Geotechnical analysis of offshore pipelines and steel ...Geotechnical analysis of offshore...
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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
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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.
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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.
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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
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Geotechnical analysis of offshore pipelines and steel catenary risers
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
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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
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Geotechnical analysis of offshore pipelines and steel catenary risers
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
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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
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Geotechnical analysis of offshore pipelines and steel catenary risers
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
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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.
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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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
David J. White and Professor Mark J. Cassidy. The paper is published as:
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;
• wrote the majority of the paper in collaboration with Professor White and Professor
Cassidy.
Paper 5
The fifth paper is presented as Chapter 6 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. (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;
• wrote the majority of the paper in collaboration with Professor White and Professor
Cassidy.
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Geotechnical analysis of offshore pipelines and steel catenary risers
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;
• wrote the majority of the paper in collaboration with Professor White and Professor
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.
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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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
Geotechnical analysis of offshore pipelines and steel catenary risers
(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
General Introduction
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
General Introduction
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
General Introduction
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
1-10
General Introduction
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
1-12
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
A Plasticity Model for Predicting the Vertical and Lateral Behaviour of Pipelines in Clay Soils
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
A Plasticity Model for Predicting the Vertical and Lateral Behaviour of Pipelines in Clay Soils
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.
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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
A Plasticity Model for Predicting the Vertical and Lateral Behaviour of Pipelines in Clay Soils
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
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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
Curve fitting parameterCurve fitting parameter
-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
Curve fitting parameterCurve fitting parameter
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
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A Plasticity Model for Predicting the Vertical and Lateral Behaviour of Pipelines in Clay Soils
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
Geotechnical analysis of offshore pipelines and steel catenary risers
Pipe invert embedment, w/D [-]
Bea
ring
capac
ity
fact
or,N
c[-]
Pipe invert embedment, w/D [-]
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
A Plasticity Model for Predicting the Vertical and Lateral Behaviour of Pipelines in Clay Soils
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
Geotechnical analysis of offshore pipelines and steel catenary risers
Pipe invert embedment, w/D [-]
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
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A Plasticity Model for Predicting the Vertical and Lateral Behaviour of Pipelines in Clay Soils
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
A Plasticity Model for Predicting the Vertical and Lateral Behaviour of Pipelines in Clay Soils
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
Geotechnical analysis of offshore pipelines and steel catenary risers
Pipe invert embedment, w/D [-]
Pea
khor
izon
talca
pac
ity,
h0
=H
max/V
0[-]
Pipe invert embedment, w/D [-]
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
A Plasticity Model for Predicting the Vertical and Lateral Behaviour of Pipelines in Clay Soils
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
Geotechnical analysis of offshore pipelines and steel catenary risers
Normalised vertical load, V/V0 [-]
Nor
mal
ised
hor
izon
tallo
ad,H
/V0
[-]
Normalised vertical load, V/V0 [-]
Nor
mal
ised
hor
izon
tallo
ad,H
/V0
[-]
Normalised vertical load, V/V0 [-]
Nor
mal
ised
hor
izon
tallo
ad,H
/V0
[-]
Normalised vertical load, V/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
A Plasticity Model for Predicting the Vertical and Lateral Behaviour of Pipelines in Clay Soils
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
A Plasticity Model for Predicting the Vertical and Lateral Behaviour of Pipelines in Clay Soils
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
Geotechnical analysis of offshore pipelines and steel catenary risers
Normalised vertical load, V/su0D [-]
Nor
mal
ised
hor
izon
tallo
ad,H
/su0D
[-]
Normalised vertical load, V/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
A Plasticity Model for Predicting the Vertical and Lateral Behaviour of Pipelines in Clay Soils
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
A Plasticity Model for Predicting the Vertical and Lateral Behaviour of Pipelines in Clay Soils
Horizontal pipe displacement, u/D [-]
Pip
ein
vert
embed
men
t,w
/D[-]
Normalised vertical load, V/V0 [-]
Pip
ein
vert
embed
men
t,w
/D[-]
Horizontal pipe displacement, u/D [-]
Nor
mal
ised
hor
izon
tallo
ad,H
/V0
[-]
Normalised vertical load, V/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
Geotechnical analysis of offshore pipelines and steel catenary risers
Horizontal pipe displacement, u/D [-]
Pip
ein
vert
embed
men
t,w
/D[-]
Normalised vertical load, V/V0 [-]
Pip
ein
vert
embed
men
t,w
/D[-]
Horizontal pipe displacement, u/D [-]
Nor
mal
ised
hor
izon
tallo
ad,H
/V0
[-]
Normalised vertical load, V/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
A Plasticity Model for Predicting the Vertical and Lateral Behaviour of Pipelines in Clay Soils
Horizontal pipe displacement, u/D [-]
Pip
ein
vert
embed
men
t,w
/D[-]
Normalised vertical load, V/su0D [-]
Pip
ein
vert
embed
men
t,w
/D[-]
Horizontal pipe displacement, u/D [-]
Nor
mal
ised
hor
izon
tallo
ad,H
/su0D
[-]
Normalised vertical load, V/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
Geotechnical analysis of offshore pipelines and steel catenary risers
Horizontal pipe displacement, u/D [-]
Pip
ein
vert
embed
men
t,w
/D[-]
Normalised vertical load, V/su0D [-]
Pip
ein
vert
embed
men
t,w
/D[-]
Horizontal pipe displacement, u/D [-]
Nor
mal
ised
hor
izon
tallo
ad,H
/su0D
[-]
Normalised vertical load, V/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 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
A Plasticity Model for Predicting the Vertical and Lateral Behaviour of Pipelines in Clay Soils
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
2-32
A Plasticity Model for Predicting the Vertical and Lateral Behaviour of Pipelines in Clay Soils
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.
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.
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.
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.
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.
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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. (1994). Physical and numerical modeling of offshore foundations undercombined loads. DPhil. thesis, The University of Oxford.
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
A Plasticity Model for Predicting the Vertical and Lateral Behaviour of Pipelines in Clay Soils
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. (2001). Geotechnical stability of offshore pipelines in calcareous sand. PhDthesis, School of Civil and Resource Engineering, The University of Western Australia.
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
2-36
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
Undrained Response of Shallow Pipelines Subjected to Combined Loading
Pipe invert embedment, w/D [-]
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
Geotechnical analysis of offshore pipelines and steel catenary risers
Normalised vertical load, V/V0 [-]
Nor
mal
ised
hor
izon
tallo
ad,H
/V0
[-]
Normalised vertical load, V/V0 [-]
Nor
mal
ised
hor
izon
tallo
ad,H
/V0
[-]
Normalised vertical load, V/V0 [-]
Nor
mal
ised
hor
izon
tallo
ad,H
/V0
[-]
Normalised vertical load, V/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
Undrained Response of Shallow Pipelines Subjected to Combined Loading
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
Undrained Response of Shallow Pipelines Subjected to Combined Loading
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
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 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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
Undrained Response of Shallow Pipelines Subjected to Combined Loading
Horizontal pipe displacement, u [mm]
Pip
ein
vert
embed
men
t,w
[mm
]
Vertical load, V [N]
Pip
ein
vert
embed
men
t,w
[mm
]
Horizontal pipe displacement, u [mm]
Hor
izon
tallo
ad,H
[N]
Vertical load, V [N]
Hor
izon
tallo
ad,H
[N]
(a) (b)
(c) (d)
SimulationExperiment
SimulationExperiment
SimulationExperiment
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
Geotechnical analysis of offshore pipelines and steel catenary risers
Horizontal pipe displacement, u [mm]
Pip
ein
vert
embed
men
t,w
[mm
]
Vertical load, V [N]
Pip
ein
vert
embed
men
t,w
[mm
]
Horizontal pipe displacement, u [mm]
Hor
izon
tallo
ad,H
[N]
Vertical load, V [N]
Hor
izon
tallo
ad,H
[N]
(a) (b)
(c) (d)
SimulationExperiment
SimulationExperiment
SimulationExperiment
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
Undrained Response of Shallow Pipelines Subjected to Combined Loading
00
30
60
50 100
Vertical load, V [N]
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
Undrained Response of Shallow Pipelines Subjected to Combined Loading
Horizontal pipe displacement, u [mm]
Pip
ein
vert
embed
men
t,w
[mm
]
Vertical load, V [N]
Pip
ein
vert
embed
men
t,w
[mm
]
Horizontal pipe displacement, u [mm]
Hor
izon
tallo
ad,H
[N]
Vertical load, V [N]
Hor
izon
tallo
ad,H
[N]
(a) (b)
(c) (d)
SimulationExperiment
Simulation
Experiment
SimulationExperiment
SimulationExperiment
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
Geotechnical analysis of offshore pipelines and steel catenary risers
Horizontal pipe displacement, u [mm]
Pip
ein
vert
embed
men
t,w
[mm
]
Vertical load, V [N]
Pip
ein
vert
embed
men
t,w
[mm
]
Horizontal pipe displacement, u [mm]
Hor
izon
tallo
ad,H
[N]
Vertical load, V [N]
Hor
izon
tallo
ad,H
[N]
(a) (b)
(c) (d)
SimulationExperiment
Simulation
Experiment
SimulationExperiment
SimulationExperiment
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
Undrained Response of Shallow Pipelines Subjected to Combined Loading
References
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.
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.
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].
Martin, C. M. (1994). Physical and numerical modeling of offshore foundations undercombined loads. DPhil. thesis, The University of Oxford.
Muir Wood, D. (2004). Geotechnical modelling. Spon Press, Oxfordshire, UK.
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. 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.
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.
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. (2001). Geotechnical stability of offshore pipelines in calcareous sand. PhDthesis, School of Civil and Resource Engineering, The University of Western Australia.
3-19
3-20
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
Geotechnical analysis of offshore pipelines and steel catenary risers
Figure 4.2: UWA geotechnical beam centrifuge
Vertical load cell
Section ofriser pipe
Figure 4.3: Model riser pipe
4-4
Centrifuge Modelling of Riser-Soil Stiffness Degradation in the Touchdown Zone of a Steel Catenary Riser
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
Centrifuge Modelling of Riser-Soil Stiffness Degradation in the Touchdown Zone of a Steel Catenary Riser
Undrained shear strength, su [kPa]
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
Centrifuge Modelling of Riser-Soil Stiffness Degradation in the Touchdown Zone of a Steel Catenary Riser
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
Centrifuge Modelling of Riser-Soil Stiffness Degradation in the Touchdown Zone of a Steel Catenary Riser
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
Centrifuge Modelling of Riser-Soil Stiffness Degradation in the Touchdown Zone of a Steel Catenary Riser
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
Centrifuge Modelling of Riser-Soil Stiffness Degradation in the Touchdown Zone of a Steel Catenary Riser
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
Centrifuge Modelling of Riser-Soil Stiffness Degradation in the Touchdown Zone of a Steel Catenary Riser
References
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.
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.
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.
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.
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.
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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. 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.
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
An Analysis of Soil Strength Degradation During Episodes of Cyclic Loading, Illustrated by the T-bar Penetration Test
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
An Analysis of Soil Strength Degradation During Episodes of Cyclic Loading, Illustrated by the T-bar Penetration Test
(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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
An Analysis of Soil Strength Degradation During Episodes of Cyclic Loading, Illustrated by the T-bar Penetration Test
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
An Analysis of Soil Strength Degradation During Episodes of Cyclic Loading, Illustrated by the T-bar Penetration Test
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
An Analysis of Soil Strength Degradation During Episodes of Cyclic Loading, Illustrated by the T-bar Penetration Test
References
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.
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., 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.
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.
Martin, C. M. and Randolph, M. F. (2006). Upper bound analysis of lateral pile capacityin cohesive soil. Geotechnique, 56(2):141–145.
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
5-18
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
Centrifuge Modelling
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
Effect of Remoulding and Reconsolidation on the Touchdown Stiffness of a Steel Catenary Riser: Observations from
Centrifuge Modelling
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
Effect of Remoulding and Reconsolidation on the Touchdown Stiffness of a Steel Catenary Riser: Observations from
Centrifuge Modelling
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
Geotechnical analysis of offshore pipelines and steel catenary risers
Undrained shear strength, su [kPa]
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
Effect of Remoulding and Reconsolidation on the Touchdown Stiffness of a Steel Catenary Riser: Observations from
Centrifuge Modelling
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
Geotechnical analysis of offshore pipelines and steel catenary risers
(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
Effect of Remoulding and Reconsolidation on the Touchdown Stiffness of a Steel Catenary Riser: Observations from
Centrifuge Modelling
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
Effect of Remoulding and Reconsolidation on the Touchdown Stiffness of a Steel Catenary Riser: Observations from
Centrifuge Modelling
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
Geotechnical analysis of offshore pipelines and steel catenary risers
∆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[-]
Change in pipe invert embedment,∆w/D [-]
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
Effect of Remoulding and Reconsolidation on the Touchdown Stiffness of a Steel Catenary Riser: Observations from
Centrifuge Modelling
∆w/D = 0.025
Ksec,cyc,1 = 14.3
Ksec,cyc,2 = 20.8,Ksec,cyc,2
Ksec,cyc,1
= 1.45
Ksec,cyc,3 = 25.3,Ksec,cyc,3
Ksec,cyc,1
= 1.77
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[-]
Change in pipe invert embedment,∆w/D [-]
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
Figure 6.8: Test 2 (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
6-15
Geotechnical analysis of offshore pipelines and steel catenary risers
∆w/D = 0.025
Ksec,cyc,1 = 16.6
Ksec,cyc,2 = 19.4,Ksec,cyc,2
Ksec,cyc,1
= 1.17
Ksec,cyc,3 = 21.8,Ksec,cyc,3
Ksec,cyc,1
= 1.32
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[-]
Change in pipe invert embedment,∆w/D [-]
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
Figure 6.9: Test 3 (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
6-16
Effect of Remoulding and Reconsolidation on the Touchdown Stiffness of a Steel Catenary Riser: Observations from
Centrifuge Modelling
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
Geotechnical analysis of offshore pipelines and steel catenary risers
(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
Effect of Remoulding and Reconsolidation on the Touchdown Stiffness of a Steel Catenary Riser: Observations from
Centrifuge Modelling
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
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
Effect of Remoulding and Reconsolidation on the Touchdown Stiffness of a Steel Catenary Riser: Observations from
Centrifuge Modelling
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
Effect of Remoulding and Reconsolidation on the Touchdown Stiffness of a Steel Catenary Riser: Observations from
Centrifuge Modelling
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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]
Change in pipe invert embedment,∆w/D [-]
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
Effect of Remoulding and Reconsolidation on the Touchdown Stiffness of a Steel Catenary Riser: Observations from
Centrifuge Modelling
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]
Change in pipe invert embedment,∆w/D [-]
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
Effect of Remoulding and Reconsolidation on the Touchdown Stiffness of a Steel Catenary Riser: Observations from
Centrifuge Modelling
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
Effect of Remoulding and Reconsolidation on the Touchdown Stiffness of a Steel Catenary Riser: Observations from
Centrifuge Modelling
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
Effect of Remoulding and Reconsolidation on the Touchdown Stiffness of a Steel Catenary Riser: Observations from
Centrifuge Modelling
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
6-32
Effect of Remoulding and Reconsolidation on the Touchdown Stiffness of a Steel Catenary Riser: Observations from
Centrifuge Modelling
References
Aubeny, C. P. and Biscontin, G. (2008). Interaction model for steel compliant riser onsoft seabed. In Proc. 40th Offshore Technology Conference, Houston, USA.
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.
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.
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].
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. (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 Quiggin, P. (2009). Non-linear hysteretic seabed model for catenarypipeline contact. In Proc. International Conference on Ocean, Offshore and ArcticEngineering, Honolulu, USA.
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.
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.
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
6-34
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
An Effective Stress Framework for the Variation in Penetration Resistance Due to Episodes of Remoulding and
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,2 = 20.8,Ksec,cyc,2
Ksec,cyc,1
= 1.45
Ksec,cyc,3 = 25.3,Ksec,cyc,3
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
An Effective Stress Framework for the Variation in Penetration Resistance Due to Episodes of Remoulding and
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
Geotechnical analysis of offshore pipelines and steel catenary risers
Undrained shear strength, su [kPa]
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
An Effective Stress Framework for the Variation in Penetration Resistance Due to Episodes of Remoulding and
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
An Effective Stress Framework for the Variation in Penetration Resistance Due to Episodes of Remoulding and
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
An Effective Stress Framework for the Variation in Penetration Resistance Due to Episodes of Remoulding and
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
Geotechnical analysis of offshore pipelines and steel catenary risers
( )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
An Effective Stress Framework for the Variation in Penetration Resistance Due to Episodes of Remoulding and
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)
Vertical effective stress, σ′
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
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ssFra
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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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
An Effective Stress Framework for the Variation in Penetration Resistance Due to Episodes of Remoulding and
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
Vertical effective stress, σ′
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
Geotechnical analysis of offshore pipelines and steel catenary risers
Vertical effective stress, σ′
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
An Effective Stress Framework for the Variation in Penetration Resistance Due to Episodes of Remoulding and
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
An Effective Stress Framework for the Variation in Penetration Resistance Due to Episodes of Remoulding and
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
An Effective Stress Framework for the Variation in Penetration Resistance Due to Episodes of Remoulding and
Reconsolidation
Operative undrained shear strength,su,op [kPa]
Cylinder
inve
rtem
bed
men
t,z m
+D
/2[m
]
Operative undrained shear strength,su,op [kPa]
Cylinder
inve
rtem
bed
men
t,z m
+D
/2[m
]
Operative undrained shear strength,su,op [kPa]
Cylinder
inve
rtem
bed
men
t,z m
+D
/2[m
]
ExperimentSimulation
ExperimentSimulation
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
Geotechnical analysis of offshore pipelines and steel catenary risers
Vertical effective stress, σ′
v[kPa]
Dep
th,z
[m]
Episode 1Episode 2Episode 3
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
An Effective Stress Framework for the Variation in Penetration Resistance Due to Episodes of Remoulding and
Reconsolidation
Vertical effective stress, σ′
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
An Effective Stress Framework for the Variation in Penetration Resistance Due to Episodes of Remoulding and
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
7-32
An Effective Stress Framework for the Variation in Penetration Resistance Due to Episodes of Remoulding and
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.
Aubeny, C. P. and Biscontin, G. (2008). Interaction model for steel compliant riser onsoft seabed. In Proc. 40th Offshore Technology Conference, Houston, USA.
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.
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.
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.
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., 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.
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.
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.
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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.
Martin, C. M. and Randolph, M. F. (2006). Upper bound analysis of lateral pile capacityin cohesive soil. Geotechnique, 56(2):141–145.
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.
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.
Schofield, A. N. and Wroth, C. P. (1968). Critical state soil mechanics. McGraw-Hill,London, UK.
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. 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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
Geotechnical analysis of offshore pipelines and steel catenary risers
(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
3D Experiments Investigating the Interaction of a Model SCR with the Seabed
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
3D Experiments Investigating the Interaction of a Model SCR with the Seabed
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
3D Experiments Investigating the Interaction of a Model SCR with the Seabed
(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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
3D Experiments Investigating the Interaction of a Model SCR with the Seabed
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
3D Experiments Investigating the Interaction of a Model SCR with the Seabed
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
3D Experiments Investigating the Interaction of a Model SCR with the Seabed
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
Geotechnical analysis of offshore pipelines and steel catenary risers
Distance from actuator, x [mm]
Pip
ein
vert
elev
atio
n,w
/D[-]
Distance from actuator, x [mm]
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
3D Experiments Investigating the Interaction of a Model SCR with the Seabed
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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.
Distance from actuator, x [mm]
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
3D Experiments Investigating the Interaction of a Model SCR with the Seabed
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
3D Experiments Investigating the Interaction of a Model SCR with the Seabed
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
3D Experiments Investigating the Interaction of a Model SCR with the Seabed
(a)
(b)
Figure 8.18: Soil deformation after cycling
8-25
Geotechnical analysis of offshore pipelines and steel catenary risers
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
3D Experiments Investigating the Interaction of a Model SCR with the Seabed
References
Aubeny, C. P. and Biscontin, G. (2008). Interaction model for steel compliant riser onsoft seabed. In Proc. 40th Offshore Technology Conference, Houston, USA.
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.
Bridge, C. D. (2005). Effects of seabed interaction on steel catenary risers. PhD thesis,School of Engineering, The University of Surrey.
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.
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.
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. (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
Geotechnical analysis of offshore pipelines and steel catenary risers
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 Quiggin, P. (2009). Non-linear hysteretic seabed model for catenarypipeline contact. In Proc. International Conference on Ocean, Offshore and ArcticEngineering, Honolulu, USA.
Randolph, M. F. and White, D. J. (2008). Pipeline embedment in deep water: processesand quantitative assessment. In Proc. 40th Offshore Technology Conference, Houston,USA.
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.
8-28
3D Experiments Investigating the Interaction of a Model SCR with the Seabed
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
Geotechnical analysis of offshore pipelines and steel catenary risers
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
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Geotechnical analysis of offshore pipelines and steel catenary risers
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.
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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
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Geotechnical analysis of offshore pipelines and steel catenary risers
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
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Geotechnical analysis of offshore pipelines and steel catenary risers
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
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., 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.
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.
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