NUMERICAL MODELLING OF PIPE-SOIL …...Numerical modelling of pipe-soil interactions i ABSTRACT This...

NUMERICAL MODELLING OF PIPE-SOIL

INTERACTIONS

By

SANTIRAM CHATTERJEE

B.Eng., M.Tech.

This thesis is presented for the degree of Doctor of Philosophy

of The University of Western Australia

Centre for Offshore Foundation Systems

School of Civil and Resource Engineering

September 2012

Numerical modelling of pipe-soil interactions

i

ABSTRACT

This thesis described research into the pipe-soil interaction forces during large

movements of deep-water pipelines, using numerical methods. Vertical penetration,

lateral break-out and steady-state lateral resistances were investigated with the help of

numerical models using a large deformation approach implemented within the

ABAQUS finite element software and sophisticated soil constitutive models.

The large deformation finite element methodology is based on a periodic

remeshing and interpolation technique which was developed for this research to

incorporate the effects of changes in the strength and geometry of the seabed during

large movements of the pipelines. Soil constitutive model that accounts for strain rate

effects and remoulding were implemented to simulate realistic behaviour. Coupled

pore-fluid stress analyses were also carried out using the modified Cam Clay plasticity

model to investigate the effects of drainage and consolidation on interaction forces.

The initial vertical penetration of a seabed pipeline is an important parameter for

design of these pipes against lateral buckling and other design conditions. The

penetration rate and strain softening have marked effects on the resistance experienced

during vertical penetration. A simple elastic perfectly plastic soil constitutive model was

modified to incorporate these effects to identify the equivalent shear strength of the soil.

A parametric study considering wide range of parameters was conducted and the results

were unified when the vertical penetration resistance was normalised using this

equivalent shear strength. Simplified equations are presented for ease of application.

Lateral pipe-soil interactions were also studied to observe the effects of the

initial embedment and different pipe weights. Two stages of lateral interaction are dealt

in this research. Firstly, the initial breakout resistance was investigated through large

deformation finite element analyses and also limit analysis using the software OxLim.


ii

Results were presented in terms of plastic failure envelopes in the V-H load space for

different initial embedments. The steady state lateral residual resistance was then

studied using large deformation analyses and an appropriate soil constitutive model. It

was found that steady state resistance is achieved after a lateral displacement of

typically three times the pipe diameter or less, even if the soil berm continues to grow in

size. The increase in berm size is counteracted by a reduction in the soil strength due to

accumulation of plastic strain. The steady state residual friction factor was linked to a

new ‘history’ parameter – termed the effective embedment – in a simple manner,

regardless of the other soil and pipeline parameters.

Finally, coupled consolidation analyses using the modified Cam Clay plasticity

model was carried out to explore the effects of consolidation on penetration and

breakout resistances. Elastoplastic modelling of consolidation beneath partially

embedded pipes was first done to study the pore pressure dissipation time history,

allowing the rate of build-up of pipe-soil resistance to be assessed. The effects of

penetration rate on the vertical resistance were examined and backbone-type curves

showing drained, undrained and partially drained behaviour were presented. It was also

shown that in contractile soil consolidation beneath a shallowly embedded pipe changes

the soil strength significantly and has a marked effect on the lateral breakout resistance.

Again, the results were presented in a normalised manner suite to application in design.

Table of contents

iii

TABLE OF CONTENTS

ABSTRACT……………………………………………………………………………..i TABLE OF CONTENTS……………………………………………………………...iii LIST OF FIGURES.......................................................................................................vii ACKNOWLEDGEMENTS………………………………………………….………xiii CHAPTER 1 INTRODUCTION AND LITERATURE REVIEW

1.1 RESEARCH MOTIVATION................................................................................1-1

1.2 LITERATURE REVIEW......................................................................................1-6

1.2.1 Theoretical solutions ...................................................................................1-7

1.2.2 Numerical analyses .....................................................................................1-9

1.2.3 Design practice..........................................................................................1-13

1.2.4 Model testing observations .......................................................................1-14

1.3 RESEARCH GOALS..........................................................................................1-15

1.4 METHODOLOGY ..............................................................................................1-17

1.5 OUTLINE............................................................................................................1-17

1.6 REFERENCES ....................................................................................................1-20

CHAPTER 2 LARGE DEFORMATION FINITE ELEMENT METHODOLOGY

2.1 NON-LINEAR FINITE ELEMENT ANALYSES................................................2-1

2.2 ANALYSIS PROCEDURES.................................................................................2-2

2.2.1 Lagrangian approach...................................................................................2-2

2.2.2 Eulerian approach........................................................................................2-2

2.2.3 Arbitrary Lagrangian Eulerian approach ....................................................2-2

2.3 RITSS APPROACH ..............................................................................................2-3

2.4 IMPLEMENTATION IN ABAQUS .....................................................................2-4

2.4.1 Superconvergent Patch Recovery – SPR ....................................................2-5

2.4.2 Steps of LDFE analysis ...............................................................................2-6

2.4.3 Effects of strain rate and softening............................................................2-10

2.4.4 Modified Cam Clay model........................................................................2-11

2.5 REFERENCES.....................................................................................................2-12

Table of contents

iv

CHAPTER 3 THE EFFECTS OF PENETRATION RATE AND STRAIN SOFTENING ON THE VERTICAL PENETRATION RESISTANCE OF SEABED PIPELINES

3.1 INTRODUCTION .................................................................................................3-1

3.2 FINITE ELEMENT MODEL ................................................................................3-2

3.2.1 Mesh, boundary conditions and material model .........................................3-2

3.2.2 Strain rate and strain softening....................................................................3-4

3.2.3 Validation of finite element model .............................................................3-5

3.3 PARAMETRIC STUDY .......................................................................................3-7

3.3.1 Effect of unit weight of soil ........................................................................3-8

3.3.2 Geotechnical resistance.............................................................................3-12

3.3.3 Effect of normalised velocity, refγ/Dpv & .................................................3-13

3.3.4 Effect of rate parameter μ .........................................................................3-15

3.3.5 Effect of sensitivity ...................................................................................3-17

3.3.6 Effect of ductility parameter ξ95................................................................3-19

3.3.7 Combining effects of strain rate and softening parameters.......................3-21

3.3.8 Effect of variation of soil shear strength profile .......................................3-23

3.4 SOIL FLOW PATTERN .....................................................................................3-23

3.5 CONCLUDING REMARKS...............................................................................3-24

3.6 REFERENCES ....................................................................................................3-26

CHAPTER 4 LARGE LATERAL MOVEMENT OF PIPELINES ON A SOFT CLAY SEABED: LARGE DEFORMATION FINITE ELEMENT ANALYSIS

4.1 INTRODUCTION .................................................................................................4-1

4.2 SOIL CONSTITUTIVE MODELLING ................................................................4-4

4.3 TYPICAL FINITE ELEMENT MESHES.............................................................4-5

4.4 IDEAL SOIL CASE ..............................................................................................4-8

4.5 REALISTIC SOIL CASE ....................................................................................4-12

4.6 EFFECTIVE EMBEDMENT APPROACH........................................................4-20


4.8 REFERENCES ....................................................................................................4-24

CHAPTER 5 MODELLING LATERAL PIPE-SOIL INTERACTIONS

Table of contents

v

5.1 INTRODUCTION .................................................................................................5-1

5.2 PARAMETRIC STUDY........................................................................................5-2

5.2.1 Input parameters..........................................................................................5-2

5.2.2 Typical results – w/D = 0.3 .........................................................................5-3

5.2.3 Initial yield envelopes and breakout resistance...........................................5-6

5.2.4 Residual friction factor..............................................................................5-11

5.3 EFFECTIVE EMBEDMENT APPROACH........................................................5-17

5.4 ASSESSMENT OF THE FULL H/V RESPONSE .............................................5-24


5.6 REFERENCES.....................................................................................................5-27

CHAPTER 6 BREAKOUT BEHAVIOUR OF PARTIALLY EMBEDDED PIPES IN UNIFORM CLAY USING LIMIT ANALYSIS

6.1 INTRODUCTION .................................................................................................6-1

6.2 METHODOLOGY.................................................................................................6-2

6.3 YIELD ENVELOPES............................................................................................6-3

6.4 INTERFACE MODIFICATION ...........................................................................6-8

6.5 EFFECT OF SOIL WEIGHT ..............................................................................6-17

6.6 EFFECT OF SOIL HEAVE.................................................................................6-20


6.8 REFERENCES.....................................................................................................6-25

CHAPTER 7 ELASTOPLASTIC CONSOLIDATION BENEATH SHALLOWLY EMBEDDED OFFSHORE PIPELINES

7.1 INTRODUCTION .................................................................................................7-1

7.2 NUMERICAL METHODOLOGY........................................................................7-2

7.3 MATERIAL MODEL............................................................................................7-3

7.4 UNDRAINED PENETRATION RESPONSE ......................................................7-6

7.5 CONSOLIDATION RESPONSE..........................................................................7-7

7.5.1 Pore pressure dissipation.............................................................................7-7

7.5.2 Consolidation settlement ...........................................................................7-13


7.7 REFERENCES.....................................................................................................7-15

Table of contents

vi

CHAPTER 8 EFFECTS OF CONSOLIDATION ON PENETRATION AND LATERAL BREAKOUT RESISTANCES 8.1 INTRODUCTION .................................................................................................8-1

8.2 MODEL DESCRIPTION ......................................................................................8-2

8.3 SOIL PARAMETERS ...........................................................................................8-4

8.4 EFFECTS OF LOADING RATE ..........................................................................8-4

8.4.1 Penetration resistance..................................................................................8-4

8.4.2 Consolidation settlement...........................................................................8-11

8.4.3 Pore pressure dissipation after undrained penetration ..............................8-13

8.5 LATERAL BREAKOUT RESISTANCE ...........................................................8-15

8.5.1 Background ...............................................................................................8-15

8.5.2 Unconsolidated undrained yield envelopes...............................................8-16

8.5.3 Consolidated undrained yield envelopes...................................................8-17

8.5.4 Simple equation fit ....................................................................................8-19


8.7 REFERENCES ....................................................................................................8-22

CHAPTER 9 CONCLUDING REMARKS

9.1 ORIGINAL CONTRIBUTIONS ...........................................................................9-1

9.1.1 Vertical penetration.....................................................................................9-1

9.1.2 Lateral pipe-soil interactions.......................................................................9-2

9.1.3 Coupled consolidation analyses ..................................................................9-4

9.2 LDFE ANALYSIS IN DESIGN............................................................................9-5

9.2.1 LDFE in support of simplified design method............................................9-5

9.2.2 LDFE directly applied in design .................................................................9-5

9.3 LIMITATIONS AND FUTURE RESEARCH......................................................9-6

9.3.1 Dynamic effects ..........................................................................................9-6

9.3.2 Full 3D model .............................................................................................9-7

9.3.3 Whole life behaviour...................................................................................9-7

List of figures

vii

LIST OF FIGURES CHAPTER 1 INTRODUCTION AND LITERATURE REVIEW

Figure 1.1 Existing and proposed pipelines at the North West Shelf of Australia ........1-2

Figure 1.2 Controlled lateral buckling of an on-bottom pipeline (Jayson et al., 2008) .1-3

Figure 1.3 Soil deformation mechanism during lateral pipe movement from centrifuge

modelling (Dingle et al., 2008) ......................................................................................1-4

CHAPTER 2 LARGE DEFORMATION FINITE ELEMENT METHODOLOGY

Figure 2.1 Overview of RITSS approach (Hu and Randolph, 1998a) ...........................2-4

Figure 2.2 Superconvergent Patch Recovery (Zienkiewicz and Zhu, 1992) .................2-5

Figure 2.3 Six noded triangulare elements in ABAQUS ...............................................2-7

Figure 2.4 Determination of position of new Gauss point;............................................2-8

Figure 2.5 Implementation of RITSS in ABAQUS .....................................................2-10

CHAPTER 3 THE EFFECTS OF PENETRATION RATE AND STRAIN SOFTENING ON THE VERTICAL PENETRATION RESISTANCE OF SEABED PIPELINES

Figure 3.1 Mesh and boundary conditions.....................................................................3-3

Figure 3.2 Comparison of penetration resistances with centrifuge result ......................3-6

Figure 3.3 Variation of vertical resistance for different submerged unit weights: (a) κ=0;

(b) κ=20........................................................................................................................3-10

Figure 3.4 Buoyancy factor fb and other non-dimensional parameters with depth: (a) κ =

0; (b) κ = 20 .................................................................................................................3-11

Figure 3.5 Variation of buoyancy factor fb with non-dimensional parameter kD/su,avg ...3-

12

Figure 3.6 Effect of normalised penetration rate on vertical resistance: (a) V normalised

by original shear strength; (b) V normalised by equivalent shear strength..................3-14

Figure 3.7 Effect of rate parameter μ on vertical resistance: (a) V normalised by original

shear strength; (b) V normalised by equivalent shear strength ....................................3-16

Figure 3.8 Effect of sensitivity on vertical resistance: (a) α = 1/St ; (b) constant α (=

0.33) .............................................................................................................................3-18

List of figures

viii

Figure 3.9 Vertical resistances normalised by equivalent shear strength for different

sensitivity values (fs = 0.8)...........................................................................................3-19

Figure 3.10 Effect of softening parameter ξ95 on vertical resistance: (a) V normalised by

original shear strength; (b) V normalised by equivalent shear strength.......................3-20

Figure 3.11 Best fit power law curve for vertical resistance with depth......................3-22

Figure 3.12 Best fit power law curves for vertical resistances for different κ.............3-22

Figure 3.13 Deformation pattern and instantaneous velocity field at w/D = 0.5 for

different κ.....................................................................................................................3-24

CHAPTER 4 LARGE LATERAL MOVEMENT OF PIPELINES ON A SOFT CLAY SEABED: LARGE DEFORMATION FINITE ELEMENT ANALYSIS

Figure 4.1 Mesh and boundary conditions.....................................................................4-6

Figure 4.2 Soil mesh at different stages of movement (Case G) ...................................4-7

Figure 4.3 Trajectory of pipe invert during lateral motion (Ideal soil model, Cases A-D)

........................................................................................................................................4-9

Figure 4.4 Normalised horizontal resistance during lateral motion (Ideal soil model,

Cases A-D) ...................................................................................................................4-10

Figure 4.5 Equivalent friction factor during lateral motion .........................................4-10

Figure 4.6 Trajectory of pipe invert during lateral motion ..........................................4-13

Figure 4.7 Normalised horizontal resistance during lateral motion (Realistic soil model,

Cases E-G) ...................................................................................................................4-14

Figure 4.8 Equivalent friction factor during lateral motion (Realistic soil model, Cases

E-G)..............................................................................................................................4-14

Figure 4.9 Failure mechanisms during Case G ............................................................4-16

Figure 4.10 Soil deformation mechanism from a centrifuge model test (u/D = 3) (Dingle

et al. 2008)....................................................................................................................4-16

Figure 4.11 Soil softening during Case G....................................................................4-17

Figure 4.12 Pipe invert trajectory during lateral motion (Varying vertical loads, Cases

H-J )..............................................................................................................................4-18

Figure 4.13 Normalised horizontal resistance during lateral motion (Varying vertical

loads, Cases H-J)..........................................................................................................4-19

Figure 4.14 Equivalent friction factor during lateral motion (Varying vertical loads,

Cases H-J) ....................................................................................................................4-19

Figure 4.15 Effect of vertical load on steady state embedment ...................................4-20

List of figures

ix

Figure 4.16 Schematic diagram explaining the effective embedment concept (as per

White and Dingle, 2011) ..............................................................................................4-21

Figure 4.17 Variation of normalised lateral resistance with effective embedment......4-22

CHAPTER 5 MODELLING LATERAL PIPE-SOIL INTERACTIONS

Figure 5.1 Typical trajectories of pipes during lateral movement for different pipe

weights ...........................................................................................................................5-3

Figure 5.2 Typical lateral responses of pipe for different pipe weights.........................5-4

Figure 5.3 Friction ratios for pipes with different operating vertical loads ...................5-4

Figure 5.4 Idealisation of pipe response during lateral motion for ‘light’ and ‘heavy’

pipes ...............................................................................................................................5-6

Figure 5.5 Yield envelopes in V-H space (LDFE and parabola fit)...............................5-8

Figure 5.6 Yield envelopes from present study and Merifield et al. (2008) ..................5-8

Figure 5.7 Variation of residual friction factor with initial embedment ......................5-12

Figure 5.8 Variation of residual friction factor with normalised vertical load ............5-13

Figure 5.9 Variation of residual resistance with vertical load normalised by (a) Dsuo,init;

(b) Dsum ........................................................................................................................5-14

Figure 5.10 Variation of residual friction factor with normalised final embedment ...5-16

Figure 5.11 Variation of Hres/su0,finalD with (w/D)final ..................................................5-16

Figure 5.12 Lateral and vertical response using effective embedment approach ........5-18

Figure 5.13 Variation of residual effective embedment with initial embedment ........5-19

Figure 5.14 Ratios of (Hres/V)calculated to (Hres/V)LDFE varying with (a) winit/D; (b)

V/Dsu0,init ......................................................................................................................5-23

Figure 5.15 Typical friction ratio responses with lateral displacement fitted with

exponential equation: (a) Lighter pipes; (b) Heavier Pipes .........................................5-26

CHAPTER 6 BREAKOUT BEHAVIOUR OF PARTIALLY EMBEDDED PIPES IN UNIFORM CLAY USING LIMIT ANALYSIS

Figure 6.1 Schematic of the problem and notation ........................................................6-3

Figure 6.2 Yield envelopes for smooth pipes (Case A) .................................................6-4

Figure 6.3 Yield envelopes for rough pipes (Case B)....................................................6-5

Figure 6.4 Comparison of results for a typical pipe embedment (embedment = 0.4D).6-5

Figure 6.5 Stresses and corresponding displacement vectors of a horizontal interface.6-6

Figure 6.6 Flow vectors for smooth interface ................................................................6-6

List of figures

x

Figure 6.7 Flow directions as per conventional plasticity analysis for rough interface6-7

Figure 6.8 Direction of flow during loss of contact in no-tension surface (after Houlsby

and Puzrin, 1999) ...........................................................................................................6-8

Figure 6.9 Schematic of pipe movement and combination of smooth and rough interface

for OxLim analysis.........................................................................................................6-9

Figure 6.10 Comparison of result with Randolph and White (2008) for w/D = 0.5 after

interface modification (Case C) ...................................................................................6-10

Figure 6.11 Optimizing OxLim Result for modified interface; (a) Before optimisation,

(b) After optimisation...................................................................................................6-11

Figure 6.12 Simple wedge failure mechanism with corresponding hodograph...........6-12

Figure 6.13 Difference between optimised OxLim result and analytical solution for low

vertical loads ................................................................................................................6-13

Figure 6.14 Failure mechanism for pipe movement direction of 1 degree to the vertical

......................................................................................................................................6-14

Figure 6.15 Failure mechanisms for different directions of pipe movement...............6-15

Figure 6.16 Optimised yield envelopes for rough pipe soil interface ..........................6-16

Figure 6.17 Adaptive mesh refinement for pure vertical and horizontal pipe movements

in flat seabed (w/D = 0.5).............................................................................................6-17

Figure 6.18 Growth of yield envelopes due to introduction of soil self-weight (Case D

and E) ...........................................................................................................................6-18

Figure 6.19 Schematic for calculating fb for any direction of pipe movement ............6-19

Figure 6.20 fb values for different directions of pipe movement .................................6-20

Figure 6.21 Heave geometries for different embedments............................................6-21

Figure 6.22 Comparison of yield envelopes from OxLim and LDFE analyses for heaved

soil (Case G).................................................................................................................6-22


in heaved soil (w/D = 0.5)............................................................................................6-23

CHAPTER 7 ELASTOPLASTIC CONSOLIDATION BENEATH SHALLOWLY EMBEDDED OFFSHORE PIPELINES

Figure 7.1 Schematic diagram of the problem solved....................................................7-2

Figure 7.2 Yield envelope and critical state line for MCC model .................................7-5

Figure 7.3 Comparison of penetration responses for smooth and rough pipes..............7-6

Figure 7.4 Contours of excess pore water pressure after penetration (w/D = 0.5) ........7-8

List of figures

xi

Figure 7.5 Excess pore pressure distribution around pipe periphery after penetration

(w/D = 0.5) .....................................................................................................................7-9

Figure 7.6 Excess pore pressure dissipation time history at pipe invert for smooth pipe7-

10

Figure 7.7 Excess pore pressure dissipation time history at pipe invert for rough pipe ..7-

10

Figure 7.8 Average pore pressure dissipation and rise in effective stress along the pipe

periphery ......................................................................................................................7-13

Figure 7.9 Time settlement response for different initial embedments (smooth pipe) 7-14

Figure 7.10 Time settlement response for different initial embedments (rough pipe).7-14

CHAPTER 8 EFFECTS OF CONSOLIDATION ON PENETRATION AND LATERAL BREAKOUT RESISTANCES

Figure 8.1 Schematic of the problem studied.................................................................8-2

Figure 8.2 Finite element meshes before and after pipe penetration .............................8-3

Figure 8.3 Normalised penetration resistances with embedment for different pipe

velocities (smooth pipe) .................................................................................................8-5

Figure 8.4 Normalised penetration resistances with embedment for different pipe

velocities (rough pipe) ...................................................................................................8-6

Figure 8.5 Contours of excess pore water pressure normalised by penetration resistance

........................................................................................................................................8-8

Figure 8.6 Backbone curves for different initial embedment levels (smooth pipe).....8-10

Figure 8.7 Backbone curves for different initial embedment levels (Rough pipe)......8-10

Figure 8.8 Backbone curves for different initial embedment levels (smooth pipe, 1 kPa

surcharge).....................................................................................................................8-11

Figure 8.9 Pipe settlements with time for different initial embedments and pipe

velocities ......................................................................................................................8-12

Figure 8.10 Consolidation settlements following penetration at different speeds under

the same consolidation load (smooth pipe)..................................................................8-13

Figure 8.11 Dissipation of excess pore water pressure with non-dimensional time T

(smooth interface) ........................................................................................................8-14

Figure 8.12 Yield envelopes for different initial embedments for unconsolidated

undrained case (smooth pipe).......................................................................................8-16

List of figures

xii

Figure 8.13 Yield envelopes for different initial embedments for consolidated undrained

case (smooth pipe) .......................................................................................................8-18

Figure 8.14 Comparison of yield envelopes for unconsolidated undrained and

consolidated undrained conditions for w/D = 0.1 and 0.5 (smooth pipe) ....................8-18

Figure 8.15 Contours of ratios of consolidated shear strength to the original shear

strength (smooth pipe)..................................................................................................8-19

Figure 8.16 Maximum vertical penetration resistances for unconsolidated undrained and

consolidated undrained conditions (smooth pipe)........................................................8-21

Acknowledgements

xiii

ACKNOWLEDGEMENTS I would like to thank my thesis supervisors, Professor David White and Professor Mark

Randolph for their insightful guidance and continuous encouragement throughout my

candidature. I could not have expected a better combination of mentors for my research

and this dissertation would not have been possible without their support at key stages of

my candidature.

I also want to express my sincere gratitude to Dr. Dong Wang for his help with

programming the large deformation methodology during the first year of my

candidature.

I wish to thank Engineering Science department of Oxford University, especially

Dr. Byron Byrne and Dr. Chris Martin, for hosting me as a visiting student to work on a

collaborative project. A chapter of this thesis was constructed with the work done at

Oxford. Special thanks are extended to Dr. Chris Martin for allowing me use his limit

analysis software OxLim and for many fruitful discussions.

I would also like to thank Professor Deepankar Choudhury of Indian Institute of

Technology Bombay and Professor Ramendu Sahu of Jadavpur University, India for

recommending me to the University of Western Australia.

Centre for Offshore Foundation Systems at UWA has been a stimulating

working environment and I am indebted to all its faculty members, staffs and post

graduate students for making it such a fun place to work.

Throughout my candidature, I was financially supported by an International

Postgraduate Research Scholarship, a University Postgraduate Award and an ad-hoc

scholarship from COFS, which are gratefully acknowledged.

Finally, I would like to thank my parents, other family members and wife, Divya

for their continuous support, encouragement and love.


Centre for Offshore Foundation Systems 1-1

CHAPTER 1

INTRODUCTION AND LITERATURE REVIEW

1.1 RESEARCH MOTIVATION

Much of Australia’s remote sub-sea oil and gas resources remain undeveloped. Over the

last two decades, offshore oil and gas developments have gradually extended to deeper

water further from shore. This has led to a shifting of focus from fixed platforms to

floating production systems, which in turn has resulted in increasing importance of

pipelines and risers (Randolph & White, 2008a). Australia’s gas industry relies on ultra-

long sea-bed pipelines to bring the oil and gas from remote offshore hydrocarbon fields

to shore.

Figure 1.1 shows the existing (red lines) and proposed (white lines) pipelines at

the North-West Shelf of Western Australia. As seen in this figure, many hundreds of

kilometres of new pipelines are being proposed to transport hydrocarbon fluids from far

field locations. The further from shore, the deeper the water (in general) with seabed

comprised of finer-grained sediments than typically encountered in shallow water.

Within each field development, considerable lengths of flowlines link individual wells

to subsea manifolds and processing plants, prior to export to shore.

In deep water, where hydrodynamic loading is much reduced, pipelines are

generally laid directly on the seabed without trenching or other form of secondary

stabilisation. Assessment of the as-laid pipe embedment is an important step for proper

design of deep-water offshore pipelines, since other aspects such as lateral and axial

resistance, and thermal transfer rates are strongly influenced by embedment. Adopting

CHAPTER 1: Introduction and literature review


conservative design values is not a safe approach because high and low embedment, and

consequently the probable axial and lateral resistance, may work for or against a

particular design consideration. Design values of pipe-soil interaction forces, which

depend on the embedment, are key input in determining the practicability of a design

solution. Considerable amounts of capital expenditure can be saved by slight fine-tuning

of these values, through reduced requirements for stabilisation and anchoring measures

and a reduced need to tolerate end expansions (Randolph & White, 2008b, Hill & Jacob

2008).

Figure 1.1 Existing and proposed pipelines at the North West Shelf of Australia

In the case of deep-water pipelines, forces from hydrodynamic loading are

generally small and the dominant forces are from high internal temperature and pressure,

which tend to cause expansion (Bruton et al., 2008). Axial resistance between the pipe

and the seabed opposes this expansion. Excessive compressive forces lead to buckling,

but the buckling response depends critically on the lateral soil resistance. When



buckling occurs, it significantly reduces the net axial load in the pipe. On the other hand,

excessive buckling may lead to high bending strains in the pipe section. So, controlled

buckling (Figure 1.2) may be a feasible solution for relief of thermal loading.

Accumulated axial movement due to repeated thermal cycles may lead to global

displacement of pipes. This phenomenon is termed ‘walking’ (Carr et al., 2006). For

design purposes, it is very important to assess pipeline buckling and walking accurately.

Recent design approaches to control buckling and walking have necessitated predicting

the available soil resistance on pipelines undergoing movement, accounting for the

associated changes in seabed geometry and strength. The existing models are mainly

derived for stability analyses. The challenge is to extend existing models to account for

geometry changes, remoulding and reconsolidation effects that influence large

amplitude cyclic displacements.

Figure 1.2 Controlled lateral buckling of an on-bottom pipeline (Jayson et al., 2008)



During pipe-lay, deep-water pipelines typically embed by between 10 and 50 % of

their diameter, due to their own weight and the dynamic motions during laying

(Westgate et al., 2009, 2010). Once embedded, pipelines undergo cycles of large

horizontal movement in zones where buckling occurs, due to thermal expansion and

contraction. Key design parameters are the initial peak lateral resistance during the first

‘breakout’ cycle, and then the steady state resistance during subsequent cycles.

Load-displacement responses during lateral breakout have been reported from

centrifuge model studies (Dingle et al., 2008). Figure 1.3 shows soil deformation

mechanisms at several stages during lateral movement.

Figure 1.3 Soil deformation mechanism during lateral pipe movement from centrifuge modelling (Dingle et al., 2008)

At peak breakout resistance, evidence of two-sided mechanisms can be seen. Although

clear slip surfaces can be observed in front of the pipe, no clear slip surface is developed

in the soil behind the pipe, which means full soil strength was not mobilised in this

region prior to separation of the pipe from the soil. After breakout, distinct slip planes

can be seen in front of the pipe, matching mechanisms calculated from plasticity limit



analysis. At this stage, tensile resistance at the rear is lost and there is full pipe-soil

separation. During large amplitude lateral movement, soil is swept ahead of the pipe and

a berm is generated. Numerical results (Aubeny et al., 2005; Merifield et al., 2008) and

plasticity solutions (Randolph & White, 2008c, Cheuk et al., 2008) have been used to

assess breakout resistance. Although these solutions are theoretically rigorous, they do

not capture the changing seabed geometry or strength and are strictly applicable only for

a horizontal soil surface.

Vertical penetration and lateral movement of pipelines on a soft seabed are typical

examples of large deformation problems. Small strain finite element analyses cannot

replicate the full response because soil elements near the pipeline become extremely

distorted. In recent studies, large deformation finite element (LDFE) analyses of vertical

as well as lateral movements of pipes have been performed (Wang et al., 2010). The

“remeshing and interpolation technique with small strain” (RITSS, Hu & Randolph,

1998) has been used in these methods to divide the total displacement into a series of

small incremental steps, performing small strain analysis for each step. After a given

number of steps, the deformed geometry is remeshed prior to the next series of small

strain analyses. Field variables, e.g. stress and material properties, are updated from the

old mesh to the new mesh. The advantage of this method is that it can be combined with

commercial finite element packages such as AFENA (Carter & Balaam, 1995) or

ABAQUS (Dassault Systèmes, 2007, 2011). This methodology has been implemented

in ABAQUS by the author of this thesis for the current research and various problem-

specific refinements of the approach have been performed wherever necessary.

Most existing finite element studies of (deep-water) pipe-soil interaction assume

simple undrained soil models. However, pipelines undergoing large cyclic deformations

on fine-grained soil cause intermittent episodes of remoulding of the soil (during

pipeline motion) followed by reconsolidation (following movement). For correct



assessment of the resulting response, it is important to predict the operative soil strength.

Soil strength is decreased by remoulding, but it will increase again during

reconsolidation, as excess pore pressures dissipate. However, there is a scarcity of

models in the literature that can simulate cycles of softening due to remoulding,

followed by strength recovery due to consolidation.

Coupled consolidation finite element analyses to study the consolidation time

history beneath partially embedded seabed pipelines have typically been limited to

small strain elastic solutions in the past. Consolidation analyses using elasto-plastic soil

models, combined with large amplitude displacement of pipelines, have not been

reported in the literature prior to the present work.

1.2 LITERATURE REVIEW

Before proceeding to the original contribution of this research, a detailed review of the

literature on pipe-soil interactions is presented first. Chapters in the book edited by

McCarron (2011) summarised the design considerations for subsea flowlines against

lateral and upheaval buckling. Simple modelling techniques of pipe-soil interactions

based on numerical techniques are also discussed in this book. The chapter called

‘pipeline and riser geotechnics’ in the book by Randolph & Gourvenec (2011) also

discussed key aspects of offshore pipeline design and current practices.

The literature available to date on pipe-soil interaction can be divided into three

main categories. First are solutions based on classical plasticity theory, second are finite

element analysis based solutions and finally there are empirical approaches based on

centrifuge modelling or other physical modelling studies.



1.2.1 Theoretical solutions

Randolph & Houlsby (1984) first gave a theoretical solution for the limiting pressure on

a circular pile moving laterally through soil under undrained conditions. Although the

context was for laterally loaded piles, in a broader sense the solution applies to any

cylindrical object (such as a pipeline) moving laterally through soil. In that paper,

classical plasticity theory was used to establish lower and upper bound solutions. The

soil was assumed to be a perfectly plastic cohesive material and the pile as a long

cylinder moving horizontally in the infinite medium, reducing the calculations to a

plane strain problem of plasticity theory. In the lower-bound approach, a stress

distribution in equilibrium with a given applied load is assumed. Provided the stress

field does not conflict with the failure criterion, the calculated load is less than or equal

to the true collapse load. On the other hand, in the upper-bound approach, a failure

mechanism is assumed. The collapse load is found by equating the rate of plastic work

within the deforming soil to the work done by the external load. In this case, the

estimated load is greater than or equal to the true collapse load. If both these solutions

match, the solution is said to be exact if an additional conditions is satisfied – that the

stress field is extensible without violating the yield criterion. For the laterally loaded

pile problem the solution is expressed in terms of a resistance factor expressed as N =

P/suD, where P is the lateral capacity per unit length, su is the undrained shear strength

of the soil and D is the diameter of the pile.

At the time it was published, the Randolph & Houlsby solution was considered

exact (having equal upper and lower bounds). However, subsequent work by Murff et al.

(1989), who applied a modified form of the solution to evaluate the ultimate load

capacity of a pipe penetrating into perfectly plastic cohesive material, revealed an error

in the upper-bound solution, apart from the case of a fully rough pile. The authors

showed that the reason for this was the presence of a region of localised conflict



between the strain rate field and the stress field for any value of α < 1, where α is the

ratio of the limiting pile-soil friction to the shear strength of the soil. The solution was

corrected by taking the absolute value of the maximum shear strain rate, integrating the

particular component of plastic work numerically. This led to divergence of the lower

and upper-bound solutions, with a maximum discrepancy of 9.1% for the case of a

smooth pile.

Martin & Randolph (2006) made an attempt to minimize the gap between lower-

bound and upper-bound solutions for laterally loaded piles in undrained clay. Three

upper-bound solutions were provided for the ultimate load capacity of a circular pile

undergoing lateral translation in undrained clay. The first solution, referred to as the

Randolph mechanism, based on Randolph & Houlsby (1984), was shown to work well

for large α. A second solution was based on what is referred to as the Martin mechanism,

which consists of a crescent-shape body of soil undergoing rigid body rotation about a

point located on the axis of the pile perpendicular to the direction of the motion of the

pile. This mechanism works well for small α. In an effort to obtain an upper-bound

solution that will give close bracketing of the exact collapse load for all values of α,

these two mechanisms were combined in the third mechanism. This mechanism gave

upper-bound solutions that are very close to the lower-bound solution for all values of α.

The solution reduced the maximum discrepancy between upper and lower bound

solutions to 0.65% in the case of a smooth pile compared with the previous 9.1% (Murff

et al., 1989).

Upper-bound yield envelopes for shallowly embedded pipes in clay under

combined vertical and horizontal undrained loading were developed in a study by

Randolph & White (2008c). A plane strain plasticity model was assumed and the

solution was based on a generalisation of the mechanism as devised by Martin &

Randolph (2006). The generalisation is that the centre of rotation of the main block of



failing soil is not constrained to lie on the diameter normal to the direction of the pipe.

‘Break away’ at the trailing edge of the pipe was also assumed. Solutions were

presented for both homogeneous soil and for soil with shear strength varying

proportionally with depth below the soil surface.

Cheuk et al. (2008) also presented results of upper-bound analyses based on

simple slip circle failure mechanism. The results from this study are less optimal than

Randolph & White (2008), but consider non-breakaway cases and soil self weight as

well.

In an effort to allow for the strain-rate dependence of shear strength, and also the

gradual loss of strength due to remoulding, Einav & Randolph (2005) introduced a new

theoretical method involving a modified version of the Tresca soil model to evaluate the

penetration resistance for rigid ‘full-flow’ T-bar (cylindrical) and ball (spherical)

penetrometers. The method, which combines conventional strain path method and

classical upper-bound solutions, was referred to as the upper-bound-based strain path

method (UBSPM). Unlike the conventional strain path method, where the kinematic

mechanisms are based on flow solutions for irrotational inviscid fluid, the analysis was

based on the flow pattern derived from an upper-bound mechanism. The upper-bound

mechanism was optimized for ideal rigid plastic soil and was integrated with the strain

path method. Using this approach, the effects of rigidity index, strain rate and strain

softening on penetration resistance were investigated. The modification to the Tresca

constitutive model proposed by Einav & Randolph (2005) has been applied in the

present research.

1.2.2 Numerical analyses

Aubeny et al. (2005) reported results of small-strain finite element analyses for vertical

loading of pipes ‘wished-in’ place in a vertical trench in clay. Plane strain analyses were



carried out for different embedment depths. Most of the studies in this area considered

pipes with shallow embedment up to half the diameter of the pipe, whereas this study

was performed for embedments varying from 0.1 times the diameter to 5 times the

diameter of the pipe. Solutions for soils with constant shear strength and for soils with

linearly varying shear strength were presented. The results were compared with

approximate lower-bound and upper-bound plasticity solutions. Curve fitting of the FE

results allowed simplified equations to be developed relating the collapse load to

embedment depth and the shear strength of the soil at the pipe invert.

Merifield et al. (2008) reported results of finite element analyses of shallowly

embedded pipes under combinations of horizontal and vertical load. The results were

compared with the yield envelopes drawn from the upper-bound analyses of Randolph

& White (2008c). The limiting loads obtained from finite element analyses were in

very good agreement with the upper-bound curves. The authors also showed a good

match between the internal displacements calculated from FE analysis and those from

centrifuge tests. For simple assessment of the ultimate resistance of shallowly

embedded pipes, the yield curves were fitted with simple equations.

The above mentioned finite element solutions mainly dealt with small strain

analyses. Hesar (2004) made a first attempt to capture the large movements of pipelines

in soft clay using finite element software ABAQUS. ABAQUS explicit was used along

with adaptive meshing to avoid severe mesh distortion. The effects of initial pipe

embedment and submerged pipe weight on pipe soil lateral interaction forces were

explored. The paper also stressed the importance of obtaining high quality soil data for

very shallow depths which has marked influence on the design of pipelines. Only results

for a few specific cases were presented, and no attempt was made to provide general

solutions.



Konuk & Yu (2007) and Yu & Konuk (2007) studied large displacement pipe-

soil interaction problem using an Arbitrary Lagrangian Eulerian (ALE) approach

implemented in FE software LS-DYNA. Two-dimensional and three-dimensional

models were prepared and a cap plasticity soil constitutive model was used. These

papers emphasised the inadequacy of traditional design methods of pipelines against

lateral buckling, which are based on Winkler or Coulomb type models. The importance

of large deformation finite element techniques to design high temperature and high

pressure pipelines undergoing cyclic lateral motions was shown through a number of

2D and 3D models.

Merifield et al. (2009) studied the vertical penetration response of pipes and

subsequent horizontal resistance for pushed-in-place (PIP) pipes. A large deformation

finite element methodology, following an ALE approach, was adopted in ABAQUS to

limit mesh distortion problems. The effects of soil weight and local heave generated

during pipe penetration were explored. Simple expressions for vertical and horizontal

bearing capacities were presented incorporating these effects. Archimedes’ principle

was revisited and a modification was suggested to account for the effect of heave.

Zhou & Randolph (2007) performed numerical simulations of deep penetration

of full flow penetrometers (cylindrical T-bar and spherical ball). The RITSS approach

proposed by Hu & Randolph (1998) was adopted to perform the large deformation finite

element analysis, using AFENA as the finite element programme. The simple elastic-

perfectly plastic Tresca soil model was modified to incorporate the effects of strain-

softening and strain-rate. At any stage of analysis, the shear strength was modified to

account for reduction due to strain softening as well as enhancement due to high strain

rate, with the strength given by (Einav & Randolph 2005)



[ ] 0u/3

remrem

ref

.

ref

.

max

.

u se)1(.max

log1s 95ξξ−δ−+δ

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

γ

⎟⎠

⎞⎜⎝

⎛ γγμ+=

1.1

The first part of this relationship captures the effect of strain rate, with the reference

shear strain, ref

.γ , taken as 3x10-6 s-1 and the rate parameter, μ, giving the rate of strength

increase per decade, taken in the range of 0.05-0.2. The maximum shear strain rate,

max

.γ , was deduced as

tn31

max

.

ΔεΔ−εΔ

=γ 1.2

where 1εΔ and 3εΔ are cumulative major and minor principal strains, respectively, over

n increments between remeshing steps. The time period tΔ is given by

fieldp d/vd/t δ

=Δ 1.3

where δ is the specified incremental displacement for each increment, d and dfield are the

penetrometer diameters in the finite element calculations and field tests respectively,

and vp is the field penetrometer velocity (generally standard at 20 mm/s). The second

part of the equation represents the effect of strain softening. Here, suo denotes the

original shear strength at the reference shear strain rate prior to any softening, δrem is the

ratio of fully remoulded and initial shear strength, ξ is the accumulated absolute plastic

shear strain at the Gauss point and ξ95 is the value of ξ to cause 95% remoulding.

Parametric studies were carried out to investigate the effects of soil ductility,

rigidity index and rate parameter on penetration resistance for both T-bar and ball

probes. The phenomena of periodic shear bands and oscillations in the resistance were

observed in this study, with the peaks in the resistance-penetration response



corresponding to development of new shear bands and the troughs reflecting the

subsequent softening within each shear band.

Wang et al. (2010) studied large amplitude lateral motion of the pipe following

the RITSS approach, but implemented for the first time in finite element software

ABAQUS. Trajectories and horizontal resistance during lateral motion of the pipe for

different pipe weights were studied. A simple interpretation of the steady-state lateral

resistance was presented for pipes in rate dependent and softening clay. It was shown

that the effects of soil softening and berm build-up ahead of the pipe could be

encapsulated by defining an ‘effective embedment’ of the pipe. The results matched

well with available plasticity solutions and centrifuge test data.

Krost et al. (2011) studied consolidation around partially embedded pipelines

with the help of small strain finite element analysis but assuming the soil response to be

elastic. The generation and dissipation of pore water pressure at different levels of

embedment were studied. The results were compared to those for a strip footing. A

good match of the result was observed with available field data. The mobilisation of

effective contact force due to consolidation was presented. It was shown that up to 35%

increase in the average normal effective stress and hence axial resistance is possible due

to pore pressure dissipation under partially embedded pipes.

1.2.3 Design practice

Cathie et al. (2005) provided a state-of-the-art review of many aspects of pipeline

geotechnics. The paper summarised current models (Wagner et al. 1987, Lieng et al.

1988, Verley & Sotberg 1992, Verley & Lund 1995) used for assessing lateral

resistance of partially embedded pipelines. These two component models, consisting of

a sliding resistance component and a lateral passive pressure component, are totally

empirical and are based on a few model tests. Although these models are practically



useful they do not capture the underlying mechanics and are not applicable outside the

soil types forming the database.

Bruton et al. (2006), with the help of large and small-scale tests, provided

recommendations for using key parameters that affect the lateral pipe-soil interaction

response in soft clay soils. Different stages of pipe-soil response, including embedment

of pipe during installation, break-out during buckling, large amplitude displacement and

repeated cyclic behaviour, were defined. Suitable empirical equations were developed

for each of these steps to provide design guidelines for lateral buckling of pipelines.

Dendani & Jaeck (2008) presented simplified methods and practical calculations

for assessing pipe-soil interactions. This paper discussed soil-pipe interaction behaviour

properties based on site-specific data. Several phases of lateral resistance including peak

resistance, post-peak resistance, increase of resistance due to build-up of soil berms and

large displacement residual resistance were defined.

1.2.4 Model testing observations

Cheuk et al. (2007) reported results of full scale model tests on kaolin clay and West

African soft offshore clay to study pipe-soil lateral interactions due to repetitive cycles.

Four stages of the force-displacement response were identified: breakout, suction

release, steady berm growth and dormant berm collection. Breakout resistance was

shown to be the peak resistance followed by a drop due to loss of suction at the rear of

the pipe. Increase in resistance due to activating the dormant berm was also shown in

this study. An upper-bound model was proposed which proved to be reasonably

accurate in predicting the experimental results.

Dingle et al. (2008) reported centrifuge model test data for assessing vertical

penetration and lateral break-out resistance of pipelines laid on soft sea-bed sediments.

An advanced digital image analysis technique, using particle image velocimetry (PIV)



(White et al., 2003), was implemented to observe the soil deformation. The results

closely matched plasticity solutions, with minor differences attributed to the difficulties

in accurately assessing the shear strength of near mud-line soft sediments.

Cheuk & White (2009) reported results of centrifuge model tests using different

clays to investigate dynamic lay effects on pipeline embedment. Results showed that

only a few cycles of small amplitude oscillation were sufficient to double or triple the

static embedment. The combined effects of lateral ploughing and softening were

considered responsible for this additional embedment. The authors also proposed a new

model incorporating the concepts of plasticity theory to estimate dynamic pipe

embedment.

Cardoso & Silveira (2010) reported results of full scale model tests to study the

large deformation lateral resistance of pipe in soft clay. A wide range of parameters

including ‘heavy’ and ‘light’ pipes were chosen and a number of model tests were

performed. Results were expressed in non-dimensional form and empirical equations

were fit. Expressions for breakout resistance, residual resistance and berm resistance,

i.e. the pipeline resistance at different stages of lateral motion, were presented in the

form of simple expressions.

1.3 RESEARCH GOALS

As seen in the review of the literature, most of the available theoretical studies dealt

with small strain finite element analyses. These studies do not capture the change of

geometry during large amplitude movements of the pipe. The limited number of large

deformation studies did not consider all aspects that affect the pipe-soil interaction

forces on moving pipelines. Also, most of these studies assumed non-softening

constitutive soil models, which do not account for remoulding of the soil as it undergoes

large strains, and therefore are not suitable for predicting realistic pipe-soil interaction



forces. Coupled consolidation stress analyses for drained behaviour of soil under a

partially embedded pipe are scarce in the literature. Experimental studies have been

performed in the industry to study large amplitude movements of pipelines, but these

are mostly case specific, and the results have rarely been generalised other than using

empirical expressions without theoretical basis. A significant quantity of experimental

data related to the topic is becoming available through industry studies and also from

recent academic research. The goal of the present research has been to provide a

theoretical basis in which these experimental results can be framed and also to help to

predict results for the cases where experimental results are not available or experiments

are difficult to conduct. The specific goals of this research are listed below.

1) To develop a methodology based on large deformation finite element (LDFE)

analysis to simulate the movement of offshore pipelines in soft seabed sediments

in the horizontal and vertical directions. The effects of strain rate and strain

softening will be incorporated in the model.

2) To develop a calculation approach to predict pipeline embedment during the

laying process. This will be based on parametric studies, using the methodology

developed in (1), varying parameters such as the relative weight of the pipe

compared with the soil shear strength, the sensitivity of the soil, and the pipeline

motions.

3) To quantify the lateral resistance of pipes in soft soil, with particular focus on

the breakout resistance and the steady state lateral resistance relevant for

buckling analysis. The effects of initial embedments and operating pipe weight

will be explored in detail.

4) To improve the available plasticity-based solutions to predict pipe-soil

interaction forces for pipelines under combined vertical and horizontal loads.



The specific improvement will be to incorporate uneven berm geometry

available from LDFE analyses.

5) To introduce the effect of soil consolidation into this topic. Coupled

consolidation analysis using the modified Cam Clay soil model will be

incorporated in the LDFE methodology to study partially drained behaviour of

soil around partially embedded pipes.

1.4 METHODOLOGY

A two-dimensional large deformation finite element model was adopted with the help of

“Remeshing and interpolation technique with small strain” (RITSS, Hu & Randolph,

1998). RITSS is a variation of the Arbitrary Lagrangian Eulerian (ALE) method (Ghosh

& Kikuchi, 1991), involving periodic remeshing followed by interpolation of the field

variables from the old mesh to the new mesh, in order to model ‘convection’ of the soil

through the mesh. The approach was implemented in the commercial finite element

software ABAQUS (Dassault Systèmes, 2007, 2011).

Two different soil constitutive models were used. The first was based on the

simple Tresca soil model for undrained response of clays. However, the effects of strain

rate and strain softening were implemented in the analysis according to the model

suggested by previous researchers (Einav & Randolph, 2005; Zhou & Randolph, 2007).

The second model was the more sophisticated constitutive model, modified Cam Clay

(MCC). This was implemented in the LDFE methodology to perform coupled

consolidation analyses.

1.5 OUTLINE

The thesis consists of nine chapters. A brief outline of each chapter is given below.



1. The first chapter is an introductory chapter outlining the motivation for the

research and providing a review of current literature on pipe-soil interactions.

2. The second chapter explains the large deformation finite element methodology

developed for this study.

3. In the third chapter, pipe-soil interaction during vertical embedment of pipelines

on the seabed is studied using a simple Tresca soil model, modified to

incorporate the combined effects of strain rate and softening. The large

deformation finite element method is validated by comparing the results with

data from centrifuge model tests. Results of a parametric study are then

presented, varying the strain rate and softening parameters to explore their

effects on penetration resistance. Simple expressions for penetration resistance,

incorporating the effects of strain rate and softening, are provided. The effects of

soil strength vertical heterogeneity and buoyancy are also explored.

4. In the fourth chapter, the lateral response of pipelines on a soft seabed is studied

for very large amplitude lateral movement. Initially, pipe soil interaction

simulations are presented for the case of ideal soil, with non-softening strength.

Lateral resistance profiles and trajectories of the pipe during lateral motion are

investigated for different initial embedment of the pipe. A more realistic soil

model incorporating the effects of strain rate and strain softening is then

explored. Lateral resistance profiles and trajectories of the pipes from this

realistic model are compared with the ideal soil case. Finally, the concept of

effective pipe embedment – which accounts for the soil softening and the

geometric changes caused by the soil berm ahead of the pipe – is applied to both

the ideal and realistic soil model responses. The normalized horizontal resistance



response is shown to be linked to the effective embedment in a simple manner,

regardless of the other soil and pipeline parameters.

5. The fifth chapter also focuses on lateral pipe-soil interactions. Results of a

parametric study varying the pipe weight and initial embedment are presented.

The results show that a steady state is generally reached at large displacements,

reflecting a balance between the growth of a soil berm ahead of the pipe and the

softening of the disturbed soil. The initial breakout response is shown to match

well with previously established failure envelopes and a new interpretation is

proposed to capture the large-displacement response. The ‘effective embedment’

concept is used to rationalise the influence of the soil berm ahead of the pipe.

This leads to simple new relationships for predicting the steady state residual

lateral resistance, which provide more accurate predictions of the LDFE

response than previously published solutions. The complete load-displacement

response over large movements is also shown to be well-fitted by an exponential

relationship, albeit for the specific case of lateral movements under constant

vertical load.

6. In the sixth chapter, the breakout resistance and trajectory of partially embedded

pipelines in seabed is investigated using finite element limit analysis software

OxLim. Although OxLim analyses conform to classical plasticity theory, a slight

modification of the interface condition which violates normality has been

adopted. The pipe-soil interface can sustain neither tension nor shear stress when

separation occurs, providing a more natural solution. Results are compared with

those available in the literature and marginal improvements are demonstrated.

The effect of considering self-weight on the resulting yield envelopes is

explored. Also, the effect of soil heave around the pipe, the geometry of which

has been obtained from large deformation finite element analyses, is investigated.



7. In the seventh chapter, the consolidation behaviour under partially embedded

pipelines is investigated using large deformation finite element analyses based

on the modified Cam Clay plasticity model. Initially results from undrained

analyses are presented and the effects of initial embedment and pipe-soil

interface friction are explored in a systematic manner. The dissipation responses

are fitted by simple equations to facilitate practical design.

8. In the eighth chapter, results of partially drained analyses are presented for

different penetration rates of the pipe. Backbone-type curves are provided for

both smooth and rough pipes. The lateral breakout resistance and the direction of

pipe movement on breakout depend on the consolidated strength of the soil

around the pipe, as well as the applied loading. The effect of consolidation on

the lateral breakout resistance has also been explored in this chapter. It has been

shown that the envelopes of vertical-lateral combined loading bearing capacity

differ markedly from those predicted assuming undrained behaviour throughout.

9. In the last chapter, concluding remarks based on the research in this thesis are

presented. Future research and challenges in this area are also discussed at the

end of this chapter.

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Randolph, M. F. & Houlsby, G. T. (1984). The limiting pressure on a circular pile

loaded laterally in cohesive soil. Géotechnique 34, No. 4, 613-623.

Randolph, M. F., Wang, D., Hossain, M. S., Zhou, H. & Hu, Y. (2008). Large

deformation finite element analysis for offshore applications. Proc. of 12th



International Conference of International Association for Computer Methods

and Advances in Geomechanics, Goa, India.

Randolph, M. F. & White, D. J. (2008a). Offshore Foundation Design – A Moving

Target. Proc. BGA International Conference on Foundations, Dundee, IHS BRE

Press, London, 27-59.

Randolph, M. F. & White, D. J. (2008b). Pipeline embedment in deep water: process

and quantitative assessment. Proc. Offshore Technology Conference, Houston, Paper

OTC 19128.

Randolph, M. F. & White, D. J. (2008c). Upper-bound yield envelopes for pipelines at

shallow embedment in clay. Géotechnique 58, No. 4, 297-301.

Verley, R. L. P. & Lund, K. M. (1995). A soil resistance model for pipelines placed on

clay soils. Proc. Offshore Mechanics and Arctic Engineering Conf, Copenhagen,

18–22, Vol V: 225–232.

Verley, R. L. P. & Sotberg, T. (1992). A soil resistance model for pipelines placed on

sandy soils. Proc. Offshore Mechanics and Arctic Engineering Conf, Vol V-A

pipeline technology: 123–131.

Wagner, D. A. Murff J. D. & Brennodden, H. (1987). Pipe-soil interaction model. Proc.

Offshore Technology Conf., Houston, OTC 5504: 181–190.

Wang, D, White, D. J. & Randolph, M. F. (2010). Large deformation finite element

analysis of pipe penetration and large-amplitude lateral displacement. Can. Geotech.

J. 47, No. 8, 842-856.

Westgate, Z., White, D. J. & Randolph, M. F. (2009). Video observations of dynamic

embedment during pipelaying on soft clay. Proc. Conf. on Offshore Mechanics

and Arctic Engineering, Honolulu. Paper OMAE2009-79814



Westgate, Z. W., White, D. J., Randolph, M. F. & Brunning, P. (2010). Pipeline laying

and embedment in soft fine-grained soils: Field observations and numerical

simulations. Proc. Offshore Technology Conference, Houston. Paper 20407

White, D. J., Take, W. A. & Bolton, M. D. (2003). Soil deformation measurement using

Particle Image Velocimetry (PIV) and photogrammetry. Géotechnique, 53, No.

7, 619-631.

Yu, S. & Konuk, I. (2007). Continuum FE modelling of lateral buckling. Proc. Offshore

Technology Conf., Houston, OTC 18934.

Zhou, H. & Randolph, M. F. (2007) Computational techniques and shear band

development for cylindrical and spherical penetrometers in strain-softening clay.

Int. J. Geomech., 7, No. 4, 287-295.



CHAPTER 2

LARGE DEFORMATION FINITE ELEMENT

METHODOLOGY

2.1 NON-LINEAR FINITE ELEMENT ANALYSES

Over the past several decades, numerical solutions of non-linear problems have received

attention of researchers because of many practical applications. Unlike linear analyses,

the stiffness matrix does not remain constant in a non-linear analysis. Non-linear

behaviours associated with finite element analyses can be classified in to three main

categories – material non-linearity, geometric non-linearity and boundary non-linearity

(Bathe, 1996). In material non-linear analyses, displacements and strains are

infinitesimal, but stress-strain relations are non-linear. Geometric non-linearity is

mainly associated with large deformation of the domain. As per Bathe (1996),

geometric non-linear analyses can be of two types – (i) large displacements, large

rotations, but strains are small and (ii) large displacements, large rotations and strains

are also large. In boundary non-linearity problems, the boundary conditions change

during the motion of the body. As far as geotechnical non-linear analyses are concerned,

material non-linearity, which is an inherent characteristic of soil behaviour, has been the

most studied aspect to date. Thorough and dedicated research to address geometrical

non-linear analyses of geomechanics problems involving large deformations has not

been commenced until recent years. The complexity of large deformation geotechnical

problems coupled with complex constitutive model has encouraged researchers to

invent novel techniques to solve them.

CHAPTER 2: Large deformation finite element methodology


2.2 ANALYSIS PROCEDURES

There are three widely used finite element techniques to solve large deformation

problems - Lagrangian approach, Eulerian approach and Arbitrary Lagrangian Eulerian

approach.

2.2.1 Lagrangian approach

In the Lagrangian approach, the nodes of the finite element mesh move with the

associated material point during analysis. The advantages of this approach are that it

only has to satisfy relatively simple governing equations and it allows easy tracking of

free surfaces. In the Total Lagrangian (TL) approach all variables are referred to the

undeformed geometry. In the Updated Lagrangian (UL) approach, all variables are

referred to the current and updated reference geometry. The major limitation that both

these techniques suffer from is gross mesh distortion and entanglement when large

deformations occur within the body.

2.2.2 Eulerian approach

In the Eulerian approach, the computational mesh remains fixed and the material moves

through it as time progresses. This approach is particularly suitable for fluid flow

problems and when there is no moving boundary. This technique was successfully

applied to deep penetration problem in geomechanics by van den Berg (1991).

2.2.3 Arbitrary Lagrangian Eulerian approach

The Arbitrary Lagrangian Eulerian approach was developed to combine the advantages

of the above two techniques and minimise the limitations to address large deformation

problems. This methodology was proposed in a finite difference context by Noh (1964)

and Franck & Lazarus (1964), and later adapted by Hirt et al. (1974). The methodology



was implemented in finite element analysis of fluid problems by researchers such as

Donea et al. (1977), Belytschko et al. (1978) and Hughes et al. (1991). Ghosh &

Kikuchi (1988) and Ghosh & Kikuchi (1990) introduced the technique to non-linear

solid mechanics problems. In the Arbitrary Lagrangian Eulerian (ALE) technique, mesh

and material displacements are uncoupled to avoid mesh distortion and entanglement.

As the name suggests, the extent to which material moves through the finite element

mesh or the mesh moves with material is arbitrary. In this description, the motions of

both grid and material are defined, but strictly ALE involves a finite element grid of

constant topology (i.e. without periodic remeshing).

2.3 RITSS APPROACH

All the techniques stated above implement large strain formulations. However, from a

geotechnical perspective, complex constitutive models make large strain formulations

more difficult to be implemented. Hu & Randolph (1998a, b) developed a simple

technique called Remeshing and Interpolation Technique with Small Strain (RITSS). A

series of small strain Lagrangian calculations are performed, followed by remeshing of

the deformed regime and interpolation of stress, strain and material properties from the

old mesh to the new mesh. This is repeated until the required displacement is achieved.

An overview of the technique, as per Hu & Randolph (1998a), is shown in Figure 2.1.

The main advantage of the method is that, due to the Lagrangian small strain

incremental steps, it can be coupled with any commercially available finite element

software. Initially, RITSS was successfully implemented in finite element software

AFENA (Carter & Balaam, 1995) to study several geotechnical applications – shallow

foundations (Hu & Randolph, 1998a, 1998b, 1998c; Hu et al., 1999; Zhou & Randolph,

2006), spudcan foundations (Hu & Randolph 1998a; Hossain et al., 2005; Hossain &



Randolph, 2009, 2010), subsea pipelines (Barbosa-Cruz & Randolph 2005; Zhou et al.,

2008) and penetrometers (Lu et al., 2004; Zhou & Randolph, 2007, 2009a, 2009b, 2011).

Initial mesh generation (and optimisation)

Small strain incremental analysis step

Updating of external and internal boundary node positions and remeshing

Interpolation of stresses and material properties from old to new mesh

Loop

as n

eces

sary

Initial mesh generation (and optimisation)

Small strain incremental analysis step

Updating of external and internal boundary node positions and remeshing

Interpolation of stresses and material properties from old to new mesh

Loop

as n

eces

sary

Figure 2.1 Overview of RITSS approach (Hu & Randolph, 1998a)

2.4 IMPLEMENTATION IN ABAQUS

Recently Wang et al. (2006, 2010a, 2010b) implemented RITSS in the commercial

software ABAQUS (Dassault Systèmes, 2007) due to its powerful mesh generation

tools and computational efficiency. The numerical procedure developed for this

research has been based on the same methodology and various problem specific

modifications have been incorporated where necessary.

The finite element software ABAQUS was used for making the model, mesh

generation, analysis and post-processing. The problem was solved using a

displacement-controlled approach. Following the RITSS method, the whole

displacement is divided into a series of small displacement steps. Python, which is the

in-built scripting language of ABAQUS software, is used to execute different ABAQUS



functions. The superconvergent patch recovery (SPR) technique (Zienkiewicz & Zhu,

1992) was used for recovery of stresses from the Gauss points to the nodes. Stress-SPR

interpolation scheme was chosen to transfer stress from the old mesh to the new mesh.

2.4.1 Superconvergent Patch Recovery – SPR

There are certain points in each element of a mesh that exhibit superconvergent

properties. At these sampling points, the convergence order of the finite element

functions is at least one order higher than at others. It is seen that the Gauss points are

the superconvergent sampling points for second order triangular elements (Figure 2.2).

Patch assembly point

Superconvergent sampling pointsNodal values recovered





Figure 2.2 Superconvergent Patch Recovery (Zienkiewicz & Zhu, 1992)

Let ∧

σ be the stress at superconvergent points. If the values of ∧

σ at these points are

accurate to order p+1, it is possible to find superconvergent stresses *σ at all points in

the element defined by a polynomial of degree p. The polynomial is of the same order

as that in the shape function for displacement and can be fitted to the superconvergent

points using a least squares approach.

The recovered stress component *iσ can be written as



a].y,...,y,x,1[pa p*i ==σ 2.1

where, a is a vector of unknown parameters.

An error estimate is provided by

∑=

∧

−σ=∏n

1k

2kkki ]ap)y,x([

2.2

where pk corresponds to the vector associated with the coordinates of the

superconvergent sampling point, (xk, yk).

The value of Π is minimised for a patch with n sampling points. Then, the parameter

vector, a, is deduced as

BAa 1−= 2.3

where

∑=

=n

1kk

Tk ppA 2.4

and

)y,x(pB kkiTk

∧

σ=

2.5

The solution of Equation 2.3 is done component by component .Thus, by means of the

superconvergent sampling points, stress values can be smoothed at each node of a patch.

It should be noted that there are many nodes that belong to more than one patch. In

those cases, the recovered stresses from different patches are averaged to obtain the

final value. In the case of external boundary nodes, the stresses are discontinuous. So,

the nodal values are calculated from the nearest patches for those cases.

2.4.2 Steps of LDFE analysis

The steps of the LDFE analysis are as follows.



1. First, a Python script provides details of the model and generates the mesh for

the first step. The model is used as input to ABAQUS for standard analysis with

very small displacement increment.

2. After completion of this standard analysis step, the output database is post-

processed with the help of another Python script. The coordinates of the nodes

of the displaced model, and also stresses at integration points and reaction forces,

are recorded. The python script also generates the list of elements forming the

top free surface. The order of the nodes and faces of a six noded triangular

element in ABAQUS are numbered in the following manner as shown in Figure

2.3.

1 4 2

5

3

6Face 3 Face 2

Face 1

Y

X 1 4 2

5

3

6Face 3 Face 2

Face 1

1 4 2

5

3

6Face 3 Face 2

Face 1

Y

X

Y

X

Figure 2.3 Six noded triangulare elements in ABAQUS

The list generated by the python script groups three types of elements – S1

which have face 1 at the top surface, S2 which have face 2 at the top surface and

S3 which have face 3 at the top surface. From this list of elements, the nodes

that are at the top surface are identified, although it should be remembered that

they are not arranged in order to define the new surface. With the help of a

Fortran subroutine, the nodes at the top boundary are arranged in order and, after

calculating the displaced coordinates, the new top boundary is defined. The old



deformed mesh is deleted and with the help of another python script, a new

mesh is generated for the deformed regime.

3. Following the recovery procedure mentioned in the previous section, stresses are

recovered from the old Gauss points to the old nodes. Now, the stress

components are interpolated from the old nodes to the new Gauss points

following the scheme described below.

i. First, one old triangle is chosen at a time. Two horizontal boundaries

passing through the extreme top and bottom points of the triangle are

drawn as shown in Figure 2.4. Two vertical boundaries passing through

the extreme left and right points of the triangle are also drawn.

ii. Then, the new integration points that fall between these boundary lines

are identified. Each integration point (G) falling within the rectangular

region is connected to the vertices of the old triangle. This forms three

sub-triangles for each integration point. These three sub-triangles are

ABG, BCG and CAG.

A

G

C

B

G

A

B

C

(a) (b)

A

G

C

B

A

G

C

B

G

A

B

C

G

A

B

C

(a) (b)

Figure 2.4 Determination of position of new Gauss point;

(a) Gauss point inside old triangle; (b) Gauss point outside old triangle



iii. If a new Gauss point is inside the old triangle ABC, the sum of the area

of the sub-triangles is equal to the area of the old triangle. The case is

shown in Figure 2.4a. If not, the sum is greater than the area of the

original triangle - this case is shown in Figure 2.4b. In this way, it is

determined which old element contains the new Gauss point.

iv. The above steps are repeated for all old elements to determine the

position of all the new Gauss points. The stresses at the new integration

points are then interpolated from recovered stresses at the neighbouring

old nodes.

4. For interpolation of the shear strength of the soil from the old mesh to the new

mesh, there is no need to perform the recovery step. The shear strengths at the

new nodes are interpolated directly by quadratic interpolation from the old nodes.

5. The in-built ABAQUS user subroutine SIGINI is used to define the initial

stresses at the new Gauss points. Then, the new remeshed domain with these

initial conditions is submitted to ABAQUS for another incremental small strain

step.

6. All these steps are repeated until the desired displacement is achieved.

The whole process is controlled by a master Fortran program, which repeatedly calls

Fortran subroutines and Python scripts to accomplish the analysis automatically without

the intervention of the user. The default equilibrium and convergence criteria available

in ABAQUS are implemented and convergence is checked at the end of each

incremental step. A flow diagram is shown in Figure 2.5 to describe the entire process.

Essentially this follows the procedure outlined by Wang et al. (2010b), although it has

been implemented in a slightly different way for the present work.



Python Script for initial mesh generation

Small strain ABAQUS analysis

Python Script for post-processing to obtain nodal displacements and stresses

and parameters on integration points

Recovery of stresses and other parameters from integration

points to nodes Coordinates of displaced

boundary nodes

Python script for remeshing

Interpolation of stresses and other parameters from old

nodes to new integration points

Small strain ABAQUS analysis

Loop

as n

eces

sary

Figure 2.5 Implementation of RITSS in ABAQUS

2.4.3 Effects of strain rate and softening

To incorporate the effects of strain rate and strain softening, the original shear strength

of the soil, defined within the Tresca soil model, is modified according to the model

proposed by Einav & Randolph (2005). As far as the LDFE methodology is concerned,

two new variables are recorded at each Gauss point – shear strain rate and cumulative

plastic strain. Shear strain rate and cumulative plastic strain are then interpolated to the

new mesh, in addition to stresses and other parameters as described previously. The

original shear strength at each new Gauss point is then modified and updated as a

function of these two variables. The details of this procedure are given in Chapters 3, 4

and 5.



2.4.4 Modified Cam Clay model

In the later stages of this research, coupled consolidation analyses were performed to

study partially drained behaviour and consolidation effects. The simple Tresca model is

suitable for total stress analyses, but is not able to replicate soil behaviour under

partially drained conditions. The modified Cam Clay (MCC) critical state soil model

was implemented in the LDFE methodology to perform the study and all details are

provided in Chapter 7. There are several new parameters that are required to be defined

within the MCC model. The effective stresses are recovered at old nodes and

interpolated to the new Gauss points as described earlier. The pore water pressure is a

new parameter in this model and is a nodal variable. Pore water pressure was

interpolated from the old nodes directly to the new nodes as initial conditions and

therefore there was no need for a special recovery technique.

Another parameter that needs to be updated during incremental steps is the pre-

consolidation pressure, a0, which defines the current size (half) of the yield surface. The

current yield surface size is recovered from the Gauss points to the old nodes at the end

of each step and then interpolated from the old nodes to the new Gauss points by

interpolation. At this stage, the yield status is checked at the new Gauss points to

identify whether the initial stress components are inside or on the initial yield surface. If

the stress components are outside the yield surface, the following procedure is adopted

to bring it back to the surface. A line is drawn from the centre of the initial yield surface

to the current stress state. This line cuts the yields surface at a point and the initial stress

components are defined based on that point. This correction is important to ensure an

accurate and smooth response.



2.5 REFERENCES

Barbosa-Cruz, E. R. & Randolph, M. F. (2005). Bearing capacity and large penetration

of a cylindrical object at shallow embedment. Proc. Int. Symp. on Frontiers in

Offshore Geotechnics - ISFOG, Perth, Australia, 19-21 September 2005, 615-621.

Bathe, K-J. (1996). Finite element procedures. Prentice Hall, Upper Saddle River, New

Jersey.

Belytschko, T., Kennedy, J. M. & Schoeberle, D. F. (1978). Quasi-Eulerian finite

element formulation for fluid-structure interaction. Proceedings of Joint

ASME/CSME Pressure Vessels and Piping Conference. ASME: New York, 13,

ASME paper 78-PVP-60.

Carter, J. P. & Balaam, N. P. (1995). AFENA User Manual 5.0. Geotechnical Research

Centre, The University of Sydney, Sydney, Australia.

Dassault Systèmes (2007) Abaqus analysis users’ manual, Simula Corp, Providence,

RI, USA.

Donea, J, Fasoli-Stella, P. & Giuliani, S. (1977). Lagrangian and Eulerian finite element

techniques for transient fluid-structure interaction problems. In Trans. 4th Int. Conf.

on Structural Mechanics in Reactor Technology, San Francisco.

Einav, I., & Randolph, M. F. (2005). Combining upper bound and strain path methods

for evaluating penetration resistance. Int. J. Numer. Methods Eng. 63, No. 14, 1991-

2016.

Franck, R. M. & Lazarus, R. B. (1964) Mixed Eulerian-Lagrangian method. In Methods

in Computational Physics, Vol. 3: Fundamental methods in Hydrodynamics,

Academic Press: New York, 47–67.



Ghosh, S. & Kikuchi, N. (1988). Finite element formulation for the simulation of hot

sheet metal forming process. Int. J. Eng. Sci. 26, 143-161.




Hirt, C. W., Amsden, A. A. & Cook, J. L. (1974) An arbitrary Lagrangian-Eulerian

computing method for all flow speeds. J. Comput. Phys. 14, 227–253.

Hossain, M. S., Hu, Y., Randolph, M. F. & White, D. J. (2005). Limiting cavity depth

for spudcan foundations penetrating clay. Géotechnique 55, No. 9, 679-690.

Hossain, M. S. & Randolph, M. F. (2009). Effect of strain rate and strain softening on

the penetration resistance of spudcan foundations on clay. Int. J. Geomech. 9, No. 3,

122-132.

Hossain, M. S. & Randolph, M. F. (2010). Deep-penetrating spudcan foundations on

layered clays: numerical analysis. Géotechnique 60, No. 3, 171–184.


deformation problems in soil. Int. J. Numer. Analyt. Meth. Geomech. 22, No. 5, 327-

350.



Hu, Y. & Randolph, M. F. (1998c). Deep penetration of shallow foundations on

nonhomogeneous soil. Soils and Foundations 38, No. 1, 241-246.

Hu, Y., Randolph, M. F. & Watson, P. G. (1999). Bearing response of skirted

foundation on nonhomogeneous soil. J. Geotech. Geoenviron. Eng. 125, No. 11, 924-

935.



Hughes, T. J. R., Liu, W. K. & Zimmerman, T. K. (1981). Lagrangian–Eulerian finite

element formulation for viscous flows. Comput. Methods Appl. Mech. Eng. 29, 329-

349.

Lu, Q., Randolph, M. F., Hu, Y. & Bugarski, I. C. (2004). A numerical study of cone

penetration in clay. Géotechnique 54, No. 4, 257-267.

Noh, W. F. (1964). A time-dependent two-space-dimensional coupled Eulerian-

Lagrangian code. Methods in Computational Physics, Academic Press, New York,

3,117-179.

van den Berg, P., Teunissen, J. A. M. & Huetink, J. (1991). Cone penetration in layered

media, an ALE element formulation, Proc. Int. Conf. on Computer Methods and

Advances in Geomechanics, 3, 1957-1962.

Wang, D., Hu, Y. & Jin, X. (2006). Two-dimensional large deformation finite element

analysis for the pulling-up of plate anchor. China Ocean Engineering 20, No. 2, 269-

279.

Wang, D., Hu, Y. & Randolph, M. F. (2010a). Three-dimensional large deformation

finite-element analysis of plate anchors in uniform clay. J. Geotech. Geoenviron.

Engng, ASCE 136, No. 2, 355-365.

Wang, D., White, D. J. & Randolph, M. F. (2010b). Large deformation finite element


J. 47, No. 8, 842-856.

Zhou, H. & Randolph, M. F. (2006). Large deformation analysis of suction caisson

installation in clay. Can. Geotech. J. 43, No.12, 1344-1357.




development for cylindrical and spherical penetrometers in strain-softening clay. Int.

J. Geomech. 7, No. 4, 287-295.

Zhou, H. & Randolph, M. F. (2009a). Resistance of full-flow penetrometers in rate-

dependent and strain-softening clay. Géotechnique 59, No. 2, 79-86.

Zhou, H. & Randolph, M. F. (2009b). Numerical investigations into cycling of full-flow

penetrometer in soft clay. Géotechnique 59, No. 10, 801–812.

Zhou, H. & Randolph, M. F. (2011). Effect of shaft on resistance of a ball penetrometer.

Géotechnique 61, No. 11, 973–981.

Zienkiewicz, O. C. & Zhu, J. Z. (1992). The superconvergent patch recovery and a

posterior error estimates. Part 1: The recovery technique. Int. J. Numer. Meth.

Engng. 33, No.7, 1331-1364.



CHAPTER 3

THE EFFECTS OF PENETRATION RATE AND STRAIN

SOFTENING ON THE VERTICAL PENETRATION

RESISTANCE OF SEABED PIPELINES

3.1 INTRODUCTION The problem of pipeline embedment in fine-grained sediments has been an active topic

of research for many years. Failure mechanisms and ultimate loads have been identified

based on classical plasticity theory (Randolph & Houlsby, 1984; Murff et al., 1989;

Martin & Randolph, 2006; Randolph & White, 2008c), small-strain finite element

analyses (Aubeny et al., 2005; Merifield et al., 2008; Merifield et al., 2009) and on

model tests (Verley & Lund, 1995; Dingle et al., 2008). Most of the theoretical studies

assume the pipe to be ‘wished-in-place’ and do not capture the change in geometry

during large amplitude deformation. Model tests performed in the centrifuge (Dingle et

al., 2008) are available, but they are too limited in number and confined to specific

cases to provide general guidance. A recent study has demonstrated the potential of

large deformation finite element (LDFE) analysis for estimating the vertical and lateral

response of pipes over significant displacements (Wang et al., 2010).

Dynamic motions during pipe lay, and potential entrainment of water, result in a

decrease in the shear strength of the seabed soil in the vicinity of the pipe. The amount

of softening depends on the sensitivity and ductility (meaning rate of softening) of the

soil. The effect of strain rate on the shear strength of soil has also been explored widely

(Casagrande & Wilson, 1951; Graham et al., 1983; Lefebvre & LeBoeuf, 1987;

CHAPTER 3: The effects of penetration rate and strain softening…


Biscontin & Pestana, 2001; Lunne et al., 2006; Lunne & Andersen, 2007; Yafrate &

DeJong, 2007, Low et al., 2008). The combined effects of strain rate and softening on

the shear strength of the soil have been modelled recently in theoretical studies of deep

penetration problems (Einav & Randolph, 2005; Zhou & Randolph, 2007, 2009) but has

yet to be applied to the problem of pipe penetration resistance.

This chapter presents the results of a detailed and systematic parametric study of

the vertical embedment of pipelines in clay, incorporating the effects of strain rate and

softening on soil strength. Large deformation finite element analysis has been

performed using the commercial finite element software ABAQUS (Dassault Systèmes,

2007). The simple Tresca soil model was modified to account for the effects of strain

rate and softening. Rate parameters, sensitivity and ductility of the soil were varied to

investigate their effects on penetration resistance. The effects of soil strength non-

homogeneity and buoyancy on the vertical resistance of pipelines were also evaluated.

Simple relationships were then developed, expressing the non-dimensionalised vertical

penetration resistance as a function of the normalised penetration.

3.2 FINITE ELEMENT MODEL The large deformation finite element model developed for this study is based on the

“Remeshing and interpolation technique with small strain” (RITSS, Hu & Randolph,

1998a, 1998b), as described in Chapter 2.

3.2.1 Mesh, boundary conditions and material model A two-dimensional plane strain model was used (as shown in Figure 3.1). The two side-

edges of the model were restrained horizontally but free to move vertically, whereas the

bottom edge was restrained both vertically and horizontally. The pipe was considered as

a rigid body. The 2D plane strain element CPE6 of the ABAQUS element library was

used, which has three vertex nodes and three mid-side nodes. The optimal size of the



model and mesh density were established after trying several options. An incremental

displacement, taken as 1% of the diameter of the pipe, was imposed at the centre of the

pipe.

Figure 3.1 Mesh and boundary conditions This incremental displacement was verified to be small enough by running one set of

analyses with an incremental displacement of 0.1% of the diameter and confirming

negligible variation in the overall response. Contact between the pipe and the soil was

simulated by defining the pipe surface as the master surface and the soil surface as the

slave surface in ABAQUS. For considering friction between pipe and soil, the penalty

method in ABAQUS was used, with the maximum shear stress at the interface, τmax set

as αsum , where α is the interface roughness factor and sum is the mudline shear strength

of soil. In most cases, as detailed below, a value of α = 1/St was used where St is the

sensitivity of the soil, corresponding to the ratio of the intact and remoulded values. As

a result, the interface resistance was generally equal to the remoulded strength at the

mudline.



All the analyses were performed using an undrained total stress approach, based

on the Mohr-Coulomb soil model with zero friction angle (equivalent to the simple

Tresca model). For the elastic part of the linear-elastic-perfectly-plastic soil model, a

Poisson’s ratio of 0.499 (~0.5) was adopted to impose negligible volume change. The

Young’s modulus, E, of the soil was taken as 500 times the shear strength, su, at the

given depth.

3.2.2 Strain rate and strain softening The effects of strain rate and strain softening on shear strength were incorporated in the

analysis according to the model suggested by previous researchers (Einav & Randolph,

2005; Zhou & Randolph, 2007). The simple elastic-perfectly plastic Tresca soil model

was modified accordingly. At each remeshing and interpolation stage of the analysis,

the shear strength was modified to account for a reduction due to strain softening as

well as an enhancement due to high strain rate, with the strength due to the combined

effects given by

[ ] 0u/3

remremref

refmaxu s.e)1(),max(log1s 95ξξ−δ−+δ⎥

⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛γ

γγμ+=

&

&&

3.1

The first part of this relationship captures the effect of strain rate, γ& , with the reference

shear strain, refγ& , taken as 1%/hr or 3×10-6 s-1 and the rate parameter, μ, giving the rate

of strength increase per decade, taken in the range of 0.05-0.2 (Biscontin & Pestana,

2001; Lunne & Andersen, 2007). The maximum shear strain rate at a given location,

maxγ& is defined by

Dv

D/)( p31

max

.

δεΔ−εΔ

=γ

3.2



Where, 1εΔ and 3εΔ are major and minor principal strain, respectively, resulting from a

displacement increment, δ, D is the pipe diameter and vp is the pipe velocity.

The second part of Equation 3.1 represents the effect of strain softening. Here, su0

denotes the original shear strength at the reference shear strain rate prior to any

softening, δrem is the ratio of fully remoulded and initial shear strength and hence is the

inverse of sensitivity of soil. The sensitivity of the soil (St) ranges from 2 to 6 in the

case of marine clays (Randolph, 2004). ξ is the accumulated absolute plastic shear strain

( )pp 31 εΔ−εΔ at the Gauss point, where 1pεΔ and 3pεΔ are major and minor principal

plastic strain, respectively. ξ95 is the cumulative plastic shear strain for 95% shear

strength degradation, with typical value ranging from 10 to 50 (Randolph, 2004).

3.2.3 Validation of finite element model To validate the finite element model, initially a set of parameters were chosen that

matched those from a centrifuge study (Dingle et al., 2008). The prototype diameter of

the pipe was D = 0.8 m. Shear strength, su0 at any depth z for this simulation was taken

as 2.3+3.6z kPa (with z the equivalent prototype depth in m). Submerged (i.e. effective)

unit weight of the kaolin clay was 6.5 kN/m3. The sensitivity of the clay was considered

as 3.2, reflecting results from cyclic T-bar tests. The friction ratio at the pipe-soil

interface, α, was taken equal to the inverse of sensitivity (0.31).

The pipe was penetrated down to a depth of 0.45 times the diameter of the pipe.

The vertical reaction force during embedment, V was non-dimensionalised by Dsu0,

with su0 the nominal intact (reference shear strain rate) shear strength of the soil at a

level corresponding to the invert of the pipe. The measured and computed variations of

normalised vertical resistance on the pipe, V/Dsu0, with non-dimensionalised

embedment, w/D, are plotted in Figure 3.2.



0.0

0.1

0.2

0.3

0.4

0 1 2 3 4 5 6 7

V/Dsu0w

/D α=0.31, no strain effects

α=0.31, μ=0.1, St=3.2, ξ95=10,

reference strain rate = 0.000003 s-1, vp/D=0.015 s-1

centrifuge data

Figure 3.2 Comparison of penetration resistances with centrifuge result

When the effects of strain-rate and softening were not considered, the numerical results

are quite different from the centrifuge data. If both strain rate and softening effects are

taken into account, the computed response gives a good match with the centrifuge data

(Figure 3.2) and hence provides some validation of the large deformation finite element

approach. It should be noted that there are some jaggedness in the LDFE results for

normalised penetration resistance which are generally not observed in case of small

strain analyses. This is due to spatial variation of softened and rate dependent shear

strength in the soil domain. Also, this could happen due to interpolation of the shear

strength values from the previous step to the next step.



3.3 PARAMETRIC STUDY Details of the parameters chosen for the parametric study are shown in Table 3.1. A

base case for rate and softening parameters were chosen with 1000refD/pv =γ& ,

μ = 0.1, St = 3 and ξ95 = 20. The submerged unit weight of the soil, γ' = 5 kN/m3 was

considered for this case, since this is typical of deep water sediments. Keeping other

parameters equal to this base case, one parameter was varied at a time (as in Table 3.1).

Table 3.1 Parameters chosen for LDFE analyses

kD/sum γ'D/sum refp D/v γ& μ St ξ95

0 0.25 0, 100, 1000, 10000

0.1 3 20

0 0.25 1000 0, 0.05, 0.1, 0.15

3 20

0 0.25 1000 0.1 1, 2, 3, 6

20

0 0.25 1000 0.1 3 10, 20, 30

0 0.15, 0.25, 0.35

1000 0.1 3 20

1 1.25 0, 100, 1000, 10000

0.1 3 20

1 1.25 1000 0, 0.05, 0.1, 0.15

3 20

1 1.25 1000 0.1 1, 2, 3, 6

20

1 1.25 1000 0.1 3 10, 20, 30

20 10 0, 100, 1000, 10000

0.1 3 20

20 10 1000 0, 0.05, 0.1, 0.15

3 20

20 10 1000 0.1 1, 2, 3, 6

20

20 10 1000 0.1 3 10, 20, 30

20 6, 10, 14 1000 0.1 3 20

The pipe diameter, D was taken as 0.5 m for all the cases, although all results are

presented in normalised form and may be generalised to other diameters. The shear



strength of the soil, su0, at any depth z is assumed to vary according to the following

linear variation.

kzss um0u += 3.3

Where, sum is the (intact) shear strength at the mudline and k is the shear strength

gradient. Three values of κ (= kD/sum) corresponding to 0 (sum = 10 kPa and k = 0), 1

(sum = 2 kPa and k = 4 kPa/m) and 20 (sum = 0.25 kPa and k = 10 kPa/m) were selected.

The parametric study was repeated for these three values of κ. The maximum shear

stress at the pipe soil interface, τmax, was taken as αsum, with α equal to the inverse of

the soil sensitivity. So, the maximum shear stress at the interface is actually the mudline

remoulded shear strength. For each case, the pipe was penetrated down to a depth of 1D

and vertical resistance forces were recorded at every increment of displacement (1% of

the diameter of the pipe).

3.3.1 Effect of unit weight of soil The vertical penetration resistance may be considered as the sum of the geotechnical

resistance and a component due to buoyancy as the pipe becomes embedded within the

soil. The geotechnical resistance is generally expressed as a power law (Aubeny et al.,

2005), so the total vertical resistance can be written as:

0u2s

b

b

0u sD

DA

fDwa

DsV γ′

+⎟⎠⎞

⎜⎝⎛=

3.4

Where the first part of the right hand side of the equation denotes geotechnical

resistance (with power law parameters, a and b) and the second part represents the

resistance due to buoyancy. As is the submerged cross-sectional area of the pipe, so that

Asγ' is the (nominal) weight of soil displaced by the pipe. This is adjusted by a factor, fb,



which accounts for the enhanced buoyancy effect due to heave of the soil adjacent to the

pipe. Merifield et al. (2009) found that fb should be taken around 1.5.

Keeping all other parameters as in the base case, the effect of unit weight was

explored for soils with κ = 0 and κ = 20, taking submerged unit weights of 3, 5 and

7 kN/m3. It is evident from Figure 3.3 that the effect of unit weight is more pronounced

for soil with a high value of κ; this is because the value of the non-dimensional

parameter γ'D/sum lies in the range 0.15 to 0.35 for soil with κ = 0, whereas it is far

higher, varying from 6 to 14, for soil with κ = 20.

To evaluate appropriate values of fb for these cases, parallel sets of analyses

were run with and without considering the self-weight of soil. This allowed the

geotechnical resistance term to be isolated, and then the buoyancy term quantified by

subtracting the geotechnical resistance from the total resistance for analyses that

included self-weight of the soil. The value of fb was thus deduced, albeit on the

assumption that the geotechnical resistance is unchanged between the two cases,

implying no significant change to the penetration mechanism.

As shown in Figure 3.4(a), the average value of fb was ~1.4 for κ = 0. For soil

with a high shear strength gradient (κ = 20), the average value of fb was ~1.75 (Figure

3.4b). A value of fb = 1.5 was obtained for κ = 1. The value of fb is therefore a function

of the shear strength gradient, k. It was found to vary linearly with the non-dimensional

term kD/su,avg, where, su,avg is the average of shear strengths at the mudline and at a

depth of one pipe diameter. Hence kD/su,avg is bounded by 0 (for k = 0) and 2 (for

sum = 0). Figure 3.5 shows the variation of fb with kD/su,avg for these three cases, with a

simple linear trend line given by



( ) 38.1s/kD2.0f avg,ub += 3.5

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8

V/Dsu0w

/D

κ = 0

γ'D/sum = 0.15, 0.25, 0.35

(a)

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8

V/Dsu0

w/D

κ = 20

γ'D/sum = 6, 10, 14

(b)

Figure 3.3 Variation of vertical resistance for different submerged unit weights: (a) κ = 0; (b) κ = 20



0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8

Non-dimensional Parameters

w/D

κ = 0γ'D/su0 = 0.25

(V/Dsu0)weighty - (V/Dsu0)weightless

(V/Dsu0)weightless

(V/Dsu0)weighty

fb

(a)

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8

Non-dimensional Parameters

w/D

κ = 20

(V/Dsu0)weighty - (V/Dsu0)weightless

(V/Dsu0)weightless

(V/Dsu0)weighty

fb

γ'D/su0

(b)

Figure 3.4 Buoyancy factor fb and other non-dimensional parameters with depth: (a) κ = 0; (b) κ = 20



0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 0.4 0.8 1.2 1.6 2

kD/su,avg

f b

Figure 3.5 Variation of buoyancy factor fb with non-dimensional parameter kD/su,avg

3.3.2 Geotechnical resistance It is convenient to quantify the geotechnical resistance using closed-form expressions

suitable for routine design. Previously, power law relationships for the coefficients ‘a’

and ‘b’ in Equation 3.4 have been obtained as a function of embedment (Aubeny et al.,

2005; Merifield et al., 2009). Aubeny et al. (2005) gave power-law fit coefficients for a

‘wished-in-place’ pipe with an open trench directly above it, and hence did not consider

the change in geometry and formation of heave during continuous penetration. They

also did not consider the effects of strain rate and softening. Merifield et al. (2009) gave

results for ‘pushed-in-place’ pipes in uniform strength soil, and also did not consider the

effects of strain rate and softening. Aubeny et al. (2005) gave results for two extreme

values of κ, (0 and ∞) and plotted a best-fit curve between them to predict the resistance

for intermediate values of κ. The present study extends the previous work by



establishing simple relationships for a range of κ values, but also accounting for rate

effects and strain softening.

To compare results with Aubeny et al. (2005), the geotechnical resistances for different

κ values in this study were averaged for displacements down to 0.5D and fitted to a

best-fit power law curve.

Table 3.2 Comparison of coefficients ‘a’ and ‘b’ from literature and this study

Base case values for strain rate and softening parameters were adopted, as detailed

earlier. Coefficients ‘a’ and ‘b’ of Equation 3.4 for this base case and those from other

researchers are shown in Table 3.2 for rough pipes only. The coefficients are applicable

for the particular strain rate and softening parameters adopted in the base case. The

effect of these parameters on the response is explored below and a more refined set of

coefficients are derived.

3.3.3 Effect of normalised velocity refγ/Dpv &

Three values of refγ/Dpv & , 100, 1000 and 10000, were investigated for the parametric

study with all other parameters similar to the base case. Soil with zero rate-dependency

was also included for comparison. For κ = 1, the variation of vertical resistance for

different values of refγ/Dpv & is shown in Figure 3.6a.

a b Comments Aubeny et al.

(2005) 6.73 0.29 Wished-in-place, no strain effects

Merifield et al. (2008) 7.4 0.4 Wished-in-place,

no strain effects Merifield et al.

(2009) 7.1 0.33 Pushed-in-place, no strain effects

Base Case of Present Study 6.81 0.25

Pushed-in-place, Strain rate and strain

softening effects



0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7

V/Dsu0w

/D

κ = 1μ = 0.1ξ95 = 20St = 3

= 100, 1000, 10000

No rate effect

(a)

ref

.

p D/v γ

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7

V/Dsu0,eq

w/D

κ = 1μ = 0.1ξ95 = 20St = 3

(b)

Figure 3.6 Effect of normalised penetration rate on vertical resistance: (a) V normalised by original shear strength; (b) V normalised by equivalent shear strength



As the normalised velocity increases from 100 to 10000, the vertical resistance

increases by more than 20%. It is helpful to identify what equivalent soil strength, su0,eq,

would reflect the effect of the increasing strain rate in the soil. Thus, instead of

normalising V by Dsu0, V was normalised by Dsu0,eq, where

( )[ ]refpr0ueq,0u D/vflog1ss γμ+= & 3.6

The factor fr reflects the average operative shear strain during each increment of pipe

penetration relative to the penetration rate, refp D/v γ& . This factor was varied in order

to find a suitable value to bring the various curves together, and a value of 0.7 was

found to be appropriate. It can be seen from Figure 3.6b that now points from all the

above cases fall in a narrow band, implying that a representative operative strength

during shallow pipe penetration is that at a strain rate corresponding to D/v7.0 p .

3.3.4 Effect of rate parameter μ The rate parameter, μ, was varied across values of 0.05, 0.1 and 0.15 to evaluate the

effect on the vertical resistance. Figure 3.7a shows the variation of vertical resistance

with normalised depth for different values of μ for κ = 1. The response for μ = 0 is also

included for comparison purpose. In this case also, vertical resistance increased by more

than 20% as μ was increased from 0.05 to 0.15. Normalising the vertical resistance by

su0,eq, using Equation 3.6 with fr = 0.7, all these curves fall in a narrow band (Figure

3.7b).



0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8

V/Dsu0w

/D

κ = 1ξ95 = 20St = 3

μ = 0, 0.05, 0.1, 0.15

(a)

1000D/v ref

.

p =γ

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8

V/Dsu0,eq

w/D

κ = 1ξ95 = 20

St = 3

(b)

1000D/v ref

.

p =γ

Figure 3.7 Effect of rate parameter μ on vertical resistance: (a) V normalised by original shear strength; (b) V normalised by equivalent shear strength



3.3.5 Effect of sensitivity The sensitivity of the soil causes the operative strength during pipe penetration to be

lower than the original intact strength. Three values of sensitivity, St = 2, 3 and 6, were

considered and other parameters for all these cases were kept equal to the base case.

Higher sensitivity results in a higher rate of softening and lower penetration resistance.

Figure 3.8a shows variations of vertical resistance for different values of sensitivity for

soil with κ = 1. Results for soil with no softening, i.e. a sensitivity of unity, are also

shown in this figure. The vertical resistance reduces by more than 20% at shallow

depths as the sensitivity increases from 1 to 6. In all cases, the interface resistance was

taken equal to the inverse of the sensitivity times the mudline shear strength (i.e an

interface resistance = 0.167sum, 0.33sum, 0.5sum and sum for sensitivity values of 6, 3, 2

and 1 respectively). If a single value of interface friction is used for all cases,

corresponding to the base case value of 0.33sum, the variation in vertical resistance is

much less (as shown in Figure 3.8b). This is because now there is only the effect of the

change of sensitivity within the soil mass itself, while previously there was an

additional effect of the interface initially being at the different values of fully remoulded

strength, sum/St.

To characterise the effect of the change in soil sensitivity, an equivalent shear strength

was back-calculated as

( )[ ]95s /)D/w(f3remrem0ueq,u e1ss ξ−δ−+δ= 3.7

The term fs(w/D) in Equation 3.7 reflects the equivalent plastic strain (proportional to

w/D) undergone by the soil as it is deformed by the pipe. A value of 0.8 for the constant

fs was required to bring together the curves for the cases with different sensitivities and



the same α (Figure 3.9), implying that a representative operative strength during shallow

pipe penetration is that at a plastic strain corresponding to 0.8w/D.

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8V/Dsu0

w/D

κ = 1ξ95 = 20μ = 0.1

St = 6, 3, 2, 1

(a)

1000D/v ref

.

p =γ

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8

V/Dsu0

w/D

κ = 1ξ95 = 20μ = 0.1

St = 6, 3, 2, 1

(b)

1000D/v ref

.

p =γ

Figure 3.8 Effect of sensitivity on vertical resistance: (a) α = 1/St ; (b) constant α (= 0.33)



0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8

V/Dsu0,eq

w/D

κ = 1ξ95 = 20μ = 0.1fs = 0.8

1000D/v ref

.

p =γ

Figure 3.9 Vertical resistances normalised by equivalent shear strength for different sensitivity values (fs = 0.8)

3.3.6 Effect of ductility parameter ξ95

The value of the ductility parameter, ξ95, was varied between 10, 20 and 30 to examine

its effect on the vertical resistance, as shown in Figure 3.10a for κ = 1. The penetration

resistance increases by more than 10% as the soil becomes more ductile, with ξ95

increasing from 10 to 30. Vertical resistances were normalised using an equivalent shear

strength based on Equation 3.7 and a value of fs = 0.8, which brought all the curves of

Figure 3.10a together, as shown in Figure 3.10b.



0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8

V/Dsu0w

/D

κ = 1μ = 0.1St = 3

ξ95 = 10, 20, 30

(a)

1000D/v ref

.

p =γ

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8

V/Dsu0,eq

w/D

κ = 1μ = 0.1St = 3fs = 0.8

(b)

1000D/v ref

.

p =γ

Figure 3.10 Effect of softening parameter ξ95 on vertical resistance: (a) V normalised by original shear strength; (b) V normalised by equivalent shear strength



3.3.7 Combining effects of strain rate and softening parameters It may be seen from the above results that the strain rate and softening parameters have

marked effects on the overall penetration response of pipelines. An attempt is made here

to derive a single curve for the vertical penetration resistance with depth that accounts

for the effects of all these parameters. The current practice is to unify the penetration

response in soils of different strength profiles by normalizing the vertical force by the

shear strength of the soil at the invert of the pipe. In strain rate dependent, softening soil,

this approach is extended by normalizing the vertical resistance force by an equivalent

shear strength of the soil at the pipe invert, incorporating the effects of strain rate and

softening parameters. The equivalent shear strength, su0,eq is expressed as

( )[ ] ( )[ ] 0u)/)D/w(f3(

remremrefpreq,0u se1D/vflog1s 95s ξ−δ−+δγμ+= & 3.8

where fr and fs are the two constant factors introduced earlier and all other symbols are

as in Equation 3.1. The vertical resistance force, V, is normalised by Dsu0,eq. For a

particular κ value, the vertical resistance normalised by the equivalent shear strength at

the pipe invert was plotted in a single graph for all the cases of Table 3.1. It is seen from

Figure 3.11 that all the points fall into a narrow band when fr = 0.7 and fs = 0.8 are used.

These sets of values can be fitted by power law curves of the form V/Dsu0,eq = a.(w/D)b,

although two separate portions are required to provide a good fit, matching the curves at

w/D = 0.1. The best fits are expressed as:

0.1for w/D Dw2.5

DsV

0.1for w/D Dw103.3

Dw10

DsV

DsV

19.0

eq,0u

5.0

1.0D/weq,0ueq,0u

>⎟⎠⎞

⎜⎝⎛=

≤≈⎟⎠⎞

⎜⎝⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛=

= 3.9



0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6

V/Dsu0,eq

w/D

LDFE pointsFitted Curve

κ = 1

V/Dsu0,eq = 5.2.(w/D)0.19

V/Dsu0,eq =

V/Dsu0,eq,w/D=0.1x(10.w/D)0.5

Figure 3.11 Best fit power law curve for vertical resistance with depth

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6

V/Dsu0,eq

w/D

κ = 20, 1, 0

Figure 3.12 Best fit power law curves for vertical resistances for different κ



3.3.8 Effect of variation of soil shear strength profile The power law equation fit stated above is valid for a particular shear strength profile

(or value of κ). Two other shear strength profiles were considered: uniform soil with

κ = 0 and soil with high shear strength gradient, κ = 20. The previous procedure for

κ = 1, was repeated for these two cases. For normalised displacement w/D ≥ 0.1,

V/Dsu0,eq = a.(w/D)b equations were fitted and values of coefficients ‘a’ and ‘b’ were

obtained. These coefficients, together with the value of V/Dsu0,eq at w/D = 0.1, are

tabulated in Table 3.3 for different values of κ. For w/D ≤ 0.1, the same curve as in

Equation 3.9 is used. The resulting curves are shown on Figure 3.12. For other values of

κ, the fitted curves can be interpolated.

Table 3.3 Power law fit coefficient ‘a’ and ‘b’ for different shear strength profile

3.4 SOIL FLOW PATTERN The main advantage of the present large deformation finite element analysis is its ability

to capture the changes in geometry and subsequent formation of heave when the pipe is

pushed into the soil. It is of interest to consider the shape and size of the soil heave for

different shear strength profiles, and also the soil flow mechanism during pipe

penetration for different cases. These are illustrated for a normalised displacement

w/D = 0.5 in Figure 3.13. It may be seen that for soil with low κ values, the mechanism

is relatively deep and wide with the heave decaying gradually with distance from the

κ a b (V/Dsu0,eq)w/D=0.1

0 5.4 0.23 3.18

1 5.2 0.19 3.35 20 4.7 0.17 3.18



pipe. On the other hand, for soil with high κ the mechanism is shallower – tending to

favour the weaker shallower soil – and with the heave concentrated close to the pipe.

κ = 0 κ = 0

κ = 1 κ = 1

κ = 20 κ = 20

Figure 3.13 Deformation pattern and instantaneous velocity field at w/D = 0.5 for different κ

3.5 CONCLUDING REMARKS The large deformation finite element analysis approach described in this chapter

provides a more rigorous analysis for vertical penetration of seabed pipelines than other

theoretical methods currently available in the literature. The method accounts for



geometry changes in the surface of the seabed in the form of heave, and also the effects

of strain rate and softening by modifying the simple linearly-elastic perfectly-plastic

Tresca soil model. Profiles of vertical penetration resistance with normalised

displacement obtained from this study were compared with results from a centrifuge

model test. Good agreement between these two results was obtained, supporting the

validity of the finite element approach.

The shear strength was modified in each step of the LDFE analysis by

multiplying it with two factors, accounting for (a) enhancement of strength at increasing

strain rates (relative to a reference value) and (b) softening as the soil is remoulded. It

was found that the strain rate and softening parameters have significant effect on the

vertical resistance. However, it was found that normalising the vertical resistance by an

equivalent shear strength, accounting for the strain rate and softening parameters, led to

a narrow band of values when plotted against normalised penetration of the pipe. These

sets of values were fitted by power law expressions, using two different equations for

w/D ≤ 0.1 and w/D > 0.1.

The effect of buoyancy was also explored in this chapter by varying the

submerged unit weight of the soil. The total vertical resistance was divided into a

geotechnical resistance and resistance due to buoyancy. Values for fb (a multiplication

factor on Archimedes’ buoyancy) were provided for different strength profiles, refining

the previous published value of 1.5.

The effect of soil non-homogeneity was also investigated in this chapter, leading

to different power law fit coefficients for soils with different shear strength profile,

expressed as κ = kD/sum. The heave patterns and associated soil flow kinematics were

illustrated for different values of κ.



It should be noted that the present chapter does not deal with excess embedment of

pipes due to dynamic lay effects. Another limitation of the present work is that due to

numerical difficulty, constant interface shear strength as a fraction of the original

mudline shear strength is assumed. In reality, the interface shear strength should be a

fraction of the remoulded shear strength at the penetration depth.

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Bruton, D. A. S., White, D. J., Cheuk, C. Y., Bolton M. D. & Carr M. C. (2006). Pipe-



Paper OTC 17944.

Casagrande, A. & Wilson, S. D. (1951). Effect of rate of loading on the strength of

clays and shales at constant water content. Géotechnique 2, No. 3, 251-263.

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Einav, I., & Randolph, M. F. (2005). Combining upper bound and strain path methods

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Low, H. E., Randolph, M. F., DeJong, J. T. & Yafrate, N. J. (2008). Variable rate full-

flow penetration tests in intact and remoulded soil. Proc. 3rd Int. Conf. on

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Lunne, T. & Andersen, K. H. (2007). Soft clay shear strength parameters for deepwater

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Lunne, T., Berre, T., Andersen, K. H., Strandvik, S. & Sjursen, M. (2006). Effects of

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in cohesive soil. Géotechnique 56, No. 2, 141-145.







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Murff, J. D., Wagner, D. A. & Randolph, M. F. (1989). Pipe penetration in cohesive

soil. Géotechnique 39, No. 2, 213-229.

Randolph, M. F., & Houlsby, G. T. (1984). The limiting pressure on a circular pile

loaded laterally in cohesive soil. Géotechnique 34, No. 4, 613-623.

Randolph, M. F. (2004). Characterization of soft sediments for offshore applications.

Keynote Lecture, Proc. 2nd Int. Conf. on Site Characterization, Porto, Portugal, Vol.

1, Millpress Science Publishers, Rotterdam, 209-231.

Randolph, M. F. & White, D. J. (2008a). Offshore Foundation Design – A Moving

Target. Proc. BGA International Conference on Foundations, Dundee, IHS BRE

Press, London, 27-59.

Randolph, M. F. & White, D. J. (2008b). Pipeline embedment in deep water: process


OTC 19128.

Randolph, M. F. & White, D. J. (2008c). Upper-bound yield envelopes for pipelines at


Verley, R. & Lund, K. M. (1995). A soil resistance model for pipelines placed on clay

soils. Proc. Int. Conference on Offshore Mechanics and Arctic Engineering,

Copenhagen, ASME, Vol. 5, 225-232.



J. 47, No. 8, 842-856.



Yafrate, N. J. & DeJong, J. T. (2007). Influence of penetration rate on measured

resistance with full-flow penetrometers in soft clay. Proc. GeoDenver 2007-

Advances in Measurement and Modelling of Soil Behaviour, ASCE, GSP No. 173.


development for cylindrical and spherical penetrometers in strain-softening clay. Int.

J. Geomech. 7, No. 4, 287-295.

Zhou, H. & Randolph, M. F. (2009). Resistance of full-flow penetrometers in rate-

dependent and strain-softening clay. Géotechnique 59, No. 2, 79-86.



CHAPTER 4

LARGE LATERAL MOVEMENT OF PIPELINES ON A

SOFT CLAY SEABED: LARGE DEFORMATION FINITE

ELEMENT ANALYSIS

4.1 INTRODUCTION Lateral buckling due to internal temperature and pressure can move deepwater pipes a

large distance across the seabed, and can provide an effective mitigation against the

high loads that are generated if the pipe is fully constrained. During on-bottom lateral

buckling a pipeline might sweep laterally by 10 or 20 diameters across the seabed. To

model this behaviour in design, it is necessary to estimate the pipe-soil force-

displacement response. This behaviour cannot be assessed via a single conservative

response – it must be bracketed because both high and low geotechnical resistance can

hamper a design (Bruton et al. 2007).

The existing models for lateral pipe-soil resistance are mainly derived for the

analyses of pipeline stability under hydrodynamic loading, and are not suited to the

large-amplitude movements associated with buckling. The challenge is to extend

existing models to account for changes in the seabed geometry and the soil remoulding

effects that influence pipe-soil resistance during large amplitude cyclic displacements.

An important design parameter is the large-amplitude (‘residual’) lateral resistance,

which is generally assumed to be a steady value, once the pipe has ‘broken out’.

In recent years, lateral pipe soil interaction has been studied extensively by

researchers, with a particular focus on the undrained conditions that generally prevail

during pipe movements on the fine-grained soils found in deep water. It is now well

CHAPTER 4: Large lateral movement of pipelines on a soft clay seabed…


known that the resistance from soil during lateral movement is not governed by a

Coulomb friction force at the pipe soil interface. When a pipe is laid on the seabed, it

partially penetrates into the soil due to its self weight and due to other factors such as

the dynamic movement created by the laying process (Randolph & White, 2008a). This

initial embedment has a significant influence on the lateral pipe resistance. When the

pipe is forced to move laterally, it rises or dives depending on its weight relative to the

current bearing capacity (Zhang et al., 2002; Randolph & White, 2008b). The passive

resistance from the soil berm ahead of the pipe governs the lateral pipe-soil interaction

force (White & Cheuk, 2008; White & Dingle, 2010). Also, the large amplitude

movement of the pipe across the seabed during thermal expansion causes remoulding of

the soil. This remoulding has a marked influence on the operative soil strength and the

resulting lateral pipe resistance.

Relatively few previous studies have investigated pipe-soil resistance during

large displacements. Experimental investigations into this behaviour have been

performed at large scale and at reduced scale in a centrifuge, as reported by Bruton et al.

(2006), Cheuk et al. (2007), Bruton et al. (2008) and Cardoso & Silveira (2010). These

studies have led to empirical expressions for the lateral breakout resistance and the

subsequent steady residual resistance. These methods are commonly used in design, but

are subject to significant scatter and uncertainty (AtkinsBoreas 2008). More recently,

studies have examined the detailed mechanisms of soil movement during large

amplitude pipe displacements. Physical modelling of pipe-soil interaction in a

geotechnical centrifuge, using particle image velocimetry (PIV) to quantify the

observed movements, has been performed (Dingle et al. 2008). This study measured

lateral pipe-soil interaction forces and linked them to the observed failure mechanisms.

A more limited number of numerical studies have been performed. Hesar (2004)

reported one of the first finite element studies of large-amplitude lateral movement of



pipelines using ABAQUS/Explicit together with an ALE (Arbitrary Lagrangian-

Eulerian) adaptive meshing algorithm. The large-amplitude lateral behaviour of pipes

with different self weights was presented. Konuk & Yu (2007) also developed ALE

finite element models for the lateral movement of pipelines, using the software package

LS-DYNA. Both these studies showed the influence of initial embedment and pipe

weight on lateral pipe soil interactions, but did not include any attempt to generalise the

observed behaviour.

Physical model tests have shown the controlling influence of two large deformation

effects: (i) the changing topography of the seabed and (ii) the changing strength of the

sediment, as it is disturbed and remoulded. This chapter shows how finite element

analyses can capture both of these important effects. It is shown that with the help of the

large deformation finite element technique and a particular soil model that can capture

remoulding effects, the key aspects of lateral pipe-soil interaction that are observed in

physical model tests can be reproduced.

In this chapter, the large deformation finite element methodology implemented in

ABAQUS (Dassault Systèmes, 2007) is used to study the lateral movement of a pipe

embedded in soft clay. The pipe is moved a significant distance (seven times its

diameter) to ensure steady state soil resistance is reached. Initially, studies are presented

for ideal soil with shear strength not depending on the strain rate or softening. After that,

a rate dependent and softening soil model is adopted and the results are compared with

the ideal case. The concept of effective embedment – which is a summation of the

original embedment and an increase of embedment due to the berm ahead of the pipe –

is presented. It is shown that the normalised horizontal resistance may be related to the

effective embedment through a simple relationship, regardless of the other parameters.



4.2 SOIL CONSTITUTIVE MODELLING

Within each small strain analysis, the soil is modelled as an elastic perfectly-plastic

material, with failure according to the Tresca yield criterion. The particular value of the

Tresca shear strength for each element within the mesh is calculated when each small

strain analysis is initialised. This calculation accounts for the influences of cumulative

strain (i.e. the level of disturbance or remoulding) on the soil strength, as well as the

current strain rate.

The same methodology as described in previous chapters has been adopted to

modify the simple Tresca soil model to incorporate the effects of strain rate and

softening. After each analysis step, the original shear strength of the soil at every node,

su0, is modified to an updated value, su, according to the following formula.

( )[ ] 0u/3

remremref

p31u se1

D/vD/

)(,1maxlog1s 95ξξ−δ−+δ×

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛γδ

εΔ−εΔμ+=

& 4.1

Where the first part of the equation adjusts the strength according to the strain rate

effect and the second part allows for strain softening. 1εΔ and 3εΔ are the major and

minor principal strains, respectively, resulting from a displacement increment, δ/D,

where D is the pipe diameter. vP is the pipe velocity. μ is the rate of strength increase

per decade of strain rate, refγ& is the reference strain rate. Softening is taken as an

exponential function of the cumulative absolute plastic shear strain ξ. Here δrem denotes

the ratio of fully remoulded strength to the initial strength, hence is the inverse of

sensitivity, St. The parameter ξ95 reflects the relative ductility of soil and is the value of

ξ at which the soil has undergone 95% remoulding.



Incompressible – i.e. undrained – conditions were imposed and a rigidity index,

E/su = 500 and Poisson’s ratio, ν = 0.49 were prescribed. The penalty method within

ABAQUS was used to model the interaction between the pipe and the soil surfaces. A

constant limiting shear stress, τmax = αsum, with α = 0.5, was imposed at the pipe- soil

interface, along with a zero tension condition. Here, sum denotes the undrained shear

strength of the soil at the mudline and α is termed the interface friction ratio.

4.3 TYPICAL FINITE ELEMENT MESHES A two-dimensional plane strain model with the pipe as rigid and the soil as deformable

was established. Six-noded triangular elements (CPE6 in the ABAQUS standard library)

were used for discretisation. The details of the mesh and boundary conditions are

illustrated in Figure 4.1. Very fine meshing with a minimum size equal to 0.05 times the

pipe diameter is used near the pipe. In each small displacement step, the pipe was

moved by a displacement of 1% of its diameter, before the remeshing and interpolation

procedure was performed.

The extent of the finest meshing from the centre of the pipe at the start of the

analysis was up to 1.5 times the pipe diameter on both sides and 1 time the diameter

below from the mudline. The sufficiency of these criteria is confirmed by the results

shown later in Figure 4.11, where it can be seen that soil in this zone undergoes

extensive strain softening by the pipe movement.



Figure 4.1 Mesh and boundary conditions

The advantage of this methodology is that the frequent remeshing does not allow

the mesh to become distorted. However, the pipe can be displaced by significant

cumulative distances. Snapshots of the finite element mesh of the soil domain at

different stages of pipe movement are shown in Figure 4.2 for the analysis described

later as Case G (Table 4.4). The initially low mesh density in the far field is replaced by

progressively finer elements as the pipe approaches. This updating is performed

automatically according to the refinement criteria described above. There is no manual

intervention during the analysis. The mesh is not ‘unrefined’ in regions that are no

longer undergoing intensive deformation, with the small elements being combined into

larger elements. However, this could potentially be an additional strategy within the

refinement process if it was desirable to reduce the total number of elements to facilitate

more rapid analysis. However, the distribution of strength and other material parameters

(e.g. the cumulative plastic strain) is highly variable within the ‘trail’ of deformation



behind the pipe. Any coarsening of the previously-refined mesh would smear these relic

features that are left within the seabed behind the pipe.

(a) Prior to horizontal movement

(b) u = 1D

(c) u = 4D

(d) u = 7D

(a) Prior to horizontal movement

(b) u = 1D

(c) u = 4D

(d) u = 7D

Figure 4.2 Soil mesh at different stages of movement (Case G)

Figure 4.2 shows clearly the growth of a soil berm ahead of the pipe as it sweeps

laterally.



4.4 IDEAL SOIL CASE Firstly, four cases with soil strength that is independent of strain rate or softening were

simulated. The soil shear strength increased with depth with a linear gradient k and a

mudline strength, sum. The soil and pipe parameters adopted in these cases are tabulated

in Table 4.1 and the details of the four cases are shown in Table 4.2. The parameters

tabulated in Table 4.1 were chosen because they allow the results to be compared with

the centrifuge modelling results presented by Dingle et al. (2008); the model test data

provide an excellent means to validate the present finite element analysis. Vmax in Table

4.2 denotes the penetration resistance experienced by the pipe at the end of initial

vertical embedment and V is the vertical load applied to the pipe during lateral motion.

Table 4.1 Pipe and soil parameters adopted in the study Parameters Values

Pipe Diameter, D 0.8 m

Shear strength of soil at mudline, sum 2.3 kPa

Shear strength gradient, k 3.6 kPa/m

Submerged unit weight of soil, γ' 6.5 kN/m3

Interface friction ratio, α 0.5

Initially the pipe was pushed vertically to different depths, unloaded to a specified

vertical load, and then moved laterally up to a distance of 7 times its diameter (D) under

a constant vertical load. Different initial embedments of w = 0.15D, 0.3D and 0.45D

(centrifuge test) were considered (cases B, C and D respectively). This range represents

typical values of as-laid pipe embedment. The vertical load applied during lateral

movement for all the cases was 0.19 times the maximum vertical load at the 0.45D

vertical penetration (as in the model test). Case A involved no over-penetration - i.e. the

initial embedment was achieved with the same vertical load as during the lateral

sweeping stage.



Table 4.2 Simulation details for cases of ideal soil

Case V (kN/m) V/Vmax (w/D)ini (w/D)fin (H/V)fin

A 2.96 1.00 0.02 0.026 0.63

B 2.96 0.33 0.15 0.021 0.63

C 2.96 0.24 0.30 0.011 0.78

D 2.96 0.19 0.45 0.002 0.86

The vertical movement of the pipe during the lateral motion – i.e. trajectory of the

pipe – is shown in Figure 4.3. In all cases except for Case A (no over-penetration) the

pipe moves upwards back to the original surface or just below the surface. For the no

over-penetration case, the pipe first moves downward for some distance and then moves

upward.

0

0.1

0.2

0.3

0.4

0.5

0 1 2 3 4 5 6 7Horizontal displacement, u/D

Pipe

inve

rt em

bedm

ent,

w/D

Centrifuge dataNo over-penetrationInitial embedment = 0.15DInitial embedment = 0.30DInitial embedment = 0.45D

Centrifuge data, Cases A, B, C and D

Figure 4.3 Trajectory of pipe invert during lateral motion (Ideal soil model, Cases A-D)



0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7

Horizontal displacement, u/D

Nor

mal

ised

horiz

onta

l res

istan

ce, H

/Ds u

0 Centrifuge dataNo over-penetrationInitial embedment = 0.15DInitial embedment = 0.30DInitial embedment = 0.45D


Figure 4.4 Normalised horizontal resistance during lateral motion (Ideal soil model, Cases A-D)

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7


Equi

vale

nt fr

ictio

n fa

ctor

, H/V

Centrifuge dataNo over-penetrationInitial embedment = 0.15DInitial embedment = 0.30DInitial embedment = 0.45D


Figure 4.5 Equivalent friction factor during lateral motion (Ideal soil model, Cases A-D)

The horizontal resistance during lateral motion, H, can be normalised by Dsu0,

where su0 is the shear strength of the soil at the invert of the pipe. The variation in



normalised lateral resistance, H/Dsu0 during lateral displacement, u/D, is shown in

Figure 4.4. As the shear strength of the soil changes with depth, the change in su0 is also

reflected in the normalised lateral response if H is normalised by Dsu0. For this reason, it

is useful also to normalize H by the operating vertical load, V, which remains constant

throughout the lateral movement. H/V is referred to as the equivalent lateral friction

factor and is shown in Figure 4.5.

Comparing Cases A-D, it is evident that over-penetration of the pipe leads to a

lateral response that softens after the pipe breaks out, as the pipe moves upwards

towards the ground surface. In terms of normalised resistance, H/Dsu0, this effect is

masked by the changing soil strength at the invert elevation. In all cases, a steady

residual resistance is reached after ∼3-4 diameters of lateral movement, when the pipe

invert is located at an embedment of < 0.03D below the original soil surface (and in

cases A and B the pipe was continuing to rise even closer to the surface at the end of the

simulation). This residual resistance is higher for a higher initial embedment (noting

that all cases involved the same weight of pipe). This is because a deeper initial

embedment leads to a larger soil berm being pushed ahead of the pipe.

The same general trend is apparent in the model test – the over-loaded pipes rise

upwards to the surface, and an approximately steady resistance is reached. However,

some significant differences are evident when the large displacement behaviour is

considered:

1. The LDFE trajectories are curved throughout the movement, whereas the model

test trajectory is approximately straight over the range 0.1 < u/D < 0.75.

2. The LDFE trajectories are tending towards an embedment of zero, rather than

the steady value of approximately w/D ∼ 0.05 seen in the model test.



3. The lateral resistance does not show a significant fall as the pipes move towards

the soil surface. The steady LDFE resistance is H/suD ~ 1.4 but the model test

plateau is H/suD ~ 0.8.

These three effects can all be linked to the influence of soil softening. Although the

LDFE reproduces the initial resistance accurately, once the soil is disturbed and

remoulded (which causes a drop in strength, in reality – i.e. the model tests), the

resistance is over-predicted. Softening is also an explanation for the differences in

trajectory. If a shear plane softens, then it forms a preferential failure mechanism which

the pipe will tend to favour during subsequent motion – hence the straight trajectory

during the initial movement in the model tests and the softening LDFE. Once a failure

plane forms in a particular direction, this is favoured and the pipe does not deviate. In

contrast, the LDFE without soil softening shows a curved trajectory, with a

continuously-changing direction.

Finally, if the soil becomes weaker with accumulating strain then it is possible for

the soil berm to grow in size, but continue to provide the same lateral resistance. The

increase in berm size is counteracted by a reduction in the soil strength. As a result, the

pipe can continue to scrape soil away from the seabed, growing the soil berm, whilst the

resistance remains constant.

4.5 REALISTIC SOIL CASE The influence of soil softening on the pipe trajectory and lateral resistance is confirmed

by the results from a further three LDFE analyses. These use the more realistic modified

Tresca model, which incorporated soil softening and strain rate-enhanced strength, as

defined through Equation 4.1. The adopted parameters for these aspects of the soil

constitutive model are shown in Table 4.3. The effects of rate and softening parameters



on the lateral response were not explored independently. It should be noted that practical

problems may have different pipe movement velocities and softening parameters.

Three initial embedments of w = 0.45D (the centrifuge test), 0.3D and zero over-

penetration (0.02D) were chosen for the realistic soil cases (Table 4.4). In each case, the

pipe was then moved laterally by 7 times its diameter. For all cases, the operating

vertical load was 0.19 times the maximum vertical load during penetration for the 0.45D

initial embedment case (see Dingle et al. 2008 for further details of the centrifuge

modelling procedures).

Table 4.3 Rate and softening parameters chosen Parameters Values Reference shear strain rate, refγ& 3 x 10-6 s-1

Vertical pipeline penetration rate, vp 0.015 D/s

Horizontal pipeline penetration rate, vp 0.05 D/s Rate of strength increase per decade, μ 0.1 Sensitivity of clay, St 3.2 Accumulated plastic strain at which 95% soil strength reduction occurs by remoulding, ξ95

10

0

0.1

0.2

0.3

0.4

0.5

0 1 2 3 4 5 6 7


Pipe

inve

rt em

bedm

ent,

w/D

No over-penetration

Initial embedment = 0.3D

Initial embedment = 0.45D

Centrifuge data

Cases E, F, centrifuge data and case G

Figure 4.6 Trajectory of pipe invert during lateral motion (Realistic soil model, Cases E-G)



Table 4.4 Parameters for realistic soil cases with same load, V


E 3.4 1.00 0.02 0.051 0.46 F 3.4 0.23 0.30 0.049 0.49 G 3.4 0.19 0.45 0.045 0.54

0

1

2

3


Nor

mal

ised

horiz

onta

l res

istan

ce, H

/Ds u

0

No over-penetrationInitial embedment = 0.3DInitial embedment = 0.45DCentrifuge data

Cases E, F and G

Figure 4.7 Normalised horizontal resistance during lateral motion (Realistic soil model, Cases E-G)

0

1

2

3

0 1 2 3 4 5 6 7


Equi

vale

nt fr

ictio

n fa

ctor

, H/V

No over-penetration

Initial embedment = 0.3DInitial embedment = 0.45DCentrifuge data

Cases E, F and G

Figure 4.8 Equivalent friction factor during lateral motion (Realistic soil model, Cases E-G)



Figure 4.6 shows the pipe trajectory; Figure 4.7 and Figure 4.8 show the normalised

lateral resistance and equivalent friction factor responses respectively. The centrifuge

data from Dingle et al. (2008), which extends up to 3D lateral displacement, is also

superimposed on all three figures for comparison. It is clear that these cases – using a

soil model with softening – capture better the behaviour observed in the centrifuge

model tests. The initial steep increase in friction factor within 0.05D of lateral

movement observed in the centrifuge test is from the mobilisation of tensile resistance

at the rear of the pipe. This phenomenon is not captured in the present finite element

methodology and is hence not seen in the numerical results.

Figure 4.8 shows that the pipe experiences a steady state resistance after travelling

around 2 times its diameter, which is a shorter distance than the ideal soil cases (Figure

4.5). This is consistent with the steeper initial trajectory, which causes the pipe to

approach the soil surface more rapidly (compare Figure 4.6 and Figure 4.3).

It is also evident from Figure 4.6 that, unlike the ideal case, the pipe invert does not

reach as close to the original soil surface. For all cases it stabilizes at an embedment of

w ∼ 0.05D. As the invert of the pipe remains below the original surface, the pipe

continues to displace a significant volume of soil ahead of it, causing the size of the

berm to grow continuously – despite the lateral resistance remaining constant. It is

concluded that the increase in resistance from the growing berm area during the steady

resistance state is counterbalanced by the decrease in the operative soil strength due to

softening. It should be noted that the value of V for the realistic case is slightly larger

than the ideal case – this also has a minor influence on the elevation that the pipe

reaches.

The failure mechanisms associated with Case G are shown in Figure 4.9. Figure

4.10 shows the equivalent failure mechanism, identified through particle image

velocimetry (PIV) analysis of the model test, which was conducted behind a transparent



window by Dingle et al. (2008). This allowed images to be captured and analysed,

revealing the soil failure mechanism. Again, good agreement is evident between the

centrifuge model test observations (Figure 4.10) and the LDFE results (Figure 4.9d).

(b) u/D = 0.5(a) u/D = 0.1

(c) u/D = 1 (d) u/D = 7

(b) u/D = 0.5(a) u/D = 0.1

(c) u/D = 1 (d) u/D = 7

(b) u/D = 0.5(a) u/D = 0.1

(c) u/D = 1 (d) u/D = 7

Figure 4.9 Failure mechanisms during Case G

Figure 4.10 Soil deformation mechanism from a centrifuge model test (u/D = 3) (Dingle et al. 2008)



(a) u/D = 0.1

(b) u/D = 0.5

(c) u/D = 1

(d) u/D = 7

(a) u/D = 0.1

(b) u/D = 0.5

(c) u/D = 1

(d) u/D = 7

(a) u/D = 0.1

(b) u/D = 0.5

(c) u/D = 1

(d) u/D = 7

Figure 4.11 Soil softening during Case G

The calculated distributions of soil softening, expressed as the current strength

relative to the initial strength of that soil element, su/su0, are shown in Figure 4.11. These

plots illustrate clearly the softened failure plane that develops initially, and continues to

be mobilised for the first ∼ 0.75D of lateral movement. Once the pipe reaches the stable



embedment of w/D ∼ 0.05, the failure mechanism is predominantly a sliding failure

beneath the soil berm, but with further shear deformation occurring within the soil berm

(which causes continued softening).

The simulated pipe weight during the lateral sweep is the same for all Cases E - G,

and the steady state embedment is virtually identical for all analyses in each soil type.

To explore the influence of pipe weight on the steady condition, variations on Case G

(0.45D initial embedment) were performed using three other load ratios, V/Vmax = 0.1,

0.3 and 0.4 (Cases H – J, Table 4.5).

Table 4.5 Parameters for realistic soil cases with varying load, V


H 1.78 0.1 0.45 0.000 0.59 I 5.35 0.3 0.45 0.098 0.54 J 7.12 0.4 0.45 0.170 0.64

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 1 2 3 4 5 6 7


Pipe

inve

rt em

bedm

ent,

w/D

V/Vmax = 0.40V/Vmax = 0.30V/Vmax = 0.19V/Vmax = 0.10

Cases H, G, I and J

Figure 4.12 Pipe invert trajectory during lateral motion (Varying vertical loads, Cases H-J )

For these cases, the pipe invert trajectory, normalised lateral response and equivalent

friction factors are shown in Figure 4.12, Figure 4.13 and Figure 4.14 respectively,



together with Case G. These four cases cover a fourfold range in simulated pipe weight,

with all other parameters being the same.

0

0.5

1

1.5

2

2.5

3

3.5

0 1 2 3 4 5 6 7


Nor

mal

ised

horiz

onta

l res

istan

ce, H

/Ds u

0 V/Vmax = 0.40

V/Vmax = 0.30V/Vmax = 0.19V/Vmax = 0.10Cases H, G, I and J

Figure 4.13 Normalised horizontal resistance during lateral motion (Varying vertical loads, Cases H-J)

0

0.5

1

1.5

2

2.5

3


Equi

vale

nt fr

ictio

n fa

ctor

, H/V

V/Vmax = 0.40

V/Vmax = 0.30V/Vmax = 0.19V/Vmax = 0.10

Cases H, G, I and J

Figure 4.14 Equivalent friction factor during lateral motion (Varying vertical loads, Cases H-J)

It may be seen from Figure 4.12 that, for a higher vertical load, a greater steady state

pipe embedment is observed. The normalised steady state embedment of the pipe,



denoted by wres/D, can be related to the normalised vertical load, V/Dsu0. Figure 4.15

shows the LDFE results (taken at u/D = 7) and a simple power law fit with the

following equation:

47.20ures )Ds/V(01.0D/w = 4.2

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 0.5 1 1.5 2 2.5 3 3.5

V/Dsu0

wre

s/D

LDFE pointsFitted curve

Case H

Case G

Case I

Case J

47.20ures )Ds/V.(01.0D/w =

Figure 4.15 Effect of vertical load on steady state embedment

4.6 EFFECTIVE EMBEDMENT APPROACH These analyses have shown that the lateral resistance is influenced by the size of the soil

berm ahead of the pipe, as well as the strength properties of the soil and the weight of

the pipe.

An elegant way of normalizing the lateral resistances, which incorporates all of

these influences, is to use a concept termed the effective embedment, as proposed by

White & Dingle (2011). When the pipe moves laterally, the berm ahead of it can be

considered as an additional contribution to the embedment, in addition to the vertical



position of the pipe invert below the original soil surface. A schematic diagram

explaining this concept of effective embedment is shown in Figure 4.16.

Figure 4.16 Schematic diagram explaining the effective embedment concept (as per White & Dingle, 2011)

The effective embedment is the summation of the two embedment components and

can be expressed as:

D/hD/wD/w 'berm

' += 4.3

Where,

η= berm

berm,t

'berm

AS

1h

4.4

Here, the area of the berm, Aberm is idealised as a rectangle with aspect ratio η. As

the pipe moves laterally, Aberm can be calculated as the cross-sectional area swept by the

pipe (i.e. the integral w⋅du) plus the volume displaced during the initial vertical

penetration.

When the realistic (softening) soil model is used, the effective height of the berm is

reduced by a factor St,berm. St,berm is the mobilised sensitivity of the soil in the berm. As

the soil in the berm may on average be only partially softened, St,berm is lower than St by



some fraction f (Wang et al. 2010). For the ideal soil case, St,berm is taken equal to unity,

since the soil strength is unchanged within the berm.

Using values of η = 1.5 and f = 0.5, all of the normalised lateral resistances for

displacements greater than u = 1D from the ideal (A – D) and realistic cases (E – J) fall

in a narrow band when plotted against effective embedment (Figure 4.17). The data are

fitted by a simple power law expression:

95.0'

0u Dw45.2

DsH

⎟⎟⎠

⎞⎜⎜⎝

⎛=

4.5

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2 2.5

H/Dsu0

w'/D

Points from ideal soil case

Points from realistic soil case

Fitted power law expression

95.0'

0u Dw45.2

DsH

⎟⎟⎠

⎞⎜⎜⎝

⎛=

Figure 4.17 Variation of normalised lateral resistance with effective embedment

It can be concluded that the normalised horizontal resistance response is very well

correlated with the effective embedment as per the above relationship, for a wide range

of soil and pipeline parameters. This simple observation provides a useful contribution



to the development of a general model for large-amplitude lateral pipe-soil interaction,

accounting for changes in geometry and soil strength.

4.7 CONCLUDING REMARKS The large deformation finite element analysis method is a robust technique for studying

lateral pipe movements in clay. It is capable of capturing the changing seabed geometry

during large amplitude motion of pipelines on soft soils. But this method should be

coupled with a soil strength model that incorporates the effects of strain rate and

softening to predict the real behaviour.

Initially, the present study adopted an idealised soil model with shear strength not

depending on the strain rate or softening. After that, a more realistic soil model was

adopted and differences in response with the previous case were demonstrated. The

methodology and input parameters were validated by comparing the results with

available centrifuge data. Specific conclusions from the present study are as follows.

The trajectory or the vertical position of the pipe during lateral motion depends on

the weight of the pipe. The heavier the pipe the deeper it remains during lateral

movement. In the case of realistic soil, the pipe traverses with a much steeper upward

trajectory than for the ideal soil case. This phenomenon results in the pipe reaching a

steady state lateral resistance after travelling a shorter lateral distance.

For both ideal and realistic soil models, the deeper the initial embedment of the

pipe, the greater is the steady state lateral resistance. This is because deeper initial

embedment results in a larger area of the berm ahead of the pipe and hence greater

resistance.

In the case of the realistic soil model, the pipeline stays below the original soil

surface and still experiences a steady resistance from the soil. It is concluded that the

growth of the size of the berm is counterbalanced by the softening of the soil during



lateral motion. The steady state vertical embedment of the pipe is related to the

operating vertical load of the pipe. A simple power law relationship was presented to

express the steady state embedment of the pipe.

Finally, the concept of effective embedment was presented. The results of the study

showed that the large displacement lateral resistance depended on the initial embedment

of the pipe, the overloading ratio and also on the particular soil model. It is obvious that

the lateral resistance for the ideal soil cases is greater than that for the realistic soil

because there is no reduction of the soil strength in the former case. Also, the

differences in initial embedment and overloading ratio result in differences in the berm

size, which in turn result in differences in the lateral resistance.

It is therefore useful to model the lateral pipe-soil resistance with a method that

includes the actual embedment, the berm height and the sensitivity of the soil. The

effective embedment of the pipe, defined by the actual embedment of the pipe below the

mudline plus an increase of embedment due to the berm ahead of it, achieves this. The

lateral resistance responses for both the ideal soil and the realistic soil were related to

the effective embedment of the soil according to the same simple power law expression.

This relationship was valid for all the cases regardless of the other soil and pipe

parameters.

4.8 REFERENCES AtkinsBoreas (2008). SAFEBUCK JIP – Safe design of pipelines with lateral buckling.

Design Guideline. Report No. BR02050/SAFEBUCK/C, AtkinsBoreas.

Bruton, D., Carr, M. & White, D. J. (2007). The influence of pipe-soil interaction on

lateral buckling and walking of pipelines: the SAFEBUCK JIP. Proc. 6th Int. Conf.

on Offshore Site Investigation and Geotechnics, London. 133-150.



Bruton, D. A. S., White, D. J., Carr, M. & Cheuk, C. Y. (2008). Pipe-soil interaction

during lateral buckling and pipeline walk - the SAFEBUCK JIP. Proc. Offshore

Technology Conf., Houston, Paper OTC 19589.

Bruton, D. A. S., White, D. J., Cheuk, C. Y., Bolton, M. D. & Carr, M. C. (2006). Pipe-



Paper OTC 17944.

Cardoso, C. O., & Silveira, R. M. S. (2010). Pipe-soil interaction behavior for pipelines

under large displacements on clay soils – a model for lateral residual friction factor.


Cheuk, C.Y., White, D. J. & Bolton, M. D. (2007). Large scale modelling of soil-pipe

interaction during large amplitude movements of partially-embedded pipelines. Can.

Geotech. J.44, No. 8, 977-996.

Dassault Systèmes (2007) Abaqus analysis users’ manual, Simulia Corp, Providence,

RI, USA.



Hesar, M. (2004). Pipeline-seabed interaction in soft clay. Proc. 23rd Int. Conf. on

Offshore Mechanics and arctic eng., Vancouver, 225-232.

Konuk, I. & Yu, S. (2007). Continuum FE modelling of lateral buckling: study of soil

effects. Proc. of 26th Int. Conf. on Offshore Mechanics and Arctic Eng., San Diego,

OMAE2007-29376.

Randolph, M. F. & White, D. J. (2008a). Pipeline embedment in deep water: process


OTC 19128.



Randolph, M. F. & White, D. J. (2008b). Upper-bound yield envelopes for pipelines at




J. 47, No. 8, 842-856.

White, D. J. & Dingle, H. R. C. (2011). The mechanism of steady ‘friction’ between

seabed pipelines and clay soils. Géotechnique 61, No. 12, 1035–1041

White, D. J. & Cheuk, C. Y. (2008). Modelling the soil resistance on seabed pipelines

during large cycles of lateral movement. Marine Structures 21, 1, 59-79.

Zhang, J., Stewart, D. P. & M.F. Randolph, M. F. (2002). Modelling of shallowly

embedded offshore pipelines in calcareous sand, Journal of Geotechnical and

Geoenvironmental Engineering ASCE 128, N0. 5, 363–371.



CHAPTER 5

MODELLING LATERAL PIPE-SOIL INTERACTIONS

5.1 INTRODUCTION

In the previous chapter, it has been shown that real lateral pipe-soil interaction

behaviours during large movement can be modelled using large deformation finite

element analyses if a softening and rate dependent soil constitutive model is adopted.

The ‘effective embedment’ approach was shown to be successfully capturing the

‘residual resistance’ behaviour. What remains to be established is how to predict the

pipe trajectory, thus allowing the evolution of effective embedment with lateral

displacement to be predicted. In this chapter, a detailed parametric study was performed

varying the initial vertical embedment and pipe weight (a wider range) and the effective

embedment was related to the initial embedment through simple relationships. The

results of the parametric study are compared with existing empirical correlations and

new recommendations are provided.

Also, the initial ‘break-out’ resistance, an important phase of lateral pipe-soil

interaction, was not addressed in the previous chapter. The trajectory and the resistance

during pipe ‘break-out’ is best described within a plasticity framework by means of

failure envelopes. Equations of yield envelopes are available in the literature. In this

chapter, new equations derived from large deformation analyses are proposed. Also, the

entire pipe-soil lateral response from initial break-out to steady residual phases has been

modelled using a simple relationship.

CHAPTER 5: Modelling lateral pipe-soil interactions


5.2 PARAMETRIC STUDY

5.2.1 Input parameters A parametric study was undertaken, varying the initial vertical embedments and level of

overloading. Depending on whether the pipe is heavy or light, relative to the vertical

bearing capacity (Vmax) at the current embedment, lateral breakout will be accompanied

by either downward or upward movement. For this study, five values of initial

embedment (w/D = 0.1, 0.2, 0.3, 0.4 and 0.5) and five levels of overloading (V =

0.1Vmax,, 0.2Vmax, 0.4Vmax, 0.6Vmax and 0.8Vmax) were considered. In the previous

chapter, it has been shown that the pipe reaches a steady state after a lateral movement

of two times its diameter. For all the analyses in this chapter, the pipe was moved

laterally up to a distance of three times its diameter. The adopted soil parameters for this

study as given in Table 5.1, represents a typical soft seabed.

Table 5.1 Parameters used for parametric study

Parameters Values Pipe Diameter, D 0.8 m Shear strength of soil at mudline, sum 2 kPa Shear strength gradient, k 4 kPa/m Submerged unit weight of soil, γ' 5 kN/m3

Young’s modulus, E 500 su0 Poisson’s ratio, ν 0.499 Reference shear strain rate, refγ& 3 x 10-6 s-1

Vertical pipeline penetration rate, vp 0.015 D/s

Horizontal pipeline penetration rate, vp 0.05 D/s Rate of strength increase per decade, μ 0.1 Sensitivity of clay, St 3 Accumulated plastic strain at which 95% soil strength reduction occurs by remoulding, ξ95

10

Interface friction ratio, α 0.5



Interface friction between pipe and soil is a difficult parameter to choose because of

variation of soil shear strength along the pipe perimeter. A mid value of α = 0.5, in

between fully smooth and fully rough case was chosen for all analyses in this chapter.

5.2.2 Typical results – w/D = 0.3 Figure 5.1 to Figure 5.3 show the results from the parametric study for the initial

embedment of w/D = 0.3 (and the 5 values of normalised pipe weight). Figure 5.1

shows that the lighter pipes rise whereas the heavier pipes move downwards. In all

cases the pipe reaches a steady embedment after undergoing a lateral displacement of

around two diameters. The non-dimensionalised horizontal resistance H/Dsu0 for each

case is shown in Figure 5.2. The heavier the pipe, the greater is the lateral resistance,

when normalised by the local initial strength, because the heavier pipes create a higher

berm ahead.

-0.1

0.1

0.3

0.5

0.7

0.9

0 0.5 1 1.5 2 2.5 3u/D

w/D

Initial Embedment = 0.3DV/Vmax = 0.1, 0.2, 0.4, 0.6, 0.8

Figure 5.1 Typical trajectories of pipes during lateral movement for different pipe weights



0

1

2

3

4

0 0.5 1 1.5 2 2.5 3

u/D

H/D

s u0

Initial Embedment = 0.3D

V/Vmax = 0.1, 0.2, 0.4, 0.6, 0.8

Figure 5.2 Typical lateral responses of pipe for different pipe weights

0

1

2

3

0 0.5 1 1.5 2 2.5 3

u/D

H/V

Initial Embedment = 0.3D

V/Vmax = 0.1, 0.2, 0.4, 0.6, 0.8

Figure 5.3 Friction ratios for pipes with different operating vertical loads



By non-dimensionalising by the shear strength at the pipe invert, a change in su0 is

reflected in H/Dsu0. To see only the variation in resistance force during lateral motion,

instead of normalizing H by Dsu0, H can be normalised by the vertical force (V) applied

during horizontal motion, as shown in the Figure 5.3. This normalisation shows that the

lightest pipe undergoes a reduction in lateral resistance by a factor of nearly 2.5 in the

first diameter of movement, which is obscured in Figure 5.2 by the simultaneous fall in

su0 as the pipe rises.

Broad trends evident in Figure 5.2 and Figure 5.3 are that:

1. The initial breakout resistance, H/Dsu0, varies by a factor of only 1.6 across all 5

cases, even though the pipe weights different by a factor of 8, indicating the

strong influence of embedment.

2. As a corollary, when the breakout resistance is expressed as a friction factor,

H/V, a high variation is evident, spanning the range 0.3 – 1.7.

3. The residual friction factor spans a range of 2 across all 5 cases, with the highest

value corresponding to the heaviest pipe. The range is far higher in terms of

absolute resistance, H, with the highest value being 5.5 times greater than the

lowest (note that this is not directly evident in either Figure 5.2 or Figure 5.3

since both V and su0 vary among the different analyses at the residual state).

The responses of light and heavy pipes can be idealised as in Figure 5.4. Initially there

is a breakout resistance, Hbrk. After that, light pipes undergo upward movement and the

resistance approaches a steady value, referred to as the residual resistance, Hres. Heavy

pipes move downward resulting in increasing passive berm resistance. After large

displacements the pipe approaches a horizontal trajectory and a steady resistance,

although not as rapidly as in the case of light pipes.



Hbrk

Hres

Hres

Heavy Pipe

Hor

izon

tal R

esis

tanc

e

Horizontal displacement

Light Pipe

Figure 5.4 Idealisation of pipe response during lateral motion for ‘light’ and ‘heavy’ pipes

5.2.3 Initial yield envelopes and breakout resistance The maximum resistance within the initial movement of u/D = 0.1 was used to define

the breakout resistance, Hbrk. A clear way to present the lateral breakout resistance for

partially embedded pipelines with varying embedment and weight is via yield envelopes

defined in V-H space. Yield envelopes for shallowly embedded pipelines undergoing

small lateral displacements have been derived in previous studies either through

plasticity analysis (Randolph & White, 2008) or small strain finite element analysis

(Merifield et al., 2008). For a given initial embedment, the envelope defines the

different limiting combinations of vertical and horizontal load. The origin of the

envelope is at the point V = 0, H = 0 (assuming a non-bonded pipe-soil interface that

can sustain no tension). The apex point is at V = Vmax, H = 0 where Vmax is the vertical

bearing capacity at the pipe embedment. These envelopes are approximately parabolic

in shape and can be fitted to using (Merifield et al., 2008):



21

maxmaxmax

max

max VV1

VV

VH

VH

ββ

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛β= 5.1

Where

( )( )

21

21

21

21ββ

β+β

βββ+β

=β 5.2

The parameters β1 and β2 skew the ellipse, while the ratio Hmax/Vmax gives the relative

proportions of the ellipse.

For the present study, the parameters β1 and β2 and the ratio Hmax/Vmax were found to

vary with initial embedment according to the following linear best-fits:

)Dw66.0(89.01 −=β 5.3

)Dw64.0(87.02 −=β 5.4

)Dw55.0(31.0

VH

max

max += 5.5

The yield envelopes are shown in Figure 5.5 for each initial embedment. The maximum

horizontal load Hmax is reached at around V/Vmax = 0.5. Since the Tresca soil model

obeys normality, the yield envelopes for a pipe embedded in the soil will also obey

normality, so these can also be used to describe the pipe movement at yield by

redefining the axes as the conjugate plastic displacements. The point where pure

horizontal pipe movement occurs is often called the parallel point and lies close to

V/Vmax = 0.5 in the present case. For load levels lower than this point, pipe will undergo

upward movement on breakout, whereas heavier pipes will move downward.



0

0.1

0.2

0.3

0.4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

V/Vmax

H/V

max

w = 0.1D

w = 0.5D

LDFE Parabola fit

Figure 5.5 Yield envelopes in V-H space (LDFE and parabola fit)

0

0.1

0.2

0.3

0.4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

V/Vmax

H/V

max

w = 0.1D

w = 0.5D

present studyMerifield et al. (2008)

Figure 5.6 Yield envelopes from present study and Merifield et al. (2008)



Figure 5.6 shows comparison of the normalised failure envelopes from the

present study and those from Merifield et al. (2008). The parallel points for Merifield et

al. (2008) are at about V/Vmax = 0.4 compared to ~ 0.5 in the present study and the

envelopes are a slightly different shape.

The maximum values of normalised horizontal resistance, Hmax/Dsu0, from this

study are compared with the Merifield et al. (2008) values in Table 5.2. The latter

values are considerably lower than those from the present study, principally because

they are derived for a ‘wished-in-place’ pipe (without any heave from the penetration

process). In the present study the pipe is ‘pushed-in-place’, leading to local soil heave

and additional passive lateral resistance on breakout. Differences may also be attributed

to the softening and rate-dependency of the soil in this study, and the variation in soil

strength with depth (Merifield et al. 2008 considered uniform/constant strength soil).

In a different study, Merifield et al. (2009) modelled a pushed-in-place pipe

(albeit in non-softening soil) and provided an alternative expression for Hmax (Table 5.2).

These values are slightly lower but closer to those from the present study. The

maximum values of Vmax/Dsu0 from the present study and these two studies are also

compared in Table 5.3. Again, the Merifield et al. (2008) values are considerably lower

than those from Merifield et al. (2009) and from the present study. This reflects the

inclusion of heave during penetration, and also the strength profile increasing with

depth conditions (with kD/sum = 1.6), in the present study.

Merifield et al. (2009) gave expressions for vertical and lateral resistances for

fully smooth and fully rough pipes. The present LDFE analyses are based on an

interface friction ratio of 0.5. So, the results shown in Table 5.2 and Table 5.3 are

average values for fully smooth and fully rough cases presented in that paper.



Table 5.2 Comparison of Hmax/Dsu0 from present study and literature

Present study

Merifield et al. (2008)


w/D = 0.1 0.90 0.49 0.72 w/D = 0.2 1.20 0.88 1.10 w/D = 0.3 1.58 1.24 1.41 w/D = 0.4 1.78 1.58 1.68 w/D = 0.5 2.02 1.90 1.92

Table 5.3 Comparison of Vmax/Dsu0 from present study and literature

Present study



w/D = 0.1 4.48 2.95 3.27 w/D = 0.2 5.28 3.89 4.00 w/D = 0.3 5.74 4.57 4.49 w/D = 0.4 6.00 5.13 4.87 w/D = 0.5 6.27 5.61 5.19

In conclusion, the normalised shape of the V-H yield envelopes proposed by

Merifield et al. (2008) for uniform soil with constant strength are also broadly

appropriate for the present study, which considers soil softening and strain rate effects,

and slightly modified ellipse parameters to describe the failure envelope shape are

provided in Equations 5.1 to 5.5. The horizontal extent of the envelopes, defined by

Hmax/Vmax, is slightly greater due to the influence of heave during the initial embedment

process.

Although yield envelopes are rigorous methods to express pipe soil interaction

forces in the combined load spaces, they are only valid for the small lateral

displacements required to define the breakout resistance. After the pipe breaks out, the

shape of the soil berm ahead of the pipe compared to the void behind creates an

anisotropic geometry, and a change in the allowable V-H load combinations – including

an anisotropy within the failure envelopes themselves.



5.2.4 Residual friction factor As shown in Figure 5.3, the equivalent lateral friction factor, H/V, reaches a steady

residual value after the pipe is displaced by about two diameters. The residual friction

factor depends on the weight of the pipe and the initial embedment. These factors

control the pipe trajectory and the final steady embedment.

Table 5.4 Steadiness of the large displacement lateral resistance

winit/D V/Vmax

Horizontal resistance at

u/D = 2.5 (kN)

Horizontal resistance at

u/D = 3 (kN)

Variation over Δu/D = 0.5

(%)

0.1 0.12 0.15 24.5 0.2 0.81 0.82 +1.4 0.4 1.44 1.53 +5.5 0.6 2.75 2.80 +2.0

0.1

0.8 4.21 4.39 +4.1 0.1 0.73 0.66 -9.9 0.2 1.04 1.1 +6.3 0.4 2.36 2.31 -2.2 0.6 4.39 4.33 -4.1

0.2

0.8 6.48 6.75 +3.9 0.1 0.80 0.84 +4.8 0.2 1.37 1.38 +0.3 0.4 3.12 3.15 +0.9 0.6 5.97 6.27 +4.9

0.3

0.8 9.64 9.89 +2.5 0.1 1.03 1.05 +2.6 0.2 1.58 1.53 -2.8 0.4 4.20 4.18 -0.7 0.6 7.90 - -

0.4

0.8 11.50 - - 0.1 1.23 1.18 -4.8 0.2 1.90 1.87 -1.6 0.4 5.40 5.65 +4.3 0.6 9.74 - -

0.5

0.8 14.05 - -

The degree to which a steady state is reached within each analysis can be

defined by the change in lateral resistance during the last half diameter of lateral

movement, denoted by ΔH2.5<u/D<3, divided by the final value, Hu/D=3. These changes are

tabulated in Table 5.4. In most of the cases, the variation in lateral resistances is below



10%, which indicates that in these cases the pipe has reached a reasonably steady lateral

resistance. As seen from Table 5.4, in some cases the values of resistances at u/D = 3

are left blank. These are the cases where the pipe did not reach a steady state due to the

development of a very large berm; convergence in the numerical calculations was not

achieved beyond u = 2.5D in these cases due to overtopping of the soil berms.

Figure 5.7 shows the variation of residual friction factor with initial embedment

of the pipe. If the pipe starts at a deeper position, it ends up experiencing a higher

residual friction factor. Figure 5.8 shows the variation of residual friction factor with the

initial normalised vertical load. A higher vertical load leads to a higher residual friction

factor, although Hres/V for V/Vmax = 0.2 is lower than for V/Vmax = 0.1 in most cases.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.1 0.2 0.3 0.4 0.5 0.6

winit/D

Hre

s/V

V/Vmax = 0.1V/Vmax = 0.2V/Vmax = 0.4V/Vmax = 0.6V/Vmax = 0.8

Figure 5.7 Variation of residual friction factor with initial embedment A complication of this plot is that vertical load, V, is present on both axes. To see the

variation of absolute horizontal resistance with vertical load, both H and V were



normalised by Dsuo,init (Figure 5.9(a)). It is then clear that for a given initial embedment,

any increase in pipe weight leads to an increase in residual resistance.

0

0.5

1

1.5

0 1 2 3 4 5

V/Dsu0,init

Hre

s/V

initial w/D = 0.1initial w/D = 0.2initial w/D = 0.3initial w/D = 0.4initial w/D = 0.5

Figure 5.8 Variation of residual friction factor with normalised vertical load

Comparisons between different embedments remain complicated by the

variation in su0,init with depth, so Figure 5.9(b) uses Dsum for normalisation of all cases.

This shows that there is a consistent trend through the results for all embedments and

overloading ratios, except at low values of V/Dsum. It should be remembered that Figure

5.9(b) corresponds to a particular kD/sum(= 1.6) ratio and may change for different

strength parameter values.



0

1

2

3

4

5

0 1 2 3 4 5V/Dsu0,init

Hre

s/Ds u

0,in

it initial w/D = 0.1initial w/D = 0.2initial w/D = 0.3initial w/D = 0.4initial w/D = 0.5

V/Vmax = 0.1

V/Vmax = 0.2

V/Vmax = 0.4

V/Vmax = 0.6

V/Vmax = 0.8

(a)

0

2

4

6

8

10

0 2 4 6 8 10V/Dsum

Hre

s/Ds u

m

initial w/D = 0.1initial w/D = 0.2initial w/D = 0.3initial w/D = 0.4initial w/D = 0.5

V/Vmax = 0.1

V/Vmax = 0.2

V/Vmax = 0.4

V/Vmax = 0.6

V/Vmax = 0.8

(b)

Figure 5.9 Variation of residual resistance with vertical load normalised by (a) Dsuo,init; (b) Dsum



An alternative form of normalisation is to use the final embedment of the pipe

invert, relative to the initial undisturbed soil surface, (w/D)final (Figure 5.10). A greater

final embedment generally results in greater friction factor, except for the highly

unloaded pipes (low V/Vmax) which rise to the original soil surface. A spread of residual

friction factor is evident for the same final embedment and this is due to differences in

the size of the soil berm ahead of the pipe. Figure 5.11 shows the variation of residual

horizontal resistance (normalised by su0,final) with the final embedment of the pipe. The

differences in the size of the berm in this case also are responsible for different values of

lateral resistance for the same final embedment. In the same figure, the limiting

resistance, Hmax/suD, from Merifield et al. (2009) is also shown, which represents the

resistance to horizontal movement. Merifield et al. (2009) results are valid only for the

range 0 ≥ w/D § 0.5. At the residual state, the pipe is moving horizontally in all of the

LDFE analyses so the large discrepancy between this curve and the LDFE results is due

to the presence of the soil berm ahead of the pipe – which creates additional passive

resistance beyond that captured in the Merifield et al. (2009) resistance using an

embedment relative to the undisturbed soil surface. A method of accounting for this

additional passive resistance is explained in the following section.



0.4

0.6

0.8

1

-0.2 0 0.2 0.4 0.6 0.8 1 1.2

(w/D)final

Hre

s/V

V/Vmax = 0.1V/Vmax = 0.2V/Vmax = 0.4V/Vmax = 0.6V/Vmax = 0.8winit/D = 0.1

winit/D = 0.2

winit/D = 0.3

winit/D = 0.4

winit/D = 0.5

Figure 5.10 Variation of residual friction factor with normalised final embedment

0

0.5

1

1.5

2

2.5

3

3.5

-0.2 0 0.2 0.4 0.6 0.8 1 1.2

(w/D)final

Hre

s/su0

,fina

lD

V/Vmax = 0.1V/Vmax = 0.2V/Vmax = 0.4V/Vmax = 0.6V/Vmax = 0.8Merifield et al. (2009)

Figure 5.11 Variation of Hres/su0,finalD with (w/D)final



5.3 EFFECTIVE EMBEDMENT APPROACH For a lateral displacement beyond the initial breakout stage, an elegant way of

expressing the lateral resistance is by its variation with effective embedment. The

concept of effective embedment was proposed by White & Dingle (2011) and was

shown in the previous chapter. The effective embedment of the pipe invert is the

summation of the actual embedment (below the undisturbed soil surface) and an

additional term arising from the height of the soil berm ahead of the pipe. The

normalised effective embedment, w'/D, is expressed as:

η

+=+= berm

berm,t

berm ADS

1Dw

D'h

Dw

D'w 5.6

Aberm is the area of the berm and it is idealised as a rectangular block with aspect ratio η.

The height of the berm, hberm, is given byηbermA

. The value of η is generally in the

range 1.5-2.5. As the soil in the berm is remoulded, the effective berm height is

discounted by a factor of St,berm, to account for the softened soil not offering the same

level of passive resistance as if it were intact: berm,tbermberm S/h'h = . The lateral

resistance from all the LDFE analyses (5 initial embedments and 5 load ratios in each

case) are plotted against effective embedment in Figure 5.12 (the initial mobilisation

and breakout are ignored – only data from u/D > 0.5 are shown). All the responses fall

in a narrow band and are well-fitted by a power-law equation:

y'

0u Dwx

DsH

⎟⎟⎠

⎞⎜⎜⎝

⎛= 5.7

Where x = 2.82 and y = 0.72.



The results for Hmax/Dsu0 from Merifield et al. (2009), considering the actual

embedment from their study as effective embedment, are shown in the same figure

(Figure 5.12) for comparison. For a particular embedment, the horizontal resistance

from Merifield et al. is slightly higher because they did not consider softening of the

soil.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.5 1 1.5 2 2.5 3 3.5 4

H/Dsu0

w'/D

0 0.5 1 1.5 2 2.5 3 3.5 4

V/Dsu0

H/Dsu0

power law fit

H/Dsu0 by Merifield et al. (2009)

V/Dsu0

best fit curve

Figure 5.12 Lateral and vertical response using effective embedment approach

The normalised vertical load, V/Dsu0, at the end of lateral displacement, when

the lateral resistance had reached a steady value, are also shown and follow a particular

trend (Figure 5.12), which may be fitted by:

( ) ⎟⎠⎞

⎜⎝⎛ −= − qD/'wp

0ue1A

DsV 5.8



where A is a constant that corresponds to the limiting value of steady-state vertical

resistance during horizontal movement, in cases of very heavy pipes. The value of A

was estimated by analysing a case with a very heavy pipe (operating vertical load equal

to the 0.9 times the maximum vertical reaction force). The values assigned for A, p and

q to obtain the best fit curve were 3.7, 2.4 and 0.84 respectively.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.1 0.2 0.3 0.4 0.5 0.6

Initial Embedment, winit/D

Res

. Eff.

Em

b. (w

'/D) re

sidu

al

V/Vmax= 0.1

V/Vmax= 0.2

V/Vmax= 0.4

V/Vmax= 0.6

V/Vmax= 0.8

Figure 5.13 Variation of residual effective embedment with initial embedment

The steady state lateral resistance can be estimated using Equations 5.7 and 5.8.

For that, estimation of the residual effective embedment is necessary. Residual effective

embedment depends on the initial embedment and also on the loading ratios. Figure

5.13 shows the variation of residual effective embedment with initial embedment for

different values of V/Vmax. For each value of V/Vmax, the residual effective embedment

data can be fitted to linear curve as the following equation.



( ) ( ) nD/wmD/'w initialresidual += 5.9

The values of m and n for different values of V/Vmax are tabulated in Table 5.5, and may

be approximated as

( )maxV/V56.2m = 5.10

( )maxV/V38.0n = 5.11

Table 5.5 Best fit values of coefficients m and n for estimating residual effective embedment (Equation 5.9)

The value of effective residual embedment can now be predicted using

Equations 5.9 to 5.11. Using that value and Equations 5.7 and 5.8, the values of

Hres/Dsu0 and V/Dsu0 can be estimated, and hence the value of Hres/V.

The values of Hres/V predicted in this way have been compared with the four

empirical methods suggested previously. These are the relationships derived from

specific physical modelling studies by White & Dingle (2011) and Cardoso & Silveira

(2010) and the methods devised within the SAFEBUCK Joint Industry Project. White &

Dingle (2011) devised an expression for Hres/V, based on a set of 6 centrifuge model

tests, given by:

V/Vmax m n 0.1 0.31 0.02 0.2 0.45 0.06 0.4 1.03 0.10 0.6 1.57 0.21 0.8 2.03 0.35



res

initial max

H w V0.3 2V D V

⎛ ⎞= + ⎜ ⎟⎝ ⎠

5.12

Based on the results from a set of large-scale model tests, Cardoso & Silveira (2010)

proposed that Hres/V can be estimated as:

0.586 0.479

u,1Dres

u,1D

sH V0.2 0.929V 'Ds D

−⎛ ⎞ ⎛ ⎞

= + ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟γ⎝ ⎠ ⎝ ⎠ 5.13

where u,1Ds is the mean undrained shear strength between the soil surface and a depth of

one pipe diameter (i.e. for a linear strength profile, u,1D um sus s k D / 2= + ).

The SAFEBUCK studies generated simple correlations using wide databases of

model test results collated from many studies. The Phase I method was derived in White

& Cheuk (2005) and was published by Bruton et al. (2006), with Hres/V expressed as

res uH s11 0.65 1 expV 2 'D

⎡ ⎤⎛ ⎞= − − −⎢ ⎥⎜ ⎟γ⎝ ⎠⎣ ⎦

5.14

The SAFEBUCK Phase II method was derived in White & Cheuk (2009) and is

currently unpublished. Comparisons between the four methods and the LDFE results

are given in Table 5.6. In the italicised cases the pipe did not reach a steady state in the

numerical calculations (as shown in Table 5.4).

The calculated values of Hres/V using the four methods, normalised by the actual

value obtained through the finite element analyses, have been compared with the initial

embedments and initial vertical resistances, to identify whether any method exhibits

skew with respect to these input parameters (Figure 5.14). The Cardoso & Silveira

(2010) method shows a consistent bias except at very low pipe weights, over-predicting

the resistance by a factor of 2.4 on average. The SAFEBUCK Phase I method also over-

predicts the resistance consistently, with a greater discrepancy evident for lighter pipes.

The White & Dingle (2011) and SAFEBUCK Phase II methods are accurate on average,



but show more scatter than the method set out in this paper. The proposed equations in

the present study are closest to the parity line on average – which is not surprising since

the method has been calibrated against the data set being considered.

Table 5.6 Comparison of Hres/V value from present and previous studies

Calculated Hres/V

winit/D V/Vmax LDFE result Present

Method

White &

Dingle (2011)

SAFEBUCKPHASE I

SAFEBUCK PHASE II

Cardoso&

Silveira (2010)

0.1 0.20 0.50 0.36 0.83 0.45 0.67 0.2 0.46 0.50 0.39 0.83 0.45 0.91 0.4 0.43 0.53 0.43 0.83 0.45 1.26 0.6 0.56 0.58 0.45 0.83 0.45 1.55

0.1

0.8 0.65 0.63 0.48 0.83 0.45 1.80 0.1 0.59 0.49 0.43 0.81 0.54 0.76 0.2 0.45 0.51 0.48 0.81 0.54 1.04 0.4 0.52 0.57 0.55 0.81 0.54 1.46 0.6 0.66 0.64 0.61 0.81 0.54 1.80

0.2

0.8 0.75 0.72 0.66 0.81 0.54 2.10 0.1 0.61 0.50 0.49 0.79 0.63 0.83 0.2 0.49 0.53 0.57 0.79 0.63 1.14 0.4 0.58 0.61 0.68 0.79 0.63 1.62 0.6 0.76 0.70 0.76 0.79 0.63 2.00

0.3

0.8 0.89 0.80 0.84 0.79 0.63 2.33 0.1 0.63 0.50 0.55 0.76 0.70 0.89 0.2 0.51 0.54 0.66 0.76 0.70 1.23 0.4 0.67 0.65 0.81 0.76 0.70 1.75 0.6 0.82 0.77 0.92 0.76 0.70 2.16

0.4

0.8 0.93 0.89 1.02 0.76 0.70 2.52 0.1 0.66 0.51 0.62 0.74 0.78 0.94 0.2 0.55 0.56 0.75 0.74 0.78 1.32 0.4 0.76 0.69 0.93 0.74 0.78 1.87 0.6 0.90 0.84 1.07 0.74 0.78 2.32

0.5

0.8 0.98 0.98 1.19 0.74 0.78 2.71

Table 5.7 Comparison of mean and standard deviation values from different studies

Mean Standard Deviation (%) Present Study 1.03 11.2

White & Dingle (2011) 1.06 18.1 SAFEBUCK Phase I (2005) 1.38 32.8 SAFEBUCK Phase II (2009) 1.03 21.0 Cardoso & Silveira (2010) 2.44 51.1



0.1

1

10

0 0.1 0.2 0.3 0.4 0.5 0.6winit/D

(Hre

s/V) ca

lc/(H

res/V

) LD

FE

Proposed ModelParity Line

0.1

1

10

0 1 2 3 4 5V/Dsu0,init

(Hre

s /V)ca

lc/(H

res /V

)LD

FE

Proposed ModelParity Line

0.1

1

10

0 0.1 0.2 0.3 0.4 0.5 0.6winit/D

(Hre

s/V) ca

lc/(H

res/V

) LD

FE

White and Dingle (2011)Parity Line

0.1

1

10

0 1 2 3 4 5V/Dsu0,init

(Hre

s /V)ca

lc/(H

res /V

)LD

FE

White and Dingle (2011)Parity Line

0.1

1

10

0 0.1 0.2 0.3 0.4 0.5 0.6winit/D

(Hre

s/V) ca

lc/(H

res/V

) LD

FE

SAFEBUCK PHASE IParity Line

0.1

1

10

0 1 2 3 4 5V/Dsu0,init

(Hre

s /V)ca

lc/(H

res /V

)LD

FE

SAFEBUCK PHASE IParity Line

0.1

1

10

0 0.1 0.2 0.3 0.4 0.5 0.6winit/D

(Hre

s/V) ca

lc/(H

res/V

) LD

FE

SAFEBUCK PHASE IIParity Line

0.1

1

10

0 1 2 3 4 5V/Dsu0,init

(Hre

s /V)ca

lc/(H

res /V

)LD

FE

SAFEBUCK PHASE IIParity Line

0.1

1

10

0 0.1 0.2 0.3 0.4 0.5 0.6winit/D

(Hre

s/V) ca

lc/(H

res/V

) LD

FE

Cardoso and Silveira (2010)Parity Line

0.1

1

10

0 1 2 3 4 5V/Dsu0,init

(Hre

s /V)ca

lc/(H

res /V

)LD

FE

Cardoso and Silveira (2010)Parity Line

Figure 5.14 Ratios of (Hres/V)calculated to (Hres/V)LDFE varying with (a) winit/D; (b)

V/Dsu0,init

(a) (b)



However, it is significant that the standard deviation for the new method, at ~11%,

is significantly lower than the standard deviation values for the other methods (Table

5.7), suggesting that the governing mechanisms are better captured by this new analysis

approach.

It is important to note, however, that the method set out in this paper has not been

tested for other soil strength profiles, or against a range of experimental data. A

comparison with the databases used to generate the other calculation methods would be

an important part of validating (and perhaps refining) the proposed method in order to

establish that it is appropriate for use in practice.

5.4 ASSESSMENT OF THE FULL H/V RESPONSE Once the breakout and residual resistances are obtained (as discussed in section 5.2.3

and 5.2.4 respectively), it may be useful to model the complete resistance response for

the laterally sweeping pipeline, assuming that this takes place under constant vertical

pipe-soil load. The friction ratio responses shown in Figure 5.3 are well fitted by the

following expression:

( ) ( )⎟⎠⎞

⎜⎝⎛ −⎟

⎠⎞

⎜⎝⎛ −+⎟

⎠⎞

⎜⎝⎛ −=

μλ−− D/ubrkresD/uabrk e1V

HV

He1V

HVH b

5.15

The first term only controls the initial mobilisation of the breakout resistance, and is not

the main focus of this study. The second term provides a smooth exponential transition

from the breakout resistance to the residual value. To fit the LDFE results, the values of

coefficients a, b and μ remain essentially constant for all values of initial embedment

and pipe weight, but the value of λ (which determines the distance required to mobilise

the steady resistance) changes with pipe weight and initial embedment.



For any given initial embedment, the values of λ were fitted by a linear

relationship with V/Vmax, given by

d)V/V(c max +=λ 5.16

The values of c and d for different initial embedments are given in Table 5.8 and may be

approximated as

9.4D

w2.8c init −⎟

⎠⎞

⎜⎝⎛= 5.17

5.4D

w8.5d init +⎟

⎠⎞

⎜⎝⎛−= 5.18

The values of a, b and μ were assigned to be 25, 0.5 and 1.5 respectively for all cases.

The parameters a and b only relate to the initial mobilisation of Hbrk, not the transition to

Hres.

Table 5.8 Values of coefficients c and d for different values of initial embedments (Equation 5.16)

Typical fits for an initial embedment value of 0.3 times the diameter are shown in

Figure 5.15(a) and Figure 5.15(b) for ‘light’ and ‘heavy’ pipes respectively. Here ‘light’

pipes are those that rise during lateral movement. As shown previously, pipes with

V/Vmax lower than 0.5 respond in this way. ‘Heavy’ pipes have V/Vmax > 0.5 and dive

winit/D c d 0.1 -3.96 3.94 0.2 -3.16 3.31 0.3 -2.83 3.06 0.4 -1.22 2.05 0.5 -0.83 1.68



0

0.4

0.8

1.2

1.6

2

0 0.5 1 1.5 2 2.5 3u/D

H/V

(a)

V/Vmax = 0.1

V/Vmax = 0.2V/Vmax = 0.4

0

0.4

0.8

1.2

1.6

2

0 0.5 1 1.5 2 2.5 3u/D

H/V

(b)

V/Vmax=0.8

V/Vmax=0.6

Figure 5.15 Typical friction ratio responses with lateral displacement fitted with exponential equation: (a) Lighter pipes; (b) Heavier Pipes



during lateral movement. As seen in Figure 5.15, Equation 5.15 captures the lateral

response very well.

5.5 CONCLUDING REMARKS A wide ranging parametric study was performed involving large lateral movements

under constant vertical load. A range of initial embedments and overloading ratios were

considered. Differences in the characteristic response of ‘light’ and ‘heavy’ pipes were

explored and idealised responses for these cases identified. For assessment of the initial

break-out resistance, yield envelopes in V-H load spaces were derived and fitted by

generalised parabolic equations. For lateral movements beyond 50% of pipe diameter,

the concept of effective embedment was found to provide a useful normalisation that

accounts for any berm of soil ahead of the pipe. It was found that a steady state of

embedment and lateral resistance was reached, except for the heaviest cases (highest

V/Vmax). These showed a steady growth in resistance whilst diving to an ever greater

embedment.

The ‘effective embedment’ was related to the initial embedment and the operating

weight of the pipe. Simple relationships to predict the steady residual lateral resistance

were proposed. These perform well in comparison to other empirical correlations. If this

conclusion is shown to apply generally, then the new analysis will provide a useful tool

for the design of seabed pipelines with controlled lateral buckling.

5.6 REFERENCES Cardoso, C. O., & Silveira, R. M. S. (2010). Pipe-soil interaction behavior for pipelines

under large displacements on clay soils – a model for lateral residual friction factor.




Dassault Systèmes (2007) Abaqus analysis users’ manual, Simulia Corp, Providence,

RI, USA.





ASCE 135, No. 6, 819-829.

Randolph, M. F. & White, D. J. (2008). Upper-bound yield envelopes for pipelines at




White, D. J. & Cheuk, C. Y. (2009). SAFEBUCK JIP: Pipe-soil interaction models for

lateral buckling design: Phase IIA data review. Report to Boreas Consultants

(SAFEBUCK JIP), UWA report GEO 09497. 185pp.

White, D. J. & Dingle, H. R. C. (2011). The mechanism of steady ‘friction’ between

seabed pipelines and clay soils. Géotechnique 61, No. 12, 1035–1041



CHAPTER 6

BREAKOUT BEHAVIOUR OF PARTIALLY EMBEDDED

PIPES IN UNIFORM CLAY USING LIMIT ANALYSIS

6.1 INTRODUCTION

Predicting the resistance and trajectory of a pipeline during buckling-induced lateral

movements is most elegantly described within a plasticity framework by means of yield

envelopes, which in undrained conditions are also plastic potentials, to define the load

combinations that will cause movement, and the resulting direction of that movement.

In this chapter, Finite Element Limit Analysis (FELA) software OxLim (Martin, 2011)

is used to explore the effect of the response at the pipe-soil boundary. Two conditions

are considered: a no-tension associated flow response – which is the formal condition

required for the plasticity bound theorems to apply – and the more natural condition for

an unbonded interface which is zero shear stress to be present when separation occurs

and the normal stress is equal to zero. OxLim computes strict lower and upper bound

plasticity solutions as described by Makrodimopoulos & Martin (2006, 2007 and 2008).

Adaptive mesh refinement using the approach described by Martin (2011) is used to

achieve tight bracketing of the exact collapse load. The adaptivity also reveals the

regions of highest strain, showing the form of the collapse mechanism.

The results from this study provide definitive yield envelopes for the bearing

capacity of a pipeline shallowly embedded on constant/uniform strength weightless

undrained soil for these two pipe-soil interface responses. For the case of a horizontal

soil surface, the results show that the analytical upper bounds provided by Randolph &

White (2008) are also very close to the exact lower bounds. For practical purposes, the

CHAPTER 6: Breakout behaviour…


Randolph & White (2008) solutions provide adequate accuracy, but the FELA results

highlight more optimal failure mechanisms in certain conditions. The increase in the

size of the yield envelope when soil self-weight is introduced is investigated. It is shown

that a superposition approach is adequate to capture the effect of buoyancy, indicating

that the failure mechanism is not altered by the soil self-weight, for typical values of

submerged unit weight.

The growth of the yield envelopes in the presence of soil heave around the pipe

shoulders is also assessed. The shape of the soil heave is defined based on results from

large deformation finite element analyses, the strength of the heaved soil is assumed to

be the original shear strength of the soil, and limit analyses are performed for the

corresponding geometry. These limit analyses show good agreement with the finite

element results, and confirm that the presence of soil heave leads to increase in the

breakout resistance.

6.2 METHODOLOGY

The schematic of the problem studied is shown in Figure 6.1, which introduces the

notation used throughout this chapter. The pipe was modelled as a rigid body with the

shape of a regular polygon with 200 sides. The pipe was rigid and free to move in the

vertical and horizontal directions, but no rotation was allowed. The soil domain was

extended to five times the pipe diameter in the vertical as well as the horizontal

directions from the centre of the pipe, which was sufficient to eliminate boundary

effects. In each OxLim analysis, lower and upper bounds to the exact solution were

calculated iteratively using successive meshes that were automatically refined

adaptively. This automated process was repeated until the difference between the lower

and upper bounds was less than 1%.



D

w

θ

φ

10D

5D

Direction of pipe movement at failure

Figure 6.1 Schematic of the problem and notation

6.3 YIELD ENVELOPES

All cases analysed in this study are tabulated in Table 6.1. Initially, simple cases were

considered, with the pipe wished-in-place into weightless soil with a horizontal surface.

The soil was idealised as a rigid plastic material, as required in plasticity limit analysis,

failing according to a Tresca yield criterion at constant volume (which is representative

of undrained conditions) mobilising a shear strength of su. The soil strength was

uniform throughout the domain. Initially the pipe-soil interface was modelled in a

manner that obeys normality, and was either fully smooth (i.e. zero shear stress) or fully

rough (i.e. mobilising a shear stress of su).

Five pipe invert embedment cases equalling 0.1, 0.2, 0.3, 0.4 and 0.5 times the

diameter were studied. The pipe was probed in different directions making angles of 0°

to 180° with the vertical at intervals of 5°. The vertical and horizontal resistance forces

have been non-dimensionalised using the pipe diameter D and the shear strength su. The

resulting yield envelopes for smooth and rough interfaces are shown in Figure 6.2 and

Figure 6.3 respectively. The bearing capacity of the pipe increases with embedment and



with interface roughness. The aspect ratio of the envelopes decreases as the embedment

increases: for a given increase in embedment there is a greater rise in horizontal

capacity than vertical capacity.

Table 6.1 Different cases of OxLim analysis

Case Embedment Pipe-soil interface Soil weight Seabed

geometry Soil shear Strength

A 0.1D, 0.2D, 0.3D, 0.4D and 0.5D

Smooth Weightless Flat Uniform strength

B ,, Fully Rough ,, ,, ,,

C ,,

Fully rough at the front and smooth when breaks away

,, ,, ,,

D ,,

Roughness factor, α = 0.5

at the front and smooth when breaks

away

,, ,, ,,

E ,, ,, Soil weight considered, γ΄D/su = 0.8

,, ,,

F ,, ,, Weightless With soil heave ,,

G ,, ,, Soil weight considered, γ΄D/su = 0.8

,, ,,

0

0.5

1

1.5

2

2.5

3

-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

H /D

s u

V/Dsu

initial embedment = 0.1D, 0.2D, 0.3D, 0.4D and 0.5D

Figure 6.2 Yield envelopes for smooth pipes (Case A)



0

0.5

1

1.5

2

2.5

3

-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

H /D

s u

V/Dsu

initial embedment = 0.1D, 0.2D, 0.3D, 0.4D and 0.5D

Figure 6.3 Yield envelopes for rough pipes (Case B)

These results are compared with the analytical upper-bound solution given by Randolph

and White (2008) for an embedment of w/D = 0.4 for smooth and rough pipes in Figure

6.4. The results show excellent agreement for the case of smooth pipes, indicating that

the failure mechanism assumed in the Randolph & White (2008) analytical upper-bound

is near-optimal. In contrast, there is a significant discrepancy between the results of

these two studies for the rough pipe-soil interface.

0

1

2

3

-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

H /D

s u

V/Dsu

Smooth pipe (Oxlim analysis)Smooth pipe (Randolph and White, 2008)Rough pipe (Oxlim analysis)Rough pipe (Randolph and White, 2008)

Figure 6.4 Comparison of results for a typical pipe embedment (embedment = 0.4D)



This difference for rough pipes is due to the different interface behaviour assumed in

each analysis. The response of an interface is defined according to the notation set out in

Figure 6.5, which shows the normal stress σ and shear stress τ acting on the lower half

of the interface and the corresponding displacements of the upper half relative to the

lower half. If the interface is smooth, τ = 0 the yield surface is as shown in Figure 6.6.

From normality the yield surface is also the plastic potential, so the flow at failure is as

shown by the arrows. In the case of rough interface, a shear stress of su is sustained for

all σ > 0, leading to the yield envelope given by the bold line in Figure 6.7. The plastic

displacement vectors at failure are normal to this yield surface.

στ v

u

(a) Stresses (b) Displacement vectors

Figure 6.5 Stresses and corresponding displacement vectors of a horizontal interface

σ

τ

, dv

, du

Figure 6.6 Flow vectors for smooth interface



σ, dv

τ , du

su

Figure 6.7 Flow directions as per conventional plasticity analysis for rough interface If the two surfaces of the interface are moving apart at an angle (i.e. du ≠ 0) then a shear

stress of su is mobilised. The exception is the special case of zero tangential movement,

in which case the stress state can lie anywhere along the line σ = 0 at ⏐τ⏐ ≤ su. The

implication is that even when the pipe is separating from the soil, and a gap is opening,

the full shear strength of the interface is mobilised. These ‘phantom’ shear stresses are

required by classical plasticity theory, since they emerge from the requirement of

normality. However, they are unrealistic: if the interface is assumed to sustain no

tension and instead separates, then it cannot transmit shear stress through the opening

gap. Instead, a loss of contact means the normal and shear stresses reduce to zero (σ = 0,

τ = 0) so the stress point jumps to origin (O) meaning that whilst the yield envelope

remains unchanged, the plastic flow vectors all radiate from the origin as shown in

Figure 6.8, after Houlsby & Puzrin (1999). In this case the normality condition is

violated. The upper-bound solutions provided by Randolph and White (2008) are

consistent with Figure 6.8 because they do not consider any tangential traction in the

regions where the pipe separates from the soil.



, du

σ

su

τ

, dv

oA B

Figure 6.8 Direction of flow during loss of contact in no-tension surface (after Houlsby and Puzrin, 1999)

OxLim, following plasticity limit analysis theory, includes tangential traction even

when separation occurs, which leads to the discrepancy compared to the Randolph &

White (2008) solutions for a rough pipe (Figure 6.4). For pure downward vertical

movement of the pipe, when no breakaway occurs, the results agree closely. This

distinction between yield envelopes for no-tension interfaces that either sustain shear

stress at failure obeying normality, or which do not, has been studied in relation to the

bearing capacity of strip foundations by Houlsby & Puzrin (1999).

6.4 INTERFACE MODIFICATION

To replicate more natural condition for an unbonded interface, the pipe yield envelopes

were recalculated in OxLim after modifying the interface condition so that zero shear

stress was mobilised where separation occurs. To do this, the pipe was modelled as fully

rough (A-B in Figure 6.9) except for the portion where separation occurs, which was

modelled as fully smooth (B-C in Figure 6.9). The OxLim analyses were performed by

prescribing a specified direction of pipe movement, consistent with the modelled

interface conditions.



Smooth interfaceRough interface

Direction of pipe movement

A

B

C

Smooth interfaceRough interface


A

B

C

Figure 6.9 Schematic of pipe movement and combination of smooth and rough interface for OxLim analysis

The locus of the OxLim results using this interface modification for an embedment of

0.5D is shown in Figure 6.10 and compared with the results from Randolph and White

(2008). The OxLim results for high V/Dsu now match closely with the Randolph and

White (2008) results, compared with the poor agreement in Figure 6.4. However the

OxLim envelope lies slightly outside the Randolph & White (2008) solution for very

low (and negative) vertical loads. Also, the OxLim envelope, if mirrored into the

negative H domain, would not be convex.

These discrepancies at low V/Dsu arise because the OxLim envelope in Figure

6.10 is formed by simply joining the raw (V, H) results from each case. However, these

results all correspond to different boundary value problems because in each case the

separation point is different and so the relative lengths of rough and smooth pipe

interface are different. Following the usual FELA approach, each (V, H) result is

derived by firstly assessing the vector of load combinations that gives the minimum

dissipation rate for the specified direction of pipe movement. From that vector of

resultant loads, the actual (V, H) result is the point on the vector that is tangential to the

yield envelope for that boundary value problem.



0

0.5

1

1.5

2

2.5

3

-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

H /D

s u

V/Dsu

Randolph and White (2008)

Oxlim with smooth interface at the rear of the pipe

Figure 6.10 Comparison of result with Randolph and White (2008) for w/D = 0.5 after interface modification (Case C)

However, when considering a hybrid yield envelope, composed of segments related to

different separation points and therefore different boundary value problems, the full

load vectors from each solution must be considered, since the relevant (V, H) load point

may no longer be tangential to the yield envelope for the problem analysed.

To obtain the true yield envelope for the hybrid case in which the separation

point and the rough-smooth interface boundary varies with the pipe movement direction,

the load vectors from each solution have been re-combined to define the collapse loads

based on the hybrid case. To illustrate this re-combination process, the case with an

initial embedment of 0.5D is used. The pipeline was displaced upwards at angles from 0

< θ < 50 degrees, at one degree increments, with the separation point and rough-smooth

interface boundary changing for each case. For each raw OxLim (V, H) result – which

is applicable only to the non-varying interface case – the vector of potential load

combinations that would cause this collapse mechanism was reconstructed. These

vectors are perpendicular to the specified direction of movement. Figure 6.11(a) shows

the reconstructed vectors for θ = 10°, 20°, 30° and 40°, along with the full locus of raw

(V, H) results at 1° intervals.



0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0 0.1 0.2 0.3 0.4

H /D

s u

V/Dsu

Analytical solution (Randolph & White, 2008)OxLim result after optimization

(b)

0

0.2

0.4

0.6

0.8

1

1.2

-0.2 0 0.2 0.4

H /D

s u

V/Dsu

OxLim result

Analytical solution (Randolph & White, 2008)

Vectors perpendicular to the direction of pipe movement

(a)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0 0.1 0.2 0.3 0.4

H /D

s u

V/Dsu

Analytical solution (Randolph & White, 2008)OxLim result after optimization

(b)

0

0.2

0.4

0.6

0.8

1

1.2

-0.2 0 0.2 0.4

H /D

s u

V/Dsu

OxLim result

Analytical solution (Randolph & White, 2008)

Vectors perpendicular to the direction of pipe movement

(a)

Figure 6.11 Optimizing OxLim Result for modified interface; (a) Before optimisation, (b) After optimisation

The intersections between the reconstructed vectors and the adjacent cases (i.e. at higher

and lower values of θ) then define the new yield envelope that represents the hybrid

case. This process recovers the normality condition (Figure 6.11(b)).

Analytical solution for low vertical loads

For low vertical loads, an analytical solution for the (V, H) collapse can be obtained

using a simple wedge failure mechanism (Randolph & White 2008, Figure 6.12(a)).

When the pipe is displaced at angle θ the only work dissipated is along failure plane L,

which is of length 0.5.D.tanθ. The hodograph for displacement components is shown in

Figure 6.12(b). If the shear strength of the soil is su, the internal work done is equal to

suLδ. The external work done is H.δsinθ - Vδcosθ.



θθ

θV

H

D/2L

Δu= δ.sinθ

θ

Δw= δ.cosθ

δ

(a) Schematic (b) Hodograph

Figure 6.12 Simple wedge failure mechanism with corresponding hodograph From the principle of virtual work:

H.δsinθ - Vδcosθ = suLδ = 0.5.suDtanθδ 6.1

Hence

H = Vcotθ + 0.5.suD.secθ 6.2

For a particular value of V, the minimum H can be obtained by differentiating with

respect to θ, to give

θθ+θ−=θ

tan.secDs5.0eccosVddH

u2 = 0

6.3

and hence

θθ= 2

u

tan.sin5.0DsV

6.4

Substituting this into Equation 6.2 leads to the maximum value of H, given by

θθ+

=cos2

)sin1(DsH 2

u

6.5

So, for a particular angle of pipe movement θ, Equations 6.4 and 6.5 give optimum

values of V and H. The Randolph and White (2008) analytical upper-bound degenerates

to this simple wedge failure for low vertical loads.

Figure 6.13 compares the wedge solution with the reconstructed upper and lower

bound results from OxLim. For 0º < θ < 32º, the reconstructed OxLim solutions are

better than the simple wedge mechanism. Beyond this angle, the OxLim results bracket

the wedge case.



0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

1.01

0 5 10 15 20 25 30 35 40 45 50 55

Hox

lim/ H

wed

ge

Angle of pipe movement with the vertical, θ

Upper bound

Lower bound

θ0ο < θ < 50ο

Figure 6.13 Difference between optimised OxLim result and analytical solution for low vertical loads

The adaptive mesh refinement in OxLim reveals the detail of the failure mechanism,

showing how the breakout resistance is reduced to below the simple wedge case. The

adapted mesh for a near-vertical breakout (θ = 1º) is shown in Figure 6.14. The

adaptivity scheme focuses the elements according to the magnitude of shear strain. The

zoomed portion of this figure shows that the failure mechanism involves distributed

shear strain within a vertical wedge. However, close to the ground surface there is a

hinge point and a rigid block adjacent to a 45º wedge of distributed shear.

This feature is similar to the near-surface detail in the trapdoor failure

mechanism reported by Martin (2009). Although this mechanism is of little practical

relevance, the parallel with the trapdoor solution is interesting, and provides an

explanation for the ∼5% reduction in breakout resistance compared to the simple wedge

case (Figure 6.13). Failure mechanisms for pipe movement at θ = 15˚, 25˚, 35˚ and 45˚

are also shown in Figure 6.15(a-d). The mechanisms show details that differ from the

simple wedge case, explaining the divergence in Figure 6.13.



Wedge mechanism with an ear near surface

Figure 6.14 Failure mechanism for pipe movement direction of 1 degree to the vertical

To generate the full failure envelopes using this interface modification technique,

further OxLim analyses were performed, spanning all initial embedment cases. These

led to the definitive yield envelopes for the no-tension interface condition, which are

shown in Figure 6.16. For comparison, the results of Randolph & White (2008) are

shown, as well as small strain finite element analyses that were performed for this study,

using the same interface idealisation. In general, the Randolph & White (2008)

analytical upper-bound are equal to or marginally greater than the OxLim results. The

FE results are also generally close to the OxLim results, but are in error for purely

vertical loading by an underestimation of up to 10%.

This error is attributed to some separation occurring in ABAQUS analyses near

the pipe shoulder for pure vertical movement. If the same analysis is repeated with the

pipe and soil surfaces tied together, there is no separation and the FE results fall close to,

but marginally outside the theoretical results – as is typically found in similar plane

strain problems (e.g. Gourvenec & Randolph 2003). This approach cannot be used for

the other directions of loading, since breakaway would not then occur.



Failure mechanisms revealed by the adaptive mesh refinement in OxLim for

pure vertical and pure horizontal pipe movements are shown in Figure 6.17(a) and

Figure 6.17(b) respectively. These illustrate the similarity between the optimal

mechanism identified by OxLim and the analytical upper-bound reported by Randolph

& White (2008).

(a) 15˚ with vertical (b) 25˚ with vertical

(c) 35˚ with vertical (d) 45˚ with vertical

Figure 6.15 Failure mechanisms for different directions of pipe movement



0

0.5

1

1.5

2

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

H/D

s u

V/Dsu


Optimized OxLim result

ABAQUS small strain analysis

w/D = 0.1

0

0.5

1

1.5

2

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

H/D

s u

V/Dsu




w/D = 0.2

0

0.5

1

1.5

2

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

H/D

s u

V/Dsu




w/D = 0.3

0

0.5

1

1.5

2

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

H/D

s u

V/Dsu



ABAQUS small stra in analysis

w/D = 0.4

0

0.5

1

1.5

2

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

H/D

s u

V/Dsu

Randolph and White (2008)Optimized OxLim resultABAQUS small strain analysis

w/D = 0.5 A

B

Figure 6.16 Optimised yield envelopes for rough pipe soil interface



(a) Vertical pipe movement (point B in Figure 6.16)

(b) Horizontal pipe movement (point A in Figure 6.16)


in flat seabed (w/D = 0.5)

6.5 EFFECT OF SOIL WEIGHT

To extend the previous analyses, the effect of including soil self weight on the resulting

yield envelopes was explored. The results from analyses denoted as Cases D and E in

Table 6.1 are shown in Figure 6.18. In both cases the interface roughness factor was

chosen to be 0.5. For the weighty soil case, the non-dimensional term γ΄D/su was taken

equal to 0.8, which is typical for a soft seabed soil, where γ΄ is the submerged unit



weight of the soil. An increase in breakout resistance due to introduction of soil weight

can be observed for all embedment ratios in Figure 6.18.

0

0.5

1

1.5

2

2.5

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

H /D

s u

V/Dsu

w/D = 0.1, 0.2, 0.3, 0.4 and 0.5dashed lines - weightless soilsolid lines - weighty soil (γ'D/su = 0.8)

interface roughness factor, α = 0.5

Figure 6.18 Growth of yield envelopes due to introduction of soil self-weight (Case D and E)

Buoyancy factor

For pure vertical loading, the normalised vertical load V can be expressed as the sum of

components due to soil strength and self-weight as follows:

u

sbc

u DsA

fNDsV γ′

+= 6.6

where, Nc is the bearing capacity factor, As is the area of the soil displaced by the pipe.

fb is a buoyancy factor and is equal to 1 according to Archimedes’ principle, if the soil

surface is horizontal. For pipe motion in a direction other than pure vertical movement,

the resultant load F and the direction of pipe movement are not same. Instead they make

an angle ζ (= π - θ - tan-1(H/V)) as shown in Figure 6.19. To back-calculate fb for any

direction of pipe movement, the component of resultant forces in the direction of pipe

movement should be taken. Equation 6.6 can be rewritten for generalised direction of

movement in the following form:

u

sb0 Ds

Af)cosF(cosF γ′+ζ=ζ =γ

6.7



Where, ζcosF and ( ) 0cosF =γ′ζ are the components of F in the direction of pipe

movement for weighty (case E) and weightless (case D) soil cases. The value of fb

calculated this way can be confirmed by simple theoretical calculations as described in

the following section.


F

h

θ ζ

ψ

dψ

P Q

R S w

R

Figure 6.19 Schematic for calculating fb for any direction of pipe movement

A very small arc, ‘P-S’ in the periphery of the pipe in contact with the soil is considered

(Figure 6.19). This makes an angle ψ with the pipe radius. The arc itself makes a small

angle dψ in the centre of the pipe. When the pipe moves at an angle θ to the vertical, the

area of soil lifted with ‘P-S’ is denoted by an approximate rectangle ‘PQRS’, the area of

which is equal to R.dψ.δ.sin(θ - ψ). Here, δ is an incremental pipe movement in the

direction of pipe movement. The normalised depth of this portion from the mudline can

be calculated as:

Dw5.0sin5.0

Dh

−−ψ= 6.8



Therefore, the incremental work done (ΔW) for this small arc can be expressed as:

')Dw5.0sin5.0)(sin(RdW γ−−ψψ−θψδ=Δ

6.9

If this incremental work is integrated around the pipe periphery in contact with the soil

and divided by the work done by the component of F in the direction of pipe movement

against the weight of the soil displaced by the pipe, fb is obtained. The theoretically

calculated fb values are shown in solid lines and the buoyancy factors calculated using

OxLim results are shown by different symbols in Figure 6.20. As seen from this figure,

an excellent match is obtained between the theoretical calculation and the OxLim results.

0

0.2

0.4

0.6

0.8

1

1.2

0 30 60 90 120 150 180

Angle of pipe movement with vertical, θ

Buo

yanc

y fa

ctor

, f b

w/D = 0.1w/D = 0.2w/D = 0.3w/D = 0.4w/D = 0.5

Solid lines - theoretical calculationsMarkers - OxLim results

Figure 6.20 fb values for different directions of pipe movement

6.6 EFFECT OF SOIL HEAVE

The effect of soil heave around the pipe was also investigated. Initially, large

deformation finite element analysis using ABAQUS was performed to study the

breakout resistances of partially embedded pipelines to explore more realistic cases.

This analysis used the approach described in Chapters 2. The pipe was gradually pushed



into the soil and a berm was generated on each side. The pipe-soil interface was

assigned a roughness value of α = 0.5, in between the fully smooth and rough cases.

OxLim analyses were performed with the same soil conditions and using the berm

geometry extracted from the LDFE analyses after the initial penetration. The heave

geometries for w/D = 0.1 to 0.5 are shown in Figure 6.21.

(a) w/D = 0.1

(b) w/D = 0.2 (c) w/D = 0.3

(d) w/D = 0.4 (e) w/D = 0.5

Figure 6.21 Heave geometries for different embedments Two cases (Case F and Case G) without and with soil self-weight were considered. The

breakout resistance for pure horizontal motion for w/D = 0.5 was increased by 9.1% due



to the effect of soil self weight. For Case G, with heaved soil and γ'D/su = 0.8, the value

of fb for pure vertical loading was found to be in the range of 1.35 to 1.38 for uniform

soil. Yield envelopes for the berm soil case with soil weight are shown in the Figure

6.22.

0

0.5

1

1.5

2

2.5

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

H /D

s u

V/Dsu

w/D = 0.1, 0.2, 0.3, 0.4 and 0.5

solid lines - OxLim resultscircles - LDFE points

A

B

Figure 6.22 Comparison of yield envelopes from OxLim and LDFE analyses for heaved soil (Case G)

Results of Case D (no soil heave, weightless soil) and Case G (weighty soil with soil

heave) were compared to explore the effects of soil heave and soil weight together on

the breakout resistance. An increase of 10% (w/D = 0.1) – 18% (w/D = 0.5) in breakout

resistance for pure horizontal motion was observed in the case of heaved soil compared

to the weightless flat seabed. Case F (weightless soil with soil heave) and Case D

(weightless soil with no soil heave) were compared to see the effect of heave only. An

increase of 8.1% in the horizontal capacity for w/D = 0.5 for pure horizontal movement

was observed. The sum of the effect of heave (8.1%) and the effect of soil self weight

(9.1%) gives a total increase of 17.2%, which is close to the combined effect of 18%

increase. This indicates that superposition is an acceptable approach for assessing these

two effects.



Data points from LDFE analyses are also superimposed in the same figure and a

good match is observed. Displacement vectors revealing the failure mechanisms for

vertical penetration and pure horizontal movement for heaved soil case are shown in

Figure 6.23(a) and Figure 6.23(b). There are no fundamental differences in the failure

mechanism compared to the flat seabed case (as shown in Figure 6.17(a) and Figure

6.17(b)). The additional resistance is primarily due to the additional weight of soil to be

lifted, and the slight increase in the length of the failure planes that extend to the soil

surface.

(a) Vertical pipe movement (point B in Figure 6.22)

(b) Horizontal pipe movement (point A in Figure 6.22)


in heaved soil (w/D = 0.5)



6.7 CONCLUDING REMARKS In this chapter, the breakout resistance of shallowly embedded pipelines has been

addressed using finite element limit analysis methodology and verification has been

carried out using finite element software ABAQUS.

In the initial part of this study, a flat seabed and weightless soil was considered

and fully smooth and fully rough pipe soil interfaces were explored. The results were

compared with previously published solutions. In the case of a no-tension rough pipe-

soil interface, differences were highlighted between cases with an interface obeying an

associated flow rule, and a more natural one where the shear stress was limited to zero

where the pipe separates from the soil. In the latter case, although the associated flow

rule of classical plasticity theory is violated, the solution relates to a more logical

condition and leads to a different solution for a rough pipe soil interface. The OxLim

analysis was repeated using a modified interface behaviour, to mimic the more natural

breakaway condition. This led to results that are equivalent to published upper-bound

results in which breakaway is modelled. The resulting failure envelopes are definitive

solutions for the breakaway case. The OxLim approach revealed marginal

improvements in the collapse loads relative to analytical upper-bounds.

After exploring the weightless case in detail, the effect of soil self-weight was

investigated. It was shown that, for a flat seabed, a superposition approach is adequate

to capture the influence of buoyancy for a typical value of normalised soil self-weight.

This is because the soil failure mechanism is negligibly altered due to introduction of

self-weight.

The effect of soil heave around the pipe was also investigated. Initially, large

deformation finite element analyses were performed to simulate gradual penetration of

pipe and formation of heave around its shoulder. The seabed geometry with soil heave

was then extracted to perform upper-bound analyses in OxLim to study the breakout



resistance. It was confirmed that the buoyancy factor fb exceeds unity for purely

downward motion in the case of heaved soil surface. It was also concluded that the

presence of a soil berm around the pipe has a marked effect on the breakout resistance,

with an increase of up to 18% in capacity due to cumulative effect of soil weight and

berm observed. The results were compared with LDFE analyses and a good match was

observed.

6.8 REFERENCES Bruton, D. A. S., White, D. J., Carr, M. & Cheuk, C. Y. (2008). Pipe-soil interaction

during lateral buckling and pipeline walk – the SAFEBUCK JIP. Proc. Offshore

Technology Conf., Houston, Paper OTC 19589.

Chatterjee, S., Randolph, M. F. & White, D. J. (2012).The effects of penetration rate

and strain softening on the vertical penetration resistance of seabed pipelines.


Dassault Systemes (2007). Abaqus analysis users’ manual, Simulia Corp, Providence,

RI, USA.

Gourvenec, S. and Randolph, M. F. (2003). Effect of strength non-homogeneity on the

shape and failure envelopes for combined loading of strip and circular foundations on

clay. Géotechnique, 53, No. 6, 575-586.

Houlsby, G. T. & Puzrin, A. M. (1999). The bearing capacity of a strip footing on clay

under combined loading. Proc. R. Soc. Lond. A, 455, 893-916.

Martin, C. M. (2009). Undrained collapse of a shallow plane-strain trapdoor.


Martin, C. M. (2011). The use of adaptive finite-element limit analysis to reveal slip-

line fields. Géotechnique Letters, pp. 1-7.




response of partially embedded pipelines on clay. J. Geotech. Geoenviron. Engng.,

ASCE 135, No 6, 819-829.

Makrodimopoulos, A. & Martin, C. M. (2006). Lower bound limit analysis of cohesive

frictional materials using second-order cone programming. Int. Journal for Numerical

Methods in Engineering 66, No. 4, 604-634.

Makrodimopoulos, A. & Martin, C. M. (2007). Upper bound limit analysis using

simplex strain elements and second-order cone programming. Int. Journal for

Numerical and Analytical Methods in Geomechanics 31, No. 6, 835-865.

Makrodimopoulos, A. & Martin, C. M. (2008). Upper bound limit analysis using

discontinuous quadratic displacement fields. Communications in Numerical Methods in

Engineering 24, No. 11, 911-927.

Randolph, M. F. & White, D. J. (2008). Upper-bound yield envelopes for pipelines at




CHAPTER 7

ELASTOPLASTIC CONSOLIDATION BENEATH

SHALLOWLY EMBEDDED OFFSHORE PIPELINES

7.1 INTRODUCTION

In the fine grained, low permeability soils typically encountered in deep-water,

undrained conditions prevail during laying, resulting in excess pore pressures and

relatively low effective stresses in the vicinity of the pipe-soil interface. Estimation of

the axial friction available between pipeline and soil, which is required for design

calculations such as expansion and contraction of the pipeline due to temperature

changes, must therefore consider the time-scale of consolidation beneath the pipeline.

Pore pressure dissipation under shallowly embedded pipes has been addressed by

Gourvenec & White (2010) and Krost et al. (2011), but those results were limited to

elastic response of the seabed, and with a uniform coefficient of consolidation, cv. This

chapter extends those results to a more realistic elasto-plastic response of the soil.

Coupled consolidation finite element analyses have been undertaken using the

Modified Cam Clay soil model. Results from large deformation finite element (LDFE)

analyses are compared with the previous findings for elastic soil. Extremes of pipe

roughness (fully smooth or fully rough) and cv profiles (either uniform or increasing

proportionally with depth according to the effective stress level) are considered.

CHAPTER 7: Elastoplastic consolidation…


7.2 NUMERICAL METHODOLOGY

The large deformation finite element methodology developed for total stress analysis as

described in previous chapters was extended to coupled effective stress analysis for this

chapter.

The problem was solved as a two-dimensional plane strain problem with elasto-

plastic soil response and a rigid pipe, as shown in Figure 7.1. A sequence of small strain

analyses, with the pipe advanced by 1 % of its diameter at each step, were combined

with remeshing and interpolation of stress and material properties to penetrate the pipe

to the target embedment level.

Impe

rmea

ble

Impe

rmea

ble

Impermeable pipe-soil interface

Rigid pipe

Permeable surface Permeable surface

Impermeable

D

Uniform surcharge = 200 kPa Uniform surcharge = 200 kPa

Impe

rmea

ble

Impe

rmea

ble


Rigid pipe


Impermeable

D


Impe

rmea

ble


Rigid pipe


Impermeable

D


Figure 7.1 Schematic diagram of the problem solved

A graded mesh of second order (coupled consolidation-stress) triangular

elements, type CPE6MP in ABAQUS, was used with the smallest element of side equal

to 2 % of the pipe diameter. No drainage was allowed during the penetration process.

After the pipe had reached the target embedment, drainage was allowed at the top

surface to dissipate pore pressures generated during penetration. As for the small strain



analyses, extremes of a perfectly smooth and fully rough pipe-soil interface were

modelled.

The initial consolidation time increment, Δtinitial, was chosen according to the

criterion (Vermeer & Verruijt, 1981):

k'E6ht w2

initialγ

=Δ 7.1

where h is a typical element dimension, γw is the unit weight of water, E' is the effective

Young’s modulus of the soil (calculated here using the MCC reloading stiffness,

inversely proportional to κ) and k is the permeability of the soil.

7.3 MATERIAL MODEL

The soil response was modelled using Modified Cam Clay (MCC, Roscoe & Burland,

1968), as implemented in ABAQUS. The soil is defined as a porous elastic material

before yielding. All parameters used for the numerical analyses are listed in Table 7.1.

Table 7.1 Input parameters for numerical study Parameter Value Slope of CSL in p'-q space, Μ, (friction angle in triaxial compression, φ'tc)

0.92 (23.5°)

Void ratio at p' = 1 kPa on CSL, ecs 2.14 Slope of NCL in e-ln(p') space, λ 0.205 Slope of swelling and recompression line in e-ln(p´) space, κ 0.044 Poisson’s ratio, ν (LDFE) 0.3 Saturated bulk unit weight, γsat 15.0 kN/m3 Unit weight of water, γw 10.0 kN/m3 Permeability of soil, k 1.0e-9 m/s Pipe diameter, D 0.5 m

A limitation of the MCC model is that the soil stiffness, and hence the coefficient of

consolidation, cv, varies in proportion to the mean effective stress. In order to

investigate how the time-scale for consolidation varies with the distribution of cv,

separate series of analyses were undertaken: (a) with an artificial surcharge of 200 kPa

applied at the soil surface (including beneath the pipe) (Figure 7.1), giving an



approximately uniform value of cv within the soil domain; and (b) with a very small

surcharge (1 kPa – the smallest to allow numerical stability), giving cv approximately

proportional to depth. Comparison of the two series allowed assessment of an

equivalent cv for the latter case in order to obtain similar consolidation timescale for the

homogeneous case. For the large deformation analyses, heave grows on either side of

the pipe. The curved soil surface is modelled as a series of small straight lines and the

surcharge is maintained throughout the analysis by applying that pressure on each

straight line.

In all analyses the soil was considered to be K0 (normally) consolidated, with K0

given by

tc0 sin1K φ−= ~ 0.6 7.2

where φtc is the friction angle for triaxial compression conditions. In situ effective

stresses and pore pressure varied according to the respective self-weights (see Table

7.1).

The initial size of the yield envelope is determined by p'c, expressed as

tc

tc0

02

20

c sin3sin6

M withppM

qp

φ−φ

=′+′

=′ 7.3

where '0p and 0q are the initial effective mean stress and deviatoric stress. Initial void

ratio, e0, is calculated from

c010 pln)(plnee ′κ−λ−′κ−= 7.4

where

)2ln()(ee cs1 κ−λ+= 7.5

and κ and λ are the usual swelling and compression indices in MCC.



For these initial conditions, the starting point of the analysis for a given depth is denoted

by ‘O’ in p' - q and e – ln p' spaces, as shown in Figure 7.2.

q

p'

M1

Critical state line

C

O

BA

pa' pb' po' pc'

ln p'

e

λ1

A

BO

C

Critical state line

Normal compression line

κ1

q

p'

M1

Critical state line

C

O

BA

pa' pb' po' pc'

ln p'

e

λ1

A

BO

C

Critical state line

Normal compression line

κ1

Figure 7.2 Yield envelope and critical state line for MCC model

The stress path to reach critical state during undrained penetration is denoted by OB.

For triaxial compression conditions, the undrained shear strength ratio, su/σ'v, for K0

consolidated soil can be calculated from the MCC parameters using (Wroth, 1984):

Λ

⎟⎟⎠

⎞⎜⎜⎝

⎛ +φ=

σ 21a

a2sins 2

tc'v

u 7.6

For plane strain conditions the undrained shear strength ratio can be expressed as,



Λ

⎟⎟⎠

⎞⎜⎜⎝

⎛ +φ=

σ 21a

a2sin

32s 2

tc'v

u 7.7

where

)sin23(2sin3

atc

tc

φ−φ−

= and λ

κ−λ=Λ 7.8

This leads to (su/σ'v0)nc for plane strain conditions of 0.29 and mudline strengths of

0.29 kPa and 57.2 kPa for the 1 kPa and 200 kPa surcharge cases.

7.4 UNDRAINED PENETRATION RESPONSE

Normalised undrained penetration responses are shown in Figure 7.3.

0

0.1

0.2

0.3

0.4

0.5

0 1 2 3 4 5 6V/Dsu0

w/D

MCC Model -Smooth

Tresca Mode - Smooth

MCC Model - Rough

Tresca Model - Rough

1 kPa surcharge, smooth

1 kPa surcharge, rough

Figure 7.3 Comparison of penetration responses for smooth and rough pipes

The majority of the results, unless otherwise stated, are for uniform strength soil with a

surcharge of 200 kPa at the soil surface, although comparative LDFE results are also



shown for the nominal surcharge of 1 kPa. The geotechnical penetration resistance, V,

has been calculated by subtracting the buoyancy effect, assessed following Chatterjee et

al. (2012). V is normalised by the pipe diameter, D, and the undrained shear strength,

su0, at the invert level, calculated from the in situ profile based on Equation 7.7.

Comparative results of LDFE analyses using a simple Tresca soil model are also shown,

giving close agreement.

Comparison with the rigid plastic limit analyses of Randolph & White (2008)

shows that the partial mobilisation effect applies to the LDFE analyses at shallow

penetration, for the soil stiffnesses used here. The responses in Figure 7.3 lie slightly

below the equivalent rigid plastic solutions for w/D less than 0.2 (smooth) to 0.3

(rough). However, the relative trends agree, so the 1 kPa surcharge cases (increasing

strength with depth) show a higher normalised penetration resistance at shallow

embedment compared to uniform soil, reversing at greater embedment. The latter effect

is enhanced by dragdown of weaker sediments from the surface – an effect neglected in

the limit analysis solutions.

7.5 CONSOLIDATION RESPONSE

7.5.1 Pore pressure dissipation After penetration, the final resistance was maintained as a constant load while

consolidation was permitted. Contours of initial excess pore pressure normalised by the

value at the pipe invert for w/D = 0.5 are shown in Figure 7.4, and the corresponding

variation around the pipe periphery is shown in Figure 7.5. For the 1 kPa surcharge case,

the excess pore pressure is concentrated at the pipe invert, reflecting the increasing soil

strength with depth, and therefore the concentration of load at the pipe invert. In

uniform soil conditions the excess pore pressure is almost uniform (+/-15%) across

most of the pipe (-0.4 < x/D < 0.4).



Figure 7.4 Contours of excess pore water pressure after penetration (w/D = 0.5)



0

0.2

0.4

0.6

0.8

1

1.2

0 0.1 0.2 0.3 0.4 0.5 0.6

x/D

Δu/

Δu i

nv

Pipe embedment, w/D = 0.5Results shown for both sides of pipe (x/D positive and negative)

Rough, 200 kPa

Smooth, 200 kPa

Rough, 1 kPa

Smooth, 1 kPa

Figure 7.5 Excess pore pressure distribution around pipe periphery after penetration (w/D = 0.5)

The differences in the shape of the initial excess pore pressure field contribute to

differences in consolidation rate. Consolidation time is normalised as T = cvt/D2, where

cv is expressed in terms of the permeability, k, and (plastic) isotropic compressibility,

mv, as

( )w

0

wvv

pe1km

kcλγ

′+=

γ= 7.9

For simplicity, the initial value of cv has been used for the normalisation.

Figure 7.6 and Figure 7.7 show variations of excess pore water pressure at the

pipe invert, normalised by the initial value, with non-dimensional time T.



0

0.2

0.4

0.6

0.8

1

1.2

0.00001 0.0001 0.001 0.01 0.1 1 10 100T = cvt/D

2

Δu/

Δu

iw/D = 0.1w/D = 0.2w/D = 0.3w/D = 0.4w/D = 0.5

w/D = 0.1, 1 kPa surcharge


Markers: LDFE resultsLines: Equation 10

Figure 7.6 Excess pore pressure dissipation time history at pipe invert for smooth pipe

0

0.2

0.4

0.6

0.8

1

1.2

1E-05 0.0001 0.001 0.01 0.1 1 10 100T = cvt/D

2

Δu/

Δu i

w/D = 0.1w/D = 0.2w/D = 0.3w/D = 0.4w/D = 0.5



Markers: LDFE resultsLines: Equation 10

Figure 7.7 Excess pore pressure dissipation time history at pipe invert for rough pipe

Simple hyperbolic equations (solid lines) have been fitted to the FE data (symbols),

according to



m50i )T/T(1

1uu

+=

ΔΔ 7.10

where T50 is the value of T for 50% dissipation and m is a constant. The values of T50

and m for different embedment levels are tabulated in Table 7.2.

Table 7.2 Values of T50 and constant ‘m’ of hyperbolic fits

Smooth pipe Rough pipe Initial embedment ratio, w/D

T50 m T50

m

0.1 0.022 0.028 0.2 0.040 0.055 0.3 0.060 0.075 0.4 0.081 0.110 0.5 0.096

1.05

0.135

1.05

It can be seen from Figure 7.7 that, for a rough pipe, there is an initial increase in excess

pore pressure for all embedments. This is due to the Mandel-Cryer effect (stress transfer

phenomenon in which the dissipation process creates a local rise in total stress, resulting

in an increase rather than a decrease in excess pore pressure) (Mandel, 1950; Cryer,

1963 and as discussed for this problem by Gourvenec & White, 2010). In contrast to the

elastic consolidation results of Krost et al. (2011), the effect is evident for each

embedment, although in the LDFE analyses is more prominent for shallower

embedments. Due to the Mandel-Cryer effect, the hyperbolic fit does not capture the

initial portion of the dissipation response.

The majority of the results in Figure 7.6 and Figure 7.7 are for the uniform cv

case, but two example responses for the LDFE analyses using 1 kPa surcharge (cv

approximately proportional to depth) are shown. For those cases, the cv value that gives

a good match to the uniform cases at T50 and during the latter part of the consolidation

curve is higher than the invert value. The ratio, χ, of the operative value, cv,operative to the

invert value is given in Table 7.3.



Table 7.3 Operative cv for different initial embedment values

χ = cv,operative/cv,invert Depth of operative cv

(normalised by pipe diameter) Initial

embedment ratio, w/D Smooth pipe Rough pipe Smooth pipe Rough pipe

0.1 1.19 1.19 0.20 0.20 0.2 1.54 1.54 0.55 0.55 0.3 1.53 1.78 0.70 0.90 0.4 1.69 1.91 1.00 1.20 0.5 1.61 2.00 1.10 1.50

The increase in cv by 1.2 - 2 times indicates more rapid dissipation than if the

entire soil domain had the same cv value as at the pipe invert. This can be linked to (i)

the higher cv within the consolidating soil beneath the pipe invert and (ii) the different

initial pore pressure field (Figure 7.4 and Figure 7.5). An alternative interpretation of

this effect is to consider the depth at which this operative cv is found, which is also

given in Table 7.3.

The decay in the average excess pore pressure around the pipe periphery, Uav

(= Δuav/Δuav,init), and the corresponding rise in average normal effective stress, Σ, are

useful quantities since they indicate the build-up of potential axial resistance between

the pipe and the seabed. Σ is defined as:

( )( )'

init,av,n'

f,av,n

'init,av,n

'av,n

σ−σ

σ−σ=∑ 7.11

where σ'n,av denotes the average normal effective stress around the pipe periphery and

σ'n,av,init and σ'n,av,f are the values before and after dissipation. These trends are shown in

Figure 7.8 for a smooth pipe. The pore pressure and inverted effective stress responses

agree to within 4% throughout the decay process, indicating that changes in total stress

– which can occur due to the wedging effect, even if the applied pipe weight is constant

– are small. The MCC results are similar to the elastic results, but show more rapid



dissipation as consolidation progresses compared to the elastic solution, reflecting the

increasing stiffness as the effective stress rises.

0

0.2

0.4

0.6

0.8

1

0.00001 0.0001 0.001 0.01 0.1 1 10 100

T = cvt/D2

Uav

or (

1-Σ

)w/D = 0.1w/D = 0.2w/D = 0.3w/D = 0.4w/D = 0.5

MCC analyses:Lines: Effective stress, (1 - Σ)Markers: Pore pressure, Uav

Elastic analysis, w/D = 0.1(Gourvenec & White, 2010)

Elastic analysis, w/D = 0.5(Gourvenec & White, 2010)

Figure 7.8 Average pore pressure dissipation and rise in effective stress along the pipe periphery

7.5.2 Consolidation settlement Consolidation settlement, wc normalised by the diameter of the pipe is plotted against

non-dimensional time T in Figure 7.9 (smooth pipe) and Figure 7.10 (rough pipe). The

settlement increases with increasing initial embedment, consistent with the increase in

load applied during consolidation. Apart from the shallowest embedment, where the

pipe-soil interface condition makes little difference, the rough interface leads to a slight

delay in the onset of consolidation settlement, and T50 values that are up to twice as high.

Since the pipe is subjected to the full vertical bearing capacity throughout consolidation,

these settlements are greater than will typically occur in practice. The duration of the

consolidation settlement is substantially less than the equivalent elastic results – scaled

to give the same total consolidation settlement (Figure 7.9, Krost et al., 2011).



0

0.05

0.1

0.15

0.2

0.25

1E-05 1E-04 0.001 0.01 0.1 1 10 100 1000T = cvt/D

2w

c/D

w = 0.1Dw = 0.2Dw = 0.3Dw = 0.4Dw = 0.5D

V/Dsu0=2.13

V/Dsu0=3.29

V/Dsu0=3.84

V/Dsu0=4.13V/Dsu0=4.35

Elastic solutionKrost et al. (2011)

Figure 7.9 Time settlement response for different initial embedments (smooth pipe)

0

0.05

0.1

0.15

0.2

0.25

1E-05 1E-04 0.001 0.01 0.1 1 10 100 1000T = cvt/D

2

wc/D

w = 0.1Dw = 0.2Dw = 0.3Dw = 0.4Dw = 0.5D

V/Dsu0 = 2.16

V/Dsu0 = 3.52

V/Dsu0 = 4.48

V/Dsu0 = 5.26

V/Dsu0 = 5.91

Figure 7.10 Time settlement response for different initial embedments (rough pipe)



7.6 CONCLUDING REMARKS The consolidation process after partial embedment of pipelines is an important

consideration for design, as it governs the rate at which axial friction develops. The

effects on consolidation of embedment, pipe-soil interface condition and the large

deformations associated with the penetration have been investigated. In an advance over

previously-published elastic solutions, the more realistic Modified Cam Clay plasticity

soil model was used.

For both smooth and rough pipe-soil interfaces, consolidation time increased with

increasing initial embedment, and was greater for the rough case. An initial increase in

excess pore water pressure was observed at the invert for rough pipes due to the

Mandel-Cryer effect. Simple hyperbolic equations were fitted to the dissipation curves

at the pipe invert, with parameters tabulated for ease of use in design. Also, the

averaged pore pressure and effective stress quantities around the pipe-soil contact were

assessed, since these control the available friction.

The dissipation responses were compared to those from elastic solutions,

highlighting the effects of different initial excess pore pressure distributions and some

stiffness increase during consolidation arising from the Modified Cam Clay model.

Comparison of results between small strain and large deformation analyses showed the

effect of the soil berms on the consolidation behaviour.

7.7 REFERENCES Chatterjee, S., Randolph, M. F. & White, D. J. (2012). The effects of penetration rate

and strain softening on the vertical penetration resistance of seabed pipelines.

Géotechnique 62, in press, doi: 10.1680/geot.10.P.075.

Cryer, C. W. (1963). A comparison of the three dimensional consolidation theories of

Biot and Terzaghi. Q. J. Mech. Appl. Math. 16, No. 4, 401–412.



Dassault Systèmes. (2010). Abaqus Analysis Users' Manual. Simula Corp, Providence,

RI, USA.




Gourvenec, S. M. & White, D. J. (2010). Elastic solutions for consolidation around

seabed pipelines. Proc. Offshore Technology Conf., Houston, Texas, USA, Paper

OTC 20554.

Hu, Y. & Randolph, M. F. (1998). A practical numerical approach for large deformation

problems in soil. Int. J. Numer. Analyt. Meth. Geomech. 22, No. 5, 327-350.

Krost, K., Gourvenec, S. M. & White, D. J. (2011). Consolidation around partially

embedded seabed pipelines. Géotechnique 61, No. 2, 167-173.

Mandel, J. (1950). Étude mathématique de la consolidation des sols. Actes du Colloque

International de Mécanique, Poitier, France, 4, 9–19.

Randolph, M. F. & White, D. J. (2008). Upper bound yield envelopes for pipelines at

shallow embedment in clay. Géotechnique, 58, No. 4, 297-301

Roscoe, K. H. & Burland, J. B. (1968). On the generalised stress-strain behaviour of

'wet clay'. Engineering Plasticity, Cambridge University Press, 535-609.

Vermeer, P. A. & Verruijt, A. (1981). An accuracy condition for consolidation by finite

elements. Int. J. Numer. Analyt. Meth. Geomech. 1, 1–14.



J. 47, No. 8, 842-856.

Wroth, C. P. (1984). The interpretation of in situ soil tests. Géotechnique 34, No. 4,

449-489.



CHAPTER 8

EFFECTS OF CONSOLIDATION ON PENETRATION

AND LATERAL BREAKOUT RESISTANCES

8.1 INTRODUCTION

To design a pipeline reliably for lateral buckling, it is necessary to predict the lateral and

axial pipe-soil resistance forces, which both depend on the pipe embedment and the

strength of the surrounding soil. In deep water, the seabed typically comprises soft fine-

grained sediments, which can consolidate and change in strength over the time periods

relevant to the operating life of a pipeline. In this chapter, the effects of consolidation on

two key aspects of deep water pipeline design are studied: firstly, the effect of

consolidation on pipeline embedment; and secondly the effect of consolidation on the

lateral breakout behaviour.

The current design practice (White & Cheuk 2005, 2009; AtkinsBoreas 2008)

assumes that undrained conditions apply throughout the lay process and subsequent

consolidation settlements are generally neglected. Also, it is usually assumed that the

soil strength during pipe breakout is unaffected by consolidation under the pipe weight

during the period between laying and breakout. The effect of these assumptions is

investigated in this chapter.

A large deformation finite element methodology combined with the Modified Cam

Clay plasticity soil constitutive model was developed as described in the previous

chapter to study the pore pressure dissipation beneath partially embedded seabed

pipelines. In this chapter, the same methodology has been used to study the effect of

consolidation on penetration behaviour and subsequent lateral breakout resistance.

CHAPTER 8: Effects of consolidation…


8.2 MODEL DESCRIPTION

The same model as described in the previous chapter is used here. A two-dimensional

plane strain model was constructed with the pipe as a rigid body and the soil as

deformable. The extent of the model was 10 times the pipe diameter in the vertical

direction and 8 times the pipe diameter in the horizontal direction on both sides of the

pipe. The side boundaries of the model were free to move in the vertical direction, but

restrained against horizontal movement. The bottom boundary was fixed, preventing

vertical and horizontal movement. Drainage was allowed only at the top soil surface and

the pipe-soil interface was taken as impermeable. A schematic diagram of the problem

studied and main notation used are shown in Figure 8.1.

10D

Impermeable pipe-soil interface (smooth / rough)

Permeable Permeable

D


w

HV

Rol

ler /

Impe

rmea

ble

Rol

ler /

Impe

rmea

ble

Hinge / Impermeable

16D

Pipe

Soil10D


Permeable Permeable

D


w

HV

Rol

ler /

Impe

rmea

ble

Rol

ler /

Impe

rmea

ble

Hinge / Impermeable

16D

Pipe

Soil


Permeable Permeable

D


w

HV

Rol

ler /

Impe

rmea

ble

Rol

ler /

Impe

rmea

ble

Hinge / Impermeable

16D

Pipe

Soil

Figure 8.1 Schematic of the problem studied

A very small displacement of 1% of the pipe diameter, D, was applied at the

pipe reference point in each step. Six-noded triangular plane strain elements of type

CPE6MP within the ABAQUS library were used for discretization of the soil domain. A

fine mesh with minimum side length of the triangular elements of 0.02D was adopted



near the pipe. The extent of the finest meshing from the centre of the pipe at the start of

the analysis was up to 1.25D on both sides and below from the mudline. Figure 8.2

shows the finite element mesh before any pipe displacement and after the pipe had been

penetrated into the soil by half its diameter.

(a) Initial Mesh

(b) Mesh after pipe penetration

Figure 8.2 Finite element meshes before and after pipe penetration



8.3 SOIL PARAMETERS

The modified Cam Clay (MCC) soil constitutive model (Roscoe & Burland, 1968;

Schofield & Wroth, 1968) was adopted and the numerical parameters used for all the

analyses are same to that of the previous chapter. A uniform pressure of 200 kPa was

applied at the top soil surface. This alleviates numerical problems associated with the

very low shear strength of the soil at the mudline when using the Cam clay soil model

and normally consolidated conditions.

As well as providing numerical stability, this surcharging technique minimises the

variation in soil properties with depth. This makes normalisation of the results more

straightforward, since properties such as the coefficient of consolidation and the initial

undrained shear strength are essentially invariant with depth. The strength heterogeneity

affects the vertical and horizontal soil resistance. Adoption of an artificial surcharge of

200 kPa restricts the study to strength heterogeneity of close to zero. However, the main

focus here is to evaluate the general trends of response observed as a result of partial

consolidation, compared with corresponding results for purely undrained conditions.

The interface between the pipe and the soil was assumed to be fully smooth

(mobilising zero shear stress during tangential movement) or fully rough (with adjacent

pipe and soil nodes being tied). The pore water pressure distribution was initially

hydrostatic.

8.4 EFFECTS OF LOADING RATE

8.4.1 Penetration resistance

Fully coupled consolidation stress analyses following the RITSS approach were

performed. The pipe was penetrated to an embedment of 50% of its diameter with

different velocities, v, and thus different values of the non-dimensional velocity vD/cv.

The consolidation coefficient, cv, can be determined from



wvv m

kcγ

= 8.1

Where, mv is the volume compressibility, wγ is the unit weight of water and k is the

permeability.

A wide range of values of vD/cv from a very high velocity (vD/cv = 100) down

to the lowest velocity corresponding to vD/cv = 0.025 were considered. The highest

velocity means that negligible excess pore water pressure can dissipate and undrained

conditions are approached. In contrast, slower velocities of the pipe lead to a partially

drained and ultimately a fully drained response. Figure 8.3 shows the variation of

normalised penetration resistance with depth for a smooth pipe-soil interface, and

Figure 8.4 shows the same results for a rough pipe-soil interface.

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8V/Dsu0

w/D

vD/Cv=0.025vD/Cv=0.1vD/Cv=1vD/Cv=10vD/Cv=30Dv/Cv=60vD/Cv=100Tresca Model

Figure 8.3 Normalised penetration resistances with embedment for different pipe velocities (smooth pipe)



0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10V/Dsu0

w/D

vD/Cv=0.05

vD/Cv=0.1

vD/Cv=1

vD/Cv=10

vD/Cv=30

vD/Cv=100

Tresca Model

Figure 8.4 Normalised penetration resistances with embedment for different pipe velocities (rough pipe)

The resistance force is normalised using the undrained shear strength, su0 at the pipe

invert obtained from the modified Cam Clay parameters for K0-consolidated soil. The

initial undrained shear strength (Wroth, 1984) obtained was 57.2 kPa at the mudline and

64.4 kPa at the bottom of the mesh.

At the two highest penetration rates, the resistance profiles are similar,

suggesting that fully undrained conditions are almost reached. This is confirmed by the

results of an analysis performed using the same numerical technique but with the Tresca

soil model and the equivalent undrained shear strength. These results are also shown in

Figure 8.3 and Figure 8.4. Excellent agreement is evident, indicating that the fastest

cases correspond to practically undrained conditions.

At lower pipe velocities, the penetration resistances are higher (Figure 8.3).

Numerical convergence problems were observed for a very low penetration rate



simulating fully drained conditions. However, there are negligible differences in the

resistance responses for vD/cv = 0.1 and vD/cv = 0.025 or 0.05. This indicates that pipe

velocities corresponding to vD/cv = 0.1 or lower lead to essentially fully drained

resistance, even though small excess pore pressures are still present. The contours of

excess pore water pressure normalised by the resistance experienced by the pipe at w/D

= 0.5 for the highest and the lowest penetration rates (nominally undrained and drained

cases) for smooth and rough pipes are shown in Figure 8.5. For the lowest pipe

penetration rate, the excess pore pressure generated beneath the pipe is much less

compared to that for the undrained cases.

The ratio between the drained and undrained penetration resistance increases

with pipe embedment. Compared to the smooth case, more resistance is observed at a

particular embedment level for the rough pipe-soil interface. However, the relative

increase in resistance from the fully undrained to the fully drained case is lower in the

case of rough pipe. At the embedment level of w/D = 0.5, for the smooth pipe, a 72%

increase in resistance is observed from the fully undrained condition to the fully drained

condition, whereas a difference of approximately 48% is found for the rough pipe.

To illustrate the transition between drained and undrained conditions, the

resistance for a particular pipe velocity (V) is normalised by the undrained resistance

(Vundrained) at that depth and plotted against the non-dimensional velocity. Figure 8.6 and

Figure 8.7 show the resulting ‘backbone’ curves at different embedment levels for

smooth and rough pipes respectively. For vD/cv ≤ 0.1, the resistance is independent of

velocity and the response is essentially drained. For vD/cv ≥ 100, the response stabilises

and the response is fully undrained. The non-dimensional velocities in between these

limits correspond to partially drained behaviour. The backbone curves for smooth and

rough pipes can be fitted to a simple hyperbolic equation of the form:



Figure 8.5 Contours of excess pore water pressure normalised by penetration resistance



[ ]c50vvundrained )c/vD/()c/vD(1ba

VV

++=

8.2

where (vD/cv)50 is the normalised penetration rate that gives a response midway

between the drained and undrained limits. For higher values of vD/cv, i.e. for undrained

cases, V/Vundrained tends to unity, so the value of parameter ‘a’ is always 1. The

parameter ‘b’ controls the drained limit of the backbone curve as vD/cv → 0. The

quantities ‘c’ and (vD/cv)50 were varied to obtain best-fit curves for all embedment

levels for smooth as well as rough pipes. It was found that values of c = 1 and (vD/cv)50

= 2 gave reasonably fitting curves for all initial embedment and smooth and rough pipes.

The parameter ‘b’ depends on the initial embedment level and can be expressed as a

power law function of the embedment depth. For a smooth pipe

b ~ 1.45(w/D) 8.3

And for a rough pipe:

b ~ 0.92(w/D)0.9 8.4

For comparison, a number of analyses were run for a low surcharge of 1 kPa at

the top surface for the smooth pipe. For the case of 1 kPa surcharge, the value of cv

varies considerably with depth. Hence, while calculating non-dimensional velocity

vD/cv, cv was chosen at depth of 1D. Figure 8.8 shows the backbone curves for different

embedments for 1 kPa surcharge. The V/Vundrained ratios are generally higher at the

drained end for this case. However, for embedment levels of w/D = 0.2 or more, the

backbone curves are closer to each other compared to the 200 kPa case. This indicates

that for 1 kPa surcharge, V/Vundrained ratio increases less as the pipe penetrates deeper.



1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

0.01 0.1 1 10 100 1000

vD/cv

V/V

undr

aine

d LDFE result, w/D=0.1LDFE result, w/D=0.2LDFE result, w/D=0.3LDFE result, w/D=0.4LDFE result, w/D=0.5

Figure 8.6 Backbone curves for different initial embedment levels (smooth pipe)

1

1.1

1.2

1.3

1.4

1.5

0.01 0.1 1 10 100 1000

vD/cv

V/V

undr

aine

d

LDFE result, w/D=0.1LDFE result, w/D=0.2LDFE result, w/D=0.3LDFE result, w/D=0.4LDFE result, w/D=0.5

Figure 8.7 Backbone curves for different initial embedment levels (Rough pipe)



1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

0.01 0.1 1 10 100 1000vD/cv

V/V

undr

aine

d

w/D = 0.1w/D = 0.2w/D = 0.3w/D = 0.4w/D = 0.5

Figure 8.8 Backbone curves for different initial embedment levels (smooth pipe, 1 kPa surcharge)

8.4.2 Consolidation settlement

At different levels of vertical embedment, i.e. at w/D = 0.1, 0.2, 0.3, 0.4 and 0.5, the

consolidation settlement behaviour was also studied. The excess pore water pressure

generated during the pipe penetration was allowed to dissipate under the full penetration

resistance load experienced at the respective embedment level. This simple case may

not represent practical conditions. In general, the maximum vertical pipe-seabed load

during pipe laying is higher than the pipe weight alone, so the applied vertical load

during consolidation is less than the full bearing capacity.

The settlement (Δw) variations for different embedment levels are shown in

Figure 8.9, as a function of non-dimensional time factor T (= cvt/D2), for initial

penetrations at speeds of vD/cv = 0.1 (drained), and 100 (undrained). For the (nominally)

drained penetration case, the pore water pressure is partially dissipated during

penetration and hence the subsequent consolidation settlement should be less than for



0

0.05

0.1

0.15

0.2

0.25

0.3

0.0001 0.001 0.01 0.1 1 10 100 1000T = cvt/D

2Δ

w/D

vD/Cv = 0.1

vD/Cv = 100

Curves in orderw/D = 0.1, 0.2, 0.3, 0.4 & 0.5


(a) Smooth interface

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.0001 0.001 0.01 0.1 1 10 100 1000T = cvt/D

2

Δw

/D

vD/Cv = 0.1vD/Cv = 100



(b) Rough interface

Figure 8.9 Pipe settlements with time for different initial embedments and pipe velocities

the undrained case. However, this is more than compensated for by the greater

resistance experienced during drained penetration, and thus higher loads applied during

the consolidation phase. If the same load were to be applied during consolidation, the



consolidation settlement would indeed be much less following drained penetration

compared to the undrained case. This phenomenon is illustrated in Figure 8.10 for the

smooth pipe, where for the drained case the loads were reduced (following penetration,

prior to consolidation) to the same as for the corresponding undrained case.

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.0001 0.001 0.01 0.1 1 10 100 1000T = cvt/D

2

Δw

/D

vD/Cv = 0.1

vD/Cv = 100



Figure 8.10 Consolidation settlements following penetration at different speeds under the same consolidation load (smooth pipe)

It may be seen that the overall time-scale of consolidation is the same, regardless

of the degree of consolidation during initial penetration. The time-scale for

consolidation settlement is essentially dictated by the far-field pore pressures, and is

nearly two orders of magnitude greater than for pore pressure dissipation adjacent to the

pipe (Chatterjee et al. 2012).

8.4.3 Pore pressure dissipation after undrained penetration The axial and lateral resistance of the pipeline are affected significantly by the degree of

consolidation following installation. This may be characterised by the average excess

pore pressure around the embedded pipe perimeter (Δuav), normalised by the initial

average value (Δuav,init), as plotted for different initial embedment levels against the



non-dimensional time T for a smooth pipe in Figure 8.11. The consolidation response

can be fitted by a simple hyperbolic equation of the form

m50init,av

av

)T/T(11

uu

+=

ΔΔ

8.5

where T50 is the non-dimensional time required for 50% dissipation of the average

excess pore pressure. The values of T50 and index ‘m’ for different embedment levels

are tabulated in Table 8.1. The T50 values from the present study are less than published

previously for elastic soil (Gourvenec & White, 2010), indicating faster dissipation

(Table 8.2).

0

0.2

0.4

0.6

0.8

1

1.2

0.00001 0.0001 0.001 0.01 0.1 1 10 100

T = cvt/D2

Δu a

v/ Δu a

v,in

it

w/D = 0.1w/D = 0.2w/D = 0.3w/D = 0.4w/D = 0.5

Symbols - LDFE resultsLines - hyperbolic fits

Figure 8.11 Dissipation of excess pore water pressure with non-dimensional time T (smooth interface)

Table 8.1 Values of T50 and constant ‘m’ of hyperbolic fits

Initial embedment ratio, w/D T50 m

0.1 0.015 0.85 0.2 0.032 0.88 0.3 0.052 0.93 0.4 0.075 1.00 0.5 0.090 1.05



Table 8.2 Comparison of values of T50 from the present study and elastic solution (Gourvenec & White, 2010)

T50 Initial embedment ratio,

w/D Present study

Gourvenec & White (2010)

0.1 0.015 0.018 0.2 0.032 0.042 0.3 0.052 0.068 0.4 0.075 0.096 0.5 0.090 0.121

8.5 LATERAL BREAKOUT RESISTANCE

8.5.1 Background After the pipe is partially embedded into the seabed, it can be displaced laterally in

response to internal temperature and pressure, or as a result of external hydrodynamic

loading. The breakout resistance, i.e. the peak lateral resistance experienced by the pipe

as it displaces laterally, depends strongly on the strength of the surrounding soil. The

direction of the pipe movement at this stage also depends on the weight of the pipe

relative to the strength of the seabed (although note that this will not be simulated well

in the present study, because of the artificially high shear strength resulting from the

surcharge of 200 kPa).

The available solutions for breakout resistance in the literature are mainly

confined to undrained breakout, with the strength of the surrounding soil being

unaffected by consolidation. In reality, there is always a significant duration between

pipe laying and operation. During this time, consolidation of the soil below and around

the pipe can occur under the weight of the pipe and contents. Dissipation of positive

excess pore water pressure leads to an increase in the shear strength of the soil near the

pipe. So, before breakout occurs, the strength distribution around the pipe is altered, and

the breakout resistance is potentially raised.



The breakout resistance depends on the load path in V-H space, so the best basis for

describing the potential breakout resistance is to determine the yield envelope in V-H

space. In this study, yield envelopes in V-H load space have been evaluated, for a

smooth pipe-soil interface only, for two conditions: (i) immediately after undrained

penetration (referred to as unconsolidated, undrained); and (ii) after full consolidation

following undrained penetration (referred to as consolidated, undrained). In both cases,

the pipeline movement during penetration and breakout was at rate corresponding to a

normalised velocity of 100, giving nominally undrained conditions. The failure loads in

V-H space were obtained by displacing the pipe by 10 % of its diameter in different

directions.

8.5.2 Unconsolidated undrained yield envelopes Firstly, the unconsolidated undrained case is considered. The limiting values of vertical

and horizontal resistances have been normalised by the initial undrained shear strength

at that depth. The resulting yield envelopes in V-H space for w/D = 0.1, 0.2, 0.3, 0.4

and 0.5 are shown in Figure 8.12.

0

1

2

3

0 1 2 3 4 5 6

V/Dsu0

H/D

s u0


Present study

Merifield et al. (2009) horizontal resistance

Merifield et al. (2009) vertical resistance

Curves in orderw/D = 0.1, 0.2, 0.3, 0.4 and 0.5

Figure 8.12 Yield envelopes for different initial embedments for unconsolidated undrained case (smooth pipe)



These results exceed the equivalent results presented by Randolph & White (2008) by

typically 15% because the latter analyses considered only a flat seabed (with the pipe

wished into place) and ignored the self-weight of the soil. Buoyancy effects due to soil

self-weight are minimal in the present study, because of the high shear strength.

However, the berm of soil displaced during penetration in the present study results in

greater soil resistance. Merifield et al. (2009) reported results of finite element analyses

using a Tresca model and also considered the effects of soil berms on the vertical

penetration and horizontal breakout resistances. Results from that study for pure vertical

and pure horizontal pipe movements are also shown in Figure 8.12. Their results are

close to the present study, with a maximum error below 9 % (except for w/D = 0.1). The

close agreement confirms the correct operation of the Modified Cam Clay soil model

for fully undrained conditions.

8.5.3 Consolidated undrained yield envelopes Figure 8.13 shows the consolidated undrained yield envelopes for different initial

embedment levels after full pore pressure dissipation. To make a comparison between

the unconsolidated and consolidated cases, results for two initial embedment levels of

w/D = 0.1 and 0.5 are plotted in Figure 8.14. The growth in the size of the yield

envelope was 66 % for pure vertical movement for both w/D = 0.1 and 0.5. For pure

horizontal movement, the horizontal resistance is 53 % greater for the consolidated case

for w/D = 0.1, whereas the increase is 83 % for w/D = 0.5.

Contours of the strength increase compared to the original undrained shear

strength at the embedment level of w/D = 0.5 (w/D ~ 0.75 following consolidation) are

shown in Figure 8.15. The consolidated strength reaches 2.1 times the original strength

just beneath the pipe. The shape of the bulb of strength increase is consistent with the

change in shape of the yield envelopes. The increase is strength is greatest beneath the

pipe – within the soil that controls the response to vertical loading – and a lower



increase in strength is evident to the side of the pipe – within the soil that controls the

response to horizontal loading.

0

1

2

3

4

0 1 2 3 4 5 6 7 8

V/Dsu0

H/D

s u0

Curves in orderw/D = 0.1, 0.2, 0.3, 0.4 and 0.5

Figure 8.13 Yield envelopes for different initial embedments for consolidated undrained case (smooth pipe)

0

1

2

3

4

0 1 2 3 4 5 6 7 8

V/Dsu0

H/D

s u0

Consolidated undrainedUnconsolidated undrainedParabola fit

w/D = 0.1

w/D = 0.5

Figure 8.14 Comparison of yield envelopes for unconsolidated undrained and consolidated undrained conditions for w/D = 0.1 and 0.5 (smooth pipe)



Figure 8.15 Contours of ratios of consolidated shear strength to the original shear strength (smooth pipe)

8.5.4 Simple equation fit

The finite element results shown in Figure 8.12 and Figure 8.13, which form the

undrained yield envelopes, can be fitted by an equation with the form of a distorted

ellipse:

21

0u0u

max

0u0u DsV

DsV

DsV.f

DsH

ββ

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛β=

8.6

where

( )( )

21

21

21

21ββ

β+β

βββ+β

=β 8.7

Here, the parameters β1 and β2 skew the ellipse and f is a factor determining the aspect

ratio of the ellipse; Vmax is the undrained resistance under pure vertical loading. The

values of the parameters f, β1 and β2 for different initial embedment levels and

unconsolidated and consolidated cases are tabulated in Table 8.3.



Table 8.3 Values of f, β1 and β2 for unconsolidated and consolidated conditions

Unconsolidated Undrained

Consolidated Undrained Initial embedment ratio,

w/D f β1 β2 f β1 β2

0.1 0.14 0.83 0.64 0.26 0.81 0.53 0.2 0.16 0.70 0.65 0.32 0.75 0.53 0.3 0.22 0.65 0.61 0.39 0.46 0.52 0.4 0.31 0.53 0.58 0.47 0.41 0.70 0.5 0.37 0.45 0.59 0.55 0.35 0.70

The values of normalised Vmax versus normalised embedment for unconsolidated and

consolidated cases are plotted in Figure 8.16. These responses can be fitted by a simple

power law equation of the form:

b

0u

max

Dwa

DsV

⎟⎠⎞

⎜⎝⎛=

8.8

Coefficients ‘a’ and ‘b’ for unconsolidated and consolidated cases are listed in Table 8.4.

In the same figure (Figure 8.16), results from Merifield et al. (2009) are also plotted for

comparison with the unconsolidated undrained case and show good agreement.

Table 8.4 Power law fit coefficient ‘a’ and ‘b’ for unconsolidated and consolidated

conditions

Results for 1 kPa surcharge are also shown for the unconsolidated and the consolidated

cases in Figure 8.16 to compare with the more natural case. There are considerable

buoyancy effects in the overall resistance for the 1 kPa surcharge case, unlike the 200

kPa case. The maximum penetration resistances for the 1 kPa surcharge case that are

plotted in Figure 8.16 are the geotechnical capacity after correction for buoyancy.

Conditions a b

Unconsolidated Undrained 5.7 0.29

Consolidated Undrained 9.3 0.28



0

0.1

0.2

0.3

0.4

0.5

0 1 2 3 4 5 6 7 8Vmax/Dsu0

w/D Unconsolidated undrained

Consolidated undrained


Unconsoildated undrained, 1kPa surchargeConsolidated undrained, 1 kPasurcharge

Fitted power law curve

Figure 8.16 Maximum vertical penetration resistances for unconsolidated undrained and consolidated undrained conditions (smooth pipe)

8.6 CONCLUDING REMARKS The consolidation of soil around deep-water pipelines is an important phenomenon to

consider for correct prediction of pipe-soil interactions. A large deformation finite

element (LDFE) methodology combined with the Modified Cam Clay plasticity soil

model was developed for this study to explore the coupled consolidation behaviour

beneath partially embedded seabed pipelines.

The penetration resistance during embedment of the as-laid pipes depends

markedly on the rate of penetration, with the resistance increasing with the degree of

consolidation during penetration. Results have been presented for both smooth and

rough pipe-soil interfaces for normalised embedment, w/D, from 0.1 to 0.5. Up to 72 %

increase in resistance was observed from fully undrained to fully drained conditions.



Backbone curves, i.e. penetration resistance versus non-dimensional velocities

for smooth and rough pipes, have also been presented. From these curves, fully drained

conditions pertain for vD/cv = 0.1 or lower, while undrained conditions pertain for

vD/cv = 100 or higher. The backbone curves are presented in terms of simple hyperbolic

equations fitted to the LDFE results.

The strength of the soil beneath and around the pipe, and hence the breakout

resistance, depends on the extent to which consolidation occurs following penetration.

The resulting changes in the size and shape of the undrained yield envelopes were

shown to be significant for initially normally consolidation conditions. It was found that

the bearing capacities during vertical and horizontal movements were increased by 66 %

and 83% respectively, for an embedment of w/D = 0.5 if consolidation under the full

vertical bearing capacity was permitted following penetration. These effects of

consolidation – which strongly affect the stability of an on-bottom pipeline – are

important to consider in design in order to provide realistic prediction of pipe-soil

interaction forces.

8.7 REFERENCES AtkinsBoreas (2008). SAFEBUCK JIP – Safe design of pipelines with lateral buckling.

Design Guideline. Report No. BR02050/SAFEBUCK/C, AtkinsBoreas.

Chatterjee, S., Yan, Y., Randolph, M. F. & White, D. J. (2012). “Elastoplastic

consolidation beneath shallowly embedded offshore pipelines.” Géotechnique

Letters , 2, 73-79.

Dassault Systèmes. (2011). Abaqus analysis users' manual, Simula Corp, Providence, RI,

USA.



Gourvenec, S. M. & White, D. J. (2010). “Elastic solutions for consolidation around

seabed pipelines.” Proc. Offshore Technology Conf., Houston, Texas, USA, Paper OTC

20554.

Merifield, R. S., White, D. J. & Randolph, M. F. (2009). “Effect of surface heave on

response of partially embedded pipelines on clay.” J. Geotech. Geoenviron. Engng,

ASCE 135, No. 6, 819-829.

Randolph, M. F. & White, D. J. (2008). “Upper-bound yield envelopes for pipelines at

shallow embedment in clay.” Géotechnique 58, No. 4, 297-301.

Roscoe, K. H., & Burland, J. B. (1968). On the generalised stress-strain behaviour of

'wet clay'. Engineering plasticity, Cambridge University Press.

Schofield, A. & Wroth, C. P. (1968). Critical State Soil Mechanics, McGraw-Hill, New

York.

White, D. J. & Cheuk, C. Y. (2005). SAFEBUCK JIP: Lateral pipe-soil interaction:

Data review. Report to Boreas Consultants (SAFEBUCK JIP), ref. SC-CUTS-0502-

R02. 77pp.

White, D. J. & Cheuk, C. Y. (2009). SAFEBUCK JIP: Pipe-soil interaction models for

lateral buckling design: Phase IIA data review. Report to Boreas Consultants

(SAFEBUCK JIP), UWA report GEO 09497. 185pp.

Wroth, C. P. (1984). “The interpretation of in situ soil tests.” Géotechnique 34, No. 4,

449-489.



CHAPTER 9

CONCLUDING REMARKS

9.1 ORIGINAL CONTRIBUTIONS

This thesis shows how large deformation finite element (LDFE) analysis can be used to

shed light on the pipe-soil interaction forces during embedment and lateral buckling of

on-bottom pipelines, and reports parametric studies that have shown the underlying soil

deformation mechanisms and led to improved calculation methods for use in design.

The remeshing and interpolation technique with small strain (RITSS) approach

combined with commercial software ABAQUS has been adopted to develop the LDFE

methodology. The specific outcomes of this research are as follows.

9.1.1 Vertical penetration

The design parameters that define the soil resistance to lateral and axial motion of the

pipeline are a function of the amount of vertical embedment. However, vertical

embedment is difficult to estimate, partly because of the effects of soil heave around the

pipeline as it penetrates, and partly because the soil shear strength depends on the strain

rate and the degree of softening as the soil is sheared and remoulded. The large

deformation finite element approach was implemented in ABAQUS firstly to study

pipe-soil interaction during vertical embedment of pipelines on the seabed. This

implementation utilises a soil constitutive model that captures the effects of penetration

rate and softening on soil shear strength.

The contributions of shearing resistance and buoyancy to penetration resistance

were characterised in simple expressions. A detailed parametric study was performed,

CHAPTER 9: Concluding remarks


varying the strain rate and softening parameters to explore their effects on geotechnical

resistance. It was found that strain rate and softening have significant effects on the

penetration resistance of shallowly embedded pipes and vertical resistances can vary

widely with the change of these parameters.

An ‘operative shear strength’ incorporating the effects of strain rate and softening

was proposed. Normalising the vertical resistance with this equivalent shear strength led

to narrow band of values. Simple power law expressions for penetration resistance

varying with normalised embedment were presented suited to application in design.

9.1.2 Lateral pipe-soil interactions

Accurate assessment of the lateral pipe-soil interaction forces during large-amplitude

movements of subsea pipelines is required to support lateral buckling design. In this

thesis, two important stages of pipe-soil lateral interactions – initial break-out behaviour

and steady-state residual behaviour – were studied in detail.

Initial yield envelopes and break-out resistance

The initial break-out behaviour of the pipe during lateral motion was studied

numerically using large deformation finite element analyses as well as limit analysis

software OxLim. The present LDFE methodology suggests improvement over the

available numerical solutions in the literature because it incorporates a softening soil

model and generation of soil heave around the pipe is accounted for. Marginal

improvement of the presently available plasticity solution is also discussed. For the first

time, yield envelopes for heaved soil, with consideration of the soil self weight, were

presented and a good match of results between LDFE and limit analyses were obtained.

It was shown that for a flat seabed the soil failure mechanism is negligibly altered due

to introduction of self-weight and a superposition approach is adequate to capture the

influence of buoyancy. It was also concluded that the presence of a soil berm around the



pipe has a significant effect on the breakout resistance and an increase of up to 18% in

lateral capacity was observed.

Residual friction factor

It was found that a steady residual resistance and embedment is achieved after the pipe

has moved laterally by 2-3 times its diameter. In the LDFE analyses, a very large lateral

displacement ranging from three to seven times the diameter was imposed to ensure the

steady state was reached. Both ideal (no rate effect and softening) and realistic (effects

of strain rate and softening incorporated) soil models were explored. If soil softening

was not included, the response differed in some critical aspects from the behaviour

observed in model tests available in the literature. The lateral resistance was over-

predicted and the trajectory of the pipe was too shallow. When softening was included

in the analysis, the trajectory deepened but this was compensated by a lower operative

soil strength in the partly-remoulded soil ahead of the pipe. Good agreement with model

test data was achieved – both the resistance and the pipe trajectory were correctly

reproduced.

A detailed parametric study was also performed to explore the effects of the

initial embedment and pipe weight on the residual friction factor. For the range of

parameters chosen, the residual friction factor varied from 0.5 to 0.98, which is

comparable to the SAFEBUCK JIP database. Initial embedment and operating pipe

weight have considerable effects on the steady state lateral resistance. The steady state

lateral friction factor was shown to depend on the ‘effective embedment’ of the pipe

irrespective of other soil and pipeline parameters. The ‘effective embedment’ is defined

as the height of the growing soil berm ahead of the pipe, discounted for remoulding

effects. The evolution of the effective embedment and the resulting lateral resistance

was shown to depend on the initial embedment and the operating pipe weight. This



conceptual approach provides a useful contribution towards the development of a

general model for describing large-amplitude lateral pipe-soil interaction. At any instant,

the effect of the soil softening and changing seabed topography can be distilled into the

effective embedment parameter. Based on this concept, simple correlations were also

provided to estimate the steady lateral resistance. These were shown to provide more

accurate predictions than other empirical relationships that have been proposed.

The complete load-displacement response over large movements was also

shown to be well-fitted by an exponential relationship interpolating between the break-

out and residual resistances.

9.1.3 Coupled consolidation analyses

Most previous studies using LDFE and the RITSS approach have been based on total

stress analyses. In this research, a further advance was to combine LDFE and RITSS

with an effective stress approach using the modified Cam Clay soil model. Analyses

were performed to study the coupled consolidation behaviour of partially embedded

seabed pipelines. The pore water pressure dissipation time history and consolidation

settlement were studied after the pipe had been partially penetrated to different

embedment levels in undrained conditions. Results were fitted by simple equations to

facilitate application in practice. The effect of the rate of penetration on the degree of

consolidation was also studied. Backbone type curves defining zones of drained,

partially drained and undrained behaviour, depending on the non-dimensional velocity

were also presented.

Changes in lateral breakout behaviour due to drainage and consolidation were

also explored. For normally consolidated soil, the shear strength near the pipe increases

significantly due to consolidation under the weight of the pipe. Yield envelopes defined

in V-H space for unconsolidated undrained and consolidated undrained cases were



compared and it was shown that the size of the V-H yield envelope can almost double

following consolidation.

9.2 LDFE ANALYSIS IN DESIGN

9.2.1 LDFE in support of simplified design method

The analyses reported in this research have shown that LDFE techniques, coupled with

an appropriate soil model, can capture faithfully some of the behaviour observed during

large-amplitude lateral pipeline movements. The geometric and soil strength changes

can be replicated well, at least for an initial lateral sweep of several diameters.

LDFE and physical model testing are complementary tools. Both allow

parametric studies to be performed. It is easier to replicate tests with controlled

variations of the input parameters via LDFE, but physical modelling has the advantage

of utilising ‘real’ soil. Given these complementary attributes, both LDFE and model

testing currently play a significant role in the development of analysis methods for the

assessment of pipe-soil interactions. Having assembled databases of results it is

convenient to devise approximate relationships that capture the same behaviour. These

are then a convenient tool for use in practice.

9.2.2 LDFE directly applied in design

LDFE techniques could be used directly in design on at least two levels. Firstly, specific

plane strain analyses could be performed to develop site-specific (and pipeline-specific)

lateral force-displacement curves, which would then be converted to non-linear ‘p-y

springs’, making some assumptions regarding generalisation to arbitrary load and

displacement paths.

A second, more detailed approach would be to model the soil and structural

responses concurrently, either by creating a full three-dimensional soil model, or by



attaching two-dimensional plane strain soil domains at each node along the structural

model of the pipeline. Both of these latter approaches are hugely demanding from a

computational perspective.

Realistically, this type of analysis still lies beyond the time constraints of real

projects. However, as computational power increases, and the obstacles to realistic

modelling of the soil response are overcome, this situation is likely to change.

9.3 LIMITATIONS AND FUTURE RESEARCH

This research has shown the capabilities of LDFE analysis in successfully modelling the

pipe-soil interaction forces during vertical penetration and lateral displacement. Despite

the promising results and findings from this research, a number of limitations still exist

and there is significant scope for future research.

9.3.1 Dynamic effects

Partial embedment of deep water as-laid pipes into the seabed depends on the weight of

the pipeline and the strength of the soil, although the laying process and dynamic

motions of the laying vessel (leading to cyclic motions of the pipe) make it significantly

more complicated. In this research, though static embedment of the pipe using an

advanced soil model incorporating the effects of strain rate and softening has been

studied, it was not possible to include the dynamic and cyclic effects within the scope of

the thesis. However, it has been observed that the as-laid pipe penetration is generally

much greater than that calculated from the effect of the self-weight alone. It is, therefore,

suggested that future research effort to numerically model embedment of deep water

pipes should be directed towards capturing cyclic effects.



9.3.2 Full 3D model

All the analyses in this thesis were based on a two-dimensional plane strain model

assuming the pipe to be a rigid body. During lateral buckling, the pipe may undergo

large lateral bending strains. Hence the assumption of a rigid pipe may be too simplistic.

As mentioned in the previous section, concurrent modelling of structural and

geotechnical responses using a full three-dimensional (3D) model may be a feasible

solution. However, full 3D modelling of large deformation effects of both structural and

soil domains is a significant challenge from a numerical perspective. Also, the high

computation time required for such analyses poses a considerable challenge for real

projects. With the advent of supercomputers, and also new solver techniques, full 3D

modelling of simultaneous structural and geotechnical responses could be achieved in

the near future.

9.3.3 Whole life behaviour

During lateral bucking, the pipe moves several times its diameter to and fro for a

number of cycles. During this time, the soil around the pipe may undergo periods of

strength reduction due to softening and strength gain due to consolidation. In the present

research, only the first cycle of lateral movement has been studied. Also, consolidation

effects after large lateral motion has not been considered. It is therefore necessary for

future work to consider the whole life behaviour of a pipe element sweeping repeatedly

within a buckle and to extend the soil constitutive modelling to capture consolidation

effects within the large lateral deformation framework.

Despite restrictions of the current work and scope for future research, it is

considered that the outcomes of this research present several useful contributions for the

investigation of pipe-soil interaction. They also provide validation and calibration of



existing calculation methods for pipe-soil interaction, and have generated new analysis

techniques that can be utilised to investigate project-specific refinements.

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