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1Optimal intensity measures for the structural assessment of buried

2steel natural gas pipelines due to seismically-induced axial

3compression at geotechnical discontinuities

4

5

6Grigorios Tsinidis1, Luigi Di Sarno2, Anastasios Sextos3, and Peter Furtner4

7

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

12

13 Corresponding Author: Dr Grigorios Tsinidis, VCE Vienna Consulting Engineers ZT GmbH,

14 Untere Viaduktgasse 2, 1030, Vienna, email: tsinidis.grigorios@gmail.com

15

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

34 infrastructure.

35

36 Keywords: Natural gas pipelines; intensity measures; efficiency; sufficiency; steel pipelines;

37 local buckling

38

39

40

41

42

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11. Introduction

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 [5]. 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) [5]. 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 [24]. 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 [26].

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

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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) [26]. 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 [27]. 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 [28]. 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

15 [28-29].

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 [37], 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

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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].

3

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.

18

19

h

Pipeline & surficial soil layer

Subdeposit 1

uA

uB

ur

H

Subdeposit 2

Elastic bedrock

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).

23

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) [38], 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

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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.

10

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).

Country

Operator

Nominal diameter range, D (mm, ΄)

Operational pressure

range, p (MPa)

Austria

TAG

914.4 mm to 1066.8 mm (36’ to 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 mm to 762 mm (20’ to

30’)

n.p.*

Germany

Gasunie

> 1066.8 mm (42’) for the supra-regional

networks; otherwise > 508 mm to 762 mm (20’ to

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 mm to 1219.2 mm (20’ to 48’)

7 - 8

Spain

Enegas

406.4 mm to 812.8 mm (16’ to 32’)

n.p.

Sweden

Swedegas

406.4 mm to 660.4 mm (16’ to 26’)

5 - 8

Switzerland

Transitgas

914.4 mm to 1066.8 mm (36’ to 48’)

7 - 8

13 * n.p. = not provided

14

15 Table 2 Summary of examined cases.

External diameter,

D (’)

External diameter,

D (mm)

Wall thickness,

t (mm)

D/t

Internal

pressure,

p (MPa)

Burial

depth,

h (m)

Depth of soil

sites,

H (m)

Surficial soil-

trench

properties

16’

406.4

9.5

42.8

8

1.0

60

TA, TB

36’

914.4

12.7

72.0

0, 4, 8

1.0, 2.0

30,60,120

TA, TB

48’

1219.2

19.1

63.8

8

1.0

60

TA, TB

16

17 Table 3 Mechanical properties of steel grades used in this study.

Steel 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

18

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

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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 [39]:

12 (1)

0.5

max 2,max

220 'm

G K

13

(b)

(a)

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.

15

16 where is the effective confining stress (in kPa) and is a constant depending on the

'm

2,max

K

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 [40]. 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

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1B - Soil C. The nonlinear response of the selected subdeposits during ground seismic shaking

2was described by means of G-γ-D curves, following [41].

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 [38]. 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.

21

22 Table 4 Relationships between density, relative density, K2,max parameter and cohesionless soil

23 characterization (after [39]).

24

Density, ρ (t/m3)

Relative density, Dr (%)

K2,max

Characterization

1.4

30

30

Loose

1.65

52.5

48

Medium

2

90

70

Fine

25

26 Table 5 Physical and mechanical properties of investigated trenches.

Density, ρ

(t/m3)

Poisson’s ratio,

v

Shear 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

63.1

44

0.78

27

28

29

30

31

32

33

34

35

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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 [25]. 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 [42]. 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. [25], 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.

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1

h

Nonlinear spring with

fixed free-end, u =0

δu

Ground surface

δu

u = 0

Critical area,

dense mesh

Pipeline shell

1

1m

D

3×D

2

uA

uB

1D soil response analyses

ur

ur

Soil nonlinear response

δu

Output:

Critical deformation patterns δue= max (uA-uB)

Seismic IMs at ground surface

3

δue

δu (m)

Step

Step

Step

p

Input:

Selected soil-pipe configurations

Ground displacement pattern δu

Output:

Input:

Selected soil configurations

Selected ground motions

l=20×D

Output:

ε- δu correlations

Pipeline-spring

connection

Constrains

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

8response analyses.

9

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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 [43], 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 [43]. 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 [24]:

35

36 (2)

max

2

max max max max max max

for

+ 2 for

x x

s

x x

s s s s s

EA k

FD

EA m

k m k k k k

37 where:

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1(3)

s

Dk

EA

2(4)

max

D

mEA

3is the backfill-pipe relative axial movement caused by the relative axial ground deformation

x

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

max

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

max

10 axial pull-out tests of the examined pipe from the trench backfill soil, as per [16]. 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. [16] 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 [43], 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 [25]. To select an adequate mesh, the half-

38 wavelength of the examined pipeline sections in the post-elastic range, , is initially

,c p

39 computed as [49]:

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1(5)

, ,c p c el p

E E

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

,c el

4Poisson’s ratio v = 0.3 for the steel grades examined herein, the latter is given as [49]:

5(6)

,1.72

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: [25]. Element lengths, ranging

, ,

0.5

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

,c p

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

17 m.

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.

23 (7)

n

y

a

E

24

25

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).

28

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

-13-

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 [25]. 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

6shell wall.

7

8(8)

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

9

10

Lcrit

2λc

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).

13

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% [50]. 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,

crit

L

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

-14-

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.

18

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 [51]. 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 [41]. An additional

28 viscous damping of 1 % is also introduced in the form of the frequency-dependent Rayleigh

29 type [52], 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.

39

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

-15-

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 [52]. 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 [52]. The computational efficiency of 1D soil response analyses allows for an

19 extended and thorough parametric analysis, such as the one presented herein.

20

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.

-16-

1

(b)

(c)

Trench-soil

Pipe

Pipe-soil interface

(a)

δx

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).

7

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].

31

-17-

1

2

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.

8

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) [40] were selected in this study. The selected records (Table

12 6), which were retrieved from the SHARE database [53], 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 [36]. 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.

25

26

27

28

29

30

-18-

1Table 6. Selected ground motion records.

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

-19-

1

2Fig. 8 Distribution of main parameters of selected ground motion records.

3

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 [80]. 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 [37] 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.

-20-

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[77], 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 [61], 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).

21

22 Table 7 Examined Intensity Measures.

Location

Intensity measure

Outcrop

Peak ground acceleration

max

r r

PGA a t

Outcrop

Peak ground velocity

max

r r

PGV v t

Outcrop

Peak ground velocity

max

r r

PGD d t

Outcrop

Arias intensity

2

0

2

r r

Ia a t dt

g

Ground surface

Peak ground acceleration

1 ,1 ,2

max max , max

soil soil

PGA a t a t

Ground surface

Peak ground acceleration

2 ,1 ,2

max ,max

soil soil

PGA avg a t a t

Ground surface

Peak ground velocity

1 ,1 ,2

max max , max

soil soil

PGV v t v t

Ground surface

Peak ground acceleration

2 ,1 ,2

max ,max

soil soil

PGV avg v t v t

Ground surface

Peak ground acceleration

1 ,1 ,2

max max , max

soil soil

PGD d t d t

Ground surface

Peak ground acceleration

2 ,1 ,2

max , max

soil soil

PGD avg d t d t

Ground surface

2 2 2

1,1 ,2

max max , max

soil soil

PGV PGA PGV PGA PGV PGA

Ground surface

2 2 2

2,1 ,2

max , max

soil soil

PGV PGA avg PGV PGA PGV PGA

23

24

-21-

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 [80]:

8(9)

b

EDP a IM

9where and are coefficients defined by the regression analysis. The above relation may be

a

b

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:

12 (10)

res

ln EPD b ln IM a

13 where is the standard normal variant with zero mean and unit standard deviation and is a

res

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.

22

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).

26

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

-22-

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.

24

-23-

1

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).

-24-

1

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).

6

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

-25-

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.

-26-

1

!" # "

$ " % "

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

-27-

1backfill properties and soil-pipe interface characteristics on values. (c, d) Effect of soil deposit depth

2H on values.

3

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.

40

-28-

1

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.

5

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).

-29-

1

(a)

(b)

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

4seismic IMs.

5

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) [28]. 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

res IM

res IM

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

res IM

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

-30-

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) [28].

4

5

6Fig. 15 Representative regression analyses of relative to magnitudes (M) and epicentral

res IM

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.

10

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

res IM

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,

res IM

-31-

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).

30

-32-

1

(a)

(b)

(c)

(d)

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

res IM

-33-

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

3pipelines).

4

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

res IM

7pipelines embedded in trench TA in soil deposits with depth H = 60 m.

8

(a)

(b)

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.

res IM

-34-

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.

res IM

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

res IM

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

res IM

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.

-35-

1

(a)

(b)

(c)

(d)

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

res IM

4pressure p and pipeline wall imperfections (w/t) on p-values. (b) Effects of trench properties and soil-

-36-

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).

3

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 =

res IM

6914.4 mm pipelines embedded in trench TA in soil subdeposits with depth H = 60 m.

7

(a)

(b)

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

res IM

10 motions.

11

-37-

1

25. Conclusions

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

res IM

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

-38-

1constitutes the first comprehensive numerical effort towards proving superiority of PGV as

2optimal seismic IM for the assessment of buried NG pipelines.

3Acknowledgements

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.

8

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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

publishing venue.

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