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A Critical Review on the Vulnerability Assessment of Natural Gas

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Pipelines Subjected to Seismic Wave Propagation. Part 1: Fragility

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Relations and Implemented Seismic Intensity Measures

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Grigorios Tsinidis1, Luigi Di Sarno2, Anastasios Sextos3, and Peter Furtner4

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1University of Sannio, Italy & Vienna Consulting Engineers ZT GmbH, Austria

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2University of Sannio, Italy & University of Liverpool, United Kingdom

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3University of Bristol, United Kingdom & Aristotle University of Thessaloniki, Greece

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4Vienna Consulting Engineers ZT GmbH, Austria

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Corresponding Author: Grigorios Tsinidis, University of Sannio, School of Engineering,

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Piazza Roma, 21, 82100, Benevento, Italy, email: tsinidis.grigorios@gmail.com

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Abstract: Natural gas (NG) pipeline networks constitute a critical means of energy

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transportation, playing a vital role in the economic development of modern societies. The

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associated socio-economic and environmental impact, in case of seismically-induced severe

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damages, highlights the importance of a rational assessment of the structural integrity of this

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infrastructure against seismic hazards. Up to date, this assessment is mainly performed by

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implementing empirical fragility relations, which associate the repair rate, i.e. the number of

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repairs/damages per unit length of the pipeline, with a seismic intensity measure. A limited

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number of analytical fragility curves that compute probabilities of failure for various levels of

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predefined damage states have also been proposed, recently. In the first part of this paper, a

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thorough critical review of available fragility relations for the vulnerability assessment of

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buried NG pipelines is presented. The paper focuses on the assessment against seismically-

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induced transient ground deformations, which, under certain circumstances, may induce non-

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negligible deformations and strains on buried NG pipelines, especially in cases of pipelines

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crossing heterogeneous soil sites. Particular emphasis is placed on the efficiency of

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implemented seismic intensity measures to be evaluated or measured in the field and, more

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importantly, to correlate with observed structural damages on buried NG pipelines. In the

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second part of this paper, alternative methods for the analytical evaluation of the fragility of

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steel NG pipelines under seismically-induced transient ground deformations are presented.

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Through the discussion, recent advancements in the field are highlighted, whilst acknowledged

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gaps are identified, providing recommendations for future research.

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Keywords: Natural gas pipelines; fragility; seismic intensity measures; transient ground

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deformations; steel pipelines

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1. Introduction

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Natural gas (NG) holds a significant share in the global energy market, whilst projections for

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the next two to three decades indicate an increasing dependence of the global energy demand

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on this fossil fuel (International Energy Agency, 2015). NG is most commonly distributed from

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wells to end-users, through extensive onshore networks of buried pipelines, made almost

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exclusively of large-diameter steel pipes.

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The increasing dependence of the energy demand of seismic prone areas on NG (e.g. south-

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eastern Europe, China, Japan, New Zealand, west USA), gives rise to the question of the

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seismic performance and resilience of NG networks. Earthquake-induced damages on NG and

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fossil-fuel networks may lead to significant downtimes, which in turn may result in high direct

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and indirect economic losses, not only for the affected area and state, but also at trans-national

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level. Moreover, severe damages may trigger ignition or explosions with life-treating

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consequences and significant effects on the environment. For instance, the rupture of an oil

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pipeline near the Santa Clara River in Colorado, USA, during the 1994 Northridge earthquake,

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caused a large oil spill, with approximately 5 miles of pipeline empty to the ground and into

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the river (Leville et al., 1995). The above aspects highlight the importance of simple, yet

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efficient, seismic analysis and vulnerability assessment methods, to be used for the design of

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new NG networks and the evaluation of the resilience of existing networks, as well as for the

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post-earthquake management of the seismic risk through rapid and rational evaluation of

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damages on existing networks. However, the seismic structural assessment of this type of

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lifelines is not a straightforward task. The structural characteristics of the pipeline segments

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(e.g. material type and strength, diameter, wall thickness, coating smoothness), the existence

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and quality of the connections (i.e. between the pipeline segments or between the pipeline and

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other network elements), the corrosion state and the operational pressure of the pipeline, as

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well as the significant variations of the geomorphologic and geotechnical conditions and the

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seismic hazard along the pipeline length, are among the parameters that may affect

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significantly the seismic behaviour and vulnerability of NG networks (O’Rourke M.J. and Liu,

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1999).

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In practice, the seismic risk assessment of pipelines is mainly performed, by implementing

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empirical fragility relations, constructed on the basis of observations of the behaviour of buried

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pipelines during past earthquakes. A limited number of analytical fragility curves that compute

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probabilities of failure in the ‘classical sense’ have also been proposed, recently (Lee et al.,

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2016; Jahangiri and Shakid, 2018). Based on the above considerations, the main objective of

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this two-part review paper is to critically revisit available tools for the seismic vulnerability

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assessment of buried NG pipelines. The discussion focuses on the vulnerability of steel NG

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pipelines subjected to transient ground deformations due to seismic wave propagation, which

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contrary to common belief may induce non-negligible strains on the pipeline, particularly in

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cases where the pipeline is crossing highly heterogeneous soil sites. In this part of the paper a

37

thorough critical review of available fragility relations for the vulnerability assessment of

38

buried pipelines is presented. Particular emphasis is placed on the efficiency of implemented

39

seismic intensity measures to be evaluated or measured in the field and, more importantly, to

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correlate with observed structural damages on NG pipelines. In the second part of this paper, a

1

thorough review of alternative methods for the analytical evaluation of the vulnerability of

2

steel NG pipelines is presented, focusing on the assessment against buckling failure modes due

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to seismically-induced transient ground deformations, which constitute a critical damage mode

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for this infrastructure. Additionally, a new methodological approach for this assessment is

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presented. The paper highlights the recent advancements in the field, reports gaps and

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challenges, which call for further investigation, and provides means for an efficient assessment

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of steel NG pipelines against seismically-induced buckling failure modes. It is worth noticing

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that seismic wave propagation may trigger liquefaction phenomena to liquefiable soil sites,

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which may lead to significant permanent soil deformations imposed on the pipelines. These

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effects are out of the scope of the present study.

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2. Seismic performance and critical failure modes of buried NG pipelines

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Contrary to above ground structures, the seismic response of which is directly related to the

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inertial response of the structure itself, the seismic response of embedded structures, including

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buried pipelines, is dominated by the kinematic response of the surrounding ground (O’Rourke

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M.J. and Liu, 1999; Hashash et al., 2001; Scandella, 2007). Post-earthquake observations have

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demonstrated that seismically-induced ground deformations may induce extensive damages on

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buried pipelines. More specifically, buried steel NG pipelines were found to be vulnerable to

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permanent ground deformations associated with seismically-induced ground failures, i.e. fault

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movements, landslides, liquefaction-induced settlements or uplifting and lateral spreading

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(O’Rourke M.J. and Liu, 1999). Although to a lesser extent, transient ground deformations,

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induced by seismic wave propagation, have also contributed to steel pipelines damage

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(Housner and Jenningst, 1972; O’Rourke T.D. and Palmer, 1994; O’Rourke M.J., 2009). An

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increasing seismic vulnerability of NG pipelines was actually reported on steel pipelines that

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were previously weakened by corrosion or poor quality welds (EERI, 1986; Gehl et al., 2014).

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Permanent ground deformations commonly induce a higher straining on the steel pipelines,

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compared to transient ground deformations; therefore, most research efforts have been mainly

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focused on this seismic hazard (Karamitros et al., 2007; Vazouras et al., 2010; Vazouras et al.,

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2012; Kouretzis et al., 2014; Vazouras et al., 2015; Vazouras et al., 2016; Karamitros et al.,

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2016; Melissianos et al., 2017a, 2017b, 2017c; Demirci et al., 2018; Sarvanis et al., 2018,;

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Tsatsis et al. 2018, among many others). However, statistically it is more likely for a pipeline

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to be subjected to transient ground deformations rather than seismically induced permanent

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ground deformations. Additionally, studies have demonstrated that pipelines embedded in

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heterogeneous sites and/or subjected to asynchronous ground seismic motions are likely to be

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affected by appreciable deformations and strains due to transient ground deformations, which

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in turn may lead to damages on the pipeline (Psyrras and Sextos, 2018; Psyrras et al., 2019).

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Along these lines, this study focuses on the transient ground deformation effects.

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A critical step in developing adequate tools for the seismic analysis, design and vulnerability

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assessment of NG pipelines under transient ground deformation effects is to identify the

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mechanisms that lead to failures on this infrastructure. The existence of joints and their

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characteristics were found to affect significantly the seismic performance of pipelines,

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generally leading to diverse damage modes on them during past earthquakes. On this basis,

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pipelines are commonly classified as continuous or segmented (O’Rourke M.J. and Liu, 1999).

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In the former case, pipeline segments are assembled by means of welding (e.g. welded, flanged

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or fused joints), with the welds being at least as strong as the pipe segments. On the contrary,

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mechanical joints are implemented for segmented pipes (e.g. coupled joints or bell and spigot

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joints), which generally constitute the weak points of the pipeline. Continuous pipelines are

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commonly preferred in NG networks. Supra-regional transmission networks are almost

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exclusively made of large diameter steel pipelines, whist for local distribution networks, steel,

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PVC or polyethylene pipelines of small diameters are commonly used.

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Under certain circumstances, transient ground deformation may trigger diverse damage modes

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on continuous buried NG pipelines, including (i) shell-mode or local buckling, (ii) beam-mode

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buckling, (iii) pure tensile rupture, (iv) flexural bending failure and (v) excessive ovaling

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deformation of the section (O’Rourke M.J. and Liu, 1999).

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Shell-mode or local buckling is associated with the loss of stability caused by compressive or

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bending loading on the pipe. Commonly, NG networks are made of high strength steel

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pipelines (i.e. σy > 350 MPa) with radius over thickness ratios R/t < 40. For these

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characteristics, shell mode instabilities are expected to occur in the inelastic range of response

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(Kyriakides and Korona, 2007). In particular, with increasing axial or bending loading on the

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pipeline, strains begin to localize at ‘critical sections’ of the pipeline. Subsequently, the axial

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stiffness of the pipe gradually decreases and wall wrinkles begin to develop at these sections,

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followed by a limit load instability or a secondary, usually non-axisymmetric, bifurcation. The

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highly localized strains and deformations may lead to wall tearing and hence gas leakage.

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Imperfections of the pipelines, such as initial deviations of the walls of the pipeline from the

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perfect geometry, may affect significantly the nonlinear load-displacement path (Kyriakides

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and Korona, 2007). This failure mode, which has been observed on steel buried pipelines

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during past earthquakes (Housner and Jenningst, 1972; O’Rourke M.J., 2009), is more likely to

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occur near geometric imperfections of the pipelines, or discontinuities such as girth welds and

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elbows. Local buckling of buried pipelines has been a subject of early and recent studies (e.g.

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Chen et al., 1980; Lee et al., 1984; Yun and Kyriakides, 1990; Psyrras et al., 2019) and is

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further examined in the second part of this paper.

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Beam-mode or ‘upheaval’ buckling leads to an upward bending of the pipe, which in some

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cases may even seen as a reveal of the pipe out of the ground surface. This failure mode, which

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is likely to occur in cases of shallow-buried pipelines with low radius over thickness (R/t)

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ratios, resembles the Euler buckling mode of a column under high compression axial loading

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and has been observed on steel oil, gas and water pipelines during past earthquakes

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(McNorgan, 1989; Mitsuya et al., 2013). Beam-mode buckling rarely leads to deformations

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localization that may cause breakages and leakages. However, it may affect the serviceability

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of the pipeline by reducing the flow of content. Along these lines, the definition of a limit state

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on a quantitative basis is not a straightforward task. A series of numerical and experimental

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studies have been recently carried out to further elaborate on the upheaval buckling mode (e.g.

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Wang et al., 2011; Mitsuya et al., 2013).

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The burial depth and the flexural stiffness of the pipe, the existence and amplitude of initial

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geometrical imperfections on the pipe walls, as well as the soil properties of the trench, are

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among the parameters that may control the occurrence of a shell- over a beam-mode buckling

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failure mode on a steel pipeline (Yun and Kyriakides, 1990). However, it is quite common the

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above failure modes to interact. Investigating this interaction, Meyersohn and O’Rourke T.D.

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(1991) proposed a critical trench depth for buried steel pipelines that govern which failure

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mode is preceded. They also suggested that a minimum cover depth of 0.5-1.0 m suffices to

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prevent a beam-mode buckling.

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Under excessive tensile axial loading, steel NG pipelines may be subjected to significant

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plastic longitudinal strains, which in turn may lead to tensile rupture or tensile fracture.

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Tensile failures rarely occur in steel pipelines with butt arc welds. On the contrary, they were

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observed in gas-welded slip joint pipelines during the 1994 Northridge earthquake (O’Rourke

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T.D. and O’Rourke M.J., 1995). Generally, X-grade steel pipelines, which are commonly used

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in NG networks, may reach ultimate tensile strains of the order of 20 %. These tensile strain

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limits are extracted from tension tests on strip specimens of base steel material, far away from

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welds. However, imperfections associated with the welding process are expected to reduce the

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ductility of steel pipelines. In an effort to account indirectly for the reduced ductility capacity

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of the welded pipe weakest locations, i.e. girth welds, as well as for wall imperfections, lower

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limits of the order of 2 - 4 %, are commonly adopted in the design practice for steel NG

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networks (e.g. JGA, 2000; EN 1998-4, CEN 2006), while other studies propose even less limit

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strains, of the order of 0.5 %, e.g. (Gantes and Bouckovalas, 2013). In any case, the

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identification of the actual ultimate strain is of great importance for the accurate evaluation of

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the response of steel pipelines under compressive axial loading, since work hardening is found

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to affect the critical buckling load of the pipe.

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Although theoretically it may occur, flexural failures of steel pipelines, associated to excessive

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bending, are rarely expected on buried NG pipelines, owing to the high ductile steel grades

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used. However, excessive bending may lead to beam buckling failures or ovalization of the

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pipeline, depending on the radius over wall thickness (R/t) ratio of the pipe.

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Large radial deformations, associated with significant bending forces, may lead to a flattening

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of the circular cross section of a pipe in an oval-like shape, a response pattern that is also know

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as the Brazier effect (Brazier, 1927). This deformation pattern is not expected to affect the

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structural integrity of the pipeline; however, it is may reduces the flowing capacity. An

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ovalization limit, i.e. , has been proposed by Gresnigt (1986), prescribing the

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change of pipe diameter over the nominal diameter of the pipe D.

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Clearly, distinct failure modes may have different consequences on the structural integrity and

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serviceability of NG networks. Understanding the main response mechanisms behind the

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0.15dDD=

dD

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identified failure modes, on the basis of rigorous experimental and numerical studies, may

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contribute towards a reliable definition and quantification of limit states for NG steel pipelines.

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3. Fragility relations for the assessment of buried pipelines under

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seismically-induced ground transient deformations

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3.1 Steps in quantitative risk assessment of NG networks

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Aleatory and epistemic uncertainties play a vital role in earthquake engineering, as they

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propagate through all the stages of analysis and assessment. The rapid evolving of the

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computational capabilities, in addition to our increasing understanding of these inherent

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uncertainties on the seismic response and vulnerability of civil infrastructure, have led to a

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shifting from conventional deterministic analysis procedures to probabilistic risk assessment

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concepts. On this basis, the quantitative risk assessment of a NG network should involve the

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following critical steps (Honegger and Wijewickreme, 2013): (i) definition of the

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characteristics of elements at risk (e.g. pipeline dimensions and steel grade, trench soil

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properties) and the target performance and acceptable levels of risk, (ii) determination of the

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expected seismic hazards and of their likehood of occurrence, accounting for the associated

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uncertainties, employing probabilistic methods, (iii) assessment of vulnerability of the

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elements at risk (e.g. pipelines) under the expected seismic hazards (e.g. ground transient

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deformations on buried NG pipelines), and (iv) evaluation of the probabilities of occurrence of

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consequences associated with predefined damage states (e.g. Omidvar et al. 2013; Jahangiri

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and Shakid, 2018). The third step of the above procedure is commonly applied in practice,

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employing fragility relations defined for the elements at risk; in the case examined herein, the

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NG pipelines.

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Contemporary standards and guidelines (e.g. ALA, 2001; JGA, 2004; EN1998-4, CEN 2006)

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provide some specifications for the seismic design of buried pipelines. However, only ALA

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(2001) provides guidelines for the seismic vulnerability assessment of buried steel pipelines,

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referring mainly to water-supply steel pipelines. In this context, available fragility relations,

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referring to other typologies of buried pipelines, constitute the basis for the assessment of NG

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pipelines (Gehl et al., 2014).

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Generally, the seismic fragility of any element at risk can be determined as the conditional

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probability that the response reaches or exceeds a structural limit state (LS), for a given seismic

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intensity measure (IM). Limit states do not necessarily refer to collapse or total failure but

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instead are related to predefined levels of damage state. Fragility relations or curves are used

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to prescribe the probability that the induced seismic demand D is equal or higher than the

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corresponding to a predefined limit state structural capacity C, for a given seismic IM, i.e.

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(1)

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A number of approaches may be used to develop fragility curves, which can be grouped under

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empirical, expert-judgement-based analytical and hybrid (Rossetto and Elnashi, 2003; Elnashai

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Fragility P D C IM=é³ ù

ëû

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and Di Sarno, 2015; Jalayer et al., 2017; Bakalis and Vamvatsikos, 2018). The definition of the

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structural limit states should be based on an adequate Engineering Demand Parameter (EDP),

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describing the response of the element at risk; the pipeline in the particular case. It is clear that

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both the definitions of the EDP and the IM are of prior importance for the development of

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adequate fragility curves.

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6

3.2 Empirical fragility curves for buried pipelines

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A variety of probabilistic empirical fragility relations have been proposed over the last 40 years

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for buried pipelines, based on post-earthquake observations of their response under

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seismically-induced permanent or transient ground deformations. The majority of these

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relations provide correlations between the pipeline repair rate, RR, i.e. the number of pipe

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repairs per unit of pipeline length, and a selected seismic IM, and are commonly expressed in

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either linear or power law forms (ALA, 2001), i.e.:

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(2)

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The parameters a and b are defined on the basis of a regression analysis of available post-

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earthquake damage reports of buried pipelines. It is worth noticing that the following terms

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have been used in relevant studies, instead of repair rate: damage rate, damage ratio or failure

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rate, all describing the number of pipe repairs per unit of pipeline length (Piccinelli and

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Krausmann, 2013). Having estimated the RR, the probability to have a total number of n

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damages (i.e. leaks or breaks) and repairs for a pipeline track of length L is given via a Poisson

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distribution, as follows (Gehl et al., 2014):

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(3)

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The probability of a pipe failure may then be computed as:

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(4)

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assuming that the pipe fails when at least one damage has been occurred along its length.

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An overview of available empirical fragility relations for buried pipelines, subjected to

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seismically-induced transient ground deformations, is presented in the ensuing, in

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chronological order, without being restricted to NG pipelines.

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Katayama et al. (1975) presented the first charts of seismically-induced damages on brittle

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buried pipes, using data from six earthquakes in Japan, USA and Nicaragua. The study did not

30

account for the pipe material, diameter and joint characteristics; however, it considered the

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effect of soil conditions on the reported damage. The seismic hazard intensity was expressed in

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terms of peak ground acceleration (PGA).

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A few years later, Ιsoyama and Katayama (1982) presented a PGA-based fragility relation

34

based on damages on cast iron pipelines reported during the 1971 San Fernando earthquake.

35

Eguchi (1983) developed fragility functions for welded steel, asbestos cement and cast iron

36

pipes, using observations from four earthquakes in USA and employing the Mercalli Modified

37

Intensity (MMI) as seismic IM. This study constitutes the first case, where pipe damages

38

( ) ( )

/ or /

oob

RR n repairs km a IM RR n repairs km a IM=´=´

( ) ( )

!

n

RR L

RR L

PN n e

n

-´

´

== ´

( )

101

RR L

f

PPN e

-´

=-= =-

-8-

caused by seismically-induced transient ground deformations and permanent ground

1

deformations were disaggregated. Barenberg (1988) proposed fragility curves for buried cast

2

iron pipes based on damage reports from three earthquakes in USA, introducing for the first

3

time the peak ground velocity (PGV) as seismic IM.

4

Ballentine et al. (1990) presented a series of MMI-based fragility functions for water steel

5

pipelines, using observations from six earthquakes in USA. Later studies also developed MMI-

6

based fragility relations for various typologies of pipelines (Eguchi, 1991; O’Rourke T.D. et

7

al., 1991) on the basis of recorded damages in USA. The Technical Council on Lifeline

8

Earthquake Engineering of the American Society of Civil Engineers (ASCE-TCLEE, 1991)

9

proposed PGA-based fragility relations, reanalyzing damage data on water-supply systems

10

from previous studies (Katayama et al., 1975). PGA-based fragility relations were also

11

proposed by Hamada (1991) and O’Rourke T.D. et al. (1991) employing damage reports from

12

earthquakes in the USA and Japan.

13

A PGV-based fragility relation was proposed by O’Rourke M.J. and Ayala (1993) for brittle

14

cast iron pipelines, using damage reports from earthquakes in USA and Japan. The study

15

highlighted the effect of corrosion state of the pipelines on their seismic vulnerability. The

16

proposed fragility relation was later adopted by FEMA in the HAZUS methodology (NIBS,

17

2004) for the evaluation of seismic vulnerability of pipes subjected to seismically-induced

18

transient ground deformations. A reduction factor, i.e. 0.3, was introduced on the initial

19

fragility relation in order this to be applicable for ductile pipelines, such as steel NG pipelines,

20

as well. It is worth noticing that the particular fragility function does not account for the critical

21

effect of the size of the pipe on its seismic vulnerability.

22

Reanalyzing the pipeline damage reports used by O’Rourke M.J. and Ayala (1993), Eidinger et

23

al. (1995) developed a new PGV-based fragility relation. The study that was further described

24

in Eidinger et al. (1998) examined the effect of a number of salient parameters on the seismic

25

vulnerability of buried pipelines, i.e. the pipe diameter, material, joint type, coating, the trench-

26

soil conditions and the date of installation. The effects of the above parameters were

27

considered in the proposed fragility relation through the introduction of a modification factor

28

K1 and a quality index, the latter related with the confidence of the available empirical data set.

29

Reanalyzing damage reports from previous studies (Katayama et al., 1975; TCLEE-ASCE,

30

1991; Hamada, 1991; O’Rourke et al., 1991), Hwang and Lin (1997) developed a new PGA-

31

based fragility function for buried pipelines.

32

Trifunac and Todorovska (1997) developed fragility relations for water-supply pipelines, using

33

damage reports from the 1994 Northridge earthquake in California, USA. The fragility

34

relations were plotted on basis of damage rates per square km of land area, while the severity

35

of the ground motion was described employing the peak soil shear strain (γmax), computed near

36

the soil surface, as: , where Vs,30 is the average shear wave velocity of the top

37

30 m of the soil deposit.

38

O’Rourke T.D. et al. (1998) implemented a detailed geographic information system (GIS) to

39

examine for a first time the efficiency of various seismic IMs to correlate with observed

40

max ,30s

PGV V

g

=

-9-

damage rates of pipelines. The study employed reported damages on cast iron pipelines of the

1

water-supply system of California, induced by the 1994 Northridge earthquake. From the

2

seismic IMs that were considered in the study, i.e. MMI, PGA, PGV, spectral acceleration SA,

3

spectral intensity SI, and Arias intensity Ia, PGV was found to be more efficient in correlating

4

with observed damages. A year later, a new fragility relation was proposed by O’Rourke T.D.

5

and Jeon (1999) for cast iron pipes using data from the same earthquake in California, USA. A

6

new metric, i.e. the scaled velocity, was used seismic IM, defined by normalizing PGV by the

7

diameter of the pipe, so as to account for the effect of the pipe size on its seismic vulnerability.

8

Reported damages on the water-supply network of Kobe during the destructive 1995

9

Hyogoken-Nambu earthquake were exploited by Isoyama et al. (2000) to develop PGA- and

10

PGV-based fragility relations for steel pipes. A series of correction coefficients were proposed

11

to account for the effects of pipe material and diameter, trench-soil conditions, as well as soil

12

liquefaction occurrence, on the seismic vulnerability of pipelines.

13

In 2001 the American Lifelines Alliance (ALA, 2001) published detailed guidelines for the

14

seismic assessment of water-supply networks, which included PGV-based fragility relations for

15

buried pipelines subjected to seismically-induced transient ground deformations. The relations

16

that were defined using more than 80 damage reports from diverse seismic events in USA, are

17

provided as ‘backbone’ curves that may properly be adjusted through correction parameters, so

18

as to account for the effects of salient parameters, such as the pipe material and diameter and

19

the joint characteristics, on the seismic vulnerability of the pipe. It is worth noticing that the

20

relations were derived from very scattered damage data, which refer mainly to brittle pipes

21

made of cast iron or asbestos cement.

22

Chen et al. (2002) examined the response of NG and water-supply pipelines of the Taichung

23

City during the 1999 Chi-Chi earthquake and developed fragility relations for various pipe

24

diameters and materials (polyethylene, steel, cast iron) using relevant damage reports. A

25

variety of relations were actually developed using PGA, PGV and spectrum intensity SI, as

26

seismic IMs. Interestingly, the researchers noticed a better correlation of damage rates with

27

PGA, while PGV was found to be the worst damage indicator. However, their relations and

28

relevant observations were based on rather limited damage reports. Pineda and Ordaz (2003)

29

developed PGV-based fragility functions for brittle cast iron and asbestos cement water pipes

30

based on the observed behaviour of the water-supply system of Mexico City during the 1985

31

earthquake.

32

Reanalysing the fragility relations proposed by O’Rourke M.J. and Ayala (1993) and Jeon and

33

O’Rourke T.D. (1999), O’Rourke M.J. and Deyoe (2004) revealed differences on their

34

predictions, which were attributed to various parameters, including the seismic wave type that

35

dominated the ground-pipeline system response in each reported case, the corrosion state of the

36

pipe and the low statistical reliability of some of the used data. Classifying the statistical

37

reliable damage reports and making reasonable assumptions regarding the dominant seismic

38

wave in each case, the researchers proposed PGV-based relations in a first effort to account for

39

the type of the controlling seismic wave. The main assumption for the development of the

40

-10-

latter curves was that body shear waves, i.e. S-waves, control the response and damage

1

potential of pipelines that are located near the seismic source, whereas surface Rayleigh waves,

2

i.e. R-waves, govern the pipeline response in far-field sites. Finally, assuming an apparent

3

velocity of 500 m/s and 3000 m/s for the R-waves and the S-waves, respectively, the

4

researchers computed the Peak Ground Strain (εg) (see Section 4.2.4) for each damage case and

5

developed εg-based fragility relations. Generally, a more consistent correlation between

6

reported damages on pipelines and Peak Ground Strain (εg) was reported by the researchers

7

compared to PGV.

8

Reanalyzing pipeline damage reports from the study of O’Rourke T.D. et al. (1998), Jeon and

9

O’Rourke T.D. (2005) proposed PGV-based fragility functions for various types of pipelines,

10

i.e. welded steel, cast iron, ductile iron and asbestos cement pipelines.

11

The 1985 Michoacán earthquake in Mexico City was used as a case study by Pineda-Porras

12

and Ordaz (2007) to propose a fragility relation for the seismic vulnerability assessment of

13

brittle water-supply pipelines embedded in soft soil, introducing a new vector seismic IM, i.e.

14

PGV2/PGA. The proposed IM was claimed to correlate better with observed damages compared

15

to PGV, particularly in cases of soft soils. Two years later, an updated εg-based fragility

16

function for buried segmented pipelines was presented by O’Rourke M.J. (2009).

17

O’Rourke T.D. et al. (2014) examined the response of buried water-supply, wastewater and

18

NG pipeline networks of Christchurch, New Zealand, during the 2011 Canterbury earthquake

19

sequence. Using damage reports of brittle water-supply pipelines, they developed PGV-based

20

fragility relations, with PGV being defined as the geometric mean peak ground velocity. The

21

study highlighted the very good performance of the NG distribution network, which consisted

22

mainly of very ductile high-density polyethylene pipes. Extending his previous study

23

(O’Rourke M.J., 2009) with observed damage reports from the 1999 Kocaeli earthquake in

24

Turkey, O’Rourke M.J. (2015) proposed a new εg-based fragility relation.

25

A summary of commonly used empirical fragility relations for buried pipelines, subjected to

26

seismically-induced transient ground deformations, is provided in Table 1.

27

Based on the above overview, it is evident that most empirical fragility relations have been

28

proposed for water-supply pipeline networks. In this context, the implementation of these

29

functions in steel NG pipelines, the dimensions and the operational pressures of which, are

30

quite distinct, might be questionable. Based on comparisons of the predictions of available

31

empirical fragility relations with reported damages on buried pipeline networks during the

32

1999 Dutze earthquake, in Turkey, and the 2003 Lefkas earthquake, in Greece, Alexoudi

33

(2005) and Pitilakis et al. (2005), suggested the use of the Isoyama et al. (2000) fragility

34

relations for NG networks, while the use of ALA (2001) relations was proposed for water-

35

supply and waste-water networks.

36

Gehl et al. (2014) suggested that the empirical fragility relations by O’Rourke M.J. and Ayala

37

(1993), as adopted by HAZUS (NIBS, 2004), Eidinger et al. (1995), Isoyama et al. (2000) and

38

ALA (2001), constitute adequate candidates for the assessment of continuous ductile welded-

39

steel, PVC and HDPE pipelines that are commonly used in NG networks. The latter relations,

40

-11-

which all use PGV as seismic IM, are comparatively presented in Figure 1. O’Rourke M.J. and

1

Ayala (1993) fragility relation was defined on the basis of damage reports of cast iron pipes;

2

hence, its applicability in ductile steel NG pipes is arguable. Moreover, the relation is reported

3

to be over-conservative as the pipeline damage data on which it is based, was most probably

4

biased by the long duration ground seismic motions of the 1985 Michoacán earthquake

5

(O’Rourke, T.D., 1999; Tromans, 2004). On the other hand, the Isoyama (2000) and the ALA

6

(2001) relations offer a longer applicability range in terms of PGV values (see also Section

7

4.3.2). The former relation was proposed on the basis of damage reports in Japan; hence its

8

applicability in other sites abroad is again questionable. ALA (2001) provides a more recent

9

reference and is based on an extended database of damage reports from USA and Japan. It is

10

worth noticing the available empirical fragility relations do not consider polyethylene

11

pipelines. As mentioned above, these pipelines revealed a very good performance during the

12

2011 Canterbury earthquake sequence owing to their high ductility (O’Rourke et al., 2014).

13

Empirical fragility curves for the vulnerability assessment of continuous steel-welded NG

14

pipelines subjected to seismically-induced transient ground deformations, in the classical

15

definition of Equation 1, i.e. by computing probabilities of exceedance of particular

16

performance levels for a given level of seismic intensity, were proposed for the first time by

17

Lanzano et al. (2013). The researchers proposed three discrete damage states (DS) that were

18

associated with corresponding risk states (RS). The former states describe the type and level of

19

structural damage on the pipeline (i.e. DS0: slight damages, DS1: significant damages, DS2:

20

severe damages), whereas the latter are defined based on the potential consequences (i.e. RS0:

21

no losses - null hazard, RS1: limited losses - low hazard, RS2: non-negligible losses - high

22

hazard). Based on the above definitions, PGV-based relations were established by fitting well-

23

documented damage reports of continuous steel pipelines during past earthquakes, with a

24

lognormal cumulative distribution function (Figure 1). This study was then extended in

25

Lanzano et al. (2014) to develop fragility functions for NG pipelines subjected to seismically-

26

induced ground deformations. The list of damage reports used to construct the fragility

27

functions were presented in detail in Lanzano et al. (2014; 2015).

28

29

3.3 Analytical fragility curves for buried NG pipelines

30

A few recent studies have employed numerical methodologies to develop analytical fragility

31

curves, in the sense of Equation 1. Lee et al. (2016) presented a set of analytical PGA-based

32

fragility curves for a buried steel NG pipeline with a diameter of 762 mm (30 in) and a wall

33

thickness of 17.5 mm (i.e. radius over thickness ratio R/t = 21.8). The fragility curves were

34

developed on the basis of an incremental dynamic analysis (IDA), using simplified numerical

35

models to account for the soil-pipe interaction effects. In particular, the analyses were

36

conducted using the finite element code ZeusNL, with the pipeline being simulated with

37

inelastic cubic line elements and the soil compliance being modelled by means of discrete

38

nonlinear springs in the three translational directions (axial, transverse and vertical). The soil

39

springs were validated using the relevant regulations of ALA (2001). The total length of the

40

-12-

models was set equal to 1.2 km, whilst various assumptions were made with regard to the

1

burial depth of the pipeline, the soil properties of the trench (i.e. homogeneous, heterogeneous

2

soils along the pipeline axis) and the boundary conditions at the end-sides of the pipeline (i.e.

3

fixed or pined conditions). Unfortunately, only the strength properties of the selected soil

4

deposits were given, while no information regarding the soil stiffness was provided in the

5

relevant paper. The majority of analyses were conducted assuming a straight pipeline, while a

6

number of analyses were also carried out, by assuming over- or sag-bends on the pipeline. The

7

latter are commonly used in crossings of NG pipelines with rivers or existing civil

8

infrastructure. The maximum axial strain, which was computed at critical sections of the

9

pipeline, such as the end-boundaries and the bends (when existed), was used as EDP for the

10

construction of the fragility curves. It is inferred from the paper that no desegregation between

11

compressive or tensional axial strains was made by the researchers. For a uniform soil deposit,

12

the strains on the pipe are indeed expected on the sections that were selected by the

13

researchers. However, for heterogeneous soil deposits, high pipe straining is expected at the

14

sections where the soil properties are changing. Three limit states, i.e. minor, moderate and

15

major damages, were defined as fractions of the steel material yield strain (Table 2), following

16

Shinozuka et al. (1979). Considering the high ductility of the steel grades used in NG

17

networks, this definition might be considered as quite conservative. The analyses were carried

18

out for 12 recorded ground seismic motions, scaled to a range of earthquake intensities, i.e. 0.1

19

g to 1.5 g. An increasing pipe straining was reported with a decreasing burial depth of the

20

pipeline. Additionally, the seismic vulnerability of the examined pipe was increased when

21

looser soil deposits were considered, while it was found to be sensitive to the boundary

22

conditions adopted at the end-sides.

23

Figure 3 illustrates representative analytical fragility curves from this study, highlighting the

24

effects of soil heterogeneities along the pipeline axis (Figure 3a), as well as of the existence of

25

bends (Figure 3b) on the seismic vulnerability of the examined pipeline. A slightly higher

26

vulnerability is reported for the minor and major damage states, when the pipe is considered to

27

be embedded in a heterogeneous soil deposit, while the reverse holds for the moderate damage

28

state. Interestingly, the effect of pipe bends on the seismic vulnerability of the examined pipe

29

was found to be quite reduced. The latter results may have been biased, at least to some extent,

30

by the simplified simulation of the soil compliance and the pipeline itself.

31

In a more detailed study, Jahangiri and Shakib (2018) investigated the seismic vulnerability of

32

buried steel NG pipelines, proposing a series of analytical PGV-based fragility curves. The

33

fragility curves were developed on the basis of an IDA, implementing numerical models of the

34

examined soil-pipe configurations developed in the finite element code OpenSees. In

35

particular, the examined pipes were modelled using 3D beam elements with fiber sections in

36

the circumferential and radial directions, obeying a nonlinear Ramberg-Osgood material

37

model. The soil compliance was simulated by means of nonlinear spring elements acting in

38

axial, transverse and vertical directions, as per ALA (2001) regulations. Additionally, discrete

39

damper elements were implemented, defined following Hindy and Novak (1979). The length of

40

-13-

the soil-pipe models was set equal to 1 km, while nonlinear springs were introduced at both

1

end-sides of the examined systems, in order to account for the infinite length of the pipeline,

2

following Liu et al. (2004). Salient parameters that affect the seismic response and

3

vulnerability of NG pipelines, such as the pipe dimensions, burial depth and steel grade, and

4

the soil properties of the trench, were considered. The diameter over thickness ratios (D/t) of

5

the selected pipes ranged between 21 and 116. It is worth noticing that large diameter steel

6

pipelines, commonly found in NG transmission networks (i.e. diameters D > 800 mm) were not

7

considered. The burial depth over diameter ratios (H/D) varied between 1 and 4, while the

8

effect of steel material grade was accounted for by considering API 5L X60, X65, X70 and

9

X80 steel pipes. The shear wave velocities of the adopted soil sites ranged between 180 m/s

10

and 360 m/s. Full dynamic time history analyses were conducted using 20 far-field records.

11

The records were appropriately scaled and applied on the examined soil-pipe systems in equal

12

PGV steps of 10 cm/s. The maximum axial compressive strain computed at the most critical

13

section of the pipeline was selected as EDP. Four limit states, corresponding to various levels

14

of damage, were defined, as per Table 3, following the relevant references, also provided in the

15

table. Obviously, a more rigorous definition of limit states was made herein, compared to Lee

16

et al. (2016).

17

Figure 4 illustrates representative analytical fragility curves developed within this study. More

18

specifically, the effects of the dimensions and burial depth of the pipeline on its seismic

19

vulnerability are highlighted in Figures 4a and 4b, respectively. The comparisons indicate an

20

increase of the failure probabilities of NG pipelines with decreasing D/t ratios, as well as with

21

increasing H/D ratios (i.e. with increasing burial depth). Figures 4c and 4d compare analytical

22

fragility curves for diverse pipe-trench-soil configurations, highlighting the effects of the

23

trench soil properties and steel grade of the pipe on the seismic vulnerability of NG pipelines.

24

Higher failure probabilities are reported with an increasing stiffness of the surrounding ground,

25

as well as with a reducing steel grade of the pipe. The effects of the above parameters on the

26

axial response and vulnerability of steel pipelines are further addressed and discussed in the

27

second part of this paper.

28

29

3.4 Critical discussion on available fragility relations for buried pipelines

30

The majority of available fragility relations refer to cast-iron or asbestos cement segmented

31

pipelines, the seismic response of which is quite distinct compared to continuous pipelines

32

(O’Rourke M.J. and Liu, 1999). The lack of relevant damage reports and therefore of relevant

33

fragility relations for continuous pipelines has been attributed by some researchers to their

34

better performance, compared to the segmental pipelines, when subjected to seismically-

35

induced transient ground deformations. However, several studies have demonstrated that under

36

particular circumstances, transient ground deformations may result in appreciable strains on

37

continuous pipelines, which in turn may lead to damages as well (O’Rourke M.J., 2009;

38

Psyrras and Sextos, 2018; Psyrras et al., 2019).

39

-14-

The usage of repair rate as an EDP does not provide any information regarding the severity of

1

damage, as well as the type of required repair. The only available recommendation to define

2

the expected damage level on the pipeline is provided by HAZUS (NIBS, 2004) and is based

3

on the type of seismic hazard. For seismically-induced transient ground deformations, it is

4

simply proposed that leaks will appear at 80 % of the reported damages, while the less 20 %

5

will correspond to breaks. The reverse holds for seismically-induced permanent ground

6

deformations.

7

The quality and accuracy of the repair reports after a seismic event and the lack of knowledge

8

regarding the incident angle between the pipeline axis and the ray path of the seismic wave are

9

other acknowledged issues that may induce a high level of uncertainty to the empirical fragility

10

relations. The accuracy of the repair reports that constitute the basis for the development of

11

empirical fragility functions may be debatable, since these are commonly drafted after a short

12

period from the main event and under the pressure for rapid restorations. The incident angle

13

between the ray path and the pipeline axis that is expected to affect notably the pipeline

14

response and vulnerability (O’Rourke M.J. et al., 1980; Pineda-Porras and Najafi, 2010) is not

15

known and therefore its crucial effect on the empirical relations statistics is not considered.

16

Indeed, if a pipeline is oriented in parallel with the propagation of surface Rayleigh waves, the

17

expected straining that will be imposed on the pipe and the potential damages are increased

18

considerably. On the contrary, if the Rayleigh waves are propagating in the perpendicular

19

direction to the pipeline axis, no damage is expected on the pipe. Additionally, the reliability of

20

the repair ratio statistics is highly sensitive to the pipeline lengths sampled in each interval of

21

the selected seismic IM (O’Rourke T.D. et al., 2014).

22

The majority available empirical relations were developed on the basis of damage reports on

23

pipeline networks found in USA and Japan, whilst in southern Europe or other seismic prone

24

areas there is tremendous lack or relevant information. Among few exceptions are, the 2003

25

Lefkas earthquake, where damages were reported and examined on the water-supply network

26

of the city (Alexoudi, 2005; Pitilakis et al., 2006; Paolucci and Pitilakis, 2007), as well as the

27

reported damages on the NG network of L'Aquila during the 2009 earthquake (Esposito et al.,

28

2014). Evidently, the applicability of the empirical fragility relations is restricted to cases

29

where the network (e.g. pipe dimensions and materials, soil conditions etc), and the ground

30

motion characteristics, are similar to the relevant characteristics of the sample used to develop

31

the relations. Along these lines, a general and unconditional use of these relations might

32

introduce a significant degree of uncertainty in the seismic risk assessment of networks with

33

distinct characteristics (Psyrras and Sextos, 2018).

34

The most important drawback of empirical fragility relations is that they do not disaggregate

35

between the potential damage modes (i.e. local or beam buckling, tensile rupture and

36

ovalization for continuous pipelines). As discussed in Section 2, different damage modes are

37

associated with different risks and effects on the structural integrity and serviceability of the

38

pipeline. Along these lines, the efficiency of empirical fragility relations in a rapid and valid

39

post-earthquake risk assessment of existing NG networks might be highly arguable.

40

-15-

The available analytical fragility functions for NG pipelines that were developed recently refer

1

to rather limited number soil-pipe configurations and do not cover NG pipelines with diameters

2

larger than 800 mm that are commonly used in transmission NG networks. The analytical

3

fragility curves use more rigorous EPDs compared to the empirical fragility relations, e.g. the

4

pipeline axial compressive strain; however, the evaluation of these EPDs, as well as the

5

definition of limit states, associated with particular damage modes, are still open issues, which

6

call for further investigation. More importantly, the relevant numerical studies do not examine

7

thoroughly salient parameters that may affect the response and hence the vulnerability of

8

buried NG pipelines under seismically-induced transient ground deformations, such as the

9

effects of the internal operational pressure of the pipeline, the geometric imperfections of the

10

walls of the pipes and the spatial variability of the seismic ground motion along the axis of the

11

pipeline. The effects of the above parameters on the structural response and vulnerability of

12

NG pipelines are further discussed in the second part of this paper.

13

Along these lines, additional research is deemed necessary towards the development of

14

analytical fragility functions that will account for the above critical parameters and will cover a

15

wide range of soil-pipe typologies, commonly used in NG applications. One critical issue

16

towards the development of rigorous analytical fragility curves is the identification of

17

‘adequate’ intensity measures that may efficiently be used to describe the effect of seismic

18

intensity on the vulnerability of pipelines for the identified damage modes. In the following

19

section, a critical review of the commonly used for buried pipelines seismic IM is made,

20

focusing on their efficiency to correlate with observed damages on pipelines, as well as to be

21

determined or measured in the field.

22

23

4. Seismic intensity measures for buried pipelines

24

25

4.1 Why the selection of adequate seismic intensity measures is important?

26

The severity of a ground seismic motion in fragility relations is expressed by means of a

27

seismic intensity measure (IM) (Baker and Cornell, 2005). Generally, a seismic IM should

28

provide information regarding various characteristics of a seismic ground motion, including its

29

amplitude, duration and frequency and energy content, which are all expected to affect the

30

seismic vulnerability of any element at risk. Available seismic IMs may be classified as

31

empirical or instrumental. In the former case, the severity of the seismic hazard is described by

32

means of macro‐seismic intensity scales, whereas in the latter case analytical values, recorded

33

by an instrument or computed via a seismic hazard analysis, are used. The optimum seismic IM

34

should be efficient, in the sense that it results in reduced variability of the EDP for a given IM

35

value (Shome and Cornell, 1998) and in parallel sufficient, in the sense that it renders the

36

structural response conditionally independent of the earthquake magnitude (M), source-to-site

37

distance (R) and other seismological parameters (e.g. ε) (Luco and Cornell, 2007). An efficient

38

IM allows for a reduction of the number of numerical analyses and ground seismic motions that

39

are required to estimate the probability of exceedance of each value of the EDP for a given IM

40

-16-

value. On the other hand, a sufficient IM allows for a free selection of the seismic ground

1

motions, since the effects of seismological parameters on the prediction of the EDP are less

2

important. Both the efficiency and sufficiency of a seismic IM may rigorously be defined

3

following recently-developed analysis frameworks for the performance based design, as well as

4

the probabilistic risk assessment of the structures (Cornell and Krawinkler, 2000; Luco and

5

Cornell, 2007).

6

In particular, the Pacific Earthquake Engineering Research Center (PEER) framework allows

7

the calculation of the loss by integrating over particular levels of the seismic hazard, the

8

response and damage with the contributions of each of those variables weighted by their

9

relative likelihood of occurrence. The method accounts for the uncertainties involved in all the

10

variables and their in between relations in a mathematically rigorous formality, known as the

11

total probability theorem:

12

(5)

13

where DV is the decision variable(s), e.g. fatalities due to ignitions or explosions caused by

14

potential leakages from NG pipelines, direct or indirect monetary losses associated to

15

downtimes of a NG network etc., DM is the damage measure(s), e.g. buckling or tensile rapture

16

of the pipeline etc., EDP is the engineering demand parameter, e.g. the maximum compressive

17

or tensile strain on a steel NG pipeline, and IM is the seismic intensity measure. G(.) stands for

18

the complementary cumulative distribution function (CCDF) or probability of exceedance. The

19

CCDFs that are found in Equation 5 from left to right may be evaluated from the loss, damage

20

and response models. The term may be obtained via a probabilistic seismic hazard

21

analysis, i.e. by implementing a seismic hazard curve. Evidently, a critical step in the above

22

analysis procedure is the development of functional relationships between the EDP and the

23

selected seismic IM on the basis of predictions of relevant numerical analyses. Various

24

approaches have been proposed in the literature for this purpose, including the incremental

25

dynamic analysis (IDA) (Vamvatsikos and Cornell, 2002), the multiple-stripe analysis (Jalayer

26

and Cornell, 2009) and the cloud analysis (Jalayer et al., 2015). The EDP-IM relations

27

developed by any of the above methods may be used to evaluate in a mathematically rigorous

28

way the efficiency and sufficiency of any seismic IM. As stated, an efficient IM will result to

29

reduced variability of the EDP for a given IM value. Quantifying the sufficiency of a seismic

30

IM requires the separate regression analysis of the EDP relative to seismological parameters,

31

e.g. the magnitude M and the epicentral distance R.

32

Other concepts and quantities, namely the practicality, effectiveness, robustness, computability

33

and proficiency, have been proposed before for identifying the optimum seismic IM for

34

buildings, bridges and above ground civil infrastructure (indicatively: Shome et al., 1998,

35

Mackie and Stojadinovic, 2003, Baker and Cornell, 2005; Vamvatsikos and Cornell, 2005,

36

Luco and Cornell, 2007, Padgett and DesRoshes, 2008, Yang et al., 2009, Kostinakis et al.,

37

2015, Fotopoulou and Pitilakis, 2015, among many others). Evidently, an efficient

38

[ ] [ ]

,,

DM EDP IM

DV G DV DM dG DM EDP dG EDP IM IM

ll

=éùéùéù

ëûë ûëû

òòò

[ ]

IM

l

-17-

determination of the spatial distribution of a selected seismic IM is of great importance in the

1

assessment of an extended network (De Risi et al., 2018).

2

As indicated in Section 3, various seismic IM have been adopted in empirical and analytical

3

fragility relations for buried pipelines, including MMI, PGA, PGV, εg, Ia, SI, as well as

4

PGV2/PGA. Figure 5 illustrates the proportions of the seismic IMs used by the available

5

empirical and analytical fragility relations for buried pipelines. The graph follows Gehl et al.

6

(2014), whilst being updated by recent empirical and analytical studies. Clearly, PGV has a

7

dominant presence as seismic IM in the available functions, while PGA, MMI and εg are

8

following. A relevant comparative discussion on the efficiency (in a general sense) of the

9

above seismic IMs was made by Pineda-Porras and Najafi (2008). In a more recent study,

10

Shakid and Jahangiri (2016) examined the efficiency and sufficiency of 18 seismic IMs for NG

11

pipelines, on the basis of a numerical parametric study. More details about the latter study are

12

provided in the ensuing. Before that a critical revisit of the seismic IMs used in empirical and

13

analytical fragility relations for buried pipelines so far, as well as some elements from relevant

14

comparative studies, are presented.

15

16

4.2 Critical review of seismic IMs used in empirical fragility relations and analytical

17

fragility curves for buried pipelines

18

19

4.2.1 Modified Mercalli Intensity (MMI)

20

Modified Mercalli Intensity was used as seismic IM for buried pipelines in early studies

21

(Eguchi, 1983; Ballentine et al., 1990; Eguchi, 1991; O’Rourke T.D. et al., 1991; O’Rourke

22

T.D. et al., 1998), mainly due to the absence of extensive instrumental records of the seismic

23

ground motion. The measure is defined according to an index scale, with each level having a

24

qualitative description of earthquake effects on constructions and natural surroundings, as well

25

as on human perceptions. The subjective nature of its definition, introduces a high level on

26

uncertainty, making MMI an inadequate IM for a quantitative seismic risk assessment of

27

pipelines.

28

29

4.2.2 Peak Ground Acceleration (PGA)

30

PGA constitutes the most common measure of the amplitude of a seismic ground motion and it

31

was widely used as seismic IM for above ground structures, such as buildings and bridges. This

32

seismic IM can easily be obtained from recorded accelerograms, as follows:

33

(7)

34

In the absence of recorded data, use of Ground Motion Prediction Equations (GMPE) or shake

35

maps that are made available few minutes after a seismic event, can be made. Alternatively,

36

stochastic simulation of ground motion may be applied, particularly during pre-seismic

37

evaluations of existing networks.

38

PGA correlates directly with the inertial response of a structure, which in cases of buried

39

pipelines is of minor, if not negligible, importance. However, PGA was extensively used as

40

( )

maxPGA a t=

-18-

seismic IM in seismic fragility functions for pipelines, especially in early studies (Katayama et

1

al., 1975; Isoyama and Katayama, 1982; TCLEE-ASCE, 1991; Hamada, 1991; O’Rourke T.D.

2

et al., 1991, Isoyama et al., 2000; O’Rourke T.D. et al., 1998; Chen et al., 2002; Lee et al.,

3

2016). Figure 6 compares PGA-based empirical fragility relations developed on the basis of

4

damage reports of cast-iron buried pipelines. The comparison reveals significant deviations in

5

the prediction of repair rates, even for the area of common range of applicability of the

6

relations, as reported by Tromans (2004) and highlighted with purple box in figure. Obviously,

7

the observed deviations may be attributed to the range and quality of the dataset of damage

8

reports and the regression analysis used to develop each relation, as well as to issues related to

9

the rational evaluation of PGA, particularly in cases of earlier studies, where relevant recorded

10

data and reliable GMPE were absent. However, the high differences of the relations could be

11

an evidence of the poor ‘efficiency’ of PGA to correlate with observed damages on pipelines.

12

Various definitions of PGA may be found in the relevant literature, referring to above ground

13

structures, including the use of (i) the peak value of the two orthogonal directions at a given

14

location, (ii) the average of the peak values of the orthogonal directions, (iii) the square root of

15

the sum of squares (SRSS) of the two orthogonal directions, (iv) the maximum amplitude of

16

the resultant (RES) vector of the orthogonal directions and (v) the geometric mean of the

17

orthogonal directions. The most ‘adequate’ value for the evaluation of the seismic vulnerability

18

of pipelines is generally an open issue, calling for further investigation.

19

20

4.2.3 Peak Ground Velocity (PGV)

21

PGV was used extensively as seismic IM in fragility relations for buried pipelines (Barenberg,

22

1988; O’Rourke M.J. and Ayala, 1993; Eidinger et al., 1995; Eidinger et al., 1998; Jeon and

23

O’Rourke T.D., 1995; O’Rourke et al., 1998; Isoyama et al., 2000; ALA, 2001; Chen et al.,

24

2002; Pineda and Ordaz, 2003; O’Rourke M.J. and Deyoe, 2004; Lanzano et al., 2013;

25

Lanzano et al., 2014; Jahangiri and Shakib, 2018). The wide use of PGV is attributed to its

26

direct relation with the longitudinal ground strain, which is responsible for the induced

27

damages on buried pipelines caused by transient ground deformations. The relation between

28

PGV and ground strain is further examined in the following section. Velocity time histories

29

may be obtained through integration of accelerograms recorded at the site of interest.

30

Subsequently, PGV can be obtained as follows:

31

(8)

32

In the absence of acceleration time history recordings, PGV may be obtained either through

33

GMPEs that correlate directly PGV with multiple seismological parameters, or by the use of

34

relevant shake maps. Additionally, PGV/PGA relations have also been proposed in relevant

35

guidelines and research papers (e.g. ALA, 2001; Hashash et al., 2001), which may be used in

36

the absence of more rigorous PGV data. However, the efficiency of the latter is rather reduced,

37

particularly for soft soils, where the seismic vulnerability of pipelines is generally amplified

38

(ALA, 2001; Jahangiri and Shakib, 2018).

39

( )

maxPGV v t=

-19-

Figure 7 compares the PGV-based fragility relations, which according to Gehl et al. (2014) are

1

considered to be more adequate in describing the vulnerability of continuous NG pipelines.

2

Noticeable deviations between the fragility relations are observed again, even for the common

3

range of applicability (highlighted with the purple box in figure). However, these deviations

4

are lower compared to those observed in the relevant comparisons of PGA-based relations

5

(Figure 6), highlighting a better ‘performance’ of this metric against PGA. This observation

6

comes in line with several studies, which highlighted the superiority of PGV as seismic IM for

7

buried pipelines compared to PGA. For instance, PGV was reported as more efficient seismic

8

IM for describing the observed damages of water-supply buried pipelines in the comparative

9

study of Jeon and O’Rourke T.D. (2005). Using damage reports of the medium- and low

10

pressure NG network of L’Aquila, Italy, during the 2009 earthquake, Esposito et al. (2014)

11

estimated repair rates, which were plotted against local-scale PGV values. The latter was

12

defined using shake maps that illustrated the spatial distribution of PGV in the region. The

13

above correlations indicated a higher concentration of damages in areas with higher reported

14

PGV. However, the comparisons of the estimated repair rates with the predictions of

15

commonly used PGV-based fragility functions, i.e. NIBS (2004), Eidinger et al. (1998) and

16

ALA (2001), revealed a general under prediction of the expected damage by the latter. The

17

observed differences were associated to the differences of the structural characteristics of the

18

L’Aquila NG network, compared to the characteristics of the networks, for which the fragility

19

relations were developed. A reasonably good coloration between observed damages on buried

20

pipelines and PGV was also reported in the case of the water-supply network of the city of

21

Darfield during the 2011 earthquake sequence in New Zealand (O’Rourke T.D. et al., 2014).

22

The repair/damage spots were generally concentrated in the areas, where a higher PGV was

23

reported. It is worth noticing the different definition of PGV in the studies of Esposito et al.

24

(2014) and O’Rourke T.D. et al. (2014). In the former study, PGV was defined as the peak

25

value of one of the orthogonal directions. On the contrary, the geometric mean of PGV of the

26

two orthogonal directions was used in the latter study. These different computational

27

approaches highlight again the open issue of the ‘proper’ way of evaluating instrumental

28

seismic IMs. Similar to PGA, PGV can be defined in various ways, e.g. peak value, SRSS

29

value, RES value etc. In a relevant study, Jeon and O’Rourke T.D. (2005) reported a higher

30

level of correlation between damages/repairs of cast iron buried pipes during the 1994

31

Northridge earthquake and PGV values, the latter computed on the basis of peak values of one

32

of the orthogonal directions.

33

34

4.2.4 Peak ground strain (εg)

35

The longitudinal ground strain constitutes the main loading mechanism of buried pipelines

36

subjected to seismically-induced transient ground deformations; therefore, it is directly related

37

to the seismic performance and vulnerability of this infrastructure. In this context, the peak

38

ground strain εg was used as seismic IM for buried pipelines in some recent studies (O’Rourke

39

M.J. and Deyoe, 2004; O’Rourke M.J., 2009; O’Rourke T.D. et al., 2014; O’Rourke M.J.,

40

-20-

2015). εg may be quantified rigorously from ground displacement time histories along the axis

1

of the pipeline, as follows (Pineda-Porras and Najafi, 2008):

2

(9)

3

The required displacement time histories may be evaluated via double integration of

4

accelerographs at the site of interest. Considering the inaccuracies in the processing of the raw

5

acceleration data, including the potential effects of filtering and base line correction or

6

tapering, the accuracy of the computed displacement time histories might be debatable. More

7

importantly, the above procedure requires a number of records along the pipeline axis, which

8

should be referenced to an absolute time reference (Pineda-Porras and Najafi, 2008).

9

Therefore, the installation of dense seismic arrays along the pipeline axis is necessary.

10

However, the high installation and operation costs of such arrays impede such a selection in

11

extended NG networks. Along these lines, it is common in practice to evaluate εg in a

12

simplified fashion, using the PGV, as follows:

13

(10)

14

where C is a measure of the wave propagation velocity and κ is a correction parameter to

15

account for the maximization of strain as a function of the incidence angle φ, the latter formed

16

between the plane wave propagation and the longitudinal axis of the pipeline. The selection of

17

C and κ depends on the wave type, the incidence angle and the local soil conditions. In this

18

context, the dominant seismic wave type at the area of interest should be initially defined.

19

Generally, body waves and particularly shear S-waves, are expected to dominate the response

20

of a pipeline located near the seismic source, while for pipelines located away from the seismic

21

source, surface Rayleigh waves are manifesting the response. IITK-GSDMA (2007) guidelines

22

suggested a limit for the selection of the ‘appropriate’ seismic waves for design purposes,

23

which may potentially be used for vulnerability assessment purposes, as well. In particular, S-

24

waves should be used for the design or assessment of pipelines located at an epicentral distance

25

up to five times the focal depth, whereas for higher distances, R-waves should be considered.

26

The apparent velocity C in Equation 10 may be defined on the basis of above recommendations

27

for the dominant seismic waves.

28

Quite distinct recommendations may be found in relevant guidelines for the determination of

29

the above parameters in case of S-waves. ALA (2001) suggests the use of C = 2 km/s, and κ =

30

2.0 for S-waves. The AFPS/AFTES (2001) guidelines for the seismic design of tunnels

31

suggests κ = 2.0 and C to be taken as the minimum value between 1 km/s and a mean soil shear

32

wave velocity of the upper subsurface, the latter corresponding to a depth equal to the

33

fundamental wavelength of soil deposit. Eurocode 8 (EN1998-4, CEN 2006) proposes the

34

‘apparent wave speed’ C to be computed based on geophysical considerations, while implicitly

35

κ is set equal to 1.0. Significant differences may be found on the selection of the apparent

36

velocity of relevant studies that proposed εg-based fragility functions for buried pipelines, as

37

well. O’Rourke M.J. and Deyoe (2004) adopted in their study apparent velocities C equal to

38

500 m/s and 3000 m/s for R-waves and S-waves, respectively. Following Paolucci and

39

( ) ( )

max max

gtDtt

ee

==¶¶

gPGV C

ek

=

-21-

Smerzini (2008), O’Rourke M.J. (2009) used an apparent velocity C = 1000 m/s to update his

1

previous fragility function (O’Rourke M.J. and Deyoe, 2004). Comparing the above

2

recommendations and studies, one can get twice as high ground strains, when implementing

3

the ALA guidelines compared to AFPS/AFTES, while the empirical fragility relations

4

proposed for S-waves by O’Rourke M.J. and Deyoe (2004) and O’Rourke M.J. (2009) on the

5

basis of similar damage reports may provide highly distinct predictions for the expected

6

damage of a network.

7

For surface R-waves, κ is equal to 1.0, while C is equal to phase velocity, cph (O’Rourke M.J.

8

and Liu, 1999). The phase velocity is defined as the velocity at which a transient vertical

9

disturbance of a given frequency that originates at ground surface is propagating across the

10

surface of the soil site. This velocity is related to wavelength λ and frequency f of the

11

disturbance, as follows: . Dispersion curves have been proposed in the literature to

12

account for this frequency dependence of cph in case of layered soil profiles, resting on elastic

13

half space (O’Rourke M.J. and Liu, 1999). O’Rourke M.J. et al. (1984) highlighted that for low

14

frequencies, the effect of the characteristics of the soil deposits, overlaying the half space, on

15

the cph is negligible since the corresponding wavelength is larger than the thickness of the

16

overlying soil layer. Hence, cph is slightly lower than the shear wave velocity of the elastic half

17

space. For high frequencies, the wavelength is comparable to the thickness of the overlying soil

18

layer and therefore the phase velocity is affected highly be its characteristics. A tri-linear

19

relation between the phase velocity and the frequency was proposed by O’Rourke M.J. et al.

20

(1984) on the basis of the above observations. The correlation of the phase velocity with the

21

wavelength highlights the importance of an ‘adequate selection’ of the later in the definition of

22

the ground strain. Some suggestions on the selection of this critical parameter may be found in

23

the literature (O’Rourke M.J. et al., 1984). However, its accurate determination is still an open

24

issue.

25

The above discussion and observations highlight the uncertainty introduced in the evaluation of

26

εg, even for the cases of relatively homogeneous soil deposits. The evaluation of εg becomes

27

more complex in cases of irregular topography (e.g. variable bedrock depth, hills, canyons,

28

slopes), as well as in the presence of significant lateral soil heterogeneities. Actually, in such

29

conditions the seismic vulnerability of pipelines is expected to increase significantly (e.g.

30

Trifunac and Todorovska, 1997; Takada et al., 2002; Scandella and Paolucci, 2006; Psyrras

31

and Sextos, 2018), while a worse correlation between the εg and PGV is commonly observed

32

(Paolucci and Pitilakis, 2007). Several approaches have been proposed in the literature to

33

account for the effects of irregular topography on the ground strain in a simplified fashion.

34

Indicatively, O’Rourke M.J. and Liu (1999) presented a simplified procedure for the

35

computation of the ground strain in cases of soil deposits with inclined soil-bedrock interface,

36

while Scandella and Paolucci (2006) proposed an analytical relationship for the εg-PGV

37

correlation near the boundaries of basins with simplified geometries. Numerous studies that

38

examine the effects of topography and soil heterogeneous soil condition on the soil straining

39

ph

cf

l

=

-22-

response may be found in the literature. A detailed presentation of this aspect is out of the

1

scope of this paper.

2

The implementation of εg-based fragility relations requires the development of seismic hazard

3

maps in terms of εg. The latter can be obtained either by converting PGV shake maps,

4

implementing Equation 10 and making ‘adequate’ selections for the apparent velocity C.

5

Alternatively, εg hazard maps can be computed on the basis of 2D or even 3D soil response

6

analyses for seismic ground motions compatible with the targeted seismic hazard. The

7

implementation of numerical simulations, especially in 2D or 3D, requires a significant

8

computational effort and time; hence, this approach is not efficient for a rapid post-earthquake

9

assessment of extended pipeline networks. However, it may be used for networks of great

10

importance during pre-seismic vulnerability studies. In an alternative approach, a large number

11

of 1D soil response analyses may be employed to estimate the spatial distribution of seismic

12

hazard at the site of interest (Paolucci and Pitilakis, 2007). The 1D soil response analyses have

13

the advantage of computational efficiency, compared to 2D or 3D numerical analyses. The

14

main drawback is that 1D response analyses provide the soil strains that are of pure shear

15

nature (vertically propagated S-waves are used as input for these analyses). These strains

16

commonly have a relatively sharp variation with depth and more importantly, they cannot be

17

translated into longitudinal soil strain in a straightforward way. Another drawback of 1D soil

18

response analyses is that these analyses neglect the effects of lateral variation of the soil

19

properties, as well as the creation and propagation of surface waves, which may be important

20

for the response of pipelines, especially those located away from the epicenter of the seismic

21

event. Comparing numerically predicted shear and longitudinal soil strains, computed in

22

various depths by 1D and 2D soil response analyses, respectively, Paolucci and Pitilakis (2007)

23

reported a rather weak correlation between the two strains, which was generally increased with

24

increasing burial depth. Despite the above observations, the researchers suggested the use of

25

shear strains as a first approximation of the ground strains for the assessment of buried

26

pipelines, mainly due to the computational efficiency of 1D soil response analyses compared to

27

the other types of soil response numerical analyses. Regardless of the selected soil response

28

analysis method, the use of fully coherent ground seismic motions may lead to a significant

29

underestimation of the actual ground strains that may be developed along the axis of an

30

extended pipeline. Among others, Zerva (1993) highlighted the significant effect of variability

31

of shape of motions over the pipeline length on the induced strains on it.

32

Figure 8 compares εg-based fragility relations proposed for buried pipelines subjected to

33

seismically-induced transient ground deformations. The relations are plotted on the log-log

34

space. As reported by Psyrras and Sextos (2018), the relations provide comparable repair rates

35

for strain levels, ranging between 10-3 and 10-2, which are highlighted with the purple box in

36

the figure. These strain levels are considered quite high to induce significant damages on

37

buried NG pipelines. For strain levels other than these, significant deviations between the

38

relations are observed. However, these differences are generally lower compared to the

39

relevant deviations observed in cases of PGA- and PGV- based fragility relations. It is worth

40

-23-

noticing the increasing trend of damage rate with increasing ground strain level that is revealed

1

by the fragility relations. As pointed out by Psyrras and Sextos (2018), this observation comes

2

in contrast with early analytical studies (O’Rourke M.J. and Hmadi, 1988). The latter suggest

3

that slippage phenomena between the pipeline and the surrounding ground are expected take

4

place, even with the mobilization of small relative displacement, subsequently reducing the

5

straining induced on the pipeline. The slippage phenomena and their effect on the pipe

6

response are expected to be amplified with increasing ground strain level. Along these lines,

7

the proposed functional form that is used to develop the fragility functions needs to be re-

8

evaluated.

9

The installation of distributed fiber optic sensing, capable of recording the strain level of the

10

pipeline along its axis (e.g. Gastineau et al., 2009), in conjunction with the use of εg-based

11

fragility relations may contribute towards a rapid post-earthquake assessment of extended

12

pipeline networks, providing an almost real-time evaluation of the pipe straining and detection

13

of damages. Since the ground strains are used in the definition of the εg-based fragility

14

relations, this assessment framework might be more effective for the cases, where the pipe

15

shares the same strain level with surrounding ground. As highlighted above, this condition is

16

rarely valid, since slippage phenomena of the pipeline relative to the surrounding ground may

17

take place even for low shaking motions (O’Rourke M.J. and Hmadi, 1988). Another drawback

18

of the implementation of distributed fiber optic sensing is the high costs of installation and

19

operation of these monitoring systems.

20

21

4.2.5 PGV2/PGA

22

PGV2/PGA was proposed by Pineda-Porras and Ordaz (2007) as a seismic IM for assessment

23

of shallow pipelines embedded in soft soils. Dimensionally, this metric corresponds to

24

displacement and when modified by a relevant correction factor (the so-called shape factor λpr)

25

is shown to be an effective proxy for peak ground displacement (PGD). The latter is related

26

with the very-low frequency content of seismic ground motion, which subsequently is

27

associated with higher imposed ground deformations and strains on the pipeline. Along these

28

lines, PGV2/PGA might be a suitable candidate as seismic IM for buried pipelines. This IM

29

may be estimated through shake maps or by making use of GMPEs for PGA and PGV, as

30

shown in the previous sections. Pineda-Porras and Ordaz (2007) examined the performance of

31

this seismic IM using reported repairs/damages of the water-supply system of Mexico City

32

during the 1985 Michoacán earthquake. The study revealed a better correlation between the

33

repairs/damages and PGV2/PGA was reported, compared to PGV alone. However, this

34

constitutes the only case where this seismic IM was used and validated. Given the peculiarities

35

of the specific site and seismic event, further validation of the particular seismic IM is deemed

36

necessary.

37

38

4.2.6 Arias Intensity (Ia)

39

-24-

The seismic fragility of pipelines may be affected by the duration of strong seismic motion.

1

Under certain circumstances, repeated ground strains of moderate amplitude, imposed over an

2

extended period on the pipeline, may lead to higher levels of damage compared to

3

instantaneous higher amplitude ground strains. Actually, a number of moderate loading cycles

4

may cause cumulative cyclic damage on the pipeline, such as buckling phenomena on steel

5

pipelines or fatigue on HDPE pipelines. In this context, Arias intensity Ia, may be considered

6

as a potential seismic IM for the characterization of the structural performance of buried steel

7

NG pipelines since it embodies both the amplitude and duration characteristics of the seismic

8

ground motion. Arias intensity Ia, may be defined as follows:

9

(11)

10

where is an acceleration time history. Among other seismic IMs, O’Rourke et al. (1998)

11

examined the ‘efficiency’ (in a general sense) of Ia for buried pipelines, reporting a poor

12

correlation between this seismic IM and observed damages. Contrarily, Hwang et al. (2004)

13

reported a higher level of correlation between Ia and reported damages on the NG network of

14

Taichung City during the 1999 Chi-Chi earthquake, compared to other seismic IMs, such as

15

PGA, PGV and spectral intensity SI. However, the latter study was based on limited data from

16

one case study. A potential drawback of Ia is the large number of recorded acceleration time

17

histories that are required to obtain the spatial variability of this metric along the length of the

18

pipeline axis. Therefore, the use of a dense instrumentation array is mandatory; however, the

19

high installation and operation costs of such an array may impede the extended use of this

20

seismic IM.

21

22

4.2.7 Spectral Acceleration (Sa) and Spectrum Intensity (SI)

23

The spectral acceleration Sa constitutes a meter of the ‘strength’ of the seismic ground motion

24

that may adversely affect structures at given frequencies. It actually describes the seismic

25

motion as a function of the response of elastic single degree of freedom oscillators (SDOF)

26

with ξ % damping and natural periods T. Sa was widely used as seismic IM for above ground

27

structures, such as building and bridges, since it is related directly with the inertial response of

28

the structure, which is controlling the seismic response of the structure itself.

29

The spectrum intensity, on the other hand, is computed as:

30

(12)

31

where T is the natural period of the structure, SV is the velocity response spectrum, ξ is the

32

damping of the structure and C1, t1 and t2 are constants. In the original formulation proposed by

33

Housner (1952), C1, t1 and t2 were set equal to 1, 0.1 s and 2.5 s, respectively, while other

34

definitions for the above parameters may be found in the literature. Similar to Arias Intensity, a

35

series of records of the seismic ground motion (e.g. acceleration time histories) is required

36

along the pipeline axis, to estimate the spatial distribution of both the spectral acceleration Sa

37

( )

2

0

2

a

I a t dt

g

p

µ

=éù

ëû

ò

( )

at

( ) ( )

2

1

1

1,

t

v

t

SI S T dT

C

xx

=ò

-25-

and spectrum intensity SI. With reference to the applicability of the above seismic IM in cases

1

of buried pipelines, O’Rourke et al. (1998) investigated the efficiency (in the general sence) of

2

SA to correlate with observed damages on buried cast iron pipelines of the water-supply system

3

of California during the 1994 Northridge earthquake. In a similar study, Hwang et al. (2004)

4

examined the use of SI for embedded pipelines, by implementing damage reports on gas and

5

water-supply pipelines of Taichung City during the 1999 Chi-Chi earthquake. In both studies,

6

the above seismic IMs were found to provide very poor correlations with the reported damages.

7

These poor correlations are actually expected, since both IM are directly related to the inertial

8

response of above ground elastic single degree of freedom oscillators, the seismic response of

9

which is highly distinct compared to the one that the embedded pipelines exhibit.

10

11

12

13

4.2.8 Peak ground shear strain (γmax)

14

Trifunac and Todorovska (1997) established fragility relations using damage reports of buried

15

pipelines in California during the 1994 Northridge earthquake. In their study the peak ground

16

shear strain γmax was used as seismic IM. Despite the differences between the shear and axial

17

ground strains (see Section 4.2.3), the evaluation of the spatial distribution of peak ground

18

shear strain in a site of relatively known properties is by far an easier task compared to the

19

evaluation of the axial soil strains. In their study, Trifunac and Todorovska (1997) used the

20

following simplified formula to define approximately the peak soil shear strain:

21

(13)

22

where Vs,30 is the average shear wave velocity of the top 30 m of soil deposits. Obviously, such

23

a definition requires the knowledge of the spatial distribution of PGV, as well as Vs,30. As stated

24

above, the former may be defined by making use of shake maps that are published after a

25

particular seismic event, or via GMPEs. Vs,30 may be obtained using available geological and

26

geotechnical data for the given site. For pre-seismic assessments of existing NG networks, an

27

extended use of 1D soil response analyses, covering the area of interest and accounting for the

28

geological, geomorphic and geotechnical data of the site, could provide a better idea of the

29

spatial distribution of γmax.

30

31

4.3 On the efficiency and sufficiency of seismic IM for buried steel NG pipelines

32

Employing a numerical framework, Shakid and Jahangiri (2016) examined the efficiency and

33

sufficiency of 18 seismic IMs for buried steel NG pipelines, in a mathematically rigorous way

34

(Baker and Cornell, 2005, Luco and Cornell, 2007). The investigated seismic IM are

35

summarized in Table 4. Their analysis included IDA of six small-diameter API 5L X65 steel

36

NG pipelines embedded in soft to medium-stiff uniform soil deposits. In particular, the selected

37

pipe diameters were ranged between 356 mm and 610 mm, while the selected diameter over

38

thickness ratios (D/t) varied between 45.1 and 95.3. The internal pressure of the pipelines was

39

max

,30s

PGV

V

g

=

-26-

ranged between 1.7 MPa and 5.2 MPa, while the burial over diameter ratios (H/D) varied

1

between 2.5 and 5.4. Finally, the shear wave propagation velocity of the surrounding ground

2

was ranging between 180 m/s and 360 m/s. A finite length of the selected pipelines was

3

modelled by means of inelastic shell elements, whilst the effect of infinite length of the

4

pipeline on the actual response was considered by means of nonlinear axial springs, which

5

were introduced at both end-sides of the pipeline, following Liu et al. (2014). The surrounding

6

ground was modelled by nonlinear spring elements, acting in the axial, transverse and vertical

7

directions, defined as per ALA (2001) guidelines, while dashpots elements were also

8

introduced, following Hindy and Novak (1979). The IDA was conducted using an assembly of

9

30 real far-field seismic ground motions, scaled to various PGA in steps of 0.1 g. The

10

computed by the dynamic analyses peak axial compression strain of the pipeline was used as

11

EPD. The effects of spatial distribution and incoherence of the seismic ground motion, as well

12

as potential soil heterogeneities along the pipelines axis were not considered. In addition to the

13

previously discussed seismic IMs (e.g. PGA, PGV, PGV2/PGA, Ia), a set of new seismic IMs

14

was also examined. A brief presentation of these new seismic IMs is made in the ensuing,

15

examining their potential application in buried pipelines, while the main conclusions of this

16

study are finally discussed.

17

18

4.3.1 Peak Ground Displacement, PGD

19

PGD corresponds to the maximum absolute value of a ground displacement time history, i.e.:

20

(14)

21

The required for the computation of PGD, ground displacement time histories are commonly

22

defined through double integration of acceleration time histories recorded at the site of interest.

23

As stated already, PGD correlates better with the longer period ordinates of ground seismic

24

motion, which generally are associated with higher ground deformations and higher straining

25

on buried pipelines. Along these lines, PGD may be considered as an adequate candidate of a

26

seismic IM for buried NG pipelines. However, the inherent uncertainties associated with the

27

integration analysis of acceleration time histories are unavoidably propagate in the computation

28

of this seismic IM.

29

30

4.3.2 Root mean square acceleration, RMSa, velocity, RMSv, and displacement, RMSd

31

The root mean square acceleration is determined using acceleration recordings at a site, as

32

follows:

33

(15)

34

where t0 and te indicate the beginning and end of the duration of the seismic ground motion

35

under consideration. This seismic IM constitutes a measure of the average rate of energy

36

imparted by the ground seismic motion. The large number of recorded acceleration time

37

histories that is required to obtain the spatial variability of RMSa, impedes the wide use of this

38

( )

maxPGD d t=

( )

0

2

0

1e

t

a

et

RMS a t dt

tt

=éù

ëû

-ò

-27-

seismic IM for extended networks of buried pipelines. Similar relations with Equation 15 may

1

be found in the literature for the definitions of the root mean square velocity RMSv and the root

2

mean square displacement RMSd, which are rarely used in practice.

3

4

4.3.3 Cumulative absolute velocity, CAV

5

The cumulative absolute velocity (CAV) has a similar interpretation to RMSa, as it is actually

6

derived by integrating the entire ground acceleration recording, as follows:

7

(16)

8

The use of RMSa or CAV as seismic IMs for buried pipelines might be questionable, since both

9

measures are associated directly with the ground acceleration. As already discussed, ground

10

acceleration is related to inertial loads, which are generally of secondary importance for the

11

seismic response and vulnerability of buried civil infrastructure.

12

13

4.3.4 PGD2/RMSd

14

PGD2/RMSd constitutes a dimensionless metric of the ground displacement. The evaluation of

15

this seismic IM requires the definition of the PGD and RMSd, which both depend on the

16

estimation of displacement time histories through the double integration of acceleration time

17

histories recordings at the site of interest.

18

19

4.3.5 Sustained maximum acceleration, SMA, and velocity, SMV

20

The sustained maximum acceleration SMA and the sustained maximum velocity SMV, which

21

both were defined by Nuttli (1979), characterize the seismic ground motion using lower peaks

22

of the recorded acceleration or the velocity time histories. In particular, SMA is defined as the

23

third (or fifth) highest (absolute) value of the acceleration time history, while SMV is defined in

24

a similar manner using the velocity time history. Obviously, accelerographs from the

25

investigated site are required for the definition of these seismic IMs.

26

27

4.3.6 Spectral seismic IMs

28

The acceleration response spectrum, Sa, is commonly calculated using the Nigam and Jennings

29

(1969) algorithm. The spectral velocity, Sv, and spectral displacement, Sd, may then be

30

estimated, based on the following relations (Chopra, 1995):

31

(17)

32

Having estimated the response spectra for a given seismic ground motion time history, the

33

acceleration and velocity spectra intensities, ASI, VSI, may be defined by integrating the

34

relevant response spectra, as follows:

35

(18)

36

( )

0

t

CAV a t dt=ò

( ) ( ) ( ) ( )

2

22

,

vda d

ST ST ST ST

TT

pp

æö æö

=´=´

ç÷ ç÷

èø èø

( ) ( )

0.5 0.5

0.1 0.1

,

av

ASI S T dT VSI S T dT==

òò

-28-

In addition to the above spectral seismic IMs, Shakib and Jahangiri (2016) examined the

1

efficiency and sufficiency of the following vector seismic IM: ,

2

where is the first natural frequency of the pipe-soil configuration. According to the

3

researchers, is quantified on the basis of a natural frequency analysis, using the numerical

4

models of the soil-pipeline configuration presented above (i.e. pipe shell model on soil

5

springs). In the authors’ view, the use of spectral seismic IMs, as well as the definition of

6

for embedded structures, such as buried pipelines, are not straightforward tasks. More

7

importantly, the use of spectral seismic IMs seems to be not valid from a theoretical viewpoint,

8

especially when considering the prevailing loading mechanism of buried pipelines during

9

seismic ground shaking. As highlighted in several parts of the paper, the seismic response of

10

buried pipelines is dominated by the kinematic loading imposed by the surrounding ground on

11

them, while, contrary to above ground structures, their inertial response is of secondary, if not

12

negligible, importance. Additionally, the response of buried structures is highly distinct

13

compared to that of a single degree of freedom oscillator (SDOF), for which the response

14

spectra and the relevant spectral seismic IMs are actually defined. In this context, the use of

15

spectral seismic IM for embedded civil infrastructure, such as buried pipelines, is highly

16

arguable. These perspectives come in line with the poor correlations between spectral seismic

17

IMs, i.e. spectral acceleration and spectrum intensity, and reported damages on water-supply

18

and steel NG pipelines during past earthquakes (O’Rourke M.J. et al., 1998; Hwang et al.,

19

2004).

20

21

4.3.7 Summary

22

The study of Shakib and Jahangiri (2016) revealed different optimum seismic IM for pipelines

23

embedded in soft or medium-stiff soil deposits. More specifically, for buried pipelines in soft

24

soils, revealed the higher efficiency and sufficiency compared to

25

other seismic IMs, while the next more efficient and sufficient seismic IM was found to be

26

RMSd. On the contrary, PGD2/RMSd was found to be the optimum seismic IM for buried

27

pipelines in medium-stiff soils. It is worth noticing that the above conclusions were drawn for

28

pipelines with diameters D < 800 mm, without covering large-diameter pipelines that are

29

commonly found in transmission NG networks (diameters up to 1400 – 1800 mm).

30

Additionally, the operational pressure, which may affect significantly the axial response of a

31

pressurized steel pipeline, was restricted to 5.2 MPa. The operational pressure of transmission

32

NG networks may exceed this value, reaching 8.0 to 8.5 MPa. More importantly, the study did

33

not examine any relations between particular damage modes (e.g. local buckling) and seismic

34

IMs, neither investigated the critical effects of soil heterogeneities and spatial variability of the

35

seismic ground motion along the pipeline axis. An interesting point is that the same researchers

36

proposed in a later study numerical fragility curves for NG steel pipelines (see Section 3.3),

37

using PGV as seismic IM (Jahangiri and Shakib, 2018).

38

( )

1d

VSI PGD RMS

w

´´ +

éù

ëû

1

w

1

w

1

w

( )

1d

VSI PGD RMS

w

´´ +

éù

ëû

-29-

1

4.4 Identified gaps and challenges

2

Summarizing, MMI is considered an outdated IM, which due to its subjective definition is not

3

appropriate for a quantitative seismic assessment. Theoretically, εg may directly be related to

4

seismic vulnerability of buried pipelines. However, its evaluation might be more cumbersome

5

compared to PGV, due to difficulties and uncertainties in the definition of the apparent wave

6

velocity C. PGA is related directly with inertial forces, which for buried pipelines are not

7

important. PGV2/PGA requires the definition of two parameters, while its efficiency has not

8

been extensively validated. Ia provides information of both the duration and amplitude of a

9

seismic ground motion; however, its definition in field might be difficult, as a large number of

10

accelerograms is required to evaluate its spatial distribution at the site of interest. Peak ground

11

shear strain (γmax) is not related directly to peak ground axial strain that imposes damages on

12

buried pipelines. However, in a ground response analysis framework, γmax may be evaluated

13

easier than ground axial strain, since 1D soil response analyses suffice for its computation. The

14

additional seismic IMs used by Shakib and Jahangiri (2016), e.g. PGD, RMSa, RMSv, RMSd,

15

PGD2/PMSd, CAV, SMA, SMV, etc. have not been validated against real reported damages of

16

buried pipelines. However, some of them, such as PGD might be considered as promising

17

candidates. Finally, in the authors’ opinion, the use of spectral seismic IMs for buried pipelines

18

is highly debatable.

19

One of the main issues that prevent the definition of the optimum seismic IM for a quantitative

20

seismic assessment of NG pipelines is the lack of evidence on the efficiency (in the general

21

sence) of various seismic IMs to correlate with particular damage modes of pipelines. This

22

knowledge shortfall highlights the need for numerical and experimental studies, which will

23

allow for a thorough investigation of the level of correlation of various damage modes of NG

24

steel pipelines with various seismic IMs. A summary of numerical approaches that may be used

25

towards this direction are presented in the second part of the paper.

26

27

5. Conclusions

28

The paper summarized a critical review of available fragility relations for the vulnerability

29

assessment of buried NG pipelines subjected seismically-induced transient ground

30

deformations. Particular emphasis was placed on the efficiency of various seismic IMs to be

31

evaluated or measured in the field and, more importantly, to correlate with observed structural

32

damages of this critical infrastructure. The main conclusions and identified open issues are

33

summarized in the following:

34

• Distinct damage modes may have different consequences on the structural integrity and

35

serviceability of buried steel NG pipelines. Understanding the main response mechanisms

36

behind the identified damage modes on the basis of rigorous experimental and numerical

37

studies, may contribute towards a reliable definition and quantification of limit states for

38

this infrastructure.

39

-30-

• The majority of available empirical fragility relations refer to segmented cast-iron and

1

asbestos cement pipelines, the seismic response of which is quite distinct compared to

2

continuous pipelines, such as buried steel NG pipelines. Additionally, the implementation

3

of repair rate as an EDP does not provide any information regarding the severity of

4

damage, as well as the type of required repair. The most important drawback of empirical

5

fragility relations is that they do not disaggregate between the potential damage modes.

6

• The recently-developed analytical fragility functions for buried steel NG pipelines refer to a

7

limited number of soil-pipe configurations, while they do not consider many critical

8

parameters that may affect significantly the seismic response and vulnerability of this

9

infrastructure. Along these lines, additional research is deemed necessary towards the

10

development of analytical fragility functions, which will refer to distinct damage modes.

11

• Critical for development of efficient analytical fragility curves is the identification of

12

optimum seismic IMs for buried steel NG pipelines. The strengths and weaknesses of a

13

large number of commonly used seismic IMs for buried pipelines were discussed herein,

14

including also other potential metrics of the seismic intensity that may be found in the

15

literature. PGV, PGD, εg and PGV2/PGA seem to be reasonable candidates as optimum

16

seismic IMs for structural assessment of buried NG pipelines, due to their compatibility

17

with the loading mechanism of buried pipelines under seismically-induced transient ground

18

deformations. On the contrary, the use of ‘spectral’ seismic IMs seems to be incompatible

19

with the loading mechanism and general behaviour of buried civil infrastructure. One of the

20

main issues that prevent the definition of optimum seismic IMs for buried steel NG

21

pipelines, to date, is the lack of evidence regarding the ‘efficiency’ of various seismic IMs

22

to correlate with particular damage modes of buried pipelines. This knowledge shortfall

23

highlights the need for efficient numerical methodologies, which will allow for a proper

24

simulation of the distinct damage modes of buried steel NG pipelines and a thorough

25

investigation of the level of correlation of these damage modes with various seismic IMs.

26

Alternative methods for the analytical evaluation of the vulnerability of buried steel NG

27

pipelines under seismically-induced transient ground deformations are thoroughly discussed in

28

the second part of this paper. The discussion focuses on the assessment against seismically-

29

induced buckling failures since these constitute critical damage modes for the structural

30

integrity of this infrastructure.

31

32

Acknowledgements

33

This work was supported by the Horizon 2020 Programme of the European Commission under

34

the MSCA-RISE-2015-691213-EXCHANGE-Risk grand (Experimental and Computational

35

Hybrid Assessment of NG Pipelines Exposed to Seismic Hazard, www.exchange-risk.eu). This

36

support is gratefully acknowledged.

37

38

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