Article

Seismic Fragility of Buried Steel Natural Gas Pipelines due to Axial Compression at Geotechnical Discontinuities

Abstract and Figures

This paper presents an extended set of numerical fragility functions for the structural assessment of buried steel natural gas (NG) pipelines subjected to axial compression caused by transient seismic ground deformations. The study focuses on NG pipelines crossing sites with a vertical geotechnical discontinuity, where high compression straining of a buried pipeline is expected to occur under seismic transient ground deformations. A de-coupled numerical framework is developed for this purpose, which includes a 3D finite element model of the pipe–trench system employed to evaluate rigorously the soil–pipe interaction effects on the pipeline axial response in a quasi-static manner. One-dimensional soil response analyses are used to determine critical ground deformation patterns at the vicinity of the geotechnical discontinuity, caused by the ground shaking. A comprehensive parametric analysis is performed by implementing the proposed analytical framework for an ensemble of 40 recorded earthquake ground motions. Crucial parameters that affect the seismic response and therefore the seismic vulnerability of buried steel NG pipelines namely, the diameter, wall thickness, burial depth and internal pressure of the pipeline, the backfill compaction level, the pipe–soil interface friction characteristics, the soil deposits characteristics, as well as initial geometric imperfections of the walls of the pipeline, are systematically considered. The analytical fragility functions are developed in terms of peak ground velocity at the ground surface, for four performance limit states, considering all the associated uncertainties. The study contributes towards a reliable quantitative risk assessment of buried steel NG pipelines, crossing similar sites, subjected to seismically-induced transient ground deformations.
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Seismic fragility of buried steel natural gas pipelines due to axial1compression at geotechnical discontinuities2
3Grigorios Tsinidis1, Luigi Di Sarno2, Anastasios Sextos3, and Peter Furtner4
4
51Vienna Consulting Engineers ZT GmbH, Austria & University of Sannio, Italy6 2University of Liverpool, United Kingdom & University of Sannio, Italy7 3University of Bristol, United Kingdom8 4Vienna Consulting Engineers ZT GmbH, Austria9
10 Corresponding Author: Grigorios Tsinidis, University of Sannio, School of Engineering,11 Piazza Roma, 21, 82100, Benevento, Italy, email: tsinidis.grigorios@gmail.com12
13 Abstract: This paper presents an extended set of numerical fragility functions for the structural14 assessment of buried steel natural gas (NG) pipelines subjected to axial compression caused by15 transient seismic ground deformations. The study focuses on NG pipelines crossing sites with a16 vertical geotechnical discontinuity, where high compression straining of a buried pipeline is17 expected to occur under seismic transient ground deformations. A de-coupled numerical18 framework is developed for this purpose, which includes a 3D finite element model of the pipe-19 trench system employed to evaluate rigorously the soil-pipe interaction effects on the pipeline20 axial response in a quasi-static manner. One-dimensional soil response analyses are used to21 determine critical ground deformation patterns at the vicinity of the geotechnical discontinuity,22 caused by the ground shaking. A comprehensive parametric analysis is performed by23 implementing the proposed analytical framework for an ensemble of 40 recorded earthquake24 ground motions. Crucial parameters that affect the seismic response and therefore the seismic25 vulnerability of buried steel NG pipelines namely, the diameter, wall thickness, burial depth26 and internal pressure of the pipeline, the backfill compaction level, the pipe-soil interface27 friction characteristics, the soil deposits characteristics, as well as initial geometric28 imperfections of the walls of the pipeline, are systematically considered. The analytical29 fragility functions are developed in terms of peak ground velocity (PGV) at the ground surface,30 for four performance limit states, considering all the associated uncertainties. The study31 contributes towards a reliable quantitative risk assessment of buried steel NG pipelines,32 crossing similar sites, subjected to seismically-induced transient ground deformations.33
34 Keywords: natural gas pipelines; seismic response; fragility curves; soil-pipe interaction;35 transient ground deformations; steel pipelines; local buckling36
37 1. Introduction38 Earthquake-induced damage on Natural Gas (NG) pipeline networks may lead to significant39 downtimes, which in turn may result in high direct and indirect economic losses. The 199940 Chi-Chi earthquake in Taiwan, for instance, caused noticeable damage on natural gas supply41 systems, with the associated economic loss for the major natural gas companies exceeding $2542
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million (Chen et al. 2000; Lee et al. 2009) More importantly, severe damages may trigger1 ignition or explosions with life-treating consequences and significant effects on the2 environment. The 1995 Hyogo-Ken Nambu earthquake in Japan is a rather devastating3 example since the particular earthquake caused gas leakages from buried pipelines at 2344 different locations, which subsequently led to more than 530 fires (EQE 1995; Scawthorn et al.5 1995). The above aspects highlight the importance of simple, yet efficient, methods for6 structural vulnerability assessment of NG pipeline networks.7 Buried steel NG pipelines are found to be quite vulnerable to high strain imposed by permanent8 ground deformations, associated with seismically-induced ground failures, i.e. fault9 movements, landslides, liquefaction-induced settlements or uplifting and lateral spreading10 (O’Rourke M.J. and Liu 1999; Sarvanis et al. 2018; Lanzano et al. 2015; Karamitros et al.11 2007; 2016; Vazouras et al. 2010; 2012; Vazouras and Karamanos 2017; Melissianos et al.12 2017a, b, c; Sarvanis et al. 2018; Demirci et al. 2018; Tsatsis et al. 2018). Although to a lesser13 extent, transient ground deformations, induced by seismic wave propagation, have also14 contributed to seismic damage of steel pipelines (Housner and Jenningst 1972; O’Rourke T.D.15 and Palmer 1994; O’Rourke M.J. 2009). Indeed, transient ground deformation may trigger16 diverse damage modes on continuous NG pipelines, including (i) shell-mode or local buckling,17 (ii) beam-mode buckling, (iii) pure tensile rupture, (iv) flexural bending failure and (v)18 excessive ovaling deformation of the section (O’Rourke M.J. and Liu 1999). Recent studies19 have demonstrated that pipelines embedded in heterogeneous sites and/or subjected to20 asynchronous ground seismic motions are likely to be further affected by appreciable21 deformations and strains due to transient ground deformations, which in turn may lead to22 buckling damages on the pipeline (Psyrras and Sextos 2018; Psyrras et al. 2019).23 In practice, the seismic risk assessment of pipelines is mainly performed, by implementing24 empirical fragility relations, which were constructed on the basis of observations of the25 behaviour of buried pipelines during past earthquakes (e.g. ALA 2001; NIBS 2004; Gehl et al.26 2014). A detailed review of available empirical relations may be found in Tsinidis et al.27 (2019a). These relations normally provide correlations between the pipeline repair rate, RR,28 i.e. the number of pipe repairs per unit of pipeline length, and a selected seismic intensity29 measure, expressing the seismic intensity.30 The majority of available fragility relations refer to cast-iron or asbestos cement segmented31 pipelines, the seismic response of which is quite distinct compared to continuous pipelines,32 such as buried NG pipelines (O’Rourke M.J. and Liu 1999). The lack of relevant damage33 reports and therefore of relevant fragility relations for continuous pipelines has been attributed34 by some researchers to their better performance, compared to the segmental pipelines, when35 subjected to seismically-induced transient ground deformations. However, as stated above,36 under certain conditions, transient ground deformations may impose significant strains on37 buried pipelines.38 The implementation of repair rate as an engineering demand parameter (EDP) does not39 provide detailed information regarding the severity of damage, as well as the type of required40 repair, while the accuracy of the repair reports that constitute the basis for the development of41 empirical fragility functions may be debatable, since these are commonly drafted after a short42
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period from the main event and under the pressure for rapid restorations. Moreover, available1 empirical relations were developed on the basis of damage reports on pipeline networks found2 in USA and Japan, whilst in southern Europe or other seismic prone areas there is an evident3 lack of relevant information. Evidently, the applicability of the empirical fragility relations is4 restricted to cases where the network characteristics, e.g. pipe dimensions and materials, soil5 conditions etc, and the ground motion characteristics, are similar to the relevant characteristics6 of the sample used to develop the relations. Finally, available fragility relations do not7 disaggregate between distinct damage modes and associated effects on the structural integrity8 and serviceability of the pipeline. Along these lines, a general and unconditional use of these9 relations might introduce a degree of uncertainty in the seismic risk assessment of networks10 with distinct characteristics (Psyrras and Sextos 2018).11 A limited number of numerical fragility curves that compute probabilities of failure for well-12 defined limit states in the ‘classical sense’ have been proposed, recently (Lee et al. 2016;13 Jahangiri and Shakid 2018). However, available numerical fragility functions refer to rather14 limited number soil-pipe configurations and do not cover NG pipelines with diameters larger15 than 800 mm that are commonly used in transmission NG networks. More importantly, the16 relevant numerical studies do not examine thoroughly salient parameters that may affect the17 response and hence the vulnerability of buried NG pipelines under seismically-induced18 transient ground deformations, such as the effects of the internal operational pressure of the19 pipeline or the initial geometric imperfection of the walls of the pipes and the spatial variability20 of soil conditions.21 In the light of the above considerations and knowledge gaps, this paper presents an extended22 set of numerical fragility curves for the structural assessment of buried steel NG pipelines23 subjected to axial compression caused by transient seismic ground deformations. The study24 focuses on pipelines crossing perpendicularly a vertical geotechnical discontinuity with an25 abrupt change on the soil properties, where the potential of high compression strain and26 therefore buckling failures is expected to be increased under seismic transient ground27 deformations. A detailed analytical framework is developed for this purpose, which is28 employed in a comprehensive parametric analysis of large number of pipe-soil configurations29 and for an ensemble of 40 recorded earthquake ground motions. Crucial parameters affecting30 the response of buried steel pipelines namely the diameter, wall thickness, burial depth and31 internal pressure of the pipeline, the existence of initial geometric wall imperfections of the32 pipeline, the trench soil compaction level, the pipe-backfill interface friction characteristics and33 the variability of the characteristics of the soil deposits, are thoroughly accounted for in the34 study. The analytical fragility curves are developed in terms of peak ground velocity (PGV) at35 the ground surface, for four performance limit states, considering the associated uncertainties.36
37 2. Definition of problem38
Fig. 1 illustrates schematically the problem examined herein. A continuous buried steel NG39 pipeline of external diameter D and wall thickness t is embedded in a surficial block of soil at a40 burial depth h. The surficial block of soil is resting over a soil deposit with a vertical41 geotechnical discontinuity. The latter divides the deposit into two subdeposits, i.e. subdeposit 142
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and subdeposit 2, with abrupt changes on their physical and mechanical properties. The total1 depth of the soil deposit is H. It is noted that the selected soil deposits constitute idealized2 cases to facilitate the numerical parametric study presented herein. The soil-pipe system is3 subjected to ground seismic shaking, in the form of upward propagated, vertically polarized4 plane shear waves, which causes a dissimilar ground movement of the adjusted subdeposits.5 The dissimilar ground movement of the adjusted soil subdeposits produces a differential6 horizontal ground deformation along the pipeline axis near the critical section of the7 geotechnical discontinuity, which subsequently is transferred via the pipe-trench soil interface8 on the pipeline causing its compressive-tensional axial straining. A potential high axial9 compression strain of the pipeline might finally lead to a failure of the pipeline in the form of10 local buckling. Based on the above considerations, a numerical framework is developed to11 evaluate the vulnerability of the embedded steel NG pipeline under an ensemble of carefully12 selected real records.13
h
Pipeline & surficial soil layer
Subdeposit 1
uAuB
ur
H
Subdeposit 2
Elastic bedrock
14 Fig. 1 Schematic view of the examined problem (H: depth of the soil deposit, h: burial depth of the15 pipeline, ur: seismic displacement at bedrock, uAand uB: horizontal seismic deformations of the adjacent16 soil subdeposits).17
18 3. Analytical framework19 3.1 General flowchart20 The extended dimensions of the problem in hand, the need for refined meshes to capture21 potential buckling failure of the pipeline, the complexity in simulating the material and22 geometrical nonlinearities, i.e. sliding and/or detachment phenomena at the soil-pipe interface,23 during ground shaking, the uncertainty in the definition of the characteristics of heterogeneous24 soil sites, and issues associated with proper selection of seismic ground motions, are all reasons25 that render a fully 3D time history analysis of the coupled pipeline-trench soil system26 computationally prohibitive (Psyrras and Sextos 2018).27 Generally, the inertial soil-structure interaction (SSI) effects are not considered to be a key28 factor in the context of the dynamic soil-pipe interaction (SPI) problem mainly due to the29 reduced mass of the pipe in comparison to that of the soil (O’Rourke M.J. and Hmadi 1988).30 This allows for a decoupling of the problem in successive stages in order to reduce the high31 computational cost, associated with a fully-fledged 3D SPI dynamic analysis. Moreover, it32 allows for the investigation of the effect of transient ground deformation on the response of the33 embedded pipeline in a quasi-static manner.34
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Based on the above considerations, an analytical framework was developed within this study to1 evaluate thoroughly the seismic vulnerability of NG pipelines embedded in sites, similar to Fig.2 1. The flowchart of the analytical framework is illustrated schematically in Fig. 2.3
4
Selection of examined
soil-pipe
configurations
Selection of
earthquake ground
motions
Computation of pipe
response for an
increasing ground
displacement pattern,
δu via a 3D SPI model
Computation of soil
response via 1D soil
response analyses
Correlation of pipe
response with soil
response for various
ground motions:
δu-EDP
Evolution of EDP with
PGV at ground
surface
Definition of limit
states & uncertainties
Development of
PGV-based fragility
curves for various
soil-pipe
configurations
δ
u
δ
ue
δ
u
u=0
uAuB
u
r
uAuB
PGVA
urur
δue= max (uA-uB)
PGV = max {PGVA, PGVB}
PGVB
5
6Fig. 2 Flowchart of the analytical framework for the development of fragility curves for buried NG7pipelines crossing sites with a geotechnical discontinuity.8
9The analysis of the seismic response of the selected soil-pipe configurations is carried out in10 steps, as follows: initially, a 3D trench-pipe numerical model is developed to compute the axial11 compression response of the buried steel NG pipeline under an increasing level of seismically-12 induced relative axial ground displacement, δu, considering the soil compliance effects. The13 response of selected soil deposits is then computed by means of separate 1D nonlinear soil14 response analyses of the adjacent subdeposits. In particular, through the soil response analyses,15 the horizontal deformations of the subdeposits are computed for the selected ground motions at16 the burial depth of the examined pipelines. These are subsequently used to define maximum17 differential ground movement patterns, δue, of the soil deposits consisting of the examined18 subdeposits. The soil response analyses are also used to calculate the peak ground velocity19 PGV at the ground surface, which is used as seismic intensity measure (IM) to express the20 fragility curves. The outcomes of the 3D SPI analyses and 1D soil response analyses are finally21 combined, to correlate the pipe response, in terms of maximum axial compression strain, ε,22 which is selected as engineering demand parameter, EDP, for the pipeline, with the ground23 response computed for each of the selected pairs of subdeposits and each ground motion. The24 latter combinations result in relationships of pipe strain ε with the PGV at ground surface,25 which are finally used to define fragility curves for four predefined performance limit states,26
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considering all the associated uncertainties. The analytical framework is further elaborated in1 the following sections.2
33.2 3D trench-pipe model for SPI analysis4A 3D model of the trench soil, encasing a cylindrical shell model of the pipeline, is initially5 developed in ABAQUS (2012), aiming at computing the axial response of the pipeline under6 an increasing level of horizontal relative ground displacement, δu, developed near a7 geotechnical discontinuity (Fig. 3).8
9Fig. 3 3D trench-pipe numerical model for the computation of the axial compression response of the10 pipeline, under an increasing level of seismically-induced relative ground displacement, δu.11
12 The use of the near field 3D continuum trench-pipe model allows for a rigorous simulation of13 localized buckling modes that might potentially be developed in the pipe under axial14 compression, as well as for the proper simulation of geometric imperfections of the pipeline15 walls, which are expected to affect significantly the axial compression response of the buried16 pipeline (Yun and Kyriakides 1990; Tsinidis et al. 2018; Psyrras et al. 2019). Additionally, it17 allows for a proper simulation of the operational pressure of the pipeline and contact nonlinear18 phenomena, i.e. sliding and/or potential detachment in the normal direction, between the19 pipeline wall and the surrounding ground. The latter is of great importance since the shear20 behaviour of the trench soil-pipe interface effectively controls the level of shear stresses that21 are transmitted along the perimeter of the pipeline during shaking. The integral of these shear22 stresses constitutes the axial loading of the pipeline.23
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3.2.1 Dimensions of the 3D model1The shallow burial depth of the pipeline in addition to absence of significant inertial SSI effects2 and the assumption of in-plane ground deformation pattern, allow for the simulation of only the3 surficial soil-trench, which constitutes a surficial block from the semi-infinite 3D ground4 domain (Psyrras et al. 2019). Along these lines, the distance between the side boundaries of the5 trench model and the pipe edges is set equal to one pipe diameter, whereas the distance6 between the pipe invert and the bottom boundary of the trench model is set equal to 1.0 m.7 Evidently, the distance between the pipe crown and ground surface is defined on the basis of8 the adopted burial depth, h, of the examined pipeline.9 Generally, an ‘adequately long’ 3D continuum model is required to replicate the actual SPI10 phenomena, accounting for the ‘anchorage’ length of the pipeline on the surrounding trench11 and its effect on the transmitted shear stresses from the trench on the pipeline through the soil-12 pipe interface during the axial deformation of the trench. Additionally, there is a requirement of13 fine discretization of the pipe to adequately resolve the buckling modes of the pipeline, as14 discussed in the following. The above aspects increase significantly the relevant computational15 cost of the analysis, even if the seismic loading is considered in a quasi-static manner. To16 reduce the required length of the 3D model, while accounting for the effect of the infinite17 pipeline length on the response of the examined pipeline-trench soil configuration, nonlinear18 springs are introduced at both sides of the pipeline. The force-displacement relation of the19 nonlinear springs, which are act parallel to the pipeline axis, is given by the following20 relations:21
max
2
for
+ 2 for
x x s
x x
s s s s s
EA k
FD
EA m
k m k k k k
t
l d d
t p t t t t t
l l d l d
ì£
ï
ï
ï
=íæ ö
æ ö æ ö æ ö
ïç ÷
+ - - >
ç ÷ ç ÷ ç ÷
ïç ÷
è ø è ø è ø
ïè ø
î
(1)22
where:23
s
Dk
EA
p
l
=(2)24
max
D
m
EA
p t
=(3)25
x
d
is the ground-pipe relative axial movement caused by the relative axial ground deformation26
δu as a result of the dissimilar ground movement of the adjacent subdeposits,
max
t
is the27
maximum shear resistance that develops along the trench backfill-pipe interface, ks is the shear28 stiffness of the trench backfill-pipe interface and EA is the axial stiffness of the pipeline cross29 section. For cohesionless backfills, the maximum shear resistance depends on the adopted30 friction coefficient μ and varies along the perimeter of the pipe. Average values of
max
t
and ks
31
may be computed on the basis of numerical simulations of simple axial pull-out tests of the32 examined pipe from the examined trench soil, as discussed later. Following the above33 simulation approach, the required length of the 3D pipe-soil trench model may be reduced to34
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20 times the external diameter of the pipeline. The theoretical background behind this1 simulation approach, which is inspired by a numerical model that was developed by Vazouras2 et al. (2015), is presented in Tsinidis et al. (2019b). The validity of this proposed simulation is3 verified in the following, by comparing the stresses and strains computed at the middle critical4 section of a selected pipeline by the 3D reduced-length model with the nonlinear springs, with5 relevant predictions of an equivalent quite extended, almost ‘infinitely’ long 3D continuum6 model of the soil-pipe configuration subjected to the same axial ground deformation pattern.7 Typical static boundary conditions are applied at the bounding soil surfaces, while the ground8 surface is set free.9
10 3.2.2 Finite element discretization11 The trench soil is simulated by means of hexahedral (brick-type) elements with equivalent soil12 properties being assign on them (i.e. soil degraded stiffness), the latter being estimated by the13 separate 1D soil response analyses, as discussed in the ensuing. Inelastic, reduced integration14 S4R shell elements are used to mesh the pipeline. The particular shell elements have both15 membrane and bending stiffness. The mesh density of the pipeline at the central section of the16 3D model, i.e. at the assumed location of the geotechnical discontinuity, where the axial strain17 of the pipeline is expected to maximize under ground shaking, is selected to be fine enough, so18 that to resolve the inelastic buckling modes of an equivalent axially compressed unconstrained19 cylindrical steel shell (Psyrras et al. 2019). To facilitate the selection of mesh, the half-20 wavelength in the post-elastic range,
,
c p
l
, is initially computed for the selected pipelines, as21
per Timoshenko (1961):22
, ,c p c el p
E E
l l
» ´ (4)23
where E is the Young’s modulus of the steel grade of the pipeline, Ep is the plastic modulus of24
the steel grade of the pipeline and
,
c el
l
the elastic axial half-wavelength. Considering a25
Poisson’s ratio v = 0.3 for the steel grades examined herein, the latter is given as:26
,1.72
c el
Rt
l
»(5)27
where R is the radius of the pipeline and t is the wall thickness of the pipeline. Assuming that28
the plastic modulus Ep is equal to 0.1E, Eq. 4 yields:
, ,
0.5
c p c e
l l
»(Psyrras et al., 2019).29
Element lengths, ranging between 1.0 cm and 2.0 cm, depending on the geometric properties of30 the selected pipelines, were found capable to reproduce the theoretical axial half-wavelength31
,
c p
l
of the examined pipelines. These mesh seeds are applied over a length of 2.0 m in the32
middle section of the examined pipelines. The mesh density away from the critical central zone33 is gradually decreased, with the axial dimension of the shell elements being as high as 0.30 m,34 in an effort to reduce the computation cost. The mesh discretization of the trench soil in the35 axial direction of the model matches the exact mesh seed of the pipeline to avoid any initial36 gaps during the generation of mesh. The mesh seed of the trench in the other two directions is37 restricted to 0.30 m.38
39
40
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3.2.3 Trench soil-pipe interface1The soil-pipe interface is simulated by means of an advanced hard contact interaction model,2 available in ABAQUS (2012). The model allows for sliding and/or potential detachment in the3 normal direction between the interacting pipe and trench-soil elements during the horizontal4 deformation of the surrounding trench. The shear behaviour of the interface model is controlled5 by the classical Coulomb friction model, through the introduction of a friction coefficient, μ.6 The adopted values of friction coefficients, μ, are presented in Section 4.7
83.2.4 Behaviour of the backfill soil and pipe9The surficial soil-backfill is simulated as an elastic medium, with equivalent properties (i.e.10 degraded soil stiffness) defined as per Section 3.3. The plastic behaviour of the steel pipelines11 is modelled employing a classical flow plasticity model combined with a von Mises yield12 criterion. The model is defined by fitting Ramberg-Osgood curves (Equation 6) to bilinear13 isotropic curves, the latter describing the tensile uniaxial behaviour of the selected steel grades14 (see Section 4)15
n
y
a
E
s s
es
æ ö
= + ´
ç ÷
ç ÷
è ø
(6)16
where E is the elastic modulus,
σ
is the axial stress, ε is the axial strain,
y
σ
is the yield stress,17
n is a hardening parameter and
a
is a ‘yield offset’ which is equal to y
α σ
E
. Parameters α and18
n are defined for the selected steel grades of the examined pipelines in Section 4.19
20 3.2.5 Initial geometric imperfection of the pipeline section21 The axial compressive response of thin-walled steel pipelines is known to be highly affected by22 initial geometric imperfections of the walls (NASA 1968; Yun and Kyriakides 1990; Psyrras at23 al. 2019). To account for this effect on the structural response of the examined pipelines, both24 ‘perfect’ pipelines and equivalent pipelines with initial geometric imperfections are examined.25 For the latter cases, a stress-free, biased axisymmetric imperfection is considered. The26 imperfection is defined on the basis of a sinusoid modulated by a second sinusoid, as per27 Equation (7), following Psyrras et al. (2019):28
( )
0 1 cos cos , , 2.0 , 2
2 2
crit crit
crit c crit
c c
L L
x x
w x w w x L m N L
N
p p l
l l
é ù
æ ö æ ö
= + - £ £ = =
ê ú
ç ÷ ç ÷
è ø è ø
ë û (7)29
The positive values correspond to outward direction from the mid-surface of the pipeline shell30 wall. The peak amplitude of the imperfection is set as a function of the pipe lining thickness,31 based on the following formulation: 0 1
0.10
w w w t
= + = . The imperfection level is based on32
relevant specifications from NG pipeline manufactures, e.g., ArcelorMittal specifies a33 manufacturing tolerance for the walls of API-5L X65 pipelines in the range of + 15% to -34 12.5% (ArcelorMittal 2018). The imperfection is applied over the central critical pipeline zone35 with length equal to
crit
L
= 2.0 m, centered at the exact position, where the soil discontinuity is36
considered. Fig. 4 illustrates a detail of the mesh of the central section of an imperfect pipeline.37
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The exact same perturbation is introduced on the mesh of the trench soil, surrounding the1 pipeline, to prevent any initial gaps during the generation of the mesh that might affect the2 contact phenomena during loading. It is noted that any residual stresses on the pipelines,3 related to the manufacturing process were disregarded in the present study.4
5
Lcrit
2λc
Peak imperfection
amplitude
6Fig. 4 Detail of the mesh of the central section of a 914.4 mm pipeline with a biased axisymmetric7geometrical imperfection of the walls (the radial deformation is exaggerated by a scale factor, i.e. × 10).8
93.2.6 Analysis steps10 The stress state, associated with the gravity and the internal pressure of the pipeline, is initially11 established within a general static step. The effect of seismically-induced transient ground12 deformation is then introduced in quasi-static fashion. In particular, the nodes of the one half of13 the trench model and the free node of the relevant nonlinear spring are fixed in the axial14 direction, i.e. the right-hand side of the model in Fig. 3, whereas the nodes of the other half of15 the trench model and the free node of the relevant nonlinear spring are monotonically forced to16 move towards constraint part of the model, in a stepwise fashion, thus resulting in a relative17 axial displacement of the trench model equal to δu, the latter increasing throughout the analysis18 step. The analysis is carried out till the numerical analysis collapses, i.e. after buckling failure19 of the examined pipeline. This displacement configuration is equivalent to the case, where both20 halves of the trench model, are moving dissimilarly in the axial direction, causing the same21 differential axial ground movement δu on the examined system. The displacement pattern is22 kept constant with depth coordinates over the trench soil domain and the free-ends of the23 nonlinear springs, for the sake of simplicity. This assumption is considered valid since the24 depth of the trench domain is rather small compared to the predominant wavelength of25 common seismic waves (Psyrras et al. 2019). The above kinematic loading induces shear26 stresses along the pipe-soil interface, which in addition to the axial loading induced on the both27 ends of the pipeline through the nonlinear springs, result in an axial compression straining of28 the pipeline. The latter is traced for the increasing level of relative axial ground displacement,29
δu, via a modified Riks solution algorithm, available in ABAQUS (ABAQUS 2012). Through30 this analysis, a curve describing the relation between an increasing relative axial ground31 displacement, δu, and the corresponding peak compression axial strain ε of the critical middle32 section of the pipeline, i.e. near the assumed geotechnical discontinuity, can be established.33 The peak compression axial strain is evaluated as the envelope of the compression axial strains34 computed for all the shell elements that are located within the critical section of the pipeline. It35
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should be highlighted that the analysis focuses on the axial ground displacements and1 disregards the vertical ones that might be observed near geotechnical discontinuities since the2 former constitute the dominant loading mechanism for the buried pipeline. Since the response3 of the pipeline is computed for an increasing level of relative axial ground displacement, δu, the4 outcome of one 3D SPI analysis may be used to examine the axial straining of the pipe under a5 variety of selected ground axial relative displacements, δue, caused by diverse seismic motions.6 This is of course possible under the assumption and implementation of mean equivalent soil7 properties for the trench backfill soil, corresponding to the strain-range that is anticipated for8 the selected ground seismic motions.9
10 3.3 1D soil response analysis of adjacent soil deposits11 The response of the selected sites is evaluated through separate 1D soil nonlinear response12 analyses of the adjacent subdeposits (Fig. 5), carried out by employing the code DEEPSOIL13 v6.1 (Hashash et al. 2016). The hysteretic nonlinear response of the soil during ground shaking14 is considered in the analyses by means G-γ-D curves, which are properly selected for the15 examined deposits, following Darendeli (2001). To avoid the potential amplification of higher16 frequencies of the ground that may result in unrealistic oscillations of the acceleration time17 histories in low ground strains, additional viscous damping of 1 % is also introduced in the18 form of the frequency-dependent Rayleigh type (Hashash and Park 2002). The Rayleigh19 coefficients are properly tuned for a frequency interval range, characterizing the ‘dominant20 frequencies’ of each soil column. Through the soil response analyses, time histories of the21 horizontal deformations of the soil columns are calculated at the burial depths of the pipelines.22 These time histories are subsequently used to compute maximum differential ground23 deformation patterns δue for the selected pairs of adjusted subdeposits. Additionally, time24 histories of the horizontal velocity are computed at the ground surface, which are used to25 evaluate the peak ground velocity PGV at ground surface. The latter is used as seismic intensity26 measure for the development of the analytical fragility curves.27
uAuB
PGVA
1D soil response analyses
urur
Soil nonlinear response
δ
u
e
= max (u
A
-
u
B
)
PGV = max {PGVA, PGVB}
Surficial layer
Subd
eposit 1
u
A
u
B
u
r
H
Subd
eposit 2
Elastic bedrock
PGVB
28 Fig. 5 Schematic view of the analysis framework used to compute the response of the selected soil sites29 under ground shaking.30
31 3.4 Correlation of 3D SPI and 1D soil response analyses results32 The critical relative axial ground deformation patterns, δue, which are defined on the basis of33 the results of the 1D soil response analyses, are correlated with the predicted straining of the34
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pipeline, using the δu -maximum compressive axial strain ε relations computed by the 3D SPI1 analyses. The identified from the above correlation procedure pipeline strains ε are employed2 to define ε-PGV relationships, which are finally used to define the numerical fragility curves3 for predefined limit states in a probabilistic framework, accounting for all the associated4 uncertainties.5
63.5 Performance limit states7The development of analytical fragility curves requires the rigorous definition of performance8 limit states, which are associated with specific damage levels. In this study, four performance9 limit states are defined on the basis of peak axial compressive strain ε of the pipeline, following10 Jahangiri and Shakib (2018). The limit states, summarized in Table 1, refer to different return11 periods of earthquake, ranging between 25 and 2475 years, and are associated with different12 levels of damage on the pipeline. They are actually defined on the basis of thorough review of13 relevant studies, guidelines, codes and regulations, as per Table 1. Despite this fact, the14 definition of limit states contains a level of uncertainty, which is considered in the definition of15 fragility curves, as discussed in the ensuing. The first two limit states, i.e. operable limit state16 (OLS) and pressure integrity limit state (PILS), may be characterized as operational limit17 states, since no leakages are expected, and the flow of the pipeline is not disrupted. On the18 contrary, ultimate limit state (ULS) and global collapse limit state (GCLS), constitute ultimate19 limit states, since pipe wall tearing is expected, resulting in leakages and flow disruption. In20 terms of damage level, the four limit states may by associated with slight, moderate, extensive21 and complete damage, respectively. For a more detailed presentation of the relevant definitions22 of the limit states the reader is referred to Jahangiri and Shakib (2018).23
24 3.6 Development of fragility functions25 Fragility functions describe the probability of exceeding different performance limit states,26 given a level of ground shaking intensity (Elnashai and Di Sarno 2015). Following common27 approaches, the fragility relations in this study are developed, by employing a lognormal28 probability distribution function:29
30
( )
1ln
tot mi
PGV
P ds ds S PGV
b
é ù
æ ö
³ = F ´
ê ú
ç ÷
è ø
ë û
(8)31
where
(
)
P ds ds S
³ is the probability of exceeding a particular limit state, ds, for a given32
seismic intensity level, the latter defined by the peak ground velocity, PGV, at ground surface.33
Φ is the standard cumulative probability function, PGVmi is the median threshold value of34 PGV, required to cause the ith damage state, and βtot is the total lognormal standard deviation.35 Based on the above definitions, the analytical fragility curves may be sufficiently described by36 defining the following parameters PGVmi and βtot.37
38
39
40
-13-
Table 1. Limit states adopted Jahangiri and Shakib (2018), t: thickness of the pipeline, D: diameter of1the pipeline2
Limit state Maximum limit axial
compressive strain Description Return
period
(years)
εcdefined following:
Operable
Limit State
(OLS)
(
)
min 0.01,0.4
t D
e
= ´
Despite some minor plastic
deformations, the pipeline
will operate immediately
after the event.
25 ALA (2001);
JG(G)-206-03 (2004);
EN 1998-4 (2006)
Pressure
Integrity
Limit State
(PILS)
(
)
min 0.04,1.76
t D
e
= ´
Despite some significant
deformations on the pipe,
no leakage of containment
is taken place.
95
ALA (2001) ;
JG(G)-206-03 (2004) ;
CEN (2006) ;
Mohareb (1995) ;
Honegger et al.
(2002); Bai and Bai
(2014)
Ultimate
Limit State
(ULS)
(
)
min 0.1,4.4
t D
e
= ´ A ‘controllable’ release of
the containment of the
pipeline is expected. 475
Bai (2001);
Honegger et al.
(2014); Bai and Bai
(2014)
Global
Collapse
Limit State
(GCLS)
0.15
e
=
A structural collapse is
reported. 2475
Zhang (2008);
Nazami and Das
(2010);
Ahmed et al. (2011);
Bai and Bai (2014)
3The fragility curves are established based on the evolution of EDP, i.e. the peak axial strain of4 the pipeline ε in this study, with increasing earthquake intensity, encountering the associated5 uncertainties. In particular, PGVmi are defined on the basis of relevant regression analyses of6 the axial strain of the pipeline ε with increasing PGV at ground surface. The latter is defined in7 this study as the maximum value of the peak values computed by the 1D soil response analyses8 of the adjacent subdeposits (see Section 3.3). It is worth noticing PGV has been used9 extensively as seismic IM in fragility relations for buried pipelines (Barenberg 1988; O’Rourke10 M.J. and Ayala 1993; Eidinger et al. 1995; Eidinger et al. 1998; Jeon and O’Rourke T.D. 1995;11 ALA 2001; Chen et al. 2002; Pineda and Ordaz 2003; O’Rourke M.J. and Deyoe 2004;12 Lanzano et al. 2013; Lanzano et al. 2014; Jahangiri and Shakib 2018). The wide use of PGV is13 attributed to its direct relation with the longitudinal ground strain, which is responsible for the14 induced damages on buried pipelines caused by transient ground deformations. More15 importantly, in a recent study of the authors this measure was found to be the optimum one for16 the structural assessment of buried steel NG pipelines embedded in similar soils sites and17 subjected to similar seismic hazards. Finally, the metric satisfies the hazard computability18 criterion, since PGV hazard maps are readily available after a major earthquake event.19 With reference to the definition of the lognormal standard deviation, βtot, which describes the20 total variability associated with each fragility curve; three primary sources of uncertainty are21 considered (NIBS 2004) namely the definition of damage states, βds, the response and22
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resistance (capacity) of the element, βC, and the earthquake input motion (demand), βD. The1 total uncertainty is estimated as the root of the sum of the squares of the component2 dispersions. The uncertainty associated with the definition of damage states, βds, is set equal to3 0.4, following HAZUS suggestions for buildings (NIBS 2004). In a similar manner, the4 uncertainty due to the capacity, βC, is assigned equal to 0.25. It is worth noticing that the5 definition of both βds and βC constitutes an open issue, particularly for embedded civil6 infrastructure (Argyroudis and Pitilakis 2012; Argyroudis et al. 2017). A more rigorous7 definition of the above parameters requires further detailed investigation, something that is8 beyond the scope of the present study. The last source of uncertainty, associated with the9 seismic demand, βD, is described by the variability in response of the pipeline caused by the10 variability of ground motion, and it is calculated as the dispersion of the simulated damage11 indices with respect to the regression fit.12
13 3.7 Limitations14 Inevitably, there are some limitations of the analytical framework employed herein. The effects15 of inertial SPI and of the evolution of stresses and deformations due to temperature changes on16 the pipeline response, as well as time-dependent phenomena, such as fatigue and steel strength17 and soil stiffness degradation due to cyclic loading, are neglected. Additionally, the18 methodology does not account for all the sources that lead to spatial variability of the seismic19 ground motion along the pipeline axis, such as wave passage effect and loss of coherency.20 Although the latter parameters may further affect the response of the long buried pipelines, it21 has been reported that their effect is relatively lower as compared to the effect of soil22 variability (Psyrras et al. 2019). Moreover, complex 2D wave phenomena near the geotechnical23 discontinuity are not being thoroughly investigated, due to the implementation of 1D soil24 response analyses. However, 1D nonlinear soil response analyses offer computational25 efficiency compared to 2D or 3D analyses and may be used as a first approximation for the26 evaluation of the seismic response of the ground and pipelines at shallow depths (Paolucci and27 Pitilakis 2007). The computational efficiency of 1D soil response analyses allows for an28 extended and thorough parametric analysis, such as the one presented in the ensuing. It is also29 noted that the methodology does not consider the potential effect of the transversal seismic30 loading on the pipeline response.31
32 4. Numerical parametric study33
A comprehensive numerical parametric study was conducted for various soil-pipe34 configurations, employing the above analytical framework.35
36 4.1 NG pipelines37 The external diameter, D, and operational pressure, p, of the examined pipelines were selected38 on the basis of a preliminary investigation of the variation of these characteristics in case actual39 transmission NG networks found in several countries of Europe (Table 2). The external40 diameter, D, wall thickness, t, and examined internal pressures, p, of the selected pipelines are41 summarized in Table 3. The selected pipelines, which cover a wide range of diameter over42
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thickness ratios, D/t, that may be found in NG network applications, were designed following1 the relevant regulations of ALA (2001) for a maximum operational pressure of p = 9 MPa. For2 this maximum pressure level and by setting the external diameter of the pipeline, the wall3 thickness of the pipeline was calculated. Checks against ovaling due to earth loads were also4 carried out, as per ALA (2001). It was finally verified that the selected pipeline dimensions are5 available by the industry. The pipelines are made of API 5L X60, X65 and X70 grades, in an6 effort to cover a range of steel grades that are commonly used in this infrastructure. The7 mechanical properties of the selected grades are tabulated in Table 4, while Fig. 6 presents the8 axial stress-strain curves, which characterize the axial response of the examined pipelines and9 were defined by fitting Eq. 6 for a yield offset equal to 0.5 %. On this basis, the hardening10 exponents n are set equal to 15, 19.5 and 21, for grades X60, X65 and X70, respectively. The11 burial depth, h, of the selected pipelines, i.e. distance between the pipeline crown and ground12 surface, ranged between 1.0 m and 2.0 m, which constitute common burial depths for this13 infrastructure.14
15
16 Fig. 6 Uniaxial tensile stress-strain response of API X60, X65 and X70 steel grades adopted herein (n=17 hardening exponent, a = yield offset × E/σy).18
19 Table 2 External diameters and range of operational pressure of transmission NG pipeline networks20 found in several countries of Europe (information provided by the website of each operator).21
Country Operator Nominal diameter range Operational pressure
range (MPa)
Austria TAG 914.4 mm to 1066.8 mm (36’ - 42’) 7 - 8
Belgium Fluxys Belgium 914.4 mm, 965.2 mm, 1016.0 mm (36’, 38’, 40’) 4 - 7
Germany Gascade > 1066.8 mm (42’) for the supra-regional
networks; otherwise > 508 -762 mm (20’ - 30’) n.p*
Germany Gasunie > 1066.8 mm (42’) for the supra-regional
networks; otherwise > 508 - 762 mm (20’ - 30’) n.p
Greece DESFA 254 mm, 508 mm, 609.6 mm, 762 mm, 914.4 mm
(10’, 20’, 24’, 30’, 36’) 7
Italy SNAM 508 - 1219.2 mm (20’ to 48’) 7 - 8
Spain Enegas 406.4 - 812.8 mm (16’ to 32’) n.p
Sweden Swedegas 406.4 - 660.4 mm (16’ to 26’) 5 - 8
Switcherland Transitgas 914.4 - 1066.8 mm (36’ to 48’) 7 - 8
* n.p.: not provided22
23
-16-
Table 3 Dimensions of examined pipes.1External diameter
D (’) External diameter
D (mm) Wall thickness t (mm) D/t R/t Internal pressure,
p (MPa)
16 406.4 9.5 42.8 21.4
0, 4, 8
20 508.0 8.7 58.4 29.2
30 762.0 14.3 53.3 26.5
36 914.4 12.7 72.0 36.0
42 1066.8 15.9 67.1 33.55
48 1219.2 19.1 63.8 31.9
2Table 4 Mechanical properties of steel grades used in this study.3Steel grade X60 X65 X70
Yield stress, σy (MPa) 414 448 483
Ultimate stress, σu (MPa) 517 531 565
Ultimate tensile strain, εu(%) 14.2 13 11.2
Young’s modulus, E (GPa) 210 210 210
44.2 Selected soil sites and backfill of trenches5The depth of the selected soil sites, H, ranged between 30 m, 60 m and 120 m (Fig. 1). Both6 cohesive and cohesionless soil deposits were examined, with the properties of the examined7 pairs of subdeposits varying, in order to cover a range of anticipated sites. As stated above, a8 surficial layer of cohesionless material was considered in all examined cases. This layer,9 resting upon the examined pairs of subdeposits, had a depth equal to 3.0 m. Additionally, all10 the examined sites were assumed to rest on an elastic bedrock with mass density, ρb =2.2 t/m3
11 shear wave velocity Vs,b = 1000 m/s.12 With reference to the mechanical and physical properties of the subdeposits beneath the13 surficial layer; Fig. 7 illustrates the gradients of the shear wave propagation velocities and the14 mass densities, ρ, of the selected soil subdeposits. The variation of the small-strain shear15 modulus of the cohesionless subdeposits follows the Seed and Idriss (1970) empirical formula:16
( )
0.5
max 2,max
220 'm
G K
s
=(9)17
where
'
m
s
is the mean effective confining stress and
2,max
Kis a constant depending on the18
relative stiffness Dr of the sub-deposit (Table 5). Using Eq. 9 for the selected soil mass19 densities and following basic elasto-dynamics, the gradients of small-strain shear wave20 velocity were defined (Fig. 9a). The gradients of small-strain shear wave velocity of the21 cohesive soil subdeposits were also considered to increase with depth (Fig. 9b). The selected22 soil deposits correspond to soil classes B and C according to Eurocode 8 (CEN 2004). The23 adopted profiles were selected in pairs, in order to define subdeposits 1 and 2 (Fig. 1). In24 particular, three pairs were examined, i.e. Soil A - Soil B, Soil A - Soil C and Soil B - Soil C.25 Accounting for the cohesionless and cohesive subdeposits, as well the diverse depths H of the26 deposits, adopted herein, a total of 18 different cases was finally examined. The nonlinear27 response of the all selected soil deposits during ground seismic shaking was described by28 means of adequate G-γ-D curves provided by Darendeli (2001), which were employed in the29 1D soil response analyses carried out in DEEPSOIL.30
-17-
Table 5 Relationships between density, relative density, K2,max parameter and cohesionless soil1characterization (after Seed and Idriss 1970).2Density, ρ (t/m
3
) Relative density, Dr(%) K2,max Characterization
1.4 30 30 Loose
1.65 52.5 48 Medium
2 90 70 Fine
3
(b)
(a)
ρA = 1.5 t/m
3
ρB = 1.7 t/m
3
ρC = 1.95 t/m
3
4Fig. 7 Shear wave velocity gradients of examined (a) cohesive and (b) cohesionless soil sub-deposits.5
6Two different sets of mechanical and physical properties were examined for the surficial soil7 layer. This layer constitutes the trench backfill material for the examined pipelines and8 therefore is referred as either trench TA or trench TB in the ensuing, for the sake of simplicity.9 The selected properties, summarized in Table 6, correspond to well or very well-compacted10 conditions. For these upper bounds of backfill compaction level, an increased pipeline axial11 straining is expected under transient ground deformations. It is worth noting that the shear12 moduli, G, presented in Table 6, correspond to ‘average’ equivalent soil stiffnesses, referring to13 the ground strain range anticipated for the selected seismic ground motions, and were estimated14 on the basis of 1D soil response analyses, discussed in Section 3.3.15
16 Table 6 Physical and mechanical properties of investigated trenches.17 Density, ρ
(t/m3)Poisson’s ratio,
vShear modulus,
G (MPa) Friction angle,
φ (o)Friction
coefficient, μ
Trench TA 1.65 0.3 37.1 35 0.45
Trench TB 1.9 0.3 63.15 44 0.78
18
-18-
With reference to the selection of the friction coefficient of the trench backfill-pipe interface, μ;1 this may vary along the axis of a long-buried pipeline, while it may also change during ground2 seismic shaking. However, it is bounded between the following limits, μmin= 0.3 and μmax= 0.8.3These limits are actually derived from the linear relation between the friction coefficient μ of4
the soil-pipe interface and friction angle φ of the trench backfill soil, i.e.
(
)
0.5 0.9 tan
m j
= - ´ ,5
which was proposed by El Hmadi and O’Rourke MJ (1988) and is commonly adopted in6 practice (ALA 2001). For typical trench backfills the soil friction angle may range between 29o
7and 41 - 44o, yielding to above limits for the friction coefficients. The herein adopted friction8 coefficients are presented in Table 6.9
10 4.3 Seismic ground motions11 An ensemble of 40 real ground motions is used in this study (Table 7), following a relevant12 selection made by Fotopoulou and Pitilakis (2015), aiming for a diverse, yet unbiased sample13 of ground motions. The motions were retrieved from the SHARE database (Giardini et al.14 2013). The corresponding earthquake moment magnitudes Mw are varying between 5 and 7.62,15 while the epicentral distances, R, are ranging between 3.4 and 71.4 km. The motions were16 recorded on rock outcrop or very stiff soil (soil classes A and B according to Eurocode 8, CEN17 2004), with shear wave velocity of first 30 m, Vs,30, ranging between 650 m/s and 1020 m/s.18 Note that outcrop motions were selected since they were to applied at the bedrock level of the19 conducted 1D analyses. The input peak ground acceleration PGA varies between 0.065 g and20 0.91 g, while the peak ground velocity PGV ranges between 0.031 m/s and 0.785 m/s.21
22 5. Results and discussion23 5.1 Verification of the 3D SPI model24 The stresses and strains of a representative pipeline predicted under a particular axial ground25 deformation pattern by implemented the 3D SPI model discussed above, are compared with26 relevant results of an equivalent ‘infinitely’ long 3D continuum model of the soil-pipe27 configuration subjected to the same kinematic loading condition, to verify the efficiency of the28 selected 3D model. The length of the long ‘infinite’ model is set equal to 1000 times the29 external diameter of the pipeline, D, to ensure that its predictions are approaching those of a30 numerical model with ‘infinite’ length. In particular, the verification is carried out for a31 ‘perfect’ 914.4 mm pipeline, embedded at a burial depth, h = 1.0 m in both adopted surficial32 soil-trenches. The pipeline is pressurized at an internal pressure p = 8 MPa. The nonlinear33 springs that are introduced at the sides of the examined pipeline, as per Fig. 3, are initially34 defined, as presented in Fig. 8. Fig. 8a illustrates the numerical model used to simulate the35 axial pull-out of the pipeline. The pull-out analyses are performed examining both adopted36 surficial soil-trenches, i.e. TA and TB (Table 6). The analyses yield the shear stress-37 displacement relations provided in Fig. 8b. These relations are used to define the maximum38 shear resistance τmax and the shear stiffness ks of the trench-pipe interface, which are39 subsequently used to define the nonlinear springs, employing Eq. (1). The computed nonlinear40
-19-
springs are presented in Fig 8c. Evidently, a higher friction coefficient for the trench-pipe1 interface leads to ‘stiffer’ springs.2 Table 7. Selected records used in this study.3
Date Earthquake Country Station Name MW R (km) Preferred FS
25/07/2003 N Miyagi Prefecture Japan Oshika 6.1 32.00 Reverse
23/10/2004 Mid Niigata Prefecture Japan Tsunan 6.6 36 Reverse
12/06/2005 Anza USA Pinyon Flat Observatory 5.2 11.50 Strike-Slip
22/12/2003 San Simeon USA Ca: San Luis Obispo; Rec Center 6.4 61.5 Reverse
16/09/1978 Tabas Iran Tabas 7.35 57 Oblique
10/06/1987 Kalamata (Aftershock) Greece Kyparrisia-Agriculture Bank 5.36 17.00 Oblique
13/05/1995 Kozani Greece Kozani 6.61 17 Normal
07/09/1999 Ano Liosia Greece Athens 4 (Kipseli District) 6.04 17.00 Normal
15/04/1979 Montenegro Serbia Hercegnovi Novi-O.S.D. 6.9 65 Thrust
25/10/1984 Kremidia (Aftershock) Greece Pelekanada-Town Hall 5 16 -
17/05/1995 Kozani (Aftershock) Greece Chromio-Community Building 5.3 16.00 Normal
13/10/1997 Kalamata Greece Koroni-Town Hall (Library) 6.4 48 Thrust
06/05/1976 Friuli Italy Tolmezzo-Diga Ambiesta 6.4 21.70 Reverse
15/09/1976 Friuli (Aftershock) Italy Tarcento 5.9 8.50 Reverse
23/11/1980 Irpinia Italy Bisaccia 6.9 28.30 Normal
14/10/1997 Umbria Marche
(Aftershock) Italy Norcia 5.6 20.00 Normal
09/09/1998 App. Lucano Italy Lauria Galdo 5.6 6.60 Normal
06/04/2009 L Aquila Mainshock Italy L Aquila - V. Aterno - Colle Grilli 6.3 4.40 Normal
09/02/1971 San Fernando USA Lake Hughes #12 6.61 20.04 Reverse
28/11/1974 Hollister-03 USA Gilroy Array #1 5.14 11.08 Strike-Slip
06/08/1979 Coyote Lake USA Gilroy Array #6 5.74 4.37 Strike-Slip
02/05/1983 Coalinga-01 USA Slack Canyon 6.36 33.52 Reverse
24/04/1984 Morgan Hill USA Gilroy Array #6 6.19 36.34 Strike-Slip
23/12/1985 Nahanni, Canada Greece Site 1 6.76 6.8 Reverse
14/11/1986 Taiwan Smart1(45) Taiwan Smart1 E02 7.3 71.35 Reverse
07/02/1987 Baja California USA Cerro Prieto 5.5 3.69 Strike-Slip
18/10/1989 Loma Prieta USA Gilroy Array #6 6.93 35.47 Reverse-Oblique
18/10/1989 Loma Prieta USA Ucsc Lick Observatory 6.93 16.34 Reverse-Oblique
25/04/1992 Cape Mendocino USA Petrolia 7.01 4.51 Reverse
28/06/1992 Landers USA Lucerne 7.28 44.02 Strike-Slip
17/01/1994 Northridge-01 USA La - Griffith Park Observatory 6.69 25.42 Reverse
17/01/1994 Northridge-01 USA Pacoima Dam (Downstr) 6.69 20.36 Reverse
16/01/1995 Kobe, Japan Japan Nishi-Akashi 6.9 8.7 Strike-Slip
20/09/1999 Chi-Chi, Taiwan Taiwan Tcu071 7.62 15.42 Reverse-Oblique
28/06/1991 Sierra Madre USA Mt Wilson - Cit Seis Sta 5.61 6.46 Reverse
16//10/1999 Hector Mine USA Hector 7.13 26.53 Strike-Slip
20/09/1999 Chi-Chi, Taiwan-03 Taiwan Tcu129 6.2 18.5 Reverse
17/08/1999 Izmit Turkey Gebze-Tubitak Marmara 7.6 42.77 Strike-Slip
17/08/1999 Izmit Turkey Izmit-Meteoroloji Istasyonu 7.6 3.40 Strike-Slip
12/11/1999 Duzce 1 Turkey Ldeo Station No. C1058 Bv 7.1 15.60 Strike-Slip
-20-
(b) (c)
Trench-soil
Pipe
Pipe-soil interface
(a)
δ
x
1Fig. 8 (a) Numerical simulation of a buried pipeline subjected to axial pull-out, (b) shear stress–2displacement relationship at the pipe-soil interface computed for the D = 914.4 mm pipeline, embedded3in trench soil TA (μ = 0.45) and TB (μ = 0.78) in burial depth h = 1.0 m, (c) force-displacement relation4of the nonlinear springs computed for the D = 914.4 mm pipeline, embedded in trench soil TA (μ =50.45) and TB (μ = 0.78), h = 1.0 m.6
7Fig. 9 compares contour diagrams of the Mises stresses and axial strains computed at the8 critical central section of the pipeline by the two numerical models for a relative axial ground9 deformation δu = 20 cm. The reduced-length 3D model SPI model with the nonlinear spring at10 the sides of the pipeline provides quite similar –if not identical– results with the extended-11 length 3D SPI model, both in terms of stresses and strains, irrespectively of the assumed trench12 properties. Naturally, a higher axial response of the pipeline is reported for surficial soil-trench13 TB, where a rougher soil-pipe interface is considered. Evidently the computational cost of the14 reduced length model is significantly lower than that of the extended model. It is worth15 noticing that similarly good comparisons between the predictions of the reduced length 3D16 model with the nonlinear springs at both ends and the ‘infinitely’ long 3D model were17 observed, even when a geometric imperfection was considered on the central critical sections18 of the pipeline.19 Fig. 10 elaborates on the effect of the selected width and depth of the trench soil model,20 surrounding the pipeline, by comparing contour diagrams of the axial straining computed on an21 examined pipeline, for different widths and depths of the trench continuum model. The results22 refer to a 762 mm ‘perfect’ pipeline embedded in surficial soil-trench TA at a burial depth h=23 1.0 m. The pipeline is pressurized to an internal pressure p = 8 MPa and is subjected to a24 relative axial ground deformation δu = 20 cm. The length of the models remains constant in all25 the examined cases, while nonlinear springs are properly defined as per Fig. 8 for each26 examined ‘trench dimensions’. For the displacement loading patterns examined herein, the27 differences on the predictions of the pipeline axial strains are very small, if not negligible.28
29
-21-
Axial strain
0.0004 -0.012
3D hybrid SPI model, L= 20D
‘Infinitely’ long model, L=1000D
Mises stress (MPa)
140 490
3D hybrid SPI model, L= 20D
‘Infinitely’ long model, L=1000D
Trench TA (
μ
= 0.45)
Axial strain
0.0004 -0.15
3D hybrid SPI model, L= 20D
‘Infinitely’ long model, L=1000D
Mises stress (MPa)
190 530
3D hybrid SPI model, L= 20D
‘Infinitely’ long model, L=1000D
Trench TB (
μ
= 0.78)
1Fig. 9 Comparisons of contour diagrams of the Mises stresses and axial strain distributions computed at2the critical central section of a 914.4 mm pipeline, embedded in backfill TA or TB, by the 3D SPI3model with the nonlinear springs at both end sides and an ‘infinitely’ long equivalent 3D SPI model.4
5
Axial strain
0.0 -0.06
3D
h
+ D + 1m
h + D + 2m
h + D + 2m
5D
6Fig. 10 Contour diagrams of axial strains distributions computed on 762 mm ‘perfect’ pipeline7embedded in trench TA, pressurized to an internal pressure p = 8 MPa and subjected to a relative axial8ground deformation δu = 20 cm, using 3D trench-soil models of diverse widths and depths.9
10
11
-22-
5.2 Pipeline response under an increasing relative axial deformation of the surrounding1ground2
3Fig. 11 illustrates some representative results from 3D SPI analyses of a 1219.2 mm pipeline,4 embedded in surficial soil-trench TB at a burial depth, h = 1.0 m, elaborating on the effect of5 salient parameters on the axial response of embedded steel pressurized pipelines under an6 increasing relative axial ground deformation. In particular, contour diagrams of the axial7 stresses, developed at the critical zone of the pipeline, are plotted for two distinct steps of the8 analysis, i.e. before major concentration of stresses and buckling failure at the zone and at the9 end of the analysis, after buckling failure occurrence (end of analysis). The diagrams are10 plotted on the deformed shapes of the pipelines, so that to highlight the form of buckling11 failures that occur for higher levels of imposed relative axial ground deformations.12 Additionally, the figure portrays the evolution of maximum compressive strain of the critical13 pipeline zone with increasing relative axial ground deformation δu. The results are provided for14 various levels of internal pressure for the pipeline (i.e. p = 0, 4 MPa and 8 MPa), considering15 both a ‘perfect’ pipeline (i.e. w/t=0) and an equivalent imperfect pipeline (i.e. w/t=0.1).16 Evidently, both the pressurization level of the pipeline and the initial geometric imperfections17 of the pipeline wall affect the axial response of the examined pipelines.18 In particular, with increasing relative axial ground deformation δu, the pipeline tends to bend19 upwards, i.e. towards the free ground surface. This response results in an early concentration of20 compressive axial stresses at the invert part of the pipeline, i.e. ditch axis of the pipeline. The21 existence of geometric imperfections is found to affect the distribution of the axial stresses on22 the pipeline. Actually, these stresses tend to distribute more uniformly across the invert of the23 perfect pipeline. On the contrary concentrations of stresses are observed at the imperfection24 ‘bulges’ of the imperfect pipeline.25 The pressurization level tends to affect the buckling patterns of the examined pipelines, which26
take place under large relative axial ground deformations, i.e.
12 20
u
cm
d
» - for the examined27
cases. Inward deformations of the pipe walls (i.e. deformations towards the pipe cavity) are28
observed for the non-pressurized (i.e. p = 0 MPa) or the low pressurized (i.e. p = 4 MPa)29
pipelines, while a combination of inward and outward deformations (i.e. deformations towards30
the trench soil) are observed on the highly pressurized pipelines (i.e. p = 8 MPa).31
The effects of the wall imperfections and internal pressure are also evident on the evolution of32 maximum compressive axial strain of the critical zone of the pipeline with the increasing33 relative axial ground deformation δu.Higher stains are reported on the pressurized pipelines34 even at low δu, compared to those predicted on the non-pressurized pipelines. This observation35 is related to the combined effects of the operational internal pressure and axial compression of36 the pipeline caused by the seismic ground movement, on axial response of a steel pipeline37 (Paquette and Kyriakides 2006; Kyriakides and Corona 2007; Tsinidis et al. 2018).38 Additionally, the pipeline with the wall imperfection tends to concentrate higher strains39 throughout the analysis compared to the equivalent ‘perfect’ pipeline, with the differences40 between the two cases being as high as 18 %.41
-23-
δu (m)
σ
xx
(
M
Pa)
610.0 305.0457.5 152.5 0.0 -152.5 -305.0 -457.5 -610.0
p = 0 MPa, w/t = 0 p = 0 MPa, w/t = 0.1
p = 4 MPa, w/t = 0.1
p = 0 MPa, w/t = 0
p = 4 MPa, w/t = 0
p = 0 MPa, w/t = 0.1
p = 4 MPa, w/t = 0.1
p = 8 MPa, w/t = 0.1
p = 4 MPa, w/t = 0
p = 8 MPa, w/t = 0 p = 8 MPa, w/t = 0.1 p = 8 MPa, w/t = 0
1Fig. 11 Effects of internal pressure and geometric imperfection of the pipe walls on the axial stresses2and the evolution of the maximum compressive strain, computed at the critical pipeline section for an3increasing relative axial ground deformation δu (results for a D = 1219.2 mm pipeline, embedded in4trench TB at a burial depth, h = 1.0 m).5
6
Fig. 12 presents comparisons of relations of maximum pipeline compressive strain, ε, with7 increasing relative axial ground deformation δu, as computed by 3D SPI analyses. The relations8 are plotted for 406.4 mm and 1219.2 mm ‘perfect’ or ‘imperfect’ pipelines embedded at9 various depths, h, in surficial backfill soils TA and TB and pressurized to various levels, i.e. p10 = 0, 4, 8 MPa. The comparisons highlight the critical effects of pipeline dimensions, backfill11 properties and compaction level and backfill-pipe interface friction characteristics on the axial12 response of the steel pipelines, induced by seismically-induced relative axial ground13 deformations. Evidently, higher axial compression strains, ε, are reported for the pipelines14 embedded in backfill TB. The higher shear stresses that are developed along the ‘rougher’15 backfill-pipe interface (the friction coefficient μ is equal to 0.78 in this case), result in an16 increased axial straining of the pipelines embedded in these surficial soil conditions, compared17 to the equivalent pipelines embedded in trench TA. Additionally, the higher confinement that is18 being offered by the surrounding ground on the pipeline, as a result of its higher compaction19
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level and stiffness, partially reduces the upward bending of the pipeline during the kinematic1 loading of the system (i.e. bending towards the ground surface, see Fig. 9), which in turn leads2 to an increased localization of axial straining at the critical zone of the pipeline, near the3 geotechnical discontinuity. Additionally, the concentration of axial compression strains, which4 subsequently leads to buckling of the pipelines, occurs in higher levels of relative axial ground5 deformation, δu, in the case of 1219.2 mm pipelines with thicker walls. It is worth noticing the6 wide range of pipeline strain ε that might be computed for a given level of relative axial ground7 deformation, δu, under various assumptions regarding the initial geometric imperfections of the8 pipeline walls, the backfill properties, the backfill-pipe interface characteristics and the internal9 pressure of the pipeline. Indeed for a given relative axial ground deformation δue,n in Fig. 1210 (associated with a ground motion and computed by the 1D soil response analyses as per11 Section 3.3), a wide range of compressive strains ε may be computed on the pipeline, when12 considering all the above parameters. Hence, the consideration of these parameters is of great13 importance in the structural vulnerability assessment of this infrastructure.14
15
δu (m) δu (m)
TA TA
TB TB
δue,n δue,n
16 Fig. 12 Evolution of the maximum compressive strain, ε, computed at the critical middle section of17 ‘perfect’ or ‘imperfect’ pipelines, embedded at various depths, h, in surficial backfill soils TA and TB18 and pressurized to various levels, i.e. p = 0, 4, 8 MPa, for an increasing relative axial ground19 deformation δu.20
21 5.3 Fragility functions22 Prior to the development of the fragility functions, the limit states defined in Section 3.5, are23 quantified for the selected pipelines, as per Table 1. Table 8, summarizes the limit axial24 compression strains for the four limit states for all examined pipelines. As seen, the maximum25 strain for OLS may range between 0.56 % and 0.94% for the examined pipelines. The range of26 strains for PILS varies between 2.4 % and 4 %, while for ULS the limit strain ranges between27 6.1 % and 10 %.28
29
30
31
32
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Table 8 Quantification of the maximum compression axial strains defined for each limit state and1examined pipeline.2
Diameter, D (mm) 406.4 508 762 914.4 1066.8 1219.2
Wall thickness, t (mm) 9.5 8.7 14.3 12.7 15.9 19.1
R/t 21.4 29.2 26.6 36.0 33.5 31.9
Maximum strain for limit state OLS, εOLS 0.0094 0.0069 0.0075 0.0056 0.0060 0.0063
Maximum strain for limit state PILS, εPILS 0.0400 0.0301 0.0330 0.0244 0.0262 0.0276
Maximum strain for limit state ULS, εULS 0.1000 0.0754 0.0826 0.0611 0.0656 0.0689
Maximum strain for limit state GCLS, εGCLS 0.1500 0.1500 0.1500 0.1500 0.1500 0.1500
3Having quantified the maximum strain for each limit state and examined pipeline, regression4 analyses of the natural logarithm of the computed maximum axial strain ε of the examined5 pipeline relative to the natural logarithm of the peak ground velocity PGV at ground surface are6 carried out, as per Fig. 13. The regressions are actually conducted for each soil-pipe7 configuration, by combining the numerical predictions of the above analytical framework,8 referring to various levels of internal pressure for pipelines (i.e. p = 0, 4 and 8 MPa) and9 various assumptions regarding the initial geometric imperfection of the pipeline walls (i.e.10 combining the results referring to w/t = 0 or w/t = 0.1). The selection is made on the ground11 that existence of geometric imperfections on pipeline walls is not a-priori known. Additionally,12 the use of results, referring to a range of internal pressures, allows for a general application of13 the provided fragility curves in networks with similar ranges of operational pressure. The14 results of the regression analyses are used to define the parameters that are required to15 construct the fragility functions, i.e. PGVmi and βtot.16
17
18 Fig. 13 Example of evolution of ln(ε), with earthquake intensity measure ln(PGV) and regression19 analysis used to define PGVmi and βtot (numerical results for of a 762 mm pipeline embedded in Trench20 TA at a burial depth, h = 1.0 m in soil deposit with depth H = 30 m)21
22 Based on the above procedure, an extended set of more than 1200 fragility functions was23 constructed, referring to diverse examined soil-pipe configurations. The relevant PGVmi and βtot
24 for all the examined curves are summarized in a set of tables, summarized in Appendix A. In25 the following, some representative fragility curves are comparatively presented, aiming at26
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discussing the effects of salient parameters on the computed fragility of the examined NG1 pipelines.2 Fig. 14 compares analytical fragility relations, referring to X65 914.4 mm pipelines embedded3 in surficial soil-trench TA, highlighting the effects of the depth, H, of the soil deposit, the4 subdeposits characteristics and pipeline burial depth h, on the seismic fragility of NG pipelines.5 Generally, the seismic fragility of the examined pipelines is found to be low. Actually, the ULS6 and GCLS limit states are not reached for the examined pipelines embedded in soil deposits7 with depths, H, equal to 30 m and 60 m, while the seismic fragility of examined pipelines is8 found to increase with increasing burial depth, H, of the soil deposit. This observation is9 attributed to the higher differential ground response of the adjacent subdeposits, expected for10 deposits with higher depths, i.e. for H = 120, compared to the one of deposits with depths, H,11 equal 30 m or 60 m, when subjected to the same excitation at the bedrock. The higher12 differential ground response of the adjacent subdeposits induces a higher axial straining on the13 pipeline, thus increasing the potential of damage under a given seismic intensity.14 The seismic fragility of the examined pipelines embedded in cohesionless soils is found to be15 slightly lower compared to the one predicted for the cases where the pipelines are embedded in16 cohesive soils (see subplots on the left-hand side of Fig. 14). The differences are again17 attributed to the distinct ground response characteristics of the examined soil subdeposits,18 which induce distinct axial straining on the embedded pipelines.19 The higher contrast on the soil properties of the adjacent soil subdeposits, leads naturally to a20 more dissimilar response of the subdeposits, which induces a higher straining on the pipeline,21 thus resulting in a higher potential for damage, under a given intensity. This hypothesis is22 verified by comparing the fragility curves developed for the pairs of subdeposits A-B and A-C.23 Indeed, a higher fragility is reported in case of pipelines embedded in soil with subdeposits A-24 C, where the differences on the soil properties of the subdeposits (i.e. shear wave velocity and25 mass density) are higher compared to the case of the soil that consists of subdeposits A-B.26 Comparing the fragility of pipelines embedded in soils with subdeposits A-B and B-C, a much27 higher fragility is reported in the former soil site, even though the level of contrast of the28 properties of the adjacent subdeposits is the same for both cases. This is actually expected,29 given the lower ground seismic response of ‘stiffer’ soil deposits, i.e. the soil with subdeposits30 B-C in this case, compared to soft soil deposits (i.e. soil with subdeposits A-B), under a given31 seismic intensity.32 A higher fragility is systematically reported for pipelines embedded at a burial depth, h = 1.033 m, compared to the cases, where the equivalent pipelines are embedded deeper, i.e. h = 2.0 m.34 This should be attributed to the higher horizontal ground movement of the soil deposits35 towards the ground surface, during ground shaking, which causes higher relative ground36 deformations on the shallow-buried pipelines, hence increasing their axial response and37 damage potential.38
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1Fig. 14 Fragility functions of X65 914.4 mm pipelines embedded in surficial soil-trench TA. Effects of2soil deposit depth, H, subdeposits characteristics and burial depth, h, of the pipelines on the seismic3fragility.4
5It is worth noticing that the general low fragility of the buried pipelines in surficial soil-trench6 TA comes in line with the reported good performance of buried NG pipelines and their reduced7 fragility reported during past earthquakes. It is recalled that the first two limit states, adopted in8 this study, constitute operational limit states that do not lead to wall tearing and leakages and9 basically do not affect the flow of containment - at least not significantly. This makes the10 observation of relevant actual damages rather difficult after an earthquake event.11 Fig. 15 compares similar fragility relations, referring to the same pipelines, i.e. X65 914.4 mm12 pipelines, embedded in surficial soil-trench TB. Evidently, a much higher fragility is reported13 in this case, compared to the previous results. All limit states are reached, even for the cases14 where the pipelines are embedded in the shallow soil deposits, i.e. for H = 30 m and 60 m. This15 observation is in line with the higher axial compressive straining of the pipeline that is16
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anticipated in cases of a dense backfill trench with a ‘rougher’ backfill-pipe interface (i.e.1 surficial soil-trench TB). In line with the previous results, the fragility of the examined2 pipelines is increased with increasing depth of the soil deposits, H, decreasing burial depth of3 the pipelines, h, and increasing contrast of the properties of the adjacent soil subdeposits. A4 slightly higher fragility is reported for the pipelines embedded in the soil deposits with5 cohesive subdeposits. It is worth noting that higher total lognormal standard deviations βtot
6were estimated for the fragility relations referring to pipelines embedded in surficial soil-trench7 TB, associated with the generally amplified axial response of pipelines for these conditions.8
9
10 Fig. 15 Fragility functions of 914.4 mm X65 pipelines embedded in surficial soil-trench TB. Effects of11 soil deposit depth, H, subdeposits characteristics and burial depth, h, of the pipelines on the seismic12 fragility.13
14
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The effect of the steel grade of the pipeline on its fragility is highlighted in Fig. 16, where1 fragility curves referring to 762 mm pipelines made of different steel grades, i.e. X60 and X70,2 are compared. The comparisons refer to pipelines embedded in surficial soil-trench TB in3 cohesive or cohesionless soil deposits A-B of depth H = 60 m. As expected, the fragility of4 X60 pipelines is found higher, compared to the equivalents made of X70 steel grade.5
6
7Fig. 16. Effect of steel grade of pipelines on their seismic fragility. Fragility functions for 762 mm8pipelines embedded in surficial soil-trench TB in cohesive or cohesionless soil deposits A-B of depth H9= 60 m.10
11 Fig. 17 compares fragility relations, referring to pipelines with diverse dimensions, embedded12 in similar trench soil conditions and burial depth, h, (i.e. soil deposit A-B of depth H = 60 m13 and pipeline burial depth h = 1.0 m), in an effort to highlight the effect of the radius over14 thickness ratio (R/t) of the pipelines on their seismic fragility. The comparisons do not provide15 a clear trend between the radius over thickness ratio (R/t) of the pipeline and its seismic16 fragility. Indeed, the highest fragility is reported for the 914.4 mm pipelines with R/t =36,17 followed by the 406.4 mm pipelines with R/t=21.4. The lowest fragility is reported for the18 1219.2 mm pipelines with R/t=31.9.19
20 6. Conclusions21
A detailed analytical framework was developed to evaluate the fragility of NG pipelines22 crossing sites with a vertical geotechnical discontinuity, when subjected to axial compression23 caused by transient seismic ground deformation. The methodological framework consists of a24 3D SPI model, aiming at evaluating the pipe-trench interaction effects on the pipeline axial25 response in quasi-static manner and 1D soil response analyses, used to determine critical26 ground deformation patterns at the geotechnical discontinuity under ground shaking. The27 efficiency of the 3D SPI model in replicating the actual soil-pipe interaction phenomena,28 associated with the extended length of this infrastructure was thoroughly verified. A29 comprehensive parametric analysis was performed, using the proposed analytical framework,30 for an extended number of soil-pipe configurations and an ensemble of 40 recorded earthquake31
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ground motions, which led to the definition of an extended set of fragility curves. The latter1 were developed in terms of PGV at the ground surface, for four performance limit states,2 considering the associated uncertainties. The main conclusions of the study are summarized in3 the following:4
5
6Fig. 17. Effect of radius over thickness (R/t) ratio of diverse pipelines, embedded in trench TB in7cohesive or cohesionless soil deposits A-B of depth H = 60 m, on their seismic fragility.8
9
·The seismic fragility of buried steel NG pipelines against seismically-induced axial10 compression near geotechnical discontinuities was found to be rather low, when the11 examined pipelines were embedded in a medium-compacted surficial layer with a medium12 friction coefficient μbeing considered for the trench soil-pipe interface (i.e. surficial soil-13 trench TA in this study). Actually, for these cases, the ULS and GCLS limit states, which14 are associated with major failures or collapse where not reached in the majority of the15 examined soil-pipe configurations. This observation is in line with the reduced16 vulnerability of this infrastructure against transient ground deformations, reported during17 past earthquakes.18
·On the contrary, a higher fragility was reported for the pipelines embedded in a ‘stiffer’19 very well-compacted surficial soil-trench, with a high friction coefficient μ being20 considered for the trench soil-pipe interface (i.e. surficial soil-trench TB). This is mainly21 attributed to the higher axial straining of the pipeline, which is caused by the higher22 stresses developed along the trench-pipe interface during the surrounding ground23 deformation. Additionally, the higher compaction level and stiffness of the surrounding24 ground lead to a higher confinement of the pipeline, which reduces the bending of the25 pipeline towards the ground surface, during the kinematic loading of the system, thus26 increasing the local straining of the pipeline, finally contributing to an increased damage27 potential. In the light of the above observations, it is very important to avoid over-28 compacting of the trench soil of buried NG pipelines, or even try to reduce the soil-pipe29 interface friction, particularly in seismically-prone regions of varying soil conditions, in30
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order to reduce the fragility of this infrastructure under seismically-induced transient1 ground deformations.2
·Regardless of the trench backfill properties and backfill-pipe interface characteristics the3 seismic fragility of the examined NG pipelines was increased with increasing depth, H, of4 the soil deposit. This was attributed to the higher differential ground response of deeper5 adjacent subdeposits, e.g. for H = 120 m, under a given excitation at bedrock. The higher6 differential ground response of the adjacent subdeposits induced a higher axial straining on7 the pipeline, thus increasing the potential of damage.8
·The seismic fragility of pipelines was found to be slightly lower for the cohesionless9 subdeposits, studied herein, compared to the one predicted for equivalent pipelines in10 cohesive subdeposits.11
·The higher contrast on the soil properties of the adjacent soil subdeposits, led to a more12 dissimilar seismic response of the subdeposits under a given excitation at bedrock, which13 subsequently led to a higher axial straining for the embedded pipeline and hence to a higher14 damage potential.15
·A higher fragility was systematically reported for pipelines embedded at a burial depth, h =16 1.0 m, compared to the cases, where the equivalent pipeline was embedded at a higher17 depth, i.e. h = 2.0 m. Naturally, pipelines made of X60 steel grade were found to be more18 vulnerable to the particular seismic hazard, compared to those made of higher steel grades,19 e.g. X65 and X70, while it was not possible to define a clear trend between the radius over20 thickness (R/t) of the pipeline and its seismic fragility.21 Inevitably, there are some limitations of the analytical framework used herein. The effects of22 inertial SPI and of the evolution of stresses and deformations due to temperature changes on23 the pipeline response, as well as time-dependent phenomena, such as fatigue and steel strength24 and stiffness degradation due to cyclic loading, are not considered in the present analysis25 framework. Moreover, complex 2D wave phenomena near the geotechnical discontinuity are26 not being thoroughly investigated. However, the study covers a wide range of salient27 parameters that may affect the response and vulnerability of buried steel NG pipelines, crossing28 similar sites. In this context, the use of the provided analytical fragility curves may contribute29 towards a more reliable quantitative risk assessment of buried steel NG pipelines, subjected to30 seismically-induced transient ground deformations, particularly if combined with the practical31 recommendations reported above.32
33 Acknowledgements34
This work was supported by the Horizon 2020 Programme of the European Commission under35
the MSCA-RISE-2015-691213-EXCHANGE-Risk grant (Experimental and Computational36
Hybrid Assessment of NG Pipelines Exposed to Seismic Hazard, www.exchange-risk.eu). This37
support is gratefully acknowledged.38
39
40
41
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9
10 Appendix A11
A series of tables, summarizing the parameters required for the definition of the fragility curves12 developed in the framework of this study, i.e. the median peak ground velocities corresponding to the13 limit states, PGVm,iand total lognormal standard deviation βtot, are summarized in this appendix.14
15
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Table A1 Median peak ground velocities corresponding to the limit states, PGVm,i, and total lognormal1standard deviation, βtot, for 406.4 mm pipelines embedded in soil deposit of depth H = 30 m ( - : the2limit state is not reached).3
4
Cohesive soil deposit – Trench type TA Cohesionless soil deposit – Trench type TA
Soil Steel
Grade
Burial
depth,
h (m)
PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot
A-B X60 1 0.458 2.840 - - 0.773 1.133 3.199 - - 0.769
A-B X65 1 1.167 3.407 - - 0.749 1.303 3.955 - - 0.740
A-B X70 1 1.278 3.915 - - 0.725 1.424 4.527 - - 0.717
A-B X60 2 1.952 - - - 0.642 2.274 - - - 0.631
A-B X65 2 2.045 - - - 0.659 2.339 - - - 0.650
A-B X70 2 2.341 - - - 0.625 2.681 - - - 0.615
A-C X60 1 1.070 3.101 - - 0.758 1.016 3.154 - - 0.761
A-C X65 1 1.240 3.886 - - 0.734 1.284 4.049 - - 0.725
A-C X70 1 1.371 4.529 - - 0.711 1.374 4.220 - - 0.676
A-C X60 2 2.175 - - - 0.629 2.296 - - - 0.623
A-C X65 2 2.288 - - - 0.649 2.388 - - - 0.644
A-C X70 2 2.647 - - - 0.612 2.750 - - - 0.607
B-C X60 1 4.315 - - - 0.621 4.655 - - - 0.606
B-C X65 1 4.296 - - - 0.612 - - - - -
B-C X70 1 4.691 - - - 0.601 - - - - -
B-C X60 2 - - - - - - - - - -
B-C X65 2 - - - - - - - - - -
B-C X70 2 - - - - - - - - - -
Cohesive soil deposit – Trench type TB Cohesionless soil deposit – Trench type TB
Soil Steel
Grade h (m) PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot
A-B X60 1 0.458 0.913 1.411 1.711 0.961 0.488 0.990 1.546 1.882 0.995
A-B X65 1 0.516 1.031 1.596 1.936 0.973 0.518 1.079 1.714 2.103 1.019
A-B X70 1 0.505 1.048 1.661 2.036 1.020 0.558 1.205 1.959 2.428 1.027
A-B X60 2 0.486 0.990 1.551 1.892 1.114 0.551 1.197 1.953 2.426 1.085
A-B X65 2 0.544 1.176 1.913 2.372 1.112 0.625 1.452 2.470 3.125 1.067
A-B X70 2 0.621 1.445 2.461 3.114 1.066 0.715 1.791 3.194 4.125 1.009
A-C X60 1 0.432 0.862 1.333 1.616 0.969 0.447 0.900 1.399 1.701 0.968
A-C X65 1 0.449 0.911 1.422 1.731 1.011 0.473 0.978 1.544 1.891 0.999
A-C X70 1 0.492 1.047 1.686 2.081 1.011 0.520 1.129 1.840 2.284 0.994
A-C X60 2 0.482 1.019 1.632 2.011 1.088 0.512 1.118 1.830 2.275 1.055
A-C X65 2 0.549 1.243 2.082 2.615 1.078 0.586 1.377 2.358 2.992 1.038
A-C X70 2 0.568 1.252 2.062 2.571 1.077 0.603 1.370 2.299 2.891 1.045
B-C X60 1 1.290 3.727 - - 0.812 1.414 4.231 - - 0.765
B-C X65 1 1.305 3.780 - - 0.811 1.709 - - - 0.767
B-C X70 1 1.455 4.447 - - 0.786 1.591 4.657 - - 0.713
B-C X60 2 1.440 4.427 - - 0.834 2.047 - - - 0.749
B-C X65 2 1.652 - - - 0.812 2.407 - - - 0.718
B-C X70 2 1.908 - - - 0.770 2.845 - - - 0.671
5
6
-37-
Table A2 Median peak ground velocity corresponding to the limit states, PGVm,i and total lognormal1standard deviation βtot for 406.4 mm pipelines embedded in soil deposit of depth H = 60 m ( - : the limit2state is not reached).3
4
Cohesive soil deposit – Trench type TA Cohesionless soil deposit – Trench type TA
Soil Steel
Grade
Burial
depth,
h (m)
PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot
A-B X60 1 0.809 2.176 4.059 - 0.741 0.902 2.482 4.700 - 0.755
A-B X65 1 0.924 2.660 - - 0.719 1.013 2.949 - - 0.724
A-B X70 1 1.044 3.212 - - 0.697 1.069 3.187 - - 0.731
A-B X60 2 1.525 - - - 0.634 1.811 - - - 0.630
A-B X65 2 1.781 - - - 0.621 1.811 - - - 0.662
A-B X70 2 2.081 - - - 0.593 2.144 - - - 0.618
A-C X60 1 0.700 1.749 3.117 4.024 0.742 0.742 1.878 3.374 4.372 0.758
A-C X65 1 0.791 2.106 3.904 - 0.723 0.845 2.287 4.286 - 0.738
A-C X70 1 0.877 2.468 4.739 - 0.705 0.952 2.752 - - 0.717
A-C X60 2 1.245 4.194 - - 0.646 1.376 4.867 - - 0.652
A-C X65 2 1.495 - - - 0.623 1.595 - - - 0.641
A-C X70 2 1.744 - - - 0.598 1.859 - - - 0.610
B-C X60 1 1.533 4.740 - - 0.741 1.775 - - - 0.703
B-C X65 1 1.724 - - - 0.700 2.172 - - - 0.674
B-C X70 1 1.810 - - - 0.687 2.399 - - - 0.646
B-C X60 2 2.895 - - - 0.611 3.422 - - - 0.614
B-C X65 2 3.711 - - - 0.592 4.016 - - - 0.590
B-C X70 2 3.711 - - - 0.577 4.588 - - - 0.575
Cohesive soil deposit – Trench type TB Cohesionless soil deposit – Trench type TB
Soil Steel
Grade h (m) PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot
A-B X60 1 0.345 0.647 0.961 1.145 0.903 0.380 0.727 1.094 1.310 0.870
A-B X65 1 0.354 0.665 0.989 1.180 0.935 0.396 0.766 1.162 1.397 0.892
A-B X70 1 0.376 0.725 1.098 1.319 0.952 0.423 0.847 1.310 1.590 0.911
A-B X60 2 0.366 0.697 1.048 1.255 1.051 0.410 0.816 1.260 1.526 1.008
A-B X65 2 0.400 0.795 1.227 1.487 1.061 0.456 0.958 1.530 1.883 0.998
A-B X70 2 0.439 0.918 1.462 1.796 1.059 0.522 1.183 1.983 2.492 0.964
A-C X60 1 0.432 0.862 1.333 1.616 0.938 0.336 0.607 0.883 1.042 0.927
A-C X65 1 0.324 0.578 0.833 0.979 0.961 0.341 0.616 0.893 1.053 0.960
A-C X70 1 0.340 0.620 0.906 1.072 0.972 0.359 0.665 0.981 1.165 0.964
A-C X60 2 0.330 0.591 0.854 1.005 1.070 0.351 0.652 0.962 1.143 1.045
A-C X65 2 0.353 0.654 0.965 1.146 1.090 0.387 0.754 1.148 1.383 1.032
A-C X70 2 0.389 0.760 1.158 1.395 1.080 0.427 0.880 1.387 1.696 1.018
B-C X60 1 0.689 1.599 2.721 3.442 0.936 0.801 1.961 3.449 4.428 0.900
B-C X65 1 0.733 1.744 3.014 3.839 0.956 0.828 2.055 3.644 4.696 0.929
B-C X70 1 0.796 1.978 3.511 4.526 0.930 0.874 2.220 3.998 - 0.917
B-C X60 2 0.796 1.989 3.544 4.575 0.985 0.809 1.984 3.492 4.485 1.003
B-C X65 2 0.843 2.157 3.901 - 0.986 0.891 2.294 4.164 - 0.978
B-C X70 2 0.966 2.663 - - 0.920 1.000 2.736 - - 0.924
5
-38-
Table A3 Median peak ground velocity corresponding to the limit states, PGVm,i, and total lognormal1standard deviation, βtot, for 406.4 mm pipelines embedded in soil deposit of depth H = 120 m ( - : the2limit state is not reached).3
4
Cohesive soil deposit – Trench type TA Cohesionless soil deposit – Trench type TA
Soil Steel
Grade
Burial
depth,
h (m)
PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot
A-B X60 1 0.548 1.390 2.498 3.239 0.718 0.613 1.526 2.710 3.495 0.712
A-B X65 1 0.591 1.549 2.842 3.718 0.721 0.680 1.784 3.275 4.286 0.691
A-B X70 1 0.657 1.817 3.451 4.584 0.702 0.757 2.104 4.006 - 0.669
A-B X60 2 0.958 3.226 - - 0.642 1.145 4.013 - - 0.615
A-B X65 2 1.169 4.389 - - 0.605 1.396 - - - 0.591
A-B X70 2 1.274 4.994 - - 0.622 1.493 - - - 0.608
A-C X60 1 0.454 1.062 1.813 2.298 0.747 0.497 1.147 1.941 2.450 0.726
A-C X65 1 0.498 1.219 2.141 2.748 0.737 0.547 1.322 2.307 2.951 0.714
A-C X70 1 0.549 1.415 2.570 3.346 0.715 0.603 1.538 2.773 3.600 0.688
A-C X60 2 0.764 2.338 4.731 - 0.655 0.852 2.635 - - 0.625
A-C X65 2 0.907 3.042 - - 0.623 1.596 - - - 0.608
A-C X70 2 1.049 3.816 - - 0.598 1.170 4.302 - - 0.583
B-C X60 1 1.208 3.868 - - 0.704 1.463 4.406 - - 0.673
B-C X65 1 1.395 4.796 - - 0.677 1.640 - - - 0.663
B-C X70 1 1.417 4.890 - - 0.696 1.812 - - - 0.653
B-C X60 2 2.519 - - - 0.590 2.751 - - - 0.611
B-C X65 2 2.630 - - - 0.608 3.092 - - - 0.600
B-C X70 2 2.863 - - - 0.593 2.940 - - - 0.616
Cohesive soil deposit – Trench type TB Cohesionless soil deposit – Trench type TB
Soil Steel
Grade h (m) PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot
A-B X60 1 0.267 0.480 0.694 0.818 0.997 0.303 0.542 0.782 0.920 0.992
A-B X65 1 0.274 0.494 0.716 0.843 1.034 0.312 0.559 0.807 0.950 1.037
A-B X70 1 0.288 0.530 0.778 0.923 1.039 0.331 0.610 0.897 1.063 1.037
A-B X60 2 0.279 0.502 0.726 0.855 1.145 0.317 0.574 0.836 0.987 1.131
A-B X65 2 0.296 0.546 0.803 0.952 1.158 0.343 0.647 0.964 1.150 1.130
A-B X70 2 0.325 0.629 0.953 1.146 1.124 0.375 0.740 1.135 1.372 1.097
A-C X60 1 0.246 0.432 0.615 0.719 1.012 0.269 0.464 0.655 0.763 0.998
A-C X65 1 0.250 0.436 0.618 0.721 1.031 0.273 0.470 0.661 0.769 1.036
A-C X70 1 0.262 0.465 0.666 0.782 1.046 0.286 0.501 0.713 0.834 1.051
A-C X60 2 0.255 0.442 0.626 0.729 1.166 0.273 0.470 0.661 0.769 1.179
A-C X65 2 0.268 0.472 0.675 0.790 1.206 0.289 0.508 0.726 0.850 1.206
A-C X70 2 0.288 0.526 0.768 0.908 1.194 0.313 0.571 0.836 0.989 1.193
B-C X60 1 0.498 1.111 1.844 2.308 0.905 0.614 1.453 2.501 3.180 0.841
B-C X65 1 0.543 1.255 2.128 2.688 0.933 0.656 1.613 2.844 3.656 0.867
B-C X70 1 0.601 1.464 2.566 3.289 0.919 0.743 1.954 3.595 4.708 0.841
B-C X60 2 0.590 1.429 2.494 3.192 0.991 0.728 1.910 3.507 4.589 0.889
B-C X65 2 0.678 1.766 3.228 4.216 0.960 0.866 2.491 4.849 - 0.840
B-C X70 2 0.812 2.340 4.560 - 0.887 1.036 3.295 - - 0.802
5
-39-
Table A4 Median peak ground velocity corresponding to the limit states, PGVm,i, and total lognormal1standard deviation, βtot, for 508.0 mm pipelines embedded in soil deposit of depth H = 30 m ( - : the2limit state is not reached).3
4
Cohesive soil deposit – Trench type TA Cohesionless soil deposit – Trench type TA
Soil Steel
Grade
Burial
depth,
h (m)
PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot
A-B X60 1 1.139 3.356 - - 0.791 0.802 2.336 4.524 - 0.758
A-B X65 1 0.841 2.648 - - 0.774 0.901 2.803 - - 0.738
A-B X70 1 0.962 3.306 - - 0.734 1.031 3.503 - - 0.700
A-B X60 2 1.535 0.000 - - 0.628 1.816 - - - 0.618
A-B X65 2 1.895 0.000 - - 0.599 2.243 - - - 0.593
A-B X70 2 2.201 0.000 - - 0.581 2.564 - - - 0.578
A-C X60 1 0.752 2.333 4.697 - 0.773 0.798 2.530 - - 0.761
A-C X65 1 0.861 2.894 - - 0.754 0.933 3.244 - - 0.738
A-C X70 1 1.001 3.713 - - 0.714 1.065 4.045 - - 0.700
A-C X60 2 1.630 - - - 0.619 1.758 - - - 0.613
A-C X65 2 2.044 - - - 0.592 2.192 - - - 0.589
A-C X70 2 2.393 - - - 0.576 2.475 - - - 0.572
B-C X60 1 2.214 - - - 0.711 2.328 - - - 0.687
B-C X65 1 2.155 - - - 0.700 3.133 - - - 0.671
B-C X70 1 2.410 - - - 0.681 3.537 - - - 0.646
B-C X60 2 2.683 - - - 0.625 3.985 - - - 0.609
B-C X65 2 3.670 - - - 0.607 4.552 - - - 0.597
B-C X70 2 3.847 - - - 0.597 4.918 - - - 0.596
Cohesive soil deposit – Trench type TB Cohesionless soil deposit – Trench type TB
Soil Steel
Grade h (m) PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot
A-B X60 1 0.328 0.639 0.967 1.319 1.051 0.356 0.693 1.046 1.426 1.019
A-B X65 1 0.342 0.679 1.038 1.428 1.066 0.373 0.743 1.138 1.567 1.033
A-B X70 1 0.363 0.750 1.174 1.643 1.053 0.398 0.825 1.295 1.818 1.021
A-B X60 2 0.486 1.224 2.166 3.326 0.863 0.486 1.224 2.166 3.326 0.863
A-B X65 2 0.562 1.551 2.906 4.658 0.857 0.742 2.413 - 0.000 0.781
A-B X70 2 0.954 3.830 - - 0.635 0.890 3.277 - 0.000 0.726
A-C X60 1 0.314 0.627 0.960 1.322 1.027 0.329 0.667 1.034 1.437 1.017
A-C X65 1 0.329 0.667 1.033 1.435 1.045 0.345 0.717 1.126 1.581 1.039
A-C X70 1 0.350 0.740 1.176 1.665 1.035 0.369 0.800 1.290 1.848 1.026
A-C X60 2 0.571 1.694 3.320 - 0.732 0.645 2.079 4.287 - 0.697
A-C X65 2 0.724 2.523 - - 0.684 0.832 3.178 - - 0.654
A-C X70 2 0.920 3.806 - - 0.640 1.056 4.766 - - 0.614
B-C X60 1 0.847 2.480 4.817 - 0.917 0.898 2.714 - - 0.854
B-C X65 1 0.717 1.907 3.493 - 0.909 0.987 3.134 - - 0.847
B-C X70 1 0.919 2.820 - - 0.899 1.075 3.596 - - 0.826
B-C X60 2 1.188 4.101 - - 0.879 1.902 - - - 0.696
B-C X65 2 1.375 - - - 0.851 2.431 - - - 0.660
B-C X70 2 1.392 - - - 0.815 2.715 - - - 0.628
5
6
-40-
Table A5 Median peak ground velocity corresponding to the limit states, PGVm,i, and total lognormal1standard deviation, βtot, for 508.0 mm pipelines embedded in soil deposit of depth H = 60 m ( - : the2limit state is not reached).3
4
Cohesive soil deposit – Trench type TA Cohesionless soil deposit – Trench type TA
Soil Steel
Grade
Burial
depth,
h (m)
PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot
A-B X60 1 0.491 1.226 2.158 3.301 0.860 0.548 1.407 2.521 3.907 0.844
A-B X65 1 0.531 1.381 2.495 3.889 0.879 0.605 1.643 3.047 4.846 0.833
A-B X70 1 0.962 3.306 - - 0.734 0.658 1.883 3.606 0.000 0.846
A-B X60 2 0.956 3.504 - - 0.693 1.137 4.529 - - 0.648
A-B X65 2 1.133 4.594 - - 0.668 1.283 - - - 0.672
A-B X70 2 1.303 0.000 - - 0.632 1.629 - - - 0.631
A-C X60 1 0.445 1.044 1.770 2.631 0.864 0.470 1.120 1.915 2.867 0.873
A-C X65 1 0.472 1.140 1.965 2.959 0.888 0.508 1.247 2.174 3.301 0.861
A-C X70 1 0.515 1.311 2.338 3.610 0.877 0.554 1.450 2.630 4.113 0.875
A-C X60 2 0.832 2.803 - - 0.679 0.964 3.565 - - 0.655
A-C X65 2 1.001 3.781 - - 0.651 1.063 4.150 - - 0.681
A-C X70 2 1.157 4.807 - - 0.628 1.217 - - - 0.643
B-C X60 1 1.013 3.215 - - 0.802 1.061 3.358 - - 0.790
B-C X65 1 1.072 3.513 - - 0.771 1.223 4.167 - - 0.800
B-C X70 1 1.096 3.622 - - 0.772 1.312 4.655 - - 0.764
B-C X60 2 1.880 - - - 0.636 2.224 - - - 0.658
B-C X65 2 2.211 - - - 0.619 2.690 - - - 0.624
B-C X70 2 2.193 - - - 0.652 3.099 - - - 0.605
Cohesive soil deposit – Trench type TB Cohesionless soil deposit – Trench type TB
Soil Steel
Grade h (m) PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot
A-B X60 1 0.260 0.493 0.733 0.987 0.976 0.275 0.513 0.753 1.005 0.987
A-B X65 1 0.268 0.506 0.751 1.011 0.994 0.285 0.536 0.791 1.060 1.002
A-B X70 1 0.281 0.548 0.827 1.126 0.981 0.302 0.587 0.885 1.205 0.984
A-B X60 2 0.310 0.623 0.960 1.327 0.983 0.328 0.657 1.008 1.392 1.005
A-B X65 2 0.339 0.714 1.133 1.602 0.985 0.368 0.789 1.264 1.801 1.011
A-B X70 2 0.381 0.869 1.448 2.124 0.951 0.406 0.929 1.550 2.278 0.961
A-C X60 1 0.244 0.441 0.636 0.838 0.988 0.258 0.475 0.693 0.921 0.985
A-C X65 1 0.253 0.460 0.667 0.881 0.994 0.267 0.493 0.722 0.961 0.997
A-C X70 1 0.264 0.490 0.719 0.959 0.980 0.278 0.527 0.782 1.052 0.977
A-C X60 2 0.294 0.568 0.853 1.159 0.994 0.305 0.603 0.919 1.261 0.969
A-C X65 2 0.320 0.649 1.006 1.398 0.968 0.340 0.719 1.142 1.617 0.930
A-C X70 2 0.352 0.762 1.229 1.760 0.930 0.367 0.812 1.328 1.921 0.914
B-C X60 1 0.456 1.027 1.699 2.478 1.012 0.508 1.185 2.001 2.966 1.008
B-C X65 1 0.483 1.115 1.872 2.761 1.033 0.550 1.344 2.337 3.540 1.010
B-C X70 1 0.522 1.269 2.198 3.322 1.006 0.599 1.551 2.794 4.346 0.973
B-C X60 2 0.661 1.819 3.401 - 0.967 0.689 1.878 3.490 - 0.979
B-C X65 2 0.682 1.880 3.521 - 0.984 0.789 2.307 4.481 - 0.947
B-C X70 2 0.832 2.625 - - 0.886 0.863 2.696 - - 0.906
5
-41-
Table A6 Median peak ground velocity corresponding to the limit states, PGVm,i, and total lognormal1standard deviation, βtot, for 508.0 mm pipelines embedded in soil deposit of depth H = 120 m ( - : the2limit state is not reached).3
4
Cohesive soil deposit – Trench type TA Cohesionless soil deposit – Trench type TA
Soil Steel
Grade
Burial
depth,
h (m)
PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot
A-B X60 1 0.380 0.904 1.542 2.305 0.893 0.437 1.043 1.786 2.676 0.863
A-B X65 1 0.405 0.989 1.717 2.599 0.901 0.470 1.163 2.037 3.102 0.861
A-B X70 1 0.445 1.151 2.072 3.222 0.876 0.518 1.364 2.481 3.889 0.827
A-B X60 2 0.737 2.566 - - 0.663 0.860 3.087 - - 0.646
A-B X65 2 0.892 3.493 - - 0.635 1.032 4.142 - - 0.623
A-B X70 2 1.044 4.521 - - 0.609 1.178 - - - 0.611
A-C X60 1 0.290 0.569 0.863 1.181 0.997 0.361 0.785 1.269 1.821 0.927
A-C X65 1 0.303 0.602 0.922 1.268 1.028 0.380 0.841 1.376 1.991 0.936
A-C X70 1 0.320 0.654 1.017 1.419 1.024 0.400 0.855 1.370 1.951 0.973
A-C X60 2 0.601 1.864 3.754 - 0.698 0.623 1.876 3.707 - 0.723
A-C X65 2 0.697 2.367 - - 0.668 0.739 2.469 - - 0.681
A-C X70 2 0.778 2.819 - - 0.662 0.881 3.315 - - 0.640
B-C X60 1 0.815 2.678 - - 0.759 0.858 2.718 - - 0.755
B-C X65 1 0.890 3.070 - - 0.746 1.030 3.631 - - 0.739
B-C X70 1 0.944 3.351 - - 0.736 1.071 3.840 - - 0.749
B-C X60 2 2.028 - - - 0.595 2.063 - - - 0.610
B-C X65 2 2.211 - - - 0.619 2.037 - - - 0.635
B-C X70 2 2.037 - - - 0.619 2.352 - - - 0.609
Cohesive soil deposit – Trench type TB Cohesionless soil deposit – Trench type TB
Soil Steel
Grade h (m) PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot
A-B X60 1 0.201 0.363 0.523 0.687 1.081 0.229 0.407 0.581 0.760 1.076
A-B X65 1 0.210 0.380 0.549 0.723 1.117 0.236 0.419 0.598 0.781 1.117
A-B X70 1 0.220 0.410 0.601 0.802 1.107 0.246 0.449 0.650 0.858 1.098
A-B X60 2 0.237 0.443 0.653 0.873 1.129 0.267 0.499 0.733 0.980 1.125
A-B X65 2 0.255 0.491 0.737 1.001 1.130 0.289 0.561 0.845 1.151 1.135
A-B X70 2 0.273 0.550 0.848 1.173 1.115 0.309 0.627 0.972 1.350 1.087
A-C X60 1 0.188 0.328 0.463 0.599 1.087 0.206 0.352 0.491 0.629 1.085
A-C X65 1 0.193 0.335 0.471 0.608 1.113 0.212 0.361 0.503 0.645 1.117
A-C X70 1 0.205 0.368 0.528 0.694 1.096 0.223 0.395 0.561 0.731 1.106
A-C X60 2 0.227 0.421 0.617 0.822 1.119 0.237 0.425 0.610 0.800 1.160
A-C X65 2 0.230 0.420 0.610 0.807 1.188 0.250 0.457 0.665 0.880 1.190
A-C X70 2 0.259 0.514 0.785 1.080 1.114 0.273 0.530 0.798 1.086 1.147
B-C X60 1 0.337 0.729 1.175 1.681 1.012 0.390 0.877 1.448 2.110 0.948
B-C X65 1 0.350 0.769 1.252 1.804 1.025 0.417 0.969 1.633 2.418 0.958
B-C X70 1 0.373 0.853 1.422 2.088 1.012 0.450 1.100 1.912 2.897 0.940
B-C X60 2 0.431 1.037 1.784 2.682 1.029 0.527 1.378 2.498 3.907 0.943
B-C X65 2 0.487 1.261 2.271 3.534 1.007 0.690 2.019 3.922 - 0.868
B-C X70 2 0.585 1.700 3.289 - 0.925 0.717 2.300 4.727 - 0.814
5
6
-42-
Table A7 Median peak ground velocity corresponding to the limit states, PGVm,i, and total lognormal1standard deviation, βtot, for 762.0 mm pipelines embedded in soil deposit of depth H = 30 m ( - : the2limit state is not reached).3
4
Cohesive soil deposit – Trench type TA Cohesionless soil deposit – Trench type TA
Soil Steel
Grade
Burial
depth,
h (m)
PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot
A-B X60 1 1.230 3.962 - - 0.767 1.407 4.789 - - 0.754
A-B X65 1 1.321 4.391 - - 0.772 1.521 - - - 0.747
A-B X70 1 1.656 - - - 0.690 1.736 - - - 0.708
A-B X60 2 2.013 - - - 0.648 2.333 - - - 0.644
A-B X65 2 2.321 - - - 0.637 2.636 - - - 0.629
A-B X70 2 2.685 - - - 0.603 3.159 - - - 0.597
A-C X60 1 1.343 4.740 - - 0.732 1.407 4.789 - - 0.754
A-C X65 1 1.471 - - - 0.739 1.521 - - - 0.747
A-C X70 1 1.696 - - - 0.700 1.736 - - - 0.708
A-C X60 2 2.233 - - - 0.637 2.394 - - - 0.629
A-C X65 2 2.561 - - - 0.625 2.733 - - - 0.616
A-C X70 2 3.108 - - - 0.590 3.159 - - - 0.597
B-C X60 1 - - - - - - - - - -
B-C X65 1 - - - - - - - - - -
B-C X70 1 - - - - - - - - - -
B-C X60 2 - - - - - - - - - -
B-C X65 2 - - - - - - - - - -
B-C X70 2 - - - - - - - - - -
Cohesive soil deposit – Trench type TB Cohesionless soil deposit – Trench type TB
Soil Steel
Grade h (m) PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot
A-B X60 1 0.649 1.711 3.118 4.609 0.989 0.574 1.350 2.291 3.233 1.030
A-B X65 1 0.557 1.297 2.188 3.075 1.079 0.628 1.552 2.715 3.908 1.034
A-B X70 1 0.612 1.507 2.632 3.784 1.052 0.696 1.828 3.321 4.900 0.993
A-B X60 2 0.515 1.295 2.293 3.326 1.067 0.664 1.744 3.169 4.677 1.010
A-B X65 2 0.648 1.683 3.035 4.457 1.059 0.783 2.275 4.400 - 0.986
A-B X70 2 0.722 2.005 3.770 - 1.013 0.855 2.623 - - 0.927
A-C X60 1 0.513 1.195 2.015 2.834 1.015 0.529 1.238 2.095 2.951 1.020
A-C X65 1 0.566 1.393 2.432 3.496 1.030 0.597 1.502 2.658 3.854 1.005
A-C X70 1 0.616 1.591 2.862 4.195 1.021 0.649 1.711 3.118 4.609 0.989
A-C X60 2 0.618 1.627 2.962 4.377 1.022 0.685 1.697 2.973 4.284 1.032
A-C X65 2 0.685 1.932 3.670 - 1.011 0.736 2.172 4.241 - 0.968
A-C X70 2 0.786 2.425 4.867 - 0.947 0.883 2.929 - - 0.897
B-C X60 1 1.484 - - - 0.818 2.008 - - - 0.751
B-C X65 1 1.831 - - - 0.806 2.270 - - - 0.734
B-C X70 1 2.039 - - - 0.784 2.611 - - - 0.701
B-C X60 2 1.922 - - - 0.804 2.680 - - - 0.697
B-C X65 2 2.505 - - - 0.747 3.004 - - - 0.670
B-C X70 2 2.375 - - - 0.747 3.744 - - - 0.628
5
-43-
Table A8. Median peak ground velocity corresponding to the limit states, PGVm,i, and total lognormal1standard deviation, βtot, for 762.0 mm pipelines embedded in soil deposit of depth H = 60 m ( - : the2limit state is not reached).3
4
Cohesive soil deposit – Trench type TA Cohesionless soil deposit – Trench type TA
Soil Steel
Grade
Burial
depth,
h (m)
PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot
A-B X60 1 0.921 2.827 - - 0.772 1.034 3.259 - - 0.778
A-B X65 1 1.101 3.732 - - 0.741 1.180 3.988 - - 0.755
A-B X70 1 1.656 - - - 0.712 1.431 - - - 0.719
A-B X60 2 1.474 - - - 0.649 1.824 - - - 0.629
A-B X65 2 1.890 - - - 0.611 2.331 - - - 0.602
A-B X70 2 2.235 - - - 0.593 2.403 - - - 0.610
A-C X60 1 0.774 2.158 4.069 - 0.795 0.832 2.370 4.530 - 0.792
A-C X65 1 0.889 2.675 - - 0.771 0.985 3.089 - - 0.760
A-C X70 1 1.066 3.568 - - 0.712 1.160 4.005 - - 0.717
A-C X60 2 1.304 - - - 0.645 1.324 - - - 0.667
A-C X65 2 1.470 - - - 0.642 1.683 - - - 0.626
A-C X70 2 1.831 - - - 0.598 1.970 - - - 0.608
B-C X60 1 1.995 - - - 0.720 2.071 - - - 0.724
B-C X65 1 1.873 - - - 0.735 2.664 - - - 0.702
B-C X70 1 2.280 - - - 0.684 2.887 - - - 0.673
B-C X60 2 3.177 - - - 0.615 4.127 - - - 0.611
B-C X65 2 3.552 - - - 0.603 4.956 - - - 0.592
B-C X70 2 4.083 - - - 0.588 - - - - -
Cohesive soil deposit – Trench type TB Cohesionless soil deposit – Trench type TB
Soil Steel
Grade h (m) PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot
A-B X60 1 0.375 0.763 1.183 1.575 1.035 0.431 0.922 1.477 2.007 0.982
A-B X65 1 0.404 0.854 1.357 1.835 1.048 0.461 1.021 1.668 2.296 1.019
A-B X70 1 0.424 0.919 1.482 2.024 1.093 0.499 1.154 1.940 2.721 1.042
A-B X60 2 0.413 0.897 1.449 1.980 1.084 0.472 1.089 1.826 2.559 1.029
A-B X65 2 0.477 1.131 1.929 2.731 1.032 0.596 1.606 2.963 4.416 0.935
A-B X70 2 0.525 1.321 2.338 3.392 1.057 0.652 1.853 3.534 - 0.926
A-C X60 1 0.338 0.645 0.961 1.246 1.052 0.367 0.725 1.104 1.452 1.008
A-C X65 1 0.359 0.703 1.064 1.395 1.076 0.389 0.786 1.215 1.614 1.044
A-C X70 1 0.383 0.778 1.206 1.604 1.089 0.419 0.886 1.406 1.901 1.061
A-C X60 2 0.380 0.786 1.233 1.653 1.094 0.395 0.830 1.315 1.774 1.071
A-C X65 2 0.403 0.855 1.362 1.843 1.119 0.456 1.049 1.754 2.453 1.045
A-C X70 2 0.428 0.941 1.530 2.101 1.141 0.524 1.320 2.338 3.393 1.012
B-C X60 1 0.791 2.125 3.916 - 0.946 0.866 2.370 4.417 - 0.953
B-C X65 1 0.874 2.480 4.727 - 0.923 0.892 2.458 4.602 - 0.975
B-C X70 1 0.961 2.879 - - 0.893 0.910 2.526 4.750 - 0.971
B-C X60 2 0.888 2.589 - - 0.950 0.988 2.985 - - 0.916
B-C X65 2 1.074 3.513 - - 0.886 1.181 3.934 - - 0.871
B-C X70 2 1.239 4.413 - - 0.854 1.121 3.614 - - 0.914
5
-44-
Table A9. Median peak ground velocity corresponding to the limit states, PGVm,i, and total lognormal1standard deviation, βtot, for 762.0 mm pipelines embedded in soil deposit of depth H = 120 m ( - : the2limit state is not reached).3
4
Cohesive soil deposit – Trench type TA Cohesionless soil deposit – Trench type TA
Soil Steel
Grade
Burial
depth,
h (m)
PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot
A-B X60 1 0.715 2.099 4.086 - 0.746 0.835 2.491 4.898 - 0.703
A-B X65 1 0.858 2.788 - - 0.706 0.938 2.962 - - 0.702
A-B X70 1 1.018 3.659 - - 0.669 1.173 4.253 - - 0.635
A-B X60 2 1.157 4.600 - - 0.636 1.303 - - - 0.637
A-B X65 2 1.431 - - - 0.612 1.685 - - - 0.603
A-B X70 2 2.235 - - - 0.593 1.933 - - - 0.595
A-C X60 1 0.572 1.499 2.722 4.014 0.799 0.623 1.620 2.926 4.301 0.778
A-C X65 1 0.656 1.852 3.520 - 0.777 0.717 2.019 3.828 - 0.749
A-C X70 1 0.770 2.393 4.824 - 0.726 0.833 2.560 - - 0.691
A-C X60 2 0.899 3.139 - - 0.659 0.995 3.523 - - 0.644
A-C X65 2 1.121 4.436 - - 0.624 1.257 - - - 0.608
A-C X70 2 1.370 - - - 0.595 1.461 - - - 0.597
B-C X60 1 1.596 - - - 0.714 1.674 - - - 0.703
B-C X65 1 1.628 - - - 0.720 1.963 - - - 0.687
B-C X70 1 2.020 - - - 0.668 2.214 - - - 0.669
B-C X60 2 3.177 - - - 0.615 3.119 - - - 0.609
B-C X65 2 3.552 - - - 0.603 3.728 - - - 0.577
B-C X70 2 4.083 - - - 0.588 4.199 - - - 0.575
Cohesive soil deposit – Trench type TB Cohesionless soil deposit – Trench type TB
Soil Steel
Grade h (m) PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot
A-B X60 1 0.289 0.560 0.842 1.098 1.092 0.334 0.649 0.979 1.280 1.078
A-B X65 1 0.305 0.603 0.919 1.209 1.115 0.354 0.704 1.078 1.424 1.095
A-B X70 1 0.329 0.676 1.055 1.410 1.105 0.378 0.782 1.226 1.643 1.079
A-B X60 2 0.308 0.615 0.943 1.246 1.158 0.359 0.741 1.160 1.554 1.105
A-B X65 2 0.339 0.714 1.132 1.528 1.146 0.402 0.890 1.454 2.003 1.088
A-B X70 2 0.374 0.837 1.376 1.903 1.120 0.448 1.060 1.804 2.552 1.029
A-C X60 1 0.259 0.474 0.689 0.879 1.143 0.283 0.511 0.736 0.934 1.140
A-C X65 1 0.272 0.507 0.745 0.958 1.169 0.297 0.546 0.796 1.017 1.180
A-C X70 1 0.288 0.549 0.819 1.064 1.179 0.311 0.581 0.856 1.102 1.194
A-C X60 2 0.266 0.486 0.706 0.900 1.267 0.295 0.552 0.814 1.048 1.233
A-C X65 2 0.303 0.600 0.915 1.206 1.232 0.334 0.673 1.039 1.379 1.207
A-C X70 2 0.320 0.652 1.014 1.352 1.227 0.349 0.723 1.134 1.521 1.209
B-C X60 1 0.620 1.670 3.082 4.595 0.912 0.714 1.971 3.695 - 0.887
B-C X65 1 0.683 1.951 3.734 - 0.900 0.769 2.200 4.213 - 0.881
B-C X70 1 0.781 2.419 4.866 - 0.857 0.813 2.384 4.639 - 0.883
B-C X60 2 0.749 2.311 4.638 - 0.864 0.817 2.489 4.957 - 0.879
B-C X65 2 0.887 3.023 - - 0.840 1.174 4.521 - - 0.786
B-C X70 2 1.088 4.200 - - 0.783 1.337 - - - 0.741
5
-45-
Table A10. Median peak ground velocity corresponding to the limit states, PGVm,i, and total lognormal1standard deviation, βtot, for 914.4 mm pipelines embedded in soil deposit of depth H = 30 m ( - : the2limit state is not reached).3
4
Cohesive soil deposit – Trench type TA Cohesionless soil deposit – Trench type TA
Soil Steel
Grade
Burial
depth,
h (m)
PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot PGVm,OLS
(m/s) PGVm,PILS
(m/s) PGVm,ULS
(m/s) PGVm,GLS
(m/s) βtot
A-B X60 1 0.736 2.160 4.205 - 0.879 0.826 2.563 - - 0.850
A-B X65 1 0.922 3.101 - - 0.807 1.042 3.716 - - 0.779
A-B X70 1 1.081 4.021 - - 0.761 1.228 4.858 - - 0.735
A-B X60 2 0.945 3.426 - - 0.816 1.009 3.729 - - 0.833
A-B X65 2 1.286 - - - 0.720 2.073 - - - 0.556
A-B X70 2 1.336 - - - 0.733 1.536 - - - 0.723
A-C X60 1 0.763 2.411 4.912 - 0.861 0.796 2.546 - - 0.836
A-C X65 1 1.203 - - - 0.755 1.011 3.740 - - 0.763
A-C X70 1 1.079 4.184 - - 0.768 1.323 - - - 0.755
A-C X60 2 0.927 3.460 - - 0.840 1.958 - - - 0.541
A-C X65 2 1.832 - - - 0.625 1.268 - - - 0.745
A-C X70 2 1.437 - - - 0.723 1.519 - - - 0.717
B-C X60 1 3.185 - - - 0.545 2.905 - - - 0.736
B-C X65 1 2.974 - - - 0.702 4.900 - - - 0.697
B-C X70 1 3.646 - - - 0.678 - - - - 0.669
B-C X60 2 2.819 - - - 0.705 - - - - 0.688
B-C X65 2 4.159 - - - 0.655 - - - - 0.646
B-C X70 2 - - - - - - - - - -
Cohesive soil deposit – Trench type TB Cohesionless soil deposit – Trench type TB
Soil
Steel
Grade h (m)
PGV
m,OLS
(m/s)
PGV
m,PILS
(m/s)
PGV
m,ULS
(m/s)
PGV
m,GLS
(m/s) βtot
PGV
m,OLS
(m/s)
PGV
m,PILS
(m/s)
PGV
m,ULS
(m/s)
PGV
m,GLS
(m/s) βtot
A-B X60 1 0.351 0.738 1.169 1.836 1.148 0.376 0.813 1.310 2.091 1.173
A-B X65 1 0.401 0.900 1.484 2.424 1.101 0.427 0.983 1.646 2.728 1.110
A-B X70 1 0.440 1.045 1.783 3.011 1.090 0.480 1.193 2.095 3.637 1.056
A-B X60 2 0.357 0.769 1.234 1.963 1.233 0.391 0.894 1.491 2.461 1.200
A-B X65 2 0.409 0.946 1.589 2.641 1.166 0.427 1.004 1.702 2.856 1.178
A-B X70 2 0.614 1.954 4.000 - 0.870 0.587 1.758 3.463 - 0.951
A-C X60 1 0.333 0.709 1.131 1.787 1.155 0.337 0.706 1.115 1.745 1.198
A-C X65 1 0.374 0.836 1.373 2.235 1.138 0.383 0.852 1.397 2.269 1.144
A-C X70 1 0.432 1.067 1.866 3.229 1.066 0.451 1.134 2.007 3.511 1.040
A-C X60 2 0.347 0.773 1.269 2.063 1.221 0.347 0.773 1.269 2.063 1.221
A-C X65 2 0.384 0.885 1.483 2.460 1.210 0.392 0.911 1.536 2.563 1.197
A-C X70 2 0.546 1.669 3.329 - 0.950 0.553 1.693 3.383 - 0.938
B-C X60 1 0.852 2.614 - - 0.955 0.858 2.628 - - 0.916
B-C X65 1 0.927 2.959 - - 0.894 1.200 4.450 - - 0.838
B-C X70 1 1.131 4.130 - - 0.823 1.475 - - - 0.769
B-C X60 2 0.993 3.549 - - 0.877 1.067 3.870 - - 0.888
B-C X65 2 0.962 3.222 - - 0.907 1.385 - - - 0.798
B-C X70 2 1.571 - - - 0.710 1.884 - - -