C_CORE PRCI Extended Model PSI Rpt (1).pdf

Catalog No. L51990

Extended Model for Pipe Soil Interaction Contract PR- 271-0184

Prepared for the Design, Construction & Operations Technical Committee of Pipeline Research Council International, Inc.

Prepared by the following Research Agencies: C-CORE & Doug Honegger, D.G. Honegger Consulting Publication Date: August 2003 2003

“This report is furnished to Pipeline Research Council International, Inc. (PRCI) under the terms of PRCI PR-271-0184, between PRCI and C-CORE. The contents of this report are published as received from C-CORE. The opinions, findings, and conclusions conclusions expressed in the report are those of the authors and not necessarily those of PRCI, its member companies, or their representatives. Publication and dissemination dissemination of this report by PRCI should not be considered an endorsement by PRCI or C-CORE, or the accuracy or validity of any opinions, findings, or conclusions expressed herein. In publishing this report, PRCI makes no warranty or representation, expressed or implied, with respect to the accuracy, completeness, usefulness, or fitness for purpose of the information contained herein, or that the use of any information, method, process, or apparatus disclosed in this report may not infringe on privately owned rights. rights. PRCI assumes no liability with respect respect to the use of, or for damages resulting from the use of, any information, method, process, or apparatus disclosed in this report. The text of this publication, or any part thereof, may not be reproduced or transmitted in any form by any means, means, electronic or mechanical, mechanical, including photocopying, photocopying, recording, storage in an information retrieval system, or otherwise, without the prior, written approval of PRCI.”

Pipeline Research Council International Catalog No. L51990 Copyright, 2003 All Rights Reserved by Pipeline Research Council International, Inc.

PRCI Reports are Published by Technical Toolboxes, Inc. 3801 Kirby Drive, Suite 340 Houston, Texas 77098 Tel: 713-630-0505 Fax: 713-630-0560 Email: [email protected]

Committee Recognition Rosters PRCI Board, the executive committee members, and PRCI staff are credited for the completion of this report. The project is supervised and supported by Design, Construction & Operations Technical Committee Roster, Chairman R. Gailing,

Southern California Gas Company

M. Al-Sannaa, Saudi Aramco M. Brown, Enron Corp. K. Champagne, Shell Pipeline Company LP A. Drake, Duke Energy Company R. Healy, El Paso Corporation S. Kitt, Foothills Pipe Lines Ltd. W. Lambright, Lambright, Consumers Energy Company Company K. Leewis, Gas Technology Institute G. Mallette, Westcoast Energy Inc. M. McLamb, BP p.l.c. C. Parker, TransGas Ltd. E. Roelofsen, N.V. Nederlandse Gasunie P. Ruppert, Dominion Resources, Inc. I. Taka-Aho, Gasum Oy J. E. Thygesen, Thygesen, DONG A/S R. Verley, Statoil ASA R. Weninger, Williams Energy J. Zhou, TransCanada PipeLines Ltd.

Ad hoc Committee Committee Member

GTI Project Coordinator Ad hoc Committee Member

Project Coordinator

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Extended Model for Pipe Soil Interaction - Final Report

EXECUTIVE SUMMARY

GENERAL The objective of this study is to extend and improve guidelines on differential landslide ground movement effects and to quantify practical mitigative methods for reduction of these effects on buried gas pipelines. This program contributes to maintaining and improving the integrity and safety of existing pipelines with regard to ground movement hazards, and reducing the capital costs of new pipeline systems. The research program focused on the axial, lateral and complex loading of pipeline due to soil movements. It includes (1) a literature review: it presents significant issues related to modelling pipe-soil interaction with a focus to recent development since ASCE (1984); (2) axial loading: it includes a summary of the methods to estimate the axial soil forces on pipeline and recent field measurements on decommissioned pipe sections in weak to desiccated, cohesive to sandy silts in California; (3) lateral loading of buried pipeline: it covers the effects of cover depth, soil strength, loading rate, trench geometry and backfill strength on pipe-soil interaction; (4) complex loading of buried pipeline: the interaction between the lateral and axial soil forces on pipeline are studied; and (5) quantification of mitigative methods: a physical testing program including a total of 20 laterally loaded pipelines are used to identify and quantify the effects of various mitigative methods on reducing lateral loads transferred to a buried pipeline. LITERATURE REVIEW In the literature review, significant issues related to modelling pipe-soil interaction are presented. This includes representation of soil-pipe interaction forces, their validation based on field, experimental and numerical results and discussions on the historical record. It has also focused on the issues addressed by this research. NUMERICAL MODELLING Analyses using ABAQUS/Standard finite element code were mainly focused on a rigid elastic pipe in clay. The Von-Mises and Mohr-Coulomb plasticity soil models are selected according to the research objectives. Numerical analyses were validated using experimental data. The effects of cover depth, strength of native and backfill soils, and trench geometry on horizontal movement of pipes were investigated. The movements of the pipe in the field are not always in one direction (e.g. axial or lateral), unlike the simplification used in many theoretical and experimental analyses. The analyses of combined translation (axial and horizontal) of a pipe on a horizontal plane show that a small lateral movement (angle of pipe translation) significantly increases the contact force between the pipe and surrounding soil. However, a large translation angle decreases the overall contact force because of the formation of a gap behind the pipe.

C-CORE Report R-02-044-113 29 August 2003

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The study also investigated the effects of the soil movement rate. The state-of-practice pipe-soil interaction analysis uses undrained shear strength to calculate interaction forces on pipelines buried in clay. Consequently, the effects of the soil movement rate are not considered. This assumption is correct only when the pipeline moves rapidly through soil. Under many pipeline working-conditions, the relative rate of displacement between a pipe and the surrounding soil is small, consolidation of soil inevitably occurs in the process of soil deformation. Experimental evidence of consolidation of soil around pipelines was reported from the literature. Numerical analyses were performed to investigate the effects of soil movement rate on pipe-soil interaction in uniform clay by imposing displacement with different rates on the pipeline. PHYSICAL MODELLING The physical model tests were conducted in the C-CORE centrifuge using the methodology developed by Paulin et al. (1995, 1996). There is good agreement between experimental and recommended interaction factors. The force-displacement curves measured from the experimental tests have much lower initial stiffness than those predicted by PRCI, ASCE and numerical modeling. Trench width has significant effects on force-displacement curves. An increase in the trench width results in increasing the pipe displacement to peak load. The lateral interaction force is much lower in a pipe with a wider trench than a narrower trench prior to reaching the peak load. The peak load occurs after pipe passes the trench wall. The peak load is controlled by native soil strength; it decreases slightly with increase in the trench width. Upward movements of pipeline result in the slight decrease in the peak load. The mitigative effects of inclined trench are demonstrated. An inclination of 45° is required for pipeline buried in cohesive backfill to mobilize the mitigative effects of trench wall inclination. For sand material used, the inclination of 45° was not enough to observe the mitigative effects. A larger inclination (e.g. 30° suggested by PRCI guidelines) is needed. CONCLUSIONS For pipes buried in uniform clay, there is significant interaction between the axial and lateral pipe response, for which an equation is proposed for primarily lateral loading. Under near axial loading, the pipe resistance is very sensitive to slight misalignments. The axial relationships, using adhesion factor, provided in the new PRCI guidelines is endorsed. The transition from undrained to drained behaviour is defined using a normalized displacement rate. A hyperbolic curve is recommended to capture the undrained p-y response. New interaction factors are proposed which account for soil weight and are consistent with the lateral resistance of a pile for deep burial. The p-y curve stiffness should be based on the soil deformation properties. The presence of a trench backfilled with material weaker than the native soil softens the p-y response compared to that of the same pipe buried in native soil. Increased trench


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width and softer backfill strengths are potential strategies to reduce pipe distress, as is having trench walls inclined at 45° or less. Further work to develop this program is proposed. The studies recommended changes to guidelines on differential landslide ground movement effects from axial and lateral loading, including trench effects, on buried gas pipelines are summarised in Appendix B.


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TABLE OF CONTENTS

EXECUTIVE SUMMARY .................................................. .............................................. II 1

REVIEW OF STUDIES RELEVANT TO PIPE/SOIL INTERACTION.................. 1 1.1

Representation of Soil-Pipeline Interaction Forces: Theoretical Analysis and Laboratory Testing ................................................... ....................................... 1

1.2

1.3

1.4

1.5

2

3

1.1.1

Longitudinal Interaction........................... ......................................... 2

1.1.2

Transverse Horizontal Interaction......................... ............................ 7

1.1.3

Transverse Vertical Interaction ....................................................... 16

Validation ...................................................................................................... 19 1.2.1

Field Tests ................................................ ....................................... 19

1.2.2

Laboratory Tests ................................................. ............................ 20

1.2.3

Centrifuge Modelling ............................................... ....................... 20

Numerical Modelling of Pipe/Soil Interaction ............................................ .. 22 1.3.1

Finite Element Analysis – Structural Models ................................. 22

1.3.2

Finite Element Analysis – Continuum Models ............................... 23

Summary of Past Efforts to Characterize Pipe-soil Interaction..................... 23 1.4.1

Current State of Practice .................................................. ............... 23

1.4.2

State-of-the-Art ........................................................ ....................... 24

1.4.3

Open Issues/Challenges .................................................................. 26

Issues Addressed by This Research Project .................................................. 28 1.5.1

Introduction............................................ ......................................... 28

1.5.2

Non-linear Soil-Spring Characteristics ........................................... 29

1.5.3

Axial Pipe-Soil Interaction............................................... ............... 29

1.5.4

Lateral Pipe-Soil Interaction ........................................... ................ 29

1.5.5

Complex Loading........................................................................ .... 30

1.5.6

Quantifying Mitigative Measures ................................................... 30

SUMMARY OF METHODS TO ESTIMATE AXIAL FRICTION ....................... 41 2.1

Comparisons of Proposed Adhesion Factor Relationships with Test Data ... 42

2.2

Variation of Axial Load with Axial Displacement........................................ 44

CONSTITUTIVE MODELS ............................................ ........................................ 49 3.1

Constitutive Models....................................................... ................................ 49 3.1.1

Constitutive Model for Sand .................................................. ......... 49

3.1.2

Constitutive Models for Clay.............................................. ............ 49

3.2

Analysis Procedure .............................................. .......................................... 50

3.3

Treatment of Pipe-Soil Interface ................................................... ................ 50

3.4

Numerical Model Verification ................................................ ...................... 51 3.4.1

Pipe in Sand: Lateral Loading......................................................... 51


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3.4.2 3.5 4

Pipe in Clay: Lateral Loading ...................................... ................... 52

Comments........................................................ .............................................. 52

EFFECT OF COVER

DEPTH AND SOIL STRENGTH: HORIZONTAL

LOADING ................................................................................................................ 61 4.1

Introduction ................................................................................................... 61

4.2

Finite Element Analysis Set-up ................................................. .................... 61

4.3

4.2.1

Finite Element Set-up...................................... ................................ 61

4.2.2

Material Properties ............................................... ........................... 62

4.2.3

Analysis Procedure and Cases Analyzed ........................................ 62

Pipes in Uniform Clay ............................................ ....................................... 63 4.3.1

Ultimate Soil Resistance: Bearing Capacity Factor ........................ 63

4.3.2

Failure Mechanisms ................................................. ....................... 63

4.3.3

Discussion ............................................... ........................................ 64

4.3.4

Force-Displacement Curves and Pipe Displacement at ultimate state ............................................... .......................................................... 65

5

6

7

RATE EFFECT ON SOIL-PIPELINE INTERACTION ......................................... 91 5.1

Effective Stress Analysis ................................................... ............................ 91

5.2

Representative Soil Parameters ........................................................... .......... 91 5.2.1

Soil consolidation during loading ............................................. ...... 92

5.2.2

Effect of loading rate on pipe responses ......................................... 92

TRENCH EFFECT ON SOIL-PIPELINE INTERACTION.................................. 103 6.1

Studied Cases........................................ ................................................... .... 103

6.2

Effect of Trench Width................................... ............................................. 103

6.3

Effect of Burial Depth at a Given Trench Width ........................................ 104

6.4

Effect of Backfill Strength Relative to Native Soil Strength ...................... 105

6.5

Trench with Inclined Walls ......................................................................... 105

PIPE/SOIL INTERACTION UNDER COMPLEX LOADING.............................. 126 7.1

Studied Cases.................................... ............................................... ............ 126

7.2

Effect of the Angle of Pipe Translation on Pipe-Soil Interaction ................. 127

7.3

Effect of Soil Strength on Pipe-Soil Interaction with Combined Pipe Movement .................................................................................................... 127

7.4 8

Effect of Pipe-Soil Frictional Angle δ and Burial Depth Ratio................... 128

PHYSICAL MODELLING .................................................................................... 142 8.1

Introduction ............................................... .................................................. 142

8.2

Summary Program...................................................... ................................. 142

8.3

Experimental Procedure and Testing.......................................... ................. 143 8.3.1

Pipelines .................................................. ...................................... 143

8.3.2

Soil Preparation and Testing .................................................. ....... 144

8.3.3

Instrumentation and Measurement ................................................ 144


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8.3.4 8.4 9

11

Shear Strength and Water Content of Native Soil....................................... 145

QUANTIFICATION OF MITIGATIVE METHODS............................................ 155 9.1

10

Test Procedure.............................. ................................................. 145

Summary of Experimental Results ................................................... ........... 155 9.1.1

Force-Displacement Curves .......................................................... 155

9.1.2

Comparison of Test Results with Existing Methods..................... 156

9.1.3

Mitigative Effects.......................................................................... 158

9.2

Comparison of Experimental and Numerical Results ................................. 160

9.3

Numerical Back-Analysis...................................................................... ...... 162

DISCUSSION AND RECOMMENDATIONS........................ .............................. 187 10.1

Complex Loading ................................................... ..................................... 187

10.2

Axial Pipe-Soil Interaction ................................................... ....................... 188

10.3

Lateral Pipe-Soil Interaction................................................ ........................ 189

10.4

Quantifying Mitigative Measures............................................... ................. 190

10.5

Future Work................................................................................................. 191

REFERENCES .................................................. ................................................... .. 202

APPENDIX A

EXAMPLE FOR PIPELINE RESPONSE TO P-Y CURVE

INITIAL STIFFNESS.................................................................. ........................... 213 APPENDIX B

RECOMMENDED CHANGES TO STRUCTURAL ANALYSIS

DESIGN GUIDELINES ................................................. ........................................ 216


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LIST OF FIGURES

Figure 1-1 Figure 1-2 Figure 1-3 Figure 1-4 Figure 1-5 Figure 1-6 Figure 1-7 Figure 1-8 Figure 1-9 Figure 1-10 Figure 1-11 Figure 2-1 Figure 2-2 Figure 3-1 Figure 3-2

Figure 3-3

Figure 3-4

Figure 3-5 Figure 3-6 Figure 3-7 Figure 3-8 Figure 4-1 Figure 4-2

(a) Schematic illustration of continuum pipe/soil interaction, (b) Idealization of pipe/soil interaction based on structural model. .................. 31 Generalized load−displacement relationships for modelling soil behaviour ................................................. .................................................... 32 Plotted values for the adhesion factor, α .................................................. ... 33 ASCE horizontal bearing capacity factor: adapted from Hansen (1961) .... 34 ASCE horizontal bearing capacity factor: after Trautmann and O'Rourke (1983a) ......................................................................................................... 35 Lateral bearing coefficients recommended in PRCI guidelines .................. 36 Definition of ε50 ................................................... ........................................ 36 Comparison of p-y curves for clays: ASCE (1984) for pipes and lateral loaded pile in soft clay .................................................. ............................... 37 Differences between ASCE (1984) for pipes and the practice of pile engineering............................................. ...................................................... 38 Dependency of soil force on loading rate: pipelines buried in saturated sand ......................................................................................................... 39 Dependency of soil force on loading rate: pipelines buried in saturated clay .............................................. ........................................................... 40 Adhesion Factors Recommended in API RP2A and ALA Guidelines........ 47 Comparison of Adhesion Factor Relationships with Test Data................... 48 Finite element mesh for verification analyses ............................................. 53 Model parameters: (a) dependency of soil elastic modulus on effective mean stress used in finite element analysis, and (b) mobilization of soil strength parameters during deformation (adapted from Nobahar et al., 2000 and Popescu et al., 2001) .................................................................... 54 Experimental and calculated force-displaceme nt curves for lateral loading of a rigid pipe in dense sand: using a perfectly elasto-plastic model with constant dilation angle and E = E ave ......................................... 55 Experimental and calculated force-displaceme nt curves for lateral loading of a rigid pipe in dense sand: elasto-plastic hardening model with variable dilation angle: (a) constant Young’s modulus; and (b) variable Young’s modulus ........................................................................... 56 Experimental and calculated force-displacement curves of rigid pipe in loose sand..................................................................................................... 57 Recorded and predicted force-displacement relations for large-scale tests in clay, using the Von-Mises soil model: (a) soft clay; and (b) stiff clay.... 58 Comparison between predicted (a) and observed (b) failure in stiff clay.... 59 Recorded and predicted force-displacement relations for large-scale tests in clay, using the Cam-Clay model: (a) soft clay; (b) stiff clay................... 60 Typical finite element mesh and boundary conditions ................................ 67 Predicted force-displace curves for pipelines in uniform clay at different burial depth: (a) cu = 10 kPa, (b) cu = 20 kPa, and (c) cu = 45 kPa.............. 68


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Figure 4-3 Figure 4-4 Figure 4-5 Figure 4-6 Figure 4-7 Figure 4-8 Figure 4-9 Figure 4-10 Figure 4-11 Figure 4-12 Figure 4-13

Figure 4-14 Figure 4-15 Figure 4-16 Figure 4-17 Figure 4-18 Figure 4-19

Figure 4-20

Figure 4-21

Effect of burial depth on the bearing capacity factor of pipe in uniform clays 69 Effect of burial depth ratio on soil displacement distribution around a pipeline: cu = 20 kPa, δ /D = 0.35 ........................................................ ......... 70 Effect of burial depth ratio on plastic strains (PEMAG) in soil around a pipeline: cu = 20 kPa, δ /D = 0.35 ........................................................ ......... 71 Effect of burial depth ratio on soil displacement distribution around a pipeline: cu = 45 kPa, δ /D = 0.35 ........................................................ ......... 72 Variation of plastic zone with burial depth: cu = 45 kPa, δ /D = 0.35 .......... 73 Effect of burial depth ratio on soil displacement distribution around a pipeline: cu = 10 kPa, δ /D = 0.35 ........................................................ ......... 74 Effect of burial depth ratio on plastic strains in soil around a pipeline: cu = 10 kPa, δ/D = 0.35 .................................................................................... 75 Effects of soil strength on soil displacement distribution around a pipeline: H/D = 1.97, δ /D = 0.35 ................................................................. 76 Effect of burial depth ratio on plastic strains, PEMAG in soil around a pipeline: H/D = 1.97, δ /D = 0.35 ................................................................. 77 Onset of ultimate deformation: cu = 45kPa................................ .................. 78 Contours of plastic strains, PEMAG: Influence of burial depth ratio on plastic deformation zone at the onset of ultimate soil deformation using cu = 45 kPa ................................................................................................... 79 The relationship between (H/D)cr and N ch ................................................. .. 81 Hansen’s failure mechanism for an anchor slab: the basic case .................. 82 Effects of soil unit weight of bearing capacity factor .................................. 83 Lateral interaction factor for weightless cohesive soil ................................ 84 Values of ⇓ , increase in the lateral interaction factor vs. . h/cu .................... 85 Comparison of calculated force-displacement curves and recommendations of ASCE (1984) for cu = 20kPa: (a) H/D =1.03; (b) H/D = 4.08 ................................................ ................................................... 86 Comparison of calculated force-displacement curves and recommendations of ASCE (1984) for cu = 45kPa: (a) H/D =1.03; (b) H/D = 4.08 ................................................ ................................................... 87 Variation of A '' yu and B” with burial depth ratio H/D at cu = 10 and 45

kPa 88 Figure 4-22 Calculated force-displacement curves and the curve fitting with A = 0.075 and B = 0.925: cu = 10kPa ................................................................. 89 Figure 4-23 Pipe displacement yu: predicted and recommended by ASCE (1984)......... 90 Figure 5-1 Effective and undrained strength comparison of some clays ...................... 95 Figure 5-2 Mean effective stress distribution in soil mass under drained conditions (relative pipe displacement δ /D = 0.45).............................................. ......... 96 Figure 5-3 Strengths of soil around the pipeline in total and effective stress analyses . 97 Figure 5-4 Distributions of mean effective stresses in soil under (a) drained, (b) undrained and (c) partially drained conditions: H/D = 1.3, c∋ = 35kPa, φ∋ = 30°, relative pipe displacement δ /D = 0.15 .......................................... 98


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Figure 5-5 Figure 5-6 Figure 5-7 Figure 5-8 Figure 6-1 Figure 6-2 Figure 6-3 Figure 6-4 Figure 6-5 Figure 6-6 Figure 6-7 Figure 6-8 Figure 6-9 Figure 6-10

Figure 6-11 Figure 6-12 Figure 6-13 Figure 6-14 Figure 6-15 Figure 6-16 Figure 6-17 Figure 6-18 Figure 6-19 Figure 6-20 Figure 6-21 Figure 7-1

Effect of loading rate on predicted force-displacement curves with different clays, burial depth ratio H/D = 1.3................................................ 99 Force displace responses at small displacement at different loading rates 100 Dependency of ultimate pipe force on loading rate ................................... 101 Mobilization of cohesion and friction angle with strain ............................ 102 Definition of trench configuration ............................................................. 107 Effect of trench width: cun /cub=45kPa/20kPa, H/D = 1.03......................... 108 Effect of trench width on soil deformation: displacement distribution (relative pipe displacement δ /D = 0.08).......................................... ........... 109 Effect of trench width on soil deformation: plastic strain distribution, PEMAG (relative pipe displacement, δ /D = 0.08)..................................... 110 Soil deformations and contours of shear strain (PEMAG) in uniform soft clay (cu = 20 kPa) at relative pipe displacement δ /D = 0.08; B/D = 3.16.. 111 Effect of trench width at cun /cub =45kPa/20kPa: (a) H/D = 1.30 and (b) H/D = 2.0 .................................................. ................................................. 112 Differences of force-displacement curves of trenched pipes and pipes in uniform native soil ................................................. .................................... 113 Plastic strain distribution, PEMAG and deformations of native soil: B/D = 2.1, H/D = 1.03, at pipe relative displacement, δ /D = 0.79................... 114 Plastic strain distribution, PEMAG and deformations of native soil: B/D = 1.6, H/D = 1.03, at pipe relative displacement, δ /D = 0.38.................... 115 Plastic strain distribution, PEMAG and deformations of soil for a pipe buried in uniform native clay of cu = 45kPa: at pipe relative displacement, δ /D = 0.21 ........................................................................... 116 Effect of burial depth at different trench widths: (a) B/D = 1.6; (b) B/D = 2.1 117 Influence of burial depth ratio on bearing capacity factor for trenched pipelines: cun /cub = 45kPa/20kPa ............................................................... 118 Effects of burial depth on the distribution of plastic strain developed in soil at δ /D = 0.08: trenched pipelines, B/D = 2.16, cub/cun = 20kPa/45kPa119 Effects of burial depth on soil displacements at δ /D = 0.08: trenched pipelines, B/D = 2.16, cub /cun = 20kPa/45kPa............................................ 120 Calculated force-displacement curves for backfill strength of cun /cub = 45kPa/10kPa: H/D =1.3 .............................................. ............................... 121 Effects of backfill strength on force-displacement curves: (a) H/D = 1.3, B/D = 1.58; and (b) H/D = 2.0, B/D = 2.11 ............................................... 122 Effects of backfill strength on bearing capacity of trenched pipelines...... 123 Influence of burial depth ratio on bearing capacity factor for trenched pipelines: cun /cub = 45kPa/10kPa.............................................. .................. 123 Effects of backfill strength on the bearing capacity factor of trenched pipelines ..................................................................................................... 124 The configuration of trench with inclined walls ........................................ 124 Influence of trench wall inclination on calculated force-displacement curves ....................................................................................................... 125 Buried pipe subjected to combined axial and lateral translation ............... 130


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Figure 7-2

Simulation of a buried rigid pipe subjected to complex loading: a & b. finite element meshes; c. positioning of the pipe and result output section .............................................. ......................................................... 131 Figure 7-3 The maximum normalized axial interaction forces (a) and lateral forces (b) predicted for the central zone of the pipe: H/D = 1.8, δ = 20° and cu = 45kPa ................................................ ...................................................... 132 Figure 7-4 Contact between pipe and soil at relative axial displacement z/D = 0.35: cu = 45kPa, H/D = 1.8 ............................................................................... 133 Figure 7-5 Relationship between calculated axial interaction factor Nz and lateral interaction factor N x: H/D = 1.8, δ = 20° and cu = 45kPa.......................... 134 Figure 7-6 The maximum normalized axial interaction forces predicted for the central zone of the pipe: H/D =1.8, δ = 20°, cu = 20, 45, 100 and 200kPa 135 Figure 7-7 The maximum normalized lateral forces predicted for the central zone of the pipe: H/D = 1.8 , δ = 20°, cu = 20, 45, 100 and 200kPa ....................... 136 Figure 7-8 Variation of axial forces with soil strength in ax ial loading: (a) normalized force and (b) axial force on 1m long pipe segment ................ 137 Figure 7-9 Effect of pipe-soil frictional angle δ on pipe-soil interactions with combined axial and lateral loading: H/D = 1.8, cu = 45kPa ...................... 138 Figure 7-10 Effect of pipe-soil frictional angle on the interaction diagrams: H/D = 1.8, cu = 45kPa............................ ................................................... ............ 139 Figure 7-11 Effect of burial depth ratio on pipe-soil interactions with combined axial and lateral loading: cu = 45kPa, δ = 20° .................................................... 140 Figure 7-12 Effect of burial depth ratio on the interaction diagrams: cu = 45kPa , δ = 20° ................................................ ....................................................... 141 Figure 8-1 Typical layout of centrifuge model test after Paulin (1998)...................... 147 Figure 8-2 (a) Layout of Pipes in Test bed-2; and (b) location of pipe in the trench. . 148 Figure 8-3 Consolidated soil testbed before placing pipelines.................................... 149 Figure 8-4 Testbed surface is covered by Vaseline ..................................................... 150 Figure 8-5 Test 5: undrained shear strength using Equation 9-2 (left) and Equation 9-3 (right)................................................................................................... 151 Figure 8-6 Laterally loaded pipeline and surrounding soil after test........................... 152 Figure 8-7 Soil deformations in front of pipeline captured by spaghetti mesh ........... 153 Figure 8-8 Sketch of pipe location after test for T2P3 ................................................ 154 Figure 9-1 Force-displacement curves for test 1, pipes 1-4 ........................................ 164 Figure 9-2 Force-displacement curves for test 2, pipes 1-4 ........................................ 165 Figure 9-3 Force-displacement curves for test 3, pipes 1-4 ........................................ 166 Figure 9-4 Force-displacement curves for test 4, pipes 1-4 ........................................ 167 Figure 9-5 Force-displacement curves for test 5, pipes 1-4 ........................................ 168 Figure 9-6 Force-displacement curves for all centrifuge tests .................................... 169 Figure 9-7 Horizontal Interaction Factor Comparison ................................................ 170 Figure 9-8 Comparison of test T2P1 (uniform soil) in terms of normalized force – normalized displacement with ASCE and PRCI guidelines ...................... 171 Figure 9-9 Comparison of test T2P4 (uniform soil) in terms of normalized force – normalized displacement with ASCE and PRCI guidelines ...................... 172


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Figure 9-10 Comparison of pipe response in terms of normalized force vs. normalized displacement for pipe buried in uniform soil (T2P1) and pipe with trench (T2P3) .............................................. ....................................... 173 Figure 9-11 Comparison of pipe response in terms of normalized force vs. normalized displacement for pipes with vertical trench wall .................... 174 Figure 9-12 Comparison of pipe response in terms of normalized force vs. normalized displacement for pipes T1P1 to 4 ........................................... 175 Figure 9-13 Normalized force-displacement curves for pipelines buried in inclined trench ....................................................................................................... 176 Figure 9-14 Comparison of soil reactions in terms of normalized force vs. normalized displacement for T2P2 buried in inclined trench (45 degrees) and T2P3 buried in trench with vertical wall............................................. 177 Figure 9-15 Comparison of soil reactions in terms of normalized force vs. normalized displacement for T3P1 buried in inclined trench (60 degrees) and T3P4 buried in trench with vertical wall............................................. 178 Figure 9-16 Normalized force-displacement for pipelines buried in trenches with sand backfill............................................................................................... 179 Figure 9-17 Comparison of soil reactions for test T2P3 (cub = 20 kPa) and T4P3 (sand backfill) ........................................................... ................................. 180 Figure 9-18 Comparison of soil reactions for test T5P3 (vertical trench –sand backfill) and T5P2 (inclined trench – sand backfill) ................................. 181 Figure 9-19 Force-displacement curve comparisons, Tests T1P3 and T1P4 ................ 182 Figure 9-20 Force-displacement curve comparisons, Test series T2 ............................ 183 Figure 9-21 Force-displacement curve comparisons, Test series T3 ............................ 184 Figure 9-22 Force-displacement curve comparisons, Tests T2P1 and T4P1 ................ 185 Figure 9-23 Back-analysis of T2P3 using finite element method ................................. 186 Figure 10-1 Typical axial - lateral resistance interaction diagram ................................ 193 Figure 10-2 Proposed maximum normalized axial force .............................................. 194 Figure 10-3 Proposed maximum normalized lateral force ............................................ 195 Figure 10-4 Comparison of lateral interaction factor accounting for soil weight effects 196 Figure 10-5 Comparison of lateral interaction factor for weightless soil...................... 197 Figure 10-6 Normalized force-displacement relationship: (a) experimentally recorded shown by continuous lines; and (b) proposed approximation shown by dashed lines ............................................................................... 198 Figure 10-7 Normalized force-displacement relationship: (a) experimentally recorded shown by continuous lines; and (b) proposed approximation shown by dashed lines ............................................................................... 199 Figure 10-8 Normalized force-displacement relationship: (a) experimentally recorded shown by continuous lines; and (b) proposed approximation shown by dashed blue line ............................................ ............................. 200 Figure 10-9 Normalized force-displacement relationship: (a) experimentally recorded shown by continuous lines; and (b) proposed approximation shown by dashed blue line ............................................ ............................. 201 Figure B - 1 Plotted values for the adhesion factor, α .................................................. . 221 C-CORE Report R-02-044-113 29 August 2003

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Figure B - 2 Lateral interaction factor for weightless cohesive soil .............................. 222 Figure B - 3 Values of ⇓ , increase in the lateral interaction factor vs. . h/cu .................. 223 Figure B - 4 ASCE horizontal bearing capacity factor: after Trautmann and O'Rourke (1983a) 224 Figure B - 5 Effects of lateral spring load on axial spring capacity based on angle of loading 225 Figure B - 6 Comparison of lateral interaction factors estimated from replacement model (dashed-line) and 3D finite element analysis.................................. 226 Figure B - 7 Comparison of axial interaction factors estimated from replacement model (dashed-line) and 3D finite element analysis.................................. 227 Figure B - 8 Proposed p-y curve for laterally loaded trenched pipeline ........................ 228


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LIST OF TABLES

Table 2-1 Table 2-2 Table 4-1 Table 5-1 Table 6-1 Table 7-1 Table 8-1 Table 8-2 Table 9-1 Table 9-2 Table 9-3

Key Parameters for Tests Discussed in Honegger (1999) ........................... 44 Key Information from Tests Performed by Honegger in Sandy Soil .......... 45 Summary of cases studied........................................... ................................. 61 Studied case: rate effects.............................................................................. 94 Studied cases: trench effects ............................................................... ....... 107 Studied cases: combined axial and lateral loading .................................... 129 Summary of experimental tests....................................................... ........... 143 Shear strength and water content of native soil before and after acceleration ................................................... ............................................. 146 Experimental results and theoretical predictions ....................................... 155 Initial stiffness: experimental and theoretical values................................. 158 Estimated responses for T2P3 and T4P3 ................................................... 159

Table A - 1 Parameters used for the analysis ................................................................ 214 Table A - 2 Finite element results in terms of peak values........................................... 215


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Extended Model for Pipe Soil Interaction – Final Report

1

REVIEW OF STUDIES RELEVANT TO PIPE/SOIL INTERACTION

A literature review of significant issues related to modelling pipe-soil interaction is presented in this section. Discussions on the historical record, empirical and analytical studies on pipe-soil interaction and related mechanisms, and numerical procedures are presented. 1.1

Representation of Soil-Pipeline Interaction Forces: Theoretical Analysis and Laboratory Testing

In engineering design practice, the soil-pipeline system is represented by a structural beam (for the pipe) and spring elements (for the soil) in the axial (longitudinal), transverse horizontal, and transverse vertical directions (ASCE, 1984), Figure 1-1. This simplification is derived from the concept of sub-grade reaction originally proposed by (Winkler, 1867). The nonlinear, stress-dependent load-deformation characteristics of the springs are denoted as t-x, p-y, and q-z curves, representing the behaviour of soil in the axial, transverse horizontal, and transverse vertical directions, respectively. The general forms of the resistant forces can be expressed as: t = f x ( x ) , p = f y ( y ) , q = f z ( z ) where t, x ( p, y; q, z ) are soil forces per unit pipeline length and pipeline displacement in the axial (horizontal; vertical) directions, respectively. Usually, the force-displacement relationships of soil are nonlinear and there exist upper limits for t , p and q. Furthermore, all soil springs are independent and the effect of shear stress between two adjacent soil springs is not considered. In Figure 1-1, three frequently used dimensions about pipe location are defined, i.e., pipe cover depth C , burial depth H and embedment depth h. One of the critical tasks in the beam/spring model for buried pipelines is to determine the analytical expressions of soil resistance functions f x , f y and f z . Various relationships have been proposed for axial t-x, transverse horizontal p-y, and transverse vertical interaction q-z . Hyperbolic and bilinear forms are the most widely used force-displacement relationships, as shown in Figure 1-2 for normalized transverse horizontal p-y curves. The characterization of soil loads on pipeline is performed by two distinct approaches: (1) use of theoretical soil mechanics to derive equivalent simplified relationships, and (2) use of physical (small- or large-scale) test data to develop empirical relationships. The first approach consists of two methodologies based on the continuum theory and the Winkler theory considering the shear deformation effect of soil. In continuum models (see Reissner, 1958; and Vlazov & Leontiev, 1966 among others), assumptions about the distribution of displacements and stresses are made based on physical laws. The springs describing the soil resistance to deformation are usually assumed independent of one another, therefore no connection between adjacent soil zones is considered. This


1


assumption of independent soil slices does not truly replicate the observed behaviour (Kettle, 1984; Popescu and Konuk, 2001). Winkler models considering shear effects of soil proceed from the conventional discontinuous Winkler theory and eliminate its discontinuous behaviour by providing mechanical interaction between individual spring elements. Such theoretical models of soil behaviour have been proposed by Hetenyi (1946) among others. Either elastic membranes provide the interaction between the spring elements, elastic beams or elastic layers capable of pure shearing deformation. More details can be found in Selvadurai (1979). Following the model of Hetenyi, C-FER (1993) proposed two-dimensional soil spring models with shear elements linking adjacent soil springs and obtained improved pipe strain predictions of a full-scale buried pipeline subjected to frost heave. Winkler-type soil models, however, are unable to describe complicated soil behaviour, such as dilatancy, stress path dependency and to some extent strain softening. When soil is under large deformations, these phenomena may have significant effects on the soil loads and can only be simulated by using more sophisticated constitutive models and continuum numerical modelling techniques. 1.1.1

Longitudinal Interaction

For a buried pipeline, loads are induced in the pipeline when differential motion between the pipeline and the surrounding soil occurs. The axial interaction force between the pipeline and the soil is the friction force at the pipeline-soil interface. ASCE (1984) suggests that the axial soil load along the pipeline can be considered similar to the skin friction for piles. As such, the well-developed load displacement relationships for simulating pile-soil interactions can be readily implemented to buried pipelines. For pipelines buried in sand, no adhesion at the interface between pipeline and soil is considered. The axial yield stress σ t that can be transferred by the interface is then expressed as

σ t = σ n tan δ

(Eq. 1-1)

where σ n is the average effective normal stress along the periphery of the pipeline, and δ is the friction angle between soil and pipeline (ASCE, 1984). The value of δ can vary from 0.5φ to 1.0φ with φ being the internal friction angle of soil, depending on the characteristics of the interface between the pipe material and the surrounding soil. Kulhawy et al. (1983) found that δ varies from 0.5φ to 0.7φ for smooth steel pipes and 0.7φ to 1.0φ for rough steel pipes. Trautmann and O’Rourke (1983a) reported an indicative δ value of 0.6φ between sand and plastic pipelines. Long-term creep of wrap or insulation may significantly reduce the axial interaction forces. Machan and Squier (1983) found that bitumen coating significantly reduces skin friction along steel pipe piles. Similar applications to buried pipelines will be helpful to reduce the axial load transfer when a section of the pipeline is subjected to lateral soil C-CORE Report R-02-044-113 29 August 2003

2


movement, provided that the rate of ground movement allows the bitumen to deform at a sufficiently reduced level of stress. This finding reveals that, for long-term soil pipeline interaction, the friction angle δ based on short-time tests cannot be directly used. By integrating σ t in Equation 1-1 around the circumference of pipeline, the maximum soil load per unit pipeline length, t u, can be expressed as t u

1

' (1 + K o ) tan δ = π D. H 2

(Eq. 1-2)

where K o is the coefficient of earth pressure at rest; H is the depth to the centre of pipeline; D is the external pipeline diameter; and .∋ is the effective unit weight of soil. For large diameter pipelines, Dutch code NEN 3650 (1991) states that the weight of the pipeline and its contents has a significant effect on the friction acting on the pipeline and should be considered. The axial load transfer between pipelines and clays is also similar to that observed on piles ASCE (1984). By assuming that no drainage occurs during deformation processes, the maximum axial soil resistance per unit length of pipeline can be expressed as t u

= π Dcuα

(Eq. 1-3)

where α is an empirical adhesion factor decreasing with the undrained shear strength of soil, cu. The recommended values of α are given in Figure 1-3. The value of α , the adhesion factor, as a function of the undrained shear strength, is generally estimated based on back-calculations from pipe load test results. The value of α for piles is usually selected to be low for safe design; for imposed displacement problems such as buried pipelines subjected to soil movement, a relatively high estimation of α is required for safe design. ASCE (1984) presents a graphical relationship between the adhesion factor α and soil undrained shear strength cu for buried pipelines. The values of α are approximately 1.0, 0.65 and 0.44 when the values of cu are assumed to be 40, 80 and 120kPa respectively. For a cu value of less than 40kPa, the α value of ASCE (1984) is often assumed to be a constant of 1.0 (Rizkalla et al., 1996 and Cappelletto et al., 1998). Rizkalla et al. (1996) presented recent developments of longitudinal pipeline/soil interaction of coated pipelines in cohesive soils. Research programs supported by TransCanada Pipelines Ltd. have investigated the key parameters governing the longitudinal pipe-soil interaction based on both controlled experiments and full-scale field tests. It is found that the present state-of-practice models used for cohesive soils over-predict the value of α . The authors present new interaction models and discuss the potential implications of applying the new models. The value of the empirical adhesion factor α obtained from their test programs are significantly lower than that presented by ASCE (1984). The α values of Rizkalla et al. (1996) are approximately 0.65, 0.37, 0.20 C-CORE Report R-02-044-113 29 August 2003

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and 0.15 when the values of undrained shear strength (cu) of soil are 20, 40, 80 and 160kPa respectively. Cappelletto et al. (1998) also obtained consistent α values from two field tests. The adhesion factor α proposed by ASCE (1984) overestimates the adhesive forces by a factor ranging from 2 (for low cu soil) to 4 (for high cu soil). The prudent use of the adhesion factor proposed in this work is likely to contribute to more cost-effective design and maintenance of pipelines. The consideration for axial loading in Dutch code NEN 3650 is slightly different from ASCE (1984). According to Dutch Code NEN 3650, the friction per metre of pipeline length can be calculated by the following equation

& 1 + K o σ k tan δ + a #! % 2 "

t u = π D $

(Eq. 1-4)

in which D = the outer diameter of pipe K 0 = ratio between horizontal and vertical soil pressure σ k = vertical soil pressure at pipeline axis δ = angle of friction between soil and pipe wall, as a function of soil type and surface roughness of pipeline or coating a = adhesion, as a function of type of soil and time elapsed since backfilling, approximately equal to drained cohesion c∋ . Dutch code claims that it is cohesion that mainly determines the shear strength in clay soils. However, the contribution of inter-particle friction is not excluded. For saturated clay, the undrained friction angle φ is usually less than 5°. Consequently, at normal pipeline depths, the effects of friction angle are negligible compared with the effect of adhesion. As the water content is reduced, however, the undrained friction angle will increase rapidly for the same adhesion. Cappelletto et al. (1998) conducted field tests of eight longitudinally loaded pipes of 203mm (8in.) and 610mm (24in.) in diameter and interpreted the test results using the effective stress based models for both frictional soil and cohesive soil. Four pipes of 203mm in diameter were coated with coal tar and were tested in undisturbed silt and clayey fill, loose backfilled silt and clay, loosely backfilled silt and clay with granulite around the pipe, and uniform sand, respectively. Another four pipes of 610mm in diameter were coated with wrapped polyethylene and tested in undisturbed silt and clayey fill, loose backfilled silt and clay, loosely backfilled silt and clay with granulite around the pipe, and gravelly soil, respectively. The length of the pipes ranged from 16.2m to 18.3m and the burial depth was from 1.58m to 2.25m. During testing, the axial pull-out rate was 1mm per minute for the 203mm pipes and 0.7mm per minute for the 610mm pipes. The test results have been analysed using different methods. The limit skin friction per unit area at the pipe-soil interface is expressed with total stress analysis following ASCE (1984) α-method as C-CORE Report R-02-044-113 29 August 2003

4


f s

= α cu

(Eq. 1-5)

and with effective stress analysis (⇓-method) as f s

1

' (1 + K o ) tan δ = ⇓σ v ' = . H 2

(Eq. 1-6)

where σ v∋ is the effective vertical stress at pipe axis depth. The suggested values for α in ASCE (1984) overestimate adhesion at the interface by a factor of 2 to 2.5, while the results of effective stress analysis (⇓-method) match tests data well. The test results of Cappelletto et al. (1998) indicate that the use of an effective stress model (the ⇓-method), which is recommended by the Dutch code NEN3650, rather than a total stress one appears to be more appropriate to predict the longitudinal pipe-soil interaction forces for both frictional soil and cohesive soil at these displacement rates. This is because the thickness of the shear zone adjacent to the pipe is very thin and excess shear generated pore pressures dissipate very quickly with time. The axial force transferred by the pipe-soil interface depends greatly on the friction coefficient of the interface for quasi-static loads. The wrapped polyethylene coating is much smoother than the coal tar coating and results in larger reduction of skin friction. Direct shear box tests of different pipe-soil interfaces show that to minimize the friction between pipe and backfill soils, hard and smooth coatings are preferred to soft and rough coatings, almost irrespective of the types of surrounding soils, Scarpelli et al. (1999). Draft PRCI guidelines (Honegger and Nyman, 2001) consider both the frictional and cohesion components in the ultimate longitudinal soil resistance on pipe movement as follows:

& 1 + K 0 # ! tan δ 2 % "

t = π Dα c + π DH . $

(Eq. 1-7)

where: pipe outside diameter soil cohesion representative of the soil backfill depth to pipe centreline . effective unit weight of soil K o coefficient of pressure at rest adhesion factor (curve fit to plots of recommended values in Figure α 0.274 0.695 1-3) α = 0.608 − 0.123c − 2 where c is in ksf or kPa/100 + c + 1 c3 + 1 = interface angle of friction for pipe and soil = f φ δ internal friction angle of the soil φ = f = coating dependent factor relating the internal friction angle of the soil to the friction angle at the pipe-soil interface. Representative values of f for various types of external pipe coatings are provided below: D c H

= = = = = =


5


PIPE COATING Concrete Coal Tar Rough Steel Smooth Steel Fusion Bonded Epoxy Polyethylene

f

1.0 0.9 0.8 0.7 0.6 0.6

The ultimate axial soil resistance is significantly influenced by K o, the coefficient of earth pressure at rest, see Equations (1-2), (1-4) and (1-6). The ASCE (1984) guidelines make no recommendation for the coefficient of soil pressure at rest, although usually it is taken to be 0.5. In engineering practice, Jaky's Equation is well-accepted for loose sand and normally consolidated clay (Jaky, 1944) K o

= 1 - sin φ

(Eq. 1-8)

For dense sand, experimental evidence indicates that K 0 is intricately linked to the density. Based on experimental results, Sherif et al. (1984) suggested the following empirical relationship for dense sand K o

= 1 - sin φ + 5.5(. d /. d min − 1)

(Eq. 1-9)

where φ = friction angle of sand; . d = dry unit weight of sand; and . dmin = the minimum dry unit weight of sand. Furthermore, the friction resistance of soil along pipeline results from the normal stress, which may vary with soil deformation. In other words, the normal stress applied on pipe is only a representative value instead of the actual one, which influences the pipe-soil interaction. For overconsolidated clay, K 0 is related to OCR, the overconsolidation ratio, and can be estimated as follows (Mayne and Kulhawy, 1982) K o

= (1 - sin φ )(OCR) sin φ

(Eq. 1-10)

ASCE (1984) recommended that the maximum axial load (t u) typically occurs at a displacement xu of 0.1 to 0.2inches for pipelines buried in sand, 0.2 to 0.4inches for pipelines buried in clays; these displacements were obtained using research on piles and tests results of buried pipelines. These values are very close to the suggested values in PRCI guidelines: 0.1inches for dense sand, 0.2inches for loose sand, 0.3inches for stiff clay, and 0.4inches (10mm) for soft clay. The axial load-displacement relationships can be approximated by a hyperbolic (Holloway, 1976) or a bilinear relationship.


6


1.1.2

Transverse Horizontal Interaction

Many pipeline-soil interaction models have been developed based on research in pile-soil interaction and anchor plate-soil interaction. Research on anchor behaviours related to pipe-soil interaction will also be covered in this section. Mackenzie (1955) carried out small-scale tests of rectangular and long deadman anchors in clay in a steel tank in which the anchors were displaced horizontally to failure. The model anchor was 25.4mm high and 254mm long, with a thickness of 25.4mm. The soil used was a silty-clay with a liquid limit of 92% and a plastic limit of 30%. Tests were 3 conducted with water contents of 63% (cu = 2.5 kPa, . = 15.7 kN/m ) and 45% (cu = 21 3 kPa, . = 16.5 kN/m ). The thickness of soil cover ranged from 0 to 432mm. To simulate deep anchors, a water surcharge was placed on the soil surface. Lubricated steel plates were placed adjacent to the ends of the anchor to eliminate end effects so as to achieve plane-strain conditions. The test results indicate that when the cover was shallow (the ratio of cover depth to anchor height C/D = 0 to 2, see Figure 1-1), the anchor acted as a continuous wall and a conventional passive wedge type failure was observed. For deep anchors, the failure surfaces were similar to those of the deep failure mechanism assumed for laterally loaded piles. The data suggest a definite trend towards a limiting resistance for deep anchors. For shallow to medium depths up to approximately 200mm (or C/D = 7.9), in order to fit the experimental data, corrections were made to the passive wedge theory and the ultimate soil resistance was finally expressed as

pu

=

D & 1

# 2 $ . h + 2hcu ! h % 2 "

(Eq. 1-11)

where h is the depth of soil to the bottom of the anchor (or the embedment depth, see Figure 1-1); D is the height of the anchor; cu is the undrained strength of soil; and . is the unit weight. For deep anchors with depth greater than 250mm (or the ratio of cover depth to pipe diameter C/D = 10), the ultimate resistance resulted as pu

= 8 Dcu

(Eq. 1-12)

Mackenzie (1955) concluded that the passive wedge theory could be used only for horizontally loaded surface anchors (h = D) in clay. For deadman anchors with substantial cover, this theory results in unsafe prediction of anchor resistance. Due to the limited information on p-y curves for pipelines, Audibert and Nyman (1977) conducted an experimental investigation to determine the p-y curves for buried pipelines in sand, to reveal failure mechanism, and to examine the effects of pipe diameter, cover depth and soil density. Three model pipes with diameters of 25mm, 60mm and 111mm were tested in loose and dense sand. The ratios of cover depth to pipe diameter were from 1 to 24. The failure mechanisms were observed through a plexiglass wall on one side of the testing box. For shallow to intermediate burial depth (cover depth to pipe diameter


7


ratios equal to 1 - 6), a front passive wedge bounded by a logarithmic failure surface was observed. For deep burial conditions, confined zones of soil flow were observed. Based on the test results, a p-y relationship was recommended for analytical prediction of forcedisplacement curves of pipelines in sand, expressed as p =

y / y u A + By / yu

pu

(Eq. 1-13)

where A = 0.145, B = 0.855, pu is the predicted ultimate lateral force imposed on the pipeline corresponding to a displacement of yu. The above equation is the same as that proposed by Das and Seeley (1975) for vertical anchor in sand. Audibert and Nyman (1977) found good agreement between the experimentally obtained ultimate loads ( pu) and those predicted by the method of Hansen (1961), and recommended that the method of Hansen (1961) be used to predict the ultimate lateral load for the above equation. A yu value of about 1.5% to 2% of embedment depth was also recommended. It is also stated that the hyperbolic p-y curve can be represented by a bilinear relationship. It was confirmed from the field test data of a 229 mm diameter pipe that the proposed method for p-y curves gave a reasonable approximation to the field results. Trautmann and O’Rourke (1985) conducted tests of laterally loaded pipelines buried in sand. The experimental program was designed to characterize force-displacement behaviour in terms of a simple model suitable for design practice and to compare the test results with other published data. The pipe diameters were 102mm and 324mm. A loose sand, a medium dense sand and a dense sand were used, with peak friction angles of 31°, 36°, and 44°, respectively. Thirty tests were conducted with various burial depth-todiameter ratios ( H/D, Figure 1-1) ranging from 1.5 to 11. The test results showed that the roughness of pipelines had little effect on the soil response. Soil density had a significant influence on the resisting force of the pipelines. The value of the lateral dimensionless resistance factor N qh obtained from the test data increases with both the soil friction angle and the burial depth-to-diameter ratio, H/D. The displacement, yu, for reaching the maximum soil resistance were 0.13h, 0.08h and 0.03h for loose, medium and dense sand respectively, where h = H+D/2 is the embedment depth (Figure 1-1). The N qh values of the larger pipe are only 8% greater than the smaller one on average in loose sand and are only about 1% higher in the dense sand. The results show that the effect of pipe diameter on N qh is limited. Trautmann and O’Rourke (1985) made a comparison of test results with the analytical models of Hansen (1961), Ovesen (1964), Neely et al. (1973) and Rowe and Davis (1982b). The best agreement was with the model of Ovesen (1964) and Rowe and Davis (1982b), while the models proposed by Hansen (1961) and Neely et al. (1973) over predicted the lateral soil resistance by 150% to 200%. Based on the work of Ovesen (1964), design curves of N qh versus H/D were developed for different values of soil friction angle. It was also found from the experimental data that there is a hyperbolic relationship between lateral force ( p) and displacement ( y). C-CORE Report R-02-044-113 29 August 2003

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Wantland et al. (1982) conducted field and laboratory tests to determine the effect of pipe weight, pipe diameter, embedment depth, loading rate and type of soil on the lateral resistance to a pipeline buried in clay. The N c values increase with the embedment ratio h/D, with an upper limit on the order of 5 to 6. For h/D = 1, 2 and 5, the values of N c (approximate average of test data) were about 2.2, 3.4 and 5 respectively. It is noticed that N c is not significantly affected by pipeline diameter. It is suggested that lateral soil resistance to pipeline in clay is similar to the bearing capacity of a foundation and an upper bound plasticity mechanism for bearing capacity could be applied to a laterally loaded pipeline. Using the foundation analogy, the maximum lateral resistance to pipeline movement would be 5.14cu D at h = 2 D. It is recognized that the actual maximum lateral resistance for a pipeline may be different from the value suggested by the plasticity theory and a deeper embedment may be necessary to achieve the maximum value. Wantland et al. (1982) suggest that the ultimate lateral resistance of the cohesive soil is expressed as pu

= cu − avg N c D

(Eq. 1-14)

where N c is a lateral bearing capacity factor related to embedment ratio h/D and pipe shape; cu-avg is the average strength from a distance of 2 D above the pipe base. Rizkalla et al. (1992) proposed an expression of pu for pipes buried in clay as follows pu

= cu N ch D

(Eq. 1-15)

The interaction factor N ch can be derived according to Rowe and Davis (1982a) or ASCE (1984). However, there was significant effect of ditch/trench geometry on loads transferred to a buried pipeline due to soil movement. Rizkalla et al. concluded that most attention related to the soil spring models had been focused on predicting the ultimate resistance to pipeline movements. The experimental work available for verifying the predictive capacity of the soil spring models is largely laboratory based, using idealized soil and not adequately addressing the influence of construction-related factors influencing pipe/soil interaction, such as the geometry and/or the backfill properties. Rowe and Davis (1982a) conducted an elasto-plastic finite element analysis of vertical anchor plates subjected to lateral loading in cohesive soil. The anchor under plane-strain conditions was thin and rigid, with a height of D and a depth of h (embedment depth, Figure 1-1). The effects of embedment depth, overburden pressure, breakaway conditions, anchor roughness, thickness and shape were investigated. In the case of “immediate breakaway”, the back of the anchor separates from the surrounding soil. However, for “no breakaway” condition, the back of the anchor is maintained in contact with the soil. The failure of a shallow anchor was characterized by plastic flow to the soil surface while the failure of deep anchor was more characterized by local failure. The resistance of soil increases with depth up to a critical depth ratio (h/D). If the depth ratio is further increased, the anchor capacity does not change very much with depth. This critical depth ratio is about 3 for horizontally loaded anchors in both “immediate C-CORE Report R-02-044-113 29 August 2003

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breakaway” and “no breakaway” conditions. Furthermore, the value of N c is greatly influenced by breakaway conditions. For example, for depth ratios of 1, 2 and 3, the corresponding values of N c are approximately 2, 4 and 5 for “immediate breakaway” condition and about 4, 9.5, 11.5 for “no breakaway”. The results were found comparable with small-scale anchor tests of Mackenzie (1955) and Ranjan & Aurora (1980). For vertical anchor plates subjected to lateral loading in cohesionless soil , Rowe and Davis (1982b) found that soil dilatancy has a significant effect on anchor response and appreciably increase the ultimate capacity of anchors at moderate depth (embedment ratio h/D>3) in medium to dense sand. On the other hand, the influence of K 0 is usually less than 10% and may be neglected for typical values of K 0 ( K 0 =0.4~1). For an anchor at shallow depth (embedment h/D<3), the roughness of the anchor may increase the ultimate load by 15% to 60%, depending on the dilational properties of the soil. Similar to anchors in clay, the failure of a shallow anchor in sand was characterized by plastic flow to the soil surface while the failure of a deep anchor was more characterized by local failure. ASCE (1984) presents guidelines for the seismic design of pipeline systems. When the soil and the pipeline are subjected to relative transverse horizontal movement, a soil resistance will be applied to the pipeline. This load depends upon soil properties, pipeline geometry and buried conditions. The transverse horizontal (lateral) soil loading theory presented is inferred from footing and vertical anchor plate pull out capacity theory and laboratory tests on model pipelines particularly by Audibert and Nyman (1977) and Trautmann and O’Rourke (1983a). The hyperbolic p-y curve by Audibert and Nyman (1977) and given in Equation (1-13) is adopted. The ultimate lateral soil load to unit length of pipeline, pu, and the corresponding displacement, yu, are expressed as

= . HN qh D y u = . ( H + D / 2) pu

(Eq. 1-16)

In the equations above, H is the burial depth to pipe centre line (springline). The values of coefficient . are 0.07 to 0.10 for loose sand, 0.03 to 0.05 for medium sand, and 0.02 to 0.03 for dense sand. ASCE (1984) provides two models to calculate the horizontal bearing factor, N qh, see Figures 1-4 and 1-5. The first is based on the work of Audibert and Nyman (1977), who adapted Hansen (1961) model for vertical piles subjected to lateral loading and found good agreement with experimental data. The value of N qh increases with soil friction angle and burial depth-diameter ratio, H/D. The second model for the bearing factor, N qh, is based on the work of Trautmann and O’Rourke (1983a), who found good agreement between experimental results and the theory for vertical plate anchors subjected to horizontal loading Ovesen and Stromann (1972). ASCE (1984) has pointed out that for the same burial geometry and soil properties, the factor N qh obtained from the model of Hansen (1961) is 50 to 100% greater than that obtained from the Ovesen and Stromann (1972) based model.


10


For clays, ASCE (1984) suggests that the ultimate soil resistance of pipelines be calculated using Equation (1-15). The bearing capacity factor N ch can be derived after Hansen (1961), increasing with the burial depth-diameter ratio H/D, Figure 1-4. The values of N ch are approximately 5, 6, 7 and 7.5 when the values of H/D are 1, 2, 5 and 10 respectively. The guidelines suggest that the p-y curve for cohesive soils is similar to the hyperbolic p-y curve for sands. The value of yu displacement for clays ranges approximately from 3% to 5% of the embedment depth h. The ultimate pipe displacements recommended by ASCE (1984) are in the form of yu = . (H+D/2 ), where . = 0.07-0.10 for loose sand, 0.03-0.05 for medium sand, 0.02-0.03 for dense sand, and 0.03-0.05 for clay. In the Dutch code NEN3650, the Brinch Hansen theory (Hansen, 1961) is used to determine the horizontal bearing capacity in both sand and clay. For sand, a nominal frictional angle φ n is introduced in calculation by using a contingency factor of 1.2 such that tan φ n = (tanφ ) / 1.2. In other words, by using this contingency factor, a reduced friction angle is used in estimating force transferred to the pipe instead of directly using the friction angle of sand, such as in ASCE (1984). The upper limit of horizontal ultimate bearing capacity for sand is given as q hor = D0 K qσ k in which α z with

(Eq. 1-17)

σ k = vertical pressure at pipeline axis, K q = load factor in the form of K q = K q0

α z = 1 +

h

K 0 sin φ

D sin(45° + φ / 2)

(Eq. 1-18)

where h is embedment depth of a pipeline; D is the pipe diameter. The load factor K q0 is given as

K q 0

= exp[(π / 2 + φ ) tan φ ] cos φ tan(45° + φ / 2) . factor of passive pressure − exp[− (π / 2 − φ ) tan φ ] cos φ tan(45° − φ / 2) . factor of active pressure Eq. 1-19

Details can be found in Hansen (1961). However, no functional form of the p-y curve or pipe displacement at ultimate state is recommended in the Dutch code. For clay and peat, a contingency factor of 1.2 is recommended for modifying the cohesion of soil. When the soil surface is horizontal, the lateral bearing c apacity for C > 2 D is given as qhor

= aDo K c cu

(Eq. 1-20)

where


11


cu = undrained cohesion (undrained shear strength) K c = load factor, K c = 6 for C/D = 2, 7 for C/D = 6, and 8 for C/D > 15 a = 0.6 for open trench construction, 1.0 for jacked sections C = depth of cover Remark: The recommendations in Dutch code NEN3650 are made for pipeline construction. As such, qhor should be regarded as the lateral bearing capacity of soil, i.e. the support the soil can provide to a pipeline. The introduction of a contingency factor larger than unity decreases both soil friction angle and cohesion to consider the variation in soil bearing capacity due to some uncertainty in soil properties. However, when the soil loads transferred to the pipeline are of concern, the use of contingency factor under-estimates the load applied on the p ipe. Consequently, the contingency factor should not be introduced in this case. The PRCI guidelines (Honegger and Nyman, 2001) consider the contributions of both soil friction and cohesion to lateral soil resistance in the following form Pu

= N ch cD + N qh. HD

(Eq. 1-21)

where N ch = horizontal bearing capacity factor for cohesive effects (0 for c = 0), N qh = horizontal bearing capacity factor for frictional effects (0 for φ = 0 °). The expressions for N ch and N qh are closed form fits to published empirical results, and Nqh can be interpolated for intermediate values of φ between 20° and 45°, see Figure 1-6. The displacements at P u suggested in PRCI guidelines are yu = 0.04( H + D/2), but no less than 0.10 D to 0.15 D with D being the outer diameter of the pipeline. Rizkalla et al. (1992) suggested that in routine design of laterally loaded pipelines, both the work of Rowe and Davis (1982a) based on the elasto-plastic finite element analysis of vertical smooth anchors, and the recommendation of ASCE (1984) based on the work of laterally loaded piles Hansen (1961) should be included. Theoretical procedures to calculate the ultimate resistance of shallow anchors embedded in sand have been proposed by Teng (1962), Ovesen & Stromann (1972) and Neely et al. (1973). Teng (1962) considered anchors with embedment ratio h/D ! 1.5~2 and suggested that the ultimate soil resistance can be calculated as pu

= P p − P a

(Eq. 1-22)

where P p and P a are Rankine passive force in front of the anchor and active force behind the anchor, respectively. Obviously, Teng’s method does not consider the friction between the anchor and the surrounding soil. Further, this method overestimates the ultimate anchor resistance, since in most cases the mobilized soil resistance in front of the anchor is less than the passive Rankine force.


12


Luscher et al. (1979) suggest that the lateral pipeline force is resisted by the passive resistance of the soil and is analogous to a buried deadman anchor undergoing horizontal displacement. The lateral resistance is related to the shear strength parameters of the soil and the burial depth of the pipeline. For granular soils, the lateral resistance is based on the Rankine passive earth pressure reduced by a factor, a, as suggested by Ovesen and Stromann (1972). The ultimate soil resistance per unit length of pipeline is pu

1

= . ' ( H + D / 2) 2 K p a

(Eq. 1-23)

2

where H represents the burial depth to the centre of the pipeline (springline); . is the (effective) unit weight of soil. The reduction factor, a, increases with the diameterembedment depth ratio, D/( H+D/2). The coefficient of passive earth pressure is in the form of

= tan 2 (45 + φ / 2) !

K p

(Eq. 1-24)

For cohesive soils, the ultimate resistance is expressed as pu

= cu N c D

(Eq. 1-25)

where cu is the undrained shear strength of soil; D is the diameter of pipeline; and N c is the lateral resistance coefficient based on the work of Mackenzie (1955) on deadman anchorages. N c increases with the embedment-diameter ratio, h/D, where h = ( H+D/2). Based on the model tests conducted by Ovesen (1964), Ovesen & Stromann (1972) proposed another procedure to determine the ultimate resistance of anchors in sand. In this method, curved failure surfaces behind and in front of the anchor are assumed based on experimental observations. Furthermore, the surface of the anchor is assumed to be rough and the friction between the anchor and the surrounding soil is considered. Finally, the ultimate resistance is obtained by performing equilibrium analyses of the anchor. Biarez et al. (1965) presented a method to determine the ultimate resistance of anchors by means of limit analysis. They found that the resistance of anchors with embedment ratio h/D ! 4 is influenced by the roughness and weight of anchors. Dickin and Leung (1985) gave a simplified form of the original expression of Biarez et al. (1965) in the following form K p sin 2φ & h # & h 1 # ( K K ) = − − + $ ! $ − 1! p a b. H 2 % D 2 " 2 tan(45 + φ / 2) % D " pu

2

(Eq. 1-26)

where K p and K a are the horizontal components of passive and active earth pressure coefficients respectively; and h/D is the embedment ratio.


13


As for the load-displacement relationship, Ovesen (1964) studied the effect of sand density on shallow anchors with the embedment ratio h/D = 1. For a dense sand with relative density, Dr = 81%, a peak point was obtained at the displacement δ = 0.036h followed by gradually decreasing anchor resistance at large deformations. However, for a loose sand with Dr = 20%, the applied load monotonically increased until the test was terminated at δ = 0.10h. In this case, the ultimate load may be defined as the point at which the load-displacement relationship becomes practically constant, i.e. a large deformation only induces a small increase in load. For deep anchors in sand, theoretical analyses can be conducted by following the same principle for shallow anchors, however, different deformation mechanisms and failure modes should be used. As such, Ovesen (1964) gave an approximate estimation for the ultimate resistance of deep strip anchors as N q

=

pu

. hBD

= (1.6 + 4.1 tan 4 φ )(1 − sin φ )eπ tan . tan(45 + φ / 2)

(Eq. 1-27)

Meyerhof (1973) also proposed the variation of N q with the soil friction angle, φ . For a given soil friction angle φ , the value of N q obtained by Meyerhof is smaller than that calculated from Equation 1-27. Ng (1994) conducted a numerical analysis of buried pipelines subjected to external loads and to simulate in situ pipe loading tests to improve the understanding of the behaviour of buried pipelines under differential ground displacements. The results of lateral loading tests were used for the validation of a two-stage analysis technique, developed by British Gas. In Stage 1, a 2-D plane-strain finite element analysis was performed to predict the lateral resistance of the soil as a function of pipe displacement. The predicted soil resistance was then used in Stage 2 for modelling the lateral behaviour of the pipe using an elastic beam on elastic foundation. The program has been modified to include the effects of plasticity of pipe material, change in shape of pipe cross-section, and shear deformation in the pipe. Different soil models were used to represent the backfill in the FE analysis and assume different interface conditions between the soil and the pipe and between the backfill and natural ground. Satisfactory agreement between the field test data and the results of the numerical analysis has been found. Ng (1994) compared the results of the field lateral loading tests to the empirical relationships for N c, proposed by Matlock (1970), Poulos and Davis (1980), Rowe and Davis (1982a), Randolph and Houlsby (1984) and ASCE (1984). It was found that most formulations from the literature under-predicted the value of N c. As for the pipe displacement to ultimate load, Ng pointed out that the values suggested by ASCE (1984) under-predict the actual values measured from field tests. The results of a parametric study showed that the pipe displacement at ultimate load is a function of the strength ratio of natural ground to backfill for different W/D ratios for trenches. In summary, Ng concluded that a non-linear p-y curve can be estimated using the equation suggested by ASCE (1984) with the parameters as A = 0.16 and B = 0.84 in Equation (1-13). The ultimate load factor N c can be taken to be the Hansen bearing capacity factor suggested by ASCE (1984) and the effect of the presence of a backfilled trench should be accounted for. C-CORE Report R-02-044-113 29 August 2003

14


The softening phenomenon in static loading has also been observed in both physical and numerical modelling on soil-pipeline interaction (Paulin et al., 1997, 1998; Popescu et al. 1999). However, no attempts are made so far to describe the decrease in soil resistance at large pipe displacement by using force-displacement curves. It should be pointed out that the ASCE (1984) are in fact consistent with the methodology of pile design in geotechnical engineering practices, especially for deep buried pipes. In piling engineering, the p-y curve of a laterally loaded pile in soft clay is usually expressed by a parabolic function such as P pu

= 0.5 ( y/yc ) n

(Eq. 1-28)

where n is a constant with a value of 0.25 to 0.33 for soft clay and 0.33 to 0.53 for stiff clay (e.g. Reese and Welch, 1975; Welch, 1972; Matlock, 1970), yc = 2.5 Dε 50 is a reference displacement with ε 50 being the strain at one-half of the maximum principal stress difference in a laboratory stress-strain curve obtained from triaxial compression test (Figure 1-7), and D the width or diameter of the pile. The typical value of ε 50 for most clays may be assumed between 0.005 (stiff clay) and 0.02 (soft clay), while ε 50 = 0.01 is typical for normally consolidated clays. The displacement yu at p = pu is larger than yc. In static loading, if n = 0.33 as suggested by Matlock, then yu = 8 yc. Figure 1-8 shows the comparison between the p-y curves of a horizontally loaded pipe and a laterally loaded pile with D = 200mm. The displacements of pile to mobilize the ultimate soil resistance pu using ε 50 = 0.005 (stiff clay) to 0.02 (soft clay) is yu = (0.1~0.4) D, while the average value of yu for pipelines is suggested as 0.04( H+D/ 2) for clay in ASCE (1984), where H is burial depth to pipe springline. For typical values of H/D = 1~11, yu = 0.04(H+D/2 ) = (0.06~0.44) D which is overall in agreement with yu for piles. For a given pipe/pile diameter, pipe displacement to ultimate soil resistance ( yu) in ASCE (1984) is a function of burial depth while pile displacement to ultimate soil resistance is a constant. For shallow buried pipes in stiff clays and deep buried pipes in soft clays, yu in both pile engineering practice and ASCE (1984) are very similar. Scott (1981) suggested another method to evaluate the reference pile displacement, yc based on elastic deformation of soil, such that

yc

=

2.5c D E

(Eq. 1-29)

where E is a secant modulus of elasticity of the soil; c is the shear strength of clay. For piles in stiff clay, softening behaviour during static loading, i.e. the decrease in lateral loads with pile displacements, is accounted for and Equation (1-28) is modified to reflect this phenomenon, see Sulliva et al. (1979).


15


For piles in sand , experimental evidence shows yu = 3 D/ 80 (Reese et al, 1974), which is much smaller than that in clay. The range of yu in ASCE (1984) for pipes is (0.02~0.10) (H+D/2) for typically 1< H/D <11. Obviously, the pipe displacements to mobilize pu in ASCE (1984) are much higher than those experimentally observed for piles. Furthermore, on p-y curves for a pile in sand, elastic response is recognized at a pile displacement less than D/60, followed by a parabolic response until yu is achieved. The p-y curves for piles are also very different from ASCE (1984) for pipes. The determination of ultimate horizontal soil resistance in ASCE (1984) follows the same principles as in pile engineering. Consequently, no significant difference is found in pu for both clays and sands if suitable soil strength parameters are selected. However, the resulting stiffness of soil springs based on ASCE (1984) is remarkably different from that in pile engineering Pipe in sand:

pu y u

=

. ' HN qh D . ' N qh D = . ' N qh D / x 1 x ( H + D / 2) x(1 + ) 2 H / D

Pile in sand: Pipe in clay:

Pile in clay:

pu

. ' HN qh D

y u

xD

pu y u

=

= . ' N qh H / x

N ch cD x ( H + D / 2)

pu

N ch cD

y u

xD

=

N ch c H 1 x( + ) D 2

= N ch c / x

For sand, the secant stiffness based on ASCE (1984) is almost constant with depth, while that in pile engineering is linearly increasing with depth. For clay, the conclusion is just opposite: the secant stiffness based on ASCE (1984) decreases with depth, while that in pile engineering is a constant. The differences between ASCE (1984) for pipe engineering and the practice of pile engineering are illustrated in Figure 1-9. Further investigations on this issue are necessary. 1.1.3

Transverse Vertical Interaction

The pipe-soil interactions in the axial direction and in the transverse horizontal direction are assumed symmetric. However, the transverse vertical restraint component is unsymmetrical. The magnitude of soil resistance and the failure mechanism of upward pipeline/soil interaction are quite different from those in the downward direction. The downward and upward movements must be evaluated separately. 1.1.3.1 Downward Motion The soil resistance to pipelines subjected to relative downward movement can be estimated using the bearing capacity theories for strip foundations. It is assumed that the pipeline acts as a cylindrically-shaped strip footing. The ultimate soil resistance on C-CORE Report R-02-044-113 29 August 2003

16


pipeline per unit length is given by a general expression for both clays and sands, written as (e.g. Honegger and Nyman, 2001) qu

1

= cN c D + . HN q D + . D 2 N . 2

(Eq. 1-30)

where c is the cohesion of soil or the undrained shear strength; . is the total unit weight of soil; and D is the diameter of pipeline. The bearing capacity factors N c, N q and N . can be derived after Meyerhof (1955), depending on the friction angle of soil. The downward q- z curve for pipeline/soil interaction can be represented by a hyperbolic or bilinear relationship. The ultimate soil resistance, qu, is generally considered to occur at a displacement, z u, of 10% to 15% of the pipeline diameter, see ASCE (1984). Both the ASCE (1984) and the Dutch code calculate the ultimate bearing capacity of clay by using the undrained shear strength of clay. In Dutch code NEN 3650, Hansen’s method is recommended for both sand and clay, however, the friction angle and cohesion are reduced by the contingency factor of 1.2 and 1.5, respectively. Remark: Similar to what has been discussed in Section 1.2, the contingency factor is introduced to account for some uncertainties in the determination of soil strength or bearing capacity. However, when the loads transferred to a pipeline by soil are concerned, the contingency factor should not be used. 1.1.3.2 Upward Motion A number of researchers have investigated the upward lift force-displacement relationships (q-z curves) and the ultimate soil resistance on buried pipelines. Audibert et al. (1978) proposed that the models of Vesic (1969) and Reese and Casbarian (1968) can estimate the ultimate upward soil resistance, qu, for pipelines buried in clays and sands. For shallow horizontal anchors, both models assume curved failure surfaces that extend to the ground surface. The soil resistance per unit length of pipeline is related to the cohesion and friction angle of soil and a general expression of qu for pipelines in sands and clays can be given as (Honegger and Nyman, 2001) qu

= cN cv D + . ' HN qv D

(Eq. 1-31)

where c is the cohesion or undrained shear strength of soil; D is the diameter of pipeline; H represents the burial depth of pipeline to springline; .∋ is effective unit weight of soil; and N cv and N qv the are vertical uplift factors. For clays, the ultimate vertical lift resistance is usually expressed as qu

= cu N cv D


(Eq. 1-32)

17


where cu is the undrained shear strength of soil. Vesic (1971) proposed the vertical uplift factor N factor N cv cv from theoretical solutions for buried cylinders. Based on the tests of pipelines buried in dry, uniform sand, Trautmann and O’Rourke (1983a) proposed a hyperbolic q- z z relationship relationship as q

=

z 0.07 z u

+ 0.93 z

qu

(Eq. 1-33)

The value of z u ranges from 0.005 to 0.015 H for 4-inch diameter pipelines in dense, medium and loose sand Trautmann and O’Rourke (1983a). Similarly, Esquivel-Diaz (1967) reported test results of 3-inch diameter circular plate anchors, indicating that the ultimate pull-out resistance occurs at a displacement, z displacement, z u, of approximately 0.01 to 0.02 H for dense and loose sand. According to the model test results of Ali (1968) and Reese and Casbarian (1968), relatively large displacements, in the range of 0.1 to 0.1 to 0.2H ( ( z z u = 0.1H to to 0.2H ), ), are required to fully mobilize the uplift resistance to pipelines buried in clays. Here H Here H is is burial depth to the pipe spring line. For sands, the ultimate vertical lift resistance of pipeline is in the form of qu

= . 'hN qv D

(Eq. 1-34)

Based on the results of Trautmann and O’Rourke (1983b) and Rowe and Davis (1982b), ASCE (1984) summarizes the values of the uplift factor N factor N qv qv for dry and saturated sands. This factor is found to increase with the burial depth-diameter ratio ( H ( H / D) D) and soil friction angle ( φ ). ). The data of Trautmann and O’Rourke (1983b) were obtained from the tests of pipelines in sand while the results of Rowe and Davis (1982b) were finite element solutions of horizontal plates with no soil dilatancy and no interface friction. Rowe and Davis (1982a&b) conducted elasto-plastic finite element analyses of horizontal anchor plates subjected to upward vertical loading in both clay and sand. For horizontal anchors in sand, the effects of anchor embedment, soil friction angle, dilatancy, initial stress state and anchor roughness were investigated. For anchors in sand, soil dilatancy has a significant effect on anchor response and appreciably increases the ultimate capacity of anchors at moderate depth (embedment ratio h/D > 3) 3) in medium to dense sand. The influence of K 0 is usually less than 10% 10% and may be neglected for typical values of K 0 ( K K 0 = 0.4~1), while the effect of the anchor roughness is negligible at all burial depth. Furthermore, the normalized resistance of sand almost linearly increases with depth ratio h/D. h/D. For anchors in clay, the undrained behaviour of anchor plates was considered. Considerations were given to the effects of anchor embedment depth, overburden pressure, anchor roughness, and breakaway conditions. Different from anchor plates in sand, the normalized resistance of clay, N clay, N c, increases with depth up to a critical depth ratio (h/D (h/D). ). If the depth ratio is further increased, the anchor capacity does not change very much with respect to depth. This critical depth ratio is about 3 for horizontally loaded anchors in both “immediate breakaway” and “no breakaway” C-CORE Report R-02-044-113 29 August 2003

18


conditions. What is more important, the value of N c is greatly influenced by breakaway conditions, which is similar to the behaviour of vertical anchor plates subjected to horizontal loading in clay. If drained condition is considered, the value of N of N c is a function of both soil friction angle and embedment depth ratio. In general, there is good agreement between the finite element simulations (Rowe and Davis, 1982b) and the measured pipeline forces for dense sand (Trautmann and O’Rourke, 1983b). For medium dense sand, the finite element model tends to over predict uplift forces when H/D H/D is greater than 4, however, the difference is in a reasonable range (less than 15%). For loose sand, the FEM solutions by Rowe and Davis over-predict uplift forces for H/D for H/D > 3 by approximately 1.4 times. 1.2

1.2.1

Validation

Field Tests

Honegger (1999) investigated axial soil friction forces on buried pipelines through field measurement. The results have been reflected in PRCI guidelines, see Honegger and Nyman (2001). Rizkalla et al. (1996) reported a series of field longitudinal pullout tests tests under typical pipeline right-of-way (RoW) field conditions and controlled field-testing conditions for the purpose of validating and/or refining the state-of-practice (SoP) longitudinal pipeline/soil interaction factors for cohesive soils. NPS 16 and NPS 36 pipelines with different types of coating were tested. A total of 14 tests were performed on pipeline segments of 5.6m to 18.5m long. It was found that the ASCE’s (1984) recommendations overestimate the longitudinal interaction factor, or adhesive factor, α by by factors of 2 (for soils of low undrained shear strength) to 4 (for soils of high undrained shear strength). Field longitudinal pullout tests were also carried out at SNAM (Cappelletto et al., 1998; Scarpelli et al., 1999). Two series of four tests each were performed in different soils (including clay, silt, sand and gravel) on pipeline segments of about 11.5m and 19.0m long, respectively. The pipes were pulled out at a constant speed of 0.7mm/min or 1mm/min. It was clearly recognized that the soil response around the pipe is essentially drained, whatever the nature of the backfill, granular or cohesive. The values of measured longitudinal interaction factors are close to, but slightly larger than, those obtained by Rizkalla et al. (1996). Again, it is confirmed that the ASCE (1984) overestimates the adhesive factor by a factor of 2 to 2.5. Further analysis of the in-situ test in-situ test results shows that the effective stress method provides a reliable mean to evaluate the longitudinal soil pipeline interaction force. The "aging" effect in clay or a loose backfill was also observed in this research. Some of the pipeline damage in the 1994 Northridge earthquake provided case histories for comparison with longitudinal pipe/soil interaction models (O’Rourke and O’Rourke, 1995). In this analysis, Equation (1-2) is used to evaluate the interaction force at the pipesoil interface. The friction angle of dense sand is assumed to be φ = = 37°, the friction angle C-CORE Report R-02-044-113 29 August 2003

19


on pipe/soil interface is δ = = 0.87φ and and δ = = φ for for coal tar epoxy and cement mortar coating, 3 respectively. The average effective unit weight of soil is . ' = = 18.8 kN/m . When an elastic pipe response model is assumed, the calculated critical strain due to longitudinal soil movement is less than the seismic strain for all three pipes under investigation. Here, seismic strain is a calculated maximum pipe strain by assuming a different seismic ground movement pattern (see O'Rourke and Liu, 1999 for details). Consequently, failure is predicted for each of these pipes observed. Together with a non-linear pipe model, Equation (1-2) also successfully predicted local buckling of two pipelines during the earthquake. 1.2.2

Laboratory Tests

A series of tests were performed under an international program to evaluate the forcedisplacement response of buried pipelines in various sands and clays at full-scale. Five different loading conditions were investigated: upward movement, lateral movement, downward movement, axial movement and diametral deflection monitoring. Some of the tests were performed at C-CORE (Paulin et al., 1998) under both lateral and axial loading. The relative density of sand had a significant effect on the interaction forces. The post-peak lateral loads in dense sand were on average 160% of those in loose sand at large deformation. Some methods from the literature gave reasonable estimation for peak loads in dense sand, however, the peak loads in loose sand were over predicted. A similar conclusion was obtained for axial loading. C-CORE test results in clay revealed that the ASCE recommendations over-estimated the ultimate load, t u in axial loading. 1.2.3

Centrifuge Modelling

Various centrifuge tests have been conducted to investigate soil/pipe interaction. Investigations include the effect of groundwater level on buried pipes (English and Schofield, 1973), the behaviour of flexible circular pipes subjected to surface loads (Valsangkar and Britto, 1979), thaw induced settlement of pipelines (Smith, 1991), the influence of excavation on buried pipes (Kusakabe, 1984; Phillips, 1986), and the effect of earth pressure on buried flexible pipes (Tohda et al., 1988; Takada et al., 1985). Dickin (1988) studied the lateral displacement of vertical anchor plates and pipelines in both loose and dense sands by centrifuge tests. The lateral soil restraint on buried pipelines was successfully predicted based on the results of vertical anchor plates, even though the behaviour of anchor plates and pipelines was different. Therefore, centrifuge tests were conducted to examine the force-displacement response of 1m high vertical anchor plates and 1m diameter pipelines with buried depths from 1 to 11m. No significant difference in the force-displacement relations was observed between the plates and the pipelines, especially at large burial depths. The test results broadly validated the assumption that a laterally displaced pipeline can be treated as a laterally loaded vertical anchor plate in theoretical estimation of lateral resistance. For dense sand, the method of Ovesen and Stromann (1972) yields reasonable results compared with test data, while the theory of Rowe and Davis (1982b) over predicted predicted the experimental breakout loads. loads. For


20


loose sand, both analytical methods over predicted the lateral resistances by approximately 100%. Krstelj (1996) conducted a series of centrifuge tests of pipelines with a prototype diameter of 0.1m to 1.3m with embedment ratio h/D h/D = 3, 5 and 7 to investigate the behaviour of pipes buried in dry and saturated sand under both static and s eismic loading. The relative densities of sand in this study ware 40% and 60% for tests on dry and saturated sand, respectively. 1-g model tests on 20 to 40 mm diameters pipes buried in dry sand were also carried out to compare with centrifuge test results. He found that the normalized lateral load in dry sand decreases with increasing pipe diameter. When the scaled pipe diameter is larger than 0.7m, the normalized lateral load approaches a constant for a given density of sand. However, if the pipe diameter is decreased to D = 0.2 m, the normalized force is increased by approximately 25%. The model test results match the predictions from the methods of Ovesen (1964) and Rowe & Davis (1982b) very well. However, the model proposed by Hansen over-predicts the measurements by as much as 100%. For pipes in saturated sand under undrained conditions, the normalized force can increase by 80% or more over its "drained" value, depending on velocity of applied loading. The higher the loading rate, the larger larger the normalized force, see Figure 1-10. The negative pore pressure due to shearing induces the increase in normalized force under undrained conditions. Krstelj (1996) also carried out a series of small-scale, 1g model tests. The tests confirmed that the normalized ultimate loads dropped by approximately 20% for a ten-fold increase of pipe diameter. The experimental data were compared with the recommendations of ASCE (1984). The theoretical results of Ovesen (1964) were in good agreement with experimental data while the formulation of Hansen (1961) over-predicted soil resistances by as much as 100%. Paulin (1998) presented a series of centrifuge tests of pipelines with a prototype diameter of 0.95m to investigate the effects of trench geometry, soil preconsolidation stress, pipeline displacement rate and backfill type on the pipe/soil interaction. The pipes were placed in trenches with widths of 1.5 to 3m while the under cover depth varied from 0 to 3.25m. The testbed soil was a kaolin-silt mixture preconsolidated to either 140 or 400 kPa. The type of trench backfills included slurry, chunks of backfill, remoulded material and fine sand. The experimental data for H/D for H/D ratios ratios from 1 to 1.84 show the normalized lateral load increases with H/D with H/D;; however, the effect of cover depth on lateral load is not significant when H/D when H/D > 1.84. On the other hand, when partial drainage is permitted or the loading velocity is decreased, the lateral load on pipeline increases, Figure 1-11. For the tests performed under undrained conditions (i.e. at high loading speed), experimental data appear to be bounded by the interaction curves from Rowe and Davis (1982a) and Hansen (1961) for embedment ratio H/D ratio H/D less less than 2. For greater embedment ratios, the experimentally derived lateral soil resistance was similar to that according to Rowe and Davis (1982a). Opposite dependencies of pipe-soil interaction on loading speed are observed from studies by Krstelj (1996) and Paulin (1998). However, this can be explained by the principle of effective stress. stress . For Krstelj's tests on sand with relative density o f Dr = = 60%, the material is dilative. When sheared, the volume of sand tends to increase and hence


21


induces negative pore pressure, which in turn increases the effective stress. The dissipation of negative pore pressure increases with time or the lasting period of testing; as a result, the effective stresses in soil around the pipe, and hence pipe-soil interaction forces at fast loading are larger that those at slow loading. On the contrary, the clay used in Paulin's study is contractive, positive pore pressure generates during shearing and causes decrease in effective stress in soil. Since positive excess pore pressure dissipates more at slow loading, the pipe-soil interaction forces decrease with loading speed. In short, under undrained conditions, pipe-soil interaction forces increase with loading speed for dilatant soils, while they decrease for contractive soils. Paulin et al. (1998) initiated a number of 1:50 scale centrifuge tests of lateral pipe/soil interaction in cohesive soil (overconsolidated kaolin clay). The tests were performed at C-CORE. The objectives of this research included: (1) to prove that the centrifuge technique is suitable for soil/pipeline interaction, (2) to determine the interaction factors for a particular soil and (3) to determine the effect of trench geometry. From the test results, it was concluded that centrifuge modelling is a valid technique for investigating lateral pipe/soil interaction. It was pointed out that the current state-of-practice formulations according to Rowe and Davis (1982a) and Hansen (1961) appeared to not be conservative, predicting resistance loads on the pipelines approximately 50% lower than those obtained experimentally. However, a re-examination of the experimental data in light of desiccated soil condition in centrifuge tests by Paulin et al. yielded interaction factors consistent with the preceding formulations. 1.3

Numerical Modelling of Pipe/Soil Interaction

Analytical solutions are advantageous in terms of the simplicity, functionality and utility for conducting preliminary assessment of pipeline integrity and parametric analysis. The procedures, however, are limited by the underlying assumptions and idealizations considered. Furthermore, analytical difficulties are encountered for pipe/soil interaction events that consider non-uniform boundary conditions, spatial variation in characteristics of the pipeline and soil media, large amplitude, accumulated or cyclic deformational loading mechanisms, and nonlinear material behaviour. For these issues, numerical methods provide a rational basis for conducting pipe/soil interaction studies. Two commonly employed numerical procedures are the finite difference method and finite element method. 1.3.1

Finite Element Analysis – Structural Models

The current state of practice for analyzing pipe/soil interaction events by the finite element method is based on a structural-type finite element model. The structural model is a relatively simple tool and can be used for pipe lengths of the order of kilometres. The procedure is significantly more efficient and requires substantially less computational resources than equivalent continuum analysis, which will be further addressed in the next section.


22


The basic components of the numerical model are beam and spring elements, illustrated schematically in Figure 1-1, which are idealizations of the continuum pipe/soil response. The pipeline response is typically modelled by specialized beam elements that can account for internal pressure and thermal strain due to temperature differential. Additional variables that consider ovalization, warping, pressure stiffening, and nonlinear curved beam effects are also available with some commercial software packages. The soil continuum is discretized by spring elements that represent the load−displacement response per unit length of pipeline and are generally considered mutually uncoupled. The numerical model may also account for nonlinear geometric (i.e. displacement, strain) and material (i.e. elasticity, p lasticity) analysis. A number of studies have been conducted to investigate pipe/soil interaction using structural-type models, such as Kim et al. (1998) for buried pipeline response to ground subsidence; Bruschi et al. (1996) for long-term pipe/soil interaction; Bruschi et al. (1995) for the effects of pipeline route geometry with respect to the soil displacement field magnitude, distribution and direction. 1.3.2

Finite Element Analysis – Continuum Models

Continuum finite element models are robust and comprehensive numerical tools that can address a number of limitations in the structural-type finite element analysis in reproducing: 1. soil constitutive behaviour, 2. soil deformation mechanisms (e.g. shear load transfer), 3. soil/pipe interaction (e.g. variable circumferential or longitudinal pressure distribution), 4. complex pipeline response mechanisms (e.g. ovalization, or wrinkling). The significant disadvantages of continuum finite element modelling are the demands on computational resources, limited availability of realistic soil constitutive models, and the requisite experience and knowledge of the analyst. In addition, lack of data and uncertainty in determining input parameters (soil properties) always limit the application of more complex analysis such as finite element analysis. A number of studies have been conducted to investigate pipe/soil interaction using continuum finite element modelling, such as Popescu et al. (1999), Popescu and Konuk (2001), Altaee et al. (1996) and Bruschi et al. (1995); or pipeline response, such as Yoosef-Ghodsi et al. (2000) and Yoshizaki et al. (1998). 1.4

1.4.1

Summary of Past Efforts to Characterize Pipe-soil Interaction

Current State of Practice

The current state of practice is fully reflected in the ASCE (1984) guidelines, Dutch Code NEN 3650, and more recently, PRCI guidelines (Honegger and Nyman, 2001). The C-CORE Report R-02-044-113 29 August 2003

23


pipeline is represented as an elastic beam, while the so il along the pipeline is modelled by a series of discrete nonlinear springs (i.e. elasto-plastic, multi-linear). The maximum soil spring forces and associated relative displacement necessary to mobilize these forces are computed using different equations corresponding to assumed conditions. 1.4.1.1 Determination of ultimate soil forces Even though the above mentioned three guidelines/code follow the same basic principles, the calculations of soil forces are very different, since they are based on different considerations and assumptions. For pipelines buried in cohesive soil, ASCE (1984) assumed soil as fully saturated clay under undrained conditions. As such, the components of soil force due to the frictional properties of real soil are neglected and only undrained shear strength is considered. In the Dutch code NEN 3650, the frictional property of cohesive soil is not accounted for in the calculation of horizontal and vertical soil forces. However, the frictional contribution of clay to longitudinal soil force is considered and the effective stress method is adopted. Draft PRCI guidelines reflect the most recent progress in the research of pipeline/soil interaction. In the calculation of soil forces under different displacement conditions, both frictional and cohesive components are considered. Furthermore, it is clearly pointed out that soil properties representative of the backfill should be used to compute axial soil spring forces, while in cases of transverse loading, the properties of backfill can be used only when the pipeline movement is not influenced by the native soil outside the pipe trench. 1.4.1.2 Force-displacement relationships In both ASCE and PRCI guidelines (ASCE, 1984; Honegger and Nyman, 2001), the force-displacement relationships are assumed to be either hyperbolic or bilinear, while the bilinear relationship is implied in Dutch code NEN3650. For hyperbolic forcedisplacement relationships, the mathematical formulas are recommended only for transverse horizontal and vertical (upward) loadings in ASCE (1984). There is a significant difference in the recommended bilinear and hyperbolic force-displacement relationships by ASCE (1984), see Figure 1-2 in which the normalized p-y curves of both hyperbolic and bilinear relationships are presented. Overall, the hyperbolic curve gives larger soil resistance than the bilinear relationship. This may result in a significant difference in predicting forces applied on a pipeline due to relative pipe-soil displacements. 1.4.2

State-of-the-Art

1.4.2.1 Contact between soil and pipeline Correct modelling of the soil-structure interaction is very important for accurate simulation of the load transfer to the pipeline. Relative movements often take place at the interface, involving slip and/or separation. In the state-of-the-art approach, the pipe and C-CORE Report R-02-044-113 29 August 2003

24


the soil are discretized into 2D/3D finite elements. The pipe-soil interface is modelled with true interface elements that can account for relative displacements. Various types of interface elements have been used, such as: zero-thickness elements (e.g. double nodes with allowable relative motion), thin layer elements, modified quadrilateral/brick elements. Ng et al. (1997) compared the performance of three such interface elements implemented in the finite element code CRISP. They upgraded one of them, and performed 2D simulations of lateral pipe loading in an elastic-perfectly plastic soil, to test the ability of the interface element in simulating gapping. An interesting comparison between results of a 2D discrete analysis using PIPLIN (1991) and a 3D continuum analysis using SPIA (Selvadurai, 1991) of a pipeline subjected to frost-heave in a discontinuous permafrost was presented by C-FER (1993). It was concluded that the discrete model could handle situations with slow variations in pipesoil interaction along the pipeline. However, the discrete representation of the soil was deemed inappropriate in case of rapid variations in soil properties. A full continuum 3D representation of the soil was considered necessary for such situations. On the other hand, the computational effort for the 3D analyses was two orders of magnitude higher than that required by the 2D discrete analyses. Popescu and Konuk (2001) and Popescu et al. (1999) use the contact surface approach implemented in ABAQUS/Standard. It allows for separation and sliding of finite amplitude and arbitrary relative rotation of the contact surfaces, and includes an equivalent shear stress limit. Also mentioned in the literature, are a series of dynamic solutions based on combined boundary element – finite element methods. The pipeline is discretized in finite elements. The loads at the pipe-soil interface are evaluated with boundary elements using, for example, the cavity theory. Manolis et al. (1995) found, based on such a study, that seismically induced stresses in a buried pipeline are more pronounced in the case of transverse vibrations than for longitudinal vibrations. Though boundary element solutions are less demanding computationally than corresponding finite element approaches, they are only appropriate for linear or mildly nonlinear problems, and therefore offer a poor representation of soil nonlinear behaviour. There are reported efforts to improve on several computational aspects (e.g. Liolios et al., 1998 simulate the no tension behaviour and gapping at pipe-soil interface). Tehrani-Zadeh (1995) performs such hybrid dynamic analyses in the frequency domain, addressing aspects such as angle of incidence of the seismic waves. 1.4.2.2 Soil constitutive models Numerous constitutive models have been proposed for simulating the surrounding soil. Some authors assume linear behaviour, modelling the soil either with elastic springs (e.g. Zhou and Harvey, 1996; Karadeniz, 1997; Zhuang and O’Donoghue, 1998), or as an elastic continuum (e.g. Tohda et al., 1988 & 1994; Fernando and Carter, 1998). However, the linear elastic assumption is only applicable to situations involving a relatively low strain level, such as compressor-induced vibrations, or moderate vertical loads on the backfill. The next step was to assume elastic–perfectly plastic behaviour of the soil materials. Workman (1992), Popescu and Konuk (2001) simplify soil as an elastic-plastic


25


continuum. Studies using non-linear hyperbolic soil models are also reported (e.g. Javanmard and Valsangkar, 1998). However, to correctly simulate the pipe-soil interaction in problems involving large deformations, the use of an appropriate soil model, able to reproduce both strain hardening and softening, is necessary. Also, in the case of saturated soil materials, coupled field equations capabilities are required to reproduce pore water pressure buildup and suction phenomena induced by pipe movements through soil. Examples of such finite element analyses are listed here: Altaee and Boivin (1995) and Altaee et al. (1996) conducted 2D plane strain analyses of pipes moved laterally through soil to investigate the performance of various nonlinear soil constitutive models implemented in CRISP and AGAC. Cam-Clay models were deemed to provide satisfactory results for normally consolidated and slightly overconsolidated clays. A boundary surface soil constitutive model was recommended for overconsolidated clays. In those analyses, no special consideration was given to the pipe-soil interface. Yang and Poorooshasb (1997) studied the effects of ice scour on buried pipelines. They conducted 3D finite element analyses to investigate the effects of ice scour on pipelines buried in a sandy seabed, using the Drucker-Prager soil model implemented in ABAQUS. The pipeline was modelled as an elastic beam, and no slip was allowed at the interface. An extensive experimental and numerical research on interaction between soil and buried pipes subjected to very large relative deformations (e.g. Popescu et al., 1999, Nobahar et al., 2001) indicated that (1) a modified Cam-Clay model with isotropic hardening was adequate for analyzing pipes loaded in clay under drained conditions, and (2) a non-associated Mohr-Coulomb model with isotropic hardening/softening provided good results for pipes loaded in sand. A contact surface approach allowing for separation and sliding of finite amplitude and arbitrary relative rotation of the contact surfaces was used. It was mentioned, however, that kinematic hardening would be needed for capturing hysteretic effects in saturated soils subjected to cyclic loading. 1.4.3

Open Issues/Challenges

1.4.3.1 Applicability over wide range of “real” soils The response of pipelines is very much dependent upon the properties of the surrounding soil. For a pipeline buried in loose sand or soft clay, the measured force-displacement curves are almost hyperbolic. However, a peak point followed by a decrease in force is observed in dense sand, see Paulin et al. (1997) for example. This is termed as strain softening, which is mainly induced by dilatancy of dense sand under shearing. The strain softening behaviour is also very often observed in stiff clays. Examples of such calculations, accounting for strain softening of granular soil materials and using a full continuum representation of the pipe and the soil are presented by Nobahar et al. (2001) and Popescu and Konuk (2001). For pipelines buried in medium sand or firm clay, the gradient of the force-displacement curve may become constant, i.e. the soil force C-CORE Report R-02-044-113 29 August 2003

26


increases linearly with pipe displacement, see C-CORE (2001a) for example. Obviously, this is different from the assumed hyperbolic or bilinear force-displacement relationships in the state-of-practice. 1.4.3.2 Dependency of soil interaction forces on stress state and stress history Soil behaviour is influenced by stress histories and current stress state. For example, the stress- strain response and strength of overconsolidated clay are different from those of normally consolidated clay. The maximum friction angle of soil under plane strain conditions is about 5% higher than that of the same soil under triaxial stress conditions. All these have effects on interaction between a pipeline and the surrounding soil. As the loading mechanisms of soil surrounding buried pipes is quite complex, a viable (but expensive) solution would be use of soil constitutive models based on the continuum plasticity theory that are able to address any stress combinations. The coupling between shear and normal stresses in soil may change dramatically the force-displacement response in terms of p-y curves and the soil failure mechanism, as shown in C-CORE (2001a). However, they are not reflected in the simplified sub-grade reaction models based on Winkler concept. 1.4.3.3 Large deformation (meters) vs. small deformation (millimetres) Large scale experimental investigations by Paulin et al. (1997 & 1998) and field fullscale tests reported by Cappelletto et al. (1998) reveal that softening force-displacement responses at relatively large displacement are common in densely compacted soils. At the residual state, the soil force may decrease to only 50% of the maximum mobilized soil force at small relative displacement. These very large relative soil/pipeline displacements may occur for example during landslides. In these cases, the soil properties at residual state should be used instead of those at small deformations. However, this is not considered in the current analysis procedures. 1.4.3.4 Load rate effects According to tests on soil samples, fast loading rates on soil usually result in higher stiffness and higher strength (e.g. Ishihara, 1996). In pipe-soil interaction problems, the effects of loading rate are significant for pipelines buried in clay. However, the experimental results are different from those obtained from tests on soil samples. Largescale model tests on axial pullout of pipe in clay shows that slow loading (0.5 mm/hr) caused 25% larger axial force than fast loading (10 mm/hr), see Paulin et al. (1998b). A series of centrifuge model tests (Paulin, 1998) on pipes subjected to lateral loading shows that slower loading leads to larger soil resistance than fast loading, especially at large pipe displacement. In that research, the load rates vary between 0.0095 m/day and 0.74 m/day, and the soil force at slow loading can even be 2.5 times of that at fast loading. This has been attributed to the influence of loading rate (or time) on the dissipation of excess pore pressure in clay around the pipe. The test results from these experimental investigations support the use of effective stress concept in estimating soil/pipeline


27


interaction. In seismic analysis, effective stress analysis is the only appropriate approach to consider the effect of excess pore pressure due to cyclic loading. 1.4.3.5 Characterizing basic soil parameters Due to the dependency of soil properties on the type of soil, current stress state, deformation history, loading or deformation rate, and drainage conditions, the characterization of representative soil parameters, e.g. φ , c, K o, becomes a challenge. The somehow simplistic recommendations in the current guidelines (e.g. ASCE, PRCI guidelines) and design codes (e.g. Dutch code NEN 3650) do not reflect all these effects in determining soil parameters, especially for pipelines buried in clay. More research is necessary in this direction. 1.5

1.5.1

Issues Addressed by This Research Project

Introduction

C-CORE developed a continuum finite element model for pipe-soil interaction involving large relative displacements using the ABAQUS Standard finite element code. The analysis procedure accounts for the nonlinear behaviour of soil and pipe materials, relative slip and separation at the pipe-soil interface, and ovalization and buckling of the pipe. The calculations were performed in terms of large displacements/finite strains. The model was calibrated and validated based on full-scale experimental data (e.g. C-CORE, 1998; Paulin et al., 1997 & 1998b), including various soil materials, pipe-soil relative flexibility and loading mechanisms. The validations were performed considering four different soil materials used in the full-scale experiment, and for both lateral loading (Popescu, 1999, Popescu et al., 1999) and moment loading (Popescu et al., 2001). Several aspects of pipe/soil interaction that are not addressed by the standards used in current practice have been studied to indicate improvements to existing soil spring based structural models. Such preliminary studies addressed the effects of various factors, such as: (1) soil failure mechanism (including embedment ratio, soil type and strength, pipe loading mechanism); (2) pipeline trenching (including trench geometry and backfill vs. native soil strength ratio); (3) pipeline ovalization and collapse (including pipe thickness-to-diameter ratio, boundary conditions, soil type, internal pressure); (4) complex loading (including pipe translation + rotation, axial + lateral translation, axial + moment loading). The objectives of this research are (1) to improve current pipe-soil interaction guidelines on differential ground movement effects and upgrade simple structural pipe-soil interaction models used in current practice, and


28


(2) to quantify practical mitigative methods for reduction of these effects on buried gas pipelines. The continuum 3D finite element model for pipe-soil interaction developed at C-CORE will be used for this purpose, along with full-scale and centrifuge experimental results of pipe-soil interaction, and also recent results of field measurements performed by Honegger (2000) on decommissioned pipe sections in weak-to-desiccated, cohesive-to-sandy silts in California. Some of the issues to be addressed are briefly described hereafter. 1.5.2

Non-linear Soil-Spring Characteristics

The improvements under this research focus on better definition of the nonlinear spring characteristics of the axial (t-x) and lateral ( p-y) soil response. Soil behaviour is very different between dilatant soils (e.g. firm to stiff clay, medium to dense sand) and contractive ones (e.g. soft clay and loose sand) under either drained or undrained conditions. In this study, soil constitutive models available in ABAQUS, a commercial software, will be selected and customized so as to capture most of the salient deformation features of soil materials, such as nonlinear deformations, shear induced volume change under drained conditions and excess pore pressure under undrained conditions. The findings of the study will then be translated into recommendations for defining non-linear spring characteristics for various soil materials. 1.5.3

Axial Pipe-Soil Interaction

The field tests of Rizkalla et al. (1996) showed that the peak axial soil reaction (t u) in clay is about 50% of that calculated using ASCE (1984). These measurements will be compared to other more recent field measurements made by Honegger (2000) on decommissioned pipe sections in weak to desiccated, cohesive to sandy silts in California. The axial interaction (t-s springs) occurs over a very thin shear zone between the pipe and soil and consolidation in this zone happens very quickly. It may therefore be more appropriate to base the t-s clay springs on effective stress parameters. This position is supported by field tests by Scarpelli et al. (1999) and the Dutch Code NEN 3650. Efforts will be made in this research to find the appropriate method, total stress or effective stress analyses, for axial pipe-soil interaction. 1.5.4

Lateral Pipe-Soil Interaction

Improvements can also be made to the lateral soil response springs. ASCE (1984) assumes that the secant stiffness ( pu/ yu) decreases with increased pipe burial depth in clay. Actually, the secant stiffness will increase with increased burial depth (Paulin et al., 1995). Paulin et al. (1996) also indicate a significant rate effect in cohesive soils. For fast rates of interaction ASCE p-y curves based on undrained shear strength may be sufficient, but for slow interaction rates an effective stress analysis should be used (that is 'sand' type curves). Moreover, a recent study by C-CORE (1999) of p-y response in sands showed that the ASCE (1984) provided a reasonable prediction of pu in dry and submerged sands. However, the yu value was halved between the submerged and dry tests for the same test


29


geometry. That is, there is an effective stress effect on yu that is currently not considered in the guidelines. 1.5.5

Complex Loading

ASCE (1984) recognizes that the lateral soil pressure acting on the pipe significantly affects the effective axial soil resistance. Kennedy et al. (1977) estimated this effect, but the effect needs to be quantified. The ASCE (1984) soil/pipeline interaction model assumes that the soil response can be approximated by a series of independent non-linear springs, attached to the pipe structure. Three independent orthogonal springs are assumed to represent the axial, vertical and lateral response of the soil with respect to the pipeline. However, the coupling effects between axial and lateral interactions cannot be modelled. Significant advances have been made by analysing the pipe-soil interaction as a continuum, rather than as discrete systems (e.g. Popescu and Konuk, 2001). Recognizing that more complex loading, including pipe rotations and bending, as well as combinations of rotations and translations may occur in the field, Popescu and Konuk (2001) analysed the effects of shear interaction between different soil zones along pipe axis. It was also found that soil pressure induced by lateral relative displacement of the pipe, as well as soil failure induced by inclined loads may change significantly the actual pipe-soil interaction forces. All those findings resulted from continuum finite element analyses of pipe-soil interaction. Discrete structural models represent, however, the state of practice in soil/pipeline interaction analysis. The focus of this project will be therefore to provide recommended improvements consistent with discrete analyses commonly used in practice. 1.5.6

Quantifying Mitigative Measures

The ASCE (1984) guidelines do not discuss mitigative measures in detail but a variety of potential mitigation measures will be addressed in the PRCI guidelines. Through a limited number of tests, research has shown promise in mitigating the effect of lateral soil movement by use of lightweight backfill (Scarpelli et al., 1999) and consideration of the trench effect around the pipeline, Ng (1994) and Paulin et al. (1995). In order to realize the potential benefits, a proper pipe-soil interaction model to account for the low strength of the backfill materials is required. A recent study by TransCanada (C-CORE, 2000) has demonstrated that significant cost savings can be materialized if the low-strength backfill materials are properly accounted for in pipe-soil interaction analysis, in conjunction with the most appropriate trench geometry.


30


Hs Y

X

Z

(a)

ka ka

kh

kh Y

X

kv

kv

Z (b) Figure 1-1

(a) Schematic illustration of continuum pipe/soil interaction, (b) Idealization of pipe/soil interaction based on structural model.


31


1.2

) u p / 1 p ( d a o L0.8 l a t n o0.6 z i r o H d0.4 e z i l a m r0.2 o N 0

Hyperbolic − p p u

y # = y y & $ 0.15 + 0.85 y ! u u " %

Idealized Bilinear

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Normalized Horizontal Displacement (y/y ) u

Figure 1-2

Generalized load−displacement relationships for modelling soil behaviour


32


1.6 ASCE (1984) Tomlinson (1957) Rizkalla et al. (1996) Balboa Potrero Canyon Paulin et al. (1998)

1.4 1.2 o t c 1 a F n 0.8 o i s e h 0.6 d A

Rizkalla et al. (1996) Data Proposed Equation by

Honegger and Nyman (2001)

0.4 0.2 0 0

25

50

75

100

125

150

Undrained Shear Strength, kPa

Figure 1-3

Plotted values for the adhesion factor, α


33


Figure 1-4

ASCE horizontal bearing capacity factor: adapted from Hansen (1961)


34


Figure 1-5

ASCE horizontal bearing capacity factor: after Trautmann and O'Rourke (1983a)


35


100

Nqh, φ = 45 h q

N &

Nqh, φ = 40

h c

N , s t n e i c i f f e 10 o C g n i r a e B l a r e t a L

Nqh, φ = 35 Nqh, φ = 30

Nch Nqh, φ = 25 Nqh, φ = 20

1 0

2

4

6

8

10

12

14

16

18

20

H/D

Figure 1-6

Lateral bearing coefficients recommended in PRCI guidelines

q = σ1 - σ3 q max

0.5q

max

ε50 Figure 1-7

axial strain

Definition of ε50


36


n

/pu = 0.5( y/yc) , n = 1/3, c = 2.5ε 50 D = 5 mm u = 8 yc = 40 mm ASCE pipe guidelines

yc

Figure 1-8

yu

Comparison of p-y curves for clays: ASCE (1984) for pipes and lateral loaded pile in soft clay


37


Figure 1-9

Differences between ASCE (1984) for pipes and the practice of pile engineering


38


Figure 1-10 Dependency of soil force on loading rate: pipelines buried in saturated sand


39


300 TW 0.5D 1D , ) p ( D 200 A O L E P I 100 P

0 0

0.007 m/week

0.064 m/week 0.58 m/week

5.25 m/week

1 2 3 PIPE DISPLACEMENT (y), D

4

Figure 1-11 Dependency of soil force on loading rate: pipelines buried in saturated clay


40


2

SUMMARY OF METHODS TO ESTIMATE AXIAL FRICTION

The axial (longitudinal) displacement of a buried pipeline relative to the surrounding soil generates axial forces on the pipeline related to shear failure of the soil at the pipe-soil interface. Several theories have been proposed and implemented in practice to estimate the magnitude of the axial soil loads and the relationship between the axial loads and relative displacement, as reviewed in Section 1.1.1. Most approaches used for quantifying axial soil loads on buried pipelines relevant for engineering uses were originally developed for application to pile design and represent soil resistance on the pipeline by an equivalent non-linear spring. For onshore pipelines, the most common relationships for defining equivalent axial soil springs are summarized in guidelines for the seismic design of oil and gas pipeline systems prepared by the American Society of Civil Engineers (ASCE, 1984). These relationships have been modified slightly in a recent project undertaken by the American Lifelines Alliance (ALA, 2001). For offshore applications, axial soil loads on buried pipelines are typically derived from recommended practice for piles used for fixed offshore platforms provided in American Petroleum Institute RP 2A (API, 1993). For both onshore and offshore applications, the most commonly used relationships are based on characterizing the soil as either clay or sand. The general form of the equations for estimating axial soil load is identical for both onshore and offshore relationships provided in ALA (2001) and API RP2A (API, 1993) as provided below: 1

tu

= π DH . (1 + Ko ) tan δ

for sand

(Eq. 2-1a)

tu

= π Dα c

for clay

(Eq. 2-1b)

2

where: t u = D = H = . =

ultimate axial soil force in units of force per unit length of pipe pipe outside diameter depth from the ground surface to the pipeline centerline effective unit weight of soil

K o = φ = δ = α = c =

coefficient of earth pressure at rest = 1-sin(φ ) internal friction angle of soil interface friction angle between the pipeline and the soil adhesion factor undrained shear strength for clay soil

The primary differences offshore applications is guidelines (ALA, 2001) the definition of soil components.

in the implementation of the recommendations for onshore and in the definition of δ and α . Recent changes in the ALA combine equations (10a) and (10b) to account for cases where properties includes both frictional and cohesive strength


41


The interface angle of internal friction in API RP2A, is simply taken as the internal friction angle of the soil minus 5 degrees with a range of internal friction angles for sand varying from 20° to 35° primarily because these angles are more typical of offshore sediments. The ALA guidelines define the interface angle of friction as the internal friction angle of the soil multiplied by a factor less than one and is based upon the coating characteristics of the pipeline. Equivalent multiplicative factors for the API RP2A recommendations vary from 0.75 to 0.85, regardless of pipeline coating. The lack of a coating dependence in API RP2A is logical considering the recommendations are intended for pile design where the intent of the coating is to maximize the ultimate axial soil load. The ALA guidelines recommend factors that vary from 0.6 for pipelines with a smooth hard coating to 1.0 for pipelines with coatings such as concrete that are expected to bond to the soil. There are no limits on the soil angle of internal friction in the ALA guidelines and it is noted that if the same approach in API RP2A is extended to soil angles of internal friction as high as 40° to 45° (highly unlikely for offshore deposits), the equivalent multiplication factors increase to approximately 0.9. From this comparison, it is concluded that the onshore and offshore equations used to estimate ultimate axial soil loads are quite similar with the API RP2A approach leading to slightly higher loads than the ALA guidelines for smooth, hard pipe coatings. Except for highly plastic clays, there is little difference between API RP2A and the ALA guidelines in the definition of the adhesion coefficient, α , for estimating axial soil loads on pipeline. Both the API RP2A and ALA approaches define α as a function of the undrained shear strength, c, as shown in Figure 2-1. There is a considerable difference in the recommended values of the adhesion factor in API RP2A for the highly plastic clays specifically identified in the Gulf of Mexico. Such materials are infrequently encountered in onshore pipeline applications. 2.1

Comparisons of Proposed Adhesion Factor Relationships with Test Data

Other recommendations for defining adhesion factors have been proposed for pipeline applications based on information from laboratory and field tests of buried pipelines and piles or theoretical grounds (Tomlinson, 1957, ASCE, 198 4; Sladen, 1992; Rizkalla et al., 1996; Terzaghi et al., 1996; Paulin et al., 1998; Honegger, 1999). Provisions in the ALA guidelines are based on a comparison of new data and past data and recommendations discussed by Honegger (1999). A comparison of several relationships and data sets from Honegger (1999) is provided in Figure 2-2. It is immediately apparent that the tests of Rizkalla et al., (1996) and Paulin et al. (1998) indicate adhesion factors well below those in the ALA or API RP2A guidelines and the test data reported by Honegger (1999). Several factors are likely responsible for this apparent discrepancy: 1. The tests reported by Rizkalla et al. (1996) and Paulin et al. (1998) were carried out at much lower displacement rates than those by Honegger (1999). The displacement rate was approximately 1 mm per minute for the Rizkalla et C-CORE Report R-02-044-113 29 August 2003

42


al. tests and either .01 or 0.2 mm per minute for the Paulin et al. tests. The tests by Honegger were performed at a rate of approximately 18 mm per minute. The reason for the difference in displacement rates is related to the fact that Rizkalla et al. and Paulin et al. were focused on pipeline response in creeping slide zones while Honegger’s interest was earthquake generated ground movement. 2. The Rizkalla et al. (1996) tests included field tests of sections of an existing pipeline coated with asphalt emulsion and controlled field tests of eight pipe specimens with fusion bonded epoxy and extruded polyethylene coatings. The adhesion factors for the controlled field tests tended to be consistently lower. This may be a result of the pipe coatings or differences in the soil characteristics between the controlled and existing pipe tests. 3. The results of Paulin et al. (1996) are based on laboratory tests in reconstituted Grade D kaolin clay with the moisture content used to control the shear strength. Although the tests were performed for two shear strengths that varied by about a factor of two, the data indicates a constant adhesion factor. In addition to the very slow load rate, the characteristics of the young kaolin clay, in comparison to aged “real” soil may be a factor in the reported results. 4. Axially loaded piles are installed to maximize their interaction with the surrounding soil by pile driving to post installation grouting. Pipes are not installed with this strategy. The consequential reduction in the normal effective stresses acting on the pipe surface, compared to that on a pile, will reduce the pipes axial resistance. 5. Slight misalignment in field and large-scale laboratory tests increase the axial soil loads significantly, section 7. Under perfect axial alignment, the axial soil loads are very low and controlled by the soil/pipe interface properties. The relationship proposed by Sladen (1992) for estimating the adhesion factor is also indicated in Figure 2-2 for a representative effective stress value. Sladen’s work is based on theoretical soil mechanics principles and derives an expression for the adhesion factor as a function of the effective stress, consolidation ratio, swelling and compression indices, and internal friction angle. The relationship plotted in Figure 2-2 is based on typical values for the various parameters. The relationship proposed by Sladen is not considered useful for engineering applications to pipelines because of the information necessary to apply Sladen’s relationship for specific soil. In particular, cautions raised in Sladen (1992) question the applicability of the “typical” equation to backfill soils. In assessing pipeline response to ground displacements, it is generally conservative to overestimate the soil loads generated by relative displacement between the pipeline and the soil. While it appears that there may be justification for reducing the adhesion factor for very low displacement rates, there are insufficient experimental or theoretical grounds for quantifying the effect of displacement rate and a purely axial load is unlikely. Considering the questions that remain regarding the potential load rate effects and the trends from field tests of in-place pipe in natural soil, preference should be given to adopting the relationship for adhesion factor provided in the ALA guidelines. C-CORE Report R-02-044-113 29 August 2003

43


A summary of key information from the tests reported on in Honegger (1999) is summarized in Table 2-1. All of the pipelines in Table 2-1 were protected with a coal tar coating. Since 1999, three additional field tests have been performed by Honegger for Southern California Gas Company. These tests were performed using the identical methodology described in Honegger (1999) on pipelines in soil characterized as a dry sand with some silt. The information from two tests conducted in 2000 is summarized in Table 2-1. The third test, conducted in 2001 was on an existing pipeline in similar soil as the 2000 tests. However, a miscommunication with field construction personnel led to the isolation of a test section of approximately 11.5m in length that had approximately 4.3m of soil cover. The pipeline could not be moved with the maximum hydraulic actuator force of 890 kN. Data collection on the initial test for 2000-1 was compromised when the load cell used to measure the force applied to the pipeline became misaligned and gave faulty readings. The ALA recommended equation for axial soil resistance provides a reasonable estimate of the maximum soil resistance for test 2000-2. However, the tests indicate a reduction in maximum soil resistance when load is removed and the test is repeated.

Table 2-1

Key Parameters for Tests Discussed in Honegger (1999)

Test

Pipe Size (NPS)

Soil Cover (m)

Undraine d Shear Strength (kPa)

Initial Test Peak Load (kN/m)

Displ. at Initial Peak (mm)

Retest Peak Load (kN/m)

Displ. at Retest Peak (mm)

C-1

12

0.64

18-28

18.6

13

16.7

9

C-2

12

0.66

18-28

19.9

19

19.9

4

C-3

12

0.69

18-28

16.8

2

14.2

2

C-4

12

0.66

>150

(1)

32.8

13

26.0

8

C-5

22

1.30

50-104

49.9

18

50.0

14

(1) Test C-4 was performed in similar soil as tests C-1 through C-3 but the soil was in a highly desiccated state, and could not be excavated by hand, and could not be penetrated for torvane measurements.

2.2

Variation of Axial Load with Axial Displacement

The relative pipe displacement to achieve the maximum axial soil force is typically very small for all soil types. For granular soils, this displacement is likely related to several factors including the embedment of soil particles in the pipe coating, the size of the soil particles, the density of the soil, and grain size distribution. For cohesive soils, the displacement is likely related to soil plasticity. For the tests in kaolin clay, Paulin et al. (1998) reports displacements of 0.3 to 0.6 mm to achieve the peak axial soil load. Rizkalla et al. (1996) do not report information on the load displacement characteristics in their tests. C-CORE Report R-02-044-113 29 August 2003

44


Data collected by Honegger include five tests in cohesive soil and two tests in granular soil. The cohesive soil tests were in similar soil material but one of the cohesive soil tests was in a desiccated deposit. For the cohesive tests in most material, the displacement to initially achieve the maximum soil load ranged from 2 to 19mm and was 13mm for the desiccated material. When axial load was reapplied, the displacement to reach maximum soil load were reduced to 2 to 14mm and 8mm for the moist and desiccated soil, respectively. The maximum difference in displacements between the initial and reapplied load cases was a reduction from 19 to 4mm. The one valid initial load test in sandy soil (2000-2 in Table 2-2) achieved the maximum axial soil load at a relative displacement of 6mm and reduced to 3mm on the reapplication of load. As previously noted, the initial loading of the other test (2000-1 in Table 2-2 performed in sandy soil by Honegger suffered from load cell misalignment. The reapplication of load for this test reached an intermediate plateau in the applied load at a displacement of approximately 3 mm. However, the axial load continued to increase with the maximum load in Table 2-2 obtained at the end of the test when the maximum displacement was approximately 25 mm. This increase in load with displacement was not observed in any other tests conducted by Honegger. In general, the displacements to achieve maximum axial load measured by Honegger are consistent with the recommended displacements in ASCE (1984) and the ALA guidelines for cohesive and cohesionless soil. Table 2-2

Key Information from Tests Performed by Honegger in Sandy Soil Parameter

Test 2000-1

Test 2000-2

NPS 30

NPS 30

5.58

5.52

fusion bonded epoxy

coal tar enamel tape

18.9

18.1

1.63

1.50

45°

44°

Fines Content, %

12

12

Initial Test Maximum Load (kN/m)

(1)

50.3

Displ. at Maximum Initial Test Load (mm)

(1)

6

20.5 / 21.9

32.5

Pipe Size Specimen Length, m Coating Soil Unit Weight, pcf Soil Cover,m Internal Friction Angle

(3)

Retested Maximum Load (kN/m) Displ. at Maximum Retest Load (mm) ALA Load (kN/m)

3 / 25

(2)

29.8

3 51.3

(1) load cell misaligned during test and under measured load as 11.0 kN/m (2) initial peak load of 20.5 kN/m reached at 3 mm, load continued to increase to 21.9 kN/mm for 25 mm applied displacement at end of test (3) Direct shear test on soil as-is, for example partially saturated

It should be noted that in most practical applications, the amount of displacement to achieve maximum axial soil load is not a critical parameter for assessing pipeline C-CORE Report R-02-044-113 29 August 2003

45


response because the ground displacements of interest are typically several orders of magnitude greater than the displacement to achieve the maximum axial soil load.


46


2.0 1.8 1.6 1.4 r o t c 1.2 a F n 1.0 o i s e h 0.8 d A

0.6 0.4 0.2 0.0 0

20

40

60

80

100

120

140

Undrained Shear Strength, kPa ALA Guidelines API RP2A (other clay soils) API RP2A (highly plastic overconsolidated clay at shallow depth) API RP2A (highly plastic unconsolidated or normally consolidated cl ay)

Figure 2-1

Adhesion Factors Recommended in API RP2A and ALA Guidelines


47


1.6 1.4 1.2 r o 1 t c a F n 0.8 o i s e h d 0.6 A

0.4 0.2 0 0

25

50

75

100

125

150

Undrained Shear Strength, kPa ALA Equation ASCE(1984) Tomlinson (1957) Rizkalla et al. (1996) Sladen (1992) for effective stress of 20 kPa Rizkalla et al. (1996) Pipeline Data Rizkalla et al. (1996) Test Specimen Data Paulin et al. (1998) Data Honegger (1999) Data (3 locations) Honegger (1999) Data (1 location)

Figure 2-2

Comparison of Adhesion Factor Relationships with Test Data


48


3

CONSTITUTIVE MODELS

3.1

Constitutive Models

In this study, the Von-Mises and Mohr-Coulomb plasticity models are selected to fulfill the research objectives. The pipe was considered as purely elastic with large stiffness to simulate a rigid pipe. Analyses were performed using the finite element code ABAQUS/Standard (Hibbitt et al., 1998). The program has been used in the past at CCORE for 2D and 3D finite element analyses of pipe-soil interaction involving large relative deformations, and has been validated based on results of full-scale tests (e.g. Nobahar et al., 2000; Popescu et al., 2001). 3.1.1

Constitutive Model for Sand

The Mohr-Coulomb (MC) plasticity model implemented in ABAQUS/Standard is intended for pressure-dependent materials. It has isotropic hardening, defined in terms of material cohesion. The plastic flow rule is non-associated, with the flow potential described as a hyperbolic function in the p-q plane, and a smooth elliptic function in the deviatoric plane. The dilation angle, defining the slope of plastic potential in p-q plane, can be different from the friction angle, which defines the slope of the yield surface. However, only non-negative values are allowed for the dilation angle. Thus the model cannot reproduce shear induced plastic compaction. Since sands are typical frictional materials, the Mohr-Coulomb model is chosen as the constitutive model for sand materials in this study. However, the hardening law provided in ABAQUS/ Standard does not correctly reflect the frictional deformation mechanism of sand. In this study, the simulation of hardening is achieved by customizing ABAQUS using a user-defined field. Perfectly elasto-plastic models are also used for sand materials to verify the effects of the material model with hardening/softening. 3.1.2

Constitutive Models for Clay

3.1.2.1 Von-Mises Plasticity model In Chapter 4, the effects of cover depth and soil strength on pipe-soil interaction are investigated for pipelines buried in clay. The clay materials are assumed to be under undrained condition (i.e. purely cohesive) and the Von-Mises plasticity model is chosen as the constitutive law in which the yield stress is determined by the undrained shear strength, cu, of clay. No hardening or softening occurs during deformation. The elastic deformation of clay is calculated by using linear elasticity. Different values for the undrained shear strength cu and the elastic modulus E are selected, while Poisson’s ratio of . = 0.33 is used in all cases.


49


3.1.2.2 Mohr-Coulomb model When analyzing the influence of loading rate on pipe-soil interaction, the variation of effective stresses as well as the deformation induced excess pore pressure have to be determined. The dependency of soil strength on effective stresses is described by the Mohr-Coulomb constitutive model, in which two strength parameters (i.e. the effective cohesion c∋ and the effective friction angle φ∋ ) are used. No hardening or softening occurs during deformation. The elastic deformation of clay is calculated by using linear elasticity. Different effective cohesion, friction angle and elastic modulus E are selected for firm and soft clays, while Poisson’s ratio of . = 0.33 is used in all cases. 3.2

Analysis Procedure

First, a geostatic step is performed to establish the initial stress state in the soil. Next, the desired pipe movement is imposed as displacement controlled. Nodal displacements are prescribed in the horizontal direction, while the pipe is free to move in the vertical direction. Large deformations and finite strain analysis options are used throughout the study. The interaction forces are output by the program only at contact nodes in the soil (“slave” surface). Owing to the large relative deformations at soil/pipe interface, it is difficult to follow the position of soil nodes relative to the pipe, and therefore those nodes are not appropriate for calculating the forces on the pipe. The predicted soil/pipe interaction forces are obtained in this study by two methods: (1) from driving forces, as nodal reactions – for nodes with imposed displacements, and (2) from element forces, using the balance of the internal element forces over each node at the pipe-soil interface. The first method is certain to provide correct numerical results, while the second may be affected by numerical errors induced by adding numbers that can differ by several orders of magnitude. However, the first method could not be used for all the situations analyzed, as driving forces can only be inferred at nodes with prescribed displacements. 3.3

Treatment of Pipe-Soil Interface

The interface between pipe and soil is simulated using the contact surface approach implemented in ABAQUS/Standard. This approach allows for separation and sliding of finite amplitude and arbitrary rotation of contact surfaces. With this procedure, ABAQUS automatically generates the necessary interface nodes besides the ones defined by user for proper description of the interface. If a pipeline is buried in sand, the Coulomb friction model is used to simulate the frictional interaction between pipe and soil. In this method, an appropriate friction angle, δ , between the pipe and soil is assumed. If no experimental data is available, the typical values of δ vary from 0.5φ to 0.7φ for smooth steel and 0.7φ to φ for rough steel (ASCE, 1984). For pipe in clay, the pipe-soil interface is assumed to be adhesive, i.e. no sliding occurs before the shear stress on the interface reaches an ultimate value τ max. This is numerically achieved by assuming a large friction coefficient in the Coulomb friction C-CORE Report R-02-044-113 29 August 2003

50


model. In general, the maximum shear stress along the pipe-soil interface is in the range of (1/2~2/3)cu with cu being the undrained shear strength of clay. 3.4

3.4.1

Numerical Model Verification

Pipe in Sand: Lateral Loading

In this verification, numerical modeling results are compared with experimental data from a large-scale model study. The results of the large-scale tests, reported here, are part of a Joint Industry Project (C-CORE, 2001). Due to confidentiality of results, the values are not shown. However, Nobahar et al. (2000) presented the details of the numerical model, described the large-scale tests and presented the following information used for verification of the numerical model. The finite element mesh used in this verification is shown in Figure 3-1. Based on experimental results, the interface friction angles between pipe and sands are 28.5° and 26.5° for dense and loose sand respectively, which correspond to the friction coefficient of 0.54 and 0.49. The pressure dependency of elastic moduli of soil is expressed as, n

E = E 0 (p/p0 )

(Eq. 3-1)

where n is a constant; E o is the elastic Young 's modulus at a reference pressure of po. Usually po is taken as the atmospheric pressure. The value of the power exponent for dense sand is chosen as n = 0.75 from the best curve fitting of data from direct shear box tests. However, for most cohesionless soil the value of n is usually around 0.5 (Richard et. al, 1970). The value of E 0 varies between 17.5 MPa and 25 MPa (Figure 3-2a). The average of elastic modulus, E ave, in the stress range encountered in this study is also given in Figure 3-2a. When a strain hardening of sand is considered, the mobilization of friction with plastic shear strain is presented in Figure 3-2b. It should be mentioned that the cohesion shown in Figure 3-2b should be regarded only as an apparent cohesion (resulting from dilatancy) in calculating the shear s trength of sand. If sand is assumed to be perfectly elasto-plastic and its failure follows the Mohr-Coulomb criterion, when the Young’s modulus take the value of E = E ave = 8MPa, the calculated force-displacement is presented in Figure 3-3. As the large-scale test data are proprietary at the present time, only relative pipe displacements and no pull force values are shown. Relatively close predictions of the recorded test values were obtained for the ultimate values of pull forces, and for the initial, elastic, portion of the force-displacement response. The numerical model correctly reproduces the experimental results in terms of the force-displacement relationship prior to the peak load. However, the decrease of soil resistance with pipe displacement after the peak is not captured. When strain hardening and shear induced volume change (i.e. stress dilatancy) of sand during deformation is correctly described in the procedure of numerical modeling, the calculated force-displacement curve matches the complete experimental forceC-CORE Report R-02-044-113 29 August 2003

51


displacement curves, including the decrease of soil resistance after the peak as shown Figure 3-4. The dilation angle, . , is estimated using Rowe’s (1962) relation: sin .

=

sin φ − sin φ cv 1 − sin φ sin φ cv

(Eq. 3-2)

where φ cv is the friction angle at constant volume. In Figure 3-5, the calculated and measured force-displacement curve for rigid pipelines buried in very loose sand is compared with experimental curves obtained from three repeated tests. In this numerical simulation, sand is assumed to be a perfectly elasto plastic material following the Mohr-Coulomb failure criterion. 3.4.2

Pipe in Clay: Lateral Loading

Comparisons between finite element predictions using the Von-Mises model and experimental measurements in terms of force-displacement curves are presented in Figure 3-6. Again, the force values are not shown. Figure 3-7 presents the comparison of the calculated plastic strain distribution and the deformed mesh to the experimentally observed deformation – showing the failure mechanism – in stiff clay after excavation. The implementation of the more advanced Cam-Clay model leads to numerical results that are closer to the measured data, Figure 3-7 (Popescu et al., 2000). 3.5

Comments

The comparisons between the results of numerical modelling and large-scale model tests on pipelines buried in both sand and clay show that, when soil parameters are correctly estimated, the proposed numerical procedure (including the constitutive model of soil) can reasonably reproduce pipe-soil interactions under different soil conditions.


52


Figure 3-1

Finite element mesh for verification analyses


53


(a)

Eave

(b)

Figure 3-2

Model parameters: (a) dependency of soil elastic modulus on effective mean stress used in finite element anal ysis, and (b) mobilization of soil strength parameters during deformation (adapted from Nobahar et al., 2000 and Popescu et al., 2001)


54


Figure 3-3

Experimental and calculated force-displacement curves for lateral loading of a rigid pipe in dense sand: using a perfectly elasto-plastic model with constant dilation angle and E = E ave


55


a.

measured calculated using E0 = 17.5 MPa

e c r o F

0.00 0%

25%

50%

75%

100%

125%

pipe displacement

measured

b.

calculated using E0 = 25.0 MPa

e c r o F

0.00 0%

25%

50%

75%

100%

125%

pipe displacement

Figure 3-4

Experimental and calculated force-displacement curves for lateral loading of a rigid pipe in dense sand: elasto-plastic hardening model with variable dilation angle: (a) constant Young’s modulus; and (b) variable Young’s modulus


56


e c r o F

measured calculated

0.00 0%

25%

50%

75%

100%

125%

Displacement (%)

Figure 3-5

Experimental and calculated force-displacement curves of rigid pipe in loose sand


57


a.

e c r o f l a r e t a l

Measured Calculated

soft caly 0 0%

25%

50%

75%

100%

125%

pipeline displacement

b.

e c r o f

measured calculated

firm clay 0.00 0%

25%

50%

75%

100%

125%

displacement Figure 3-6

Recorded and predicted force-displacement relations for large-scale tests in clay, using the Von-Mises soil model: (a) soft clay; and (b) stiff clay


58


(a)

(b)

Figure 3-7

Comparison between predicted (a) and observed (b) failure in stiff clay


59


Figure 3-8

Recorded and predicted force-displacement relations for large-scale tests in clay, using the Cam-Clay model: (a) soft clay; (b) stiff clay


60


4

EFFECT OF COVER DEPTH AND SOIL STRENGTH: HORIZONTAL LOADING

4.1

Introduction

As pointed out in the literature review, the current state of practice for pipe-soil interaction is reflected in the ASCE (1984) guidelines, Dutch Code NEN 3650, and more recently, PRCI guidelines (Honegger and Nyman, 2001). The soil along the pipeline is represented by a series of discrete nonlinear springs (i.e. elasto-plastic, multi-linear). The maximum soil spring forces and associated relative displacement necessary to mobilize these forces are usually functions of burial depth ratio, H/D. In all these methods, less attention is placed to the stiffness of the soil springs, except the ASCE (1984), in which the force-displacement curves are assumed to be hyperbolic. The correct estimation of soil spring stiffness (or force-displacement curves) will significantly affect the mobilized soil forces on a pipeline. Assuming plane strain conditions, this chapter investigates the effects of burial depth and soil strength on the predicted force-displacement curves. A total of 54 finite element runs in 18 configurations were analyzed, as summarized in Table 4-1. Table 4-1

Summary of cases studied c u (kPa)

Native soil

H/D

B/D

Backfill

1.03, 1.34, 1.97, 2.50, Uniform clay 10, 20, 45 3.03, 4.08 Trenched pipe 45 5, 10, 20 1.03, 1.34, 1.97, 2.50 1.58, 2.11, 3.16

Total number of cases analyzed

18 36

* Note: Outer diameter of pipe, D = 95cm

4.2

4.2.1

Finite Element Analysis Set-up

Finite Element Set-up

For both trenched pipes and pipes buried in uniform clay, four burial depth ratios are selected with H/D = 1.03, 1.34, 1.97 and 3.13, where H is the depth to pipeline centre and D is the pipe diameter (Rowe and Davis, 1982a, suggested an embedment ratio of 3 as the transition from shallow to deep cover). D = 0.95m is used in the analyses. Typical finite element meshes are shown in Figure 4-1. In all cases, the soil was discretized using quadratic plane strain finite elements with 8node and reduced integration (i.e. element CPE8R in ABAQUS). These second order elements are known to yield higher accuracy than linear elements at the same computational effort.


61


The contact surface approach implemented in ABAQUS/Standard, which allows for separation and sliding of finite amplitude and arbitrary relative rotation of the contact surfaces, is used to simulate the pipe/soil interface. The contact is assumed frictional, with isotropic Coulomb friction. The shear stress between the surfaces in contact is limited by a critical stress τ crit = ∝ p, where p is the normal contact pressure; and ∝ is the friction coefficient. For clay materials, a maximum value is also assumed for the shear stress at the interface, τ max, irrespective of the normal contact pressure; the critical shear stress is expressed as τ crit = min(∝ p, τ max ). Practical values of τ max on pipe-soil interface are about one third of the undrained shear strength (e.g. Paulin et al., 1998). In this study " the interface between the soil and the pipe is assumed to be adhesive, hence a large friction coefficient of ∝ = 1 and τ max = 0.5cu were assumed. For trenched pipes, the maximum shear stress on the trench wall was assumed equal to the strength of the backfill. 4.2.2

Material Properties

Clay materials under undrained conditions were assumed. Other soil material properties are summarized as follows: Young’s modulus, E = 400 cu Poisson’s ratio, . = 0.33 Shear stress limit at trench wall, τ max = cu-backfill The stiffness and thickness of pipeline were selected to represent a virtually rigid behaviour. 4.2.3

Analysis Procedure and Cases Analyzed

First, a geostatic step is performed to establish the initial stress state in the soil. Next, the desired pipe movement is imposed as displacement controlled. Nodal displacements are prescribed in the horizontal direction (direction x in Figure 4-1), while the pipe is free to move in the vertical direction. The interaction forces are obtained as discussed in Section 3.2. In the following sections, the predicted interaction forces are presented as normalized force–displacement curves, in which the normalized force is calculated as N

= F /(cu D)

(Eq. 4-1)

where F is the interaction force per meter of pipe; D is the pipe diameter; and cu is the undrained shear strength of clay. For trenched pipes, cu is taken as the undrained shear strength of the native soil so that it is convenient to determine the effect of the backfill properties. The normalized force corresponding to the ultimate force F u is termed as the bearing capacity factors N ch

N ch

= Fu /(cu D)


(Eq. 4-2)

62


4.3

4.3.1

Pipes in Uniform Clay

Ultimate Soil Resistance: Bearing Capacity Factor

Figure 4-2 presents the normalized force-displacement curves for pipelines buried at different burial depths in uniform clays with the undrained shear strength cu = 10, 20 and 45kPa, respectively. Figure 4-3 summarizes the variation of the bearing capacity factor with burial depth ratio H/D. The bearing capacity factor N ch increases with the burial depth ratio, however, it tends to be constant above H/D = 3 for a given soil strength, especially for soft clays with cu = 20kPa . The values of N ch in ASCE and PRCI guidelines are also presented for comparison. For H/D > 2, the values of predicted N ch are larger than those recommended in both ASCE and PRCI guidelines. The ultimate value of N ch for deeply buried pipelines is 35% to 76% higher than that in the ASCE (1984). 4.3.2

Failure Mechanisms

The burial depth ratio also significantly affects the displacement pattern and the failure mechanisms of soil around the pipelines. Figure 4-4 presents the distribution of soil displacements in the vicinity of the pipeline at the relative horizontal pipe displacement δ /D = 0.35 in the case of cu = 20 kPa (δ is the pipe horizontal displacement; and D is the pipe diameter). The corresponding plastic strain distributions in the soil are given in Figure 4-5. For the pipe with a shallow burial depth of H/D = 1.03, the soil in front of the pipe moves upward, with failure surfaces fully developed throughout the soil. The failure can be regarded as a typical general failure. When the burial depth ratio is increased to H/D = 3.13, the deformation of soil is mainly constrained in the vicinity of the pipe and the soil displacement is almost symmetric with respect to the pipeline horizontal axial: it is a typical local failure. In all these cases, no active failure zone is observed in the soil behind the pile. The same deformation and failure modes phenomenon are observed in the case of cu = 45kPa (Figure 4-6 and Figure 4-7). The soil displacement pattern and the failure mechanism also depend on soil strength. For pipes buried in very soft clay with the undrained shear strength as cu = 10kPa, when H/D < 2, the failure mode of soil is generally the same as that observed in the case of cu = 20kPa. However, when H/D = 3.13, the soil in the vicinity of the pipe deforms as if it rotated around the pipe, Figure 4-8c and Figure 4-9c. The variation of failure modes with soil strengths at H/D = 1.97 is presented in Figure 4-10 and Figure 4-11. Active failure surfaces behind the pipe fully developed when cu = 5 and 10 kPa, while only the passive surfaces formed in front of the pipe when cu = 20 and 45 kPa. According to the distributions of displacement and plastic zones presented in Figure 4-4 through Figure 4-9, depending on both burial depth and soil strength, two failure mechanisms, i.e. general failure and local failure, are observed. However, the results presented are at the same pipe displacement δ /D = 0.35 which is larger than that required C-CORE Report R-02-044-113 29 August 2003

63


to mobilize the ultimate soil resistance, Figure 4-2. The critical burial depth ratio at which the failure mechanism changes can be determined by checking the distribution of the plastic zone in soil at the onset of ultimate soil deformation. Figure 4-12 shows the dependency of the pipe displacement at the onset of ultimate soil deformation on burial depth ratio for cu= 45kPa. The corresponding distributions of plastic deformation zones are presented in Figure 4-13, from which the critical burial depth ratio is found to be about 2. When H/D > ( H/D)cr , local failure will predominate the failure mechanism. Similarly, (H/D)cr corresponding to different undrained shear strengths can be determined. Figure 4-14 presents the relationship between (H/D)cr and the corresponding bearing capacity factors. The (H/D)cr ~ N ch relationship is very close to that recommended in ASCE and PRCI guidelines. The recommended values of bearing capacity factor in ASCE and PRCI guidelines appear to assume the general failure mechanism. In fact, the horizontal bearing capacity factors in ASCE (1984) are based on the method proposed by Hansen (1961). In his basic analysis, Hansen assumed that a passive and an active failure zone developed in front of and behind a slab, respectively, while the slab translates through soil only in the horizontal direction (Figure 4-15). The resistance to pipe translation through soil is the difference of the mobilized passive and active soil forces in front of and behind the pipe, i.e. F

= E p − E a

(Eq. 4-3)

Hansen’s theory assumed a general failure mechanism. 4.3.3

Discussion

Figure 4-3 shows that the calculated bearing capacity factor tends to decrease with the increase of the shear strength of clay. Some researchers attributed the variation of bearing capacity factor with shear strength to the effect of the clay weight. The results shown in 3 Figure 4-3 are attained by assuming the uniform unit weight . = 17.5 kN/m , except for 3 the cases of cu = 5 kPa in which the unit weight is assumed to be . = 13.5 kN/m . Further simulations are carried out to investigate the effect of the unit weight of soil on bearing capacity factors. Figure 4-16 presents the comparison of bearing capacity factor 3 3 at cu = 20kPa when . = 17.5 kN/m and 13.5 kN/m respectively. The increase in the unit weight of soil leads to larger values of bearing capacity factor when all other conditions are the same. However, this effect tends to disappear for deep buried pipes. It is concluded that the difference in calculated bearing capacity factors presented in Figure 4-3 cannot be only attributed to the variation in the unit weight of soil, especially at deeply burial depths. More exactly, bearing capacity factors should be expressed as a function of both the shear strength and the unit weight of soil. Inferring from Rowe and Davis (1982a), the following equation may be suggested to account for the effects of soil shear strength and soil weight,


64


= min( N ch* + ⇓

N ch

. H cu

, N chmax )

(Eq. 4-4)

*

where N ch is the interaction factor for weightless soil (e.g. Figure 4-17); ⇓ is a factor max including the effects of soil weight and shear strength (e.g. Figure 4-18); N ch is the limiting values for the horizontal interaction factor. A series of analysis is performed assuming undrained shear strength of 10kPa and 20 kPa. Each analysis is performed 3 twice: (1) assuming a soil unit weight of 17.5 kN/m and (2) assuming no soil weight. * max = 12 (Figure Based on these analysis, values of N ch (Figure 4-17), ⇓ = 0.85 , and N ch 4-18) are obtained. This latter limiting value is consistent with that obtained for laterally loaded rough piles in clay, Fleming et al (1985), as expected. The value of N chmax may be expected to decrease to about 9 as the pipe interface becomes smoother. 4.3.4

Force-Displacement Curves and Pipe Displacement at ultimate state

The predicted force-displacement curves for pipelines in uniform clay with cu = 10 and 20 kPa at different burial depths have already been presented in Figure 4-2. In ASCE (1984), the following expression is recommended to express the relationship between force per unit length and horizontal displacement p =

y

with A ' = 0.15

A '+ B ' y

yu pu

, B' =

0.85 pu

(Eq. 4-5)

where pu is the lateral bearing capacity at the critical pipe displacement yu. Eq. (3-5) can be rearranged into the following forms p pu

=

p Fmax

y / yu A + By / yu

=

with A = 0.15, B = 0.85

y A '' yu

+y

(Eq. 4-6)

(Eq. 4-7)

where A '' = A / B , F u is the ultimate force per unit length at pipe displacement approaches infinite and F max = pmax = pu/0.85 =1.1765 pu. The comparisons of the predicted normalized force-displacement curves with those obtained from Equation (4-5) are presented in Figure 4-19 and Figure 4-20 for cu = 10 and 45 kPa respectively. The initial stiffness given by ASCE (1984) is less than the calculated one. When the formula expressed by Equation (4-7) is used to fit calculated forcedisplacement curves, the variation of A '' yu with burial depth ratio H/D at cu = 10kPa is shown in Figure 4-21. The values of A '' yu almost linearly increase with burial depth ratio following the relationship


65


A '' yu

= 0.0019H / D + 0.0036

(Eq. 4-8)

for D = 0.95m. It is found that A = 0.075 and B = 0.925 give best fits to the predicted force-displacement curves (Figure 4-22) while the corresponding yu is expressed as yu

= 0.025(H + 1.85D)

(Eq. 4-9)

The comparison between the calculated values of yu and that recommended in ASCE (1984) is presented in Figure 4-23. The calculated values of yu are in accordance with the recommendations in ASCE (1984), however, slightly larger pipe displacements are predicted at shallow burial depth in this study.


66


y x

y x

Figure 4-1

Typical finite element mesh and boundary conditions


67


(a)

(b)

(c)

Figure 4-2

Predicted force-displace curves for pipelines in uniform clay at different burial depth: (a) cu = 10 kPa, (b) cu = 20 kPa, and (c) cu = 45 kPa


68


Figure 4-3

Effect of burial depth on the bearing capacity factor of pipe in uniform clays


69


(a) H/D = 1.03

(b) H/D = 1.34

(c) H/D = 3.13

Figure 4-4

Effect of burial depth ratio on soil displacement distribution around a pipeline: cu = 20 kPa, δ /D = 0.35


70


(a) H/D = 1.03

(b) H/D = 1.34

(c) H/D = 3.13

Figure 4-5

Effect of burial depth ratio on plastic strains (PEMAG) in soil around a pipeline: cu = 20 kPa, δ /D = 0.35


71


(a) H/D = 1.03

(b) H/D = 1.34

(c) H/D = 3.13 Figure 4-6



72


(a) H/D = 1.03

(b) H/D = 1.34

(c) H/D = 3.13

Figure 4-7

Variation of plastic zone with burial depth: cu = 45 kPa, δ /D = 0.35


73


(a) H/D = 1.03

(b) H/D = 1.97

(c) H/D = 3.13

Figure 4-8



74


Figure 4-9

Effect of burial depth ratio on plastic strains in soil around a pipeline: cu = 10 kPa, δ/D = 0.35


75


(a) cu = 5 kPa

(b) cu = 10 kPa

(c) cu = 20 kPa

(d) cu = 45 kPa Figure 4-10 Effects of soil strength on soil displacement distribution around a pipeline: H/D = 1.97, δ /D = 0.35 C-CORE Report R-02-044-113 29 August 2003

76


Figure 4-11 Effect of burial depth ratio on plastic strains, PEMAG in soil around a pipeline: H/D = 1.97, δ /D = 0.35


77


Figure 4-12 Onset of ultimate deformation: cu = 45kPa


78


(a) H/D = 1.03

(b) H/D = 1.34

(c) H/D = 1.97

Figure 4-13 Contours of plastic strains, PEMAG: Influence of burial depth ratio on plastic deformation zone at the onset of ultimate soil deformation using cu = 45 kPa


79


(d) H/D = 2.50

(e) H/D = 3.13

Figure 4-13(Continue of Contours of plastic strains, PEMAG: Influence of burial depth ratio on plastic deformation zone at the onset of ultimate soil deformation: cu = 45 kPa


80


General

local failure

Figure 4-14 The relationship between (H/D)cr and N ch


81


Figure 4-15 Hansen’s failure mechanism for an anchor slab: the basic case


82


Figure 4-16 Effects of soil unit weight of bearing capacity factor


83


3.5

4

0

4.5

5

5.5

6

6.5

7

7.5

Lateral interaction factor

1 o i t 2 a r h t p 3 e d l a 4 i r u B

5 6 7 8

Figure 4-17 Lateral interaction factor for weightless cohesive soil


84


5 r o t c a f l 4 a r e t a l n3 o i t c a r e t n2 i n i e s a e r 1 c n I

α∼0.85 ⇓∼0.85 cu = 20 kPa cu = 10 kPa

0

0 2 4 6 8 10 12 . Normalized overburden pressure (from weight), H cu Figure 4-18 Values of ⇓ , increase in the lateral interaction factor vs. . h/cu


85


(a)

H/D=1.03, Cu=10kPa

(b) H/D=4.08, Cu=10kPa

Figure 4-19 Comparison of calculated force-displacement curves and recommendations of ASCE (1984) for cu = 20kPa: (a) H/D =1.03; (b) H/D = 4.08


86


(a)

(b)

Figure 4-20 Comparison of calculated force-displacement curves and recommendations of ASCE (1984) for cu = 45kPa: (a) H/D =1.03; (b) H/D = 4.08


87


Figure 4-21 Variation of A '' yu and B” with burial depth ratio H/D at cu = 10 and 45 kPa


88


Figure 4-22 Calculated force-displacement curves and the curve fitting with A = 0.075 and B = 0.925: cu = 10kPa


89


Cu=10kPa

Figure 4-23 Pipe displacement yu: predicted and recommended by ASCE (1984)


90


5

RATE EFFECT ON SOIL-PIPELINE INTERACTION

In the state-of-practice pipe-soil interaction analysis for pipelines buried in clay, it is assumed that no drainage occurs during soil deformations. Consequently, soil undrained shear strength is used in a total stress analysis and the effect of the rate of pipe movement is not considered. These assumptions are correct only when the pipeline moves rapidly through the soil. Under many pipeline working-conditions, the relative rate of displacement between a pipe and the surrounding soil is small, consolidation of soil inevitably occurs in the process of soil deformations. Experimental evidences of consolidation of soil around pipelines was found in a large-scale model test of pipe-soil interaction research program (C-CORE, 2001); and Paulin (1998) reported the effect of loading rate on soil-pipeline interaction in a se ries of centrifuge model tests. In this section, a numerical modeling procedure is developed to investigate the effect of pipe moving through soil on pipe-soil interaction for pipelines buried in uniform clay. No attempts are made to compare with any experimental data. 5.1

Effective Stress Analysis

When subjected to normal or shear stresses, a soil mass tends to change its volume. For saturated soil, this can only be achieved when pore water has sufficient time for flow out or into the soil mass. Otherwise, excess pore water pressure (either positive or negative) is induced and causes the variation of effective stress, which governs the shear strength of soil. In order to analyze the effect of the rate of pipe moving through soil, effective stress analysis has to be performed. In this study, the dependency of soil strength on effective stresses is described by the Mohr-Coulomb constitutive model, in which two strength parameters (i.e. the effective cohesion c∋ and the effective friction angle φ∋ ) are used. No hardening or softening is assumed during deformation. The elastic deformation of clay is calculated by using linear elasticity. Different effective cohesion, friction angle and elastic modulus are selected for firm and soft clays; and a Poisson’s ratio of . = 0.33 is used in all cases. 5.2

Representative Soil Parameters

Many investigations have been performed to estimate the undrained shear strength of clay using various methods. Correlations between undrained shear strength of clay and its plasticity index are also available. However, the effective stress shear strength parameters as reported in literature are highly scattered. The strength parameters of some clays (Bell, 1992) in Figure 5-1 shows that for the considered undrained shear strength in this study (cu= 15 to 45kPa for pipes in uniform clay), the reasonable estimation of effective stress shear strength parameters is c∋ = 10 to 20kPa and φ∋ =15° to 30°. The effective stress shear strength parameters c∋ and φ∋ can be measured from direct simple shear tests. In order to compare with the results based on total stress analysis, the representative effective stress shear strength parameters are selected so that the strengths of soil around C-CORE Report R-02-044-113 29 August 2003

91


pipelines are in the same range in total and effective stress analyses. According to the mean effective stresses in soil in front of the pipe (Figure 5-2), the effective strength parameters are chosen as c∋ = 20kPa, φ∋ = 30° and c∋ = 13kPa, φ∋ = 20° for firm and soft clay respectively (Figure 5-2 only shows the deformed soil in front and behind the pipeline; it does not include the pipeline section). The difference in soil strength in total and effective stress analyses is shown in Figure 5-3. The boxes in Figure 5-3 show the ranges of undrained shear strength calculated using the effective strength parameters for the ranges of possible effective stresses. Table 5-1 summarizes the cases analyzed in the investigation of loading rate effects. 5.2.1

Soil consolidation during loading

The evidence of soil consolidation is shown in Figure 5-4, which shows the effective stresses in soil under partially or fully drained conditions are much higher than those under undrained conditions. The overall mean effective stress increases with decreasing the pipe displacement rate. 5.2.2

Effect of loading rate on pipe responses

The variation of calculated force-displacement curves for pipelines in soft and firm clays are presented in Figure 5-5 (enlarged at small displacements in Figure 5-6). The overall mobilized soil resistances at drained conditions are larger than those in undrained conditions due to soil consolidation during the loading process. The variation of the ultimate pipe force with normalised loading rate is given in Figure 5-7. Due to the presence of higher effective stresses caused by soil consolidation, it is natural that higher mobilized soil resistance is obtained in partially or fully drained conditions. For the three cases studied (Figure 5-5), the maximum forces in drained conditions are approximately 20, 28 and 33% larger than that in undrained conditions. Except for the difference in the maximum values of mobilized soil resistance, the forcedisplacement curves are also affected by drainage conditions through the rate of pipe displacement. When undrained, the force monotonically increases until its ultimate value appears at a relative pipe displacement δ /D of approximately 0.05. Then, the force on the pipe remains constant, while the pipe displacement continues to increase. However, if consolidation of clay is considered, depending upon the rate of pipe displacement, the force on the pipeline increases monotonically at partially drained conditions before the maximum appears at very large pipe displacements. When drained, a peak point appears on the force-displacement curves at a relatively small value of δ /D, followed by a gradual decrease in the force until a residual force is achieved at very large pipe displacement. About 15 to 20% larger than the ultimate force under undrained conditions, the ultimate (or residual) forces in partially (or fully) drained conditions are the same irrespective of the loading rate. This can be attributed to the consolidation of soil around a pipeline in drained conditions. However, there is no significant effect of loading rate on the initial stiffness of soil spring, Figure 5-6.


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According to Figure 5-5 and Figure 5-6, when the pipe is loaded with various displacement rates, the initial parts of force-displacement curves are almost the same as the curve under undrained conditions. However, when the soil force on pipe reaches to the undrained ultimate force value, it remains constant in undrained conditions, whereas it increases with pipe displacement in drained conditions. This is partially caused by the non-uniform soil consolidation in front of the pipe. For c∋ =13kPa, φ∋ = 20°, when the pipe displacement reaches 0.01m, the corresponding time of consolidation varies between 6 100 seconds and 1 ⋅ 10 seconds for different loading rates. If the approximation of parabolic isochrones (Schofield & Worth, 1968) is assumed, the consolidation front will move a distance L = 12 cv t , which is approximately 21mm and 2.1m for loading rate, v -4

-8

=10 m/s and 10 m/s respectively. t is time and cv is the coefficient of consolidation, which expresses the rate of primary consolidation settlement with time. The coefficient of consolidation can be determined using oedometer tests or using empirical correlations with field tests. However, even within the consolidation zone, the excess pore water pressure does not completely dissipate, leading to less increase in effective stress and shear strength of soil. Consequently, there is no significant variation in the soil force applied on the pipeline. When the ultimate force under undrained condition is obtained at the pipe displacement 2 of 0.03 to 0.08m, the corresponding time of consolidation varies between (3~8) ⋅ 10 6 seconds and (3~8) ⋅ 10 seconds for these different loading rates. The length of -4 -8 consolidation area increases to 64mm and 9m for v =10 m/s and 10 m/s respectively. For cases of slow loading, most of the excess pore water pressure in soil around the pipe is already dissipated, causing the increase in soil strength and the force on the pipeline. From the range of the consolidation zone and the dissipation of excess pore pressure, it is -4 concluded that, at the pipe displacement of 0.03 to 0.08 m, the force at v =10 m/s is almost the same as that obtained under undrained condition, while the calculated force at -8 v =10 m/s very close to the force under drained condition. This conclusion is in agreement with the force-displacement curves shown in Figure 5-5 and Figure 5-6. This transition from undrained through partially drained to drained behaviour can be considered by normalizing the displacement rate, v using the pipe diameter D and the coefficient of consolidation, cv, Figure 5-7. The normalised displacement rate, V shows undrained behaviour for values greater than 10 and drained behaviour for values less than 0.1. These normalised rate values and the S shaped transition curve are consistent with those reported by House et al. (2001) for transverse vertical loading of deeply buried ‘pipeline segments’ in calcareous sands. The difference in the mobilization of cohesion and friction angle with soil deformation also plays an important role. Figure 5-8 shows the mobilization of cohesion and friction of clay in a triaxial test. The cohesion of clay is fully mobilized at a small strain level while a higher strain level is required to mobilize the fictional angle. The residual force is achieved at the pipe displacement of approximately 0.5m irrespective of the rate of displacement.


93


Table 5-1

Studied case: rate effects

Parameters Soft Strength parameters c∋ = 13kPa, φ∋ = 20° 3 Effective unit weight (kN/m ) 5.0 Target undrained shear strength, cu 15 (kPa) Burial depth ratio, H/D 1.3 Elastic modulus, E 400cu Poisson’s ratio, . 0.33 Coefficient of consolidation, cv 2 (mm /s) 0.38 Pipe diameter, D (m) 0.95 -10 Permeability, k (m/s) 10 -4 -5 -6 -7 -8 Loading rate (m/s) 10 , 10 , 10 , 10 , 10


Firm c∋ = 20kPa, φ∋ = 30° 7.0

22.5 1.3 400cu 0.33 0.56 0.95 -10 10 -4 -5 -6 -7 -8 10 , 10 , 10 , 10 ,10

94


Figure 5-1

Effective and undrained strength comparison of some clays


95


(a) cu = 38kPa

(b) cu = 22.5kPa

(c) cu = 15kPa

Figure 5-2

Mean effective stress distribution in soil mass under drained conditions (relative pipe displacement δ /D = 0.45)


96


Figure 5-3

Strengths of soil around the pipeline in total and effective stress analyses


97


(a) drained condition

(b) undrained condition

-6

(c ) rate of pipe displacement v = 10 m/s Figure 5-4

Distributions of mean effective stresses in soil under (a) drained, (b) undrained and (c) partially drained conditions: H/D = 1.3, c∋ = 35kPa, φ∋ = 30°, relative pipe displacement δ /D = 0.15


98


(a)

(b)

(c)

Figure 5-5

Effect of loading rate on predicted force-displacement curves with different clays, burial depth ratio H/D = 1.3


99


Figure 5-6

Force displace responses at small displacement at different loading rates


100


1.4

drained

1.3 d e n i a r d n u , u

1.2

F / u F

H/D =

1.3 c' = 20kPa φ ' = 30°

1.1

c v

-7

undrained

2

= 5.6 ⋅ 10 m /s

1 0.01

0.1

1

10

100

1000

vD/c v

1.4

1.3 d e n i a r d n u , u

drained 1.2 H/D =1.3 c' = 35 kPa φ ' = 30°

F / u

F

1.1

-7

2

c v = 5.6⋅ 10 m /s undrained 1 0.01

0.1

1

10

100

1000

vD/c v

Figure 5-7

Dependency of ultimate pipe force on loading rate


101


Cohesion

Friction angle

Figure 5-8

Mobilization of cohesion and friction angle with strain


102


6

TRENCH EFFECT ON SOIL-PIPELINE INTERACTION

Since pipelines are usually laid in a trench; the pipe-soil interaction is influenced by trench geometry as well as the properties of the native soil and the backfill. The presence of the backfill, usually weaker or softer than the native soil, decreases the constraint on the pipeline, including the force transferred to the pipeline. On the other hand, the confinement of the backfill by the native soil results in an increase in backfill soil strength, depending on the geometry of the trench. It is obvious that the interaction between soil and a trenched pipe cannot be analyzed by simply using the properties of the native soil or the backfill alone. In this section, the numerical modeling procedures developed in Chapters 3 and 4 are used to investigate the effects of trench on pipe-soil interaction. The influence of trench configuration (including trench width and shape), the backfill properties will be systematically studied. No attempts are made to compare the results with any experimental data in this chapter. 6.1

Studied Cases

The trench effects on pipe-soil interaction are investigated by varying trench configuration and ratios of the undrained shear strength of native soil to backfill, Figure 6-1. The undrained shear strength of the native soil is kept constant while the strength of the backfill is chosen as cub = 5, 10 and 20 kPa respectively. A rigid pipe, with the diameter of 0.95m, is placed in a trench with the ratio between the trench width and the pipe diameter varying between 1.5 and 3.1 at the depth ratio H/D = 1.0 to 2.5. Furthermore, trench walls inclined at the angles of 45° and 60° are also studied. Table 6-1 summarizes all the cases reported here. In the following analysis, the normalized force, N , applied on a trenched pipe is calculated using the undrained shear strength of the native soil, cun, i.e. N = F /(cun D)

(Eq. 6-1)

where F is the force on a 1m long pipe segment; and D is the pipe diameter. cu represents native soil strength in the figures of this chapter. 6.2

Effect of Trench Width

The influence of trench width on normalized force-displacement curves is shown in Figure 6-2, in which the burial depth ratio H/D = 1.03 and the undrained shear strength of backfill is cub = 20kPa. All calculated force-displacement curves are bounded by forces obtained for pipes buried in the uniform firm clay (native soil) and the uniform soft clay (the backfill). The confining effect of the native soil on the soft backfill is clearly shown in Figure 6-3 and Figure 6-4, which present the distributions of soil displacement and plastic strain at δ /D = 0.08 for different trench widths. Compared with the deformations C-CORE Report R-02-044-113 29 August 2003

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of soil for pipelines buried in uniform soft clay (Figure 6-5), it is found that the confinement of native soil at B/D = 3.16 becomes very small. Due to the confinement of the strong native soil on the soft backfill, the normalized forces on trench pipe are larger than that of a pipe buried in uniform soft clay (backfill). A decrease in trench width results in an increase in the calculated forces on pipeline. However, when the burial depth is very small ( H/D = 1.03), the backfill tends to move upward and hence the effect of the confinement from the native soil is relatively small. The normalized force-displacement curves with different burial depth ratio H/D = 1.3 and 2.0 are presented in Figure 6-6. The general trend of the force-displacement curves is as follows: the force increases with displacement until the resistance is fully mobilized in the backfill; as the pipe enters the native soil, the force increases again with displacement and approaches an ultimate value corresponding to the failure in the native soil. This phenomenon is consistent with experimental observations (Paulin, 1998). However, the ultimate force corresponding to the failure of native soil is less than that when the pipe is buried in uniform native clay, Figure 6-7. This is explained as follows: When a trenched pipe translates through the soft backfill in the horizontal direction, the movement in the vertical direction takes place simultaneously; thus the burial depth is reduced when the pipe eventually reaches the trench wall, see Figure 6-8 and Figure 6-9. Compared to the deformations of soil when the pipe is buried in uniform native clay (Figure 6-10), a smaller volume of native soil is mobilized to resist the pipe movement in a trenched pipe, which leads to a smaller force on the pipeline. The reduction of the ultimate force corresponding to the failure in native soil may vary for various H/D and B/D in a trenched pipeline; thus the reduction magnitude shown in Figure 6-7 should not be used quantitatively for all cases. 6.3

Effect of Burial Depth at a Given Trench Width

Figure 6-11 presents the dependency of the normalized force-displacement curves on burial depth ratio ( H/D) at different trench widths with the undrained shear strength of backfill as cub = 20 kPa. Here the force is normalized using the strength of native soil cun = 45 kPa. Similar to pipelines buried in uniform clay (see Figure 4-2), the forces applied on trenched pipelines also increase with burial depth ratio. Figure 6-12 presents the bearing capacity factor, N ch, before the pipe penetrates through the trench wall. Compared to pipelines buried in uniform native soil, the force transferred to the pipe is reduced significantly. When the trench width ratio B/D is larger than 2, the effects of native soil on soil response become negligible. As already discussed in Section 6.2, due to the confinement from relative strong native soil, soil deformation mainly takes place within the backfill. Figure 6-13 and Figure 6-14 show the effect of burial depth on the deformation of soil for trenched pipelines. For shallow buried pipes, the backfill within the trench tend to move upward along trench while the deformation of native soil is very small before the pipe reaches the trench wall. With the increase of burial depth ratio, due to the increase in vertical stress, which provides more confinement to soil deformation, the deformation of soil in the trench tends to be more localized around the pipe. Consequently, a larger force is transferred to native soil and deformations of native soil are more pronounced. Compared to Figure 3.6,


104


the effects of burial depth ratio on the modes of soil deformation are the same for pipelines in uniform clay and the trenched ones. Figure 6-15 shows that for B/D larger than 2, the force on a trenched pipe is very close to that on a pipe buried in uniform backfill (normalized forces shall be multiplied by a factor of cun /cub = 45/10 = 4.5), as if there were no presence of native soil. 6.4

Effect of Backfill Strength Relative to Native Soil Strength

Figure 6-15 and Figure 6-16 show the effect of backfill strength on the forcedisplacement curves on trenched pipelines. As shown in Figure 6-6, Figure 6-15 reveals that the normalized force on pipelines decreases with increasing trench width for a given burial depth ratio for a backfill soil weaker than native soil. When B/D is larger than 2, the ultimate forces are almost a constant irrespective of trench width in the studied cases. However, the maximum normalized forces are influenced significantly by backfill strength and burial depth, Figure 6-16. The maximum force decreases approximately 60% when the backfill strength decreases from 20 kPa to 5 kPa, Figure 6-17. Figure 6-18 summarizes the variation of bearing capacity factors with burial depth ratio at different trench width when the undrained shear strength of backfill is 10kPa. Similar to Figure 6-12, which presents the bearing capacity factor with backfill strength of 20kPa, the soft backfill remarkably decreases the forces on the pipelines. Due to the interaction between native soil and backfill along trench wall, the forces at B/D = 2.1 and 3.1 are less than those corresponding to uniform soft clay which has the same shear strength as the backfill. The influence of backfill strength on the bearing capacity factor is summarized in Figure 6-19. 6.5

Trench with Inclined Walls

In modeling the influence of trench wall inclination on pipe soil interaction, the burial depth ratio is taken as H/D = 1.3 and the distance between trench walls at the location of pipe spring line is B = 2.0 m (or B/D = 2.1), Figure 6-20. The inclination angle . is defined as the angle of the trench wall with a horizontal plane. Only the horizontal movements are applied while the pipe is allowed to move freely in the vertical direction together with soil. The variation of calculated force-displacement curves relative to the trench wall inclination angle is presented in Figure 6-21. When trench walls are inclined, there exists a peak on the calculated force-displacement curve. After the peak, the force almost remains constant while the pipe continues translating through the backfill until it touches the trench wall, Figure 6-21a. Before the peak point, the inclination of trench wall has less effect on force-displacement curves. Due to inclination of trench walls, the restraint on the backfill decreases, resulting the pipe moving together with the backfill along the inclined trench wall. When the pipe eventually contacts the trench wall, the pipe displacement is larger than the initial distance between pipe and trench wall, ( B-D)/2. Also, the soil resistance to pipe movements is smaller for pipelines in inclined trenches. It is expected that the maximum force on the pipeline increases with angle . , as shown in C-CORE Report R-02-044-113 29 August 2003

105


Figure 6-21b in which the undrained shear strength of the backfill is cub = 20 kPa. However, for cub = 10 kPa, the calculated forces are very close for . = 45° and 60°, both less than that of vertical trench wall.


106


Table 6-1

Studied cases: trench effects

Native Backfill Total unit weight Native 3 (kN/m ) Backfill Trench width depth ratio, B/D Burial depth ratio, H/D Elastic modulus, E Poisson’s ratio, . Trench geometry Pipe diameter, D (m) Soil strength

Figure 6-1

cun = 45 kPa cub = 5, 10, 20 kPa 17.5 13.5 1.5, 2.1, 2.6, 3.1 1.0, 1.3, 2.0, 2.5 400cu 0.33 45°, 60°, vertical 0.95

Definition of trench configuration


107


Figure 6-2

Effect of trench width: cun /cub=45kPa/20kPa, H/D = 1.03


108


(a) B/D = 1.58

(b) B/D = 2.11

(c) B/D = 3.16

Figure 6-3

Effect of trench width on soil deformation: displacement distribution (relative pipe displacement δ /D = 0.08)


109


(a) B/D = 1.58

(b) B/D = 2.11

(c) B/D = 3.16

Figure 6-4

Effect of trench width on soil deformation: plastic strain distribution, PEMAG (relative pipe displacement, δ /D = 0.08)


110


Figure 6-5

Soil deformations and contours of shear strain (PEMAG) in uniform soft clay (cu = 20 kPa) at relative pipe displacement δ /D = 0.08; B/D = 3.16


111


(a)

(b)

Figure 6-6

Effect of trench width at cun /cub =45kPa/20kPa: (a) H/D = 1.30 and (b) H/D = 2.0


112


Figure 6-7

Differences of force-displacement curves of trenched pipes and pipes in uniform native soil


113


Figure 6-8

Plastic strain distribution, PEMAG and deformations of native soil: B/D = 2.1, H/D = 1.03, at pipe relative displacement, δ /D = 0.79


114


Figure 6-9

Plastic strain distribution, PEMAG and deformations of native soil: B/D = 1.6, H/D = 1.03, at pipe relative displacement, δ /D = 0.38


115


Figure 6-10 Plastic strain distribution, PEMAG and deformations of soil for a pipe buried in uniform native clay of cu = 45kPa: at pipe relative displacement, δ /D = 0.21


116


(a)

(b)

Figure 6-11 Effect of burial depth at different trench widths: (a) B/D = 1.6; (b) B/D = 2.1


117


Figure 6-12 Influence of burial depth ratio on bearing capacity factor for trenched pipelines: cun /cub = 45kPa/20kPa


118


(a) H/D = 1.03

(b) H/D = 1.34

(c) H/D = 1.97

(d) H/D = 3.13

Figure 6-13 Effects of burial depth on the distribution of plastic strain developed in soil at δ /D = 0.08: trenched pipelines, B/D = 2.16, cub/cun = 20kPa/45kPa


119


(a) H/D = 1.03

(b) H/D = 1.34

(c) H/D = 1.97

(d) H/D = 3.13 Figure 6-14 Effects of burial depth on soil displacements at δ /D = 0.08: trenched pipelines, B/D = 2.16, cub /cun = 20kPa/45kPa C-CORE Report R-02-044-113 29 August 2003

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Uniform native clay

Figure 6-15 Calculated force-displacement curves for backfill strength of cun /cub = 45kPa/10kPa: H/D =1.3


121


(a)

(b)

Figure 6-16 Effects of backfill strength on force-displacement curves: (a) H/D = 1.3, B/D = 1.58; and (b) H/D = 2.0, B/D = 2.11


122


Figure 6-17 Effects of backfill strength on bearing capacity of trenched pipelines

Figure 6-18 Influence of burial depth ratio on bearing capacity factor for trenched pipelines: cun /cub = 45kPa/10kPa


123


Figure 6-19 Effects of backfill strength on the bearing capacity factor of trenched pipelines

Figure 6-20 The configuration of trench with inclined walls


124


Figure 6-21 Influence of trench wall inclination on calculated force-displacement curves


125


7

PIPE/SOIL INTERACTION UNDER COMPLEX LOADING

The pipe/soil interaction models provided by different guidelines, including ASCE (1984), PRCI (2002) guidelines, are appropriate for simple loading (axial, lateral, upwarddownward). Since soil behaviour is highly nonlinear, loading in one direction has significant effects on the deformation properties of soil in other directions. Simple pipe-soil interaction models may not adequately address this phenomenon. Furthermore, more complex loading, including pipe rotations and bending, as well as combinations of rotations and translations may occur in the field. Shear interaction between different soil zones along pipe axis (e.g. Popescu and Konuk, 2001), as well as soil failure induced by inclined loads may change significantly the actual soil/pipe interaction forces. In this section, the numerical modelling procedure developed in previous sections is applied to investigate pipe/soil interaction under complex loading. Emphases are placed on the combined translation of rigid pipelines in both axial and horizontal direction as shown in Figure 7-1. These analyses consider a range of soil strengths, pipe displacement angles (. ), amount of concurrent lateral displacement, and pipe-soil interface friction angles (δ ). No attempts are made to compare the results with experimental data. 7.1

Studied Cases

In this study, rigid pipes with outside diameter D = 203mm are buried in clay at the burial ratio H/D = 4.6 and 1.8 respectively. The undrained shear strength of clay varies in the range of cu = 20 to 200kPa. The direction of pipe movement changes from axial to laterally horizontal by changing the angle of pipe translation . , Figure 7-1. Coulomb friction is assumed at the soil/pipe interface. Based on ASCE (1984), the interface angle of friction between soil and pipeline, δ , may vary from 0.5φ to 1.0 φ where φ is the angle of shearing resistance for granular soil. The value of δ depends on the characteristics of the interface between the structural material of interest and the soil in contact with it. Trautmann and O'Rourke (1983) report a value of δ of 0.6φ for the interface friction angle between sand and plastic pipelines. If the steel pipeline surface is covered with a coating that is smooth, relatively hard, and resistant to weathering, then the interface friction could be reduced sufficiently to result in a δ of 0.5φ to 0.7φ . In this research, the value of the pipe soil interface friction angle is assumed in the range of δ = 10° to 20°. A total of 77 analyses were conducted (Table 7-1). Finite element meshes used in the analyses are given in Figure 7-2. Due to effects of existing boundaries, soil forces are not uniformly distributed along the pipeline. A pipe segment of L = 0.822 m in the middle of the pipe is used to calculate the representative forces on the pipe. In the following analysis, both axial and lateral forces are normalized by the undrained shear strength of soil using N x = F x/(cu DL), N z = F z /(cu DL) C-CORE Report R-02-044-113 29 August 2003

(Eq. 7-1) 126


where F x and F z are lateral and axial forces respectively; cu is the undrained shear strength of clay; and D is the external pipe diameter. 7.2

Effect of the Angle of Pipe Translation on Pipe-Soil Interaction

For the cases of burial depth ratio H/D = 1.8, friction angle δ = 20° and undrained shear strength cu = 45 kPa, the variation of the maximum axial and lateral forces with the angle of pipe translation α is plotted in Figure 7-3. Very small normalized axial interaction forces were predicted for a pure axial displacement, N z = 0.092. A very small inclination in the direction of pipe translation leads to remarkable increases in axial interaction forces, the maximum is achieved at the angle of . # 10°. Further increase in α almost has no effect on the maximum axial interaction forces until α exceeds 30°. For larger values of . (. > 30°), the predicted peak axial forces gradually reduce due to failure of the soil on inclined planes. On the other hand, the mobilized lateral forces monotonically increase with the translation angle . . o

When the angle of pipe translation is small (say less than 2.5 ), the relative pipe-soil displacement mainly takes place in the axial direction. The small lateral movement causes significant increase in contact forces on the interface of pipe and the surrounding soil. Since the displacement of pipe in lateral direction is very small, when sliding occurs along pipe surface in the axial direction, only a small section of pipe looses contact with soil behind the pipe, Figure 7-4a. The net effect of the increase in contact forces in front of the pipe and the decrease in contact area at the rear of the pipe leads to an increase in frictional force along the pipe. When the angle of pipe translation is large enough (say greater than 30°), the movement of the pipe in the lateral direction causes a gap behind the pipeline. This gap significantly decreases the overall contact area on pipe surface, Figure 7-4c. Even though the contact stresses between pipe and soil increase, the total contact forces decrease due to the gap behind the pipe and the shear failure in soil in front of the pipe. Consequently, the axial interaction forces decrease with angle . . The interaction diagram is presented in Figure 7-5. When the angle of pipe translation is . < 15o, there exists a linear relationship between the normalized axial and lateral forces N z and N x, which are almost constant in the range of 15° < . < 30°. When . exceeds 30°, the value of N z decreases while N x increases. 7.3

Effect of Soil Strength on Pipe-Soil Interaction with Combined Pipe Movement

Figure 7-6 and Figure 7-9 present the dependency of pipe-soil interaction factors on translation angle at various soil strength, i.e. cu = 20, 45, 100 and 200kPa. When normalized with the undrained shear strength of clay, the predicted interaction factors, both axial and lateral, slightly decreases with soil strength. For the translation angle . > 5°, the difference in the normalized axial forces is less than 10%. However, the difference is as high as 45% for . < 5° (Figure 7-6).


127


The maximum lateral force (when normalized with cu D) also tends to decrease with soil strength (Figure 7-7). When cu increases from 20 to 100kPa, N x is reduced by approximately 15%. However, there is no further change in N x if cu further increases. Under axial loading, the axial force on a unit pipe segment is not expected to change with soil strength if the pipe-soil friction angle and the unit weight of soil do not change. The variation of axial forces with soil strength is presented in Figure 7-8. Even though the normalized axial force decreases with soil strength, the total force on a unit length of pipe segment is almost constant. 7.4

Effect of Pipe-Soil Frictional Angle δ δ and Burial Depth Ratio

The interface friction angle δ between a pipe and the surrounding soil plays a key role in determining the axial forces in the presence of relative pipe soil displacement. A large friction angle leads to higher axial forces in the pipe. Figure 7-9a presents the normalized axial forces at various pipe translation angle with different pipe soil frictional angle δ . When δ changes, the overall dependencies of normalized axial force N z on pipe translation angle . are the same, however, the value of N z increases with frictional angle δ . This is expected because N z is directly a function of tan δ . Figure 7-9b presents the effect of pipe-soil frictional angle on the variation of normalized lateral force with . , the angle of pipe translation. While the mobilized lateral forces N x increase with translation angle . , N x is smaller at a larger value of δ is smaller when . < 15°. However, when . > 15°, a larger friction angle δ induces higher lateral forces. This can be attributed to changes in failure mechanism from an interface one to a soil shear failure by variation of angle of loading .. The influence of pipe-soil frictional angle is more clearly reflected in the interaction diagrams shown in Figure 7-10. The normalized axial force N z increases with the value of δ , however, a larger mobilized lateral force is obtained at a small frictional angle when the angle of translation is small. The effects of burial depth ratio on pipe-soil interaction are presented in Figure 7-11 and Figure 7-12.


128


Table 7-1 Studied cases: combined axial and lateral loading (a) Base analyses Soil strength (kPa) 20, 45, 100, 200 3 Effective unit weight (kN/m ) 17.5 Burial depth ratio, H/D 1.8 Elastic modulus, E 400cu Poisson’s ratio, . 0.33 Pipe-soil friction angle, δ 20° 0° (axial), 1°, 2.5°, 5°, 10°, 15°, Pipe displacement angle, . 30°, 45°, 60°, 75°, 90° (lateral) Pipe diameter, D (m) 0.203 (b) Effect of pipe-soil friction Soil strength (kPa) 3 Effective unit weight (kN/m ) Burial depth ratio, H/D Elastic modulus, E Poisson’s ratio, . Pipe-soil friction angle, δ Pipe displacement angle, . Pipe diameter, D (m) (c) Effect of burial depth Soil strength (kPa) 3 Effective unit weight (kN/m ) Burial depth ratio, H/D Elastic modulus, E Poisson’s ratio, . Pipe-soil friction angle, δ Pipe displacement angle, . Pipe diameter, D (m)


45 17.5 1.8 400 cu 0.33 15°, 20°, 25° 0° (axial), 1°, 2.5°, 5°, 10°, 15°, 30°, 45°, 60°, 75°, 90° (lateral) 0.203

45 17.5 1.8, 4.6 400 cu 0.33 20° 0° (axial), 1°, 2.5°, 5°, 10°, 15°, 30°, 45°, 60°, 75°, 90° (lateral) 0.203

129


.

Figure 7-1

Buried pipe subjected to combined axial and lateral translation


130


Figure 7-2

Simulation of a buried rigid pipe subjected to complex loading: a & b. finite element meshes; c. positioning of the pipe and result output section


131


(a)

angle of translation, .

(b)

angle of translation, .

Figure 7-3

The maximum normalized axial interaction forces (a) and lateral forces (b) predicted for the central zone of the pipe: H/D = 1.8, δ = 20° and cu = 45kPa


132


(a) . = 2.5°

(b) . = 15°

(c) . = 45°

Figure 7-4

Contact between pipe and soil at relative axial displacement z/D = 0.35: cu = 45kPa, H/D = 1.8


133


o

30 < . < 90 o

15 < . < 30

o

o

o . < 15

Figure 7-5

Relationship between calculated axial interaction factor Nz and lateral interaction factor N x: H/D = 1.8, δ = 20° and cu = 45kPa


134


angle of translation, . (deg.)

angle of translation, Figure 7-6

. (deg.)

The maximum normalized axial interaction forces predicted for the central zone of the pipe: H/D =1.8, δ = 20°, cu = 20, 45, 100 and 200kPa


135


angle of translation,

Figure 7-7

. (deg.)

The maximum normalized lateral forces predicted for the central zone of the pipe: H/D = 1.8 , δ = 20°, cu = 20, 45, 100 and 200kPa


136


. =0 o (a)

. =0 o

(b)

Figure 7-8

Variation of axial forces with soil strength strength in axial loading: loading: (a) normalized force and (b) axial force on 1m long pipe segment


137


angle of translatio n,

. (deg.)

(a) Normalized axial forces


. (deg.)

(b) Normalized lateral forces Figure 7-9

Effect of pipe-soil frictional angle δ on on pipe-soil interactions with combined axial and lateral loading: H/D loading: H/D = 1.8, cu = 45kPa


138


. < 150

Figure 7-10 Effect of pipe-soil frictional angle on the interaction diagrams: H/D diagrams: H/D = 1.8, c 1.8, cu = 45kPa


139



. (deg.)

(a) Normalized horizontal forces

angle of translatio n, . (deg.) (b) Normalized lateral forces Figure 7-11 Effect of burial depth ratio on pipe-soil interactions with combined axial and lateral loading: cu = 45kPa, δ = 20°


140


Figure 7-12 Effect of burial depth ratio on the interaction diagrams: cu = 45kPa , δ = 20°


141


8 8.1

PHYSICAL MODELLING Introduction

The physical modelling program included centrifuge tests of lateral loading of pipeline sections in cohesive soil. Various mitigative methods were examined to quantify their effects on lateral loads transferred to a buried pipeline. These methods included trench geometries, backfill soil types and backfill soil strengths. These model tests complemented the numerical analyses in Chapters 3-8. Centrifuge modelling has been shown to be a useful tool when modelling gravitydependent phenomena (e.g. Schofield, 1980; Murff, 1996). Centrifugal acceleration is used to simulate increased gravity and allows for correspondence of stress fields between model and full-scale, permitting accurate modelling of geotechnical and other gravitydependent phenomena. Such modelling increases general understanding, and permits calibration and verification of numerical and theo retical models of full-scale situations. 8.2

Summary Program

A total of 20 tests were performed in five testbeds. Table 8-1 summarizes all test conditions. The physical model tests were conducted in the C-CORE centrifuge using the methodology developed by Paulin et al. (1995, 1996). The soil used in all tests is a mixture of 50% speswhite kaolin clay and 50% Sil-CoSil silt by weight. Paulin (1998) discussed some reasons for the selection of this soil. All tests were done under an acceleration of 50 g . The pipes were pulled at a displacement rate of ~ 0.5 to 0.7mm/s, which was sufficiently fast for undrained loadin g Paulin (1998). Figure 8-1 shows a typical layout of the pipes tested in the centrifuge. Tests with vertical trench walls (tests T1P1 to 4, T2P3, T3P2, T3P4, T4P3 to 4, and T5P3 to 4) were done to investigate the effects of trench width, burial depth, and backfill material. Tests T2P2, T3P1, T4P1, T4P2, and T5P1 to 2 were performed to study the mitigative effects of inclined trench walls. T3P3, T4P2 to 4, and T5P2 to 3 used a sand backfill to investigate the effects of different backfill types.


142


Table 8-1 Testbed

Summary of experimental tests Pipe No.

1

2

3

4

5

Test Name

H /D

1

T1P1

0.5

2

T1P2

3 4

B /D

Trench wall

c ub

c un

(kPa)

(kPa)

2

20

40

Vertical

0.5

3.2

20

40

Vertical

T1P3 T1P4

1 1

3.2 2

20 20

40 40

Vertical Vertical

1

T2P1

1.5

N/A

Uniform

40

N/A

2

T2P2

1.5

2

20

40

Inclined (45°)

3

T2P3

1.5

2

20

40

Vertical

4

T2P4

3

N/A

Uniform

40

N/A

1

T3P1

2.5

2

20

40

Inclined (60°)

2 3

T3P2 T3P3

2.5 2.5

3.2 2

20 Sand

40 40

Vertical Vertical

4

T3P4

2.5

2

20

40

Vertical

1

T4P1

1.5

2

20 $ 40

40

Inclined (60°)

2

T4P2

1.5

2

Sand

40

Inclined (60°)

3

T4P3

1.5

2

Sand

40

Vertical

4

T4P4

1.5

2

Sand *

40

Vertical

1

T5P1

2

2

10

40

Inclined (45°)

2

T5P2

2

2

Fine sand

40

Inclined (45°)

3

T5P3

2

2

Fine sand

40

Vertical

4

T5P4

2

2

10

40

Vertical

* Sand to pipe the crown then 20kPa backfill 8.3

8.3.1

Experimental Procedure and Testing

Pipelines

The pipelines used here were a series of aluminium tubes fitted with strain gauges to measure lateral load. The model pipelines had a diameter of 19mm and length of 250mm corresponding to a prototype pipelines with diameter of 0.95m and length of 12.5m (1:50 scale). The pipe was pulled horizontally using two 3mm (1/8. φ) steel cables attached at each end. C-CORE Report R-02-044-113 29 August 2003

143


8.3.2

Soil Preparation and Testing

Test beds of native soil were prepared from a slurry of 50% speswhite kaolin clay and 50% Sil-CoSil silt. The initial water content of the slurry was 70%, which is approximately twice the liquid limit. It was then consolidated to a vertical stress of 400 kPa. A consolidated soil testbed is shown in Figure 8-3. The expected undrained shear strength of this soilbed is 40 kPa. The thickness of the consolidated soil layer was always more than the required thickness. The centre of all pipes was at 110 mm above the bottom of the tank. For a given H / D ratio, the thickness of soil required is H +110mm. As an example, the layout of pipe-2 and pipe-4 in testbed 2 is shown in Figure-8.2(a). Once the soil surface is levelled to the required height, four trenches were made using templates of desired cross sections. At this stage Vaseline was applied on trench wall and bottom. Vaseline separates the native soil from backfill, and also prevents possible migration of pore water between, and softening of, these two soils. Bedding material of 3-4mm thickness was placed at the bottom of all trenches except the trenches in testbed3, where a 10mm thick bedding was placed (see Figure 8-2b). A 19mm diameter aluminium pipe was placed at the centre of the trench and then filled with backfill soil. The same material (50% speswhite kaolin clay and 50% Sil-CoSil silt) was used for clay backfill. The weaker clay backfill was prepared by adding water to some soil that has been removed from the top of the soil bed. In case of sand backfill, two types of sand were used; (i) well-graded sand (in test T3P3, T4P2, T4P3), and (ii) uniformly graded fine sand (in test T5P2 & T5P3). In front of the pipe, five vertical spaghetti strands (@ 10-15 mm) were inserted near both ends of the pipe. From these vertical spaghettis (strands), the movements and failure mechanism in the soil were observed after the test. Finally, Vaseline was also applied on whole soil surface to prevent any surface desiccation (Figure 8-4). 8.3.3

Instrumentation and Measurement

Instrumentation for this test program included: Potentiometers Load cells Pore pressure transducers Piezocone penetrometers LVDT Four high-torque DC motors were used to pull the pipes horizontally at a constant displacement rate. These motors were attached to a bulkhead and linked to a shaft via a 1/8. stainless steel cable. This shaft had two pulleys on either end that linked to the steel cables attached to the pipelines. A rotary potentiometer on the shaft measured the displacement of the pipe. The pipelines themselves acted as the load cells in this series of tests. Two half Wheatstone bridges were located at either end of a rectangular shaft inside the aluminium casing. They were calibrated using point and distributed load. C-CORE Report R-02-044-113 29 August 2003

144


Four pore pressure transducers (PPTs) were used to verify the constant level of water table during the test. Two of them were inserted into the native clay, one at 100 mm and another at 70 mm depth. The other two PPTs were inserted behind the bulkhead and in the standpipe, respectively. A piezocone penetrometer was used to measure in-flight undrained shear strength of soil, for example Figure 8-5. A linear vertical displacement transducer (LVDT) was used to measure the height of the soil during consolidation. 8.3.4

Test Procedure

The test procedure is briefly described in this section. Further details can be found in Paulin et al. (1995, 1996). The total activities can be divided into four phases: (1) consolidation of the slurry, (2) preparation of test package, (3) centrifuge test, and (3) post-test activities. In-flight centrifuge activities included the re-consolidation of soil under self-weight, cone penetration tests, and pulling of the pipes. Undrained shear strength of native and backfill soil is measured at 2-3 locations using the piezocone. The piezocone was moved to the targeted position using the vertical and horizontal drives and penetrated into the soil at a rate of 3 mm/s. Tests were done in both native clay and sand/clay backfill. The pipes were pulled horizontally using a DC controller and relay. The pulling was conducted at a constant rate until a peak was observed or a prescribed displacement limit was reached. After all in-flight activity had been completed, the centrifuge was stopped and the package was removed. Hand shear vane tests were done to confirm the undrained shear strength of native and backfill soil. Testbed soil was then cut to measure the soil displacement and to investigate the failure mechanism (Figure 8-6 and Figure 8-7). The measured pipe displacement agreed well with the values obtained from data acquisition system. As an example, the displacement of pipe T2P3 is shown in Figure 8-8. 8.4

Shear Strength and Water Content of Native Soil

Undrained shear strength using hand vane, and water content were also measured for native soil before and after each test. Table 8-2 shows that the native soil properties in all five testbeds are reasonably the same in terms of water content and undrained shear strength, although slight differences exist in testbeds 4 and 5. This could be due to the uncertainties of vane shear tests. The undrained shear strength from vane shear tests could be different from in-flight shear strength. The vane shear tests were performed in 1 g , while the pipes were pulled under C-CORE Report R-02-044-113 29 August 2003

145


much higher effective stresses at 50g level. To have a better estimate of soil undrained shear strength during test under 50 g acceleration, piezocone penetrometer tests were performed as part of the in-flight activity. The undrained shear strength (cu) was then calculated as, cu

= (qc − " vo ) / N k

(Eq. 8-1)

where qc, N k , and σ vo are cone tip resistance, cone bearing factor, and total overburden pressure, respectively. Considering the effect of overconsolidation, Paulin (1998) recommended the following two equations for N k for the soil used in these experiments: (1) based on back calibration of undrained shear strength using the vane test results by Lin (1995), N k

= 10.1 − 0.94 ln OCR

(Eq. 8-2)

and (2) based on back calculation of undrained shear strength using direct shear box tests, N k

= 7.2 + 1.9 ln OCR

(Eq. 8-3)

where OCR is the overconsolidation ratio. As an example, undrained shear strength of native soil in testbed 5 is shown in Figure 8-5. As the primary goal of the physical modelling was to determine the mitigative effect, a shear strength of 40kPa was taken as a reasonable value for the undrained shear strength of native soil above the pipeline elevation. Table 8-2

Shear strength and water content of native soil before and after acceleration Pre-test

Testbed 1

Post-test

Average native Average native Average native Average native Vane strength Vane strength water content water content (kPa) (kPa) (%) (%) 28.1 27 29.0 28.7

2

29.2

30.4

29.7

28.7

3

31.4

28.3

28.3

28.1

4

39.9

35

28.5

27.5

5

26.7

35

28.6

29.0


146


Plan view

Drive #1

CPT Site

Cable

Drive #3

Drive #2 Drive #4

Strongbox

Section Pipeline

Trench Bulkhead Kaolin - Silt

Figure 8-1

Typical layout of centrifuge model test after Paulin (1998)


147


(a) Soil surface

H=3D= 57 mm H=1.5D= 28 mm Pipe-2

Pipe-4

110 mm

110 mm

(b) Backfill

Native

H Trench pipe

10 mm for test bed-3 3-4 mm for other tests

Figure 8-2

(a) Layout of Pipes in Test bed-2; and (b) location of pipe in the trench.


148


Figure 8-3

Consolidated soil testbed before placing pipelines


149


Figure 8-4

Testbed surface is covered by Vaseline


150


0

undrained shear strength, kPa 20 40 60

0

10

0 0

undrained shear strength, kPa 10 20 30 40 50

10 Pipe location

20

20

30

30

m m , e c a f r 40 u s l i o s m o r 50 f h t p e D

m m , e c a f r 40 u s l i o s m o r 50 f h t p e D

60

60

70

70

80

80

90

90

100

100

Figure 8-5

Test 5: undrained shear strength using Equation 9-2 (left) and Equation 9-3 (right)


151


Figure 8-6

Laterally loaded pipeline and surrounding soil after test


152


Figure 8-7

Soil deformations in front of pipeline captured by spaghetti mesh


153


285 217.5 Initial soil surface

Deformed soil surface

2 6 1

9 3 1

Figure 8-8

8 1 1

0 1 1

Sketch of pipe location after test for T2P3


154


9

QUANTIFICATION OF MITIGATIVE METHODS

9.1

Summary of Experimental Results

9.1.1

Force-Displacement Curves

The force-displacement curves for each testbed are shown in Figures 10-1 to 10-5. Four pipes were tested in each testbed, Table 8-1. Figure 9-6 shows the force-displacement of all tests and that, other conditions remaining constant, force increases with burial depth. The soil shear strength (cub and cun), and depth of the pipe mainly control the response. The force increases with displacement until a peak value and then it decreases or remains constant except in testbed-3. Note that, the tests in bed3 were done for deep buried pipes and that test T3P3 is unreliable due to a mechanical problem. Table 9-1 Pipe

Experimental results and theoretical predictions

/D B /D H

Peak Displ. to model peak force, force, mm kN

= F u /c N nD ch u Test

Normalized Normalized displ. at peak displacement PRCI Rowe & force at 90% peak Davis force δ δ/ (H +D /2) (1982a) δ δ/ (H +D /2)

T1P1

0.5

2

0.57

9.8

3.0

4.06

4.08

0.52

0.23

T1P2 T1P3 T1P4

0.5 1 1

3.2 3.2 2

0.55 0.57 0.63

28.5 24.5 13.0

2.9 3.0 3.3

4.06 4.90 4.90

4.08 4.30 4.30

1.50 0.86 0.46

1.10 0.52 0.25

T2P1

1.5

N/A

0.86

13.4

4.5

5.35

4.43

0.35

0.14

T2P2 T2P3 T2P4

1.5 1.5 3

2 2 N/A

0.59 0.70 1.37

20.1 15.0 12.1

3.1 3.8 7.2

5.35 5.35 6.36

4.43 4.43 4.65

0.53 1.25 0.18

0.31 0.22 0.09

T3P1 T3P2 T3P4

2.5 2.5 2.5

2 3.2 2

1.39 1.23 1.34

27.6 21.2 20.6

7.3 6.5 7.1

6.11 6.11 6.11

4.59 4.59 4.59

0.48 0.37 0.36

0.23 0.29 0.24

T4P1

1.5

2

0.83

17.0

5.0

5.35

4.43

0.45

0.29

T4P2

1.5

2

0.79

14.6

4.8

5.35

4.43

0.39

0.21

T4P3 T4P4

1.5 1.5

2 2

0.77 0.80

15.0 15.9

4.7 4.8

5.35 5.35

4.43 4.43

0.40 0.42

0.21 0.19

T5P1

2

2

1.00

28.0

6.0

5.78

4.52

0.59

0.41

T5P2 T5P3 T5P4

2 2 2

2 2 2

0.84 0.86 0.93

35.7 32.7 43.1

5.1 5.2 5.6

5.78 5.78 5.78

4.52 4.52 4.52

0.75 0.69 0.91

0.45 0.30 0.49


155


Table 9-1 compares the experimental results and theoretical predictions. The maximum force, F max and displacement to the maximum force, ymax, were obtained for each test. However, maximum loads often happen at very large deformations. It is difficult to determine a peak load particularly in soft to medium stiff soil (e.g. Paulin, 1998). Thus, pipe displacements at 90 percent of maximum loads were therefore also obtained for comparison. The force is normalized by, F n

=

F

(Eq. 9-1)

LDcu

where F n, F , L, D, and cu are normalized force, force, pipe length, pipe external diameter, and native soil shear strength, respectively. A native soil shear strength cun of 40 kPa was used in the normalisation. A large lag is observed in T5P4 in Figure 9-5. Measurements after test indicated that this lag is caused by the initial off-centre position of the pipeline in trench. 9.1.2

Comparison of Test Results with Existing Methods

PRCI Guidelines PRCI guidelines recommend that discrete bi-linear springs can be used to model soil loading a pipeline for seismic engineering purposes. The properties of springs should be defined using native soil properties to calculate the axial, horizontal, upward and downward soil responses. The maximum force of the lateral spring in cohesive soil is obtained by, pu

= N ch cu D

(Eq. 9-2)

where pu, cu, and D are the ultimate lateral load per unit length of pipeline, soil undrained shear strength, and pipe diameter. N ch is the horizontal bearing capacity adapted from Hansen (1961), N ch

H

= 6.898 + 0.056( ) − D

8.742 + H 2 ( ) +1 D

4.639 H ( )3 + 1 D

(Eq. 9-3)

PRCI suggests that pipe displacement at P u be calculated as yu = 0.04 ( H+ D/2). This displacement is adapted from ASCE (1984), recognizing that variation of yu = 0.03( H+ D/2) to 0.05( H+ D/2) was inconsequential for seismic analysis. ASCE (1984) Guidelines For lateral loading, the guidelines present a hyperbolic p-y curve of the form, p = y/(A∋ + B∋ ’ y), C-CORE Report R-02-044-113 29 August 2003

A∋ = 0.15 yu / pu , B∋ = 0.85 / pu

(Eq. 9-4) 156


The ASCE (1984) also adapted Hansen’s (1961) model for cohesive soils to estimate the maximum horizontal force, pu, which is given by: pu = cu N ch D

(Eq. 9-5)

where N ch is the horizontal bearing capacity factor. The variation of N ch with depth of pipe was shown in Figure 1-4. These values are identical to the values suggested by PRCI in Equation 9-3. The guidelines also suggest that yu occurs at 0.03 to 0.05 of h =. Note that, h is the depth to the bottom of the pipe ( H +D/2). ASCE (1984) also refer to the numerical analysis by Rowe and Davis (1982a&b). The values of N ch suggested by Rowe and Davis (1982a) based on immediate separation are lower than those by Hansen (1961). The experimental interaction factors in Table 9-1 are in reasonable agreement with the values predicted by PRCI or Rowe and Davis (1982a), Figure 9-7. The experimental results are slightly lower than those from Rowe & Davis to about H/D of 1.5 and slightly greater than those by PRCI for deeper burials above H/D of 2, due to the transition in the failure mechanism. The experimental results are well bounded by the numerical prediction for the associated strength, weight and uniform (no trench) conditions. Most experimental results lie lower than the numerical prediction due the mitigative trench effect. Experimental displacements to F u are much larger than suggested values of yu by PRCI and ASCE – compare a range of yu/( H +D/2) = 0.03-0.05 to normalized displacements to F u in Table 9-1. The values of yu suggested by ASCE and PRCI are not necessarily pipe displacements to maximum soil reaction. PRCI and ASCE predictions of yu are closer to values of displacement to 90% of maximum load in uniform soil (T2P1 and T2P4) – compare a range of 0.03-0.05 to 0.09 and 0.14. The larger displacements to F u in nonuniform tests can be partially attributed to trench effects. Initial lags in centrifuge tests may attribute to a larger displacement at peak – a lag of 1mm in model test is equal to 5.5% of pipe diameter. More importantly, the lateral pipeline movement causes a surcharge to build up in front of the pipe above the soil surface, see Figure 8-7 and Figure 8-8. This build up increases the soil weight being lifted by the pipe with a consequential increase in horizontal force, Section 4.3.3. This effect was particularly pronounced in Tests T3P1, 2 & 4, Figure 9-3. Removing the surcharge effect, that is the near linear increase of load with pipe displacement post yield, reduces the interaction factors to the range between those proposed by PRCI and Rowe & Davis. Uniform soil Test T2P1 and T2P4 were performed on uniform soil to be compared to previous studies. Figure 9-8 and Figure 9-9 shows comparison of results of T2P1 and T2P4 with ASCE and PRCI guidelines.


157


The measured peak loads are close to the predicted values. For burial depth ratio, H/D = 1.5, the peak load is close to the value predicted by Rowe and Davis (1982a) assuming immediate separation. For burial depth ratio, H/D = 3.0, the peak load is closer to the value suggested by PRCI. However, the soil reactions observed in shallow centrifuge tests are lower than those predicted by PRCI and ASCE guidelines. Initial stiffness Initial stiffnesses of force-displacement curves are calculated in Table 9-2. These values are compared to suggested values by PRCI and ACSE. It is also possible to calculate the stiffness from the reloading curve for test T2P1. The experimental initial stiffness is lower than the predicted values by PRCI and ASCE (1984). Table 9-2

Initial stiffness: experimental and theoretical values

Pipe

Experimental ASCE initial PRCI stiffness, 2 initial stiffness stiffness using (kN/m ) 2 (kN/m ) Rowe and Davis (1982a), 2 (kN/m )

9.1.3

T2P1

1500

15700

3600

T2P4

2400

8300

2100

Reloading stiffness, 2 (kN/m )

2200

Mitigative Effects

Trench Effects Figure 9-10 shows comparison between tests T2P1 and T2P3 buried at the same depth in a vertical trench with width B/D = 2. The pipe in T2P1 is buried in uniform soil, while in T2P3, the pipe was buried in backfill soil with shear strength of 20kPa. The comparison shows that soil response has a smaller magnitude initially in trenched pipe (T2P3). However, when the pipe approaches the trench wall (after 0.3 D), the soil resistance increases. Due to upward movement of pipe through the backfill, the soil response on the pipe buried in backfill never reaches that of the pipe buried in uniform soil. Mitigative Effects of Trench Width Figure 9-11 shows a comparison of all tests performed on a pipe buried in trench with vertical walls. Comparison between pipe response for tests T1P1 to 2 and T1P4 to 3 shows how a wider trench increases the displacement required to reach peak load. (T3P2 & 4 shows a similar effect for deeper burial). T1P3 has a slightly smaller peak load than T1P4, Figure 9-12, due to the upward movement of the pipeline while moving through the backfill.


158


Mitigative Effects of Inclined Trenches Figure 9-13 shows normalized force versus normalized displacement for pipelines buried in trenches with inclined walls and clayey backfill. Figure 9-14 demonstrates the mitigative effects of inclined trench wall at an angle of 45 degrees. Both pipes T2P2 and T2P3 have the same burial depth; the only difference is that trench wall is inclined in test T2P2 and is vertical in T2P3. This trench inclination did not have a mitigative effect on the initial stiffness (elastic part of reactions), however when the load increases to half of the ultimate load, the soil reactions on the pipeline with inclined trench (45 degrees) are about 30% to 35% of those for the pipeline in a vertical trench. At larger displacements, this difference decreases to about 10% to 15%. However, the inclination of 60 degrees (from the horizontal plane) does not have a significant mitigative effect on reducing the pipeline load, Figure 9-15. Initially the soil response is also stiffer for the pipe in inclined trench than the pipe in uniform soil for this test. PRCI recommends that trench walls should be sloped at an angle of about 30 degrees to mobilize the mitigative effects of loose backfill for horizontal ground displacements. However, trench wall inclination of 45 degrees have significant a mitigative effect for cohesive soft backfill. Effects of Sand Backfill Figure 9-16 compares normalized force-displacement curves for pipelines buried in trenches with loose sand backfill. Figure 9-17 shows comparison of soil reactions for test T2P3 (cub = 20 kPa) and T4P3 (sand backfill). Both tests have the same geometry. The soil reactions are relatively close. Soil reactions estimated for cohesive native soil, cohesive backfill and frictional backfill are reported in Table 9-3. These values confirm the relatively close response for T2P3 and T4P3. Soil reactions are softer for loose sand backfill. ASCE (1984) also suggest softer response for loose sand than clay – a range of 0.03h to 0.05h for stiff to soft clay compare to 0.07 to 0.1h for loose sand (h = H+D/2). Table 9-3

Estimated responses for T2P3 and T4P3

N qh Vertical pressure (estimated), σ∋ v Ultimate soil loads on the pipe (kN/m)

Cohesive native soil (c = 40 kPa) u 5.35/4.43 N/A

203.3/168.3

Cohesive backfill (c = 20 kPa) ub 5.35/4.43 N/A

101.6/84.2

Loose sand backfill (φ φ = 30 degrees) 6.57 22.8 kPa

142.9

Figure 9-18 shows comparison of soil reactions for test T5P2 and T5P3. Both tests have loose sand backfill with B/D ratio of 2 at springline. Trench wall is vertical in T5P3, C-CORE Report R-02-044-113 29 August 2003

159


whereas is inclined with angle 45 degrees in T5P2. The 45 degrees inclination in sand material has a mitigative effect on reducing the pipe response. 9.2

Comparison of Experimental and Numerical Results

The numerical analyses described in Chapters 3-8 were done, using ABAQUS/Standard FE code, before the centrifuge tests. The analyses were done mainly for clay. The undrained behaviour of clay was modelled using the von-Mises plasticity model. Many parameters influence the response of a pipeline under horizontal loading (Chapters 3-8). In this section the effects of three main parameters will be discussed: (i) shear strength of backfill (cub), (ii) shear strength of native soil (cun), and (iii) trench geometry ( B/ D, H / D, and the inclination of trench wall, see Table 8-1). The rate of loading has also a significant effect, as the soil behaviour can be categorized into drained, undrained, or partially drained. The numerical analysis in Chapter 5 shows that when the rate of horizontal displacement of this pipe is more than 0.1 mm/s the behaviour is undrained. As the pipes in the physical model tests were pulled horizontally at a rate of 0.5-0.7 mm/s, the loading is considered undrained. A total of 9 tests from 5 test beds with clay backfill are compared with numerical analyses. Some of the tests (e.g. T1P1, T1P2, and all tests in test bed-5) are not compared, because the trench geometries or backfill materials of these tests do not match with those used in numerical analysis. The parameters of the selected numerical cases are slightly different from the centrifuge tests; however, these slight differences do not affect the comparisons. Test bed-1 Test bed-1 had an undrained shear strength of the native soil (cun) of about 40 kPa. Four pipes were placed in vertical trenches. Two of them were at a depth of 1.0 D while the other two were at 0.5 D. The widths of the trenches were 2.0D or 3.2D (see Table 8-1). The shear strength of backfill material (cub) was 20 kPa. The responses of two pipes (T1P3 and T1P4) from this test bed are compared with the numerical prediction. Test conditions of these two tests are same except the width of the trenches ( B/D = 3.2 in T1P3 and B/ D = 2.0 in T1P4). The force-displacement curves of these two pipes are shown in Figure 9-19. As shown in the x-axis of this figure, the horizontal displacement (δ ) is normalized with pipe diameter ( D). In the y-axis, the developed force on the pipe per unit length ( F ) is normalized with (cun D). The normalized force is higher for T1P4, which was in a narrower trench ( B/D = 2.0). However, these two curves become closer at large displacement ( # / D > 0. 9 ). That is, the response of the pipe was controlled mainly by native soil at large displacement. As cun was same for both cases, the force-displacement curves are close at large displacement.


160


Predicted force-displacement curves for T1P3 and T1P4 are also shown in Figure 9-19. A very small difference between these two predicted curves has been found. That is, the effect of trench width on the predicted force-displacement curves for these two cases is very small. The comparison between the numerical and centrifuge test results shows that the normalized force-displacement curves for these two tests do not match very well at low displacement. The predicted force-displacement curves are initially too stiff. This discrepancy comes from the modelling of soil, and is addressed in Section 9.3. However, the predicted force at large displacement is very close to the centrifuge test result. That is, ultimate force is predicted well using this model. Test bed-2 Four pipes were tested in this bed. Two of them (T2P1 and T2P4) were in uniform native soil (cun = 40 kPa). The other two pipes (T2P2 and T2P3) were tested in same native soil but with a clay backfill of cub= 20 kPa. The geometry of the trenches is shown in Table 8-1. Figure 9-20 shows the normalized force-displacement curves of four tests in this test bed. Tests T2P1 and T2P4 were in the same condition except for the depth of cover. Test T2P4 had a deep-seated pipe ( H/D = 3) while T2P1 had a shallow pipe ( H/D = 1.5). The normalized force is larger for the deep-seated pipe. The other two pipes in this test bed (T2P2 and T2P3) were tested with same H/D (1.5) and B/D (2.0). However, the trench wall in T2P2 was inclined at 45° while the trench wall in test T2P3 was vertical. Figure 9-20 shows a higher normalized force at large displacement for vertical trench (T2P3), as the backfill was weaker than the native clay. Predicted force-displacement curves for these four pipes are also plotted in this figure (solid lines). In this case, the initial part of the force-displacement curve obtained from numerical analysis is also stiffer than that obtained from the centrifuge test results. However, the predicted forces at large displacement are close to the test results. Test bed-3 In this test bed four pipes were tested. The pipe T3P1 was in an inclined trench, while other three pipes were tested with vertical trenches. Three pipes (T3P1, T3P2 & T3P4) were tested using clay backfill material. The backfill material for the other test T3P3 was sand. Normalized force-displacement curves of these four tests were shown in Figure 9-3. The comparison between centrifuge test and numerical analysis is done only for the pipes with clay backfill. The results of test T3P1 were found to be similar to T3P4, Section 9.1.3. Therefore, only two tests (T3P2 & T3P4) are compared with numerical results in Figure 9-21. Both tests (T3P2 & T3P4) were done with the same burial depth, H/D = 2.5.


161


The width of the trenches are different; B/D = 3.2 for T3P2 and B/D = 2.0 for test T3P4. The numerical analyses with B/D = 2.0 or 3.2 were not done. Therefore, the numerical results with B/D = 2.1 and H/D = 2.5 is used for comparison. The centrifuge test results and numerical predictions are shown in Figure 9-21. This figure shows that the numerical result compares quite well with the centrifuge test results, except again for the initial stiffness. Test bed-4 Four pipes were tested in Test bed-4. Test T4P1, the only one with clay backfill, is compared with numerical analysis. This test was done with H/D = 1.5 and B/D = 2.0 at the level of springline of the pipe. The wall of the trench is inclined at 60° with horizontal. Unlike other tests (Test bed1-3), the strength of clay backfill in this test is very close to the native clay (cun = cub = 40 kPa). Figure 9-22 shows the normalized force-displacement curve of test T4P1. The result of test T2P1, which was in uniform soil of cun = 40 kPa, is also plotted in this figure. The two tests compare very well. This is a good indication of repeatability of the tests. The numerical prediction for uniform soil predicts the ultimate force ver y well. 9.3

Numerical Back-Analysis

The previous numerical analyses described in Section 9.2 assumed that soil deformation is elastic within the yield surface. However, in real soils there is a gradual change from elastic to elasto-plastic behaviour pre-yield. Also, use of a high value of elastic modulus ( E = 400cu) in numerical analysis produced very stiff initial force-displacement relationship, for example Figure 9-20. Back-analysis of one of the centrifuge tests, T2P3 addressed the latter issue by decreasing the elastic modulus. The soil elastic deformation modulus, E , was calibrated by matching finite element results to the initial part of the recorded results. Figure 9-23 compares the experimental and numerical results using a value of E of 1MPa. This value is much lower than the initial value used in the initial numerical modelling ( E = 400cu) of 16MPa. The deformation modulus varies for different types of soil (e.g. D’Appolonia et al., 1971). Finite element results were able to match the recorded results till half of ultimate force was mobilized. The finite element analysis was not able to match the centrifuge results in the transition from initial stiffness to ultimate load. This limitation can be attributed to several factors. The constitutive model used here was an elastic perfectly plastic Von Mises model (see Chapters 3 and 4). This model does not include hardening/softening parameters; thus it is not able to capture complex behaviour of soil prior to peak load. A more sophisticated constitutive model like the one used for sand materials in Chapters 3 and 8 is required.


162


This back-analysis indicates that better predictions of the force-displacement curves in the guidelines and design codes should account for the effect of the deformation modulus on pipe-soil interaction forces.


163


Load-displacement curves for test 1 pipes 1-4 0.8 0.7 B/D = 2 B/D = 3.2

0.6

H/D = 1.0

0.5

H/D = 0.5

N k , d0.4 a o L

0.3 0.2 T1P1 T1P2 T1P3 T1P4

0.1 0 0

Figure 9-1

10

20 30 Displacement, mm

40

50

Force-displacement curves for test 1, pipes 1-4


164


Load-displacement curves for pipes 1-4 1.4

1.2 uniform soil 1

vertical trench, B/D = 2

0.8

N k , d a o l 0.6

inclined trench (45 degrees) B/D = 2

0.4

T2P1 T2P2 T2P3 T2P4

0.2

0 0

10

20

30

40

50

60

displacement, mm

Figure 9-2



165


Load-displacement curves for pipes 1-4 1.4

inclined trench 60 degrees B/D = 2

vertical trench

1.2 mechanical problem 1

N0.8 k , d a o L0.6

sand backfill

0.4 T3P1 T3P2 T3P3 T3P4

0.2

0 0

Figure 9-3

5

10

15 20 Displacement, mm

25

30

35



166


Load-displacement curves for pipes 1-4 0.9 uniform 0.8 0.7 sand backfill 0.6 N0.5 k , d a o L0.4

0.3 0.2 T4P1 T4P2 T4P3 T4P4

0.1 0 0

5

10

15

20

25

30

35

40

Displacement, mm

Figure 9-4



167


Load-displacement curves for pipes 1-4 1.2 Vertical trench wall Inclinded trench wall

1

0.8 N k , d0.6 a o l

Sand backfill

0.4

T5P1 T5P2 T5P3 T5P4

0.2

0 0

Figure 9-5

5

10

15

20 25 displacement, mm

30

35

40

45



168


1.4

1.2

T1P1 T1P2 T1P3 T1P4 T2P1 T2P2 T2P3 T2P4 T3P1 T3P2 T3P3 T3P4 T4P1 T4P2 T4P3 T4P4 T5P1 T5P2 T5P3 T5P4

1

0.8 N k , d a o L

0.6

0.4

0.2

0 0

10

20

30

40

50

60

Displacement, mm

Figure 9-6

Force-displacement curves for all centrifuge tests


169


8.5 7.5 h c N6.5 , s r o t c 5.5 a f n o i t 4.5 c a r e t n i 3.5 l a t n o 2.5 z i r o H

Centrifuge test s Numerical predictions PRCI

1.5

Rowe and Davis (1982a) 0.5 0.5

Figure 9-7

1

1.5

2 2.5 Burial depth ratio, H/D

3

3.5

Horizontal Interaction Factor Comparison


170


7

6 PRCI (Hansen, 1961) 5

D u c / F , e4 c r o f d e z i l 3 a m r o N

ASCE , 1984 (Rowe and Dav is, 1 982a) T2P1

2

1

0 0

0.2

0.4

0.6

0.8

1

Normalized displacement, δ /D

Figure 9-8

Comparison of test T2P1 (uniform soil) in terms of normalized force – normalized displacement with ASCE and PRCI guidelines


171


8 T2P4

7 PRCI (Hansen, 1961) 6 ASCE , 1984 (Rowe and Davis, 1982a)

D u c / F 5 , e c r o f 4 d e z i l a 3 m r o N

2 1 0 0

0.2

0.4

0.6

0.8

1


Figure 9-9

Comparison of test T2P4 (uniform soil) in terms of normalized force – normalized displacement with ASCE and PRCI guidelines


172


5 Uniform soi,l c = 40 kPa u

4.5 4

With trench, B/D = 2; c /c un

ub

= 20kPa/40kPa

3.5

D u c / F 3 , e c r o f 2.5 d e z i l a 2 m r o N1.5

1 0.5 0 0

T2P1 T2P3 0.5

1

1.5

2

2.5

3


Figure 9-10 Comparison of pipe response in terms of normalized force vs. normalized displacement for pipe buried in uniform soil (T2P1) and pipe with trench (T2P3)


173


8 7 B/D = 2.0 H/D =2.5

6 D u c / F5 , e c r o f 4 d e z i l a 3 m r o N

H/D =1.5 H/D =1.0

2

H/D =0.5

1 0 0

T1P1 T1P2 T1P3 T1P4 T2P3 T3P2 T3P4

B/D = 3.2

0.5

1 1.5 2 Normalized displacement, δ /D

2.5

3

Figure 9-11 Comparison of pipe response in terms of normalized force vs. normalized displacement for pipes with vertical trench wall


174


3.5 B/D = 2.0

H/D = 1 B/D = 3.2

3

2.5

D u c / F , e 2 c r o f d e z i l 1.5 a m r o N

H/D = 0.5

1 T1P1 T1P2 T1P3 T1P4

0.5

0 0

0.5

1 1.5 Normalized displacement, δ /D

2

2.5

Figure 9-12 Comparison of pipe response in terms of normalized force vs. normalized displacement for pipes T1P1 to 4


175


8 H/D = 2.5; B/D = 2.0

7 60° wall trench

6

H/D = 2.0; B/D = 2.0

D u c / F5 , e c r o f 4 d e z i l a 3 m r o N

45° wall trench

H/D = 2.0; B/D = 2.0

2 T2P2 T3P1 T5P1

1 0 0

0.2

0.4

0.6 0.8 1 1.2 Normalized displacement, δ /D

1.4

1.6

1.8

Figure 9-13 Normalized force-displacement curves for pipelines buried in inclined trench


176


4 Vertical wall trench 3.5 45° inclined trench wall 3 D u c / F2.5 , e c r o f 2 d e z i l a 1.5 m r o N

H/D = 1.5; B/D = 2.0

1 0.5 T2P2 T2P3 0 0

0.5


2.5

3

Figure 9-14 Comparison of soil reactions in terms of normalized force vs. normalized displacement for T2P2 buried in inclined trench (45 degrees) and T2P3 buried in trench with vertical wall


177


8 7 6

60° inclined trench wall

D u c / F5 , e c r o f 4 d e z i l a 3 m r o N

Vertical wall trench

H/D = 2.5; B/D = 2.0

2 T3P1 T3P4

1 0 0

0.2

0.4

0.6 0.8 1 Normalized displacement, δ /D

1.2

1.4

1.6

Figure 9-15 Comparison of soil reactions in terms of normalized force vs. normalized displacement for T3P1 buried in inclined trench (60 degrees) and T3P4 buried in trench with vertical wall


178


5 H/D = 2.0

4.5 4

H/D = 1.5

3.5


B/D = 2.0

T4P2 T4P3 T4P4 T5P2 T5P3

1 0.5 0 0

0.5

1 Normalized displacement, δ /D

1.5

2

Figure 9-16 Normalized force-displacement for pipelines buried in trenches with sand backfill


179


4.5 4 3.5 D 3 u c / F , e 2.5 c r o f d e 2 z i l a m r o1.5 N

H/D = 1.5; B/D = 2.0

1 0.5 0 0

T2P3 T4P3 0.5


2.5

3

Figure 9-17 Comparison of soil reactions for test T2P3 (cub = 20 kPa) and T4P3 (sand backfill)


180


5 4.5 4 3.5


H/D = 2.0; B/D = 2.0

1 0.5 0 0

T5P2 T5P3 0.5

1 Normalized displacement, δ /D

1.5

2

Figure 9-18 Comparison of soil reactions for test T5P3 (vertical trench –sand backfill) and T5P2 (inclined trench – sand backfill)


181


8

7

Dashed line: Centrifuge tests Solid line: Numerical Prediction

6

)

D

n u

c / F ( e c r o f d e z i l a m r o N

5

4

3

T1P4 T1P3

2

1

0 0

0.1

0.2

0.3

0.4

0.5

0.6

Relative pipe displacement ( δ /D )

Figure 9-19 Force-displacement curve comparisons, Tests T1P3 and T1P4


182


8 T2P1 T2P2 T2P3 T2P4

Dashed line: Centrifuge tests Solid line: Numerical Prediction 7

6

)

D5 u c / F ( e c r 4 o f d e z i l a m r o3 N

2

1

0 0

0.1

0.2 0.3 0.4 Relative pipe displacement ( δ /D )

0.5

0.6

Figure 9-20 Force-displacement curve comparisons, Test series T2


183


8 T3P2 T3P4 Numerical (B/D=2.1)

Dashed line: Centrifuge tests Solid line: Numerical Prediction 7

c ub /c un=20/40, H /D =2.5

6

)


2

1

0

0

0.1

0.2

0.3

0.4

0.5

0.6

Relative pipe displacement ( δ /D )

Figure 9-21 Force-displacement curve comparisons, Test series T3


184


8 Dashed line: Centrifuge tests Solid line: Numerical Prediction

T2P1 T4P1 Numerical

7

6

)


2

1

0 0

0.2

0.4 0.6 0.8 Relative pipe displacement ( δ /D )

1

1.2

Figure 9-22 Force-displacement curve comparisons, Tests T2P1 and T4P1


185


5 4.5

T2P3: recorded T2P 3:numerical back-analysis

4 3.5

D u c / F 3 , e c r o2.5 f d e z i l 2 a m r o N1.5

H/D = 1.5; B/D = 2.0

1 0.5 0 0

0.5 1 Normalized displacement, δ /D

1.5

Figure 9-23 Back-analysis of T2P3 using finite element method


186


10 DISCUSSION AND RECOMMENDATIONS 10.1 Complex Loading

Most guidelines propose a soil/pipeline interaction design model that assumes that the soil response can be approximated by a series of independent non-linear springs, attached to the pipe structure. The set of three orthogonal springs are assumed to represent the axial, vertical and lateral response of the soil with respect to the pipeline. However, the coupling effects between the springs are generally ignored. This deficiency is recognised by ASCE (1984). Analysing the pipe-soil interaction as a continuum, rather than as discrete system (e.g. Popescu and Konuk, 2001) has addressed this deficiency, but continuum analyses are only practical for local effects due to section computation resources. This project addressed the interaction of axial and lateral movements of a pipe in undrained clay using FEA continuum analyses, Section 7, to provide initial recommendations for use with the discrete analyses used in practice. Figure 7-12 summarised the typical interaction between lateral and axial loading in undrained medium strength clay, which is repeated in Figure 10.1. The interface friction between the pipe and soil controls the axial load when the pipe displacement is inclined at less than 15° to the pipe axis. For these conditions the ultimate axial soil resistance can be calculated using an equation similar to Equation 1-7, which appears in the draft PRCI guidelines. However, the lateral effective stress K o. H in the right hand term should be increased to account for the mobilized lateral resistance, p. o

Currently, the mobilized lateral resistance, p for inclinations less than 15 is not readily calculable, and significant axial resistance is generated for inclination angles greater than 1°. So it is recommended that the axial resistance be calculated using the left-hand term of Equation 1.7 only for undrained loading, as proposed in Section 2. This recommendation is reasonable as purely axial pipe displacement is rare, and pipe sections contain bends, curves and coating discontinuities that effectively increase the axial resistance. However, pipe failures have been experienced in slopes due to excessive soil movement that was primarily parallel to the pipe axis (Novacorp, 1992). Back-analyses of such failures using current methods have failed to capture the observed pipe distress. This may be due in part to the current over-prediction of high axial resistance in straight pipe sections. However, there are many other factors that may also be contribute. The axial-lateral interaction envelope, Figure 10-1 can be expressed as 2

2

2

N x + 3 N z = N x90


with N z < απ

(Eq. 10-1)

187


where N x90 is the lateral interaction factor under pure lateral loading, α is the adhesion factor given in Figure 2-2 and other terms are defined in Equation 7.1. The “3” is an approximate analytical factor to account for the difference in the shear and bearing stress limits associated with axial and lateral loading respectively. The cap on N z for an adhesion factor of 0.6, typical for 45kPa undrained strength, is shown in Figure 10-1. It is recommended at present that Equation 10-1 be considered to limit the axial resistance available under predominantly lateral loading. This is also illustrated in Figure 10-2. Full axial adhesion is recommended for loading with angle of translation smaller than 60 degrees. For larger inclinations (i.e. dominantly lateral loadings), the axial resistance should be decreased as shown by the inclined dashed line in Figure 10-2. This is the case in many loading scenarios: the pipeline is often loaded nearly perpendicular to its axes. However, axial movements occur in due to the load inclination. In current practise, the full axial soil capacity is assumed in such a loading scenario but the interaction diagrams, Figure 10-1 and Figure 10-2 show the mobilized axial resistance is reduced as the majority of the soil strength resists lateral motion. This reduction may have a considerable effect in strain-based design, which requires large deformation analysis. For example, an analysis of a pipeline subjected to lateral soil movements showed around a 30% decrease in tensile and compression strains respectively when the reduction in axial resistance was considered. For translation angles less than 30 degrees (i.e. dominantly axial loading), the lateral resistance is slightly decreased by Equation 101, Figure 10-3. This decrease is negligible when N x > 4 N z , where N x is the lateral interaction factor; and N z is the axial interaction factor. Equation 10-1 should be further developed to include vertical loading and other soil conditions. In reality soil reactions are dependent on loading history. Thus, the results of this study may not be directly applied for the loading cases in which loading paths change. There is also a need to validate these numerical results for complex loading using physical testing. Further more, a similar study should be developed for frictional materials. The following conclusions and recommendations apply to primarily axial or lateral loading only, that is coupling between axial and lateral loading is not considered. 10.2 Axial Pipe-Soil Interaction

Section 2 showed there might be justification for reducing the adhesion factor for very low displacement rates, but there are insufficient experimental or theoretical grounds for quantifying the effect of displacement rate, and purely axial load is unlikely. Slight misalignment in field and large-scale laboratory tests increase the axial soil loads significantly, Section 7. Considering the questions that remain regarding the potential load rate effects and the trends from field tests of in-place pipe in natural soil, preference should be given to adopting the relationship for adhesion factor provided in the draft PRCI guidelines (Honegger and Nyman, 2001). Under perfect axial alignment, the axial soil loads are very low and controlled by the soil/pipe interface properties in a very thin shear zone between the pipe and soil and consolidation in this zone happens very quickly. C-CORE Report R-02-044-113 29 August 2003

188


In most practical applications, the amount of displacement to achieve maximum axial soil load is not a critical parameter for assessing pipeline response because the ground displacements of interest are typically several orders of magnitude greater than the displacement to achieve the maximum axial soil load. 10.3 Lateral Pipe-Soil Interaction

This report focussed on pipe response in clay soils. Previous reports by C-CORE in CCORE (1999) and Popescu et al. (2001) studied the p-y response in sands. The former showed that the ASCE (1984) guidelines provided a reasonable prediction of pu in dry and submerged sands. However, the yu value was halved between the submerged and dry tests for the same test geometry. That is, there is an effective stress effect on yu that is currently not considered in the guidelines. The latter showed that the p-y response curve can be well predicted by FEA including post-peak softening in dense sand, Section 3. In clay soils, C-CORE found a significant rate effect, Paulin et al. (1996). For slow interaction rates, the guidelines’ drained analysis is recommended, that is to use the apparent cohesion and friction angle approach rather than the undrained strength. C-CORE has consistently found however, e.g. Paulin et al. (1998b), that the Trautmann and O’Rourke method for such frictional analyses is consistently better for the ultimate resistance calculation, than the Hansen based methods, which significantly over-predicts. It is recommended that the transition from undrained to drained behaviour can be considered by normalizing the displacement rate, v using the pipe diameter D and the coefficient of consolidation, cv, Figure 5-7. The normalised displacement rate, V shows undrained behaviour for values greater than 10 and drained behaviour for values less than 0.1. Analyses for partially drained behaviour will require consideration of the excess pore pressures in the soil around the pipe. A hyperbolic curve is recommended to capture the observed p-y response, Sections 5.3.4 and 10.1.2. The interaction factors in uniform clay are in reasonable agreement with the values predicted by PRCI or Rowe and Davis (1982a), Figure 9-7. The experimental results are slightly less than those from Rowe and Davis to about H/D of 1.5 and slightly more than those from PRCI for deeper burials above H/D of 2. This transition is associated with a change in failure mechanism from a passive wedge type below H/D of 2 to local flow around the pipe. The experimental factors in uniform clay are well predicted by Equation 4-4 developed from the FEA. This recommended equation captures the importance of the soil weight in the passive wedge mechanism and is consistent with the lateral resistance of a pile for deep burial. Figure 10-4 show the applicability of the Equation 4-4 and compare its resulting factors with previous results. Finite element predictions were performed for clayey soil with soil shear strength of 3 45kPa, unit weight of 17.5kN/m , and pipe diameter of 0.9m. Figure 10-5 compares the results of Equation 4-4 for a weightless soil (i.e. FE results assuming weightless soil) with small-scale tests; PRCI recommendations and centrifuge data from Section 9 are also plotted in the same figure. There is a negligible weight effect in small-scale tests.


189


The measured initial stiffness of the p-y curve is less than that proposed in the guidelines. Paulin et al. (1995), using Equation 1-28, and Section 9.3 demonstrate that soil deformation properties, for example shear modulus, are required to correctly predict the stiffness response. A further comprehensive laboratory element-testing program is required to obtain the soil deformation properties to associate with the experimental results and develop new stiffness relations. Such a new relation would also address a serious deficiency in the guidelines that predict that the secant stiffness ( pu/ yu) decreases with increased pipe burial depth in clay, Figure 1-9. The secant stiffness actually increases with increased burial depth, Section 9.1 and Paulin et al. (1995). The importance of response stiffness (which it is a function of yield displacement and shape of p-y curve) is investigated through an example in Appendix A. For slope movements less than about 1.0m, the yield displacement and p-y curve shape are shown to be important in quantifying the pipe response.

10.4 Quantifying Mitigative Measures

The ASCE (1984) does not discuss mitigative measures in detail but a variety of potential mitigation measures will be addressed in the PRCI guidelines. The presence of the trench softens the pipe response, Sections 6 and 9.1.3. This study addressed the effects of trench geometry (width and wall inclination) and backfill strength on the lateral pipe-soil interaction, using physical models and FEA. The backfill is weaker than the native soil. The FEA idealisation exaggerated the contrast between the pipe response in the backfilled trench and native soil. The physical model results provided a moderated response as summarised below. The presence of a trench backfilled with material weaker than the native soil softens the p-y response compared to that of the same pipe buried in native soil. This p-y response is the same or stiffer than the pipe buried completely in backfill, that is no native soil. This stiffer response is due to the confinement of the backfill by the surrounding native soil. Soil deformation properties of the backfill and the native soil need to be assessed to quantify this effect. The lateral interaction force is much lower in a pipe with a wider trench than a narrower trench prior to reaching the peak load. For a wide trench ( B/D = 3.16), the effect of the native clay is minimal, and the p-y response is similar to the pipe in backfill alone. The effects of the native clay are further reduced for shallow burial as the pipe moves upward under horizontal displacement. In general, the force increases with displacement until the resistance is fully mobilized in the backfill, then it continues without significant increase, the force again increases when the pipe comes closer to the trench wall. The peak load occurs after pipe touches the trench wall. This ultimate force is less than the ultimate force developed on a pipe embedded only in stronger native soil. In a vertical trench, an increase in the trench width results in increasing the pipe displacement to peak load.


190


A simple approach is recommended to predict soil reactions on a trenched pipeline based on numerical and experimental results in Sections 6 and 9. This method is demonstrated in Figures 10-6 to 10-9 (dash-lines). Two yield loads are considered. The first yield load can be calculated using soil strength parameters of backfill materials (i.e. assuming a uniform backfill material). The second yield load is calculated using native soil parameters. The first yield load can be assumed to correspond to the yield displacement given by ASCE or PRCI guidelines – i.e. 0.04( H + D/2). The second yield load corresponds to the displacement of pipeline when it enters the native soil that is “B-D/2”. Figures 10-6 to 10-9 validate the applicability of the proposed method. The mitigation effects of trenches were more pronounced in the finite element results. This is partially attributed to difference in deformability of m aterials assumed in the finite element analyses and those of the actual soil tested in the centrifuge. Thus, it can be concluded that the proposed method is a conservative assessment of the forcedisplacement relationship that can be used in design. The second yield load could be further reduced to account for the mitigative effects caused by upward movements of pipeline. However, quantification of this reduction needs further numerical and experimental studies. PRCI recommends that trench walls should be sloped at an angle of about 30 degrees to mobilize the full mitigative effects of loose backfill for horizontal ground displacements. o However, trench wall inclination of 45 also has a significant mitigative effect. Compared to a vertical trench of the same width at the pipe springline, a trench with o walls at 45 does not have a mitigative effect on the initial p-y stiffness however when the load increased to half of the ultimate load, the soil reactions on the pipeline with inclined trench (45 degrees) are about 32% of those for the pipeline in a vertical trench. At larger displacements this difference decreases to about 12% as the pipe is interacting with mainly native soil. A similar conclusion was observed for a trench backfilled with loose sand rather than soft clay. Wall inclinations of 60° to horizontal did not have a significant mitigative effect on reducing the pipeline load.

10.5 Future Work

1. The coupled axial – lateral interaction has been shown to be very significant. The assumption of independent springs in each direction (i.e. axial, lateral, downward, and upward) is suspect. This interaction should be confirmed through physical tests. This study focused on cohesive materials. A similar study should be developed for frictional materials. It is expected to see a more pronounced difference in the response predicted assuming independent behaviour in axial, lateral, upward, and downward directions and a full 3D analysis in frictional materials because their strength is load-dependent. For clayey soil, practical values, used for adhesion, over-predict axial loading in full 3D loading conditions. However, for frictional material, the practical values may under-predict axial loading in full 3D loading conditions. In addition, load path independence is assumed in this study. This assumption should be verified through numerical


191


2.

3. 4.

5. 6.

study to provide a more general application for the results. Finally, special spring element formulations should be developed to able to account for 3D interaction in discrete analyses. The soil reactions on a buried pipeline are affected by native and backfill soil strength and stiffness as well as trench geometry. The current practise is able to estimate the peak loads with in reasonable ranges. However, more accurate forcedisplacement predictions can be made if the soil deformation properties are known. Further work should be done in correlating observed p-y responses to these soil properties. The program should be extended to include vertical, including combined, loading effects. The burial depth ratio in this study was limited to 3 and 8 in experimental and numerical studies, respectively. It is recommended to extend numerical and experimental studies to include deeper burial depth ratios and different pipe diameters. Deeper burial depth in order of 10 or more is important in river crossings. This will help to extend, and verify the cap on, Equation 4-4. At this time, it is recommended to cap Equation 4-4 as discussed in Section 4.3.3 for deep burial. The effects of stratigraphy (layered soil) and non-uniformity of soil reactions along the pipeline on pipeline responses should be studied. Field work should be extended to investigate the effects of “real” soil, which can be characterized as sand or clay. This is particularly important for pipelines that may often lie within the upper desiccation zone.


192


7 H/D=3.6

Eqn 10-1

6 5 H/D=1.8

4

x N

3

Cu = 45 kPa,

δ =20o

2 1

α =0.6

0 0

0.5

1

1.5

2

Nz Figure 10-1 Typical axial - lateral resistance interaction diagram


193


απ =1.88

2 z N , e c r 1.5 o f l a i x a d e 1 z i l a m r o n m0.5 u m i x a m

Proposed axial load

H/D=3.6

H/D=1.8

0

Cu = 45 kPa, δ =20

0

0

15

30

45

60

75

90

angle of translation (deg.) Figure 10-2 Proposed maximum normalized axial force


194


8

. x N , e c r 6 o f l a r e t a l d 4 e z i l a m r o n 2 m u m i x a m

H/D=3.6

H/D=1.8

0

Cu = 45 kPa, δ =20

0 0

15

30

45

60

75

90

angle of translation (deg.)

Figure 10-3 Proposed maximum normalized lateral force


195


12

10

H c

N , r o t c a f n o i t c a r e t n i l a t n o z i r o H

8

6

4 FE results using D = 0.95m, c u = 45kPa, . = 17.5 kN/m PRCI Rowe and Davis (1982a) Centrifuge tests FE results for weightless soil 3 Eq. 4-4 using D = 0.95m, c = 40kPa, . = 17.5 kN/m u

2

0

3

0

2

4

6

8

10

12

Burial depth ratio, H/D

Figure 10-4 Comparison of lateral interaction factor accounting for soil weight effects


196


PRCI Centrifuge tests FE results for weightless soil

Ranjan and Arora (1980) Mackenzie (1955), cu = 3.9kPa Mackenzie (1955), cu = 21.4kPa

Figure 10-5 Comparison of lateral interaction factor for weightless soil


197


10

9

8

7 D u c 6 / F , e c r o f 5 d e z i l a m r 4 o N

3

2

1 T1P1 T1P2 0

0

0.2

0.4

0.6

0.8 1 1.2 /D Normalized displacement, δ

1.4

1.6

1.8

2

Figure 10-6 Normalized force-displacement relationship: (a) experimentally recorded shown by continuous lines; and (b) proposed approximation shown by dashed lines


198


10

9

8


3

2

1 T1P3 T1P4 0

0

0.2

0.4

0.6


1.4

1.6

1.8

2

Figure 10-7 Normalized force-displacement relationship: (a) experimentally recorded shown by continuous lines; and (b) proposed approximation shown by dashed lines


199


10

9

8


3

2

1 T3P1 T3P4 0

0

0.2

0.4

0.6


1.4

1.6

1.8

2

Figure 10-8 Normalized force-displacement relationship: (a) experimentally recorded shown by continuous lines; and (b) proposed approximation shown by dashed blue line


200


10

9

8


3

2

1 T3P2 0

0

0.2

0.4

0.6


1.4

1.6

1.8

2

Figure 10-9 Normalized force-displacement relationship: (a) experimentally recorded shown by continuous lines; and (b) proposed approximation shown by dashed blue line


201


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Application and Limitations. Canadian

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surface

loading.

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212


APPENDIX A EXAMPLE FOR PIPELINE RESPONSE TO P-Y CURVE INITIAL STIFFNESS

The effects of displacement to peak pressure (at yield displacement, yu) and the shape of pressure-displacement relationship of soil reactions ( p-y curve) on pipeline were investigated. Obviously, the yield displacement and shape of p-y curve have significant impacts when small soil movements are considered (this is the case for most routine analysis using working stress design approach). Here, these effects were studied for pipeline subjected to large soil deformations. Such an analysis is required in strain-based design (e.g. Honegger and Nyman, 2001). A pipeline subjected to subscour deformation is considered. Soil deposit under ice-scour undergoes large deformations (e.g. Poorooshasb and Clark, 1990). Practical methods were developed by C-CORE to predict subscour soil deformations under a research program named PRISE. PRISE, the Pressure Ridge Ice Scour Experiment, was a jointly funded program to develop the capability to design pipelines and other seabed installations in regions scoured by ice, taking into account the sediment deformations and stress changes which may be caused during a scour event, Clark et al. (1998). Here, a pipeline buried in an overconsolidated clayey deposit subjected to ice-scour with characteristics given in Table A - 1 were considered. Soil deformations at pipeline springline were calculated based on C-CORE routines (Table A - 1; see WoodworthLynas, 1996). The complex sub-scour loading mechanism was simplified to allow for meaningful comparison. Thus, only horizontal movements of soil and one loading condition were considered. First, finite element analyses were performed for four cases (#1 to 4 in Table A - 2) varying yield displacement and shape of p-y curve. Two yield displacements were considered: 0.12 and 0.6m. The displacement of yu = 0.12m was calculated based on PRCI recommendations – yu = 0.04( H + D/2) for the specifications given in Table A - 1. The displacement of yu = 0.6m is inferred from Table 9.1; it is appropriate for soil used in physical testing program. To study pipeline responses under very large soil movements, four additional finite element analyses were performed (#5-8). In these analyses, the maximum movement of soil (i.e. 0.64m in Table A - 1) was increased to a value of 3.2m. For the maximum soil movement of 0.64m (cases 1 to 4), yield displacement and p-y curve shape have significant effects on the responses. The smaller yield displacement and the hyperbolic p-y curve resulted in significant larger tensile and compression strains as tabulated in Table A - 2 (cases 1 to 4). However, for a very large soil movement (here 3.2m), the differences were small as shown in Table A - 2 (cases 5 to 8). In conclusion, yield displacement and p-y curve shape may have a significant impact on pipeline responses depending on the magnitude of soil movements. Common slope movements are smaller than 1.0m (C-CORE, 2000); thus, the yield displacement and p-y curve shape are deemed to be important in design.


213


Table A - 1 Parameters used for the analysis PIPELINE CHARACTERISTICS

Parameter Pipeline grade Yield strength for X52 Ultimate strength for X52

Value/Type X52 358 MPa @ 0.5% strain 430 MPa

Outside pipe diameter including coating Steel wall thickness Pipeline internal pressure Depth below keel bottom to top of pipeline Temperature

0.95 m

Type Backfill material over pipeline Undrained shear strength, cu Unit weight, % Gouge Orientation Gouge width, B Gouge depth, D Keel angle Maximum horizontal movement


Explanation/ Reference Typical steel Ramber_Osgood hardening model (Walker and Williams, 1995) A typical example

22.8 mm 2.0 MPa 1.0 m No temperature loading SOIL CHARACTERISTICS Clay A typical example based on CCORE routines Clay 100 kPa 3 17.5 kN/m GOUGE CHARACTERISTICS Perpendicular to pipeline 8m 1.0 m 15 (degrees) 0.64/3.2m

A typical example based on CCORE routines

C-CORE routines (see Woodworth-Lynas, 1996)

214


Table A - 2 Finite element results in terms of peak values Axial Run Strain Number Tens. (#) (%)

Displa cement to Bend. peak Moment pressu re, y (kN-m) (m)

Axial Strain Axial Mises Comp. Stress Stress p-y Curve (%) (MPa) (MPa) Shape Maximum soil horizontal movement = 0.64m u

Maximum Soil Movement (m)

1

1.07

0.86

391.6

376.9

4503.3

0.12

Bilinear

0.64

2

0.29

0.26

350.8

336.2

3805.4

0.6

Bilinear

0.64

3

1.24

1.00

395.1

380.4

4557.2

0.12

Hyperbolic

0.64

4

0.79

0.65

383.4

368.7

4384.6

0.6

Hyperbolic

0.64

Maximum soil horizontal movement = 3.2m 5

2.33

1.36

411.3

396.5

4529.3

0.12

Bilinear

3.2

6

2.26

1.18

410.6

395.9

4406.7

0.6

Bilinear

3.2

7

2.93

1.62

416.5

401.7

4492.8

0.12

Hyperbolic

3.2

8

2.63

1 .41

413.9

399.1

4469.1

0.6

Hyperbolic

3.2


215


APPENDIX B RECOMMENDED ANALYSIS DESIGN GUIDELINES

CHANGES

TO

STRUCTURAL

In this appendix, some spring characteristics representing soil response in the pipe – soil structural analyses of landslide ground movement effects on buried gas pipelines are presented. These characteristics are only those recommended by this study for axial and lateral loading and include consideration of trench effects. Some of these recommendations may require further work for confirmation. This study did not address upward/downward movements. The approach adopted by PRCI (Honegger and Nyman, 2001) for vertical loading appears reasonable based on the literature review presented. List of symbols

.

Pipe external diameter soil undrained shear strength empirical adhesion factor − coating dependent factor relating the internal friction angle of the soil to − the friction angle at the pipe-soil interface peak axial load − peak lateral load − – displacement to peak load – displacement rate – coefficient of consolidation – depth to the centre of pipeline – effective unit weight of soil – total unit weight of soil – horizontal interaction factor (bearing capacity factor) for cohesive soil – horizontal interaction factor (bearing capacity factor) for frictional soil – coefficient of earth pressure at rest – internal friction angle of soil – interface angle of friction – normalised displacement rate, V = vD/ cv – trench width – angle of loading in degrees

B1

Axial Soil Springs

D cu

α f t u pu yu v cv H

.∋ . N ch N ch K o

φ δ V B

– –

For cohesive material (e.g. clay) – undrained loading: Purely axial spring capacity can be calculated using


216


t u

= π Dcuα

B-1

The values of α by Honegger and Nyman (2001) can be used (Figure B - 1). Under perfect axial alignment, the axial soil resistance may be much lower and controlled by the soil/pipe interface properties in a very thin shear zone between the pipe and soil as consolidation (drainage) in this zone happens very quickly. However, slight misalignment in field increases the axial resistance due to increased volume of soil shear zone. Thus, the relationship for adhesion factor provided in the draft PRCI guidelines is recommended. The effects of misalignment observed in numerical analysis can be further verified from physical tests. For frictional material (e.g. sand) – drained loading: Peak axial capacity can be calculated using t u

1

' (1 + K o ) tan δ = π D. H

B-2

2

The value of δ can vary from 0.5φ to 1.0φ with φ being the internal friction angle of soil, depending on the characteristics of the interface between the pipe material and the surrounding soil. Some suggested values of f (δ = f φ) are given in draft PRCI guidelines Force displacement relationship A bilinear relationship as suggested by ASCE (1984) and PRCI is recommended for the force-displacement curve. B2

Lateral Soil Spring

For cohesive material (e.g. clay) – undrained loading: A similar approach as used by PRCI and ASCE (1984) is suggested, however it is recommended to account for weight terms as detailed in Section 4.3.3. In summary, spring capacity is pu

= cu N ch D

B-3

and interaction factor accounting for the weight ef fect is


217


= min( N ch* + ⇓

N ch

. H cu

, N chmax )

B-4

⇓ = 0.85 *

where N ch is the interaction factor for weightless soil (Figure B - 2); ⇓ is a factor max including the effects of soil weight and shear strength (Figure B - 3); N ch is the limiting values for the horizontal interaction factor (its value estimated to range from 9 to 12). For frictional material (e.g. sand) – drained loading: This study did not focus on frictional materials. Based on the past studies and the literature review, the approach selected by ASCE is recommended. C-CORE has consistently found, e.g. Paulin et al. (1998b), that the Trautmann and O’Rourke (1983a) factors (Figure B - 4) for such frictional analyses are consistently better for the estimating the ultimate resistance. The spring capacity is, pu

= . ∋ HN qh D

B-5

Slow rate of loading In clay soils, C-CORE found a significant rate effect, Paulin et al. (1996). For slow loading rates, it is recommended use a drained (frictional) analysis using the apparent cohesion and friction angle (see the following section for quantification of slow loading rates). Also in many cases, real soil strength properties have both cohesive and frictional parts. For all these cases, a combination of Equations B - 3 and B - 5 can be u sed pu

= N ch c + . ∋ HN qh D

B-6

Rate Effects It is recommended that the transition from undrained to drained behaviour can be considered by normalised displacement rate, V = vD/ cv. The normalised displacement rate, V shows undrained behaviour for values greater than 10 and drained behaviour for values less than 0.1. Analyses for partially drained behaviour will require consideration of the excess pore pressures in the soil around the pipe.


218


Force-displacement relationship A hyperbolic curve is recommended to capture the observed p-y response, Sections 5.3.4 and 9.1.2. A bilinear relationship can replace the hyperbolic relationship when soil displacement, u are considerably larger than yield displacement, yu . Soil yield displacement, yu and p-y curve stiffness prior to peak load may significantly vary with soil deformation properties. Correct estimation of yield displacement, yu and p-y curve stiffness requires knowledge of soil deformation properties and further research. They may or may not have significant effects on pipe responses depending on loading type and its magnitude, see Appendix A. B3

Interaction Under Complex Loading

Interaction between axial load and lateral can be accounted for in cohesive soil based on the angle of loading. Axial and lateral spring capacity can be calculated using Equation B - 1 & B - 3 and then modified based on angle of loading as (Figure B - 5),

* t u ' t u = ) . (2 − )t u '( 45 *' pu = pu − 3t u2 pu = ) '( pu

. = 45°

B-7

. > 45° . = 45° . > 45°

where . is angle of loading in degrees. If loading on pipeline changes its direction or in case of a combined force and displacement controlled loading, the above equation may not be directly applicable. The estimated interaction factor (loads) in lateral and axial directions using Equations B 1, B - 3 & B - 7 (replacement model for practical application) are compared with 3D finite element results from Section 7 in Figure B - 6and Figure B - 7. They show relatively good agreement. It is recommended that findings for complex loading be verified using physical testing. B4

Trench Effects

For a laterally loaded pipeline, buried in a wide trench, two peak loads can be considered. The first peak load can be calculated using soil strength parameters of backfill materials (i.e. assuming a uniform backfill material). The second peak load is calculated using native soil parameters. These two peak loads correspond to displacements of “0.04( H + D/2)” and “B-D/2” respectively as illustrated in Figure B - 8. The first peak load should not exceed the second. The second peak load can be further reduced to account for the mitigative effects caused by upward movements of pipeline. However, quantification of this reduction needs further numerical and experimental studies. This result is obtained


219


for cohesive materials. It is recommended to confirm its application to frictional materials through further studies.


220


1.6 ASCE (1984) Tomlinson (1957)

1.4

Rizkalla et al. (1996) Balboa Potrero Canyon Paulin et al. (1998)

1.2

r o t c 1 a F n 0.8 o i s e h 0.6 d A

Rizkalla et al. (1996) Data Proposed Equation by

Honegger and Nyman (2001)

0.4 0.2 0 0

25

50

75

100

125

150

Undrained Shear Strength, kPa Figure B - 1 Plotted values for the adhesion factor, α


221


3.5

4

0

4.5

5

5.5

6

6.5

7

7.5

Lateral interaction factor

1 o i t 2 a r h t p 3 e d l a 4 i r u B

5 6 7 8

Figure B - 2 Lateral interaction factor for weightless cohesive soil


222


5 r o t c a f l 4 a r e t a l n3 o i t c a r e t n2 i n i e s a e r 1 c n I

α∼0.85 ⇓∼0.85 cu = 20 kPa cu = 10 kPa

0

0 2 4 6 8 10 . Normalized overburden pressure (from weight), H cu

12

Figure B - 3 Values of ⇓ , increase in the lateral interaction factor vs. . h/cu


223


Figure B - 4 ASCE horizontal bearing capacity factor: after Trautmann and O'Rourke (1983a)


224


1.0tu

. e c r o f l a i x 0.5tu a

0.0tu 0

15

30

45

60

75

90

angle of translation . (deg.) Figure B - 5 Effects of lateral spring load on axial spring capacity based on angle of loading


225


8 . e c r o f l 6 a r e t a l d e z i l 4 a m r o n m u 2 m i x a m

H/D=3.6

H/D=1.8

Cu = 45 kPa, δ =20

0

0 0

15

30

45

60

75

90

angle of translation (deg.) Figure B - 6 Comparison of lateral interaction factors estimated from replacement model (dashed-line) and 3D finite element analysis


226


3 e 2.5 c r o f l a i x 2 a d e z i l a 1.5 m r o n m 1 u m i x a 0.5 m

H/D=3.6

H/D=1.8

Cu = 45 kPa, δ =20

0

0 0

15

30

45

60

75

90

angle of translation (deg.) Figure B - 7 Comparison of axial interaction factors estimated from replacement model (dashed-line) and 3D finite element analysis


227


pu2

e c r o F pu1

0.04( H + D/2)

B-D/2

Displacement Figure B - 8 Proposed p-y curve for laterally loaded trenched pipeline


228

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