to equal the ratio of the

yield surface curvature parameters, β1/β2. This ensures the load path in a numerical swipe

test reaches the ‘parallel point’ at the peak of the theoretical yield surface, consistent with

2-23


Normalised vertical load, V/su0D [-]

Nor

mal

ised

hor

izon

tallo

ad,H

/su0D

[-]


Nor

mal

ised

hor

izon

tallo

ad,H

/su0D

[-]

(a) (b)

22.5◦

45◦

67.5◦

22.5◦

45◦

67.5◦

0 2 4 6 8 100 2 4 6 8 10

0.5

-1

0

1

2

3

4

5

6

7

0

1

2

3

4

5

Figure 2.12: Loads paths during inclined penetration tests from (a) surface and (b) 1Dembedment

the experimental observations. Values of β3 = β4 = 0.65 were found to give the best fit to

the results, indicating only slight non-association.

None of the experiments conducted provided information on the flow rule at low V/V0

ratios. Bransby et al. (2008) indicated the possibility of a marked deviation from normality

for low values of V/V0. Nevertheless, the simplified approach of defining a plastic potential

of similar form to the yield surface is adopted in this model.

2.5 Retrospective Simulations

Numerical simulations of a number of representative experiments have been performed to

investigate the capabilities of the pipe-soil interaction model. In each of these simulations

the values of the experimentally prescribed displacements were taken as input, and the

loads were calculated as output for comparison with the experiments. The model has been

implemented as a FORTRAN90 program for these simulations. For numerical stability, the

model requires a small initial vertical plastic displacement for the solution to progress. The

results that follow are from retrospective simulations that began with an initial embedment

of 0.01D.

The simulations are carried out for the swipe tests 1.305.2(a) and 1.311 and the inclined

penetration tests 1.401 and 1.404.1, using the recommended model parameters described

in Table 2.7. No attempt to adjust parameters to fit individual tests was made, thereby

demonstrating the generic applicability of the model. All of the simulation results have

been normalised for presentation in this paper. The displacements have been presented

2-24


normalised by the pipe diameter. In the presentation of the swipe test simulation results,

loads are normalised by the vertical load capacity V0 at the swipe embedment, and in the

inclined penetration simulations, loads are normalised by su0D at every point throughout

the test.

2.5.1 Swipe tests

Simulated swipe tests were conducted to test the model’s ability to track the yield surface,

predict the peak horizontal capacity and the displacement at which it occurs. Both a

normally loaded and an overloaded swipe test were simulated.

In the normally loaded swipe test simulation, the pipe was displacement controlled

in the vertical direction until it reached a prescribed embedment. It was then displaced

horizontally whilst maintaining the vertical displacement. Figure 2.13 shows the results of

a retrospective simulation of test 1.305.2(a), a normally loaded swipe test at an embedment

of 0.5D. During the initial penetration phase of the test, the model prediction follows the

experimental results closely. The horizontal swipe phase also shows good agreement, with

the model tracking a yield surface slightly outside the experimental load path. The model

over predicts the peak horizontal load to a small degree and slightly under predicts the

vertical load that occurs at horizontal yield. The model shows a stiffer horizontal response,

reaching horizontal yield within a smaller horizontal displacement than observed in the

experiment.

Figure 2.14 shows the results of a retrospective simulation of test 1.311, an overloaded

swipe test at an embedment of 0.2D. The simulation was conducted using the same phases

as the normally loaded swipe. However, between the initial penetration and the horizontal

swipe phases, the vertical load was unloaded to Vt using load control. In addition to the

characteristics tested in the normally loaded swipe simulation, this style of simulation

checks the ability of the model to unload elastically and follow a yield surface in negative

vertical load space. Initially, the model simulation follows a similar penetration curve to

that recorded in the experiment, before unloading elastically to Vt. During unloading,

both the stiffness and the vertical load at the end of the unload phase are well simulated

and the horizontal swipe phase shows general agreement between the experiment and the

model prediction. As observed in the normally loaded swipe simulation, the model slightly

over predicts the horizontal load. In contrast to the normally loaded swipe simulation,

the model slightly over predicts the vertical load that occurs at horizontal yield.

2.5.2 Inclined penetration tests

Constant gradients of horizontal to vertical displacement were used as inputs to simulate

an inclined penetration test from the surface and an embedment of one diameter. These

simulations are not intended to replicate any realistic behaviour encountered in practice.

Instead they serve as a robust test of the model’s capability. The resulting horizontal and

vertical loads are compared against the experimental results.

2-25


Figure 2.15 shows the results from a model simulation of test 1.401 in which the pipe

was penetrated at an angle of 45◦ to the horizontal starting from the surface. Both

the vertical and horizontal response predicted by the model are in agreement with the

experiment and the results display the model’s ability to predict the combined loading

behaviour when penetrated from the surface.

Figure 2.16 shows the results from a model simulation of test 1.404.1. In this test the

pipe was initially penetrated to an embedment of one diameter before being displaced at

an angle of 22.5◦ to the horizontal. The initial vertical penetration phase of the simulation

displays good agreement with the experimental observation. During the beginning of the

combined displacement path phase of the experiment, the horizontal load rapidly increased

coupled with a reduction in the vertical load. This behaviour is well simulated by the

model. However, the vertical load reduces to a slightly smaller value than that observed

in the experiment. After the initial rapid increase in horizontal load and reduction in

vertical load, there was a change in horizontal stiffness which is also well predicted by the

model. Due to the vertical load unloading to a slightly smaller value in the initial stage

of the combined displacement path phase, the vertical load continued to remain less than

observed in the experiment throughout the latter stages of the simulation.

2.5.3 Summary of retrospective simulations

The horizontal load-displacement response predicted by the model can be seen to follow

the experimental data well up to several diameters displacement in both of the inclined

penetration simulations. However, in a situation much nearer the surface or one that does

not involve a component of continuously increasing vertical penetration, the model would

not be expected to perform as well over such large lateral displacements. This is due to

the influence of berms beside the pipe.

The choice of elastic stiffness within this single surface model was also seen to be

crucial in the retrospective simulations. Simulated swipe tests with small displacements

displayed a stiffer response than in the experiments, but in the larger displacement inclined

penetration tests the stiffness was predicted well. Possible future refinement of the model

could include the degradation of stiffness with strain amplitude for load combinations

within the yield surface. Several approaches are possible, including boundary surface

models or the use of multiple (or even infinite) numbers of yield surfaces.

2-26


Horizontal pipe displacement, u/D [-]

Pip

ein

vert

embed

men

t,w

/D[-]


Pip

ein

vert

embed

men

t,w

/D[-]


Nor

mal

ised

hor

izon

tallo

ad,H

/V0

[-]


Nor

mal

ised

hor

izon

tallo

ad,H

/V0

[-]

(a) (b)

(c) (d)

Experiment

Simulation Experiment

Simulation

Experiment

Simulation

Experiment

Simulation

0 0.25 0.5 0.75 10 0.05 0.1 0.15 0.2

0 0.25 0.5 0.75 10 0.05 0.1 0.15 0.2

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0

0.1

0.2

0.3

0.4

0.5

0.6

0

0.1

0.2

0.3

0.4

0.5

0.6

Figure 2.13: Simulated normally loaded swipe at pipe invert embedment of 0.5D

2-27



Pip

ein

vert

embed

men

t,w

/D[-]


Pip

ein

vert

embed

men

t,w

/D[-]


Nor

mal

ised

hor

izon

tallo

ad,H

/V0

[-]


Nor

mal

ised

hor

izon

tallo

ad,H

/V0

[-]

(a) (b)

(c) (d)

Experiment

Simulation

Experiment

Simulation

Experiment

Simulation

Experiment

Simulation

-0.5 0 0.5 10 0.05 0.1 0.15 0.2

-0.5 0 0.5 10 0.05 0.1 0.15 0.2

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0

0.05

0.1

0.15

0.2

0.25

0

0.05

0.1

0.15

0.2

0.25

Figure 2.14: Simulated overloaded swipe at initial pipe invert embedment of 0.2D

2-28



Pip

ein

vert

embed

men

t,w

/D[-]


Pip

ein

vert

embed

men

t,w

/D[-]


Nor

mal

ised

hor

izon

tallo

ad,H

/su0D

[-]


Nor

mal

ised

hor

izon

tallo

ad,H

/su0D

[-]

(a) (b)

(c) (d)

Experiment

Simulation

Experiment

Simulation

Experiment

Simulation

Experiment

Simulation

0 2 4 6 80 0.5 1 1.5 2 2.5

0 2 4 6 80 0.5 1 1.5 2 2.5

0

0.5

1

1.5

2

2.5

3

3.5

4

0

0.5

1

1.5

2

2.5

3

3.5

4

0

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

Figure 2.15: Simulated inclined penetration test from surface

2-29



Pip

ein

vert

embed

men

t,w

/D[-]


Pip

ein

vert

embed

men

t,w

/D[-]


Nor

mal

ised

hor

izon

tallo

ad,H

/su0D

[-]


Nor

mal

ised

hor

izon

tallo

ad,H

/su0D

[-]

(a) (b)

(c) (d)

Experiment


Simulation

Experiment


Simulation

0 2 4 6 80 1 2 3 4 5

0 2 4 6 80 1 2 3 4 5

-1

0

1

2

3

4

5

6

7

-1

0

1

2

3

4

5

6

7

0

0.5

1

1.5

2

2.5

3

3.5

0

0.5

1

1.5

2

2.5

3

3.5

Figure 2.16: Simulated inclined penetration test from embedment of 1D

2-30


2.6 Conclusions

This paper details a displacement hardening plasticity model that represents the undrained

combined loading behaviour of pipelines in clay soils, a description of the centrifuge ex-

periments used to derive its main components and example retrospective simulations of

the experiments verifying its predictive capabilities.

The model’s hardening relationship applies to the pipe’s purely vertical response, for

penetration and uplift capacity, and it agrees well with the experimental data. It is valid

for a partially embedded pipe through to conditions of deep penetration. Based on a suite

of swipe tests, a description for the increase in yield surface size and change in shape with

embedment is provided. Swipe tests at deep conditions were used to determine a limiting

horizontal capacity, which was observed to occur after approximately three diameters of

embedment. The flow rule and vertical elastic stiffness factor were also empirically derived

to fit the experimental data. The experimental evidence indicates slight non-association.

However, with only minor adjustment of the yield surface shape a simple plastic potential

was provided. Information regarding the flow rule at low values of V/V0 was not obtained.

Further research is required to verify the shape of the plastic potential at low normalised

vertical loads.

The model has been developed from monotonic loading experiments. In many situa-

tions an offshore pipe in clay soil will be subjected to numerous cyclic loads, reducing the

surrounding soil strength and possibly creating berms of soil on either side of the pipe. It

may also be subjected to significant lateral movements. These have not been incorporated

in this model. However, the model provides a framework for the simpler case and is a step

towards formulating a more advanced plasticity model that accounts for cyclic loading

effects and large lateral deformations.

2-31


References

AGA (1993). Submarine pipeline on-bottom stability. Vol. 1: Analysis and design guide-lines. Technical report, American Gas Association (AGA).


Aubeny, C. P., Gaudin, C., and Randolph, M. F. (2008). Cyclic tests of a model pipe inkaolin. In Proc. 40th Offshore Technology Conference, Houston, USA.

Aubeny, C. P., Shi, H., and Murff, J. D. (2005). Collapse loads for a cylinder embeddedin trench in cohesive soil. International Journal of Geomechanics, 5(4):320–325.

Audibert, J. M. E., Nyman, D. J., and O’Rourke, T. D. (1984). Differential groundmovement effects on buried pipelines. In Guidelines for the Seismic Design of Oil andGas Pipeline Systems. ASCE.

Barbosa-Cruz, E. R. and Randolph, M. F. (2005). Bearing capacity and large penetrationof a cylindrical object at shallow embedment. In Proc. International Symposium onFrontiers in Offshore Geotechnics, pages 615–621, Perth, Australia.

Barrett, D. (2005). Model testing to prove up applicability of plasticity modelling of sub-sea pipelines in purely undrained soils. Honours thesis, School of Civil and ResourceEngineering, The University of Western Australia.

Bransby, M. F., Amman, S., and Zajac, P. (2008). Numerical analysis of the capacity of ‘on-bottom’ offshore pipelines. In Proc. 2nd British Geotechnical Association InternationalConference on Foundations, Dundee, Scotland.


Calvetti, F., di Prisco, C., and Nova, R. (2004). Experimental and numerical analysisof soil-pipe interaction. Journal of Geotechnical and Geoenvironmental Engineering,130(12):1292–1299.

Cassidy, M. J., Byrne, B. W., and Randolph, M. F. (2004). A comparison of the combinedload behaviour of spudcan and caisson foundations on soft normally consolidated clay.Geotechnique, 54(2):91–106.


Chung, S. F. and Randolph, M. F. (2004). Penetration resistance in soft clay for differentshaped penetrometers. In Proc. 2nd International Conference on Geotechnical SiteCharacterization, volume 1, pages 671–678, Porto, Portugal.

di Prisco, C., Nova, R., and Corengia, A. (2004). A model for landslide-pipe interactionanalysis. Soils and Foundations, 44(3):1–12.

DNV (2007). Recommended practice RP-F-109: On-bottom stability design of submarinepipelines. Technical report, Det Norske Veritas (DNV).

2-33


Finnie, I. M. (1993). The behaviour of shallow foundations on calcareous soil. PhD thesis,School of Civil and Resource Engineering, The University of Western Australia.

Gazetas, G., Dobry, R., and Tassoulas, J. L. (1985). Vertical response of arbitrarily shapedembedded foundations. Journal of Geotechnical Engineering, 111(6):750–771.

Gazetas, G. and Tassoulas, J. L. (1987). Horizontal stiffness of arbitrarily shaped embed-ded foundations. Journal of Geotechnical Engineering, 113(5):440–457.

Gottardi, G., Houlsby, G. T., and Butterfield, R. (1999). Plastic response of circularfootings on sand under general planar loading. Geotechnique, 49(4):453–469.

Hodder, M. S., Cassidy, M. J., and Barrett, D. (2008). Undrained response of shallowpipelines subjected to combined loading. In Proc. 2nd British Geotechnical AssociationInternational Conference on Foundations, Dundee, Scotland. [presented as Chapter 3of this thesis].

House, A., Randolph, M. F., and Watson, P. G. (2001). In-situ assessment of shear strengthand consolidation characteristics of soft sediments. In Proc. International ConferenceOTRC ‘01, pages 52–63, Houston, USA.

Hu, Y. and Randolph, M. F. (1998). A practical numerical approach for large deforma-tion problems in soil. International Journal for Numerical and Analytical Methods inGeomechanics, 22(5):327–350.


Martin, C. M. and Houlsby, G. T. (2000). Combined loading of spudcan foundations onclay: laboratory tests. Geotechnique, 50(4):325–337.

Martin, C. M. and Randolph, M. F. (2006). Upper bound analysis of lateral pile capacityin cohesive soil. Geotechnique, 56(2):141–145.

Merifield, R. S., White, D. J., and Randolph, M. F. (2008). The ultimate undrainedresistance of partially embedded pipelines. Geotechnique, 58(6):461–470.

Murff, J. D., Wagner, D. A., and Randolph, M. F. (1989). Pipe penetration in cohesivesoil. Geotechnique, 39(2):213–229.

Randolph, M. F., Hefer, P. A., Geise, J. M., and Watson, P. G. (1998). Improved seabedstrength profiling using T-bar penetrometer. Technical Report Res. Report No. G1320,Centre for Offshore Foundation Systems, The University of Western Australia.

Randolph, M. F. and Houlsby, G. T. (1984). The limiting pressure on a circular pile loadedlaterally in cohesive soil. Geotechnique, 34(4):613–623.

Stewart, D. P. (1992). Lateral loading on piles due to simulated embankment construc-tion. PhD thesis, School of Civil and Resource Engineering, The University of WesternAustralia.

Stewart, D. P., Boyle, R. S., and Randolph, M. F. (1998). Experience with a new drumcentrifuge. In Proc. International Conference Centrifuge ‘98, volume 1, pages 35–40,Tokyo, Japan.

2-34


Stewart, D. P. and Randolph, M. F. (1991). A new site investigation tool for the centrifuge.In Proc. International Conference on Centrifuge Modelling — Centrifuge ‘91, pages531–538, Boulder, Colorado, USA.

Stewart, D. P. and Randolph, M. F. (1994). T-bar penetration testing in soft clay. Journalof the Geotechnical Engineering Division, 120(12):2230–2235.

Tan, F. S. C. (1990). Centrifuge and theoretical modeling of conical footings on sand. PhDthesis, The University of Cambridge.

Verley, R. and Lund, K. M. (1995). Soil resistance model for pipelines placed on clay soils.In Proc. 14th International Offshore Mechanics and Arctic Engineering Conference,volume 5, pages 225–23, Copenhagen, Denmark.

Wagner, D. A., Murff, J. D., Brennodden, H., and Sveggen, O. (1987). Pipe-soil interactionmodel. In Proc. 19th Offshore Technology Conference, Houston, USA.

Watson, P. G. (1999). Performance of skirted foundations for offshore structures. PhDthesis, School of Civil and Resource Engineering, The University of Western Australia.

White, D. J. and Randolph, M. F. (2007). Seabed characterisation and models for pipeline-soil interaction. International Journal of Offshore and Polar Engineering, 17(3):193–204.


Zhang, J. and Erbrich, C. T. (2005). Stability design of untrenched pipelines — geotech-nical aspects. In Proc. International Symposium on Frontiers in Offshore Geotechnics,pages 623–628, Perth, Australia.

Zhang, J., Randolph, M. F., and Stewart, D. P. (1999). Elasto-plastic model for pipe-soil interaction of unburied pipelines. In Proc. 9th International Offshore and PolarEngineering Conference, volume 2, pages 185–192, Brest, France.

Zhang, J., Stewart, D. P., and Randolph, M. F. (2002). Modeling of shallowly embeddedoffshore pipelines in calcareous sand. Journal of Geotechnical and GeoenvironmentalEngineering, 128(5):363–371.

2-35

3Undrained Response of Shallow Pipelines Subjected to

Combined Loading

3.1 Abstract

The evaluation of unburied pipeline response when subjected to combined vertical and

horizontal loading conditions is a significant problem facing offshore geotechnical engineers.

Typical circumstances where an assessment of the response is required include a pipeline

being subjected to hydrodynamic forces, riser motions at the touchdown point due to vessel

motions or lateral buckling of a pipeline due to thermal expansion. In this paper, a model

that describes the undrained, monotonic response of a pipe on soft clay is assessed against

a different series of experimental conditions from which it was originally derived. These

combined loading experiments were conducted using a 20 or 70mm diameter model pipe

on the laboratory floor in an overconsolidated kaolin clay sample. The tests concentrated

on investigating behaviour at embedments shallower than half a diameter and on expected

load paths of a partially embedded pipe subjected to hydrodynamic forces. Retrospective

numerical simulations of the model show its applicability to a variety of conditions.

3.2 Introduction

Pipelines act as the critical conduit for the transport of oil and gas between offshore devel-

opments and the mainland. With any failure of a pipeline disastrous for the environment

and economy, a reliable prediction of a pipeline’s response to various loading conditions

is a considerable problem in offshore geotechnical engineering. Traditionally, lateral fric-

tion factors are used to assess the stability of subsea pipelines. However, a more realistic

interpretation of combined vertical and lateral resistance is espoused (Cathie et al., 2005;

White and Randolph, 2007) as an unconservative design can result in instability of the

pipeline during loading events and a too conservative design can result in significantly

increased cost due to weight coating or wall thickness requirements.

A more accurate and practicable option is to incorporate the pipeline behaviour as

a ‘macro element’ expressed purely in terms of the loads (force resultants) on the pipe

3-1


w

u

D

V

H

Figure 3.1: Sign convention of load and displacement

and the corresponding displacements (Cathie et al., 2005; White and Randolph, 2007)

(see Figure 3.1). The popularity of this force-resultant modelling technique (Muir Wood,

2004) has seen application in spudcan, caisson and pipeline analysis. As an example of

the latter, Zhang (2001) developed a suite of models describing the response of partially

embedded pipes on drained calcareous sand. More recently, a model applicable to the

combined vertical and lateral behaviour of pipelines on clay soils in undrained conditions

was outlined (Hodder and Cassidy, 2010). The model is based on displacement hardening

plasticity theory and has four components:

1. A yield surface in combined vertical and horizontal loading space that describes the

boundary of elastic and plastic states;

2. A hardening law relating the evolution of yield surface size with vertical plastic

displacement;

3. A description of elastic response; and

4. A flow rule that determines the ratio between plastic displacement components dur-

ing a plastic step.

The model parameters were calibrated using data obtained from a series of tests con-

ducted in the University of Western Australia’s drum centrifuge facility (Hodder and

Cassidy, 2010). The model includes the negative vertical load capacity that was observed

during uplift in the centrifuge experiments. At shallow embedments this is due to negative

pore pressures in the soil below the pipe and suction developing at the pipe-soil interface.

At deeper embedments backfilling over the top of the pipe was observed, further contribut-

ing to the uplift capacity (Hodder and Cassidy, 2010).

Suction is rate dependant and for many applications at shallow embedments it maybe

appropriate to employ no tensile resistance. This approach is taken in this paper. A

force-resultant model that describes the behaviour of shallowly embedded pipelines is

outlined. It is applicable to half a diameter of embedment, monotonic loading and small

displacements. It extends the applicability of the original model of Hodder and Cassidy

(2010) by providing the parameters required to make the assumption of no tensile vertical

capacity. It is not feasible to repeat all of the model derivation and components in this

3-2

Undrained Response of Shallow Pipelines Subjected to Combined Loading

paper, with readers encouraged to refer to Hodder and Cassidy (2010) for such details.

Only the changes to the original model parameters are described.

To demonstrate the application of the revised model, the results of retrospective sim-

ulations of several experiments conducted on shallow pipelines (Barrett, 2005) are shown.

The purpose of these is to further test the generic applicability of the model by reproducing

types of tests that were not conducted in the original drum centrifuge testing programme

(Hodder and Cassidy, 2010).

3.3 Experimental Programme

The experiments were conducted on saturated, heavily overconsolidated kaolin clay (Stew-

art, 1992), prepared in a 600 mm diameter tub and to the methodology described by Vlahos

et al. (2005). Six different samples were prepared, with up to five tests in each. Undrained

strength characterisation tests were undertaken using a T-bar penetrometer (Stewart and

Randolph, 1991) of projected area 100 mm2 (5 mm x 20 mm) before, during and after the

pipe model tests. An interpreted average of the shear strength profiles is provided for all

of the experiments presented in this paper in Tables 3.1 and 3.2.

Two model pipes were used in the testing programme. The smaller pipe was 20 mm

in diameter, D, and 160 mm in length. For very shallow embedment tests (w/D ≤ 0.1) a

70 mm diameter pipe with 350 mm length was used. With length to diameter ratios of 8

and 5 respectively, three dimensional end effects are believed to be negligible (Chung and

Randolph, 2004) and plane-strain conditions are assumed. Two bending and one axial

strain gauge located on the vertical loading shaft holding the model pipe were used to

derive the vertical and horizontal loads on the pipe (Barrett, 2005). Either displacement

or load control in each degree of freedom could be maintained by the actuator system.

The goal of the model tests was to investigate the behaviour of pipelines embedded

up to half a diameter and subjected to combined vertical and lateral loads. However, the

experiments were selected to allow derivation of the force-resultant model parameters:

• Purely vertical penetration tests checked the theoretical hardening law solution

(Barbosa-Cruz and Randolph, 2005; Hodder and Cassidy, 2010);

• Swipe tests investigated the yield surface shape;

• Probe tests (occasionally known as constant vertical load tests) derived the flow rule,

and;

• Constant load path tests simulated realistic hydrodynamic loading conditions.

Though the latter tests were used to derive the flow rule parameters, they also provided

an opportunity to evaluate the performance of the completed model in simulating an

installed pipeline loading scenario. Details of all of the tests with results shown in this

paper are provided in Tables 3.1 and 3.2. Further details of the experiments are provided

in Barrett (2005).

3-3

Geote

chnic

alanaly

sisofoffsh

ore

pip

elin

es

and

steelcate

nary

risers

Table 3.1: Summary of swipe tests

Test details Soil propertiesaV

initialbMeasured

peak valuescDerived

propertiesFigure

TestdD

[mm]w/D[-]

sum

[kPa]ρ

[kPa/mm]V0

[N]Hmax

[N]V at Hmax

[N]h0

[-]V/V0 at Hmax

[-]

2-1 70 0.05 2.2 0.2 229.3 51.8 69.6 0.23 0.30 3.23-2 20 0.05 3.0 0.0 181.3 40.7 53.5 0.22 0.30 3.2, 3.3a, 3.54-1 70 0.05 2.13 0.33 270.9 43.0 92.3 0.16 0.34 3.23-1 70 0.1 3.0 0.0 280.6 59.1 90.5 0.21 0.32 3.24-2 20 0.1 2.13 0.33 45.8 8.6 16.4 0.19 0.36 3.21-5 20 0.25 1.5 0.145 66.2 15.9 22.6 0.24 0.34 3.21-4 20 0.5 1.5 0.145 82.7 28.6 22.9 0.35 0.28 3.2, 3.3d, 3.63-3e 20 0.41 3.0 0.0 59.1 18.5 23.3 0.31 0.39 3.3c

asum is the undrained shear strength at the soil surface and ρ is the strength gradientbLoads are presented here as the total load recorded on the pipe element, not load per unit lengthcLoads are presented here as the total load recorded on the pipe element, not load per unit lengthdThe first number represents the sample and the second the test in that sample (Barrett, 2005)eTest 3-3 was an overloaded swipe with initial vertical loading to V0 = 59.1 N before being unloaded to V/V0 = 0.15 prior to the swipe

3-4

Undra

ined

Resp

onse

ofShallo

wPip

elin

es

Subje

cte

dto

Com

bin

ed

Loadin

g

Table 3.2: Experiments investigating the flow rule

Test details Soil properties Load paths followed Figure

TestD

[mm]w/Dinitial

[-]sum

[kPa]ρ

[kPa/mm]V0

[N]V/V0

[-]Load path

V : H

Pro

be:

const

.ve

rtic

allo

ad

5-1 20 0.83 4.5 0.026 80.0 1 - 3.45-2 20 0.14 4.5 0.026 45.0 1 - 3.45-3 20 0.33 4.5 0.026 65.0 1 - 3.4, 3.75-4 20 0.65 4.5 0.026 80.0 0.5 - 3.45-5 20 0.59 4.5 0.026 80.0 0.275 - 3.4, 3.86-1 20 0.42 4.0 0.181 80.0 0.287 - 3.4

Loa

dpat

h 6-2 20 0.2 4.0 0.181 50.0 0.8 -1:1 3.46-3 20 0.144 4.0 0.181 50.0 0.58 -1:1 3.4, 3.10, 3.116-5 20 0.13 4.0 0.181 50.0 0.44 -1:1 3.4

3-5


3.4 Numerical Model

Of the force resultant model (Hodder and Cassidy, 2010), only the yield surface and flow

rule are discussed in detail in this paper as the hardening law and elastic relationship are

unchanged. In brief, the hardening law uses traditional bearing capacity theory with fac-

tors derived from large deformation finite element analysis (Barbosa-Cruz and Randolph,

2005) and a non-coupled matrix describes elastic behaviour with stiffness proportional to

the undrained shear strength at the pipe invert (Hodder and Cassidy, 2010).

3.4.1 Yield surface

The yield surface is a boundary in vertical and horizontal load space that separates elastic

and elasto-plastic states. The size and shape of the yield surface is defined purely in terms

of the vertical plastic displacement. The yield surface presented in Hodder and Cassidy

(2010) requires adjustment to remove the vertical tensile capacity and therefore reverts

back to the original form presented for the application of spudcan foundations on clay

(Martin, 1994):

f =

(

H

h0V0

)1/β2

−

(

(β1 + β2)(β1+β2)

ββ11 ββ2

2

)1/β2(

V

V0

)β1/β2(

1 −V

V0

)

= 0 (3.1)

h0 = Hmax/V0 defines the ratio of the peak horizontal load Hmax to vertical capacity

at a given depth and β1 and β2 are parameters controlling the curvature of the surface.

The removal of the tensile capacity term from the yield surface formulation requires an

adjustment of the curvature parameters β1 and β2 with respect to the original model

(Hodder and Cassidy, 2010). Values of β1 and β2 equal to 0.55 and 0.99 respectively

provide good agreement with the yield surface shapes observed in the swipe tests. Values

of 0.75 and 0.75 were adopted in the original model (Hodder and Cassidy, 2010). The

variation in h0 with embedment is defined by the relationship:

h0 = h0,surface + φh (h0,deep − h0,surface) (3.2)

where h0,surface is the value of h0 at zero embedment, h0,deep is the limiting value of h0

and describes the horizontal capacity at several diameters embedment (when h0 becomes

independent of embedment) and φh is a transition factor defined as:

φh =

[

1 −

(

1 − min

(

1,w

wh,deep

))Ah]1/Bh

(3.3)

where w = w/D is the pipe invert embedment normalised by the pipe diameter and

wh,deep is the normalised embedment at which h0,deep occurs. Using the peak horizontal

loads observed in the swipe tests conducted in both the centrifuge and on the laboratory

floor (Barrett, 2005), values of h0,surface = 0.147, h0,deep = 0.8, wh,deep = 3.5, Ah = 1.26,

3-6



Pea

khor

izon

talca

pac

ity,

h0

=H

max/V

0[-]

CentrifugeLaboratory floorEquation 3.2

0 0.125 0.25 0.375 0.50

0.1

0.2

0.3

0.4

0.5

Figure 3.2: Variation of h0 with embedment

Bh = 1.59 provide a good fit. This is shown in Figure 3.2.

Using the above yield surface formulation, Figure 3.3 shows examples of yield surfaces

for swipe tests conducted in the laboratory floor (Barrett, 2005) and centrifuge tests

(Hodder and Cassidy, 2010). Both normally and overloaded loaded swipes are shown.

The former refers to a test that is immediately driven laterally after the pipe is penetrated

to the desired embedment (Figures 3.3a, 3.3b and 3.3d), whilst in the latter the pipe is

unloaded to a vertical load less than V0 before being swiped (Figure 3.3c).

3.4.2 Flow rule

A flow rule that predicts the correct ratio of footing displacements during yield is required.

Slight non-association was observed in experiments where the pipe was penetrated and

horizontally displaced at a fixed ratio in the drum centrifuge (Hodder and Cassidy, 2010).

However, this could be reliably modelled by a plastic potential surface of the same for-

mulation as the yield surface, but with its curvature modified. As the yield surface of

Equation 3.1 accounts for no tensile capacity, the plastic potential (Hodder and Cassidy,

2010) can be written as:

g =

(

H

h0V ′

0

)1/β4

−

(

(β3 + β4)(β3+β4)

ββ33 ββ4

4

)1/β4(

V

V ′

0

)β3/β4(

1 −V

V ′

0

)

= 0 (3.4)

where β3 and β4 are the modified curvature parameters and V ′

0 is a dummy parameter

defining the intersection of the plastic potential surface with the vertical load axis.

Six probe and three load path tests are used to evaluate appropriate curvature factors

3-7



Nor

mal

ised

hor

izon

tallo

ad,H

/V0

[-]


Nor

mal

ised

hor

izon

tallo

ad,H

/V0

[-]


Nor

mal

ised

hor

izon

tallo

ad,H

/V0

[-]


Nor

mal

ised

hor

izon

tallo

ad,H

/V0

[-]

Yield surfaceExperimental swipe test

(a) (b)

(c) (d)

w/D = 0.05 w/D = 0.2

w/D = 0.41 w/D = 0.5

0 0.25 0.5 0.75 10 0.25 0.5 0.75 1

0 0.25 0.5 0.75 10 0.25 0.5 0.75 1

0

0.1

0.2

0.3

0.4

0

0.1

0.2

0.3

0.4

0

0.1

0.2

0.3

0.4

0

0.1

0.2

0.3

0.4

Figure 3.3: (a) Normally loaded laboratory floor swipe at w/D = 0.05; (b) normallyloaded centrifuge swipe at w/D = 0.2; (c) overloaded laboratory floor swipeat w/D = 0.41; (d) normally loaded centrifuge and laboratory floor swipes atw/D = 0.5

3-8


tan−1 (h0∆up/∆wp)

tan−

1(H

/h0V

)

Associated flow

Non-associated flow

Probe from V/V0 = 1

Probe from V/V0 < 0.5

Constant load path

0 20 40 60 80 100 120 140 160 1800

10

20

30

40

50

60

70

80

90

Figure 3.4: Comparison of experimental and theoretical flow results

for Equation 3.4. In Figure 3.4, the angle of the normalised force ratio tan−1 (H/h0V )

against the angle of the normalised plastic displacement ratio, tan−1 (h0∆up/∆wp) (where

the superscript p denotes the plastic component of the total displacement), for all nine

tests in Table 3.2 are shown. These results can be compared to theoretical estimates

derived from Equation 3.4. As the tests were conducted at a changing depth, normalising

the angles by h0 allows the theoretical estimates to reduce to one curve (per set of β3 and

β4). The theoretical associated flow curve (where β3 = β1 = 0.55 and β4 = β2 = 0.99)

does not fit the experimentally measured results to the degree of accuracy required. A

better fit occurs with β3 and β4 values of 0.44 and 0.8 respectively (labelled non-associated

in Figure 3.4) and these should be used with the no tensile capacity assumption of this

paper. In deriving this solution the ratio of the plastic potential parameters β3/β4 was

constrained to be equal the ratio of the yield surface parameters β1/β2. This ensures

the load path of the numerical swipe test reaches the ‘parallel point’ at the peak of the

theoretical yield surface. This is consistent with the experimental results with the pipe

displacing horizontally at the yield surface peak with limited change in load state.

3.5 Retrospective Simulations

This section demonstrates the applicability of the model by retrospectively simulating

a selection of the experiments (Barrett, 2005). All shear strength profiles used in the

simulations were obtained from a fit to the experimental shear strength profile over a

3-9


depth relevant to the specific test, as specified in Tables 3.1 and 3.2. The simulations are

run on a purpose written FORTRAN program, which allows two of the experimentally

measured quantities (e.g. the loads) to be taken as input and the other quantity (e.g. the

displacement) to be calculated for comparison with the experiment. Although the model

is formulated per unit length of pipe, the results are presented as total loads to allow for

comparison to the loads recorded directly in the experiments.

3.5.1 Swipe tests

The results from two simulated normally loaded swipe tests are discussed. The exper-

iments were simulated numerically using the same phases used to conduct the physical

experiments. Firstly, the pipe was penetrated using displacement control to the desired

embedment, followed by a displacement controlled lateral swipe while holding the verti-

cal displacement constant. These simulations test the model’s ability to track the yield

surface and predict the peak horizontal load and the displacement at which it occurs.

Figure 3.5 shows a retrospective simulation of normally loaded swipe test 3-2 (see

Table 3.1 for description). Both the vertical-horizontal load path and the horizontal load

versus horizontal displacement show general agreement with the experimental data. The

vertical load at the end of the swipe is a little higher than in the experiment, with the

peak horizontal load predicted well. The simulated horizontal behaviour is slightly stiffer,

yielding at a smaller horizontal displacement than in the experiment.

Figure 3.6 shows a retrospective simulation of test 1-4 (Table 3.1). Similar to the

swipe at 0.05D, both the vertical-horizontal load path and the horizontal load versus

horizontal displacement show general agreement with the experimental data. Both the

vertical and horizontal loads at the end of the simulated swipe are slightly higher than in

the experiment. The slight over prediction in horizontal load is due to the variation in h0

with embedment. Equation 3.2 is a fit to all of the experimental swipes conducted (Hodder

and Cassidy, 2010; Barrett, 2005) and therefore can over predict the horizontal load when

compared to the physical experiment in specific tests. Of course, it under predicts for

other cases. As with the swipe at 0.05D, the simulated horizontal behaviour is slightly

stiffer, yielding at a smaller horizontal displacement than in the experiment.

3.5.2 Probe tests (constant vertical load)

The results from a simulated normally loaded and an overloaded probe test are discussed.

Again the numerical simulations use the same phases as the physical experiments. In the

normally loaded case the pipe was initially penetrated using displacement control to the

desired embedment, and then while holding the vertical load constant the pipe was dis-

placed laterally using displacement control. The procedure in the overloaded simulation

was as per the normally loaded simulation, except, prior to displacing the pipe laterally,

the vertical load was unloaded to a situation of V < V0. This smaller vertical load was

then held constant using load control throughout the lateral displacement. These probe

3-10


Vertical load, V [N]

Hor

izon

tallo

ad,H

[N]

Horizontal pipe displacement, u [mm]

Hor

izon

tallo

ad,H

[N]

(a) (b)

Simulation

Experiment

Simulation

Experiment

0 2.5 5 7.5 100 50 100 150 2000

15

30

45

0

15

30

45

Figure 3.5: Normally loaded swipe simulation at w/D = 0.05


Hor

izon

tallo

ad,H

[N]


Hor

izon

tallo

ad,H

[N]

(a) (b)

Simulation

Experiment

Simulation

Experiment

0 1 2 3 4 50 20 40 60 800

10

20

30

40

0

10

20

30

40

Figure 3.6: Normally loaded swipe simulation at w/D = 0.5

3-11


simulations test the model’s ability to simulate the change in vertical plastic displacement

required to maintain a constant vertical load. This variation in vertical plastic displace-

ment causes an expansion or contraction of the yield surface, depending on whether the

pipe penetrates or heaves.

Figure 3.7 shows a retrospective simulation of a normally loaded probe test from an

initial penetration of 0.33D (test 5-3 in Table 3.2). Up to a horizontal displacement of

0.5D (10 mm), the simulation displays excellent agreement with the experimental data,

with both the additional pipe penetration and horizontal load predicted well. For horizon-

tal displacements greater than 0.5D, the model over predicts both the vertical penetration

and the peak horizontal load. Throughout the test the horizontal load continues to in-

crease due the expansion of the yield surface size caused by the increase in plastic vertical

displacement at constant vertical load.

Figure 3.8 shows a retrospective simulation of test 5-5; an overloaded probe test from

an initial penetration of 0.59D that was unloaded to V/V0 = 0.275 (Table 3.2). The

simulation shows excellent agreement with the experimental data in predicting the heave

of the pipe over the full horizontal displacement. The predicted peak horizontal load is

approximately 25% greater than that recorded in the experimental data, which is due to

Equation 3.2 over predicting the horizontal capacity for this particular test.

At the beginning of the horizontal displacement, the horizontal load rapidly increases

to a peak before decreasing. This is in contrast to the normally loaded probe simulation,

in which the horizontal load steadily increases during the simulation. In the overloaded

case this rapid increase in horizontal load demonstrates elastic behaviour inside the yield

surface, which continues until the load combination is on the yield surface. Figure 3.9

shows that at this stage the V :H load point is on the ‘left side’ of the yield surface

peak (low V/V0), resulting in the vertical component of a vector normal to the plastic

potential surface to be pointed towards negative vertical displacement. Therefore, in

order to maintain a constant vertical load the pipe begins to heave, causing a contraction

of the yield surface and a subsequent gradual reduction in horizontal load. While the peak

horizontal load is slightly over predicted in the simulation, the reduction in horizontal load

is replicated well.

3.5.3 Constant load path test

The constant load path tests were conducted to simulate a realistic loading scenario. The

pipe is initially penetrated using displacement control and then unloaded to V < V0. This

approximates the pipe laying process where the underlying soil is subjected to a vertical

load larger than the pipe’s self weight. Hydrodynamic forces on a partially buried pipe can

have the effect of applying an uplift and lateral force simultaneously. This was investigated

experimentally by applying a constant load path ratio V : H of −1 : 1.

Figures 3.10 and 3.11 show retrospective simulations of test 6-3, an overloaded constant

load path test from an initial penetration of 0.144D (Table 3.2). Figure 3.10 shows the

3-12



Pip

ein

vert

embed

men

t,w

[mm

]


Pip

ein

vert

embed

men

t,w

[mm

]


Hor

izon

tallo

ad,H

[N]


Hor

izon

tallo

ad,H

[N]

(a) (b)

(c) (d)

SimulationExperiment




0 20 40 60 800 5 10 15 20

0 20 40 60 800 5 10 15 20

0

15

30

45

60

0

15

30

45

60

0

10

20

30

0

10

20

30

Figure 3.7: Normally loaded probe simulation

3-13



Pip

ein

vert

embed

men

t,w

[mm

]


Pip

ein

vert

embed

men

t,w

[mm

]


Hor

izon

tallo

ad,H

[N]


Hor

izon

tallo

ad,H

[N]

(a) (b)

(c) (d)




Simulation

Experiment

0 25 50 75 1000 5 10 15 20

0 25 50 75 1000 5 10 15 20

0

10

20

30

40

0

10

20

30

40

0

5

10

15

0

5

10

15

Figure 3.8: Overloaded probe simulation

3-14


00

30

60

50 100


Hor

izon

tallo

ad,H

[N] Yield surface

Plastic potential surface

iii

iii

i. Load

ii. Unload to V/V0 < 1

iii. Probe at constant V

Figure 3.9: Load path during overloaded probe simulation

results of a simulation using the same test phases as the physical experiment; penetrating

vertically using displacement control, unloading vertically using load control and tracking a

V :H load path of -1:1 using load control. The V :H load path recorded in the experiment

shows that while initially the load path is tracked successfully, the system could not

sustain the increase in H with decreasing V . A peak horizontal load is reached followed

by a reduction due to failure in the soil. Numerically, a similar event occurs. The model

successfully tracks the requested load path until the load combination reaches the yield

surface, after which the simulation becomes unstable. This again is failure being predicted,

as the input command of increasing horizontal load with decreasing vertical load can not

be sustained by a model predicting a contracting yield surface and pipe heave.

As an alternative, the vertical and horizontal displacement signals from the actuator

control system used in the physical experiment were used as the input to a second model

simulation of test 6-3. The results from this simulation are shown in Figure 3.11, with

this essentially being a comparison of the experimentally recorded load path and the nu-

merically predicted. In this simulation, the model displays general agreement with the

experimental observations. In the unload phase, the model unloads to a vertical load

approximately 30% higher than the experiment. However, at the end of the test similar

vertical loads are obtained. Horizontally, the model predicts an initial peak load slightly

higher than in the experiment but then shows excellent agreement in simulating the hori-

zontal load versus horizontal displacement relationship. This simulation also demonstrates

the model’s ability to handle very small input permutations.

3-15


3.6 Conclusions

This paper outlines a force-resultant model applicable to predicting the undrained response

of shallow pipelines subjected to combined vertical and lateral loading. The model is a

variation of that presented in Hodder and Cassidy (2010) adjusted for the condition of

zero uplift capacity. The changes required to the original model are presented. The model

is limited to small displacements and monotonic loading.

To investigate the capability of the model, a range of experiments conducted by Bar-

rett (2005) were retrospectively simulated using a purpose built program written in FOR-

TRAN. Swipe, probe and constant load path tests were simulated and generally displayed

good agreement with the experimental behaviour.

3-16



Pip

ein

vert

embed

men

t,w

[mm

]


Pip

ein

vert

embed

men

t,w

[mm

]


Hor

izon

tallo

ad,H

[N]


Hor

izon

tallo

ad,H

[N]

(a) (b)

(c) (d)


Simulation

Experiment



0 12.5 25 37.5 500 5 10 15

0 12.5 25 37.5 500 5 10 15

0

5

10

15

0

5

10

15

0

1

2

3

0

1

2

3

Figure 3.10: Constant load path simulation

3-17



Pip

ein

vert

embed

men

t,w

[mm

]


Pip

ein

vert

embed

men

t,w

[mm

]


Hor

izon

tallo

ad,H

[N]


Hor

izon

tallo

ad,H

[N]

(a) (b)

(c) (d)


Simulation

Experiment



0.7

0 12.5 25 37.5 500 5 10 15

0 12.5 25 37.5 500 5 10 15

0

5

10

15

0

5

10

15

0

1

2

3

0

1

2

3

Figure 3.11: Constant load path simulation using actuator displacements

3-18


References


Barrett, D. (2005). Model testing to prove up applicability of plasticity modelling of sub-sea pipelines in purely undrained soils. Honours thesis, School of Civil and ResourceEngineering, The University of Western Australia.


Chung, S. F. and Randolph, M. F. (2004). Penetration resistance in soft clay for differentshaped penetrometers. In Proc. 2nd International Conference on Geotechnical SiteCharacterization, volume 1, pages 671–678, Porto, Portugal.

Hodder, M. S. and Cassidy, M. J. (2010). A plasticity model for predicting the verticaland lateral behaviour of pipelines in clay soils. Geotechnique, 60(4):247–263. [presentedas Chapter 2 of this thesis].


Muir Wood, D. (2004). Geotechnical modelling. Spon Press, Oxfordshire, UK.



Vlahos, G., Martin, C. M., Prior, M. S., and Cassidy, M. J. (2005). Development of amodel jack-up unit for the study of soil-structure interaction on clay. InternationalJournal of Physical Modelling in Geotechnics, 5(2):31–48.



3-19

4Centrifuge Modelling of Riser-Soil Stiffness Degradation in

the Touchdown Zone of a Steel Catenary Riser

4.1 Abstract

Steel catenary risers (SCRs) are economical to assemble and install compared to conven-

tional vertical risers. However, accurate evaluation of the fatigue life of an SCR remains a

major challenge due to uncertainty surrounding the interaction forces at the seabed within

the touchdown zone (TDZ). Fatigue life predictions are heavily dependant on the assumed

stiffness between the riser and the seabed and therefore an accurate assessment of seabed

stiffness — or more specifically the non-linear pipe-soil resistance — is required. During

the lifespan of an SCR, vessel motions due to environmental loading cause repeated pen-

etration of the riser into the seabed within the TDZ. This behaviour makes assessment of

seabed stiffness difficult due to the gross deformations of the seabed and the resulting soil

remoulding and water entrainment.

This paper describes a model test in which the movement of a length of riser pipe was

simulated within the geotechnical beam centrifuge at the University of Western Australia.

The model soil was soft, lightly over-consolidated kaolin clay with a linearly increasing

shear strength profile with depth, typical of deepwater conditions. The pipe was cycled

over a fixed vertical distance from an invert embedment of 0.5 diameters to above the

soil surface. This range represents a typical vertical oscillation range of a section of riser

within the TDZ during storm loading.

The results indicate a significant degradation in the vertical pipe-soil resistance during

cyclic vertical movements. Due to the cyclic degradation in soil strength, the component

of the vertical resistance created by buoyancy was significant, particularly due to the

influence of heave. A new approach to the interpretation of heave-enhanced buoyancy was

used to extract the separate influences of soil strength and buoyancy, allowing the cyclic

degradation in strength to be quantified.

During cycling, the soil strength reduced by a factor of 7.5 relative to the initial pen-

etration stage. This degradation was more significant than the reduction in soil strength

during a cyclic T-bar penetration test. This contrast can be attributed to the breakaway

4-1


of the pipe from the soil surface which allowed water entrainment. This dramatic loss of

strength and therefore secant stiffness, and the significance of the buoyancy term in the

total vertical pipe-soil resistance, has implications for the fatigue assessment of SCRs.

4.2 Introduction

With the continuing depletion of fossil fuel reserves in shallow water there is an increasing

trend to develop fields further offshore in deeper water. A deepwater facility typically

consists of a floating platform, a mooring system and risers that transport the product

between the platform and the seabed. Steel catenary risers (SCRs) are a cost effective

option in deep water and consist simply of a steel pipe, 200-500 mm in diameter.

SCRs were initially used in the Gulf of Mexico, attached to spars or tension leg plat-

forms (TLPs) which undergo low amplitude dynamic motions. The first SCRs were in-

stalled 14 years ago on Shell’s Auger TLP in the Gulf of Mexico in 900 m of water (Phifer

et al., 1994). SCRs have subsequently been used in the Campos Basin offshore Brazil

(Serta et al., 1996; Gonzalez et al., 2005) and within the Gulf of Guinea, off the coast

of West Africa (Nolop et al., 2007). The majority of these newer risers are connected to

FPSOs and semi-submersible vessels, so must withstand larger amplitude motions.

Fatigue stresses can be a critical design consideration at the connection to the platform

and in the region where the SCR touches down on the seabed (the touchdown zone or

TDZ). The fatigue life assessment is heavily dependant on the assumed seabed stiffness

conditions (Bridge et al., 2004; Clukey et al., 2007). Failure of an SCR has obvious

environmental and economic implications.

The interaction between the riser pipe and the seabed in the touchdown zone is con-

ventionally modelled by linking the force per unit length of pipe, V , to the embedment, w,

using linear vertical springs, sometimes with zero-tension lift-off (Figure 4.1a), although

advanced analyses include vertical non-linearity, and tensile forces during uplift of the riser

(Bridge et al., 2004) (Figure 4.1b). Bridge (2005) and Clukey et al. (2007) demonstrate

that the tensile component of the non-linear model significantly increases the fatigue dam-

age within the TDZ, and that stiffer linear springs create increased damage compared to

compliant linear springs.

The non-linear response during the initial penetration of the riser into the virgin seabed

can be assessed from the in situ soil strength, using conventional bearing capacity-type

expressions. However, during the in-service life of the riser, the pipe movement at the

touchdown zone involves episodes of cyclic loading linked to the hydrodynamic and envi-

ronmental loading experienced by the riser and the vessel.

When idealised as purely vertical motion, these episodes of cyclic loading lead to

changes in the soil strength compared to the in situ conditions. The changes in soil strength

are due to remoulding of the soil, and subsequent reconsolidation. Large amplitude pipe

movements cause additional strength loss, particularly if the pipe breaks away from the

soil surface leading to entrainment of water into the disturbed soil. The strength and

4-2

Centrifuge Modelling of Riser-Soil Stiffness Degradation in the Touchdown Zone of a Steel Catenary Riser

(a) (b)

ww

VV

k

Figure 4.1: Models for vertical pipe-soil interaction

stiffness can recover, at least temporarily, if a period of reconsolidation is permitted.

If non-linear pipe-soil interaction is considered, the effect of the remoulding process

is to reduce both the compressive penetration resistance and the tensile uplift resistance,

narrowing the width of the vertical force-displacement hysteresis loop. If the seabed

response is idealised as linear, the remoulding effect can be incorporated as a reduction in

the pipe-soil stiffness.

This paper describes the results of a test that was conducted with the aim of quantifying

the reduction in soil strength due to repetitive cycling near the soil surface, when the pipe

breaks away, allowing entrainment of water. The vertical cyclic amplitude was chosen to

simulate riser movements that would occur in the field during a significant storm event.

The variation in back-calculated soil strength is compared to that predicted by the soil

sensitivity derived from a typical cyclic T-bar test.

4.3 Experimental Apparatus

The experiments described in this paper were conducted using the geotechnical beam

centrifuge at the University of Western Australia (UWA). A complete description of this

beam centrifuge, as commissioned in 1989, is provided by Randolph et al. (1991). The

centrifuge is an Accutronic Model 661 geotechnical centrifuge. It has a swinging platform

radius of 1.8 m with a nominal working radius of 1.55 m, and has a rated capacity of 40 g-

tonnes (which equates to a maximum payload of 200 kg at an acceleration of 200 g). A

recent photograph of the centrifuge is shown in Figure 4.2.

A geotechnical centrifuge is required to accurately model the behaviour of geotechnical

processes at small scale. The strength and stiffness of soil is governed by the effective

stress, so small scale models conducted at unit gravity do not correctly mimic full scale

behaviour. If a small scale model is accelerated within a centrifuge, the self-weight of the

soil is enhanced by the ratio of the centrifuge acceleration to Earth’s gravity. This ratio is

4-3


Figure 4.2: UWA geotechnical beam centrifuge

Vertical load cell

Section ofriser pipe

Figure 4.3: Model riser pipe

4-4


the scaling factor required to convert dimensions in a centrifuge model to the dimensions

of the corresponding field scale situation. In this paper, all results are presented in field

scale units, unless stated otherwise.

The general arrangement for conducting pipe-soil interaction tests is for the model pipe

section to be rigidly fixed to an actuator which has two degrees of freedom (vertical and

horizontal). In these tests, the model pipe section was 20 mm in diameter and 122.5 mm

in length (Figure 4.3). At the test acceleration level of 50 g these dimensions correspond

to a pipe diameter of 1.0 m and a length of 6.125 m. The ratio of pipe length to diameter

is sufficiently high that end effects can be neglected.

The model pipe was attached to a vertical load cell which was in turn connected to

a loading arm that was instrumented to measure the horizontal load applied to the pipe.

The loading arm was attached to the actuator.

4.4 Sample Preparation and Characterisation

The model seabed used in this experiment consisted of kaolin clay, consolidated from a

slurry within the centrifuge. The mechanical properties of kaolin are well documented

(Stewart, 1992) and kaolin has been extensively used in geotechnical modelling at UWA

and elsewhere.

To prepare the sample, dry kaolin powder was mixed with water to produce a slurry

with a moisture content of approximately twice the liquid limit. The slurry was mixed in

a barrel mixer for six hours with a vacuum applied for the final two hours to de-air the

slurry. The slurry was then carefully transferred from the mixer to the strongbox, which

had a 15 mm thick sand drainage layer in the base. The sample was then spun at an

acceleration of 50 g for four days, after which time primary consolidation was complete.

The centrifuge was then stopped and approximately 45 mm of clay was scraped from the

surface of the sample to provide a strength intercept at the mudline. Before testing, the

sample was spun at 50 g for one day to achieve pore pressure equilibration. The final

sample depth was ≈ 130 mm.

A T-bar penetrometer (Stewart and Randolph, 1991) with a diameter of 5 mm and

length of 50 mm (Figure 4.4) was used to determine the profiles of intact and remoulded

shear strength. The T-bar was initially penetrated to a depth of 80 mm (at model scale)

before being cycled between depths of 35 and 60 mm. The undrained shear strength su

was back-calculated from the net penetration resistance, q, following the usual approach:

su =q

NT−bar

(4.1)

It is conventional to use a single value of NT−bar = 10.5, which is derived from the-

oretical solutions for the flow of soil around a deeply embedded cylinder (Martin and

Randolph, 2006). However, in this investigation it was necessary to accurately quantify

the soil strength near the surface, which requires an adjustment of NT−bar to account for

4-5


Figure 4.4: Miniature T-bar penetrometer

the changing penetration mechanism within this zone. At very shallow embedment the

T-bar is effectively a surface foundation with a curved base, for which a bearing capacity

factor of ≈ 5 is required to link strength and penetration resistance.

The variation in NT−bar from the surface to the depth at which the deep flow-round

mechanism is mobilised can be captured by the following expression:

NT−bar = φNNT−bar,deep (4.2)

where φN is an elliptical transition factor defined as:

φN =

[

1 −

(

1 − min

(

1,z

zN,deep

))AN]1/BN

(4.3)

where z is the depth of the T-bar invert normalised by the T-bar diameter, NT−bar,deep =

9.87 is the limiting value of NT−bar and occurs at a normalised depth zN,deep = 4.63. AN

and BN are curvature parameters controlling the abruptness of the transition at zN,deep and

the initial steepness of the relationship respectively and are equal to 1.26 and 3.24. These

parameters are fitted to the numerical analyses of shallow pipe penetration presented by

Barbosa-Cruz and Randolph (2005).

The resulting profile of undrained strength is shown in Figure 4.5, overlain by a simple

linear fit defined by a mudline intercept of sum = 1.5 kPa and a strength gradient of

ρ = 1 kPa/m (at prototype scale).

A cyclic phase was included in the T-bar test (Figure 4.5) to provide an indication of the

reduction in soil strength with remoulding, which is commonly referred to as the sensitivity.

4-6



Sam

ple

dep

th,z

[m]

su = 1.5 + z kPa

(z in metres)

-6 -4 -2 0 2 4 60

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Figure 4.5: Calculated shear strength from cyclic T-bar test

The progressive reduction in strength is quantified by a degradation factor, defined as the

current strength normalised by the intact strength from the initial penetration (Figure 4.6).

The majority of the strength degradation occurs within the first 3 cycles.

Two definitions of T-bar sensitivity are considered. In-out sensitivity, St,in−out, is the

penetration resistance (or inferred strength) during the initial downward penetration di-

vided by the resistance as the T-bar is withdrawn. Cyclic sensitivity, St,cyc, is the ratio of

the initial downward penetration resistance to the steady value of downward penetration

resistance reached after many cycles of movement. Based on the degradation shown in

Figure 4.6, values of St,in−out = 1.5 and St,cyc = 2.4 are found.

During these cyclic stages the T-bar remained embedded within the soil, so free water

from above the soil surface was unable to become entrained during the remoulding process.

4.5 Cyclic Riser Test

4.5.1 Cyclic total resistance

A total of 16 tests were conducted in the same soil sample to observe the vertical response

of a section of riser pipe under a variety of imposed load and displacement sequences,

including periods of reconsolidation.

This paper focuses on a single test that was conducted to simulate vertical cycling

over a fixed distance ranging from a pipe invert embedment of 0.5 diameters below the

original soil surface to a pipe invert elevation of 1D above the original soil surface. This

4-7


Cycle number

Deg

radat

ion

fact

or[-]

Penetration phase

Extraction phase

St,in−out = 1.5

St,cyc = 2.4

0 5 10 15 200

0.2

0.4

0.6

0.8

1

Figure 4.6: Strength degradation during cyclic T-bar test

Vertical bearing pressure, qt [kPa]

Pip

ein

vert

embed

men

t,w

/D[-]

Trench

D = 1 m

Trench after

2 cycles

-5 0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

Figure 4.7: Vertical resistance during cyclic movement

4-8


large amplitude of motion, forcing the soil to break away from the pipe, was selected to

illustrate the effect of robust cyclic motion and highlight the influence of breakaway. A

total of 20 cycles were imposed, prior to a period of reconsolidation followed by further

cycling. The response subsequent to reconsolidation is not discussed in this paper.

The measured load, after a minor adjustment for the changing effective weight of

the model pipe and loading arm with radial position within the centrifuge, indicates the

variation in total vertical resistance qt = V/D (in units of stress), where V is the vertical

force per unit length of pipe and D is the pipe diameter. It is this total force which is

represented in the structural analysis of risers by the idealised models shown in Figure 4.1.

Figure 4.7 shows the variation in qt over the 20 cycles. The data from above the soil

surface, when the load was zero, has been omitted for clarity. The resistance degrades

sharply within the first few cycles. A trench forms during the first 2 cycles, such that no

vertical resistance is encountered until an embedment of 0.175D relative to the original

soil surface.

The shape of the response during the first cycle is comparable to the non-linear ‘suction’

model shown in Figure 4.1b. Significant tensile resistance is encountered during the first

uplift phase, although this never exceeds 50% of the initial penetration resistance.

Beyond the first ≈ 5 cycles the response stabilises, with minimal further degradation of

strength occurring. At this stage it is notable that the total resistance remains compressive

even after the pipe begins to move upwards. The fully remoulded response is ‘banana-

shaped’ and represents a superposition of the linear model (Figure 4.1a) and a weak version

of the non-linear suction model (Figure 4.1b).

To clarify the underlying behaviour it is necessary to include the contribution of buoy-

ancy to the vertical resistance, by dividing the total resistance, qt, into separate compo-

nents: (i) resistance due to buoyancy, qb, and (ii) resistance due to soil strength, qs.

4.5.2 Buoyancy effect: modified Archimedes’ principle

For a conventional foundation embedded in undrained soil at some depth, w, below the soil

surface, the total bearing capacity, qt, comprises of two contributions which arise from (i)

the shear strength (denoted qs in Equation 4.4) and (ii) the self-weight of the foundation

soil (denoted qb).

qt = qs + qb = Ncsu + γ′w (4.4)

The second term — often referred to as the surcharge term — arises from buoyancy. If

the undrained strength is reduced to zero then the soil is a heavy fluid and a hydrostatic

pressure of γ′w acts upwards on the foundation leading to a resultant force equal to the

(submerged) weight of the displaced fluid.

For the case of a pipeline, the buoyancy term is influenced by the surface heave gen-

erated as the pipe penetrates into the soil, which increases the buoyancy effect (Merifield

et al., 2009; Randolph and White, 2008a). Once soil has heaved above the original sur-

4-9


face, then the potential energy to be transferred to the soil as the pipe penetrates deeper

is increased. This is because any subsequent penetration is achieved by lifting the dis-

placed soil to the top of the pre-existing heave, rather than to the original ground surface

elevation.

To account for this effect, Equation 4.4 can be adjusted by introducing an additional

bearing capacity factor, Nb, linked to the buoyancy term:

qt = qs + qb = Ncsu + Nbγ′w (4.5)

The buoyancy term can be expressed in terms of the nominal submerged pipe area,

As:

qt = Ncsu + fbAsγ′1

Dso Nb =

fbAs

Dw(4.6)

where w = w/D and:

As =D2

4

[

sin−1(

√

4w (1 − w))

− 2 (1 − 2w)√

w (1 − w)]

(4.7)

The enhanced heave effect is captured by increasing the buoyancy term in Equation 4.6

by a factor fb. The physical origin of this adjustment can be illustrated by the idealised

heave geometry shown in Figure 4.8. The zone of heaved soil on each side of the pipe has

a cross-sectional area of As/2 (due to undrained conditions), and can be idealised as a

rectangular block with width defined as λD′/2, where D′ is the nominal pipe-soil contact

width and λ is a parameter used to define the geometry of the heave (Figure 4.8). For

this soil surface geometry, any additional heave must be accommodated on top of the

existing heave profile at an elevation of h∗

heave, rather than at the original soil surface level.

Potential energy considerations can be used to show that (Merifield et al., 2009):

fb = (1 + 1/λ) (4.8)

If the soil strength is zero the heave will spread sideways so that λ → ∞, fb = 1 and

the buoyancy term reverts to Archimedes’ principle. A higher heave block, located close

to the pipe, corresponds to a lower value of λ and therefore a higher value of fb and an

enhanced buoyancy term.

The height of the idealised heave block h∗

heave can be approximated as (Merifield et al.,

2009):

h∗

heave

D≈

w

1.4λ(4.9)

4-10


Pipe

V

D

w = wD

w

D′

As

Bheave

Soil

γ′, su

hheave

Aheave

h∗

heave

B∗

heave= λD′/2

Idealised heave

Figure 4.8: Heave geometry

4.5.3 Back-calculation of buoyancy effect

Comparisons between large deformation FE analyses and plasticity solutions show that a

heave parameter of λ = 3 is appropriate for describing the initial penetration of a pipe into

undrained soil (Merifield et al., 2009). For the initial penetration and extraction cycle,

the profile of resistance due to buoyancy, qb, with depth can therefore be calculated from

Equations 4.5–4.8 and applied as an adjustment to the measured resistance, qt, to derive

the resistance created by the soil strength, qs — as shown on Figure 4.9.

For the subsequent cycles, however, this definition of qb does not directly apply because

of the trench formed during the initial cycle. The surface of this trench is a distance, t,

below the original ground surface (Figure 4.10). The presence of the trench and the pre-

existing heave created in the initial penetration and extraction cycle means that the qb

term must be modified.

Firstly, the pipe embedment is calculated relative to the trench surface, so the effective

embedment, w′ = w−t, replaces w in Equations 4.5–4.7. Secondly, the existing high mound

of heave next to be pipe leads to a lower value of the heave geometry parameter, λ. If

it is assumed that the heave profile on either side of the pipe formed during the initial

penetration cycle undergoes minimal change in shape throughout the following cycles,

then the heave elevation relative to the trench surface is h′

heave (Figure 4.10) instead of

hheave, where h′

heave = hheave + t (Figure 4.8).

Using Equation 4.9 and the modified heave height for the trench case, the heave ge-

ometry parameter associated with cycles into the pre-existing trench, λt, and the heave

parameter used in the initial penetration, now denoted λs, can be related as follows, taking

w as the deepest previous embedment:

λt =w − t

w/λs + 1.4t(4.10)

where t is the trench depth, t, normalised by the pipe diameter, D. The response shown

4-11


Buoyancy pressure, qb [kPa]

Pip

ein

vert

embed

men

t,w

/D[-] Equations 4.5–4.8

t/D = 0, λs = 3

t/D = 0, λs = ∞

t/D = 0.175, λt = 0.8

t/D = 0.175, λt = ∞

0 1 2 30

0.1

0.2

0.3

0.4

0.5

0.6

Figure 4.9: Buoyancy contribution to vertical resistance

hheave

w

h′

heave

w′

t

Figure 4.10: Effect of trench formation on heave geometry

4-12


in Figure 4.7 indicates a trench depth of t = 0.175, which leads to a value of λt = 0.8

based on Merifield et al.’s (2009) value for the initial heave parameter of λs = 3.

The resulting variation in qb with depth for the later cycles is shown in Figure 4.9.

To illustrate the significance of heave in enhancing the buoyancy effect, the self weight

resistance due purely to Archimedes’ principle of buoyancy within a fluid (i.e. λ = ∞)

are also shown. Inclusion of heave leads to a ≈ 40% increase in buoyancy during the

initial penetration and more than doubles the buoyancy contribution during the cyclic

penetration, based on the assumed geometry of heave (quantified by λt = 0.8).

4.5.4 Back-calculation of cyclic soil strength response

The buoyancy component of the total penetration resistance shown in Figure 4.9, can be

subtracted from the total resistance, qt, to identify the resistance arising from the soil

strength, qs. It is this component of the resistance which is directly influenced by changes

in soil strength due to remoulding.

Figure 4.11 shows the variation of qs with depth. The response during the initial pene-

tration stage matches the response predicted based on plasticity solutions (e.g. Randolph

and White, 2008a,b; Merifield et al., 2008), with a bearing capacity factor of Nc ≈ 5 evi-

dent at w/D = 0.5. The response calculated using the linear shear strength profile derived

from the T-bar data and the Nc relationship in Equations 4.2–4.3, but substituting the

sample depth, z, with the pipe invert embedment, w, is also shown.

The shape of the cyclic response is significantly different to the total resistance, qt,

shown in Figure 4.7. As the pipe begins to move upwards the resistance immediately

becomes tensile, indicating that the soil resistance opposes the motion. Comparable re-

sistance is mobilised during penetration and extraction of the pipe, indicating the sym-

metrical form of response which is expected as the soil is repeatedly failed in opposite

directions.

The symmetry of the qs response indicates that the banana-shaped curvature of the qt

response can be attributed to the non-linear buoyancy term, which is shown in isolation

in Figure 4.9. The remaining component of resistance shows the symmetrical degradation

with cycles that matches cyclic T-bar tests (Figures 4.5, 4.6).

The cyclic degradation in soil strength is summarised in Figure 4.12, which shows qs at

the cyclic mid-depth (relative to the trench level) normalised by the value of qs from the

initial penetration. The resistance from the soil strength degrades to only 13.5% (1/7.5)

of the initial resistance. This represents a far greater loss of strength compared to the

cyclic T-bar test, which showed cyclic sensitivity of 2.4. The additional loss of strength

in the pipe test can be attributed to the entrainment of water into the remoulded soil,

permitting an increase in moisture content and therefore a reduction in strength.

During the cyclic T-bar test the bar remained embedded within the soil, so free water

from above the soil surface was unable to become entrained during the remoulding pro-

cess. In the future, it may be preferable to conduct near-surface cyclic T-bar tests which

4-13


Resistance component from soil strength, qs [kPa]

Pip

ein

vert

embed

men

t,w

/D[-]

Predicted penetration curve

-5 0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

Figure 4.11: Soil strength contribution to vertical resistance

Cycle number

Deg

radat

ion

fact

or[-]

Penetration phase

Extraction phase

Steady degradation reached

in cyclic T-bar test (Figure 4.6)

0 5 10 15 200

0.2

0.4

0.6

0.8

1

Figure 4.12: Cyclic strength degradation in riser section test

4-14


may be able to capture the tendency for additional strength degradation through water

entrainment.

4.6 Conclusions

The pipe-soil interaction forces within the touchdown zone of a steel catenary riser (SCR)

strongly influence the fatigue damage that accumulates within the riser pipe. Structural

analyses of SCRs usually consider only vertical pipe-soil forces and incorporate the pipe-

soil interaction via linear springs. Non-linear models which incorporate tensile pipe-soil

forces have been recently developed, and indicate significantly increased fatigue damage

compared to the linear idealisation.

This paper describes an experimental investigation conducted in a geotechnical cen-

trifuge. The pipe-soil interaction forces during large-amplitude cyclic vertical motion of a

section of riser pipe resting on soft clay were simulated.

The key observations can be summarised as follows:

1. The initial vertical penetration resistance follows the general form predicted from

the intact soil strength and conventional bearing capacity theory.

2. During large-amplitude cyclic movements, in which the pipe lifts away from the soil

surface, the vertical penetration and extraction resistance reduces significantly, and

a steady cyclic pattern is reached within 5–10 cycles.

3. The steady profile of vertical resistance with depth is ‘banana-shaped’, and comprises

of two significant components: a buoyancy term (acting upwards) which increases

non-linearly with depth, and a soil strength term, which opposes the pipe movement.

4. The contribution of buoyancy is significant due to the low remoulded strength of the

soft clay, and is enhanced by the presence of heave around the pipe. A modification

of Archimedes’ conventional buoyancy expression is required to accommodate heave.

The development of a trench and the consequent lowering of the soil surface adjacent

to the pipe also affects the resistance profile.

5. The component of resistance due to the soil strength reduces by a factor of 7.5 during

cycling, which is greater than the T-bar cyclic sensitivity of 2.4 measured in the same

sample. This increased degradation can be attributed to the entrainment of water

as the pipe repeatedly breaks away from the soil.

These observations shed light on the vertical pipe-soil interaction forces during large-

amplitude cyclic motion of an SCR. The importance of buoyancy forces in heavily re-

moulded soft clay is highlighted, and the possibility of enhanced soil strength degradation

due to the presence of free water at the soil surface is shown. The resulting cyclic vertical

pipe-soil response is idealised in Figure 4.13. This banana-shaped response represents an

4-15


w

V

Total resistance

Trench

Soil resistance

Buoyancy resistance

Figure 4.13: ‘Banana-shaped’ cyclic vertical pipe-soil response

amalgam of the features present in current linear and non-linear models for riser-soil in-

teraction. The increased degradation in soil strength compared to the existing non-linear

model (Bridge et al., 2004) leads to reduced hysteresis, which would reduce the calculated

fatigue damage. The enhanced buoyancy force generates a non-cyclic component of resis-

tance which increases with depth, and can cause the pipe-soil force to remain compressive

even during upwards motion.

It should be noted that the degradation in soil strength quantified in this paper for

a single episode of cycling is not necessarily a permanent effect. Tests not reported in

this paper showed that the strength loss was at least partially recovered after a period of

reconsolidation, and the remoulded strength evident in a subsequent cyclic episode was

different to the remoulded strength found in the initial episode.

4-16


References





Gonzalez, E. C., Mourelle, M. M., Maurico, J., Lima, T. G., and Moreira, C. C. (2005).Steel catenary riser design and analysis for Petrobras Roncador field development. InProc. 37th Offshore Technology Conference, Houston, USA.


Merifield, R. S., White, D. J., and Randolph, M. F. (2008). The ultimate undrainedresistance of partially embedded pipelines. Geotechnique, 58(6):461–470.

Merifield, R. S., White, D. J., and Randolph, M. F. (2009). Effect of surface heave onresponse of partially embedded pipelines on clay. Journal of Geotechnical and Geoenvi-ronmental Engineering, 135(6):819–829.

Nolop, N., Elholm, E., Wang, H., Hoyt, D., Kan, W., Montbarbon, S., and Quintin, H.(2007). Steel catenary risers and offloading system for the Erha field development. InProc. 39th Offshore Technology Conference, Houston, USA.

Phifer, E. H., Kopp, F., Swanson, R. C., Allen, D. W., and Langner, C. G. (1994).Design and installation of Auger steel catenary riser. In Proc. 26th Offshore TechnologyConference, Houston, USA.

Randolph, M. F., Jewell, R. J., Stone, K. J. L., and Brown, T. A. (1991). Establishing anew centrifuge facility. In Proc. International Conference on Centrifuge Modelling —Centrifuge ‘91, pages 2–9, Boulder, Colorado.

Randolph, M. F. and White, D. J. (2008a). Pipeline embedment in deep water: processesand quantitative assessment. In Proc. 40th Offshore Technology Conference, Houston,USA.

Randolph, M. F. and White, D. J. (2008b). Upper-bound yield envelopes for pipelines atshallow embedment in clay. Geotechnique, 58(4):297–301.

Serta, O. B., Mourelle, M. M., Grealish, F. W., Harbert, S. J., and Souza, L. F. A.(1996). Steel catenary riser for the Marlim field FPS P-XVIII. In Proc. 28th OffshoreTechnology Conference, Houston, USA.

4-17




4-18

5An Analysis of Soil Strength Degradation During Episodes of

Cyclic Loading, Illustrated by the T-bar Penetration Test

5.1 Abstract

Pipelines and risers form an essential part of the infrastructure associated with offshore

oil and gas facilities. During installation and operation, these structures are subjected

to repetitive motions which can cause the surrounding seabed soil to be remoulded and

soften. This disturbance leads to significant changes in the operative shear strength,

which must be assessed in design. This paper presents an analytical framework that aims

to quantify the degradation in undrained shear strength as a result of gross disturbance

— in this case through repeated vertical movement of a cylindrical object embedded in

undrained soil. The parameters of the framework were calibrated using data obtained in a

geotechnical centrifuge test. In this test a T-bar penetrometer — which is a cylindrical tool

used to characterise the strength of soft soils — was cycled vertically in soil with strength

characteristics typical of a deep water seabed. Using simple assumptions regarding the

spatial distribution of ‘damage’ resulting from movement of the cylinder, and by linking

this damage to the changing undrained shear strength via a simple degradation model, the

framework is shown to simulate well the behaviour observed in a cyclic T-bar test. This

framework can potentially be extended to the similar near-surface behaviour associated

with seabed pipelines and risers.

5.2 Introduction

Seabed pipelines and catenary risers, which are used to transport oil and gas, undergo

episodes of movement during installation and operation that cause remoulding and soft-

ening of the surrounding seabed soil. In deep water environments, the seabed is typically

soft clay. Seabed pipelines are often designed to buckle laterally to relieve the thermal

loading during operating cycles. During each cycle the crown of the buckle may displace

laterally by several diameters, disturbing and remoulding the seabed soil (Bruton et al.,

2008; Dingle et al., 2008). Similarly, at the touchdown zone of a catenary riser — which

5-1


is essentially a pipeline hanging from a floating structure down to the seabed — the pipe

undergoes many cycles of displacement in response to vessel motion. This movement re-

moulds and softens the surrounding soil (Palmer, 2000; Clukey et al., 2005). Observations

of riser touchdown zones indicate that the pipe may penetrate up to 5 diameters beneath

the original seabed elevation, and undergo lateral movements of more than 10 diameters

(Bridge and Howells, 2007).

In design, it is necessary to undertake a structural analysis of a pipeline or riser to

assess the response within the buckles or the touchdown zone. Prediction of the soil

strength is essential to provide an appropriate idealisation of the soil-structure interaction

forces. Theoretical solutions — such as plasticity-based bearing capacity factors — link the

operative soil strength to the resistance offered to vertical penetration or lateral movement

of a pipeline or riser in contact with the seabed (Aubeny et al., 2005; Randolph and White,

2008). However, due to the severity of the cyclic action, it is important to account for the

changing soil strength during episodes of disturbance.

For the analysis of a catenary riser, current guidance to account for remoulding recom-

mends simply scaling the peak soil resistance during uplift by an experimentally calibrated

cyclic loading factor (Bridge et al., 2004). For pipeline analysis, it has been recognised

that cyclic movement leads to softening of the surrounding soil, and a reduction in the

soil resistance (Dingle et al., 2008), but no methodology for accounting for this behaviour

in a cycle-by-cycle manner has been proposed.

This paper outlines a framework which provides a basis for improved models for cyclic

riser and pipeline movement — and general large-amplitude cyclic disturbance of soft soils.

The aim of this model is to account for progressive remoulding and softening in a more

accurate manner. The cyclic degradation of soil strength in the vicinity of a penetrating

cylindrical object — in this case a T-bar penetrometer rather than a pipeline or riser —

is modelled in a simple fashion. The aim is to allow the progressive loss of soil strength

to be captured for any sequence of movement, with the spatial variation in softening

captured in a manner that avoids the need for a full analysis of the penetration process.

The framework assumes undrained conditions and ignores rate effects. It is shown that

the framework captures well the response observed in a cyclic T-bar penetrometer test

conducted using kaolin clay in a geotechnical centrifuge.

5.3 Model Framework

To predict the operative undrained shear strength experienced by a cylinder during one-

dimensional vertical cycling, the framework illustrated in Figure 5.1 is proposed. The

current depth of the cylinder normalised by the diameter is defined as zm as shown in

Figure 5.2. The vertical location of a point relative to the centre of the cylinder, normalised

by the diameter, is denoted η (Figure 5.1a). A damage influence zone is defined around

the cylinder (Figure 5.1b). As the cylinder advances, ‘damage’ is accumulated in the

surrounding soil within this vertical zone. Damage is used here as a general term for a

5-2

An Analysis of Soil Strength Degradation During Episodes of Cyclic Loading, Illustrated by the T-bar Penetration Test

process that reduces the operative soil strength, and it is common for plastic shear strain to

be used as a measure of damage (Einav and Randolph, 2005). The damage influence zone

represents an idealisation of the full two-dimensional flow process (Martin and Randolph,

2006; Einav and Randolph, 2005; Zhou and Randolph, 2009). For any vertical movement

of the cylinder, increments of damage are progressively accumulated to form a distribution

of damage with depth (Figure 5.1c). By linking damage to degraded shear strength via a

soil strength degradation model, the current undrained shear strength at all depths can

be calculated (Figure 5.1d). At any instant the operative shear strength available to resist

movement of the cylinder depends on a weighted average of local shear strength around

it. Therefore, a strength influence zone is also defined (Figure 5.1e) for this weighting

function, in order to derive the average undrained shear strength at the current depth

(Figure 5.1f). Finally, the mobilisation of this undrained strength takes place over a finite

distance, defined as λ, due to the finite stiffness of soil. An exponential function is used

to capture the pre-failure resistance, with the displacement since the last change in the

direction of motion denoted ∆zm (Figure 5.1g).

The mathematical details of this framework are described in the following sections. Fi-

nally, the applicability of this framework is demonstrated by comparing a simulated cyclic

T-bar penetrometer test with results from a test conducted in a geotechnical centrifuge.

5-3

Geote

chnic

alanaly

sisofoffsh

ore

pip

elin

es

and

steelcate

nary

risers

(a) (b) (c) (d) (e) (f) (g)

Current cylinder

location

Damage influence

zone/function

Current damage

distribution

Current undrained shear

strength distribution

Strength influence

zone/function

Averaged undrained shear strength

at the cylinder mid-depth

Mobilisation of operative

undrained shear strength

Soil strength

degradation

model

su,av =

zm+α∫

zm−α

su(z)ν(z) dzsu,op

su,av

= 1 − e−3

∆zmλ

η

η = −β

η = 0

η = β

η = −α

η = α

µ(z) N(z) su(z) ν(z)

zzzz

µ(zm) = 1/β N(zm) ν(zm) = 1/α

Figure 5.1: Components of analysis framework

5-4


5.4 Cumulative Damage Number Interpretation

The damage accumulated at a given soil horizon — denoted N — increases progressively

as the penetrometer approaches and passes that horizon. The damage scale is based on

N = 1 being accumulated during one penetration and extraction cycle of the penetrometer

(Figure 5.2). Each full passage of the soil element completely through the damage influence

zone causes N to increase by 0.5, with a return event accumulating a damage of unity.

Alternatively, the penetrometer may approach the soil element and then reverse direction,

without the soil element passing fully through the damage influence zone. In this case a

damage less than unity is accumulated.

The detailed distribution of strain rate and damage accumulation around a penetrome-

ter is extremely complex and has been tackled using various models of material behaviour,

including analytical modelling with inviscid fluid flow, rigid plasticity and linear elasticity

(Einav and Randolph, 2005; Klar and Osman, 2008) and numerical analysis with soften-

ing and rate dependent strength (Zhou and Randolph, 2009). The calculated distributions

of strain rate vary between the different types of analysis. A practical simplification is

to model the rate of damage as a one-dimensional function — since only one-dimensional

movement is being considered — and to use a triangular function, µ(z), with limits extend-

ing by a normalised distance β above and below the penetrometer centreline (Figure 5.1b).

The damage influence function is therefore defined as:

µ(z) =1

β

(

1 −|η|

β

)

(5.1)

where η = z − zm is the normalised distance of the T-bar centerline from an element

of soil at depth z. If the soil element lies outside the damage influence zone, µ(z) = 0.

A triangular distribution has been adopted here for simplicity, but any function in the

form of a probability density expression (i.e.zm+∞∫

zm−∞

µ(z) dz = 1) can be adopted without

changing the calculation framework. The same flexibility applies to the strength influence

function, ν(z), which is introduced later.

For continuous movement of the penetrometer, the instantaneous local distribution of

damage due to the current passage can be found by integrating the triangular damage

influence function:

N(z) =

N(zm) + 0.25, if η ≤ −β

N(zm) − 0.25η

β(1 + βµ(z)) , if −β < η < β

N(zm) − 0.25, if η ≥ β

(5.2)

where N(zm) is the value of N at the mid-depth of the T-bar and the bar is moving

in the positive direction (Figure 5.1c). Equation 5.2 provides the shape of the damage

distribution around the T-bar during steady penetration. To generalise this behaviour

5-5


penetration

extraction

Cylinder diameter, D

N = 0 N = 1

N = 0.25

N = 0.75

N = 0.5

Soil surface

Normalised

soil depth,

z = z/D

Normalised cylinder

mid-depth embedment,

zm = zm/D

Figure 5.2: Depth nomenclature and cycle number definition for initial penetration andextraction (after Randolph et al., 2007)

to arbitrary sequences of movement, the accumulation of damage, ∆N(z), due to an

incremental movement of the T-bar, ∆zm, can be described as:

∆N(z) = 0.5µ(z)∆zm (5.3)

5.5 Strength Degradation and Accumulation of Damage

The soil strength is assumed to decay exponentially with accumulated strain from the

initial value, su,initial, to the fully remoulded value, su,rem (Figure 5.3a). This approach is

similar to the model used by Einav and Randolph (2005), but the direct use of plastic

shear strain to assess the level of strain softening is replaced with a scaled parameter that

is referred to as the damage number, N . Rather than defining a nominal value of shear

strain to represent some averaged value of shear strain accumulated within a relevant

zone of soil as the T-bar passes, the accumulated damage at a given depth, z, associated

with a single pass of the T-bar is simply defined as ∆N = 0.5. This definition provides

a convenient scale for the softening behaviour as the current strength, su, decays from

su,initial to su,rem:

su(z)

su,initial(z)= δrem + (1 − δrem) e

−3(N(z)−0.25)N95,rem

(5.4)

where the relative magnitude of the initial and remoulded strengths is denoted by:

δrem =su,rem

su,initial

=1

St,cyc

(5.5)

5-6


(a) (b)

Log damage number, N Log damage number, N

Undra

ined

shea

rst

rengt

h,s u

0.250.25 N95,remN95,rem N95,str

su,remsu,rem

su,initialsu,initial

su,intact

su,intact

su,initial − su,str

(1 − δrem) su,initial δstrsu,initial

(1 − δstr − δrem) su,initial

Figure 5.3: Idealisations of strength degradation with accumulated damage

N95,rem+0.25 is the damage that causes a 95% drop in strength from intact to remoulded

conditions, indicating the brittleness of the response. Both St,cyc and N95,rem are parameters

that can be obtained from cyclic T-bar penetrometer tests. The (N − 0.25) term ensures

that when N = 0.25 (i.e. the average value during the initial penetration), su = su,initial.

The strength degradation model can be refined by introducing two stages of degrada-

tion to additionally capture a highly brittle strength component (Randolph et al., 2007),

which can be attributed to structure or cementation (Figure 5.3b):

su(z)

su,initial(z)= δrem + (1 − δstr − δrem) e

−3(N(z)−0.25)N95,rem

+ δstre

−3(N(z)−0.25)N95,str

(5.6)

where δstr = su,str/su,initial and su,str is the structure or cementation component of the

strength which is 95% destroyed at an accumulated damage of N95,str + 0.25.

su,initial is the apparent undrained shear strength, which is calculated by dividing the

net T-bar resistance, qt,initial, during the initial penetration by a bearing factor, Nkt, that is

usually taken as a theoretical value derived using plasticity theory based on the assumption

that the soil is a rigid plastic Tresca material (Martin and Randolph, 2006). However,

it is recognised that in a soil that softens with shear strain — which is the topic of this

model — the value of strength calculated as su,initial = qt,initial/Nkt is not the ‘intact’ soil

strength, which would be the peak value measured by failure of a single soil element in

a triaxial test, for example. Due to the high shear strains accumulated during the initial

penetration of a T-bar penetrometer, the apparent undrained shear strength, su,initial, can

be below the intact strength, su,intact, if rate effects are neglected (Lehane et al., 2009;

Zhou and Randolph, 2009). This is because at any instant of steady penetration, the high

strains induced by the T-bar cause some soil elements to exist beyond the peak strength

value, and therefore, the operative strength at any instant of steady penetration is lower

5-7


than the peak value.

For brevity, Equations 5.4–5.6 can be rewritten in terms of a structure damage factor,

Ψstr:

Ψstr(z) = 1 − e

−3(N(z)−0.25)N95,str

(5.7)

and a remoulding damage factor, Ψrem:

Ψrem(z) = 1 − e

−3(N(z)−0.25)N95,rem

(5.8)

which allows the two-stage degradation model to be written as:

su(z)

su,initial(z)= 1 − δstrΨstr(z) − (1 − δstr − δrem) Ψrem(z) (5.9)

For a damage number, N , equal to 0.25, the damage factors are equal to zero and the

undrained shear strength equals the initial value. When the damage number reaches N95,str

and N95,rem, the damage factors Ψstr and Ψrem approach the maximum of 1. A negative

damage factor implies an undrained shear strength greater than that apparent during first

penetration. The intact undrained shear strength can be found by substituting N = 0

into Equations 5.7–5.9:

su,intact(z)

su,initial(z)= 1 − δstr

(

1 − e

0.75N95,str

)

− (1 − δstr − δrem)

(

1 − e

0.75N95,rem

)

(5.10)

5.6 Operative Shear Strength Calculation

The shear strength that governs the penetration resistance is determined from the local

distribution of shear strength by a weighted average according to the strength influence

zone. This zone is defined by a triangular function extending by a distance α above and

below the T-bar centerline in the same manner as the damage influence zone:

ν(z) =1

α

(

1 −|η|

α

)

(5.11)

The averaged undrained shear strength, su,av, at the current position of the T-bar is:

su,av =

zm+α∫

zm−α

su(z)ν(z) dz (5.12)

5.7 Mobilisation of Operative Shear Strength

The final component of the framework is a simple rule for the progressive mobilisation of

resistance after a change in the direction of the penetrometer movement. An exponential

5-8


function is assumed, with 95% of the available resistance being mobilised over a normalised

penetrometer movement of λ. This behaviour is captured by defining the operative soil

strength, su,op, as a fraction of the averaged soil strength:

su,op

su,av

= 1 − e−3∆zm

λ (5.13)

where ∆zm is the change in the penetrometer’s mid-depth embedment after a change

in direction (Figure 5.1g).

5.8 Example Application of Framework

5.8.1 Derivation of framework parameters

The analysis framework is illustrated with the results from a cyclic T-bar penetrometer

test conducted in soft, lightly overconsolidated kaolin clay using the geotechnical beam

centrifuge at the University of Western Australia. A full description of the apparatus and

methodology is given by Hodder et al. (2008). The sample was prepared from a slurry

by in-flight consolidation at a centrifuge acceleration of 50 g. The T-bar penetrometer

test was then conducted whilst the centrifuge continued to spin. The test was performed

at a displacement rate of 1 mm/s (at model scale) which ensured undrained conditions.

The test followed the usual pattern of a cyclic T-bar penetration test, with a series of

constant-amplitude cycles being conducted part way through the extraction stage. The

operative soil strength during the test is shown in Figure 5.4a and was calculated from

the experimentally measured unit penetration resistance, qt, using a constant bearing

capacity factor of Nkt = 10.5 (Martin and Randolph, 2006). All dimensions are shown in

prototype scale units — i.e. multiplied from the model scale by the centrifuge acceleration.

Also shown in Figure 5.4a is an undrained shear strength profile calculated based on the

approach described by Wroth (1984):

su/σ′

v0

[su/σ′

v0]nc

= OCRΛ (5.14)

where σ′

v0 is the in situ vertical effective stress, [su/σ′

v0]ncis the normally consolidated

strength ratio, OCR is the overconsolidation ratio and Λ is the plastic volumetric strain

ratio. The values of each parameter are given in Table 5.1.

The resistance measured at the mid-depth of the cycles has been used to derive the

parameters for the analysis framework. These parameters were then used in a simulation of

the entire test, including the initial penetration and extraction stages and the full cycles

of movement, to illustrate how the framework outlined in this paper can be applied to

general cyclic penetration behaviour.

5-9


Operative undrained shear strength, su,op [kPa]

T-b

arin

vert

embed

men

t,z m

+D

/2[m

]

Operative undrained shear strength, su,op [kPa]

T-b

arin

vert

embed

men

t,z m

+D

/2[m

]

Nor

mal

ised

T-b

arin

vert

embed

men

t,(z

m+

D/2

)/D

[-]

Nor

mal

ised

T-b

arin

vert

embed

men

t,(z

m+

D/2

)/D

[-]

(a)

(b)

Experimental data

Simulation

su,op = qt/Nkt

Nkt = 10.5

Strength profile

from Wroth (1984)

-6 -4 -2 0 2 4 6

-6 -4 -2 0 2 4 6

0

2

4

6

8

10

12

14

16

18

0

2

4

6

8

10

12

14

16

18

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Figure 5.4: Cyclic T-bar penetrometer test (a) experimental data (b) comparison of dataand simulation

5-10

An

Analy

sisofSoil

Stre

ngth

Degra

datio

nD

urin

gEpiso

des

ofCyclic

Loadin

g,Illu

strate

dby

the

T-b

ar

Penetra

tion

Test

Table 5.1: Summary of framework parameters

FrameworkComponent

Parameter Dimension Description Value

Geometry D [L] Cylinder diameter 0.25 m

Soil strength[su/σ′

v0]nc

Λ[−][−]

Normally consolidated strength ratioPlastic volumetric strain ratio

0.160.785

Soil sensitivityδstr

a [−]‘Structural’ component of soil strength

0.35normalised by initial strength

δrem [−]Remoulded soil strength normalised by

0.42initial strength (inverse of cyclic sensitivity, St,cyc)

Soil ductilityN95,str

N95,rem

[−][−]

‘Structure’ ductility parameterRemoulding ductility parameter

0.756.5

Influence limitsβα

[−][−]

Damage influence zone extentStrength influence zone extent

11

Mobilisation λ [−] Strength mobilisation distance 1

aImplemented in simulation as δstr = 1 − 1/St,in−out where St,in−out is the sensitivity in the first cycle, i.e. qt,in/qt,out

5-1

1


Figure 5.5 compares the degradation in strength recorded at the middle of each pene-

tration cycle (at a depth of zm = 2.375 m, Figure 5.4a) with the one-stage and two-stage

degradation models. The parameters δrem and N95,rem are fitted to the later cycles. For

the two-stage model, a good fit to the data is achieved if it is assumed that the structure

of the soil is destroyed during the first penetration and extraction of the T-bar, so that:

N95,str = 0.75 (5.15)

and

δstr = 1 −1

St,in−out

(5.16)

where St,in−out is the sensitivity of the soil in the first cycle, calculated as the ratio of the

initial penetration to extraction resistance and equal to 1.54 in this case. This assumption

captures well the observed strength degradation, with the two-stage model reproducing the

initial brittle behaviour, followed by a more gentle reduction in resistance. In contrast, the

optimal fit of the single stage degradation model shows too high a strength in the initial

few cycles, but too low a strength during the later cycles.

Using the two-stage degradation parameters, an intact to initial strength ratio equal

to 1.63 is calculated at N = 0. As shown in Table 5.1, a normally consolidated strength

ratio, [su/σ′

v0]nc, of 0.16 was used in Equation 5.14 to fit the experimentally recorded initial

penetration of the T-bar. If the [su/σ′

v0]ncvalue for the T-bar is multiplied by the intact

to initial strength ratio implied by the two-stage degradation model, an ‘intact’ [su/σ′

v0]nc

value equal to 0.26 is obtained, which lies in the typical range for element tests conducted

on the UWA kaolin clay (Lehane et al., 2009). This observation further supports the

adoption of a two-stage degradation model. The single-stage model predicts an intact

[su/σ′

v0]ncvalue of 0.19 which is lower than measured in laboratory tests.

Based on the derived two-stage degradation parameters, the increase in each damage

factor, Ψstr and Ψrem, with cycles is shown in Figure 5.6. The structure damage factor,

Ψstr, increases rapidly and reaches unity after a single cycle, whilst the remoulding damage

factor, Ψrem, shows a more gradual increase with cycling.

Using the assumptions concerning δstr and N95,str, given by Equations 5.15–5.16, Equa-

tion 5.9 can be rewritten in terms of the two sensitivities measured directly in a cyclic

T-bar test:

su(z)

su,initial(z)= 1 −

(

1 −1

St,in−out

)

Ψstr(z) −

(

1

St,in−out

−1

St,cyc

)

Ψrem(z) (5.17)

The parameters required in the framework and the values adopted in the simulation

are summarised in Table 5.1. The values of α and β were chosen to match the experimental

data, particularly where the T-bar moves up into stronger soil after the cyclic phase. The

four parameters in the two-stage degradation model were all obtained directly from the

cyclic T-bar test: δstr and δrem by relating to St,in−out and St,cyc respectively, N95,str = 0.75

5-12


Damage number, N

Deg

radat

ion

fact

or,s u

,op/s

u,in

itia

l[-]

Damage number, N

Deg

radat

ion

fact

or,s u

,op/s

u,in

itia

l[-]

Cyclic T-bar data

One-stage degradation model

N95,rem = 2.5

δrem = 1/St,cyc = 0.42

δstr = 0

Two-stage degradation model

N95,rem = 6.5

δrem = 1/St,cyc = 0.42

N95,str = 0.75

δstr = 1 − 1/St,in−out = 0.35

Cyclic T-bar data

One-stage degradation model

Two-stage degradation model

(a) (b)

N = 0.25

(initial penetration)

10−2 10−1 100 101 1020 2 4 6 8 100

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Figure 5.5: Degradation model comparison against experimental data

Damage number, N

Dam

age

fact

or,Ψ

Ψrem

Ψstr

N = 0.25 (initial penetration)

0 2 4 6 8 10-2

-1.5

-1

-0.5

0

0.5

1

1.5

Figure 5.6: Damage factor accumulation based on derived parameters

5-13


and N95,rem by inspection of the degradation curve.

5.8.2 Simulation results

Figure 5.4b compares the result of the simulated cyclic T-bar test with the data recorded

in the experiment. It should be noted that the operative undrained shear strength is

always positive. When the T-bar is traveling upwards, su,op calculated in the simulation

is simply plotted as negative for comparison against the experimental data.

The simulation displays close agreement with the experimental data. The soil proper-

ties fitted to the mid-cycle response appear to capture the behaviour throughout the test,

including the transition as the penetrometer emerges from the cyclic zone into soil which

is less disturbed. The mobilisation distance throughout the cyclic phase, and also after

the initial change of direction, appears well fitted by a single value of the mobilisation

parameter, λ = 1.

As the penetrometer initially enters the soil, the operative shear strength in the sim-

ulation is greater than inferred from the experiment. The raised strength very close to

the surface in the simulation arises because the soil does not experience a full sequence of

damage as the T-bar passes it. Until the T-bar is in contact with the soil, no damage can

be accumulated, even if the proximity of the penetrometer puts the surface soil within the

damage influence zone. As a result, the damage number does not increase fully to 0.25

and therefore the operative shear strength for the near surface soil lies between the intact

and initial shear strengths.

The basis for this effect also applies in practice. However, the experimental data does

not show a raised operative strength near the surface because, for simplicity, the operative

shear strength was back calculated using a constant bearing capacity factor of Nkt = 10.5,

which is incorrect for a shallowly embedded cylinder.

The profiles of soil strength and damage after the cyclic T-bar test are shown in

Figure 5.7. The damage factors have reached the maximum values (Ψstr, Ψrem = 1) in

the region where the T-bar was cycled, creating a fully remoulded shear strength profile.

Below the zone disturbed by the T-bar the shear strength remains at the intact value of

su,intact/su,initial ≈ 1.6, as calculated from Equation 5.10.

5-14

An

Analy

sisofSoil

Stre

ngth

Degra

datio

nD

urin

gEpiso

des

ofCyclic

Loadin

g,Illu

strate

dby

the

T-b

ar

Penetra

tion

Test

Damage number, N

Sam

ple

dep

th,z

[m]

Damage factor, Ψ

Sam

ple

dep

th,z

[m]

su/su,initial [-]

Sam

ple

dep

th,z

[m]

su [kPa]

Sam

ple

dep

th,z

[m]

(a) (b) (c) (d)

su,initial

su,rem

su,intact

Ψrem

Ψstr

0 4 8 120 0.5 1 1.5 2-2 -1 0 10 5 10 15 20 250

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Figure 5.7: Profiles of damage number, damage factor and shear strength after cycling

5-1

5


5.9 Conclusions

This paper outlines an analytical framework for calculation of the operative shear strength

experienced by a buried cylinder subjected to general cycles of vertical displacement within

a soil that softens. Using soil parameters obtained directly in a cyclic T-bar test, a

numerical simulation was conducted and was shown to capture the experimental behaviour.

The analysis framework assesses the operative soil strength at any instant by calculat-

ing the accumulated damage caused by previous disturbance. Simple models are used to

assess the accumulation of damage, the resulting change in soil strength and the weighting

of the local soil strength to derive the resistance to penetration. It is shown that the

observed strength degradation during a cyclic T-bar penetrometer test is best captured

by a two-stage exponential function, with a highly brittle component being fully degraded

within a single cycle. This two-stage model also reconciles the different strength ratios

evident during T-bar penetration and in laboratory soil element tests.

In this paper the analysis framework has been applied to a cyclic T-bar penetration

test. The same approach could be used in pipeline and riser applications, where large-

amplitude cyclic movements lead to significant changes in the operative soil strength. In

these cases it would be necessary to include the variation in bearing capacity factor close

to the soil surface, reflecting the different failure mechanism. In the analysis of pipelines

and risers, the operative soil strength is as significant an uncertainty as the appropriate

bearing capacity factor to link strength and resistance, and the framework described in

this paper provides a simple approach to tackle this assessment.

The framework is constructed without reference to the underlying mechanics that

cause strain-softening, which is the case for many other methods that tackle this form

of constitutive behaviour. However, it is noted that if softening occurs along thin shear

bands, and has a length scale, then the present behaviour may not scale directly to larger

boundary value problems without the model parameters potentially varying. Since soil

can soften whilst deforming as a continuum there may not be a need to introduce a length

scale to faithfully capture the response of both small T-bars and larger pipes or risers, but

this question remains to be resolved.

5-16


References


Bridge, C. D. and Howells, H. A. (2007). Observations and modeling of steel catenaryriser trenches. In Proc. 17th International Offshore and Polar Engineering Conference,pages 803–813, Lisbon, Portugal.


Bruton, D. A. S., White, D. J., Carr, M. C., and Cheuk, C. Y. (2008). Pipe-soil interac-tion during lateral buckling and pipeline walking: the SAFEBUCK JIP. In Proc. 40thOffshore Technology Conference, Houston, USA.

Clukey, E. C., Haustermans, L., and Dyvik, R. (2005). Model tests to simulate riser-soilinteraction in touchdown point region. In Proc. International Symposium on Frontiersin Offshore Geotechnics, pages 651–658, Perth, Australia.

Dingle, H. R. C., White, D. J., and Gaudin, C. (2008). Mechanisms of pipe embedmentand lateral breakout on soft clay. Canadian Geotechnical Journal, 45(5):636–652.

Einav, I. and Randolph, M. F. (2005). Combining upper bound and strain path methodsfor evaluating penetrometer resistance. International Journal of Numerical Methods inEngineering, 63:1991–2016.

Hodder, M. S., White, D. J., and Cassidy, M. J. (2008). Centrifuge modelling of riser-soilstiffness degradation in the touchdown zone of a steel catenary riser. In Proc. Inter-national Conference on Offshore Mechanics and Arctic Engineering, Estoril, Portugal.[presented as Chapter 4 of this thesis].

Klar, A. and Osman, A. S. (2008). Continuous velocity fields for the T-bar problem. In-ternational Journal for Numerical and Analytical Methods in Geomechanics, 32(8):949–963.

Lehane, B. M., O’Loughlin, C. D., Gaudin, C., and Randolph, M. F. (2009). Rate effectson penetrometer resistance in kaolin. Geotechnique, 59(1):41–52.


Palmer, A. C. (2000). Catenary riser interaction with the seabed at the touchdown point.In Proc. Deepwater Pipeline and Riser Technology Conference, Houston, USA.

Randolph, M. F., Low, H. E., and Zhou, H. (2007). In situ testing for design of pipeline andanchoring systems. In Proc. 6th International Conference on Offshore Site Investigationand Geotechnics, pages 251–262, London, UK. Society for Underwater Technology.

Randolph, M. F. and White, D. J. (2008). Upper-bound yield envelopes for pipelines atshallow embedment in clay. Geotechnique, 58(4):297–301.

Wroth, C. P. (1984). Interpretation of in situ soil tests. Geotechnique, 34(4):449–489.

Zhou, H. and Randolph, M. F. (2009). Resistance of full-flow penetrometers in rate-dependent and strain-softening clay. Geotechnique, 59(2):79–86.

5-17

6Effect of Remoulding and Reconsolidation on the Touchdown

Stiffness of a Steel Catenary Riser: Observations from

Centrifuge Modelling

6.1 Abstract

Steel catenary risers (SCRs) can be economical to construct and install compared to

conventional vertical risers. However, accurate evaluation of the fatigue life of an SCR

remains a major challenge due to uncertainty surrounding the interaction forces where the

riser ‘touches down’ on the seabed. Fatigue life predictions for the pipe in the vicinity

of the touchdown zone (TDZ) are heavily dependant on the assumed vertical stiffness

between the riser and the seabed. For accurate fatigue life predictions to be made, a

reliable evaluation of the seabed stiffness is required.

This paper describes a series of model tests that were conducted within the University

of Western Australia’s geotechnical beam centrifuge. These tests aimed to assess typical

vertical stiffness values during large and small amplitude cycles of riser motion, and the

influence of remoulding and reconsolidation effects. The tests used a short section of riser

pipe which simulated part of an SCR. The soil comprised soft kaolin clay, consolidated

to an undrained strength that increased approximately linearly with depth, mimicking

typical field conditions.

A wide range of riser motions were simulated, encompassing sequences of both large

and small amplitude movements, under load and displacement control, with intervening

pause periods to investigate the effects of reconsolidation. The associated changes in

vertical pipe-soil resistance are reported, and converted into appropriate values of secant

stiffness which would correspond to a linear idealisation of the vertical pipe-soil response.

It is shown that the vertical pipe-soil stiffness rapidly reduces during an episode of large-

amplitude cyclic motion, with a steady cyclic stiffness being reached within ≈ 10 cycles

as the soil remoulds. The influence of cyclic load amplitude is identified, and is shown to

match a hyperbolic model. Episodes of reconsolidation are found to create a significant

increase in vertical pipe-soil stiffness. This recovery can lead to a pipe-soil stiffness that

6-1


exceeds the initial intact stiffness (prior to remoulding). The implications for design are

summarised.

The riser pipe test results are supported by data from a site investigation of the

centrifuge soil sample using a miniature T-bar penetrometer. Cyclic T-bar tests were used

to assess the strength and cyclic sensitivity of the soil, and the tendency for a recovery of

undrained strength after periods of reconsolidation. The trends of changing soil strength

from these T-bar tests match the patterns of changing pipe-soil stiffness from the riser

tests.

6.2 Introduction

As fossil fuel reserves in shallow water continue to be depleted and offshore technology

advances, the development of fields located in deep water is increasingly common. Typ-

ically, a deep water offshore development consists of a floating vessel or platform with a

mooring system, and risers that transport the hydrocarbon product between the seabed

and the platform. Steel catenary risers (SCRs) can be a more cost effective option than

vertical or flexible risers in deep water and consist of a 200-500 mm diameter steel pipe,

suspended from the platform.

Storm loading on an offshore vessel can cause large amplitude motions of the SCR

at the TDZ. While these events impose large strains on the riser pipe and cause gross

deformations of the underlying seabed material, they occur relatively infrequently. In

certain locations, such as the Gulf of Mexico, storm seasons are generally an annual event.

During a storm the riser will be subjected to large amplitude cycling, after which time

the loading regime will return to the regular day-to-day, small motions and will generally

remain so for the remainder of the year. The period of inactivity following the severe

cycling allows the pore pressure in the seabed soil in the vicinity of the pipeline to return

to hydrostatic. In normally or lightly overconsolidated soils, which are typical in deep

water, dissipation of excess pore pressure results in a reduction in moisture content and

an increase in undrained shear strength.

The fatigue life of an SCR can be highly dependent on the dynamic stiffness of the

pipe-soil response where the SCR touches down on the seabed and the shape of the SCR,

which is influenced by any trench that forms within the touchdown zone. These two

separate considerations — the stiffness of the response to dynamic motion and the static

deformed shape — must be assessed during design. In an analysis, the vertical pipe-soil

interaction at the touchdown zone is commonly idealised as a bed of linear springs with

stiffness k (with units of F/L2). The change in vertical pipe-soil load transfer, ∆V , per

unit length of pipe can then be related to the change in the pipe embedment, ∆w (or vice

versa), as:

∆V = k∆w (6.1)

6-2

Effect of Remoulding and Reconsolidation on the Touchdown Stiffness of a Steel Catenary Riser: Observations from


Pipe diameter = D

w = w/D

qs,initialD

Vertical load per

unit length of pipe,

V [F/L]

Reloading

Initial

penetrationLinear idealisationsof unload-reload

behaviour

Unloading

Pipe invert

embedment, w [L]slope k = Ksecqs,initial

Ksec ∝ 1/∆w

Figure 6.1: Linear idealisation of vertical pipe-soil response

The linear spring stiffness, k, is related to the plastic penetration resistance of the intact

seabed, which in undrained conditions is given by the bearing capacity, qs,initial = Ncsu,initial

(Figure 6.1):

k = Ksecqs,initial = KsecNcsu,initial (6.2)

In practice, both Nc and su,initial are parameters that can be obtained in a conventional

manner. Various formulations of Nc — the bearing capacity factor applicable to undrained

loading — exist in the literature (as examples see Aubeny et al., 2005; Randolph and

White, 2008a,b). The initial undrained shear strength, su,initial, refers to the value at the

depth of the pipe invert — which is usually assessed from in situ penetration tests. The

initial strength does not account for any changes in this value over the operating life of the

SCR. It is common for the initial seabed strength to be used as a reference condition, and

Ksec can be modified to account for any changes in stiffness that arise from remoulding or

reconsolidation of the seabed soil.

The dimensionless parameter Ksec is often referred to as the ‘secant stiffness ratio’ or

‘normalised secant stiffness’. The change in normalised embedment, ∆w/D, associated

with unloading from the ultimate penetration resistance, qs,initial, to zero load is equal

to 1/Ksec. The term Ksecw/D represents the ratio of stiffness, k, of the unload-reload

response at a depth of w/D to the secant stiffness during plastic penetration to that same

depth. Therefore, for a constant value of Ksec, the ratio between the ‘elastic’ unload-reload

stiffness and the ‘plastic’ penetration stiffness increases with embedment.

It has been shown that Ksec varies with the magnitude of cyclic displacement, ∆w, due

6-3


to the non-linearity of the pipe-soil response (Bridge et al., 2004; Aubeny and Biscontin,

2008; Clukey et al., 2008). In practice, the value of Ksec in a fatigue analysis is typically

chosen based on an initial approximation of anticipated vertical riser displacements at

the TDZ. An iterative process is required to achieve agreement between the calculated

displacements and the displacement used in selecting Ksec. The non-linear response means

that the secant stiffness for small amplitude day-to-day movements of the SCR is higher

than for large amplitude motions during storm events.

The stiffness and strength of the seabed soil at the TDZ varies during the life of an

SCR due to remoulding, water entrainment and reconsolidation. Storm events lead to

large riser movements that cause softening due to remoulding, which is exacerbated by

water entrainment. The seabed soils found in deep water are typically very soft, normally

to lightly overconsolidated clays. In these fine grained soils, riser movements induce an

undrained response in the seabed soil. In normally or lightly overconsolidated material,

undrained loading generates positive excess pore water pressures in the soil near the riser

pipe. During reconsolidation, dissipation of positive excess pore pressure can lead to a

decrease in moisture content, causing the strength and stiffness to recover. This recovery

can potentially cause the strength to rise above the initial intact value.

This paper focuses on the evaluation of vertical seabed stiffness, quantified by the

parameter Ksec, using experimental data from centrifuge model tests of a short pipe section,

oscillated close to the surface of a soft clay seabed. The aim is to identify the variation of

seabed stiffness with cycle amplitude, remoulding and reconsolidation. The study includes

results from three tests in which the pipe was subjected to displacement-controlled cycles

(see Table 6.2) and two tests in which load-controlled cycles were imposed (see Table 6.3).

The displacement controlled tests were conducted to investigate the response during large

amplitude cyclic motions that might occur during a severe storm loading event. The cyclic

movement was imposed until a steady state response was observed, then the pipe motions

were stopped and the surrounding soil was permitted to reconsolidate. A total of three

episodes of cycling, with intervening reconsolidation periods between each episode, were

conducted. The load controlled tests involved smaller pipe movements and were conducted

to investigate the response during small amplitude, day-to-day oscillations.

6.3 Experimental Apparatus

The experiments described here were conducted using the University of Western Aus-

tralia’s geotechnical beam centrifuge (Figure 6.2) at an acceleration of 50 g. A complete

description of the centrifuge as commissioned in 1989 is provided by Randolph et al. (1991).

It has a swinging platform radius of 1.8 m with a nominal working radius of 1.55 m, and

has a rated capacity of 40 g-tonnes (which equates to a maximum payload of 200 kg at an

acceleration of 200 g).

A geotechnical centrifuge is required to accurately model the behaviour of geotechnical

processes at small scale. The strength and stiffness of soil is governed by the effective

6-4



Figure 6.2: UWA geotechnical beam centrifuge

stress, so small scale models conducted at unit gravity do not correctly mimic full scale

behaviour. If a small scale model is accelerated within a centrifuge, the self-weight of the

soil is enhanced by the ratio of the centrifuge acceleration to Earth’s gravity. This ratio is

the scaling factor required to convert dimensions in a centrifuge model to the dimensions

of the corresponding field scale situation. In this paper, all results are presented in field

scale units, unless stated otherwise. The scaling factors relevant to this paper are shown

in Table 6.1, where N is equal to the ratio of the centrifuge acceleration to Earth’s gravity

and is equal to 50.

The model pipe section was 20 mm in diameter and 122.5 mm in length, which corre-

sponds to a diameter of 1 m and a length of 6.125 m at prototype scale (Figure 6.3). The

ratio of pipe length to diameter was sufficiently high that end effects could be neglected.

The pipe segment was attached to a sensitive load cell to record vertical load. The loading

Table 6.1: Scaling factors for centrifuge modelling

Parameter Model-Prototype Ratio

Gravity NStress 1Strain 1Length 1/NForce 1/N2

Time (consolidation) 1/N2

6-5


arm was attached to an actuator which was used to provide load or displacement control

in the vertical direction. All measured vertical loads were adjusted to account for the

changing effective weight of the model pipe and the loading arm with the radial position

within the centrifuge.

6.4 Sample Preparation and Site Characterisation

The model seabed used in these experiments consisted of kaolin clay, consolidated from

a slurry within the centrifuge. The mechanical properties of kaolin are well documented

and kaolin has been extensively used in geotechnical modelling at UWA and elsewhere.

To prepare the sample, dry kaolin powder was mixed with water to produce a slurry

with a moisture content of approximately twice the liquid limit. The slurry was mixed in

a barrel mixer for six hours with a vacuum applied for the final two hours to de-air the

slurry. The slurry was then carefully transferred from the mixer to the strongbox, which

had a 15 mm thick sand drainage layer in the base. The sample was then spun at an

acceleration of 50 g for four days, after which time primary consolidation was complete.

The centrifuge was then stopped and approximately 45 mm of clay was scraped from the

surface of the sample to provide a strength intercept at the mudline. Before testing, the

sample was spun at 50 g for one day to achieve pore pressure equilibrium. The final sample

depth was ≈ 130 mm.

A T-bar penetrometer (Stewart and Randolph, 1991) with a diameter of 5 mm and a

length of 50 mm (Figure 6.4) was used to determine the profiles of intact and remoulded

shear strength. The T-bar was initially penetrated to a depth of 80 mm (at model scale)

before being cycled between depths of 35 and 60 mm. The undrained shear strength, su,

was back-calculated from the net penetration resistance, q, following the usual approach:

su =q

Nkt

(6.3)

A bearing capacity factor of Nkt = 10.5 was used, which is applicable to a deeply buried

cylinder (Martin and Randolph, 2006). Figure 6.5 shows the back calculated undrained

shear strength profile. A simple linear fit with a mudline intercept of sum = 1 kPa and

a gradient of ρ = 1.2 kPa/m provides a good fit to the initial penetration resistance. A

cyclic phase was included in the T-bar test to provide an indication of the reduction in soil

strength with remoulding, which is commonly referred to as the sensitivity. The sensitivity

parameters for the soil were calculated as St,in−out = 1.5 and St,cyc = 2.4, where St,in−out is

the ratio of the initial penetration to initial extraction resistance and St,cyc is the ratio of

the initial to the fully remoulded resistance.

6-6



Instrumentcables

20 mmdiameter

122.5 mm

Model riserpipe section

Vertical

load cell

Figure 6.3: Model riser pipe section

Load cell

5 mm diameter

50 mm

Figure 6.4: Miniature T-bar penetrometer

6-7



Sam

ple

dep

th,z

[m]

Nor

mal

ised

T-b

arin

vert

embed

men

t,w

/D[-]

su = q/Nkt

Nkt = 10.5

su = 1 + 1.2z kPa

(z in metres)

-4 -2 0 2 4 60

2

4

6

8

10

12

14

16

0

0.5

1

1.5

2

2.5

3

3.5

4

Figure 6.5: Undrained shear strength profile of model seabed

6.5 Test Parameters

Three displacement-controlled tests were conducted, involving different patterns of vertical

displacement, as shown schematically with Table 6.2. The three different patterns allowed

the effect of separation of the pipe from the seabed during cycles to be explored (since

Test 3 did not involve separation), and also provided results for two different depths of

penetration — w/D = 0.5 and 1.0. Each test involved three episodes, each comprising

20 cycles of motion, with approximately one year of consolidation permitted between

each episode. Two load-controlled tests involving continuous cycling were also conducted

(Table 6.3). These tests initially involved compressive cycles, but near the end of the

tests the minimum load was progressively reduced, encouraging the pipe to pull from the

seabed.

In the displacement-controlled tests the pipe was driven at a velocity of 1 mm/s (at

model scale). In the load-controlled tests the displacement rate was 0.25 mm/s, and was

reduced to avoid the load limits being exceeded as a result of the very high stiffness

encountered in the later stages of the tests.

6.6 Interpretation of Results

The tests provided measurements of the vertical load per unit length of pipe, V , and

the associated pipe embedment below the original mudline, w. In order for the experi-

mental data to be analysed in the context of a linear idealisation of the vertical response

6-8



Table 6.2: Displacement-controlled test information

TEST NUMBER

1 2 3

CO

NT

RO

L

INP

UT

Pipe invert embedmentat cycle limits, w/D [-]

Maximum 0.5 1 1

Minimum -1 -1 0.5

Number of cycles per episode 20 20 20

Approximate reconsolidation period1 1 1

between cyclic episodes [years]

ASSU

MED

AN

ALY

SIS

PA

RA

MET

ER

S

BOUYANCY

Trench depthnormalised by pipediameter, t/D [-]

Episode 1 0.175 0.175 0

Episode 2 0.275 0.275 0

Episode 3 0.325 0.375 0

fb,initial 1.33 1.18 1.13

STIFFNESS

FORMULATION

V0/Vu(w0),Vu−suc/Vu

Episode 1 0.15 0.17 0.2

Episode 3 0.27 0.37 0.3

Kmax

Episode 1200 200 200

Episode 3

FIGURES6.66.76.12

6.86.12

6.96.12

Table 6.3: Load-controlled test information

TEST NUMBER

4 5

CO

NT

RO

L

INP

UT

Load cycle limits,qt [kPa]

Maximum 11.25 18.8

Initial minimum 2.25 0

Final minimum -8.25 -35.25

Approximate testlength

Cycles 7250 4500

Duration (for consolidation) [years] 1.15 2

FIGURES 6.13 6.14

6-9


(Equations 6.1–6.2, Figure 6.1), values of the unloading secant stiffness ratio, Ksec, were

calculated within each cycle. However, it is first necessary to make a distinction between

the resistance that arises from the soil strength and from the soil buoyancy.

The total unit vertical resistance during penetration of the pipe, qt = V/D, arises from

the soil buoyancy, qb = Vb/D, and the resistance due to the soil strength, qs.

V

D= qt = qb + qs =

Vb

D+

Vs

D(6.4)

During the first penetration of the pipe into the seabed, the soil resistance is related

to the initial (or in situ) shear strength, and is denoted qs,initial.

To express the unload-reload stiffness in a dimensionless form, it is necessary to nor-

malise the change in load by a penetration resistance, which can be either the total pen-

etration resistance, qt, or the resistance arising from the soil strength, qs. The change in

load can also include or neglect the influence of buoyancy.

In this paper, the buoyancy contribution is first eliminated from the response, and the

resistance arising from the soil strength is used to assess both the penetration resistance

and the changing load within cycles. This approach is likely to provide more consistency

across different conditions, since the unload-reload behaviour arises from the stress-strain

response of the soil, as does qs,initial. In contrast, the soil buoyancy is linked to the unit

weight and does not unload or reload, but always acts upwards, independent of the pipe

movement. This approach also follows the usual convention for the linear spring stiffness, k,

to be calculated from the initial undrained shear strength, su,initial, as given in Equation 6.2.

The normalised secant stiffness is therefore derived from the experimental data as:

Ksec =∆Vs

∆wqs,initial

(6.5)

where ∆Vs and ∆w are the change in the vertical load due to soil strength and the

change in the pipe invert embedment since the change in the direction of the pipe section

at the start of the cycle. qs,initial is the soil strength component of the bearing resistance

at the depth where the pipe changed direction using the initial undrained shear strength

profile.

6.6.1 Buoyancy adjustment

The total pipe-soil resistance, which is measured during the experiments, qt = V/D, must

be adjusted to account for the soil buoyancy, in order to assess qs, which is the resistance

due to the strength of the soil. In soil with very low operative shear strength, the soil

buoyancy can represent a significant proportion of the penetration resistance (Hodder

et al., 2008). The buoyancy component of resistance, qb, can be expressed as:

Vb

D= qb = fbAsγ

′/D (6.6)

6-10



Asγ′/D is the soil buoyancy based on Archimedes’ principle, where D is the pipe

diameter, γ′ is the effective unit weight of the soil and As is the submerged cross-sectional

area of the pipe which can be expressed in terms of the normalised pipe invert embedment,

w = w/D:

As

D2=

1

4

[

sin−1(

√

4w (1 − w))

− 2 (1 − 2w)√

w (1 − w)]

, if 0 ≤ w ≤ 0.5

1

4

(

π −[

sin−1(

√

4w (1 − w))

− 2 (2w − 1)√

w (1 − w)])

, if 0.5 < w < 1

π

4, if w ≥ 1

(6.7)

Included in Equation 6.6 is a heave enhancement term, fb, which accounts for the

increased buoyancy experienced by a penetrating object due to the effect of surface heave

(Randolph and White, 2008a; Merifield et al., 2009). Typical values of fb range from

approximately 1.5 for shallow pipe penetrations (Merifield et al., 2009) down to 1 for deep

behaviour, where the penetration does not cause additional surface heave and so buoyancy

arises purely from Archimedes’ principle.

If the pipe is embedded in a small trench, of normalised depth t = t/D, the soil

displaced during penetration is heaved at the soil surface, which is now at a greater

elevation relative to the base of the trench. A simple approximation for the value of fb

which captures the buoyancy during re-penetration into a small trench can be written as

(Hodder et al., 2008):

fb,t = 1 +(fb,initial − 1) w + 1.4t

w − t(6.8)

where fb,initial and fb,t are the heave enhancement terms for the initial penetration from

the surface and penetrations into the trench respectively.

Using Equations 6.6–6.8 and the parameters in Table 6.2, Figure 6.6 shows the response

from Test 1 before and after buoyancy adjustment. Before adjustment (Figure 6.6a), the

remoulded response shows a clear bias towards compressive bearing resistance, with the

soil resistance acting upwards on the pipe even after extraction by a significant distance.

This indicates that the buoyancy component of the total resistance (which acts upwards

on the pipe) is significant relative to the soil shear strength component (which acts to

oppose the pipe motion). This feature is particularly relevant for riser-soil interaction in

soft clay, due to the low operative soil shear strength caused by remoulding and water

entrainment. A more symmetrical remoulded response is observed after the buoyancy

component is subtracted from the measured resistance (Figure 6.6b).

6-11


Total bearing resistance, qt [kPa]

Pip

ein

vert

embed

men

t,w

/D[-]

Resistance component from soil strength, qs [kPa]

Pip

ein

vert

embed

men

t,w

/D[-]

Episode 1

Episode 2

Episode 3

Episode 1

Episode 2

Episode 3

(a) (b)

-5 0 5 10 15-5 0 5 10 150

0.1

0.2

0.3

0.4

0.5

0

0.1

0.2

0.3

0.4

0.5

Figure 6.6: Test 1 response (a) before and (b) after buoyancy adjustment

6-12



6.6.2 Displacement controlled tests

Throughout its lifetime, an SCR will be subjected to large amplitude cycles caused by

severe storm events, which can induce gross deformations of the underlying seabed. Tests

where the pipe segment was cycled between fixed displacement limits were conducted to

investigate the pipe-soil response when subjected to large amplitude oscillations and the

behaviour after periods of reconsolidation. Three tests each involving three episodes of

cycling with reconsolidation periods between the episodes were performed. Each episode

of cycling comprised 20 cycles of penetration and extraction, which was sufficient to fully

remould the soil, leading to a steady pattern of cyclic resistance. The intervening recon-

solidation periods were approximately one year at prototype scale (Table 6.2).

The results from Tests 1, 2 and 3 are presented in Figure 6.7, Figure 6.8 and Figure 6.9

respectively. Plot (a) of the figures shows the variation in soil resistance with vertical

embedment. A steady remoulded response is observed within 10 cycles. In the tests where

the pipe segment was lifted clear of the mudline (Tests 1 and 2), the onset of resistance

during penetration was encountered at progressively lower elevations after each period of

reconsolidation. This is due to the settlement of the soil surface during each reconsolidation

period, reflecting the expulsion of pore water.

In plot (b) of Figures 6.7–6.9, the variation in unloading secant stiffness ratio, Ksec,

during cycling is shown. In these plots, Ksec was calculated at a normalised pipe uplift of

∆w/D = 0.025. Ksec values of 51, 48 and 47 were observed in Tests 1, 2 and 3 respectively

during the first unloading stage, which are similar to the values reported in previous studies

at the same uplift displacement (∆w/D = 0.025) (Bridge et al., 2004; Aubeny et al., 2008;

Clukey et al., 2008). The general reduction in soil resistance with increasing cycle number

evident in plot (a) leads to a degradation of Ksec. After ≈ 10 cycles, the stiffness stabilises.

This steady cyclic stiffness, denoted Ksec,cyc, was in the range ≈ 10–20, increasing with

episode number.

The degradation in Ksec during the first episode of cycling can be quantified by calcu-

lating the ratios of the initial Ksec to Ksec,cyc (observed after ≈ 10 cycles), with ratios of

4.3, 3.4 and 2.9 obtained for Tests 1, 2 and 3. After each period of reconsolidation, the

response displayed a distinct increase in Ksec,cyc. For Tests 1, 2 and 3, the ratios of Ksec,cyc

in cyclic episode 3 to that in episode 1 were calculated as 1.55, 1.77 and 1.32.

In practice, choice of the linear spring stiffness, k, depends on Ksec. These results show

that within a given episode of cycling, beyond the first few cycles of motion, the stiffness

of the response stabilises at a value which is related to remoulded conditions. It is this

steady behaviour which is relevant to a fatigue analysis, and not the stiffer initial response.

Focussing on this stable behaviour, the values of the Ksec,cyc in episodes 1, 2 and 3 were

calculated at normalised pipe uplifts ranging between 0.005 and 0.5 as shown in plot (c)

of Figures 6.7–6.9.

6-13


∆w/D = 0.025

Ksec,cyc,1 = 11.7

Ksec,cyc,2 = 16.1,Ksec,cyc,2

Ksec,cyc,1

= 1.38

Ksec,cyc,3 = 18,Ksec,cyc,3

Ksec,cyc,1

= 1.55

Resistance component from soil strength,qs [kPa]

Pip

ein

vert

embed

men

t,w

/D[-]

Change in pipe invert embedment,∆w/D [-]

Ste

ady

unlo

adin

gse

cant

stiff

nes

sra

tio,

Ksec,cyc=

∆V

/∆w

q s,in

itia

l[-]

Cycle

Unlo

adin

gse

cant

stiff

nes

sra

tio,

Ksec=

∆V

/∆w

q s,in

itia

l[-]


Ksec,cyc,n/K

sec,cyc,1

[-]

Episode 1

Episode 2

Episode 3

Episode 1

Episode 2

Episode 3

Episode 1

Episode 2

Episode 3

Episode 2

Episode 3

(a) (b)

(c) (d)

10−3 10−2 10−1 100

0 10 20 30 40 50 60

10−3 10−2 10−1 100

-5 0 5 10

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0

10

20

30

40

50

60

0

10

20

30

40

50

60

70

0

0.1

0.2

0.3

0.4

0.5

Figure 6.7: Test 1 (a) vertical response, (b) unloading stiffness ratio variation with cycling,(c) steady unloading stiffness ratio variation with uplift and (d) change insteady unloading stiffness ratio relative to first cyclic episode

6-14



∆w/D = 0.025

Ksec,cyc,1 = 14.3


Ksec,cyc,1

= 1.45


Ksec,cyc,1

= 1.77


Pip

ein

vert

embed

men

t,w

/D[-]


Ste

ady

unlo

adin

gse

cant

stiff

nes

sra

tio,

Ksec,cyc=

∆V

/∆w

q s,in

itia

l[-]

Cycle

Unlo

adin

gse

cant

stiff

nes

sra

tio,

Ksec=

∆V

/∆w

q s,in

itia

l[-]


Ksec,cyc,n/K

sec,cyc,1

[-]

Episode 1

Episode 2

Episode 3

Episode 1

Episode 2

Episode 3

Episode 1

Episode 2

Episode 3

Episode 2

Episode 3

(a) (b)

(c) (d)

10−3 10−2 10−1 100

0 10 20 30 40 50 60

10−3 10−2 10−1 100

-15 -10 -5 0 5 10 15

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0

10

20

30

40

50

60

0

10

20

30

40

50

60

70

80

90

0

0.2

0.4

0.6

0.8

1


6-15


∆w/D = 0.025

Ksec,cyc,1 = 16.6


Ksec,cyc,1

= 1.17


Ksec,cyc,1

= 1.32


Pip

ein

vert

embed

men

t,w

/D[-]


Ste

ady

unlo

adin

gse

cant

stiff

nes

sra

tio,

Ksec,cyc=

∆V

/∆w

q s,in

itia

l[-]

Cycle

Unlo

adin

gse

cant

stiff

nes

sra

tio,

Ksec=

∆V

/∆w

q s,in

itia

l[-]


Ksec,cyc,n/K

sec,cyc,1

[-]

Episode 1

Episode 2

Episode 3

Episode 1

Episode 2

Episode 3

Episode 1

Episode 2

Episode 3

Episode 2

Episode 3

(a) (b)

(c) (d)

10−3 10−2 10−1 100

0 10 20 30 40 50 60

10−3 10−2 10−1 100

-10 -5 0 5 10 15

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0

10

20

30

40

50

60

0

10

20

30

40

50

60

70

0

0.2

0.4

0.6

0.8

1


6-16



6.6.3 Comparison with hyperbolic model

The secant stiffness through the unloading and reloading response can also be assessed

using a hyperbolic formulation following the approaches described by Bridge et al. (2004),

Aubeny and Biscontin (2008) and Randolph and Quiggin (2009). The change in vertical

load through unloading, ∆V , can be calculated as (Randolph and Quiggin, 2009):

∆V = HUL(w) (V0 − Vu−suc(w)) (6.9)

where

HUL(w) =∆wKmax

AUL(w) + ∆wKmax

(6.10)

and

AUL(w) =V0 − Vu−suc(w)

Vu(w0)(6.11)

where V0 is the vertical load at the point just prior to uplift, Vu(w0) is the ultimate

penetration capacity at the starting depth of the current unload cycle (denoted w0) and

Vu−suc is the ultimate suction capacity, which is a function of the current embedment, w.

The formulation is defined by three parameters:

1. Kmax is the value of Ksec as the normalised change in pipe embedment, ∆w, ap-

proaches zero (Figure 6.10a).

2. The ratio V0/Vu is the load mobilised at the point of unloading at the start of the

current cycle, expressed as a proportion of the resistance mobilised during the initial

penetration at the current depth (Figure 6.10b).

3. The ratio Vu−suc/Vu is the maximum load that can be mobilised in tension at the

current depth divided by the corresponding load in compression (Figure 6.10b).

In this analysis, all loads are calculated based on the soil resistance, Vs, rather than

the total resistance, Vt, by including an adjustment for buoyancy. As noted previously,

this is a more consistent approach for assessing the hysteretic unload-reload behaviour,

since this arises from the soil resistance rather than the buoyancy. The same approach is

adopted by Randolph and Quiggin (2009).

For small movements (such that the changes in Vu and Vu−suc with w can be neglected),

the hyperbolic model can be reduced to the following expression for Ksec:

Ksec =Kmax

1 + ∆wKmax

(

Vu

V0 − Vu−suc

) (6.12)

Values of V0/Vu at the depth of unloading, w0, as detailed in Table 6.2 were used to fit

lower and upper bounds to the experimental data. A value of Kmax = 200 was adopted.

6-17


(a)

(b)

V

V

w

w

Vu(w0)

V0

w0

w0

∆wKsecVu(w0)/D

KsecVu(w0)/D

Vu(w) = qs,initialD

KmaxVu(w0)/D

Vu−Vu−suc−Vu

Figure 6.10: Features of hyperbolic secant stiffness formulation

6-18



The model has been applied on the basis that Vu remains tied to the in situ strength

profile, so that V0/Vu is equal to the reduction in resistance at the lowest point of the

displacement cycles relative to the initial penetration. Also, Vu−suc/Vu is assumed to equal

V0/Vu since buoyancy effects have been removed from the data and the remaining soil

resistance can then be assumed equal for both penetration and extraction.

The hyperbolic model is also shown on Figures 6.7–6.9 (the solid lines in plot (c))

in terms of Ksec,cyc calculated via Equation 6.5, but with the change in vertical load,

∆V , derived from Equations 6.9–6.11. This hyperbolic formulation, applied using the

approach described, provides good agreement with the experimental data and provides a

simple analytical format to capture the non-linearity of the response.

6.6.4 Effect of reconsolidation periods on response

Plot (d) in Figures 6.7–6.9 shows how the ratio of Ksec,cyc in episodes 2 and 3 to that

calculated in episode 1 varies with the normalised uplift displacement. A relatively uniform

increase in Ksec,cyc is evident in episodes 2 and 3 relative to episode 1. The increase in soil

stiffness due to an episode of reconsolidation appears not to alter significantly the form of

the uplift response. Instead, the stiffness at any displacement rose by 20–40% per episode

in Tests 1–2, in which the pipe broke away from the seabed within each cycle. A smaller

increase in stiffness of ≈ 10% per episode was observed during Test 3, in which the pipe

remained within the soil throughout the cycles.

6.6.5 Comparison to T-bar site investigation

To allow the cyclic riser results to be viewed in the context of site investigation parameters,

a special type of T-bar test was conducted to quantify the drop in operative soil strength

due to remoulding and the potential for recovery with reconsolidation. The model T-bar

shown in Figure 6.4 was used. Three episodes of 20 penetration and extraction cycles

with reconsolidation periods of 1 year (at prototype scale) were performed, matching the

sequence that was carried out in the displacement controlled cyclic pipe tests. The results

from the T-bar test are shown in Figure 6.11.

During the first episode of cycling, the remoulded resistance dropped to 40% of the

initial value. This reduction can be compared to the drop in secant stiffness observed in

the cyclic riser tests during the first episode. Ratios of Ksec,cyc to initial Ksec equal to 0.23,

0.29 and 0.35 were calculated for Tests 1, 2 and 3 respectively. It appears that tests in

which the pipe broke away from the soil surface (Tests 1 and 2), allowing the entrainment

of water, experienced a greater reduction in Ksec when compared to the reduction in T-bar

resistance. During the test in which the pipe remained in contact with the soil (Test 3)

the reduction in Ksec (0.35) was similar to the reduction in T-bar resistance (0.40).

The trends of increasing pipe-soil stiffness after an episode of reconsolidation (Fig-

ures 6.7–6.9) are matched by similar increases in the steady, remoulded T-bar resistance

after similar reconsolidation periods. The ratios between the steady degradation factor

6-19


Bearing pressure, qt [kPa]

Sam

ple

dep

th,z

[m]

T-b

arin

vert

embed

men

t,w

/D[-]

Cycle

Deg

radat

ion

fact

or,D

F=

q t/q

t,in

itia

l[-]

Episode 1Episode 2Episode 3


Steady DF1 = 0.4

Steady DF2 = 0.6, DF2/DF1 = 1.49

Steady DF3 = 0.79, DF3/DF1 = 1.95

(a)

(b)

0 10 20 30 40 50 60

-80 -60 -40 -20 0 20 40 60 80

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

2

4

6

8

10

12

0

0.5

1

1.5

2

2.5

3

Figure 6.11: T-bar (a) response and (b) increase in steady degradation factor after periodsof reconsolidation

6-20



Test 1

Test 2

Test 3

Steady T-bar degradation factor, DFn/DF1 [-]

Ksec,cyc,n/K

sec,cyc,1

[-] Episode 2

Episode 3

Ksec,cyc at ∆w/D = 0.025

1 1.25 1.5 1.75 21

1.25

1.5

1.75

2

Figure 6.12: Comparison of cyclic riser test change in steady unloading stiffness andchange in steady T-bar resistance after reconsolidation episodes

reached in episodes 2 and 3 to that reached in episode 1 are 1.49 and 1.95 respectively.

The remoulded undrained shear strength approximately doubled after two periods of full

reconsolidation. This mechanism of behaviour, and the corresponding increase in pipe-soil

contact stiffness, can be attributed to the generation of positive excess pore pressure dur-

ing cycling, leading to a reduction in moisture content during subsequent reconsolidation

(White and Hodder, 2009).

Of the three displacement-controlled cyclic pipe tests performed, Test 2 displayed the

highest increase in Ksec,cyc over reconsolidation episodes (a factor ≈ 1.8). This value is

closely aligned with the increase in remoulded undrained shear strength observed in the

T-bar site investigation (as summarised in Figure 6.12). The generation of excess pore

pressure is linked to undrained shearing of the soil. Test 2 would be expected to display

the largest relative increase in Ksec because it involved cycles of the greatest amplitude,

and therefore, would have generated the highest potential for strength gain during recon-

solidation.

The simple comparison shown in Figure 6.12 indicates that penetrometer tests have

the potential to provide a simple basis for assessing changes in touchdown stiffness through

episodes of remoulding and reconsolidation.

6-21


6.6.6 Load controlled tests

During the majority of its lifetime, a riser will be subjected to small amplitude cycles

induced from day-to-day loading. When a linear idealisation of the pipe-soil response is

adopted, the stiffness is higher for small amplitude cycles than for large amplitude. Since

the predicted fatigue life of a riser is strongly influenced by the pipe-soil stiffness, the

choice of spring stiffness for day-to-day loading is a critical design decision.

Two tests were performed to investigate riser response when subjected to many cycles

of small-amplitude loading and unloading — representative of day-to-day conditions (Ta-

ble 6.3). Test 4 involved cycling between the load mobilised during initial penetration to

an embedment of approximately 0.5 diameters and 20% of this load (Figure 6.13). Test 5

involved cycling between the load at a penetration of approximately 1 diameter and zero

load (Figure 6.14).

In both tests, a state was reached where the pipe reached a stable embedment, with

negligible continued penetration. From this point, the unloading limit was gradually

decreased (i.e. made more negative) until the unload limit exceeded the uplift capacity,

and the pipe segment extracted fully from the soil in response to the actuator load control

system ‘hunting’ for the desired load. The inputs to the tests can be seen on Figures 6.13–

6.14 in plots (a) and (c). Plot (a) shows the total imposed vertical load (including the

buoyancy contribution). Plot (c) shows in blue the variation in the load amplitude with

cycle number.

During the initial phase of each test the pipe displacement rate was fixed at 0.25 mm/s

(at model scale). Near the end of the tests, when the vertical stiffness of the response

became extremely high, the displacement rate was decreased to 0.1 mm/s to avoid the

load limits being exceeded. These points are indicated on Figures 6.13–6.14.

The data was analysed to examine the variation in normalised secant stiffness through-

out the test. It was processed by firstly identifying the unloading points of each cycle.

The stiffness during the unloading phase was then calculated using Equation 6.5 and the

change in vertical load and pipe embedment from the point of unloading to the subse-

quent point of reloading. The initial soil resistance profile used in the calculation of Ksec

at the depth of unloading is shown in Figure 6.13a and Figure 6.14a and was derived from

a separate test in which the pipe element was monotonically penetrated deep into the

sample.

Point (i) on Figures 6.13–6.14 corresponds to the start of the load controlled cycling.

As the test progressed, the pipe was observed to ‘sink’, requiring further embedment

with each cycle to generate the bearing capacity defined by the upper load limit. During

this phase, the change in pipe invert embedment, ∆w/D, during unloading progressively

reduced, leading to a corresponding increase in Ksec.

Point (ii) on Figures 6.13–6.14 corresponds to the stage in each test when the pipe

reached an essentially stable elevation. At this point in both tests, Ksec values of approxi-

mately 200 and normalised cyclic amplitudes of ∆w/D ≈ 0.003 were calculated. Between

6-22



points (ii) and (iii), the minimum load limit targeted by the control system was progres-

sively reduced (as shown by the blue line in plot (c)). The amplitude of pipe movement to

mobilise the desired load range remained almost constant, so Ksec was observed to increase

following the changing load range. Maximum values of Ksec ≈ 250 were observed in both

tests, associated with cycles of amplitude ∆w/D ≈ 0.003.

At point (iii) on Figures 6.13–6.14, the increasing load range leads to a tensile compo-

nent of resistance being mobilised within the cycle. This onset of tensile loading triggers

a reduction in the stiffness, Ksec. The cyclic load amplitude is progressively raised and the

corresponding hysteretic stiffness reduces. Eventually the pipe is pulled from the soil as a

result of the unload limit exceeding the current uplift capacity. The minimum load reached

in the final cycle was qt ≈ −8 kPa in the shallow test (Figure 6.13a) and qt ≈ −35 kPa in

the deeper test (Figure 6.14a). In the latter test this value is significantly higher than the

initial penetration resistance at the same embedment. This increased resistance could be

due to a gain in the strength of the overlying material following the repeated disturbance

as the pipe was cyclically embedded, following a similar mechanism to the T-bar behaviour

shown in Figure 6.11.

Although these tensile loads mobilised during the final cycle of each test are significant

— exceeding the initial penetration resistance for Test 5 — it is likely that the pipe

would pull out from the seabed under a cyclic load with a smaller tensile component.

Close inspection of the displacement response showed that the pipe embedment began to

reduce once the mean imposed soil resistance, qs, became negative. A tentative conclusion

that can be reached from this observation is that a stable cyclic response — which can

be modeled by an equivalent linear spring — can be expected only for loads which are

on average compressive. If the mean load within the cycle is tensile then the soil will

eventually weaken due to the softening effect of the negative pore pressures associated

with the tensile mean loading.

Even before the mean cyclic load is tensile, the response softens, as shown by the drop

in Ksec evident at point (iii) in Figure 6.13c and Figure 6.14c. At this point the cyclic

load includes a tensile component, but the mean value remains positive and the mean

embedment does not reduce.

Plot (d) of Figures 6.13–6.14 shows that Ksec calculated as the pipe gradually extracted

(between points (iii) and (iv)) was significantly higher than when the pipe embedded (be-

tween points (i) and (ii)) for a given uplift, ∆w/D. This can be attributed to consolidation

of the soil surrounding the riser during the period of cycling, which would cause a ‘widen-

ing’ of the ultimate capacity curve (illustrated schematically in Figure 6.15). During this

period the net pipe-soil load was compressive which would tend to increase the strength

for the soil through consolidation, beyond the initial effects of remoulding. This increase

in soil strength would be expected to create an increase in the stiffness of the response for

a given amplitude of displacement, in the same manner as shown for Tests 1–3.

6-23


Bearing pressure, qt [kPa]

Pip

ein

ver

tem

bed

men

t,w

/D[-]

Cycle

Pip

ein

ver

tem

bed

men

t,w

/D[-]

Chan

gein

pip

ein

ver

tem

bed

men

t,∆

w/D

[-]

Cycle

Unlo

adin

gse

cant

stiff

nes

sra

tio,

Ksec=

∆V

/∆

wq s

,in

itia

l[-]

Chan

gein

bea

ring

pre

ssure

,∆

q t[k

Pa]


Unlo

adin

gse

cant

stiff

nes

sra

tio,

Ksec=

∆V

/∆

wq s

,in

itia

l[-]

w/D

∆w/D

Ksec

∆qt

(a) (b)

(c) (d)

qs,initial

unload limit decreased

test displacement rate

decreased to avoid

overshooting load limit

10−3 10−2 10−1 1000 2000 4000 6000 8000

0 2000 4000 6000 8000

-10 -5 0 5 10 15 20

0

50

100

150

200

250

300

0

4

8

12

16

20

24

0

50

100

150

200

250

300

0

0.004

0.008

0.012

0.016

0.02

0.0240

0.2

0.4

0.6

0.8

1

1.2

0

0.2

0.4

0.6

0.8

1

1.2

ivi

iii

ii

ivi

iii

ii

iv

i

iiiii

Figure 6.13: Test 4 (a) vertical response, (b) pipe invert embedment and uplift magnitude,(c) unloading stiffness ratio and change in bearing pressure and (d) unloadingstiffness ratio variation with uplift

6-24



Bearing pressure, qt [kPa]P

ipe

inver

tem

bed

men

t,w

/D[-]

Cycle

Pip

ein

ver

tem

bed

men

t,w

/D[-]

Chan

gein

pip

ein

ver

tem

bed

men

t,∆

w/D

[-]

Cycle

Unlo

adin

gse

cant

stiff

nes

sra

tio,

Ksec=

∆V

/∆

wq s

,in

itia

l[-]

Change

inbea

ring

pre

ssure

,∆

q t[k

Pa]


Unlo

adin

gse

cant

stiff

nes

sra

tio,

Ksec=

∆V

/∆

wq s

,in

itia

l[-]

w/D

∆w/D

Ksec

∆qt

(a) (b)

(c) (d)

unload limit

decreased

test displacement rate

decreased to avoid

overshooting load limit

qs,initial

10−3 10−2 10−1 1000 1000 2000 3000 4000 5000

0 1000 2000 3000 4000 5000

-40 -20 0 20 40

0

50

100

150

200

250

300

0

10

20

30

40

50

60

0

50

100

150

200

250

300

0

0.01

0.02

0.03

0.04

0.05

0.060

0.5

1

1.5

2

2.5

3

0

0.5

1

1.5

2

2.5

3

ivi

iii

ii

iv

i

iii

ii

iv

i

iii

ii

Figure 6.14: Test 5 (a) vertical response, (b) pipe invert embedment and uplift magnitude,(c) unloading stiffness ratio and change in bearing pressure and (d) unloadingstiffness ratio variation with uplift

6-25


V

w

∆w

original stiffness

post-consolidation stiffness

Initial ultimate capacity curvecorresponding to early life

Increased ultimate capacity curve afterstrength gain through consolidation

Figure 6.15: Influence on vertical stiffness of increased ultimate capacity due to reconsol-idation effects

6.7 Summary of Observed Seabed Stiffness

The results from these model tests provide an indication of how the vertical seabed stiff-

ness varies through the types of loading event associated with the behaviour of an SCR.

Table 6.4 and Table 6.5 summarise the values of normalised stiffness observed at different

amplitudes of movement in the displacement and load controlled tests respectively.

The results from the displacement controlled tests are applicable to conditions where

cyclic amplitude of the motion is significant and the overall response is dominated by

remoulded soil behaviour. The minimum amplitude of cycling investigated in the dis-

placement controlled tests was 0.5 pipe diameters, which was large enough to remould the

soil within 10 cycles. The field loading conditions and position along the TDZ where the

remoulded response observed in these tests would be applicable are during storm events

and the portion of riser pipe nearest the vessel — where displacements are largest.

Table 6.4 shows the values of Ksec,cyc calculated during the steady, remoulded condi-

tions reached in the displacement controlled tests in cyclic episodes 1–3 over a range of

uplift magnitudes. At a given uplift, broadly consistent Ksec,cyc values were calculated over

Tests 1–3 for a particular cyclic episode. After only two severe cyclic loading events, with

intervening periods of reconsolidation, an average increase in steady Ksec,cyc of approxi-

mately 50% was recorded, reflecting reconsolidation of the disturbed soil after each event.

Many episodes of disturbance would be expected over the entire life of the riser. Therefore,

the use of very low values of Ksec,cyc which are associated with the remoulded undrained

shear strength relative to the initial soil conditions derived from site investigation data,

without consideration given to the possibility of an increase in remoulded shear strength,

could result in unconservative fatigue life estimates.

6-26



In the context of fatigue life prediction, the choice of an appropriate high stiffness

associated with small amplitude, day-to-day motions that the SCR is subjected to for

the majority of its life, is also important. The load controlled experiments involved small

amplitude loadings relevant to the portion of riser furthest from the vessel within the TDZ.

Table 6.5 shows the values of Ksec calculated during the load controlled tests over a

range of uplift magnitudes. Separate values are reported for the early phase — where

further penetration took place with every cycle (‘embedding’ in Table 6.5) to generate the

bearing capacity required by the upper load limit — and the later phase — where the

lower load limit was gradually decreased until the load exceeded the uplift capacity and

the pipe section extracted completely (‘extracting’ in Table 6.5). For a particular phase,

consistent values of Ksec were calculated for both Tests 4 and 5 for a given uplift. The

increase in Ksec in the later phase relative to the early phase varied between ≈ 70% and

≈ 125%. On average, the stiffness approximately doubled between these two phases of

the tests. These results further illustrate the importance of considering changes in Ksec

associated with reconsolidation of the surrounding soil over the life of an SCR and that

these effects are not only limited to large amplitude cycling.

6-27

Geote

chnic

alanaly

sisofoffsh

ore

pip

elin

es

and

steelcate

nary

risers

Table 6.4: Summary of steady unloading secant stiffness ratio, Ksec,cyc, observed during large amplitude/displacement controlled tests

Steady, Episode 1 Steady, Episode 3 Average of Tests 1–3∆w/D Test 1 Test 2 Test 3 Test 1 Test 2 Test 3 Episode 1 Episode 3 Episode 3/Episode 1

0.005 46 48 55 65 87 67 50 73 1.470.01 26 30 35 39 53 44 30 45 1.490.025 12 14 17 18 25 22 14 22 1.510.05 6.3 7.9 9.2 10 14 12.3 7.8 12.1 1.550.1 3.4 4.3 5.2 5 7.3 6.9 4.3 6.4 1.490.5 0.5 0.8 1.2 0.8 1.1 1.5 0.8 1.1 1.36

Table 6.5: Summary of unloading secant stiffness ratio, Ksec, observed during small amplitude/load controlled tests

‘Embedding’ phase ‘Extracting’ phase∆w/D Test 4 Test 5 Average Test 4 Test 5 Average ‘Extracting’/‘Embedding’

0.005 125 125 125 210 210 210 1.680.01 63 63 63 120 140 130 2.060.025 NA 27 27 53 68 61 2.240.05 NA 17 17 25 35 30 1.76

6-2

8



Figure 6.16 compares the secant stiffness ratios obtained from the displacement and

load controlled tests at a normalised pipe uplift of ∆w/D = 0.005.

• The ‘first unload’ value of Ksec is from the initial upwards motion in the displace-

ment controlled tests. This value is a high stiffness, representative of unloading of

the intact soil, without any influence of cyclic remoulding or reconsolidation. The

measured value at the small movement of ∆w/D = 0.005 is close to the common

recommendation of Kmax = 200 (which is the stiffness from the hyperbolic model as

∆w/D tends to zero when unloading from the intact penetration resistance). There

is excellent agreement between the measured stiffnesses in the three tests, despite

the normalised embedment in Test 1 being half of the embedment in Tests 2–3.

• The next stiffness values shown in Figure 6.16 are the steady remoulded values

reached in the first episode of the displacement controlled tests. These values are

lower than the ‘first unload’ values by a factor of 3–4, reflecting the softening that

arises from the remoulding process, and perhaps also water entrainment. This pro-

portionate drop in stiffness exceeds the sensitivity of the soil, but the two parameters

are likely to be related.

• However, the stiffness values from the steady phase of the third cyclic episode show

the influence of reconsolidation, which causes the stiffness to recover by a factor of

1.5–2 through the two intervening periods. This gain in stiffness between episodes of

pipe movement is lower than the gain in strength evident between episodes of cyclic

T-bar penetration. The largest amplitude of pipe movement (Test 2: 1 diameter of

soil penetration) showed the greatest increase in stiffness, which was within ≈ 10%

of the strength gain in the T-bar case. It is assumed that the strength gain during

reconsolidation arises from the dissipation of excess pore pressure generated dur-

ing undrained remoulding. The higher-amplitude pipe movement generates greater

excess pore pressure, leading to a greater gain in strength during reconsolidation.

• The final pair of stiffness values shown in Figure 6.16 is from the load controlled tests

which consisted of continuous small-amplitude cycling. This long period of cycling

induced both remoulding and reconsolidation. During the early phase of the test,

the influence of remoulding appears dominant, since the secant stiffness is lower than

the ‘first unload’ values. However, in the later life stage the effect of reconsolidation

leads to a stiffness of Ksec ≈ 210, which exceeds the ‘first unload’ value.

A simple summary of the changing stiffnesses observed in this set of tests is that an

initial episode of remoulding led to a reduction in the vertical pipe-soil stiffness by a factor

of 4–5 compared to the initial unloading step. However, the reconsolidation that occurred

concurrent with a long period of small amplitude movement led to an increase in the

vertical pipe-soil stiffness to ≈ 30% above the initial unloading stiffness. Although these

values will be specific to the lightly overconsolidated kaolin clay used in this study, the

6-29


Large Amplitude Motion

(displacement controlled tests)Small Amplitude Motion

(load controlled tests)

First unload Episode 1 Episode 3

Steady, remoulded

Early life

(‘embedding’

phase)

Later life

(‘extracting’

phase)

Test 1 Test 2 Test 3 Test 4 Test 5

Normalised pipe uplift, ∆w/D = 0.005

Unlo

adin

gse

cant

stiff

nes

sra

tio,

Ksec

[-]

0

50

100

150

200

250

Figure 6.16: Comparative summary of results from large and small amplitude cyclic risertests

6-30



observed trends of changing pipe-soil stiffness match the changing soil strength observed

in cyclic (and episodic) T-bar penetration tests. It may therefore be possible to use this

type of in situ test to assess the corresponding changes in pipe-soil stiffness in other soil

types and conditions, as proposed by Clukey et al. (2008).

The full pipe-soil interaction response within the touchdown zone of an SCR involves

interaction between the structural response and the soil response. The actual conditions

imposed on an element of pipe are neither load controlled nor displacement controlled, so

it is difficult to distill these observations into generalised predictions of the local behaviour.

However, these results emphasise the significance of the changes in soil strength and stiff-

ness when disturbed by large or small-amplitude pipeline movements. Remoulding effects

tend to reduce the soil strength and the pipe-soil stiffness whereas reconsolidation effects

tend to raise the soil strength and the pipe-soil stiffness.

6.8 Conclusions

An accurate assessment of the vertical pipe-soil stiffness is critical to the long-term fatigue

analysis at the touch down zone of deep water steel catenary risers. To observe the

stiffness values under a range of conditions, a series of five centrifuge models tests on a

pipe section has been conducted. The tests were designed to investigate the behaviour

of a section of riser moving at shallow embedment in a soft clay typical of deep water

conditions. The experimental results presented in this paper have been back-analysed in

a manner that separates the effects of soil buoyancy and soil strength. The results show

that the amplitude of motion and processes including soil remoulding, water entrainment

and reconsolidation influence the vertical secant stiffness. The remoulding process creates

a significant reduction in the vertical stiffness, by a ratio higher than the sensitivity of the

soil — which is hypothesised to be due to water entrainment. In contrast, reconsolidation

of the soil after disturbance is shown to create a significant increase in the stiffness of the

response. The reconsolidation effect can entirely compensate for the remoulding effect.

A hyperbolic formulation provides a simple framework to capture the non-linearity of

the response at each stage. A good fit to the measured experimental data from constant

displacement cycles was displayed. However, because the secant pipe-soil stiffness is influ-

enced by episodes of remoulding and reconsolidation, as well as the amplitude of motion,

the use of a single stiffness value for all conditions during a riser’s service life will lead to

inaccurate fatigue assessments. The results in this paper show how modifications due to

cyclic amplitude, the duration of cyclic loading, embedment, as well as the intervening pe-

riods of limited activity, might be considered. The use of cyclic T-bar penetrometer tests

that include periods of reconsolidation may provide a basis for assessing these changes in

touchdown stiffness.

6-31



References





Clukey, E. C., Young, A. G., Garmon, G. S., and Dobias, J. R. (2008). Soil response andstiffness laboratory measurements of SCR pipe/soil interaction. In Proc. 40th OffshoreTechnology Conference, Houston, USA.

Hodder, M. S., White, D. J., and Cassidy, M. J. (2008). Centrifuge modelling of riser-soilstiffness degradation in the touchdown zone of a steel catenary riser. In Proc. Inter-national Conference on Offshore Mechanics and Arctic Engineering, Estoril, Portugal.[presented as Chapter 4 of this thesis].


Merifield, R. S., White, D. J., and Randolph, M. F. (2009). Effect of surface heave onresponse of partially embedded pipelines on clay. Journal of Geotechnical and Geoenvi-ronmental Engineering, 135(6):819–829.

Randolph, M. F., Jewell, R. J., Stone, K. J. L., and Brown, T. A. (1991). Establishing anew centrifuge facility. In Proc. International Conference on Centrifuge Modelling —Centrifuge ‘91, pages 2–9, Boulder, Colorado.


Randolph, M. F. and White, D. J. (2008a). Pipeline embedment in deep water: processesand quantitative assessment. In Proc. 40th Offshore Technology Conference, Houston,USA.

Randolph, M. F. and White, D. J. (2008b). Upper-bound yield envelopes for pipelines atshallow embedment in clay. Geotechnique, 58(4):297–301.


White, D. J. and Hodder, M. S. (2009). A simple model for the effect on soil strength ofepisodes of remoulding and reconsolidation. Canadian Geotechnical Journal, in press.

6-33

7An Effective Stress Framework for the Variation in

Penetration Resistance Due to Episodes of Remoulding and

Reconsolidation

7.1 Abstract

Steel catenary risers (SCRs) are used to transport hydrocarbon products between offshore

floating platforms and the seabed. Like many offshore structures, SCRs are subjected to

gross cyclic movements during operation, which remould the seabed soil. The fatigue life

of these structures is highly sensitive to the stiffness and strength of the seabed response.

Accurate modelling of this behaviour requires a framework that can capture the changes in

soil strength and stiffness that occur throughout the design life, accounting for remoulding

during extreme events, and reconsolidation during the intervening periods. This paper

describes such a framework, which is couched in effective stress terms. Soil softening

during remoulding is predominantly associated with excess pore pressure generation, and

the subsequent regain in strength is linked to the dissipation of excess pore pressure. The

framework can describe the variation of resistance on a cylinder (i.e. a pipe) during any

sequence of vertical cyclic motion, interspersed with pause periods. The framework is

based on a critical state approach, with the current strength being linked to the current

moisture content. The framework is shown to capture well the load-penetration response

during an episodic T-bar penetrometer test. The operative soil strength is shown to vary

dramatically throughout this event, with the softening effect of remoulding being almost

entirely negated by a regain in strength associated with periods of partial or complete

reconsolidation. The framework provides a basis for capturing these dramatic effects

to aid pipeline and riser design (and other processes that involve gross remoulding and

reconsolidation), without recourse to a full numerical simulation of the entire soil domain.

7-1


7.2 Introduction and Motivation

7.2.1 Geotechnical design of steel catenary risers

The continuing depletion of hydrocarbon reserves in shallow water coupled with the ad-

vancement of offshore technology has led to the development of fields located further

offshore in water depths exceeding 1000 m. A typical deep water offshore oil or gas facility

consists of a floating platform or vessel, a mooring system, and risers that transport the

hydrocarbon product between the platform and seabed. Steel catenary risers (SCRs) can

be economical to construct and install in deep water conditions compared to traditional

vertical or flexible risers. SCRs consist of a steel pipe, typically of 200-500 mm in diameter,

suspended in the form of a catenary from the vessel to the seabed.

The repetitive loading that an SCR is subjected to throughout its lifetime can cause

fatigue damage to the riser pipe in the region where it meets the seabed (known as the

‘touchdown zone’). Fatigue life calculations are sensitive to the assumed pipe-soil interac-

tion stiffness in the touchdown zone (Bridge et al., 2004; Bridge, 2005; Clukey et al., 2007).

The predicted response obtained from pipe-soil interaction models such as those presented

by Bridge et al. (2004), Aubeny and Biscontin (2008) and Randolph and Quiggin (2009) is

strongly influenced by the strength of the seabed soil. Therefore, accurate quantification

of the seabed strength, including any variation from the initial in situ strength throughout

the lifetime of the riser, is necessary for meaningful fatigue life predictions.

Other applications that require the effects of episodes of remoulding and reconsoli-

dation to be assessed include the installation, extraction and subsequent re-installation

of the spudcan foundations of a jack-up drilling rig (e.g. Stewart and Finnie, 2001), the

horizontal pipe movement of the crown of a lateral buckle, created by thermal cycles dur-

ing pipeline operation (e.g. Bruton et al., 2008) and cyclic penetrometer tests, using a

flow-round T-bar or ball device (e.g. Randolph et al., 2007).

The seabed soils found offshore in deep water where these challenges are commonly

encountered are usually very soft, normally to lightly overconsolidated clays. In these

fine-grained soils, riser movements typically occur at a rate which induces an undrained

response in the surrounding seabed soil. However, the cyclic nature of the loading can

soften and remould the surrounding soil in the touchdown zone. Within this zone the pipe

can move by several diameters during storm events. During intervening periods of calm

weather the soil undergoes minimal disturbance, and significant changes in strength can

occur due to consolidation.

In normally or lightly overconsolidated material, repeated undrained shearing due to

cyclic loading tends to generate positive excess pore water pressure, which reduces the

effective stress, and, therefore, reduces the strength of the soil. With time, consolidation

occurs and these positive excess pore water pressures dissipate, allowing the soil strength to

recover. The dissipation of positive excess water pressure ultimately reduces the moisture

content of the soil which causes an increase in the undrained shear strength. Clukey et al.

(2005) noted the potential for SCR fatigue life to be reduced as a result of higher pipe-

7-2

An Effective Stress Framework for the Variation in Penetration Resistance Due to Episodes of Remoulding and

Reconsolidation

soil interaction stiffness due to an increase in soil strength associated with consolidation

following cyclic loading. Recent experimental investigations have confirmed that the pipe-

soil stiffness can increase following a period of inactivity between packets of cyclic loading.

This is linked to the dissipation of excess pore pressure (Hodder et al., 2009).

7.2.2 Remoulding and reconsolidation of soft soils

There exists a considerable amount of literature concerning the weakening of soils due to

excess pore pressure generation. Typical applications include the assessment of liquefac-

tion potential due to earthquakes and the stability of gravity-based offshore structures

on coarse-grained soils subjected to storm loading (see for example, Bjerrum, 1973; Lee

and Focht, 1975; France and Sangrey, 1977; Andersen, 2009). However, there is no es-

tablished design methodology for assessing the strength recovery of fine-grained soils after

cyclic loading, or the resulting change in bearing capacity (or penetration resistance) of

a pipeline or riser. Furthermore, only minimal soil disturbance occurs during liquefaction

or storm loading of a gravity-based structure and the design aims for the soil to remain in

a pre-failure state. In contrast, the gross soil deformation associated with the large riser

movements in an SCR touchdown zone (or the initiation of controlled lateral buckles —

Bruton et al., 2008) involves taking the soil far beyond initial failure.

7.2.3 Analysis procedure for remoulding and reconsolidation

This paper outlines an analysis framework to predict the variation of undrained shear

strength due to both remoulding and reconsolidation effects. It is presented in the context

of the observed experimental behaviour of a T-bar penetrometer test. The framework

extends that presented in Hodder et al. (2010) — for the prediction of the degraded

undrained shear strength experienced during vertical motion — to include the recovery of

soil strength induced by consolidation effects.

In Hodder et al. (2010), the degradation of strength was associated with the accu-

mulation of shear strain via ‘damage’ of the nearby soil. However, in this paper, the

degradation is linked to a reduction in effective stress via the incremental development of

excess pore pressure during undrained shearing. This allows the recovery of soil strength

to be incorporated in the framework by including the dissipation of excess pore pressure

during periods of consolidation.

The analysis framework is based around principles of critical state soil mechanics,

in which the effective stress state during undrained failure (and therefore the strength)

depends on the current specific volume. It builds on an interpretation of cyclic T-bar pen-

etrometer behaviour in soft clay during remoulding and reconsolidation that was presented

by White and Hodder (2009), based on an idea set out by Palmer (1997). The strength

of a given soil horizon is assumed to be related to the current vertical effective stress.

This stress is reduced during each increment of undrained remoulding caused by vertical

movement of the cylinder when it is in the vicinity of the horizon. A vertical distribution

7-3


of excess pore pressure through the soil sample is obtained from the incremental increases

of pore pressure as the cylinder passes a horizon. Similarly, the current operative strength

experienced by the cylinder is obtained by integrating the soil strength in the vicinity

of the cylinder. Reconsolidation effects are included in the framework by assuming that

the excess pore pressure dissipates according to a simple one-dimensional solution. This

dissipation leads to a recovery of strength after each remoulding event.

Before the model is presented, a brief set of experimental observations of the varying

resistance when a model pipeline is moved vertically causing remoulding and subsequent

consolidation are presented. This is to illustrate the underlying behaviour and its impor-

tance in governing pipe-soil interaction. The pipe-soil stiffness results are then supported

by a similar trend observed in a T-bar penetrometer test (a T-bar being a cylindrical

penetrometer commonly used in soft soils, Randolph et al., 2007). The link between pipe-

soil interaction behaviour and the behaviour observed during a cyclic T-bar penetrometer

test is illustrated. The components of the framework are then presented along with the

derivation of key framework parameters. Finally, the framework is demonstrated by simu-

lating a cyclic T-bar penetrometer test with intervening pause periods between the cyclic

episodes.

7.3 Observed Effects of Remoulding and Reconsolidation

7.3.1 Effect on vertical pipe-soil stiffness

A suite of experiments were performed using the University of Western Australia’s geotech-

nical beam centrifuge to investigate pipe-soil interaction behaviour in the touchdown zone

of a SCR when subjected to a range of vertical cyclic loading conditions. Detailed results

are presented in Hodder et al. (2009). It is well known that a geotechnical centrifuge is

required to model soil behaviour accurately at small scale, since the response of soil is

governed by the effective stress level. The ratio of the centrifuge acceleration to Earth’s

gravity is the scaling factor used to relate model and prototype geometry. Lengthy con-

solidation events which would ordinarily be impractical to explore at prototype scale are

relatively straightforward to investigate in a geotechnical centrifuge because model consoli-

dation time is scaled by the square of the centrifuge scaling factor — meaning consolidation

times are greatly reduced in the centrifuge model. Details of the scaling laws and general

information on centrifuge modelling procedures are given by Taylor (1995), Muir Wood

(2004) and Garnier et al. (2007).

The experiments were performed at an acceleration level of 50 g using a model riser

pipe, 20 mm in diameter and 122.5 mm in length (1 m and 6.125 m at prototype scale).

The model soil was soft, lightly overconsolidated kaolin clay with a shear strength profile

that increased linearly with depth — typical of seabed conditions found in deep water

environments. Results from a test involving large amplitude cycling are shown in Figure 7.1

and Figure 7.2. The test consisted of vertical displacement cycles where the pipe was

7-4


Reconsolidation

Total bearing pressure, qt [kPa]

Pip

ein

vert

embed

men

t,w

/D[-]

Cycle

Unlo

adin

gse

cant

stiff

nes

sra

tio,

Ksec=

∆V

/∆w

q s,in

itia

l[-]

Episode 1

Episode 2

Episode 3

Episode 1

Episode 2

Episode 3

(a) (b)

∆w/D = 0.025

Ksec,cyc,1 = 14.3


Ksec,cyc,1

= 1.45


Ksec,cyc,1

= 1.77

0 10 20 30 40 50 60

-10 0 10 20

0

10

20

30

40

50

600

0.25

0.5

0.75

1

Figure 7.1: Large-amplitude cyclic pipe-soil interaction with pause periods between cyclicepisodes

repeatedly extracted clear above the soil surface before being re-penetrated. The test

involved three episodes of cyclic motion with intervening pause periods of approximately

1 year duration (at prototype scale) between the cyclic episodes. This is similar to field

conditions, where periods of relative inactivity occur between successive annual storm

seasons.

The variation of total vertical bearing pressure, qt = V/D (where V is the vertical

pipe-soil contact load per unit length of pipe and D is the pipe diameter), against pipe

invert embedment normalised by the pipe diameter, w/D, recorded throughout the test

is shown in Figure 7.1a. Figure 7.1b shows the variation of the unloading secant stiffness

ratio, Ksec = ∆V/∆wqs,initial (where ∆V/∆w is the unloading secant stiffness measured

from the onset of upward movement and qs,initial is the component of the initial bearing

capacity at the depth of unloading that arises from the soil strength (i.e. after subtracting

the influence of buoyancy)). The Ksec parameter is often used to specify elastic springs

to simulate the seabed in a structural analysis of an SCR (Bridge et al., 2004; Clukey

et al., 2005; Aubeny et al., 2008; Clukey et al., 2008). The equivalent elastic stiffness of

the pipe-soil response, ∆V = k∆w, is k = Ksecqs,initial.

Within each cyclic episode, the pipe-soil stiffness degraded rapidly due to soil remould-

ing. However, a significantly stiffer steady remoulded response was observed after each

period of reconsolidation (Figure 7.1b). After two reconsolidation periods the increase of

steady remoulded secant stiffness, Ksec,cyc, relative to the value recorded during the first

cyclic episode, Ksec,cyc,1, was approximately 75%.

7-5


Excess pore pressure, u [kPa]P

ipe

inve

rtem

bed

men

t,w

/D[-]

Prototype time (consolidation), tp [years]

Exce

sspor

epre

ssure

,u

[kPa]

(a)

(b)

Episode 1

Episode 2

Episode 3

0 0.5 1 1.5 2 2.5 3

-10 0 10 20 30

-10

0

10

20

30

0

0.25

0.5

0.75

1

Figure 7.2: Generation and subsequent dissipation of excess pore pressure at pipe invert

7-6


Reconsolidation

Figure 7.2a illustrates the generation of excess pore pressure that was recorded at the

pipe invert as the pipe was cycled in the soil. Subsequent dissipation of pore pressure

during the pause periods is evident in Figure 7.2b. The stiffer remoulded response ob-

served after reconsolidation periods is due to a reduction in the specific volume of the soil

associated with reconsolidation during the pause periods. The analytical framework set

out in this paper aims to describe this observed behaviour: remoulding within a cyclic

episode due to excess pore pressure generation, coupled with the recovery of strength and

increased stiffness due to consolidation.

7.3.2 Effect on T-bar penetration resistance

To compare the pipe-soil interaction results against observations that could be obtained

via an in situ site investigation, the testing programme also included a novel form of T-bar

penetrometer test. The test was performed in the same soil sample using a test sequence

similar to the sequence imposed during the cyclic pipe experiment. The test involved three

episodes of cycling with intervening pause periods between cyclic episodes, allowing both

remoulded and reconsolidation to be quantified. The model T-bar was 5 mm in diameter

(0.25 m at prototype scale).

The results from the T-bar test are shown in Figure 7.3. The undrained shear strength

was back-calculated from the bearing pressure recorded throughout the test as su = q/Nc,

where Nc is a bearing capacity factor applicable to the undrained loading of a deeply

buried cylinder, and was assumed equal to 10.5 (Randolph and Houlsby, 1984; Martin and

Randolph, 2006). Figure 7.3a shows the variation in undrained shear strength during the

three episodes of cycling. The strength variation was quantified by defining a degradation

factor, DF = su/su,initial, where su,initial is the undrained shear strength recorded during

the initial penetration. The degradation factor calculated at a prototype sample depth of

1.75 m is shown in Figure 7.3b. The soil strength degrades rapidly within a cyclic episode.

However, a significantly higher remoulded strength was recorded after each reconsolidation

episode — almost doubling after two periods of reconsolidation.

7.3.3 Comparison of pipe-soil and T-bar behaviour

The results from the T-bar test show a clear similarity with the changing pipe-soil inter-

action stiffness seen in Figure 7.1b. The link is further illustrated in Figure 7.4, where

the T-bar degradation factor is plotted against Ksec measured during the pipe test nor-

malised by the secant stiffness ratio recorded during the first unload, Ksec,initial. Within

an episode of cycling, the T-bar degradation factor varies in the same manner as the nor-

malised Ksec value. The ultimate increase of remoulded strength and Ksec also displays an

approximately linear trend after each reconsolidation period.

This link illustrates a potential end-use of the analysis framework presented in this

paper. An episodic cyclic T-bar test with phases specifically designed to reveal both

remoulding and reconsolidation effects could be used to calibrate the parameters of an

7-7



Pro

toty

pe

sam

ple

dep

th,z

[m]

Cycle

Deg

radat

ion

fact

or,D

F=

s u/s

u,in

itia

l[-]

(a)

(b)

Episode 1

Episode 2

Episode 3

Episode 1

Episode 2

Episode 3

Steady DF1 =0.4

Steady DF2 =0.6, DF2/DF1 =1.49

Steady DF3 =0.79, DF3/DF1 =1.95

0 10 20 30 40 50 60

-6 -4 -2 0 2 4 6

0

0.2

0.4

0.6

0.8

1

0

0.5

1

1.5

2

2.5

3

Figure 7.3: Cyclic T-bar penetration test with pause periods between cyclic episodes

7-8


Reconsolidation

T-bar degradation factor [-]

Ksec/K

sec,in

itia

l[-]

Episode 1

Episode 2

Episode 3

Ksec at ∆w/D =0.025

0 0.25 0.5 0.75 10

0.25

0.5

0.75

1

Figure 7.4: Comparison of normalised pipe-soil interaction stiffness and T-bar strengthdegradation

analytical framework accounting for this behaviour, which can then be used to capture

this form of pipe-soil interaction response. This is currently beyond the capabilities of

existing models. The purpose of the framework presented in this paper is to reproduce

the behaviour shown in Figure 7.3.

7.4 Model Framework

7.4.1 Framework overview

The framework uses the nomenclature for defining the depth to a soil horizon, the diameter

of the penetrating cylinder (which could be a pipeline or T-bar), the embedment and cycle

counting convention at a given soil horizon as illustrated in Figure 7.5. The cycle number

is used to quantify the disturbance and remoulding process. The framework is written

to allow for arbitrary cyclic movements, but the full passage of a soil element completely

into and out of the zone of influence of the cylinder results in a cycle number increase of

∆N = 0.5. This follows the convention of Randolph et al. (2007) and allows framework

to be linked directly to cyclic T-bar data.

The framework consists of several components that are set out in Figure 7.6. The

vertical distance between the current cylinder mid-depth and a given soil horizon nor-

malised by the cylinder diameter is denoted η (Figure 7.6a). A ‘cycle number influence

function’, µ(z), is defined above and below the cylinder (Figure 7.6b). This dictates the

rate of incremental increase of cycle number (and therefore remoulding) throughout the

soil sample, ∆N(z), in response to an increment of vertical displacement of the cylinder,

7-9


penetration

extraction

Cylinder diameter, D

N = 0 N = 1

N = 0.25

N = 0.75

N = 0.5

Cycle number, N

Soil surface

Normalised depth

to soil horizon,

z = z/D

Normalised cylinder

mid-depth embedment,

zm = zm/D

Figure 7.5: Depth nomenclature and cycle number definition for initial penetration andextraction (after Randolph et al., 2007)

∆zm. The vertical spatial distribution of excess pore pressure throughout the soil, ∆u(z)

(with the overbar denoting excess), is assumed to increase incrementally in response to

vertical displacement of the cylinder and is calculated via the incremental increase of the

soil horizon cycle number at each soil horizon (Figure 7.6c).

Consolidation effects are included in the framework by linking the excess pore pressure

distribution to a simplified one-dimensional lateral dissipation model (Figure 7.6d). The

current vertical effective stress profile, σ′

v(z), is obtained by subtracting u(z) from the in

situ vertical effective stress profile, σ′

v0(z). The undrained shear strength profile, su(z), is

then calculated directly from the current vertical effective stress, σ′

v(z) (Figure 7.6e). By

integrating the current soil strength in the vicinity of the cylinder according to a ‘strength

influence function’, ν(z) (Figure 7.6f), the average soil strength, su,av, can be obtained

(Figure 7.6g). During steady movement the resistance on the cylinder (per unit length) is

then calculated as Ncsu,avD, where Nc is an appropriate bearing factor.

After a change in direction of the cylinder motion, the progressive mobilisation of

the operative strength, su,op, is calculated by factoring su,av using a simple exponential

expression (Figure 7.6h).

7-10

An

Effectiv

eStre

ssFra

mework

for

the

Varia

tion

inPenetra

tion

Resista

nce

Due

toEpiso

des

ofRem

ould

ing

and

Reconso

lidatio

n

(a) (b) (c) (e) (f) (g) (h)

Current cylinder

location

Cycle number

influence

zone/function

Current excess

pore pressure

distribution

Current undrained

shear strength

distribution

Strength influence

zone/function

Averaged undrained shear strength

at the cylinder mid-depth

Mobilisation of operative

undrained shear strength

(d)

Excess pore pressure

dissipation model

su,av =

zm+α∫

zm−α

su(z)ν(z) dzsu,op

su,av

= 1 − e−3

∆zmzmob

µ(zm) = 1/β ν(zm) = 1/α

µ(z) u(z) su(z) ν(z)

zzzz

η

η = −β

η = 0

η = β

η = −α

η = α

Soil surface

zm

Figure 7.6: Schematic of model framework

7-1

1


To include the recovery of soil strength due to the effects of consolidation observed in

Figure 7.3, a critical state framework that links specific volume, v, and vertical effective

stress, σ′

v, as illustrated in Figure 7.7, is used. Prior to the initial penetration of the

cylinder, the soil is assumed to be at an intact state and may exist on a normal compression

line (NCL) as illustrated at point A in Figure 7.7, or in a lightly overconsolidated state

(point B). The undrained shearing of the soil when first disturbed by the cylinder generates

positive excess pore pressure which causes the effective stress to drop below the in situ

stress as shown at point C. After several cycles, the strength drops to the fully remoulded

value (point D) and is defined by the vertical effective stress on the ‘remoulded strength

line’ (RSL).

Later, as the excess pore pressure dissipates and consolidation progresses, the soil state

follows a reconsolidation line with slope κ (point E). Subsequent undrained cycling at the

reduced specific volume causes the RSL to be encountered at a higher vertical effective

stress as shown at point F, which results in a higher remoulded undrained shear strength

than the previous cyclic episode (White and Hodder, 2009).

7.4.2 Accumulation of excess pore pressure

Excess pore pressure, u, is generated in response to undrained shearing caused by dis-

turbance by the cylinder. For convenience, the rate of excess pore pressure increase as a

function of the remaining potential excess pore pressure (for the current specific volume),

(umax(z) − u(z)), is related to the increase of cycle number, N , at a given soil horizon:

∆u(z)

∆N(z)= f (umax(z) − u(z)) (7.1)

Equation 7.1 follows, in a simplified form, van Eekelen (1977) and van Eekelen and

Potts (1978) who presented various models for cyclic strength degradation via progressive

pore pressure generation. The maximum potential excess pore pressure, umax(z), at a given

specific volume is defined as:

umax(z) = σ′

v0(z) − σ′

v,RSL(z) (7.2)

where the in situ vertical effective stress is σ′

v0(z) = γ′z and σ′

v,RSL(z) is the effective

stress at the intercept of the RSL with the current specific volume (Figure 7.8).

The increase of cycle number due to a small vertical displacement increment of the

cylinder, ∆zm, is defined as:

∆N(z) = 0.5µ(z)∆zm (7.3)

where µ(z) is the cycle number influence function (Figure 7.6b), and controls the in-

crease of cycle number — and, therefore, excess pore pressure — according to the proximity

of a soil horizon to the cylinder. The 0.5 is included in Equation 7.3 for consistency with

7-12


Reconsolidation

Log mean vertical

effective stress, ln(σ’v)

Sp

ecif

ic v

olu

me, v

BA

CD

NCLRSL

λ

κ

ΓNCL

σ’v = 1kPa

Remoulding

cycles

E

κ

σ’v0

in situ vertical

effective stress

F

ABC

D

EF

κ

κ

λ

ΓNCL

Remoulding

cycles

in situ vertical

effective stress

Log mean vertical

effective stress, ln(σ′

v)

σ′

v0σ′

v= 1 kPa

Spec

ific

volu

me,

v

RSL NCL

Figure 7.7: Simplified critical state interpretation of remoulding and reconsolidation

Vertical effective stress, σ’v

Spec

ific

volu

me,

v

current vmaxu

zv γ′=σ′0RSLv,σ′

Remoulded strengh line

(RSL)

Vertical effective stress, σ′

v

σ′

v0= γ′zσ′

v,RSL

umax

current v

Remoulded strength line

(RSL)

Spec

ific

volu

me,

v

Figure 7.8: Definition of maximum potential excess pore pressure based on in situ verticaleffective stress and RSL

7-13


the cycle counting convention illustrated in Figure 7.5. A simple triangular expression is

adopted for µ(z) with limits which extend a normalised distance β above and below the

cylinder mid-depth:

µ(z) =1

β

(

1 −|η|

β

)

(7.4)

where η = z − zm defines the normalised distance of a soil horizon from the cylinder

mid-depth. If the soil horizon lies outside the influence zone (i.e. if |η| ≥ β), then µ(z) = 0,

and the soil horizon is unaffected by the current cylinder displacement increment. Even

though a triangular function is used here, any function in the form of a probability density

expression (i.e.zm+∞∫

zm−∞

µ(z) dz = 1) can be used without affecting the basis of the framework.

7.4.3 Calculation of operative undrained shear strength

Undrained shear strength in triaxial stress conditions can be described as su = Mp′/2,

where M is the critical state stress ratio and p′ is the mean effective normal stress. If the

stresses at failure are assumed to be σ′

v and σ′

h = Kσ′

v, then:

su =M

6(1 + 2K) σ′

v (7.5)

For convenience, the analysis framework assumes the undrained shear strength distri-

bution through the depth of the soil sample is proportional to the current vertical effective

stress, σ′

v(z), via a lumped strength parameter, Φ, which neglects the influence of stress

anisotropy:

su(z) = Φσ′

v(z) (7.6)

where σ′

v(z) = σ′

v0(z) − u(z). This simplification means that any reduction in the

mobilised friction angle from peak to critical state conditions due to overconsolidation or

the destruction of fabric or cementation, combined with the variability of K due to changes

of lateral stress state or OCR are incorporated into the lumped strength parameter, Φ.

The average undrained shear strength at the current location of the cylinder, su,av, is

obtained by the weighted integration of current soil strength in the vicinity of the cylinder

according to a ‘strength influence function’, ν(z) (Figure 7.6f):

su,av =

zm+α∫

zm−α

su(z)ν(z) dz (7.7)

The strength influence function is of similar form to the cycle number influence func-

tion, µ(z), as expressed in Equation 7.4, but with limits extending a normalised distance

7-14


Reconsolidation

α above and below the cylinder mid-depth:

ν(z) =1

α

(

1 −|η|

α

)

(7.8)

To account for the gradual mobilisation of strength after a cylinder direction change,

the operative strength, su,op, is calculated by factoring su,av using an exponential expression

with 95% of su,av being mobilised at a normalised cylinder displacement of zmob:

su,op

su,av

= 1 − e−3 ∆zm

zmob (7.9)

where ∆zm is the change in cylinder displacement since a change of direction.

7.4.4 Excess pore pressure dissipation

The initial value of each ‘packet’ of excess pore pressure generated by an increment of

displacement of the cylinder is denoted u0 and occurs at time t0. The current excess pore

pressure at a given soil horizon, uc, at the current time, tc, is related to u0 by the degree

of dissipation, U :

uc = u0 (1 − U) (7.10)

where U is a function of ∆t as described below. The time since the packet of pore

pressure was generated is ∆t = tc − t0. The total current excess pore pressure at a given

soil horizon used in the calculation of the current soil strength is obtained by summing

the uc packets up until the current time, tc:

u =

tc∑

t=0

uc (7.11)

Vertical cycling of the cylinder is assumed to result in a column of excess pore pressure

that dissipates one-dimensionally in the lateral direction away from the plane of motion.

The increase in excess pore pressure generated by cycling is idealised as uniform across

a lateral influence zone of width 2χD (Figure 7.9). This allows use of a solution for

the lateral dissipation of an initially rectangular pore pressure distribution presented by

Bolton (1979, pp. 173–181). The lateral variation of excess pore pressure as consolidation

progresses can be calculated using Bolton’s solution, and converted to the average value

within the lateral influence zone.

There are two phases to the Bolton solution. Phase 1 accounts for the first 1/6 of the

consolidation and is valid up to ∆t = (χD)2/12cv, at which time the dissipation front has

spread inwards and reached the cylinder centreline. Phase 2 comprises the final 5/6 of the

consolidation and is valid for all ∆t > (χD)2/12cv. The degree of dissipation, U , which

is applicable to the average excess pore pressure acting over the width 2χD is (Bolton,

7-15


( )zu �Current excess pore

pressure distribution ,

z�

1�z

2�z

3�z

Cylinder

diameter , D

( )1�zu

( )2�zu

( ) 0�3 =zu

2χDCurrent excess pore

pressure distribution, u(z)

Cylinder

diameter, D

u(z1)

u(z2)

u(z3)

z1

z2

z3

z

2χD

Figure 7.9: Generation of an increment of excess pore pressure, uniformly across a widthof 2χD, during passage of the cylinder

1979):

U =

1

6

√

12cv∆t

(χD)2, 0 ≤ ∆t ≤

(χD)2

12cv

1 −

(

χD

X−

(χD)3

6X3

)

, ∆t >(χD)2

12cv

(7.12)

The parameter X defines the distance from the cylinder centreline to the mid-point of

the laterally spreading pressure distribution, and can be solved at ∆t from:

1

2

[

X2

(χD)2−

5

6− ln

(

X

χD

)]

=cv∆t

(χD)2(7.13)

Figure 7.10 illustrates the resulting consolidation curve obtained from the dissipation

solution. By solving for the incremental change in excess pore pressure, ∆u(z), between

solution iterations, the reduction in specific volume, ∆v(z), can be calculated by relation

to the increase in effective stress, since ∆σ′

v(z) = −∆u(z):

∆v(z) = −κ ln

(

σ′

v(z) + ∆σ′

v(z)

σ′

v(z)

)

(7.14)

where κ is the slope of the reconsolidation line as shown in Figure 7.11.

7-16


Reconsolidation

Dimensionless time factor, T = cv∆t/(χD)2 [-]

Deg

ree

ofdis

sipat

ion,U

[-]

Phase 1Phase 2

Phase 2Phase 1

10−4 10−3 10−2 10−1 100 101 102 103 104 105 106

0

0.2

0.4

0.6

0.8

1

Figure 7.10: Consolidation curve for lateral dissipation of a rectangular block of pore pres-sure (Bolton, 1979)


v

σ′

v+ ∆σ′

vσ′

v

∆v

κ∆σ′

v

(−∆u)

Spec

ific

volu

me,

v

Figure 7.11: Change in specific volume, ∆v, associated with a consolidation-induced in-crease in effective stress

7-17


7.5 Calibration of Framework Parameters

This section outlines the methodology used to select appropriate parameter values for the

framework. Primarily, the framework parameters are calibrated using the data gathered

from the cyclic T-bar penetrometer experiment described earlier. In addition, reasonable

values are adopted for parameters that were not measured as part of the experimental

programme. The framework parameters along with appropriate values are detailed in

Table 7.1.

7.5.1 Initial specific volume profile

An initial profile of specific volume must be defined throughout the depth of the soil sample

against which changes can be compared, to quantify the variation in soil strength caused

by consolidation effects. The initial specific volume of the soil can be expressed in terms of

the overconsolidation ratio, OCR, and the in situ vertical effective stress, σ′

v0(z), following

usual critical state soil mechanics notation (Schofield and Wroth, 1968; Muir Wood, 1990):

vinitial(z) = ΓNCL − λ ln(

OCR(z)σ′

v0(z))

+ κ ln (OCR(z)) (7.15)

where ΓNCL is the specific volume at σ′

v = 1 kPa on the normal compression line.

The moisture content, w, of the intact model soil was measured at various depths after

conducting the experiments described earlier. The specific volume was evaluated from the

measured moisture content by applying the relationship, v = 1 + wGs. For the kaolin clay

used in these experiments, a specific particle density, Gs = 2.6, was assumed (Stewart,

1992). The calculated specific volumes along with the associated σ′

v0 and OCR at the four

depths where moisture content was measured are shown in Table 7.2. The OCR values

indicate a lightly overconsolidated sample, as a layer of soil 45 mm thick (at model scale)

was scraped off the soil surface prior to testing.

Using the moisture content measurements along with the known OCR and σ′

v0 profiles

(assuming an effective unit weight of γ′ = 5.5 kN/m3), best-fit values of ΓNCL = 3.74 and

λ = 0.311 were obtained by minimising the residuals between the measured and predicted

specific volumes from Equation 7.15. During the fitting of the parameters, the ratio of the

slope of the normal compression line, λ, to the slope of the swelling line, κ, was constrained

to equal 4.66, to match the value given by Stewart (1992) for kaolin clay. Although the

actual moisture content measurements provide appropriate values of ΓNCL and λ, only the

ratio λ/κ affects the model response.

Using the fitted values of ΓNCL, λ and κ, the variation of initial specific volume plotted

against in situ vertical effective stress is shown Figure 7.12. The normal compression line

(NCL) is also shown.

7-18

An

Effectiv

eStre

ssFra

mework

for

the

Varia

tion

inPenetra

tion

Resista

nce

Due

toEpiso

des

ofRem

ould

ing

and

Reconso

lidatio

n

Table 7.1: Summary of framework parameters

Framework

Component Parameter Dimensions Description Value Notes

Geometry D [L] Cylinder diameter 0.25 m

Soil characteristics

γ′ [F/L3] Effective unit weight 5.5 kN/m3 Used to define the in situ vertical effective stress, σ′

v0 = γ′z

[su/σ′

v0]NC

Λ[−][−]

Normally consolidated strength ratioPlastic volumetric strain ratio

0.2050.557

Used to calculate the remoulded vertical effective stress (Equa-tion 7.16) via definition of an initial undrained shear strength profile(Equation 7.18)

Soil specific volume -vertical effective

stress relationship

λΓNCL

[−][−]

Slope of normal compression line (NCL)Specific volume, v, at σ′

v = 1 kPa on NCL0.3113.74

Used to define the initial specific volume profile (Equation 7.15)

κ [−] Slope of swelling/reconsolidation line 0.0667Used to define the initial specific volume profile (Equation 7.15) andthe change of specific volume due to consolidation (Equation 7.14)

Soil strength

Φsteady [−] Strength parameter at steady, remoulded conditions 0.6

Used to calculate the undrained shear strength from the current ver-tical effective stress (Equation 7.6) via the current lumped strengthparameter (Equation 7.19), and to define the remoulded verticaleffective stress (Equation 7.16)

b [−] Peak strength parameter, kΦ = OCRb 0.3

Used to define the current lumped strength parameter (Equa-tion 7.19) via a peak strength component (Equation 7.20)

N95,Φ [−] Peak strength ductility 0.75Number of cycles to cause a 95% degradation from kΦΦsteady toΦsteady (Equation 7.19)

St,cyc [−] Soil sensitivity 2.48Ratio of initial to remoulded undrained shear strength and used tocalculate the remoulded vertical effective stress (Equation 7.16)

Operative strengthα [−] Strength influence zone extent 1

Used to define the average undrained shear strength in the vicinityof the cylinder (Equations 7.7 and 7.8)

zmob [−] Strength mobilisation distance 1Used to calculate the operative undrained shear strength experi-enced by the cylinder (Equation 7.9)

Remoulding

β [−] Cycle number influence zone extent 1Use to calculate the incremental increase of cycle number (Equa-tion 7.3) via definition of a cycle number influence zone (Equa-tion 7.4)

N95,u1[−] Pore pressure rate parameter 0.25

Number of cycles to cause a 95% generation of pore pressure com-ponent u1 maximum (Equations 7.21 and 7.22)

N95,u2[−] Pore pressure rate parameter 11

Number of cycles to cause a 95% generation of pore pressure com-ponent u2 maximum (Equations 7.21 and 7.22)

a [−] Pore pressure component parameter 0.77Used to define the proportion of umax allocated to pore pressurecomponents u1 and u2 (Equations 7.21 and 7.22)

Consolidationχ [−] Lateral extent of excess pore pressure column 1

Used to define the lateral width of the excess pore pressure columnfor consolidation solution (Equations 7.12 and 7.13)

cv [L2/T] Coefficient of consolidation 2 m2/year

7-1

9


7.5.2 Initial remoulded stress profile

The relationship between specific volume and the remoulded stress state, coupled with the

reload stiffness, κ, dictates strength increase after the dissipation of excess pore pressure.

Throughout the depth of the soil sample, the initial remoulded vertical effective stress,

σ′

v,RSL, can be expressed in terms of the initial undrained shear strength, su,initial:

σ′

v,RSL(z) =su,initial(z)

ΦSt,cyc

(7.16)

where Φ is the lumped strength parameter and St,cyc is the cyclic sensitivity of the soil

(defined as the ratio of su,initial to the fully remoulded undrained shear strength during the

first episode of cycling). The remoulded stress can also be expressed directly in terms of

the initial specific volume profile:

σ′

v,RSL(z) =

[

su

σ′

v0

]

NC

σ′

v0(z)

ΦSt,cyc

exp

(

Λ (ΓNCL − vinitial(z) − λ ln (σ′

v0(z)))

λ − κ

)

(7.17)

The relationship between specific volume and remoulded vertical effective stress re-

quired to define the updated σ′

v,RSL as v varies with consolidation is the same as for the

initial conditions. Equation 7.17 is obtained by linking Equations 7.15 and 7.16, and sub-

stituting the initial undrained shear strength, su,initial, in Equation 7.16 with the following

expression in terms of σ′

v0 and OCR (Wroth, 1984):

su,initial(z) = σ′

v0(z)

[

su

σ′

v0

]

NC

OCR(z)Λ (7.18)

where [su/σ′

v0]NCis the normally consolidated strength ratio and Λ is the plastic volu-

metric strain ratio. Optimum values of [su/σ′

v0]NC= 0.205 and Λ = 0.557 were obtained

by fitting the expression given by Equation 7.18 to the initial undrained shear strength

profile recorded during the T-bar penetrometer experiment.

7.5.3 Lumped strength parameter

The lumped strength parameter, Φ, links the current vertical effective stress with the

undrained shear strength. By using the remoulded undrained shear strength measured

experimentally during the three episodes of cycling, an appropriate value of Φ = Φsteady

can be back-calculated which is valid for steady, fully remoulded conditions.

As illustrated in Figure 7.13, the remoulded stress line in σ′

v : v space can be adjusted by

varying Φsteady in Equation 7.16 whilst retaining the initial specific volume profile calculated

via Equation 7.15. To select Φsteady, a value of St,cyc = 2.48 was back-calculated from the

experimental T-bar data and the swelling line slope, κ = 0.0667 was used from the fitting

of the initial specific volume profile. With these two parameters, and the remoulded

undrained strength measured after each reconsolidation episode a value of Φsteady = 0.6 is

obtained.

7-20


Reconsolidation

Table 7.2: Measured specific volume of centrifuge model soil sample

Prototypedepth,

In situ verticaleffective stress,

Overconsolidationratio,

Specificvolume,

z σ′

v0OCR v = 1 + wGs

[m] [kPa] [−] [−]

0.75 4.1 4.00 2.952.25 12.4 2.00 2.793.75 20.6 1.60 2.725.25 28.9 1.43 2.58


v[kPa]

Spec

ific

volu

me,

v[-]

Measured specific volume

Initial specific volume profile

Equation 7.15

NCL

v(z) = ΓNCL − λ ln σ′

v(z)

10−1 100 101 102

2.5

2.75

3

3.25

Figure 7.12: Initial specific volume profile of centrifuge model soil sample

7-21



v[kPa]

Spec

ific

volu

me,

v[-]

3

1

2κ

κ

σ′

v0

Cyclic

episode:Decreasing

Φsteady

Increasing

Φsteady

Remoulded stress line

(RSL)

100 101

2.5

2.6

2.7

2.8

2.9

3

Figure 7.13: Back-calculation of Φsteady using fully remoulded undrained shear strengthmeasured during each episode of cyclic loading (with full consolidation be-tween episodes)

This value represents the steady strength parameter. During the initial penetration,

and the first few cycles of the first episode, it was found that a higher value of Φ was

needed to match the measured data. This suggests that a brittle component of peak

strength exists.

This behaviour, and the progressive generation of excess pore pressure within all

episodes of cycling, is governed by the expressions adopted for the initially higher lumped

strength parameter and for the excess pore pressure generation.

To allow for the prediction of a higher, non-linear initial undrained shear strength

profile associated with overconsolidation, a peak lumped strength parameter is introduced

and related to Φsteady. A simple exponential is adopted, where Φ decays from a peak value,

kΦΦsteady, to Φsteady:

Φ(z) = kΦ(z)Φsteady − (kΦ(z) − 1)

(

1 − e−3

N(z)N95,Φ

)

Φsteady (7.19)

The number of cycles required to cause a 95% drop from kΦΦsteady to Φsteady is N95,Φ

(since e−3 ≈ 0.05). The strength parameter multiplier, kΦ, is linked to the OCR, in

the same way that the ratio between the peak and critical state strength of soil is also

dependent on OCR, as idealised via the Hvorslev surface (Schofield and Wroth, 1968;

Muir Wood, 1990):

kΦ(z) = OCR(z)b (7.20)

7-22


Reconsolidation

where b is a ‘peak’ strength parameter. N95,Φ is assigned a value of 0.75 (i.e. the average

cycle number within the cycle number influence zone after one complete penetration and

extraction of the cylinder). This implies that the strength decay occurs within the first

penetration-extraction cycle. The use of N95,Φ = 0.75 is also consistent with the number

of cycles to cause a 95% reduction of the structure or cementation component of strength

in the framework presented in Hodder et al. (2010).

To achieve good agreement with the measured data, it was found that the generated

excess pore pressure, u, should consist of two components, u1 and u2 (where u = u1 + u2).

The two components are exponentials with different rates, such that the incremental rise

in excess pore pressure with cycle number, ∆N , is:

∆u1(z)

∆N(z)=

3

N95,u1

(aumax(z) − u1(z))

∆u2(z)

∆N(z)=

3

N95,u2

((1 − a)umax(z) − u2(z))

(7.21)

Integrating these expressions with the boundary condition u1 = u2 = 0 at N = 0, gives

the following expression for continuous cycling (with no intervening drainage):

u(z)

umax(z)= 1 − ae

−3N(z)

N95,u1 − (1 − a) e−3

N(z)N95,u2 (7.22)

The components are linked via a parameter, a, where the maximum potential excess

pore pressure available to components u1 and u2 are aumax and (1 − a)umax respectively.

The parameters, N95,u1and N95,u2

, define the number of cycles to cause a rise of the excess

pore pressure components equal to 95% of their maximum. Here, N95,u1is assumed equal

to 0.25 — which results in a 95% rise of u1 to its maximum value, aumax, within 0.25

cycles (i.e. the average cycle number within the cycle number influence zone during the

initial penetration of the cylinder). Equation 7.22 defines the shape of the pore pressure

generation with continuous cycling, but the incremental form of Equation 7.21 is used in

the framework. This allows the incremental rise of excess pore pressure to be calculated

relative to a general pore pressure distribution.

Using the framework parameter values derived earlier, along with the assumed values of

N95,Φ = 0.75 and N95,u1= 0.25, optimum values of b = 0.3, a = 0.77 and N95,u2

= 11 were

obtained by minimising the error between the framework prediction and the experimentally

recorded initial undrained shear strength profile and cyclic degradation during the first

cyclic episode. The operative undrained shear strength experienced by the cylinder, su,op,

is affected by α and β — the cycle number and strength influence zone extents. Values

of α = 1 and β = 1 were adopted during the parameter calibration, which are consistent

with the values adopted in Hodder et al. (2010).

The resulting decay of Φ calculated via Equation 7.19 is illustrated in Figure 7.14 for

various overconsolidation ratios using the value of b = 0.3 obtained during the calibration.

7-23


Cycle number, N

Str

engt

hpar

amet

er,Φ

OCR = 1

OCR = 2

OCR = 3

OCR = 4

OCR = 5

Φsteady = 0.6

N95,Φ = 0.75

b = 0.3

Φsteady

Φ − Φsteady

kΦΦsteady

0.8

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

Figure 7.14: Effect of OCR on peak strength component (Φ − Φsteady)

Cycle number, N

u/u

max

Total excess pore pressure, u

Excess pore pressure component 1, u1

Excess pore pressure component 2, u2

a = 0.77

N95,u1= 0.25

N95,u2= 11

0 2.5 5 7.5 100

0.2

0.4

0.6

0.8

1

Figure 7.15: Two-component excess pore pressure generation model

7-24


Reconsolidation

Φ is observed to reduce to Φsteady at a cycle number N = 0.75 for all OCR > 1, while for

an OCR = 1 (i.e. a normally consolidated soil), Φ = Φsteady throughout the cycling.

Figure 7.15 shows the generation of the excess pore pressure components calculated

using Equation 7.21 with a = 0.77 and N95,u2= 11. The excess pore pressure component,

u1, increases rapidly, reaching 77% of the maximum potential excess pore pressure, umax,

soon after a cycle number of 0.25. u2 shows a more gradual increase, reflecting the milder

rate parameter: N95,u2= 11. When the components are summed, the total excess pore

pressure, u, has an initially rapid increase followed by a more gradual accumulation.

7-25


7.6 Example Simulation Using Framework

A full simulation of the in situ T-bar penetrometer experiment described earlier was

performed to demonstrate the framework. The parameter values used in the simulation are

detailed in Table 7.1. The strength mobilisation distance parameter, zmob, was assumed

equal to 1, which is consistent with the value adopted in the fully undrained analysis

presented by Hodder et al. (2010). χ, which defines the lateral extent of the excess pore

pressure column was assumed equal to β — the extent of the cycle number influence zone.

A consolidation coefficient of cv = 2 m2/year was adopted (Stewart, 1992).

7.6.1 Discussion of simulation results

Figure 7.16 shows the variation of undrained shear strength that was recorded throughout

the in situ T-bar penetrometer experiment (also shown in Figure 7.3a, based on Nc = 10.5).

The framework prediction is overlain. Cyclic episode 1 is shown in Figure 7.16a, and good

agreement is evident between the experimental results and the simulation prediction. The

limiting remoulded strength is predicted well over the full travel of the cylinder. However,

the framework under-predicts the operative strength slightly during the first penetration

of the cylinder, up to a depth of 1.5 m.

The results for cyclic episodes 2 and 3 are shown in Figure 7.16b and Figure 7.16c

respectively. Pause periods of 1 year were imposed between the cyclic episodes in the

simulation, matching the prototype scaled time allowed during the experiment. There is

good agreement when comparing the simulated and experimental responses during cyclic

episodes 2 and 3, even though the strength parameter degradation and pore pressure

generation components of the framework were calibrated using only the experimental

strength degradation behaviour observed during the first cyclic episode. However, the

framework under-predicts the remoulded strength near the vertical limits of the cycling

range during cyclic episodes 2 and 3 (and possible improvements to the framework to solve

this are discussed later).

The calculated profiles of vertical effective stress immediately after the three cyclic

episodes are shown in Figure 7.17. The limiting remoulded stress increases with each

cyclic episode, due to the successive reduction of specific volume associated with each

reconsolidation period. Above and below the cyclic zone, the vertical effective stress

profiles revert to the in situ profile over a distance dictated by the extent of the cycle

number influence zone, β.

The calculated and observed variation in operative shear strength with cycle number

at the approximate mid-depth of the cycles is shown in Figure 7.18. The softening during

the initial cycles followed by a more gradual reduction of strength is replicated well by the

framework across all three cyclic episodes. The ultimate increase of remoulded strength

after each reconsolidation period observed experimentally is also reproduced.

The calculated vertical effective stress-specific volume path at the cycle mid-depth is

presented in Figure 7.19. This shows the progressive reduction of vertical effective stress

7-26


Reconsolidation

Operative undrained shear strength,su,op [kPa]

Cylinder

inve

rtem

bed

men

t,z m

+D

/2[m

]


Cylinder

inve

rtem

bed

men

t,z m

+D

/2[m

]


Cylinder

inve

rtem

bed

men

t,z m

+D

/2[m

]

ExperimentSimulation



(a)

(b)

(c)

-6 -4 -2 0 2 4 6

-6 -4 -2 0 2 4 6

-6 -4 -2 0 2 4 6

0

0.5

1

1.5

2

2.5

3

3.5

0

0.5

1

1.5

2

2.5

3

3.5

0

0.5

1

1.5

2

2.5

3

3.5

Figure 7.16: Comparison of experimental and simulation prediction of operative undrainedshear strength during (a) cyclic episode 1, (b) cyclic episode 2 and (c) cyclicepisode 3

7-27



v[kPa]

Dep

th,z

[m]


in situ vertical effective stress profile

limiting remoulded

stress profiles

0 5 10 15 200

0.5

1

1.5

2

2.5

3

3.5

4

Figure 7.17: Vertical effective stress profiles calculated immediately after cyclic episodes

Cycle number, N

Oper

ativ

eundra

ined

shea

rst

rengt

h,

s u,op

[kPa]

Experiment

Simulation

Cyclic episode 1

Cyclic episode 2

Cyclic episode 3

0 10 20 30 40 50 600

0.5

1

1.5

2

2.5

3

3.5

Figure 7.18: Comparison of calculated and measured operative undrained shear strengthat mid-depth of cyclic range (z = 1.75 m)

7-28


Reconsolidation


v[kPa]

Spec

ific

volu

me,

v[-]

in situ vertical effective stress

Remoulded stress line (RSL)

Episode 1

Episode 2

Episode 3

100 101

2.5

2.6

2.7

2.8

2.9

3

Figure 7.19: Calculated variation in effective stress and specific volume throughout test(at z = 1.75 m)

7-29


at constant specific volume within each cyclic episode, and the recovery of effective stress

and an associated reduction in specific volume during each reconsolidation period. The

reconsolidation periods between the cyclic episodes do not result in full excess pore pressure

dissipation. A reconsolidation period of 1 year is equivalent to a dimensionless time factor

of T = 32 for the parameters used in the simulation. From the lateral excess pore pressure

dissipation solution used in the framework, the associated degree of dissipation is U = 0.88

at T = 32. The incomplete dissipation of excess pore pressure during the reconsolidation

periods is the source of the slightly lower remoulded strengths predicted by the framework

in cyclic episodes 2 and 3. This is because the lumped steady strength parameter, Φsteady,

was back-calculated using the remoulded strengths measured experimentally during the

three cyclic episodes, based on the assumption of full reconsolidation.

7.6.2 Possible refinements of framework

A disparity between the experimental results and the framework prediction is the increased

remoulded strength (when compared to the initial strength) evident in the experimental

results at the vertical limits of the cyclic zone. The increased strength is clear in the results

of cyclic episode 3, although the effect is observed to a lesser degree in cyclic episode 2.

The reason for the discrepancy is that at the vertical limits of cycling, dissipation of the

resulting excess pore pressure column is likely to be two-dimensional, particularly near the

soil surface, which provides a drainage boundary. In contrast, dissipation of excess pore

pressure at a soil horizon at the mid-depth of the cylinder cycle — with a zone of roughly

equal excess pore pressure above and below — would likely occur one-dimensionally in

the lateral direction — with an additional component in the orthogonal lateral direction,

along the axis of the pipe or T-bar near its ends. Therefore, consolidation would be

expected to occur at a higher rate, particularly near the vertical limits of the excess pore

pressure column. These effects are not simulated by the framework in its current form.

As a result, the soil at the vertical limits of the cyclic zone would drain more rapidly, and

therefore have a higher remoulded undrained shear strength prior to full reconsolidation.

The consolidation component of the framework could be modified from the simple one-

dimensional lateral dissipation model to include this effect, with the rate of excess pore

pressure dissipation at a given soil horizon determined as a function of the horizon’s

location within the current vertical distribution of excess pore pressure.

7.7 Conclusions

This paper presents an analytical framework that describes the variable operative undrained

shear strength experienced by a vertically cycled cylinder due to the effects of remoulding

and reconsolidation. The framework is an extension of that presented in Hodder et al.

(2010), where the degradation of soil strength within an episode of robust cyclic loading

was quantified via the spatial accumulation of ‘damage’ around the penetrating object.

7-30


Reconsolidation

In this paper, damage is explicitly modelled as a reduction in effective stress due to the

generation of excess pore pressure. The current soil strength is related to the vertical

effective stress via a lumped strength parameter. Consolidation effects are included in the

framework by linking the excess pore pressure to a dissipation model, and a consequent

reduction in specific volume.

The framework was shown to simulate well the behaviour observed during a T-bar

penetrometer test, reproducing the cyclic strength degradation within a cyclic episode,

along with the recovery of strength and ultimate increase of remoulded undrained shear

strength with successive cyclic episodes due to reconsolidation. Degradation of the lumped

strength parameter from a peak to a steady value coupled with a two-component excess

pore pressure generation model were implemented in order to simulate the softening re-

sponse during cycles. A simple one-dimensional lateral dissipation model was shown to

predict the reduction of specific volume associated with consolidation, causing an increase

in undrained shear strength.

Accurate fatigue life predictions of SCRs require consideration be given to the variation

of operative seabed strength from in situ conditions. This paper presented experimental

evidence of the effects of remoulding and reconsolidation on vertical cyclic pipe-soil re-

sponse, which were supported by similar trends observed during a T-bar penetrometer

test. The link between vertical cyclic pipe-soil response and the remoulding and recon-

solidation behaviour observed during a T-bar penetrometer test demonstrate a possible

end-use for the framework presented, with data from episodic T-bar tests being useful to

calibrate the framework. It would then be possible to analyse soil-structure interaction

processes that involve episodes of remoulding and reconsolidation, without recourse to a

full numerical analysis of the soil domain. More accurate assessment of the fatigue life of

an SCR in the touchdown zone is one potential application of the framework.

7-31


Reconsolidation

References

Andersen, K. H. (2009). Bearing capacity under cyclic loading — offshore, along thecoast, and on land. The 21st Bjerrum Lecture presented in Oslo, 23 November 2007.Canadian Geotechnical Journal, 46(5):513–535.



Bjerrum, L. (1973). Geotechnical problems involved in foundations of structures in theNorth Sea. Geotechnique, 23(3):319–358.

Bolton, M. D. (1979). A guide to soil mechanics. Macmillan, London, UK.



Bruton, D. A. S., White, D. J., Carr, M. C., and Cheuk, C. Y. (2008). Pipe-soil interac-tion during lateral buckling and pipeline walking: the SAFEBUCK JIP. In Proc. 40thOffshore Technology Conference, Houston, USA.


Clukey, E. C., Haustermans, L., and Dyvik, R. (2005). Model tests to simulate riser-soilinteraction in touchdown point region. In Proc. International Symposium on Frontiersin Offshore Geotechnics, pages 651–658, Perth, Australia.


France, J. W. and Sangrey, D. A. (1977). Effects of drainage in repeated loading of clays.Journal of the Geotechnical Engineering Division, 103(GT7):769–785.

Garnier, J., Gaudin, C., Springman, S. M., Culligan, P. J., Goodings, D., Konig, D.,Kutter, B., Phillips, R., Randolph, M. F., and Thorel, L. (2007). Catalogue of scalinglaws and similitude questions in geotechnical centrifuge modelling. International Journalof Physical Modelling in Geotechnics, 7(3):1–23.

Hodder, M. S., White, D. J., and Cassidy, M. J. (2009). Effect of remolding and reconsoli-dation on the touchdown stiffness of a steel catenary riser: observations from centrifugemodeling. In Proc. 41st Offshore Technology Conference, Houston, USA. [presented asChapter 6 of this thesis].

7-33


Hodder, M. S., White, D. J., and Cassidy, M. J. (2010). An analysis of soil strengthdegradation during episodes of cyclic loading, illustrated by the T-bar penetration test.International Journal of Geomechanics, 10(3):117–123. [presented as Chapter 5 of thisthesis].

Lee, K. L. and Focht, J. A., J. (1975). Liquefaction potential at Ekofisk Tank in North Sea.Journal of the Geotechnical Engineering Division, 101(GT1):1–18.


Muir Wood, D. (1990). Soil behaviour and critical state soil mechanics. Cambridge Uni-versity Press, Cambridge, UK.

Muir Wood, D. (2004). Geotechnical modelling. Spon Press, Oxfordshire, UK.

Palmer, A. C. (1997). Geotechnical evidence of ice scour as a guide to pipeline burialdepth. Canadian Geotechnical Journal, 34(6):1002–1003.

Randolph, M. F. and Houlsby, G. T. (1984). The limiting pressure on a circular pile loadedlaterally in cohesive soil. Geotechnique, 34(4):613–623.

Randolph, M. F., Low, H. E., and Zhou, H. (2007). In situ testing for design of pipeline andanchoring systems. In Proc. 6th International Conference on Offshore Site Investigationand Geotechnics, pages 251–262, London, UK. Society for Underwater Technology.


Schofield, A. N. and Wroth, C. P. (1968). Critical state soil mechanics. McGraw-Hill,London, UK.


Stewart, D. P. and Finnie, I. M. S. (2001). Spudcan-footprint interaction during jack-up workovers. In Proc. 11th International Offshore and Polar Engineering Conference,volume 1, pages 61–65, Stavanger, Norway.

Taylor, R. N. (1995). Geotechnical centrifuge technology. Chapman and Hall, London,UK.

van Eekelen, H. A. M. (1977). Single-parameter models for the progressive weakening ofsoils by cyclic loading. Geotechnique, 27(3):357–368.

van Eekelen, H. A. M. and Potts, D. M. (1978). The behaviour of Drammen Clay undercyclic loading. Geotechnique, 28(2):173–196.

White, D. J. and Hodder, M. S. (2009). A simple model for the effect on soil strength ofepisodes of remoulding and reconsolidation. Canadian Geotechnical Journal, in press.

Wroth, C. P. (1984). Interpretation of in situ soil tests. Geotechnique, 34(4):449–489.

7-34

83D Experiments Investigating the Interaction of a Model

SCR with the Seabed

8.1 Abstract

Steel catenary risers (SCRs) are used to transport hydrocarbon products between the

seabed and floating production facilities, particularly in deep offshore environments. As

developments move into deeper water the understanding of structural performance of the

riser can become critical to operational longevity. SCRs can be prone to fatigue damage,

especially in the region where the riser pipe reaches the seabed — known as the ‘touchdown

zone’. The results of a fatigue assessment depend significantly on the assumed pipe-soil

interaction conditions at the touchdown zone, which remains an area of uncertainty for

designers.

Typical experimental investigations into the problem focus on the two-dimensional ele-

mental response of a short section of riser pipe with the soil in order to calibrate interaction

models. This paper describes a different approach, where the three-dimensional response

of the riser with the seabed is explored experimentally. The experimental equipment de-

scribed represents the first such apparatus used to investigate 3D riser-soil interaction

under controlled conditions in a laboratory. The model riser pipe was 7.65m long and

110 mm in diameter and was loaded by both monotonic and cyclic motions via a computer-

controlled actuation system. A range of instrumentation was used to assess the structural

response of the model riser as well as trench formation and the development of excess

water/pore pressures. In these experiments the pipe was placed on a bed of sand for

benchmarking purposes although future experiments will explore the response in clay soils

which are typically encountered in the locations where SCRs are used.

Numerical analysis was used to determine an appropriate form for the distribution

of soil reaction along the length of the pipe, in response to the uplift of the model pipe.

Results from the numerical analysis displayed good agreement with the experimental data.

A simple methodology is outlined for the back-calculation of the distribution of soil bearing

stress beneath the model pipe. This provides a link between the 3D test results and

the more typically conducted 2D tests, allowing the verification of pipe-soil interaction

8-1


models derived from 2D experiments. A number of observations are drawn from the

work regarding 3D riser response including the effect of riser geometry and stiffness on

soil reaction and vertical pipe-soil load paths and hydrodynamic ‘jetting’ induced trench

evolution.

8.2 Introduction

Recent developments in offshore oil and gas extraction have taken place in ever deeper

water due to the depletion of shallow water fossil fuel reserves. The operation of fixed

production platforms is usually not feasible at these depths where a more viable option

consists of a floating vessel or platform. These usually consist of a mooring system and

risers that transport the hydrocarbon product between the seabed and the platform, as

illustrated in Figure 8.1a. Steel catenary risers (SCRs) can be a more cost effective option

than conventional vertical or flexible risers in deep water and typically consist of a 200-

600 mm diameter steel pipe suspended in a catenary from the platform.

One of the key issues for SCR design is the assessment of fatigue damage due to repet-

itive loading over the lifetime of the riser. This assessment depends significantly on the

assumed pipe-soil interaction behaviour at the location where the riser reaches the seabed

surface. This is generally known as the ‘touchdown zone’. There is still considerable

uncertainty over the riser-soil mechanics in this region and it is a major concern for indus-

try. The pipe-soil interaction response is dependent on a range of parameters such as the

seabed soil strength, loading conditions and pipe displacement magnitude. The schematic

of the touchdown zone presented in Figure 8.1b illustrates the typical method of modelling

the riser-seabed interaction as a series of springs, which may include a non-linear response.

It is worth considering the detail contained in Figure 8.1b. As the riser is laid, it will

initially penetrate a certain distance into the seabed. This initial penetration depth is

generally observed to be greater than would be expected solely from the self-weight of the

riser. The enhanced embedment is primarily due to two effects which occur during pipe

lay; concentration of pipe-soil contact stress in the touchdown zone and dynamic motion

of the pipe (Lund, 2000; Cathie et al., 2005; Randolph and White, 2008; Palmer, 2008).

Some distance from the touchdown zone (point B), the curvature of the riser will become

zero and the vertical displacement relative to the initial penetration depth will also be

zero. The loads applied to the riser, due to the motion of the floating facility as well

as from water currents on the riser, will result in cyclic rotations as well as vertical and

horizontal displacements at some location above the seabed (point A in Figure 8.1b). The

pipe-soil response between point A and point B is the subject of the work described in

this paper.

Two types of experiments can be carried out to investigate this problem. As shown

in Figure 8.1d, a typical approach is to carry out 2D experiments on a short, rigid sec-

tion of pipe, and — assuming plane strain conditions — explore the elemental behaviour

of the riser interaction with the soil under a range of different amplitudes and velocities

8-2

3D Experiments Investigating the Interaction of a Model SCR with the Seabed

of vertical motion. This type of work has been carried out by a variety of researchers

including recently by Aubeny et al. (2008), Clukey et al. (2008), Langford and Aubeny

(2008), Hodder et al. (2009) and Hu et al. (2009). The results from these 2D tests provide

invaluable information regarding the elemental pipe-soil response and can be used to di-

rectly calibrate interaction models such as described in Bridge et al. (2004), Aubeny and

Biscontin (2008) and Randolph and Quiggin (2009). However, it is important to be able

to verify results from 2D elemental tests by comparison to 3D experimental data in order

to gain confidence in the interaction models that are developed.

The approach described in this paper is to consider the three-dimensional effects, as

shown in Figure 8.1c, and therefore represents a more complete investigation of the pipe

behaviour at the touchdown zone. The testing involved subjecting a large section of flexible

pipe to cyclic vertical displacement at one end, with observation of the pipe response in

the touchdown zone by use of suitable instrumentation. As the motions of the riser are

complex, a simplifying assumption was made by only applying cyclic vertical motion to the

pipe via the actuator. This greatly simplified the loading arrangement but was considered

still to be a realistic idealisation of the cyclic lay-down and pull-up behaviour of the riser.

The pipe used during the testing was 110 mm in diameter, 7.65 m long and made from

PVC. The work was carried out on a sand seabed so as to provide benchmark data for

both numerical studies and future experimental work.

Whilst the work involved the commissioning of a unique testing facility, the main con-

tribution is the description and analysis of tests conducted. The results obtained include

bending moment profiles, cumulative displacements and water pressure measurements at

various positions along the length of the pipe under both monotonic and cyclic loading.

The instrumentation allows for the quantification of the distribution of soil reaction be-

neath the model riser, trench formation and excess water pressure — including soil suction.

The sign convention for the results shown in this paper is given in Figure 8.2.

8.3 Previous Work

The only piece of experimental work conducted previously to explore the three-dimensional

aspects of riser-soil interaction formed part of the STRIDE JIP (Steel Risers in Deepwater

Environments Joint Industry Project) as described by Bridge et al. (2003) and Bridge

(2005). The large scale testing was conducted at Watchet Harbour in the South West of

England. The soil at the site consisted of clay with properties similar to a deepwater Gulf

of Mexico seabed.

The test set-up consisted of a riser pipe, 110 m long and 168 mm in diameter, slung

in a catenary from an actuating device across the natural seabed of the harbour. The

actuator was fixed to the harbour wall. The actuating device was able to apply vertical

and horizontal motions to the end of the riser. The applied displacements at the actuator

were intended to simulate those that would occur at some distance above the seabed as

a result of slow drift vessel motions as well as higher frequency motions that might be

8-3


(a) (b)

(c) (d)

wa

ua

θa

wb = 0θb = 0

Figure 8.1: (a) Overview of problem showing (b) schematic of touchdown zone and twotypes of possible tests for investigation: (c) 3D experiments in a long tank,and, (d) 2D plane strain experiments for elemental response

Distance from soil

surface to pipe invert , w

Pipe diameter , D

(a)

Vertical load at

actuator support , P

(b) (c)

Sag = positive bending

(a) (b) (c)

Vertical load atactuator support, P

Sag = positive bendingDistance from soilsurface to pipe invert, w

Pipe diameter, D

Figure 8.2: (a) Nomenclature and positive sign convention of vertical pipe displacement,(b) vertical load at actuator support and (c) bending moment

8-4


associated with wave loading (both extreme and serviceable loadings). Instrumentation

was attached along the length of the riser and included strain gauging, an accelerometer

and load cells.

Some important insights were reported by Bridge et al. (2003) and Bridge (2005) re-

garding the 3D response of riser-soil interaction. The development of soil suction beneath

the pipe when subjected to motion simulating a slow vessel drift was illustrated by com-

paring the bending moment results from tests where the pipe rested on the natural soil

and where it rested on wooden planks — simulating an artificially rigid seabed. The fact

that the results recorded were similar throughout laying and lifting of the pipe when rest-

ing on planks, but differed significantly when it rested on the clay was attributed to the

development of soil suctions beneath the pipe as it was lifted. Suction was identified as

significant for large, slow vessel motions and therefore potentially damaging to the riser

from an ultimate strength perspective, but less significant for dynamic motions — where

the suctions were thought to dissipate with the amplitudes of cycling imposed. Through-

out the course of testing, a trench was observed to evolve and was believed to form from

a combination of plastic deformations of the soft clay seabed as a result of riser cycling

and hydrodynamic effects.

While the Watchet Harbour 3D riser experiment provided creditable information into

the problem, there were some shortcomings. Because the testing was conducted at a nat-

ural site the soil conditions were not able to be controlled or varied and the measurement

of additional parameters could have been beneficial. For example there was no direct mea-

surement of suction beneath the riser pipe, and as such it was only possible to estimate the

longitudinal variation of suction through differences in the measured bending moment at

discrete points along the riser during laying and lifting. The evolution of trench formation

could not be linked directly to the imposed motion due to the lack of vertical displacement

measurements along the pipe throughout testing. The inclusion of this additional instru-

mentation would have allowed the characterisation of the soil-riser interaction in detail,

and therefore, determine its effect on the structural response of the riser.

The work described in this paper looks to address some of the shortcomings described

above by developing an experiment in laboratory-controlled conditions within which 3D

riser-soil interaction effects can be explored. In developing the experimental set-up, par-

ticular attention was paid to ensuring that there was sufficient instrumentation to properly

characterise both the soil behaviour and pipe behaviour along with the ability to ‘design’

or control the desired model seabed conditions.

8.4 Experimental Set-Up

8.4.1 Flume

The experiments were carried out in a long flume, shown in Figure 8.3a, developed at

Oxford University to explore soil-structure interaction problems related to pipelines using

8-5


various soil types and conditions. The key dimensions of the flume are 8 m in length, 0.64 m

wide and 0.8 m deep. It has been designed so that it can be tilted about one axis to allow

for fluid flow experiments. A water distribution and pumping system (plus reservoir) has

been incorporated to allow the bed of soil to be fully liquefied by using upward hydraulic

gradients. The design allows the tank to be completely filled with saturated soil, although

for the experiments described in this paper, the soil bed was approximately 350 mm deep.

The soil used in the testing was Redhill 110, a reasonably uniform silica sand, with an

average particle size of 0.138 mm.

8.4.2 Actuator and pipe connection

Shown in Figure 8.3b is the actuation system located at one end of the tank. This was used

to apply specified displacement paths to the end of the pipe. The actuator is controlled

by a computer and it is possible to move at either constant velocity or cyclically in the

form of a sine wave at a range of amplitudes and frequencies. More complex motions can

be applied but require specific control programs to be developed. The actuator can move

at speeds up to 150 mm/s and apply loads up to 15 kN.

The pipe was connected to the actuator via a pin-joint and a horizontal linear guide

and carriage as shown in Figures 8.3c and 8.3d. The linear guide allowed free motion

along the longitudinal axis of the pipe. In reality there will be a large tension in the

riser, which leads to axial stresses at the pipe-soil interface. The linear guide used in the

experiment meant that axial stress was not transferred to the soil, allowing for comparison

of the interpreted data with ‘elemental’ 2D plane strain test results. The pipe was allowed

to rotate freely about its transverse axis by imposing the vertical motion via a 20 mm

diameter brass pin slotted through the centre of the pipe with the pin housed in sealed

pillow block bearings on either side of the pipe. The pipe therefore displaced vertically

with the actuator motion, but was free to translate horizontally or rotate at the connection

point. This was considered to be an appropriate approximation to the behaviour in the

field. The far end of the pipe was not attached and sat freely on the soil.

8.4.3 Pipe and instrumentation

The instrumented pipe in the flume is shown in Figure 8.3e. The photo was taken as a lift-

up test was in progress. The riser was modelled using a 110 mm diameter PVC pipe with

a length of 7.65 m with details in Table 8.1. PVC was chosen for its low material stiffness,

which ensured the portion of pipe furthest from the actuator would remain stationary at

the maximum actuator travel whilst also permitting a relatively large diameter to be used.

The bending stiffness of the pipe was chosen to suit the geometry of the flume and was not

intended to model SCR bending stiffness in the field. The Young’s modulus was estimated

by measuring the deflection of the pipe in response to the application of various weights in

a simply-supported beam bending exercise. To achieve the full length, two pieces of pipe

were joined together using a pipe socket. The joint was 6 m from the actuator. Galvanised

8-6


PipePin to allow

free rotation

Vertical load cell

Actuator to provide

vertical motion

Linear guide and carriage

to allow free longitudinal

displacement

(a) (b)

(c) (d)

(e)(e)

Vertical load cell

Pin

Linear guideand carriage

Pin to allowfree rotation

Pipe

Verticalload cell

Actuator to providevertical motion

Linear guide and carriageto allow free longitudinal

displacement

Figure 8.3: Large scale pipe test facility for 3D tests showing (a) overall view, (b) linearactuating device at one end of the testing tank, (c) schematic of pipe-actuatorconnection, (d) photo of pipe-actuator connection and (e) view of instrumentedmodel riser in flume

8-7


steel wire rope inserted inside the pipe was used to provide additional self-weight. The

steel wire rope was flexible and fitted loosely inside the pipe, thereby not affecting the

bending stiffness.

The layout of the instrumentation is illustrated in Figure 8.4. The instrumentation

consisted of:

• A load cell used to record the vertical load at the actuator during lifting of the pipe.

• Four draw wire displacement sensors mounted above the pipe to monitor local dis-

placements and quantify any trench formation. The displacement at the actuator

was also recorded.

• Five sets of strain gauges along the pipe to measure the bending moments.

• Three pressure transducers to measure water pressure at the pipe invert. These were

protected by a vyon filter and completely de-aired prior to testing to ensure a quick

response to pressure changes.

The strain gauges were configured in a four gauge full Wheatstone bridge circuit with

one strain gauge in each arm of the bridge as shown in Figure 8.5a. The circuit was

designed for axial strain and temperature compensation. To prevent water ingress during

testing, waterproofing consisted of two thin layers of polyurethane followed by a coating

of microcrystalline wax (Figure 8.5b) and a sheet of plastic which was sealed using ad-

ditional wax (Figure 8.5c). The area was then taped to provide mechanical protection

(Figure 8.5d).

The instrumentation was powered and amplified by signal conditioning equipment

supplied by RDP electronics. The data were logged on a computer using a LABVIEW

program via a National Instruments 16-bit data acquisition card. A logging frequency of

10 Hz was used during the majority of the testing. The data logging program was also

responsible for the control of the actuation system.

Table 8.1: Model pipe parameters

Parameter Value Units

Diameter 110 mmWall thickness 5.3 mm

Length 7650 mmYoung’s modulus 2.6 GPa

Submerged weight (including steel rope) 79.8 N/m

8-8

3D

Experim

ents

Investig

atin

gth

eIn

tera

ctio

nofa

ModelSCR

with

the

Seabed

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 6500 7000 7500

Distance from actuator,

x [mm]

DW = draw wire displacement sensor

BM = bending moment strain gauge

PPT = water/pore pressure transducer

Load

cell

PPT1 PPT2 PPT3

BM1 BM2 BM3 BM4 BM5

DW1 DW2 DW3 DW4

Figure 8.4: Schematic of model pipe measurement positions

8-9


8.4.4 Instrument calibration

The bending strain gauges were calibrated by placing the pipe into a simply-supported

condition and hanging combinations of weights at various positions along its length. The

theoretical bending moment at each of the gauge locations was then compared to the

recorded output voltage to form a relationship between voltage and bending moment.

Both sag and hog bending states (relative to a particular gauge) were imposed during the

calibration by rotating the pipe 180◦ about its longitudinal axis. An example result of a

strain gauge calibration is shown in Figure 8.6.

The vertical load cell was calibrated by using weights of known mass to subject the load

cell to various tension and compression loads. The pressure transducers were calibrated,

after being de-aired, by using a column of water of different heights to apply various

hydrostatic pressures to the transducer.

8.5 Numerical Analysis of Physical Model

To facilitate a comparison of the pipe-soil interaction force experienced by an ‘element’ of

pipe during a three-dimensional experiment with results obtained from the more typically

performed two-dimensional plane strain experiments using a short length of pipe, the

distribution of vertical soil reaction throughout the touchdown zone must be quantified.

Solutions describing the response of a riser pipe in the touchdown zone have been presented

(for example see Pesce et al., 1998; Lenci and Callegari, 2005; Palmer, 2008; Randolph

and White, 2008). Such solutions are dependent on a number of parameters; the water

depth, the riser tension, lay angle, bending stiffness and submerged weight along with

the soil stiffness. The simplified arrangement of the experimental apparatus described in

this paper allows the distribution of soil bearing pressure, S(x), along the base of the

pipe to be investigated using simple small displacement beam bending theory according

to the balance of external forces on the model riser described by the free body diagram

shown in Figure 8.7. Along with the comparison of results against behaviour observed

during two-dimensional experiments, the quantification of pipe-soil reaction throughout

the model touchdown zone also enables interpolation between the experimental bending

moment and displacement data points obtained.

To explore an appropriate form of the distribution of soil bearing pressure below the

model riser pipe, a simple numerical model was constructed using the finite element pro-

gram ABAQUS. The numerical model also allowed for the comparison between the nu-

merical and experimental results. The soil was modelled as a bed of linear springs, as

highlighted in Figure 8.1b, with zero stiffness for pipe invert elevations above the soil

surface, allowing the pipe to lift from the soil without resistance. The stiffness for pipe

invert elevations below the soil surface, k, was calculated as a secant stiffness to a nominal

embedment from the theoretical bearing capacity curve for a strip footing in drained soil

with width, B, equal to the contact width of the pipe for a particular embedment. This is

8-10


(a) (b)

(c) (d)

Figure 8.5: (a) Strain gauging, (b) wax coating, (c) plastic coating and (d) taping

Output voltage [V]

Theo

reti

calben

din

gm

omen

t[N

m]

R2 = 0.9991

-2 -1.5 -1 -0.5 0 0.5 10

20

40

60

80

100

120

140

Figure 8.6: Example of strain gauge calibration

8-11


Pipe length , L

Vertical load

at actuator

support, P

Pipe self weight , Q

Distance from actuator to touchdown point , xTDP

Distance from actuator , x

Soil pressure

distribution, S(x)Distance from actuatorto touchdown point, xTDP

Pipe self weight, Q

Pipe length, L

Distance from actuator, x

Soil pressuredistribution, S(x)

Vertical loadat actuatorsupport, P

Figure 8.7: Free body diagram of physical model

Vertical load per unit length of pipe , V [F/L]

Pip

e i

nv

ert

em

bed

ment,

w[L

]

.

Theoretical vertical

penetration curve from

drained bearing capacity

2γγ′+γ′== BNwNBVq q

B = pipe contact width

wVk ∆∆=w∆

V∆

Theoretical verticalpenetration curve from

drained bearing capacity

q = V/B = γ′wNq + γ′BNγ/2

B = pipe contact width

Pip

ein

vert

embed

men

t,w

[L]

Vertical load per unit length of pipe, V [F/L]

∆w

k = ∆V/∆w

∆V

Figure 8.8: Determination of linear spring stiffness for input into ABAQUS model

8-12


Distance from actuator, x [mm]

Soi

lre

acti

on/

pip

ew

eigh

t[-]

ABAQUS soil reactionCalculated approximation of soil reaction

Actuator uplift, w/D = 0.045

Actuator uplift, w/D = 3

0 1000 2000 3000 4000 5000 6000 7000 80000

0.5

1

1.5

2

2.5

Figure 8.9: Soil bearing pressure distribution from numerical simulation

illustrated in Figure 8.8. The bearing capacity factors Nq and Nγ were calculated from the

well-known exact solution and from Martin (2005) respectively. Due to the relative linear-

ity of the penetration curve, the spring stiffness, k, was assumed constant with embedment

for this investigation.

The distributions of bearing pressure, represented as a fraction of the pipe self weight,

from the numerical analysis are shown in Figure 8.9 at two values of pipe uplift at the

actuator. These can be described by a two-stage exponential association function:

S(x) = H (x − xTDP)[

A(

1 − e−B(x−xTDP))

− C(

1 − e−D(x−xTDP))]

(8.1)

where H (x − xTDP) is the Heaviside step function, equal to 0 for (x − xTDP) < 0 and

1 for (x − xTDP) ≥ 0 whilst A, B, C, D are fitting parameters and xTDP is the distance

from the actuator support to the touchdown point. By varying the five parameters, the

form of Equation 8.1 has the ability to describe the bearing pressure below the pipe over

a range of pipe uplift magnitudes.

One of the important products of the experimental data analysis is to be able to

back-calculate the bearing pressure distribution and touchdown point given the bending

moment at discrete points along the pipe and the measured vertical reaction at the ac-

tuator. Appendix 8.A outlines the methodology developed and used for this calculation.

The approach was tested initially with the numerical ABAQUS results and is shown in

Figure 8.9, where a good match between the numerical results and the calculated approx-

imation to the actual results is evident. This gave confidence that the methodology could

be used to back-analyse the experimental results.

Figure 8.9 also shows that the maximum soil reaction predicted by the numerical

8-13


Soil reaction / pipe weight [-]

Pip

ein

vert

elev

atio

nat

actu

ator

,w

/D[-]

x = 2000 mm

x = 3000 mm

x = 4000 mm

x = 5000 mm

x = 6000 mm

x = 7000 mm

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

3

Figure 8.10: Numerically predicted soil bearing pressure at various positions along pipethroughout pipe uplift

analysis is over twice the pipe self weight. The magnitude of this ‘overstressing’ effect —

which causes the pipe to exert a load on the soil exceeding that of the pipe self-weight —

is a function of geometry and pipe stiffness and increases with soil stiffness (Cathie et al.,

2005; White and Randolph, 2007) and so the results presented here are specific to the test

conditions. However, as shown in Figure 8.10, the numerical results do provide insight

into the load paths experienced by the soil at various positions along the pipe as it is

lifted. Initially, the soil reaction at all positions is equal to the pipe weight. As the pipe is

lifted, the soil reaction does not decrease immediately at all positions along the pipe, but

increases due to the effect of bending stiffness of the pipe before finally decreasing to zero

in some cases as the pipe loses contact with the soil at that position. This illustrates that

although the numerical simulation was conducted in simple displacement control by lifting

the pipe at one end; the resulting load transmitted to the underlying soil by an element

of pipe is governed by a combination of load and displacement control and is a complex

function of the 3D geometry, pipe and soil stiffness. This ‘3D effect’ results in different

load paths than imposed by the typical displacement or load controlled 2D tests where a

short section of pipe is cycled between upper and lower displacement or load limits (as

examples, see Aubeny et al., 2008; Hodder et al., 2009).

8.6 Experimental Results

This section presents the results of the experiments conducted on a sand model seabed.

Two tests were carried out:

8-14


1. A ‘monotonic’ lift-up and lay-down test performed at a slow, constant velocity on a

medium density sand bed. This test was conducted as a benchmark static experiment

and to compare against the numerical analysis described above.

2. A cyclic test performed at a variety of amplitudes and frequencies on a loose sand

bed. This test was conducted to investigate the potential of trench formation as

a result of cycling and assess any differences in the results when compared to the

monotonic test. Details of the amplitudes and frequencies and the number of cycles

imposed are shown in Table 8.2.

Both tests were conducted using saturated soil. The model riser remained submerged

throughout the full range of imposed displacements, with approximately 350 mm of water

above the soil surface. In processing the data, an adjustment was made to the vertical

load cell readings to account for the effect of the variation in effective weight of the pipe-

actuator connection due to the changing submerged volume with travel of the actuator.

8.6.1 Monotonic test

A monotonic lift-up and lay-down test was conducted to a maximum normalised pipe

invert elevation of three diameters above the soil surface. In addition to providing data as

a static benchmark experiment, the test also served as a verification of the experimental

instrumentation, actuator control and data acquisition systems. The sand bed for the test

was not prepared with the use of the pumping system and the soil surface was manually

smoothed. While the relative density was not explicitly calculated for this test, the sand

sample was believed to be in a medium dense state. Draw wire displacement sensor DW2

was not used in the monotonic test.

After preparation of the sand bed was complete, the model riser was carefully lowered

onto the soil surface before being connected to the actuator. A displacement rate of 1 mm/s

was imposed throughout the lift-up and lay-down. All instrumentation was zeroed prior

to the lifting phase of the experiment.

Figure 8.11 shows the vertical load at the actuator and the bending moments recorded

throughout the monotonic test. There is a small amount of hysteresis apparent in the ac-

tuator load, with a slightly larger load recorded in the lift-up phase than during lay-down.

This hysteresis is likely due to plastic deformation of the soil as a result of ‘overstressing’

Table 8.2: Details of cyclic test

Uplift amplitude / Pipe diameter FrequencyCycles

[−] [Hz]

0.1 0.5 20000.825 0.23 27001.55 0.18 20002.275 0.16 2400

3 0.15 6000

8-15


as the pipe was lifted. Also shown in Figure 8.11 are the results from the ABAQUS numer-

ical analysis for comparison. Generally, there is good agreement between the experimental

and numerical results for the both the actuator load and the bending moments over the

range of uplift; however, the numerical analysis predicted a slightly higher actuator load

in the early stages of the uplift and a slightly lower actuator load in the later stages than

observed experimentally.

To examine the variation in bending moment and displacement along the pipe, the

recorded experimental readings at normalised pipe uplifts of one and three diameters at

the actuator are compared to the bending moment diagram and displaced shape predicted

by the ABAQUS numerical analysis in Figure 8.12. It can be seen that the experimental

readings follow the numerical prediction acceptably.

Using the methodology outlined in the previous section, the variation in the touchdown

point and peak soil reaction throughout the uplift was investigated using the array of

bending moment and actuator load readings with the results shown in Figure 8.13. For

comparison, the numerical results are also shown. Table 8.3 provides details of the bearing

pressure distribution parameters xTDP, A, B, C and D calculated from the experiments

for a range of normalised uplift positions. The experimental and numerical predictions of

the touchdown point and peak soil reaction are observed to follow similar trends. This

result confirms that it is possible to back-calculate an estimate of the touchdown point

and distribution of soil reaction that occurred during an experiment, given an array of

measured bending moments and the load required to lift the pipe.

8.6.2 Cyclic test

A riser will be subjected to many cycles of loading throughout its lifetime. The influence of

cycling on the overall model response and the possibility of trench formation was assessed

by imposing a series of cyclic motions at the actuator in the form of a sine wave. Details

of the amplitudes, normalised by the pipe diameter, frequencies and number of cycles

imposed are detailed in Table 8.2. The minimum pipe invert elevation was equal to zero

(i.e. the soil surface) for all cyclic amplitudes. The maximum pipe uplift was restricted to

Table 8.3: Summary of calculated soil bearing pressure distribution parameters

Actuator uplift,w/D [−]

Bearing pressure distribution parameters

xTDP A B C D(

×10−3) (

×10−3)

0.1 640 3.50 1.5 3.42 1.470.5 1842 3.65 1.5 3.57 1.451.0 2700 3.25 1.5 3.17 1.401.5 3423 3.25 1.6 3.18 1.442.0 3837 3.40 1.6 3.35 1.422.5 4274 4.00 1.6 3.96 1.423.0 4576 3.49 1.5 3.46 1.31

8-16


Actuator load, P [N]

Pip

ein

vert

elev

atio

nat

actu

ator

,w

/D[-]

Bending moment [Nm]

Pip

ein

vert

elev

atio

nat

actu

ator

,w

/D[-]

ExperimentalABAQUS

Experimental

ABAQUS

(a) (b)

Phase 1:

lift up

Phase 2:

lay down

BM1

BM2

BM3

BM4BM5

-100 0 100 200 3000 50 100 150 200 2500

0.5

1

1.5

2

2.5

3

0

0.5

1

1.5

2

2.5

3

Figure 8.11: Comparison of ABAQUS and experimental (a) actuator load and (b) bendingmoment throughout monotonic lift up/lay down test on medium dense sandbed

8-17



Pip

ein

vert

elev

atio

n,w

/D[-]


Ben

din

gm

omen

t[N

m]

ABAQUS displaced shape

Experimental displacement readings

(a)

(b)

Pipe invert elevation

at actuator, w/D = 3

ABAQUS bending moment diagram

Experimental bending moment readings

Pipe invert elevation

at actuator, w/D = 1

0 1000 2000 3000 4000 5000 6000 7000 8000

0 1000 2000 3000 4000 5000 6000 7000 8000

-50

0

50

100

150

200

250

300

-0.5

0

0.5

1

1.5

2

2.5

3

Figure 8.12: Comparison of ABAQUS and experimental (a) displaced shape and (b) bend-ing moment from monotonic test on medium dense sand bed for 1 and 3 pipediameters actuator uplift

8-18


Touchdown point, xTDP [mm]

Pip

ein

vert

elev

atio

nat

actu

ator

,w

/D[-]

Peak soil reaction / pipe weight [-]

Pip

ein

vert

elev

atio

nat

actu

ator

,w

/D[-]

Experimental

ABAQUS

Experimental

ABAQUS

(a) (b)

1 1.5 2 2.5 30 2000 4000 60000

0.5

1

1.5

2

2.5

3

0

0.5

1

1.5

2

2.5

3

Figure 8.13: Comparison of ABAQUS and calculated experimental touchdown point andpeak soil reaction

three diameters to ensure the pipe remained submerged throughout the range of imposed

vertical displacement. The frequencies adopted in the cyclic test were not intended to

replicate realistic behaviour expected in field conditions. The frequencies were reduced

with increasing amplitude, due to limitations with the actuation system.

The soil sample was prepared by fluidising the sand by applying upward hydraulic

gradients via the pumping system. As the pumping system resulted in vigorous surges of

water to exit the outlets and travel up through the sample, once the pump was turned

off, the flow of water in the flume meant the sand settled with slight undulations in the

surface. Therefore, when the pipe was lowered into the flume, there were areas where the

pipe invert was not in contact with the soil, and ‘free spanned’ slightly between zones of

mounded sand. This was circumvented by very briefly turning on the pumping system

once again with the pipe resting on the sand, which caused an amount of settlement of the

pipe. The result was a relatively uniformly embedded pipe with an average embedment

of 0.17 diameters. The relative density of the sand sample was calculated as 28% and

was therefore classified as loose. The profile of the pipe prior to and after commencement

of the cyclic test is presented in Figure 8.14. The profile was obtained by measuring the

distance from the water surface to the top of the pipe at 500 mm increments along the

pipe.

Figure 8.15 and Figure 8.16 show the envelopes of the maximum and minimum actuator

support loads, bending moments and pipe invert elevations that were recorded throughout

the cyclic test. Shown for comparison in broken lines are the values observed in the

8-19


monotonic test at a pipe uplift corresponding to the relevant cyclic amplitude.

It can be seen in Figure 8.15a that after the first lift-up and lay-down cycle, a significant

negative load (compressive) at the actuator of approximately 100 N was recorded as the

pipe was returned to its initial position. This was likely due to backfilling of loose soil into

the void left by the pipe as it was first lifted which meant that the pipe invert encountered

resistance at a slightly higher elevation upon re-laying. The very high stiffness or rate of

change of actuator load as the pipe invert elevation approaches the soil surface observed

in Figure 8.11a explains the relatively large load required to return the pipe to its original

elevation and the scatter of the minimum recorded load value with cycling. The envelope

of the maximum actuator load recorded during cycling does not vary considerably when

compared to the monotonic results.

Plots b–f of Figure 8.15 show the envelopes of the maximum and minimum bending

moments recorded at the locations of the five strain gauges throughout the cyclic test. A

similar scatter to that observed in the minimum actuator load is apparent in the envelope

of minimum bending moment recorded by strain gauge BM1. Negative (hog) bending

moments are also observed in the minimum envelope of BM1, which are linked to the

downward actuator loads recorded as the pipe returned to its original elevation. The en-

velopes of the maximum bending moment for gauges BM1, BM2 and BM3 do not show

significant differences to the monotonic results, while the maximum envelope for gauge

BM4 shows that larger bending moments were recorded with cycling when compared to

the monotonic results. Gauges BM2 and BM3 generally recorded the largest variation

between the maximum and minimum bending moment envelopes throughout cycling and

would therefore be identified with the critical fatigue region along the model riser. The

strain gauge furthest from the actuator, BM5, recorded very little variation between the

maximum and minimum envelopes and, in general, recorded more negative bending mo-

ments as the cycling progressed and exceeded the values observed during the monotonic

test. The minimum envelopes of BM2, BM3 and BM4 in general recorded positive bending

moments throughout cycling.


Ele

vati

on[m

m]

Draw wire displacement sensor readings

Pipe invert - initial

Pipe invert - after cycling

0 1000 2000 3000 4000 5000 6000 7000 8000-15

-10

-5

0

5

10

15

Figure 8.14: Pipe profile at the beginning and end of cyclic test

8-20


Cycle

Ver

tica

llo

adat

actu

ator

,P

[N]

Cycle

Ben

din

gm

omen

t[N

m]

Cycle

Ben

din

gm

omen

t[N

m]

Cycle

Ben

din

gm

omen

t[N

m]

Cycle

Ben

din

gm

omen

t[N

m]

Cycle

Ben

din

gm

omen

t[N

m]

Cyclic maximum

Cyclic minimum

Monotonic maximum

Monotonic minimum

(a) (b)

(c) (d)

(e) (f)

BM1

BM2 BM3

BM4

BM5

0 3000 6000 9000 12000 150000 3000 6000 9000 12000 15000

0 3000 6000 9000 12000 150000 3000 6000 9000 12000 15000

0 3000 6000 9000 12000 150000 3000 6000 9000 12000 15000

-20

-15

-10

-5

0

5

-30

0

30

60

90

120

150

-50

0

50

100

150

200

250

300

0

50

100

150

200

250

-50

0

50

100

150

200-250

-125

0

125

250

Figure 8.15: (a) Envelope of maximum/minimum vertical load at actuator and envelopesof maximum/minimum bending moment at (b) BM1, (c) BM2, (d) BM3, (e)BM4 and (f) BM5 throughout cycling

8-21


Figure 8.16 shows the envelope of the maximum and minimum pipe elevations recorded

throughout cycling by the actuator and the four draw wire displacement sensors, measured

relative to the profile of the pipe prior to commencement of the test. For DW1 — the

draw wire sensor located nearest to the actuator — both the maximum and minimum

envelopes of pipe elevation show a negligible difference to the monotonic results. Cycling

also appeared to have little effect on the maximum and minimum elevation of the pipe

at this location, which is expected due to the proximity of the draw wire sensor to the

actuator. Because DW2 was not used in the monotonic experiment, the envelopes at DW2

could not be compared to monotonic results. However, cycling did appear to have a small

effect on the maximum and minimum envelopes of positions at this location and the pipe

can be observed to settle slightly. This settlement behaviour is also seen in the envelopes

of DW3 and DW4. The largest final settlement of almost 0.1 diameters was recorded by

draw wire sensor DW3 which was located 3750 mm from the actuator; approximately half

way along the pipe. The final displacement readings are summarised and compared to the

initial pipe profile in Figure 8.14.

The source of the settlement observed in the data recorded by the draw wire displace-

ment sensors was likely due to hydrodynamic ‘jetting’ effects as the pipe was laid down

onto the soil. This issue was touched on by Cathie et al. (2005) and Clukey et al. (2008)

and is important as trench shape has been shown to influence fatigue life assessments (see

for example, Bridge and Howells, 2007; Clukey et al., 2007). The erosion of soil as water

is forced out of the space between the pipe and soil surface can lead to progressive trench

formation in very soft, remoulded clays. This effect also applies here as the very small

particle size of the fine sand used in the experiment requires a low critical fluid velocity

to induce scour. This was confirmed visually by observation of the transportation of sand

particles by the flow of water beneath the pipe as it was laid onto the soil.

Figure 8.17 shows an example of the data recorded by a water pressure transducer

throughout a period of cycling. Here, ‘excess water pressure’ is defined as the hydrostatic

pressure at the location of the transducer subtracted from the recorded total water pres-

sure. It can be seen that positive excess water pressures were generated as the pipe invert

was lowered into the trench. Upon lifting of the pipe, the excess water pressure imme-

diately recorded negative pressure or suction, before decaying with further uplift of the

pipe. While the excess water pressures recorded were small (approximately 0.05 kPa), the

response was very repeatable with similar peak pressures recorded over a large number of

cycles.

The soil deformation after cycling is shown in Figure 8.18. The lateral extent of

deformation can be seen to increase with proximity to the actuator, where pipe velocities

were largest. This follows the description of trenches in the field investigated by remote

operated vehicle surveys as reported by Bridge and Howells (2007). The soil deformation

further confirms the dependency of trench formation on hydrodynamic ‘jetting’ effects.

8-22


Cycle Cycle

Cycle Cycle

Cycle

Pip

ein

vert

elev

atio

n,w

/D[-]

Pip

ein

vert

elev

atio

n,w

/D[-]

Pip

ein

vert

elev

atio

n,w

/D[-]

Pip

ein

vert

elev

atio

n,w

/D[-]

Pip

ein

vert

elev

atio

n,w

/D[-]

Cyclic maximum

Cyclic minimum

Monotonic maximum

Monotonic minimum

(a) (b)

(c) (d)

(e)

Actuator DW1

DW2 DW3

DW4

0 3000 6000 9000 12000 15000

0 3000 6000 9000 12000 150000 3000 6000 9000 12000 15000

0 3000 6000 9000 12000 150000 3000 6000 9000 12000 15000

-0.03

-0.02

-0.01

0

0.01

-0.1

-0.05

0

0.05

0.1

-0.15

0

0.15

0.3

0.45

0.6

0.75

-0.25

0

0.25

0.5

0.75

1

1.25

1.5

0

0.5

1

1.5

2

2.5

3

Figure 8.16: Envelope of maximum and minimum pipe invert elevations at (a) actuatorand position transducers (b) DW1, (c) DW2, (d) DW3 and (e) DW4 through-out cycling

8-23


Excess water pressure [kPa]

Pip

ein

ver

tel

evat

ion,w

/D[-]

Generation of positive

excess water pressure as

pipe lays into trench

Generation and

decay of negative

excess water

pressure as pipe

lifts out of trench

-0.06 -0.04 -0.02 0 0.02 0.04 0.06-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

Figure 8.17: Example of excess water pressure recorded during cycling

8-24


(a)

(b)

Figure 8.18: Soil deformation after cycling

8-25


8.7 Conclusions

This paper has presented the first controlled experiment of a riser-soil interaction prob-

lem in the laboratory exploring three-dimensional effects. Instrumentation was used to

quantify riser performance, trench formation and the development of excess water/pore

pressures. A simple methodology was outlined for the back-calculation of the touchdown

point and distribution of bearing pressure with pipe uplift to compare to 2D test results.

The results from the numerical analysis compared favourably to the monotonic experi-

mental results. The data gathered form the basis for benchmarking numerical studies as

well as for providing a benchmark for further testing on clay soils, where suctions and

deformations are expected to be significant.

The observations include that large amplitude displacement controlled uplift induces

different behaviour than typically imposed in two-dimensional displacement controlled

tests due to the three-dimensional ‘overstressing’ effect. The cycling caused a negligible

effect in the test conducted, which for a light pipe on sand, was to be broadly expected.

Trench formation was observed, and this appeared to be due to hydrodynamic ‘jetting’

effects as the pipe moved in and out of the trench and can attributed to the low critical

velocity for scouring for the fine sand used in the experiments. This effect would be

much more significant in the field where many more cycles would be applied. Trench

formation is significant as it has been shown that the geometry of the trench can influence

fatigue life predictions. Current pipe-soil interaction models used in the analysis of SCRs

cannot replicate the trench formation observed in the cyclic experiments. Further testing

in this facility could be used to calibrate a model that could quantify trench evolution as

a function of pipe velocity.

8-26


References




Bridge, C. D. and Howells, H. A. (2007). Observations and modeling of steel catenaryriser trenches. In Proc. 17th International Offshore and Polar Engineering Conference,pages 803–813, Lisbon, Portugal.

Bridge, C. D., Howells, H. A., Toy, N., Parke, G., and Woods, R. (2003). Full scale modeltests of a steel catenary riser. In International Conference Fluid Structure Interaction2003, Cadiz, Spain.





Hodder, M. S., White, D. J., and Cassidy, M. J. (2009). Effect of remolding and reconsoli-dation on the touchdown stiffness of a steel catenary riser: observations from centrifugemodeling. In Proc. 41st Offshore Technology Conference, Houston, USA. [presented asChapter 6 of this thesis].

Hu, H. J. E., Leung, C. F., Chow, Y. K., and Palmer, A. C. (2009). Centrifuge modelstudy of SCR motion in touchdown zone. In Proc. International Conference on Ocean,Offshore and Arctic Engineering, Honolulu, USA.

Langford, T. and Aubeny, C. P. (2008). Model tests for steel catenary riser in marine clay.In Proc. 40th Offshore Technology Conference, Houston, USA.

Lenci, S. and Callegari, M. (2005). Simple analytical models for the J-lay problem. ActaMechanica, 178:23–39.

Lund, K. H. (2000). Effect of increase in pipeline soil penetration from installation. InProc. International Conference on Offshore Mechanics and Arctic Engineering, NewOrleans, USA.

8-27


Martin, C. M. (2005). Exact bearing capacity calculations using the method of character-istics. In Proc. 11th International Conference of IACMAG, volume 4, pages 441–450,Turin, Italy.

Palmer, A. C. (2008). Touchdown indentation of the seabed. Applied Ocean Research,30:235–238.

Pesce, C. P., Aranha, J. A. P., and Martins, C. A. (1998). The soil rigidity effect in thetouchdown boundary-layer of a catenary riser: static problem. In Proc. 8th InternationalOffshore and Polar Engineering Conference, pages 207–213, Montreal, Canada.


Randolph, M. F. and White, D. J. (2008). Pipeline embedment in deep water: processesand quantitative assessment. In Proc. 40th Offshore Technology Conference, Houston,USA.


8-28


8.A Appendix A – Analysis of the Experimental Data

Using the parameters measured in the experiment it is possible to back-calculate the

touchdown point and the distribution of bearing pressure experienced by the soil along

the pipe. The back-calculated distribution of bearing pressure can then be related to

the measured displacements to investigate the vertical load-displacement response for an

‘element’ of pipe. This is important as it can then be compared to results obtained from 2D

element tests conducted using a short section of pipe and to verify the pipe-soil interaction

models developed from pipe element tests.

Using statics, and assuming small displacements, a free body diagram of the physical

model is shown in Figure 8.7. The relationship between a general distribution of bearing

pressure, S(x), and the support reaction at the actuator, P , the pipe self weight, Q, the

pipe length, L, and the distance from the actuator to the touchdown point, xTDP, must

satisfy global equilibrium, such that:

∑

V = 0 = P − QL +

L∫

xTDP

S(x) dx (8.A.1)

and

∑

M = 0 =QL2

2−

L∫

xTDP

xS(x) dx (8.A.2)

where∑

V and∑

M are the sum of the external vertical forces and moments respec-

tively. Here, the sum of external moments about the actuator connection is used.

For a general distribution of bearing pressure below the pipe, S(x), the internal bending

moment, M(x), can be written as:

M(x) = Px −Qx2

2+

∫∫

S(x) dx (8.A.3)

For the form of bearing pressure distribution in Equation 8.1, the integrals required in

Equations 8.A.1 - 8.A.3 are:

L∫

xTDP

S(x) dx = (A − C) (L − xTDP)−A

B

(

1 − e−B(L−xTDP))

+C

D

(

1 − e−D(L−xTDP))

(8.A.4)

8-29


L∫

xTDP

xS(x) dx =1

2B2D2

[

B2D2 (A − C)(

L2 − x2TDP

)

+ 2AD2(

(BL + 1) e−B(L−xTDP) − BxTDP − 1)

− 2CB2(

(DL + 1) e−D(L−xTDP) − DxTDP − 1)

]

(8.A.5)

∫∫

S(x) dx =H (x − xTDP)

2B2D2

[

B2D2 (A − C)(

x2 + x2TDP

)

+ 2AD2(

1 − e−B(x−xTDP) − B (xTDPxB + x − xTDP))

− 2CB2(

1 − e−D(x−xTDP) − D (xTDPxD + x − xTDP))

]

(8.A.6)

The bending moments at the positions of the bending strain gauges were used to fit

a function of the form of Equation 8.A.3 such that the residuals between the predicted

bending moments and the actual values were minimised, subject to the constraints of

Equations 8.A.1 and 8.A.2 and using the bearing pressure distribution function of Equa-

tion 8.1.

8-30

9Concluding Remarks

9.1 Introduction

This thesis investigates various geotechnical aspects of the interaction of pipelines and

risers with the seabed and has contributed to the field through research of the following

areas:

1. combined loading response of pipelines;

2. the effects of cyclic loading on pipe-soil interaction, and;

3. physical modelling of the touchdown zone of a steel catenary riser.

This chapter will present the outcomes of the thesis followed by recommendations for

future work.

9.2 Original Contributions and Main Findings

This section will present the contributions and findings of the thesis in line with the specific

areas of research and associated aims outlined in Chapter 1.

9.2.1 Combined loading response of pipelines

A displacement hardening ‘force-resultant’ model was outlined in Chapter 2. It can be used

to predict the response of a pipe subjected to combined vertical and horizontal loading on

soft clay soil in undrained conditions. The model can function as a boundary condition el-

ement between the pipeline and soil in a structural analysis. The components of the model

were primarily derived using data gathered from a suite of experiments conducted within

the University of Western Australia’s drum centrifuge. A simple elasto-plastic model was

proposed, where the response for load combinations inside the vertical-horizontal load

yield surface are assumed to be fully elastic. The hardening law adopted for the model

was shown to predict well the purely vertical penetration response observed experimentally

9-1


from conditions of shallow embedment through to deep penetration. Relationships defin-

ing the variation of uplift and horizontal capacity with pipe penetration were proposed and

were identified to become independent of penetration after 4 and 3.5 pipe diameters em-

bedment respectively. The predictive capability of the model was demonstrated through

numerical retrospective simulation of several combined loading pipe-soil experiments using

a purpose written FORTRAN program. Good agreement was generally evident between

the experimental observation and the numerical prediction.

With a focus on the behaviour of shallowly embedded pipelines, Chapter 3 presented

alternative components of the model described in Chapter 2 for applications where an

assumption of zero pipe uplift capacity is necessary. At conditions of shallow pipe embed-

ment, resistance to pipe uplift requires tensile stress capacity at the pipe-soil interface.

Alternative model components were presented because conservatism may warrant the ex-

clusion of uplift capacity due to the time dependency of the response or the possibility

of preferential drainage paths to occur along the pipe-soil interface which would break

the required tensile stress capacity. The alternative model components were validated

by numerical retrospective simulation of several shallowly embedded pipeline experiments

conducted on the laboratory floor using soft, overconsolidated clay. Conditions of vertical

load control were assessed, and the model successfully predicted ‘sinking’ or ‘heaving’ of

the pipe depending on the vertical load ratio.

9.2.2 The effects of cyclic loading on pipe-soil interaction

The results from a test which was conducted to investigate the effects of vertical cycling

on pipe-soil response was described in Chapter 4. The experiment was performed using

a short length of riser pipe within the University of Western Australia’s beam centrifuge.

The test was conducted in a soft clay sample with a linearly increasing undrained shear

strength gradient — typical of deep water seabed conditions. A large cyclic amplitude

was imposed to explore the effects of the entrainment of water into the surrounding soil.

This might occur during storm loading of such severity that the pipe breaks away from the

seabed surface. A cyclic site investigation was conducted using a T-bar penetrometer to

characterise the remoulded undrained shear strength of the soil to allow for the comparison

of the degraded pipe-soil resistance and the soil sensitivity magnitudes. A steady cyclic

response was observed after 5–10 cycles and the cyclic pipe-soil resistance degraded by

a factor of 7.5 relative to the initial penetration resistance. Using the soil sensitivity

of 2.4 calculated from the cyclic site investigation, the degradation of pipe-soil stiffness

was over three times that predicted by soil sensitivity alone and can be attributed to the

entrainment of water into the soil. While significant uplift resistance (or ‘suction’) was

recorded during the initial extraction, rapid degradation was observed to occur over only

2–3 cycles. During large-amplitude cycling, the steady pattern of pipe-soil response was

observed to be ‘banana-shaped’ with an upwards pipe-soil contact force recorded even as

the riser pipe was extracted.

9-2

Concluding Remarks

Continuing the soil strength degradation theme explored experimentally in Chapter 4,

an analytical framework was presented in Chapter 5 which can be used to predict the de-

graded operative undrained shear strength experienced by a cylinder subjected to cycles

of general vertical motion in clay soil. The framework uses soil sensitivity and ductility

parameters which can be obtained from site investigation data to describe the soil soften-

ing response. The gradual reduction of undrained shear strength of a soil element from

an intact to fully remoulded state is captured by linking the soil strength degradation to

the incremental accumulation of ‘damage’. By associating the damage increase of a soil

element with the proximity of the element to the cylinder according to a damage influ-

ence function, a one-dimensional spatial variation of damage, and therefore, soil strength

throughout the depth of the soil sample is achieved. The weighted average soil strength in

the vicinity of the cylinder is calculated using a strength influence function. Application of

the framework was demonstrated by numerically simulating a cyclic site investigation test

with a cylindrical tool. The simulated response showed close agreement against experi-

mental observations with the gradual reduction in operative soil strength, unload-reload

resistance after a change in direction of the cylinder, and the increase in resistance as the

cylinder experienced less damaged soil well predicted.

The results from a suite of tests conducted to investigate the effects of various forms of

vertical cyclic loading on pipe-soil response were presented in Chapter 6. The experiments

were again performed using a short length of riser pipe within the University of Western

Australia’s beam centrifuge using a soft clay sample with a linearly increasing undrained

shear strength gradient. A wide range of tests were performed, investigating the effects

of large and small-amplitude cycling under both load and displacement controlled con-

ditions. The effects of reconsolidation were explored by imposing pause periods between

episodes of robust loading — similar to a field condition of periods of relative inactiv-

ity between successive storm seasons. The results were processed into a ‘secant stiffness

ratio’ for adoption within a linear idealisation of the unload-reload response. The ‘first

unload’ stiffnesses recorded during the initial extraction of the large-amplitude displace-

ment controlled tests agreed well with recommendations found in the current literature.

A hyperbolic stiffness model captured the unload response well over a large range of pipe

uplift magnitudes. During large-amplitude cycling, the stiffness dropped to approximately

30% of the first unload value after reaching a steady, remoulded state within 10 cycles.

After two additional episodes of large-amplitude cycling with intervening reconsolidation

periods of 1 year between episodes, the remoulded stiffness increased by 50% relative to

the remoulded stiffness observed in the first cyclic episode. A novel site investigation was

perfomed where a T-bar penetrometer was cycled in the soil until fully remoulded condi-

tions were observed before pausing, allowing the dissipation of excess pore pressure, and

the process repeated. After two periods of full reconsolidation, the remoulded undrained

shear strength approximately doubled. The increase of steady pipe-soil secant stiffness

during robust loading after reconsolidation periods was shown to generally follow the

trend of remoulded undrained shear strength increase observed in the site investigation

9-3


experiment. During the early phase of many small-amplitude cycles, a stiffness 75% of

the first unload value was observed, while after many cycles (approximately 1.5 years) this

value approximately doubled.

The analytical framework presented in Chapter 5 was extended in Chapter 7 to include

the recovery of soil strength through reconsolidation observed experimentally in Chapter 6.

For the normally consolidated or lightly overconsolidated clays typical of seabed conditions

in deep offshore environments, reconsolidation generally induces a reduction in specific vol-

ume and hence an increase in undrained shear strength. The framework is presented in

a ‘critical state’ style — where the behaviour of a soil element is dictated by the current

effective stress and specific volume. The degradation of undrained shear strength due to

the accumulation of ‘damage’ presented in Chapter 5 is replaced by a reduction in effec-

tive stress via an increase of excess pore pressure generated during undrained loading. By

linking the excess pore pressure generation to a dissipation model, the change in specific

volume with time can be defined and reconsolidation effects included. Application of the

framework was demonstrated by numerically simulating a cyclic site investigation test

with intervening pause periods between cyclic episodes using a cylindrical tool. The simu-

lated response showed close agreement against experimental observations with the gradual

reduction in operative soil strength within a cyclic episode and the recovery of strength

and ultimate increase of remoulded undrained shear strength through reconsolidation after

periods of inactivity well predicted.

9.2.3 Physical modelling of the touchdown zone of a steel catenary riser

The details of a novel experimental apparatus developed for the investigation of the re-

sponse of the lower section of a steel catenary riser in the touchdown zone were presented

in Chapter 8. The purpose was to develop an apparatus which could be used to explore the

overall response of the riser in the touchdown zone with controlled model seabed soil con-

ditions and to gather data to validate pipe-soil interaction models derived from the more

traditionally performed two-dimensional experiments using a short length of model riser

pipe. The apparatus consisted of a 7.65 m long 110 mm diameter PVC pipe instrumented

to measure the bending moment, vertical displacement and water pressure at several po-

sitions along the pipe. A computer-controlled actuation system provided displacement

to one end of the pipe. The displacement and vertical load to lift the pipe were also

recorded at the actuator. The results from monotonic and cyclic experiments performed

on sandy soil were presented and also compared to predictions from a simple numerical

model. During the cyclic experiment, trench formation was observed and quantified us-

ing the displacement measurements along the pipe. A simple analysis methodology was

outlined for the back calculation of the distribution of vertical reaction throughout the

touchdown zone using the vertical load required to lift the pipe and the array of bending

moment measurements.

9-4

Concluding Remarks

9.2.4 Summary

The contributions to the field, findings and associated implications for design arising from

the research conducted for this thesis are summarised as follows.

1. A coupled vertical-horizontal pipe-soil interaction model for the application of a

pipeline on soft clay in undrained conditions was presented. Model components to

either include or exclude pipe uplift capacity were given. The model can be ‘attached’

to structural elements in a numerical analysis and function as a boundary condition

containing the geotechnical behaviour linking the pipe-soil interaction forces and

displacements within the element.

2. During large-amplitude vertical cycling of an unburied pipe in soft clay — repre-

sentative of storm loading conditions where the pipe breaks away from the seabed

— resistance to uplift (or ‘suction’) was observed to decay rapidly. Therefore, pipe-

soil interaction models should not include suction capacity in conditions of extreme

loading which result in pipe displacement magnitudes such that breakaway occurs.

3. Pipe breakaway allowing the entrainment of water into the soil was found to exacer-

bate pipe-soil resistance degradation. The steady-state degraded pipe-soil stiffness

during large-amplitude vertical cycling of a pipe in soft clay was over three times

that predicted by soil sensitivity alone.

4. The vertical pipe-soil response is a superposition of a soil shear strength component

— which acts in a direction to oppose the pipe motion, and therefore, dictates the

width of the unload-reload hysteresis loop — and a soil self-weight (or soil buoyancy)

component — which acts upwards on the pipe. In very soft soils, such as those

characteristic of seabed conditions associated with large-amplitude cycling, the pipe-

soil response is dominated by the soil self-weight component of resistance. The

dominance of the soil self-weight component causes the pipe-soil interaction force

to remain compressive, acting upwards on the pipe even as the pipe extracts from

very soft soil. The influence of surface heave significantly enhances soil self-weight

resistance and should be accounted for in an accurate representation of vertical pipe-

soil response in very soft soil conditions.

5. Results from a suite of tests investigating pipe-soil response when subjected to var-

ious vertical cyclic loading conditions were processed into a ‘secant stiffness ratio’

for adoption within a linear idealisation of vertical unload-reload pipe-soil response.

For a given pipe uplift magnitude, the secant stiffness varied by a factor of over four

across the tests depending on loading conditions. The wide variability of stiffness ob-

served across the experimental programme illustrates that accounting for the change

in soil strength induced by loading conditions throughout the lifetime of the riser

is essential. The experimental observations indicate that the effects of reconsolida-

tion can compensate entirely for the softening effects of remoulding and potentially

9-5


cause the stiffness to rise above that calculated using current prediction methods

when using an in situ value of seabed undrained shear strength. The calculation of

an unload-reload stiffness appropriate for a given pipe displacement amplitude rel-

ative to the seabed strength conditions obtained from initial site investigation data

without consideration given to remoulding and reconsolidation effects could result

in inaccurate fatigue life predictions.

6. The tendency for pipe-soil interaction stiffness to recover during robust loading con-

ditions subsequent to reconsolidation periods followed the increase of undrained shear

strength observed during a novel site investigation experiment conducted using a T-

bar penetrometer. This relationship indicates that results from site investigation

tests performed specifically to quantify undrained shear strength variation induced

from reconsolidation effects could be used to provide an estimate of potential pipe-soil

interaction stiffness increase to occur as a function of loading conditions throughout

the service life of the riser.

7. Analytical frameworks were presented which can be used to calculate the change

from in situ soil strength conditions to a one-dimensional spatial variation of soil

strength through the depth of a soil sample as a result of loading induced from

general vertical displacement of a cylinder. The operative soil strength experienced

by the cylinder is calculated using a weighted average of the current soil strength in

the cylinder’s vicinity. Examples of potential applications of the frameworks include

the quantification of additional pipe embedment due to dynamic laying effects which

soften the surrounding seabed soil or the tendency for pipe-soil stiffness to vary due

to the accumulation and subsequent dissipation of excess pore pressure through

reconsolidation.

8. An instrumented model pipeline was developed for the investigation of the response

of the lower section of a steel catenary riser in the touchdown zone. Trenching

of the model riser was observed to occur via a hydrodynamic ‘jetting’ mechanism

as water was expelled from the gap between the pipe and seabed and appeared

proportional to pipe velocity. A simple analysis methodology was described for the

back-calculation of the distribution of vertical pipe-soil bearing reaction from the

measured experimental data. The calculated soil reaction distribution facilitates

a possible comparison of the vertical pipe-soil force experienced by an ‘element’

of pipe during the experiment against results obtained from two-dimensional pipe-

soil testing performed using a short length of model riser pipe. The comparison

provides a methodology for validating pipe-soil interaction models derived from two-

dimensional testing.

9-6

Concluding Remarks

9.3 Recommendations for Future Work

The following are possible avenues to further develop the findings of this thesis.

1. The combined vertical-horizontal pipe-soil interaction model presented in Chapters 2

and 3 could be refined to include stiffness degradation for load combinations inside

the yield surface using a boundary or multiple surface model approach. This would

extend the predictive capability of the model to cyclic loading conditions.

2. The model presented in Chapters 2 and 3 could also be extended to include large

lateral displacement response. Repetitive lateral motions of the pipe can cause soil

berms to form. Incorporating the interaction of soil berms with the pipe, including

the ability to quantify the evolution and track the relative location of a berm as a

function of the lateral pipe motion, would enhance the capability of the model.

3. The analytical frameworks presented in Chapters 5 and 7 which capture the spatial

variation of soil strength caused by general vertical displacement of a cylinder could

be incorporated into pipe-soil interaction models, such as those presented by Bridge

et al. (2004), Aubeny and Biscontin (2008) and Randolph and Quiggin (2009). By

substituting the in situ or remoulded undrained shear strength input parameter

required in the pipe-soil interaction model with an operative strength value which is

calculated using an average of the current soil strength distribution in the vicinity

of the riser or pipe — which is a function of loading history — more accurate

analyses could be performed. The use of refined pipe-soil interaction models into an

integrated fluid-soil-structure analysis of the system would allow more accurate riser

fatigue life predictions to be made. This would provide further confidence in a SCR

design. Investigation of the effect of these models on structural fatigue life would

also be of interest.

4. The experimental apparatus described in Chapter 8 could be used to perform testing

using a soft clay seabed. Using the back-calculated distribution of pipe-soil reaction

along the length of the model riser, the vertical load-displacement history at the

locations of each of the displacement transducers could be experimentally derived.

A two-dimensional pipe-soil experiment could then be performed where the displace-

ment history recorded during the ‘overall behaviour’ experiment is applied to a short

length of pipe in the same soil sample. This would allow for the direct comparison of

the vertical pipe-soil load recorded during the two-dimensional experiment against

the back-calculated load recorded during the ‘overall behaviour’ experiment. These

results could be used to determine the influence of effects not able to be captured in

two-dimensional tests such as the scour of seabed material caused by the longitudinal

‘jetting’ of water beneath the pipe.

5. The apparatus described in Chapter 8 could also be used to investigate trench evo-

lution as a function of vertical pipe velocity. The actuator could be used to apply

9-7


various cyclic frequencies and amplitudes to the end of the model riser. Using the

displacement transducers along the length of the model riser, trench formation and

pipe velocity could be recorded and related.

6. SCR field data would provide insight into the bevahiour of risers in the field and

allow further development and calibration of riser-soil interaction models.

7. The application of pipe-soil interaction models is influenced by the nature of loading.

Geotechnical engineers would gain further understanding of SCR loading regimes by

working closely with riser engineers.

9-8

Concluding Remarks

References




9-9

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