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A Critical Review on the Vulnerability Assessment of Natural Gas Pipelines Subjected to Seismic Wave Propagation. Part 1: Fragility Relations and Implemented Seismic Intensity Measures

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A Critical Review on the Vulnerability Assessment of Natural Gas Pipelines Subjected to Seismic Wave Propagation. Part 1: Fragility Relations and Implemented Seismic Intensity Measures

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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
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thorough critical review of available fragility relations for the vulnerability assessment of
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buried pipelines is presented. Particular emphasis is placed on the efficiency of implemented
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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
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thorough review of alternative methods for the analytical evaluation of the vulnerability of
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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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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
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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
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based on damages on cast iron pipelines reported during the 1971 San Fernando earthquake.
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Eguchi (1983) developed fragility functions for welded steel, asbestos cement and cast iron
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pipes, using observations from four earthquakes in USA and employing the Mercalli Modified
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Intensity (MMI) as seismic IM. This study constitutes the first case, where pipe damages
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( ) ( )
/ or /
oob
RR n repairs km a IM RR n repairs km a IM=´=´
( )
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
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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.
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Ballentine et al. (1990) presented a series of MMI-based fragility functions for water steel
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pipelines, using observations from six earthquakes in USA. Later studies also developed MMI-
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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
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Earthquake Engineering of the American Society of Civil Engineers (ASCE-TCLEE, 1991)
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proposed PGA-based fragility relations, reanalyzing damage data on water-supply systems
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from previous studies (Katayama et al., 1975). PGA-based fragility relations were also
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proposed by Hamada (1991) and O’Rourke T.D. et al. (1991) employing damage reports from
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earthquakes in the USA and Japan.
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A PGV-based fragility relation was proposed by O’Rourke M.J. and Ayala (1993) for brittle
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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
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proposed fragility relation was later adopted by FEMA in the HAZUS methodology (NIBS,
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2004) for the evaluation of seismic vulnerability of pipes subjected to seismically-induced
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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
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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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