DOWNSLOPE PIPELINE WALKING AND SOIL VARIABLES

DOWNSLOPE PIPELINE WALKING AND SOIL

VARIABLES

by

Adriano Condez Gondarém Castelo

B.E., MSc

A thesis submitted for the degree of

Doctor of Philosophy

at

The University of Western Australia

Centre for Offshore Foundation Systems

School of Civil and Resource Engineering

February 2020

Downslope pipeline walking and soil variables

i

ABSTRACT

Operational loading cycles of startup and shutdown phases have a major impact on a

pipeline’s behaviour over its lifetime. Some pipelines are long enough to generate a soil

reaction that anchors the pipeline in an overall fixed position on the seabed. For these

pipelines, the loading cycles generate symmetric expansion and contraction at the ends

of the pipeline caused by variations in temperature and pressure. A related phenomenon

named “pipeline walking” causes the pipeline to migrate globally in one direction.

Pipeline walking occurs whenever a pipeline extension is shorter than necessary thereby

leading to axial instability associated with an asymmetry between expansions and

contractions over the total length of the pipeline.

Current analytical methodologies used during early design stages of pipelines, provide

results to estimate the pipe walking susceptibility and the corresponding walking pattern

for rigid-plastic soils. However, the basic rigid-plastic soil assumption of these

methodologies leads to an overestimation of the walking response. As a result, protracted

and costly finite element analyses need to be performed, so that a more realistic walking

prediction may be achieved. Further, while it is common practice in the industry to

assume an elastic-perfectly-plastic soil reaction, field and laboratory tests show that soils

may behave very differently from elastic-perfectly-plastic. To account for these

differences, the industry assumes two different conditions of elastic-perfectly-plasticity:

the “Stiff Fit” and the “Soft Fit”. They represent the lower and upper bounds to create a

case envelope of soil resistance. Thus, there is a demand to improve the accuracy, the

cost- and time-effectiveness of the current analyses.

This thesis starts by assuming an elastic-perfectly-plastic idealization for elastic-plastic

soils followed by the analysis of the non-linear elastic-plastic soil models. For these soil

considerations, a number of innovative analytical solutions for pipeline walking are

proposed and benchmarked against finite element analyses. The reasons for the difference

between the new and the current solutions are explored and corrections to the current

analytical methodologies are proposed to make them applicable to all types of soil

conditions (elastic-plastic soils with a linear or a non-linear behaviour). These corrections

reduce time and financial demands of a project since finite element analyses are no longer

required.


ii

However, field and laboratory tests show that some soils may present a breakout peak

resistance. For instance, for clayey soils the peak breakout resistance depends largely on

the over consolidation ratio and for sandy soils it depends on dilatancy. The loading

process, potentially even including intermittent consolidation cycles, may also influence

peak resistance occurrence. These particularities of loading processes complicate the soil

reaction models considered by this research.

In this thesis, breakout peak resistance was initially idealized as a tri-linear peaky spring

to account for peak resistance. Two different cases were investigated: (1) peak breakout

resistance for the loading and unloading steps; and (2) peak breakout for just the loading

step. These two cases represent the variability that soils may impose on pipe-soil

interaction behaviours, when breakout resistance must be accounted for. Based on our

elastic-plastic modelling, finite element models were used as a general platform to

numerically determine how to correct the rigid-plastic analytical solution to account for

the breakout resistance. The corrections were then used to account for tri-linear soil

behaviours to accurately calculate the walking rates.

A more detailed approach was then taken to consider the non-linearities of a peak

breakout resistance soil model thereby further improving the peaky soil model and the

interpretation of the impact of the non-linearities of peaky soils. The numerical results

were used to establish the necessary corrections for the walking rate calculations resulting

in a valid correction – similar to the non-linear elastic-plastic – of the original rigid-plastic

solution.

The influence of different slope geometries was investigated, given the fact that real

pipelines traverse routes that often slope continuously down, but at a varying pace.

Numerical results were used to show that an average slope throughout the entire route

can be assumed so that the previous findings could still be successfully applied for these

bathymetric conditions.

Overall, this thesis presents a significant improvement to commonly applied methods for

estimating pipeline walking rates. Using the proposed solutions, realistic walking patterns

are now quickly and easily obtained. The methodology presented can optimize any

pipeline project by reducing turn-around time, costs and increasing the accuracy of the

walking patterns estimated.

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Thesis Declaration

v

I, Adriano Condez Gondarém Castelo, certify that:

This thesis has been substantially accomplished during enrolment in this degree.

This thesis does not contain material which has been submitted for the award of any other

degree or diploma in my name, in any university or other tertiary institution.

In the future, no part of this thesis will be used in a submission in my name, for any other

degree or diploma in any university or other tertiary institution without the prior approval

of The University of Western Australia and where applicable, any partner institution

responsible for the joint-award of this degree.

This thesis does not contain any material previously published or written by another

person, except where due reference has been made in the text and, where relevant, in the

Authorship Declaration that follows.

This thesis does not violate or infringe any copyright, trademark, patent, or other rights

whatsoever of any person.

This thesis contains published work and/or work prepared for publication, some of which

has been co-authored.

Signature:

Date: February 2020


vi

ACKNOWLEDGEMENTS

First of all, I would like to express my gratitude to my PhD supervisors Dave, Yinghui,

Mark and Christophe, without your help this thesis would never be achieved.

I also thank my MSc supervisor and evaluator, Nelson and Gilberto, for all the help

provided during the PhD application process.

Thanks also to the friends from UWA for touch rugby, soccer and uncountable hours of

lunch, discussions (technical or not) and fun. Special mentions to Colm, Simon, Dunja

and Wensong – all from Room 2.63; along with Liang, Susie, Dana, Lisa, Yuxia, Behnaz,

Charlie, Andrew, Diego, Fillippo, Jiayue, João, Maria, Manu, Mark, Max, Mike, Mirko,

Nicole, Pauline, Raffa, Serena, Tao, Youkou and Yusuke.

I couldn’t fail to mention some people, who we met in Perth; and made life here a lot

easier: Alex & Mickle, CC, Daniel & Rô, Edu & Monique, Flávio & Marcinha, Francisco

& Olivia, Gabriel & Andrea, Laerte & Luana, Leo & Lu, Luiz & Raquel, Marcelo &

Aline, Murray & Patrica, Shelley and Tiago & Sara.

Finally, my deepest thanks to my parents, Paulo and Guiomar, for giving me the best start

in life one could ever ask for and your constant support.

This thesis is dedicated to an incredible woman, whom I have the pleasure and honour

to refer to as “my dearest and beloved wife”, Lorena.

This research was supported by an Australian Government Research Training Program (RTP) Scholarship.

“Dans un axiome que vous appliquez à vos sciences: il n'y a pas d'effet sans cause.

Cherchez la cause de tout ce qui n'est pas l'oeuvre de l'homme, et votre raison vous

répondra.”

⸻ Allan Kardec, Le Livre Des Esprits


vii

TABLE OF CONTENTS

Abstract ............................................................................................................................ i

Publications arising from this thesis ............................................................................ iii

Acknowledgements ........................................................................................................ vi

Table of contents ........................................................................................................... vii

List of tables ................................................................................................................. xiii

List of figures ................................................................................................................ xv

Nomenclature ............................................................................................................... xix

Chapter 1. Introduction ................................................................................................. 1

1.1 Pipeline walking ................................................................................................ 2

1.2 Thesis objectives ............................................................................................... 5

1.3 Thesis organisation ............................................................................................ 5

Chapter 2. Literature review ......................................................................................... 8

2.1 Pipelines and pipeline walking .......................................................................... 9

2.2 Current analytical method ............................................................................... 11

2.2.1 Mathematical Shortcuts .................................................................. 13

2.3 Axial Pipe-soil Interaction ............................................................................... 13

2.3.1 Axial pipe-soil interaction models ................................................. 15

2.4 Possible Mitigation Strategies ......................................................................... 18

2.5 Final Remarks .................................................................................................. 22

Chapter 3. Simple solutions for downslope pipeline walking on elastic-perfectly-

plastic soils ..................................................................................................................... 31

3.1 Abstract ........................................................................................................... 32

3.2 Introduction ..................................................................................................... 32

3.3 Background to pipeline walking ...................................................................... 34

3.4 Problem Definition .......................................................................................... 35

3.5 Rigid-plastic analytical solutions .................................................................... 36

3.6 Finite element analyses methodology ............................................................. 37

3.7 Finite element analyses comparison with rigid-plastic solution ..................... 39

3.8 Xab for elastic-perfectly-plastic soil ................................................................. 40

3.9 ΔSS for elastic-perfectly-plastic soil ................................................................ 40

3.9.1 δx Boundary Conditions .................................................................. 41

3.9.2 Effective Axial Force Boundary Conditions .................................. 41

3.9.3 Effective Axial Force Pipe Differential Equation .......................... 42

3.9.4 ΔSS Revision ................................................................................... 43


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3.10 Walking rate for elastic-perfectly-plastic soil ................................................. 43

3.11 Finite element analyses parametric study ....................................................... 44

3.12 Conclusions & final remarks ........................................................................... 46

Chapter 4. Solving downslope pipeline walking on non-linear elastic-plastic

soils ................................................................................................................................. 60

4.1 Abstract ........................................................................................................... 61

4.2 Introduction ..................................................................................................... 61

4.3 Background to pipeline walking ..................................................................... 62

4.3.1 Downslope mechanism .................................................................. 62

4.3.2 Pipe-soil response ........................................................................... 63

4.4 Problem definition ........................................................................................... 63

4.5 Elastic-perfectly-plastic solution for pipeline walking ................................... 65

4.6 Finite element methodology ............................................................................ 66

4.6.1 Introduction .................................................................................... 66

4.6.2 Dual-spring pipe-soil interaction model ......................................... 67

4.6.3 Multi-spring pipe-soil interaction model ........................................ 67

4.6.4 Loads .............................................................................................. 67

4.7 Finite element analysis results and comparison with elastic-perfectly-

plastic solution ................................................................................................ 67

4.8 New analytical solutions for non-linear elastic-plastic soil ............................ 68

4.8.1 Displacement profile ...................................................................... 68

4.8.2 Displacement boundary conditions ................................................ 69

4.8.3 Effective axial force boundary conditions ..................................... 69

4.8.4 Effective axial force profile ............................................................ 71

4.8.5 Analytical solution for walking rate ............................................... 72

4.9 Revised solution for the distance between stationary points for non-linear

elastic-plastic soil - XAB,NLEP ............................................................................ 73

4.10 Revised solution for walking rate for non-linear elastic-plastic soil –

WRNLEP............................................................................................................. 73

4.11 Equivalent mobilisation distance – δmobEQ ...................................................... 74

4.12 Finite element analyses parametric study for dual-spring strategy ................. 74

4.12.1 Equivalent mobilisation distance – δmobEQ ..................................... 75

4.12.2 Distance between stationary points for non-linear elastic-plastic

soil – Xab,NLEP ................................................................................................... 77


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4.12.3 Walking rate for non-linear elastic-plastic soil – WRNLEP .............. 78

4.13 Finite element analysis for multi-spring strategy ............................................ 78

4.13.1 Rigid-plastic preliminary calculations ............................................ 78

4.13.2 Non-linear elastic-plastic calculations ............................................ 78

Equivalent mobilisation distance – δmobEQ ....................................................... 78

Distance between stationary points for non-linear elastic-plastic soil –

Xab,NLEP 78

Walking rate for non-linear elastic-plastic soil – WRNLEP ............................... 79

4.13.3 Non-linear elastic-plastic finite element model results .................. 79

Distance between stationary points from finite element analysis – Xab,FEM .... 79

Walking rate from finite element analysis – WRFEM ....................................... 79

4.14 Conclusions & final remarks ........................................................................... 79

Chapter 5. Solutions for downslope pipeline walking on peaky tri-linear soils ..... 93

5.1 Abstract ........................................................................................................... 94

5.2 Introduction ..................................................................................................... 94

5.3 Background to pipeline walking ...................................................................... 96

5.3.1 Downslope mechanism ................................................................... 96

5.3.2 Pipe-soil response ........................................................................... 96

5.4 Problem definition ........................................................................................... 96

5.5 Elastic-perfectly-plastic solution for pipeline walking ................................... 98

5.6 Finite element methodology ............................................................................ 99

5.6.1 Peaky tri-linear pipe-soil interaction models ................................ 100

5.6.2 Loads ............................................................................................ 100

5.7 Finite element analysis results and comparison with rigid-plastic solution .. 100

5.8 Revised analytical solution for the distance between stationary points for

peaky tri-linear soils – Xab,3L .......................................................................... 101

5.9 Revised analytical solution for the walking rate for peaky tri-linear soils –

WR3L .............................................................................................................. 102

5.10 Ideal mobilisation distance - δmob’ ................................................................. 102

5.11 Finite element analyses parametric study for peaky tri-linear pipe-soil

interaction ...................................................................................................... 104

5.11.1 Ideal mobilisation distance - δmob’ ................................................ 104

5.11.2 Distance between stationary points for peaky tri-linear soil –

Xab,3L 104


x

5.11.3 Walking rate for peaky tri-linear soil – WR3L .............................. 105

5.12 Observations about the effective axial force variation over the distance

between stationary points for peaky tri-linear soils – ΔSS,3L ......................... 106

5.13 Conclusions & final remarks ......................................................................... 106

Chapter 6. Solving downslope pipeline walking on non-linear soil with brittle

peak strength and strain softening ........................................................................... 117

6.1 Abstract ......................................................................................................... 118

6.2 Introduction ................................................................................................... 119

6.2.1 Pipeline walking mechanisms ...................................................... 119

6.2.2 Walking phenomenon on a rigid-plastic basis ............................. 120

6.2.3 Walking consequences ................................................................. 121

6.2.4 Axial pipe-soil non-linearity ........................................................ 122

6.3 Problem definition ......................................................................................... 123

6.3.1 General Properties of Study-Case ................................................ 123

6.3.2 Variations in axial pipe-soil response .......................................... 124

6.4 Rigid-plastic analytical solutions .................................................................. 125

6.4.1 Calculations .................................................................................. 125

6.4.2 Rigid-plastic analytical results ..................................................... 125

6.5 NLBPSS FEM solution ................................................................................. 126

6.5.1 FEM architecture .......................................................................... 126

Loads 126

Pipe-soil interaction representation ............................................................... 127

6.5.2 FEM results .................................................................................. 128

FEM results ................................................................................................... 128

6.5.3 Axial displacement ....................................................................... 129

FEM results crosscheck ................................................................................. 129

FEM results summary ................................................................................... 130

6.6 Results comparison ....................................................................................... 131

6.6.1 Effective axial force ..................................................................... 131

6.6.2 Stationary points ........................................................................... 131

6.6.3 Axial displacements & walking rates ........................................... 132

6.7 Equivalent mobilisation distance .................................................................. 133


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6.7.1 Back evaluation ............................................................................ 133


Chapter 7. Gravity-driven pipeline walking on variable slopes ............................ 147

7.1 Abstract ......................................................................................................... 148

7.2 Introduction ................................................................................................... 148

7.3 Background to pipeline walking .................................................................... 149

7.3.1 Downslope walking mechanisms ................................................. 149

7.3.2 Route topography ......................................................................... 150

7.4 Problem definition ......................................................................................... 150

7.5 Elastic-perfectly-plastic solution for pipeline walking on single slope ........ 152

7.6 Finite element methodology .......................................................................... 152

7.7 Range of parametric studies .......................................................................... 154

7.7.1 Dual slope – convex ..................................................................... 154

7.7.2 Dual slope – concave .................................................................... 155

7.7.3 Triple slope – flat-slope-flat ......................................................... 157

7.7.4 Triple slope – flat-slope-flat ......................................................... 158

7.8 Finite element model results .......................................................................... 159


Chapter 8. Concluding remarks ................................................................................ 170

8.1 Principal findings and contributions .............................................................. 171

8.1.1 Pipe-soil interaction models ......................................................... 171

Elastic-perfectly-plastic ................................................................................. 171

Non-linear elastic-plastic ............................................................................... 172

Tri-linear with a peak .................................................................................... 172

Non-linear with a peak .................................................................................. 172

General notes ................................................................................................. 173

8.1.2 Variable slopes ............................................................................. 173

8.1.3 A new assessment of downslope pipeline walking ...................... 173

8.2 Further research recommendations ............................................................... 175


xii

REFERENCES ........................................................................................................... 176

Appendix A ................................................................................................................. 180

Appendix B .................................................................................................................. 184

Appendix C ................................................................................................................. 185

Appendix D ................................................................................................................. 190


xiii

LIST OF TABLES

Table 2.1: Summary of possible walking mitigation strategies (Rong et al., 2009).

................................................................................................................... 21

Table 2.2: Summary of causes of uncertainty and thesis chapters. ................................ 24

Table 3.1: Preliminary example properties. ................................................................... 36

Table 3.2: Rigid-plastic analytical results. ..................................................................... 37

Table 3.3: Elastic-perfectly-plastic FEA results. ............................................................ 39

Table 3.4: Pipeline zoning. ............................................................................................. 41

Table 3.5: EAF boundary conditions.............................................................................. 42

Table 3.6: FEA parametric variables. ............................................................................. 44

Table 4.1: Preliminary example properties – Dual-Spring UEL. ................................... 64

Table 4.2: Preliminary example properties – Multi-Spring UEL. .................................. 65

Table 4.3: Elastic-perfectly-plastic analytical results. .................................................... 66

Table 4.4: Elastic-perfectly-plastic general results. ....................................................... 68

Table 4.5: Pipeline zoning. ............................................................................................. 69

Table 4.6: Mobilisation distance, δmob, combination cases. ........................................... 75

Table 4.7: Resultant equivalent mobilisation distance, δmobEQ. ...................................... 76

Table 4.8: Resultant non-walking mobilisation distance, δnull. ...................................... 77

Table 5.1: General properties. ........................................................................................ 97

Table 5.2: Case properties. ............................................................................................. 97

Table 5.3: Tri-linear finite element analysis results for soil case ii. ............................. 101

Table 5.4: Rigid-plastic calculation results. ................................................................. 101

Table 5.5: Analytical results. ........................................................................................ 103

Table 5.6: Tri-linear finite element analyses results. ................................................... 105

Table 6.1: Pipeline properties. ...................................................................................... 123

Table 6.2: Axial pipe-soil interaction model parameters. ............................................ 124

Table 6.3: Analytical results. ........................................................................................ 125

Table 6.4: Key aspects from rigid-plastic solution. ...................................................... 126

Table 6.5: EAF notable results. .................................................................................... 129


xiv

Table 6.6: δx notable results. ........................................................................................ 129

Table 6.7: FEM crosscheck results. ............................................................................. 130

Table 6.8: FEM summary results. ................................................................................ 130

Table 6.9: EAF comparison. ........................................................................................ 131

Table 6.10: SPs comparison. ........................................................................................ 131

Table 6.11: Walking rates for different soil approaches. ............................................. 132

Table 6.12: Equations (6.9) and (6.11) results. ............................................................ 133

Table 7.1: Environmental properties ............................................................................ 151

Table 7.2: Operational properties ................................................................................. 151

Table 7.3: Physical pipeline properties ........................................................................ 151

Table 7.4: Dual slope convex model properties ........................................................... 154

Table 7.5: Dual slope concave model properties ......................................................... 156

Table 7.6: Triple slope flat-slope-flat model properties ............................................... 157

Table 7.7: Triple slope slope-flat-slope model properties ............................................ 158

Table 7.8: Dual slope – Convex model results ............................................................. 159

Table 7.9: Dual slope – Concave model results ........................................................... 160

Table 7.10: Triple slope flat-slope-flat model results .................................................. 162

Table 7.11: Triple slope slope-flat-slope model results ............................................... 163

Table 8.1: Preliminary example properties. ................................................................. 173

Table B.1: Base cases comparison ............................................................................... 184

Table C.1: Mesh sensitivity checks .............................................................................. 185

Table D.1: Lateral buckling check ............................................................................... 190


xv

LIST OF FIGURES

Figure 1.1: Axial stability design stairs ............................................................................ 7

Figure 2.1: Example for field architecture of infield pipelines and production

infrastructure units from White (2011). ..................................................... 25

Figure 2.2: Effective axial force diagrams for start-up and shutdown loading

phases. ........................................................................................................ 25

Figure 2.3: Axial displacement diagrams for start-up and shutdown loading

phases. ........................................................................................................ 26

Figure 2.4: Rigid-plastic soil behaviour. ........................................................................ 27

Figure 2.5: Axial friction curves (no peak) – adapted from White et al. (2011)............ 27

Figure 2.6: Axial friction curve (peak in one direction) – adapted from Hill and

Jacob (2008). .............................................................................................. 28

Figure 2.7: Different soil resistance behaviours. ............................................................ 28

Figure 2.8: Walking mitigation devices from Frazer et al. (2007). ................................ 29

Figure 2.9: Pipeline walking accumulated displacement from Frankenmolen et al.

(2017). ........................................................................................................ 29

Figure 2.10: Pipe-clamping mattress from Frankenmolen et al. (2017). ....................... 30

Figure 2.11: Post pipe-clamping mattresses installation walking monitoring from

Frankenmolen et al. (2017). ....................................................................... 30

Figure 3.1: EAF diagrams for SUp and SDown phases. ................................................ 47

Figure 3.2: δx diagrams for SUp and SDown phases. ..................................................... 48

Figure 3.3: Rigid-plastic & elastic-plastic soil responses. ............................................. 49

Figure 3.4: Finite element model sketch. ....................................................................... 49

Figure 3.5: EAF plot (zoom). ......................................................................................... 50

Figure 3.6: δx plot for Stiff Fit (zoom). .......................................................................... 51

Figure 3.7: δx plot for Soft Fit (zoom). ........................................................................... 51

Figure 3.8: x coordinate for the stationary points. .......................................................... 52

Figure 3.9: Xab,EP results against δmob. ............................................................................ 52

Figure 3.10: Schematic plot accounting physical boundaries. ....................................... 53

Figure 3.11: Schematic EAF plot with the partial areas highlight. ................................ 53

Figure 3.12: Xab,EP results for 1° slope. .......................................................................... 54


xvi

Figure 3.13: Xab,EP results – numerical & calculated for 1° slope. ................................. 54





Figure 3.18: WREP results for 1° slope. .......................................................................... 57

Figure 3.19: WREP results – numerical & calculated for 1° slope. ................................. 57





Figure 4.1: Effective axial force diagrams for start-up and shutdown phases. .............. 81

Figure 4.2: Axial displacement diagrams for start-up and shutdown phases. ................ 82

Figure 4.3: Rigid-plastic, elastic-perfectly-plastic and non-linear elastic-plastic

soil responses. ............................................................................................ 83

Figure 4.4: Dual-spring finite element analysis methodology (as per values from

Table 4.1). .................................................................................................. 83

Figure 4.5: Multi-spring finite element analysis methodology (as per values from

Table 4.2). .................................................................................................. 84

Figure 4.6: Effective axial force for non-linear elastic-plastic soil – dual-spring

(zoom). ....................................................................................................... 85

Figure 4.7: Axial displacement for non-linear elastic-plastic soil – dual-spring

(zoom). ....................................................................................................... 86

Figure 4.8: x coordinate for the stationary points – dual-spring. ................................... 86

Figure 4.9: Effective axial force for non-linear elastic-plastic soil – multi-spring

(zoom). ....................................................................................................... 87

Figure 4.10: Axial displacement for non-linear elastic-plastic soil – multi-spring

(zoom). ....................................................................................................... 88

Figure 4.11: x coordinate for the stationary points – multi-spring. ................................ 88



Figure 4.14: Mobilisation distance, δmob, combination spectrum. .................................. 90


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Figure 4.15: Non-linear elastic correction results. ......................................................... 90

Figure 4.16: Walking rate from finite element models, WRFEM, results for selected

cases. .......................................................................................................... 91

Figure 4.17: Distance between stationary points results. ............................................... 91

Figure 4.18: Walking rate results. .................................................................................. 92

Figure 5.1: Effective axial force diagrams for start-up and shutdown phases. ............ 108

Figure 5.2: Axial displacement diagrams for start-up and shutdown phases. .............. 109

Figure 5.3: Tri-linear soil responses. ............................................................................ 110

Figure 5.4: Tri-linear soil responses for cyclic movements. ........................................ 111

Figure 5.5: Effective axial force for tri-linear strategy case ii – EqualPeaks

(Zoom). .................................................................................................... 112

Figure 5.6: Axial displacement for tri-linear strategy case ii – EqualPeaks (Zoom).

................................................................................................................. 113

Figure 5.7: Effective axial force for tri-linear strategy case ii – NoSUpPeak

(Zoom). .................................................................................................... 114

Figure 5.8: Axial displacement for tri-linear strategy case ii– NoSUpPeak (Zoom).

................................................................................................................. 115

Figure 5.9: Tri-linear correction results........................................................................ 115

Figure 5.10: Distance between stationary points results. ............................................. 116

Figure 5.11: Walking rate results. ................................................................................ 116

Figure 6.1: EAF diagram and sketch of acting loads. .................................................. 135

Figure 6.2: EAF diagrams for start-up and shutdown. ................................................. 135

Figure 6.3: Axial displacement – 1st cycle. .................................................................. 136

Figure 6.4: Axial displacement – further cycles. .......................................................... 137

Figure 6.5: Axial PSI non-linear approach. .................................................................. 138

Figure 6.6: Axial PSI boundaries. ................................................................................ 139

Figure 6.7: Analytical EAF plot. .................................................................................. 139

Figure 6.8: Schematic behaviours plot. ........................................................................ 140

Figure 6.9: Subroutine flowchart. ................................................................................. 141

Figure 6.10: EAF results for Cases A and B. ............................................................... 142

Figure 6.11: EAF zoom for Cases A and B. ................................................................. 143


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Figure 6.12: δx results for Cases A and B..................................................................... 144

Figure 6.13: δx zoom for Cases A and B. ..................................................................... 145

Figure 6.14: Obtaining δmobEQ – for Cases A and B. .................................................... 146

Figure 7.1: Effective axial force diagrams ................................................................... 166

Figure 7.2: Axial displacement diagrams ..................................................................... 166

Figure 7.3: Finite element model sketch ...................................................................... 167

Figure 7.4: User element behavior ............................................................................... 167

Figure 7.5: Dual slope general shapes .......................................................................... 168

Figure 7.6: Triple slope general shapes ........................................................................ 168

Figure 7.7: Walking rate results ................................................................................... 169


xix

NOMENCLATURE

The nomenclature has been selected in an effort to retain consistency with previously

published work.


xx

Latin Symbols

A pipeline steel cross-sectional area

AUnload-Reload unload-reload area

A1 parabola 1 factor A



B1 parabola 1 factor B



CorrEP elastic correction

CorrNLEP non-linear elastic correction

Corr3L tri-linear correction

C1 parabola 1 factor C



D water depth

E steel Young’s modulus

FA mobilised axial resistance force

FElastic elastic limit force

FP soil peak elastic force

FR soil residual plastic force

F1 soil spring limiting force 1




FS1 plastic force for spring S1



xxi




FTotal total spring plastic force

FS_m final mobilised axial soil spring force

FS_Ref initial mobilised axial soil spring force

KSoil tangential soil stiffness

K1 differential equation constant 1

K2 differential equation constant 2

L pipeline physical length

LTotal total pipeline physical length

L1 partial pipeline physical length 1



OD cross section steel outside diameter

R2 coefficient of determination

s distance to stationary point

t steel wall thickness

UA_m final node axial position

UA_Ref initial node axial position

W pipeline operational submerged weight

Wcomp pipeline operational submerged weight longitudinal component

WR walking rate

x longitudinal axis along pipe length

x12 physical boundary between Z1 and Z2




xxii



Xab distance between stationary points


xxiii

Greek Symbols

steel thermal expansion coefficient

β seabed slope angle

βave average seabed slope angle

β1 partial seabed slope angle 1



δ general displacement

mob mobilisation distance

mobEQ equivalent mobilisation distance

mobP peak elastic force mobilisation distance

mobR residual plastic force mobilisation distance

mobS1 mobilisation distance for spring S1





mobSoft mobilisation distance for “Soft Fit”

mobStiff mobilisation distance for “Soft Fit”

mob’ ideal mobilisation distance

null non-walking mobilisation distance

x axial displacement

δ1 limiting displacement 1





xxiv

FR variation in residual friction

p pressure variation

P change in fully constrained force

Ss change in effective axial force over Xab

T temperature variation

Mech mechanical strain

Thermal thermal strain

Total total strain

soil axial residual friction coefficient

WZ1 soil resistance in Z1






steel Poisson coefficient

exponential factor


xxv

Abbreviations

Calc calculated

CAPEX capital expenditure

COFS Centre for Offshore Foundation Systems

EP elastic-perfectly-plastic

EAF effective axial force

EPCorr elastic-perfectly-plastic correction

EqualPeaks soil behaviour with equal peaks for both loading phases – start-up

and shutdown.

FE finite element

FEA finite element analysis

FEM finite element model

FxD soil force-displacement curve

HPHT high pressure high temperature

JIP joint industry project

KP kilometre post

NLEP non-linear elastic-plastic

NLBPSS non-linear soil with brittle peak strength and strength softening

NoSUpPeak soil behaviour with no peak for start-up phases, while peaky for

shutdown phases

OPEX operating expenses

PCM pipe-clamping mattress

PSI pipe-soil interaction

PW pipeline walking

RP rigid-plastic

SCR steel catenary riser

SDown shutdown phase


xxvi

SUp start-up phase

SP stationary point

S1 partial spring S1





UEL user-element

UWA The University of Western Australia

VAS virtual anchor section

WR walking rate

Z1 pipeline zone 1

Z2 pipeline zone 2

Z3 pipeline zone 3

Z4 pipeline zone 4

Z5 pipeline zone 5

Z6 pipeline zone 6

3L tri-linear peaky soil idealization

Introduction

1

CHAPTER 1. INTRODUCTION

Chapter context: This chapter introduces the research topic of this thesis highlighting

its importance and impact for the engineering community. The objectives and

organisation of this thesis are also presented.

Chapter 1

2

1.1 PIPELINE WALKING

Hydrocarbon fluids need to be transported from their natural reservoirs to consumption

centres. There are two main methods of transporting hydrocarbons: in a ship’s tank or in

a pipeline. Although pipelines require a large capital investment and are a fixed asset,

they present advantages when compared to voyages of cargo, which demand high

operating costs and represent a higher risk to the environment (Palmer and King, 2008).

Offshore pipelines became important as the hydrocarbon sources become more difficult

to be reached. Pipelines became an essential facility for the oil and gas industry when the

North Sea area arose as a major hydrocarbons producer in the 1970s (Kyriakides and

Corona, 2007).

As exemplified by Kumar and Mcshane (2009); Palmer and Croasdale (2012); Leckie et

al. (2016); and Azevedo et al. (2018), some hydrocarbon resources could not be feasible

for production without the presence of pipelines in areas such as the Gulf of Mexico, the

Arctic, the Australian Northwest Shelf, and the Brazilian Pre-Salt.

Given the relevance of pipelines, it is understandable that pipeline stability is a major

issue for both pipeline and geotechnical engineering (through the pipe-soil interaction).

Pipeline stability is determined by hydrodynamic loads and the effects of expansion and

contraction triggered by the high pressure/ high temperature operational conditions.

These two characteristics constitute the major focus of geotechnical design for pipelines.

Unlike other types of engineered solutions for foundations, pipelines can support some

movements across the seabed without exceeding a limit state (exceptions must be made

for regions where pipelines are connected to other structures). Hence, pipelines may be

designed to not be stable at the position at which they were installed; but in these cases,

it is necessary to predict and assess all movements that may occur during a pipeline

operational lifetime.

These movements may occur in the vertical plane, as a progressive burial or exposure of

the pipeline, and in the horizontal plane, as lateral or axial sliding (White and Cathie,

2011). These movements may be combined in many different ways, that have been

studied (isolated and combined) by many authors – (Palmer and Baldry, 1974; Tornes et

al., 2000; Carr et al., 2003; Bruton et al., 2008, 2009; Randolph and White, 2008; Sinclair

et al., 2009; Watson et al., 2010; Bruton et al., 2010; Bruton and Carr, 2011b, 2011a;

Watson et al., 2011; White et al., 2011; Smith and White, 2014).

Introduction

3

The movements may be related to different phenomena, which mainly are: lateral

buckling, upheaval buckling and pipeline walking. Other phenomena examples are: route

curve pull-out and lateral ratcheting. These phenomena are called global buckling

(DNVGL, 2018), which together form the general pipeline response to internal pressure

and temperature cycles. This thesis addresses the axial sliding movement that relates to

the pipeline walking phenomenon that can affect pipelines under thermal and pressure

cyclical loads.

Tornes et al. (2000), based on Konuk (1998), developed the concept of “axial creeping”,

which is the phenomenon of the net axial displacement of pipelines induced by thermal

and pressure increments and decrements associated with the operational cycles, after

monitoring operating offshore pipelines in the North Sea when this anomaly was first

observed. Later, the “axial creeping” phenomenon was renamed “pipeline walking”,

which is induced by the same principles as axial creeping, but with a broader

understanding of its causes, effects and consequences (Carr et al., 2003).

Different causes of pipeline walking have been understood (Bruton et al., 2010); but now

it is important to better understand the relationship between the pipeline subjected to

walking and the seabed soil.

Figure 1.1 illustrates the current industry methodology for pipeline walking assessment.

It shows a staircase with multiple steps representing the different steps of the design

procedure applied to the assessment of pipeline walking. The first step represents the

input data set; a step where basic information should be gathered to support the

assessments. General information such as pipeline route and fluid characterization are

considered to be given. The second step highlights the analytical solutions. The analytical

assessments are to be performed according to Carr et al. (2003). If the pipeline is not

proved stable, the third step of the methodology should be applied: simple Finite Element

Model (FEM). Simple finite element models account for simplified route geometry,

simplified flow assurance, and pipe-soil interaction models; which represent more basic

data. Even though simplified data deliver basic pipeline walking results, these results are

reliable and robust for the level of simplifications applied to the assessment. In case the

pipeline could not be proved stable by the simple finite element analyses, the fourth step

of the methodology is applied: a detailed finite element model. These models require

detailed data such as flow assurance, detailed tri-dimensional route geometry, realistic

pipe-soil interaction models and detailed pipeline geometry so that a design digital twin

Chapter 1

4

could be generated, and the assessment provides a final answer for the pipeline walking

evaluation. For cases that the detailed finite element analyses cannot prove the pipeline

stable, a mitigation design should be prepared. The mitigation design is the fifth step in

the axial stability design stairs. The mitigation is an engineered solution to prevent

pipeline walking from occurring and to eliminate any related issue to axial stability. The

next step is where all construction data come together to enable a finite element model

that should account for every construction detail in order to forecast the walking

behaviour. Finally, the last step of additional intervention is a safety net which allows

rectification in case discrepancies are found between operational surveys and as-built

forecast.

When results inform that mitigation is required, different types of apparatus have been

used to provide an additional resistance to axial displacement, which aims to cease

pipeline walking. Various anchoring structures, that provide the additional resistance,

have been used to moor different pipelines to their installation position on the seabed

(Rong et al., 2009; Carneiro and Murphy, 2011; Perinet and Simon, 2011). Regardless of

the method of choice, the methods proposed by these authors increase the axial resistance

available. However, they all consider some sort of intervention in the pipeline, which

increases costs and time requirements.

Thus, an evaluation of the previous design steps can be performed to assess potential

improvements that could assist to avoid the mitigation step. To do so, it is mandatory to

look for improvements in the previous models (analytical and computational) and how

they can be adjusted. Especially when the relationship between soil and pipeline (i.e.

pipe-soil interaction) is considered, which is the main source of uncertainty of this type

of assessment.

The traditional analytical solution considers an idealized pipe-soil interaction model

commonly called “rigid-plastic” (Carr et al., 2006). This idealization clearly opposes the

realistic pipe-soil interaction behaviour observed in various published sample tests

(White and Cathie, 2011; White et al., 2011, 2012; Hill et al., 2012). Therefore, this thesis

aims to extend the validity of analytical techniques by generating alternative solutions

that are shown to properly represent more complex and realistic soil conditions than the

idealized rigid-plastic interaction.

Introduction

5

By extending the validity of analytical solutions, this thesis also contributes to cheaper

and quicker engineering assessments because it sits in a lower step of the investment

staircase (Figure 1.1) when compared to other solutions (finite element analyses).

1.2 THESIS OBJECTIVES

This thesis’s goal is to extend the analytical solutions so that cost and time efficient

assessments could be done reliably. This thesis improves the quality of analytical and

numerical models for pipeline walking assessments by accounting for an extended range

of potential soil conceptualizations and also evaluates the impact of different slope

geometries on pipeline walking as many pipelines are deployed in such conditions

(Leckie et al., 2016).

To successfully improve our understanding of pipeline walking, the following

intermediate goals are defined: (i) establish a perfectly elastic-plastic soil spring and

investigate its influence on pipeline walking, (ii) develop a non-linear elastic-plastic soil

model and inspect its impact on walking pattern, (iii) elaborate and investigate the

consequences of the use of a tri-linear peaky soil on the walking rates, (iv) create a non-

linear peaky soil behaviour and understand its effect on the pipeline walking phenomenon

and (v) investigate the effects of different slope geometries on pipeline walking.

1.3 THESIS ORGANISATION

This thesis has 8 chapters, including the Introduction (Chapter 1), Literature Review

(Chapter 2) and the Conclusion (Chapter 8). Chapter 2 provides an extended literature

review covering concepts associated with pipeline walking and engineering topics

essential for the research presented in this thesis.

In Chapter 3, perfectly elastic-plastic soils are treated and their impact on pipeline

walking is explored, by establishing how such soil springs can be mimicked and by

investigating its influence on pipeline walking.

Chapter 4 considers a non-linear non-peaky behaviour (non-linear elastic-plastic soil

models). The non-linear elastic-plastic soil models are developed and their influence on

pipeline walking is inspected.

In Chapter 5, peaky linear soils are treated (peaky tri-linear); while Chapter 6 considers

a non-linear soil approach (non-linear peaky). In such chapters the soil models are created

Chapter 1

6

to mimic peaky soil behaviour and their impact on pipeline walking could be understood,

for the peaky tri-linear and non-linear peaky soil behaviours, respectively.

Chapter 7 investigates the impact variable slopes have on pipeline walking, regardless

the pipe-soil interaction model.

Chapter 8 concludes this thesis by covering the research findings generated in the

previous chapters and presenting some suggestions for future research.

Appendix A gives more details on the pile/ pipe equivalence as stated by Section 3.9

accordingly with Randolph (1977).

Appendix B helps a better understanding by providing a base case comparison in one

(cheat) sheet for all pipe-soil interaction models used in this thesis (Chapters 3, 4, 5, and

6).

Appendix C provides some additional information about finite element model details.

Appendix D provides the calculation check for lateral buckling for all models used in this

thesis (Chapters 3, 4, 5, 6 and 7). Although the coupled problem of walking and lateral

buckling is not the aim of this thesis, these calculations are provided here in order to show

that some cases studied are not susceptible to lateral buckling; whilst some other cases

are. Therefore, it can be understood that even illustration cases (i.e. cases that could suffer

lateral buckling) of the different soil characterization still have value for practical and

real situations. All cases (with or without lateral buckling susceptibility) follow through

the patterns established by this study.

Introduction

7

FIGURES

Figure 1.1: Axial stability design stairs

Chapter 2

8

CHAPTER 2. LITERATURE REVIEW

Chapter context: Pipeline walking is a complex and a relatively new phenomenon that

is yet not fully understood. This chapter reviews the relevant literature on pipeline

walking, including relevant information on supporting topics, such as offshore

geotechnics experimental investigations, numerical modelling and industry adopted

strategies/ mitigation measures, among others.

Literature review

9

2.1 PIPELINES AND PIPELINE WALKING

Since the 1970s, offshore pipelines became increasingly essential facilities for

hydrocarbon production (Kyriakides and Corona, 2007) and nowadays they are seen as

the arteries of offshore oil and gas production systems (Palmer and King, 2008).

For various reasons, certain hydrocarbon resources need a complex production network

as exemplified in Figure 2.1. Despite having many different parts and pieces of

infrastructure, this type of production network became very usual in areas such as the

Gulf of Mexico, Australasia, Offshore Brazil and West Africa (Jayson et al., 2008;

Carneiro and Castelo, 2011; Roberts et al., 2018). Such arrangements of production

network require short pipelines, typically in the vicinity of 2km (Carr et al., 2003; Carr

et al., 2006); while, export pipelines are significantly longer. For example, Solano et al.

(2014) and Charnaux et al. (2015) reported pipeline lengths of approximately 40km.

In 2000 (Tornes et al., 2000), unpredicted pipeline movements were noticed in a few

short infield pipelines in the North Sea – UK Sector. These movements occurred while

operating under high pressure and high temperature conditions and could potentially have

caused an environmental disaster. This phenomenon was named pipeline walking (Carr,

et al., 2003), and represents a major challenge to pipelines’ operations.

Pipeline walking consists of a global axial migration of the pipeline. This migration is a

progressive pattern of movements that accumulates over the operational design life of a

pipeline. The movements are induced by asymmetries in expansion and contraction

cycles due to start-up and shutdown loading stages.

Further, industry based research found more information on this engineering topic, which

established the foundation for following designs and applications (Bruton et al., 2010).

Four distinct mechanisms have been identified to date to incite pipeline walking:

1. Thermal transients along the line (Tornes et al., 2000);

2. Tension at the end of the flowline (Carr et al., 2003);

3. Seabed slopes along the pipeline route (Carr et al., 2006);

4. Multiphase fluid behaviour during restart operations (Bruton et al., 2010).

The tension at the end of the flowline causes the pipeline to walk towards the tensioned

end (Carr et al., 2003). For example, this tension might be created by a riser directly

connected to the pipeline. Direct connections are normally avoided by including some

infrastructure piece to the connection. In Figure 2.1 it can be seen that the pipeline system

Chapter 2

10

includes holdback suction anchors (near the spar platform) and the pipeline end

termination structures (near the floating production, storage and offloading, FPSO, unit).

Thermal transient is the mechanism originally reported by Tornes et al. (2000) and occurs

when the operational conditions imposed a variable temperature profile along the length

of the pipeline. Although this is a common issue in operating pipelines, in assessments

the temperature variation along the entire length could generally be approximated to the

steady state operational temperature variation.

The multiphase fluid behaviour during restart operations is related to not so trivial

operational conditions where gasses and liquids are conveyed together in the same

pipeline (Bruton et al., 2010). The problem arises when the pipeline is shutdown and the

fluids separate due to different individual densities. The separation creates a variation of

total weight along the line, which increases the chances of pipeline walking.

The seabed slopes mechanism generates a weight component along the longitudinal

pipeline axis thereby increasing the likelihood of the pipeline walking occurrence (Carr

et al., 2006). This weight component modifies the pipe-soil interaction behaviour in a

way that allows the pipeline to slip downhill. The seabed slopes mechanism is the most

commonly observed cause of pipeline walking, and as such it is the focus of the research

developed in this thesis.

Changes in temperature and pressure can lead to unexpected pipeline movements caused

by physical expansion and contraction. In start-up phases, increments in temperature and

pressure generate a pipeline axial expansion. Pipe-soil interaction resists this expansion,

resulting in effective compression of the pipeline. During shutdown phases, decrements

in temperature and pressure can cause physical contraction; inducing effective tension

due to the physical contraction of the pipeline.

For pipelines in which these cycles of compression and tension do not cancel each other,

pipeline walking may occur as a result of asymmetric effective axial force along the

pipeline. Each of the four mechanisms is capable of creating the referred unbalance in

axial displacements and the asymmetric pipeline effective axial force. Therefore, pipeline

walking appears because of the pipeline effective axial force asymmetry, causing unequal

pipeline displacements between cycles of start-up and shutdown loading phases.

Industry research (Carr et al., 2003) also highlights two categories of pipelines regarding

downslope pipeline walking:

Literature review

11

1. “Long” pipelines;

2. “Short” pipelines;

These categories are not exclusively related to the pipeline physical length because they

also involve pipe-soil interaction characteristics (e.g., friction factors and mobilisation

distances). As an example, the exact same pipeline may behave as “long” for a certain set

of pipe-soil interaction, while it may behave as “short” for another set of pipe-soil

interaction. The soil resistance would help determine conditions in which the pipeline

would behave as “long” or “short”.

For “long” pipelines, the soil provides resistance so that the effective compression build-

up occurs along a sufficient length to induce enough mechanical strain to fully

compensate for the thermo-mechanical expansion during the hot stages. For “short”

pipelines, the compression build-up, due to soil resistance, is not sufficient to fully

compensate for the expansion.

When “short” pipelines are located on a sloping seabed and are not anchored, cycles of

expansion and contraction may cause the pipelines to move with geometric asymmetries

between the start-up and shutdown phases. The sloping seabed generates a component of

weight to act parallel with the seabed in a downslope direction.

Even if pipeline walking may not present a serious structural issue to the pipeline itself,

it may result in several design challenges, including:

1. Overstressing of end connections (and in-line connections);

2. Loss of tension in a SCR;

3. Increased loading leading to lateral buckling;

4. Route instability (curve pull out);

5. Need for anchoring mitigation.

Therefore, pipeline walking must be avoided since its consequences may create

downtime and environmental risk, as pointed out by Tornes et al. (2000).

2.2 CURRENT ANALYTICAL METHOD

For the downslope mechanism of pipeline walking, the effective axial force plot

demonstrates the asymmetry, as referred in Section 2.1 and shown in Figure 2.2. This

asymmetry, which accounts for the weight component action, controls the offset distance

Xab, which is the distance between the virtual anchor sections as defined by Carr et al.

Chapter 2

12

(2003). Xab is also noticeable in the different profiles of axial displacement, δx, as shown

in Figure 2.3.

The current design practice defined by Carr et al. (2006) – involves three different

calculation steps to analytically assess the pipeline walking rate under the influence of

seabed slope for a rigid-plastic, RP, soil idealization.

The first calculation step assesses the distance between the virtual anchor sections, Xab,RP,

as presented by equation (2.1):

𝑋𝑎𝑏,𝑅𝑃 =𝐿 tan𝛽

𝜇 (2.1)

where L stands for the pipeline physical length, β for the seabed slope angle and µ for the

soil axial residual friction coefficient.

The second calculation step assesses the change in effective axial force in the pipeline,

ΔSS,RP, between start-up and shutdown conditions over the length of the pipeline denoted

by Xab,RP:

𝛥𝑆𝑆,𝑅𝑃 = −𝑊𝐿(𝜇 cos 𝛽 − |sin 𝛽|) (2.2)

where W stands for the pipeline operational submerged weight.

This change in force, occurring over the distance Xab,RP, creates the asymmetry in axial

movement of the pipeline over a single temperature cycle, which is the origin of the

walking behaviour. The walking distance per cycle, also called the walking rate for a

rigid-plastic soil idealization, WRRP can then be determined in the third and last step by

combining equations (2.1) and (2.2):

𝑊𝑅𝑅𝑃 =(|𝛥𝑃| +𝑊𝐿|sin 𝛽| −𝑊𝐿𝜇 cos 𝛽)𝐿 tan 𝛽

𝐸𝐴𝜇 (2.3)

where ΔP is the change in fully constrained force, as per Carr et al. (2003) and based on

Hobbs (1984), E is the steel Young’s modulus and A is the pipeline steel cross sectional

area.

However, equation (2.3) can be entirely rewritten as:

𝑊𝑅𝑅𝑃 =(𝛥𝑆𝑆,𝑅𝑃 − 𝛥𝑃)𝑋𝑎𝑏,𝑅𝑃

𝐸𝐴 (2.4)

Equation (2.4) might also be rewritten more fundamentally as:

Literature review

13

𝑊𝑅𝑅𝑃 = −1

𝐸𝐴(∫ (𝛥𝑃)𝑑𝑥

𝑉𝐴𝑆𝑆𝑈𝑝,𝑅𝑃

𝑉𝐴𝑆𝑆𝐷𝑜𝑤𝑛,𝑅𝑃

−∫ (𝛥𝑆𝑆)𝑑𝑥𝑉𝐴𝑆𝑆𝑈𝑝,𝑅𝑃


) (2.5)

where VAS stands for virtual anchor section, as per Carr et al., (2003).

Section 2.2.1 provides additional information on the mathematical steps performed for

this analysis.

The analytical solutions shown above – equations (2.1), (2.2), (2.3), (2.4) and (2.5) – have

been used to calculate pipeline walking rates based on the rigid-plastic soil assumption,

which is schematically presented in Figure 2.4. Unfortunately, the rigid-plastic

assumption is a simple idealization that does not reflect reality, where soils may behave

in various ways.

2.2.1 Mathematical Shortcuts

In this section some auxiliary equations are listed. Equations (2.6), (2.7), (2.8), and (2.9)

present the mathematical shortcuts that are used as secondary equations (Section 3.5).

𝑋𝑎𝑏,𝑅𝑃 = (𝑉𝐴𝑆𝑆𝑈𝑝 − 𝑉𝐴𝑆𝑆𝐷𝑜𝑤𝑛) (2.6)

𝑉𝐴𝑆𝑆𝑈𝑝,𝑅𝑃 = (𝐿 + 𝑋𝑎𝑏,𝑅𝑃

2) (2.7)

𝑉𝐴𝑆𝑆𝐷𝑜𝑤𝑛,𝑅𝑃 = (𝐿 − 𝑋𝑎𝑏,𝑅𝑃

2) (2.8)

𝛥𝑃 = −(𝑝2 − 𝑝1)𝐴𝑖(1 − 2𝜈) − 𝐸𝐴𝑠𝛼(𝑇2 − 𝑇1) (2.9)

2.3 AXIAL PIPE-SOIL INTERACTION

Many authors have published research on soil behavior including site geotechnical

investigations, theoretical framework, and potential advances in numerical modelling of

soil behavior. A few selected examples are: Hill and Jacob (2008); Tian and Cassidy

(2008); Ballard and Falepin (2009); White and Cathie (2011); White et al. (2011); and,

Hill et al. (2012) However, for the purpose of this study, the overall findings across

different research programs might be summarized by the findings of White et al. (2011)

and Hill and Jacob (2008).

White et al. (2011) tests a soil sample with a moving piece of pipeline. The pipeline probe

was cyclically displaced back and forth in the axial direction, while instrumentation took

Chapter 2

14

readings from the soil resistance. The results from the test program (White et al., 2011)

are summarized in Figure 2.5 and are given in terms of equivalent friction versus axial

displacement for distinct sweep cycles. Figure 2.5 was adapted from the original, so that

a stronger visual comparison could be achieved. The slow and fast sweeps results are

superimposed with their hypothetical rigid-plastic pipe-soil interaction models to

highlight the deviation between realistic behaviour and current engineering analytical

considerations. This deviation is the point where this thesis aims to contribute by

generating a reliable and realistic analytical solution, which accounts for the axial soil

resistance particularities avoiding unrealistic and potentially over-conservative and

onerous situations.

Other literature, such as, Bruton et al., (2008); Hill and Jacob (2008); and, Carneiro and

Murphy (2011) clarify that some soils might resist with the appearance of a peak breakout

before the residual plateau, which is a slightly different behaviour to White et al. (2011).

Similarly to Figure 2.5 (White et al. 2011), Figure 2.6 summarizes the results of the tests

conducted in Hill and Jacob (2008). Figure 2.6 was also adapted from the original for a

visual comparison between the realistic behaviour and a hypothetical rigid-plastic pipe-

soil interaction model. The results shown in Figure 2.6 were obtained applying a similar

methodology(White et al. 2011); where, Hill and Jacob (2008) displaced a probe of

pipeline back and forth, while taking measurements .

DNVGL-RP-F114 (DNVGL, 2017a) summarizes the recommended engineering

practices for representing the pipe-soil interaction (in axial, lateral and vertical directions)

in submarine pipeline engineering studies. In terms of axial pipe-soil interaction models,

DNVGL-RP-F114 covers in depth the description of the axial response and equivalent

friction factors during different stages of a pipeline’s operational lifetime. In addition, it

states: “The axial pipe-soil interaction is usually idealized in structural modelling with

an elastic-plastic model that consists of two parameters: the limiting (or residual) axial

resistance, and a mobilization distance”. Unfortunately, it does not draw any conclusion

to pipeline walking assessment results; even though, it acknowldges the influence of axial

pipe-soil interaction in such assessments. This thesis drives attention to the influence of

axial pipe-soil interaction on the pipeline walking behaviour.

It was also noticed in the literature that in certain circumstances the pipe-soil interaction

might present a variable behaviour. The reasons for these variable interactions have been

attributed to some aspects of operation and construction. Pre-operational embedment and

Literature review

15

volumetric hardening (Smith and White, 2014) are examples of these circumstances. The

changes in the pipe-soil interaction models are commonly related to increased (or

decreased) axial residual friction coefficients due to physical changes originated in

operational or construction phases.

Taking pre-operational embedment as an example, White et al. (2012) clarify that this

might represent an equivalent increase in axial resistance of 10 to 20%, which in the

literature is commonly referred to as “wedging factor”. As later explained (Section 2.3.1),

this research uses beams and macro-elements to represent the pipelines and the pipe-soil

interaction models, respectively; where the embedment is not explicitly simulated in the

finite element models. Rather, the pre-operational embedment is equivalently represented

by the chosen soil axial resistance – i.e. a pipe-soil friction coefficient of 0.6 might

correspond to a situation where the interface friction between pipe and soil is 0.5 but

enhanced by a 20% wedging effect results in an overall axial resistance of 0.6.

In summary, for cases where the soil resistance varies during the pipeline life, the pipeline

walking behaviour will also vary because of the pipe-soil interaction variation. The

methods proposed by this thesis can be applied for cases that deal with varying resistance

through updating the inputs used in the analyses, such as the axial residual friction

coefficient or other properties of the pipe-soil interaction models described in Chapter 3

to Chapter 6.

2.3.1 Axial pipe-soil interaction models

To represent the soil behaviour in pipeline walking analyses, the relationship between

pipe displacement and soil resistance is conventionally treated as the pipe-soil interaction

model. Currently, for analytical assessments of pipeline walking, the pipe-soil interaction

model used is the limited rigid-plastic model, as clarified in Section 2.2 and as illustrated

in Figure 2.4, Figure 2.5 and Figure 2.6.

Consequently, the analytical formulation ends up being used as a screening method to

point out what cases need further attention – going up, at least, one step on Figure 1.1

into the finite element modelling steps. Usually, the finite element analyses considers

spring-slider elements to model the pipe-soil interaction (Chan and Matlock, 1973).

Chan and Matlock (1973) establish how multiple spring-sliders can be added together

generating a highly non-linear structure-soil interaction model for vibrations of beam

columns elements on elastic or inelastic supports. Based on the same principle of

Chapter 2

16

superimposing various spring-slider elements, different pipe-soil interaction models can

be achieved for the finite element analyses of downslope pipeline walking. Figure 2.7

was developed, based on the results shown in Figure 2.5 and Figure 2.6, to exemplify

four different pipe-soil interaction behaviours when loaded by a piece of moving pipeline.

Figure 2.7 provides a schematic view of force - displacement curves showing the rigid-

plastic behaviour in grey, two elastic-perfectly-plastic behaviours (stiff and soft fits in

red and black lines, respectively), a non-linear elastic-plastic curve in dark blue, a tri-

linear peaky soil model in green and a non-linear peaky behaviour in light blue. The two

elastic-perfectly-plastic approaches – ideal representations for the real non-linear soil, are

commonly used by the industry as later explained in Chapter 3.

Rigid-Plastic model

The less realistic pipe-soil interaction model, the rigid-plastic model is most frequently

used because of the simplicity of the model. This is the pipe-soil interaction model used

in the assessment presented in Section 2.2. It requires a simple friction coefficient which

links the pipeline operational submerged weight to the available soil resistance to axial

movement. Its behaviour is shown in Figure 2.7 (in grey) in terms of axial displacement

of the pipe and mobilised axial resistance. In this pipe-soil interaction model, regardless

of the pipe displacement level, the soil always resists with a residual plastic force, FR.

Elastic-Perfectly-Plastic model

The elastic-perfectly-plastic pipe-soil interaction models are described by two main

properties: the residual plastic force, FR, and the mobilisation distance, δmob, where FR is

attained. The soil loading transitional behaviour, from unloaded to the residual plastic

level, is governed by a linear-elastic Hooke’s Law (Halliday et al., 2010). Therefore, the

tangential soil stiffness, Ksoil, can be obtained by:

𝐾𝑠𝑜𝑖𝑙 =𝐹𝑅𝛿𝑚𝑜𝑏

(2.10)

However, this model approximates and idealizes the real behaviour, which is non-linear,

as shown in Figure 2.5. Industry has commonly approached the pipeline walking finite

element modelling using this simplification through an envelope of pipe-soil interaction

cases: the “Soft” and the “Stiff” Fits (later explained in further details in Chapter 3).

Although the elastic-perfectly-plastic pipe-soil interaction model has been extensively

used; so far, no satisfactory justification has been given for the deviation between rigid-

Literature review

17

plastic and elastic-perfectly-plastic results, nor has a direct relationship been drawn.

Therefore, this research endeavours to present a robust justification for the deviation

noticed in the results, and to draw a set of equations which would make a simpler and

quicker assessment possible.

Non-Linear Elastic-Plastic model

The non-linear elastic-plastic interaction loading process, between the unloaded and the

residual plastic level can be described by Hooke’s Law (Halliday et al., 2010), similarly

to elastic-perfectly-plastic pipe-soil interaction models. However, for non-linear elastic-

plastic models, it is not a direct relationship, as presented by equation (2.10), given the

non-linear behaviour. The non-linear behaviour also prevents a mobilisation distance,

δmob, to be attributed to the pipe-soil interaction model. As an example, if the non-linearity

can be described as a parabola, the soil stiffness in the tangential direction between the

pipeline and the seabed, Ksoil, can be obtained by the derivative of the parabola at a given

point as:

𝐾𝑠𝑜𝑖𝑙 =𝑑𝐹𝐴𝑑𝛿𝑥

= 2𝑎𝛿𝑥 + 𝑏 (2.11)

where FA is the mobilised axial resistance force, δx is the axial displacement, and a and b

are parabolic factors for a parabola which the general equation is:

𝑦 = 𝑎𝑥2 + 𝑏𝑥 + 𝑐 (2.12)

where x and y are arbitrary abscissa and ordinate axes, respectively.

Tri-Linear with a Peak model

The tri-linear with a peak pipe-soil interaction model is an approximation for the non-

linear models with a peak. However, given its more intricate nature, the tri-linear with a

peak model requires four properties to be defined: the peak elastic force, FP, the residual

plastic force, FR, the peak elastic force mobilisation distance, mobP, and the residual

plastic force mobilisation distance, mobR.

From the unloaded to the residual plastic states, the soil is governed by a set of two linear-

elastic Hooke’s Law (Halliday et al., 2010) where the tangential soil stiffness, Ksoil, can

be described (between unload and peak) as:

𝐾𝑠𝑜𝑖𝑙 =𝐹𝑃

𝛿𝑚𝑜𝑏𝑃 (2.13)

Chapter 2

18

And (between peak and residual) as:

𝐾𝑠𝑜𝑖𝑙 =(𝐹𝑅 − 𝐹𝑃)

(𝛿𝑚𝑜𝑏𝑅 − 𝛿𝑚𝑜𝑏𝑃) (2.14)

Although the tri-linear model with a peak interaction is an approximation/ idealization

from the realistic non-linear behaviour; this thesis drives attention to this pipe-soil

interaction model because of the potential advances in pipeline engineering it represents.

This thesis also seeks to revise the equations used in the pipeline walking analytical

assessment, so that results for this model can be more easily achieved.

Non-Linear with a Peak model

Given the higher non-linearity degree of the non-linear model with a peak (when

compared to the non-linear elastic-plastic model), for this research it will be described as

a linear-elastic starting part to be followed by a set of three different consecutive parabolic

curves fitted to properly represent a highly non-linear behaviour, such as the one

presented in Figure 2.7.

Consequently, the tangential soil stiffness can be obtained by the derivative of the non-

linear Hooke’s Law (Halliday et al., 2010) at a given point as:

𝐾𝑠𝑜𝑖𝑙 =𝑑𝐹𝐴𝑑𝛿𝑥

= 2𝑎𝑖𝛿𝑥 + 𝑏𝑖 (2.15)

where ai and bi are parabolic factors for a parabola i which general equation is:

𝑦𝑖 = 𝑎𝑖𝑥2 + 𝑏𝑖𝑥 + 𝑐𝑖 (2.16)

while, the linear-elastic part of the pipe-soil interaction regime general equation is:

𝑦 = 𝑚𝑥 + 𝑐 (2.17)

where x and y are arbitrary abscissa and ordinate axes, respectively, and m is the line’s

gradient.

2.4 POSSIBLE MITIGATION STRATEGIES

This section details the fifth step of current industry methodology (Figure 1.1), where a

mitigation workflow is designed to eliminate downslope pipeline walking, as described

by Bruton and Carr (2011b). Although mitigation strategies (and how to design them) are

not part of this study, this section is included in this thesis to detail the industry efforts in

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mitigating pipeline walking and show how these efforts could potentially be improved by

better pipeline walking analytical assessments.

For pipelines suffering downslope pipeline walking, industry has normally dealt with this

phenomenon by adding extra axial resistance. A few examples of available bibliography

on mitigation strategies are: Frazer et al. (2007); Rong et al. (2009); and, Frankenmolen

et al. (2017). These references illustrate the proposed mitigation strategies, which aim to:

1. Achieve a greater pipe-soil friction by adding extra weight to the pipeline, or;

2. Strengthen the pipeline structural response by anchoring a pipeline section, or;

3. Supplement the pipeline system response by anchoring an ancillary equipment.

Frazer et al. (2007) overviews the mechanisms related to pipeline movements, in both

directions – lateral and axial, triggered by temperature and pressure cyclic loads. The

paper then presents a set of mitigating strategies and recommends that pipeline walking

should always be prevented by restraining the pipeline axial displacement rather than

designing the pipeline system to accommodate such displacements. The design of the

walking mitigating strategies should be engineered considering the pipeline system and

project constraints, such as, laying direction, budget, etc.

Figure 2.8 provides a brief summary of the mitigation devices suggested by Frazer et al.

(2007). Note the suction anchor with connecting chain for pipelay initiation when the

laying direction moves away from the represented pipeline end. Also, there is a pair of

suction anchors with connecting chains and a pipeline clamp when the laying direction

moves towards the represented pipeline end, and finally there is a mid-line axial restrain

when the laying direction passes by the anchoring location.

Rong et al. (2009) explore the walking behaviour of a deep-water pipeline system by

using a set of finite element analyses and also present a comprehensive summary on the

walking mitigation strategies that could be used to cease the walking phenomenon. Three

different situations were considered, accounting for two different walking creating

mechanisms (as per Section 2.3), to guide the finite element analyses:

1. Flat seabed and thermal transients;

2. Sloped seabed and thermal transients in the same direction;

3. Sloped seabed and thermal transients in the opposite direction.

The first situation accounts for mechanism number 2 (thermal transients) only, as per the

list in Section 2.3. The second and the third situations account for mechanisms number 2

Chapter 2

20

(thermal transients) and 4 (seabed slopes), as per the list in Section 2.3, firstly in the same

direction, then in the opposite direction. Although mechanism number 2 is beyond the

scope of this thesis, the published studies by Rong et al. (2009) are very interesting for

the development of this topic.

Rong et al. (2009) explore the possible mitigation strategies including increased pipe-soil

interface friction, anchoring pipeline sections, and present an overall list of mitigation

strategies highlighting the advantages and disadvantages from each strategy. The

mitigation strategy list, alongside their advantages and disadvantages, is summarized in

Table 2.1.

The paper then considers the anchoring strategy as the most appropriate option to mitigate

the walking behaviour for the case studied and performs a more detailed analysis of the

anchoring influence for the operational regime. The simulation results are shown in terms

of effective axial force and the walking rate is derived from it. It also gives attention to

estimating the anchor load due the walking phenomenon.

Rong et al. (2009) concludes by presenting a brief discussion on anchor location

optimization, which should account for many aspects including the susceptibility of

lateral buckling.

Frankenmolen et al. (2017) present an innovative approach to increase the friction

resistance, such as the spot rock dump/mattresses strategy from Table 4.1, but with a

higher degree of reliability, and a better cost-effective alternative. The invention of Pipe-

Clamping Mattress (PCM) came from the necessity of mitigating a walking pipeline in

the Malampaya field, offshore Philippines.

When the Malampaya development was engineered, pipeline walking was not well

known; so, the design did not account for such phenomenon. Over the operational years

since constructed, the Malampaya pipeline accumulated a total displacement of 1.8m at

one of its ends, which raised concerns over the integrity of the jumper connection. The

accumulated axial displacement can be seen in Figure 2.9.

In the walking mitigation engineering processes a few finite element analyses were used

to define the optimized location for the mitigation to be installed. The optimum location

is where walking can be stopped with the minimum required load capacity. The load

capacity and the location required to arrest the pipeline studied, obtained from the finite

element analyses, indicated that spot rock dumping would be unfeasible for the example

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Table 2.1: Summary of possible walking mitigation strategies (Rong et al., 2009).

Mitigation Strategy Advantages Disadvantages

Increase Jumper/ Spool Expansion

Capacity Little additional cost Walking related displacement levels can easily exceed jumpers/ spools capacity

Site Specific Pipe-Soil Geotechnical

Investigation Improves confidence in geotechnical properties

Extremely time consuming

Accurate analysis of deep water soils is challenging and not rarely may fall outside common experience

May not eliminate walking

Concrete Weight Coating Increases friction resistance

May increase the likelihood of uncontrolled lateral buckling with localized strains due to increased

friction

Impractical for deep water installation

Trench And/ Or Bury Efficient method to increase friction resistance

Extremely costly

Trenching and burying equipment limitation

Thermal insulating effect (increases upheaval buckling susceptibility)

Spot Rock Dump/ Mattresses

Increases friction resistance Massive quantities of materials are required

Increases construction time and cost requirements

Decreases corresponding axial feed-in to lateral buckles

Specialist vessels are required

Might be uncapable to mitigate walking (Carneiro et al., 2017)

Impractical for ultra-deep waters

Controlled Buckles

Snake-Lay Reduces walking by absorbing its effects as lateral buckles feed-in Snake-Lay installations are challenging for deep waters (embedment related uncertainties)

Applicable to both (snake-lay and sleepers)

Walking effects into lateral buckles (axial feed-in) may overstress the pipe and its joints

Pipeline may behave as a “short” pipe, which does not guarantee lateral buckle(s) initiation

Buckling-Walking interaction is highly complex to analyse and predict

Sleepers Reduces walking by absorbing, in a controlled manner, its effects as lateral buckles

feed-in Higher cost related to engineering, supply, and deployment of the sleepers

Anchoring

Most likely mitigation method to succeed in mitigating walking Anchors are normally large and heavy requiring substantial vessels to install them

Allows optimization (anchor location) Anchors and anchor connections need to be properly engineered to prevent excessive movement near

anchor location Helps controlling end expansion (instead of expanding from VAS, the pipe

expands from the anchor location)

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studied. Adding regular concrete mattresses could be inefficient, because the pipeline

might settle into deeper soil levels, due the increase in vertical load in a phenomenon

known as “wedging” (White et al., 2012); and then, the combination of regular concrete

mattresses and “wedging” increased soil axial resistance could not provide sufficient

axial restrain, since regular concrete mattresses would go from membrane tension to

compression, similar to the process studied in Carneiro et al. (2017) for rock dumps.

Therefore, the Pipe-Clamping Mattress (PCM) was created as a solution which instead

of resting on the pipeline, clamps the pipeline, generating a situation where 100% of the

weight increase generate an equivalent axial resistance increase. If necessary, extra

weight might be provided by adding further regular concrete mattresses. Noteworthy

additional stresses in the pipeline wall should be checked against pipeline integrity

requirements, such as those from DNVGL-ST-F101 (DNVGL, 2017b).

Figure 2.10 shows the Pipe-Clamping Mattress (PCM) in four different views: (a) in

deployment above sea level; (b) in deployment below sea level; (c) installed on top of

pipeline; and, (d) installed on pipeline with extra weight concrete mattresses.

The paper then concludes by presenting a performance monitoring over the period of time

between PCMs deployment and after three operational load cycles, which means a period

of time that the pipeline was estimated to walk a distance around 8cm. As can be seen in

Figure 2.11, the resulting displacement during the aforementioned period of time was

found to apparently be zero. In the case the displacements related to walking are very

small, a longer period of time is required for such observations to be made; therefore,

further inspections are programmed, as stressed in Frankenmolen et al. (2017).

Figure 2.11 shows the walking monitoring results after the PCMs installation on the

Malampaya pipeline: (a) right after the PCMs installation – December 2015; and, (b) after

three operational load cycles – January 2016.

2.5 FINAL REMARKS

Pipeline walking is a complex phenomenon that affects pipelines in various operational

conditions such as tensioned end, thermal transients, multiphasic flow, and seabed slopes.

Although pipeline walking has been known and documented for the last two decades, the

efforts of providing broad and general guidance has not kept up to the amount of site-

specific investigations.

Chapter 2

23

For a pipeline laid in a seabed sloping route, downslope pipeline walking may affect such

pipeline depending on several parameters, which range from operational and

environmental conditions to certain pipeline structural properties. A few examples of

downslope walking pipelines have been found in the literature, in areas across the globe,

such as, the North Sea (Tornes et al., 2000) , Offshore Brazil (Solano et al., 2009) , Gulf

of Mexico (Kumar and Mcshane, 2009; Thompson et al., 2009), West Coast of Africa

(Jayson et al., 2008), and South East Asia (Frankenmolen et al., 2017); including system

failures being reported. Previous studies have cemented the methodology for downslope

pipeline walking assessment and derived analytical formulations; however, such

formulations are based in a rigid-plastic pipe-soil interaction idealization. To overcome

such limitation, industry related publications have documented the use of finite element

models with an elastic-perfectly-plastic pipe-soil interaction model, which is known to

slightly deviate from realistic behaviours (Bruton et al., 2008).

Rong et al. (2009) acknowledge the influence of the axial pipe-soil interaction model by

mentioning: “The axial mobilization distances may have significant effects on the axial

walking. Unfortunately, limited literature is available about this topic.” Regrettably, the

latest research program SAFEBUCK JIP (Bruton et al., 2007; Bruton and Carr, 2011b,

2011a) has also not been clear on the treatment of axial pipe-soil interaction non-

linearities, in terms of pipeline walking behaviour. It has focused in the ideal rigid-plastic

pipe-soil interaction.

At the same time, the most broadly applied engineering standard for pipe-soil interaction,

DNVGL-RP-F114 (DNVGL, 2017a), states: “In assessments of pipe walking, a low value

of mobilisation distance creates a higher rate of axial walking. To be conservative, a bi-

linear fit to the non-linear response should be a tangent fit to the initial part of the axial

force-displacement response, which represents the elastic recoverable part”. As can be

seen, no clear guidance has yet been provided on how to treat non-rigid-plastic soil

models on pipeline walking assessments. At the same time, the conservatism referred by

DNVGL-RP-F114 (DNVGL, 2017a) in the quote above might lead to an overestimation

of walking, as proved by this thesis, which could imply in avoidable costs and delays for

an engineering project.

Although the existing studies and publications have established essential knowledge

about the downslope pipeline walking problem and a few palliative actions that might be

taken in order to control such effects, no analytical formulation has been proposed to

Literature review

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reliably assess the downslope walking rate for more intricate pipe-soil interaction models.

Additionally, there is still a gap in understanding how such pipe-soil interaction models

and pipe-soil interaction changes due to construction and operational loads impact the

downslope pipeline walking behaviour. The referred knowledge and understanding gaps

can be related to the fact that this is still a new research topic and a little unusual in the

perspective of the number of operational pipelines that never suffered such problems

versus the number of pipelines dealing with this issue. Currently, finite element

modelling is becoming more and more accessible; however, it is still time demanding,

and usually requires a period of time to deliver final results that pipeline engineering

teams simply might not have, especially in early conceptual engineering phases.

Also, there is an increasing demand for probabilistic approaches, in which risk levels are

quantified and the likelihood of different scenarios is estimated. This is important for

design solutions that balance CAPEX and OPEX, such as the ‘wait and see’ approach to

pipeline walking, with planned mitigation in mid- or late-life. In this case, a large number

of simulations must be run to consider all possible operational scenarios. Rapid simple

design tools are required for this approach, rather than finite element analysis. Therefore,

having a quick, accurate and reliable analytical assessment tool is of paramount

importance to deliver solid and secure results.

Finally, this thesis investigates how the current analytical methodology should be

expanded to allow more complex assessments of pipeline walking; which are depending

on the level of pipe-soil interaction complexity (as it has been shown that there are many

more intricate pipe-soil interaction models than rigid-plastic), as well as accounting for

slope variability. Table 2.2 summarises where the different pipe-soil interaction models

are treated in this thesis, along with the slope variability.

Table 2.2: Summary of causes of uncertainty and thesis chapters.

Cause of uncertainty Chapter in thesis

Elastic-perfectly-plastic pipe-soil interaction Chapter 3

Non-linear elastic-plastic pipe-soil interaction Chapter 4

Peaky linear pipe-soil interaction Chapter 5

Non-linear peaky pipe-soil interaction Chapter 6

Slope angle variability Chapter 7

Chapter 2

25

FIGURES

Figure 2.1: Example for field architecture of infield pipelines and production

infrastructure units from White (2011).

Figure 2.2: Effective axial force diagrams for start-up and shutdown loading

phases.

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26

Figure 2.3: Axial displacement diagrams for start-up and shutdown loading

phases.

Chapter 2

27

Figure 2.4: Rigid-plastic soil behaviour.

Figure 2.5: Axial friction curves (no peak) – adapted from White et al. (2011).

Hypothetical rigid-plastic

pipe-soil interaction models

Literature review

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Figure 2.6: Axial friction curve (peak in one direction) – adapted from Hill and

Jacob (2008).

Figure 2.7: Different soil resistance behaviours.

Hypothetical rigid-plastic

pipe-soil interaction model

Chapter 2

29

Figure 2.8: Walking mitigation devices from Frazer et al. (2007).

Figure 2.9: Pipeline walking accumulated displacement from Frankenmolen et al.

(2017).

Literature review

30

Figure 2.10: Pipe-clamping mattress from Frankenmolen et al. (2017).

Figure 2.11: Post pipe-clamping mattresses installation walking monitoring from

Frankenmolen et al. (2017).

Chapter 3

31

CHAPTER 3. SIMPLE SOLUTIONS FOR DOWNSLOPE

PIPELINE WALKING ON ELASTIC-PERFECTLY-

PLASTIC SOILS

Chapter context: The published paper presented in this thesis’ chapter details the

research performed to provide the pipeline engineering community with a better

analytical solution that correctly accounts for elastic-perfectly-plastic soil properties. It

explains the required update for the distance between stationary points (initially referred

to as “virtual anchor sections”) and introduces the novel methodology that allows

accurate analytical solutions for elastic-perfectly-plastic pipe-soil interaction.

This chapter contains material that has been prepared for publication as:

Castelo, A., White, D. and Tian, Y., 2019. Simple solutions for downslope pipeline

walking on elastic-perfectly-plastic soils. Journal of Ocean Engineering (Volume 172,

15 January 2019, Pages 671-683).

Elastic-perfectly-plastic soils

32

3.1 ABSTRACT

Pipeline Walking is a phenomenon that occurs when High Pressure and High

Temperature (HPHT) pipelines experience axial instability over their operational

lifetime, and migrate globally in one direction. Existing analytical solutions treat the axial

soil response as rigid-plastic but this does not match the response observed in physical

model tests. In this paper, the authors develop a new analytical strategy using elastic-

perfectly-plastic axial pipe-soil interaction, which leads to more realistic walking rate

predictions. The new analytical methodology is benchmarked with a series of Finite

Element Analyses (FEA), which constitutes a parametric study performed to test the

proposed expressions and improve on the understanding of the influence of axial

mobilisation distance.

3.2 INTRODUCTION

Offshore pipelines are becoming increasingly important as hydrocarbon sources become

more difficult to reach. The global stability of these pipelines in response to operational

loading is a critical issue for the design of oil and gas projects. Such stability comprises

the actions of hydrodynamic loads and the effects of expansion and contraction triggered

by the High-Pressure and High-Temperature (HPHT) operational conditions (usually

imposed by frontier reservoirs), which both constitute the major focus of geotechnical

design for pipelines.

The stability of offshore pipelines is also impacted by the slope of the seabed. New

hydrocarbon sources are commonly located in regions with noticeable depth variations,

in deep water far from shore. These operational conditions are particularly common in

the Gulf of Mexico and Northwest Australia, which are currently in operation, and others

that are in development, such as the Brazilian Pre-Salt and the Arctic Area.

Threats to the integrity of offshore pipelines by the combination of HPHT conditions and

a sloping seabed were first observed by Tornes et al. (2000). Later, industry-supported

research documented many cases of “axial creeping” now known as the “Pipeline

Walking”, as per Carr et al. (2003).

Four mechanisms have been found to incite pipeline walking, as per Bruton et al. (2010):

1. Tension at the end of the flowline;

2. Thermal transients along the line;

Chapter 3

33

3. Multiphase fluid behaviour during restart operations;

4. Seabed slopes along the pipeline route.

Each of the four mechanisms creates an asymmetry in the profile of Effective Axial Force

(EAF). This asymmetry generally results in pipeline walking, by causing unequal pipeline

displacements during cycles of loading and unloading. This paper focuses on the fourth

mechanism.

When pipelines are subjected to changes in temperature and pressure, pipeline walking

can occur. During the Start-Up (SUp) phase, temperature and pressure increments cause

the pipelines to expand axially. This expansion is resisted by the pipe-soil interaction

forces which results in effective compression of the pipeline. When pipelines are

submitted to temperature and pressure reductions in the Shutdown (SDown) phase,

effective tension is induced in the pipeline.

For “long” pipelines, the effective compression build up occurs along a sufficient length

to induce enough mechanical strain to fully compensate for the thermo-mechanical

expansion during the hot stages. For “short” pipelines, the compression build up, due to

soil resistance, is not sufficient to fully compensate for the expansion.

When “short” pipelines are located on a sloping seabed and are not anchored, cycles of

expansion and contraction may cause the pipelines to move with geometric asymmetries

between the start-up and shutdown phases. The sloping seabed generates a component of

weight to act parallel with the seabed in a downslope direction.

Even if pipeline walking is not a limit state in itself, it may present several design

challenges, which include:

• Overstressing of end connections (and in-line connections);

• Loss of tension in a steel catenary riser;

• Increased loading leading to lateral buckling;

• Route instability (curve pull out);

• Need for anchoring mitigation.

Therefore, pipeline walking must be avoided since its consequences may create

downtime and environmental risk, as pointed out by Tornes et al. (2000).

It is known that pre-operational phases may influence the soil resistance during the

operational lifetime of a pipeline through the pre-operational embedment. As noticed by

White et al. (2012), typical pipeline embedments can increase the soil axial resistance by


34

10-20%. This study considers a range of axial resistance so the results cover the range of

conditions that could be created by different values of embedment. In practice, the soil

resistance may vary during the pipeline life, in which case the walking rate will also vary

as a result of this. The authors would like to clarify that the suggested solutions also apply

in cases of varying resistance during the field life requiring only an update on the

assessments’ inputs.

In this paper, focusing exclusively on the seabed slope mechanism, the authors develop

a new analytical strategy extending the traditional solution, which uses a Rigid-Plastic

(RP) soil idealization, to a new set of formulations accounting for the Elastic-Perfectly-

Plastic (EP) soil behaviour, which is a simple pipe-soil interaction model Bruton et al.

(2008). A parametric study is developed with the help of a Finite Element Analysis (FEA)

set, which will serve as proof for the proposed set of new equations, leading to more

realistic walking rate predictions.

3.3 BACKGROUND TO PIPELINE WALKING

Different papers have been published on pipeline walking in the last two decades. Nearly

all publications found on this topic are very site-specific (Jayson et al., 2008; Carneiro

and Castelo, 2011), with few exceptions providing generalizations and broad guidance

on this issue (Carr et al., 2003; Carr et al., 2006; Bruton et al., 2010).

When the downslope mechanism is taken into consideration the effective axial force plot

demonstrates the asymmetry, as referred in Section 3.2 and shown in Figure 3.1, for three

operational loading cycles. This asymmetry, which accounts for the weight component

action, controls the offset distance Xab, which is the distance between the Virtual Anchor

Sections (VAS) as defined by Carr et al. (2003). Xab is also present in the different profiles

of Axial Displacement, δx, as shown by Figure 3.2. In Figure 3.2, the axial displacements

are shown for the same three operational cycles shown in Figure 3.1, throughout the entire

pipeline length. In addition, Figure 3.2 also provides a detailed progression of the VAS

transition along the three operational cycles considered. More attention is given to Xab in

a latter part of this paper.

So far pipeline walking has been dealt with through a series of equations which account

for a rigid-plastic soil response. In this paper, an extended version of the analytical

solution is described for elastic-perfectly-plastic soil behaviour.

Figure 3.3 provides a schematic view of the Force - Displacement curve (FxD) for a given

Chapter 3

35

non-linear soil. It also accounts for rigid-plastic resistance behaviour and presents two

different elastic-perfectly-plastic approaches – commonly used as ideal representations

for the real non-linear soil. While the magnitude of the limiting axial resistance depends

on soil strength, pipe roughness and drainage conditions White et al. (2011), these effects

are beyond the scope of the present study. Instead, the focus of this paper’s work is the

influence of mobilisation distance, δmob, on the pipeline walking phenomenon.

The pipe-soil interaction varies with many different properties (Hill et al., 2012). Since

this paper simplifies the pipe-soil interaction as an elastic-perfectly-plastic (Bruton et al.,

2008), it is simpler to treat the mobilisation distance as an independent parameter, which

allows covering the full parameter space for a wider range of soils. The authors

acknowledge that different techniques might be used to obtain the pipe-soil interaction

model, but these are not part of this paper’s scope.

Two different elastic-perfectly-plastic fits are shown in Figure 3.3. One is a “Stiff Fit” in

which the mobilisation distance is denoted δmobStiff. The other is a more compliant case,

“Soft Fit”, in which the mobilisation distance is denoted δmobSoft. In this paper, the

mobilisation distances differ by a factor of 3.33, and span the typical range of plausible

elastic-perfectly-plastic fits. This is a typical uncertainty range for the non-linear response

observed in model tests of axial pipe-soil interaction. Typically, δmobStiff and δmobSoft differ

by a factor of up to 5 (White et al., 2011).

Figure 3.3 brings to light two derived parameters that are explored in the finite element

analyses parametric study (Section 3.10): Load and Unload-Reload Areas (the shaded

areas presented for the Soft Fit only). They represent the area loss between rigid-plastic

and elastic-perfectly-plastic resistance approaches in terms of the FxD curves. They are

very useful for the “elastic correction” explanation developed later.

During a reversal in the mobilised friction, the displacement required to reach the limiting

resistance in the opposite direction is 2δmob, and the unloading stiffness matches the

loading stiffness.

3.4 PROBLEM DEFINITION

To illustrate the behaviour involved in downslope pipeline walking, the properties of a

typical example are given in Table 3.1. General properties, such as temperature loads and

geometric data are in keeping with the values presented in Table 3.1, to allow the results

to be applied more broadly in the future.


36

Table 3.1: Preliminary example properties.

Parameter Value

Steel Outside Diameter, OD 0.3239m

Steel Wall Thickness, t 0.0206m

Length, L 5000m

Seabed Slope, β 2.0°

Temperature Variation, ΔT 100°C

Pipe Submerged Weight, W 0.8kN/m

Friction factor, μ 0.5

Steel Young's Modulus, E 2.07x1011Pa

Steel Poisson Coefficient, ν 0.3

Steel Thermal Expansion Coefficient, α 1.165x10-5°C-1

Mobilisation Distance for Stiff Fit, δmobStiff 0.03OD

Mobilisation Distance for Soft Fit, δmobSoft 0.10OD

3.5 RIGID-PLASTIC ANALYTICAL SOLUTIONS

The current design practice – in accordance with Carr et al. (2006) – involves three

different calculation steps to analytically assess pipeline walking rate under the influence

of seabed slope.

The first calculation step assesses the distance between the VASs, Xab,RP, as presented by

equation (3.1):


𝜇 (3.1)

The second calculation step assesses the change in force in the pipeline, ΔSS,RP, between

start-up and shutdown phases over the length of the pipeline denoted by Xab,RP:


This change in force, occurring over the distance Xab,RP, creates the asymmetry in axial

movement of the pipeline over a single temperature cycle, which is the origin of the

walking behaviour. The walking distance per cycle, WRRP can then be determined in the

Chapter 3

37

third and last step by combining equations (3.1) and (3.2):

𝑊𝑅𝑅𝑃 =[|𝛥𝑃| +𝑊𝐿|sin 𝛽| −𝑊𝐿𝜇 cos 𝛽]𝐿 tan 𝛽

𝐸𝐴𝜇 (3.3)

where ΔP is the change in fully constrained force, as per Carr et al. (2003).

However, equation (3.3) can be entirely rewritten as:

𝑊𝑅𝑅𝑃 =(∆𝑆𝑆,𝑅𝑃 − ∆𝑃)𝑋𝑎𝑏,𝑅𝑃

𝐸𝐴 (3.4)

Equation (3.4) might also be rewritten more fundamentally as:

𝑊𝑅𝑅𝑃 = −1

𝐸𝐴(∫ (∆𝑃)𝑑𝑥

𝑉𝐴𝑆𝑆𝑈𝑝,𝑅𝑃


−∫ (∆𝑆𝑠)𝑑𝑥𝑉𝐴𝑆𝑆𝑈𝑝,𝑅𝑃


) (3.5)

The rigid-plastic soils equation (3.5) is equal to ΔSS,RP integral (see Section 2.2.1 for

additional steps in this analysis).

The analytical solutions shown above – equations (3.1), (3.2), (3.3), (3.4) and (3.5) – have

been used to calculate pipeline walking rates based on the rigid-plastic assumption. Table

3.2 summarizes the analytical results for Carr et al. (2006) based on the general pipeline

properties given in Table 3.1.

Table 3.2: Rigid-plastic analytical results.

Parameter Value

Xab,RP 349.208m

ΔSS,RP -1859.184kN

WRRP 0.247m/cycle

3.6 FINITE ELEMENT ANALYSES METHODOLOGY

The finite element model used for this paper was a simplified model of a straight pipeline

laid on a uniformly sloping seabed using the parameters presented in Table 3.1.

The pipeline was represented by 5001 nodes connected by 5000 equal Euler Bernoulli

beams (B33 elements in Abaqus) representing the 5000m long pipeline. Each element,

therefore, is 1 metre in length.


38

The pipe-soil interaction was modelled as elastic-perfectly-plastic spring-slider elements

connected to each pipeline node. The spring-slider elements were developed as User

Elements (UELs) described by a subroutine in FORTRAN.

Figure 3.4 shows an overall sketch of the finite element model. It presents the uniformly

sloped pipeline and provides information about the boundary conditions imposed to all

nodes, which can only displace along the local longitudinal axis given the UEL reaction.

The spring-slider provided a constant stiffness between zero and a certain prescribed

displacement (mobilisation distance) and a corresponding force (according to Hooke’s

law). If the displacement level exceeds the mobilisation distance, the UEL provides zero

tangent stiffness and a constant force, as per the plastic plateau. On reversal, the same

stiffness is considered, until the resultant force equals the plastic plateau.

The UEL behaviour shown in Figure 3.3 is presented in terms of the loads normal to the

seabed.

This paper considers only weight and temperature as the loads acting on the pipeline.

Pressure was disregarded since it can be equally represented by an extra temperature load

(Hobbs, 1984).

The effect of the uniform slope is considered as an axial or longitudinal load equivalent

to the component of the pipeline weight, as given by:

𝑊𝑐𝑜𝑚𝑝 = 𝑊 sin 𝛽 (3.6)

The temperature loads were considered by temperature increments applied directly to the

pipeline. Operational cycling was performed taking into account the steady operational

profile (start-up) and the rest condition (shutdown).

The analyses were performed by:

1. Generating pipeline (nodes and elements) geometry;

2. Applying boundary conditions and UEL properties;

3. Applying gravity to pipeline;

4. Applying temperature increment (start-up temperature);

5. Applying temperature decrement (shutdown temperature);

6. Iterating phases 4 and 5 (9 times);

7. Extracting results from simulations’ outputs.

Chapter 3

39

3.7 FINITE ELEMENT ANALYSES COMPARISON WITH

RIGID-PLASTIC SOLUTION

Figure 3.5 presents the effective axial force responses for the EP Stiff and the Soft fits;

while Figure 3.6 and Figure 3.7 present the δx plots for the EP Stiff Fit and the EP Soft

Fit, respectively.

From the rigid-plastic case (Bruton et al., 2010), the zero displacement point is exactly

the same as the maximum effective axial force point (Table 3.3). However, the elastic-

perfectly-plastic FE results show that the point of zero displacement no longer coincides

with the point of maximum effective axial force.

Table 3.3: Elastic-perfectly-plastic FEA results.

Parameter Source Value

Xab,RP EAF & δx - Figure 3.1, Figure 3.2 and equation (3.1) 349m

Xab,EP_Stiff EAF - Figure 3.5

347m

Xab,EP_Stiff δx - Figure 3.6 321m

Xab,EP_Soft EAF - Figure 3.5 343m

Xab,EP_Soft δx - Figure 3.7 258m

As defined by Carr et al. (2003), the VASs are the sections where the δx is zero and for

the rigid-plastic soil response the VAS and the point of highest effective axial force

coincide, which makes the solution proposed by Carr et al. (2006) perfectly applicable

for rigid-plastic soils.

However, elastic-perfectly-plastic soil behaviour complicates the Xab definition, as used

by Bruton et al. (2010) and Carr et al. (2006). Thus, Xab needs to be redefined. In addition,

the points on the pipe with zero net movement (δx=0) over the period of temperature

change (either start-up or shutdown) are not stationary over this period but they move

initially in one direction then return to their original position. Here, these sections with

zero net movement are called “Stationary Points” (SP). While δx during the temperature

change phase is ideally zero for these sections, in fact they move through a cycle of

displacement and return to the original position at the end of the expansion or contraction.

Figure 3.8 shows the mentioned behaviour for stationary points during some load phases

(for the EP Stiff Fit) along with a schematic plot of the finite element model to clarify the


40

location of these stationary points. It is important to highlight that there will be one

stationary point per loading phase, which will remain at the same pipeline Kilometre Post

(KP), represented by the model nodes, as long as the conditions (temperature, soil,

geometry, etc.) also remain the same during the operational lifetime.

In the following analysis, Xab is defined as the distance between the stationary points.

This definition is more useful than the distance between the maxima in the effective axial

force profiles because the walking rate per cycle is fundamentally related to the integrated

change in effective axial force in the length of pipe between the stationary points.

3.8 XAB FOR ELASTIC-PERFECTLY-PLASTIC SOIL

The three different values for Xab (Xab,RP, Xab,EP_Stiff and Xab,EP_Soft) are compared to δmob,

in Figure 3.9, which shows the linear dependence of Xab on δmob. Imagining there is a

certain level of mobilisation distance which makes Xab to be equal to zero (and

consequently ceases the walking pattern), represented by δnull, which will be given later

in this paper, the following linear equation might be written:

𝑋𝑎𝑏,𝐸𝑃 = 𝑋𝑎𝑏,𝑅𝑃 (1 −𝛿𝑚𝑜𝑏𝛿𝑛𝑢𝑙𝑙

) (3.7)

This definition of Xab,EP for use in equation (3.4) is now defined for elastic-perfectly-

plastic soils; thus the only element missing is ΔSS,EP to analytically derive the elastic-

perfectly-plastic walking rate.

3.9 ΔSS FOR ELASTIC-PERFECTLY-PLASTIC SOIL

For rigid-plastic soils, ΔSS can be obtained directly from the basic problem parameters

using equation (3.2). For elastic-perfectly-plastic soils, however, ΔSS is not straight

forward, as the effective axial force profile is not triangular. For this reason, the effective

axial force equations need to be redefined by adopting the solution for an elastic column

compressed within an elastic medium, as used in the analysis of piles. This leads to a

second order linear differential equation which represents the displacement, δ, along the

longitudinal axis, x, as shown by equation (3.8) from Randolph (1977).

𝛿 = 𝐾1𝑒𝜉𝑥 + 𝐾2𝑒

−𝜉𝑥 (3.8)

where K1 and K2 are arbitrary constants, and ξ is exponential factor. More detail about

these parameters is given in Appendix A.

Chapter 3

41

However, before solving the differential equation, the boundary conditions among the

different behaviour patterns along the pipe route need to be defined.

Table 3.4 presents the physical boundaries that should be considered for the elastic-

perfectly-plastic effective axial force calculation, which segregates the different zones of

the pipeline. For pipeline zones Z1 and Z4 effective axial force is equivalent to the rigid-

plastic solution with straight line behaviour and constant gradient – equations (3.9) and

(3.10):

Table 3.4: Pipeline zoning.

Zone Initial KP Final KP

Z1 0 x12

Z2 x12 x23

Z3 x23 x34

Z4 x34 L

𝑊(μcos 𝛽 + sin 𝛽) (3.9)

𝑊(μcos 𝛽 − sin 𝛽) (3.10)

In contrast to zones Z1 and Z4, the behaviour of the Z2 and Z3 central zones (in the

vicinity of the highest effective axial force section), creates two different parabolic curves

(within the effective axial force plot), whose gradients vary from 0 to the values given by

equations (3.9) and (3.10).

Figure 3.10 presents a schematic plot accounting the physical boundaries and also the

revised solution for a hypothetic case.

3.9.1 δx Boundary Conditions

Considering the physical boundaries and their outcomes in terms of displacement, δ, it is

clear that displacements at x23 are zero, while at x12 and x34 displacements are equal to

δmob, where the soil resistance is fully mobilised.

3.9.2 Effective Axial Force Boundary Conditions

From Figure 3.10 it is clear that some boundary conditions must be respected when

obtaining the analytical elastic-perfectly-plastic effective axial force response; which are:

• Continuity of slope for the three zone boundaries;


42

• Continuity of effective axial force at the three zone boundaries.

These effective axial force boundary conditions might be rewritten as shown in Table

3.5.

Table 3.5: EAF boundary conditions.

x coordinate EAF 𝑑𝐸𝐴𝐹

𝑑𝑥

0 0 𝑊(μcos 𝛽 + sin 𝛽)

x12 𝑥12[𝑊(μcos 𝛽 + sin 𝛽)] 𝑊(μcos 𝛽 + sin 𝛽)

x23 ? 0

x34 𝑥34[𝑊(μcos 𝛽 − sin 𝛽)] 𝑊(μcos 𝛽 − sin 𝛽)

L 0 𝑊(μcos 𝛽 − sin 𝛽)

The question mark in Table 3.5 might only be answered after the differential equation is

solved and an expression for the effective axial force calculation is reached.

Hence, a general equation was written as follows:

(𝑑𝐹

𝑑𝑥)𝑥=

{

𝜇𝑊𝑍1, 𝛿𝑥 ≤ −𝛿𝑚𝑜𝑏

(𝜇𝑊𝑍1

𝛿𝑚𝑜𝑏) 𝛿𝑥, −𝛿𝑚𝑜𝑏 < 𝛿𝑥 < 0

(𝜇𝑊𝑍4

𝛿𝑚𝑜𝑏) 𝛿𝑥, 0 < 𝛿𝑥 < 𝛿𝑚𝑜𝑏

𝜇𝑊𝑍4, 𝛿𝑥 ≥ 𝛿𝑚𝑜𝑏

(3.11)

where µWZ? represents the soil resistance plus or minus, depending on the zone

considered, the weight component acting on the pipe due to the seabed slope.

3.9.3 Effective Axial Force Pipe Differential Equation

Observing the effective axial force boundary conditions and their implications, the

effective axial force differential equation could be written as:

Chapter 3

43

𝐸𝐴𝐹(𝑥)

=

{

𝜇𝑊𝑍1 ∗ 𝑥, 0 ≤ 𝑥 ≤ 𝑥12

𝐸𝐴𝐹(𝑥12) +√𝐸𝐴𝜇𝑊𝑍1

𝛿𝑚𝑜𝑏[𝐾1(𝑥)(𝑒

𝜉𝑍1𝑠𝑖 − 𝑒𝜉𝑍1𝑠𝑖−1) + 𝐾2(𝑥)(𝑒−𝜉𝑍1𝑠𝑖−1 − 𝑒−𝜉𝑍1𝑠𝑖)] ,

𝑥12 < 𝑥 ≤ 𝑥23




𝑥23 ≤ 𝑥 < 𝑥34𝜇𝑊𝑍4 ∗ (𝐿 − 𝑥), 𝑥34 ≤ 𝑥 ≤ 𝐿

(3.12)

See Appendix A for details on the mathematical development of equation (3.8) towards

equation (3.12).

With equation (3.12) the unknown values in Table 3.5 are derived and the full effective

axial force profiles can be deduced via iteration on the position of x23.

This solution scheme for the effective axial force profile for elastic-perfectly-plastic soils

leads to the last step of the new calculation approach.

3.9.4 ΔSS Revision

ΔSS can be directly described as the summation of areas, as given by equation (3.13), and

as schematically shown by Figure 3.11.

∫ (∆𝑆𝑠)𝑑𝑥𝑆𝑃𝑆𝑈𝑝

𝑆𝑃𝑆𝐷𝑜𝑤𝑛

= −(|𝐴𝑟𝑒𝑎1| + |𝐴𝑟𝑒𝑎2| + |𝐴𝑟𝑒𝑎3| + |𝐴𝑟𝑒𝑎4|) (3.13)

where each area represents the partial integral of effective axial force in terms of x

coordinate accounting the physical boundaries as seen in Figure 3.11.

3.10 WALKING RATE FOR ELASTIC-PERFECTLY-PLASTIC

SOIL

Based on the above expressions, the walking rate for elastic-perfectly-plastic soils can be

derived. Taking into account equation (3.5), the general modifications are:

𝑊𝑅𝐸𝑃 = −1


𝑆𝑃𝑆𝑈𝑝,𝐸𝑃

𝑆𝑃𝑆𝐷𝑜𝑤𝑛,𝐸𝑃

−∫ (∆𝑆𝑠)𝑑𝑥𝑆𝑃𝑆𝑈𝑝,𝐸𝑃

𝑆𝑃𝑆𝐷𝑜𝑤𝑛,𝐸𝑃

) (3.14)

To validate this revised expression for WREP, a parametric finite element analyses study

was conducted.


44

3.11 FINITE ELEMENT ANALYSES PARAMETRIC STUDY

The parametric study used a range of values for the following parameters:

• Pipeline length;

• Pipeline submerged weight;

• Friction factor;

• Route overall slope.

For these core properties three different values were attributed for each, resulting in 81

different combinations. The different values used are shown in Table 3.6.

Table 3.6: FEA parametric variables.

Parameter Value A Value B Value C

Length (m) 3000 4000 5000

Weight (kN/m) 0.4 0.6 0.8

Friction (-) 0.5 0.7 0.9

Slope (°) 1 2 3

Since the focus of this paper is the influence of axial mobilisation distance, eight different

values of δmob were considered, in terms of pipeline steel outside diameter (OD),

(0.03OD, 0.05OD, 0.06OD, 0.10OD, 0.15OD, 0.20OD, 0.33OD and 0.50OD), giving a

total of 648 cases.

All 648 cases were modelled using the same finite element analyses solution. All

respected the general behaviour for the pipeline walking phenomenon as expected

(including the revised solutions).

Figure 3.12 presents the finite element analyses results for Xab,EP plotted against δmob for

the 1° seabed slope while Figure 3.13 compares Xab achieved through finite element

analyses and the equations proposed in this paper. Figure 3.14, Figure 3.15, Figure 3.16

and Figure 3.17 provide the same results for 2° and 3° seabed slopes, respectively.

In Figure 3.13, Figure 3.15 and Figure 3.17 the results were plotted along with a line

representing the equation (3.7) for each case. The finite element analyses results clearly

validate equation (3.7).

At this stage, the results obtained for Xab using the suggested formulation (equation (3.7))

Chapter 3

45

and the finite element analyses’ results were statistically analysed. For the 1° slope, the

coefficient of determination, R2, is equal to 0.986; whilst for 2° and 3°, R2 is equal to

0.997 and 0.998, respectively. It is clear that the proposed methodology has a very strong

accuracy. The authors also looked into the reason for the difference noticed in the 1°

models, and it was found that some finite element models had an accidental limitation in

terms of mesh. This generated a numerical noise that was reflected in the overall results.

The noise can be eliminated through the use of a finer mesh in the models, thus retaining

their applicability to any slope.

Figure 3.18 shows the finite element model results for WREP plotted against δmob for the

1° seabed slope. Figure 3.20 and Figure 3.22 give the same results for 2° and 3° seabed

slopes. Figure 3.19, Figure 3.21 and Figure 3.23 present the comparison between finite

element analyses and equation results.

Again, applying some statistics to the results shown by Figure 3.19, Figure 3.21 and

Figure 3.23, the coefficient of determination, R2, was calculated to be 0.985 (for 1° slope),

0.997 (for 2° slope) and 0.999 (for 3° slope). These results confirm the level of accuracy

of the findings of this paper and reinforce the applicability of the proposed methodology.

As it can be seen, the analytical expressions shown in Sections 3.8, 3.9 and 3.10 agree

closely with the finite element analyses results, as shown by the plots from Figure 3.12

to Figure 3.23.

Hence, for any straight pipeline resting on any sloping seabed with an elastic-perfectly-

plastic soil we can conclude that the realistic walking rate might be written as:

𝑊𝑅𝐸𝑃 = 𝑊𝑅𝑅𝑃 − 𝐶𝑜𝑟𝑟𝐸𝑃 (3.15)

where the elastic correction, CorrEP, is equivalent to:

𝐶𝑜𝑟𝑟𝐸𝑃 = 2(𝐴𝑟𝑒𝑎𝑈𝑛𝑙𝑜𝑎𝑑−𝑅𝑒𝑙𝑜𝑎𝑑

𝛥𝐹) (3.16)

The unload-reload area and the ΔF are exemplified in Figure 3.3. Then, considering the

single-spring elastic-perfectly-plastic approach, the entity elastic correction equals:

𝐶𝑜𝑟𝑟𝐸𝑃 = 2(2𝜇𝑊 cos 𝛽 𝛿𝑚𝑜𝑏2𝜇𝑊 cos 𝛽

) = 2𝛿𝑚𝑜𝑏 (3.17)

Equation (3.17) also allows us to define the non-walking mobilisation distance, δnull, to

be:


46

𝛿𝑛𝑢𝑙𝑙 =𝑊𝑅𝑅𝑃2

(3.18)

3.12 CONCLUSIONS & FINAL REMARKS

This paper provides an analytical solution that solves pipeline walking problems for

elastic-perfectly plastic (EP) pipe-soil response, benchmarked and validated against finite

element analyses performed with an elastic-perfectly-plastic user-defined element. These

revised solutions improve understanding of the parameters involved in elastic-perfectly-

plastic soil behaviour for pipeline walking assessment. The paper resolves how the

fundamental solution for rigid-plastic pipe-soil interaction requires expansion to allow

for elasticity. It is shown that the “Stationary Points”, which have zero movement during

changes in the pipe temperature, do not coincide with the positions of maximum effective

axial force (EAF). This is an important distinction compared to the rigid-plastic solution,

in which the term “Virtual Anchor Point” is well-established as both the Stationary Point

and the position of maximum effective axial force. Using the revised Stationary Points,

the resulting mathematical proof shows the swept area within the effective axial force

plot during a change in temperature remains a valid method to assess the pipeline

expansion and contraction and therefore the pipeline walking. Relative to the rigid-plastic

solution, the correction for elasticity is equivalent to the loss in area represented by the

Unload-Reload Area inherent to the FxD soil curve.

Common solutions for pipeline walking, in which the soil is treated as rigid-plastic,

invariably derive overestimates of walking action. Besides being unrealistic, a magnified

walking rate can be onerous for projects, leading to additional effort and cost to mitigate

pipeline walking.

Therefore, it is important to identify and apply realistic soil properties, and the solution

in this paper allows the elastic-perfectly-plastic rather than rigid-plastic approach to be

used.

The walking mechanism, explored in this paper, can now be assessed by a set of analytical

expressions for walking evaluation, based on the general problem properties, such as,

overall route slope, temperature variation and pipeline geometric data. These expressions

were validated against a finite element analyses set.

Chapter 3

47

FIGURES

Figure 3.1: EAF diagrams for SUp and SDown phases.


48

Figure 3.2: δx diagrams for SUp and SDown phases.

Chapter 3

49

Figure 3.3: Rigid-plastic & elastic-plastic soil responses.

Figure 3.4: Finite element model sketch.


50

Figure 3.5: EAF plot (zoom).

Chapter 3

51

Figure 3.6: δx plot for Stiff Fit (zoom).

Figure 3.7: δx plot for Soft Fit (zoom).


52

Figure 3.8: x coordinate for the stationary points.

Figure 3.9: Xab,EP results against δmob.

Chapter 3

53

Figure 3.10: Schematic plot accounting physical boundaries.

Figure 3.11: Schematic EAF plot with the partial areas highlight.


54

Figure 3.12: Xab,EP results for 1° slope.

Figure 3.13: Xab,EP results – numerical & calculated for 1° slope.

Chapter 3

55




56



Chapter 3

57

Figure 3.18: WREP results for 1° slope.

Figure 3.19: WREP results – numerical & calculated for 1° slope.


58



Chapter 3

59



Non-linear elastic-plastic soils

60

CHAPTER 4. SOLVING DOWNSLOPE PIPELINE

WALKING ON NON-LINEAR ELASTIC-PLASTIC SOILS

Chapter context: This thesis’ chapter presents the research done to generate an improved

analytical solution to properly account for non-linear elastic-plastic soil properties. It

establishes how a non-linear elastic-plastic soil behaviour can be satisfactorily

approximated to an elastic-perfectly-plastic pipe-soil interaction model. It clarifies that

certain levels of mobilization distance might impede the pipeline walking phenomenon

from happening. Finally, it concludes by showing adjustments to the analytical solutions

that improve the results’ accuracy when non-linear elastic-plastic soils are considered.


Castelo, A., White, D. and Tian, Y., in press. Solving downslope pipeline walking on

non-linear elastic-plastic soils. Journal of Marine Structures (submitted to journal)

Chapter 4

61

4.1 ABSTRACT

Over their operational lifetime, offshore pipelines can experience an accumulation of

axial movement, referred to as “pipeline walking”, due to high pressures and

temperatures resulting in asymmetric expansion and contraction. Treating the axial soil

response as elastic-perfectly-plastic, as is conventional in design, does not fully account

for the pipe-soil interaction response observed in physical model tests and can give

inaccurate estimates of walking rate per cycle. In this paper, modifications to the elastic-

perfectly-plastic approach are made to give a new set of formulations involving non-

linear axial pipe-soil interaction, which leads to more accurate walking rate predictions.

It is shown that an equivalent elastic-perfectly-plastic model can be defined from the non-

linear response. This equivalent approach allows existing analytical expressions for

walking rate on elastic-perfectly-plastic soil to be applied, therefore providing an efficient

new design tool. This work is based on a parametric study using finite element analysis,

focused on the case of downslope pipeline walking.

4.2 INTRODUCTION

Offshore pipelines have been increasingly employed as the industry further explores deep

water hydrocarbon reservoirs. The stability of these pipelines is dependent on a number

of factors, including environmental and geotechnical aspects. For example, a pipeline

expands and contracts due to temperature and pressure changes. When the pipeline is on

a seabed slope, these changes become asymmetric, which might lead to net movement in

one direction – a phenomenon known as pipeline walking. This phenomenon increases

cost and risk and may cause severe consequences through the overstressing of

connections, altered loading and strain in any engineered lateral buckles and an increased

need for anchoring (Bruton et al., 2010). Therefore, properly quantifying pipeline

walking is necessary to reduce the risk of a loss of production and damage to the

environment (Tornes et al., 2000). If engineered well, the system can benefit from

significant cost-savings.

Currently, pipeline walking is often estimated during the design phase of offshore

pipelines using analytical formulae. These analyses need to account for various factors,

such as soil behaviour, seabed slope and operational temperature. Providing accurate

estimates for high-pressure and high-temperature operational conditions for downslope

pipelines is particularly relevant to the industry as such conditions are commonly found


62

in major oil and gas regions, including the Gulf of Mexico, West Africa and Northwest

Australia, as well as frontier locations, including the Brazilian Pre-Salt and the Arctic

area. However, current analytical formulae used by the industry are idealised, which can

produce inaccurate walking rates and further analyses are done to account for the known

limitations, such as the assumption of a linear elastic-perfectly-plastic form of pipeline-

seabed interaction.

When the pipeline walking tendency is identified through the analytical formulae, time

demanding and costly finite element analyses are performed to confirm the walking

behaviour and provide a reliable walking rate. However, as demonstrated by Castelo et

al., (2019), if more appropriate soil behaviours are accounted for in the initial analytical

formulae, the industry could avoid unnecessary additional expensive steps.

The formulation identified by Castelo et al., (2019) assume an elastic-perfectly-plastic

soil model, which requires improvement to realistically represent real soil conditions, and

thus generate more accurate pipeline walking rates.

This paper examines the influence on pipeline walking of a non-linear elastic-plastic soil

response, to see the influence of adopting a realistic soil condition. It begins with a

literature review of current methods used for estimating the walking rate for rigid-plastic

and elastic-perfectly-plastic soil behaviour. It then sets out a theoretical framework for

estimating the walking rate for non-linear elastic-plastic soils. Next, finite element

analyses are conducted to confirm this theoretical framework for non-linear elastic-

plastic soil types. Finally, this paper generates a solution that allows the non-linearity to

be captured in an analytical formula, so that the requirement for costly finite element

analysis can be reduced.


4.3.1 Downslope mechanism

For a sloping seabed, the effective axial force plot of a fully mobilised pipeline shows an

asymmetry between the start-up and shutdown phases, as illustrated in Figure 4.1, where

the pipe-soil interaction is considered as rigid-plastic. This asymmetry creates a

separation Xab between the Virtual Anchor Sections (VASs), which for rigid-plastic soils

coincide with the points of maximum absolute effective axial force, as proved by Castelo

et al. (2019). Xab is then related to the net axial displacement, δx, from a cycle of start-up

and shutdown phases as shown by Figure 4.2. The asymmetry in the profile of effective

Chapter 4

63

axial force is currently understood by the industry to be the root cause of pipeline walking,

as it tends to generate unbalanced movements during different loading cycles (start-up

and shutdown phases).

For soil conditions that are not rigid-plastic, Xab is not related to the point of maximum

effective axial force. The separation Xab is exclusively related to the stationary points, as

explained in further detail by Castelo et al. (2019).

4.3.2 Pipe-soil response

While the pipe-soil response has traditionally been treated in pipe walking analyses as

rigid-plastic or elastic-perfectly-plastic, in reality most soils behave non-linearly.

Figure 4.3 shows a typical axial force-displacement response for four different types of

pipe-soil interaction: rigid-plastic, non-linear elastic-plastic and two different elastic-

perfectly-plastic approximations (soft and stiff). The unload-reload area in the figure

represents the area loss in the pipe-soil response between the rigid-plastic and the non-

linear elastic-plastic models. This is explored further in this paper, where a “non-linear

elastic correction” is proposed. This allows the non-linear elastic-plastic response to be

simplified into an equivalent linear elastic-perfectly-plastic response, for use in analytical

solutions of walking rate.


To illustrate the method being proposed in this research, this paper will use two cases.

The first case is for dual-spring strategy and the second is for multi-spring strategy, to

better mimic realistic pipe-soil interactions. In both cases, multiple elastic-perfectly-

plastic pipe-soil responses have been combined to generate the non-linear elastic-plastic

response.

Downslope pipeline walking is dependent on three types of properties: environmental,

operational and those of the pipeline. Our parametric studies use typical parameter ranges

for these three properties; the multi-spring case has slightly more demanding parameters,

to test the rigour of our proposed methodology.

For the dual-spring case, the environmental parameters include seabed slope and friction

coefficient, taken to be 2° and 0.5, respectively in the first examples shown, but with a

wider range used later to generalise the solutions. The operational parameters include

temperature variation and pipe submerged weight, assumed to be 100°C and 0.8kN/m,


64

respectively. The physical pipeline properties include steel outside diameter, steel wall

thickness and length, taken to be 0.3239m, 0.0206m and 5000m, respectively.

The multi-spring case has a steeper slope, assumed to be 3°, lighter pipe submerged

weight of 0.4kN/m and the exact same physical pipeline properties. The full list of

properties and the parameters used in our study are provided in Table 4.1 and Table 4.2.

Table 4.1: Preliminary example properties – Dual-Spring UEL.

Parameter Value



Length, L 5000m




Friction coefficient, μ 0.5




Mobilisation Distance for Spring S1, δmobS1/OD 0.030

Plastic Force for Spring S1, FS1 0.259842kN



Chapter 4

65

Table 4.2: Preliminary example properties – Multi-Spring UEL.

Parameter Value



Length, L 5000m




Friction coefficient, μ 0.5














4.5 ELASTIC-PERFECTLY-PLASTIC SOLUTION FOR

PIPELINE WALKING

From Castelo et al. (2019), it is known that the walking rate for an elastic-perfectly-plastic

pipe-soil response, WREP, can be obtained simply by subtracting twice the mobilisation

distance from the walking rate for a rigid-plastic soil - as shown by equation (4.1):


66

𝑊𝑅𝐸𝑃 = 𝑊𝑅𝑅𝑃 − 2𝛿𝑚𝑜𝑏 (4.1)

where WRRP is the walking rate for rigid-plastic soil, which can be estimated from Carr

et al. (2006). δmob is the mobilisation distance for an elastic-perfectly-plastic pipe-soil

response, as illustrated in Figure 4.3.

As shown in Figure 4.3, the “soft” fit approximation intersects the non-linear elastic-

plastic response at the displacement where the full resistance is mobilised. For the “stiff”

fit approximation, the initial stiffness is matched, leading to a much lower mobilisation

distance.

Table 4.3 provides the calculated walking rate results from using analytical solution (4.1)

and using the mobilisation distance values from the two different fit approximations in

Figure 4.3. This paper has conducted a parametric study using finite element analysis, to

explore the non-linear elastic-plastic pipe-soil interaction response seen in Figure 4.3,

with the goal of building on equation (4.1) to generate a more accurate calculation of the

pipeline walking rate.

Table 4.3: Elastic-perfectly-plastic analytical results.

Parameter Mobilisation Distance Walking Rate

WRRP N/A 0.247m/cycle

WREP,Stiff 9.717x10-3m 0.227m/cycle

WREP,Soft 3.239x10-2m 0.182m/cycle

4.6 FINITE ELEMENT METHODOLOGY

4.6.1 Introduction

The finite element model used in this paper is based on a straight pipeline laid on a

uniformly sloping seabed. The properties of this model are presented in Table 4.1.

The 5000m pipeline was represented by 5001 nodes connected by 5000 equal Euler

Bernoulli beam elements (B33 – 3 dimensional 3 noded elements in Abaqus), creating a

1 metre “mesh” size.

To represent the non-linear elastic-plastic pipe-soil interaction, the soil was modelled as

a set of macro elements connected to each pipeline node, which were described as user

elements in FORTRAN.

Chapter 4

67

4.6.2 Dual-spring pipe-soil interaction model

The user element was modelled with a dual-spring-slider strategy. Each individual spring

had a constant stiffness between zero and a certain prescribed displacement, also called

the mobilisation distance, and a corresponding force (according to Hooke’s law). If the

displacement went beyond the mobilisation distance, the user element provided zero

stiffness and a constant force, as per the plastic plateau. Non-linear elastic-plastic

behaviour was modelled by adding the two spring-sliders. The user element

representation is shown in Figure 4.4 for the dual-spring pipe-soil interaction model.

4.6.3 Multi-spring pipe-soil interaction model

The user element was modelled as a multiple spring-slider consisting of five springs. This

allowed the modelling of a higher degree of non-linearity as shown in Figure 4.5, and

latter validation of the methodology proposed by this paper to higher degrees of non-

linearity within the elastic-plastic soils range.

4.6.4 Loads

In the analysis, the pipeline was heated up uniformly with a temperature increase of

100°C. This value includes an additional temperature amount that represents the pipe

internal pressure (Hobbs, 1984).

The self-weight of the pipeline, W, and slope angle, β, generate a sliding component to

the weight:


Operational cycling took into account the steady operational profile (start-up) and the rest

condition (shutdown).

4.7 FINITE ELEMENT ANALYSIS RESULTS AND

COMPARISON WITH ELASTIC-PERFECTLY-PLASTIC

SOLUTION

Figure 4.6 and Figure 4.7 present the effective axial force and the axial displacement

distribution, respectively, using the dual-spring strategy. Figure 4.8 shows the dual-spring

stationary points’ behaviour for various loading cycles.

Figure 4.9 and Figure 4.10 present the effective axial force and the axial displacement

distribution, respectively, using the multi-spring strategy. Figure 4.11 shows the multi-


68

spring stationary points’ behaviour for various loading cycles.

As can be seen in Figure 4.8 and Figure 4.11, a “stationary” point has no net displacement

through the sequence of thermal cycles but it is not motionless within the cycles (Castelo

et al., 2019).

The two new finite element strategies (dual- and multi-spring) gave different results for

the distance between stationary points when compared to the elastic-perfectly-plastic

solution used in Castelo et al. (2019). This is explained by the fact that the non-linear soil

model is more realistic and accounts for the partial mobilisations in the soil non-linear

spring, instead of using an approximation (“stiff” and “soft” fits) of the soil behaviour.

The results for the four elastic-plastic soil resistance cases are provided in Table 4.4.

Table 4.4: Elastic-perfectly-plastic general results.

Parameter Source Value

Xab,EP,Stiff Equation (4.14) and Castelo et al. (2019) 321m

Xab,EP,Soft Equation (4.14) and Castelo et al. (2019) 258m

Xab,NLEP,DUAL Figure 4.7 290m

Xab,NLEP,MULTI Figure 4.10 380m

To estimate the realistic results for distance between stationary points, a new analytical

solution is now outlined for the non-linear elastic-plastic pipe-soil response.

4.8 NEW ANALYTICAL SOLUTIONS FOR NON-LINEAR

ELASTIC-PLASTIC SOIL

To devise the revised solution for the walking rate with a non-linear elastic-plastic pipe-

soil interaction response, it is first necessary to develop a new definition for the position

of the stationary points, as well as the effective axial force profile, extending those given

by Carr et al. (2006) for rigid plastic pipe-soil interaction. This same process was

followed for elastic-perfectly-plastic soils (Castelo et al., 2019).

4.8.1 Displacement profile

Where the pipe-soil response is fully mobilised, the effective axial force profile is linear,

and the pipe displacement, δ, varies with the pipe’s position, x. In the zone where the

pipe-soil response is within the non-linear elastic range, a second order linear differential

Chapter 4

69

equation represents the displacement, δ, along the pipeline axis, as shown by equation

(4.3) from Randolph (1977).

𝛿 = 𝐾1𝑒𝜉𝑥 + 𝐾2𝑒

−𝜉𝑥 (4.3)

where K1 and K2 are arbitrary constants, and ξ is the exponential factor.

4.8.2 Displacement boundary conditions

Boundary conditions between sections of the pipeline’s length with different behaviours

were used to define the arbitrary constants in equation (4.3). To simplify this task, only

the non-linear dual-spring strategy was considered in this section.

The displacements’ boundaries are listed in Table 4.5, and illustrated in Figure 4.12,

where the boundaries of these different zones are highlighted for a dual-spring

hypothetical case. Figure 4.12 also provides a schematic plot of the resulting effective

axial force.

Table 4.5: Pipeline zoning.

Zone Initial KP Final KP

Z1 0 x12

Z2 x12 x23

Z3 x23 x34

Z4 x34 x45

Z5 x45 x56

Z6 x56 L

As was done for elastic-perfectly-plastic soils (Castelo et al., 2019), at this stage the

displacements at x34 were considered as nil. At x12 and x56 the displacements are equal to

the mobilisation distance for spring number 2, δmobS2, where the soil starts to behave as

“fully mobilised”. At x23 and x45 the displacements are equal to the mobilisation distance

for spring number 1, δmobS1. However, given the displacement dependency on the total

strain – mechanical plus thermal strains – the displacements need to be confirmed by the

effective axial force calculations, as follows.

4.8.3 Effective axial force boundary conditions

For a dual-spring soil, the pipeline is divided into 6 different zones, Z1 to Z6, and their


70

boundaries are provided in Table 4.5.

Zones Z1 and Z6, where the soil response is fully mobilised, are equivalent to the rigid

plastic solution with straight line behaviour and constant slopes – equations (4.4) and

(4.5):

(𝑑𝐹

𝑑𝑥)𝑍1= 𝑊(μcos 𝛽 + sin 𝛽) (4.4)

(𝑑𝐹

𝑑𝑥)𝑍6= 𝑊(μcos 𝛽 − sin 𝛽)

(4.5)

where W stands for the pipeline operational submerged weight, β for the seabed slope, μ

for the seabed friction coefficient and dF/dx for the force derivative in terms of the x

coordinate.

Zones Z2, Z3, Z4, and Z5 are the central zones. Their behaviour creates four different

parabolic curves, whose slopes vary from zero up to the values given by equations (4.4)

and (4.5).

As for Castelo et al. (2019) and as shown by Figure 4.12, the continuity of slope and

value around the five physical boundaries must be maintained. When these effective axial

force limiting conditions are rewritten, to better align with the prescriptions of the

displacement boundary conditions, the following general equations are generated for each

of the zones:

(𝑑𝐹

𝑑𝑥)𝑍1= [

𝐹𝑆1𝐹𝑇𝑜𝑡𝑎𝑙

] [−𝑊(𝜇 𝑐𝑜𝑠 𝛽 − 𝑠𝑖𝑛 𝛽)]

+ [𝐹𝑆2𝐹𝑇𝑜𝑡𝑎𝑙

] [−𝑊(𝜇 𝑐𝑜𝑠 𝛽 − 𝑠𝑖𝑛 𝛽)], 𝛿𝑥 ≤ −(𝛿𝑚𝑜𝑏𝑆2)

(𝑑𝐹

𝑑𝑥)𝑍2= [


] [−𝑊(𝜇 𝑐𝑜𝑠 𝛽 − 𝑠𝑖𝑛 𝛽)]

− [𝐹𝑆2𝐹𝑇𝑜𝑡𝑎𝑙

] [𝛿𝑥

(𝛿𝑚𝑜𝑏𝑆2)] [−𝑊(𝜇 𝑐𝑜𝑠 𝛽 − 𝑠𝑖𝑛 𝛽)],

−(𝛿𝑚𝑜𝑏𝑆2) < 𝛿𝑥 ≤ −(𝛿𝑚𝑜𝑏𝑆1)

(𝑑𝐹

𝑑𝑥)𝑍3= −[


] [𝛿𝑥

(𝛿𝑚𝑜𝑏𝑆1)] [−𝑊(𝜇 𝑐𝑜𝑠 𝛽 − 𝑠𝑖𝑛 𝛽)]

− [𝐹𝑆2𝐹𝑇𝑜𝑡𝑎𝑙

] [𝛿𝑥

(𝛿𝑚𝑜𝑏𝑆2)] [−𝑊(𝜇 𝑐𝑜𝑠 𝛽 − 𝑠𝑖𝑛 𝛽)],

−(𝛿𝑚𝑜𝑏𝑆1) < 𝛿𝑥 < 0

(4.6)

Chapter 4

71

(𝑑𝐹

𝑑𝑥)𝑍4= [


] [𝛿𝑥

(𝛿𝑚𝑜𝑏𝑆1)] [𝑊(𝜇 𝑐𝑜𝑠 𝛽 + 𝑠𝑖𝑛 𝛽)]


] [𝛿𝑥

(𝛿𝑚𝑜𝑏𝑆2)] [𝑊(𝜇 𝑐𝑜𝑠 𝛽 + 𝑠𝑖𝑛 𝛽)],

0 ≤ 𝛿𝑥 < (𝛿𝑚𝑜𝑏𝑆1)

(𝑑𝐹

𝑑𝑥)𝑍5= [


] [𝑊(𝜇 𝑐𝑜𝑠 𝛽 + 𝑠𝑖𝑛 𝛽)]


] [𝛿𝑥

(𝛿𝑚𝑜𝑏𝑆2)] [𝑊(𝜇 𝑐𝑜𝑠 𝛽 + 𝑠𝑖𝑛 𝛽)],

(𝛿𝑚𝑜𝑏𝑆1) ≤ 𝛿𝑥 < (𝛿𝑚𝑜𝑏𝑆2)

(𝑑𝐹

𝑑𝑥)𝑍6= [


] [𝑊(𝜇 𝑐𝑜𝑠 𝛽 + 𝑠𝑖𝑛 𝛽)] + [𝐹𝑆2𝐹𝑇𝑜𝑡𝑎𝑙

] [𝑊(𝜇 𝑐𝑜𝑠 𝛽 + 𝑠𝑖𝑛 𝛽)],

𝛿𝑥 ≥ (𝛿𝑚𝑜𝑏𝑆2)

4.8.4 Effective axial force profile

As with Castelo et al. (2019), the differential equation solution – equation (4.3) – was

applied to model the non-linear elastic-plastic soil behaviour. Two different sets of

calculations were performed with each set related to one of the two partial springs, as

suggested by the proportional ratios from equation (4.6). The results from each

calculation set were then overlapped. This procedure could be extended to as many partial

springs as necessary.

Equations from Castelo et al. (2019) are included below for completeness:

𝐸𝐴𝐹(𝑥)

=

{

−𝑊(𝜇 cos 𝛽 − sin 𝛽) ∗ 𝑥, 0 ≤ 𝑥 ≤ 𝑥12




𝑥12 < 𝑥 ≤ 𝑥23




𝑥23 ≤ 𝑥 < 𝑥34𝑊(𝜇 cos 𝛽 + sin 𝛽) ∗ (𝐿 − 𝑥), 𝑥34 ≤ 𝑥 ≤ 𝐿

(4.7)

Where zones Z1 and Z4 have direct solutions; and zones Z2 and Z3 are calculated using

the exponential equation. The properties ξ, K1 and K2 are presented by equations (4.8),

(4.9) and (4.10):


72

𝜉𝑍_ =

{

𝑍1,√(

𝜇𝑊𝑍1

𝐸𝐴𝑠 ∗ 𝛿𝑚𝑜𝑏)

𝑍4,√(𝜇𝑊𝑍4

𝐸𝐴𝑠 ∗ 𝛿𝑚𝑜𝑏)

(4.8)

𝐾1𝑍_ =

{

𝑍1,

1

2√𝐸𝐴𝑠 ∗ 𝛿𝑚𝑜𝑏𝜇𝑊𝑍1

휀𝑇𝑜𝑡𝑎𝑙

𝑍4,1



(4.9)

𝐾2𝑍_ =

{

𝑍1,−

1



𝑍4, −1



(4.10)

The six zones shown in equation (4.6) represent the intersection of four partial zones as

follows:

𝑍1𝐷𝑢𝑎𝑙𝑆𝑝𝑟𝑖𝑛𝑔 = 𝑍1𝑆1 + 𝑍1𝑆2






(4.11)

Now, with the effective axial force profile defined, the effective axial force variation over

the distance between stationary points, or ΔSS can be described as the summation of areas,

as given by equation (4.12), and shown in Figure 4.13.

∫ (∆𝑆𝑠)𝑑𝑥𝑆𝑃𝑆𝑈𝑝

𝑆𝑃𝑆𝐷𝑜𝑤𝑛

= −(∑|𝐴𝑟𝑒𝑎𝑖|

6

𝑖=1

) (4.12)

where each area represents the partial integral of the effective axial force in terms of the

x coordinate which takes into account the physical boundaries.

4.8.5 Analytical solution for walking rate

Similar to the revised solution for the walking rate for elastic-perfectly-plastic soils,

Chapter 4

73

WREP, in Castelo et al. (2019), the walking rate for non-linear elastic-plastic soils,

WRNLEP, can be revised to:

𝑊𝑅𝑁𝐿𝐸𝑃 = −1


𝑆𝑃𝑆𝑈𝑝,𝑁𝐿𝐸𝑃

𝑆𝑃𝑆𝐷𝑜𝑤𝑛,𝑁𝐿𝐸𝑃

−∫ (∆𝑆𝑠)𝑑𝑥𝑆𝑃𝑆𝑈𝑝,𝑁𝐿𝐸𝑃

𝑆𝑃𝑆𝐷𝑜𝑤𝑛,𝑁𝐿𝐸𝑃

) (4.13)

where ΔP stands for the change in fully constrained force (Carr et al., 2003).

While the form of the expressions are similar for non-linear elastic-plastic and elastic-

perfectly-plastic soils, the integral limits and ΔSS expression are different, which explains

the difference and leads to more accurate results.

4.9 REVISED SOLUTION FOR THE DISTANCE BETWEEN

STATIONARY POINTS FOR NON-LINEAR ELASTIC-PLASTIC

SOIL - XAB,NLEP

As an alternative to the demanding analytical method described by section 4.8, a revised

solution may be directly obtained. From Castelo et al. (2019) where the soil is treated as

a single elastic-perfectly-plastic spring, it is known that:

𝑋𝑎𝑏,𝐸𝑃 = 𝑋𝑎𝑏,𝑅𝑃 (1 −𝛿𝑚𝑜𝑏𝛿𝑛𝑢𝑙𝑙

) (4.14)

where δnull is the non-walking mobilisation distance, as per Castelo et al. (2019), and can

be obtained by:


(4.15)

However, in this paper, the soil is treated as the combination of two or more elastic-plastic

springs. Under these conditions, equation (4.14) becomes:

𝑋𝑎𝑏,𝑁𝐿𝐸𝑃 = 𝑋𝑎𝑏,𝑅𝑃 (1 −𝛿𝑚𝑜𝑏𝐸𝑄𝛿𝑛𝑢𝑙𝑙

) (4.16)

where δmob is substituted with an equivalent mobilisation distance, δmobEQ.

4.10 REVISED SOLUTION FOR WALKING RATE FOR NON-

LINEAR ELASTIC-PLASTIC SOIL – WRNLEP

Replicating the Xab solutions, from Section 4.9, the non-linear elastic-plastic walking rate


74

can be obtained from:

𝑊𝑅𝑁𝐿𝐸𝑃 = 𝑊𝑅𝑅𝑃 (1 −𝛿𝑚𝑜𝑏𝐸𝑄𝛿𝑛𝑢𝑙𝑙

) (4.17)

where δnull is the non-walking mobilisation distance, given in equation (4.15).

Equation (4.17) might be rearranged into:

𝑊𝑅𝑁𝐿𝐸𝑃 = 𝑊𝑅𝑅𝑃 − 2𝛿𝑚𝑜𝑏𝐸𝑄 (4.18)

which is an analogous solution to the solution given by Castelo et al. (2019), shown here

as equation (4.1).

4.11 EQUIVALENT MOBILISATION DISTANCE – δmobEQ

The elastic correction can be obtained by doubling the division of the unload-reload area,

AUnload-Reload, by the variation of the plastic force. These properties are shown in Figure

4.3 and the referred ratio can be calculated using equation (4.19):

𝐶𝑜𝑟𝑟𝐸𝑃 = 2( 𝐴𝑈𝑛𝑙𝑜𝑎𝑑−𝑅𝑒𝑙𝑜𝑎𝑑

𝛥𝐹𝑅) (4.19)

Following the same principles, the equivalent mobilisation distance can be acquired with

a similar procedure, as defined by equation (4.20):

𝛿𝑚𝑜𝑏𝐸𝑄 =𝐶𝑜𝑟𝑟𝑁𝐿𝐸𝑃

2= (

𝐴𝑈𝑛𝑙𝑜𝑎𝑑−𝑅𝑒𝑙𝑜𝑎𝑑𝛥𝐹𝑅

) (4.20)


FOR DUAL-SPRING STRATEGY

The following parametric study validates the above solutions for effective axial force and

stationary points’ locations as well as walking rate for a non-linear elastic-plastic soil

using a dual-spring strategy.

The parametric study uses the values provided in Table 4.1 and previously explained in

Section 4.4 but varies the seabed slope. For simplicity, the pipeline length, pipeline

submerged operational weight and friction coefficient were kept constant, although the

shape of the non-linear response up to the limiting friction was varied. Three different

slopes (1°, 2° and 3°) were used.

Chapter 4

75

Two dual-spring parameters, δmobS1 and δmobS2, were tested in various combinations as

shown in Figure 4.14. For this paper, δmobS2 equals δmob,Soft from Castelo et al. (2019). The

elastic-perfectly-plastic soil approximations “soft” and “stiff” were used as boundary

values as shown in Figure 4.14. The region bounded by these approximations was divided

in four quadrants for displacement and four quadrants for force.

To generate the cases to be considered for the parametric study, the intersection points

were defined as the mobilisation distance, δmob, combinations. A total of six different

δmobS1 and δmobS2 pairs were used in this paper as shown in Table 4.6. Three pairs presented

in Figure 4.14 (25100, 50100, and 75100) were disregarded as they represented an elastic-

perfectly-plastic soil approach, which is not the focus of this paper.

Table 4.6: Mobilisation distance, δmob, combination cases.

Force Mobilisation Distance

Stiff “25%” “50%” “75%”

“25%” I25 SOFT FIT Not Applicable Not Applicable

“50%” I50 2550 SOFT FIT Not Applicable

“75%” I75 2575 5075 SOFT FIT

“100%” STIFF FIT 25100 50100 75100

The six different mobilisation distance, δmob, combinations, three different slopes and the

five different levels of δmobS2 allowed 90 cases to be tested in the parametric experiment.

The 90 cases were modelled using the dual-spring FEM solution.

4.12.1 Equivalent mobilisation distance – δmobEQ

Table 4.7 presents the equivalent mobilisation distance, δmobEQ, for each of the parametric

cases tested according to equation (4.20) and shown in Table 4.7. The repeated values

observed in Table 4.7 are a mathematical coincidence resulting from the values selected

for the cases.


76

Table 4.7: Resultant equivalent mobilisation distance, δmobEQ.

Slope δmobS2/OD Cases

I25 (m) I50 (m) I75 (m) 2550 (m) 2575 (m) 5075 (m)

1°

0.100 0.027 0.021 0.015 0.027 0.021 0.027

0.150 0.040 0.032 0.023 0.040 0.032 0.040

0.200 0.053 0.042 0.031 0.053 0.042 0.053

0.333 0.089* 0.070* 0.051 0.089* 0.070* 0.089*

0.500 0.134* 0.105* 0.077* 0.134* 0.105* 0.134*

2°

0.100 0.027 0.021 0.015 0.027 0.021 0.027

0.150 0.040 0.032 0.023 0.040 0.032 0.040

0.200 0.053 0.042 0.031 0.053 0.042 0.053

0.333 0.089 0.070 0.051 0.089 0.070 0.089

0.500 0.134* 0.105 0.077 0.134* 0.105 0.134*

3°

0.100 0.027 0.021 0.015 0.027 0.021 0.027

0.150 0.040 0.032 0.023 0.040 0.032 0.040

0.200 0.053 0.042 0.031 0.053 0.042 0.053

0.333 0.089 0.070 0.051 0.089 0.070 0.089

0.500 0.134 0.105 0.077 0.134 0.105 0.134

Figure 4.15 presents the non-linear elastic correction results from the numerical solutions

(finite element models) plotted against the values calculated using equation (4.19). The

slopes of 1°, 2° and 3° are represented by square, circular and triangular markers,

respectively.

Figure 4.15 shows a very strong agreement between the non-linear elastic correction

obtained from the finite element analysis and the results calculated using the equation

proposed by this paper.

For Figure 4.15, 14 cases were disregarded from the 90 cases tested as the pipeline

* Values of equivalent mobilisation distance that are greater than the non-walking mobilisation distance, as

per Table 4.8 values (δmobEQ>δnull).

Chapter 4

77

walking would cease after a few loading cycles, if not immediately. These 14 cases had

an equivalent mobilisation distance greater than non-walking mobilisation distance, δnull,

as indicated in Table 4.7. The equivalent mobilisation distance, δmobEQ, values are

presented in Table 4.7 and non-walking mobilisation distance, δnull, values are given in

Table 4.8.

Table 4.8: Resultant non-walking mobilisation distance, δnull.

Slope Non-Walking Mobilisation Distance (m)

1° 0.060

2° 0.124

3° 0.190

Closer inspection of the walking rate from the finite element models, WRFEM, for four of

these 14 cases shows that the walking rate is zero after the first loading cycle, suggesting

that the non-linearity of the soil spring resisted the walking phenomenon. In the

remaining 10 cases, walking ceased after approximately four load cycles, as shown in

Figure 4.16.

Therefore, it can be concluded that once the equivalent mobilisation distance, δmobEQ,

reaches the non-walking mobilisation distance, δnull, the soil non-linearity will cause the

pipeline walking to cease.

4.12.2 Distance between stationary points for non-linear elastic-plastic soil

– Xab,NLEP

As equation (4.20) is applicable to finding the equivalent mobilisation distance, this

suggests that equation (4.16) is applicable to finding the distance between the stationary

points. To confirm this, the finite element model outputs were compared with the

calculated values from equation (4.16).

Figure 4.17 presents the finite element model results for 1°, 2° and 3° slopes with distance

between stationary points for non-linear elastic-plastic soil, Xab,NLEP, plotted against the

values obtained from equation (4.13). It is important to keep in mind that the 14 cases

highlighted in the previous section were disregarded at this stage, as they have a non-

walking pattern as illustrated by Figure 4.16.


78

4.12.3 Walking rate for non-linear elastic-plastic soil – WRNLEP

Figure 4.18 presents the walking rate results for the 1°, 2° and 3° slopes – shown in

square, circular and triangular markers for equation (4.13); and cross, plus and minus sign

markers for equation (4.17), respectively.

Overall, the results show that equation (4.17) gives a true representation of the effects of

non-linear elastic-plastic soil springs on pipeline walking.

4.13 FINITE ELEMENT ANALYSIS FOR MULTI-SPRING

STRATEGY

In this section, the work is extended to a multi-spring case to validate the equivalent

mobilisation distance rules, as initially drawn with equation (4.20). The multi-spring case

followed the properties stated by Table 4.2. In addition, this case serves as an example

for future industry and academic applications.

4.13.1 Rigid-plastic preliminary calculations

From the rigid-plastic approach, two properties can be obtained (Carr et al., 2006):

𝑊𝑅𝑅𝑃 = 0.495m/cycle (4.21)

𝑋𝑎𝑏,𝑅𝑃 = 524m (4.22)

4.13.2 Non-linear elastic-plastic calculations

Equivalent mobilisation distance – δmobEQ

Equation (4.20) was applied to the multi-spring case, as shown in Figure 4.3. Using the

values from Table 4.2, equation (4.20) gives the following value:

𝛿𝑚𝑜𝑏𝐸𝑄 = 0.067m (4.23)

Resulting in:

𝐶𝑜𝑟𝑟𝑁𝐿𝐸𝑃 = 2𝛿𝑚𝑜𝑏𝐸𝑄 = 0.134m (4.24)

Distance between stationary points for non-linear elastic-plastic soil – Xab,NLEP

Equation (4.16) was used to obtain Xab,NLEP:

𝑋𝑎𝑏,𝑁𝐿𝐸𝑃 = 524 (1 −0.067

0.248) = 382m (4.25)

Chapter 4

79

Walking rate for non-linear elastic-plastic soil – WRNLEP

Equation (4.18) was used to calculate WRNLEP:

𝑊𝑅𝑁𝐿𝐸𝑃 = 0.495 − 0.134 = 0.361m/cycle (4.26)

4.13.3 Non-linear elastic-plastic finite element model results

Distance between stationary points from finite element analysis – Xab,FEM

From the finite element analysis, the obtained Xab value was:

𝑋𝑎𝑏𝐹𝐸𝑀 = 380m (4.27)

Walking rate from finite element analysis – WRFEM

From the finite element model, the obtained walking rate value was:

𝑊𝑅𝐹𝐸𝑀 = 0.359m/cycle (4.28)

Overall, the outcome for the finite element model multi-spring strategy shows a very

good agreement with the proposed analytical methods and demonstrates that they can be

used for modelling more complex forms of non-linearity of elastic-plastic soils, resulting

in a very small deviation.


This paper provides a new strategy to solve downslope pipeline walking problems

considering non-linear elastic-plastic soil representations. Different shapes and properties

of non-linearity (within the elastic-plastic range) have been considered leading to an

innovative analytical solution. This new solution improves understanding of the main

properties involved in the non-linear elastic-plastic soil behaviour by providing a set of

analytical expressions for pipe walking, which were benchmarked and validated against

a set of finite element analyses.

Current solutions do not consider the non-linearity of soil response, and this idealisation

is known to affect the resulting walking pattern. It is also difficult to specify a suitable

elastic stiffness when the soil response observed in model tests is strongly non-linear.

Therefore, this paper resolves how the fundamental solution must be adjusted to allow

for non-linear elastic-plastic soils.

Finally, the paper presents how the non-linear elastic-plastic problem might be translated

into an elastic-perfectly-plastic soil spring by using the equivalent mobilisation distance,


80

δmobEQ. This very simple and direct solution provides an accurate estimate of the walking

rate of offshore pipelines in a non-linear soil and avoids numerical modelling which can

be time- and resource-consuming.

Chapter 4

81

FIGURES

Figure 4.1: Effective axial force diagrams for start-up and shutdown phases.


82

Figure 4.2: Axial displacement diagrams for start-up and shutdown phases.

Chapter 4

83

Figure 4.3: Rigid-plastic, elastic-perfectly-plastic and non-linear elastic-plastic soil

responses.

Figure 4.4: Dual-spring finite element analysis methodology (as per values from

Table 4.1).


84

Figure 4.5: Multi-spring finite element analysis methodology (as per values from

Table 4.2).

Chapter 4

85

Figure 4.6: Effective axial force for non-linear elastic-plastic soil – dual-spring

(zoom).


86

Figure 4.7: Axial displacement for non-linear elastic-plastic soil – dual-spring

(zoom).

Figure 4.8: x coordinate for the stationary points – dual-spring.

Chapter 4

87

Figure 4.9: Effective axial force for non-linear elastic-plastic soil – multi-spring

(zoom).


88

Figure 4.10: Axial displacement for non-linear elastic-plastic soil – multi-spring

(zoom).

Figure 4.11: x coordinate for the stationary points – multi-spring.

Chapter 4

89




90

Figure 4.14: Mobilisation distance, δmob, combination spectrum.

Figure 4.15: Non-linear elastic correction results.

Chapter 4

91

Figure 4.16: Walking rate from finite element models, WRFEM, results for selected

cases.

Figure 4.17: Distance between stationary points results.


92

Figure 4.18: Walking rate results.

Chapter 5

93

CHAPTER 5. SOLUTIONS FOR DOWNSLOPE PIPELINE

WALKING ON PEAKY TRI-LINEAR SOILS

Chapter context: In this chapter, it is presented the research done to prove that

adjustments (similar to Chapters 3 and 4) are applicable to tri-linear with a peak pipe-soil

interaction behaviour. It also covers why such peaks can be ignored – due to marginal

and negligible impact to final results – for downslope pipeline walking assessments.


Castelo, A., White, D. and Tian, Y., in press. Solutions for downslope pipeline walking

on peaky tri-linear soils. Journal of Offshore Mechanics and Arctic Engineering

(approved for publication)

Tri-linear soils with a peak

94

5.1 ABSTRACT

Offshore pipelines used for transporting hydrocarbons are cyclically loaded by great

variations of pressure and temperature. These variations can induce axial instability in

such pipelines. This instability may cause the pipelines to migrate globally along their

length; an effect known as pipeline walking. Traditional models of pipeline walking have

considered the axial soil response as rigid-plastic; however, such behaviour does not

match observations from physical soil tests. It leads to poor estimates of walking rate per

cycle and over design. In this paper, the impact of a tri-linear (3L) soil idealization

accounting for a peak break-out behaviour on pipeline walking is investigated. Different

shapes and properties of tri-linearity (within the peaky soil range) have been considered

leading to an innovative analytical solution. The new solution improves understanding of

the main properties involved in the peaky tri-linear soil behaviour by providing a set of

analytical expressions for pipe walking, which were benchmarked and validated against

a set of finite element analyses.

5.2 INTRODUCTION

As the hydrocarbon industry increasingly explores deep water reservoirs, offshore

pipelines become progressively important. When these pipelines are exposed to

operational load cycles, they expand and contract in response to temperature and pressure

changes. However, these expansion and contraction cycles may have an asymmetric

behaviour due to seabed slopes or other factors, such as multiphasic flow (Bruton et al.,

2010), and thermal transients (Carr et al., 2006). The asymmetric expansion and

contraction directly impacts the stability of these pipelines causing them to migrate in

one direction, which generates the phenomenon known as pipeline walking (Carr et al.,

2003). Pipeline walking increases cost and risk and may severely impact the subsea

system (Tornes et al., 2000). It may overstress connections, alter loads and strains in any

engineered lateral buckle and may also present the need for anchoring. Hence, accurately

identifying and estimating pipeline walking is necessary to decrease the risk of

production loss and environmental damage, and it can significantly decrease project

development costs.

Presently, the common practice in the industry is to evaluate pipeline walking during the

design phase using a set of analytical formulations as per Bruton et al. (2010). These

calculations consider various aspects, such as operational (temperature, pressure, etc.),

Chapter 5

95

environmental (seabed overall slope angle, soil friction coefficient, etc.) and physical

pipeline properties (length, steel wall thickness, etc.). Accurately evaluating high-

temperature and high-pressure pipelines for downslope pipeline walking is of paramount

importance to the industry because these conditions are commonly found in fully

operational areas, such as the Gulf of Mexico, North Sea and Northwest Australia, as well

as in frontier locations, which are still in early stages of exploration, such as the Brazilian

Pre-Salt and the Arctic Region. The analytical formulation is idealised and can provide

inaccurate walking rates. Then, the assessment requires further analyses to overcome the

aforementioned limitations.

Costly and time-demanding finite element analyses are used to confirm walking

behaviour and to generate a reliable walking rate. However, emerging academic research

(Castelo et al., 2019, in press b) demonstrates that, if the adequate soil behaviour is

considered in the initial analytical formulae, the requirement for time demanding and

expensive analyses can be reduced.

Although the formulation developed by Castelo et al. (2019, in press b) generate

significant cost-savings and improve efficiency, they are limited to a single soil range,

i.e. elastic-plastic (elastic-perfectly-plastic and non-linear elastic-plastic, respectively).

Therefore, further improvement is needed to capture the walking behaviour with soils

that develop a peak breakout resistance before reaching a plastic plateau, as commonly

seen in the operational areas mentioned above, and thus the accuracy of pipeline walking

results for analytical formulae is increased.

This paper investigates the impact on pipeline walking of a tri-linear soil idealization

accounting for a peak break-out behaviour. It starts by a brief literature review of the

present methodology used to estimate the walking rate for elastic-plastic soils (Castelo et

al., 2019, in press b). It then builds on the previous knowledge to generate theoretical

expressions for pipeline walking on peaky tri-linear soils. Next, finite element analyses

are performed to provide confirmation of the theoretical framework. Finally, this paper

generates a solution that allows an adjustment for the original rigid-plastic analytical

formulation (Bruton et al., 2010), so that the requirement for finite element analyses can

be reduced.


96


5.3.1 Downslope mechanism

The seabed slope generates an asymmetry between the start-up and shutdown phases in

the effective axial force profile for a fully mobilised pipeline, as illustrated in Figure 5.1,

where the rigid-plastic soil condition is considered. This asymmetry causes the virtual

anchor sections to be separated by a given distance, Xab. For rigid-plastic soil

representations, the virtual anchor sections correspond to the maximum absolute effective

axial force along the pipeline length. Then, the distance Xab can be associated to the axial

displacement, δx, from a particular load phase (start-up and shutdown phases), as

presented by Figure 5.2. Because it tends to create unbalanced displacements during

different loading stages, the asymmetry in the effective axial force profile is presently

understood to be the root cause of pipeline walking.

Accounting for more realistic soil conditions, the distance Xab cannot be associated with

maximum effective axial force. Therefore, Xab must be associated with the stationary

points, as thoroughly explained in Castelo et al. (2019).

5.3.2 Pipe-soil response

Previous research on pipeline walking has treated soils as rigid-plastic (Carr et al., 2003;

2006; Bruton et al., 2010) or as elastic-plastic (Castelo et al., 2019, in press b). However,

it is known that some soils behave differently, producing first a breakout peak resistance

and then decreasing their resistance to a residual plastic level.

Although many other studies, such as White et al. (2011), have already investigated

peaky soils in general terms, none has gone through the specific impact of these soils on

pipeline walking. This paper focuses on a soil representation that accounts for breakout

soil resistance using a peaky tri-linear (3L) soil representation and how pipeline walking

may change due to this different soil condition.


Downslope pipeline walking is dependent on three types of properties: environmental,

operational and those of the pipeline. This paper’s parametric study uses typical

parameter ranges for these three properties.

The environmental parameters include seabed slope angle and residual friction

coefficient, taken to be 2ᵒ and 0.25, respectively. The operational parameters include

Chapter 5

97

temperature variation and pipe submerged weight, assumed to be 100°C and 0.4kN/m,

respectively. The physical pipeline properties include steel outside diameter, steel wall

thickness and length, taken to be 0.3239m, 0.0206m and 5000m, respectively. Some

additional environmental properties were taken as variables for the parametric study, and

they are related to the pipe-soil response (cases i - iv). The full list of properties and

parameters used in this study are provided in Table 5.1 and Table 5.2.

Table 5.1: General properties.

Parameter Value

Steel outside diameter, OD 0.3239m

Steel wall thickness, t 0.0206m

Length, L 5000m

Seabed slope angle, β 2.0°

Temperature variation, ΔT 100°C

Pipe submerged weight, W 0.4kN/m

Residual friction coefficient, μ 0.25

Steel Young's modulus, E 2.07x1011Pa

Steel Poisson coefficient, ν 0.3

Steel thermal expansion coefficient, α 1.165x10-5°C-1

Table 5.2: Case properties.

Property Cases

i ii iii iv

Peak Elastic Force, FP (kN) 0.200 0.400 0.300 0.250

Peak Elastic Force Mobilisation distance,

δmobP (m) 0.129 0.129 0.129 0.129

Residual Plastic Force, FR (kN) 0.100 0.100 0.100 0.100

Residual Plastic Force Mobilisation distance,

δmobR (m) 0.162 0.162 0.162 0.162

Ideal Mobilisation distance, δmob’ (m) 0.065 0.032 0.043 0.052


98

Figure 5.3 presents a schematic axial force-displacement response for an ideal set of

peaky tri-linear soil cases. As investigated in White et al. (2011), it is known that various

aspects affect the cyclic behaviour of peaky soils. These aspects may be related, but not

limited, to the time interval between distinct movements, the varying pipeline

embedment, etc. As a result, this paper takes into account two different extreme

conditions:

• “EqualPeaks”;

• “NoSUpPeak”.

As the conditions’ names suggest, the first condition, “EqualPeaks”, behaves with equal

peaks for both loading phases – start-up and shutdown. Alternatively, the second

condition, “NoSUpPeak”, behaves with no peak for start-up phases, while peaky for

shutdown phases. There is no clear understanding in the literature as to why the peak

dissipation may occur for one load phase, while it may not occur for another load phase.

Consequently, the axial force-displacement responses, shown in Figure 5.3, need to be

updated to account for cyclic movements. Figure 5.4 shows the update to Figure 5.3,

presenting three hypothetical load steps for “EqualPeaks” and “NoSUpPeak” conditions.

Although the authors acknowledge that intermediate peak cases may occur in between

“EqualPeaks” and “NoSUpPeak” conditions, these intermediate conditions would be

enveloped by these two extreme conditions. For this reason, the intermediate cases are

disregarded in this paper. For simplicity, it is also assumed that the first load phase does

not peak.


PIPELINE WALKING

From Castelo et al. (in press b) it is known that the walking rate for an elastic-plastic

pipe-soil response, WREP, can be obtained simply by subtracting twice the equivalent

mobilisation distance, δmobEQ, from the walking rate for rigid-plastic soil, WRRP, as shown

by equation (5.1):

𝑊𝑅𝐸𝑃 = 𝑊𝑅𝑅𝑃 − 2 ∗ 𝛿𝑚𝑜𝑏𝐸𝑄 (5.1)

where the walking rate for rigid-plastic soil can be estimated from Carr et al. (2006) and

the equivalent mobilisation distance for a non-linear elastic-plastic pipe-soil response can

be obtained from Castelo et al. (in press b).

Chapter 5

99

As another option, reorganizing equation (5.1), as also explained by Castelo et al. (in

press b), the walking rate for an elastic-plastic pipe-soil response can be established by

multiplying the walking rate for rigid-plastic soil by a reduction factor based on the

equivalent mobilisation distance and the non-walking mobilisation distance, δnull, as

presented by equation (5.2):

𝑊𝑅𝐸𝑃 = 𝑊𝑅𝑅𝑃 ∗ (1 −𝛿𝑚𝑜𝑏𝐸𝑄𝛿𝑛𝑢𝑙𝑙

) (5.2)

where the non-walking mobilisation distance, δnull, can be achieved using equation (5.3)

– (Castelo et al., 2019):


(5.3)

As confirmed by Castelo et al. (in press b), the same reduction factor can be applied to

the distance between stationary points for an elastic-plastic pipe-soil response, Xab,EP, as

presented below by equation (5.4):

𝑋𝑎𝑏,𝐸𝑃 = 𝑋𝑎𝑏,𝑅𝑃 ∗ (1 −𝛿𝑚𝑜𝑏𝐸𝑄𝛿𝑛𝑢𝑙𝑙

) (5.4)

where the distance between stationary points for rigid-plastic soil, Xab,RP, can be estimated

from Bruton et al. (2010).

A parametric study has been performed using finite element analyses, to investigate the

peaky tri-linear pipe-soil responses seen in Figure 5.4, aiming on building on equation

(5.1) to create an accurate, simple and fast methodology to estimate pipeline walking for

this pipe-soil response type.


The finite element model used in this paper is based on a straight pipeline laid on a

uniformly sloping seabed. The properties of this model are presented in Table 5.1 and

Table 5.2 (soil case ii). Table 5.2 also presents data used for the parametric study

developed later in this paper.

The 5000m pipeline was represented by 5001 nodes connected by 5000 equal Euler

Bernoulli beam elements (B33 – 3 dimensional 3 noded elements in Abaqus), creating a

1 metre “mesh” size.


100

To represent the peaky tri-linear pipe-soil interaction, the soil was modelled as a set of

macro elements connected to each pipeline node, which were described as user elements

in FORTRAN.

5.6.1 Peaky tri-linear pipe-soil interaction models

Two different soil conditions were modelled for this paper: the “EqualPeaks” and

“NoSUpPeak” extreme conditions as shown in Figure 5.4.

For the “EqualPeaks” condition, the user element interface applied a constant (positive)

stiffness until a predefined peak force was attained. At this peak force a constant

(negative) stiffness was applied, so that the reaction force reduced up to a residual plateau.

If the displacement was reversed, the same behaviour could be observed for the spring-

slider in the opposite direction.

For the “NoSUpPeak” condition, the user element interface applied the same forces

during loading as applied in the “EqualPeaks” condition. However, for start-up phases,

the forces did not present the peak, because once the reaction force achieved the residual

plateau, no further reaction was provided and the applied stiffness at this point was zero,

where the forces remained in the residual plateau.

5.6.2 Loads

In the analysis, the pipeline was heated up uniformly with a temperature increase of

100°C. This value includes an additional temperature amount that represents the pipe

internal pressure (Hobbs, 1984).

The self-weight of the pipeline, W, and seabed slope angle, β, generate a sliding

component to the weight:


Operational cycling took into account the steady operational profile (start-up) and the rest

condition (shutdown).

5.7 FINITE ELEMENT ANALYSIS RESULTS AND

COMPARISON WITH RIGID-PLASTIC SOLUTION

Figure 5.5 and Figure 5.6 show the effective axial force and the axial displacement

distribution, respectively, for the “EqualPeaks” condition applied to ideal case ii.

Figure 5.7 and Figure 5.8 show the effective axial force and the axial displacement

Chapter 5

101

distribution for “NoSUpPeak” condition applied to ideal case ii.

Although these two finite element analyses (“EqualPeaks” and “NoSUpPeak”) provided

similar results when compared to each other, as shown in Table 5.3, when compared to

the analytical calculations from Bruton et al. (2010), as shown in Table 5.4, the deviation

presented a remarkable margin.

Table 5.3: Tri-linear finite element analysis results for soil case ii.

Case Distance Between Stationary Points Walking Rate

ii EqualPeaks 637m 0.674m/cycle

NoSUpPeak 638m 0.675m/cycle

Table 5.4: Rigid-plastic calculation results.


Rigid-plastic (Carr et al., 2006) 698m 0.740m/cycle

The deviation between rigid-plastic calculations and finite element results (61m for the

distance between stationary points and 0.066m/cycle for the walking rate) is justified by

the fact that the finite element analyses considered a more realistic soil. Instead of using

a basic soil approximation, rigid-plastic, the analyses considered a more realistic soil

response, peaky tri-linear pipe-soil interaction.

To estimate the realistic results for the distance between stationary points and for the

walking rate, a new analytical solution is outlined for the peaky tri-linear pipe-soil

response, as was done in Castelo et al. (2019, in press b).

5.8 REVISED ANALYTICAL SOLUTION FOR THE

DISTANCE BETWEEN STATIONARY POINTS FOR PEAKY TRI-

LINEAR SOILS – Xab,3L

From Castelo et al. (in press b) where the soil is treated as a non-linear elastic-plastic

spring, it is known that the distance between stationary points, Xab,EP, is equal to the

distance between stationary points for rigid-plastic soils, Xab,RP, multiplied by a reduction

factor, which is based on the equivalent mobilisation distance, δmobEQ, and the non-


102

walking mobilisation distance, δnull, as shown by equation (5.4).

Alternatively, for a peaky tri-linear pipe-soil behaviour, the equivalent mobilisation

distance, δmobEQ, might be substituted by an ideal mobilisation distance, δmob’.

𝑋𝑎𝑏,3𝐿 = 𝑋𝑎𝑏,𝑅𝑃 ∗ (1 −𝛿𝑚𝑜𝑏′

𝛿𝑛𝑢𝑙𝑙) (5.6)

5.9 REVISED ANALYTICAL SOLUTION FOR THE

WALKING RATE FOR PEAKY TRI-LINEAR SOILS – WR3L

From Castelo et al. (in press b), which treated the soil as a non-linear elastic-plastic

spring, it is known that the walking rate, WREP, is equal to the walking rate for rigid-

plastic soils, WRRP, multiplied by a reduction factor based on the equivalent mobilisation

distance, δmobEQ, and the non-walking mobilisation distance, δnull, as previously shown by

equation (5.2).

Analogously to Xab,3L, for a peaky tri-linear pipe-soil behaviour, the equivalent

mobilisation distance, δmobEQ, might be substituted by an ideal mobilisation distance,

δmob’.

𝑊𝑅3𝐿 = 𝑊𝑅𝑅𝑃 ∗ (1 −𝛿𝑚𝑜𝑏′

𝛿𝑛𝑢𝑙𝑙) (5.7)

5.10 IDEAL MOBILISATION DISTANCE - δmob’

As firstly developed by Castelo et al. (2019) and further expanded by Castelo et al. (in

press b) for the elastic correction, the tri-linear correction, Corr3L, for the walking rate

predictions can be obtained by doubling the division of the unload-reload area, AUnload-

Reload, by the variation of residual plastic force, ΔFR. However, differently to elastic-

plastic soils, peaky tri-linear pipe-soil interactions have an additional area, created by the

peak resistance, but the influence of the peak resistance is so small, that this additional

area can be safely ignored resulting in:

𝐶𝑜𝑟𝑟3𝐿 = 2(𝐴𝑈𝑛𝑙𝑜𝑎𝑑−𝑅𝑒𝑙𝑜𝑎𝑑

𝛥𝐹𝑅) (5.8)

Then, following the same principles, the ideal mobilisation distance, δmob’, can be

described with a similar procedure from Castelo et al. (2019, in press b), as outlined by

Chapter 5

103

equation (5.9):

𝛿𝑚𝑜𝑏′ =𝐶𝑜𝑟𝑟3𝐿2

= (𝐴𝑈𝑛𝑙𝑜𝑎𝑑−𝑅𝑒𝑙𝑜𝑎𝑑

𝛥𝐹𝑅) (5.9)

As another option, since the soil behaves linearly, δmob’ can also be written as:

𝛿𝑚𝑜𝑏′ =𝐹𝑅 ∗ 𝛿𝑚𝑜𝑏𝑃

𝐹𝑃 (5.10)

where FR is the residual plastic force, FP is the peak elastic force, and δmobP is the

mobilisation distance where the peak elastic force is achieved.

Now, using the values provided in Table 2, δmob’ was calculated for cases i - iv to be

0.065, 0.032, 0.043 and 0.052m, respectively; while, equations (5.4) and (5.7) were

rewritten, accounting for equation (5.10), as:

𝑋𝑎𝑏,3𝐿 = 𝑋𝑎𝑏,𝑅𝑃 (1 −𝐹𝑅𝐹𝑃

𝛿𝑚𝑜𝑏𝑃𝛿𝑛𝑢𝑙𝑙

) (5.11)

𝑊𝑅3𝐿 = 𝑊𝑅𝑅𝑃 ∗ (1 −𝐹𝑅𝐹𝑃


) (5.12)

Hence, using equations (5.11) and (5.12) in association to the values provided by Table

5.1, Table 5.2 and Table 5.4, the distance between stationary points and the walking rate

were obtained, as presented by Table 5.5†.

Table 5.5: Analytical results.


i 576m 0.610m/cycle

ii 637m 0.675m/cycle

iii 617m 0.653m/cycle

iv 600m 0.636m/cycle

† The authors understand that 1m lies inside the acceptable deviation given that this is the mesh spacing.


104


FOR PEAKY TRI-LINEAR PIPE-SOIL INTERACTION

The following parametric study validates the above solutions for the distance between

stationary points’ and walking rate for peaky tri-linear soils.

The parametric study uses the values provided in Table 5.1 and Table 5.2 as previously

explained in Section 5.4. For simplicity, pipeline length, pipeline submerged operational

weight (accounting for content), residual friction coefficient and the overall route slope

were kept constant, although the soil resistance was varied, as shown, for the ideal cases

i - iv, in Table 5.2, Figure 5.3 and Figure 5.4.

5.11.1 Ideal mobilisation distance - δmob’

Each of the parametric study cases tested had their own ideal mobilisation distance, δmob’,

value according to equation (5.10) as shown in Section 5.10.

Figure 5.9 presents the tri-linear correction results from the numerical solutions (finite

element models) plotted against the values calculated using equation (5.10). The

“EqualPeaks” and the “NoSUpPeak” soil conditions are represented by square and

circular markers, respectively. The triangles represent elastic-perfectly-plastic

conditions, accounting for the ideal mobilisation distance – these were used to prove the

applicability of the ideal mobilisation distance methodology. Cases i, ii, iii and iv are

indicated in the figure.

Figure 5.9 shows a very strong agreement between the tri-linear correction obtained from

the finite element analysis and the results calculated using the proposed equation.

For elastic-plastic soil conditions, when the equivalent mobilisation distance, δmobEQ,

nears the value of the non-walking mobilisation distance, δnull, the walking rate tends to

diminish up to zero and the walking phenomenon ceases (Castelo et al., 2019, in press

b). Analogously, to peaky tri-linear soils, when the ideal mobilisation distance, δmob’,

nears δnull the walking rate also tends to diminish up to zero and the walking phenomenon

ceases.

5.11.2 Distance between stationary points for peaky tri-linear soil – Xab,3L

Equation (5.10) is applicable to finding the ideal mobilisation distance. Consequently,

equation (5.11) must be applicable to finding the distance between the stationary points.

To confirm, the finite element model outputs were compared with the calculated values

Chapter 5

105

from equation (5.11).

Figure 5.10 presents the results for the distance between stationary points using numerical

solutions (finite element models) plotted against the values calculated using equation

(5.11). The “EqualPeaks” and the “NoSUpPeak” soil conditions are represented by

square and circular markers, respectively. The triangles represent elastic-perfectly-plastic

conditions, accounting for the ideal mobilisation distance. Cases i, ii, iii and iv are

indicated in the figure.

Figure 5.10 shows a very strong agreement for the distance between stationary points

obtained from the finite element analysis and the results calculated using the proposed

equation.

5.11.3 Walking rate for peaky tri-linear soil – WR3L

Figure 5.11 presents the walking rate results from the numerical solutions (finite element

models) plotted against the values calculated using equation (5.12). The “EqualPeaks”

and the “NoSUpPeak” soil conditions are represented by square and circular markers,

respectively. The triangles represent elastic-perfectly-plastic conditions, accounting for

the ideal mobilisation distance. Cases i, ii, iii and iv are indicated in the figure.

Figure 5.11 shows a very strong agreement between the walking rates obtained from the

finite element analysis and the results calculated using the proposed equation.

Overall, the results show that equation (5.12) – as presented by Table 5.6 – gives a true

representation of the effects of peaky tri-linear soil springs on pipeline walking.

Table 5.6: Tri-linear finite element analyses results.


i EqualPeaks 577m 0.611m/cycle


ii EqualPeaks 637m 0.674m/cycle


iii EqualPeaks 616m 0.652m/cycle


iv EqualPeaks 600m 0.635m/cycle



106

Finally, Equation (5.1) can be translated for peaky tri-linear soils as equation (5.13):

𝑊𝑅3𝐿 = 𝑊𝑅𝑅𝑃 − 2𝛿𝑚𝑜𝑏′ (5.13)

where the walking rate for peaky tri-linear soils, WR3L, may be directly obtained by

subtracting twice the ideal mobilisation distance, δmob’, from the walking rate for rigid-

plastic soils, WRRP.

5.12 OBSERVATIONS ABOUT THE EFFECTIVE AXIAL

FORCE VARIATION OVER THE DISTANCE BETWEEN

STATIONARY POINTS FOR PEAKY TRI-LINEAR SOILS – ΔSS,3L

For Castelo et al. (2019, in press b), the effective axial force variation over the distance

between stationary points, ΔSS, solution was mathematically revised by making

adjustments for the effective axial force physical boundaries, the axial displacement, δx,

boundary conditions and the effective axial force boundary conditions. These factors

directly impact the differential equation used to obtain the effective axial force values

and ultimately change the ΔSS expression.

While obtaining the effective axial force variation over the distance between stationary

points is important, previous experience (Castelo et al., 2019, in press b), shows that ΔSS

revision will not have a significant impact on finding the walking rate for peaky tri-linear

soils. Furthermore, confidence in the numerical solutions obtained in previous research,

and the use of similar approaches (Castelo et al., 2019, in press b), suggest that the

numerical results will be sufficient to prove the applicability of equations (5.10), (5.11),

(5.12) and (5.13).


This paper provides a new strategy to solve downslope pipeline walking problems

considering peaky tri-linear soil representations. Different shapes and properties of tri-

linearity (within the peaky soil range) have been considered leading to an innovative

analytical solution. This new solution improves understanding of the main properties

involved in the peaky tri-linear soil behaviour by providing a set of analytical expressions

for pipe walking, which were benchmarked and validated against a set of finite element

analyses.

Current solutions do not consider the tri-linearity of soil response, and it is known that

Chapter 5

107

they can provide inaccurate walking patterns. Therefore, this paper resolves how the

fundamental solution for rigid-plastic soils must be adjusted to allow for peaky tri-linear

soils. The solution also shows how peaky tri-linear soils can be adapted to an elastic-

perfectly-plastic circumstance, using the ideal mobilisation distance, δmob’, strategy and

then treated accordingly, as per (Castelo et al., 2019), avoiding numerical modelling

which can be time- and resource-consuming.


108

FIGURES

Figure 5.1: Effective axial force diagrams for start-up and shutdown phases.

Chapter 5

109

Figure 5.2: Axial displacement diagrams for start-up and shutdown phases.


110

Figure 5.3: Tri-linear soil responses.

Chapter 5

111

Figure 5.4: Tri-linear soil responses for cyclic movements.


112

Figure 5.5: Effective axial force for tri-linear strategy case ii – EqualPeaks (Zoom).

Chapter 5

113

Figure 5.6: Axial displacement for tri-linear strategy case ii – EqualPeaks (Zoom).


114

Figure 5.7: Effective axial force for tri-linear strategy case ii – NoSUpPeak

(Zoom).

Chapter 5

115

Figure 5.8: Axial displacement for tri-linear strategy case ii– NoSUpPeak (Zoom).

Figure 5.9: Tri-linear correction results.


116

Figure 5.10: Distance between stationary points results.

Figure 5.11: Walking rate results.

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117

CHAPTER 6. SOLVING DOWNSLOPE PIPELINE

WALKING ON NON-LINEAR SOIL WITH BRITTLE PEAK

STRENGTH AND STRAIN SOFTENING

Chapter context: This chapter presents the published paper which was prepared to show

that adjustments (similar to previous chapters) are required for the analytical assessment

of downslope pipeline walking phenomenon when non-linear with a peak pipe-soil

interactions are considered. It demonstrates that different non-linearities will alternatively

impact the assessments and how these impacts can be estimated.


Castelo, A., White, D. and Tian, Y., 2017. Solving downslope pipeline walking on non-

linear soil with brittle peak strength and strain softening, OMAE2017-61168,

Proceedings of the International Conference on Ocean, Offshore and Arctic Engineering,

Trondheim, Norway

Non-linear soils with a peak

118

6.1 ABSTRACT

In 2000 the first case of pipeline walking (PW) was properly documented when this

phenomenon seriously impacted a North Sea high pressure and high temperature

(HP/HT) pipeline (Tornes et al., 2000).

On the other hand, to study other aspects related not only to PW, the industry joined

forces in the SAFEBUCK Joint Industry Project (JIP) with academic partners. As a result,

other drivers, which lead a pipeline to walk, have been identified (Bruton et al., 2010).

Nowadays, during the design stage of pipelines, estimates are calculated for pipeline

walking. These estimates often use a Rigid-Plastic (RP) soil idealization and the Coulomb

friction principle (Carr et al., 2006).

Unfortunately, this model does not reflect the real pipe-soil interaction behavior, and in

practice, time consuming finite element computations are often performed using an

Elastic-Perfectly-Plastic (EP) soil model. In reality, some observed axial pipe-soil

responses are extremely non-linear and present a brittle peak strength before a strain

softening response (White et al., 2011).

This inaccuracy of the soil representation normally overestimates the walking rate, WR,

(a rigid plastic soil model leads to greater walking). A magnified WR invariably leads to

false interpretations besides being unrealistic. Finally, a distorted WR might also demand

mitigating measures that could be avoided if the soil had been adequately treated.

Unnecessary mitigation has a very strong and negative effect on the project as whole. It

will require more financial and time investments for the entire development of the project

– from design to construction activities. Therefore, having more realistic and pertinent

estimates becomes valuable not only because of budgetary issues but also because of time

frame limits.

The present paper will show the results of a set of Finite Element Analyses (FEA)

performed for a case-study pipeline. The analyses – carried out on ABAQUS software –

used a specific subroutine code prepared to appropriately mimic Non- Linear Brittle Peak

with Strain Softening (NLBPSS) axial pipe-soil interaction behavior.

The specific subroutine code was represented in the Finite Element Models (FEMs) by a

series of User Elements (UELs) attached to the pipe elements.

The NLBPSS case is a late and exclusive contribution from the present work to the family

Chapter 6

119

of available pipeline walking solutions for different forms of axial pipe-soil interaction

model.

The parametric case-study results are benchmarked against theoretical calculations of

pipeline walking showing that the case study results deliver a reasonable accuracy level

and are reliable. The results are then distilled into a simplified method in which the WR

for NLBPSS soil can be estimated by adjusting a solution derived for RP and EP soil.

The key outcome is a genuine method to correct the WR resultant from a RP soil approach

to allow for peak and softening behaviour. It provides a design tool that extends beyond

the previously-available solutions and allows more rapid and efficient predictions of

pipeline walking to be made.

This contribution clarifies, for the downslope walking case, what is the most appropriate

basis to incorporate or idealize the soil characteristics within the axial Pipe-Soil

Interaction (PSI) response when performing PW assessments.

6.2 INTRODUCTION

6.2.1 Pipeline walking mechanisms

Pipeline walking is a long term cyclic movement of the pipeline in one direction, and can

be accompanied by an asymmetric build-up of effective force within the pipe due to a

restraint or a slope. The Pipeline Walking (PW) phenomenon was described in details by

Carr et al. (2006) and Bruton et al. (2010), who set out four driving mechanisms.

The mechanisms are:

• Seabed slope along the pipeline length;

• Tension at the end of the flowline (associated with a steel catenary riser - SCR);

• Thermal transients along the pipeline – leading to different temperature profiles

during Start-Up (SUp) and Shutdown (SDown);

• Multiphase fluid behavior during restart operations (e.g. gas-liquid separation on

SDown).

The most important aspect which relates these mechanisms to the phenomenon itself is

the fact that each of the mechanisms is able to create an asymmetry in the profile of axial

force along the pipeline. This loading asymmetry generally causes the appearance of the

pipeline walking, by causing unequal pipeline displacements during SUp and SDown

stages.


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The present work is focused on the first mechanism listed above – the effect of seabed

slope – since this is the simplest case. However, the conclusions are applicable to all

mechanisms of pipeline walking.

6.2.2 Walking phenomenon on a rigid-plastic basis

When a pipeline is subjected to temperature and pressure increments it tends to expand

axially. This expansion will be resisted by the PSI forces – referred to simply as axial

friction – and effective compression will be induced into the pipeline.

On the other hand, when the same pipeline is exposed to temperature and pressure

decrements, it tends to contract and return to its original configuration. This time, the soil

reacts with a friction resisting force in the opposite direction in relation to the previous

behavior, introducing tension into the pipeline.

In the course of the SUp phase, considering a pipeline laid on the seabed and no

equipment attached to the pipeline (meaning that the ends are free and the soil resistance

is uniform), the effective axial compression develops from zero at pipeline ends to a

maximum value, approximately at its midlength point.

During the SDown phase, the pipeline temperature and internal pressure are set back to

their original (unloaded) values. In the same way, this tension will build up from zero at

the ends up to a maximum value approximately at the pipeline mid-length point.

For some pipelines, free of lateral buckling, the effective axial compression build up

occurs along sufficient length to induce compressive mechanical strain, which entirely

compensates the thermo-mechanical expansion. These are called “long” pipelines, while

those with insufficient effective axial compression are not able to fully compensate this

expansion, and are called “short” pipelines.

A non-anchored “short” pipeline, after contracting (SDown), may not go back to the same

position as previously on expansion (SUp). In this case, the cyclic expansion and

contraction behavior may result in geometric asymmetries between the expansion and

contraction cycles, if any of the four mechanisms listed above are present. These

asymmetries accumulate and cause large net axial global displacements over many

cycles.

Considering the case of a sloping seabed, it will cause a component of the pipe weight to

act parallel with the seabed in a downslope direction, while the axial friction will act in

interchanging directions opposing the current pipe movement direction. The effect of the

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121

interchanging component direction will also impact the effective compression and

tension along the pipeline length during its operational lifetime.

Figure 6.1 presents an example of effective axial force (EAF) diagram for the SUp

condition, showing the profile of EAF accounting for both slope and soil friction. As

sketched, the downslope weight component is added to or subtracted from the nominal

soil resistance. Therefore, the force diagram is not symmetrical and the maximum point,

corresponding to the Stationary Point (SP) on the pipe, is not at its mid-point.

Figure 6.2 shows the asymmetry between the effective compression and tension profiles,

due to the weight component always acting downwards. It can be noted that this

asymmetry causes an offset between the SPs for the SUp and SDown conditions.

Figure 6.3a shows the axial displacement (δx) for the first SUp phase, highlighting the

stationary point after 0.5L. The aforementioned temperature increase generates this

behavior. Figure 6.3b presents how the pipeline contracts without moving to its original

position, when the temperature decreases – for the first SDown step. The SPSDown lies

at the pipe section where the diagrams cross, as indicated, before 0.5L.

During the next or second loading cycle (Figure 6.4a), the intersection point is back after

0.5L; and when unloaded, before 0.5L again. Figure 4a also indicates the net axial shift,

which is induced by the difference between the SPs. Loaded and unloaded graphs for the

second cycle are similar to those for first cycle, but offset by this net axial shift, which

might typically be of some centimeters. Figure 6.4b shows how this shift accumulates

through 3 cycles, possibly resulting in several meters of longitudinal displacement over

the lifetime of the pipeline.

These results illustrate the axial ratcheting induced by an overall slope in the bathymetry,

which is only one of the pipeline walking drivers and is the case considered in the present

work.

6.2.3 Walking consequences

The pipeline walking phenomenon is not a limit state itself, but it may lead to several

other design challenges (Bruton et al., 2010), such as:

• Overstressing connections;

• Loss of tension in a SCR;

• Increase the loading in a lateral buckling;

• Route instability (curve pull out).


122

Any of the listed consequences might lead the pipeline system to fail, locally or globally;

and, they might appear separately or associated to other mentioned consequences.

Hence, the phenomenon and its consequences must be prevented in order to keep the

safety of the system and its entire environment.

On the other hand, simplifying the PSI behavior for PW assessments might not be

beneficial for the project. Inaccurately representing the PSI performance might lead to

overestimates of WR.

Besides being unrealistic, the referred overestimates regularly bring misunderstandings

to the design activities. A magnified WR might require mitigation to PW, which could be

avoided if the soil was properly described.

Mitigation activities have a very strong impact in any project. From designing to

installing the mitigation devices, more time and capital will be needed.

Therefore, it is essential to properly represent the PSI, so that the project can be

adequately developed avoiding any unnecessary expenditure.

6.2.4 Axial pipe-soil non-linearity

Model testing in the laboratory and at the seabed has shown that the axial pipe-soil

response is extremely non-linear. The magnitude of the axial pipe-soil friction coefficient

depends on the soil strength, pipe roughness and the drainage condition – White et al.

(2011) and White et al. (2012) – but these effects are beyond the scope of the present

study. Instead, the focus of this study is on the shape of the axial load displacement

response during both loading and unloading.

In the present paper, the soil considered is a soft natural clay as per the one presented by

White et al. (2011), although some parameters have been adjusted for this work. The aim

of this work is to show how more accurate PSI responses can be incorporated in a PW

assessment, because this offers a clear advance to the methodology of design compared

to the one currently applied by industry, which might be regarded as a too simply design

approach, that carries unwanted consequences in relation to more onerous walking

mitigation requirements.

The axial resistance measured during a typical cycle of movement from a field test using

an in situ testing tool is shown in Figure 6.5a, which is based on previously published

data (White et al., 2011). The extremely nonlinear axial response shows a smooth

transition between an initial high tangent stiffness which reduces until it reaches a zero

Chapter 6

123

tangent stiffness at a limiting axial friction. This limiting axial friction represents a peak

resistance which is followed by a negative tangent stiffness taking the resistance to a

residual/ plastic plateau.

In other words, this soil presents a brittle peak strength with a strain softening resistance,

which is the approximated non-linear behavior used in the present work.

For the present study, the non-linearity of the axial response has been captured using a

non-linear spring-slider of the form illustrated in Figure 6.5b.

It is important to stress, at this point, that Figure 6.5b also serves the purpose of

contrasting the soil model used by the present work and how the current methodology

considers the soil spring.

The non-linear approach is used by this paper, while the current industry methodology

usually uses the Rigid-Plastic approach (Figure 6.5b).


6.3.1 General Properties of Study-Case

As mentioned previously, this paper considers a pipeline resting on a sloped seabed. The

case study considers a straight steel pipeline, laid on a uniformly sloped seabed.

The general properties are shown in Table 6.1.

Table 6.1: Pipeline properties.

Property Value



Water Depth, D 1200m

Length, L 5000m


Axial Friction Coefficient, µ 0.25





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The pipe operational submerged weight, W, has been calculated considering the overall

volume of steel and content in one meter of pipe. Then, the one meter volume has been

used, along with the specific density of each material, to calculate the final buoyancy per

meter of pipe (plus contents), as per Archimedes’ Principle.

6.3.2 Variations in axial pipe-soil response

Two different pipe-soil property sets have been considered for the numerical analysis

(Case A and Case B). Axial pipe-soil resistance has been modelled based on the example

illustrated in Figure 6.6, adopting the parameters given in Table 6.2.

Table 6.2: Axial pipe-soil interaction model parameters.

Property Case A Case B

Limiting Displacement 1, δ1 0.049m 0.012m




Limiting Force 1, F1 0.150kN 0.050kN




As can be seen from the parameters presented in Table 6.2, the main difference among

Cases A and B was the limit defining the interaction between linear-elastic and parabola

1 behaviors.

For Case A, the couple (δ1,F1) lies above the plastic residual plateau (F4), while for case

B it lies below the same plateau – Figure 6.6; and, the present work examines the

divergence originated from this aspect.

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125

6.4 RIGID-PLASTIC ANALYTICAL SOLUTIONS

6.4.1 Calculations

As described by Carr et al. (2006) there are three different calculation steps to analytically

assess the pipeline WR under the influence of seabed slope for a RP soil approximation.

The first calculation step assesses the distance between the SPs, Xab,RP, presented by

Figure 6.2:


𝜇 (6.1)

The second calculation step assesses the change in force in the pipeline, ΔSS, between

SUp and SDown conditions over the length of the pipeline denoted by Xab,RP:


And finally, the third and last step is to combine these values to determine the walk rate

per loading cycle:


𝐸𝐴𝜇 (6.3)

Where:

𝛥𝑃 = −(𝛥𝑝)𝐴𝑖(1 − 2𝜈) − 𝐸𝐴𝛼𝛥𝑇 (6.4)

6.4.2 Rigid-plastic analytical results

The analytical solutions have been used to estimate the WR based on the RP assumption.

Table 6.3 summarizes the analytical results for the calculations proposed by Carr et al.

(2006) regarding the general pipeline properties.

Table 6.3: Analytical results.

RP analytical results Value

Xab,RP – Equation (6.1) 698.42m

ΔSS,RP – Equation (6.2) -429.90kN

WRRP – Equation (6.3) 0.740m/cycle

ΔP – Equation (6.4) -4.733MN

It is also worth highlighting some other general aspects concerning the analytical results.


126

Table 6.4 shows the values of these important characteristics.

Table 6.4: Key aspects from rigid-plastic solution.

General Aspects Value

SUp Max Compression Force -245kN

SUp Max Compression Force Position 2849m

SDown Max Tension Force 245kN

SDown Max Tension Force Position 2151m

SUp Stationary Point 2849m

SDown Stationary Point 2151m

Figure 6.7 shows the EAF plot in regards of the RP basis and also provides some details

about the key aspects of RP solution from Table 6.4.

At this stage, it is important to emphasize that for RP soils, SPs are the same as the

maximum EAF positions. This is not true for other soil idealizations as described by

Castelo et al. (2019).

6.5 NLBPSS FEM SOLUTION

The FEM used for this paper was a geometrically simplified model, based on a one-

dimensional pipeline laid on a uniformly sloped seabed and its general properties were

presented in Table 6.1.

6.5.1 FEM architecture

The pipeline was represented by 5001 nodes connected between them by 5000 B33 (three

dimensional three node element) pipe elements (see Dassaul, (2014) for technical details).

The soil was modeled as non-linear spring elements connected to each pipeline element

(at the pipeline nodes). Such elements were designed as UELs via a subroutine

specifically coded in FORTRAN language for this paper.

Loads

The loads acting on the pipeline are related to self-weight and temperature only.

The effect of the uniform slope is accounted for as a longitudinal load equivalent to the

component of the pipeline weight, as given by:

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127


The operational cycling was done taking in account the steady operational profile (SUp)

and the rest condition (SDown). No intermediate step of loading was manually included.

The SUp and SDown temperatures were accounted as per Table 6.1.

Pipe-soil interaction representation

As aforementioned (Sections 6.2.4 and 6.2.4), the way used to represent the PSI was

through UELs coded in FORTRAN. The basic philosophy for the UEL was an initially

linear relation between displacement and reaction force with a constant stiffness until a

limit displacement/ force couple was achieved (δ1,F1). Then a variable and decreasing

stiffness would be provided until a second limit couple was reached (δ2,F2), where the

tangential stiffness reaches ZERO. Then, the stiffness would face a negative stretch going

through the couple (δ3,F3), until reaching a zero tangent stiffness again at (δ4,F4), where

the plastic plateau is imposed to any further displacement (at the current step).

However, the spring load history will impact the load succession as can be seen in Figure

6.8, where the different possible behaviors are schematically represented. The choice of

tangent stiffness for the next step is determined depending on the axial displacement in

the current step, UA_m, relative to the axial displacement in the previous step, UA_Ref.

For a positive displacement (UA_m - UA_Ref > 0), behaviors 1 and 2 control the spring

response depending on the initial spring force of reference, FS_Ref. If FS_Ref is bigger

than the elastic limit, Felastic, it falls into behavior 2 regime; otherwise, it remains behavior

1 regime.

For negative displacements, behaviors -1 and -2 control the spring response mirroring the

relationship between behaviors 1 and 2.

In order to provide a better understanding about the general FORTRAN subroutine logic,

a simplified flowchart is included in Figure 6.9.

The governing equation for a parabola, which is differentiated to give the tangent stiffness

at different steps, is:

𝑓(𝑥) = 𝐴𝑥2 + 𝐵𝑥 + 𝐶 (6.6)

In case a higher order of non-linearity shall be modelled, perhaps to give a better fit to

field test results, a higher order polynomial may be used or an alternative formulation, so

that it represents a better fit for the soil behavior. In other words, Figure 6.6 will show


128

more boundaries, i.e. more pairs (δ,F).

It is important to stress that FS_Ref is a just a memory entry automatically kept from the

previous iteration to the next. So, it does not really matter the displacement direction for

FS_Ref, it is just the previous resultant force, FS_m.

An extensive and exhaustive test routine was performed to verify the User Element

reliability when put to use for the walking analyses. Firstly, a single node ‘floating’ in

space would be connected to the UEL, and this point would be displaced in order to

activate the spring subroutine generating a resultant force; then, the result would be cross

checked with the preconceived NLBPSS spring – based on White et al. (2011).

Afterwards, a piece of pipe would be modelled and connected to some UELs. The same

overall displacement steps would be followed and the resultant force compared. Given

that all results, generated by displacement controlled loads, agreed with the designed

NLBPSS soil curve, it was put to practice with force loads generated by thermal

increments.

At this stage, all nodes from the aforementioned “single pipe element” tests were closely

observed to guarantee that their resultant reaction force would still agree with the desired

NLBPSS curve. Finally, after reassuring that all results respected the original non-linear

soil spring, the subroutine was awarded a “reliable” status and full length pipeline

analyses were carried out.

The results using this soil approximation show how the non-linearity of a soil model with

brittle peak strength and strain softening affects the WR.

6.5.2 FEM results

In this section, we discuss the different results of the FEMs in terms of EAF and δx in

order to summarize and to highlight important aspects concerning the results that have an

influence on the PW.

FEM results

Figure 6.10 shows the results, in terms of EAF, along the entire pipeline length for five

load cycles – both cases are presented: Case A – Figure 6.10a and Case B – Figure 6.10b.

Figure 6.11 shows the same results, but this time zooming into the vicinity of the Max

and Min Forces region – both cases are presented: Case A and Case B are shown in Figure

6.11a and Figure 6.11b, respectively.

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129

From these results, key values can be extracted so that a later comparison can be done

with the other models (Table 6.5).

Table 6.5: EAF notable results.

Result Case A Case B

SUp Max Compression Force -247.572kN -248.629kN

SUp Max Compression Force Position 2845m 2847m

SDown Max Tension Force 247.831kN 248.888kN

SDown Max Tension Force Position 2155m 2154m

6.5.3 Axial displacement

Figure 6.12 shows the results, in terms of δx, along the entire pipeline length for five load

cycles – both cases are presented: CaseA – Figure 6.12a and Case B – Figure 6.12b.

Figure 6.13 shows the same results, but this time zooming into the vicinity of the SPs –

both cases are presented: Case A and Case B are shown in Figure 6.13a and Figure 6.13b,

respectively.

From these results, key values are extracted so that a later comparison can be done with

the other models (Table 6.6).

Table 6.6: δx notable results.


SUp Stationary Point, SPSUp,NLBPSS 2819m 2827m

SDown Stationary Point, SPSDown,NLBPSS 2181m 2173m

SP Distance, Xab,NLBPSS 638m 654m

Observed Walking Rate, WRObs,NLBPSS 0.674m/cycle 0.693m/cycle

FEM results crosscheck

Using the results shown previously a mathematical solution following Carr et al. (2006)

is used to calculate the WR directly and then crosscheck the observed value.

Equation (6.7) shows the general expression that can be used for obtaining the calculated

WR:


130

𝑊𝑅𝑁𝐿𝐵𝑃𝑆𝑆 = −1

𝐸𝐴(∫ (∆𝑃 − ∆𝑆𝑠)𝑑𝑥

𝑆𝑃𝑆𝑈𝑝,𝑁𝐿𝐵𝑃𝑆𝑆

𝑆𝑃𝑆𝐷𝑜𝑤𝑛,𝑁𝐿𝐵𝑃𝑆𝑆

) (6.7)

From equation (6.4) it can be deducted that ΔP will be constant along the pipe length,

which makes its integral equals to ΔP value multiplied by the distance of the stationary

points, Xab,NLBPSS.

On the other hand, the EAF variation, ΔSS, is significantly variable – especially near the

SPs; and, therefore for Cases A and B it has been solved numerically. The resultant values

are presented in Table 6.7. Both cases returned a WR difference of only 1mm per cycles,

which might be disregarded and the cross check can be classified as successful.

Table 6.7: FEM crosscheck results.


Change in Fully Constrained Force, ΔP -4.733MN -4.733MN

EAF Variation over Xab, ΔSS -0.275MN -0.282MN

Walking Rate, WRCalc,NLBPSS 0.675m/cycle 0.692m/cycle

FEM results summary

Table 6.8 summarizes the pieces of information obtained from the FEM results, as stated

in the last three sessions.

Table 6.8: FEM summary results.

Results Case A Case B

SUp Max Compression Force -247.572kN -248.629kN

SUp Max Compression Force Position 2845m 2847m

SDown Max Tension Force 247.831kN 248.888kN

SDown Max Tension Force Position 2155m 2154m

SUp Stationary Point 2819m 2827m

SDown Stationary Point 2181m 2173m

Stationary Points Distance 638m 654m

Observed Walking Rate 0.674m/cycle 0.693m/cycle

Change in Fully Constrained Force -4.733MN -4.733MN

Chapter 6

131

EAF Variation Over Xab -0.275MN -0.282MN

Calculated Walking Rate 0.675m/cycle 0.692m/cycle

Taking into account that a 1m mesh was included in the calculated results (due to the

models architecture), the error between the FEA WR and the directly calculated value is

negligible. For consistency, the FEM results are used in the further analysis.

6.6 RESULTS COMPARISON

6.6.1 Effective axial force

Table 6.9 compares can be formed to help comparing the EAF results.

Table 6.9: EAF comparison.

Results RP Case A Case B

SUp Max Compression Force -245kN -247.572kN -248.629kN

SUp Max Compression Force Position 2849m 2845m 2847m

SDown Max Tension Force 245kN 247.831kN 248.888kN

SDown Max Tension Force Position 2151m 2155m 2154m

Approximately, the comparison between FEM and Analytical results leads to the

conclusion that the maximum values of EAF and their positions are all very similar. These

changes alone do not explain the observed change in WR.

6.6.2 Stationary points

Looking only at the SPs results, Table 6.10 is prepared, so that it becomes easier to

compare SPs results.

Table 6.10: SPs comparison.

Results RP Case A Case B

SPSUp 2849m 2819m 2827m

SPSDown 2151m 2181m 2173m

Xab 698m 638m 654m


132

Observing the SP results, the change was more dramatic than the ones observed in the

previous item (6.6.1). Case A showed a 60m change in the distance between the SPs;

while, Case B reduced Xab about 44m.

Although the soil models – for Cases A and B – present a prominent peaky behavior, the

variations observed for the SPs, as stressed in the previous paragraph, agrees with the

expected behavior, as established – for non-peak cases – in other work (Castelo et al.,

2019, in press).

Previous similar studies show that the peaky behaviors have no major influence on the

walking phenomenon relative to the same soil response but with no peak, so the peak

impact may be disregarded for this scope of the present work (Castelo et al. 2019).

Therefore, the distance between the stationary points observed for Case A returned a

value that can be approximately considered equal to – as per (Castelo et al., in press a):

𝑋𝑎𝑏,3𝐿 = 𝑋𝑎𝑏,𝑅𝑃 (1 −𝐹𝑅𝐹𝑃


) (6.8)

where δmobP is the peak mobilisation distance, FR and FP are the residual force level and

the peak force level, respectively; and δnull is an idealization for non-linear soil

approaches to represent a mobilisation distance at which walking ceases (Castelo et al.,

2019). In the present work, this has a value of δnull = 0.370m for both cases considered.

For Case B, equation (6.8) does not derive into a direct relation between the observed

FEM results and the equation products. Therefore, some algebra can be used on equation

(6.8) to generate a more general equation – alternatively to (Castelo, et al., in press b):

𝑋𝑎𝑏,𝑁𝐿𝐵𝑃𝑆𝑆 = 𝑋𝑎𝑏,𝑅𝑃 (1 −𝛿𝑚𝑜𝑏𝐸𝑄𝛿𝑛𝑢𝑙𝑙

) (6.9)

where δmobEQ is an equivalent mobilisation distance to be later explored (Section 6.7).

6.6.3 Axial displacements & walking rates

The walking rate results are now presented. Table 6.11 shows only the WR results (for

the FEM Cases A and B, the observed values were accounted for, as already clarified).

Table 6.11: Walking rates for different soil approaches.

Result RP Case A Case B

WR 0.740m/cycle 0.674 m/cycle 0.693 m/cycle

Chapter 6

133

From Table 6.11, it can be clearly seen that the WR results also varied between the RP

and NLBPSS cases, by 10%.

Again, Case A results agree with the explanation given by Castelo et al. (in press a) that

for peaky soils the WR can be calculated as:

𝑊𝑅3𝐿 = 𝑊𝑅𝑅𝑃 ∗ (1 −𝐹𝑅𝐹𝑃


) (6.10)

However, Case B does not completely match equation (6.10) definition, which requires

a further generalization as – in accordance with Castelo et al. (in press b):

𝑊𝑅𝑁𝐿𝐵𝑃𝑆𝑆 = 𝑊𝑅𝑅𝑃 ∗ (1 −𝛿𝑚𝑜𝑏𝐸𝑄𝛿𝑛𝑢𝑙𝑙

) (6.11)

6.7 EQUIVALENT MOBILISATION DISTANCE

Other research (Castelo et al., 2019, in press b, in press a) indicates that the equivalent

mobilisation distance, δmobEQ, can be obtained from dividing the unload-reload area (as

per Figure 6.14) by the residual force variation (ΔFR) – as per equation (6.12):

𝛿𝑚𝑜𝑏𝐸𝑄 = (𝐴𝑈𝑛𝑙𝑜𝑎𝑑−𝑅𝑒𝑙𝑜𝑎𝑑

𝛥𝐹𝑅) (6.12)

Figure 6.14a and Figure 6.14b show the properties involved in obtaining δmobEQ for Cases

A and B, respectively.

Considering the values and the given method in Figure 6.14, Case A provides a δmobEQ of

0.032390m, while Case B has a δmobEQ equals to 0.024872m.

6.7.1 Back evaluation

Naturally, the next step for this paper is to check the hypothesis given by the equivalent

mobilisation distance approach (equation (6.8)) so that it can be proved correct.

Then, equations (6.9) and (6.11) will be evaluated and contrasted against the FEM results

formerly presented (Sections 6.5 and 6.6).

Table 6.12: Equations (6.9) and (6.11) results.

Results Case A Case B

Xab – Equation (6.9) 637m 652m


134

WR – Equation (6.11) 0.675m/cycle 0.690m/cycle

Analyzing the distance between the stationary points, Xab, equation (6.9) provides a good

estimative within a 0.31% margin of error. 637m and 652m are obtained from equation

(6.9), for Case A and Case B, respectively; while the FEM results indicated 638m and

654m for cases A and B.

Now, checking the results of walking rate, WR, equation (6.11) also derives into results

with a good agreement with the FEM results with an acceptable and marginal deviation

(0.43%). Equation (6.11) delivers a WR of 0.675 and 0.690m/cycle for cases A and B. At

the same time, the FEM approach 0.674 and 0.693 m/cycle for A and B.

Therefore, the back evaluation concerning equations (6.9) and (6.11) can be classified as

successful. A wider set of results exploring this approach, and similar efficient walking

rate analysis methods are given in Castelo et al. (2019, in press b, in press a). These offer

a tool to assist in future walking assessments.


The industry has seen the influence from some phenomena, such as pipeline walking,

increase; as hydrocarbons reservoirs have become more difficult to access over the last

decades, leading to higher wellstream temperatures in deeper and colder waters.

Some research has been done on PW; but, it was still not fully understood how this

problem should be really treated since distortions have been noticed between several

design assessments and operational observations.

The models presented in this paper provide new insights into axial PSI and its impact on

PW evaluations.

Thus, the parametric study presented by the present work, led to a better understanding

on how PW can be assessed when a highly non-linear peaky axial PSI is observed on soil

tests. Then, in order to correct the analytical assessments based on RP basis, originally

proposed by Carr et al. (2006), a new calculation approach is suggested.

It is shown that the non-linear soil model can be simplified to determine an equivalent

mobilisation distance – for an equivalent linear elastic perfectly plastic model – and this

value can be used to give an adjustment to the rigid plastic walking rate solution (from

Carr et al. (2006)) to give the walking rate on non-linear peaky soil.

Chapter 6

135

FIGURES

Figure 6.1: EAF diagram and sketch of acting loads.

Figure 6.2: EAF diagrams for start-up and shutdown.


136

Figure 6.3: Axial displacement – 1st cycle.

Chapter 6

137

Figure 6.4: Axial displacement – further cycles.


138

Figure 6.5: Axial PSI non-linear approach.

Chapter 6

139

Figure 6.6: Axial PSI boundaries.

Figure 6.7: Analytical EAF plot.


140

Figure 6.8: Schematic behaviours plot.

Chapter 6

141

Figure 6.9: Subroutine flowchart.


142

Figure 6.10: EAF results for Cases A and B.

Chapter 6

143

Figure 6.11: EAF zoom for Cases A and B.


144

Figure 6.12: δx results for Cases A and B.

Chapter 6

145

Figure 6.13: δx zoom for Cases A and B.


146

Figure 6.14: Obtaining δmobEQ – for Cases A and B.

Chapter 7

147

CHAPTER 7. GRAVITY-DRIVEN PIPELINE WALKING

ON VARIABLE SLOPES

Chapter context: In this thesis’ chapter, variable slopes are covered. This chapter was

motivated by the lack in the literature of verification for applicability on variable slopes

topography. It brings the previous chapters closer to real-world conditions, where

pipeline routes vary in slope topography alongside with pipe-soil interaction behaviours.


Castelo, A., White, D. and Tian, Y., in press. Gravity-driven pipeline walking on variable

slopes. International Journal of Offshore and Polar Engineering (submitted to journal)

Variable slopes

148

7.1 ABSTRACT

Gravity-driven pipeline walking is a phenomenon where a pipeline migrates globally

downslope at a certain rate per loading cycle. It can significantly impact the subsea

system integrity and influences the design. The current methodology simplifies the

geometry by assuming a uniform slope along the entire route. However, real pipelines

traverse routes that slope with varying angles. The literature lacks evidence to justify such

simplification. Motivated by this, this study establishes whether uniform slope solutions

can be applied. The applicability of emerging research is also confirmed, allowing a

realistic representation of pipe-soil interaction.

7.2 INTRODUCTION

As oil and gas activities increasingly moves to deep water reservoirs, pipelines become

more important. Under operational conditions, pipelines will expand and contract due to

temperature and pressure changes. These expansion and contraction cycles might be

asymmetric because of seabed slopes or other factors, as explained by Carr et al. (2006)

and Bruton et al. (2010). As a result of this asymmetry, pipelines’ stability may be

seriously compromised, and they may globally migrate in one direction, in a phenomenon

known as pipeline walking (Carr et al., 2003).

Pipeline walking increases cost and risk and may greatly impact subsea systems (Tornes

et al., 2000). Connections may be overstressed, loads may be increased, initiating lateral

buckling, and ultimately the pipeline will need to be anchored. Therefore, properly

identifying and quantifying pipeline walking is of paramount importance to decrease risk

of production loss and environmental damage besides also reducing project development

costs.

Currently, the industry common practice is to carry out a pipeline walking evaluation in

the design phase using a set of analytical formulations, which consider a simplified

geometry by assuming a uniform slope along the entire pipeline route, from one end to

the other (Bruton et al., 2010). These calculations consider various aspects, such as

operational factors (temperature, pressure, etc.), environmental factors (seabed overall

slope angle, soil friction, etc.) and physical pipeline properties (length, steel wall

thickness, etc.).

On the other hand, real pipelines traverse routes that often slope continuously down, but

Chapter 7

149

at a varying angle (Leckie et al., 2016). Hence, adequately understanding and estimating

gravity-driven downslope pipeline walking for pipelines laid on variable slope seabeds is

extremely important since this condition is commonly found in fully operational areas,

such as Northwest Australia and West Africa, as well as in frontier locations, which are

in early stages of exploration, such as the Brazilian Pre-Salt and the Arctic Region.

However, the analytical expressions (Bruton et al., 2010) are known to provide inaccurate

walking rates, thus necessitating further analyses to overcome the known limitations. To

solve some of these limitations, emerging academic research (Castelo et al., 2017)

demonstrated that, if the adequate soil behavior is considered in the initial analytical

formulae, accurate walking rates can be easily achieved by including a reduction factor

based on the soil characteristics.

Although the formulation developed by Castelo et al. (2017) represents an improvement

in the available knowledge, it was limited to a uniform slope assumption. Therefore,

motivated by this, the present paper investigates whether uniform slope solutions can be

successfully applied to variable slope condition, by averaging the slope to be uniform

throughout the entire route using an average seabed slope, βave.

Unfortunately, there is no detailed data of field measurements or laboratory tests in the

currently available literature on downslope pipeline walking; although it is known that

operators across the globe keep track of their pipelines’ movements. Therefore, this paper

presents a numerical study, to benchmark and validate the analytical findings, which

considers a total of 104 finite element models. 52 models have a dual slope topography

(26 convex and 26 concave shapes), while the remaining 52 have a triple slope

topography (26 flat-slope-flat and 26 slope-flat-slope shapes).

Across the currently available literature, various slopes have been noticed. Some authors

register very gentle slopes, such as 0.22° (Jayson et al., 2008); while other pipelines have

presented more extreme slope angles, such as 10° (Kumar and Mcshane, 2009). For the

groups of 26 models, 13 considered gentle slopes (1° to 5°), while the remaining 13

considered extreme angles (6° to 10°) as well.


7.3.1 Downslope walking mechanisms

The seabed slope generates an asymmetry between the start-up and shutdown phases in

Variable slopes

150

the effective axial force profile for a fully mobilized pipeline, as illustrated in Figure 7.1

where the rigid-plastic soil condition is considered (Bruton et al., 2010).

This asymmetry causes the Virtual Anchor Sections (VAS), which are the non-moving

sections of the pipeline during the different load steps, to be separated by a given distance,

Xab. For rigid-plastic (RP) soil conditions, the virtual anchor sections correspond to the

maximum absolute effective force along the pipeline length, as proved by Castelo et al.

(2019). Then, the distance Xab can be associated to the axial displacement, δx, from a

particular load cycle, as represented by Figure 7.2.

Because it tends to create unbalanced displacements during different loading phases, the

asymmetry in the effective axial force profile is presently understood to be the root cause

of pipeline walking.

Accounting for more realistic soil conditions, the distance Xab cannot be associated with

the maxima effective axial force sections. Therefore, Xab must be associated with the

stationary points, as thoroughly explained in Castelo et al. (2019).

7.3.2 Route topography

Although previous research on pipeline walking has explored different geotechnical

aspects, no investigation on variable slopes along the pipeline route was conducted.

Different soil idealizations (Bruton et al., 2010; Castelo et al., 2019), and realistic soils

(Castelo et al., 2017) have been scrutinized in regards of their impact on pipeline walking.

Hence, this paper focuses solely on the impact variable slopes may have on pipeline

walking.

To conduct this investigation, a numerical study has been conducted including a set of

104 models, which consider 4 different topographies for 2 different slopes’ range (gentle

and extreme angles).


Downslope pipeline walking depends on three different kinds of properties:

environmental, operational and those of the pipeline. This paper’s numerical study uses

typical property ranges.

The environmental parameters include seabed slopes, β, mobilisation distance, δmob, and

axial residual friction coefficient, μ, as shown in Table 7.1.

Chapter 7

151

Table 7.1: Environmental properties

Properties Values

Seabed Slope, β

FLAT: 0°

GENTLE: [1°; 5°]

EXTREME: [6°; 10°]

Mobilisation distance, δmob 12.35%OD (0.04m)

Axial residual friction coefficient, μ

LOW: 0.50

MID: 0.70

HIGH: 0.90

The operational parameters include temperature variation and pipeline operational

submerged weight, as shown in Table 7.2.

Table 7.2: Operational properties

Properties Values

Temperature variation, ΔT 100°C

Pipe operational submerged weight, W 0.80kN/m

The physical pipeline parameters include steel outside diameter, steel wall thickness and

pipeline length, among others as shown in Table 7.3.

Table 7.3: Physical pipeline properties

Properties Values

Steel outside diameter, OD 0.3239m

Steel wall thickness, t 0.0206m

Steel Young’s modulus, E 2.07x1011Pa

Steel Poisson coefficient, ν 0.3

Steel thermal expansion coefficient, α 1.165x10-5/°C

Pipeline length, L LOW: 3000m

MID: 4000m

Variable slopes

152

HIGH: 5000m

As previous research has already investigated different soils’ behavior, for example

Castelo et al. (2019) and Castelo et al. (2017), this paper assumes a simpler idealization:

elastic-perfectly-plastic (Castelo et al., 2019) with the same mobilisation distance, δmob,

for the entire numerical study, as shown in Table 7.1.


PIPELINE WALKING ON SINGLE SLOPE

From Castelo et al. (2019) it is known that the walking rate for a given pipeline laid on a

single slope with an elastic-perfectly-plastic soil, WREP, can be obtained simply by

subtracting twice the soils’ mobilisation distance, δmob, from the walking rate for a rigid-

plastic soil idealization , WRRP, as shown by equation (7.1):

𝑊𝑅𝐸𝑃 = 𝑊𝑅𝑅𝑃 − 2 ∗ 𝛿𝑚𝑜𝑏 (7.1)

where the walking rate for a rigid-plastic soil can be estimated from Bruton et al. (2010)

and the mobilisation distance is an environmental property, as given by Table 7.1.

Equation (7.1) can be reorganized, as also explained in Castelo et al. (2019), into equation

(7.2), where the walking rate for an elastic-perfectly-plastic soil is established by

multiplying the rigid-plastic walking rate by a reduction factor based on the soil’s

mobilisation distance, δmob, and the non-walking mobilisation distance, δnull:

𝑊𝑅𝐸𝑃 = 𝑊𝑅𝑅𝑃 (1 −𝛿𝑚𝑜𝑏𝛿𝑛𝑢𝑙𝑙

) , 𝑖𝑓 𝛿𝑚𝑜𝑏 ≥ 𝛿𝑛𝑢𝑙𝑙 → 𝑊𝑅𝐸𝑃 = 0 (7.2)

where the mobilisation distance above which the walking rate is zero, δnull, is given by

equation (7.3), (Castelo et al., 2019):


(7.3)


The finite element models used in this paper are based on a straight pipeline laid on a

variable sloping seabed. Table 7.1 provides the environmental properties used in the finite

element models in this paper, which are: seabed slope, β, mobilisation distance, δmob, and

Chapter 7

153

the axial residual friction coefficient, µ; while Table 7.2 presents the operational

properties: temperature variation, ΔT, and pipe operational submerged weight, W.

The physical pipeline properties: steel outside diameter, OD, steel wall thickness, t, steel

Young’s Modulus, E, steel Poisson coefficient, ν, steel thermal expansion coefficient, α,

and the pipeline length, L, are provided in Table 7.3.

Variability was attributed to seabed slope, axial residual friction coefficient, and pipeline

length, so that the parametric study could be conducted. The pipelines were represented

by Euler Bernoulli beam elements (B33 – 3 dimensional 3 noded elements in Abaqus),

each 1m in length.

To represent the elastic-perfectly-plastic pipe-soil interaction, the soil was modelled as a

set of macro elements connected to each pipeline node, which were described as user

elements in FORTRAN.

Figure 7.3 shows a sketch of the finite element model between arbitrary nodes A and Z,

where the slope variation happens at a constant rate. It also provides information about

the boundary conditions imposed to all nodes, which can only displace along their local

longitudinal axis given the UEL reaction.

The spring-slider provided a constant stiffness between zero and a certain prescribed

displacement (mobilisation distance) and a corresponding force (according to Hooke's

law). If the displacement level exceeds the mobilisation distance, the UEL provides zero

tangent stiffness and a constant force, as per the residual plastic plateau. On reversal, the

same stiffness is considered, until the resultant force equals the residual plastic plateau.

The UEL behavior, as shown in Figure 7.4, is presented in terms of the loads normal to

the seabed alongside with the positive and negative residual plastic resistance forces, ±FR,

mobilisation distance, δmob.

The models used in this paper consider only weight and temperature (Table 7.2) as acting

loads on the pipeline. Pressure was disregarded due its marginal effect when compared

to the temperature effect.

The pipeline operational submerged weight, W, and the seabed slope angle, β, generate a

sliding component to the weight:


Operational cycling considered the prescribed temperature variation, as per Table 7.2,

Variable slopes

154

from the starting to the end model nodes, i.e. over the entire pipeline length, without any

intermediate temperature load case.

7.7 RANGE OF PARAMETRIC STUDIES

The present numerical study verifies the applicability of single slope pipeline walking

solutions to variable slopes topography, by using an average seabed slope, βave, applied

to the entire pipeline length, based on the environmental properties faced by a specific

pipeline route.

The numerical study uses the values provided in Table 7.1, Table 7.2 and Table 7.3 as

previously explained.

Finally, to investigate the slope variability impact on the pipeline walking phenomenon,

four different topographies were selected to be investigated. These are:

• Dual slope – convex;

• Dual slope – concave;

• Triple slope – flat-slope-flat;

• Triple slope – slope-flat-slope.

7.7.1 Dual slope – convex

Some pipelines are employed in regions where they face two different slopes with a steep

start, near the initial pipeline kilometer post, KP, and a smaller slope near the final KP.

This topography is illustrated by Figure 7.5.

These pipelines may face different angles along different stretches of their length. Hence,

these aspects were accounted for the numerical study through different models, whose

properties can be seen in Table 7.4 for gentle (models 01 – 13) and extreme (models 14

– 26) angles.

Table 7.4: Dual slope convex model properties

Model Property Values

μ L1 (m) L2 (m) β1 (°) β2 (°)

01 0.5 1500 1500 3 1

02 0.7 1500 1500 3 1

03 0.9 1500 1500 3 1

04 0.5 2000 2000 3 1

Chapter 7

155

05 0.7 2000 2000 3 1

06 0.9 2000 2000 3 1

07 0.5 2500 2500 3 1

08 0.7 2500 2500 3 1

09 0.9 2500 2500 3 1

10 0.9 2500 2500 4 2

11 0.9 1500 1500 4 2

12 0.9 2000 2000 4 2

13 0.7 2000 2000 4 2

14 0.9 2500 2500 6 4

15 0.9 2000 3000 7 3

16 0.9 1500 3500 8 2

17 0.9 1000 4000 9 1

18 0.9 1000 4000 10 0

19 0.9 2000 2000 7 3

20 0.9 2000 2000 7 2

21 0.9 2000 2000 7 1

22 0.9 2000 2000 6 3

23 0.9 1000 2000 7 3

24 0.9 1000 2000 8 2

25 0.9 2000 1000 7 1

26 0.9 2000 1000 6 1

7.7.2 Dual slope – concave

In other regions, pipelines face a small angle near the initial KP and a steeper slope near

the final KP. This shape is illustrated by Figure 7.5.

Table 7.5 presents the parameters considered for the numerical study, considering gentle

slopes (models 27 – 39) and extreme slopes (models 40 – 52).

Variable slopes

156

Table 7.5: Dual slope concave model properties


μ L1 (m) L2 (m) β1 (°) β2 (°)

27 0.5 1500 1500 1 3

28 0.7 1500 1500 1 3

29 0.9 1500 1500 1 3

30 0.5 2000 2000 1 3

31 0.7 2000 2000 1 3

32 0.9 2000 2000 1 3

33 0.5 2500 2500 1 3

34 0.7 2500 2500 1 3

35 0.9 2500 2500 1 3

36 0.9 2500 2500 2 4

37 0.9 1500 1500 2 4

38 0.9 2000 2000 2 4

39 0.7 2000 2000 2 4

40 0.9 2500 2500 4 6

41 0.9 2700 2300 2 7

42 0.9 2900 2100 1 8

43 0.9 3100 1900 0 9

44 0.9 3100 1900 1 10

45 0.9 2000 2000 3 7

46 0.9 3000 1000 3 8

47 0.9 3000 1000 2 9

48 0.9 3000 1000 3 10

49 0.9 2000 1000 4 7

50 0.9 2000 1000 3 8

51 0.9 2000 1000 2 9

52 0.9 2000 1000 1 10

Chapter 7

157

7.7.3 Triple slope – flat-slope-flat

Alternatively, pipelines may also be employed in regions where they cross a flat region

before facing a route slope and return to a flat area near their final kilometer post, KP.

This type of topography is illustrated in Figure 7.6.

These pipelines may face different angles. Then, these aspects were considered for the

numerical study through different models, whose properties are shown in Table 7.6 for

gentle angles (models 53 – 65) and extreme angles (models 66 – 78).

Table 7.6: Triple slope flat-slope-flat model properties


μ L1 (m) L2 (m) L3 (m) β1 (°) β2 (°) β3 (°)

53 0.5 1500 2000 1500 0 3 0

54 0.5 1000 3000 1000 0 3 0

55 0.5 500 4000 500 0 3 0

56 0.7 500 4000 500 0 3 0

57 0.5 1500 1000 1500 0 4 0

58 0.5 1000 2000 1000 0 4 0

59 0.5 500 3000 500 0 4 0

60 0.7 500 3000 500 0 4 0

61 0.5 1000 1000 1000 0 3 0

62 0.5 500 2000 500 0 3 0

63 0.7 500 2000 500 0 3 0

64 0.5 500 2000 500 0 5 0

65 0.5 500 4000 500 0 2 0

66 0.9 1500 2000 1500 0 10 0

67 0.9 1000 3000 1000 0 8 0

68 0.9 500 4000 500 0 6 0

69 0.7 1000 3000 1000 0 6 0

70 0.7 1750 500 1750 0 10 0

71 0.9 1500 1000 1500 0 8 0

Variable slopes

158

72 0.9 1250 1500 1250 0 8 0

73 0.9 1500 1000 1500 0 10 0

74 0.5 1000 1000 1000 0 6 0

75 0.7 1000 1000 1000 0 6 0

76 0.7 1300 400 1300 0 10 0

77 0.7 1200 600 1200 0 10 0

78 0.9 1200 600 1200 0 10 0

7.7.4 Triple slope – flat-slope-flat

Other regions may require that pipelines cross a sloped area before facing a flat area and

then cross another slope near their final KP. This shape is schematically shown in Figure

7.6.

Table 7.7 presents the parameters considered for the numerical study for gentle angles

(models 79 – 91) and extreme angles (models 92 – 104).

Table 7.7: Triple slope slope-flat-slope model properties


μ L1 (m) L2 (m) L3 (m) β1 (°) β2 (°) β3 (°)

79 0.5 1500 2000 1500 3 0 3

80 0.5 1000 3000 1000 3 0 3

81 0.5 500 4000 500 3 0 3

82 0.7 500 4000 500 3 0 3

83 0.7 1500 1000 1500 4 0 4

84 0.7 1000 2000 1000 4 0 4

85 0.5 500 3000 500 4 0 4

86 0.7 500 3000 500 4 0 4

87 0.5 1000 1000 1000 3 0 3

88 0.5 500 2000 500 3 0 3

89 0.7 500 2000 500 3 0 3

90 0.7 500 2000 500 5 0 5

Chapter 7

159

91 0.5 500 4000 500 2 0 2

92 0.9 500 4000 500 10 0 10

93 0.9 750 3500 750 9 0 9

94 0.9 1000 3000 1000 8 0 8

95 0.9 500 4000 500 8 0 8

96 0.9 1750 500 1750 5 0 5

97 0.5 500 3000 500 5 0 5

98 0.7 500 3000 500 5 0 5

99 0.9 500 3000 500 5 0 5

100 0.9 500 2000 500 6 0 6

101 0.9 1000 1000 1000 6 0 6

102 0.9 500 2000 500 7 0 7

103 0.9 500 2000 500 9 0 9

104 0.9 1000 1000 1000 7 0 7

7.8 FINITE ELEMENT MODEL RESULTS

Table 7.8 and Table 7.9 show the following properties for the dual slope cases (convex

and concave, respectively):

• Residual axial friction coefficient, μ;

• Total length of the pipeline, LTotal;

• Average seabed slope angle, βave;

• Calculated walking rate, WRCalc, as per Castelo et al. (2019); and,

• Finite element model observed walking rate, WRFEM.

Table 7.8: Dual slope – Convex model results

Model

Properties Results

μ LTotal (m) βave (°) WRCalc

(m/cycle)

WRFEM

(m/cycle)

01 0.5 3000 2.0 0.106596 0.105418

02 0.7 3000 2.0 0.035611 0.035033

Variable slopes

160

03 0.9 3000 2.0 0 0.001286

04 0.5 4000 2.0 0.143218 0.141028

05 0.7 4000 2.0 0.048026 0.046524

06 0.9 4000 2.0 0 0.001865

07 0.5 5000 2.0 0.167058 0.164796

08 0.7 5000 2.0 0.047384 0.046478

09 0.9 5000 2.0 0 0.001619

10 0.9 5000 3.0 0.016589 0.017307

11 0.9 3000 3.0 0.036176 0.035523

12 0.9 4000 3.0 0.036083 0.035627

13 0.7 4000 3.0 0.116357 0.115592

14 0.9 5000 5.0 0.098955 0.097844

15 0.9 5000 4.6 0.081275 0.078890

16 0.9 5000 3.8 0.047742 0.040380

17 0.9 5000 2.6 0.001879 0.001719

18 0.9 5000 2.0 0 0.000016

19 0.9 4000 5.0 0.125128 0.122545

20 0.9 4000 4.5 0.101952 0.099380

21 0.9 4000 4.0 0.079395 0.076810

22 0.9 4000 4.5 0.10195 0.100640

23 0.9 3000 4.3 0.091652 0.086900

24 0.9 3000 4.0 0.077549 0.068640

25 0.9 3000 5.0 0.120343 0.119994

26 0.9 3000 4.3 0.091663 0.091600

Table 7.9: Dual slope – Concave model results

Model

Properties Results


(m/cycle)

WRFEM

(m/cycle)

Chapter 7

161

27 0.5 3000 2.0 0.106580 0.104538

28 0.7 3000 2.0 0.035601 0.034397

29 0.9 3000 2.0 0 0.001184

30 0.5 4000 2.0 0.143204 0.141432

31 0.7 4000 2.0 0.048018 0.046693

32 0.9 4000 2.0 0 0.001749

33 0.5 5000 2.0 0.167045 0.164354

34 0.7 5000 2.0 0.047377 0.046532

35 0.9 5000 2.0 0 0.000996

36 0.9 5000 3.0 0.016585 0.017212

37 0.9 3000 3.0 0.036176 0.035701

38 0.9 4000 3.0 0.036083 0.035567

39 0.7 4000 3.0 0.116357 0.115395

40 0.9 5000 5.0 0.098950 0.097864

41 0.9 5000 4.3 0.068417 0.068170

42 0.9 5000 3.9 0.053435 0.053310

43 0.9 5000 3.4 0.032646 0.032755

44 0.9 5000 4.4 0.073517 0.074023

45 0.9 4000 5.0 0.125116 0.122890

46 0.9 4000 4.3 0.090586 0.090960

47 0.9 4000 3.8 0.068331 0.068488

48 0.9 4000 4.8 0.113451 0.113523

49 0.9 3000 5.0 0.120332 0.119374

50 0.9 3000 4.7 0.105910 0.105470

51 0.9 3000 4.3 0.091649 0.091810

52 0.9 3000 4.0 0.077546 0.077145

With the same table structure, Table 7.10 and Table 7.11 present the results for flat-slope-

flat and slope-flat-slope geometries, respectively, accounting for gentle and extreme

angles.

Variable slopes

162

Table 7.10: Triple slope flat-slope-flat model results

Model

Properties Results


(m/cycle)

WRFEM

(m/cycle)

53 0.5 5000 1.2 0.065240 0.059084

54 0.5 5000 1.8 0.141220 0.133603

55 0.5 5000 2.4 0.219433 0.210500

56 0.7 5000 2.4 0.074987 0.071869

57 0.5 4000 1.0 0.029641 0.027041

58 0.5 4000 2.0 0.143211 0.133256

59 0.5 4000 3.0 0.260856 0.252641

60 0.7 4000 3.0 0.116361 0.110550

61 0.5 3000 1.0 0.012180 0.010683

62 0.5 3000 2.0 0.106580 0.101793

63 0.7 3000 2.0 0.035601 0.034377

64 0.5 3000 3.3 0.236102 0.230289

65 0.5 5000 1.6 0.115653 0.110969

66 0.9 5000 4.0 0.055908 0.042230

67 0.9 5000 4.8 0.090046 0.077470

68 0.9 5000 4.8 0.090042 0.079980

69 0.7 5000 3.6 0.162266 0.159180

70 0.7 4000 1.3 0 0.000194

71 0.9 4000 2.0 0 0.000330

72 0.9 4000 3.0 0.036096 0.035460

73 0.9 4000 2.5 0.015313 0.010670

74 0.5 3000 2.0 0.106604 0.104897

75 0.7 3000 2.0 0.035616 0.031720

76 0.7 3000 1.3 0 0.000037

77 0.7 3000 2.0 0.035636 0.026360

Chapter 7

163

78 0.9 3000 2.0 0 0.000121

Table 7.11: Triple slope slope-flat-slope model results

Model

Properties Results


(m/cycle)

WRFEM

(m/cycle)

79 0.5 5000 1.8 0.141208 0.133386

80 0.5 5000 1.2 0.065266 0.057494

81 0.5 5000 0.6 0 0.000491

82 0.7 5000 0.6 0 0.000090

83 0.7 4000 3.0 0.116343 0.111040

84 0.7 4000 2.0 0.048005 0.044223

85 0.5 4000 1.0 0.029614 0.024999

86 0.7 4000 1.0 0 0.000143

87 0.5 3000 2.0 0.106556 0.100635

88 0.5 3000 1.0 0.012156 0.008746

89 0.7 3000 1.0 0 0.000070

90 0.7 3000 1.7 0.015872 0.011900

91 0.5 5000 0.4 0 0.000079

92 0.9 5000 2.0 0 0.000111

93 0.9 5000 2.7 0.005532 0.003600

94 0.9 5000 3.2 0.024151 0.023130

95 0.9 5000 1.6 0 0.000031

96 0.9 4000 4.4 0.096236 0.090840

97 0.5 4000 1.3 0.057630 0.049700

98 0.7 4000 1.3 0 0.000264

99 0.9 4000 1.3 0 0.000013

100 0.9 3000 2.0 0 0.000143

101 0.9 3000 4.0 0.077528 0.070430

Variable slopes

164

102 0.9 3000 2.3 0.009347 0.004670

103 0.9 3000 3.0 0.036196 0.035010

104 0.9 3000 4.7 0.105883 0.101833

In general terms, when accounting for all models’ results, the overall percentage error

generated by the solution proposed by this paper is 6.442% only, which is a marginal

deviation.

Figure 7.7 presents the walking rate results from the numerical solutions (finite element

models) plotted against the values calculated by equation (7.1). Cross markers represent

the dual slope convex shape, while square markers represent dual slope concave shape.

Circle markers represent flat-slope-flat shape, whilst triangle markers stand for slope-

flat-slope shapes. The colors gray and black represent gentle and extreme angles,

respectively.

As can be seen in Figure 7.7 and as previously explained, the deviation found between

the analytical formulation and the finite element models can be classified as marginal.

Therefore, the accuracy and applicability from the proposed methodology can be

regarded as appropriate.


This paper provides the technical confirmation to the available methods about pipeline

walking on a variable slopes’ topography. It shows that the analytical expressions

currently available in the literature can be applied with an average slope value; and,

proves so, by an extensive benchmark against finite element analyses test (focused solely

on seabed slope variability).

This paper also proves that emerging research on pipe-soil interaction variability can

properly solve gravity-driven downslope pipeline walking problems with slope

variability.

Different slopes and properties of slope variability have been considered in this paper;

while it also checked how currently available solutions (single-slope and rigid-plastic

pipe-soil interaction) could be adapted to allow for slope and pipe-soil interaction

variabilities. Therefore, this paper resolves how currently available solutions must be

adjusted to allow for slope variability and realistic pipe-soil interactions.

Chapter 7

165

In conclusion, the findings of this paper can be used to assess the pipeline walking

behaviors for a variable-slope laid pipeline while also accounting for realistic pipe-soil

interactions.

Variable slopes

166

FIGURES

Figure 7.1: Effective axial force diagrams

Figure 7.2: Axial displacement diagrams

Chapter 7

167

Figure 7.3: Finite element model sketch

Figure 7.4: User element behavior

Variable slopes

168

Figure 7.5: Dual slope general shapes

Figure 7.6: Triple slope general shapes

Chapter 7

169

Figure 7.7: Walking rate results

Concluding remarks

170

CHAPTER 8. CONCLUDING REMARKS

Chapter context: In the following sections are listed the principal findings and their

contributions on the assessment of downslope pipeline walking for future engineering

studies. Recommendations for further research are also presented in this chapter.

Chapter 8

171

8.1 PRINCIPAL FINDINGS AND CONTRIBUTIONS

This thesis improves the understanding about downslope pipeline walking and soil

variables by accomplishing the research goals listed in Chapter 1. As presented in Section

1.2, the goals of this thesis were fulfilled delivering four major contributions:

1. Revision of the analytical equations;

2. Interpretation of the changes in walking behaviour;

3. Expansion to any pipe-soil interaction;

4. Confirmation of applicability on variable slopes.

8.1.1 Pipe-soil interaction models

This thesis starts by reviewing the available literature on the subject, alongside with other

engineering topics that are associated to the methods of research. It shows how the current

solutions idealise the realistic pipe-soil interaction models as a rigid-plastic model.

The following subheadings provide some details on how such pipe-soil interaction

models were found to interfere on the downslope pipeline walking pattern. For the

analytical methodology updates, please refer to Section 8.1.3, where the new analytical

assessment of downslope pipeline walking is summarised.

Elastic-perfectly-plastic

In Chapter 3, the research starts by analytically investigating the elastic-perfectly-plastic

pipe-soil interaction model and its impacts on the downslope walking behaviour. In this

chapter a detailed revision of the analytical formulation is presented, which enhances the

interpretations on the walking behaviour.

The analytical investigation found that the distance between stationary points (initially

referred to as “virtual anchor sections”) has a major influence in the walking behaviour;

and, the definition primarily given by Carr et al. (2006) needed to be updated. The

findings of Chapter 3 show why the “virtual anchor sections” should be substituted by

the “stationary points” and how the distance between stationary points can be obtained

by adjusting the previously available analytical solution.

The chapter then presents a methodology allowing current analytical solutions (Carr et

al., 2006) to account for elastic-perfectly-plastic pipe-soil interaction in a similar fashion

as it was initially proposed to the distance between stationary points.

Concluding remarks

172

Non-linear elastic-plastic

Chapter 4 develops the analytical investigation initially presented in Chapter 3 by

considering non-linear elastic-plastic pipe-soil interaction model. Another detailed

revision of the analytical formulation is presented enhancing the understandings on the

walking behaviour.

It was found that the same influence was generated by the distance between stationary

points; and similar updates were required for the non-linear elastic-plastic pipe-soil

interaction model. The chapter also establishes how a non-linear elastic-plastic pipe-soil

interaction can be satisfactorily approximated to an elastic-perfectly-plastic pipe-soil

interaction model. It also drives attention to the non-walking behaviour that was found

from some simulations and provides the necessary justifications for the non-walking

behaviour.

The chapter conclude that with the proper adjustments, the currently used analytical

solutions allow for the non-linear elastic-plastic pipe-soil interaction to be analytically

assessed

Tri-linear with a peak

Based on Chapters 3 and 4 outcomes, Chapter 5 skips the analytical investigation and

starts from the numerical modelling to prove that similar adjustments could be done to

the current analytical solutions.

Aligned with the previous findings, the distance between stationary points has also been

found to generate changes in walking patterns; even though the pipe-soil interaction

presents a peak. The chapter clarifies that the referred peak can be ignored since its impact

has a marginal and negligible effect on the downslope pipeline walking phenomenon.

The chapter shows how the adjustments to the analytical solutions are done for tri-linear

soils with a peak, which perfectly aligns with the previous findings.

Non-linear with a peak

Chapter 6 findings show the necessary adjustments for the application of the new

analytical assessments of downslope pipeline walking on non-linear soils with a peak. It

clarifies that different shapes of non-linearity generate different influences in the walking

behaviour, i.e. the greater the pipe-soil interaction unload-reload area, AUnload-Reload, the

greater the over conservatism implied by the rigid-plastic solutions.

Chapter 8

173

General notes

In summary, the findings of Chapters 3, 4, 5, and 6 show that depending on the pipe-soil

interaction model to be considered, a different mobilisation distance should be accounted

for in the adjustments of the analytical solutions.

The mobilisation distance needs to be calculated based on the realistic pipe-soil

interaction Force - Displacement curve (FxD). Table 8.1 presents a “cheat-sheet” on how

the referred mobilisation distances can be achieved.

Table 8.1: Preliminary example properties.

Pipe-soil interaction model Mobilisation distance

Elastic-perfectly-plastic pipe-soil interaction Section 3.3 (Figure 3.3)

Non-linear elastic-plastic pipe-soil interaction Section 4.3.2 (Figure 4.3)

Peaky linear pipe-soil interaction Section 5.10

Non-linear peaky pipe-soil interaction Section 6.7 (Figure 6.14)

8.1.2 Variable slopes

Since current solutions have not yet been verified for the applicability on variable slopes

topography, Chapter 7 aims to establish how the fundamental solutions for single slope

topographies can be improved to allow for slope variability and realistic soil reactions.

It brings previous chapters’ findings one step closer to the real-world application by

simulating a more realistic scenario related to pipelines traversing a seabed with

significant slope changes. Therefore, various shapes and angles were accounted for

generating a reliable and representative set of study cases.

In other words, it proves that treating adequately the different slopes of a specific pipeline

route, it can be satisfactorily solved with this research’s findings, which are simple, easy

and very quick to apply into pipeline engineering activities. Finally, this confirms the

achievement of the overall thesis objective– offer the engineering community a quick and

easy way to evaluate downslope pipeline walking regardless of the soil conditions and

route topography.

8.1.3 A new assessment of downslope pipeline walking

The findings exposed in this thesis enhance the analytical solutions for pipeline walking

assessment, so that more realistic walking rates are obtained in a simple and quick manner

Concluding remarks

174

accounting for realistic pipe-soil interaction properties. The new analytical results are

more accurate than the previous formulation because it reduces the conservativeness

implied by the rigid-plastic pipe-soil calculations. It eliminates the overestimation of

walking based on the realistic pipe-soil interaction, as shown in Chapters 3 to 7; and, the

comparison between the new analytical and finite element results. This improvement in

accuracy also eliminates the need for finite element modelling.

In conclusion, the findings of this research can be summarised as:

𝑊𝑅 = 𝑊𝑅𝑅𝑃 ∗ (1 −𝛿𝑚𝑜𝑏𝛿𝑛𝑢𝑙𝑙

) , 𝑖𝑓 𝛿𝑚𝑜𝑏 ≥ 𝛿𝑛𝑢𝑙𝑙 → 𝑊𝑅 = 0 (8.1)

where WR stands for the walking rate, RP for rigid-plastic, δmob for the mobilisation

distance and δnull for the non-walking mobilisation distance.

The findings of this thesis also clarify that the mobilisation distance, δmob, to be accounted

for in equation (8.1), should be obtained using equation (8.2):

𝛿𝑚𝑜𝑏 =𝐴𝑈𝑛𝑙𝑜𝑎𝑑−𝑅𝑒𝑙𝑜𝑎𝑑

𝛥𝐹𝑅 (8.2)

where AUnload-Reload is the unload-reload area, and ΔFR is the variation in residual friction

as it is referenced prior to Table 8.1 by the realistic pipe-soil interaction Force -

Displacement curve (FxD).

And the non-walking mobilisation distance, δnull, should be obtained using equation (8.3):


(8.3)

The rigid-plastic walking rate can be calculated, as per Bruton et al. (2010):


𝐸𝐴𝜇 (8.4)

while, W stands for the pipeline operational submerged weight, L for pipeline physical

length, β for seabed slope angle, µ for the soil axial residual friction coefficient, E for the

steel Young’s modulus and A for the pipeline steel cross sectional area. And, ΔP is the

change in fully constrained force, as per Carr et al. (2003).

Therefore, it can be concluded that, for any pipe-soil interaction condition, it is now

available a simple and direct analytical solution, which makes quicker and more precise

the assessment of a pipeline in regards of downslope walking issues.

Chapter 8

175

8.2 FURTHER RESEARCH RECOMMENDATIONS

This research project resulted into several new findings concerning the downslope

pipeline walking phenomenon. The PhD candidate and his supervisors believe that

similar research processes could be applied into other problems, but which were beyond

the scope of the present work. These are:

1. Sustained tension, thermal transients and multiphase flow pipeline walking. The

suggested research here is related to the same phenomenon but driven by other

causes. These are the three other drivers of pipeline walking (Bruton et al., 2010)

and a similar strategy could be used in order to review the available analytical

expressions and then more robust analytical formulation becomes accessible for

future industry and academic activities.

2. Interaction between pipeline walking and lateral buckling. The interaction

between pipeline walking and lateral buckling has been an issue treated in a case

by case strategy; although it has been in the spotlight for a while. Lateral buckling

itself is a major issue, which may have its consequences potentiated by the

influence of pipeline walking. If not properly designed, lateral buckling may

cause serious damages to pipeline.

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176

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White, D. et al. (2011) ‘SAFEBUCK JIP - Observations of Axial Pipe-Soil Interaction

from Testing on Soft Natural Clays’, in Proceedings of the Offshore Technology

Conference. doi: 10.4043/21249-MS.

White, D. et al. (2012) ‘A New Framework for Axial Pipe-Soil Interaction, Illustrated by

Shear Box Tests on Carbonate Soils’, in Proceedings of the International Conference on

Offshore Site Investigation and Geotechnics.

White, D. and Cathie, D. (2011) ‘Geotechnics for Subsea Pipelines’, in Proceedings of

the International Symposium on Frontiers in Offshore Geotechnics II, pp. 87–123. doi:

10.1201/b10132-6.

Appendix A

180

APPENDIX A

Appendix A gives more details on the pile/ pipe equivalence as stated by Section 3.9

accordingly with Randolph (1977).

• Basic Mechanics Revision

휀𝑀𝑒𝑐ℎ =𝐹

𝐸𝐴 (A.1)

휀𝑇𝑜𝑡𝑎𝑙 =𝑑𝛿

𝑑𝑥 (A.2)

(휀𝑀𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑎𝑙 + 휀𝑇ℎ𝑒𝑟𝑚𝑎𝑙) =𝑑𝛿

𝑑𝑥 (A.3)

𝑑2𝛿

𝑑𝑥2=

1

𝐸𝐴

𝑑𝐹

𝑑𝑥+ 𝛼𝛥𝑇 (A.4)

• Longitudinal Coordinate

The longitudinal coordinate, in equation (3.8) referred to as x, was substituted by the

section distance, s, as expressed by equation (A.5); where x is the absolute KP value of

the section in question and x23 is the boundary KP value for the case assessed, as

previously explained.

𝑠 = |𝑥 − 𝑥23| (A.5)

• Factor ξ

To get this factor expression, put all zones apart and do the calculations only for Z1, the

other zones will be later checked to prove whether this result is valid or not.

Hence, putting together equations (3.8) and (3.12) we can achieve the following system

of equations:

{

𝛿 = 𝐾1𝑒𝜉𝑍1𝑠 + 𝐾2𝑒

−𝜉𝑍1𝑠

𝑑𝐹

𝑑𝑥= (

𝜇𝑊𝑍1

𝛿𝑚𝑜𝑏) 𝛿

𝑑𝐹

𝑑𝑥= 𝐸𝐴(𝐾1𝜉𝑍1

2𝑒𝜉𝑍1∗𝑠 + 𝐾2𝜉𝑍12𝑒−𝜉𝑍1∗𝑠)

(A.6)

And from this system of equations, we can extract:

𝜉𝑍1 = √(𝜇𝑊𝑍1

𝐸𝐴𝛿𝑚𝑜𝑏) (A.7)

Appendix A

181

From the final shape of its expression, we can conclude that for zones Z1 and Z2, ξ has

the same value; and, this is also valid for zones Z3 and Z4. Then, there are actually only

two values for factor ξ, ξZ1 and ξZ4 applicable for zones Z1 and Z2 and Z3 and Z4,

respectively.

• Constants K1 and K2

Analogously to Randolph’s equations (4.27) and (4.28), we needed to define a pair of

equations suited to the present problem, to be considered at a single position of the pipe.

Equation (A.8) is related to x23 displacement, while equation (A.9) is related to its third

derivative through the second derivative of force.

𝛿(𝑥23) = (𝐾1𝑒𝜉𝑍1∗𝑠 + 𝐾2𝑒

−𝜉𝑍1∗𝑠)(𝑥23)

(A.8)

𝑑2𝐹

𝑑𝑥2(𝑥23)= 𝐸𝐴𝜉𝑍1

3(𝐾1𝑒𝜉𝑍1∗𝑠 − 𝐾2𝑒

−𝜉𝑍1∗𝑠)(𝑥23)

(A.9)

For x23, we can simplify the exponential portions as equal to 1, because the s exponent

will assume the value of 0 (zero). The notation Z1 was used in this item, but it could be

used Z4, as well, because x23 is the limit between the different zones. Therefore, because

of point x23’s nature, equation (A.8) and equation (A.9) might be rewritten with Z4

indices. This also means that the force acting at x23 might be dependent on Z1 or Z4 and

they must provide the same force result.

Tackling first equation (A.8), we will have – analogously to Randolph’s equation (4.28)

– using the δx boundary conditions (Section 3.9.1):

{

𝛿(𝑥23) = 0

(𝐾1𝑒𝜉𝑍1∗𝑠 + 𝐾2𝑒

−𝜉𝑍1∗𝑠)(𝑥23)

= 0

(𝐾1 + 𝐾2)(𝑥23) = 0

(A.10)

Before handling equation (A.9), we need to take a step back and look at the following

relations:

𝑑2𝐹

𝑑𝑥2=𝑑𝑑𝐹𝑑𝑥𝑑𝑥

𝑑2𝐹

𝑑𝑥2=𝑑 (𝜇𝑊𝑍1

𝛿𝑚𝑜𝑏) 𝛿

𝑑𝑥

𝑑2𝐹

𝑑𝑥2= (

𝜇𝑊𝑍1

𝛿𝑚𝑜𝑏)𝑑𝛿

𝑑𝑥

(A.11)

Appendix A

182

𝑑2𝐹

𝑑𝑥2= (

𝜇𝑊𝑍1

𝛿𝑚𝑜𝑏) 휀𝑇𝑜𝑡𝑎𝑙

𝑑2𝐹

𝑑𝑥2= (

𝜇𝑊𝑍1

𝛿𝑚𝑜𝑏) (휀𝑀𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑎𝑙 + 휀𝑇ℎ𝑒𝑟𝑚𝑎𝑙)

𝑑2𝐹

𝑑𝑥2= (

𝜇𝑊𝑍1

𝛿𝑚𝑜𝑏) (

𝐹

𝐸𝐴+ 𝛼𝛥𝑇) =

𝜇𝑊𝑍1

𝐸𝐴𝛿𝑚𝑜𝑏∗ 𝐹 +

𝜇𝑊𝑍1𝛼𝛥𝑇

𝛿𝑚𝑜𝑏

Then, equating expression (A.9) with the final product of expression (A.11) we’ll have:

(𝐾1 − 𝐾2)(𝑥23) = (𝜇𝑊𝑍1

𝜉𝑍13𝐸𝐴2𝛿𝑚𝑜𝑏

∗ 𝐹 +𝜇𝑊𝑍1𝛼𝛥𝑇

𝜉𝑍13𝐸𝐴𝛿𝑚𝑜𝑏

)(𝑥23)

(A.12)

Working with equations (A.10) and (A.11) as a system, we’ll achieve:

𝐾1(𝑥23)= (

𝜇𝑊𝑍1

2𝜉𝑍13𝐸𝐴𝛿𝑚𝑜𝑏

[1

𝐸𝐴∗ 𝐹 + 𝛼𝛥𝑇])

(𝑥23)

𝐾2(𝑥23)= −(

𝜇𝑊𝑍1

2𝜉𝑍13𝐸𝐴𝛿𝑚𝑜𝑏

[1


(𝑥23)

(A.13)

Algebraically manipulating ξ we can simplify equation (A.13) as:

𝐾1(𝑥23)= (

1

2√𝐸𝐴𝛿𝑚𝑜𝑏𝜇𝑊𝑍1

[1


(𝑥23)

𝐾2(𝑥23)= −(

1


[1


(𝑥23)

(A.14)

Or if we prefer:

𝐾1(𝑥23)= (

1


휀𝑇𝑜𝑡𝑎𝑙)

(𝑥23)

𝐾2(𝑥23)= −(

1


휀𝑇𝑜𝑡𝑎𝑙)

(𝑥23)

(A.15)

However, both solutions for K1 and K2, shown by equations (A.14) or (A.15), depend on

the force acting at x23. At this point, the value provided by Carr’s solution is applied.

Appendix A

183

By the expressions shown in equation (A.14), it was deduced that the impact of the RP

force value would be extremely small, once the force is divided by the axial stiffness.

This prediction was later confirmed when the results were compared for K1 and K2

calculated with RP and EP soils responses (the difference was 0.003%).

Appendix B

184

APPENDIX B

Appendix B helps a better understanding by providing a base case comparison in one

(cheat) sheet for all pipe-soil interaction models used in this thesis (Chapters 3, 4, 5, and

6) as Table B.1. Six new assessments were performed to match models 1 and 2 from

Chapter 6 and illustrate the influence of the pipe soil interaction models into the walking

behaviour.

Table B.1: Base cases comparison

Chapter Model

Property Values

WR (m/cycle)

L (m) W (kN/m) μ β (°) δmob /OD

3 New1 5000 0.4 0.25 2 10.000% 0.674

New2 5000 0.4 0.25 2 7.679% 0.690

4 New3 5000 0.4 0.25 2 10.000% 0.674

New4 5000 0.4 0.25 2 7.679% 0.689

5 New5 5000 0.4 0.25 2 10.000% 0.673

New6 5000 0.4 0.25 2 7.679% 0.690

6 1 5000 0.4 0.25 2 10.000% 0.674

2 5000 0.4 0.25 2 7.679% 0.693

As it can be seen, negligible differences are noticed for the same mobilisation distances,

as long as, other case properties are constant regardless the pipe soil interaction model

used.

Appendix C

185

APPENDIX C

Appendix C provides more information about finite element model details.

• Mesh Sensitivity

In different parts of the research, it has been clarified that mesh sensitivity was

performed and it was found that 1m was a good enough element size at all parts.

The values obtained from the mesh sensitivity are presented below in Table

C.1Table C.1: Mesh sensitivity checks

Chapter Model Element/ Mesh Size (m) WR (m/cycle)

3

New1

0.50 0.677

1.00 0.674

2.00 0.676

New2

0.50 0.694

1.00 0.690

2.00 0.692

4

New3

0.50 0.677

1.00 0.674

2.00 0.675

New4

0.50 0.693

1.00 0.689

2.00 0.690

5

New5

0.50 0.677

1.00 0.673

2.00 0.675

New6

0.50 0.693

1.00 0.690

2.00 0.692

6 1

0.50 0.678

1.00 0.674

2.00 0.678

Appendix C

186

Chapter Model Element/ Mesh Size (m) WR (m/cycle)

2

0.50 0.694

1.00 0.693

2.00 0.694

• Analysis Input File Example

Appendix C

187

Appendix C

188

Appendix C

189

Appendix D

190

APPENDIX D

Appendix D provides the calculation check for lateral buckling for all models used in this

thesis (Chapters 3, 4, 5, 6 and 7). Although the coupled problem of walking and lateral

buckling is not the aim of this thesis, these calculations are provided here in order to show

that some cases studied are not susceptible to lateral buckling; whilst some other cases

are. Therefore, it can be understood that even illustration cases (i.e. cases that could suffer

lateral buckling) of the different soil characterization still have value for practical and

real situations. All cases (with or without lateral buckling susceptibility) follow through

the patterns established by this study.

Table D.1: Lateral buckling check

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)

μ β (°) δmob /OD

3 1 3000 0.4 0.5 1 0.03 No

3 2 3000 0.4 0.5 1 0.05 No

3 3 3000 0.4 0.5 1 0.06 No

3 4 3000 0.4 0.5 1 0.1 No

3 5 3000 0.4 0.5 1 0.15 No

3 6 3000 0.4 0.5 1 0.2 No

3 7 3000 0.4 0.5 1 0.33 No

3 8 3000 0.4 0.5 1 0.5 No

3 9 3000 0.6 0.5 1 0.03 No

3 10 3000 0.6 0.5 1 0.05 No

3 11 3000 0.6 0.5 1 0.06 No

3 12 3000 0.6 0.5 1 0.1 No

3 13 3000 0.6 0.5 1 0.15 No

3 14 3000 0.6 0.5 1 0.2 No

3 15 3000 0.6 0.5 1 0.33 No

3 16 3000 0.6 0.5 1 0.5 No

3 17 3000 0.8 0.5 1 0.03 No

3 18 3000 0.8 0.5 1 0.05 No

Appendix D

191

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


3 19 3000 0.8 0.5 1 0.06 No

3 20 3000 0.8 0.5 1 0.1 No

3 21 3000 0.8 0.5 1 0.15 No

3 22 3000 0.8 0.5 1 0.2 No

3 23 3000 0.8 0.5 1 0.33 No

3 24 3000 0.8 0.5 1 0.5 No

3 25 3000 0.4 0.7 1 0.03 No

3 26 3000 0.4 0.7 1 0.05 No

3 27 3000 0.4 0.7 1 0.06 No

3 28 3000 0.4 0.7 1 0.1 No

3 29 3000 0.4 0.7 1 0.15 No

3 30 3000 0.4 0.7 1 0.2 No

3 31 3000 0.4 0.7 1 0.33 No

3 32 3000 0.4 0.7 1 0.5 No

3 33 3000 0.6 0.7 1 0.03 No

3 34 3000 0.6 0.7 1 0.05 No

3 35 3000 0.6 0.7 1 0.06 No

3 36 3000 0.6 0.7 1 0.1 No

3 37 3000 0.6 0.7 1 0.15 No

3 38 3000 0.6 0.7 1 0.2 No

3 39 3000 0.6 0.7 1 0.33 No

3 40 3000 0.6 0.7 1 0.5 No

3 41 3000 0.8 0.7 1 0.03 No

3 42 3000 0.8 0.7 1 0.05 No

3 43 3000 0.8 0.7 1 0.06 No

3 44 3000 0.8 0.7 1 0.1 No

Appendix D

192

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


3 45 3000 0.8 0.7 1 0.15 No

3 46 3000 0.8 0.7 1 0.2 No

3 47 3000 0.8 0.7 1 0.33 No

3 48 3000 0.8 0.7 1 0.5 No

3 49 3000 0.4 0.9 1 0.03 Yes

3 50 3000 0.4 0.9 1 0.05 Yes

3 51 3000 0.4 0.9 1 0.06 Yes

3 52 3000 0.4 0.9 1 0.1 Yes

3 53 3000 0.4 0.9 1 0.15 Yes

3 54 3000 0.4 0.9 1 0.2 Yes

3 55 3000 0.4 0.9 1 0.33 Yes

3 56 3000 0.4 0.9 1 0.5 Yes

3 57 3000 0.6 0.9 1 0.03 Yes

3 58 3000 0.6 0.9 1 0.05 Yes

3 59 3000 0.6 0.9 1 0.06 Yes

3 60 3000 0.6 0.9 1 0.1 Yes

3 61 3000 0.6 0.9 1 0.15 Yes

3 62 3000 0.6 0.9 1 0.2 Yes

3 63 3000 0.6 0.9 1 0.33 Yes

3 64 3000 0.6 0.9 1 0.5 Yes

3 65 3000 0.8 0.9 1 0.03 Yes

3 66 3000 0.8 0.9 1 0.05 Yes

3 67 3000 0.8 0.9 1 0.06 Yes

3 68 3000 0.8 0.9 1 0.1 Yes

3 69 3000 0.8 0.9 1 0.15 Yes

3 70 3000 0.8 0.9 1 0.2 Yes

Appendix D

193

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


3 71 3000 0.8 0.9 1 0.33 Yes

3 72 3000 0.8 0.9 1 0.5 Yes

3 73 4000 0.4 0.5 1 0.03 No

3 74 4000 0.4 0.5 1 0.05 No

3 75 4000 0.4 0.5 1 0.06 No

3 76 4000 0.4 0.5 1 0.1 No

3 77 4000 0.4 0.5 1 0.15 No

3 78 4000 0.4 0.5 1 0.2 No

3 79 4000 0.4 0.5 1 0.33 No

3 80 4000 0.4 0.5 1 0.5 No

3 81 4000 0.6 0.5 1 0.03 No

3 82 4000 0.6 0.5 1 0.05 No

3 83 4000 0.6 0.5 1 0.06 No

3 84 4000 0.6 0.5 1 0.1 No

3 85 4000 0.6 0.5 1 0.15 No

3 86 4000 0.6 0.5 1 0.2 No

3 87 4000 0.6 0.5 1 0.33 No

3 88 4000 0.6 0.5 1 0.5 No

3 89 4000 0.8 0.5 1 0.03 Yes

3 90 4000 0.8 0.5 1 0.05 Yes

3 91 4000 0.8 0.5 1 0.06 Yes

3 92 4000 0.8 0.5 1 0.1 Yes

3 93 4000 0.8 0.5 1 0.15 Yes

3 94 4000 0.8 0.5 1 0.2 Yes

3 95 4000 0.8 0.5 1 0.33 Yes

3 96 4000 0.8 0.5 1 0.5 Yes

Appendix D

194

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


3 97 4000 0.4 0.7 1 0.03 No

3 98 4000 0.4 0.7 1 0.05 No

3 99 4000 0.4 0.7 1 0.06 No

3 100 4000 0.4 0.7 1 0.1 No

3 101 4000 0.4 0.7 1 0.15 No

3 102 4000 0.4 0.7 1 0.2 No

3 103 4000 0.4 0.7 1 0.33 No

3 104 4000 0.4 0.7 1 0.5 No

3 105 4000 0.6 0.7 1 0.03 Yes

3 106 4000 0.6 0.7 1 0.05 Yes

3 107 4000 0.6 0.7 1 0.06 Yes

3 108 4000 0.6 0.7 1 0.1 Yes

3 109 4000 0.6 0.7 1 0.15 Yes

3 110 4000 0.6 0.7 1 0.2 Yes

3 111 4000 0.6 0.7 1 0.33 Yes

3 112 4000 0.6 0.7 1 0.5 Yes

3 113 4000 0.8 0.7 1 0.03 Yes

3 114 4000 0.8 0.7 1 0.05 Yes

3 115 4000 0.8 0.7 1 0.06 Yes

3 116 4000 0.8 0.7 1 0.1 Yes

3 117 4000 0.8 0.7 1 0.15 Yes

3 118 4000 0.8 0.7 1 0.2 Yes

3 119 4000 0.8 0.7 1 0.33 Yes

3 120 4000 0.8 0.7 1 0.5 Yes

3 121 4000 0.4 0.9 1 0.03 Yes

3 122 4000 0.4 0.9 1 0.05 Yes

Appendix D

195

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


3 123 4000 0.4 0.9 1 0.06 Yes

3 124 4000 0.4 0.9 1 0.1 Yes

3 125 4000 0.4 0.9 1 0.15 Yes

3 126 4000 0.4 0.9 1 0.2 Yes

3 127 4000 0.4 0.9 1 0.33 Yes

3 128 4000 0.4 0.9 1 0.5 Yes

3 129 4000 0.6 0.9 1 0.03 Yes

3 130 4000 0.6 0.9 1 0.05 Yes

3 131 4000 0.6 0.9 1 0.06 Yes

3 132 4000 0.6 0.9 1 0.1 Yes

3 133 4000 0.6 0.9 1 0.15 Yes

3 134 4000 0.6 0.9 1 0.2 Yes

3 135 4000 0.6 0.9 1 0.33 Yes

3 136 4000 0.6 0.9 1 0.5 Yes

3 137 4000 0.8 0.9 1 0.03 Yes

3 138 4000 0.8 0.9 1 0.05 Yes

3 139 4000 0.8 0.9 1 0.06 Yes

3 140 4000 0.8 0.9 1 0.1 Yes

3 141 4000 0.8 0.9 1 0.15 Yes

3 142 4000 0.8 0.9 1 0.2 Yes

3 143 4000 0.8 0.9 1 0.33 Yes

3 144 4000 0.8 0.9 1 0.5 Yes

3 145 5000 0.4 0.5 1 0.03 Yes

3 146 5000 0.4 0.5 1 0.05 Yes

3 147 5000 0.4 0.5 1 0.06 Yes

3 148 5000 0.4 0.5 1 0.1 Yes

Appendix D

196

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


3 149 5000 0.4 0.5 1 0.15 Yes

3 150 5000 0.4 0.5 1 0.2 Yes

3 151 5000 0.4 0.5 1 0.33 Yes

3 152 5000 0.4 0.5 1 0.5 Yes

3 153 5000 0.6 0.5 1 0.03 Yes

3 154 5000 0.6 0.5 1 0.05 Yes

3 155 5000 0.6 0.5 1 0.06 Yes

3 156 5000 0.6 0.5 1 0.1 Yes

3 157 5000 0.6 0.5 1 0.15 Yes

3 158 5000 0.6 0.5 1 0.2 Yes

3 159 5000 0.6 0.5 1 0.33 Yes

3 160 5000 0.6 0.5 1 0.5 Yes

3 161 5000 0.8 0.5 1 0.03 Yes

3 162 5000 0.8 0.5 1 0.05 Yes

3 163 5000 0.8 0.5 1 0.06 Yes

3 164 5000 0.8 0.5 1 0.1 Yes

3 165 5000 0.8 0.5 1 0.15 Yes

3 166 5000 0.8 0.5 1 0.2 Yes

3 167 5000 0.8 0.5 1 0.33 Yes

3 168 5000 0.8 0.5 1 0.5 Yes

3 169 5000 0.4 0.7 1 0.03 Yes

3 170 5000 0.4 0.7 1 0.05 Yes

3 171 5000 0.4 0.7 1 0.06 Yes

3 172 5000 0.4 0.7 1 0.1 Yes

3 173 5000 0.4 0.7 1 0.15 Yes

3 174 5000 0.4 0.7 1 0.2 Yes

Appendix D

197

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


3 175 5000 0.4 0.7 1 0.33 Yes

3 176 5000 0.4 0.7 1 0.5 Yes

3 177 5000 0.6 0.7 1 0.03 Yes

3 178 5000 0.6 0.7 1 0.05 Yes

3 179 5000 0.6 0.7 1 0.06 Yes

3 180 5000 0.6 0.7 1 0.1 Yes

3 181 5000 0.6 0.7 1 0.15 Yes

3 182 5000 0.6 0.7 1 0.2 Yes

3 183 5000 0.6 0.7 1 0.33 Yes

3 184 5000 0.6 0.7 1 0.5 Yes

3 185 5000 0.8 0.7 1 0.03 Yes

3 186 5000 0.8 0.7 1 0.05 Yes

3 187 5000 0.8 0.7 1 0.06 Yes

3 188 5000 0.8 0.7 1 0.1 Yes

3 189 5000 0.8 0.7 1 0.15 Yes

3 190 5000 0.8 0.7 1 0.2 Yes

3 191 5000 0.8 0.7 1 0.33 Yes

3 192 5000 0.8 0.7 1 0.5 Yes

3 193 5000 0.4 0.9 1 0.03 Yes

3 194 5000 0.4 0.9 1 0.05 Yes

3 195 5000 0.4 0.9 1 0.06 Yes

3 196 5000 0.4 0.9 1 0.1 Yes

3 197 5000 0.4 0.9 1 0.15 Yes

3 198 5000 0.4 0.9 1 0.2 Yes

3 199 5000 0.4 0.9 1 0.33 Yes

3 200 5000 0.4 0.9 1 0.5 Yes

Appendix D

198

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


3 201 5000 0.6 0.9 1 0.03 Yes

3 202 5000 0.6 0.9 1 0.05 Yes

3 203 5000 0.6 0.9 1 0.06 Yes

3 204 5000 0.6 0.9 1 0.1 Yes

3 205 5000 0.6 0.9 1 0.15 Yes

3 206 5000 0.6 0.9 1 0.2 Yes

3 207 5000 0.6 0.9 1 0.33 Yes

3 208 5000 0.6 0.9 1 0.5 Yes

3 209 5000 0.8 0.9 1 0.03 Yes

3 210 5000 0.8 0.9 1 0.05 Yes

3 211 5000 0.8 0.9 1 0.06 Yes

3 212 5000 0.8 0.9 1 0.1 Yes

3 213 5000 0.8 0.9 1 0.15 Yes

3 214 5000 0.8 0.9 1 0.2 Yes

3 215 5000 0.8 0.9 1 0.33 Yes

3 216 5000 0.8 0.9 1 0.5 Yes

3 217 3000 0.4 0.5 2 0.03 No

3 218 3000 0.4 0.5 2 0.05 No

3 219 3000 0.4 0.5 2 0.06 No

3 220 3000 0.4 0.5 2 0.1 No

3 221 3000 0.4 0.5 2 0.15 No

3 222 3000 0.4 0.5 2 0.2 No

3 223 3000 0.4 0.5 2 0.33 No

3 224 3000 0.4 0.5 2 0.5 No

3 225 3000 0.6 0.5 2 0.03 No

3 226 3000 0.6 0.5 2 0.05 No

Appendix D

199

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


3 227 3000 0.6 0.5 2 0.06 No

3 228 3000 0.6 0.5 2 0.1 No

3 229 3000 0.6 0.5 2 0.15 No

3 230 3000 0.6 0.5 2 0.2 No

3 231 3000 0.6 0.5 2 0.33 No

3 232 3000 0.6 0.5 2 0.5 No

3 233 3000 0.8 0.5 2 0.03 No

3 234 3000 0.8 0.5 2 0.05 No

3 235 3000 0.8 0.5 2 0.06 No

3 236 3000 0.8 0.5 2 0.1 No

3 237 3000 0.8 0.5 2 0.15 No

3 238 3000 0.8 0.5 2 0.2 No

3 239 3000 0.8 0.5 2 0.33 No

3 240 3000 0.8 0.5 2 0.5 No

3 241 3000 0.4 0.7 2 0.03 No

3 242 3000 0.4 0.7 2 0.05 No

3 243 3000 0.4 0.7 2 0.06 No

3 244 3000 0.4 0.7 2 0.1 No

3 245 3000 0.4 0.7 2 0.15 No

3 246 3000 0.4 0.7 2 0.2 No

3 247 3000 0.4 0.7 2 0.33 No

3 248 3000 0.4 0.7 2 0.5 No

3 249 3000 0.6 0.7 2 0.03 No

3 250 3000 0.6 0.7 2 0.05 No

3 251 3000 0.6 0.7 2 0.06 No

3 252 3000 0.6 0.7 2 0.1 No

Appendix D

200

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


3 253 3000 0.6 0.7 2 0.15 No

3 254 3000 0.6 0.7 2 0.2 No

3 255 3000 0.6 0.7 2 0.33 No

3 256 3000 0.6 0.7 2 0.5 No

3 257 3000 0.8 0.7 2 0.03 No

3 258 3000 0.8 0.7 2 0.05 No

3 259 3000 0.8 0.7 2 0.06 No

3 260 3000 0.8 0.7 2 0.1 No

3 261 3000 0.8 0.7 2 0.15 No

3 262 3000 0.8 0.7 2 0.2 No

3 263 3000 0.8 0.7 2 0.33 No

3 264 3000 0.8 0.7 2 0.5 No

3 265 3000 0.4 0.9 2 0.03 Yes

3 266 3000 0.4 0.9 2 0.05 Yes

3 267 3000 0.4 0.9 2 0.06 Yes

3 268 3000 0.4 0.9 2 0.1 Yes

3 269 3000 0.4 0.9 2 0.15 Yes

3 270 3000 0.4 0.9 2 0.2 Yes

3 271 3000 0.4 0.9 2 0.33 Yes

3 272 3000 0.4 0.9 2 0.5 Yes

3 273 3000 0.6 0.9 2 0.03 Yes

3 274 3000 0.6 0.9 2 0.05 Yes

3 275 3000 0.6 0.9 2 0.06 Yes

3 276 3000 0.6 0.9 2 0.1 Yes

3 277 3000 0.6 0.9 2 0.15 Yes

3 278 3000 0.6 0.9 2 0.2 Yes

Appendix D

201

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


3 279 3000 0.6 0.9 2 0.33 Yes

3 280 3000 0.6 0.9 2 0.5 Yes

3 281 3000 0.8 0.9 2 0.03 Yes

3 282 3000 0.8 0.9 2 0.05 Yes

3 283 3000 0.8 0.9 2 0.06 Yes

3 284 3000 0.8 0.9 2 0.1 Yes

3 285 3000 0.8 0.9 2 0.15 Yes

3 286 3000 0.8 0.9 2 0.2 Yes

3 287 3000 0.8 0.9 2 0.33 Yes

3 288 3000 0.8 0.9 2 0.5 Yes

3 289 4000 0.4 0.5 2 0.03 No

3 290 4000 0.4 0.5 2 0.05 No

3 291 4000 0.4 0.5 2 0.06 No

3 292 4000 0.4 0.5 2 0.1 No

3 293 4000 0.4 0.5 2 0.15 No

3 294 4000 0.4 0.5 2 0.2 No

3 295 4000 0.4 0.5 2 0.33 No

3 296 4000 0.4 0.5 2 0.5 No

3 297 4000 0.6 0.5 2 0.03 No

3 298 4000 0.6 0.5 2 0.05 No

3 299 4000 0.6 0.5 2 0.06 No

3 300 4000 0.6 0.5 2 0.1 No

3 301 4000 0.6 0.5 2 0.15 No

3 302 4000 0.6 0.5 2 0.2 No

3 303 4000 0.6 0.5 2 0.33 No

3 304 4000 0.6 0.5 2 0.5 No

Appendix D

202

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


3 305 4000 0.8 0.5 2 0.03 Yes

3 306 4000 0.8 0.5 2 0.05 Yes

3 307 4000 0.8 0.5 2 0.06 Yes

3 308 4000 0.8 0.5 2 0.1 Yes

3 309 4000 0.8 0.5 2 0.15 Yes

3 310 4000 0.8 0.5 2 0.2 Yes

3 311 4000 0.8 0.5 2 0.33 Yes

3 312 4000 0.8 0.5 2 0.5 Yes

3 313 4000 0.4 0.7 2 0.03 No

3 314 4000 0.4 0.7 2 0.05 No

3 315 4000 0.4 0.7 2 0.06 No

3 316 4000 0.4 0.7 2 0.1 No

3 317 4000 0.4 0.7 2 0.15 No

3 318 4000 0.4 0.7 2 0.2 No

3 319 4000 0.4 0.7 2 0.33 No

3 320 4000 0.4 0.7 2 0.5 No

3 321 4000 0.6 0.7 2 0.03 Yes

3 322 4000 0.6 0.7 2 0.05 Yes

3 323 4000 0.6 0.7 2 0.06 Yes

3 324 4000 0.6 0.7 2 0.1 Yes

3 325 4000 0.6 0.7 2 0.15 Yes

3 326 4000 0.6 0.7 2 0.2 Yes

3 327 4000 0.6 0.7 2 0.33 Yes

3 328 4000 0.6 0.7 2 0.5 Yes

3 329 4000 0.8 0.7 2 0.03 Yes

3 330 4000 0.8 0.7 2 0.05 Yes

Appendix D

203

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


3 331 4000 0.8 0.7 2 0.06 Yes

3 332 4000 0.8 0.7 2 0.1 Yes

3 333 4000 0.8 0.7 2 0.15 Yes

3 334 4000 0.8 0.7 2 0.2 Yes

3 335 4000 0.8 0.7 2 0.33 Yes

3 336 4000 0.8 0.7 2 0.5 Yes

3 337 4000 0.4 0.9 2 0.03 Yes

3 338 4000 0.4 0.9 2 0.05 Yes

3 339 4000 0.4 0.9 2 0.06 Yes

3 340 4000 0.4 0.9 2 0.1 Yes

3 341 4000 0.4 0.9 2 0.15 Yes

3 342 4000 0.4 0.9 2 0.2 Yes

3 343 4000 0.4 0.9 2 0.33 Yes

3 344 4000 0.4 0.9 2 0.5 Yes

3 345 4000 0.6 0.9 2 0.03 Yes

3 346 4000 0.6 0.9 2 0.05 Yes

3 347 4000 0.6 0.9 2 0.06 Yes

3 348 4000 0.6 0.9 2 0.1 Yes

3 349 4000 0.6 0.9 2 0.15 Yes

3 350 4000 0.6 0.9 2 0.2 Yes

3 351 4000 0.6 0.9 2 0.33 Yes

3 352 4000 0.6 0.9 2 0.5 Yes

3 353 4000 0.8 0.9 2 0.03 Yes

3 354 4000 0.8 0.9 2 0.05 Yes

3 355 4000 0.8 0.9 2 0.06 Yes

3 356 4000 0.8 0.9 2 0.1 Yes

Appendix D

204

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


3 357 4000 0.8 0.9 2 0.15 Yes

3 358 4000 0.8 0.9 2 0.2 Yes

3 359 4000 0.8 0.9 2 0.33 Yes

3 360 4000 0.8 0.9 2 0.5 Yes

3 361 5000 0.4 0.5 2 0.03 Yes

3 362 5000 0.4 0.5 2 0.05 Yes

3 363 5000 0.4 0.5 2 0.06 Yes

3 364 5000 0.4 0.5 2 0.1 Yes

3 365 5000 0.4 0.5 2 0.15 Yes

3 366 5000 0.4 0.5 2 0.2 Yes

3 367 5000 0.4 0.5 2 0.33 Yes

3 368 5000 0.4 0.5 2 0.5 Yes

3 369 5000 0.6 0.5 2 0.03 Yes

3 370 5000 0.6 0.5 2 0.05 Yes

3 371 5000 0.6 0.5 2 0.06 Yes

3 372 5000 0.6 0.5 2 0.1 Yes

3 373 5000 0.6 0.5 2 0.15 Yes

3 374 5000 0.6 0.5 2 0.2 Yes

3 375 5000 0.6 0.5 2 0.33 Yes

3 376 5000 0.6 0.5 2 0.5 Yes

3 377 5000 0.8 0.5 2 0.03 Yes

3 378 5000 0.8 0.5 2 0.05 Yes

3 379 5000 0.8 0.5 2 0.06 Yes

3 380 5000 0.8 0.5 2 0.1 Yes

3 381 5000 0.8 0.5 2 0.15 Yes

3 382 5000 0.8 0.5 2 0.2 Yes

Appendix D

205

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


3 383 5000 0.8 0.5 2 0.33 Yes

3 384 5000 0.8 0.5 2 0.5 Yes

3 385 5000 0.4 0.7 2 0.03 Yes

3 386 5000 0.4 0.7 2 0.05 Yes

3 387 5000 0.4 0.7 2 0.06 Yes

3 388 5000 0.4 0.7 2 0.1 Yes

3 389 5000 0.4 0.7 2 0.15 Yes

3 390 5000 0.4 0.7 2 0.2 Yes

3 391 5000 0.4 0.7 2 0.33 Yes

3 392 5000 0.4 0.7 2 0.5 Yes

3 393 5000 0.6 0.7 2 0.03 Yes

3 394 5000 0.6 0.7 2 0.05 Yes

3 395 5000 0.6 0.7 2 0.06 Yes

3 396 5000 0.6 0.7 2 0.1 Yes

3 397 5000 0.6 0.7 2 0.15 Yes

3 398 5000 0.6 0.7 2 0.2 Yes

3 399 5000 0.6 0.7 2 0.33 Yes

3 400 5000 0.6 0.7 2 0.5 Yes

3 401 5000 0.8 0.7 2 0.03 Yes

3 402 5000 0.8 0.7 2 0.05 Yes

3 403 5000 0.8 0.7 2 0.06 Yes

3 404 5000 0.8 0.7 2 0.1 Yes

3 405 5000 0.8 0.7 2 0.15 Yes

3 406 5000 0.8 0.7 2 0.2 Yes

3 407 5000 0.8 0.7 2 0.33 Yes

3 408 5000 0.8 0.7 2 0.5 Yes

Appendix D

206

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


3 409 5000 0.4 0.9 2 0.03 Yes

3 410 5000 0.4 0.9 2 0.05 Yes

3 411 5000 0.4 0.9 2 0.06 Yes

3 412 5000 0.4 0.9 2 0.1 Yes

3 413 5000 0.4 0.9 2 0.15 Yes

3 414 5000 0.4 0.9 2 0.2 Yes

3 415 5000 0.4 0.9 2 0.33 Yes

3 416 5000 0.4 0.9 2 0.5 Yes

3 417 5000 0.6 0.9 2 0.03 Yes

3 418 5000 0.6 0.9 2 0.05 Yes

3 419 5000 0.6 0.9 2 0.06 Yes

3 420 5000 0.6 0.9 2 0.1 Yes

3 421 5000 0.6 0.9 2 0.15 Yes

3 422 5000 0.6 0.9 2 0.2 Yes

3 423 5000 0.6 0.9 2 0.33 Yes

3 424 5000 0.6 0.9 2 0.5 Yes

3 425 5000 0.8 0.9 2 0.03 Yes

3 426 5000 0.8 0.9 2 0.05 Yes

3 427 5000 0.8 0.9 2 0.06 Yes

3 428 5000 0.8 0.9 2 0.1 Yes

3 429 5000 0.8 0.9 2 0.15 Yes

3 430 5000 0.8 0.9 2 0.2 Yes

3 431 5000 0.8 0.9 2 0.33 Yes

3 432 5000 0.8 0.9 2 0.5 Yes

3 433 3000 0.4 0.5 3 0.03 No

3 434 3000 0.4 0.5 3 0.05 No

Appendix D

207

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


3 435 3000 0.4 0.5 3 0.06 No

3 436 3000 0.4 0.5 3 0.1 No

3 437 3000 0.4 0.5 3 0.15 No

3 438 3000 0.4 0.5 3 0.2 No

3 439 3000 0.4 0.5 3 0.33 No

3 440 3000 0.4 0.5 3 0.5 No

3 441 3000 0.6 0.5 3 0.03 No

3 442 3000 0.6 0.5 3 0.05 No

3 443 3000 0.6 0.5 3 0.06 No

3 444 3000 0.6 0.5 3 0.1 No

3 445 3000 0.6 0.5 3 0.15 No

3 446 3000 0.6 0.5 3 0.2 No

3 447 3000 0.6 0.5 3 0.33 No

3 448 3000 0.6 0.5 3 0.5 No

3 449 3000 0.8 0.5 3 0.03 No

3 450 3000 0.8 0.5 3 0.05 No

3 451 3000 0.8 0.5 3 0.06 No

3 452 3000 0.8 0.5 3 0.1 No

3 453 3000 0.8 0.5 3 0.15 No

3 454 3000 0.8 0.5 3 0.2 No

3 455 3000 0.8 0.5 3 0.33 No

3 456 3000 0.8 0.5 3 0.5 No

3 457 3000 0.4 0.7 3 0.03 No

3 458 3000 0.4 0.7 3 0.05 No

3 459 3000 0.4 0.7 3 0.06 No

3 460 3000 0.4 0.7 3 0.1 No

Appendix D

208

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


3 461 3000 0.4 0.7 3 0.15 No

3 462 3000 0.4 0.7 3 0.2 No

3 463 3000 0.4 0.7 3 0.33 No

3 464 3000 0.4 0.7 3 0.5 No

3 465 3000 0.6 0.7 3 0.03 No

3 466 3000 0.6 0.7 3 0.05 No

3 467 3000 0.6 0.7 3 0.06 No

3 468 3000 0.6 0.7 3 0.1 No

3 469 3000 0.6 0.7 3 0.15 No

3 470 3000 0.6 0.7 3 0.2 No

3 471 3000 0.6 0.7 3 0.33 No

3 472 3000 0.6 0.7 3 0.5 No

3 473 3000 0.8 0.7 3 0.03 No

3 474 3000 0.8 0.7 3 0.05 No

3 475 3000 0.8 0.7 3 0.06 No

3 476 3000 0.8 0.7 3 0.1 No

3 477 3000 0.8 0.7 3 0.15 No

3 478 3000 0.8 0.7 3 0.2 No

3 479 3000 0.8 0.7 3 0.33 No

3 480 3000 0.8 0.7 3 0.5 No

3 481 3000 0.4 0.9 3 0.03 Yes

3 482 3000 0.4 0.9 3 0.05 Yes

3 483 3000 0.4 0.9 3 0.06 Yes

3 484 3000 0.4 0.9 3 0.1 Yes

3 485 3000 0.4 0.9 3 0.15 Yes

3 486 3000 0.4 0.9 3 0.2 Yes

Appendix D

209

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


3 487 3000 0.4 0.9 3 0.33 Yes

3 488 3000 0.4 0.9 3 0.5 Yes

3 489 3000 0.6 0.9 3 0.03 Yes

3 490 3000 0.6 0.9 3 0.05 Yes

3 491 3000 0.6 0.9 3 0.06 Yes

3 492 3000 0.6 0.9 3 0.1 Yes

3 493 3000 0.6 0.9 3 0.15 Yes

3 494 3000 0.6 0.9 3 0.2 Yes

3 495 3000 0.6 0.9 3 0.33 Yes

3 496 3000 0.6 0.9 3 0.5 Yes

3 497 3000 0.8 0.9 3 0.03 Yes

3 498 3000 0.8 0.9 3 0.05 Yes

3 499 3000 0.8 0.9 3 0.06 Yes

3 500 3000 0.8 0.9 3 0.1 Yes

3 501 3000 0.8 0.9 3 0.15 Yes

3 502 3000 0.8 0.9 3 0.2 Yes

3 503 3000 0.8 0.9 3 0.33 Yes

3 504 3000 0.8 0.9 3 0.5 Yes

3 505 4000 0.4 0.5 3 0.03 No

3 506 4000 0.4 0.5 3 0.05 No

3 507 4000 0.4 0.5 3 0.06 No

3 508 4000 0.4 0.5 3 0.1 No

3 509 4000 0.4 0.5 3 0.15 No

3 510 4000 0.4 0.5 3 0.2 No

3 511 4000 0.4 0.5 3 0.33 No

3 512 4000 0.4 0.5 3 0.5 No

Appendix D

210

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


3 513 4000 0.6 0.5 3 0.03 No

3 514 4000 0.6 0.5 3 0.05 No

3 515 4000 0.6 0.5 3 0.06 No

3 516 4000 0.6 0.5 3 0.1 No

3 517 4000 0.6 0.5 3 0.15 No

3 518 4000 0.6 0.5 3 0.2 No

3 519 4000 0.6 0.5 3 0.33 No

3 520 4000 0.6 0.5 3 0.5 No

3 521 4000 0.8 0.5 3 0.03 Yes

3 522 4000 0.8 0.5 3 0.05 Yes

3 523 4000 0.8 0.5 3 0.06 Yes

3 524 4000 0.8 0.5 3 0.1 Yes

3 525 4000 0.8 0.5 3 0.15 Yes

3 526 4000 0.8 0.5 3 0.2 Yes

3 527 4000 0.8 0.5 3 0.33 Yes

3 528 4000 0.8 0.5 3 0.5 Yes

3 529 4000 0.4 0.7 3 0.03 No

3 530 4000 0.4 0.7 3 0.05 No

3 531 4000 0.4 0.7 3 0.06 No

3 532 4000 0.4 0.7 3 0.1 No

3 533 4000 0.4 0.7 3 0.15 No

3 534 4000 0.4 0.7 3 0.2 No

3 535 4000 0.4 0.7 3 0.33 No

3 536 4000 0.4 0.7 3 0.5 No

3 537 4000 0.6 0.7 3 0.03 Yes

3 538 4000 0.6 0.7 3 0.05 Yes

Appendix D

211

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


3 539 4000 0.6 0.7 3 0.06 Yes

3 540 4000 0.6 0.7 3 0.1 Yes

3 541 4000 0.6 0.7 3 0.15 Yes

3 542 4000 0.6 0.7 3 0.2 Yes

3 543 4000 0.6 0.7 3 0.33 Yes

3 544 4000 0.6 0.7 3 0.5 Yes

3 545 4000 0.8 0.7 3 0.03 Yes

3 546 4000 0.8 0.7 3 0.05 Yes

3 547 4000 0.8 0.7 3 0.06 Yes

3 548 4000 0.8 0.7 3 0.1 Yes

3 549 4000 0.8 0.7 3 0.15 Yes

3 550 4000 0.8 0.7 3 0.2 Yes

3 551 4000 0.8 0.7 3 0.33 Yes

3 552 4000 0.8 0.7 3 0.5 Yes

3 553 4000 0.4 0.9 3 0.03 Yes

3 554 4000 0.4 0.9 3 0.05 Yes

3 555 4000 0.4 0.9 3 0.06 Yes

3 556 4000 0.4 0.9 3 0.1 Yes

3 557 4000 0.4 0.9 3 0.15 Yes

3 558 4000 0.4 0.9 3 0.2 Yes

3 559 4000 0.4 0.9 3 0.33 Yes

3 560 4000 0.4 0.9 3 0.5 Yes

3 561 4000 0.6 0.9 3 0.03 Yes

3 562 4000 0.6 0.9 3 0.05 Yes

3 563 4000 0.6 0.9 3 0.06 Yes

3 564 4000 0.6 0.9 3 0.1 Yes

Appendix D

212

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


3 565 4000 0.6 0.9 3 0.15 Yes

3 566 4000 0.6 0.9 3 0.2 Yes

3 567 4000 0.6 0.9 3 0.33 Yes

3 568 4000 0.6 0.9 3 0.5 Yes

3 569 4000 0.8 0.9 3 0.03 Yes

3 570 4000 0.8 0.9 3 0.05 Yes

3 571 4000 0.8 0.9 3 0.06 Yes

3 572 4000 0.8 0.9 3 0.1 Yes

3 573 4000 0.8 0.9 3 0.15 Yes

3 574 4000 0.8 0.9 3 0.2 Yes

3 575 4000 0.8 0.9 3 0.33 Yes

3 576 4000 0.8 0.9 3 0.5 Yes

3 577 5000 0.4 0.5 3 0.03 Yes

3 578 5000 0.4 0.5 3 0.05 Yes

3 579 5000 0.4 0.5 3 0.06 Yes

3 580 5000 0.4 0.5 3 0.1 Yes

3 581 5000 0.4 0.5 3 0.15 Yes

3 582 5000 0.4 0.5 3 0.2 Yes

3 583 5000 0.4 0.5 3 0.33 Yes

3 584 5000 0.4 0.5 3 0.5 Yes

3 585 5000 0.6 0.5 3 0.03 Yes

3 586 5000 0.6 0.5 3 0.05 Yes

3 587 5000 0.6 0.5 3 0.06 Yes

3 588 5000 0.6 0.5 3 0.1 Yes

3 589 5000 0.6 0.5 3 0.15 Yes

3 590 5000 0.6 0.5 3 0.2 Yes

Appendix D

213

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


3 591 5000 0.6 0.5 3 0.33 Yes

3 592 5000 0.6 0.5 3 0.5 Yes

3 593 5000 0.8 0.5 3 0.03 Yes

3 594 5000 0.8 0.5 3 0.05 Yes

3 595 5000 0.8 0.5 3 0.06 Yes

3 596 5000 0.8 0.5 3 0.1 Yes

3 597 5000 0.8 0.5 3 0.15 Yes

3 598 5000 0.8 0.5 3 0.2 Yes

3 599 5000 0.8 0.5 3 0.33 Yes

3 600 5000 0.8 0.5 3 0.5 Yes

3 601 5000 0.4 0.7 3 0.03 Yes

3 602 5000 0.4 0.7 3 0.05 Yes

3 603 5000 0.4 0.7 3 0.06 Yes

3 604 5000 0.4 0.7 3 0.1 Yes

3 605 5000 0.4 0.7 3 0.15 Yes

3 606 5000 0.4 0.7 3 0.2 Yes

3 607 5000 0.4 0.7 3 0.33 Yes

3 608 5000 0.4 0.7 3 0.5 Yes

3 609 5000 0.6 0.7 3 0.03 Yes

3 610 5000 0.6 0.7 3 0.05 Yes

3 611 5000 0.6 0.7 3 0.06 Yes

3 612 5000 0.6 0.7 3 0.1 Yes

3 613 5000 0.6 0.7 3 0.15 Yes

3 614 5000 0.6 0.7 3 0.2 Yes

3 615 5000 0.6 0.7 3 0.33 Yes

3 616 5000 0.6 0.7 3 0.5 Yes

Appendix D

214

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


3 617 5000 0.8 0.7 3 0.03 Yes

3 618 5000 0.8 0.7 3 0.05 Yes

3 619 5000 0.8 0.7 3 0.06 Yes

3 620 5000 0.8 0.7 3 0.1 Yes

3 621 5000 0.8 0.7 3 0.15 Yes

3 622 5000 0.8 0.7 3 0.2 Yes

3 623 5000 0.8 0.7 3 0.33 Yes

3 624 5000 0.8 0.7 3 0.5 Yes

3 625 5000 0.4 0.9 3 0.03 Yes

3 626 5000 0.4 0.9 3 0.05 Yes

3 627 5000 0.4 0.9 3 0.06 Yes

3 628 5000 0.4 0.9 3 0.1 Yes

3 629 5000 0.4 0.9 3 0.15 Yes

3 630 5000 0.4 0.9 3 0.2 Yes

3 631 5000 0.4 0.9 3 0.33 Yes

3 632 5000 0.4 0.9 3 0.5 Yes

3 633 5000 0.6 0.9 3 0.03 Yes

3 634 5000 0.6 0.9 3 0.05 Yes

3 635 5000 0.6 0.9 3 0.06 Yes

3 636 5000 0.6 0.9 3 0.1 Yes

3 637 5000 0.6 0.9 3 0.15 Yes

3 638 5000 0.6 0.9 3 0.2 Yes

3 639 5000 0.6 0.9 3 0.33 Yes

3 640 5000 0.6 0.9 3 0.5 Yes

3 641 5000 0.8 0.9 3 0.03 Yes

3 642 5000 0.8 0.9 3 0.05 Yes

Appendix D

215

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


3 643 5000 0.8 0.9 3 0.06 Yes

3 644 5000 0.8 0.9 3 0.1 Yes

3 645 5000 0.8 0.9 3 0.15 Yes

3 646 5000 0.8 0.9 3 0.2 Yes

3 647 5000 0.8 0.9 3 0.33 Yes

3 648 5000 0.8 0.9 3 0.5 Yes

4 1 5000 0.8 0.5 1 0.0825 Yes

4 2 5000 0.8 0.5 1 0.065 Yes

4 3 5000 0.8 0.5 1 0.0475 Yes

4 4 5000 0.8 0.5 1 0.0825 Yes

4 5 5000 0.8 0.5 1 0.0650 Yes

4 6 5000 0.8 0.5 1 0.0825 Yes

4 7 5000 0.8 0.5 1 0.1237 Yes

4 8 5000 0.8 0.5 1 0.0975 Yes

4 9 5000 0.8 0.5 1 0.0712 Yes

4 10 5000 0.8 0.5 1 0.1237 Yes

4 11 5000 0.8 0.5 1 0.0975 Yes

4 12 5000 0.8 0.5 1 0.1237 Yes

4 13 5000 0.8 0.5 1 0.165 Yes

4 14 5000 0.8 0.5 1 0.13 Yes

4 15 5000 0.8 0.5 1 0.095 Yes

4 16 5000 0.8 0.5 1 0.1650 Yes

4 17 5000 0.8 0.5 1 0.13 Yes

4 18 5000 0.8 0.5 1 0.165 Yes

4 19 5000 0.8 0.5 1 0.2747 Yes

4 20 5000 0.8 0.5 1 0.2164 Yes

Appendix D

216

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


4 21 5000 0.8 0.5 1 0.15818 Yes

4 22 5000 0.8 0.5 1 0.2747 Yes

4 23 5000 0.8 0.5 1 0.2164 Yes

4 24 5000 0.8 0.5 1 0.2747 Yes

4 25 5000 0.8 0.5 1 0.4125 Yes

4 26 5000 0.8 0.5 1 0.325 Yes

4 27 5000 0.8 0.5 1 0.2375 Yes

4 28 5000 0.8 0.5 1 0.4125 Yes

4 29 5000 0.8 0.5 1 0.3250 Yes

4 30 5000 0.8 0.5 1 0.4125 Yes

4 31 5000 0.8 0.5 2 0.0825 Yes

4 32 5000 0.8 0.5 2 0.065 Yes

4 33 5000 0.8 0.5 2 0.0475 Yes

4 34 5000 0.8 0.5 2 0.0825 Yes

4 35 5000 0.8 0.5 2 0.065 Yes

4 36 5000 0.8 0.5 2 0.0825 Yes

4 37 5000 0.8 0.5 2 0.12375 Yes

4 38 5000 0.8 0.5 2 0.0975 Yes

4 39 5000 0.8 0.5 2 0.07125 Yes

4 40 5000 0.8 0.5 2 0.1237 Yes

4 41 5000 0.8 0.5 2 0.0975 Yes

4 42 5000 0.8 0.5 2 0.1237 Yes

4 43 5000 0.8 0.5 2 0.165 Yes

4 44 5000 0.8 0.5 2 0.13 Yes

4 45 5000 0.8 0.5 2 0.095 Yes

4 46 5000 0.8 0.5 2 0.165 Yes

Appendix D

217

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


4 47 5000 0.8 0.5 2 0.13 Yes

4 48 5000 0.8 0.5 2 0.165 Yes

4 49 5000 0.8 0.5 2 0.2747 Yes

4 50 5000 0.8 0.5 2 0.2164 Yes

4 51 5000 0.8 0.5 2 0.1581 Yes

4 52 5000 0.8 0.5 2 0.2747 Yes

4 53 5000 0.8 0.5 2 0.2164 Yes

4 54 5000 0.8 0.5 2 0.2747 Yes

4 55 5000 0.8 0.5 2 0.4125 Yes

4 56 5000 0.8 0.5 2 0.325 Yes

4 57 5000 0.8 0.5 2 0.2375 Yes

4 58 5000 0.8 0.5 2 0.4125 Yes

4 59 5000 0.8 0.5 2 0.325 Yes

4 60 5000 0.8 0.5 2 0.4125 Yes

4 61 5000 0.8 0.5 3 0.0825 Yes

4 62 5000 0.8 0.5 3 0.065 Yes

4 63 5000 0.8 0.5 3 0.0475 Yes

4 64 5000 0.8 0.5 3 0.0825 Yes

4 65 5000 0.8 0.5 3 0.0645 Yes

4 66 5000 0.8 0.5 3 0.0825 Yes

4 67 5000 0.8 0.5 3 0.1237 Yes

4 68 5000 0.8 0.5 3 0.0975 Yes

4 69 5000 0.8 0.5 3 0.0712 Yes

4 70 5000 0.8 0.5 3 0.1237 Yes

4 71 5000 0.8 0.5 3 0.0975 Yes

4 72 5000 0.8 0.5 3 0.1237 Yes

Appendix D

218

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


4 73 5000 0.8 0.5 3 0.165 Yes

4 74 5000 0.8 0.5 3 0.13 Yes

4 75 5000 0.8 0.5 3 0.095 Yes

4 76 5000 0.8 0.5 3 0.1650 Yes

4 77 5000 0.8 0.5 3 0.13 Yes

4 78 5000 0.8 0.5 3 0.165 Yes

4 79 5000 0.8 0.5 3 0.2747 Yes

4 80 5000 0.8 0.5 3 0.2164 Yes

4 81 5000 0.8 0.5 3 0.1582 Yes

4 82 5000 0.8 0.5 3 0.2747 Yes

4 83 5000 0.8 0.5 3 0.2164 Yes

4 84 5000 0.8 0.5 3 0.2747 Yes

4 85 5000 0.8 0.5 3 0.4125 Yes

4 86 5000 0.8 0.5 3 0.325 Yes

4 87 5000 0.8 0.5 3 0.2375 Yes

4 88 5000 0.8 0.5 3 0.4125 Yes

4 89 5000 0.8 0.5 3 0.325 Yes

4 90 5000 0.8 0.5 3 0.4125 Yes

4 91 5000 0.4 0.5 3 0.2068 Yes

5 1 5000 0.40 0.25 2 0.2 No

5 2 5000 0.40 0.25 2 0.2 No

5 3 5000 0.40 0.25 2 0.2 No

5 4 5000 0.40 0.25 2 0.1 No

5 5 5000 0.40 0.25 2 0.1 No

5 6 5000 0.40 0.25 2 0.1 No

5 7 5000 0.40 0.25 2 0.1333 No

Appendix D

219

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


5 8 5000 0.40 0.25 2 0.1333 No

5 9 5000 0.40 0.25 2 0.1333 No

5 10 5000 0.40 0.25 2 0.16 No

5 11 5000 0.40 0.25 2 0.16 No

5 12 5000 0.40 0.25 2 0.16 No

6 1 5000 0.40 0.25 2 0.1 No

6 2 5000 0.40 0.25 2 0.0768 No

7 1 3000 0.8 0.5 2 0.1235 Yes

7 2 3000 0.8 0.7 2 0.1235 Yes

7 3 3000 0.8 0.9 2 0.1235 Yes

7 4 4000 0.8 0.5 2 0.1235 Yes

7 5 4000 0.8 0.7 2 0.1235 Yes

7 6 4000 0.8 0.9 2 0.1235 Yes

7 7 5000 0.8 0.5 2 0.1235 Yes

7 8 5000 0.8 0.7 2 0.1235 Yes

7 9 5000 0.8 0.9 2 0.1235 Yes

7 10 5000 0.8 0.9 3 0.1235 Yes

7 11 3000 0.8 0.9 3 0.1235 Yes

7 12 4000 0.8 0.9 3 0.1235 Yes

7 13 4000 0.8 0.7 3 0.1235 Yes

7 14 5000 0.8 0.9 5 0.1235 Yes

7 15 5000 0.8 0.9 4.6 0.1235 Yes

7 16 5000 0.8 0.9 3.8 0.1235 Yes

7 17 5000 0.8 0.9 2.6 0.1235 Yes

7 18 5000 0.8 0.9 2 0.1235 Yes

7 19 4000 0.8 0.9 5 0.1235 Yes

Appendix D

220

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


7 20 4000 0.8 0.9 4.5 0.1235 Yes

7 21 4000 0.8 0.9 4 0.1235 Yes

7 22 4000 0.8 0.9 4.5 0.1235 Yes

7 23 3000 0.8 0.9 4.3333 0.1235 Yes

7 24 3000 0.8 0.9 4 0.1235 Yes

7 25 3000 0.8 0.9 5 0.1235 Yes

7 26 3000 0.8 0.9 4.3333 0.1235 Yes

7 27 3000 0.8 0.5 2 0.1235 Yes

7 28 3000 0.8 0.7 2 0.1235 Yes

7 29 3000 0.8 0.9 2 0.1235 Yes

7 30 4000 0.8 0.5 2 0.1235 Yes

7 31 4000 0.8 0.7 2 0.1235 Yes

7 32 4000 0.8 0.9 2 0.1235 Yes

7 33 5000 0.8 0.5 2 0.1235 Yes

7 34 5000 0.8 0.7 2 0.1235 Yes

7 35 5000 0.8 0.9 2 0.1235 Yes

7 36 5000 0.8 0.9 3 0.1235 Yes

7 37 3000 0.8 0.9 3 0.1235 Yes

7 38 4000 0.8 0.9 3 0.1235 Yes

7 39 4000 0.8 0.7 3 0.1235 Yes

7 40 5000 0.8 0.9 5 0.1235 Yes

7 41 5000 0.8 0.9 4.3 0.1235 Yes

7 42 5000 0.8 0.9 3.94 0.1235 Yes

7 43 5000 0.8 0.9 3.42 0.1235 Yes

7 44 5000 0.8 0.9 4.42 0.1235 Yes

7 45 4000 0.8 0.9 5 0.1235 Yes

Appendix D

221

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


7 46 4000 0.8 0.9 4.25 0.1235 Yes

7 47 4000 0.8 0.9 3.75 0.1235 Yes

7 48 4000 0.8 0.9 4.75 0.1235 Yes

7 49 3000 0.8 0.9 5 0.1235 Yes

7 50 3000 0.8 0.9 4.6667 0.1235 Yes

7 51 3000 0.8 0.9 4.3333 0.1235 Yes

7 52 3000 0.8 0.9 4 0.1235 Yes

7 53 5000 0.8 0.5 1.2 0.1235 Yes

7 54 5000 0.8 0.5 1.8 0.1235 Yes

7 55 5000 0.8 0.5 2.4 0.1235 Yes

7 56 5000 0.8 0.7 2.4 0.1235 Yes

7 57 4000 0.8 0.5 1 0.1235 Yes

7 58 4000 0.8 0.5 2 0.1235 Yes

7 59 4000 0.8 0.5 3 0.1235 Yes

7 60 4000 0.8 0.7 3 0.1235 Yes

7 61 3000 0.8 0.5 1 0.1235 Yes

7 62 3000 0.8 0.5 2 0.1235 Yes

7 63 3000 0.8 0.7 2 0.1235 Yes

7 64 3000 0.8 0.5 3.3333 0.1235 Yes

7 65 5000 0.8 0.5 1.6 0.1235 Yes

7 66 5000 0.8 0.9 4 0.1235 Yes

7 67 5000 0.8 0.9 4.8 0.1235 Yes

7 68 5000 0.8 0.9 4.8 0.1235 Yes

7 69 5000 0.8 0.7 3.6 0.1235 Yes

7 70 4000 0.8 0.7 1.25 0.1235 Yes

7 71 4000 0.8 0.9 2 0.1235 Yes

Appendix D

222

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


7 72 4000 0.8 0.9 3 0.1235 Yes

7 73 4000 0.8 0.9 2.5 0.1235 Yes

7 74 3000 0.8 0.5 2 0.1235 Yes

7 75 3000 0.8 0.7 2 0.1235 Yes

7 76 3000 0.8 0.7 1.3333 0.1235 Yes

7 77 3000 0.8 0.7 2 0.1235 Yes

7 78 3000 0.8 0.9 2 0.1235 Yes

7 79 5000 0.8 0.5 1.8 0.1235 Yes

7 80 5000 0.8 0.5 1.2 0.1235 Yes

7 81 5000 0.8 0.5 0.6 0.1235 Yes

7 82 5000 0.8 0.7 0.6 0.1235 Yes

7 83 4000 0.8 0.7 3 0.1235 Yes

7 84 4000 0.8 0.7 2 0.1235 Yes

7 85 4000 0.8 0.5 1 0.1235 Yes

7 86 4000 0.8 0.7 1 0.1235 Yes

7 87 3000 0.8 0.5 2 0.1235 Yes

7 88 3000 0.8 0.5 1 0.1235 Yes

7 89 3000 0.8 0.7 1 0.1235 Yes

7 90 3000 0.8 0.7 1.6667 0.1235 Yes

7 91 5000 0.8 0.5 0.4 0.1235 Yes

7 92 5000 0.8 0.9 2 0.1235 Yes

7 93 5000 0.8 0.9 2.7 0.1235 Yes

7 94 5000 0.8 0.9 3.2 0.1235 Yes

7 95 5000 0.8 0.9 1.6 0.1235 Yes

7 96 4000 0.8 0.9 4.375 0.1235 Yes

7 97 4000 0.8 0.5 1.25 0.1235 Yes

Appendix D

223

Chapter Model

Property Values

Buckle? L (m) W

(kN/m)


7 98 4000 0.8 0.7 1.25 0.1235 Yes

7 99 4000 0.8 0.9 1.25 0.1235 Yes

7 100 3000 0.8 0.9 2 0.1235 Yes

7 101 3000 0.8 0.9 4 0.1235 Yes

7 102 3000 0.8 0.9 2.3333 0.1235 Yes

7 103 3000 0.8 0.9 3 0.1235 Yes

7 104 3000 0.8 0.9 4.6667 0.1235 Yes

.

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DOWNSLOPE PIPELINE WALKING AND SOIL VARIABLES