1Optimal intensity measures for the structural assessment of buried
2steel natural gas pipelines due to seismically-induced axial
3compression at geotechnical discontinuities
6Grigorios Tsinidis1, Luigi Di Sarno2, Anastasios Sextos3, and Peter Furtner4
81Vienna Consulting Engineers ZT GmbH, Austria & University of Sannio, Italy
92 University of Liverpool, United Kingdom & University of Sannio, Italy
10 3University of Bristol, United Kingdom
11 4Vienna Consulting Engineers ZT GmbH, Austria
13 Corresponding Author: Dr Grigorios Tsinidis, VCE Vienna Consulting Engineers ZT GmbH,
14 Untere Viaduktgasse 2, 1030, Vienna, email: email@example.com
16 Abstract: This paper investigates the efficiency and sufficiency of various seismic intensity
17 measures for the structural assessment of buried steel natural gas (NG) pipelines subjected to
18 axial compression caused by transient seismic ground deformations. The study focuses on
19 buried NG pipelines crossing perpendicularly a vertical geotechnical discontinuity with an
20 abrupt change on the soil properties, where the potential of high compression strain is expected
21 to be increased under seismic wave propagation. A detailed analytical framework is developed
22 for this purpose, which includes a 3D finite element model of the pipe-trench system, to
23 evaluate rigorously the pipe-soil interaction phenomena, and 1D soil response analyses that are
24 employed to determine critical ground deformation patterns at the geotechnical discontinuity,
25 caused by seismic wave propagation. A comprehensive numerical parametric study is
26 conducted by employing the analytical methodology in a number of soil-pipeline
27 configurations, considering salient parameters that control the axial response of buried steel
28 NG pipelines, i.e. diameter, wall thickness and internal pressure of the pipeline, wall
29 imperfections of the pipeline, soil properties and backfill compaction level and friction
30 characteristics of the backfill-pipe interface. Using the peak compression strain of the pipeline
31 as engineering demand parameter and a number of regression analyses relative to the examined
32 seismic intensity measures, it is shown that the peak ground velocity PGV at ground surface
33 constitutes the optimum intensity measure for the structural assessment of the examined
36 Keywords: Natural gas pipelines; intensity measures; efficiency; sufficiency; steel pipelines;
37 local buckling
2Earthquake-induced damage on Natural Gas (NG) pipeline networks may lead to important
3direct and indirect economic losses. The 1999 Chi-Chi earthquake in Taiwan, for instance,
4caused noticeable damage on natural gas supply systems, with the associated economic loss for
5the relative industry exceeding $ 25 million [1,2]. More importantly, severe damage may
6trigger ignitions or explosions with life-treating consequences and significant effects on the
7environment. As an example, the 1995 Hyogo-Ken Nambu earthquake in Japan, caused gas
8leakages from buried pipelines at 234 different locations, which subsequently led to more than
9530 fires [3, 4]. Based on the above observations, efficient methods for the vulnerability
10 assessment of NG pipeline networks seem to be of great importance.
11 A critical step towards the development of adequate tools for the vulnerability assessment of
12 NG pipelines is the identification of the expected failures, as well as of the mechanisms that
13 lead to these failures. Post-earthquake observations have demonstrated that seismically-induced
14 ground deformations may induce significant damage on buried pipelines [5-8]. Buried steel NG
15 pipelines were found quite vulnerable to high straining imposed by permanent ground
16 deformations, associated with fault movements, landslides and liquefaction-induced
17 settlements or uplifting and lateral spreading . Seismically-induced transient ground
18 deformations, caused by seismic wave propagation, have also contributed to damage of this
19 infrastructure [9-11]. Permanent ground deformations tend to induce higher straining on buried
20 steel pipelines, compared to transient ground deformations. Hence, most researchers focused
21 their investigations on this seismic hazard [12-23]. However, it is more likely for a buried
22 pipeline to be subjected to transient ground deformations rather than seismically-induced
23 permanent ground deformations. Transient ground deformations may trigger a variety of
24 damage modes on continuous buried steel NG pipelines, such as: shell-mode buckling or local
25 buckling, beam-mode buckling, pure tensile rupture, flexural bending failure or excessive
26 deformation of the section (i.e. ovaling) . Additionally, recent studies have demonstrated
27 that pipelines embedded in heterogeneous sites or subjected to asynchronous seismic motion
28 are more likely to be affected by appreciable strains due to transient ground deformations,
29 which in turn may lead to exceedance of predefined performance limits, reaching even
30 excessive damage on the pipeline [24-25]. Based on the above considerations, the present study
31 focuses on the transient ground deformation effects, as these have not yet been studied in
32 adequate depth.
33 An important aspect for the integrity assessment of NG pipeline networks is the aleatory and
34 epistemic uncertainty that is associated with their seismic response and vulnerability. In fact, a
35 shift from conventional deterministic analysis procedures to probabilistic analysis and risk
36 assessment concepts is deemed necessary . Critical elements of the latter analysis
37 frameworks are: (i) the definition of a proper Engineering Demand Parameter (EDP), which
38 shall be used as a representative metric of the response of the examined element at risk, and (ii)
39 the identification of adequate seismic intensity measures (IMs), which shall express the
40 severity of the ground seismic motion .
41 Evidently, the amplitude, frequency characteristics, energy content and duration of seismic
42 ground motions are all expected to have a considerable effect on the seismic vulnerability of
1any structural element at risk. However, it is not possible for all the above ground motion
2characteristics to be described effectively by one parameter, i.e. one seismic intensity measure
3(IM) . Therefore, the definition of optimal seismic IMs for the assessment of any structural
4system is of great importance. An optimal seismic IM should be efficient, in the sense that it
5should result in a reduced variability of the EDP for a given IM value . Additionally, it
6should be sufficient, so that it renders the computed structural response conditionally
7independent of earthquake characteristics, such as the earthquake magnitude (M), the epicentral
8distance (R) or other earthquake characteristics . An efficient seismic IM leads to a
9reduction of the number of analyses and ground seismic motions that are required to estimate
10 the probability of exceedance of each value of the EDP for a given IM value. A sufficient IM,
11 on the other hand, allows for free selection of the, employed in the analysis, seismic ground
12 motions, since the effects of seismological parameters, e.g. the magnitude, epicentral distance
13 etc., on the prediction of the EDP become less important. As discussed in the ensuing, the
14 efficiency and sufficiency of a seismic IM may be both quantified following existing literature
16 Concepts and measures like proficiency, practicality, effectiveness, robustness and hazard
17 computability, have also been proposed in the literature for identifying optimal seismic IMs for
18 the assessment of buildings and aboveground civil infrastructure [27-36, 86-87]. However, the
19 investigation of optimal seismic IMs for embedded infrastructure, including buried steel NG
20 pipelines, has received considerably less attention by the scientific community. To the authors’
21 knowledge, the only relevant study is the one by Shakid & Jahangiri , who developed and
22 employed a numerical framework, in order to examine the efficiency and sufficiency of a
23 variety of seismic IMs in case of NG pipelines subjected to seismic wave propagation. The
24 study focused on NG pipelines embedded in uniform soils, with the soil-pipe interaction being
25 considered in a simplified fashion, by employing beam on soil-springs models. The study did
26 not examine thoroughly salient parameters affecting the seismic response and vulnerability of
27 this infrastructure.
28 Based on the above considerations, the aim of this study is to identify the optimum seismic IM
29 that shall be adopted for the assessment of buried steel natural gas (NG) pipelines, when these
30 are subjected to compression axial loading due to transient seismic ground deformations. The
31 study focuses on NG pipelines crossing perpendicularly a vertical geotechnical discontinuity
32 with an abrupt change on the soil properties. In such soil sites, the potential of high
33 compression straining of the pipeline during ground shaking is expected to increase
34 significantly, compared to the case where the pipeline is embedded in a homogeneous soil site
35 [24-25]. A de-coupled numerical framework is developed to fulfil our objective, which
36 includes 1D soil response analyses of selected soil sites and 3D quasi-static analyses of
37 selected soil-pipe configurations. The former analyses aim at computing critical ground
38 deformation patterns at the vicinity of the geotechnical discontinuity, caused by seismic wave
39 propagation. Through the 3D soil-pipe interaction analyses, critical parameters affecting the
40 seismic response and vulnerability of buried steel pipelines are thoroughly considered. A
41 comprehensive study is conducted for an ensemble of 40 seismic motions, by employing the
42 proposed numerical methodology in a number of soil-pipe configurations. Various seismic
1IMs, referring to both outcrop and ground surface conditions, are tested and rated on the basis
2of two criteria namely their efficiency and sufficiency [27-28].
42. Numerical parametric analysis
52.1 Problem definition and selection of soil-pipe configurations
6A continuous buried steel NG pipeline of external diameter D and wall thickness t is embedded
7in a backfilled trench at a burial depth h (Fig. 1). The backfill-pipe configuration is located in a
8soil deposit of total depth H and crosses perpendicularly a vertical geotechnical discontinuity.
9The latter divides the soil deposit into two subdeposits (i.e. subdeposit 1 and subdeposit 2 in
10 Fig. 1) with abrupt changes on their physical and mechanical properties. The whole system is
11 subjected to upward propagated seismic shear waves, which cause a dissimilar ground
12 movement of the adjusted subdeposits. The dissimilar ground movement of the subdeposits
13 produces a differential horizontal ground deformation along the pipeline axis near the critical
14 section of the geotechnical discontinuity. This differential ground deformation is subsequently
15 transferred through the pipe-soil interface on the pipeline, causing its compressional-tensional
16 axial straining. A potential high axial compression straining of the pipeline might lead to a
17 failure of the pipeline in the form of local buckling.
Pipeline & surficial soil layer
20 Fig. 1 Schematic view of the examined problem (H: depth of soil deposit, h: burial depth of the
21 pipeline, ur: seismic ground movement of the bedrock, uA, uB seismic ground movement of subdeposit 1
22 and 2, at the burial depth of the pipeline).
24 A number of parameters affecting the seismic response of buried steel pipelines namely wall
25 thickness, diameter, and burial depth of the pipeline, internal pressure of the pipeline, existence
26 of wall imperfections of the pipeline, backfill compaction level, pipe-backfill interface friction
27 characteristics and soil properties of the site, are all considered in the present numerical study.
28 In particular, most analyses were carried out on pipelines with external diameter D = 914.4 mm
29 and wall thickness t =12.7 m, while additional analyses were conducted for pipelines with
30 external diameters D = 406.4 mm and D = 1219.2 mm and wall thicknesses, t = 9.5 mm and t =
31 19.1 mm, respectively. The selected pipelines were designed for a maximum operational
32 pressure of p = 9 MPa (i.e. 90 bar), following relevant regulations of ALA (2001) , while it
33 was verified that the selected pipeline dimensions are available by the industry. Most of
34 analyses were conducted for an operational pressure, p = 8 MPa, while sensitivity analyses
1were also carried out for an internal pressure p = 4 MPa, as well as for non-pressurized
2pipelines (i.e. p = 0 MPa). It is worth noticing that the external diameters, D, and operational
3pressures, p, of the investigated pipelines were all selected on the basis of a preliminary
4investigation of the variation of these characteristics in case of actual transmission NG
5networks found in several countries of Europe (Table 1). The external diameter, wall thickness
6and examined internal pressures of the selected pipelines are summarized in Table 2. The
7pipelines were assumed to be made of API 5L X60, X65 and X70 grades, in an effort to cover
8a range of steel grades that are commonly used in NG transmission networks. The mechanical
9properties of the selected grades are tabulated in Table 3.
11 Table 1 External diameters and range of operational pressure of transmission NG pipeline networks in
12 Europe (information provided by the website of each operator).
Nominal diameter range, D (mm, ΄)
range, p (MPa)
914.4 mm to 1066.8 mm (36’ to 42’)
7 - 8
914.4 mm, 965.2 mm, 1016.0 mm (36’, 38’, 40’)
4 - 7
> 1066.8 mm (42’) for the supra-regional
networks; otherwise > 508 mm to 762 mm (20’ to
> 1066.8 mm (42’) for the supra-regional
networks; otherwise > 508 mm to 762 mm (20’ to
254 mm, 508 mm, 609.6 mm, 762 mm, 914.4 mm
(10’, 20’, 24’, 30’, 36’)
508 mm to 1219.2 mm (20’ to 48’)
7 - 8
406.4 mm to 812.8 mm (16’ to 32’)
406.4 mm to 660.4 mm (16’ to 26’)
5 - 8
914.4 mm to 1066.8 mm (36’ to 48’)
7 - 8
13 * n.p. = not provided
15 Table 2 Summary of examined cases.
Depth of soil
0, 4, 8
17 Table 3 Mechanical properties of steel grades used in this study.
Yield stress, σy (MPa)
Ultimate stress, σu (MPa)
Ultimate tensile strain, εu (%)
Young’s modulus, E (GPa)
19 The study was conducted assuming a soil site depth H = 60 m, while additional analyses were
20 also carried out for soil sites with depths H = 30 m and 120 m. The burial depth, h, of the
1selected pipelines, i.e. distance between the pipeline crown and ground surface, was set equal
2to 1.0 m, which constitutes a common burial depth for this infrastructure. A sensitivity study
3was conducted for D = 914.4 mm pipelines buried at a burial depth h = 2.0 m.
4Both cohesive and cohesionless soil deposits were examined, with the properties of the
5examined pairs of subdeposits varying, so that to cover a range of anticipated soil sites. A 3.0
6m deep surficial layer of cohesionless material was assumed in all examined cases, regardless
7of the adopted underlying subdeposits. Additionally, all examined sites were assumed to rest
8on an elastic bedrock with mass density, ρb =2.2 t/m3 and shear wave velocity Vs,b = 1000 m/s.
9Fig. 2 illustrates the gradients of shear wave propagation velocities, as well as the mass
10 densities, ρ, of the selected soil subdeposits. The variation of the small-strain shear modulus of
11 the cohesionless subdeposits is actually estimated as follows :
ρA = 1.5 t/m3 ρB = 1.7 t/m3 ρC = 1.95 t/m3
Vs(m/s), H = 30 m
Vs(m/s), H = 60 m
Vs(m/s), H = 120 m
Vs(m/s), H = 30 m
Vs(m/s), H = 60 m
Vs(m/s), H = 120 m
14 Fig. 2 Shear wave velocity gradients of examined (a) cohesionless and (b) cohesive soil sub-deposits.
16 where is the effective confining stress (in kPa) and is a constant depending on the
17 relative stiffness Dr of the subdeposit (Table 4). By employing Eq. 1 for the selected soil mass
18 densities and based on basic elasto-dynamics, the gradients of small-strain shear wave velocity
19 were defined, as per Fig. 2a. The gradients of the small-strain shear wave velocity of the
20 cohesive soil subdeposits were also considered to be increased with depth, as per Fig. 2b. The
21 selected soil subdeposits correspond to soil classes B and C according to Eurocode 8 . The
22 above profiles were selected in pairs, in order to define the properties of subdeposits 1 and 2
23 (Fig. 1). In particular, three pairs were examined, i.e. Soil A - Soil B, Soil A - Soil C and Soil
1B - Soil C. The nonlinear response of the selected subdeposits during ground seismic shaking
2was described by means of G-γ-D curves, following .
3Two different sets of mechanical and physical properties were examined for the surficial soil
4layer, which actually constitutes the trench backfill material for the examined pipelines and
5therefore is referred as either trench TA or trench TB in the ensuing, for the sake of simplicity.
6The selected properties, summarized in Table 5, correspond to well or very well-compacted
7conditions. It is worth noting that the shear moduli G, presented in Table 5, correspond to
8‘average’ equivalent soil stiffnesses, referring to the ground strain range anticipated for the
9selected seismic ground motions. These values were estimated on the basis of nonlinear 1D soil
10 response analyses, discussed in the following.
11 With reference to the selection of the friction coefficient of the backfill-pipe interface, μ; this
12 may vary along the axis of a long pipeline and may also change during ground shaking.
13 However, for steel pipelines without external coating it is bounded between μmin= 0.3 and
14 μmax= 0.8. These limits are resulted from the relation between the interface friction coefficient
15 μ and friction angle of the backfill φ: [38, 42], by assuming typical
0.5 0.9 tan
16 values for the backfill soil friction angle, i.e. from 29o to 44o. It is worth noting that the
17 existence of external pipe coating may affect the friction coefficient of the interface . This
18 effect was disregarded in this study, since the focus was set on more critical cases where higher
19 shear stresses are developed along the pipe-soil interface, leading to a higher axial straining on
20 the embedded pipeline.
22 Table 4 Relationships between density, relative density, K2,max parameter and cohesionless soil
23 characterization (after ).
Density, ρ (t/m3)
Relative density, Dr (%)
26 Table 5 Physical and mechanical properties of investigated trenches.
12.2 Analytical methodology
2A 3D full dynamic analysis of the soil-pipe interaction (SPI) phenomena during ground
3shaking may be seen as computationally prohibitive, when considering complications in
4simulating rigorously material or geometrical nonlinearities associated with the problem, as
5well as uncertainties in the definition of the characteristics of heterogeneous soil sites and the
6inherently random varying ground seismic motion . Hence, a simplified, yet efficient,
7numerical analysis framework should be developed and used, instead.
8Generally, the inertial soil-structure interaction (SSI) effects are not important in the dynamic
9soil-pipe interaction problem . This allows for a decoupling of the problem in successive
10 stages, in an effort to reduce the computational cost, as compared to the one associated with a
11 3D SPI dynamic analysis. It also allows for the investigation of the effect of transient ground
12 deformation on the response of the embedded pipeline in a quasi-static form.
13 Based on the above considerations, a numerical framework was developed within this study.
14 The framework, which is inspired by Psyrras et al. , is illustrated schematically in Fig. 3
15 and consists of three main steps. A 3D trench-pipe numerical model is constructed within the
16 first step to compute the axial compressive response of the buried steel NG pipeline under an
17 increasing level of relative axial ground displacement, caused by the dissimilar ground
18 movement of adjacent soil subdeposits near the geotechnical discontinuity (Step 1 in Fig. 3). In
19 the second step (Step 2 in Fig. 3), the ground response is computed under vertically propagated
20 seismic waves via 1D nonlinear soil response analyses, which are carried out separately for
21 each subdeposit. More specifically, critical relative axial ground deformation patterns, δue, are
22 computed at the pipeline depth, for the selected pairs of subdeposits, using the numerically
23 predicted horizontal deformations of the adjacent soil subdeposits. Time histories of
24 acceleration, velocity and displacement are also computed at the ground surface, which are
25 then employed in the definition of some of the examined seismic IMs in the present study. The
26 outcomes of the 3D SPI analyses and the 1D soil response analyses are combined in the third
27 step of the analytical framework (Step 3 in Fig. 3). In particular, the pipe response, expressed
28 in terms of maximum axial compression strain, is correlated with the ground response, the
29 latter computed for each of the selected pairs of subdeposits and each seismic record. The
30 analytical framework is further analysed in the following sections.
Nonlinear spring with
fixed free-end, u =0
u = 0
1D soil response analyses
Soil nonlinear response
Critical deformation patterns δue= max (uA-uB)
Seismic IMs at ground surface
Selected soil-pipe configurations
Ground displacement pattern δu
Selected soil configurations
Selected ground motions
ε- δu correlations
2Fig. 3 Schematic view of the analysis framework: Step 1: 3D numerical model of the trench-pipe
3configuration to evaluate the pipeline response under an increasing level of relative axial ground
4deformations, δu, accounting for the SPI effects. Step 2: 1D soil response analyses of selected soil
5subdeposits to compute the ground response for selected ground motions, including the seismic IMs at
6ground surface, and define relative axial ground deformations δue, at the vicinity of the geotechnical
7discontinuity. Step 3: combination of the results of the 3D SPI analyses with the results of the 1D soil
12.2.1 Step 1: 3D trench-pipe model to analyse the SPI phenomena
2A 3D continuum trench model, encasing a cylindrical shell model of the pipeline, is initially
3developed in ABAQUS , aiming at computing the axial response of the pipeline under an
4increasing level of relative axial ground displacement, caused by the dissimilar horizontal
5ground shaking of the adjacent subdeposits near a geotechnical discontinuity (Step 1 in Fig. 3).
6The utilization of a 3D continuum model allows for a rigorous simulation of pressurization
7level of the pipeline, as well as of initial geometric imperfections of the wall of the pipeline,
8which both are expected to affect significantly the axial compressional response of a buried
9steel pipeline, including potential localized buckling modes [24, 45-48]. Additionally, it allows
10 for a rigorous simulation of potential sliding and/or detachment (i.e. in the normal direction)
11 between the pipeline wall and the surrounding ground, by employing rigorous interaction
12 models available in advanced finite element codes, like ABAQUS . Finally, it allows for a
13 proper simulation of the initial stress state and deformation of the trench-pipe system caused by
14 gravity and the operational pressure of the pipeline, before the application of the seismically-
15 induced ground deformations.
16 The selection of a surficial block from the semi-infinite 3D ground domain, i.e. a part of the
17 surficial layer-trench TA or TB herein, is made on the ground of absence of significant inertial
18 SSI effects, in addition to the shallow burial depth of the pipeline and the assumption of in-
19 plane ground deformation pattern. In this context, the dimensions of the 3D model are defined
20 as follows; the distance between the pipe invert and the bottom boundary of the trench model is
21 set equal to 1.0 m, while the distance between the side boundaries of the trench model and the
22 pipe edges is set equal to one pipe diameter. The distance between the pipe crown and ground
23 surface is defined according to the adopted burial depth, h, of the examined pipeline.
24 An ‘adequately long’ 3D continuum model is generally required to account for the effect of the
25 ‘anchorage’ length of the pipeline by the surrounding ground on the shear stresses that are
26 being developed along the soil-pipe interface during seismic ground deformation. This aspect
27 in addition to the requirement of fine meshes of the pipeline, to adequately resolve its buckling
28 modes (see following), may lead to a significant increase of the relevant computational cost of
29 the analyses, even if these analyses are conducted in a quasi-static fashion. On this basis,
30 generalized nonlinear springs are calculated and introduced at both sides of the pipeline, in an
31 effort to reduce the required length of the 3D SPI model, while considering the effect of the
32 infinite pipeline length on the response of the examined pipeline-soil configurations. The
33 springs are acting parallel to the pipeline axis, with the force-displacement relation of the
34 nonlinear springs being given as follows :
max max max max max max
+ 2 for
s s s s s
k m k k k k
3is the backfill-pipe relative axial movement caused by the relative axial ground deformation
4δu of the trench backfill soil, as a result of the dissimilar ground movement of the adjacent sub-
5deposits, ks is the shear stiffness of the backfill-pipe interface, is the maximum shear
6resistance that develops along the backfill-pipe interface and EA is the axial stiffness of the
7pipeline cross section. The maximum shear resistance in case of cohesionless backfills depends
8on the adopted friction coefficient μ of the interface and varies along the perimeter of the pipe.
9Therefore, mean values of and ks should be evaluated via numerical simulations of simple
10 axial pull-out tests of the examined pipe from the trench backfill soil, as per . The proposed
11 simulation of the end-boundaries of the pipeline is inspired from a numerical model that was
12 developed by Vazouras et al.  to account for the effect of the infinite length of a buried
13 steel pipeline subjected to seismically-induced strike-slip faulting. Based on the above
14 considerations, the length of the 3D pipe-soil trench model is reduced to 20 × D (D: external
15 diameter of the pipeline). This length is selected on the grounds of a sensitivity analysis, by
16 comparing the axial stresses and strains computed at the critical middle section of the pipeline
17 by the 3D SPI model, with relevant predictions of an equivalent quite extended, almost
18 ‘infinite’, 3D continuum model of the soil-pipe configuration subjected to the same axial
19 ground deformation pattern.
20 The boundary at the bottom of the soil model is fixed in the vertical direction, whereas the
21 side-boundaries are fixed in the horizontal direction. The ground surface is set free, while the
22 pipe-ends are connected to the relevant springs by means of rigid constraints, as per Fig. 3a.
23 The backfill-pipe interface is simulated using an advanced ‘hard contact’ interaction model,
24 available in ABAQUS , which allows for potential sliding and/or detachment in the normal
25 direction between the interacting pipe and backfill soil elements during the horizontal
26 deformation of the ground. The shear behaviour of the interface model is simulated via the
27 classical Coulomb friction model, by introducing a friction coefficient, μ. The latter follows the
28 values provided in Table 5.
29 A critical aspect for the efficiency of the 3D numerical model is the discretization of the
30 pipeline and surrounding soil. Linear hexahedral (brick-type) elements are used to model the
31 trench backfill, employing the equivalent soil properties (i.e. degraded soil stiffness) presented
32 in Table 5. The pipeline is simulated by means of inelastic, reduced integration S4R shell
33 elements, having both membrane and bending stiffness. The mesh density of the pipeline at the
34 critical central section of the 3D numerical model, i.e. at the location of the geotechnical
35 discontinuity where the axial strain of the pipeline is expected to maximize, is selected
36 adequately, in order to resolve the inelastic buckling modes of an equivalent axially
37 compressed unconstrained cylindrical steel shell . To select an adequate mesh, the half-
38 wavelength of the examined pipeline sections in the post-elastic range, , is initially
39 computed as :
, ,c p c el p
2where E is the Young’s modulus of the steel grade of the pipeline, Ep is the plastic modulus of
3the steel grade of the pipeline and the elastic axial half-wavelength. Considering a
4Poisson’s ratio v = 0.3 for the steel grades examined herein, the latter is given as :
c el Rt
6where R and t are the radius and wall thickness of the pipeline, respectively. By setting the
7plastic modulus Ep is equal to 0.1E, Eq. 5 yields: . Element lengths, ranging
c p c e
8between 1.0 cm and 2.0 cm, were found capable to reproduce the theoretical axial half-
9wavelength of the examined pipelines. The above mesh seeds were applied in the middle
10 section of the examined pipelines and for a length equal to 2.0 m. The mesh density away from
11 the critical central zone was gradually decreased, with the axial dimension of the shell elements
12 being as high as 0.30 m, to reduce the computation cost of the 3D analyses. This was done on
13 the ground of the small strain amplitudes and radial deflections expected away from the central
14 section of the pipeline. The mesh discretization of the trench soil in the axial direction of the
15 model matches the exact mesh seed of the pipeline, to avoid any initial gaps during the
16 generation of mesh. The mesh seed of the trench in the other two directions is restricted to 0.3
18 The plastic behaviour of the steel pipelines is modelled through a classical J2-flow plasticity
19 model combined with a von Mises yield criterion. Ramberg-Osgood curves (Eq. 7) are fitted to
20 bilinear isotropic curves that describe the tensile uniaxial behaviour of the selected steel grades
21 (Fig. 4). The curves are characterized by a yield offset equal to 0.5 %, and a hardening
22 exponent n equal to 15, 19.5 and 21, for grades X60, X65 and X70, respectively.
26 Fig. 4 Uniaxial tensile stress-strain response of API X60, X65 and X70 steel grades adopted herein (n =
27 hardening exponent, a = yield offset × E/σy).
29 The axial compression response of thin-walled steel pipelines is known to be highly affected
30 by initial geometric imperfections of the walls [25, 44]. In this context, both ‘perfect’ pipelines
31 and equivalent pipelines with initial geometric imperfections were examined. The simulation of
32 imperfections of the pipeline walls is not a straightforward task since the shape of these
33 imperfections might be rather complex. In this study, a ‘fictious’ imperfection shape is
1considered, following previous studies [25, 45]. In particular, a stress-free, biased
2axisymmetric imperfection is considered, following a sinusoid function modulated by a second
3sinusoid, which results in a peak amplitude of the imperfection at the middle section of the
4length, where it is applied . The function of radial deflection is defined as per Eq. (8),
5where positive values correspond to outward direction form the mid-surface of the pipeline
0 1 cos cos , , 2.0 , 2
crit c crit
w x w w x L m N L
11 Fig. 5 Detail of the mesh of the central section of a D = 914.4 mm pipeline with a biased axisymmetric
12 geometrical imperfection (the radial deformation is exaggerated by a scale factor × 10).
14 The peak amplitude of the imperfection is set as a function of the pipe wall thickness equal to
15 . This latter selection is made following specifications, of ArcelorMittal
0 1 0.10w w w t
16 which provide a manufacturing tolerance for the walls of API-5L X65 pipelines in the range of
17 + 15% to -12.5% . Generally, the location of a pipeline imperfection is not easily
18 detectable. In the present study it was decided to select the worst-case scenario, i.e. the
19 imperfection is applied over the central critical pipeline zone with length equal to = 2.0 m,
20 centered at the exact position of the geotechnical discontinuity. Fig. 5 illustrates a detail of the
21 mesh of the central section of an imperfect pipeline. The mesh of the backfill soil, surrounding
22 the pipeline, follows the perturbated mesh of the pipeline, in order to prevent any initial gaps
23 during the generation of the mesh that might affect the contact phenomena during loading, thus
24 decreasing the computational efficiency of the model. Residual stresses due to manufacturing
25 process of the pipelines were disregarded by the present study.
26 With reference to the loading pattern of the 3D SPI model; the effects of gravity and internal
27 pressure of the pipeline are initially considered within a general static step. The effect of
28 transient ground deformation is then simulated in quasi-static manner as follows: the nodes of
29 the one half of the trench model and the free node of the relevant nonlinear spring are fixed in
30 the axial direction, i.e. u = 0, in Fig. 3. The nodes of the other half trench model and the free
31 node of the relevant nonlinear spring are displaced towards the constraint part of the model in a
32 stepwise fashion. This deformation pattern causes a relative axial deformation of the backfill
33 model (i.e. δu), which is equivalent to the case where both halves of the model, are moving
34 differently but in the same axial direction, causing the same differential ground displacement δu
35 on the examined system. Since the depth of the trench domain is much smaller than the
36 common predominant wavelengths of seismic waves, the above-described deformation pattern
1is kept constant with depth coordinate over the trench backfill domain. The adopted
2deformation pattern leads to the development of shear stresses along the pipe-soil interface,
3which in addition to the axial loading induced on both ends of the pipeline via the generalized
4nonlinear springs, result in an axial compression straining of the pipeline. This axial response
5of the pipeline is evaluated for an increasing level of relative axial ground displacement, δu,
6through a modified Riks solution algorithm. The main outcome of this analysis is a curve that
7describes the relation between an increasing relative axial ground displacement, δu, and the
8corresponding maximum compressive axial strain of the critical middle section of the pipeline,
9i.e. around the geotechnical discontinuity (see Step 3 in Fig. 3). It is noted that the analysis
10 focuses on the axial ground displacements, which constitute the dominant loading mechanism
11 for buried pipelines under seismic wave propagation, while it disregards the vertical ground
12 displacements. Since the response of the pipeline is computed for an increasing level of relative
13 axial ground displacement, δu, the outcome of one 3D SPI analysis may be used to evaluate the
14 axial straining of the pipe under a variety of selected ground axial relative displacements, δue,
15 caused by diverse seismic motions. This may be possible with the utilization of ‘mean’
16 equivalent soil properties for the backfill soil, the latter corresponding to the strain-range that is
17 anticipated for the selected ground seismic motions.
19 2.2.2 Step 2: Soil response analyses
20 In a second step, the seismic response of the selected soil sites is evaluated via 1D nonlinear
21 soil response analyses, which are carried out separately for each subdeposit of the adopted
22 pairs, employing DEEPSOIL . Numerical models of the selected subdeposits presented in
23 Section 2.1, are initially developed, accounting also for the properties of the surficial ground
24 layers (i.e. backfills) and the elastic bedrock. The models are then employed in a series of
25 nonlinear time history analyses, using an ensemble of seismic records (see Section 2.4). The
26 hysteretic nonlinear response of the soil during ground shaking is considered by means G-γ-D
27 curves, which are properly selected for the examined deposits, following . An additional
28 viscous damping of 1 % is also introduced in the form of the frequency-dependent Rayleigh
29 type , in order to avoid the potential amplification of higher frequencies of the ground that
30 may result in unrealistic oscillations of the acceleration time histories in low ground strains.
31 The Rayleigh coefficients are properly selected for a frequency interval range, characterizing
32 the ‘dominant frequencies’ of each soil column. Through the soil response analyses, time
33 histories of the horizontal deformations of the soil columns are calculated at the burial depths
34 of the pipelines, which are then employed to compute maximum differential ground
35 deformation patterns δue for the selected pairs of adjusted subdeposits (see Section 2.1).
36 Additionally, time histories of the horizontal acceleration, velocity and deformation are
37 computed at the ground surface, in order to evaluate a variety of seismic IMs that are examined
38 in the framework of this study.
40 2.2.3 Step 3: Combination of 3D SPI with 1D soil response analyses
41 The critical relative axial ground deformation patterns, δue that are defined based on the results
42 of the 1D soil response analyses are finally correlated with the predicted straining of the
1pipeline, using the δu - maximum compressive axial strain, ε, relations computed through the
23D SPI analyses.
3Summarizing, the applying analytical framework accounts for critical parameters affecting the
4seismic response of buried steel pipelines. Additionally, the pseudo-static simulation of the
5seismically-induced transient ground deformations is computationally more efficient compared
6to an analysis conducted in a full-dynamic fashion.
7Inevitably, the proposed analysis framework has some limitations. The inertial SPI effects, as
8well as effects of the evolution of stresses and deformations due to temperature changes on the
9pipeline response are not considered in the present study. Moreover, phenomena related to
10 fatigue and steel strength and stiffness degradation due to cyclic loading, are neglected. The
11 effect of soil nonlinearity, during ground shaking, on the stiffness of the backfill and therefore
12 on the confinement level of the pipeline, is considered in an approximate manner through the
13 introduction of equivalent soil properties (i.e. strain-depended degraded stiffness) on the
14 backfill. Additionally, the 1D soil response analyses cannot capture the potential 2D wave
15 phenomena near the geotechnical discontinuity . However, 1D nonlinear soil response
16 analyses offer computational efficiency compared to 2D or 3D analyses and may be used as a
17 first approximation for the evaluation of the seismic response of the ground and pipelines at
18 shallow depths . The computational efficiency of 1D soil response analyses allows for an
19 extended and thorough parametric analysis, such as the one presented herein.
21 2.2.4 Verification of the 3D SPI model
22 As stated already, the length of the 3D trench soil-pipe model was selected by examining
23 various lengths and comparing the axial stresses and strains, computed at the middle critical
24 section of the pipeline, with relevant predictions of equivalent ‘infinitely’ long 3D continuum
25 models of the examined soil-pipe configurations, subjected to the same axial ground
26 deformation pattern. An example is provided in this section, referring to the D = 914.4 mm
27 pipeline, embedded in a burial depth h = 1.0 m. The procedure followed to evaluate the
28 nonlinear springs for the end-sides of the pipeline model in Fig. 3, is initially presented in Fig.
29 6. More specifically, Fig. 6a illustrates the numerical model used to simulate the axial pull-out
30 of the pipeline from the surrounding ground. The pull-out analyses were performed assuming a
31 length for the model equal to 20 m and examining both adopted trench backfills, i.e. TA and
32 TB (Table 5). The analyses yielded the shear stress-displacement relations presented in Fig. 6b.
33 These relations were then used to define the maximum shear resistance τmax and the shear
34 stiffness ks of the backfill soil-pipe interface, which were then employed in the definition of the
35 nonlinear springs, following Eq (1). The computed force-displacement relations of the
36 nonlinear springs for the present example are presented in Fig 6c. A higher friction coefficient
37 for the backfill-pipe interface leads to ‘stiffer’ springs for the end-sides of the pipeline.
2Fig. 6 (a) Numerical simulation of an axial pull-out test of a D = 914.4 mm pipeline, embedded at burial
3depth h = 1.0 m, (b) interface shear stress–displacement relationship estimated for the examined system
4when the pipeline is embedded in trench TA (μ = 0.45) or in trench TB (μ = 0.78), (c) force-
5displacement relations of the nonlinear springs, estimated as per Eq.1, when the examined pipeline is
6embedded in trench TA (μ = 0.45) or in trench TB (μ = 0.78).
8The nonlinear springs were introduced at the end-sides of the examined pipeline and the
9numerical model was subjected gradually to a relative axial ground deformation up to δu = 20
10 cm, as per Fig. 3. The analyses were carried out for a ‘perfect’ pipeline (i.e. w/t=0), as well as
11 for an equivalent pipeline with an initial geometric imperfection at the middle section (i.e.
12 w/t=0.1). In both cases the pipeline was pressurized to an internal pressure p = 8 MPa. Fig. 7
13 compares representative numerical results of the pipelines response computed by the proposed
14 3D SPI model, with relevant numerical predictions of extended 3D trench-pipe models of the
15 examined pipelines (i.e. models with lengths equal to 500 times and 1000 times the diameter of
16 the pipeline). In particular, the axial stress (normalized over the yield Mises stress) and the
17 axial strain computed along the ditch axis of the examined pipelines at the end of the analysis,
18 i.e. after local buckling occurred, are compared. The extended models yield in almost identical
19 results; therefore, it may be assumed that they may provide the response of an ‘infinitely’ long
20 trench-pipeline model and can be used for verification purposes of the reduced length 3D
21 model. The reduced length model provides similar results with the extended length models in
22 terms of stresses and strains for both the perfect and imperfect pipelines, irrespectively of the
23 adopted trench backfill properties. Evidently the computational cost of the reduced length
24 model is highly reduced compared to the one of the extended models. It is worth noticing the
25 significant effects of geometric imperfections of the walls of the pipeline, as well of the trench
26 properties and backfill-pipe interface characteristics, on the axial response of the pipeline.
27 Clearly, a much higher axial response is reported for the imperfect pipeline, embedded in
28 trench TB (i.e. case of very-well compacted backfill soil and higher soil-pipe interface friction
29 coefficient). The critical effects of pipeline wall imperfections or backfill compaction level on
30 the axial response of buried steel pipelines are further examined in [47-48].
3Fig. 7 Comparisons of axial stress (normalized over yield Mises stress) and axial strain along the ditch
4axis of a D = 914.4 mm perfect (i.e. w/t=0) and imperfect (i.e. w/t=0.1) pipeline, embedded in trench
5TA (μ = 0.45) or TB (μ = 0.78) at a burial depth h = 1.0 m, computed by the 3D SPI model with the
6nonlinear springs at end-sides, (i.e. L = 20 D) and extended 3D SPI models (L = 500 D and L = 1000
7D), the latter simulating the ‘infinitely’ long soil-pipeline system.
92.3 Seismic ground motions
10 An ensemble of 40 real ground motions, recorded on rock outcrop or very stiff soil (soil classes
11 A and B according to Eurocode 8)  were selected in this study. The selected records (Table
12 6), which were retrieved from the SHARE database , represent ground motions from
13 earthquakes with moment magnitudes Mw, varying between 5 and 7.62, recoded at epicentral
14 distances, R, between 3.4 and 71.4 km . The shear wave velocity of first 30 m depth, Vs,30,
15 of the recordings locations, ranges between 650 m/s and 2020 m/s. The peak ground
16 acceleration PGA of the selected records varies between 0.065 g to 0.91 g. The peak ground
17 velocity PGV ranges between 0.031 m/s to 0.785 m/s, while the Arias Intensity Ia, ranges from
18 0.015 m/s and 10.97 m/s. Scatter plots of the Mw-ln(R), PGA-PGV and PGA-Ia relations for the
19 selected records are provided in Fig. 8. It is noted that no existing selection techniques that
20 employ spectra for the selection of ground motions [e.g. as in 55-58] were used herein. This
21 was done on the ground that the response of the extended buried pipelines is highly distinct
22 compared to that of above ground structures (e.g. [59-60]), for which the ‘target’ spectra are
23 actually defined. The selection is further strengthened by the fact that buried pipelines do not
24 have an individual period of vibration, to which a spectrum could be conditioned.
1Table 6. Selected ground motion records.
N Miyagi Prefecture
Mid Niigata Prefecture
Pinyon Flat Observatory
Ca: San Luis Obispo; Rec Center
Athens 4 (Kipseli District)
Koroni-Town Hall (Library)
L Aquila Mainshock
L Aquila - V. Aterno - Colle Grilli
Lake Hughes #12
Gilroy Array #1
Gilroy Array #6
Gilroy Array #6
Gilroy Array #6
Ucsc Lick Observatory
La - Griffith Park Observatory
Pacoima Dam (Downstr)
Mt Wilson - Cit Seis Sta
Ldeo Station No. C1058 Bv
2Fig. 8 Distribution of main parameters of selected ground motion records.
43. Selection of seismic intensity measures
5A variety of seismic IMs has been employed in the existing literature to describe seismic
6intensity in empirical fragility functions for the structural assessment of buried pipelines [61-
762], including the Modified Mercalli Intensity MMI [63-67], the peak ground acceleration PGA
8[68-70], the peak ground velocity PGV [6-7,38,67,71-79], the peak ground strain (εg)
9[11,77,79], as well as PGV2/PGA . The efficiency of Arias intensity Ia, spectral
10 acceleration SA and spectral intensity SI, in predicting the damage of buried pipelines under
11 transient ground deformations was also examined in previous studies [67, 81]. The limited
12 available analytical fragility curves for buried steel NG pipelines make use of PGA and PGV as
13 seismic IMs [82-83]. From the above seismic IMs, PGV and εg, are those that are directly
14 related to the main loading condition, which is responsible for the induced damage on buried
15 pipelines caused by seismically-induced transient ground deformations.
16 Shakib and Jahangiri  examined the efficiency and sufficiency of various seismic IMs for
17 buried steel NG pipelines, employing a numerical parametric study on selected pipe-soil
18 configurations. In addition to the above seismic IMs (e.g. PGA, PGV, PGV2/PGA, Ia), a set of
19 new measures was also examined, including the peak ground displacement, PGD, the root
20 mean square acceleration, velocity and displacement, RMSa, RMSv, RMSd, PGD2/RMSd, the
21 cumulative absolute velocity, CAV, the sustained maximum acceleration and velocity, SMA,
22 SMV and a series of spectral IMs. The researchers proposed spectral seismic IMs as optimal
23 ones for some of the examined pipe-soil configurations. However, to the authors’ view, the use
24 of spectral seismic IMs for embedded structures, such as buried pipelines, might be highly
25 debatable, when considering the kinematic loading, which is imposed by the surrounding
26 ground on the embedded pipeline under ground shaking and is prevailing over the pipeline’s
27 inertial response [5, 59-60]. Actually, buried structures (including pipelines) exhibit a highly
28 distinct seismic response compared to that of single degree of freedom oscillators (SDOF), for
29 which the response spectra and the relevant spectral seismic IMs are defined. This perspective
30 comes in line with the poor correlations between spectral seismic IMs, i.e. spectral acceleration
31 and spectrum intensity, and observed damage on water-supply and steel NG pipelines during
32 past earthquakes [67, 81]. Based on the above observations, no spectral seismic IMs were
33 examined herein.
1Table 7 summarizes the tested seismic IMs. The selected IMs have been widely used in
2previous studies, e.g. for the development of empirical fragility functions or analytical fragility
3relations, while most of them may be evaluated easily. Hazard maps and hazard curves are
4readily available in terms of PGA or PGV, while other seismic IMs, such as Arias intensity Ia
5require more effort to be evaluated. Along these lines, PGA or PGV might be more desirable
6, particularly in the framework of a rapid post-seismic assessment of an extended NG
7network and management of the post-seismic risk. The peak longitudinal ground strain εg was
8not examined herein, due to the nature of the soil response analyses that were carried out
9within this study (i.e. 1D soil response analyses). Despite the direct correlation of longitudinal
10 ground strain with pipeline axial response, its rigorous computation or even its evaluation in a
11 simplified fashion via PGV and wave propagation velocity C of the site (i.e. εg = PGV/C) may
12 be cumbersome , particularly in the presence of strong soil heterogeneities along the
13 pipeline axis, like in the cases examined herein. The selected seismic IMs refer to either
14 outcrop conditions or ground surface conditions. For the latter cases, two computation
15 approaches were examined since multiple values of the seismic IMs are available near the
16 geotechnical discontinuity of the examined soil deposits, i.e. those computed at the ground
17 surface above subdeposit 1 and those computed at the ground surface above subdeposit 2 (Fig.
18 1). In particular, the seismic IMs at the ground surface refer to either the maximum value of the
19 peak values computed at the surface adjacent subdeposits, or to the mean value of the peak
20 values predicted at the adjacent subdeposits (see Table 7).
22 Table 7 Examined Intensity Measures.
Peak ground acceleration
PGA a t
Peak ground velocity
PGV v t
Peak ground velocity
PGD d t
Ia a t dt
Peak ground acceleration
1 ,1 ,2
max max , max
PGA a t a t
Peak ground acceleration
2 ,1 ,2
PGA avg a t a t
Peak ground velocity
1 ,1 ,2
max max , max
PGV v t v t
Peak ground acceleration
2 ,1 ,2
PGV avg v t v t
Peak ground acceleration
1 ,1 ,2
max max , max
PGD d t d t
Peak ground acceleration
2 ,1 ,2
max , max
PGD avg d t d t
2 2 2
max max , max
PGV PGA PGV PGA PGV PGA
2 2 2
max , max
PGV PGA avg PGV PGA PGV PGA
14. Intensity measure testing
24.1 Efficiency of tested seismic IMs
3To test the efficiency of the selected seismic IMs, regression analyses of the EDP, i.e. the
4numerically predicted maximum compression strain ε of the examined pipelines at the critical
5middle section, relative to each seismic IM were carried out. A power model was initially
6employed to describe the relationship between the pipe compression strain ε and the tested
7seismic IM :
EDP a IM
9where and are coefficients defined by the regression analysis. The above relation may be
10 rearranged in a linear regression analysis of the natural logarithm of the EPD relative to the
11 natural logarithm of the tested seismic IM, as follows:
ln EPD b ln IM a
13 where is the standard normal variant with zero mean and unit standard deviation and is a
14 dispersion parameter, describing the conditional standard deviation of the regression. The latter
15 is defined in natural logarithm units and constitutes a metric of the efficiency of the tested
16 seismic IM with respect to the EPD. Lower values mean reduced dispersion around the
17 estimated median of the results, which in other words means a more efficient seismic IM. A
18 representative example of a regression analysis of the EPD versus PGV1 is presented in Fig. 9,
19 referring to a D = 914.4 mm ‘perfect’ pipeline pressurized at p = 8 MPa and embedded in
20 trench TA. The examined soil-pipe system is assumed to be located over the examined pairs of
21 soil subdeposits (see Section 2.1), while the ground depth H is equal to 60 m.
23 Fig. 9 Regression analysis of the natural logarithm of the maximum compression strain ε of the pipeline
24 (computed at the critical middle section) relative to the natural logarithm of the PGV1 at ground surface
25 (results for a D = 914.4 mm ‘perfect’ pipeline embedded in trench TA in soil deposits with H = 60 m).
27 Fig. 10 summarizes representative regression analyses of the maximum pipeline compression
28 strain, ε, relative to various seismic IMs, tested herein. The regressions refer to a X60 D =
29 914.4 mm ‘perfect’ pipeline, pressurized at p = 8 MPa and embedded in trench TA in soil
30 deposits with depth H = 30 m. The seismic IMs, referring to ground surface conditions, are
31 computed as the maximum value of the peak values of the measures computed at the adjacent
32 subdeposits, i.e. IMs1, according to Table 7. It is noted that the regressions were conducted in
33 the log-log space; however, both the compression strains and the seismic IMs are displayed in
34 their actual units in Fig. 10. Similar regressions are provided in Fig. 11, referring to the same
1pipeline, embedded this time in trench TB in soil deposits with depth H = 30 m. In both cases,
2the lowest standard deviations are reported for the peak ground velocity at the ground
3surface, PGV1 (i.e. σ = 0.52 and 0.66 for pipelines embedded in trench TA and TB,
4respectively), implying that this seismic IM is the most efficient one, compared to other tested
5measures. This observation is in line with the theoretically expected superiority of PGV over
6the other seismic IMs tested herein. As stated above, PGV is related directly with the ground
7strains that are imposed along buried pipelines during ground shaking and constitute the main
8loading mechanism of this infrastructure under this loading condition. A reduced standard
9deviation (compared to the other seismic IMs) is also reported for PGV2/PGA1, i.e. σ = 0.55
10 and 0.72 for pipeline in trench TA and TB, respectively). The most inefficient seismic IMs for
11 the examined soil-pipe configurations are found to be PGA1 (σ = 0.64), when the pipeline is
12 embedded in trench TA and PGVr (σ = 1.07), when the pipeline is embedded in trench TB.
13 Interestingly, higher standard deviations σ are computed when the pipeline is embedded in the
14 trench TB. It is recalled that in this case, a denser backfill material and a higher friction
15 coefficient for the backfill-pipe interface are considered. For a given ground deformation
16 pattern, the above conditions will lead to the higher shear stresses along the perimeter of the
17 pipeline, compared to the shear stresses developed along the pipeline, when this is embedded
18 in a looser backfill with reduced friction at soil-pipeline interface (i.e. trench TA). The higher
19 shear stresses along the perimeter of the pipeline will result in its higher axial loading of, thus
20 increasing the potential of its yielding or buckling failure. The higher nonlinear axial response
21 of the pipeline increases the scatter of the numerically predicted pipe strain ε for a given value
22 of the seismic IMs, finally leading to higher σ values, as observed in the regression analyses of
23 Fig. 11.
2Fig. 10 Regression analyses for testing the efficiency of various seismic IMs, referring to outcrop
3conditions or ground surface conditions (results for a X60 D = 914.4 mm ‘perfect’ pipeline, pressurized
4at p = 8 MPa and embedded in trench TA in soil deposits of depth H = 30 m; ε: compression axial strain
5computed at the critical middle section of the pipeline).
2Fig. 11 Regression analyses for testing the efficiency of various seismic IMs, referring to outcrop
3conditions or ground surface conditions (results for a X60 D = 914.4 mm ‘perfect’ pipeline, pressurized
4at p = 8 MPa and embedded in trench TB in soil deposits of depth H = 30 m; ε: compression axial strain
5computed at the critical middle section of the pipeline).
7Figs. 12-14 compare the standard deviations computed for all tested seismic IMs in all
8examined cases. Through the comparisons, the effects of salient parameters controlling the
9axial response of the buried steel pipelines, on the computed σ values are reported.
10 Fig. 12a summarizes standard deviations computed for D = 914.4 mm pipelines, embedded
11 at a burial depth h = 1.0 in trench TA in diverse soil deposits with depth H = 30 m. The
12 comparisons highlight the effects of steel grade and internal pressure of the pipeline, as well as
13 of imperfections of the walls of the pipeline on the computed standard deviations . In this
14 context, the standard deviations are plotted for X60, X65, X70 ‘perfect’ (i.e. w/t = 0) or
15 imperfect (i.e. w/t = 0.1) pipelines, pressurized at various levels of internal pressure (i.e. p = 0,
16 4 or 8 MPa). The standard deviations computed for all tested seismic IMs are generally
1increasing with decreasing steel grade, i.e. higher values are reported for X60-grade
2pipelines compared to those calculated for X65- or X70-grade pipelines. Similarly, higher
3standard deviations are reported for the imperfect pipelines (i.e. w/t = 0.1) compared to the
4equivalent ‘perfect’ ones (i.e. w/t = 0). Moreover, in case of imperfect pipelines (i.e. w/t = 0.1)
5it is found that the increase of the internal pressure of the pipeline leads to an increase of the
6standard deviations . The latter observation is found to be invalid for perfect pipelines (i.e.
7w/t = 0), as higher standard deviations are reported for non-pressurized pipelines (p = 0
8MPa) compared to those calculated for pipeline pressurized at p = 4 MPa. The above
9observations should be attributed to the effect of the examined parameters (i.e. pressure level,
10 pipeline wall imperfections and steel grade) on the axial response of the pipeline under
11 seismically-induced ground deformations. For a given soil-pipeline configuration subjected to
12 a given seismic ground deformation pattern, the reduction of the steel grade of the pipeline will
13 lead to an increased nonlinear axial response of the pipeline, which will finally result in the
14 higher standard deviations , reported for lower steel grade pipelines in Fig. 12a. The
15 existence of wall imperfections on the pipeline is again expected to lead in a higher nonlinear
16 axial response of the pipeline, compared to that of an equivalent ‘perfect’ pipeline-soil system
17 subjected to the same ground deformation pattern [44, 47-48]. This may explain the higher
18 values reported for imperfect pipelines (i.e. w/t = 0.1), compared to those reported for
19 equivalent ‘perfect’ pipelines (i.e. w/t = 0).
20 Previous studies [44-48] have demonstrated that pressurization of steel pipelines leads to initial
21 circumferential tensile stresses, which interact with the axial straining of the pipeline, caused
22 by the seismically-induced ground deformation. In particular, the increase of the internal
23 pressure level of the pipeline tends to lower the axial load-displacement path, leading faster to
24 yielding or instability phenomena. In other words, for a given soil-pipeline configuration
25 subjected to a given seismic ground deformation pattern, the increasing pressurization of the
26 pipeline is expected to lead to an increasing nonlinear axial response of the pipeline under the
27 induced ground deformation, which subsequently will lead to a higher scatter of the pipeline
28 strain ε against the tested seismic IMs. This is confirmed in Fig. 13a since higher σ values are
29 indeed computed for pipelines pressurized at p = 8 MPa, compared to those predicted for p = 0
30 or 4 MPa.
31 Regardless of the effects of the above parameters on the computed σ values, the lowest
32 standard deviations are reported for PGV1, followed by PGV2 and PGVr. PGV2/PGA1 and
33 PGV2/PGA2 are also found to give relatively low σ values. On the contrary the highest standard
34 deviations are reported for PGA2 followed by PGA1 and PGAr. Iar and PGD1, PGD2 and PGDr
35 are found to be rather inefficient IMs as compared to the PGV metrics.
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2Fig. 12 Comparisons of standard deviations computed for D = 914.4mm pipelines through
3regression analyses of the axial compression strain ε of pipelines relative to tested seismic IMs. (a)
4Effects of internal pressure p and pipeline wall imperfections (w/t) on values. (b) Effect of trench
1backfill properties and soil-pipe interface characteristics on values. (c, d) Effect of soil deposit depth
2H on values.
4Fig. 12b elaborates on the effects of backfill properties and backfill-pipeline interface friction
5characteristics on the standard deviations , estimated for all tested seismic IMs, by
6comparing values computed for X60, X65 or X70 D = 914.4 mm pipelines, embedded at a
7burial depth h = 1.0 in either trench TA or TB. The comparisons are provided for soil deposits
8with depth H = 30 m and refer to both ‘perfect’ (i.e. w/t = 0) and imperfect pipelines (i.e. w/t =
90.1), pressurized at a pressure level p = 8 MPa. Higher σ values are clearly observed for the
10 cases where the pipelines are embedded in trench TB, where a higher compaction level of the
11 backfill and a higher backfill-pipe interface friction coefficient are considered. These
12 observations, which are related to the increased axial response of the pipelines when embedded
13 in trench TB, are in line with the observations made above (i.e. by comparing the regression
14 analyses in Figs. 10 and 11). Regardless of the trench properties and the soil-pipeline interface
15 characteristics, PGV1 exhibits again the lowest standard deviations in all examined cases,
16 whereas the highest standard deviations are reported for PGA2. Similar conclusions are drawn
17 when the examined pipelines (i.e. X60, X65 or X70 D = 914.4 mm ‘perfect’ or imperfect
18 pipelines) are embedded in soil deposits with higher depths, i.e. H = 60 m (i.e. Fig. 12c) or H =
19 120 m (i.e. Fig. 12d). In both cases PGV1 exhibits the lowest standard deviations, whereas the
20 highest standard deviations are reported for PGA2. It is worth noticing the increasing σ values
21 that are reported for all tested seismic IMs with increasing depth, H, of the soil deposits. The
22 latter observation should be attributed to the higher differential ground response of deeper
23 adjacent subdeposits, under a given seismic excitation at bedrock. The higher differential
24 ground response of the adjacent subdeposits is expected to induce a higher axial straining on
25 the pipeline, thus increasing the potential of a more ‘nonlinear’ response of the pipeline, which
26 results in the higher standard deviation values in the relevant comparisons.
27 Fig. 13 examines the effect of burial depth of the pipeline on the standard deviations σ
28 computed for all tested seismic IMs, by comparing the relevant σ values computed for X60 D =
29 914.4 mm pipelines embedded at depths h = 1.0 m or 2.0 m in trench TA in soil deposits with
30 depth H = 60 m. The relevant comparisons refer to both ‘perfect’ (i.e. w/t = 0) and ‘imperfect’
31 (i.e. w/t =0 .1) pipelines, pressurized at a pressure level p = 8 MPa. Higher standard deviations
32 are computed for the shallow-embedded pipelines (i.e. for h = 1.0 m) compared to the
33 equivalent pipelines embedded at h = 2.0 m. This observation should be attributed to the
34 increased ground response of the soil subdeposits towards ground surface, which yields in a
35 higher relative axial ground deformation along the pipeline axis, therefore triggering a higher
36 nonlinear axial response of shallower pipelines compared to the equivalent deeper pipelines. In
37 line with the previous results, higher σ values are reported for all tested seismic IMs in case of
38 imperfect pipelines (i.e. w/t = 0.1). Irrespectively of the pipeline’s burial depth, PGV1 exhibits
39 the lowest σ values, while the highest values are reported for PGA2 and PGA1.
2Fig. 13 Effect of burial depth, h, of the pipeline on standard deviations computed through regression
3analyses of the axial compression strain ε of pipeline, relative to tested seismic IMs. Results for X60 D
4= 914.4 mm pipelines embedded in trench TA in soil subdeposits with depth H = 60 m.
6Fig. 14a summarizes the standard deviations σ computed for all tested seismic IMs in case of D
7= 406.4 mm pipelines. More specifically, the presented σ values refer to X60, X65 and X70
8perfect (w/t =0) and imperfect (w/t=0.1) pipelines, pressurized at a pressure level p = 8 MPa
9and embedded in trench TA or TB in diverse soil deposits with depth H = 60 m. Similar to the
10 previous results, higher standard deviations are computed for imperfect pipelines (w/t =0.1)
11 embedded in trench TB. Additionally, higher σ values are reported for lower steel grade
12 pipelines compared to those predicted for equivalent higher steel grade pipelines; however, the
13 differences between the σ values computed for various steel grade pipelines are found reduced
14 as compared to the D =914.4 mm pipelines. Similar observations and conclusions are made for
15 D = 1219.2 mm pipelines examined in this study (Fig. 14b). Regardless of the geometrical
16 properties of the examined pipelines, PGV1, reveals the lowest standard deviations , for all
17 examined cases.
18 Summarizing, the lowest standard deviations are reported for PGV1 for all examined soil-pipe
19 configurations. Hence, this seismic IM is considered the most efficient from the tested ones. On
20 the contrary, PGA-based measures at top of ground surface (i.e. PGA1, PGA2) are found to be
21 the most inefficient ones, as they exhibit the highest standard deviations for all examined
22 configurations. The above observations are valid, irrespectively of the diameter and wall
23 thickness of the pipeline. However, lower dispersion values are generally identified for the D =
24 1219.2 mm pipelines with the thicker walls (i.e. R/t = 31.9).
2Fig. 14 Comparisons of standard deviations computed for D = 406.4mm (a) and D = 1219.2 mm (b)
3pipelines through regression analyses of the axial compression strain ε of pipelines relative to tested
64.2 Sufficiency of tested seismic IMs
7As stated above, a sufficient seismic IM is conditionally independent of the seismological
8characteristics, such as the magnitude (M) and the epicentral distance (R) . To determine
9the sufficiency of the tested seismic IMs, regression analyses were performed on the residuals
10 of the compression axial strain ε of the pipeline (referring at the middle critical section of the
11 pipeline), relative to the magnitude and the epicentral distance of the selected seismic records
12 (i.e. ). The residuals were defined as the differences between the numerically
13 computed maximum pipeline axial strains and the strains computed by the regression fit line,
14 the latter defined by the regression analysis on the maximum axial strain ε relative to the tested
15 seismic IM (i.e. regression analysis conducted in the framework of identifying the efficiency of
16 the tested IM, e.g. Fig. 9). The sufficiency was quantified by extracting the relevant p-values
17 from the regressions of relative to the seismological characteristics of the selected
18 ground motions, i.e. M and R. Fig. 15 illustrates examples of such regression analyses,
19 referring to X60 D = 914.4 mm ‘perfect’ pipelines embedded at a burial depth h =1.0 m in
20 trench TA in soil deposits with depth H = 30 m. The analyses were conducted for the selected
1ground motions to examine the sufficiency of PGV1. Sufficient seismic IMs should generally
2lead to high p-values. A cut-off p-value of 0.05 was set here to differentiate between sufficient
3and insufficient seismic IMs (Luco & Cornell 2007) .
6Fig. 15 Representative regression analyses of relative to magnitudes (M) and epicentral
7distances (ln(R)) of selected ground motions, aiming at evaluating the sufficiency of PGV1. Results for
8X60 D = 914.4 mm ‘perfect’ pipelines, embedded in trench TA in soil deposits with depth H = 30 m
9and pressurized at p = 8 MPa.
11 Figs. 16-18 summarize the p-values computed for all tested seismic IMs in all examined cases,
12 based on regression analyses of the residuals of the compression axial strain ε of the pipeline (
13 ) relative to the magnitude of the selected seismic records. In particular, Fig. 16a
14 summarizes p-values computed for D = 914.4 mm pipelines, embedded at a burial depth h =
15 1.0 in trench TA in diverse soil deposits with depth H = 30 m. The comparisons aim at
16 highlighting the effects of steel grade and internal pressure of the pipeline, as well as of
17 imperfections of the walls of the pipeline on the computed p-values. No clear trends can be
18 identified regarding the effects of pipeline internal pressure on the p-values. However, slightly
19 higher p-values (up to 5%) are computed for most of tested seismic IMs and examined
20 configurations with decreasing internal pressure of the pipeline. The same trend, i.e. increased
21 p-values, is observed with increasing steel grade of the pipeline, while a slight decrease of p-
22 values is observed for imperfect pipelines (i.e. w/t =0.1) compared to ‘perfect’ equivalent ones
23 (i.e. w/t = 0). Irrespectively of the steel grade, internal pressure and shape of the walls of the
24 pipeline, it can be clearly seen that PGV1 exhibits the highest p-values compared to the other
25 tested seismic IMs. Relatively high values are reported for the PGV2 and PGVr, while PGDr,
26 IAr, PGD1, PGD2, PGV2/PGA1 and PGV2/PGA1 are found to pass the threshold limit of 0.05 for
27 the p-value, in most of examined cases. On the contrary, the p-values computed for PGA1,
28 PGA2 and PGAr are in most of examined cases lower than the threshold (i.e. 0.05), indicating
29 that these measures are insufficient IMs for the examined systems.
30 Fig. 16b-d aim at highlighting the effects of soil deposit depth, H, backfill properties and
31 backfill-pipeline interface friction characteristics on the computed p-values, estimated again
32 via regression analyses of the residuals of the compression axial strain ε of the pipeline (
33 ) relative to the magnitudes of the selected seismic records. The results refer to X60,
1X65 or X70 D = 914.4 mm ‘perfect’ (i.e. w/t = 0) and imperfect pipelines (i.e. w/t = 0.1)
2pipelines, embedded at a burial depth h = 1.0 in either trench TA or TB in soil deposits of
3depth H = 30 m (Fig. 16b), H = 60 m (Fig. 16c) and H = 120 m (Fig. 16d). All examined
4pipelines are pressurized at a pressure level p = 8 MPa. In most of examined cases, higher p-
5values are reported for ‘perfect’ pipelines (i.e. w/t = 0), which generally exhibit a more ‘elastic’
6axial response for a given ground deformation compared to the equivalent imperfect pipelines
7(i.e. w/t = 0.1). Similarly, higher p-values are reported for pipelines embedded in trench TA,
8compared to equivalent pipelines embedded in trench TB. Regardless of the effects of the
9above parameters, the highest p-values are reported for PGV1 followed by PGV2. On the
10 contrary the lowest values are found for PGA1 and PGA2.
11 Fig. 17 compares p-values computed for X60 D = 914.4 mm ‘perfect’ (i.e. w/t = 0) and
12 ‘imperfect’ (i.e. w/t = 0.1) pipelines embedded at diverse burial depths (i.e. h = 1.0 m or 2.0 m)
13 in trench TA in soil deposits with depth H = 60 m. The pipelines are pressurized at a pressure
14 level p = 8 MPa. The higher embedment of the pipeline seems to lead in higher p-values for
15 some of the tested seismic IMs (i.e. PGAr, PGA1, PGA2), compared to those computed for the
16 equivalent pipelines that are embedded in shallower depth (i.e. h = 1.0 m). However, for other
17 measures, a higher embedment lead to either comparable or reduced p-values, compared to
18 those referring to shallower equivalent pipelines (e.g. PGV1, PGV2, PGD1, PGD2 etc).
19 Regardless of the above deviations, PGV1 is again found to provide the highest p-values.
20 Fig. 18a compares p-values computed for all tested seismic IMs, in case of the D = 406.4 mm
21 pipelines examined herein. The p-values refer to perfect (w/t = 0) and imperfect (w/t = 0.1)
22 pipelines, embedded in trench TA or TB in soil deposits with depth H = 60 m and pressurized
23 at a pressure level p = 8 MPa. No clear trends may be identified in these cases, regarding the
24 effects of backfill properties, backfill-pipe interface characteristics, steel grade of the pipeline
25 and imperfections of the pipeline walls, on the computed p-values. However, higher p-values
26 are reported for PGV-based IMs (i.e. PGV1, PGV2, PGVr), while the lowest values are again
27 reported for PGA-based IMs (i.e. PGA1, PGA2). The same observations are made by comparing
28 the p-values computed for all tested seismic IMs in case of the D = 1219.2 mm pipelines,
29 examined herein (Fig. 18b).
2Fig. 16 Comparisons of p-values computed for all tested seismic IMs through regression analyses of
3relative to magnitudes (M) of the selected ground motions. (a) Effects of internal pressure p
1and pipeline wall imperfections (w/t) on p-values. (b) Effects of trench properties and soil-pipe interface
2characteristics on p-values. (c, d) Effect of soil deposit depth H on p-values (results for D = 914.4mm
5Fig. 17 Effect of burial depth h of the pipeline on p-values computed through regression analyses of
6relative to magnitudes (M) of the selected ground motions. Results for X60 D = 914.4 mm
7pipelines embedded in trench TA in soil deposits with depth H = 60 m.
9Fig. 18 Comparisons of p-values computed for (a) D = 406.4 mm and (b) D = 1219.2 mm pipelines
10 through regression analyses of relative to magnitudes (M) of selected ground motions.
1Figs. 19-21 summarize comparisons of p-values, computed for all tested seismic IMs in all
2examined cases, based on regression analyses of the residuals of the compression axial strain ε
3of the pipeline ( ) relative to the epicentral distance of the selected seismic records.
4More specifically, Fig. 19a summarizes p-values referring to X60, X65 or X70 D = 914.4 mm
5‘perfect’ (i.e. w/t =0) or imperfect (i.e. w/t =0.1) pipelines, pressurized at various levels of
6pressure (p = 0, 4, 8 MPa) and embedded at a burial depth h = 1.0 in trench TA in soil deposits
7with depth H = 30 m. Generally, lower p-values are computed here, compared to those
8predicted from regression analyses of the residuals of the compression axial strain ε of the
9pipeline ( ) relative to the magnitudes of the selected seismic records. Additionally, in
10 most of examined cases the computed p-values are found to be lower than the threshold of
11 0.05, indicating insufficiency of the tested IMs. However, the computed p-values for PGV1 and
12 PGV2 are always slightly higher or higher than 0.05. Similar observations are made by
13 comparing the computed p-values for all tested seismic IMs, in cases where the examined
14 pipelines (D = 914.4 mm ‘perfect’ or imperfect pipelines) are embedded at a burial depth h =
15 1.0 in either trench TA or TB in soil deposits of depth H = 30 m (Fig. 19b), H = 60 m (Fig.
16 19c) and H = 120 m (Fig. 19d). The highest p-values are reported for PGV1 followed by PGV2.
17 On the contrary the lowest values are found for PGAr. PGV1 reveals the highest p-value
18 compared to other tested seismic IMs, even when the examined D = 914.4 mm pipeline is
19 embedded deeper (i.e. at h = 2.0 m) (Fig. 20).
20 Fig. 21a compares p-values computed for all tested seismic IMs, based on regression analyses
21 of the residuals of the compression axial strain ε of the pipeline ( ) relative to the
22 epicentral distance of the selected seismic records, in case of X60, X65 and X70 D = 406.4 mm
23 pipelines. The results refer to both perfect (w/t = 0) and imperfect (w/t = 0.1) pipelines,
24 pressurized at a pressure level p = 8 MPa and embedded in trench TA or TB in diverse soil
25 deposits with depth H = 60 m. The trends regarding the effects of backfill properties, backfill-
26 pipe interface characteristics, steel grade of the pipeline and imperfections of the pipeline
27 walls, on the computed p-values are again not clear in these cases. Higher p-values are reported
28 for PGV1, PGV2 and PGVr. On the contrary, the lowest values are again reported for PGA-
29 based measures. The same observations are made by comparing the p-values computed for all
30 tested seismic IMs, in case of the D = 1219.2 mm pipelines examined herein (Fig. 21b).
31 Based on the discussion made above, PGV1 is found to satisfy the sufficiency criterion in a
32 mathematically rigorous way.
2Fig. 19 Comparisons of p-values computed for all tested seismic IMs through regression analyses of
3relative to epicentral distances (ln(R)) of the selected ground motions. (a) Effects of internal
4pressure p and pipeline wall imperfections (w/t) on p-values. (b) Effects of trench properties and soil-
1pipe interface characteristics on p-values, (c, d) Effect of soil deposit depth H on p-values (results for D
2= 914.4 mm pipelines).
4Fig. 20 Effect of burial depth, h, of the pipeline on p-values computed through regression analyses of
5relative to epicentral distances (ln(R)) of the selected ground motions. Results for X60 D =
6914.4 mm pipelines embedded in trench TA in soil subdeposits with depth H = 60 m.
8Fig. 21 Comparisons of p-values computed for (a) D = 406.4 mm and (b) D = 1219.2 mm pipelines
9based on regression analyses of relative to epicentral distances (ln(R)) of the selected ground
3This study examined the efficiency and sufficiency of various seismic IMs for the structural
4assessment of buried steel natural gas (NG) pipelines subjected to axial compression strains,
5the latter developed as a result of seismically-induced differential ground movement near
6geotechnical discontinuities. A de-coupled numerical framework was developed for this
7purpose, including a 3D soil-pipe numerical model, to rigorously evaluate the pipeline axial
8response, accounting for the soil-pipe interaction phenomena, and 1D soil response analyses
9that were used to determine critical ground deformation patterns at the geotechnical
10 discontinuity caused by ground shaking. A comprehensive numerical parametric study was
11 performed for an ensemble of seismic records, considering critical parameters that control the
12 axial response of buried steel NG pipelines, such as the dimensions of the pipeline, the
13 pressurization level of the pipeline, the initial geometric imperfections of the pipeline walls, the
14 backfill and soil properties and the backfill-pipeline interface characteristics. The peak
15 compression strain of the pipeline, ε, computed at the location of the assumed geotechnical
16 discontinuity, was used as EDP to quantify the efficiency and sufficiency of the selected
17 seismic IMs on the basis of regression analyses of this parameter, relative to the tested IMs.
18 The main conclusions of the study are summarized in the following:
19 The regression analyses of the peak compression strain of the pipeline, ε, relative to the
20 peak ground velocity PGV, computed at ground surface as the maximum value of the peaks
21 of the adjacent soil subdeposits, i.e. PGV1, revealed the lowest standard deviations ,
22 regardless of the ground characteristics and pipeline dimensions. On the contrary, the
23 regression analyses of the peak compression strain of the pipeline ε relative to PGA-based
24 IMs revealed the highest standard deviations . Additionally, the regression analyses of the
25 peak compression strain of the pipeline, ε, relative to PGD and PGV2/PGA revealed higher
26 standard deviations , compared to the relevant regression analyses relative to PGV.
27 Therefore, PGV1 found to be the most efficient intensity measure for the structural
28 assessment of buried steel NG pipelines, crossing similar sites, when subjected to
29 seismically-induced axial ground deformations.
30 The regression analyses of the residuals relative to the magnitude (M) and the
31 epicentral distance (ln(R)) of the selected records, revealed the highest p-values for peak
32 ground velocity PGV computed at ground surface as the maximum value of the peaks of
33 the adjacent soil subdeposits, i.e. PGV1. This observation indicates that this IM satisfies the
34 sufficiency criterion in a mathematically rigorous way. On the contrary, PGA-based IMs
35 where found to be the most inefficient ones.
36 Summarizing, PGV1 was found to be the optimum seismic IM for the structural assessment of
37 buried steel NG pipelines, crossing similar sites, when subjected to seismically-induced axial
38 ground deformations. This observation is in line with the theoretically expected superiority of
39 PGV. Indeed, PGV, is directly associated with the longitudinal ground strains, which constitute
40 the main loading mechanism of this infrastructure during ground shaking. This study
1constitutes the first comprehensive numerical effort towards proving superiority of PGV as
2optimal seismic IM for the assessment of buried NG pipelines.
4This work was supported by the Horizon 2020 Programme of the European Commission under
5the MSCA-RISE-2015-691213-EXCHANGE-Risk grant (Experimental and Computational
6Hybrid Assessment of NG Pipelines Exposed to Seismic Hazard, www.exchange-risk.eu). This
7support is gratefully acknowledged.
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Conflict of Interest
The Authors declare that there is no conflict of interest regarding the manuscript titled:
Optimum intensity measures for buried steel natural gas pipelines subjected to seismically-
induced axial compression at geotechnical discontinuities’, submitted for evaluation and
potential publication in Soil Dynamics and Earthquake Engineering Journal.
Author’s name Affiliation
Dr Grigorios Tsinidis Vienna Consulting Engineers ZT GmbH, Austria
Dr Luigi Di Sarno University of Liverpool, UK
Prof. Anastasios Sextos University of Bristol, United Kingdom
Mr. Peter Furtner Vienna Consulting Engineers ZT GmbH, Austria
Authorship Conformation Form
Manuscript title: ‘Optimum intensity measures for buried steel natural gas pipelines subjected
to seismically-induced axial compression at geotechnical discontinuities’
All authors have participated in drafting of the article and approved its final version.
This manuscript has not been submitted to, nor is under review at, another journal or other
Author’s name Affiliation
Dr Grigorios Tsinidis Vienna Consulting Engineers ZT GmbH, Austria
Dr Luigi Di Sarno University of Liverpool, UK
Prof. Anastasios Sextos University of Bristol, United Kingdom
Mr. Peter Furtner Vienna Consulting Engineers ZT GmbH, Austria