Geohazards and Pipelines: State-of-the-Art Design Using Experimental, Numerical and Analytical Methodologies 9783030498917, 9783030498924

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Spyros A. Karamanos Arnold M. Gresnigt Gert J. Dijkstra Editors

Geohazards and Pipelines State-of-the-Art Design Using Experimental, Numerical and Analytical Methodologies

Geohazards and Pipelines

Spyros A. Karamanos Arnold M. Gresnigt Gert J. Dijkstra •

•

Editors

Geohazards and Pipelines State-of-the-Art Design Using Experimental, Numerical and Analytical Methodologies

123

Editors Spyros A. Karamanos Mechanical Engineering University of Thessaly Volos, Greece

Arnold M. Gresnigt Gresnigt Consultancy Berkel en Rodenrijs, The Netherlands

Gert J. Dijkstra GJ-D Consult Maasland, The Netherlands

ISBN 978-3-030-49891-7 ISBN 978-3-030-49892-4 https://doi.org/10.1007/978-3-030-49892-4

(eBook)

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

Quite often, pipelines transporting water and energy resources, cross regions with extreme terrains associated with geohazards, including seismic fault action, landslides, soil subsidence or liquefaction. On the other hand, the growing society demands for energy resources require unhindered delivery. These two requirements, in conjunction with the increasing stringency of environmental restrictions, impose important challenges to pipeline engineers. Nowadays, “Geohazards and Pipelines” constitutes a hot topic in pipeline engineering research and practice. Nevertheless, despite the fact that this topic started attracting significant attention in the late 2000s and in the 2010s, there is still a lack of relevant pipeline design guidance, and this has been the principal motivation for the GIPIPE project. The idea for the GIPIPE project has been discussed extensively in the late 2000s, among the three Editors of the present book, to develop state-of-the-art design guidelines for analysis and design of buried steel pipelines against ground-imposed hazards. The long time experience of the two Dutch Editors in designing and assessing steel pipelines in settlement areas in The Netherlands, constituted a solid know-how and motivation for this research effort. Furthermore, the multi-discipline research cooperation, started in 2007 at the University of Thessaly, between the Departments of Mechanical and Civil Engineering, in simulating soil–pipe interaction, has been another strong starting point for this research. Finally, the longtime cooperation between the Delft University of Technology and the University of Thessaly in numerous research activities on steel pipelines and tubular structures had already built a common research framework that facilitated the development of the GIPIPE project. Toward the thorough investigation of this topic, it was necessary to involve the GIPIPE project at the European level. This was dictated by: (a) the international importance of the project objectives; (b) the innovative features of this research, requiring the involvement of international research institutes and engineering organizations with high technological skills, capabilities, and experience, including the development of nonstandard testing facilities; (c) the “complexity” and cost of research activities (experimental and numerical); and (d) the required synergy of partners with different expertise. v

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Preface

The GIPIPE proposal was submitted to the European Commission for funding through the Research Fund for Coal and Steel (RFCS) in September 2010. The GIPIPE consortium consisted of six partners, including both academic institutions and industrial organizations, and was coordinated by the University of Thessaly. The GIPIPE proposal was approved in early 2011, and the Grant Agreement (GA) between the consortium and the European Commission was signed in Spring 2011 (GA number: RFSR-CT-2011-00027). The project started in July 01, 2011, was completed in June 30, 2014 and approved by the European Commission in May 2015. In the context of strain-based pipeline design, consideration of pipe–soil interaction is fundamental for determining extreme ground-induced actions, toward increasing pipeline structural safety. GIPIPE has been an innovative multidiscipline project, which tackles the problem of buried pipelines in geohazard areas through an integrated and rigorous manner, with special emphasis on soil–pipe interaction. It involves novel experimental techniques and advanced numerical simulations, which led to design guidelines, complementing existing design practice. In this perspective, the GIPIPE project has been a unique project on pipeline integrity against geohazards: its results are aimed at reducing the geohazard risk to the population and the environment, increasing pipeline operational reliability, and safeguarding the unhindered transportation of energy (oil and gas) and water resources. The academic value of the GIPIPE project has been immense. The project sponsored and supported three Ph.D. dissertations at the participating Universities, and motivated quite a few Master theses on this subject. The research conducted in the course of the GIPIPE project has been published in several refereed international scientific journals and presented in international conferences. The strong impact of this research within the academic community reflects the high quality of the GIPIPE project, and motivated numerous subsequent research efforts in this area. In all these efforts, the GIPIPE project and its relevant publications have been referred to as landmarks in the topic of “Geohazards and Pipelines”. This book includes the main contributions of the GIPIPE project. The book is divided into three parts. Part I comprises Chaps. 1–3, and offers an introduction to the topic of geohazard actions, and their connection with pipeline mechanical design. The main results of the GIPIPE project are summarized in Part II (Chaps. 4–6); in those chapters, advanced numerical simulations are presented, supported, and validated by innovative experimental testing. Finally, the design guidelines developed within the GIPIPE project are presented in Part III; more specifically, tools for determining ground-induced actions on the pipeline are presented in Chap. 7 (strain-demand), limit states related to strain-based design of pipelines are summarized in Chap. 8, whereas Chap. 9 describes simplified analytical methods for pipeline design in fault crossings and in landslide areas. It is expected that the contents of the present book will be of great help to researchers, practicing engineers, and members of code-drafting committees.

Preface

vii

The Editors of the GIPIPE book would like to thank all the contributing authors (research members of the consortium) and, on behalf of the research consortium, acknowledge the European Commission for its financial support, through the GIPIPE project. The meticulous work of Kyriaki (Kelly) Georgiadi-Stefanidi and Gregory Sarvanis, at the University of Thessaly, in putting together the information from all authors in a concise document, as well as formatting and proof-reading the document, is greatly appreciated. Furthermore, the Editors wish to acknowledge the valuable contribution of Dr. Giuseppe Demofonti, Senior Engineer at Centro Sviluppo Materialli S.p.A., during the preparation of the GIPIPE proposal and throughout the duration of the GIPIPE project. Finally, the Editors would like to thank Springer International Publishing AG for supporting the publishing of this book. Volos, Greece Berkel en Rodenrijs, The Netherlands Maasland, The Netherlands February 2020

Spyros A. Karamanos Arnold M. Gresnigt Gert J. Dijkstra

Contents

Part I

Introductory Concepts of Pipeline Behavior in Geohazard Areas

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spyros A. Karamanos, Gert J. Dijkstra, Arnold M. Gresnigt, Wouter Huinen, and Kyriaki A. Georgiadi-Stefanidi

3

2 Pipeline Design Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gert J. Dijkstra, Arnold M. Gresnigt, Sjors H. J. van Es, Spyros A. Karamanos, and Wouter Huinen

17

3 Actions Due to Severe Ground-Induced Deformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gert J. Dijkstra, Spyros A. Karamanos, Arnold M. Gresnigt, Gregory C. Sarvanis, and Panos Dakoulas Part II

35

Main Results of the GIPIPE Project

4 Experimental Testing Conducted in the Course of the GIPIPE Project and Their Numerical Simulation . . . . . . . . . . . . . . . . . . . . . . Spyros A. Karamanos, Sjors H. J. van Es, Angelos Tsatsis, Gregory C. Sarvanis, Polynikis Vazouras, Giuseppe Demofonti, Elisabetta Mecozzi, Antonio Lucci, Panos Dakoulas, Rallis Kourkoulis, Arnold M. Gresnigt, and George Gazetas 5 Pipeline Response in Strike-Slip (Horizontal) Fault Crossings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polynikis Vazouras, Panos Dakoulas, Kyriaki A. Georgiadi-Stefanidi, and Spyros A. Karamanos

51

89

6 Pipeline Response Under Landslide Action . . . . . . . . . . . . . . . . . . . . 107 Angelos Tsatsis, George Gazetas, and Rallis Kourkoulis

ix

x

Part III

Contents

Design Guidelines for Buried Pipeline Design Under Ground-Induced Actions

7 Numerical Models for Pipelines Under Large Ground-Induced Deformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Spyros A. Karamanos, Gert J. Dijkstra, Gregory C. Sarvanis, Polynikis Vazouras, Angelos Tsatsis, Sjors H. J. van Es, Wouter Huinen, Panos Dakoulas, George Gazetas, Arnold M. Gresnigt, and Rallis Kourkoulis 8 Modes of Failure, Limit States and Limit Values . . . . . . . . . . . . . . . 171 Arnold M. Gresnigt, Gert J. Dijkstra, Wouter Huinen, Ioannis Gourousis, Gregory C. Sarvanis, Athanasios Tazedakis, and Nikolaos Voudouris 9 Simplified Analytical Models for Pipeline Deformation Analyses Due to Permanent Ground Deformation . . . . . . . . . . . . . . . . . . . . . . 183 Gregory C. Sarvanis, Spyros A. Karamanos, Polynikis Vazouras, Panos Dakoulas, and Kyriaki A. Georgiadi-Stefanidi

Contributors

Panos Dakoulas Department of Civil Engineering, University of Thessaly, Volos, Greece Giuseppe Demofonti Rina Consulting—Centro Sviluppo Materiali S.p.A., Roma, Italy Gert J. Dijkstra GJ-D Consult, Maasland, The Netherlands; Tebodin Consultants & Engineers BV (Bilfinger Tebodin), The Netherlands

Schiedam,

George Gazetas School of Civil Engineering, National Technical University of Athens, Athens, Greece Kyriaki A. Georgiadi-Stefanidi Department of Mechanical Engineering, University of Thessaly, Volos, Greece Ioannis Gourousis Corinth Pipeworks S.A., Thisvi, Domvraina, Greece Arnold M. Gresnigt Faculty of Civil Engineering, Delft University of Technology, Delft, The Netherlands; Gresnigt Consultancy, Berkel en Rodenrijs, The Netherlands Wouter Huinen Bilfinger Tebodin Netherland B.V., Schiedam, The Netherlands Spyros A. Karamanos Department of Mechanical Engineering, University of Thessaly, Volos, Greece Rallis Kourkoulis School of Civil Engineering, National Technical University of Athens, Athens, Greece Antonio Lucci Rina Consulting—Centro Sviluppo Materiali S.p.A., Roma, Italy Elisabetta Mecozzi Rina Consulting—Centro Sviluppo Materiali S.p.A., Roma, Italy

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xii

Contributors

Gregory C. Sarvanis Department of Mechanical Engineering, University of Thessaly, Volos, Greece Athanasios Tazedakis Corinth Pipeworks S.A., Thisvi, Domvraina, Greece Angelos Tsatsis School of Civil Engineering, National Technical University of Athens, Athens, Greece Sjors H. J. van Es Faculty of Civil Engineering, Delft University of Technology, Delft, The Netherlands; TNO, Structural Reliability, Delft, The Netherlands Polynikis Vazouras Department of Civil Engineering, University of Thessaly, Volos, Greece Nikolaos Voudouris Corinth Pipeworks S.A., Thisvi, Domvraina, Greece

Part I

Introductory Concepts of Pipeline Behavior in Geohazard Areas

Chapter 1

Introduction Spyros A. Karamanos, Gert J. Dijkstra, Arnold M. Gresnigt, Wouter Huinen, and Kyriaki A. Georgiadi-Stefanidi

Abstract This introductory chapter presents the main scope of this book and the relevant background. The main objective is the development of guidelines for the analysis and design of buried steel pipelines under ground-induced actions, to be used by researchers, engineers and code-drafting committees. The GIPIPE project is summarized and an outline of the main results is offered. Finally, the last part of the chapter describes pipeline damages due to major seismic and landslide events since the early twentieth century, pin-pointing the influence of ground-induced actions on pipeline structural integrity.

1.1 Scope, Background and Objective Steel buried pipeline networks are of paramount importance for the international economy. A possible threat to these networks is the occurrence of severe ground– induced deformations, resulting from landslides and liquefaction of soils or seismic activity. These large deformations may cause high inelastic strains in the pipe wall and, ultimately, lead to rupture and interruption of delivery. S. A. Karamanos (B) · K. A. Georgiadi-Stefanidi Department of Mechanical Engineering, University of Thessaly, 38334 Volos, Greece e-mail: [email protected] G. J. Dijkstra GJ-D Consult, 3155 BV Maasland, The Netherlands e-mail: [email protected] Tebodin Consultants & Engineers BV (Bilfinger Tebodin), 3122 HD Schiedam, The Netherlands A. M. Gresnigt Faculty of Civil Engineering, Delft University of Technology, 2628 CN Delft, The Netherlands e-mail: [email protected] Gresnigt Consultancy, 2651 XT Berkel en Rodenrijs, The Netherlands W. Huinen Bilfinger Tebodin Netherland B.V., 3122 HD Schiedam, The Netherlands © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. A. Karamanos et al. (eds.), Geohazards and Pipelines, https://doi.org/10.1007/978-3-030-49892-4_1

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S. A. Karamanos et al.

The present book focuses on the structural safety of buried butt-welded continuous carbon steel pipelines under severe ground-induced deformations. It refers mainly to the design of new buried steel pipelines in areas where ground displacements and deformations may occur, resulting from seismic action or landslides. Nevertheless, it can also be employed for the seismic assessment of existing pipelines. The guidelines in the present book constitute the final deliverable of the GIPIPE project, sponsored by the European Commission. The content of the book can be regarded as an integration of results from the GIPIPE project with existing standards and literature on the mechanical design of buried pipelines in geohazard areas. More specifically, the present book is aimed at defining the topic and the relevant scientific background, presenting the important design issues related to the topic of “Geohazards and Pipelines” and providing guidance/methods to solve the problem using efficient numerical and analytical methodologies, validated by novel experimental testing. The guidelines of this book should be used cautiously for non-metallic pipelines. In particular, the basic principles for predicting ground-induced actions on the pipeline, consisting a procedure referred to as “strain demand”, can be used for pipes of different material. However, the ultimate strength and deformation capacity of non-metallic pipelines can be quite different. In addition, the present guidelines do not refer to above-ground industrial piping systems in power plants, or in chemical/petrochemical industries. The guidelines focus mainly on continuous butt welded steel pipeline applications (gas, oil and water pipelines). They are not directly applicable to welded pipelines with lap joints, used extensively in the United States for water transmission. The structural response and deformation capacity of lap welded joints require special treatment, which is not part of the present book. The reader interested in this topic is referred to the recent works by Keil et al. (2018) and Chatzopoulou et al. (2018). In addition, the case of segmental pipelines, usually composed by pipeline segments connected with gasketed joints, also used extensively for water transmission, requires special attention, which is out of the scope of the present book. Finally, this book does not contain specific guidance on the retrofit of existing pipeline systems; nevertheless, parts of the book and the methodologies presented may contain useful information towards this purpose. The present European standards on design of buried pipelines, such as EN 1594 and EN 14161, provide only limited information for the design of pipeline systems against large ground deformations, e.g. resulting from seismic faults or landslides. The design methods and design criteria in these standards do not fully cover the calculation of forces, stresses and strains in buried pipelines when these large ground-induced deformations occur and the required pipeline strength to sustain these actions. Such information can be also found in the 2006 edition of EN 19984, the European standard for seismic design of tanks, silos and pipelines, but the proposed design framework in that standard requires significant enhancement. The GIPIPE research project was aimed at fulfilling this gap, including a study of the relevant international standards and guidelines, with emphasis on pipe-soil interaction of buried pipelines. The outcome of this project is summarized in Part II and

1 Introduction

5

comprises results from extensive analyses of pipeline components undergoing large ground-induced deformations, including pipe-soil interaction. The GIPIPE project included extensive testing and related numerical analyses of pipelines, enhancing current knowledge on the response of buried pipelines and pipe-soil interaction when the pipe is subjected to severe ground-induced deformations. The testing program within the GIPIPE program was meant for validation of numerical models (rigorous and more simplified), and the main experimental results of this testing program are outlined in Chap. 4 of this book. In addition, analytical tools are developed that enable pipeline analysis and design in a simple and efficient form. The present book, as outcome of the GIPIPE project, is aiming at providing guidance for researchers and practicing engineers dealing with buried steel pipelines. In particular, this book provides: • identification of critical steps and parameters in the design of buried steel pipelines under severe ground-induced deformation; • recommendations for developing efficient pipe-soil interaction models; • calculation examples for pipelines under seismic fault and/or landslide, both with advanced and with simple and efficient calculation models; • information for the calibration and validation of numerical models developed within the GIPIPE project, using the results of laboratory experiments and field testing in pipe segments, subjected to large ground-induced deformations; • definition of structural resistance (ultimate limit states) of pipeline components, i.e. straight pipe segments and pipe bends. The ultimate goal of the GIPIPE design guidelines was to assure that buried steel pipelines, fulfilling the preset requirements, after the occurrence of a severe groundinduced deformation will remain operational without loss of pressure containment. In pipeline design, two limit states need to be considered: serviceability and ultimate. Serviceability refers to the operation of the pipeline after a seismic event (limitations on ovalization and local buckling), while the ultimate limit states refer to loss of pressure containment, which is associated with rupture of the pipe wall.

1.2 Description of the GIPIPE Project (2011–2014) The GIPIPE project has been a pioneering research project, sponsored by the European Commission, within the Research Fund of Coal and Steel (RFCS) in the area of steel pipeline safety for transportation of energy resources. The project was entitled “Safety of Buried Steel Pipelines Under Ground-Induced Deformations”. It has been coordinated by the University of Thessaly, Volos, Greece. It started in July 2011 and finished in June 2014 (36-month duration). The project combined experimental, numerical and analytical tools to perform high-level research on the inter-disciplinary area of buried steel pipelines under severe ground-induced actions. Extensive experimental and numerical work has been conducted, with main purpose to investigate

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the interaction between the pipe and the surrounding soil; this is the key issue for determining actions on the steel pipeline in a reliable manner. The GIPIPE consortium has been composed by the following partners: • • • • • •

University of Thessaly (Volos, Greece) [coordinator] Centro Sviluppo Materiali S.p.A. (Rome, Italy) Delft University of Technology (Delft, The Netherlands) National Technical University of Athens (Athens, Greece) Corinth Pipeworks S.A. (Thisvi, Greece) Tebodin Consultants and Engineers B.V. (Bilfinger-Tebodin, Schiedam, The Netherlands).

The project combined geotechnical engineering concepts and structural design principles with mechanical and pipeline engineering practice and was aimed at developing design guidelines/recommendations for safeguarding structural integrity of buried welded steel pipelines subjected to severe ground-induced actions. More specifically, permanent ground-induced actions were considered, such as fault motion, landslides or liquefaction-induced lateral spreading. The proposed guidelines improve and extend current design practice, considering the particularities of steel pipeline behaviour, with emphasis on soil-pipe interaction. The following targets have been achieved within the GIPIPE project: • Critical evaluation of current design practice towards identification of specific needs for developing pipeline provisions in geohazard areas. • Development of rigorous three-dimensional models for analyzing buried pipelines in cohesive and non-cohesive soils under permanent ground actions (faults, landslides, lateral spreading) with special emphasis on soil material modeling. • Performance of large-scale experiments, supported by small-scale tests, to determine pipeline mechanical behavior under various ground conditions, within the purpose of examining the interaction between the soil and the steel pipe. • Extensive parametric analyses for buried pipelines under ground-induced actions due to fault action and landslide action. • Proposal of well-calibrated analytical methodologies for the simple and efficient stress analysis of buried pipelines, to be used for design purposes. • Presentation of a set of guidelines for buried pipeline design against permanent ground-induced actions, which summarizes existing knowledge and incorporates all results from the present research program. • Dissemination of GIPIPE results and interaction with the pipeline engineering community, through a dedicated workshop, organized by the project consortium (June 2014, Delft, The Netherlands). More information on the project can be found in the final report of the project (Vazouras et al. 2015). Three major points that characterize this research program should be underlined: 1. Most of the research work on steel pipelines and piping within the Research Fund for Coal and Steel program has been directed towards pipeline resistance,

1 Introduction

7

mainly failure against fracture referred to as “strain capacity”. The present work is the first project that focuses on pipeline “strain demand”, which is an equally important issue towards reliable and safe pipeline design. 2. The present work refers to extreme loading conditions for the steel pipeline, associated with large deformation and strains well into the inelastic range of the steel material. Therefore, the results of the GIPIPE project should be considered within a strain-based design framework. Furthermore, it should be underlined that traditional analytical tools for pipeline stress analysis, based on the concept of stressbased design (developed mainly for pipeline design under pressure containment), may not be applicable in pipeline design against geohazards. 3. The particularities of buried pipeline performance have been taken into account. In particular, one has to consider that: – loss of containment is the major limit state and refers to a severe local damage situation. This is in contrast with building structures, where local damage may not necessarily be catastrophic due to the possibility of redistribution of internal forces, if the structure is designed for this possibility; – for the particular case of seismic action in welded steel pipelines, due to soil embedment, permanent ground-induced actions are the primary actions in pipeline design. Transient (wave shaking) phenomena are much less important than permanent ground-induced actions and may be given less attention. The main results of the GIPIPE project can be summarized as follows: • Experimental work has been conducted for supporting numerical models towards accurate predictions of strain demand in the pipeline. A good comparison has been achieved between test results and numerical predictions. • Experimental results offered a substantial contribution towards understanding soil-pipe interaction (axial and transverse direction). Distribution of pipeline pressure on the surrounding soil is measured. • Test results have also indicated that the formation of a local buckle in pressurized pipelines, in several instances, may be associated with loss of containment, given the fact that other detrimental factors (e.g. girth welds, unfavorable material properties) are also present. • Important results have been obtained for curved pipeline components (referred to as “bends” or “elbows”); their unique structural response under bending and, in particular, their increased flexibility may allow their use as mitigation devices, but require a detailed strain analysis to avoid failure of the elbow itself. • Simplified methodologies that employ “pipe” finite elements have been employed and compared successfully with more rigorous finite element models. Furthermore, simplified analytical methodologies, which can be used for preliminary pipeline design against geohazards, have also been proposed. • Finally, the design guidelines/recommendations developed can be used by Code Drafting Committees, for the amendment of existing design standards (e.g. EN 1998-4 for pipeline seismic design).

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The results and deliverables of GIPIPE are both novel and unique, leading to • construction of innovative state-of-the-art devices for experimental simulation of buried pipeline response; • development and validation of rigorous and simplified models, capable of describing large permanent deformations of buried pipelines with a good level of accuracy; • better understanding of soil-pipe interaction under severe ground-induced actions; • significant improvement of the state-of-the-art of pipeline design in geohazard areas. The entire GIPIPE work is reported in the final report of the project (Vazouras et al. 2015), available in digital form in the website of the Publications Office of the EU, and the corresponding deliverables, which are available upon request to the project coordinator. Furthermore, a significant number of relevant publications in international scientific journals and conferences have been presented and constitute a well-documented background for Code Drafting Committees, for developing or updating standards and guidelines towards safer and more reliable pipeline design against geohazards.

1.3 Overview of Ground Movement Induced Damage to Pipelines The reference list at the end of this Chapter contains a brief database of literature concerning the share of ground movement induced damage to pipelines in the incident frequency (Porter et al. 2004; Savigny et al. 2005; Bolt 2006; NEB 2009; Davis et al. 2011; EGIG 2018; Girgin and Krausmann 2016; Goodfellow et al. 2018). Some examples of pipeline incident data (PID) and ground movement induced damage to buried pipelines are also provided in the present section.

1.3.1 Share of Ground Movement Induced Damage to Buried Pipelines In this section, an overview of the share of ground movement induced damage to pipelines in different parts of the world is provided. According to the 10th Report of the European Gas Pipeline Incident Data Group (EGIG 2018), ground movement induced damage attributes approximately 15% to the total amount of incidents for the period 2007–2016 and respectively, 8% for the period 1970–2013. The primary failure frequency due to ground movement is reported to be more or less constant over the years: its value was approximately 0.026 per 1000 km.year over the period

1 Introduction Table 1.1 Distribution of the sub-causes of ground movement in Western Europe for 1970–2016 and 2007–2016 (EGIG 2018)

9 Type of ground movement

1970–2016 (%)

2007–2016 (%)

Landslide

64.66

90.32

Flood

14.66

3.23

River

4.31

0

Mining

3.45

0

Dike break

0.86

0

Other Unknown

1.72 10.34

0 6.45

1970–2016, with a small peak in the period 2012–2016 at 0.031 per 1000 km.year. Furthermore, ground movement is the second leading cause for the failure mode of rupture of the pipeline, after external interference. There are many types of “Ground Movement” incidents and Table 1.1 presents the distribution of the different sub-causes in the category of ground movement that cause a pipeline incident, according to the recent EGIG report (EGIG 2018). Based on this data, it is clear that the vast majority of the ground movement incidents are caused by landslides, especially in the recent 10 years. In the United Kingdom, ground-induced damage in pipelines attributes approximately 4% to the total amount of incidents, according to the UKOPA Pipeline Product Loss Incidents and Faults Report for the period 1962–2016 (Goodfellow et al. 2018). It should be noted though, that the UK is not a seismic country and this justifies the low percent of incidents due to ground movement. Nevertheless, ground movement is the second leading cause related to pipeline rupture (full bore). The natural gas transmission data for the period 1984–2001 reported by the US Department of Transportation (US DOT) shows that ground movement induced damage accounted for 8.5% of the total amount of incidents (Porter et al. 2004). However, the property damage cost caused by ground movement induced damage is only exceeded by the costs caused by third party damage. From the above information, it can be concluded that, although in some parts of the world the pipeline incidents caused by ground movement represent a rather small percentage of the total amount of incidents, they are generally related to severe damage, associated with pipe-wall rupture, greater property damage costs and longer periods required for the restoration of the damaged infrastructure and the disrupted services, with respect to other types of hazard (Porter et al. 2004). In other parts of the world, where pipelines are constructed in a more geologically active terrain, ground movement can be proved rather significant as far as pipeline incidents are concerned. The risk for a pipeline incident due to ground movement becomes greater if the specific characteristics of the “difficult” terrain are not appropriately taken into account during the pipeline design and construction stage. For example, data for a typical pipeline in the South American Andes indicate that ground movement may be the cause for 50% of the total amount of pipeline incidents, leading to an average failure frequency that exceeds 2.5 per 1000 km·yr,

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as reported by Savigny et al. (2005). This frequency is about two orders of magnitude greater than the corresponding frequency reported in Western Europe.

1.3.2 Examples of Ground Movement Induced Damage to Buried Pipelines 1.3.2.1

North American Earthquakes from 1900–1975

Table 1.2 offers a summary of various North American earthquakes that occurred in the 20th century, up to 1975, in terms of pipeline and cable damage. The data in this table are obtained by the relevant publication of O’ Rourke and McCaffrey (1984). In most instances, pipeline damage can be attributed directly to permanent ground movements. For example, the locations of cast iron water main breaks after the 1906 San Francisco earthquake show a strong correlation with the zones of lateral spreading. Approximately 57% of all water main breaks occurred within three zones of lateral spreading, which involved approximately 10% of the area covered by the distribution system. During the 1971 San Francisco earthquake, the area of surface faulting accounted for approximately 0.5% of the area affected by strong ground shaking. Nevertheless, 25 to 50% of all pipeline breaks in the area of strong ground shaking occurred at fault crossings or at the vicinity of these locations.

1.3.2.2

Manjil Earthquake, Iran, 1990

The Manjil-Rudbar Earthquake in Iran occurred at 00:30:09 on June 21, 1990. It caused widespread damage in areas within a one hundred kilometer radius of the epicenter near the city of Rasht and approximately two hundred kilometers northwest of Tehran. The cities of Rudbar, Manjil, and Lushan and 700 villages were destroyed and over 300 villages were affected. The earthquake, which had a (moment) magnitude of 7.4, also affected multiple pipelines. Towhata (2008) reports also buckling failure of a major water pipeline that crosses a seismic reverse fault; this tectonic movement across the fault induced significant compression and bending to the pipeline, resulting in its failure.

1.3.2.3

Northridge Earthquake, California, 1994

In the 1994 Northridge earthquake, in California, there were 209 repairs required to distribution lines made of metallic materials, and 27 to polyethylene lines. The 20-inch-diameter Kinder Morgan product line was ruptured in Palm Springs. The pipeline was aligned directly over the fault. The earthquake resulted in the shortening of the pipeline by five meters, causing it to wrinkle and rupture as reported by

1 Introduction

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Table 1.2 Summary of North American earthquakes (1900–1975) with significant reported pipeline and cable damage (O’ Rourke and McCaffrey 1984) Seismic event (year and Earthquake location)

Magnitude

Maximum intensity

Type of permanent ground movement

Pipeline performance

1906 San Francisco

8.3

XI

Strike-slip faulting with max. offset of 6.4 m. Extensive slope stability problems. Lateral spreads and flow failures

Water pipeline ruptured at nine locations along San Andreas fault. Extensive damage to water and gas pipeline from liquefaction- induced movements in San Francisco

1929 Grand Banka

7.2

Not reported Submarine landslides Western Union and and flow failures French communication cables broken as far as 500 km from epicenter

1931 Managua

Not reported

Not reported One main zone of faulting. Landslides along steep natural slopes

Principal water main for Managua ruptured at fault. Steel pipeline ruptured by landslide

1933 Long Beach

6.3

VIII

Ground cracks with seeping water, sand boils, and local subsidence

Over 500 pipeline breaks. Greatest concentration of pipeline failures near bays, rivers, and flood control channels

1952 Kern County

7.7

X–XI

Reverse oblique surface faulting. Many landslides. Ground cracks in terraces along creek beds

Oil pipeline ruptured along western extension of surface faulting. Gas transmission line deformed but not ruptured at fault crossing

1958 Alaska

8.0

Not reported Strike-slip faulting with max. offset of 6.5 m. Many submarine landslides. Lateral spreads and subsidence

Submarine cables of the Alaska Communication System were severed at several locations (continued)

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S. A. Karamanos et al.

Table 1.2 (continued) Seismic event (year and Earthquake location)

Magnitude

Maximum intensity

Type of permanent ground movement

Pipeline performance

1964 Alaska

8.4

XI–XII

Two reverse faults. Extensive landslides and submarine slope failures. Lateral spreads, flow failures, and subsidence

Over 200 breaks in gas and 100 breaks in water pipelines in Anchorage. Three petroleum transmission lines undamaged except for one circumferential crack

1971 San Francisco

6.4

XI

Reverse oblique surface faulting. Over 1000 landslides. Lateral spreads at Upper Van Norman Reservoir

Over 2400 breaks in water, gas and sewage pipelines. Majority of damage at faults and lateral spreads

1972 Managua

5.6

Not reported Four main surface faults with max. strike slip of 0.4 m. Landslides along steep natural slopes and granular embankments

Extensive damage to water distribution system. Many pipelines ruptured at fault crossings. Electric cables deformed by landslide

Ballantyne (2008). The pipeline was carrying diesel, which was sprayed into the air and, ultimately, 200,000 gallons of product was discharged into the local drainage system before the isolation of the line. The fault displacement also caused the rupture of a smaller natural gas distribution pipeline with similar location. Due to shaking, the Kinder Morgan Pipeline failed at 15 additional locations along the 60 km alignment parallel to the fault trace. Each failure location required environmental cleanup of the discharged diesel product.

1.3.2.4

Chi-Chi Earthquake, Taiwan, 1999

The Chi-Chi earthquake occurred on September 21, 1999 and its magnitude was recorded equal to 7.3. Apart from the thousands of houses and buildings that were completely destroyed or severely damaged, the earthquake resulted in the extensive damage of infrastructure, including bridges, dams and lifeline systems, such as electricity and telecommunication systems, water distribution and gas supply lines (Chen et al. 2002; Hamada 2014). Buckles and ruptures of buried pipes were attributed mainly to fault crossing.

1 Introduction

1.3.2.5

13

Kocaeli Earthquake, Turkey, 1999

The Kocaeli earthquake, with a magnitude equal to 7.4, occurred on August 17, 1999. It has been a landmark earthquake because of its devastating effects, not only for urban areas, but also for the significant damage on industrial facilities. In particular, the damage caused to the infrastructure of many cities was severe; about 20,000 buildings collapsed or were partially damaged, several bridges, tunnels and viaducts were extensively damaged. Furthermore, its effects on industrial facilities have been immense (Suzuki 2002) and motivated a series of relevant research programs, e.g. Pappa et al. (2012). During this earthquake, numerous water and gas pipes crossing earthquake faults were buckled and ruptured (Hamada 2014). For example, the buttwelded Thames steel water pipeline, with a diameter of 2.2 m, was crossing the Sapanca segment of the North Anatolian Fault and was severely damaged due to right lateral movement of the strike-slip fault. The steel pipeline was crossing the fault-line with an angle equal to 55o . As a result, damage and leaks were recorded at three different locations of the pipeline, where one minor and two major local buckles were observed (Kaya et al. 2017).

1.3.2.6

Canterbury Earthquakes, New Zealand, 2010–2011

Underground pipelines in Christchurch, New Zealand, were severely damaged during the Canterbury earthquake sequence. The main earthquakes were: (a) the Mw7.1 earthquake on 4 September 2010, (b) the Mw6.2 earthquake on 22 February 2011 and (c) the Mw6.0 earthquake on 13 June 2011. The main aspect of earthquake action was soil liquefaction, which caused more damage to underground pipes than the ground movement and this action was associated with large amounts of lateral and vertical ground movement (O’Rourke et al. 2012). As a result of this sequence of earthquakes, the water pipe networks were affected in various ways and impacted their ability to provide adequate service to large areas of Christchurch. More specifically: (a) gravity reticulation experienced reduced capacities; (b) potable water networks and pressure sewers experienced leakage and loss of pressure; (c) wastewater reticulation had increased flows; (d) pump stations were incapacitated; (e) all networks experienced damage leading to blockage or leakage at the interface with structures (Cubrinovski et al. 2011).

1.3.2.7

Great East Japan Earthquake, 2011

The Mw9.0 Great East Japan Earthquake took place on March 11, 2011 and had significant effects on human resources, buildings and infrastructure in many areas of the East Pacific region in Japan. The earthquake generated a tsunami of unprecedented height and special extent along the Pacific coast of east Japan. The earthquake and the subsequent tsunami caused approximately 20,000 deaths and missing and were

14

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responsible for the injury of 6,000 people. This earthquake attracted a lot of international attention mainly because of the Fukushima nuclear power plant incident, caused by the tsunami. However, despite the immense intensity of the earthquake event, the high-pressure transmission gas pipeline owned by Japan Petroleum Exploration (JAPEX), did not incur any severe damages and maintained its structural integrity despite the fact that several locations were subjected to permanent ground deformations, especially in mountain areas (Mori et al. 2012). On the other hand, related facilities to the pipeline underwent damage. After the event, the pipeline and its relevant facilities were rapidly restored, and their operation was successfully restarted two weeks after the earthquake. The 2011 Great East Japan Earthquake has been the first case in Japan, where the transmission seismic performance highly qualified gas pipeline was verified against significantly large earthquakes. This earthquake has caused significant damage to the water transmission and distribution system in the area of the seismic event. A suspension of water supply occurred at about 2,300,000 households in the wide area from Tohoku to Kanto regions just after the earthquake (Miyajima 2012). About 90% of water outrage was recovered one month after the event, except for flooded areas by the tsunami. More damage, however, occurred by the strong aftershocks that happened in the middle of April 2011.

1.3.2.8

Camisea Pipeline System Failures Due to Landslide Action, Peru, 2004–2007

All incidents described in the previous paragraphs refer to major seismic events. On the other hand, in landslide areas, pipelines may be subjected to severe groundinduced action, not necessarily due to seismic events. The Camisea pipeline system, Peru, constitutes a typical example of pipeline failure, not caused by a major earthquake. It consists of two buried pipelines within the same alignment; a natural gas line (714 km) and a natural gas liquids (NGL) line (540 km). The pipelines originate at the Camisea gas field, near Malvinas in the Amazon jungle (Selva), and continue across the Andes (Sierra) to the Pacific coast (Costa). During the first 30 months of operation, the NGL line ruptured six times; four of these incidents were caused by landslide movements. Following an audit, three key issues were identified: • during the design stage, there was a general failure to recognize landslides as a major threat along the pipeline alignment. Additional attention would have been necessary for selecting the final pipeline alignment, and for designing the mitigation measures; • the pipeline in those landslide areas should have been designed to sustain high strains without pipe wall rupture, through appropriate specification of welding and materials; • during construction, the strict timetable requirements and the associated financial penalties forced the contractor to minimize field geological investigations and

1 Introduction

15

the corresponding geotechnical analyses. This led to an inadequate definition and characterization of geohazards, and increased the risk of failure. As a consequence of the failures and the audit report, the operating company of the Camisea pipeline made significant post-incident investments in order to minimize the risk of further pipeline damage. A main conclusion from the above failures of the Camisea pipeline system is that: (a) recognition of geohazard threats during the design stage and (b) strain-based design supported by appropriate geological/geotechnical study, would have minimized the risk of pipeline failure in landslide areas. For more information on these incidents, the reader is referred to the paper by Lee et al. (2009).

References Ballantyne D (2008) Southern San Andreas fault earthquake scenario: oil and gas pipelines. SPA Risk LLC, Denver CO Bolt R (2006) A guideline: using or creating incident databases for natural gas transmission pipelines. In: Proceedings of the 23rd world gas conference. Amsterdam, The Netherlands Chatzopoulou G, Fappas D, Karamanos SA et al (2018) Numerical simulation of steel lap welded pipe joint behavior in seismic conditions. In: Proceedings of ASCE pipelines 2018 conference. Toronto, Canada Chen WW, Shih B-J, Chen Y-C et al (2002) Seismic response of natural gas and water pipelines in the Ji-Ji earthquake. Soil Dyn Earthq Eng 22:1209–1214 Comité Européen de Normalisation (2003) Petroleum and natural gas industries—Pipeline transportation systems, EN 14161 Standard (ISO 13623:2000 modified). Belgium, Brussels Comité Européen de Normalisation (2006) Eurocode 8, Part 4: Silos, tanks and pipelines, CEN EN 1998-4. Belgium, Brussels Comité Européen de Normalisation (2013) Gas supply systems—Pipelines for maximum operating pressure over 16 bar, Functional requirements, EN 1594 Standard. Belgium, Brussels Cubrinovski M, Hughes M, Bradley B et al (2011) Liquefaction impacts on pipe networks, research report 2011–04. Civil & Natural Resources Engineering, University of Catenbury, New Zealand Davis P, Dubois J, Gambardella F et al (2011) Performance of European cross-country oil pipelines: statistical summary of reported spillages in 2010 and since 1971. CONCAWE, Brussels European Gas Pipeline Incident Data Group (2018) Gas pipeline incidents, 10th Report of EGIG. EGIG VA 17.R.0395 Girgin S, Krausmann E (2016) Historical analysis of U.S. onshore hazardous pipeline accidents triggered by natural hazards. J Loss Prevent Proc 40:578–590 Goodfellow GD, Lyons CJ, Haswell JV (2018) UKOPA pipeline product loss incidents and faults report (1962–2016). UKOPA/17/002 Hamada M (2014) Engineering for earthquake disaster mitigation. Springer Series in Geomechanics and Geoengineering, Springer Kaya E, Uckan E, O’ Rourke MJ et al (2017) Failure analysis of a welded steel pipe at Kullar fault crossing. Eng Fail Anal 71:43–62 Keil BD, Gobler F, Mielke RD et al (2018) Experimental results of steel lap welded pipe joints in seismic conditions. In: Proceedings of ASCE pipelines 2018 conference. Toronto, Canada Lee EM, Audibert JME, Hengesh JV, Nyman DJ (2009) Landslide-related ruptures of the Camisea pipelien system, Peru. Q J Eng Geol Hydroge 42:251–259 Miyajima M (2012) Damage analysis of water supply facilities in the 2011 great east Japan Earthquake and Tsunami. In: Proceedings of the 15th world conference on earthquake engineering, Lisbon, Portugal, 24–28 Sept 2012

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Mori S, Chiba K, Koike T (2012) Seismic performance analysis of the transmission gas pipeline in the 2011 great East Japan Earthquake. In: Proceedings of the 15th world conference on earthquake engineering, Lisbon, Portugal, 24–28 Sept 2012 National Energy Board (2009) Focus on safety and environment a comparative analysis of pipeline performance. NEB, Calgary O’Rourke TD, McCaffrey M (1984) Buried pipeline response to permanent earthquake ground movements. In: Proceedings of the 8th World conference on earthquake engineering, vol 8, pp 215–222 O’Rourke TD, Jeon S-S, Toprak S et al (2012) Underground lifeline system performance during the canterbury earthquake sequence. In: Proceedings of the 15th World conference on earthquake engineering, Lisbon, Portugal, 24–28 Sept 2012 Pappa P, Varelis GE, Vathi M et al (2012) Structural safety of industrial steel tanks, pressure vessels and piping systems under seismic loading (INDUSE). Final Report, Research Fund for Coal and Steel (RFCS), European Commission, Brussels, Belgium Porter M, Logue C, Savigny KW et al (2004) Estimating the influence of natural hazards on pipeline risk and system reliability. In: Proceedings of international pipeline conference, Cargary Savigny K, Porter M, Leir M (2005) Geohazard management trends in the onshore pipeline industry. Geoline, Lyon Suzuki K (2002) Report on damage to industrial facilities in the 1999 Kocaeli earthquake Turkey. J Earthq Eng 6(2):275–296 Towhata I (2008) Geotechnical earthquake engineering. Springer Series in Geomechanics and Geoengineering, Springer Vazouras P, Sarvanis G, Karamanos SA et al (2015) Safety of buried steel pipelines under groundinduced deformations (GIPIPE). Final Report, RFSR-CT-2011-00027, Research Fund for Coal and Steel (RFCS), European Commission, Brussels, Belgium

Chapter 2

Pipeline Design Basics Gert J. Dijkstra, Arnold M. Gresnigt, Sjors H. J. van Es, Spyros A. Karamanos, and Wouter Huinen

Abstract The framework of pipeline design in geohazard areas is presented in this Chapter. Following a brief overview of relevant design standards and recommendations, the main procedures for pipeline design against geohazards is outlined and a flowchart is presented. The concept of importance factor is introduced and pipeline classification is presented and defined using a risk assessment matrix. Furthermore, the important issues of route study and geological investigation are pin-pointed, and indicative values of soil properties for a variety of soil types are presented, to be used in the numerical models, to be employed in subsequent chapters of this book. Finally, a short introduction to indicative measures for mitigating ground movement effects on pipelines is offered.

G. J. Dijkstra (B) GJ-D Consult, 3155 BV Maasland, The Netherlands e-mail: [email protected] Tebodin Consultants & Engineers BV (Bilfinger Tebodin), 3122 HD Schiedam, The Netherlands A. M. Gresnigt · S. H. J. van Es Faculty of Civil Engineering, Delft University of Technology, 2628 CN Delft, The Netherlands e-mail: [email protected] A. M. Gresnigt Gresnigt Consultancy, 2651 XT Berkel en Rodenrijs, The Netherlands S. H. J. van Es TNO, Structural Reliability, 2628 CK Delft, The Netherlands S. A. Karamanos Department of Mechanical Engineering, University of Thessaly, 38334 Volos, Greece e-mail: [email protected] W. Huinen Bilfinger Tebodin Netherland B.V., 3122 HD Schiedam, The Netherlands © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. A. Karamanos et al. (eds.), Geohazards and Pipelines, https://doi.org/10.1007/978-3-030-49892-4_2

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2.1 An Overview of Pipeline Standards Referring to Geohazards The topic of “pipelines and geohazards” is one of the most challenging topics in pipeline design. It is a rather new topic that motivates quite some research in the engineering community. A significant part of this research has been motivated by the relatively recent need for constructing pipelines in areas of severe seismic activity. Furthermore, the development of advanced numerical simulation methodologies, such as finite elements, enable the investigation of ground-induced actions on pipelines in a more rigorous manner. This new research constitutes the necessary background for the development of recent design provisions and gradually enters into design standards and recommendations for pipeline design against geohazard action. The ASCE (1984) guidelines have been the first document that transferred and adjusted existing knowledge and design tools of seismic engineering into the earthquake analysis and design of buried pipelines. In particular, the document has been based mainly on the relevant work by Newmark, Hall and their associates at the University of Illinois (e.g. Newmark 1968; Newmark and Hall 1975). That document has also been the basis for the ALA (2005) guidelines, which contains the most complete set of provisions for this subject and has also constituted the basis for the recent Indian NICEE guidelines (2007) for the earthquake design of buried pipelines. The PRCI (2004) guidelines for the pipeline earthquake design and assessment can be considered as an update of the ASCE (1984) guidelines for buried pipelines transporting natural gas and liquid hydrocarbons. In particular, they accounted for more recent research on soil loading on buried pipelines, on strain-based pipeline limit states and proposed more advanced tools for pipeline stress analysis. More recently, PRCI (2009) has published design guidelines for the design of oil and gas pipelines in landslide areas, which adopt analysis and design methodologies similar to the ones proposed in PRCI (2004). ASME B31.4 and ASME B31.8 standards, widely used for oil and gas pipeline design, respectively, state that earthquake loading should be considered in pipeline design as an accidental (environmental) load. Nevertheless, those standards do not contain information on how seismic action on the pipeline should be computed. Similarly, Canadian standard CSA Z662 specifies fault movements, slope movements and seismic-related earth movements as additional loading that should be taken into account for pipeline design, but does not provide any further information on how those actions should be quantified. European standard EN 1594 has been a popular standard for the general design of high-pressure gas pipelines. Annexes D and E of this standard refer to landslide and high-seismicity areas respectively; in both Annexes, it is suggested that these geohazards should be taken into account in pipeline analysis and design, whereas some mitigation measures are also proposed. Similarly, European standard EN 14161, the European implementation of the ISO 13623 standard, in Sect. 6.3.3.3 provides

2 Pipeline Design Basics

19

general information and suggestions on seismic design. European standard EN 19984 provides guidance for the earthquake analysis and design of buried pipelines. One should notice that this standard has been developed primarily for the seismic design of liquid storage tanks, whereas limited information on buried pipelines is contained in Chap. 6 and Annex B. Furthermore, EN 1998-4 has been intended to cover all possible materials (steel, concrete, plastic), and therefore, it may not be a standard suitable for the seismic design of buried steel pipelines. However, some clauses of EN 1998-4 can be useful for pipeline design. Finally, among numerous national standards for pipeline design, the Dutch standard NEN 3650 is highlighted; despite the fact that earthquake action may not be an issue in The Netherlands, NEN 3650 contains important information for ground-induced actions on pipelines, especially for soil-pipe interaction in settlement areas. The latest edition of NEN 3650 (2020) contains, in addition, specific information for the design of pipelines under seismic loads, mainly caused by human activity, in particular due to the natural gas extractions in the north of the country.

2.2 Pipeline Design Procedures in Geohazard Areas 2.2.1 General Requirements and Design Procedure The basic design of buried pipelines in geohazard areas shall be aimed at public and environmental safety and safety of supply of energy, chemicals or water resources after a severe event associated with severe ground-induced actions. Towards this purpose, the pipeline design should include route studies and geological data collection and identify all potential risks that might influence the integrity of the pipeline throughout its service life, including the potential risk to the public in case of pipeline failure and the risk with regard to the required operation and safety of supply. If necessary, measures should be taken to mitigate the risks to a preset acceptable level imposed by legislation, national or international standards and by the pipeline owner. It is required that in the design phase of a buried pipeline, all operational, environmental and incidental actions that might influence the structural integrity of the pipeline are identified and accounted for. Geohazards, and in particular earthquake actions, may constitute major threats for pipeline integrity. Design guidelines for buried pipelines should therefore, incorporate guidance on the collection of possible loads and loading combinations, describe the relevant material properties, define limit states and safety margins related to failure of the pipeline and, last but not least, give guidance on how to apply reliable calculation models that provide reliable results. Stochastic variation of loads and of material properties must be accounted for. Large ground-induced deformations are caused by seismic activity, landslides, flooding, liquefaction of soils and sometimes even by leaking pipelines. In case of seismic activity, the return period has to be established in the design basis (see Sect. 2.2.3). Seismic activity may lead to large ground movement at faults where

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the related ground shaking may give rise to secondary damage such as landslides, liquefaction, etc. These large ground deformations often cause a loading pattern to the pipelines of exceptional magnitude, stretching the pipe materials to their utmost. For steel pipes, strain based design is then needed for a good analysis. Limit states have to be defined clearly. When analyzing the pipe-soil interaction, the non-linear behavior of both the chosen pipe steel grade, as well as the surrounding soil, should be incorporated in the calculation models. To be of use for a wide scope of possible users, guidance on the possible use of both advanced analyses, such as three-dimensional finite element (FEM) analyses, as well as more traditional analyses like Beams on Nonlinear Winkler Foundation, (BNWF; beam-type analyses with soil springs), is given. A comparison between the results of the more traditional analyses and the newly developed FEM methods and analytical methods will provide more insight in the practical range of application of each modeling technique. Figure 2.1 presents a possible design procedure, in relation to the scope and results of the GIPIPE project. In this chart, between brackets, the related chapters of this book, giving more explanation, are given.

2.2.2 Pipeline Integrity Assessment Due to Ground-Induced Action (General Methodology) When planning a new pipeline in areas where large ground-induced deformations may occur, a “risk inventory and evaluation” study (sometimes referred to as “R, I & E”), identifying and quantifying all possible risks for the pipeline, should be carried out. The steps to follow and the relevant activities are shown in Table 2.1, focusing on the possible occurrence of seismic events, landslides, liquefaction of soils, mining subsidence, frost heave (in areas of permafrost), etc. It is noted that seismic activity might also trigger other actions, such as liquefaction and/or landslides. Furthermore, one should notice that, during an earthquake, those ground-induced actions may not necessarily follow strong seismic action. In several cases, a rather small seismic action may result in a large ground movement. A typical example is the triggering of a landslide movement in an unstable slope. Furthermore, in a few instances, landslide movement may not be associated to an earthquake event. The steps stated in Table 2.1 should be accompanied and supported by a detailed route (alignment) study and by all possible geological, geotechnical and geomorphical data along the proposed pipeline route, including: • Route data, affected population, environmental data; • Soil data (including Geotechnical Hazardous areas); – stratigraphy, deep geology, ground water; – historical data, susceptible for landslides, frost heave, liquefaction; – seismic data, seismic zones e.g. EEA Technical Report (2010).

2 Pipeline Design Basics route study,field study and data collection (Sect. 2.3)

21

basic design, RI&E study (Sect. 2.2)

detailed geotechnical study (Sect. 2.4, 2.5)

mitigation measures to reduce risk possible? (Sect. 2.6,5.4) select design basis (Chap. 2)

large ground-induced deformations (Chap. 3) faults crossings: axial and transversal deformation (Chap. 5) landslide action: axial deformation (Sect. 6.3; Par.7.3.11) transversal deformation (Sect. 6.4)

pipe geometry material properties • steel grade • yield/tensile strength • stress-strain curve • toughness • weld imperfections • D/t ratio • initial ovality (Chap. 8)

limit states (Chap. 8)

experimental test programs & validation (Chap. 4) calculation models (Chap. 5, 6, 7, 9)

analytical models (Chap. 9)

BNWF models (Sect. 7.2)

calculation results (Chap. 5, 6 ,7, 9)

finite element models (FEM) (Chap. 5, 6; Sect. 7.3)

testing, calculation results vs. limit states (Chap. 5, 8)

Fig. 2.1 Design procedure and calculation models for buried pipelines under severe ground induced deformation

Based on all available data, possible measures for mitigating the potential risk must be evaluated, including re-routing of the pipeline. Where possible, mitigation measures should be applied, as briefly discussed in Sects. 2.6 and 5.4.

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Table 2.1 Steps and activities of risk inventory and evaluation R, I & E study for geohazards and pipelines Step

Activity

1

Planning the design process: definition of the level of detail and the tools to be used in the analysis

2

Hazard identification: identify all hazards, related to large ground induced displacements, with respect to the examined pipeline system

3

Qualitative analysis: screening activities aimed at identifying the critical pipeline locations that may require more detailed analyses

4

Quantitative analysis: quantify actions and the expected consequence on the pipeline. At local level the analysis is usually deterministic whereas at global level, especially in the cases of seismic hazard analysis, a probabilistic approach may be followed

5

Planning of mitigation measures: implementation of all the prevention and protection measures necessary to reduce the geohazard actions on the pipeline and minimize the consequences of ground displacements on the pipeline

2.2.3 Risk Evaluation, Reliability Level and Selection of Design Basis The pipeline must have the required level of reliability, at the envisaged operational, environmental and incidental loads, during its entire service life. When selecting the required level of reliability, both the failure probability of the pipeline under consideration, as well as, the consequences in terms of the risk to the public in case of pipeline failure, possible harm to the environment and economical losses, should be considered. One method for achieving the required level of reliability of the pipeline suffering from large, ground-induced deformations is to adjust appropriately the value of the annual probability of exceedance of the design ground-induced action, introducing the importance factor. For ground induced-actions resulting from seismic events the required level of reliability is normally acquired by multiplying the reference peak ground acceleration agr by the importance factor γ I . This has been elaborated in the Eurocode 8 (EN 19981) standard and is well established in regular seismic design of civil structures. The importance factor can also be applied in pipeline seismic design. In particular, it can be accounted for by designing the pipeline for a higher (seismic) hazard, which corresponds to a higher return period, or by designing the pipeline for the design basis earthquake and multiply the design action by the importance factor. Adopting this concept, the importance factor should multiply the value of permanent ground deformation (PGD), resulting from seismic action, calculated with the empirical expressions stated in Chap. 3. A note to clause 2.1 (4) of EN1998-1 provides the following relationships for determination of γ I : γ I ∼ (TLR /TL )−1/k

(2.1)

2 Pipeline Design Basics

23

Table 2.2 Criteria for determination of the importance factor, according to EN 1998-4 Importance class according to EN1998-4, clause 2.1.4

Recommended values for the importance factor (EN 1998-4, clause 2.1.4)

Importance class

Risk to life

γ I value

Class I

Low

Negligible

0.8

≈200

Class II

Medium

Medium

1.0

≈500

Class III

High

Large

1.2

≈1000

Class IV

Exceptional

Extreme

1.6

≈3000

Economical and social risk

Return period (years)

or γ I ∼ (PL /PLR )−1/k

(2.2)

where: γ I is the importance factor;k is an exponent, depending on seismicity, but generally in the order of 3;TL is the (design) period with the same probability of exceedance by the design seismic action as the reference probability of exceedance of the reference seismic action in TL R years;TL R is the period for which the reference seismic action is defined;PL is the required probability of exceedance of the seismic action in TL years;PL R is the reference probability of exceedance of the seismic action in TL years. Reliability differentiation and recommendations for the values of the importance factor for piping and pipeline systems are given in clause 2.1.4 of EN 1998-4. This is summarized in Table 2.2, indicating the approximate return period of the seismic action. However, the matrix introduced in Table 2.2 does not evaluate environmental risk. Also, the judgement whether a risk is low, medium or high is not very detailed. Table 2.3 introduces a more detailed risk assessment matrix that may be of help for the evaluation of all types of pipelines under all types of large, ground-induced deformations, and should be used in conjunction with Table 2.2.

2.3 Route Study and Evaluation of Landslide Hazard From the point of view of landslide hazard, the selection of a possible route for a new pipeline needs an appropriate documental analysis based on topographic maps, geological maps, aerial/satellite photos, risk maps edited by regional authorities and internal experience on pipelines buried in the same area. Topographic analysis allows individuating the best potential routes that usually are ridges and valley floors. Geological maps give information about lithotypes,

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Table 2.3 Detailed risk assessment matrix Importance class Consequence areas and impact level Environment

Health

Safety

Property

IV

Major contamination. Fast and widespread spill and release of hydrocarbons to sensitive environmental area

Major health impact. Widespread effects (irreversible or irreversible to a larger community like a village

Major safety impact. Large scale explosion and fire with potential to ignite other sources. One or more fatalities

Major property damage. Loss of infrastructure. Extended duration of production loss (>1 month duration)

III

Medium contamination. Release of hydrocarbons with limited potential to impact sensitive environment

Medium health impact. Reversible health effects to small community

Medium fire with potential to ignite other sources. No fatalities but potential for serious injuries

Damage to infrastructure that requires significant effort to repair. Production loss limited to less than 1 month duration

II

Minor impact. Localized spillage and minimum potential to impact sensitive populations

Minor health impact. Health impact (reversible limited to 1 or 2 individuals)

Minor safety impact. Fire with no potential to ignite other sources. Minor injuries. Treat and release cases

Short term production shutdown ( dcrit 2

(4.1)

In the above equation, σ (d  ) and μ(d  ) are given by Eqs. 4.2 and 4.3 respectively, where dcrit is the maximum displacement at which maximum soil resistance occurs. According to ALA guidelines (2001), dcrit can be taken equal to 0.1–0.2 in for dense-to-loose sand and d  is the difference between d and dcrit , (d  = d − dcrit ).

     σ d  = σr es − σr es − σ peak e−ad

(4.2)

     μ d  = tan δϕr es − tan δϕr es − tan δϕ peak e−ad

(4.3)

The finite element model that simulates the axial (pull-out) test is shown in Fig. 4.4. The pipeline was pulled outwards at the near end, whereas the far end remained free. For the accurate simulation of the axial pipe-soil interaction in the developed finite element model, a contact algorithm was implemented in ABAQUS, following the decay law of Eq. 4.1. More details concerning the numerical model can be found in the paper by Sarvanis et al. (2018). Figure 4.5 presents the comparison between the experimental results and the numerical predictions for tests AX1 and AX2. It is clear that there exists a very good agreement between the results obtained by the finite element analyses and the respective tests.

4.2.2 Transverse Pipe-Soil Interaction Tests and Numerical Simulation Pipe-soil interaction in the transverse direction of a buried pipeline is a significant parameter for the deformation of the pipe in the case of permanent ground deformations. Three transverse tests were conducted, using the experimental setup schematically shown in Fig. 4.6. The pipe was contained within a steel box and buried in sand. It was then pulled horizontally in the transverse direction with respect to its axis at a slow constant speed by means of two pulling bars that penetrated the box wall through small openings. These bars were connected to a stiff beam, bolted to the hydraulic actuator system. The vertical displacement of the pipe was prevented by

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a

b

c

d

Fig. 4.4 Finite element model for the numerical simulation of the pull-out (axial) tests: a 3D view, b front view, c side view and d top view

two parallel horizontal guide rails at the two ends of the pipe specimen, which also supported the self-weight of the pipe. To avoid possible bending or buckling of the pipe due to forces exerted by the soil, the pipe was filled with concrete. Figure 4.7 presents the test setup before backfilling, as well as, the deformed shape of the free soil surface after testing. The test instrumentation included a load cell to measure the pulling force, while the stroke was measured by the hydraulic actuator displacement sensor. The pipe surface was also instrumented with a flexible contact pressure sensor, wrapped around a sector of 180o at the front side of the pipe, in order to measure the pressure applied by the soil upon pipe displacement. Further details and discussion on the test results are reported by Sarvanis et al. (2018). A finite element model has been developed, to simulate the described transverse tests. The finite element model shown in Fig. 4.8 employs shell elements for the simulation of the pipe and solid elements for the soil and uses the modified MohrCoulomb model (Sarvanis et al. 2016) for the surrounding soil behavior. In order to reduce the computational effort without losing accuracy, only a slice of width equal to 1 m was modeled. The analysis proceeds moving the pipeline in the direction of x axis, as shown in Fig. 4.9, while the displacements in the direction of z axis are restricted, representing exactly the test procedure. A comparison between experimental results

4 Experimental Testing Conducted in the Course …

59

40 AX 1

35

FEM

Load [kN]

30 25 20 15 10 5 0 0

50

100

150

200

250

300

350

400

a

Axial Displacement [mm] 40 AX 2

35

FEM

Load [kN]

30 25 20 15 10 5 0 0

50

100

150 200 250 Axial Displacement [mm]

300

350

400

b

Fig. 4.5 Comparison between the finite element predictions and the results of a test AX1 and b test AX2

and the results obtained from finite element model described above is shown in Fig. 4.10 for experiments TR1, TR2 and TR3. The predictions of pipe-soil interaction obtained from the finite element model are quite satisfactory.

4.2.3 Large-Scale Landslide/Fault Tests and Numerical Simulation Four large-scale tests have also been performed by CSM in order to investigate the complex behavior of pipe-soil interaction in a special “landslide/fault” device. The setup has been composed by two fixed concrete boxes and one sliding box in-between and is schematically represented in Fig. 4.11. Specifically, the device consisted of three adjacent soil boxes, 25-m-long in total, in which the 219 mm-diameter 5.56mm-thick L450 (X65) steel pipe specimen was buried. During testing, the central soil

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Fig. 4.6 Experimental setup for transverse pipe-soil interaction

a

b

Fig. 4.7 Transverse soil-pipe interaction: a test setup before the test and b soil surface after the test

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a b

c

Fig. 4.8 Finite element model of transverse test: a 3D view, b different views of the 3D FE mesh and c front view of FE mesh

a

b

Fig. 4.9 Deformed shape of the FE model simulating the transverse test: a 3D view of displacement field and b 2D view of displacement field

box was being pulled by two hydraulic actuators in a direction transverse to pipe axis and slided on rails, while the other two boxes remained fixed. Each actuator could apply a maximum force equal to 400 tons, while the stroke exceeded 5 meters. As the pipe deformed transversally, its two ends were free to translate axially, while end rotations, vertical and transverse displacements were prevented. Test specimens were composed by five pipes welded by manual Shielded Metal Arc Welding (SMAW), adopting a welding procedure specification specifically developed for the GIPIPE project. The test instrumentation mainly included strain gauges to measure the local strains on pipe and to evaluate global pipe deflections by integrating strain measure over the pipe length, as well as laser LVDTs to measure the pipe displacement at

S. A. Karamanos et al. 175

175

150

150

125

125

100

100

Load [kN]

Load [kN]

62

75 TR 1

50

ASCE (1984)

0 50

100

150

200

250

300

350

FEM

25

ASCE (1984) 0

TR 2

50

FEM 25

75

400

0 0

50

100

Transverse Displacement [mm]

150

200

250

300

350

400

450

Transverse Displacement [mm]

a

b 175 150

Load [kN]

125 100 75 TR 3

50

FEM

25

ASCE (1984)

0 0

50

100

150 200 250 300 350 Transverse Displacement [mm]

400

450

c

Fig. 4.10 Comparison between the results of a TR1, b TR2 and c TR3 and the respective finite element predictions

Fig. 4.11 Three-dimensional representation of experimental setup for “landslide/fault” tests

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Fig. 4.12 Soil boxes and setup ready for large-scale testing

the two ends. Moreover, the force applied by the hydraulic pulling system was also measured. Figure 4.12 shows the soil boxes before sand filling and the setup ready for testing. A three-dimensional finite element model, shown in Fig. 4.13, which simulates the “landslide/fault” tests, was developed. The soil was simulated with reducedintegration solid elements, while for the pipe, reduced-integration shell elements were used. The middle box slides along the x axis, as shown in Fig. 4.13, while the two far boxes remain fixed. The comparison between the experimental results from the four tests and the respective finite element analysis results is shown in Fig. 4.14, for a middle box displacement equal to 600 mm (i.e. corresponding to 2.74

a

b

c Fig. 4.13 FE model of the landslide/fault test: a general configuration, b deformed shape of the FE model and c distribution of plastic strains in the middle block

64

S. A. Karamanos et al. 0.6

0.6

LD 1

0.5

0.4 FEM

0.3

Longitudinal strain [%]

Longitudinal strain [%]

0.5

0.2 0.1 0 -0.1 -0.2 -0.3

FEM

0.3 0.2 0.1 0 -0.1 -0.2 -0.3

-0.4 0

1

2

3

4 5 6 7 8 9 Longitudinal position [m]

10

11

-0.4

12

0

1

2

3

4 5 6 7 8 9 Longitudinal position [m]

10

11

12

0.6

0.6 0.5

0.5

LD 3

0.4

Longitudinal strain [%]

Longitudinal strain [%]

LD 2

0.4

FEM

0.3 0.2 0.1 0 -0.1 -0.2

LD 4

0.4 FEM

0.3 0.2 0.1 0 -0.1 -0.2 -0.3

-0.3

-0.4

-0.4 0

1

2

3

4 5 6 7 8 9 Longitudinal position [m]

10

11

12

0

1

2

3

4 5 6 7 8 9 Longitudinal position [m]

10

11

12

Fig. 4.14 Comparison between landslide/fault test results and respective finite element predictions on longitudinal strains along the pipe for imposed displacement equal to 600 mm

pipe diameters). The experimental measurements are in a very good agreement with the numerical results, indicating that the proposed finite element model is capable of predicting accurately the mechanical response of a buried pipe subjected to permanent transverse earthquake-induced ground deformation, such as fault action or landslide. For further information on the test setup, the finite element model and the numerical results the reader is referred to Sarvanis et al. (2018). In conclusion, rigorous numerical models, which employ solid elements and shell elements for simulating the soil and the pipe, referred to as 3D FEM, are capable of describing accurately the load-displacement response and the strains developed in buried pipelines under permanent ground deformations. Comparisons between numerical results and experimental measurements have indicated that horizontaltransverse soil-pipe interaction depends on both the residual internal angle of friction and the dilation angle, and that the use of a classical Mohr-Coulomb model can simulate soil resistance using the residual value of internal angle of friction and assuming a dilation angle equal to zero. Moreover, the mechanical response of a buried steel pipeline subjected to complex loading conditions has been examined using a special-purpose, large-scale “landslide/fault” testing device. Those largescale tests have been simulated with 3D FE models and the comparison between the numerical predictions and the relevant experimental measurements indicates that the proposed type of models is capable of predicting quite satisfactorily the mechanical response of a buried steel pipeline subjected to permanent ground actions.

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4.3 Experiments Performed in the TU Delft Laboratory 4.3.1 Experimental Procedure and Results Experiments modeling a pipeline crossing a strike-slip fault, under “virtual” soil conditions have been performed by TU Delft at laboratory conditions. The test setup aims at simulating a pipeline crossing a strike-slip fault. In such an event, lateral soil pressure and axial soil friction act on the pipeline. The test setup consisted mainly of two rectangular frames, one of which was moveable, simulating a fault movement of maximum displacement equal to 1480 mm. In the tests, the soil was simulated with appropriate nonlinear springs, herein referred to as “ringsprings”. In the laboratory setup, the 20-m-long pipeline specimen was connected to the two frames by means of the ringsprings, shown schematically in Fig. 4.15. The ringsprings consisted of a collapsing steel ring with appropriate diameter, thickness and yield strength, as shown in Fig. 4.16. Such ringsprings approximately have a linear elastic-perfectly plastic force-deformation behavior. The geometric and material characteristics of the ringsprings were chosen in a way that

moving frame

constant frame

ringsprings ringsprings pipe specimen

a constant frame

moving frame

pipe specimen

b Fig. 4.15 Schematic representation of the laboratoy test setup, with the ringsprings; a undeformed configuration; b deformed configuration

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F steel rods

undeformed ring

F collapsed ring

b a

deformed ring

F

F Fig. 4.16 Ringsprings representing the deformable soil surrounding the pipeline; a schematic representation of the spring ring; b deformed (collapsed) configuration of the ringspring

Table 4.3 Assumed soil properties

Sand

Clay

Parameter

Value

Parameter

Value

ϕ

32o

cu

50

ϕ

0o

γ

17 kN/m3

δ

16o

γ

18

δ

16o

kN/m3

soil properties of a cohesive soil (clay) and a non-cohesive soil (sand) are represented. The assumed parameters of these soils are presented in Table 4.3. For all tests, the burial depth of the pipe centerline was assumed at 2.5 m. The properties of the lateral soil springs were then determined in accordance with the Dutch adaptation in NEN 3650-1 of the formulae by Brinch-Hansen (1970) and Audibert and Nyman (1975, 1977). This results in an elastic-perfectly-plastic behavior of the lateral soil springs, allowing them to be mechanically modeled using the proposed ringsprings. The interaction between the ringsprings and the specimen determined the deformed shape of the pipeline. Six ringsprings were installed on each side of the fault and the loads of each ringspring were transferred to the specimen through two steel rods and two flexible steel straps allowing ovalization of the pipeline. Axial soil friction has been simplified to an axial force at the two ends of the pipeline using hydraulic actuators. Since the large majority of the axial friction occurs at a large distance from the fault, the axial force in the pipe is nearly constant within the area of interest, justifying the simplification adopted in the test setup. Figure 4.17 shows an overview of the test setup after performing a test, the ringspring construction, as well as a detail of the flexible steel straps. The applied force and the ringspring deformation were monitored continuously during the test at each ringspring. Moreover, sixty

4 Experimental Testing Conducted in the Course …

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b

a

c

Fig. 4.17 a Test setup after testing, b detail of the ringspring arrangement and deformed shape and c detail of the wide steel straps to connect the pipe specimen with the testing frame

six (66) strain gauges were attached to the pipe in longitudinal direction, distributed over every side of each specimen and concentrated in the area of expected maximum deformation. Finally, ovalization of the pipe was monitored at ten locations along the length of the specimen. A total of ten tests were performed using the above setup, including variations in different parameters, such as pipeline geometry, steel grade, internal pressure, types of soil and the presence or absence of a girth weld (GW) in a critical segment on either side of the fault. Finally, zero and small fault crossing angles β were considered, by adjusting the axial force in the pipeline, as shown in Fig. 4.18. A brief presentation of the experiments is offered below. Table 4.4 summarizes the testing program. For more details and a thorough discussion of the experimental results, the reader is referred to van Es and Gresnigt (2016a, b) and van Es (2016). Two pipe geometries were available: 406 mm×7.3 mm and 219 mm×5.6 mm (see also Table 4.4). Three levels of internal pressure have been considered, resulting in a hoop stress of 0, 25 and 50% of the specified minimum yield strength of the steel. The typical S-shape pipe response (see Fig. 4.17a) is the result of significant deformation in two pipeline segments, one on either side of the fault. These segments, in which the majority of the deformation occurs, are denoted as critical segments. The influence of the presence of a circumferential weld, often called girth weld (GW), in such a segment was investigated by placing girth welds in the critical segments of

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a

b

Fig. 4.18 Schematic representation of strike-slip crossing and definition of angle β: a positive value of angle β; b negative value of angle β

some specimens, while keeping these critical parts free of girth welds in the other specimens. The experimental configuration takes into account the axial (longitudinal) force developed in the pipeline as a result of the fault movement. This force is controlled by the following factors: • Axial elongation of the pipeline considering normal fault displacement perpendicular to the pipeline axis (β = 0) and the corresponding force is denoted as NS. • Additional axial shortening or elongation: for β < 0, the corresponding force N β is compressive, while for β > 0, N β is tensile. • An additional component (N P ) refers to the restrained axial contraction of the pipeline under influence of hoop stresses caused by internal pressure.

4 Experimental Testing Conducted in the Course …

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Table 4.4 Overview of the experimental program No. specimen

Pipe size (D × t)

Soil type

angle β (degrees)

GW (girth weld)

P/PY

T1

219 × 5.6

Sand

0

No

0

T2

406 × 7.3

Sand

0

No

0

T3

219 × 5.6

Clay

3.25

Yes

0

T4

219 × 5.6

Sand

1.50

No

0

T5

219 × 5.6

Sand

2.25

Yes

0.26

T6

219 × 5.6

Sand

0

No

0.51

T7

406 × 7.3

Clay

0

Yes

0.51

T8

406 × 7.3

Sand

0

Yes

0

T9

406 × 7.3

Sand

2.0

No

0

T10

406 × 7.3

Sand

2.0

No

0.25

The total normal force applied in the tests was found by summation of N S , N β and N P . Applying the appropriate axial force with the use of hydraulic actuators at the end of the specimen, allows for considering a non-zero fault angle, despite the fact that the test setup was only able to apply “fault movements” perpendicular to the pipeline axis. It is noted that for small fault angles (−5º< β < 5º), the lateral soil pressures are assumed to remain unchanged. In that case, an adjustment of only the axial force suffices to account for those small angles of crossing. Using a range of values for the parameters described above, the testing program consisting of ten bending tests was composed, shown in Table 4.4, and the experimental results are presented in Table 4.5. In all tests, the fault angle β was chosen negative or zero. As a result, the axial tensile force in the pipeline is relatively low, allowing for the occurrence of local buckling of the pipe wall, at a fault movement referred to as “critical fault movement” (ufault;crit ). Local buckling occurred in seven out of ten tests. In non-pressurized pipes, local buckles folded inward in a diamond pattern, while in pressurized pipes a single outward fold formed (see Fig. 4.19). In the specimens that exhibited local buckling, this occurred on both sides of the fault. Due to stiffness loss of the pipeline because of the first buckle, local buckling on the opposite side of the fault has been accelerated. The presence of a girth weld was found to affect the local buckling resistance. In the specimens featuring a girth weld in the critical segment, local buckling occurred at the vicinity of the girth welded side of the fault first. A comparison of nearly identical conditions is made by analyzing the results of experiments T2 and T8 (Table 4.5). These two tests have the same test parameters, with the exception of placement of the girth welds. The first local buckle in specimen T8 occurred at the girth weld, at fault displacement about 70% of the corresponding displacement of test T2. This effect of girth welds on local buckling resistance has also been noticed in previous studies (Mohareb et al. 1994; Tsuru and Agata 2012). The geometric distortions and the corresponding residual stresses associated with the girth weld are the main causes of

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Table 4.5 Summary of TU Delft experimental results Specimen No.

T1

Side of specimen

Girth Weld

Critical fault displacement

Fault displacement at tensile strain(m): 0.5%

1%

2%

Left

No

–

0.286

0.421

0.660

Right

No

–

0.288

0.430

0.692

Left

No

0.910

0.444

0.690

1.084

Right

No

0.840

0.425

0.660

1.100

T3

Left

No

1.201

0.631

0.986

1.420

Right

Yes

0.810

0.580

0.820

1.341

T4

Left

No

0.689

0.300

0.471

0.701

Right

No

0.771

0.310

0.501

0.701

Left

Yes

0.460

0.296

0.410

0.440

Right

No

0.569

0.290

0.430

0.570

T6

Left

No

–

0.287

0.451

0.798

Right

No

–

0.289

0.477

0.804

T7

Left

Yes

–

0.552

0.971

–

Right

No

–

0.601

1.001

–

Left

No

0.891

0.405

0.652

0.997

Right

Yes

0.590

0.471

0.645

1.033

T9

Left

No

1.120

0.740

1.285

–

Right

No

1.030

0.730

1.062

–

T10

Left

No

0.560

0.391

0.576

0.821

Right

No

0.641

0.380

0.559

0.791

T2

T5

T8

this effect. In addition, possible mismatch in material properties in the two adjacent pipes may also cause concentration of deformation and accelerate buckling. Preliminary analyses have indicated that very small non-zero fault angles (β=0) may result in axial force that is quite different than the force corresponding to the case of pipeline crossing the fault at a perpendicular configuration (β = 0). An example refers to the comparison between tests T1 and T4. In test T4, a 40% reduction of axial force was applied compared with T1 (van Es and Gresnigt 2016a, b). Furthermore, in specimen T4, local buckling occurred at a displacement of 689 mm, whereas no such failure occurred in specimen T1. This difference in structural response is due to the different normal force developed in the two specimens, despite the fact that specimen T4 configuration corresponds to a fault angle of only 1.5º, whereas specimen T1 corresponds to a normal crossing configuration. The main conclusion from this observation is that the pipeline response is quite sensitive to small variations of the angle β value about the value of zero. Another interesting observation refers to the stiffness loss at the intrados of the pipe due to a local buckle, whereas strains at the extrados of the pipe increase and

4 Experimental Testing Conducted in the Course …

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a

b Fig. 4.19 Local buckling formation in the finite element models and the respective tests (van Es and Gresnigt 2016a, b)

this phenomenon has been more pronounced in internally-pressurized specimens (see Fig. 4.19a). In case of pressurized specimen T5, the buckle occurred near the girth weld and with further increase of the applied displacement, extreme localization of deformation developed at one side of the girth weld. At displacement equal to 710 mm, pipe wall fractured (see Fig. 4.20). At 15 mm away from the location of the crack, the

Fig. 4.20 Fracture of T5 specimen near the weld due to tensile bending strain

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S. A. Karamanos et al.

measured longitudinal strain reached 4.5%, a significant strain value, implying that the strains at the crack location could be even higher. Possible causes that might have contributed to fracture are: (a) material properties of the steel; (b) concentration of deformation as a result of the presence of the girth weld; (c) influence of welding on the ductility. Towards this reason, two tensile tests were performed in longitudinal direction of the pipe that fractured. In these tensile tests, Y/T ratios of 0.91 and 0.95 were found. These values are considered to be too high according to the maximum Y/T ratio allowed in international standards, such as DNVGL-ST-F101, API 1111, ISO 3183 or EN 1594, especially for pipes used in high-strain applications, referred to as PSL2 pipes, while no maximum is given for PSL1 pipes, i.e. pipes with standard Product Specification Level. Regardless of the standard, the measured values of 0.91 and 0.95 are too high, strongly contributing to the occurrence of fracture. A summary of all test results is presented in Table 4.5. For each specimen, on each side of the fault, the critical fault movement is listed, as well as the first occurrence of certain values of tensile strains located at the “extrados” of the bent pipe specimen. The tensile values may have been reached earlier in the pipe segments in-between the strain gauges, where no data are available. Displacements corresponding to tensile strain values ranging from 0.5 to 2% are reported, which are recommended as allowables in international design standards. The performed experiments have reached the ultimate limit values suggested by those standards; in all tests, tensile strains exceeded 1%, while in eight out of ten tests, tensile strains reached values beyond 2%. After local buckle formation on either side of the fault, strains and deformations increased rapidly due to loss of stiffness, and the events that occurred after buckling are displayed with italics in Table 4.5.

4.3.2 Numerical Simulation A first attempt to simulate the above experiments has been performed with a threedimensional numerical model. The model consisted of two main parts: (a) the pipe specimen, modeled with shell elements (S4R) and (b) the non-linear springs accounting for pipe-soil interaction. The pipeline was modeled using four-node reduced integration shell elements, with elasto-plastic material properties using a Von Mises plasticity model with isotropic hardening. The soil springs were modeled using axial elasto-plastic connectors, which were given the appropriate properties to simulate the interaction between the pipeline and the surrounding soil. A distributing coupling has been employed in order to connect the pipe with the nonlinear springs in an appropriate manner. The measured properties of the steel pipe and the rings have been used to model the pipeline and the soil springs. The finite element model also included initial geometric imperfections in the shape of a buckling eigenmode of a very small amplitude. Finally, in the critical segment of the pipe, the finite element mesh has been quite dense, while for the other pipe segments a coarser mesh was chosen. More information on this simulation can be found in the thesis by van Es

4 Experimental Testing Conducted in the Course …

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(2016). In Fig. 4.19, a comparison is presented in terms of the local buckle shapes observed in the experiments and those obtained with the finite element model. In Fig. 4.21, the variation of strain along the pipe for specimens T1 and T8 is presented, at a fault movement of 1480 mm. In addition to the above numerical simulation, a more elaborate finite element model has been developed, representing more accurately the physical problem of a pipeline crossing a tectonic fault. The numerical model is similar to the one employed in Sect. 4.2 for the simulation of the large-scale experiments, and consists of a main part of a 60-m-long pipeline segment embedded in soil conditions corresponding to the ones in Table 4.3, also considered in the experiments. The soil is discretized with three-dimensional eight-node solid reduced-integration “brick” elements (denoted as C3D8R in ABAQUS), whereas four-node reduced-integration shell finite elements (S4R) have been employed to simulate correctly the steel pipeline. Furthermore, appropriate contact conditions have been imposed in the soil-pipe interface to 0.03

a

Experiment Numerical

Axial strain

0.02

0.01

0

specimen T1

-0.01

-0.02 -10000

-7500

-5000

-2500

0

2500

5000

7500

10000

Distance from the fault (mm) 0.03

b

Experiment

Axial strain

0.02

Numerical

0.01

0

-0.01

-0.02 -10000

Specimen T8

-7500

-5000

-2500

0

2500

5000

7500

10000

Distance from the fault (mm)

Fig. 4.21 Strain comparison of FE model and test results for: a T1 specimen and b T8 specimen, at a fault movement of 1480 mm

74

S. A. Karamanos et al.

describe accurately the complex soil-pipeline interaction phenomena during fault movement. Apart from this basic length represented rigorously with finite elements, the pipeline extending on either side of the model boundaries is simulated with two nonlinear springs at the two ends of the main 60-m-long part, which account for the continuity of the pipeline, representing the effect of an infinite-length soil-pipeline system. The width and the height (depth) of the finite element model are 10 m and 5 m respectively and the burial depth of the pipe centerline is assumed at 2.5 m, as considered in the experiments. The central part of the steel pipeline around the fault, where maximum stresses and strains are expected, has a fine mesh of shell elements. Similarly, the finite element mesh for the soil is more refined in the region near the fault, whereas a coarser mesh has been used elsewhere. The interaction between the soil and the pipe is considered through a contact algorithm, controlled by an appropriate interface friction coefficient μ equal to 0.3, a value that has been used in several previous publications (Vazouras et al. 2010, 2012, 2015). A Von Mises plasticity model with isotropic hardening is employed for the steel pipe material, whereas the mechanical behavior of soil material is described through an elastic–perfectly plastic Mohr–Coulomb constitutive model. The fault movement is considered to occur within a narrow transverse zone of width w, taken equal to 0.33 m, a value that has been suggested in previous works (Vazouras et al. 2015). The angle β between the fault plane and the normal on the pipeline axis in the model has been considered equal to different values, so that the experiments of Table 4.5 are represented correctly. The results from the numerical simulation are reported in Table 4.6 and indicate the same trends shown by the experimental results (see Table 4.5). More specifically, case C1 refers to a 219-mm-diameter non-pressurized pipe buried in sandy soil, with a fault movement perpendicular to the pipe axis (β = 0°), a case comparable with experiment T1. At the maximum fault movement of 1500 mm, the numerical model indicated that no local buckling has occurred, a result which is in accordance with the corresponding experimental result. The diagram shows that, in the early stages of deformation, the pipeline behaves symmetrically with respect to the fault location. Furthermore, the results indicate that the tensile strains are no longer increasing for increasing fault movement after some threshold value has been reached. Instead, inelastic deformation spreads out over a longer length of the pipeline. The critical fault movement for reaching the tensile limit strains of 0.5%, 1%, 2%, 3% is somewhat larger, yet quite satisfactory, compared to the strains developed in specimen T1. Case C5 also refers to a 219-mm-diameter pipeline buried in sandy soil, but it is internally-pressurized. The analysis simulates a pipeline crossing a fault movement with an angle equal to −2.25° to its axis (β = −2.25°). The internal pressure corresponds to a hoop stress of approximately 25% of the specified minimum yield stress. In this case, local buckles are formed at fault movements equal to 420 mm and 500 mm on the left side and right side respectively. The local buckle on the left side of the fault occurred near a girth weld, which was simulated in the model with a circumferential ring of elements having overmatched material properties. The location of the weld was at the critical area of the specimen, coinciding with the

4 Experimental Testing Conducted in the Course …

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Table 4.6 Results from the finite element simulation of experiments Analysis

C1

Side of specimen

GW

Critical displacement (m)

Displacement for tensile strain (m) 0.5%

1%

2%

3%

Left

No

–

0.367

0.480

0.750

–

Right

No

–

0.367

0.480

0.890

–

Left

No

0.785

0.539

0.785

1.200

1.355

Right

No

0.800

0.491

0.800

1.350

–

C3

Left

No

0.800

0.466

0.567

0.753

0.891

Right

Yes

0.567

0.540

0.767

1.100

–

C4

Left

No

0.518

0.382

0.490

0.661

0.991

Right

No

0.591

0.384

0.500

0.700

–

Left

Yes

0.420

0.301

0.361

0.436

0.495

Right

No

0.500

0.368

0.458

0.572

0.675

C6

Left

No

–

0.337

0.428

0.504

0.564

Right

No

–

0.337

0.431

0.510

0.576

C7

Left

Yes

–

0.490

0.600

0.790

0.860

Right

No

–

0.580

0.750

0.885

1.057

Left

No

0.630

0.464

0.692

1.088

1.500

Right

Yes

0.543

0.368

0.464

0.594

0.927

C9

Left

No

0.700

0.675

0.853

1.200

–

Right

No

0.600

0.550

0.821

1.121

–

C10

Left

No

0.485

0.450

0.543

0.721

0.850

Right

No

0.517

0.456

0.563

0.835

1.210

C2

C5

C8

location in specimen T5. The numerical results regarding location of buckle, critical fault movement and the corresponding strains are very close to the ones obtained from the corresponding test of specimen T5.

4.4 Small–Scale Experiments Performed at NTUA To shed light on the near-field response in the case of fault crossing and to provide a benchmark for the validation of numerical tools, a series of small-scale experiments were conducted in the Laboratory of Soil Mechanics of NTUA. The experimental series was divided in three stages: (a) study of the fault rupture propagation without the presence of the pipe, (b) investigation of the fault–pipe interaction and (c) detailed measurement of representative cases. From the total of 26 experiments, two experiments are shown herein as representative and illustrative examples.

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4.4.1 Experimental Setup The response of a non-pressurized steel pipeline with D = 35 mm and t = 0.5 mm subjected to both normal and reverse faulting is studied. A custom-built apparatus was used to simulate fault rupture propagation and Fault Rupture–Soil–Structure Interaction (Fig. 4.22). It comprises a stationary and a movable part that electronically translates upwards or downwards, applying fault displacement (reverse or normal) in a quasi-static manner. Maintaining constant dip angle α = 45° for both fault types, bedrock dislocations up to 0.15 m are achieved. The inner dimensions of the box are 2.65 m × 0.9 m × 0.9 m (length × width × height). Determined by the dimensions of the split-box, a limited length of the pipeline (about 70D) was modeled. The pipeline was placed in the middle of the container and embedded into a 0.65 m deep stratum of dense sand. Admittedly, the experimental setup comes with two major drawbacks. Firstly, to achieve a realistic pipe flexural behavior, an unrealistically-high embedment depthto-pipe diameter ratio (h/D ≈ 16) was selected (a fundamental limitation of smallscale 1-g experiments). As a result, the available depth of the container is practically exhausted and the pipe is placed relatively close to the bottom boundaries, a fact that may have its impact on the soil—pipe interaction. Secondly, due to limited length, the boundary conditions at the ends of the pipe models are oversimplified, as no attempt was made to axially restrain them in order to simulate the effect of the far-field soil. Such a task would not be easy, since it would require the appropriate physical representation of the axial soil resistance provided by the far-field soil, an addition that would add significant uncertainty in the model. Hence, similarly to previous experimental studies (e.g. Saiyar et al. 2015), a free-end boundary condition had to be

2.65 m

pipe specimen strain gauges

0.55 m 0.65 m 0.9 m

0.9 m

actuator

Fig. 4.22 Schematic illustration of the fault rupture simulation (split-box) apparatus of the NTUA Soil Mechanics Laboratory: cross-section schematics depicting the dimensions of the box and the experimental setup

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stress (MPa) 400 D = 35 mm t = 0.5 mm

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tensile coupon test specimen 0 0

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Fig. 4.23 a Cross-section of the model pipe used for pipe specimens and b stress-strain curve of the model test material

reluctantly adopted, only for the sake of simplicity, while the numerical verification study modeled exactly this free-end boundary. However, for the simulation of an actual prototype problem one should account for the effect of the axial restriction provided by the far-field soil.

4.4.2 Pipe Specimens Welded tubes made of stainless steel grade AISI Type 444 were used as model pipes. The cross- section of those pipes is depicted in Fig. 4.23a. Their stress-strain curve obtained with uniaxial tensile loading is shown in Fig. 4.23b. The tubes are mirror polished and therefore, the coefficient of skin friction characterizing their smooth surface was very low.

4.4.3 Soil Material Longstone sand, an industrially produced quartz sand with d50 ≈ 0.15 mm and uniformity coefficient Cu ≈ 1.42 (Fig. 4.24a), was used for the experiments. Its void ratios at the loosest and densest state have been measured as emax ≈ 0.995 and emin ≈ 0.614 (according to ASTM D4253 and D4254). An electronicallycontrolled sand raining system (Fig. 4.24b) was employed in preparing a dry, uniformly dense (Dr ≈ 90%), soil profile. It is designed to produce soil samples of controllable Dr by adjusting the pluviation height, the speed and the aperture of the soil bucket. The raining system has been calibrated through a series of pluviation tests some results of which can be found in Anastasopoulos et al. (2010). A series

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passing (%)

80 60 40 20 0 0.01

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0.1

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a Fig. 4.24 a The grain size distribution of the Longstone Sand and b photo of the Fault-Rupture Box showing the sand “raining” dry pluviation process

of direct shear-box tests were conducted to characterize the soil shear strength at peak and residual conditions. As shown in Fig. 4.25 that summarizes those results, a strong dependence of the mobilized friction angle on the level of stress is evident. To account for the soil behavior at low overburden stresses that govern the small-scale experiment, a logarithmic model was fitted to the results. For the estimation of the dilation angle ψ, the Bolton (1986) expression was followed: τ

residual friction angle 50 φ (deg)

τp τres

dy dp

df

d

40 peak σv

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residual

20 0

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vertical stress σv (kPa) Fig. 4.25 Direct shear tests results of the Longstone at Dr ≈ 90%: measured peak and residual friction angle versus vertical effective stress accompanied with a legend denoting the characteristic horizontal displacements used for the calibration of the soil constitutive model

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(4.4)

4.4.4 Instrumentation and Monitoring In order to monitor the pipe response within the soil, strains along the bottom centerline of the pipe were measured using a series of 12 strain gauges. Produced by Kyowa, the strain gauges were 10 mm long with ability to measure strain deformations up to 1%. They were attached to the pipe with the aid of a chemical adhesive and were coated with scotch tape for protection from the moving soil. The two side walls of the Fault-Rupture apparatus were transparent to allow visual observation. A high-resolution camera on fixed position was used to monitor soil deformations and rupture propagation. A series of five laser transducers were used to scan the surface at progressively increasing fault displacements to monitor deformations of the surface.

4.4.5 Finite Element Modeling Figure 4.26 summarizes selected attributes of the three-dimensional FE mesh for simulating (as faithfully as possible) not reality but the small-scale physical model tests. Nonlinear material behavior of both soil and pipe, as well as nonlinear geometry effects, are considered. Eight-noded hexahedral continuum elements (C3D8) simulate the soil and elasto-plastic S4R shell elements simulate the pipeline. The soil–pipeline interface obeys a Coulomb’s friction law (with a low friction coefficient μ = 0.2) and allows for separation of the pipe surface from the soil medium. Figure 4.26a portrays a deformed snapshot of the model for the case of normal faulting. The bottom boundary represents the stiff bedrock: it is split in two parts, one remaining stationary and the other translating imposing a step-like dislocation. The analyses were conducted in two steps; in the first step the geostatic equilibrium is obtained, while in the second step the boundary differential fault displacements (“dislocation”) are applied in adequately small, quasi-static analysis increments.

4.4.6 Soil Constitutive Model Past studies (e.g. Bray et al. 1994) suggest that for the successful implementation of the FE method in the simulation of problems where shear deformations of the soil govern the response, its softening stress-strain response should be accounted for. Following this recommendation, this study has adopted the modified Mohr-Coulomb

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z y

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Fig. 4.26 3D Finite Element model: a view of the mesh used to reproduce the experiments highlighting the boundary conditions for normal faulting; b out-of-plane cross-section with c distribution with depth of secant Young’s modulus

(MC) model of Anastasopoulos et al. (2007), which linearly degrades the friction angle (from ϕ peak to ϕ res ) and the dilation angle (from ψ peak to 0) as functions of the octahedral plastic strain. Use of the elasto-plastic MC failure criterion implies the a priori selection of a constant value of the Young’s modulus E, presumed compatible with the expected level of stress and strain. This involves a quite challenging task—to estimate in advance the expected level of stress and strain. To this end, the procedure described in Tsatsis et al. (2019) is followed. According to Anastasopoulos et al. (2007), the linear pre-yield behavior can be described as:

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E y = 2G y (v + 1) = 2

81

τy (v + 1) γy

(4.5)

where γ y and τ y = yield strain and stress of the soil specimen and ν = Poisson’s ratio. Applying the above equation we can deduce a distribution of E y , plotted in Fig. 4.26c (DS yield state); this distribution corresponds to yielding conditions under minimal change in stress level. However, for the specific problem of dip-slip faulting, the stress field may alter significantly compared to the initial geostatic. More specifically, in normal faulting, horizontal stresses drop towards active state (Anastasopoulos et al. 2008). The opposite is the case with thrust faulting where the soil is loaded towards its passive state. Assuming that E sec is proportional to the square root of mean effective stress and placing our focus on the large-strain domain, soil stiffness has been here approximated according to the following relationship:  E sec =

1 + 2K e f f Ey 1 + 2K 0

(4.6)

where K O is the “at-rest” coefficient of lateral earth pressure and E y can be obtained from direct shear testing; K eff can be approximated by active earth pressure coefficient K a for normal faulting and by passive earth pressure coefficient K p for reverse faulting. In addition, this secant elastic modulus E sec refers to yielding state, corresponding to a rather large strain. In the close proximity to the rupture fault this is the indeed case, yet for the soil further away, assuming such a large strain would lead to underestimation of its stiffness that in turn directly governs any soil-pipeline interaction phenomena. Results from a preliminary sensitivity investigation showed that a local increase of stiffness, by a factor of 1.5 with respect to Eq. 4.6, within a radius of 3D around the pipeline (shaded area in Fig. 4.26b) is a reasonable compromise between the accurate reproduction of rupture propagation and the need to capture pipeline distress. Figure 4.26c indicates the E sec– z relationships adopted for the normal and reverse fault–pipe interaction simulations. Finally, to account for the inherent mesh dependency of a strain-softening model, a scaling law is considered to calculate the numerical plastic strains (dependent on the element characteristic length d FE ) based on the plastic strains measured during direct shear testing. Thus, the shear-band width is indirectly accounted for by appropriately scaling the post peak stress–strain relationship according to the following equation (Anastasopoulos et al. 2007): f

γ pl = f

d f − dp d p − dy + h dF E

(4.7)

where γ pl is the octahedral plastic shear strain at the end of softening, d y , d p , and df are the measured horizontal displacements at yield, peak strength and residual state, respectively (indicated in Fig. 4.25) and h is the thickness of the direct shear specimen.

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4.4.7 Comparison Between Experimental Results and Numerical Predictions Figure 4.27 compares the experimental results with the numerical prediction for the normal fault experiment. Figure 4.27a portrays the soil failure mechanisms developing during the evolution of normal faulting, demonstrating a satisfactory qualitative agreement between experiments and analysis. Earlier experimental studies (Cole and Lade 1984, Bransby et al. 2008) and field observations (Bray et al. 1994) have shown that normal faulting leads to progressive development of multiple rupture planes. The same trend is followed here, where the dislocation of the moving base initially provokes an almost vertically propagating rupture. However, this is a localized secondary rupture attributed to the brittleness of the material that fails to accommodate the deformation in a quasi-elastic manner. Increasing the bedrock offset reveals the main rupture that ultimately emerges at the surface, for vertical bedrock dislocation equal to 15 mm. Further increase in the imposed bedrock dislocation leads to the development of a secondary antithetic rupture. As the bedrock displacement increases further, deformation accumulates along these two ruptures, without any additional change on the rupture pattern. Between the primary and secondary rupture, a clear gravity graben is formed. The numerical model predicts quite accurately all the aforementioned propagation-related phenomena. Figure 4.27b compares the deformation of the pipe at the end of 120 mm of downward dislocation of the base with the respective numerical prediction. Evidently, the soil movement presented an adverse loading case for the buried pipe: plastic residual deformations are observed at the vicinity of the fault trace, with an apparent dent of the pipe wall (local buckling) at the bottom side. It should be noted that, in case of a normal fault and a continuous pipeline, a S-shaped deformation pattern of the pipeline will occur, showing a larger distance between the two points of maximum curvature than in case of the reversed fault, presented hereafter. This S-shape is not visible in Fig. 4.27b because the failure plane is “active” and the test facility is too short. As depicted in the deformed mesh with axial strain contours, the numerical model predicts quite satisfactorily the deformation pattern of the pipe, the location and the shape of the local buckle. In a similar manner, Fig. 4.28 presents a comparative assessment of the numerical model to predict the experimental results for the case of reverse faulting. Snapshots depicting the reverse fault rupture propagation are presented in Fig. 4.28a. Contrary to normal faulting, with thrust faulting the soil develops a single rupture plane (Ahmed and Bransby 2009; Loli et al. 2011), as shown in both experiment and analysis. The rupture now propagates at a smaller dip angle, and requires much larger bedrock dislocations to reach the surface compared to the normal faulting (“passive” versus “active” failure planes). The replication of the experiment is fairly precise: the rupture path is faithfully captured along with the magnitude of bedrock displacement that provokes fault trace emergence in the ground surface. Forced to comply with the soil deformations, the pipe acquires a double-curvature deformation pattern (S-curve), forming two points of excessive bending (Fig. 4.28b). With the increase in

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δz = -10 mm

δz = 15 mm

83

δz = 25 mm

γppl

γres pl

plasƟc shear strain

a

fault trace

b

Fig. 4.27 Comparison between experimental data and numerical predictions for the reverse fault experiment: a photos of the rupture path during the experiment and snapshots of the deformed soil model of the analysis with the corresponding plastic shear strain contours for reverse faulting and b post-testing photos of the model pipe and views of the deformed FE shape with axial strain contours for base vertical displacement of 120 mm

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δz = 20 mm

δz = 30 mm γppl

δz = 40 mm

(b)

γrespl

plastic shear strain

a

b Fig. 4.28 Comparison between experimental data and numerical predictions for the reverse fault experiment: a photos of the rupture path during the experiment and snapshots of the deformed soil model of the analysis with the corresponding plastic shear strain contours for reverse faulting and b post-testing photos of the model pipe and views of the deformed FE shape with axial strain contours for base vertical displacement of 120 mm

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the fault offset, the pipe yields and ultimately buckles at these points. Once again, the numerical calculation results closely imitate the response of the pipe, predicting the location of the two maximum curvature points and the formation of local buckling.

4.5 Conclusions The experiments conducted in the framework of the GIPIPE project have been pioneering and unique. Primarily, they have been used as benchmark to validate rigorous numerical models, also developed within the same project. The rigorous numerical models can successfully describe the pipe response and the interaction between the pipe and the surrounding soil, and constitute a powerful tool for predicting pipeline response in fault crossings. The results from the three axial tests (pull-out) show that the dilatancy of the sand can cause significant increase of pull-out force, though it is recognized that under field conditions the trench backfill may not always develop sufficient compaction to develop a dilatancy effect which is comparable to the test results. Furthermore, three transverse tests were successfully simulated in order to verify the prediction capabilities of the model for describing accurately transverse pipe-soil interaction. The large-scale “landslide/fault” experiments conducted by CSM (outdoor) and TU Delft (indoor) elucidated pipeline response and deformation in complex loading conditions. In addition, the small-scale NTUA experiments have examined the fault rupture propagation problem in free field conditions and subsequently, pipe response under fault rupture. The results of the numerical models compare very well with the experimental results for all examined cases. The agreement between the numerical and the experimental results builds confidence to the rigorous numerical tools, suggesting that these numerical models can be used for simulating a wide range of problems involving soil-pipe interaction under permanent ground deformation and for performing extensive relevant parametric analysis. Nevertheless, it should be underlined that those models require demanding computational skills in modeling and may not be suitable for everyday engineering practice. In such cases, more simplified finite element models should be used, as described in Sect. 7.2. However, it was demonstrated that the rigorous three-dimensional models constitute a powerful tool for simulating ground-induced actions in the pipeline, in cases where increased accuracy is required. A detailed description of those rigorous models is offered in Sect. 7.3.

References ABAQUS (2014) Users’ manual. Simulia Providence, RI, USA Ahmed W, Bransby MF (2009) Interaction of shallow foundations with reverse faults. J Geotech Geoenviron Eng 135(7):914–924 American Petroleum Institute (2018) Specification for line pipe. API 5L standard, Washington, DC

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American Petroleum Institute (2015) Design, construction, operation, and maintenance of offshore hydrocarbon pipelines (limit state design). API 1111 standard, Washington, DC American Society of Civil Engineers (1984) Guidelines for seismic design of oil and gas pipeline systems. Committee on Gas and Liquid Fuel Lifelines, Technical Council on Lifeline Earthquake Engineering, American Society of Civil Engineers, Reston, Virginia Anastasopoulos I, Gazetas G, Bransby MF et al (2007) Fault rupture propagation through sand: finite element analysis and validation through centrifuge experiments. J Geotech Geoenviron Eng 133(8):943–958 Anastasopoulos I, Georgarakos T, Georgiannou V et al (2010) Seismic performance of bar-mat reinforced-soil retaining wall: shaking table testing versus numerical analysis with modified kinematic hardening constitutive model. Soil Dyn Earthq Eng 30(10):1089–1105 Anastasopoulos I, Gerolymos N, Gazetas G, Bransby MF (2008) Simplified approach for design of raft foundations against fault rupture. Part I: Free-field. Earthq Eng Eng Vib 7:147–163 Audibert JME, Nyman KJ (1975) Coefficients of subgrade reaction for the design of buried pipelines. In: Proceedings of the 2nd ASCE speciality conference on structural design of nuclear plant facilities, New Orleans Audibert JME, Nyman KJ (1977) Soil restraint against horizontal motion of pipes. J Geotech Eng-ASCE 103(10):1119–1142 ASTM (1991) Test method for minimum index density and unit weight of soils and calculation of relative density. D4254, ASTM, West Conshohocken, Pa ASTM (1993b) Test methods for maximum index density and unit weight of soils using a vibratory table. D4253, ASTM, West Conshohocken, Pa Bolton MD (1986) The strength and dilatancy of sands. Geotechnique 36(1):65–78 Bransby MF, Davies MCR, Nahas AE (2008) Centrifuge modelling of normal fault–foundation interaction. B Earthq Eng 6(4):585–605 Bray JD, Seed RB, Cluff LS, Seed HB (1994) Earthquake fault rupture propagation through soil. J Geotech Eng-ASCE 120(3):543–561 Brinch Hansen J (1970) A revised and extended formula for bearing capacity. Bull No 28, The Danish Geotechnical Institute, Copenhagen, Denmark Cole DA Jr, Lade PV (1984) Influence zones in alluvium over dip-slip faults. J Geotech Eng-ASCE 110(5):599–615 Comité Européen de Normalisation (2013) Gas supply systems—pipelines for maximum operating pressure over 16 bar, Functional requirements. EN 1594 Standard, Brussels, Belgium DNVGL-ST-F101 (2017) Submarine pipeline systems. DNVGL standard (new version of DNVOS-F101), Oslo, Norway ISO 3183 (2012) Petroleum and natural gas industries—steel pipe for pipeline transportation systems Karimian H (2006) Response of buried steel pipelines subjected to longitudinal and transverse ground movement. Dissertation, The University of British Columbia Loli M, Anastasopoulos I, Bransby MF et al (2011) Caisson foundations subjected to reverse fault rupture: centrifuge testing and numerical analysis. J Geotech Geoenviron Eng 137(10):914–925 Mohareb ME, Elwi AE, Kulak GL, Murray DW (1994) Deformational behaviour of line pipe. Structural engineering Report No. 202, University of Alberta, Depatrment of Civil Engineering Nederlands Normalisatie Instituut (2020) Requirements for pipeline systems. NEN 3650, part-1: general and part-2: steel pipelines, Delft, The Netherlands Saiyar M, Ni P, Take WA, Moore ID (2015) Response of pipelines of differing flexural stiffness to normal faulting. Géotechnique 66(4):275–286 Sarvanis GC, Ferino J, Karamanos SA et al (2016) Soil-pipe interaction models for simulating the mechanical response of buried steel pipelines crossing active faults. In: Proceedings of the International society of offshore and polar engineers, ISOPE2016, Rhodes, Greece Sarvanis GC, Karamanos SA, Vazouras P et al (2018) Permanent earthquake-induced actions in buried pipelines: numerical modeling and experimental verification. Earthq Eng Struct D 47(4):966–987

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Scarpelli G, Sakellariadi E, Furlani G (2003) Evaluation of soil-pipeline longitudinal interaction forces. Rivista Italiana di Geotecnica 4:24–41 Tsatsis A, Loli M, Gazetas G (2019) Pipeline in dense sand subjected to tectonic deformation from normal or reverse faulting. Soil Dyn Earthq Eng 127. https://doi.org/10.1016/j.soildyn.2019. 105780 Tsuru E, Agata J (2012) Buckling resistance of line pipes with girth weld evaluated by new computational simulation and experimental technology for full-scale pipes. Int J Offshore Polar 22(1):76–82 van Es SHJ (2016) Inelastic local buckling of tubes for combined walls and pipelines. Dissertation, Delft University of Technology van Es SHJ, Gresnigt AM (2016a) Experimental and numerical investigation into the behavior of buried steel pipelines under strike-slip fault movement. In: Proceedings of the 11th International pipeline conference, IPC2016, Calgary, Alberta, Canada van Es SHJ, Gresnigt AM (2016b) Design and results of fault movement tests on buried pipelines: Research Report for RFCS project GIPIPE. TU-DELFT Vazouras P, Karamanos SA, Dakoulas P (2010) Finite element analysis of buried steel pipelines under strike-slip fault displacements. Soil Dyn Earthq Eng 30(11):1361–1376 Vazouras P, Karamanos SA, Dakoulas P (2012) Mechanical behavior of buried steel pipes crossing active strike-slip faults. Soil Dyn Earthq Eng 41:164–180 Vazouras P, Dakoulas P, Karamanos SA (2015) Pipe–soil interaction and pipeline performance under strike–slip fault movements. Soil Dyn Earthq Eng 72:48–65

Chapter 5

Pipeline Response in Strike-Slip (Horizontal) Fault Crossings Polynikis Vazouras, Panos Dakoulas, Kyriaki A. Georgiadi-Stefanidi, and Spyros A. Karamanos

Abstract Numerical results for strike-slip (horizontal) fault crossings are presented, using advanced three-dimensional finite element models. The model consists of a soil prism and employs shell elements for the pipeline and “brick” continuum elements for the soil. Appropriate boundary conditions are imposed, so that continuity of the pipeline outside the prism is taken into account. Some indicative mitigation measures are also proposed. In the final part of the chapter, the important issue of buried pipeline bends (elbows) is treated. Individual bends with axial tension are analyzed first, to examine their mechanical behavior and to establish a load-displacement relationship. Subsequently, using those load-displacement relationships, a strikeslip fault crossing case is analyzed, for the purpose of examining the effect of bends on pipeline response. It is concluded that, the proper use of bends at a distance from the fault line, may be beneficial for the pipeline, reducing the strain developed in the pipeline wall.

5.1 Introduction The response of continuous steel pipelines under horizontal (strike slip) fault action, apart from its significance in practical pipeline engineering applications, constitutes a benchmark for validating numerical models. The use of simplified numerical models as described in Sect. 7.2, as well as analytical models in Chap. 9, has been driven mainly by the need for simulating pipeline deformation in horizontal faults. Herein, the numerical simulation of welded steel (continuous) pipeline deformation under horizontal fault action is presented, using rigorous finite element models. A brief description of the finite element model is presented in the present chapter. More P. Vazouras (B) · P. Dakoulas Department of Civil Engineering, University of Thessaly, 38334 Volos, Greece e-mail: [email protected] K. A. Georgiadi-Stefanidi · S. A. Karamanos Department of Mechanical Engineering, University of Thessaly, 38334 Volos, Greece © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. A. Karamanos et al. (eds.), Geohazards and Pipelines, https://doi.org/10.1007/978-3-030-49892-4_5

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details on the model are offered in Chap. 7. The simple crossing case of a 914.4mm (36-inch) pipeline is described first, whereas in the second part of the chapter, the effects of pipeline bends on the structural performance of pipelines crossing horizontal faults is examined. It is also noted that, despite the fact that the present results refer to horizontal faults, the technique presented in this chapter may be applied, with appropriate adjustments, to vertical faults as well. Using three-dimensional rigorous finite element models, shown in Fig. 5.1 and described in detail in Sect. 7.3, numerical results are obtained for a DN 900 (36inch-diameter), L450 (X65-material) steel pipeline that crosses strike-slip faults at different angles, assuming infinite pipeline length, considering a pipe thickness equal  to 9.53 mm corresponding to a D t ratio equal to 96. The soft-to-firm clay used, referred to as Clay I, has a cohesion c = 50 kPa, friction angle ϕ = 0°, Young’s modulus E = 25 MPa and Poisson’s ratio v = 0.5. A very stiff clay under “undrained conditions”, referred to as Clay II is also employed for comparison purposes with soil parameters c, E and ϕ equal to 200 kPa, 100 MPa and 0°, respectively. The soil-pipeline finite element model has dimensions for the soil box equal to 60 m× 10 m×5 m in directions x, y, z, respectively, which comply with the size requirements stated in the publications of Vazouras et al. (2010, 2012, 2015). Finally, an equivalent nonlinear spring attached to the ends of the pipeline accounts for the infinite length of the pipeline and its continuity at the end of the model (see Fig. 5.1c), as described by Vazouras et al. (2015).

a

b

c

Fig. 5.1 Finite element model for simulating pipeline crossing of strike-slip (horizontal) tectonic faults: a undeformed soil prism; b deformed soil prism; c schematic representation of spring effects for simulating pipeline continuity

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5.2 Limit States for Pipeline Design Against Permanent Ground Deformation In the course of pipeline analysis and design against seismic actions and geohazards (in general), it is necessary to compare the calculated strains in the pipeline wall with the allowable values of strain corresponding to the limit states (modes of failure) relevant to pipeline integrity. Limit states are discussed more extensively in Chap. 8. Within the GIPIPE project the focus has been on the following limit states, which are considered to govern pipeline response and resistance under large permanent ground deformations: • Pipeline rupture (or fracture): this is a catastrophic failure, obviously an “ultimate limit state”, associated with loss of pressure containment of the pipeline. Pipeline fracture will occur, most likely, at the vicinity of girth welds. This mode of failure can be related to the applied tensile strain despite the fact that this relation may not be straightforward due to weld defects and other metallurgical parameters that may affect the fracture resistance of the pipeline weld zone. From the macroscopic point-of-view, if several strict fabrication rules are met, the allowable strain may reach a value of 2 or 3%. More discussion is offered in Chap. 8. • Pipeline wall buckling: using the rigorous finite element model under consideration, the formation of pipe wall buckles in the form of local wrinkles can be readily obtained from the model, without using any special strain criterion. Whether the presence of buckles and wrinkles on the pipe wall is an “ultimate” or “serviceability” state is discussed in Chap. 8. • Pipeline cross-sectional ovalization: this is mainly a serviceability limit state and refers to the reduction of cross-sectional arc due to pipeline deformation. However, large values of cross-sectional ovalization may be considered as an ultimate limit state condition. For low pressure pipelines, an ovalization of 15% is used as an ultimate limit state criterion, whereas a value of 6−8%, dependent on the equipment (pigging) used, may be employed for serviceability considerations, as suggested in NEN 3650. In high-pressure pipelines, this limit state may not be applicable (relevant) because of the “re-rounding” effect of internal pressure that keeps the pipeline cross-section nearly circular (see also Chap. 8). It should be noted that, apart from structural integrity issues, excessive ovalization will prevent proper pipeline inspection, because inspection tools, e.g. intelligent pigs, may not be able to pass through the pipeline anymore.

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5.3 Effect of Some Important Parameters on Pipeline Response in Fault Crossings 5.3.1 Effect of Crossing Angle β (Soft Clay, Internal Pressure Zero) The case of soft clay soil is examined (Clay I), for a non-pressurized pipeline, crossing a horizontal strike-slip fault at different angles. The numerical results in Fig. 5.2 show the “critical fault displacement” dcr , corresponding to the different limit states, for different values of the crossing angle. The results indicate that for non-positive and small positive (less than 5°) values of β, local buckling is the dominant limit state. For greater values of β, cross section flattening becomes the most important limit state. Under increasing angle β, the normalized displacement that causes cross-sectional distortion of 15% remains the same, whereas the displacement for reaching 3% tensile strain decreases (see Fig. 5.2).

Normalized critical fault displacement, dcr/D

3

3% tensile strain

2

1

0 -10

X65 steel D/t=96 zero pressure clay I

Crosssectional

local buckling

0

distorƟon

10

20

30

40

50

Fault angle β, degrees

Fig. 5.2 Normalized critical fault displacement for various performance limits at different angles of β (rigorous model), for infinite pipeline length (soil conditions Clay I)

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5.3.2 Effect of Pipewall Thickness (Soft Clay, Internal Pressure Zero) A non-pressurized pipeline is considered, crossing a strike-slip fault in Clay I soil conditions at different angles, considering three different values of thickness. The three values of thickness are 6.35 mm (0.25 in), 12.7 mm (0.5 in) and 15.88 mm (0.625 in), corresponding to values of diameter-to-thickness ratio equal to 144, 72 and 57.6, respectively. Figures 5.3, 5.4 and 5.5 show the effect of pipe wall thickness for the entire range of crossing angles, taking into account that the pipeline is of infinite length, using the equivalent nonlinear springs at its two ends. It is clear from the numerical results that, as the pipewall becomes thicker, the dominant criterion  switches from cross-section distortion to 3% of tensile axial strain and for D t equal to 57.6 no intersection of the two limit states is observed regarding positive fault angle β. In addition, for the specific soil conditions (Clay I), local buckling also occurs in small positive values of crossing angle β (about 5°) for all thicknesses of the X65 steel pipe analyzed.

Normalized critical fault displacement, dcr/D

2

X65 steel D/t=144 zero pressure clay I

1 3% tensile strain local buckling crosssectional distortion 0 -10

0

10

20

30

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50

Fault angle β, degrees

Fig. 5.3 Normalized critical fault displacement for various performance limits at different angles of β, for a pipeline of infinite length (X65, D/t = 144, Clay I, p = 0)

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Normalized critical fault displacement, dcr/D

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2 crosssectional distortion 1

0 -10

local buckling

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3% tensile strain

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Fig. 5.4 Normalized critical fault displacement for various performance limits at different angles of β, for a pipeline of infinite length (X65, D/t = 72, Clay I, p = 0) Normalized critical fault displacement, dcr/D

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cross-sectional distortion

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30

40

50

Fault angle β, degrees

Fig. 5.5 Normalized critical fault displacement for various performance limits at different angles of β, for a pipeline of infinite length (X65, D/t = 57.6, Clay I, p = 0)

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Normalized critical fault displacement, dcr/D

1

X65 steel D/t=96 zero pressure clay II

crosssectional distortion

local buckling

0 -10

0

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10

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30

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50

Fault angle β, degrees

Fig. 5.6 Normalized critical fault displacement for various performance limits at different angles of β, for a pipeline of infinite length (X65, D/t = 96, Clay II, p = 0)

5.3.3 Effect of Soil Stiffness (Internal Pressure Zero) For a relatively stiff soil material (a stiff clay, denoted as Clay II and described in Sect. 5.1), the limit state of 3% tensile axial strain and the ovalization limit state (15%), occur at the same fault displacement for positive fault angles, as shown in Figs. 5.6 and 5.7 for two X65 pipelines with diameter-to-thickness ratio equal to 96 and 72, respectively. Local buckling may occur in positive values of fault angle, even for values of β up to 15° for both cases, indicating that the bending action due to fault movement that develops in the pipeline is the major source of deformation, whereas the corresponding stretching deformation at those rather small positive values of β may not be dominant.

5.3.4 Effect of Internal Pressure (Soft Clay) The case of soft clay soil (Clay I) is examined, for an infinitely-long internallypressurized pipeline crossing a strike-slip fault at different angles. The pressure level is equal to 56% of the maximum (design) pressure pmax , defined by   t pmax = 0.72 × 2σY D

(5.1)

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Normalized critical fault displacement, dcr/D

1

X65 steel D/t=72 zero pressure clay II

cross-sectional distortion

3% tensile strain local buckling

0 -10

0

10

20

30

40

50

Fault angle β, degrees

Fig. 5.7 Normalized critical fault displacement for various performance limits at different angles of β, for a pipeline of infinite length (X65, D/t = 72, Clay II, p = 0)

The main conclusion from the finite element results is that pressurized pipelines do not exhibit cross-sectional distortion and the ovalization of the cross-section is really small. In such a case, the limit state for most positive fault angles is tensile failure. Nevertheless, local buckling may also occur in relatively small values of the crossing angle (e.g. up to 10°), as shown in Figs. 5.8 and 5.9.

5.4 Indicative Mitigation Measures for Fault Crossings As mentioned before, in Chap. 2, there exist several measures that can be taken to improve the structural performance of a pipeline crossing a seismic fault and limit the deformation and damage of the pipeline. The first and most obvious measure that should be examined by the designer is the re-alignment of pipeline routing in order to avoid a known geohazard area. However, in many instances, this option may not be feasible and therefore, other mitigation measures should be employed to improve pipeline performance and minimize the risk of failure because of a specific groundinduced action. A brief description of possible mitigation measures is offered below. One may note that this should be considered as a partial list and not as a complete treatment of mitigation measures, which have been outside the mainstream of the GIPIPE project. • Modifications to the pipeline configuration can increase pipeline strength against seismic actions. Such modifications include: (a) increasing the pipe wall thickness

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Normalized critical fault displacement, dcr/D

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3% tensile strain

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Fault angle β, degrees

Fig. 5.8 Normalized critical fault displacement for various performance limits at different angles of β, for a pipeline of infinite length (X65, D/t = 96, Clay I, p = 0.56pmax ) Normalized critical fault displacement, dcr/D

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2 3% tensile strain local buckling

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Fig. 5.9 Normalized critical fault displacement for various performance limits at different angles of β, for a pipeline of infinite length (X65, D/t = 72, Clay I, p = 0.56pmax )

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and (b) using higher grade pipeline material. In case of increased wall thickness, buckling and bending pipeline resistance also increases, while a higher grade material results to increased strength of the pipeline. However, attention should be paid to the reduced ductility of high-strength steel, as permanent ground actions are applied through a displacement-controlled scheme and in such a case, material ductility and deformation capacity might be more important than strength. Reducing soil loads on buried pipelines can improve their capacity to withstand ground induced displacements. This can be achieved by using softer soil for embedment of the pipeline, so that the pipeline is capable of accommodating itself more easily within the trench. More specifically, the use of loose granular soil as trench backfill material and the decrease of the burial depth of the pipe may reduce the loads from the ground to the pipeline. However, these measures should be adopted with caution, because a loose backfill material could reduce the pipeline resistance in global buckling due to high pressure and temperature gradients, or other permanent ground actions. Towards reducing soil loads on the pipe, smooth, low-friction coatings can be used to allow for the pipeline to accommodate itself within the trench and alleviate the high tension strains. Isolating the pipeline from ground displacement is a solution that can be implemented in two ways: either by constructing a tunnel around the pipeline so that it does not interact with the surrounding soil, or by above-ground installation with appropriate sliding supports in the ground, especially in case significant soil displacement is expected. Using the optimum pipeline crossing angle for strike-slip faults may limit compression strains and thus, the risk of local or flexural buckling, provided that the anticipated tensile strains are still acceptable. Measures can be taken to increase pipeline ductility in the fault crossing zone with special care for the welding process and related parameters, the non-destructive evaluation NDE procedures and the detection of welding imperfections. Stress and strain concentrations should be minimized at the welds, e.g. different material properties on either side of the weld, different wall thicknesses, and weld misalignment (“high-low”). In areas of potential ground rupture, sharp changes in direction and elevation with the use of flexible components, such as elbows, should be avoided within or very close to the fault zone due to significant local strain concentration. On the other hand, the presence of pipeline elbows at an appropriate distance from the fault may result in the reduction of ground-induced strains in the pipe, due to their flexibility. The optimum distance depends on the geometric characteristics of the pipe and elbow, the direction of the fault and the soil properties. The behavior of buried pipe elbows and the possibility of them acting as mitigating devices in pipelines crossing active faults are analyzed and discussed later in the present chapter. An investigation of this topic is offered in Sect. 5.5.

As noted above, these recommendations may not constitute an exhaustive list of possible measures, or necessarily appropriate for every real case. However, they

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can be part of the pipeline risk analyses and evaluated for each particular situation, depending primarily on pipeline location, the expected failure mode and its consequences, as well as the estimated mitigation costs.

5.5 Structural Behavior of Buried Pipeline Bends and Their Effect on Buried Pipeline Response in Fault Crossing Areas Apart from their use in industrial applications (Karamanos 2016), pipe bends are also employed in buried pipelines, mainly for the purpose of changing direction in pipeline alignment. Nevertheless, the structural behavior of elbows in buried pipelines, accounting for their interaction with the surrounding soil in a rigorous manner, has received very little attention, and the existing literature on this subject has been very limited, as described in the review offered in the recent paper by Vazouras and Karamanos (2017). The study presented in this section focuses on the mechanical behavior of buried steel elbows in fault-crossing areas and has a dual purpose: (a) to analyze the mechanical response of those buried pipeline components subjected to severe imposed deformations, accounting for soil-pipe interaction, and (b) to investigate the effects of elbow flexibility on the structural response of a pipeline crossing a tectonic fault. It is expected that, due to their flexibility, the presence of elbows at a distance from the fault would affect the distribution of stress and strain in the critical area. A 914.4-mm (36-inch)-diameter pipe with thickness equal to 9.53 mm (3/8 inch) is analyzed under fault-crossing conditions. The pipeline contains bends of radius equal to 5 pipe diameters, which refer to induction “hot” bends. The numerical models employed in the present study are three-dimensional models, enhancing the model employed in Sect. 5.3. More specifically, Sect. 5.5.1 examines the response of a buried pipeline segment that contains a bend (elbow) under axial pull-out force, examining the effects of internal pressure, bend angle and stiffness of the surrounding ground conditions. Subsequently, using the results obtained in Sect. 5.5.1, Sect. 5.5.2 analyzes the 914.4-mm-diameter pipeline crossing a strike-slip fault, and investigates the effects of the nearby elbows on pipeline performance.

5.5.1 Mechanical Response of Buried Pipe Bends The mechanical response of steel pipe elbows subjected to a pull-out force at one end is investigated first. The investgation is numerical and employs rigorous threedimensional finite element models in finite element software ABAQUS (2014) that have been proposed and discussed elsewhere (Vazouras et al. 2010, 2012, 2015; Sarvanis et al. 2018). The bends under consideration refer to a 914.4-mm (36-inch)

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diameter 9.53-mm-thick pipe, with bend angle α equal to 90o , 60o and 30o . The diameter-to-thickness ratio is equal to 96, while the radius-to-diameter ratio of the elbow is assumed equal to 5. The pipeline was an L450 (X65) steel pipe, with specified minimum yield stress equal to 450 MPa and specified ultimate stress equal to 560 MPa. Both non-pressurized and pressurized pipes were simulated, considering an internal pressure level of 3.78 MPa. The pipe was embedded in cohesive soil (clay), considering two different sets of soil parameters. The first set corresponds to a “soft to firm” soil, referred to as Clay I, while the second set of parameters corresponds to a stiffer clay, referred to as Clay II. The properties of these clay types have been presented in Sect. 5.1. More details of the model are offered by Vazouras and Karamanos (2017). In Fig. 5.10, a schematic representation of the physical problem is shown. The considered pipeline segment AE consists of the elbow BC and the straight parts of the pipeline, AB and CE. A pull-out force is applied to the end point A in the direction of the pipeline axis, while the straight part CE is assumed to extend at infinity beyond point E. Furthermore, Fig. 5.11 shows the finite element model simulating the pull-out configuration for the case of bend angle equal to 60o . Four-node reducedintegration shell elements (S4R) are used for modeling the steel pipeline segment, while eight-node reduced integration “brick” elements (C3D8R) are used to simulate the surrounding soil. For the description of the non-linear material behavior of the steel pipe and the surrounding soil, the appropriate constitutive models are employed. An appropriate contact algorithm is employed to simulate accurately the pipe-soil interface and a non-linear spring is attached to the end point E of the pipe segment to account for the considered infinite length of the pipeline (Vazouras et al. 2015). Further details on the finite element model can be found in the paper by Vazouras and Karamanos (2017). In order to quantify the damage of a buried pipeline under severe ground-induced actions, the appropriate performance criteria or limit states must be specified, as presented in the beginning of Sect. 5.2. More specifically, three criteria are considered

A

F

Lb

B

u

L1

R

plan view of buried pipe bend

C

α

D

L2 Fig. 5.10 Schematic representation of the considered pull-out problem

E

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Fig. 5.11 Numerical simulation of individual elbows, as part of a buried steel pipeline

herein: (a) tensile strain 3% associated with pipe wall rupture; (b) local buckling of the buried pipeline, caused by the concentrated compressive strains; in the specific study; (c) cross-sectional ovalization, expressed through the “flattening parameter” f , considering that an ovalization limit state is reached when f becomes equal to 0.15. It should be noticed that pipeline buckling is modeled explicitly, through the rigorous three-dimensional finite element model, and defined as the stage where localized deformation starts developing at the critical area. In Table 5.1, the results of the numerical analyses for all the cases considered are summarized, in terms of the first limit state that is reached and the corresponding critical displacement. The results indicate that, for most of the cases examined, the critical limit state of the elbow has been the tensile strain limit. The bend angle α has an important effect on the structural response of the buried elbows. Figure 5.12 shows the numerical results in terms of pull-out normalized force versus normalized displacement for the various bend angles considered, as well as, for a straight pipe. The arrows (↑ or ↓) in the diagrams point to the failure mode stated in Table 5.1. The results show that elbows with larger bend angle are more flexible and in the case of non-pressurized pipes, elbow flexibility becomes larger. However, when the pipe is embedded in stiffer soil, this variation in elbow flexibility is less pronounced (compare Fig. 5.12a with b), pointing out the significant role of the surrounding soil in the mechanical behavior of the bend. For a more extensive discussion on the aforementioned numerical results the interested reader is referred to the paper by Vazouras and Karamanos (2017).

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Table 5.1 Numerical results for the considered cases with respect to the limit states Case 1

Clay I p = 56% pmax

Elbow angle α

Limit state

Critical displacement (first limit state occurs) [m]

90

Local buckling

0.76

2

60

3% tensile strain

0.48

3

30

3% tensile strain

0.23 0.60

4

Clay I p = 0

90

Local buckling

5

60

Ovalization

0.42

6

30

3% tensile strain

0.20

7

Clay II p = 56% pmax

90

3% tensile strain

0.44

8

60

3% tensile strain

0.26

9

30

3% tensile strain

0.23

5.5.2 Effect of Pipe Elbows on Pipeline Response in Fault Crossings Following the examination of the mechanical behavior of individual elbows and their interaction with the surrounding soil, the influence of elbows on the mechanical behavior of buried pipelines crossing active seismic faultsis examined. Herein, a specific case is examined with a 914.4-mm (36-inch) diameter pipeline crossing a strike-slip fault at an angle β = 25o . The pipeline has the geometric and material properties described in the previous section, is pressurized with internal pressure equal to 56% of pmax defined in Eq. 5.1 and is embedded in Clay I soil conditions. The pipe bends are placed at a distance from the fault plane, which ranges from 45 to 345 m. Figure 5.13 presents the rigorous three-dimensional finite element model of the fault crossing configuration considered. The model consists of a 60-m-long soil block, in which the pipe is embedded and it is similar to the finite element model already described in Vazouras et al. (2015) and in Sect. 5.1. Solid elements are employed to model soil block, while shell elements are used to simulate the buried steel pipe. The three-dimensional finite element model is appropriately enhanced to account for the presence of the curved pipe segment. The presence of the pipe bends is taken into account through equivalent non-linear springs that are attached at both ends of the large-scale strike-slip fault model (see Fig. 5.13b). The axial force-displacement diagrams of the elbows, obtained from the numerical analyses of the first part of the present study presented in Sect. 5.5.1, are used to define the constitutive law of these non-linear springs, in order to represent the effects of the respective pipe bends.. Figure 5.14 summarizes the numerical results for all the cases considered, in terms of the corresponding critical fault displacement and the elbow distance from the fault plane. The results show that, when pipe bends are placed at an appropriate distance from the fault, the flexibility of the system is enhanced, increasing the deformation capacity of the pipeline. In fact, an optimum distance of the elbow from the fault

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a

normalized pull out force

1.5

p=56% py clay I 1

α=0°

elbow failure

α=30° elbow failure α=60°

0.5 α=90° elbow failure

0 0

0.2

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0.6

0.8

1

normalized pull out displacement

b

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elbow failure

α=60° α=90° elbow failure

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p=56% py clay II 0 0

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0.6

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1

normalized pull out displacement

c

normalized pull out force

1.5

p=0% py clay I α=0° 1 elbow failure

α=30° elbow failure

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α=60° α=90°

elbow failure

0 0

0.2

0.4

0.6

0.8

1

normalized pull out displacement

Fig. 5.12 Force-displacement diagrams obtained from the numerical analyses for: a Clay I soil conditions and pressurized pipe (cases 1, 2, 3), b Clay II soil conditions and pressurized pipe (cases 7, 8, 9) and c Clay I soil conditions ans non-pressurized pipe (cases 4, 5, 6)

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critical fault displacement, cm

350

105

α=60° α=90°

300 α=30° 250 200 150 α=0° 100 50 0 45

95

145

195

245

295

345

distance of elbow from fault, m Fig. 5.14 Critical fault displacement versus distance of elbow from fault, for different bend angles (36-inch-diameter 3/8-inch-thick X65 pipeline, with pressure equal to 0.56pmax and Clay I soil conditions)

is identified, which corresponds to a maximum allowable fault displacement. For the specific parameters of the study (geometry of the pipe, soil conditions and elbow angle), this optimum distance is equal to about 150 m and it appears to be independent of the value of bend angle α. The results also indicated that, when the elbows are placed at a quite a small distance from the fault plane, the pipeline capacity against fault displacement is reduced and either local buckling of the pipe or tensile strain failure of the elbow itself is observed. Moreover, when the distance of the elbow from the fault exceeds a certain value (equal to about 250 m for the specific study), the pipeline response seems to be independent of the presence of the elbows and becomes similar to that of the straight pipeline. For further details and discussion on the numerical results and the sensitivity of results in terms of uncertainty regarding the exact location of the fault plane, the reader is referred to the paper by Vazouras and Karamanos (2017). Based on the above results, it can be concluded that the presence of elbows may have a significant effect on pipeline response. If placed at an optimum distance from the fault, they can be used as “mitigating devices” reducing ground-induced action on the buried pipeline at fault crossing. Nevertheless, it must be noted that, for an efficient pipeline design, a dedicated analysis is necessary to quantify the beneficial effects of the pipe bends and determine this optimum distance, taking into account pipe and soil properties, fault characteristics and most importantly, the uncertainty regarding the fault location.

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References ABAQUS (2014) Users’ Manual. Simulia Providence, RI, USA Karamanos SA (2016) Mechanical behavior of steel pipe bends; an overview. J Press Vess-T ASME 138(4):041203 Nederlands Normalisatie Instituut (2020) Requirements for pipeline systems. NEN 3650, part-1: general and part-2: steel pipelines, Delft, The Netherlands Sarvanis GC, Karamanos SA, Vazouras P et al (2018) Permanent earthquake-induced actions in buried pipelines: numerical modeling and experimental verification. Earthq Eng Struct D 47(4):966–987 Vazouras P, Karamanos SA, Dakoulas P (2010) Finite element analysis of buried steel pipelines under strike-slip fault displacements. Soil Dyn Earthq Eng 30(11):1361–1376 Vazouras P, Karamanos SA, Dakoulas P (2012) Mechanical behavior of buried steel pipes crossing active strike-slip faults. Soil Dyn Earthq Eng 41:164–180 Vazouras P, Dakoulas P, Karamanos SA (2015) Pipe–soil interaction and pipeline performance under strike–slip fault movements. Soil Dyn Earthq Eng 72:48–65 Vazouras P, Karamanos SA (2017) Structural behavior of buried pipe bends and their effect on pipeline response in fault crossing areas. B Earthq Eng 15:4999–5024

Chapter 6

Pipeline Response Under Landslide Action Angelos Tsatsis, George Gazetas, and Rallis Kourkoulis

Abstract Numerical results for pipeline deformation subjected to landslide actions are presented, using advanced three-dimensional finite element models, similar to the ones employed in the previous two chapters. More specifically, a two-stage numerical methodology is developed. In the first stage, a “global” model is employed to simulate soil movement during the landslide event, ignoring pipeline presence. In the second stage, a “local” model is used, simulating an appropriate pipeline segment and the corresponding portion of the surrounding soil. The presented methodology is applied to study two representative cases: (a) pipeline response to soil movement parallel to its axis and (b) pipeline response to soil movement perpendicular to its axis.

6.1 Introduction Among the various geohazards (seismic motion, surface fault rupture, slope failure/landslide, liquefaction, lateral spreading, scour etc.), landslides pose the greatest threat for buried pipelines, as noted in Sect. 1.3 (EGIG 2018). This profound susceptibility should be attributed to two main reasons. First, landslides occur more frequently with respect to other types of geohazards; they are associated not only with seismic events but also with heavy rainfall, surface water erosion, bank erosion or even with third party activity. Furthermore, the evermore increasing energy demand, combined with the intensive routing limitations (avoidance of urban areas or agricultural lands, environmental restrictions), lead to routing major pipelines, carrying dangerous substances through remote mountainous terrain, often seismically active and with severe climatic conditions. In the past, the design of pipelines positioned in landslide susceptible locations was conducted based on the distress caused by drag forces applied by the sliding soil on the pipeline, using simplified structural models such as those in Georgiadis (1991). Therefore, the most important consideration was the assessment of the load A. Tsatsis (B) · G. Gazetas · R. Kourkoulis School of Civil Engineering, National Technical University of Athens, 15780 Athens, Greece e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. A. Karamanos et al. (eds.), Geohazards and Pipelines, https://doi.org/10.1007/978-3-030-49892-4_6

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exerted by the landslide on the pipeline. Studies into the impact force, as slide material flows around a pipeline, fall into two categories based broadly on a solid mechanics approach, where the loading is a function of primarily the soil shear strength and flow velocity (Marti 1976; Schapery and Dunlap 1978; Towhata and Al-Hussaini1988; Georgiadis 1991) or a fluid mechanics approach with more direct focus on the yield stress and viscosity of the flowing debris and resulting drag coefficients (Pazwash and Robertson 1973; Bruschi et al. 2006). More recently, more integrated approaches were developed that account for both the soil and the pipe response simultaneously. They fall within two broad categories: (a) analytical or semi-analytical solutions and (b) numerical approaches. Analytical approaches aim at the compilation of closed form solutions to evaluate deformation response of pipelines subjected to landslide-induced actions (e.g. Liu and O’Rourke 1997; Parker et al. 2008; Randolph et al. 2010; Yuan et al. 2012a, b, Zhang et al. 2016). Although analytical solutions are limited by significant idealizations, they constitute a useful starting point in design, providing a framework for a more detailed numerical analysis for the particular governing conditions. As with other types of permanent ground displacement, the effect of landslideinduced actions on buried pipelines is most usually addressed with simplified Winkler-type models (e.g. Gantes et al. 2013; Han et al. 2012; Chen et al. 2014; Zhang et al. 2017; Dadfar et al. 2018). Not withstanding their practical value, such methodologies are based on simplifying the soil response as independent uniaxial nonlinear springs. However, recent findings question the validity of that approach: Zhang et al. (2002), Phillips et al. (2004), Yimsiri et al. (2004), Guo and Stolle (2005), Di Prisco et al. (2004), Hsu et al. (2006), Daiyan et al. (2009, 2010) systematically estimated (both numerically and experimentally) the oblique pipeline-soil capacity and concluded that the bearing mechanisms under combined loading are strongly coupled. Cocchetti et al. (2009a, b) tackled this problem by describing the pipelinesoil interaction with the employment of the “macroelement” theory allowing thus, coupling among the loading components. As the computational capability increased, the use of continuum 3D finite element modeling was introduced (3D FEM can capture in a more realistic way the pipesoil interaction, the deformation pattern of the pipeline as well as local instability phenomena, while accounting for pressure and temperature phenomena). Liu et al. (2010) established a 3D finite element model to study the pipeline behavior under deflection displacement, analogous to transversal displacements arising from slope failure. They considered material nonlinearity for the pipeline, while the soil was assumed linear-elastic. Following their study, more refined and detailed models arose that addressed the case of pipelines subjected to transversal (e.g. Zheng et al. 2012; Wu et al. 2014; Li et al. 2016; Zhang et al. 2018) and longitudinal (e.g. Tsatsis et al. 2018) landslide-induced displacements. In the present chapter, a numerical methodology is presented for simulating the response of a pipeline subjected to slope failure-induced actions, based on the principals of 3D continuum modeling. The presented methodology is applied to study two representative examples:

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1. pipeline response to soil movement parallel to its axis 2. pipeline response to soil movement perpendicular to its axis.

6.2 Analysis Methodology Soil movement due to slope failure may often extend to several hundred meters, while the depth of the sliding mass can reach several meters. On the other hand, the pipe diameter under consideration is of the order of 1 m, while in order to model all possible structural instability phenomena (e.g. local bucking, excessive ovalization of the pipe section etc.), a very fine discretization is required (finite elements with dimension less than 5% of the diameter). Hence, preserving the same mesh requirements for the surrounding soil would yield an enormous and computationally unattractive finite element model. To overcome this obstacle, a two-step procedure is employed (Tsatsis et al. 2018) that is schematically described in Fig. 6.1.

Fig. 6.1 Outline of the proposed 2-step numerical methodology: the vectors of soil movement uff estimated by the analysis of the GLOBAL model are assumed at the bottom and lateral boundaries of the LOCAL model to estimate the induced pipeline distress

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The “global” model In the first step, a “global” model is employed to simulate the triggering and evolution of soil movement during the landslide event. The output of this first step is the soil displacement field at free field; this displacement field will be assigned as boundary condition at the appropriate soil nodes of the subsequent step. The pipeline presence is tactically ignored – it is assumed that the pipeline cannot significantly alter the overall displacements due to its low relative stiffness, a reasonable assumption for landslides geometries with an out-of-plane dimension significantly larger than the pipeline diameter. Evidently, in this global model the mesh requirements are manageable while a relatively coarse mesh is considered appropriate to model the evolution of the landslide movement. The “local” soil-pipe interaction model In the second step, an extremely fine “local” model is introduced comprising the pipeline and portion of the surrounding soil. Here, the landslide action is introduced as 3D displacement vectors (calculated by the “global” model) assigned at the bottom and lateral nodes of the local model. Understandably, the thickness d  of the local model should be small to promote computational efficiency, yet adequately large to ensure that the soil-pipe interaction is properly captured. To estimate the optimum thickness d  , a sensitivity study is performed using a simplified “test-model” (see Fig. 6.2). This model comprises two segments, a stationary and a moving part. The stationary part mimics the pipeline segment that is anchored within the stable soil, while the moving part represents the area of the pipe (close to the landslide toe) that is dragged along by the sliding soil mass. In this illustrative test model, the axial soil displacement (u x ) is tactically ignored, since it is irrelevant to the estimation of the minimum allowable thickness d  . Therefore, only vertical soil displacements in the z direction are prescribed along the bottom side of the moving part, leaving the top boundary free to move (see Fig. 6.2b). Two alternative configurations are comparatively tested: an adequately small “5diameter Model” where d  = 5 D, and a more rigorous (but computationally less attractive) “10-diameter Model”, where d  = 10 D. As the pipeline bends to accommodate the vertical dislocation of the base, and is stretched due to the imposed elongation, excessive tensile strains develop. Therefore, the two alternative local models are compared in terms of their predicted maximum axial strain along the pipe top centerline (see Fig. 6.2c). For small and medium-sized displacements ( 3Do at the level of the pipeline axis) is backfilled. After some time this soil will consolidate and q p → qn . The pipeline is a relatively rigid element in this, so that more consolidation can occur on either

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side of the pipe, than vertically above it. In this case, the pipeline is supported on the subsoil and the load is transmitted directly. The following formula, developed by Marston, can be used for calculating the maximum vertical passive soil pressure (q p ) on pipelines (actually the resistance that occurs when the pipeline is vertically “pulled out of the soil”), as a function of the trench width and trench depth, the stiffness of the sub-soil and the method of trench backfilling:   H q p = qn × 1 + f m Do

(7.4)

In principle, the value f m = 0.3 applies for cohesive soils. For sand, f m is strongly influenced by the degree of compaction of the trench backfill. If a very high degree of compaction is achieved, then the factor f m may be as high as f m = 0.8. In view of the compaction levels, normally achieved in pipeline trench backfilling, the value applied by Marston ( f m = 0.3) seems appropriate for many situations, however, for critical designs, it is recommended to verify this by suitable test methods. The modulus of sub-grade reaction can be derived by determination of the displacement z max of the pipeline, needed to increase the soil pressure from neutral soil pressure qn up to the maximum (q p ). This displacement (z max ) depends on the outside diameter of the pipeline (Do ), the soil cover, and the E modulus of the trench backfill on top of the pipe. The following formulae may be used for z max : clay/peat: Do   H Do

(7.5)

Do   E 0.5 H Do

(7.6)

z max = 0.25 E 1.5 sand: z max = 0.2

where: z max = vertical displacement [m]; Do = outside diameter [m]; E = elasticity modulus of the trench backfill material [MPa]; H = soil cover on the top of the pipe [m]. Note that the coefficients 0.25 and 0.2 in the above mentioned formulae are not dimensionless. The load-displacement relationship, up to and including a maximum displacement, can be described with a bilinear modulus of sub-grade reaction:

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kv,top =

7.2.2.3

q p − qn z max

(7.7)

Soil Reaction in Downward Direction

The limit value for the vertical load is given by the ultimate vertical bearing capacity. This is the load needed to cause the soil under the pipeline to fail over the full width of the pipe. As failure of the soil under the pipe progresses, this creates a steadily wider bedding area. Under cyclical loading, the bedding of the pipe will develop a good fit. The soil will then show greater stiffness at loading after previous unloading. Experiments have shown that the vertical ultimate bearing capacity can be predicted with the Brinch Hansen method (Brinch Hansen 1970), for sand, clay and peat. (a) Sand For sand, the ultimate bearing capacity, determined at pipe axis level, can be described with the Brinch Hansen formula for the drained situation:     Pwe = 0.95 0.5γgem × B × N y × S y × d y + Sq × Nq × dq qn + c cot φ − c cot φ

(7.8) where: Pwe =ultimate bearing capacity;  = average effective unit weight from the grade level, down to the pipe axis γgem level; B = installation width (chord), (at pipe axis level B = Do applies); Do = outside diameter of the pipeline; N y = 1.5(Nq − 1) tan φ S y = 1 − 0.4B/L; L = minimum support length, (here applies: B/L = Do /L = 0.1); d y = 1.0  Sq = 1 + sin φ × B L; Sq = plate factor for pipelines;   Nq = eπ tan φ tan2 45 + φ 2 ;    dq = 1 + 2 tan φ(1 − sin φ)2 arctan Z B Z = depth from grade level to the pipeline axis = H + Do /2; H = cover on top of the pipeline; c = effective cohesion, (for sand: c =0 applies). The spring stiffness can be calculated by the following formulae: kv,1 = 0.5 × E × PDweo from 0 to 2/3 times the vertical ultimate bearing capacity; kv,2 = 0.1 × E × PDweo from 2/3 to 1.0 times the vertical ultimate bearing capacity. The value of the elasticity modulus E is determined for the undisturbed subsoil, in accordance with Table 1 of the EN 1997-1 (Eurocode 7) standard, or through compression tests or triaxial tests.

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(b) Clay and peat, drained situation (slow deformation) For the ultimate bearing capacity at slow deformation, for instance, settlements or pipeline expansion from temperature, the same formulae are applicable as under (a). For clay (and for the time being also for peat), the vertical modulus of sub-grade reaction k v can be derived as follows. The ultimate bearing capacity Pwe is determined similarly with sand. The vertical modulus of sub-grade reaction is determined from the calculated ultimate bearing capacity as follows: kv,1 = 0.25 × cu × PDweo from 0 to 2/3 times the vertical ultimate bearing capacity; kv,2 = 0.04 × cu × PDweo from 2/3 to 1.0 times the vertical ultimate bearing capacity. The formula as derived describes the plastic penetration process of the pipe in the trench bottom, and can be used both for instantaneous applied loads (undrained situation) and for slowly applied loads (drained situation). The corresponding loaddisplacement curve is approximated here with a trilinear spring characteristic. (c) Clay and peat, undrained situation (rapid deformation) The ultimate bearing capacity for clay and peat, for an undrained (“rapid”) deformation is obtained by the formula: Pwe = 0.85 × cu (π + 2) × (1 + Sc + dc )

(7.9)

where: cu = undrained shear strength (from the trench bottom down to one diameter underneath the trench); Sc = form factor, Sc = 0.2B/L(for pipelines Sc = 0.02); dc = depth factor, dc = 0.4 arctan(Z /B), in radians.

7.2.2.4

Soil Reaction in Horizontal Direction

At rest, an underground pipe is subjected to lateral soil pressure, which normally is the neutral horizontal soil pressure. The soil pressure changes, as soon as the pipe moves transverse to its axis in a horizontal direction. As the pipe moves against the soil pressure, this will rise to a maximum passive horizontal soil resistance, and as the pipe is moving away from the soil, as a minimum an active soil pressure will develop. The upper limit value for the horizontal soil pressure is determined by the ultimate bearing capacity: (a) Sand, clay and peat (slow deformation, drained) Using the Brinch Hansen theory (Brinch Hansen 1970), the ultimate horizontal bearing capacity can be determined for sandy soil: qhe = K q × σk + 0.7α × K c × c where:

(7.10)

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100

100

Kq

10

1

45 35 30 25 25 20 15 10 5

10

Kc

45 40 35 30 25 20 15 10 5

1

0,1

0,1 0

5

10

15

20

5

10

15

20

(H+D/2)/D

(H+D/2)/D 10

Kcu

8 6 4 2 0 0

5

10

15

20

(H+D/2)/D

Fig. 7.5 Load coefficients K q , K c and K cu , according to Brinch Hansen (1970)

qhe = ultimate horizontal bearing capacity; K q = load coefficient according to Brinch Hansen, depending on φ and Z /D, see Fig. 7.5; K c = load coefficient according to Brinch Hansen, depending on φ and Z /D, see Fig. 7.5; a = 0.6 in case of open excavation; 1.0 in case of jacking methods; c = effective cohesion of the soil; σk = vertical intergranular soil stress at the level of the pipe axis. The correction factor 0.7 is related to a systematic deviation, demonstrated when the result of the formula is compared with the average of the results from practical tests. (b) Clay and peat (rapid deformation, undrained) For cohesive soil (clay and peat), it appears that the theory of Brinch Hansen (1970) can be used as well. The upper limit for horizontal soil pressure is for H > 2Do : qhe = 0.7α × K cu × cu

(7.11)

where: cu = undrained cohesion of the trench backfill, also referred to as undrained shear strength; a = 0.6 in case of open excavation; 1.0 in case of jacking methods;

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K cu = load coefficient according to Brinch Hansen, depending on Z /D, see Fig. 7.5. The load displacement diagram shows elastic soil behavior at smaller displacements (represented by the modulus of sub-grade reaction), and plastic soil behavior following large displacements, when the horizontal ultimate bearing capacity is reached. The following relationship can be used for the maximum displacement ymax :

   ymax = Do × 0.05 + 0.03 × Z Do + 0.5

(7.12)

where: Do = outside pipe diameter; Z = depth from grade level to the axis of the pipeline = H + Do /2; H = soil cover on top of the pipeline. A bilinear load displacement diagram can be used for the calculation model, whereby the modulus of sub-grade reaction is selected as a percentage of the horizontal ultimate bearing capacity, divided by the corresponding displacement. The horizontal modulus of sub-grade reaction (the secant modulus of the load displacement diagram), is determined here at 30% of the horizontal ultimate bearing capacity: kh,30 =

qh,30 qhe 1 − 0.3B = × y30 ymax A

(7.13)

The following values are applied to the constants A and B (see Table 7.1), specified for soil comparable with the sedimentary soils in Northen Europe: Test loads (GeoDelft 1985) have shown that a trilinear spring characteristic also gives a good estimation of the real load-deformation behavior (derived from tests with Z /D ratios up to approximately 3). The following has  been derived from these measurements: kh,1 = 33 × qhe Do N/mm3 from 0 to 2/3 times qhe (sand and clay); kh,1 = 4.8 × qhe  Do N/mm3 from 2/3 to 1 times qhe (sand); kh,1 = 2.2 × qhe Do N/mm3 from 2/3 to 1 times qhe (clay). A bilinear characteristic may also be used, by only utilizing kh,1 . Table 7.1 Constants A and B for determination of horizontal soil spring Sand and clay/peat (slowly loaded, drained situation)

Clay/peat (fast loading, undrained situation)

A

0.15

0.1

B =1− A

0.85

0.9

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Soil Reaction in Axial Direction

Whenever a pipeline is subjected to an axial displacement, relative to the surrounding soil, a frictional force develops in the contact surface between the pipeline and the soil, acting in a direction opposite to the axial displacement vector. The magnitude of this force is dependent on the relative displacement between the pipeline and the soil. Whenever the relative displacement reaches a certain size, this frictional force no longer increases. The magnitude of the friction per unit of contact area (shear stress) is determined by: • • • •

the intergranular pressure around the pipe; the angle of the internal friction; the adhesion of the soil to the pipe wall; the roughness of the pipe wall or the pipe coating.

The friction can be represented by the characteristics of a torsion or longitudinal frictional spring. The displacement (u max ) of the pipe relative to the surrounding soil, required to achieve the upper limit value (Wmax ) of the friction, is referred to as the frictional displacement. The frictional modulus of sub-grade reaction (kw ) (the axial spring) is the quotient of friction and displacement. The values included in Table 7.2 are based on limited information. Up to the maximum frictional resistance, an almost linear relationship between displacement and friction can be used. Compaction of sand reduces the displacement at maximum friction. The maximum friction resistance per unit of pipeline length can be determined both for axial and torsion friction with the formula:   1+K × σk × tan δ + 0.6 × a (7.14) W = π Do 2 where: π Do = outside pipe circumference; K = a relationship between the horizontal/vertical intergranular pressure; in the case of neutral horizontal soil pressure, K is equal to K o = 1 − sin φ; Table 7.2 Displacement at maximum frictional resistance for different types of soil

Type of soil

umax in mm

Tightly packed sand

1-3

Moderately packed sand

3-5

Loosely packed sand

5-8

Stiff clay

2-4

Moderately stiff clay

4-6

Soft clay

6-10

Moderately solid peat

6-10

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φ = the angle of the internal friction of the soil; σk = the vertical intergranular pressure at the pipe axis level; δ = the angle of the friction between the soil and the pipe wall, dependent upon the soil type and the surface roughness of the pipeline or its coating, δ ≈ 2φ/3; a = the adhesion (only with clay or peat), which is dependent on the soil type and the time elapsed since trench backfilling. The correction factor 0.6 for the adhesion stands in relation to the systematic deviation, demonstrated when the results of the formula are compared with the average of the results from field tests. In large diameter pipelines, the dead weight of the pipeline and its content may have a significant effect on the friction acting on the pipeline. This is incorporated into the friction equation as follows:  W = π Do

   1+K × σk × tan δ + 0.6 × a + Q eg + Q fill − Q buoyancy × tan δ 2 (7.15)

Sand is a non-cohesive material, and therefore, adhesion does not occur. With clay soil types, adhesion is still low immediately after trench backfill and it only develops in the course of time. In that case, the time elapsing between the installation of a pipeline and its being taken into operation becomes important. The adhesion of clay to the outside of a pipe wall appears to be approximately equal to the drained cohesion c . In clay soils, adhesion appears to determine primarily the shear stress between pipe and soil. In water saturated clays the frictional angle ϕ appears to amount to less than 5° (rapid loading). Consequently, at normal pipeline depths, the effect of friction angle is negligibly small, compared with the effect of adhesion. If, however, the water content is reduced, then the frictional angle will increase strongly, while the adhesion remains the same. In case of pipelines in clay soils, which are subjected to variations in diameter and degree of ovalization under the effect of temperature and internal pressure, the plastic behavior of clay soil may result in a certain relaxation of soil friction with time. Sand has an internal friction angle φ of approx. 30−35°. With strongly compacted sands, a higher φ value, up to 40o or even 45o may be encountered. This higher value is due to dilatancy phenomena. If a smooth pipe moves in such a strongly compacted sand package, dilatancy phenomena are limited along the smooth surface, but they can occur in case of a rough surface. Since trench backfill for a cross country pipeline will never have the same compaction as the original sediment, an internal friction angle of 30−35o may be a realistic assumption for sandy soil, used as trench backfill. By decoupling these two effects, the relationship f (δ) between the pipe wall to soil friction angle δ on one hand, and the angle of internal soil friction φ on the other hand can also be decoupled. After the application of this correction, the ratio δ/ϕ can be set to 2/3 for all sand types and materials. This results in a friction angle of 20°, irrespective of the density and the roughness of the pipe wall (δ = f (δ) × ϕ = 20°).

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7.2.3 Soil Spring Calculations According to ALA 2005 The methodology proposed by the ALA (2005) recommendations, for the calculation of soil springs in cases where PGDs are imposed on a pipeline, is presented in the present paragraph. It is assumed that undrained conditions prevail for clays, while drained conditions prevail in sands.

7.2.3.1

Axial Spring

Axial springs are presented herein. It is underlined that the “axial direction” refers to the longitudinal direction of the pipeline. Therefore, with respect to a global Cartesian system, this direction depends on the pipeline alignment. The following equations for the soil spring assume a bi-linear elastic-perfectly plastic soil behavior in the axial direction, and provide the maximum soil resistance and the corresponding axial relative displacement between the pipe and the soil. tu =  xu =

⎧ ⎨

π DaSu for clay π D ⎩ γ H (1 + K o ) tan kφ for sand 2

(7.16)

0.1 to 0.2 inches for dense to loose sand 0.2 to 0.4 inches for stiff to soft clay

where: tu = maximum soil resistance to the pipe axial direction having units of force per unit length of pipe; xu = axial displacement at which maximum soil resistance is developed; D = pipe outer diameter; a = adhesion factor from Fig. 7.6; Su = soil undrained shear strength; γ = soil effective unit weight; H = soil depth to centerline of pipe; K o = coefficient of lateral soil pressure at rest; φ = angle of soil shear resistance; k = a factor to represent the friction between the outer surface of the pipe and the surrounding soil (if that is the failure plane), such that (tan kφ) is in the range of about 0.6 to 0.7 for concrete coated steel pipe in compacted sand; or 0.4 to 0.5 for hard epoxy coated steel pipe in compacted sand. These soil springs are inferred from pile shaft load transfer theory. For design purposes, variation in tu should be considered, at least −33%/+ 50%, to consider the range of soil properties on the impact of pipe strain and other forces. The coefficient of soil pressure may be substantially higher in zones of large relative displacement between the pipeline and the soil. Lower bound values tend to result in lower stresses

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Fig. 7.6 Adhesion factors versus undrained shear strength (ASCE 1984)

and strains in the pipe and increase the length of pipeline needed to transfer pipeline forces to the soil. Upper bound values tend to increase the stresses and strain in the pipe and reduce the length of pipeline needed to transfer the pipeline forces to the soil.

7.2.3.2

Transverse (Horizontal) Spring

Horizontal transverse springs are of immense importance for the case of horizontal lateral ground-induced actions, e.g. strike-slip faults, lateral spreading or landslides. The following equations for the soil spring assume a bi-linear elastic-perfectly plastic soil behavior in the horizontal transverse direction, and provide the maximum soil resistance and the corresponding axial relative displacement between the pipe and the soil. These characteristic values for the transverse horizontal soil springs are based on data and analysis of footings and vertical anchor plates, under pull-out conditions, as well as laboratory tests on model pipelines subjected to horizontal pipe movements.  pu =

yu =

⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩

Su Nch D for clay γ H Nqh D for sand

0.07 to 0.10(H + D/2) for loose sand 0.03 to 0.05(H + D/2) for medium sand 0.02 to 0.03(H + D/2) for dense sand 0.03 to 0.05(H + D/2) for stiff to soft clay

(7.17)

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Horizondal bearing capacity factor, Nqh

22 20 18

ο

φ=45

16 14 ο

φ=40

12 10

ο

φ=35

8 ο

6

φ=30

4 2 0 1

2

3

4

5

6

7

8

9

10

Ratio of depth to diameter, H/D

Fig. 7.7 Horizontal bearing capacity factor for sand as a function of depth to diameter ratio of buried pipelines (ASCE 1984)

where: pu = maximum soil resistance to the pipe transverse (horizontal) direction having units of force per unit length of pipe; yu = transverse displacement at which maximum soil resistance is developed; D = pipe outer diameter; Su = soil undrained shear strength; γ = soil effective unit weight; H = soil depth to centerline of pipe; Nqh , Nch = coefficients from Figs. 7.7 and 7.8.

7.2.3.3

Transverse (Vertical Downwards) Spring

The transverse downward springs are activated mainly in the case of a vertical groundinduced action, such as soil subsidence or normal/reverse faults. It is important to notice that one has to distinguish the downward direction from the upward direction, due to the significantly different soil behavior in those two directions. More specifically, it is quite clear that the downward resistance of the soil is significantly stiffer and the corresponding resistance much higher than the corresponding ones in the upward direction. The following equations for the soil spring assume a bilinear elastic-perfectly plastic soil behavior in the downward direction, and provide the maximum soil resistance and the corresponding transverse relative displacement between the pipe and the soil. These values for the stiffness and resistance soil springs stem from bearing capacity theory for footings in foundations of structural systems.

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Horizondal bearing capacity factor, Nch

8

7

φ=0ο

6

5

4

3 0

2

4

6

8

10

12

14

16

18

20

Ratio of depth to diameter, H/D Fig. 7.8 Horizontal bearing capacity factor for clay as a function of depth to diameter ratio of buried pipelines (ASCE 1984)

 qu =

Su Nc D for clay  γ H Nq D + 1 2γ D 2 N y for sand

(7.18)

z u = 0.10D to 0.15D for both sand and clay where: qu = maximum soil resistance to the pipe transverse (vertical downwards) direction having units of force per unit length of pipe; z u = transverse displacement at which maximum soil resistance is developed; D = pipe outer diameter; Su = soil undrained shear strength; γ = soil effective unit weight; H = soil depth to centerline of pipe; γ = total unit weight of sand; Nc , Nq , N y = coefficients from Fig. 7.9.

7.2.3.4

Transverse (Vertical Upwards) Spring

The following equations for the soil spring assume a bi-linear elastic-perfectly plastic soil behavior in the upward direction, and provide the maximum soil resistance and the corresponding axial relative displacement between the pipe and the soil. These soil springs are inferred from bearing capacity theory for footings in foundations of

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60

Nq Nc

50

Vertical bearing capacity factor, Nγ

Vertical bearing capacity factor

55

45 40 35 30 25 20 15 10 5 0 0

5

10

15

20

25

30

35

40

80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0 0

5

Angle of internal friction, φ

10

15

20

25

30

35

40

Angle of internal friction, φ

Fig. 7.9 Vertical bearing capacity factors versus soil angle of internal friction (ASCE 1984)

structural systems. These characteristic values for defining the soil springs are derived from pull-out capacity theory and laboratory tests on anchor plates and model buried pipes.  qu =  zu =

Su Ncv D for clay γ H Nqv D for sand

(7.19)

0.01H to 0.015H for dense to loose sand 0.1H to 0.2H for stiff to soft clay

where: qu = maximum soil resistance to the pipe transverse (vertical upwards) direction having units of force per unit length of pipe; z u = transverse displacement at which maximum soil resistance is developed; D = pipe outer diameter; Su = soil undrained shear strength; γ = soil effective unit weight; H = soil depth to centerline of pipe; Nqv = coefficient from Fig. 7.10; Ncv = coefficient from Fig. 7.11.

7.2.4 Fault Crossing Example, Using the BNWF Model 7.2.4.1

Description of Software Used

Calculations on the response of buried pipelines under ground-induced actions have been performed with the computer program PLE4Win (r+k 2000), which is a (quasi1D) special-purpose finite element program for the analysis of buried pipelines.

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145

10

φ=44ο

Vertical uplift factor, Nqv

8

φ=36ο

6

4 φ=31ο

2

0 0

1

2

3

4

5

6

7

8

9

10

Ratio of depth to diameter, H/D Fig. 7.10 Vertical uplift capacity factor for sand as a factor of depth to diameter ratio for buried pipelines (ASCE 1984) 10

Vertical uplift factor, Ncv

8

6

4

2

0 0

1

2

3

4

5

6

Ratio of depth to diameter, H/D Fig. 7.11 Vertical uplift capacity factor for clay as a factor of depth to diameter ratio for buried pipelines (ASCE 1984)

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Fig. 7.12 a Beam model with spring support system and b ring model, calculation of actual pipeline behavior

The program uses a pipeline model consisting of a series of loaded beam elements supported by a spring support system. These spring supports represent the soil behavior surrounding the pipeline, see Fig. 7.12a. A finite element calculation is performed on this quasi-1D element configuration. This finite element calculation results in an overall pipeline behavior, including displacements, internal forces and soil reactions. The results are given for the centerline of the actual pipeline. Subsequently, based on the results of this beam calculation, the individual cross-sections are analyzed to provide results for the actual pipeline wall behavior, including stresses, strains and ovalizations, using a ring analysis at the specific cross-section, which employs a Fourier expansion of cross-sectional deformation of the pipe, see Fig. 7.12b. Apart from the standard stress-based elastic calculations, the software can also perform strain-based plastic calculations on the pipelines.

7.2.4.2

Pipe Material and Geometric Characteristics

The calculations presented in this summary describe a pressurized (50 barg) 914.4mm (36-inch) diameter pipeline with a wall thickness of 12.7 mm loaded by a lateral fault movement in soft to firm clay and loose sand. A stress-strain curve, including strain hardening was used in accordance with Fig. 7.13 (DSH curve, blue line). The elastic part of the stress-strain curve for DSH PLE is determined by Young’s modulus

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Fig. 7.13 Stress-strain curve for the BNWF model

and the yield stress, resulting in a (fictive) yield strain. The strain hardening starts at a value of strain, approximately 9 times larger than the yield strain. The initial strain hardening slope is approximately 2% of the elastic slope.

7.2.4.3

Basic Soil Properties, Soil Springs and Ultimate Soil Resistance

The basic soil properties are summarized in Tables 7.3 and 7.4. From the values of Tables 7.3 and 7.4 the ultimate soil resistance and the soil springs were determined, according to NEN 3650. The results are summarized in Table 7.5. Table 7.3 Non-cohesive soils (sand) for a soil element at vertical stress σ v = 50 kPa

Property

Loose

Dense

ϕ’

32°

40°

E’

8 MPa

25 MPa

ν’

0.3

0.3

γ’

18 kN/m3

21 kN/m3

K0

0.47

0.29

16°

22.5°

Pipe-soil interface δ’

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Table 7.4 Cohesive soils (clay) undrained conditions for a soil element at vertical stress σ v = 50 kPa Property

Soft to firm

Stiff

S u = cu (KPa)

50

100

ϕu

0°

0°

E u (MPa)

5

10

νu

0.5

0.5

γ (kN/m3 )

17

19

K 0 = (1-sinϕ’)OCR 0.4

1.06

1.5

OCR = σ ’νmax /σ ’νo

6.6

15.8

PI (%)

30

30

S (%)

100

100

16°

16°

Pipe-soil interface A thin, loose sand layer assumed around pipe with friction angle δ’

Table 7.5 Soil data for soft to firm clay and loose sand for a 914.4-mm (36-inch) diameter pipeline and soil coverage of 2.04 m Soil parameter

Unit

Soft to firm clay

Loose sand

Neutral soil load

N/mm2

0.0363

0.0385

Ultimate vertical soil reaction,upwards

N/mm2

0.0607

0.0642

Ultimate horizontal bearing capacity

N/mm3

0.2146

0.4042

Ultimate vertical bearing capacity, downwards

N/mm2

0.3295

1.5492

Horizontal modulus of sub-grade reaction

N/mm3

0.0117

0.0149

Vertical modulus of sub-grade reaction, downwards

N/mm3

0.0045

0.0068

Vertical modulus of sub-grade reaction, upwards

N/mm3

0.0018

0.0038

Pipe-to-soil friction

N/mm2

0.0125

0.0098

Axial pipe to soil displacement at max. friction

mm

5

6

7.2.4.4

Presentation of Calculation Results

The magnitude of the fault is given as the parameter d. This paragraph provides an overview of results obtained for several fault movement magnitudes (d) in both soft to firm clay and loose sand. The fault movement magnitudes for soft to firm clay vary from d = 200 mm to d = 2000 mm. For loose sand, the range of d amounts 200 to 1000 mm. For fault movement magnitudes larger than 1000 mm in loose sand, the iteration criterion in PLE4Win is not satisfied, resulting in potentially unrealistic outcomes, which are therefore not provided. To give an indication of the pipeline configuration subjected to a fault movement, the lateral horizontal displacements are calculated for both soft to firm clay (see Fig. 7.14) and loose sand (see Fig. 7.15). The horizontal displacements for a wide

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Lat. displ. horizontal (mm)

1,200 1,000

d=200

800

d=600

600

d=1000

400

d=1400

200

d=2000

0 -200 -400 -600 -800 -1,000 -1,200 -15,000

-10,000

-5,000

0

5,000

10,000

15,000

Distance from fault locaƟon (mm)

Fig. 7.14 Lateral horizontal displacements for a pipeline in soft to firm clay; p = 50 barg 600 d=200 d=400

Lat. displ. horizontal (mm)

400

d=600 d=800

200

d=1000 0

-200

-400

-600 -12,000

-8,000

-4,000

0

4,000

8,000

12,000

Distance from fault locaƟon (mm)

Fig. 7.15 Lateral horizontal displacements for a pipeline in loose sand; p = 50 barg

range of different fault sizes give a clear insight into the development of the pipeline configuration. This will be compared and evaluated with respect to the results from the ABAQUS model. The lateral horizontal soil reaction is the most dominant soil reaction for a pipeline subjected to a perpendicular horizontal fault movement. When the maximum lateral horizontal soil reaction is reached, soil breach (failure) will occur. For soft to firm clay, this phenomenon is visible at ±200 N/mm (see Fig. 7.16). For loose sand the maximum lateral horizontal soil reaction is ±370 N/mm (see Fig. 7.17). Comparison of the strains in the pipeline wall will give more insight in the pipeline behavior, as calculated with the two different models. Especially the location of occurrence of the (local) critical point can be observed from these calculation results. An

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S. A. Karamanos et al. 250 200

Lateral soil reacƟon (N/mm)

150 100 50 0 d=200

-50

d=600

-100

d=1000 -150

d=1400

-200 -250 -25,000

d=2000

-20,000

-15,000

-10,000

-5,000

0

5,000

10,000

15,000

20,000

25,000

Distance from fault locaƟon (mm)

Fig. 7.16 Total horizontal soil reaction for a pipeline in soft to firm clay; p = 50 barg 600 d=200 d=400

400

Lateral soil reacƟon (N/mm)

d=600 d=800 200

d=1000

0

-200

-400

-600 -20,000

-16,000

-12,000

-8,000

-4,000

0

4,000

8,000

12,000

16,000

20,000

Distance from fault locaƟon (mm)

Fig. 7.17 Total horizontal soil reaction for a pipeline in loose sand; p = 50 barg

interesting observation on the maximum (total) strain is the fact that the critical location moves further away from the fault location for an increasing fault displacement (d) (see Fig. 7.18 for soft to firm clay and Fig. 7.19 for loose sand). Since loose sand has a higher stiffness than soft to firm clay, the maximum total strains are higher. PLE performs a check on the initiation of local buckling (Gresnigt 1986; NEN 2020). This check is based on experimental data of actual pipeline behavior (see also Chap. 8). This check provides an indication of the occurrence of local buckling behavior of the pipeline under the given circumstances. Figure 7.20 shows an example

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Maximum total equilibrium strains (%)

16 d=200

14

d=600 d=1000

12

d=1400 10

d=2000

8 6 4 2 0 -20,000

-15,000

-10,000

-5,000

0

5,000

10,000

15,000

20,000

Distance from fault locaƟon (mm)

Fig. 7.18 Absolute maximum plastic strains for a pipeline in soft to firm clay; p = 50 barg

Maximum total equilibrium strains (%)

14 d=200 12

d=400 d=600

10

d=800 d=1000

8 6 4 2 0 -15,000

-10,000

-5,000

0

5,000

10,000

15,000

Distance from fault locaƟon (mm)

Fig. 7.19 Absolute maximum plastic strains for a pipeline in loose sand; p = 50 barg

of the check on the local buckling criteria for a pipeline in soft to firm clay and Fig. 7.21 for loose sand. For loose sand the critical buckling criterion is reached for relatively small fault movements (d ≥ 800 mm). The further deformation of the pipe and the development of strains in the pipe wall, after the initiation of local buckling can however not be calculated with the PLE4Win model.

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100 d=200

90

d=600

Check criƟcal buckling (%)

80

d=1000 70

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Fig. 7.21 Check on local buckling criteria for a pipeline in loose sand; p = 50 barg. Values larger than 100% indicate that local buckling can occur

7.3 Modeling Pipe-Soil Interaction Using Three-Dimensional Finite Element Analyses In some special cases, where the accuracy of numerical predictions is required, the response of buried steel pipelines under permanent ground deformations can be examined numerically in a rigorous manner using a general-purpose finite element

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Fig. 7.22 General configuration of the numerical model (before FE meshing) of soil-pipeline system; pipeline is embedded in a soil prism, which is composed by two blocks

program. In that type of models, referred to as “rigorous models”, the pipeline is simulated as an elongated cylinder, embedded in a soil prism with appropriate conditions at the soil-pipeline interface (see Fig. 7.22). The advantages of such a model can be summarized as follows: • • • •

rigorous representation of soil-pipe interaction; more rational simulation of soil deformation than simple springs; explicit calculation of cross-sectional deformation and local buckling; more exact calculation of local stresses and strains at very specific locations around the pipe cross-section, through the pipe wall thickness, and along the pipeline; • powerful tool for straightforward examination of mitigation measures (thickness, soil compaction, friction, trench size, etc.), mainly for fault crossing action. Nevertheless, some issues of concern should also be mentioned: • model development (solid modeling and meshing) and analyses require expertise in the use of advanced computational tools, making it less suitable for use by a wide variety of engineers; • analysis in regular computer hardware may require significant computational time; • convergence problems may arise in the analysis procedure;

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• model can be computationally expensive, especially for pipeline alignment that includes numerous bends; • modeling of large variations in soil properties along the pipe axis is more time consuming than with BNWF models. Nevertheless, this type of modeling has gained quite some attention lately and may be a powerful tool for rigorous finite element analysis of buried pipelines under permanent-induced actions. In the following, guidelines are provided for the development of such models, based on the experience obtained within the GIPIPE project. More information one may find in the works of Vazouras et al. (2010, 2012) and Sarvanis et al. (2018).

7.3.1 Finite Element Model Types In those rigorous models, shell finite elements are employed for modeling of the pipeline. Experience on finite element analyses (Vazouras et al. 2010, 2012) has shown that the use of shell elements can be very efficient in modeling the buried pipeline and can simulate the formation of cross-sectional distortion and local buckling. In particular, shell elements are suggested for modeling the cylindrical pipeline segment and solid elements are recommended to simulate the surrounding soil. The use of reduced-integration elements is advised, so that bending deformation is represented more accurately. Previous experience has also shown that “linear” elements (i.e. four-node shell elements and eight-node solid elements with linear interpolation functions) have provided very good results. Furthermore, one should notice that the use of solid (“brick”) finite elements for modeling the pipe is more expensive than shell, requiring more than 3 elements through the pipe thickness to describe accurately local buckling. Furthermore, solid elements may not provide accurate predictions for the formation of buckling. Therefore, the use of solid finite elements for modeling the pipeline is not recommended.

7.3.2 Model General Description The basic idea in those rigorous models is the consideration of an elongated prismatic model where the steel pipeline is embedded in a soil block, as shown in Fig. 7.22 for the case of a strike-slip fault. A discontinuity plane (e.g. fault plane, edge of landslide or lateral spreading) divides the soil block in two parts. One block is fixed, whereas the other block is movable, simulating ground motion due to the permanent ground action, as shown in Fig. 7.22 for an oblique horizontal fault. This is representative for the case of a fault in a quite straightforward manner but it can be used for the case of other ground-induced actions, such as the edge of a long landslide or liquefied area, as well as for soil subsidence. The interface between the two blocks is the critical

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area, around which maximum pipeline deformation occurs. A rather narrow zone of gradually increasing displacement from the fixed to the moving block can be used, to describe cases where this discontinuity plane is not as sharp as in faults.

7.3.3 Finite Element Meshing For those areas of the pipe where maximum deformation is expected to occur, the finite element mesh should be dense enough so that local deformation of the pipe wall is adequately represented. In those areas, it is recommended that for typical steel pipeline applications, the size of the shell elements in the longitudinal direction can be chosen equal to about 1/20 to 1/25 of the pipeline diameter (see Fig. 7.23). This choice of shell element size ensures that an adequate number of elements exist for describing numerically the pipe wall deformation wavelength in the case of local buckling formation (see Fig. 7.24). The mesh in the circumferential direction should correspond to similar element size. Another criterion may come from the requirement that, in the case of a local buckle, at least three elements should be included in the half wavelength of the buckle. √ This implies that the element size in the axial direction should be a fraction of Dt. In the hoop direction, the shape of buckles is smoother, allowing for a larger element size. Therefore, the element size in the hoop direction is mainly dictated by the requirement for simulating accurately the friction between the soil and the pipe at the interface. The mesh to be employed in the pipe parts away from the critical location can be significantly coarser to reduce the computational cost. The colors in the figure refer to Von Mises stress and are indicative of the development of wrinkling. The relative movement of the two soil blocks is considered to occur within a narrow zone of width w to avoid numerical problems (see Fig. 7.25) and to represent the physical problem more realistically,

Fig. 7.23 Modeling of soil-pipe system in the vicinity of a horizontal (strike-slip) fault: a soil prism and embedded pipeline; b transverse section of the prism; c pipeline cross-section

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Fig. 7.24 Buckling formation in a X65 steel pipeline with D/t equal to 72, subjected to strike-slip fault displacement

Fault

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Fig. 7.25 Three-dimensional pipeline modeling for crossing strike-slip faults; shell finite elements for the pipeline and solid elements for the surrounding soil: a soil-pipeline system, b model cross-section and c pipeline deformation

especially in cases where a gradual increase of soil displacement occurs. The size of this zone has been used equal to 0.33 to 1.0 m in the works of Vazouras et al. (2010, 2012, 2015).

7.3.4 Model Size and Boundary Conditions The top surface of the elongated soil prism represents the soil surface, and the embedment depth should be according to the construction requirements of the pipeline. For

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major pipeline projects, the soil cover on top of the pipe is usually at the order of 1–1.5 m, but deeper embedment conditions may also apply. The dimensions of the soil prism depend on the direction of the soil movement and the corresponding deformation of the soil-pipe system. Experience on numerical simulation of pipe–soil interaction of strike-slip faults has indicated that the total depth of the vertical direction should be about 5 times the pipe diameter, whereas its dimension in the transverse direction should be equal to about 10 times the pipe diameter. Those dimensions have been shown to be adequate for the case of medium-to-firm soil conditions (see Fig. 7.23). In case of very soft soils, it is suggested that, in order to take proper account of soil deformability, these dimensions can be taken larger, although such experience does not exist from the computational point-of-view. In such a case, a trial procedure is required for the specific case under consideration. The aforementioned dimensions have been based on experience from the finite element simulation of strike-slip faults; they may also apply for the case of simulating liquefaction-induced lateral spreading and landslide actions on pipelines. On the other hand, if vertical displacement of the pipeline is analyzed, due to normal/reverse faults or subsidence, the above vertical and horizontal dimensions of the soil prism should be reversed. In such cases, the vertical size of the soil prism should be increased, whereas the horizontal size can be reduced. The soil prism length in the longitudinal direction should be, as a minimum, equal to more than 50 pipe diameters. However, one may consider that this pipeline length is only a small segment of the total pipeline length. In order to adequately model soil-pipe interaction in the axial direction (influence of the pipe and the pipe-to-soil friction outside the prim on the deformations of the pipe section within the prism) the numerical model must include pipeline continuity outside the prism. This should be dealt with by appropriate boundary conditions at the two ends of the pipe segment under consideration. These boundary conditions can be modeled in two alternative ways: 1. The model can be continued outside the prism with pipe elements following the alignment of the pipeline. Soil springs can be placed along the pipe elements in the vertical, transverse and axial direction (see Fig. 7.26). The stiffness of these springs can be determined according to Sects. 7.2.2 or 7.2.3. 2. Appropriate nonlinear axial springs can be employed at each end of the pipeline segment using closed form mathematical expressions (see Fig. 7.27) (Vazouras et al. 2015). Those springs should account for the elastic deformation of the soil and pipe in axial direction and the development of sliding, when the shear stress at the pipe-soil interface reaches its shear strength. Using these nonlinear springs at the two ends of the pipeline in a refined finite-element model, allows for an efficient, accurate nonlinear analysis of the pipe-soil interaction problem at large soil movements with minimal computational cost. With the appropriate modifications in the mathematical expression, these springs can be used to model buried pipelines with both infinite and finite length. Implementation of option 1 allows for modeling accurately any change of pipeline alignment (bends) in a rigorous manner. The length of the pipeline simulated with

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soil springs at each pipeline node

vertical axial transverse horizontal

Fig. 7.26 Rigorous model, continued in the longitudinal direction with pipe elements and springs

equivalent spring

equivalent spring

Fig. 7.27 Rigorous model continued with nonlinear end springs, simulating the continuation of the pipeline in the longitudinal direction; force-displacement equation for the spring is developed in Vazouras et al. (2015)

this option depends on PGD magnitude, soil stiffness, pipe stiffness and pipe-tosoil friction including coating effects. Numerical results for a 914.4-mm (36-inch) diameter pipeline and typical soil conditions (cohesive or non-cohesive) indicated that a length of at least 300 m at either side of the fault is required (Vazouras et al. 2015), whereas for very soft soils, a longer model may be required. The use of a nonlinear axial spring at each end of the model (option 2) is computationally more efficient. However, the most important limitations of using option 2

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are that, outside the soil prism: (a) the pipe must behave elastically and (b) at the point of connection with the finite element model, bending deformation is at a negligible level so that the pipe is subjected to pure tension. This means that the length of the prism must be taken long enough, to ensure that bending deformation due to the transverse component of the ground motion has “dampened out” to a negligible level.

7.3.5 Modeling of Pipe Material Pipe deformations are quite large in the critical area, well into the inelastic range of the pipe material. Therefore, a plasticity model is necessary to describe material behavior. Pipe material can be described with Von Mises plasticity with isotropic hardening (J2 -flow plasticity model). Because of the monotonic type of loading in the case of permanent ground deformation and the absence of reverse plastic loading, the use of isotropic hardening to describe the relation between stress and strain has been shown to be quite effective in modeling the steel pipe material and its calibration can be performed through an appropriate uniaxial stress-strain curve obtained from a tensile test on a coupon specimen from the pipeline material. Most commercial programs have standard options for J2 -flow plasticity, where a specific stress-strain curve, obtained from a typical tensile test, can be considered.

7.3.6 Modeling Soil Material To model the mechanical behavior of soil material, an elastic-plastic material (constitutive) law should be used. It is suggested that the elastic-plastic Mohr-Coulomb constitutive model (Chen and Baladi 1985) can be used, characterized by the cohesion c, the friction angle φ, the elastic modulus E and Poisson’s ratio v. This material constitutive model exists in most of the commercial finite element softwares. The elasto-plastic Mohr-Coulomb constitutive model has been widely used for representing the behavior of all types of soils in numerical analysis of geotechnical applications. The model may be used in its simplest form of an elastic-perfectly plastic model or as an elasto-plastic model with isotropic hardening or softening behavior. The linear isotropic elastic behavior is defined by the Young’s modulus E and Poisson’s ratio v. The Mohr-Coulomb failure criterion assumes that failure is controlled by the maximum shear stress. The Mohr-Coulomb failure criterion is written as τ = c + σ tan φ

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where τ is the shear stress, σ is the normal stress, c is the cohesion of the material and φ is the material angle of friction. Figure 7.28 plots the Mohr circles at failure state and the Mohr-Coulomb failure envelope. The Mohr-Coulomb failure criterion in the deviatoric plane is shown in Fig. 7.29. The failure surface consists of an asymmetric hexagon, which yields lower shear strength in triaxial extension qte than the shear strength in triaxial compression qtc . The default ratio of the two strengths is given by

Fig. 7.28 Mohr-Coulomb failure criterion

Fig. 7.29 Mohr-Coulomb failure criterion in the deviatoric plane

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qtc 1 + sin φ = qte 1 − sin φ

(7.21)

The model is based on a non-associated plastic flow rule. The isotropic hardening/softening behavior may be accounted for in a simple way by varying the cohesion c and friction angle φ as functions of the equivalent deviatoric plastic strain or octahedral shear strain. Moreover, the dilatational behavior of the material is expressed with the dilation angle ψ (used to define plastic potential), which may also be given as a function of the equivalent deviatoric plastic strain or octahedral shear strain, as described by Anastasopoulos et al. (2007). Constitutive model parameters can be calibrated through the results of tests (triaxial, direct shear test). In the absence of such tests, the Mohr-Coulomb criterion can be used without the presence of hardening/softening behavior resulting in an idealized (elastically perfectly plastic) soil behavior. Finally, the Mohr-Coulomb yield criterion is usually combined with a tension-cutoff yield criterion. The predictions of the stress-strain behavior and the volumetric versus axial strain during a simulation of a standard triaxial compression test are given in Figs. 7.30 and 7.31, respectively. In this simulation, no hardening behavior is considered, but the value of the dilation angle ψ is reduced with respect to the magnitude of the equivalent deviatoric plastic strain, so that the volumetric strain remains constant at large strains (critical state). Among other elasto-plastic models commonly adopted for modeling soil behavior is the Drucker-Prager/Cap model with hardening/softening behavior (Chen and Baladi 1985). Moreover, the “modified cam clay” model may be used for modeling the behavior of cohesive soils under drained or undrained conditions. All the above

Fig. 7.30 Deviatoric stress versus axial strain in a triaxial compression test using the Mohr-Coulomb model

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Fig. 7.31 Volumetric strain versus axial strain in a triaxial compression test using the MohrCoulomb model

models can be found as built-in models in general-purpose finite element softwares and specialized geotechnical finite-element or finite-difference commercial programs.

7.3.7 Soil-Pipe Interaction The accurate simulation of both axial and horizontal-transverse soil-pipe interaction is crucial for the rigorous finite element models and an efficient pipeline analysis under large ground-induced deformations. Attention should be paid to the simulation of the axial soil-pipe interaction as, in the case of a soil with dilatancy, an extra stress σ develops at the soil-pipe interface that should be taken into account in the numerical models, as noticed in Sect. 4.2.1. Current design guidelines do not take into account this dilatancy effect and a classical Coulomb friction law cannot describe adequately the soil-pipe interaction in the axial direction. The interface between the outer surface of the steel pipe and the surrounding soil can be simulated with a contact algorithm (in most cases provided from the finite element program employed), which allows separation of the pipe and the surrounding soil surfaces and accounts for interface friction, through an appropriate friction coefficient μ, which depends on the type of the soil. As far as the transverse soil-pipe interaction is concerned, a classical Mohr-Coulomb constitutive model for the cohesionless soil can be employed to simulate quite accurately the soil resistance in this direction, using the residual value of internal angle of friction and a dilation angle equal to zero.

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7.3.8 Variation in Soil Properties The inherent variability of soil mineralogical composition, density, grain size distribution, grain angularity, loading history, etc., affects the variability of its stiffness and strength properties, which are required for accurate soil modeling for the purpose of an efficient pipe-soil interaction analysis. Also the variability of soil properties along the pipeline is associated to different depositional and loading conditions that occurred during the geologic history of the site. This spatial variability of soil properties can be accounted for using simple statistical parameters, such as the mean and variance. Such statistical parameters, evaluated at selected distances along the pipeline, can provide a measure of the spatial variation of the examined property. Also, the method described in Sect. 2.5.4 and Table 2.10 for BNWF calculations may be useful in the case of the rigorous model under consideration; to account for variability of soil properties along the pipeline, the finite element method analyst should partition the soil prism in several parts, assigning the appropriate soil properties at each part. As first example, the soil on each side of a liquefaction edge should have different properties (liquefied and non-liquefied); in such a case, the analyst should use different soil properties at the two soil blocks of the prism. Another example is the change of sediment layers at pipe level, e.g. from sandy soil to clays or even peat. A third example is the use of specific trench backfill (either loose sands, foam types etc.), which reduces the lateral soil resistance near an expected fault area.

7.3.9 Type of Analysis To conduct the pipeline analysis under permanent ground deformation, the ground displacements should be applied at the boundaries of the moving soil block. The analysis should be geometrically nonlinear, in the sense that equilibrium should be considered at the deformed configuration of soil-pipe system. Furthermore, the analysis should be conducted in three steps: 1. gravity loading (weight of pipe and fill and addition of any other top load); 2. operational loading (pressure and temperature); 3. application of PGD using a displacement-controlled scheme, holding one soil block fixed and imposing a gradually increasing displacement pattern at the external nodes of the second block, representing soil displacement. The analysis output consists of the stress and strain resultants in hoop direction of the pipe cross section, as well as the stresses and strains in the longitudinal direction. The analysis proceeds using a displacement-controlled scheme, which increases gradually the ground displacement. At each increment of the nonlinear analysis, stresses and strains at the pipeline wall are recorded. Furthermore, using a fine mesh at the critical pipeline portions, local buckling (wrinkling) formation and post-buckling deformation at the compression side of the pipeline wall can be simulated in a straightforward manner.

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7.3.10 Three-Dimensional Modeling of Pipelines in Landslides Among the various types of permanent ground displacement, the effects of landslide occurrence on a pipeline are of particular interest and require some special attention. The frequency of landslide occurrence is usually much higher compared to other types of permanent ground deformation. The latter take place during a seismic event of significant intensity (fault rupture, lateral spreading), whereas landslides can also be associated with earthquakes of rather small intensity. Sometimes, a landslide may be totally independent of seismic actions. The rapid expansion of the size and geographical distribution of today’s infrastructure (with millions of miles of transmission pipelines) increases the possibility of a pipeline crossing a precarious slope. On the other hand, the exponential growth of urbanized regions and the increasing intensity of environmental restrictions, pose severe limitations on pipeline rerouting to safer corridors. Therefore, the associated risks of landslide triggering rather often guides the pipeline design, and the effects of landslide-induced actions on the pipeline should be accounted for in a rigorous manner. A sophisticated and robust finite element methodology is proposed to simulate the pipeline response subjected to landslide-induced action, parallel and normal to the pipeline axis. It should be noted that a landslide simulation may require modeling of soil of the order of several hundred meters, while on the other hand, the pipe diameter may be up to the order of 1-2 m. In order to model all possible structural instability phenomena (e.g. local bucking, excessive ovalization of the pipe section etc.), a fine finite element mesh is required, and the simulation becomes computationally unattractive. To overcome this computational deficiency, a two-step procedure is proposed, as described in Chap. 6, summarized below for the sake of completeness. First step: the “global” model A “global” model is employed to simulate the evolution of soil movement during the landslide event. The output is a set of displacements to be assigned as boundary conditions at the respective soil nodes of the subsequent step. In the present step, the pipeline presence is tactically ignored-a reasonable assumption for typical landslides. In this global model the model size is manageable, while a relatively coarse mesh is adequate to model the landslide motion. Second step: the “local” model In the second step, a fine “local” model is introduced comprising the pipeline and portion of the surrounding soil. The landslide action is introduced as threedimensional displacement vectors (calculated by the “global” model in the previous step) assigned at the bottom and lateral nodes of the local model. This allows the calculation of pipeline distress as a function of the soil-movement amplitude.

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7.4 Comparison of Numerical (FEM) Calculations and BNWF Model Results Numerical results are obtained for a 914.4 mm (36-inch) -diameter buried pressurized pipeline with a pressure of 50 bar, which crosses strike-slip faults at two different angles (0° and 25°). More specifically, results are obtained for an X65 steel 36-inch pipeline with outer diameter D = 914.4 mm, thickness t = 12.7 mm (1/2 inch), Young’s modulus E = 210 GPa and Poisson’s ratio v = 0.3. The 50 bar pressure is 56% of the yield pressure. The pipeline is buried in a cohesive soil under “undrained” conditions, having a density ρs = 1732 kg/m3 , cohesion c = 50 kPa, friction angle φ = 0°, Young’s modulus E s = 5 MPa and Poisson’s ratio vs = 0.5 referred to as “soft clay”. The FE model used has been previously described, referred to as “rigorous model”, which uses shell elements for simulating the pipe and solid elements for modeling the soil. A nonlinear spring with properties derived through a closed form mathematical solution, proposed by Vazouras et al. (2012) is used as a boundary condition at the ends of the pipeline model to simulate pipeline continuity. At the interface of the pipe-soil model a constant friction value is used equal to 0.3. In addition, the rigorous model is compared with more simplified finite element models that use: • “elbow elements” to model the entire pipe length and springs in three directions, derived from NEN 3650 for the aforementioned soil, to model the surrounding soil. Elbow elements are essentially “pipe” elements (see below) that can additionally take into account cross-sectional deformation; • “pipe elements” to model the entire pipe length and springs in three directions, derived from NEN 3650 for the aforementioned soil, to model the surrounding soil. Figures 7.32 and 7.33 plot the distribution of axial normal strain at the most stressed generator (tension and compression) of the pipeline, for different values of fault displacement d. In particular, Fig. 7.33 shows the distribution of pipeline strain at the critical generators at a stage where the onset of local buckling occurs according to the rigorous model. Considering the convention of local buckling onset introduced in Vazouras et al. (2010, 2012), local buckling occurs at a fault displacement of dcr = 0.61 m; this is the most critical performance criterion in this analysis. The 3% tensile strain criterion, imposed by several standards and guidelines is reached at a larger fault displacement (1.51 m). It occurs at the buckled location, due to buckle folding, at a displacement quite larger than the one corresponding to the formation of the buckle. The pipeline is under pressure, therefore severe cross-sectional distortion does not occur. The BNWF model seems adequate in predicting a conservative value of the axial strain as long as local buckling does not occur. When “pipe elements” are used in ABAQUS, prediction of axial strain is less conservative. Local buckle can be captured explicitly only by the rigorous model. Figures 7.34 and 7.35 show the formation of local buckling at a fault displacement equal to 0.7 m and 1 m respectively. For the other models, an analytical formula is

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needed in order to estimate the occurrence of local buckling. The following formula estimates the axial strain needed for the pipe to exhibit local buckling under the presence of pressure proposed by the CSA Z662 standard, and can be used for design purposes:

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Fig. 7.34 Formation of local buckling at a fault displacement equal to 0.7 m, somewhat beyond buckling onset (at 0.61 m) obtained with the rigorous model

Fig. 7.35 Formation of local buckling at a fault displacement equal to 1 m obtained with the rigorous model

εCu

   σ 2 t h − 0.0025 + 3000 = 0.5 D E  pD pD , i f 2tσ ≤ 0.4 2t y σh = pD 0.4σ y , i f 2tσ y > 0.4

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Fig. 7.36 Distribution of axial strain along the pipeline for different type of models for a fault displacement equal to 1 m

The above formula is based on the work of Gresnigt (1986), and has also been adopted by the NEN 3650 standard in a similar form. According to the above formula, a value of critical axial strain equal to 0.65% is calculated for the case under consideration and is used as a limit value for the formation of local buckling when simplified finite element models (pipe or elbow elements) are used. As shown in Fig. 7.36, a strong dependency exists with different types of models. The fault displacement needed for local buckling is computed equal to 1.04 m when elbow elements and soil springs are used, 0.86 m when pipe elements and soil springs are used, whereas in the dedicated finite element code (PLE4Win) that uses pipe elements and soil springs, a fault value of 2 m is needed for the pipe to reach the above criterion which is a non-conservative value. Figure 7.37 presents the variation of hoop stress along the pipeline for the different type of models at a fault displacement equal to 1 m. Note that PLE4Win computer program uses pipe elements with no cross-sectional deformation and computes cross-sectional deformation a posteriori. That may explain the variation of circumferential stress presented in Fig. 7.37. Finally, Fig. 7.38 depicts the contact pressure at the pipe-soil interface along the pipeline, for a fault displacement equal to 1 m and for different types of models. The soil is modeled through discrete elastic-perfectly plastic springs in “pipe or elbow” element models so that the contact pressure for those types of models reaches a plastic plateau in the vicinity of the fault. This is visible, both for the elbow elements in ABAQUS, as well as the pipe elements in PLE4Win. The differences in results between the PLE/NEN model and the ASCE model may be caused by differences in the way the soil springs are calculated. On the other hand, in the rigorous model, which employs continuum elements, a smoother variation of contact pressure is obtained.

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References ABAQUS (2014) Users’ Manual. Simulia, Providence, RI, USA American Lifelines Alliance (2005) Guidelines for the design of buried steel pipe American Society of Civil Engineers (1984) Guidelines for seismic design of oil and gas pipeline systems. Committee on Gas and Liquid Fuel Lifelines, Technical Council on Lifeline Earthquake Engineering, American Society of Civil Engineers, Reston, Virginia Anastasopoulos I, Gazetas G, Bransby MF et al (2007) Fault rupture propagation through sand: finite element analysis and validation through centrifuge experiments. J Geotech Geoenviron Eng 133(8):943–958 Brinch Hansen J (1970) A revised and extended formula for bearing capacity. Bull No 28, The Danish Geotechnical Institute. Copenhagen, Denmark Comité Européen de Normalisation (2004) Eurocode 7, geotechnical design. CEN EN 1997-1, part I: general, also C1 (2009) and A1 (2013), Brussels, Belgium Canadian Standard Association (2007) Oil and gas pipeline systems. CSA-Z662, Mississauga, Ontario, Canada Chen WF, Baladi GY (1985) Soil plasticity: theory and implementation. Elsevier GeoDelft (1985) Soil investigation behaviour pipelines in clay. Delft, GeoDelft, CO-272040/75 Gresnigt AM (1986) Plastic design of buried steel pipelines in settlement areas. HERON 31(4):1– 113 Korf M, Hergarden HJAM (2002) Integraal ontwerp leidingen en riolen, Grondmechanische randvoorwaarden. Delft Cluster project 04.02.01 Nederlands Normalisatie Instituut (2020) Requirements for pipeline systems. NEN 3650, part-1: general and part-2: steel pipelines, Delft, The Netherlands r+k Consulting Engineers BV (2000) Description and Verification of a new module in PLEMicroCAD to determine the deformation and stress/strain behaviour in the elasto-plastic region of buried steel transport pipelines Sarvanis GC, Karamanos SA, Vazouras P et al (2018) Permanent earthquake-induced actions in buried pipelines: numerical modeling and experimental verification. Earthq Eng Struct D 47(4):966–987 Vazouras P, Karamanos SA, Dakoulas P (2010) Finite element analysis of buried steel pipelines under strike-slip fault displacements. Soil Dyn Earthq Eng 30(11):1361–1376 Vazouras P, Karamanos SA, Dakoulas P (2012) Mechanical behavior of buried steel pipes crossing active strike-slip faults. Soil Dyn Earthq Eng 41:164–180 Vazouras P, Dakoulas P, Karamanos SA (2015) Pipe–soil interaction and pipeline performance under strike–slip fault movements. Soil Dyn Earthq Eng 72:48–65

Chapter 8

Modes of Failure, Limit States and Limit Values Arnold M. Gresnigt, Gert J. Dijkstra, Wouter Huinen, Ioannis Gourousis, Gregory C. Sarvanis, Athanasios Tazedakis, and Nikolaos Voudouris

Abstract Having presented “strain demand” methodologies in the previous chapter, the present chapter refers to the item of “strain capacity” or “strain resistance”, which constitutes the second and final stage of “strain-based” pipeline design methodology. Strain limits are presented and discussed for ultimate and serviceability limit states, and reference to major pipeline standards is made. It is noted that the topic of “strain resistance” is very broad, and impossible to cover in a book dedicated to groundinduced actions on a buried pipeline. It is noted that some topics of strain capacity, such as weld defect tolerance and weld tensile strength require special treatment, and a substantial amount of research work is still performed. Nevertheless, this chapter provides some basic information on this topic, pin-pointing the main features of strain capacity. For more details, the interested reader is referred to relevant publications.

A. M. Gresnigt (B) Faculty of Civil Engineering, Delft University of Technology, 2628 CN Delft, The Netherlands e-mail: [email protected] Gresnigt Consultancy, 2651 XT Berkel en Rodenrijs, The Netherlands G. J. Dijkstra GJ-D Consult, 3155 BV Maasland, The Netherlands Tebodin Consultants & Engineers BV (Bilfinger Tebodin), 3122 HD Schiedam, The Netherlands W. Huinen Bilfinger Tebodin Netherland B.V., 3122 HD Schiedam, The Netherlands I. Gourousis · A. Tazedakis · N. Voudouris Corinth Pipeworks S.A., 32010 Thisvi, Domvraina, Greece G. C. Sarvanis Department of Mechanical Engineering, University of Thessaly, 38334 Volos, Greece © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. A. Karamanos et al. (eds.), Geohazards and Pipelines, https://doi.org/10.1007/978-3-030-49892-4_8

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8.1 Introduction to Pipeline Damage and Serviceability Limit States The previous chapters referred to the actions exerted by the surrounding soil on the pipeline and the calculation of local stress and strain at critical locations of the pipeline. This is called “stress/strain demand” calculation and results in the determination of seismic action (stress, strain) in the pipeline. However, this constitutes only the first part of a seismic design process of a pipeline system under large groundinduced deformations. One has to proceed to design stress/strain verification, in the sense that the relevant stresses, strains and deformations have to be within specific bounds so that the pipeline structural integrity and its operability requirements may not be threatened. For this purpose, failure modes and limit states have to be defined. The major requirement of safe pipeline design is structural integrity in terms of loss of containment. It should be always remembered that the pipeline may undergo significant deformation during a severe seismic event associated with some degree of plasticity and damage. A distinction is made between (a) ultimate limit states, normally related to (severe) loss of structural integrity and (b) serviceability limit states, related to unacceptable loss of function of the system while the structural integrity and pressure containment is maintained. Both the ultimate and the serviceability limit state may be related to the frequency of a certain adverse event, causing the large ground movements.

8.1.1 Pipeline Ultimate Limit States Within the above framework, the following specific ultimate limit states may be considered applicable for pipelines: • through-thickness rupture at a pipeline component (e.g. pipe, girth weld or longitudinal weld, elbow or T-branch connection); • loss of equilibrium or stability of the pipeline or of the supporting structure or excessive local buckling that requires immediate stop of pipeline operation because of unacceptable risk of through-thickness rupture development. Checking pipeline integrity against these ultimate limit states, requires the calculation of the so-called “engineering demand parameters”. Pressure containment requires a minimum resistance against internal pressure (hoop stress). In this case, stresses may not be the appropriate measure of action/resistance to assess pipeline structural integrity. As mentioned above, the pipeline may undergo inelastic deformation and therefore, some small degree of damage may not need to trigger an ultimate limit state. In such a case though, strains may be well beyond the yield limit. Stresses are at yield level or somewhat higher depending on the strain hardening behavior of the applied steel.

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For pipeline design against seismic/geohazard action, strain is the most suitable parameter for assessing the integrity of the pipeline. The ultimate limit state of rupture will occur if the strain exceeds the strain capacity of the pipeline element. When determining the value for the tensile strain capacity, the toughness of pipe material shall be taken into account, as well as the effect of other parameters that may influence the strain capacity, such as geometrical and metallurgical discontinuities at welds (imperfections and different strength and toughness properties of the weld metal and the metal in the heat affected zones). Furthermore, attention should be paid to differences in yield strength in the connected pipes. In case of externally-imposed deformation, the deformations will concentrate in the weaker section of the joint. In this respect, the yield-to-ultimate ratio of the steel is an important factor. When a section is strained, strain hardening will result in higher local strength and further deformations will occur in neighboring sections with less strain, a phenomenon referred to as “redistribution of strains”. Strain is also the main engineering demand parameter for assessing the possibility of local buckling formation. This refers to compressive strain and it is associated with the formation of wrinkles at the pipeline wall, due to structural instability. The last parameter that affects structural integrity is deformation: the limit state manifested by excessive deformation of the pipeline configuration, either globally or at its cross-section, such as excessive ovalization, excessive local buckling or flexural buckling, causing major folds and/or implosion and progressive plastic collapse. The occurrence of such deformations may cause large local strains but does not necessarily lead to rupture and loss of containment. However, local large strains in areas of reduced strain capacity may exceed the ultimate limit state of strain and lead to fracture of pipe wall. Figure 8.1 demonstrates a landslide situation where large tensile strains in the pipeline may occur in the upper part of the landslide, whereas large compressive stresses in the lower part can lead to local or global buckling. Another example is given schematically in Fig. 8.2, showing the impact of a reversed fault on the pipeline, leading to severe compressive strain on the pipe, local and global buckling.

pipeline pipeline in bending and tension

deformed pipeline pipeline in bending and compression

Fig. 8.1 Limit states of tensile strain and buckling developing in a pipeline subjected to landslide action

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soil surface

deformed pipeline

pipeline in bending and global compression (buckling)

pipeline axis

hanging wall

foot wall

Fig. 8.2 Deformation of a pipeline due to reverse fault action

Based on the above, it should be underlined that the classical stress-based approach for pipeline design against internal pressure may not be adequate in the case of a seismic or geohazard design. In such case, a strain-based approach is necessary, where the “engineering demand parameter” is the strain in the pipeline wall at a specific case and this should be used to check all relevant limit states through the corresponding strain limits. According to strain-based design approach, the acting strain on the pipeline wall is called “strain demand” S, whereas the set of required strain limits is often called “strain capacity” or “strain resistance” R. In other words, one may state that to safeguard pipeline structural integrity, S should always be less than R.

8.1.2 Pipeline Serviceability Limit States (Damage Limitation States) Serviceability requirements of a pipeline are necessary, so that a minimum operating level is maintained. This means that the extent and amount of damage of the considered system, including some of its components, shall be limited, so that after damage checking and control have been carried out, the capacity of the system can be restored up to a predefined level of operation. Towards this purpose, the following issues need to be underlined to keep a minimum operating level of the pipeline: • initiation of (local) buckling may occur but no tearing of the pipewall must be allowed due to high local strains; • local deformations need to be controlled so that transportation capacity is maintained to the predefined level and internal inspection tools pass through; • repair may be required but (some) time should be available;

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• pressure integrity may last for a certain period and therefore, the pipeline may be operated at a lower pressure level. In this case, analyses of pressure fluctuations are required to assess the possibility of fatigue failure at the buckled area (Dama et al. 2007). It is also possible to specify the return period of the seismic action for which the damage limitation limit state may not be exceeded. In the lack of a detailed analysis, a return period TDLR of 10 years can be considered. The following limit states are to be taken into account in the context of these guidelines, for both the full integrity requirement, as well as the minimum operating level: 1. Ovalization: the pipeline should not exhibit excessive ovalization or bending deformation, so that pigs and other measuring instruments can pass through. These deformations are associated with plastic deformation. However, also excessive elastic deformations can become a threat in violating a serviceability limit state. Examples of this occur when moving parts, which have limited tolerance (e.g. valves) get stuck, or when deformation violates the tightness, e.g. in flange connections. 2. Local or global buckling: wrinkles that develop to minor or major folds can make the pipeline unfit for use. In general, this type of large unacceptable deformations will induce plastic deformations. Also, the occurrence of local buckling and/or wrinkling causes a reduction of the bending moment capacity, leading to a concentration of the bending curvature and thereby an increase of local tensile strains at the tension side of the buckled/wrinkled cross section of the pipeline. The extent of this tensile deformation depends on the reduction of the bending moment capacity and the deformations of the soil and soil stiffness. 3. (Low cycle) fatigue: in this limit state, variations in the magnitude of load(s) cause strain variations in the steel material (and its weldments) to such a degree that crack initiation and crack growth occurs, eventually leading to fracture and loss of pipeline containments. In case of a locally buckled pipe, a fit-for-purpose analysis may be carried out: analyzing the strain variations because of load variations (mainly internal pressure) and checking these with (low-) cycle fatigue design concepts. If needed, the operating pressure may be lowered in relation to a suitable low cycle fatigue criterion and the time interval until repair. These analyses are beyond the scope of these guidelines. The interested reader is referred to the paper by Dama et al. (2007).

8.2 Tensile Strain Capacity Tensile strain capacity is directly related to pipe wall fracture. In order to guarantee sufficient deformation capacity, the yield strength to ultimate strength ratio should be preferably less than 0.90. In standard design of onshore buried pipelines, the tensile strain is usually limited to 0.5%. However, in the case of large ground-induced deformations, larger strains usually cannot be avoided. Post yielding behavior of

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the pipeline must be analyzed and safe limits for ultimate (plastic) strain must be determined.

8.2.1 Scope of Commonly Used Pipeline Standards One should note that the use of regular codes and standards for pipeline production, design and construction (e.g. API 5L, API 1104, ASME B31.4, ASME B31.8, EN 1594), does not guarantee by any means that the required strain capacity in pipelines under large ground-induced deformations (e.g. up to 3% tensile strain) can be reached. The primary focus of these standards is pressure containment, while the longitudinal stress/strain in pipeline design normally needs to be within the elastic limit. Using those standards, the maximum strain allowed is equal to 0.5%, as noted in API 1104. Higher values of strain can be allowed, as stated in EN 1594, but further requirements are necessary to qualify the pipeline for such a higher-strain demand. In other words, the above regular codes and standards establish minimum safety condition, whereas in geohazard locations (e.g. locations where significant ground-induced deformations are likely to occur), it is necessary to specify special requirements (additional to the regular standards and specifications) to qualify pipeline integrity in high-strain conditions. This imposes higher demands to pipeline resistance against failures, such as local buckling and, mainly, fracture. Useful information on the tensile strain limit of girth welds exists in offshore pipeline standards, in conjunction with “reeling” laying method (originally used for small diameter, but tending also to be used for bigger diameter nowadays) imposes axial strains in the steel pipe up to 3%, in combination with ovalization of the steel pipe cross section. Offshore pipeline codes, such as DNVGL-ST-F101 for submarine pipeline systems and the Dutch NEN 3656 standard specify rules for determination of allowable weld defects in relation to strain capacity. More specifically, DNVGL-ST-F101 considers primarily the value of crack-tip opening displacement (CTOD) obtained with a special-purpose laboratory test, whereas NEN 3656 specifies an Engineering Critical Assessment (ECA) procedure, using wide plate testing.

8.2.2 Influence of Girth Weld and HAZ and Variations in Pipe Bending Strength Assuming the absence of serious defects and damage in the base material of the pipeline, the tensile strain capacity is controlled mainly by the strain capacity of the pipeline girth welds and heat effected zone (HAZ), which are usually the weakest locations against tensile loading due to welding imperfections (in particular planar defects) and high-low induced stress/strain concentrations (sometimes also referred to as “hi-lo”), due to misalignment of the adjacent pipes.

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The weld material should always be “overmatched”, i.e. should have higher yield strength and ultimate strength than the adjacent pipe material, in order to avoid strain concentration at the girth weld. In those locations though, the strain capacity depends not only on the pipe base material and the weld material, but also on: (1) the type, size and location of imperfections in the weld and heat affected zone (HAZ) and (2) the ductility of the weld metal and the HAZ. Inevitably, there is a difference in strength, defined as the product of pipe yield stress σY and the pipe wall thickness t, between the two pipe segments that are joined at the girth weld, even if they have the same specified minimum yield strength and nominal thickness. This difference may result in strain concentration on one side of the girth weld, in the weaker pipe, as observed in a few tests in the TU Delft testing program, described in Sect. 4.3 (van Es 2016). Therefore, when ordering pipes, in addition to specifying minimum yield strength, it is also necessary to limit the yield strength value of each pipe to a maximum value. In addition, discontinuities (e.g. welding imperfections) are always present in pipeline girth (field) welds and must be limited below allowable values. Furthermore, measurements must be taken to ensure sufficient ductility in the weld and HAZ, to ensure that the pipeline is able to sustain significant deformation and reach the desired strain capacity with acceptable reliability. For more information reference is made to standards, e.g. DNVGL-ST-F101 (2017), NEN 3656 (2015) and the Canadian Standard CSA Z662 (2007) and available literature and specialists in this subject, e.g. Fairchild et al. (2016, 2017), Panico et al. (2017) and references as mentioned in next section.

8.2.3 Recommendations from Literature Tensile strain limits are experimentally determined through appropriate tensiletests on strip specimens and in wide plates (Wang et al. 2010). A straightforward approach for determining tensile strain limit of pipeline girth welds is provided by the Canadian standard CSA Z662 (CSA 2007) pipeline design standard, Annex C, for buried defects and for surface-breaking defects. It is based on Crack Tip Opening Displacement Testing (CTOD). The following equation considers surface-breaking defects:    εT u = δ (2.36−1.583λ−0.101ξ η) 1 + 16.1λ−4.45 −0.157 + 0.239ξ −0.241 η−0.315 (8.1) where, εT u is the ultimate tensile strain capacity in %, δ is the CTOD toughness of the weld (0.1 ≤ δ ≤ 1), λ is the yield-to-tensile strength ratio  (0.7 ≤ λ ≤ 0.95), ξ is the ratio of defect length over the pipe wall thickness (2c t) with 1 ≤ ξ ≤ 10, and η is the ratio of defect height over the pipe wall thickness (a / t) with η ≤ 0.5. Background information for the above equation can be found in the paper by Wang et al. (2007) and in Cakiroglu (2015). Considering a slightly defected pipe, with ξ = 0.1, η = 0.1, δ = 0.7 and λ = 0.775, one obtains a value of εT u = 4.5%. It

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is Wang’s suggestion that the value of the ultimate tensile strain εT u for butt-welded pipelines should vary between 2 and 5%. Another method to determine the strain capacity of welds, including all possible imperfections, is performing curved wide plate testing (instead of CTOD). For this method reference is made to Denys and Levevre (2009a, b), the EWI report (Mohr 2003) and the Dutch pipeline code for offshore pipelines NEN 3656. It is noted that the value of 3% is adopted by the EN 1998-4 provisions for seismicfault-induced action on buried steel pipelines. This is a very high value for strain capacity and is not justified in this standard. Research experience from the above research works clearly indicate that such a high value of tensile strain limit should be supported by an appropriate ECA procedure, involving dedicated experimental testing. A more detailed discussion of these values is offered in the next section. One should also note that the above limit values for the maximum tensile strain εT u refer to the “macroscopic” strain calculated from a stress analysis methodology, as described in the previous sections of this book. The value of this strain is quite different than the real strain that exists locally in the vicinity of the girth weld toe.

8.2.4 Requirements and Recommendations for Ultimate Tensile Strain Within the Scope of These Guidelines Adopting a 2 or 3% strain, a tensile strain capacity limit for the strength verification of the pipeline in geohazard areas constitutes a real challenge. One should note that this level is more than 10 times higher than the one corresponding to the yield strain of the pipe material and is considered as excessive loading condition. In order to safeguard the required strain capacity in welds and HAZ, the acceptance of such a high tensile strain level is related to the following additional requirements: 1. for girth welds, the weld metal must be sufficiently overmatched, both for yield and tensile strength, so that the weld metal is stronger than base metal. This aims at avoiding strain concentration in the weld zone. It should be emphasized that there is a statistic distribution of both the base metal strength and the weld metal strength and this feature should be taken into account when selecting the welding consumables for the selected pipes; 2. additional requirements should be set to the Welding Procedure Specification (WPS) and welder qualifications; 3. the acceptance criteria for weld imperfections shall be established in relation to testing and detection capacity of the non-destructive evaluation (NDE) technique to be applied. For strain based design, the use of NDE techniques capable of proper detection of planar defects is a must. Application of AUT (Automated Ultrasonic Testing) techniques is recommended; 4. in any case, suitable requirements for qualification of NDE techniques should be imposed;

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5. for girth welds within areas of possible risk for large ground-induced deformations the strain capacity of the welds and adjacent heat affected weld area shall be validated by suitable ECA procedures for determining the critical weld defect size (in terms of its length and depth), involving CTOD testing or Curved Wide Plate (CWP) testing.

8.3 Compressive Strain Limits Local buckling of the pipe wall, though not necessarily leading to direct loss of containment, is an important limit state, influencing the operability and structural integrity of the pipeline as a whole. The shape of the pipe wall deformation is strongly influenced by the diameter/wall thickness ratio and the level of internal pressure in the pipeline (see Figs. 8.3 and 8.4). A significant number of test results are available when it comes to establish a limit state for the initiation of local buckling and for a detail presentation of this

Fig. 8.3 Local buckling of pipes without internal pressure: a thin-walled pipe with D/t equal to 103; b moderately thick-walled pipe with D/t equal to 70

Fig. 8.4 Local buckling of pipes in the presence of internal pressure: a thin-walled pipe with D/t equal to 103; b moderately thick-walled pipe with D/t equal to 70

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Fig. 8.5 Strain based design: test data and design curve for local buckling initiation in steel pipelines (data from Gresnigt et al. 2017)

topic. A large number of publications is available reporting local buckling tests and analyses of the test results with the parameters that determine the critical curvature. Test results show a large scatter in critical compressive strain. In the COMBITUBE RFCS project (Bijlaard et al. 2014; van Es et al. 2016; Vasilikis et al. 2016) the various factors that are responsible for this scatter have been investigated, see also the publication by Gresnigt et al. (2017). The following formula, is plotted in Fig. 8.5, and estimates the axial strain needed for the pipe to exhibit local buckling under the presence of internal pressure (Gresnigt 1986). It has been adopted by NEN 3650 standard and, in a slightly different form, by the CSA Z662 standard, and can be used for predicting the buckling strain of a steel cylinder under compressive loading, in the presence of internal pressure:   2 t r 2r  ≤ 120, εCu = 0.25  − 0.0025 + 3000 · p · | p| if t r Et   2 2r  t r if > 120, εCu = 0.10  + 3000 · p · | p| t r Et

(8.2)

(8.3)

In the above equation, r  is the radius of the deformed cross section e.g. due to combinations of earth loads and bending. In case of bending, r  can be estimated by the formula in Fig. 8.6. Furthermore, for simplicity in the design calculations, r  may be taken as r , as suggested by the CSA Z662 standard. Simplified expressions for the calculation of the ovalization in case of bending with other loads, such as earth loads may be found in NEN 3651 and in Gresnigt et al. (2017).

8 Modes of Failure, Limit States and Limit Values

r′ =

w

181

r 3w 1− r

deformed (ovalized)

r′

D D′ w

r initial

Fig. 8.6 Change in cross-section shape and calculation of r’

8.4 Ovalization of the Cross Section The ultimate limit value for the smallest diameter of the ovalized cross-section is often taken equal to 0.85D, e.g. in NEN 3650, or D  > 0.85D (see Fig. 8.6). In tests carried out by Spangler (1956), it appeared that at D  ≤ 0.80D there is a risk of collapse. In the present guidelines, D  = 0.85D is indicated as the value for the smallest permissible diameter. For the serviceability limit state a much lower permissible value for the ovalization is taken, e.g. because of the requirements set by the passage of measuring and (intelligent) in-line inspection tools, referred to as PIGS. This is usually agreed between the operator of the pipeline system and the company performing the in-line inspection. A rule of thumb that is used in some pipeline standards specifies an allowable ovalization of approximately 6%, e.g. in NEN 3650. However, this value should be the decision of the pipeline operator.

References American Petroleum Institute (2013) Welding of pipelines and related facilities. API 1104 standard, Washington, DC American Petroleum Institute (2018) Specification for line pipe. API 5L standard, Washington, DC American Society of Mechanical Engineers (2006) Pipeline transportation systems for liquid hydrocarbons and other liquids. ANSI/ASME B31:4 American Society of Mechanical Engineers (2007) Gas transmission and distribution piping systems. ANSI/ASME B31:8 Bijlaard FSK, Gresnigt AM, van Es SHJ et al (2014) Bending resistance of steel tubes in CombiWalls (COMBITUBE), Final Report. RFSR-CT-2011-00034, Research Fund for Coal and Steel (RFCS), European Commission, Brussels, Belgium Cakiroglu C (2015) Tensile strain capacity of energy pipelines. Dissertation, Department of Civil and Environmental Engineering University of Alberta, Canada Canadian Standard Association (2007) Oil and gas pipeline systems. CSA-Z662, Mississauga, Ontario, Canada

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Combitube (2016) Bending resistance of steel tubes in CombiWalls - Final Report. European Commission, Research Programme of the Research Fund for Coal and Steel (RFCS), Brussels Comité Européen de Normalisation (2006) Eurocode 8, Part 4: Silos, tanks and pipelines. CEN EN 1998-4, Brussels, Belgium Comité Européen de Normalisation (2013) Gas supply systems - Pipelines for maximum operating pressure over 16 bar, Functional requirements. EN 1594 Standard, Brussels, Belgium Dama E, Karamanos SA, Gresnigt AM (2007) Failure of locally buckled pipelines. J Press Vess-T ASME 129(2):272–279 Denys R, Levevre A (2009a) Failure characterization of a girth weld with surface-breaking flaw under tensile load. In: Proceedings of pipeline technology conference 2009, Ostend, Belgium Denys R, Levevre A (2009b) Ugent guidelines for curved wide plate testing. In: Proceedings of pipeline technology conference 2009, Ostend, Belgium DNVGL-ST-F101 (2017) Submarine pipeline systems. DNVGL standard (new version of DNVOS-F101), Oslo, Norway Fairchild DP, Panico M, Crapps JM et al (2016) Full-Scale pipe strain test quality and safety factor determination for strain-based engineering critical assessment. In: Proceedings of the 11th International pipeline conference IPC 2016, Calgary, Alberta, Canada, September 26–30 Fairchild DP, Panico M, Crapps JM et al (2017) Benchmark examples of tensile strain capacity prediction and strain-based engineering critical assessment calculations. In: Proceedings of the 27th International ocean and polar engineering conference, San Francisco, CA, USA, June 25–30 Gresnigt AM (1986) Plastic design of buried steel pipes in settlement areas. HERON 31(4):1–113 Gresnigt AM, van Es SHJ, Karamanos SA, Vasilikis D (2017) New design rules for tubes in combined walls in EN 1993-5. In: Proceedings of EUROSTEEL, Sept 13–15, 2017, Copenhagen, Denmark Mohr W (2003) Strain-based design of pipelines. EWI Report, Columbus, Ohio Nederlands Normalisatie Instituut (2019) Requirements for pipeline systems. NEN 3651: Additional requirements for pipelines in or nearby important public works, Delft, The Netherlands Nederlands Normalisatie Instituut (2020) Requirements for pipeline systems. NEN 3650, Part-1: General and Part-2: Steel Pipelines, Delft, The Netherlands Nederlands Normalisatie Instituut (2015) Requirements for pipeline systems. NEN 3656: Requirements for submarine pipeline systems in steel, Delft, The Netherlands Panico M, Macia ML, Fairchild DP, Wentao C (2017) A case study of design and integrity management framework for strain-based pipelines. In: Proceedings of the 27th International ocean and polar engineering conference, San Francisco, CA, USA, June 25–30 Spangler MG (1956) Stresses pressure pipelines and protective casing pipes. J Struct Div-ASCE 82(5):1–33 van Es SHJ (2016) Inelastic local buckling of tubes for combined walls and pipelines. Dissertation, Delft University of Technology van Es SHJ, Gresnigt AM, Vasilikis D, Karamanos SA (2016) Ultimate bending capacity of spiralwelded steel tubes - Part I: Experiments. Thin-Wall Struct 102:286–304 Vasilikis D, Karamanos SA, van Es SHJ, Gresnigt AM (2016) Ultimate bending capacity of spiralwelded steel tubes - Part II: Predictions. Thin-Wall Struct 102:305–319 Wang YY, Horsley D, Liu M (2007) Strain based design of pipelines. In: Proceedings of the 16th Joint technical meeting, Australian Pipeline Association, Canberra, Australia Wang X, Kibey S, Tang H et al (2010) Strain-based design—advances in prediction methods of tensile strain capacity. In: Proceedings of the 12th International offshore and polar engineering conference, ISOPE 2010, Beijing, China

Chapter 9

Simplified Analytical Models for Pipeline Deformation Analyses Due to Permanent Ground Deformation Gregory C. Sarvanis, Spyros A. Karamanos, Polynikis Vazouras, Panos Dakoulas, and Kyriaki A. Georgiadi-Stefanidi Abstract A set of simplified pipeline design methodologies are outlined for the strain analysis and design of pipelines under ground-induced actions from tectonic faults and landslides. The methodologies refer mainly to “strain demand”, as alternatives to the more elaborate finite element methodologies presented in Chap. 7. These simplified methodologies have been either developed by the authors within the GIPIPE project, or adopted from relevant publications in literature. Using those methodologies, the pipeline designer obtains a quick overview of the problem, and identifies the effects of main parameters on pipeline deformation. Comparison of the results from those methodologies with more advanced analysis tools, described in Chap. 7, shows that the simplified methodologies may provide a good level of accuracy. Therefore, they can be used quite efficiently for preliminary pipeline design purposes. The use of these simplified methodologies is illustrated using appropriate design examples.

9.1 Introduction Simple analytical methodologies are presented for calculating the strain in the pipeline wall, induced by ground displacements, directed mainly in the transverse direction of the pipeline. The developed methodologies refer mainly to fault crossing, but they can be used in a broader framework of ground-induced actions (liquefaction lateral spreading, landslides, soil subsidence), where a discontinuity in the soil exists, associated with differential movement of the soil at each side of the discontinuity. The goal of this chapter is to provide the engineer with simple and efficient analytical methodologies for calculating the strain in the pipeline, given the ground-induced action. Considering the pipeline as an elongated cylinder, practically a very long G. C. Sarvanis (B) · S. A. Karamanos · K. A. Georgiadi-Stefanidi Department of Mechanical Engineering, University of Thessaly, 38334 Volos, Greece e-mail: [email protected] P. Vazouras · P. Dakoulas Department of Civil Engineering, University of Thessaly, 38334 Volos, Greece © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. A. Karamanos et al. (eds.), Geohazards and Pipelines, https://doi.org/10.1007/978-3-030-49892-4_9

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beam-like structural system, the strain in the longitudinal direction of the pipeline due to ground-induced action is of major concern in this calculation, which should be combined with the hoop strain to examine whether the pipeline is structurally safe.

9.2 Fault Crossing Analysis The fault crossing problem is shown schematically in Fig. 9.1. In Fig. 9.1a, crossing perpendicular to the fault is shown, whereas in Fig. 9.1b, the general crossing configuration is shown. In this configuration, one may use either angle β or angle θ . deformed pipeline

fault motion

dF θ=90o

β=0

pipeline

fault perpendicular to the pipeline

L a deformed pipeline

fault motion

β

dF pipeline

θ

fault

L b

Fig. 9.1 Schematic representation of the pipeline fault-crossing configuration; a pipeline direction perpendicular to the fault plane; b general crossing configuration

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Table 9.1 Coefficients to obtain design values of fault displacements Effective fault activity Pipe function

Very high

High

Moderate

Low

II

1.0

0.66

0.44

0.29

III

1.5

1.5

1.0

0.66

IV

2.3

2.3

1.5

1.0

9.2.1 Determination of the Fault Displacement Value The average surface fault displacements P G D F in meters can be estimated from the work of Wells and Coppersmith (1994), also mentioned in Sect. 3.2. According to this publication, the maximum displacement for all types of fault motion can be computed in terms of the moment magnitude M of the earthquake: log(P G D F ) = −5.46 + 0.82M   log(σ F ) = 0.42

(9.1)

Similar expressions are offered by Wells and Coppersmith (1994) for the average displacement of the fault. Furthermore, that publication offers similar expressions for specific types of faults (e.g. strike-slip, normal, reverse). Equation 9.1 was developed from data regression, using a combination of strike-slip normal and reverse faulting. The P G D F value represents the vector sum of horizontal and vertical movements along the fault strike. The recommended design fault displacement d F to be used in a pipeline analysis and design procedure is a function of the effective fault activity level. The d F value is the product of the P G D F value with the coefficient shown in Table 9.1. More details on this methodology are provided by Davis (2008). Alternatively, the design value of fault displacement can be obtained by multiplying the P G D F value with the importance factor, introduced in Table 2.2.

9.2.2 Calculation of Strains in the Pipeline In the case of crossing at an angle β equal to zero (or θ equal to 90o ) shown in Fig. 9.1a, the total longitudinal strain consists of two components: • bending strain, denoted as εb ; • longitudinal stretching (membrane strain), denoted as εm1 , due to the fact that the curved shape is always longer than the initially straight shape.

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If the crossing angle β is not zero (or equivalently, angle θ is not 90o ), as shown in Fig. 9.1b, then a third component of membrane strain should be added, denoted as εm2 , due to direct elongation of the pipeline. In addition to numerical models, there exist numerous analytical methodologies. However, most of these analytical methodologies refer to non-straightforward analytical formulations, which require iterative solution methods and are not easy to implement and use in everyday engineering practice. See for example the works by Kennedy et al. (1977), Wang and Yeh (1985) and, more recently, by Takada et al. (2001), Karamitros et al. (2007) and Trifonov and Cherniy (2010). In the following, we only refer to those methodologies that result in closed-form analytical expressions, which are easy to use in engineering practice.

9.2.2.1

Newmark and Hall (1975)

In this methodology, the pipeline is assumed to be a cable, neglecting its bending resistance, and disregarding the bending strain. The axial strain is due to stretching of the pipeline and can be computed as follows:  2 1 dF dF sin β + cos β εm = L 2 L

(9.2)

In this case, only strain components εm1 and εm2 are included. In this methodology, the length L of the deformed S-shape of the pipeline, which is defined as the distance between “inflection points” as noted by Newmark and Hall (1975), is calculated as follows: PY P − PY L = + 2 tu tu

(9.3)

where P is the axial tension in the pipeline,PY is the yield axial tension of the pipe cross-section and tu is the maximum soil resistance in the axial direction. For regular steel material, after yielding, P is practically equal to the yield force of the pipe cross-section PY , therefore, L=2

PY tu

(9.4)

Equations 9.3 or 9.4 have been shown to provide not accurate predictions for length L.

9 Simplified Analytical Models for Pipeline …

9.2.2.2

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The Newmark and Hall (1975) equation is adopted by ALA (2005). However, a factor of 2 is used, perhaps as a “safety factor” accounting for possible un-conservativeness of Eq. 9.2, as follows: εm = 2

dF sin β + L



dF cos β L

2 (9.5)

The length L of the deformed shape is also calculated from Eqs. 9.3 or 9.4 above. The calculation of a reliable value of the “deformed length” L is a crucial issue and will be discussed in the following section.

9.2.2.3

Proposed Methodology

This methodology involves quite some analytical effort for its development, but results in a convenient set of closed-form equations and is very straightforward to use. It can be considered as an amendment of the above equations used in ALA (2005), in the sense that it • considers a realistic shape function of the pipeline; • can simulate both horizontal and vertical fault action; • accounts for flexible-end conditions of the pipe segment, due to pipeline continuity; • offers a reliable and straightforward calculation of the “deformed length”. The problem under consideration can be stated schematically in Fig. 9.2, which is similar to, yet more enhanced than the one shown in Fig. 9.1a. The buried pipeline crosses a discontinuity plane in the ground at angle β (or θ ), as shown in Fig. 9.3. The discontinuity plane is here the tectonic fault plane. However, it may also represent any other type of soil discontinuity, such as the edge of a landslide or the interface between liquefied and non-liquefied soil. An outline of this methodology is offered in the following. The ground on the right side of the fault in Fig. 9.3 moves parallel to the fault direction, by an amount d F with respect to the ground on the left side. Due to this differential ground motion, the pipeline is subjected to both bending and stretching, obtaining an S-shape configuration, also shown in Fig. 9.3. The lengths L 1 and L 2 in Fig. 9.3 correspond to the curved pipe parts of the deformed S-shaped pipeline on each side of the fault, while L i is the distance of the inflection point (point where the curvature changes sign) from the fault plane. The proposed methodology is based on the decomposition of fault action d F in a transverse and longitudinal component (see Fig. 9.1b). Furthermore, it assumes the following shape function for the transverse displacement u(x):

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deformed pipeline

more general case fault motion

β

dF

flexible end conditions

flexible end conditions

θ

pipeline

fault

L2 ≠ L1

L1

Fig. 9.2 Schematic representation of the fault-crossing problem, showing a few particular issues that are accounted for in the analytical solution ⎧ ⎨





 x ˆ 1 + L i ) cos β 1 + 1 sin π x d(L − L +L 0 ≤ x ≤ L 1 +L i 4 L +L 1 i 

1 i  u(x) = ⎩ d(L ˆ 2 − L i ) cos β 1 + 1 sin π(−x+L 1 +L i ) − x+L 2 −L 1 −2L i L 1 +L i ≤ x ≤ L 4 L −L L −L 2

i

2

i

(9.6)  where, d = d F (L 1 + L 2 ) is the normalized ground displacement. This assumed shape function has the advantage of satisfying the condition of zero displacement and slope at the two ends, but also assumes zero curvature at the two ends, so that the decay of bending deformation is described properly as in a real pipeline. In the present formulation, it is always assumed that L 2 is larger than L 1 (L 2 ≥ L 1 ), which means that the soil resistance qu1 is larger than soil resistance qu2 . Assuming elastic response of the pipe, the final stage of transverse deformation in Fig. 9.3b can be decomposed in two bending deformation patterns: (a) the configuration due to differential movement of the supports in the transverse direction, which represents the permanent soil movement of the fault and (b) the configuration due to distributed loading, representing soil resistance. A key assumption is also made at this stage: upon first yielding of pipeline material, the values of lengths L 1 and L 2 remain constant. The main argument in support of this assumption is that, upon yielding at a specific location, deformation will localize at this point, so that the general shape of the pipeline in terms of lengths L 1 , L 2 and L i may not change significantly. The accuracy of this assumption has been verified numerically. More details on this formulation can be found in the recent article of Sarvanis and Karamanos (2017). The design methodology stemming from this formulation is summarized in Table 9.2. For the specific case of a horizontal (strike slip) fault, it is clear that qu1 = qu2 (both equal to a single value pu ), there exists symmetry with respect to the fault plane, so that the methodology becomes more straightforward, and it is described in

9 Simplified Analytical Models for Pipeline …

189

fault motion

z

d sin fault plane

undeformed soil block

Li

deformed pipeline axis

C E

A

d

B

x

d cos

a

L1

z

fault plane

A

d

L2 fault motion

deformed pipeline axis

C

E

deformed soil block

qu 2

undeformed soil block

B

d cos

x

d cos

Li

L1

b

qu1

L2

deformed soil block

d cos

Fig. 9.3 Sketches referring to the analytical methodology: a schematic representation of groundinduced deformation of pipeline, b deformation of pipeline considering only the transverse component of ground-induced deformation

the Table below (for the sake of completeness). In this case, the following equations apply: L 1 = L 2 = L/2, and L i = 0, and therefore, the total length L is equal to 2L 1 or 2L 2 . The methodology is summarized in Table 9.3.

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Table 9.2 Strain calculation for fault crossing; general case crossing angle Step

Methodology

0

Given the geometric and material properties of the pipe (D, t, E, σ y ), the maximum soil resistances of the surrounding soil (qu1 , qu2 , tu ) with qu1 ≥ qu2 , the axial soil displacement xu corresponding to axial soil resistance tu , the imposed fault (ground) displacement d F and the angle β  Calculate the resistance ratio b = qu1 qu2   Calculate the length ratio α = L 1 L 2 from Fig. 9.4 using b = qu1 qu2  Find parameter F(a) from Fig. 9.5a using the length ratio α = L 1 L 2   Calculate the length ratio αi = L i L 2 from Fig. 9.5b using α = L 1 L 2

1 2 3 4 5

Calculate the ground displacement d y for first yielding of the pipe cross section  σ y  t  Dσ y  dy D = E D qu2 F(α)

6

Compute the characteristic lengths of the deformed pipeline L 1 , L 2 and L i : √ 24d y E J 1/4 L 1 = α qu2 +q , L 2 = Lα1 and L i = αi L 2 u1

7

Calculate the maximum bending strain εb and the membrane strain εm :



 2) 2D ω dˆ cos β εm = (32+π dˆ 2 cos2 β + dˆ sin β ω+1 where εb = 8(Lπ1 +L 64 i)   dˆ = d F (L 1 + L 2 ) and ω = L2 xutEu A

8

Calculate the maximum tensile strain εT and the maximum compressive strain εC ; compare with the corresponding strain limits: εT = εb + εm ≤ εT u and εC = εb − εm ≤ εCu

Table 9.3 Strain calculation for “perpendicular” fault crossing with angle θ = 90o (β = 0o ) Step Methodology 0

Given the geometric and material properties of the pipe (D, t, E, σ y ), the maximum soil resistances of the surrounding soil ( pu , tu ), the axial soil displacement xu corresponding to axial soil resistance tu , the imposed ground displacement d F and the angle β

1

Calculate the ground displacement d y corresponding to first yielding of the pipe cross  σ y  t  Dσ y  d section. Dy = 42 5 E D pu

2

Compute the characteristic lengths of the deformed S-shape of the pipeline L 

12d y E J 1/4 L=2 pu

3

Calculate the maximum bending strain εb and the membrane strain εm : εb = π4LD dˆ cos β



   2) ω dˆ 2 cos2 β + dˆ sin β ω+1 εm = (32+π where dˆ = d F L and ω = L2 xutEu A 64

4

Calculate the maximum tensile strain εT and the maximum compressive strain εC ; compare with the corresponding strain limits: εT = εb + εm ≤ εT u εC = εb − εm ≤ εCu

2

9 Simplified Analytical Models for Pipeline …

191 0.200

1.0 0.9

0.175

0.8 0.150

= L1 / L2

= L1 / L2

0.7 0.6 0.5 0.4

0.125 0.100 0.075

0.3 0.050

0.2 0.025

0.1

0.000

0.0 0

1 2

3

4

5 6

7

20

8 9 10 11 12 13 14 15 16 17 18 19 20

30

40

50

60

70

80

90

100 110 120 130 140 150

b = qu1 / qu2

b = qu1 / qu2

a

b

    Fig. 9.4 Length ratio α = L 1 L 2 in terms of soil resistance ratio b = qu1 qu2 ; a diagram for b values between 0 and 20 and b diagram for b values between 20 and 150 9

0,35

8

0,30

7

0,25

αi = L /L i 2

6

F

5 4

0,20 0,15

3

0,10 2

0,05

1

0,00

0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0,0

1.0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

α = L1/L2

= L1 / L2

a

b

Fig. 9.5 Function F(α) and length ratio αi in terms of length ratio α

9.3 Examples for Fault Crossing 9.3.1 Example 1 A buried pipeline, with diameter equal to 914.4 mm (36 in), wall thickness equal to 11.91 mm (0.469 in), made of X65 steel σ y = 490 MPa crosses a strike-slip fault. The soil is cohesionless (sand) with properties shown in Table 9.4. The geometric Table 9.4 Soil parameters and geometric properties for Example 1 ϕ

KO

γ (kg/m3 )

H c (m)

D (m)

t (m)

pu (kN/m)

t u (kN/m)

yu (m)

36°

0.5

1800

1.3

0.9144

0.01191

318.6

40.5

0.003

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and material parameters of the pipe are also tabulated in Table 9.4. Compute the maximum longitudinal strain in the pipeline: • for crossing angle β equal to 30o and fault displacements equal to 0.914 and 1.371 m; • for crossing angle β equal to 60o and fault displacements equal to 0.914 and 1.371 m. The pipeline crosses a strike-slip fault, therefore the methodology described in Table 9.3 is applicable. In the present case, the fault displacement at which the pipe cross section enters the plastic zone (row 1 of Table 9.3) is        dy Dσ y 42 σ y  t 490000 0.01191 0.9144 × 490000 42 = ⇒ d y = 0.328 m = D 5 E D pu 5 210000000 0.9144 318.6

  Subsequently, considering J = π D 3 t 8 and dˆ = d L, the length L of the curved pipe segment based on the equation of the row 2 of Table 9.3 is  L=2 

12d y E J pu

1/4 ⇒

12 × 0.33 × 210000000 × L=2 318.6

π×0.91443 ×0.01191 8

1/4 = 19.62 m

It is also necessary to calculate parameter ω (end flexibility factor) as follows L ω= 2



19.62 tu = xu E A 2



40.5 = 0.425 0.003 × 210000000 × π × 0.9144 × 0.01191

Finally, for the prediction of strain in the pipeline wall the equations in row 3 and 4 of Table 9.3 are used: • for angle β = 30o and ground displacement 0.914 m. π2D ˆ π 2 × 0.9144 0.914 cos 30o = 0.464% d cos β ⇒ εb = 4L 4 × 19.62 19.62    (32 + π 2 ) ˆ 2 ω ⇒ εm εm = d cos2 β + dˆ sin β 64 ω+1    0.425 (32 + π 2 ) 0.9142 cos2 30o 0.914 sin 30o = 0.73% = + 64 19.622 19.62 0.425 + 1 εb =

Therefore the maximum tensile strain is εT = εb + εm = 1.19%

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193

• for angle β = 30o and ground displacement 1.371 m. π2D ˆ π 2 × 0.9144 1.371 d cos β ⇒ εb = cos 30o = 0.695% 4L 4 × 19.62 19.62    (32 + π 2 ) ˆ 2 ω ⇒ εm εm = d cos2 β + dˆ sin β 64 ω+1    0.425 (32 + π 2 ) 1.3712 cos2 30o 1.371 sin 30o = 1.11% = + 64 19.622 19.62 0.425 + 1 εb =

Therefore the maximum tensile strain is εT = εb + εm = 1.81% • for angle β = 60o and ground displacement 0.914 m π2D ˆ π 2 × 0.9144 0.914 cos 60o = 0.268% d cos β ⇒ εb = 4L 4 × 19.62 19.62    (32 + π 2 ) ˆ 2 ω 2 ˆ • εm = ⇒ εm d cos β + d sin β 64 ω+1    0.425 (32 + π 2 ) 0.9142 cos2 60o 0.914 sin 60o = 1.21% = + 64 19.622 19.62 0.425 + 1

• εb =

• Therefore the maximum tensile strain is • εT = εb + εm = 1.48% • for angle β = 60o and ground displacement 1.371 m π2D ˆ π 2 × 0.9144 1.371 cos 60o = 0.401% d cos β ⇒ εb = 4L 4 × 19.62 19.62    (32 + π 2 ) ˆ 2 ω 2 ˆ ⇒ εm = d cos β + d sin β 64 ω+1    0.425 (32 + π 2 ) 1.3712 cos2 60o 1.371 sin 60o = 1.83% εm = + 64 19.622 19.62 0.425 + 1 εb =

Therefore the maximum tensile strain is εT = εb + εm = 2.23% Comparison of the above predicted strains with finite element results and the predictions from the semi-numerical method proposed by Karamitros et al. (2007) is presented in Tables 9.5 and 9.6.

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Table 9.5 Comparison of predictions from proposed methodology with a semi-numerical methodology and FEM results for angle β equal to 30o

Table 9.6 Comparison of predictions from proposed methodology with a semi-numerical methodology and FEM results for angle β equal to 60o

d (m)

Max tensile strain % Proposed methodology

Semi-numerical

FEM

0.914 (1D)

1.19

1.25

1.46

1.371 (1.5D)

1.81

1.70

1.85

d (m)

Max tensile strain % Proposed methodology

Semi-numerical

FEM

0.914 (1D)

1.48

1.52

1.57

1.371 (1.5D)

2.23

2.50

2.25

9.3.2 Example 2 A 1524-mm-diameter (60 in), X42 steel (σ y = 290 MPa) pipeline with 8.1 mm (0.319 in) wall thickness crosses a normal fault with dip-angle equal to 70o , which implies a value equal to 20o for the angle β. Calculate the maximum strain in the pipeline for two different ground displacements (design values of fault movement) equal to 0.3 and 2.0 m. In the present case, cause of the normal fault, a non-symmetric soil resistance exists, and the methodology described in Table 9.2 should be applied. The soil properties in terms of the corresponding soil resistances (according to the ALA Guidelines) are presented in Table 9.7. Using the soil resistance values in Table 9.7 the soil resistance ratio is equal to  b = qu1 qu2 = 1100/50 = 22 From Figs. 9.4 and 9.5 the length ratios α, αi and the parameter F(α) are  α = L 1 L 2 = 0.144  αi = L i L 2 = 0.272 F(α) = 1.48 Table 9.7 Soil parameters for Example 2 q u upward (kN/m)

qu downward (kN/m)

tu axial (kN/m)

z u upward

z u downward

xu axial

50

1100

45

0.015

0.150

0.003

9 Simplified Analytical Models for Pipeline …

195

Therefore, the fault displacement at which the pipe cross section enters the plastic zone (row 5 of Table 9.2) is calculated as follows:    dy σy  t Dσ y F(α) = D E D qu2     0.0081 1.524 × 290000 290000 × 1.48 ⇒ d y = 0.146 m = 210000000 1.524 50 The characteristic lengths L 1 , L 2 and L i of the deformed shape of the pipeline are obtained from row 6 of Table 9.2, as follows: L1 =

√



24d y E J α qu2 + qu1

1/4

⇒ L1 =

√



24 × 0.146 × 210000000 × 0.144 50 + 1100

π ×1.5243 ×0.00811 8

1/4 = 3.497 m

 where J = π D 3 t 8, and L2 =

L1 3.497 = = 24.27 m α 0.144

L i = αi L 2 = 0.272 × 24.27 = 6.60 m L = L 1 + L 2 = 3.497 + 24.27 = 27.76 m The end flexibility parameter ω is also calculated as follows: ω=

L 2



tu 3.497 + 24.27 = xu E A 2



45 = 0.596 0.003 × 210000000 × π × 1.524 × 0.0081

Finally, strain predictions are calculated from rows 7 and 8 of Table 9.2 for angle 20o andtwo different ground displacements equal to 0.3 and 2.0 m, considering that dˆ = d F (L 1 + L 2 ): • for angle β = 20o and ground displacement equal to 0.3 m εb =

0.3 π2 D π 2 × 1.524 dˆ cos β ⇒ εb = cos 20o = 0.189% 8(L 1 + L i ) 8 × (3.497 + 6.60) 3.497 + 24.27

  (32 + π 2 ) ˆ 2 ω ⇒ d cos2 β + dˆ sin β 64 ω+1    0.596 (32 + π 2 ) 0.32 cos2 20o 0.3 sin 20o = 0.14% + εm = 64 (3.497 + 24.27)2 3.497 + 24.27 0.596 + 1 

εm =

Therefore the maximum tensile strain is

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Table 9.8 Comparison between predictions from the proposed methodology and FEM results

d F (m)

Max tensile strain % Proposed methodology

FEM

0.3

0.33

0.28

2.0

2.29

2.42

εT = εb + εm = 0.33% • for angle β = 20o and ground displacement equal to 2.0 m εb =

2.0 π2 D π 2 × 1.524 dˆ cos β ⇒ εb = cos 20o = 1.26% 8(L 1 + L i ) 8 × (3.497 + 6.60) 3.497 + 24.27



  (32 + π 2 ) ˆ 2 ω ⇒ d cos2 β + dˆ sin β 64 ω+1    0.596 (32 + π 2 ) 2.02 cos2 20o 2.0 sin 20o = 1.03% εm = + 64 (3.497 + 24.27)2 3.497 + 24.27 0.596 + 1 εm =

Therefore the maximum tensile strain is εT = εb + εm = 2.29% The strain predictions from the proposed analytical methodology are compared with finite element results in Table 9.8 showing a very good comparison. The two examples presented above indicate that the present analytical methodology can be used for predicting the strains induced in the pipeline because of fault movement, in a simple, straightforward and efficient manner. The proposed methodology constitutes a simple yet very useful tool for the preliminary design of pipeline design against geohazards.

9.4 Transverse (Horizontal) Ground-Induced Action on the Pipeline Due to Landslide The following sketch in Fig. 9.6 offers a general representation of the physical problem of a pipeline crossing a landslide area in a direction perpendicular to soil movement. In this sketch, d SG is the displacement of the moving soil mass used for pipeline design and is the product of the permanent ground displacement value of landslide displacement P G D S , computed by Eq. 3.7, and the coefficient in Table 9.9. Furthermore, d S P is the corresponding maximum transverse displacement of the pipeline. It should be underlined that the value of d S P may not always be equal to d SG , depending on the width of the moving block W.

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197

general case dLS

ground motion

deformed pipeline

dL pipeline center line

W Fig. 9.6 Graphical representation of pipeline deformation due to transverse action of landslide or lateral spreading (liquefaction)

Table 9.9 Coefficients for obtaining slope movement design value d SG (Davis 2008)

Pipe function

Design slope movement coefficient

II

1.0

III

1.6

IV

2.6

9.4.1 Methodology Proposed by Liu & O’ Rourke (1997) Two cases are considered: (a) the case of “wide” ground moving zone large value of W, as shown in Fig. 9.7 and (b) the case of “narrow” ground moving zone [small W ], as shown as shown in Fig. 9.8. Wide moving zone In this case, because of the large size of the moving soil block, it can be readily assumed that d SG = d S P and an assumed shape u(x) for the deformed pipeline is considered, as follows:   dS P 2π x u(x) = 1 − cos (9.7) 2 W The bending strain εb : is obtained by double-differentiation of Eq. 9.7 to calculate the pipeline longitudinal curvature, and subsequently it is readily calculated: εb =

π 2 Dd S P W2

(9.8)

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dSG

............ ............ ............ ............ ............ ............ ............ ............ ............ ............ ............ ............ .. ............ ............ ............ ............ ............ ............ ground motion ............ ............ ............ ............ ............ ............ .. ............ ............ ............ ............ ............ ............ ............ ............ ............ ............ ............ ............ .. ............ ............ ............ ............ ............ ............ ............ ............ ............ ............ ............ ............ .. ............ ............ ............ ............ ............ ............ ............ ............ ............ ............ ............ ............ .. ............ ............ ............ ............ ............ ............ ............ ............ ............ ............ ............ ............ ............ ............ ............ ............ ............ ............ .. d =d ............ ............ ............ ............ . ............ ............ ............ ............ ............ ............ ............ ............ SP

wide zone case

deformed pipeline

SG

pipeline

center line

L

L W

Fig. 9.7 Pipeline deformation due to transverse action of landslide or lateral spreading (liquefaction) with a “wide” ground moving zone

narrow zone case

dSG ground motion

u(x) A

dSP d S P , i.e. the entire soil movement is not transferred to the pipeline. Therefore, the axial (membrane) strain is neglected and the bending strain is calculated by the maximum moment of a pipe segment AB in Fig. 9.8, assumed with fixed-fixed end conditions. The calculation from simple mechanics readily results in the following expression for the bending strain: εb =

pu W 2 3π Et D 2

(9.10)

9.4.2 American Lifeline Alliance—ALA (2005) There is no distinction between “wide” or “narrow” zone in the ALA (2005) guidelines. On the other hand, both Eqs. 9.8 and 9.10 are considered for the bending strain, and it is stated that the real bending strain will be the smaller value from those two equations. In addition, no axial strain is given in ALA (2005).

9.4.3 An Enhanced Methodology for Transverse Landslide Action on Pipelines At this stage, an important argument is stated: suppose that the width of the zone W is very large. Then, according to Eqs. 9.8 and 9.9, the bending strain becomes negligible. Nevertheless, this may not be true. After a certain value of W, the strain should remain the same and be independent of the value of W. In such a case, the physical problem will be exactly the same as the horizontal fault crossing problem, where the fault will play the role of the “edge” of the landslide. Furthermore, the exact value of the width will be inconsequential. Therefore, the fault crossing equations in Table 9.3 can be used under the condition that W is larger than L. On the other hand, for the “narrow” ground zone i.e. when W is less than L, a similar approach would require the repetition of the methodology described in Sect. 9.2, but with a new and more appropriate shape function, which would account for the “cantilever” conditions at point C and the “decay” conditions at point O of Fig. 9.8. This is out of the scope of the present work. Alternatively, to simplify the analysis, a displacement function of the following form can be considered, as shown in Fig. 9.8 with a dotted line. u(x) =

πx  dS P

1 − cos 2 W

(9.11)

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Double differentiation of this function provides the curvature and the bending strain, whereas calculation of elongation due to stretching would provide the average axial strain. However, in this “narrow” zone case, it is clear that the value of d S P is less than the corresponding ground displacement (d SG ) and, in addition, is very difficult to calculate or estimate. Therefore, those assumed-shape approaches may not be suitable for this case. To overcome this issue, the “equilibrium-based” Eq. 9.10 can be employed for pipeline design subjected to transverse landslide action. An improvement of this equation, towards increasing the conservativeness of this approach, would be to consider that segment AB of Fig. 9.8 is pinned-pinned, instead of fixed-fixed, so that the maximum bending moment results in the following equation for the bending strain: εb =

pu W 2 2π Et D 2

(9.12)

The axial (stretching) strain in the case of a “narrow” zone should be much smaller than the bending strain. Liu and O’Rourke (1997) proposed a methodology for estimating axial strains in the case of a “narrow zone”. However, this methodology has not been validated using the present rigorous models, and is not included in the present guidelines. The interested reader is referred to the paper by Liu and O’Rourke (1997) for more relevant information.

9.5 Axial (Horizontal) Ground-Induced Action on the Pipeline Due to Landslide For continuous pipes exhibiting permanent ground-induced action in the longitudinal direction due to landslide action, no distinction between the ground displacement d SG and the corresponding pipeline displacement d S P is made. In this case, d SG = d S P = d S as shown in Fig. 9.9. According to the ALA (2005) guidelines, two axial forces F1 and F2 should be computed. The value of F1 is computed assuming the pipe is elastic and fully compliant with the soil and F2 is the ultimate force that the soil can transfer to the pipe: F1 =



E Atu (d S )

(9.13)

and  F2 = (tu L S ) 2

(9.14)

The pipeline should be designed for an axial force F, which is the minimum of F1 and F2 . In the above expressions, tu is the ultimate axial soil resistance of soil per

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dS initial soil position

ground motion pipeline

Ls

final soil position

Fig. 9.9 Schematic representation of a buried pipeline under longitudinal permanent ground deformation caused by a landslide

unit pipe length acting on the pipe in axial direction and L S is the length of the pipe in soil mass undergoing movement (see Fig. 9.9).

9.6 Examples for Landslides 9.6.1 Example for Landslide Motion Transverse to the Pipeline A buried pipeline, with diameter equal to 914.4  mm (36 in), wall thickness equal to 11.91 mm (0.469 in), made of X65 steel σ y = 490 MPa crosses a slope with potential hazard for a landslide, with a zone W equal to 10 m. The direction of the pipeline is perpendicular to the direction of the landslide movement, and soil displacement d SG equal to 2.0 m is expected in this landslide motion. The soil is cohesionless (sand) with the properties shown in Table 9.10. The geometric and Table 9.10 Soil parameters and geometric properties ϕ

KO

γ (kg/m3 )

H c (m)

D (m)

t (m)

pu (kN/m)

t u (kN/m)

yu (m)

36°

0.5

1800

1.3

0.9144

0.01191

318.6

40.5

0.003

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material parameters of the pipe are also shown in Table 9.10. Assume the same soil properties inside and outside the moving landslide block. Initially, the given width of the zone should be categorized as narrow or wide. Based on the methodology described in Sect. 9.4.3, assuming a wide landslide block, the length L of the methodology described in Table 9.3 should be computed. In the present case, the soil displacement at which the pipe cross section enters the plastic zone (row 1 of Table 9.3) is:    Dσ y d y 42 σ y  t = D 5 E D pu     490000 0.01191 0.9144 × 490000 42 ⇒ d y = 0.328 m = 5 210000000 0.9144 318.6   Subsequently, considering J = π D 3 t 8 and dˆ = d L, the length L of the curved pipe segment, using the equation in row 2 of Table 9.3 can be calculated as follows: ⎛ ⎞1/4 3  12 × 0.33 × 210000000 × π ×0.91448 ×0.01191 12d y E J 1/4 ⎠ ⇒ L = 2⎝ L=2 = 19.62 m pu 318.6 

The landslide width W is smaller than the length L. Therefore, the present block can be regarded as a narrow block. In this case, the maximum applied bending strain in the pipewall can be calculated using Eq. 9.12, as follows: εb =

pu W 2 318.6 · 102 = = 0.24% 2π Et D 2 2π · 210000000 · 0.01191 · 0.91442

The calculation provides a bending strain equal to 0.24%. If the width W of the landslide at the same location is equal to 50 m, then W is larger than the length L, and this means that the landslide zone is a “wide” zone. In such a case, the applied bending strain in the pipewall can be calculated using the methodology presented in Sect. 9.2.2.3. The length of the deformed S-shape of the pipeline was calculated previously equal to 19.62 m. Moreover, it is necessary to calculate parameter ω (end flexibility factor) as follows: ω=

L 2



19.62 tu = xu E A 2



40.5 = 0.425 0.003 × 210000000 × π × 0.9144 × 0.01191

Finally, for the prediction of strain in the pipeline wall the equations in row 3 and 4 of Table 9.3 are used considering a crossing angle β = 0o and ground displacement 2.0 m: εb =

π2D ˆ π 2 × 0.9144 2.0 cos 0o = 1.17% d cos β ⇒ εb = 4L 4 × 19.62 19.62

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  (32 + π 2 ) ˆ 2 ω 2 ˆ ⇒ εm = d cos β + d sin β 64 ω+1    0.425 (32 + π 2 ) 2.02 cos2 0o 2.0 sin 0o = 0.2% εm = + 64 19.622 19.62 0.425 + 1 

Adding these two values, the maximum tensile strain, induced in the pipewall is εT = εb + εm = 1.37%

9.6.2 Example for Landslide Motion Parallel to the Pipeline A 1524-mm-diameter pipeline (60 in), made of X42 steel (σ y = 290 MPa) with 8.1 mm (0.319 in) thickness crosses an unstable slope (from top to bottom of the slope), with potential hazard for a landslide. The soil movement is parallel to pipeline direction with length L S equal to 100 m and expected ground displacement equal to 1.0 m. The soil axial resistance (tu ), according to the ALA Guidelines, is equal to 45 kN/m. Assuming the pipe is elastic and fully compliant with the soil, the applied force in the pipeline F1 is calculated as follows: F1 =



E Atu (d S ) =

 210000000 · 3.14 · (1.524 − 0.0081) · 0.0081 · 45 · 1.0 = 19092 kN

On the other hand, the maximum load that soil can transfer to the pipeline, F2 is calculated as follows:   F2 = (tu L S ) 2 = (45 · 100) 2 = 2250 kN Therefore, the design axial force induced to the pipeline should be equal to 2250 kN. The pipeline should be capable of sustaining this axial force.

References American Lifelines Alliance (2005) Seismic Guidelines for Water Pipelines American Society of Civil Engineers (1984) Guidelines for the seismic design of oil and gas pipeline systems, prepared by the ASCE Technical Council on Lifeline Earthquake Engineering Davis CA (2008) Assessing geotechnical earthquake hazards for water lifeline systems with uniform confidence. In: Proceedings of ASCE geotechnical earthquake engineering and soil dynamics IV, Sacramento, CA, paper 4291 Karamitros DK, Bouckovalas GD, Kouretzis GP (2007) Stress analysis of buried steel pipelines at strike-slip fault crossings. Soil Dyn Earthq Eng 27:200–211

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Kennedy RP, Chow AW, Williamson RA (1977) Fault movement effects on buried oil pipeline. J Transp Eng-ASCE 103:617–633 Newmark NM, Hall WJ (1975) Pipeline design to resist large fault displacement. In: Proceedings of U.S. national conference on earthquake engineering, pp 416–425 Liu X, O’Rourke MJ (1997) Behaviour of continuous pipeline subject to transverse PGD. Earthquake Eng Struct Dynam 26:989–1003 Sarvanis GC, Karamanos SA (2017) Analytical model for the strain analysis of continuous buried pipelines in geohazard areas. Eng Struct 152:57–69 Takada S, Hassani N, Fukuda K (2001) A new proposal for simplified design of buried steel pipes crossing active faults. Earthquake Eng and Struct Dynam 30:1243–1257 Trifonov OV, Cherniy VP (2010) A semi-analytical approach to a nonlinear stress–strain analysis of buried steel pipelines crossing active faults. Soil Dyn Earthq Eng 30:1298–1308 Wang LRL, Yeh YA (1985) A refined seismic analysis and design of buried pipeline for fault movement. Earthquake Eng Struct Dynam 13:75–96 Wells D, Coppersmith K (1994) New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement. Bull Seism Soc Am 84(4):974–1002