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Evidence from past earthquakes suggests that damage inflicted to buried natural gas (NG) pipelines can cause long service disruptions, leading to unpredictably high socioeconomic losses in unprepared communities. In this review paper, we aim to critically revisit recent progress in the demanding field of seismic analysis, design and resilience assessment of buried steel NG pipelines. For this purpose, the existing literature and code provisions are surveyed and discussed while challenges and gaps are identified from a research, industrial and legislative perspective. It is underscored that, in contrast to common belief, transient ground deformations in non-uniform sites are not necessarily negligible and can induce undesirable deformations in the pipe, overlooked in the present standards of practice. It is further highlighted that the current seismic fragility framework is rich in empirical fragility relations but lacks analytical and experimental foundations that would permit the reliable assessment of the different parameters affecting the expected pipe damage rates. Pipeline network resilience is still in a developing stage, thus only few assessment methodologies are available whereas absent is a holistic approach to support informed decision-making towards the necessary mitigation measures. Nevertheless, there is ground for improvement by adapting existing knowledge from research on other types of lifeline networks, such as transportation networks. All above aspects are discussed and directions for future research are provided.
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Safety of buried steel natural gas pipelines under earthquake-
induced ground shaking: a review
Nikolaos K. Psyrras1 and Anastasios G. Sextos2
Abstract. Evidence from past earthquakes suggests that damage inflicted to buried natural gas (NG)
pipelines can cause long service disruptions, leading to unpredictably high socioeconomic losses in
unprepared communities. In this review paper, we aim to critically revisit recent progress in the
demanding field of seismic analysis, design and resilience assessment of buried steel NG pipelines. For
this purpose, the existing literature and code provisions are surveyed and discussed while challenges
and gaps are identified from a research, industrial and legislative perspective. It is underscored that, in
contrast to common belief, transient ground deformations in non-uniform sites are not necessarily
negligible and can induce undesirable deformations in the pipe, overlooked in the present standards of
practice. It is further highlighted that the current seismic fragility framework is rich in empirical fragility
relations but lacks analytical and experimental foundations that would permit the reliable assessment of
the different parameters affecting the expected pipe damage rates. Pipeline network resilience is still in
a developing stage, thus only few assessment methodologies are available whereas absent is a holistic
approach to support informed decision-making towards the necessary mitigation measures.
Nevertheless, there is ground for improvement by adapting existing knowledge from research on other
types of lifeline networks, such as transportation networks. All above aspects are discussed and
directions for future research are provided.
Keywords. Buried pipeline; natural gas; seismic resilience; gas networks; service disruption; seismic
fragility; soil-pipe interaction; structural health monitoring
1 Ph.D. Candidate, Department of Civil Engineering, University of Bristol, United Kingdom
2 Assoc. Professor, Department of Civil Engineering, University of Bristol, United Kingdom
Natural gas (NG) is nowadays a cornerstone in supplying energy to industry and households,
maintaining an important share in the global energy market. A steadily growing dependence of the
global energy demand on NG is reflected in numbers: one quarter of the total energy demand in the US
and the European Union is currently satisfied by NG delivery [1], while it is projected that by 2040
nearly one quarter of the global electricity will be generated by NG [2]. Extensive onshore networks of
buried steel pipelines are the method of choice for inland NG distribution from wells to end-users, with
steel being used almost exclusively for the large-diameter transmission network. For further details on
NG pipeline technology, the interested reader is referred to Folga [3].
However, of the heaviest dependents on NG are earthquake-prone regions, such as California in the
United States, south-eastern Europe (Italy, Greece, Turkey and the Balkans), Japan and New Zealand,
which are all exposed to significant seismic hazard. Experience from past earthquakes has repeatedly
demonstrated that buried pipelines are vulnerable to seismic effects. In line with existing literature, these
seismic effects can be divided into two main groups of ‘geohazards’, based on the temporal nature of
the damage source: (a) transient ground deformation (TGD) due to seismic wave propagation, and (b)
permanent ground deformation (PGD), with possible failure causes being active fault movements,
landslides, liquefaction-induced settlement or lateral spreading (Figure 1). Most of the damage reported
to date is attributed to PGD [4,5], but there is also strong evidence that wave propagation has contributed
to pipe damage [6–12], though to a lesser extent.
Fig. 1. Illustration of the major geohazards threatening the structural integrity of buried NG pipelines: (a) seismic
wave propagation; (b) – (d) PGD types: (b) strike-slip fault movement; (c) landslide in the form of earth flow; (d)
liquefaction-induced settlement.
From a system-wide viewpoint, the impact of a seismic shock on the network level of a NG pipeline
system can be highly adverse and spatially dispersed. A potential long-lasting flow disruption due to
earthquake damage can have excessive direct and indirect socioeconomic repercussions not only locally,
but also internationally, given the spatial dimension of a NG network. Records on the number of NG
network users that experienced service disruption and the disruption duration after past earthquake
events can be found in relevant reports [5,7,12,13]. Additionally, content leakage may have life-
threatening consequences if ignition is triggered and can pose an environmental threat. It becomes
therefore evident that underground NG networks traversing seismically active areas are exposed to
seismic risk and, consequently, securing their long-term integrity and operability with the minimum
cost to society and economy is of paramount importance. This very objective has given rise to the
concept of resilience in recent years, which is commonly perceived as the capacity to cope with
unanticipated dangers after they have become manifest, learning to bounce back, or the ability to resist,
adapt to and recover from some shock, insult or disturbance. As resilience is of paramount importance
for all lifeline systems, strategies for improvement are gradually being adopted as a desired target by
authorities and influential movements within policy-making for natural disaster mitigation in urban
Given the above challenges, the objectives of the present review study are to:
a) Identify and examine one by one essential aspects pertaining to the seismic safety of buried steel
NG pipelines, both on the component and the network level. These aspects are identified by the
section titles following,
b) For each element of this analysis, point out and discuss the most important outcomes and
conclusions found in the literature that relate to the way we design and assess NG buried pipeline
networks in seismogenic regions,
c) Highlight the primary challenges involved in each subdomain in light of the latest knowledge and
pinpoint limitations and gaps that need to be filled by new research.
Analyze interrelationships among the different elements, where possible and discuss ideas for possible
future research work, more so towards an integrated seismic resilience assessment framework.
The novelty herein lies in the fact that we attempt to approach the most critical aspects of seismic safety
of buried NG pipelines in a holistic manner. Previous similar efforts on pipelines (e.g. [14–17]) or with
a broader structural typology scope [18,19] dealt only with specific aspects independently of one another,
such as response analysis and design or fragility analysis. It must be emphasized that the scope is
focused on TGD effects. The reasons are that TGD involves more complex physics and more
uncertainties, it is statistically more likely to affect buried pipelines due to its spatially distributed
character, it is not as well documented as PGD cases and, in contrast to the above, it is often overlooked.
On the other hand, pipelines under PGD is a well-developed topic supported by a large volume of
analytical and experimental studies, especially in recent years. However, throughout this text, references
to research explicitly dealing with PGD are also made, because these two seemingly different types of
ground movement (TGD and PGD) share some common characteristics, as explained later. References
to some studies on water mains are also made when the material used is steel to provide a better insight
in the phenomena studied.
The structure of the study is as follows. First, five interlinked aspects of seismic safety of buried NG
pipelines are reviewed in detail in a bottom-up order, starting with component and ending with network
features, namely: (a) governing failure mechanisms and relevant field observations; (b) pipe response
analysis elements, including soil-pipe interaction (SPI), spatial variation of seismic ground motion along
the pipeline and applicable analysis methodologies; (c) seismic vulnerability of NG pipelines; (d)
structural health monitoring; and (e) seismic resilience at the network level. Then, existing seismic code
provisions for pipeline design are critically assessed to determine to which extent they address the latest
research findings. Finally, unaddressed issues are outlined and discussed altogether, and suggestions are
made for future research and improvement of existing codes.
In the course of earthquake-resistant design of underground steel pipeline networks, one has to first
identify the principal mechanisms leading to pipe failure due to seismic excitation in order to establish
appropriate performance criteria and select effective analysis methodologies. Extensive previous
research efforts and field surveys have been successful in classifying the most frequently occurring
failure modes into two main groups: those prevalent in continuous and those usually observed in
segmented pipelines. The first group includes line pipes assembled with welding techniques, the welds
being equally strong or stronger than the pipe barrels themselves [3]. The second group includes
pipelines in which connections are achieved by means of mechanical joints, which are the weak link of
the chain due to their lower strength. Herein, discussion is restricted to continuous pipelines, because
they are preferred for NG networks. One can distinguish five common damage states for continuous
steel-welded pipelines triggered by ground deformation: (i) shell-mode buckling, (ii) beam-mode
buckling, (iii) pure tensile rupture, (iv) flexural failure, and (v) section ovalization [20,21] as shown in
Figure 2. Each one is discussed in detail in this section.
Fig. 2. Common failure mechanisms in buried, continuous steel pipelines: (a) shell-mode buckling due to uniform
axial compression (top) and pure bending (bottom); (b) beam-mode buckling; (c) tensile fracture and (d) cross-
section ovalization.
2.1 Shell-mode buckling
Shell-mode (also referred to as local) buckling is a failure condition associated with loss of stability
arising under compressive load or bending moment. Typical radius to thickness (R/t) ratios (e.g. R/t <33
for a safety factor of 2 for pressure loading) and steel grades (σy >350 MPa) used in NG pipeline
applications dictate that shell-mode instabilities are expected in the inelastic range of response, both for
axial and bending loading [22]. Initial small deviations of the pipe walls from the perfect geometry can
destabilize the nonlinear load-displacement path causing bifurcation of the deformation, manifesting
itself as wall wrinkling. With increasing load, the stiffness gradually drops and these wrinkles will grow
and start to localize, leading to a limit load instability or a secondary bifurcation, usually in a non-
axisymmetric mode, depending on the plastic steel characteristics and the R/t ratio. The highly localized
deformation may cause wall tearing and content leakage. Local buckling is a common failure mode in
steel pipelines, as indicated by field observations of pipeline performance in past earthquakes [7,20].
Specifically, local buckling caused by TGD affected a water pipe during the 1985 Michoacan event in
Mexico City, whilst liquid fuel, water and gas pipelines suffered such damage in the 1991 Costa Rica
and 1994 Northridge earthquakes. Local buckling due to PGD was also evident in pipelines crossing
faults, both normal and reverse, in the 1971 San Fernando event. Experience so far shows that wrinkling
tends to initiate near geometric imperfections or discontinuities, such as elbows and girth welds [23]. It
is also noted that particularly for the case of buried pipelines, non-uniform compaction of the subsoil
within the trench may act as a potential imperfection of the pipe-soil system as it will be discussed later.
Elastic and inelastic buckling of standalone cylindrical shells is a well-established topic in the literature
given the long identified problems in industrial applications. On the other hand, the buckling problem
of shallow-buried cylindrical shells, which can be idealized as buckling under constraints (i.e.,
confinement by the surrounding soil), is not yet as mature. Chen et al. [24] and Lee et al. [25] used shell
stability formulations to study the elastic static and dynamic elastoplastic axial buckling of a buried
pipeline, respectively. Yun and Kyriakides [26] further provided vital insight into the parameters that
control the occurrence of shell-over beam-mode (see Section 2.2) buckling in buried pipelines under
seismically-induced axial compression. Their sensitivity analyses show qualitatively that combination
of conditions such as large diameter, large R/t ratio and deep soil covers favour shell-mode buckling.
Pipelines embedded in stiffer soils display a slight increase in the buckling loads and strains, but what
exerts greater influence on the pipe response is the amplitude of the initial imperfections.
Hall and Newmark [27], based on previous experimental results, recommended a strain-based criterion
for the onset of shell-type buckling in buried pipelines as a function of the reciprocal of R/t (adopted as
a design provision by ASCE [28]):
   
0.15 0.20
t R t R
 
where is the critical buckling strain. O’Rourke and Liu [20] note that the above criterion finds better
applicability to thin-walled pipes, while it is rather conservative for thick-walled ones. In reality, most
NG transmission pipelines lie in the intermediate range. Vazouras et al. [23] also establish a ‘no-
buckling’ condition for buried pipelines deformed by strike-slip fault movement normal to their axis:
 
0.05R t a L R
where is the length of the deformed segment of the pipeline and is a parameter depending on the
pipeline material and initial imperfections.
2.2 Beam-mode buckling
Shallow-buried NG pipelines subject to compressive ground forces are also likely to suffer from beam-
mode buckling (sometimes referred to as ‘upheaval’ buckling, but this term is only meaningful for
vertical upward pipe motion), a failure mode that resembles the well-known Euler buckling of a column.
In this failure mechanism, the pipeline is forced to bend upwards, where the soil resistance is lower,
sometimes revealing itself out of the ground, as it has been witnessed in previous earthquakes. Because
deformation localization is not as severe as in shell-mode buckling, the likelihood of pipe breakage is
generally low, therefore beam-mode buckling is considered a less catastrophic failure mode [20]. That
said, beam-mode buckling is better characterized as a serviceability peril, since the content flow is not
necessarily interrupted. A limit state criterion for beam-mode buckling depends on several parameters,
such as the flexural rigidity of the pipe section, potential imperfections and the burial depth of the
pipeline. As such, it is challenging to be reliably quantified without experimental justification.
Observations from past earthquakes verify the occurrence of beam-mode buckling in some cases. In
1959, oil pipelines embedded in a shallow trench with a depth ranging between 0.15 and 0.30m and
traversing the Buena Vista reverse fault, lifted out of the ground because of high compression stresses.
In another interesting occasion related to the 1979 Imperial Valley seismic event, there was no evidence
of upheaval buckling until local inspections by means of cover removal forced the pipelines to buckle
upwards [29]. This is also an indication that beam-mode buckling may not always interrupt the
functionality of the pipeline. Beam-mode buckling damage was also reported after the Niigataken
Chuetsu-oki earthquake in Japan [30].
Again, Yun and Kyriakides [26] analysed the factors that contribute to beam-mode buckling failure. As
anticipated, in pipelines with smaller diameters, smaller R/t ratios and shallower burial depth, beam-
mode buckling tends to dominate. However, it was claimed that in the most realistic case, shell- and
beam-mode buckling essentially interact; in fact, coupled axial compression and bending can produce
localized deformation at buckling loads lower than the ones predicted for shell-buckling alone.
Meyersohn and O’Rourke [31] noticed that pipelines covered by backfill soil with limited uplift
resistance are more likely to fail by means of beam-mode buckling. They pointed out that there is a
proportional relationship between buckling load and trench depth and calculated a critical value for the
latter, which governs the precedence of occurrence of the two modes of buckling; that is, if a pipeline
has a larger burial depth than the critical cover depth, then shell-mode buckling will occur before beam-
mode buckling and vice versa. It was also noted that a minimum cover depth of 0.5 to 1.0m is sufficient
to ensure that the pipeline will not experience beam-mode buckling.
More recently, Matheson and Zhu [32] carried out a parametric numerical study of an idealized buried
pipeline model with hill-crest overbend imperfection under service loads, in order to establish an
empirical formula and limit state for the critical upheaval buckling load. Wang et al. [33] set to
determine the upward pipe displacement required to mobilize the upheaval buckling resistance by
conducting full-scale plane-strain soil-pipe tests in order to avoid scaling law problems. It was found
that mobilization distance relates linearly to the burial depth-to-diameter ratio. Mitsuya et al. [34]
managed to reproduce the beam-mode buckling that occurred in buried pipelines during the Niigataken
Chuetsu-oki earthquake by developing a simple formula that makes use of elastic stability theory and
tangent modulus theory. The critical strain is given by:
 
1/ 1
k I n
 
 
 
where A is the pipe cross-sectional area, I its second moment of inertia, the lateral spring constant,
the 0.2% steel proof stress and the corresponding strain, n stands for a work-hardening
2.3 Tensile rupture
When the pipeline is in a state of axial tension, rupture is expected to occur if excessive plastic
longitudinal strains develop in the pipe walls. This type of failure is rarely observed in arc-welded steel
pipelines with butt connections due to the strongly ductile behaviour of the latter. On the contrary, steel
pipelines assembled with gas-welded slip joints are more vulnerable to this failure mechanism, since
they are incapable of withstanding substantial yielding prior to rupture. This finding is described in [35],
based on evidence from the 1994 Northridge event.
Although the ultimate strain of X-grade pipe steel may well reach 21% according to manufacturers’
specifications [36], usually a more conservative value of 2%, 3% [37,38] or 4% [20] is adopted in
engineering practice and research. However, there is a debate on whether these values are representative
of the real ductility capacity of steel at the weakest locations of a steel-welded pipeline: girth welds and
potential wall defects (elaborated in Section 3.4). Girth welds, although designed with higher strength
provisions than the pipe barrels [3], may exhibit lower ductility than the nominal value owing to
metallurgical alterations induced by the welding process. Considering that such geometric asperities can
attract high stresses due to their discontinuous nature, it becomes clear that their uncertain strain capacity
raises safety concerns regarding the proposed strain limits of 3% or 4%. That said, tensile tests on
representative specimens containing welds are necessary to quantify the actual strain limit.
In general, experience from previous earthquake events has shown that most steel pipelines exposed to
tensile loads performed more than sufficiently, since modern manufacturing techniques are able to
satisfy the minimum ductility requirements. When it comes to compressive axial loading, though,
emphasis should be placed on the identification of the actual ultimate strain, because the critical shell
buckling load has been shown to be highly sensitive to work hardening.
2.4 Flexural failure
Failure due to excessive bending strains of the pipe section is quite rare in steel pipelines because of the
high ductility of steel. To this conclusion points evidence from the 1971 San Fernando earthquake event,
where a number of buried gas and liquid fuel pipelines were found to have endured approximately 2.5
m of transverse soil dislocation [39]. However, large bending deformations may drive the moment-
curvature equilibrium to an ovalization limit or an instability limit, depending on the R/t ratio of the
2.5 Section ovalization
Another possible failure state associated with large radial displacements is the cross-sectional
ovalization, also known as the Brazier effect, after the researcher who first derived an analytical
ovalization limit for an elastic pipe [40]. Severe bending forces the circular cross-section of the pipe to
flatten into an oval-like shape, an effect that accelerates the loss of bending stiffness, differentiating the
behaviour as this is predicted by the classical beam bending theory. This does not entail an ultimate
limit state, but can pose a serviceability threat to the pipeline carrying capacity. An ovalization limit
state developed by Gresnigt [41] is described by the critical change in pipe diameter over the original
diameter (also known as the flattening factor):
It is important to emphasize that a different approach is needed to establish failure criteria for continuous
pipelines with slip, riveted or gas-welded joints. As opposed to pipelines assembled with butt joints, for
which failure criteria are mostly functions of pipe performance indicators, in this case failure criteria
must be formulated based on joint characteristics. The reason is because this type of joints is generally
weaker than the main pipe body. A number of studies involved the estimation of the strength of slip
joints with inner [42,43] and outer weld [44], in terms of joint efficiency, namely the ratio of joint to
pipe strength. Joint efficiency values lower than 0.40 were obtained in all cases. Damage evidence at
gas-welded joints is available from the 1971 San Fernando earthquake, where most of the failures were
related to low-quality welding.
2.6 Remarks
It can be argued that some of the existing limit state criteria for buried steel NG pipelines under TGD
effects are not well-established. The first reason is that potentially critical conditions controlling the
occurrence of the damage modes are ignored from analytical considerations due to the associated
analysis complexity. Such are, for instance, the uneven soil resistance around the pipe circumference,
the variability of soil properties along the pipeline and the nonlinear pipe-soil contact behaviour,
conditions that might be unfavourable (and not extreme cases) to the pipeline seismic performance with
regard to shell-type buckling and are not captured by current criteria. Other potentially important aspects
that have not received enough attention is the bending-induced shell buckling and the interaction
between different modes (e.g., shell- and beam-type buckling).
The second is that the overall approach to the problem lacks robust verification by experimental data.
Previous experiments have mostly focused on the derivation of equivalent soil spring constants for
analysis purposes, as discussed in Section 3.1.2. Dynamic or pseudo-static physical testing of
representative pipe specimens, including the surrounding soil, under controlled laboratory conditions
will be valuable in identifying reliably all the variables describing the damage mechanisms, and also in
clarifying the conditions under which interaction of different modes can arise. Moreover, based on [26],
it can be deduced that beam-mode buckling is more likely to affect smaller-diameter distribution
pipelines rather than large-diameter transmission ones. Given the currently available computational
demand but also the experimental capabilities, reliable quantification of NG pipeline limit states is
deemed of major importance to reduce the associated epistemic uncertainty.
The crucial factor that differentiates the seismic behavior of buried structures like pipelines from that
of aboveground structures is the restraint provided by the surrounding soil and the anticipated dynamic
interaction. In contrast to the well-understood, inertia-governed dynamic response of aboveground
structures to strong ground motion, subsurface pipelines are minimally affected by seismic inertia forces,
because these are of small magnitude as a result of the relatively small pipe mass and are anyway resisted
directly by the surrounding soil body. This observation, recognized early by researchers and reflected
in design codes [19,38,45–47], further implies that inertial soil-structure interaction (SSI) effects, in the
form they manifest in overground structures, are practically insignificant. It follows that the fully
dynamic problem can be approximated satisfactorily as a quasi-static one, provided that all important
sources of energy dissipation are accounted for. In this respect, it can be argued that the problem of a
buried pipeline under TGD is quite similar in terms of mechanics to the problem of a buried pipeline
under PGD.
The governing deformation modes are pure axial tension or compression, bending in the vertical or
horizontal plane, or combination of these, depending on dominant type of seismic waves (S-waves, P-
waves or surface waves), the pipeline alignment with respect to the ray path and the incidence angle of
the wave front. A purely axial state of stress, associated with near-uniform normal axial stresses over
the pipe section, is produced by shear stress transfer from the soil and can lead to axial buckling or
tensile rupture. A flexural state of stress, associated with curvature of the cross-section, is produced by
the direct imposition of the soil curvature on the pipe in contact and can result in bending buckling,
section ovalization or flexural failure. However, axial seismic demand is deemed more critical as it has
been found in several studies that axial strains generally tend to be larger than bending strains (e.g.
[6,48,49]), except in the case of pipe bents where the reverse holds [50].
3.1 Soil-pipe interaction
When an earthquake strikes and travelling stress waves arrive at points along a pipeline, it is usually the
relative motion between the affected pipe segment and the soil that generates stress in the pipe. We can
describe this kind of load as ‘displacement-controlled’, as the pipeline is deformed by the imposed
ground motion rather than by seismic inertial forces. For this reason, traditional force-based design is
not effective for buried pipelines, rather it is necessary to ensure that ductility levels suffice in this
instance (note here that this is underpinned by the fact that pipelines made of cast iron, a non-ductile
material, have suffered more extensive damage compared to steel pipelines in past earthquakes).
However, the occurrence of relative soil-pipe movement is not a unique condition for pipeline
deformation to occur. A pipeline embedded in soil strata having stiffness that varies along its axis is
also expected to deform under seismic wave activity due to the different vibrational characteristics of
the said strata, even if the pipeline fully conforms to the ground motion (i.e., by assuming zero relative
displacements). This case of spatially variable ground motion is of major interest and is more thoroughly
discussed in Section 3.2.
As already mentioned, inertial interaction between an NG pipeline and the soil can be ignored in most
cases. If, for the case of uniform soil conditions, one further shows that kinematic interaction effects
can also be ignored, as demonstrated in Papadopoulos et al. [51], the entire soil-pipe interaction (SPI)
problem degenerates into a local contact problem driven by the soil motion and can be modelled either
rigorously with explicit FE contact formulations or more approximately with equivalent soil springs as
discussed below.
3.1.1 Models neglecting soil-pipe interaction
A quite common yet seemingly sound assumption adopted both in design practice and research (e.g.
[52–54]) is that the supporting soil possesses considerably greater stiffness than the pipe itself, hence
the latter is actually forced to perfectly conform to soil movement; this has also been confirmed by some
field tests [6]. From this assumption, it follows that pipe strains and curvatures match the ones developed
in the near-field soil. This approach appears conservative, because it leads to higher design strains
compared to the case that the pipe is able, to some extent, to resist soil distortion [55].
Along this line of thought, fundamental was the early approach proposed by Newmark [52]. Assuming
ground shaking is triggered by a constant plane wave train propagating with velocity c parallel to the
pipeline in an infinite, homogeneous, isotropic, elastic medium, he formulated the following simplified
yet practical analytical expressions for the axial strain (in case the ground motion is parallel to the
propagation direction) and curvature (in case the ground motion is perpendicular to the propagation
direction) of a straight pipeline:
1u u
x c t
 
 
2 2
2 2 2
1v v
y c t
 
 
where and represent the free-field and, by assumption, pipe axial strain and curvature,
u x 
2 2
v y 
respectively. Eqs. (5) and (6) can be manipulated to reflect deformation in a buried pipe struck by P-,
S- or R-waves under any incidence angle. Kuesel [53] implemented this approach for the earthquake-
resistant design of the San Francisco Trans-Bay Tube. Parmelle and Ludtke [56] also conclude that the
effect of SPI is negligible. However, Newmark’s approach yields credible results mostly for highly
flexible pipes, that means pipes with high R/t ratios. Typical NG transmission pipelines often have
stiffness that may prevent them from fully conforming to soil motion. Consequently, applying
Newmark’s approach in this case would lead to strain overestimation.
3.1.2 Models considering soil-pipe interaction
When pipeline stiffness is appreciable compared to soil stiffness, as in soft soils or pipelines with
relatively low R/t ratios, pipeline movement can deviate from that of the soil and SPI effects are likely
to play a role in the pipeline response. The simplest and most popular model able to capture this effect
is the beam-on-nonlinear-Winkler-foundation (BNWF). In this case, the pipeline is represented by
elastic beam elements, while discrete equivalent translational springs of appropriate stiffness are
assigned at points along its axis in three orthogonal directions to represent the soil resistance. In a one-
dimensional treatment of the general 3D problem in the time domain, the governing equations of motion
of a pipeline subject independently to an imposed ground displacement history in the transverse
( )
w t
horizontal and in the axial direction are given by:
( )
u t
2 4
2 4 0
h h r
w w
m c k w EI
t t x
 
 
 
2 2
2 2 0
a a r
u u
m c k u EA
t t x
 
 
 
where and represent the time-dependent pipe displacement components in the transverse and axial
direction respectively, and , is the pipe-distributed mass, EI and EA are the
r g
w w w 
r g
u u u 
flexural and axial rigidities of the pipe cross-section, and , and , are the equivalent dashpot
and spring constants per unit pipeline length in the transverse horizontal and axial directions. If the
dynamic terms are ignored, the response is of quasi-static type and Eq. (7) becomes:
 
4h g
EI k w w
 
Similarly, the quasi-static response in the axial direction is described by
 
2a g
EA k u u
 
Several soil spring models are available in the literature, and various studies have considered the SPI
effect. In an early study, St. John and Zahrah [55] derived a reduction factor to estimate the internal
forces of an SPI system from that of a corresponding interaction-free system, making simplifying
assumptions about the nature of the oncoming seismic waves. The interpretation of this reduction factor
is that consideration of the SPI effects has a favourable effect on the pipe forces. This conclusion is
further supported by another study by Hindy and Novak [48]. In this case, a lumped mass beam-model
for the pipe was adopted and analysed considering dynamic SPI, in correspondence with the continuous
version of the problem described by Eqs. (7) and (8). Two different soil configurations were examined;
in the case of a homogeneous medium, it was found that SPI leads to decreased pipe stresses as
compared to the ones obtained neglecting it. On the contrary, for a soil consisting of two different layers
separated by a vertical plane, stress concentration was evident, this time located close to the vertical
boundary, while the pertinent peak values were found higher than the ones predicted without SPI.
One of the first known experimental tests to investigate SPI effects was conducted by Audibert and
Nyman [57], who explored the lateral (horizontal) response of steel pipelines buried in sand under a
wide range of burial depth-to-pipe diameter ratios. They developed a rectangular hyberbola to represent
the soil resistance as a function of the relative lateral movement and then calculated the ultimate soil
resistance as a function of the lateral pipe motion:
,U lateral q
where is the effective unit weight of the soil, is the outside pipe diameter, is the depth to the
pipe centreline and is the bearing capacity factor, estimated from appropriate charts. Hindy and
Novak [48] derived analytically linear soil spring constants and dashpot coefficients in the axial and
transverse pipeline direction by combining the complex solution of the dynamic plane strain problem
of in-phase pipe harmonic vibration and the static solution of Mindlin’s problem. The expressions are
not included here due to their complexity. O’Rourke and Wang [58] proposed that the axial soil stiffness
be twice the effective soil shear modulus.
Later, Nyman [59] investigated the restraints applied on a pipe by cohesionless soil due to oblique
vertical-horizontal pipe motion. He proposed an expression for the ultimate soil restraint against the
oblique pipe motion as the product of the ultimate soil restraint against vertical pipe motion
and an inclination factor :
, ,U oblique i U vertical
with (13)
1 1
90 0.75
U lateral
U vertical
Ra F
 
 
 
 
 
where is defined as the inclination angle in degrees between the oblique and the vertical soil restraint
and can be evaluated from (11) or other sources. To completely describe the nonlinear force-
displacement relationship, Nyman recommends the following values for the yield displacement soil
required to mobilize the oblique ultimate soil restraint:
0.015 for dense geomaterials
0.025 for loosegeomaterials
y oblique
To validate the available analytical models against experimental data, Trautmann and O’ Rourke [60]
performed a series of multi-parametric lateral loading tests to assess the response of subsurface,
typically-sized pipelines to lateral soil motion. A hyperbolic function was derived to represent the
average lateral force-displacement curve of the obtained test data, expressed in dimensionless form as:
0.17 0.83
 
 
where is the ultimate soil force, with L and standing for the length and the horizontal
U h
force factor, respectively. Appropriate values for the latter parameter may be sought in relevant charts
as a function of depth-to-diameter ratio and friction angle. Test results also indicated a strong variation
of the yield displacement of the soil with the soil density, ranging from 0.13H for loose soil, 0.08H
for medium soil and 0.03H for dense soil.
Selvadurai [61] gave the vertical elastic stiffness of a buried pipeline under ground movement as
. In order to characterize the transverse horizontal and axial SPI described by Eqs. (9)
1.3 / (1 )
 
and (10), St. John and Zahrah [55] used a foundation modulus obtained by manipulating the solution to
the Kelvin’s problem of a static point load applied within an infinite, homogeneous, elastic, isotropic
medium. The result was expressed as:
 
 
3 4
k GD
where v, G are the Poisson’s ratio and shear modulus of the medium and D the outer pipe diameter. In
the same manner, but utilizing the solution to the Flamant’s problem, they arrived at an estimate for the
foundation modulus that governs the pipe response to transverse vertical soil motion:
 
Concerned with the evaluation of axial soil springs, El Hmadi and O’ Rourke [62] aimed to verify the
theoretical and empirical predictions for the axial spring stiffness available at that time, taking advantage
of the experimental data provided by a previous full-scale field test [63]. After performing a back-
calculation on the governing displacement functions and considering the strain-dependent nature of the
soil shear modulus, they ended up with an upper and lower bound value for the axial spring constant ka
as a function of the soil shear modulus G:
1.57 1.70
G k G 
This range of values apparently lies within and consequently partly confirms the wider range provided
by the then existing literature . Another important finding of this study is that the inertial
G k G 
axial force induced in the pipeline during the test was over two orders of magnitude lower than the soil
restraint developed, thus confirming that pipeline inertia is insignificant. O’ Rourke and El Hmadi [47]
calculated the peak frictional resistance per unit length that develops at the soil-pipe interface under
relative axial motion as the product of the mean applied normal force and the coefficient of friction:
U axial
 
 
 
 
where represents the coefficient of friction, ko is the coefficient of lateral earth pressure and πD the
circumference of the pipe. Matsubara and Hoshiya [64] derived the axial elastic stiffeness using the
elasticity theory as , where λ is defined as the ratio of an imaginary outer radius at
2 / (log )G
 
 
which displacements vanish and the pipeline radius.
In another experimental effort, Hsu et al. [65] dealt with the response of pipes buried in loose sand and
subjected to oblique-horizontal increasing displacement. Specifically, a large-scale test was carried out
involving various pipe specimens and depth configuration, wherein the pipe was successively placed at
horizontal orientations in different, gradually increasing inclination angles with respect to the direction
of movement. The goal was to evaluate the longitudinal and transverse horizontal (lateral) soil restraint
components for each test setup of the oblique pipe. Their results
Table 1. Soil-pipe interaction models proposed in the literature, described by either the ultimate soil restraint or
equivalent spring constants (all parameters and variables involved are explained in the body).
Audibert and Nyman
Lateral direction; steel pipe in sand
O’Rourke and Wang
Axial direction
Nyman (1984)
Oblique direction in cohesionless soil
Trautmann and O’
Rourke (1985)
Lateral direction; ranges from 0.03H to
0.13H depending on soil density
Selvadurai (1985)
Vertical direction
St. John and Zahrah
Axial direction; elastic stiffness
El Hmadi and O’
Rourke (1988)
Axial direction
O’ Rourke and El
Hmadi (1988)
Axial direction; sand backfill
Matsubara and Hoshiya
Axial direction; infinite homogeneous soil
Hsu et al. (2001)
Lateral direction in loose sand
,U lateral q
k G
, ,U oblique i U vertical
0.17 0.83
 
 
1.3 / (1 )
k G
 
 
 
3 4
k GD
1.57 1.70
G k G 
U axial
 
 
 
 
2 / (log )k G
 
axial oblique axial
lateral oblique lateral
F F a
F F a
indicated that the axial-oblique restraint can be determined simply by multiplying the axial force of the
corresponding purely axial pipe ( ) with the cosine of the inclination angle, while to obtain the
lateral-oblique restraint, a multiplication between the lateral force of the associated purely lateral pipe
and the sine of the inclination angle is sufficient:
axial oblique axial
F F a
lateral oblique lateral
F F a
where is the inclination angle between the orientation of the pipeline and the direction of movement.
Table 1 summarizes all SPI spring models presented in this section.
The American Lifeline Alliance presented a report [66] that contains mathematical expressions
describing the constitutive behaviour of nonlinear lumped soil springs in each of four principal
Table 2. Ultimate soil force and relative displacement relationships for soil-pipe relative motion proposed by the
ALA [66].
Spring direction
Ultimate soil restraint
Ultimate relative displacement
Vertical uplift
Vertical bearing
: adhesion factor; : backfill soil cohesion; , , , , , , : bearing capacity
factors in the horizontal, vertical uplift and vertical bearing direction (subscript denotes clay,
denotes sand)
Dac H D
 
 
 
 
3 ~ 10mm
ch qh
 
0.04 2 0.10 ~ 0.15H D D D 
cv qv
0.01 ~ 0.02 0.1 dense to loose sands
0.1 ~ 0.2 0.2 stiff tosoft clays
c qb
 
 
0.1 for granular soils
0.2 for cohesive soils
directions of pipe motion, i.e. axial, lateral, vertical uplift and vertical bearing. In all cases, the
nonlinearity of the soil is idealized as an elastoplastic bilinear curve, hence it is only one point that is
actually needed to define each curve. These models provide a way to estimate both the maximum soil
restraints and the corresponding relative displacements. The relationships (Table 2), extensively used in
design practice, were derived assuming uniform soil conditions and are based on Refs. [67,68].
3.2 Spatially variable seismic demand along the pipeline
Spatial variability in earthquake ground motion (SVEGM) can be interpreted as the differences expected
in frequency content, amplitude and phase angle of seismic signals captured at distant stations on a local
scale; this observation was consolidated over three decades ago, when researchers [69,70] started
analyzing the ample accelerogram data obtained from densely installed strong motion recording arrays,
in particular the SMART-1 array in Taiwan. SVEGM is a physical phenomenon of stochastic nature, in
the sense that its occurrence can only be predicted with a degree of uncertainty due to the complex,
multi-parametric underlying mechanisms that contribute to its generation.
These variations in the seismic ground motion are attributed to three main factors [71]: (a) the
transmission of the waves at finite velocity (wave passage effect), which intuitively results in different
arrival times at different recording stations, (b) the gradual reduction in the coherency of the waves as
a result of successive scattering, such as reflections and refractions, that occurs along their path through
the inhomogeneous earth strata (ray-path effect), and due to the varying superposition of waves
originating from different points of an extended seismic source (extended source effect), collectively
known as the incoherence effect’, (c) the different local soil conditions at remote stations that primarily
affect the amplitude and frequency content of the incoming waves (local site effect). Additional causes
of the phenomenon have also been recognized: the attenuation of seismic waves along their path,
resulting from the gradual dissipation of wave energy into the soil medium, and, though not critical in
the case of pipelines, the relative flexibility of the soil-foundation system that may ‘filter’ certain
frequencies of the incoming wave field [72].
SVEGM and its effects on extended structures such as bridges, dams etc, have been rigorously
investigated by modeling the earthquake ground acceleration as a random signal of time using analytical
[73], numerical [74], field [75] and experimental [76,77] methods. Descriptors of the probabilistic
properties of the ground motions have been established and used to reflect the sources of spatial
variability [78]. Random vibration analysis or deterministic time-history analysis using simulated
spatially variable ground motions as input are employed to assess the effect of the phenomenon on the
response of various structures.
It is understood that SVEGM is very relevant to buried pipeline systems. Given the spatial extent of the
structure, the input seismic excitation can always and should be treated as a spatially variable one. Along
these lines, SVEGM in buried pipeline problems falls in two major categories: (a) due to the wave
passage effect and (b) due to local site effects. The majority of the published research has focused on
the first, as will be become obvious in Section 3.3. Local site effects have received less attention
Local site effects may result from gradients in soil properties (medium inhomogeneity), features of
irregular topography (e.g., hills, ridges, canyons and cut-and-fill slopes) and special subsurface
geomorphic conditions, such as a soft surficial sediment sharing an inclined border with stiff rock
(valley setting). The presence of any of the above along the route of a buried pipeline, combined with
‘appropriate’ seismic excitation, can profoundly amplify the ground motion, alter its frequency
characteristics and spatial profiles, prolong its duration, and induce substantial ground strains and
curvatures (e.g., see [79–83]), which in turn can cause pipeline deformation. In Figure 3, some idealized
scenarios of such sites and loading conditions are identified and sketched: (a) a site consisting of two
horizontally adjacent soil layers of different shear wave velocities and (b) a soft alluvial valley of
trapezoidal shape, both excited by vertically propagating S-waves of varying polarization. In case (a),
S-wave polarization in the pipeline direction induces axial strain in the pipeline near the boundary
(marked with red), while the generated parasitic vertical motion forces the pipeline to bend in the vertical
plane (indicated by a black curve). In this situation, coupled axial-bending shell-buckling and
ovalization may appear, while tensile fracture is generally not anticipated. Polarization in the transverse
direction induces only bending in the horizontal direction near the boundary which is likely to cause
ovalization of the cross section and bending buckling. The stress state is similar in case (b), with the
difference that peak strains and curvatures are located near the valley edges. One immediately realizes
that if the wavefield is incident under angle, or the pipeline is placed obliquely with respect to the soil
particle motion, multiple motion components will be simultaneously applied on the pipeline.
Fig. 3. Buried NG pipeline crossing: (a) two laterally adjacent soil layers of different Vs; (b) a soft alluvial valley
The effect of inhomogeneous soil on pipeline seismic demand was first studied by Hindy and Novak
[48] using dynamic equilibrium of an elastic lumped-mass beam model of the pipeline and appropriate
soil springs and dashpots. A major conclusion was that body waves travelling along a pipeline laid
through two different soils cause peak axial and bending stresses near the boundary of the two media,
and are larger than the ones in the homogeneous case. Several of the earliest contributions on the effect
of SVEGM on the response of buried pipelines are attributed to Japanese researchers. Nishio et al.
[84,85] conducted laboratory tests of buried pipelines in valley and cut-and-fill settings subject to
horizontal base excitation. Analytical methods have also been used to study the strain response of buried
pipelines laid through dipping soil layers [86], cut-and-fill embankments [87], riverbeds [88] and
multiple soil media [89].
Buried pipelines under incoherent ground motion have also been the subject of scrutiny. Zerva et al.
[90] and Zerva [72] examined in the stochastic domain the axial and transverse response of segmented
and continuous pipelines to differential ground motion. Random vibration analysis of analytical pipeline
models was carried out using as input the stochastic properties of ground motions recorded at the
SMART-1 array. By comparing results for partially and perfectly coherent motions, a close match was
found between displacements of continuous pipelines, a circumstantial finding attributed to the fact that
the same rigid body mode was excited in both cases. However, partially correlated motions gave higher
stress values. Further, it was observed that axial stresses become dominant as the slenderness of the
continuous pipeline increases, while bending stresses become sizable when the pipe diameter is large.
The results of another effort [49] revealed that axial strains are the principal source of deformation over
bending strains in continuous, large-diameter pipelines (Figure 4). It was also shown that the selection
of the incoherence parameter on the pipeline response is critical (Figure 5). Upon inspection of the
figures, it can be seen that the maximum axial strains are at least two orders of magnitude lower than
the steel elastic limit and the commonly used limit state strains.
Fig. 4. Distribution of root-mean-square strains along the pipeline longitudinal axis y for pipe orientation that
coincides with the epicentral direction of the input motion, as calculated by Zerva (1993) (adapted from [49]).
Fig. 5. Distribution of root-mean-square axial strains along the pipeline longitudinal axis y for different values of
the incoherence parameter, as calculated by Zerva (1993) (adapted from [49]).
Zerva [91] further dealt with the effect of differential ground motions on the response of various lifeline
structures, including underground pipelines. Two coherency decay models [92][93] were used and it
was found that pipeline axial strains are maximized when the motions are totally incoherent, i.e. the
differential displacements at the input stations are maximum. Specifically, for the second coherency
model, an increasing trend was observed for the seismic strains with stronger decay (denoting increasing
incoherence). More recently, Lee et al. [94] applied multiple seismic excitation on a BNWF model of a
pipeline in a 3D nonlinear time-history analysis, showing that the pipeline displays varying distribution
of the axial relative displacement along its length, with peaks appearing in the region of differing
imposed excitations. For the bending response, calculated pipeline demand for a specific input ground
motion reached half the respective capacity.
At the time of writing, the authors of this were expending efforts to investigate numerically the impact
of non-uniform site conditions on the stability of high-pressure steel natural gas pipelines. To this end,
the buckling capacity of the pipeline is evaluated in view of the demand imposed by the vibrating soil.
The originally complex problem is split in two stages: (a) determination of the time-varying site
response at the pipeline depth and subsequently (b) application of the critical response profile as a
spatially variable displacement demand on the pipeline. The latter issue is described better in Section
3.3. In terms of site response, the scenarios illustrated in Figure 3 are considered. Parametric 2D plane-
strain viscoelastic and equivalent-linear site response analyses are conducted with Ricker-type wavelets
and real ground motion records as input to detect the most critical TGD cases. Some sample results are
shown in Figures 6 and 7. Figure 6 shows contours of the axial strain synthetics at the ground surface
for equivalent-linear soil response of the sites displayed in Figure 3 under high-intensity Ricker pulses.
It is clear that peaks appear near the material discontinuity with magnitudes of one order higher (~ 2%)
than the elastic ones, a result with potential implications on the pipeline demand. In Figure 7, the critical
horizontal displacement profiles derived based on the maximum compressive strain are plotted for
different input excitations, revealing that the maximum differential displacement load on the pipeline
shows strong dependence on the exciting frequency.
Fig. 6. Time-variation of axial strain field at the surface of the equivalent-linear sites of Fig. 3 for vertically
incident acceleration Ricker pulse with 0.5 Hz and PGA=0.2g (L= half-length of the domains)
Fig. 7. Critical horizontal displacement profiles at the surface of the equivalent-linear sites shown in Fig. 3 for
vertically incident acceleration Ricker pulses with PGA=0.2g and varying frequency.
3.3 Analysis methodologies employed in literature
The choice of a suitable methodology to estimate the pipeline response to strong ground shaking is case-
specific and largely depends on the response quantity and damage mechanism of interest, as well as the
desired degree of accuracy. In general, the physical problem in its entirety is extremely complex and
uncertain, as it involves wave propagation in elastic/inelastic semi-infinite soil media, inherently
random time-varying input excitation, nonlinear surface contact between the pipeline and soil, shell pipe
mechanics, potential geometric nonlinearities, very large dimensions, nonhomogeneous site with
uncertain dynamic properties, potential geometry defects and material inelasticity of the pipeline, and
time-dependent response. All these complexities render a fully 3D numerical approach not only
computationally prohibitive, but also unjustified in view of the involved uncertainties; hence, reliable
simplification of the problem is essential.
Typically, simplification steps are taken with regard to two constituents of the physical problem: (a)
modelling of the pipeline behaviour and (b) modelling of the supporting soil and/or soil-pipe contact
conditions (SPI). As regards item (a), if one wants to obtain simply a rough estimate of the pipeline
seismic demand (axial or bending) and compare it with the respective capacity, they commonly resort
to the classical beam theory. In this manner, axial and bending deformations are assumed uncoupled,
while the hoop stress component, which might become important, cannot be captured. The ability to
capture shell buckling modes and section ovalization is also precluded.
On the other hand, if the goal is to check for the possibility of shell bifurcation or cross-section
ovalization, or account for hoop stresses due to pressurization and gravity, use of one of the available
shell theories is inevitable in order to accurately describe the cross-sectional deformation and the
distributions of membrane and bending strains. Hybrid approaches have also been reported (e.g.,[95]),
wherein the critical pipeline segment is modelled as a cylindrical shell and the remaining segments as
As for item (b), the simplest method is to neglect any relative motion between pipe and soil, as long as
this can be warranted by the problem characteristics; in this way, the assumed input excitation can be
directly applied on the pipeline and a purely structural analysis of a 2D or 3D pipeline model can be
performed. A method of better accuracy is the use of equivalent nonlinear soil springs to account for
soil resistance in the tangential and normal directions, as already presented in Section 3.1.2. In both
these methods, soil response is assumed as uncoupled and its explicit dynamic simulation is excluded
from the analysis; instead, the input excitation is taken directly from recorded outcrop ground motions
at different stations or is calculated as a function of the incidence angle for seismic waves of idealized,
typically sinusoidal, shape. The use of general 3D elasticity theory to represent soil behavior is very
rare, and so is site response analysis to propagate the oncoming wavefield from the far-field to surface.
All combinations between variants of items (a) and (b) have been reported in the literature as discussed
Sakurai and Takanashi [6] were among the first to study the dynamic stresses on a buried pipeline by
conducting field experiments during the Matsushiro earthquake sequence. They observed that axial pipe
deformations match the ground ones when the earthquake intensity is mild enough to not induce slip,
and this was confirmed by the solution they derived for Eq. (8) (ignoring the damping term). Shinozuka
and Koike [96] extended the results of [6] to calculate conversion factors between the induced soil and
(straight and bent) pipe axial strains in a homogeneous medium due to a P- or R-wave propagating
parallel to the pipeline, taking into account the possibility of slippage (nonlinear axial interaction).
Comparison between the dynamic and the quasi-static conversion factors revealed a minor effect of
pipeline inertia. From the perspective of structural stability, Lee et al. [25] used an elastic-plastic
cylindrical shell formulation for a buried pressurized pipeline in a homogeneous elastic medium, based
on the simple flow plasticity theory and a variational formulation for the equations of motion, to check
for the stability of the dynamic equilibrium of the pipe shell. In their treatment, they ignored SPI in the
axial direction and assumed a lateral soil restraint in the form of distributed elastic radial springs. Their
solutions showed that the critical axisymmetric buckling stress and strain of the pipeline under dynamic
conditions are essentially the same as under static conditions. In another seminal work, Wong et al.
[97,98] considered in its three dimensions the problem of a long pipeline shell buried in an elastic
homogeneous halfspace under obliquely incident body or surface waves. They arrived at an analytical
solution of the equations of elastodynamics describing the coupled motion of pipeline and soil by using
eigenfunction expansions of the wave potentials. In this way, they accounted for inertial and kinematic
SPI, as well as scattering of the waves by the free surface. O’Rourke and El Hmadi [47] studied the
axial behavior of a continuous elastic pipeline embedded in a homogeneous elastic soil under Rayleigh
wave propagation in the pipeline direction (Eq. (8)). Elastic-perfectly plastic frictional behaviour at the
soil-pipe interface was considered through Eq. (19). They also proposed a design methodology based
on the correlation between ground axial strain and interface frictional strain. Application of this on a
typical buried steel pipeline case showed that the axial pipe strain produced by an R-wave of
PGA=0.35g reached 35% of the yield strain. Yun and Kyriakides [26] examined in detail the conditions
under which a buried pipeline loaded in compression may bifurcate plastically into a beam- or an
axisymmetric shell-mode, as well as the potential of interaction between the two. To formulate the
problems analytically, they used large-deflection beam kinematics for the first and Sander’s nonlinear
thin shell theory for the second mode, respectively, coupled with incremental plasticity laws and initial
geometric imperfections. SPI was assumed as in [25] but through a nonlinear model calculated by
solving the problem of a circular soil cavity expanding uniformly.
In more recent works, Kouretzis et al. [99] deployed elastic shell equations to analyze the distributions
of axial and hoop strains of a long cylindrical structures in uniform elastic soil or soil-over-bedrock due
to out-of-phase vibration induced by travelling harmonic S-waves, incident under angle. Optimization
of the closed-form solutions with respect to the angle variables involved led to critical strain expressions
for seismic design. Hatzigeorgiou and Beskos [100] developed the finite element code SINUS to analyze
directly seismic SSI effects in 3D rock-tunnel systems, considering the inelastic behaviour of both
materials through the continuum theory of elastic damage. Their results showed the reliability and
efficiency of the methodology adopted, and also that SSI effects are negligible for tunnels in soft rock.
Focusing on steel pipe bends, Saberi et al. [101] used a hybrid 3D shell-beam pipeline model where the
bend part is represented by shell elements and the straight parts by beam elements. SPI was taken into
account using the ALA spring models for uniform soil, while nonlinear pipe end springs were used to
represent pipe continuity. Nonlinear response history analyses were performed in all three principal
directions using real ground motions having phase difference. Nourzadeh and Takada [102] use the
BNWF model combined with the ALA soil springs in their numerical parametric investigation of the
response of buried steel NG distribution pipelines to input earthquake ground motion in three directions.
Analyses postulate that pipelines experienced local buckling for PGAs greater than 0.6g; however,
performance criteria are too loosely defined to allow safe judgment based on this observation, since a
shell analysis was not performed. Papadopoulos et al. [51] employed a two-step numerical methodology
to shed light into the effects of SVEGM on the demand of a buried pipeline longitudinally crossing a
basin section: they first performed 2D viscoelastic site response analysis under in-plane S-wave
propagation to determine the soil response histories at the pipeline depth, and then applied these 2D
excitations on a separate BNWF pipeline model to perform a 3D nonlinear time-history analysis (Figure
Fig. 8. BNWF model of a pipeline used in Ref. [51], with equivalent soil spring support in two directions.
Following the latest trend in research necessitating the use of sophisticated numerical simulations to
capture the nonlinear behaviour and bifurcation of shell-type structures, several studies have explored
the response of buried steel pipelines under PGD effects. In a series of publications [23,103,104],
Vazouras and his co-workers used 3D shell and solid finite elements (FE) for the soil-pipe model to
analyze the static axial and bending strains in buried steel pipelines crossing active strike-slip faults
under angle, also considering the influence of pipe continuity by deriving nonlinear springs for the pipe
ends. SPI was represented rigorously by the use of contact elements at the interface. Daiyan et al. [105]
developed a similar 3D FE model to validate centrifuge tests; their findings indicate that SPI can exhibit
strong coupling for oblique loading. In the same fashion, Sarvanis et al. [106] enhanced this approach
by calibrating model parameters through full-scale tests. Vazouras and Karamanos [107] extended the
previous models to study the mechanical performance of pipe bends; their results substantiated their
increased flexibility. Chaloulos et al. [108,109] and Kouretzis et al. [110] employed 2D plane-strain
soil-pipe FE models with interface contact elements to study the trench effects on the soil-pipe response
subject to PGD. In analytical treatments of pipelines under PGD problems, Karamitros et al. [95],
adopted a BNWF model and a secant modulus solution method to develop a design methodology to
estimate inelastic pipeline axial and bending strains generated by strike-slip fault movement, while
Trifonov and Cherniy [111] contributed a plane-stress plasticity model that accounts for internal
pressure, temperature variation and bending stresses, combined with a BNWF pipeline model to
effectively predict the inelastic stress and strain distributions over the pipe cross-section due to fault
displacements. The last works concerning PGD might seem irrelevant to the topic of this study, but in
reality they are not. Given that previous research has shown that dynamic amplification in TGD-
governed problems is not important, several of the analysis approaches taken to solve PGD problems
can be effectively applied on TGD problems with the appropriate modifications.
As part of the ongoing work briefly mentioned in Section 3.2, the authors of this have undertaken a two-
level analysis approach to capture potential buckling phenomena due to SVEGM-induced compressive
axial strain and curvature in the pipeline. A long 3D shell finite element model has been encased by a
near-field, caisson-type 3D continuum soil model representing the trench. Ignoring classical SSI effects
(both kinematic and inertial), the pseudo-static nonlinear response of the pipe-soil model is computed
for the critical in-plane soil displacement profiles obtained from 2D plane-strain site-specific response
analysis (Figure 9). With this method, the contact state can be evaluated with precision over the entire
contact surface: the frictional behaviour is controlled by a Coulomb law, a separation/no-penetration
rule is used for the normal behaviour, and also their coupling is guaranteed. The initial stress equilibrium
in the domain due to gravity and pipe internal pressure loading is directly computed. For a typical
pipeline with R/t=30 and σy=450 MPa buried in a site similar to scenario (a) of Figure 3 and subject to
the axial ground strains generated by the 1979 Imperial Valley earthquake (PGA=0.31g), results reveal
that, although sliding initiates after a limit stress and spreads, there is strong interaction between the
axial load and bending moment in the vertical plane within a short critical segment near the
inhomogeneity feature, which essentially reduces the axial buckling limit load of the pipeline. The
evolution of strain localization leading eventually to the development of two nearby lobes is displayed
in Figure 10, where different stages are associated with the respective points on the average
x x cr
 
and paths.
Fig. 9. Illustration of a two-stage methodology to analyze local site effects on the seismic response of a buried
pipeline: (1) site-specific seismic response analysis and derivation of the critical motion profiles along the assumed
pipeline; (2) aspect of a 3D continuum-shell SPI FE model able to capture local buckling phenomena in the
pipeline upon static application of the critical displacement patterns from stage (1).
Fig. 10. Left: the successive stages of deformation localization in the pipeline due to axial load-moment
interaction, with axial strain contours depicted; right: nominal axial stress-shortening and bending moment-axial
curvature plots (control sections are taken to account for the response in the critical zone of the pipeline).
3.4 Implications and recommendations
There are certain key problem parameters that need first to be well understood and defined before we
gain confidence in our model predictions.
Geologic and geomorphic conditions
One major consideration is the overall geologic and geomorphic conditions in the region of interest.
Crucial to the choice of a suitable analysis methodology is the reliable knowledge of the degree of soil
stiffness variation in the direction of pipeline route, but also with depth, particularly if the bedrock is
inclined. To this end, in-situ field surveys can contribute useful data on the real soil properties. If the
soil domain where the pipeline is supposed to be buried is relatively uniform, then strains can arise only
as a result of the apparent propagation velocity of the travelling waves, depending again on the dominant
wave type and the incidence angle, or as a result of strong relative soil-pipe motion under a fully
coherent wavefront, when the wave amplitude is large. In these cases, it has been shown that the
expected pipeline strains are generally orders of magnitude smaller than steel yield limits, hence a highly
sophisticated modelling approach to predict the pipeline seismic response is rather unnecessary. If,
however, strong soil heterogeneities or special topographic features, such as basins, hill crests and toes
and cut-and-fill embankments, are present along the pipeline path, complex scattering of the wavefield
can drastically amplify motion, change the frequency content and induce significant displacement
gradients. In such cases, more elaborate models of the pipeline and SPI are recommended to predict the
biaxial state of stress, particularly if shell-mode buckling needs to be captured. Also, 2D or even 3D site
response analysis is deemed appropriate in some instances to evaluate reliably the differential surface
free-field motion. The sub-structuring DRM method [112] is another viable option, if one wants to resort
to a large-scale simulation containing both the source, path, and local site effects.
Distance to source
A second consideration is the proximity of the location of interest to the earthquake source, which has
impact on the prevailing types of seismic waves and their frequency content. A pipeline passing near
the source of an earthquake is more likely to be stricken by high-amplitude, high-frequency vertically
propagating body waves. It follows that pipeline distress can emerge in this case by in-phase relative
movement between the pipeline and the soil, where a 2D dynamic plane-strain model is suitable, or by
local site effects. On the other hand, in an apparently more complicated situation, a buried pipeline in
sufficient distance from the earthquake source can be affected simultaneously by both nearly-vertically
propagating body waves and surface waves of lower frequencies and larger amplitudes. It has been
observed that the predominant wavelength of Rayleigh waves is a controlling parameter for the level of
stresses developed in a buried pipeline [47] The above remarks have implications on the selection of
the input ground motion to be used in a site response or more directly a pipeline response analysis.
Trench soil
The trench soil also deserves special attention. In common pipeline trenching operations, the excavated
trench soil is backfilled after the pipeline is laid, and compaction follows. The initial contact state of the
soil-pipe system depends on the quality of the backfilling and compaction works. Sometimes, the
compaction can increase the lateral earth pressure coefficient up to unity or more; in turn, the frictional
resistance, taken from the Coulomb friction law as a function of soil pressures, is raised, and this can
consequently favour the development of larger pipe stresses. The tangential interface behaviour is
controlled by the coefficient of interface friction, which is usually a linear function of the angle of
shearing resistance of the trench soil. Some typical values of the coefficient of interface friction for
buried steel pipelines are given in [47], but generally its value is not known with certainty and, even if
it was known, it would possibly vary along the pipe length. Notably, the effect of pipeline steel scour
on the SPI has also been investigated [113] and it was found that tangential interaction depends on the
unsupported length of the pipe due to scour. Further, Chaloulos et al. [108,109] and Kouretzis et al.
[110] explored the effect of a narrow trench on the evolution of the soil failure surface and peak pipeline
force under lateral pipeline motion. Using experimentally validated numerical models, they show that
the commonly used assumption of an infinitely wide trench can lead to underestimation of the actual
response quantities. Moreover, the trench soil properties are a determining factor to the uplift resistance
of the pipeline, which is of interest when ground motion with significant vertical components is expected.
Internal pressure
Another key factor specific to NG pipelines is the level of internal pressure. Pipelines belonging to the
high-pressure transmission grid develop large initial circumferential tensile stresses (30-40% of the
yield stress) as a result of uniform pressurization. This can have mixed effects on the overall seismic
performance of the pipeline. In constraint-free circular cylindrical shells under uniform axial
compression, the presence of internal pressure lowers the whole inelastic part of the response as a result
of the produced state of stress, and this reduction is sharper for higher pressures. It follows that yield,
bifurcation and collapse (if occurring in the plastic range) loads are reduced compared to the no-pressure
case [114]. If the shell is under axial compression, pressure also stiffens the pre-yield response. In buried
pipelines, however, Lee et al. [25] report that pressurization has the opposite effect, i.e., it raises the
pipe buckling stress. Another intuitive effect of internal pressure is that it tends to smooth out non-
axisymmetric imperfections. Despite the aforementioned effects, the seismic performance of a
pressurized buried pipeline is not expected to be drastically modified; however, this aspect calls for
further scrutiny under simultaneous consideration of the soil restraint.
Pipeline geometric imperfections
Initial pipe wall imperfections are an issue that deserves due consideration. Thin-walled cylindrical
shells are known to be highly imperfection-sensitive structures, and this can be manifested by the severe
discrepancies in buckling loads between theoretical elastic solutions and experiments with real
specimens [115]. This sensitivity is also evident for cylindrical shells of lower R/t ratios, where buckling
is expected in the inelastic range. Pipelines may suffer from two different types of geometric
imperfections: ‘load’ imperfections caused in-situ by the depth-dependent soil pressures towards the
pipeline walls, and pre-existing geometry imperfections resulted from such operations as manufacturing
process (residual stresses), transportation, girth welding and laying, all of which can cause deviations
from the perfect geometry. For instance, ArcelorMittal states in its API-5L X65 line pipe stock
specifications [116] a manufacturing tolerance for the pipe wall thickness of +15%, -12.5%.
Traditionally, buckling analysis of shells considering imperfect geometry is facilitated by linearly
superposing eigemode shapes obtained from a linear eigenvalue buckling analysis. Other approaches
include load perturbation and explicit definition of a stress-free imperfection pattern (e.g. [117]). For
buried pipelines under compression forces, Yun and Kyriakides [26] report that the presence of even
low-magnitude axisymmetric imperfections lowers considerably the bifurcation and limit stress and
strains compared to the perfect geometry case. Therefore, care should be taken to reliably establish the
initial perturbed geometry of the buried pipeline and apply it on representative shell models. It appears
also imperative to examine the combined effect of different imperfection patterns and internal pressure
levels on the buckling load of a buried NG pipeline.
Pipe bends
Pipe bends, also known as ‘elbows’, pose further challenges, as they exhibit more complex behavior
compared to straight pipes due to their bent geometry, and can alter the earthquake response of a buried
pipeline system. As early as 1979, Shinozuka and Koike [118] used an approximate analytical model of
a continuous buried pipeline system to derive the moment- and shear force-induced longitudinal strains
developed in right-angle bends and T-junctions under out-of-phase seismic ground motion parallel to
one of the legs. Their results show that the more extended the soil-pipe slippage and the larger the
seismic wavelength, the larger these strains are (in the first case they can become over twice the free-
field strain). McLaughlin and O’Rourke [119] confirm these findings for buried elbows impinged upon
by harmonic R-waves, and further support that axial ground strains are an upper bound estimate for the
elbow bending strains, except in the case of very thick-walled elbows. Saberi et al. [101] studied the
effect of various parameters on the bending strains of a right-angle pipe elbow under seismic wave
propagation, and concluded that these are maximized for a bend angle of about 135. There are also
studies dealing experimentally [120,121] and analytically [107,122] with the static response of soil-
embedded pipe bends under PGD-induced in-plane bending. In a review study, Karamanos [123]
describes elbows as a critical component of buried pipeline systems because they exhibit more flexible
behaviour compared to straight counterparts and are more prone to section ovalization due to bending
and fatigue damage under cyclic loading.
3.5 Challenges ahead
Even though it is broadly recognized that classical SSI effects can be safely ignored in a seismically
loaded soil-pipe system, contact between soil and pipe should be considered where necessary, as it can
differentiate pipe from soil strain. The absence of consensus on the importance of SPI and the relative
dispersion observed in calculated pipe demand due to TGD, stem partly from the inability to reliably
describe the nonlinear nature of the interaction phenomenon. This has been a subject of continuous
research over the years and the substantial progress achieved has provided mainly linear or elastoplastic
idealizations of the true nonlinear soil-pipe response. Experimental tests dealing with the derivation of
equivalent soil springs are usually based on monotonic loading protocols, and for this reason their
applicability can be justified only for cases of earthquake-induced PGD. This, however, overlooks the
true cyclic nature of seismic excitation and the hysteretic characteristics of the pipe, the soil and their
interface. In view of this, further research is necessary on the development of reliable cyclic force-
displacement curves that describe the dynamic SPI under seismic shaking, including contact effects at
the soil-pipe interface. Furthermore, what most published SPI models do not reflect is the coupling
between the directional components of the relative soil-pipe motion and the subsequent coupling of
various failure modes. For instance, it is trivial to realize that when a gap opens in the normal direction
of the soil-pipe interface, the frictional behaviour cannot be defined. The same holds for a lateral oblique
Another assumption extensively used is the homogeneity of the medium along the pipeline route, which
apparently does not hold true considering that pipelines are geographically distributed systems.
Laterally varying soil conditions can profoundly affect stress distribution and magnitudes in the pipeline
due to TGD, as already indicated in some studies (e.g. [48,124,125]). This issue also calls for further
scrutiny in the framework of dynamic/quasi-static SPI analysis under SVEGM as a result of local site
conditions and topography. More importantly, it needs to be clarified whether pipe strains can arise that
can lead to critical limit states, such as shell-mode buckling and fracture.
Research so far on the susceptibility of buried pipelines to SVEGM is mostly constrained in analytical
boundaries. Further laboratory work is necessary in order to support, calibrate and extend the existing
analytical findings. Given that shell-mode buckling is one the most common damage modes observed,
particular attention has to be placed on the experimental study of local site effects on the stability of
such structures.
In the last decades, a gradual transition is seen in the interest of the structural engineering community
from conventional deterministic analysis procedures to probabilistic risk assessment concepts, as the
understanding of the effect of aleatory and epistemic uncertainty on the response of structures to natural
hazards is improved and the computational capabilities are rapidly evolving. Particularly in earthquake
engineering, where inherent uncertainties propagate through all stages of assessment and decision-
making, structural reliability tools have been widely employed to quantify them, and evaluate the risk
level the structure is exposed to. When it comes to the seismic safety of critical civil infrastructure, such
as utility systems, probabilistic approaches are deemed necessary to secure minimum functionality
disruption and overall longevity under different excitation levels. As outlined in [126], a quantitative
seismic risk assessment of oil and gas pipelines involves the following key steps: (a) definition of the
physical subject and the objectives of the analysis, which should contain a preliminary (and quite
subjective) definition of the target, acceptable risk levels; (b) identification of the expected earthquake
hazards and estimation of their likelihood of occurrence, a process that involves many uncertainties and
is typically accomplished through probabilistic methods; (c) vulnerability assessment of the pipeline
subject by correlating hazard severity to pipeline strain demand and (d) evaluation of the probabilities
of occurrence of predefined consequences incurred by pipeline damage.
Because it requires a high degree of expertise and experience to perform, a full seismic risk assessment
of buried NG pipelines is generally not required by regulations and is rarely undertaken in practice
except a-posteriori, for post-earthquake assessment purposes. Instead, most operators rely on an
intermediate output of procedure (c), that is, fragility relationships. In a broad context, fragility
expresses the conditional probability that a system or an individual component reaches or exceeds a
certain limit damage state for a given level of an intensity measure [127]. Fragility is commonly referred
to as the probability of failure, where the term ‘failure’ does not necessarily imply catastrophic damage,
but rather refers to different predefined damage states. In the sphere of earthquake engineering, fragility
curves are used to describe the probability that the imposed seismic demand D is equal to or greater
than the capacity C corresponding to a specified damage state of the structure, given a ground motion
intensity measure (IM hereafter):
 
|Fragility P D C IM 
Particularly in the context of damage analysis of buried pipelines, probabilistic seismic fragility relations
are the typically used evaluation tool, even though they are defined in a much simpler manner compared
to those defined for buildings and bridges. They establish a relationship between the spatially distributed
pipe damage rates and the different degrees of an appropriate IM. The damage rate is usually quantified
as the pipeline repair rate, i.e. the number of pipe repairs (for breaks or leaks) per unit length of pipelines,
although other measures have also been used. Seismic fragility relations are usually categorized
according to the damage source type, that is, TGD and PGD, and are expressed in the form of a power
where RR is the median repair rate and a, b are parameters estimated by regression analysis of the
available data pairs.
Several ground motion IMs have been claimed in the literature to correlate well with pipeline damage,
ranging from the standard ones MMI, PGA, PGV, AI, , to the more pipeline-specific peak ground
 
strain and . Most studies on seismic fragility of buried pipelines adhere to the fragility
relation scheme based on collected empirical data. At least to the authors’ knowledge, only few research
efforts [128,129] have advanced to producing classic fragility curves by calculating probabilities of
failure rigorously as they are produced, for instance, for the case of bridges [130].
4.1 Empirical seismic fragility relations for buried pipelines
The first studies that utilized observed pipe damage from earthquakes date back to 1975, when
Katayama et al. [131] published charts of pipe damage as a function of PGA for different soil categories,
taking into account data obtained from six events. Later, Eguchi [132] generated expressions for pipe
breaks in terms of the MMI scale for various pipe materials, being the first to distinguish between wave
propagation and PGD hazards and providing a ranking in terms of vulnerability of different pipe
materials as follows (in descending order): concrete, PVC, cast iron, ductile iron, X-grade steel.
Barenberg [133] and Ballantyne et al. [134] then developed the first fragility relations considering PGV
as the ground motion IM. Along the same lines, empirical PGA-based fragility expressions were
produced in three subsequent studies [135–137].
A remarkable effort is that of O’Rourke and Ayala [138], who proposed a PGV-based seismic fragility
relation based on damage data associated with pipelines of various materials from three earthquake
events. Their function concerning damage due to wave propagation was adopted by FEMA in HAZUS
methodology [139] and has been thereafter widely used. Further on this subject, O’Rourke et al. [140]
performed comparative damage analyses using different IMs; their conclusion was that the highest
correlation between damage and seismic motion severity is achieved with the use of PGV as IM, that
being one of the first confirmations of the enhanced efficiency of velocity- and energy- related IMs,
compared to PGA, for problems involving soil response. In an alternative approach, Trifunac and
Todorovska [141] defined the damage rate as the amount of pipe breaks per square km of land area and
used the peak soil shear strain γmax as IM to derive fragility expressions for water pipelines based on the
1994 Northridge event. O’Rourke and Jeon [142] then used cast iron pipe damage evidence from the
1994 Northridge event to develop a fragility relation for wave propagation. The combined effect of
seismic and/or abnormal loadings over time on the fragility of water networks in Cyprus has also been
derived by Fragiadakis et al. [143].
Because of the major importance of fragility estimates in decision making and lifecycle management of
lifelines, the American Lifeline Alliance published guidelines [144] that incorporate the most
comprehensive list of seismic fragility relations for water supply pipelines, based on an extensive
database of documented damage that includes 81 data points. The relations are provided in the form of
backbone functions, allowing for adjustment through correction factors to account for different pipe
materials, joint types and other parameters, and their validity has been confirmed in practice in recent
earthquake events. It should be noted that the damage data present considerable scatter and, moreover,
refer mostly to cast iron (CI) and asbestos cement pipeline. O’Rourke and Deyoe [145] accomplished a
twofold objective by re-examining previously used data sets related to segmented buried pipes: on the
one hand to illustrate that the peak ground strain is more consistent than PGV in describing seismic
damage to segmented buried pipes, on the other hand to develop improved fragility relations in terms
of . An effort was also made to derive PGV-based relations considering the type of the controlling
seismic wave. These relations assume that S-waves govern for near-source sites and R-waves for far-
source sites. Jeon and O’Rourke [146] performed comparisons among damage prediction equations
using differently estimated PGV, concluding that the maximum recorded PGV value provides better
correlation with water supply pipeline damage rates. Later, Pineda and Ordaz [147] proposed a new
vector IM for buried pipeline fragility functions, , and showed that it is more closely
related to damage patterns in soft soils. By assuming different effective wave velocity, other researchers
[148] presented a revised strain-based fragility relation for segmented pipes exposed to seismic wave
More recently, Esposito et al. [12] presented a comprehensive study analyzing the performance of the
L’Aquila medium- and low-pressure gas distribution network in the 2009 earthquake. Relying on
damage reports, seismic fragility of buried steel pipes in terms of repair rates was estimated and plotted
against local-scale PGV values interpolated using ShakeMaps illustrating the spatial distribution of
seismic intensity. Then, the obtained data were validated against existing fragility relations, giving non-
negligible damage underestimations by the latter. The deviations were attributed to the fact that the
fragility relations used were established for arc-welded steel pipes, while the L’Aquila gas pipeline
network consists of gas-welded pipes, which are more vulnerable.
Table 3. Summary of the most recent empirical fragility functions in terms of repair rate (RR/km) for buried
pipelines found in the literature; PGV in cm/s, K1 and K2: correction factors that apply to certain pipe types, PGD
in cm, : peak ground strain, GMPGV: geometric mean PGV
Fragility function
M. J. O’ Rourke and Ayala (1989)
 
Wave propagation damage
T. D. O’Rourke and Jeon (1999)
0.00109 PGV
Wave propagation damage, CI pipes
ALA (2001)
10.002416K PGV 
Wave propagation damage, various
pipe typologies
ALA (2001)
22.5831K PGD 
PGD damage, various pipe typologies
M. J. O’ Rourke and Deyoe (2004)
513 g
Wave propagation damage, segmented
M. J. O’ Rourke and Deyoe (2004)
724 g
Combined wave propagation and PGD
damage, segmented pipes
M. J. O’ Rourke and Deyoe (2004)
0.034 PGV
Wave propagation damage, surface
M. J. O’ Rourke and Deyoe (2004)
0.0035 PGV
Wave propagation damage, body waves
M. J. O’ Rourke (2009a)
1905 g
Wave propagation damage, segmented
T. D. O’Rourke et al. (2014)
4.52 2.38
Wave propagation damage, CI pipes
T. D. O’Rourke et al. (2014)
0.0839 0.41
Lateral ground strain damage, CI pipes
M. J. O’ Rourke et al. (2015)
2951 g
Wave propagation damage, segmented
Fig. 11. Comparative log-log plot of published strain-based empirical fragility relations for buried steel pipelines
under TGD.
Noteworthy is the fact that high-density polyethylene pipes exhibited no damage at all. More recently,
O’Rourke et al. [149] assessed the performance of underground water, wastewater and gas pipelines
during the 2011 Canterbury seismic sequence. By processing large amounts of damage data through
screening criteria, they developed robust fragility relations for different pipe materials, using geometric
mean PGV, angular distortion and lateral peak ground strain as IMs. Specifically, for the gas distribution
network performance, they comment that it remained almost undamaged, owing to the good ductility of
MDPE pipelines. Further, O’ Rourke et al. [150] enriched the previously proposed fragility expressions
[148] with four additional data points obtained from the 1999 Kocaeli event, in Turkey. This fragility
relation does not differ significantly from the initial one, hence demonstrating that the latter is fairly
stable. Strain-based fragility relations for steel pipelines under TGD are plotted in Figure 11, while all
empirical fragility expressions cited herein are summarized in Table 3. If we examine Figure 11, we
notice that the region of agreement for the plotted curves lies between ground strains of 10-3 and 10-2,
which are quite large and potentially damaging for the pipeline. Beyond this range, the curves diverge.
Of note also, the damage rates increase linearly with the ground strain, a trend that is in contrast with
analytical findings [47,96] suggesting that the soil-pipe slippage releases pipeline strain as soon as a
relatively small relative displacement is mobilized (of the order of 10-3 m). This effect might need to
trigger a discussion on the functional form of the fragility curves.
Lanzano et al. [128] published one of the few studies that addresses complete fragility curves, in the
sense of probability of exceedance of a specific performance level given some measure of ground
motion intensity. Their investigation regarded continuous, steel-welded, NG pipelines subject to TGD
and the IM used was PGV as well. Three discrete damage states were established: slight, significant and
severe, which then were associated with corresponding risk states, according to projected estimations
of environmental consequences. Utilizing a vast database of past earthquake damage, from which only
the well documented cases were considered, seismic fragility curves were developed by fitting the useful
data with a lognormal CDF (Figure 12). The extension of this work incorporates fragility curves due to
PGD [129]. Recently, Melissianos et al. [151] presented a probabilistic methodology for performance
assessment of fault-crossing buried steel pipelines. Using fault displacement hazard analysis, a vector
IM of the fault displacement components and structural analysis of a BNWF pipeline model, they
developed fragility surfaces for tensile and compressive strains, with and without account of demand
and capacity randomness.
Fig. 12. Seismic fragility curves for buried NG pipelines developed by Lanzano et al. (2013) (adapted from [128]).
RS1 and RS2 stand for Risk State 1 and 2, corresponding to limited and significant loss of containment
4.2 Identified challenges
It is evident that the state-of-the-art on seismic fragility of pipelines is limited to empirical expressions,
which might be yield more credible damage rates, but their applicability is restricted to cases where
ground motion, soil and pipe characteristics are similar to the sample used to derive those simplified
expressions. Therefore, generalized and unconditional use into seismic risk assessment, mitigation
methodologies and software introduces a significant degree of uncertainty. In light of this fact, analytical
fragility curves, verified against experimental results, are expected to provide a more reliable estimate
of damage of pipelines under a wider range of seismic scenarios, soil types, and for an extended typology
of buried NG pipelines, also allowing for the consideration of special phenomena affecting pipe
response, such as the SVEGM and SPI. Damage states have to be explicitly defined and linked to limit
state criteria. Further, there seems to be some bias in the available damage information, as most of it
concerns segmented water pipelines. Research on vulnerability of continuous steel-welded pipelines,
which is the norm in buried NG networks, is scarce; hence, this issue remains to be illuminated.
To achieve the goal of sustainability, two major requirements must be met during the design life of a
lifeline: regular maintenance and quick rehabilitation after an extreme event. In this respect, an integral
part of the desired service lifecycle of lifelines is the implementation of non-destructive Structural
Health Monitoring (SHM) methods during their operation towards the reliable diagnosis of their
structural condition. According to Chang [152], SHM provides the means to continuously gather (nearly)
real-time information on the integrity of infrastructure without interruption of their service, with the
final goal being hazard mitigation. A successful SHM application is typically characterized by the
following aspects [153]: (a) almost real-time health screening, (b) minimal service interruption during
the monitoring process, (c) deployment of sensing instruments able to capture on a continuous basis
variations in specific metrics that determine the state of the structure, (d) transmission of acquired data
through an established wired or wireless network and (e) data analysis in order to detect damage patterns
and assess damage modes and extent.
SHM has become standard practice for virtually every type of lifeline structure nowadays; underground
energy pipelines are no exception to this. Apart from earthquake-induced damage, pipe deterioration
may be accelerated by previous time-dependent material degradation and ageing, or even manufacturing
defects and imperfections. Pipeline SHM techniques are useful both as a prevention tool, in that they
can detect on time accumulated damage due to service loads, wearing and pre-existing flaws prior to
any failure, and as a remediation tool to rapidly localize and characterize incurred damage immediately
after the occurrence of an earthquake. Needless to say, the pipeline industry is bound to special
regulations that require the implementation of inspection procedures on existing pipelines [154].
Scheduled maintenance by means of visual in situ inspections has now been replaced to a great degree
by cutting-edge techniques that not only offer a broader insight of the structure’s integrity indicators
both in space and in time, but also minimize labor and downtime costs. Excluding the outdated and
inefficient in situ inspection, three are currently the main sensing technologies used in pipeline SHM
[155]: (a) in-line inspection techniques, (b) fiber optic sensing and (c) remote sensing. Of the three, the
first two are the dominant trends in pipeline industry, and for this reason only are treated herein.
5.1 In-line inspection techniques
Perhaps the most widely adopted approach in SHM of buried NG pipelines today is the so-called in-line
inspection. Essentially, small autonomous devices known as ‘smart pigs’ (the term ‘pig’ derives from
Pipeline Inspection Gauge) and carrying sensors, data recorders and transmitters are inserted inside the
pipeline and driven by content flow, ‘in-line’ with it. As they travel long distances in the interior of the
pipe, the mounted sensors obtain continuous measurements of various parameters, depending on the
desired inspection tasks; these are typically related to geometry checks, strain analysis, metal loss and
crack detection. In this manner, large pipeline segments can be examined at reduced times without
blocking the transportation process of NG. The basic principle behind the measuring activity that gives
meaning to the obtained data is that consecutive measurements are taken over time, thus any change
with respect to previously obtained values related to undamaged state will denote a health issue. After
proper statistical processing, these data are compared to measurements corresponding to the so-called
‘learning’ period and diagnosis is then made with respect to the integrity of the pipeline.
Commercially available in-line inspection tools are based on various sensing technologies [155].
Among them, ultrasound-based sensors are common in the market for metal loss and crack inspections.
These are sensing transducers that emit ultrasonic pulses in the direction of the pipe wall. The acoustic
signals are then reflected from both the inner and the outer wall surface and captured back from the
transducer (Figure 13a). From the knowledge of the sound velocity in the medium and by measuring
the traveling times of the signal, wall thickness is computed and any metal loss can be inferred. The
transducers may be piezo-electric or electro-magnetic, with the latter being the case for NG pipelines as
the former require a liquid medium to function, and may also be installed on the external surface of the
pipeline. Another highly popular in-line inspection technology tailored to corrosion detection of steel
pipelines is magnetic flux leakage. According to the underlying physical principle of magnetization, the
inspection unit transmits magnetic flux into the pipe-wall, creating a magnetic circuit. If metal corrosion
is present in certain regions, there will be some sort of leakage in the magnetic field, which is detected
by magnetic sensors placed on the unit (Figure 13b). Moreover, the latest industry trends suggest the
combined utilization of different sensing technologies on a single in-line inspection tool in order to carry
out more reliable, multi-purpose pipeline inspections.
Fig. 13. Schematic views of in-line inspection technologies: (a) principle of ultra-sound based sensors (reprinted
from [154]; (b) principle of magnetic flux leakage sensors
5.2 Distributed fiber optic sensing
Fiber optic sensors are one of the most promising technological developments in the field of SHM,
although their first use can be traced back as early as the 1970s [155]. The function of fiber optic systems
is based on the physical properties of light propagation: the goal is to associate unexpected variations in
the light signals as they travel along fiber strands with damage patterns. Through various configurations,
fiber optic sensing offers diverse capabilities in measuring a number of different parameters, including
strain, temperature, pressure and acceleration [153]. What is of interest in examining the condition of a
pipeline subject to earthquake effects is primarily the strain levels in the pipeline. Discrete and, lately,
distributed fiber optic sensors have been used for strain monitoring purposes. Although discrete sensors
provide unmatched resolution and accuracy in local-scale measurements, they are not suitable for global
monitoring, as this would require the installation of thousands of them along the pipeline, together with
a complex wiring system, leading to prohibitively high costs.
This significant drawback is surmounted by the distributed fiber optic sensors, which are capable of
efficiently monitoring large portions of such elongated systems as pipelines. Distributed sensors are
fairly simple in their structure; they comprise a single silicon fiber cable sensitive at its whole length,
which is tightly bonded to the pipe wall upon installation in order to allow lossless transfer of the
material strains. Low attenuation levels ensure that distributed sensors perform well over distances of
up to 25 km [156]. Other advantages of the distributed sensing technology include simple cable
connections to the data receiver and reduced installation effort and cost.
Fig. 14. Select results from the pipe strain monitoring experiment with distributed Brillouin sensors conducted by
Glisic and Yao (2012), indicating detected damage inside the strain concentration region (reprinted from [157]).
Distributed fiber sensing technology relies on one of the following three optical effects: Rayleigh
scattering [158], Raman scattering [159] and Brillouin scattering [160]. Technical details about these
fall out of the scope of this study and may be found in the relevant references. Brillouin scattering-based
implementations are usually the method of choice, since they suffer the least from signal losses and they
are capable of long-range monitoring [157]. Several experimental studies have been conducted that
demonstrate the effectiveness of the method. For instance, Inaudi and Glisic [156] present the results of
the field application of a previously developed Brillouin distributed strain, temperature and combined
strain-temperature sensing instrument (DiTeSt) [161]. Excellent performance of distributed strain
monitoring on a buried gas pipeline subjected to landslide loading was reported, as well as successful
detection of the leakage spot by the distributed temperature sensors during a gas leakage simulation. In
an earlier laboratory test, Ravet et al. [162] took advantage of the unique capability of distributed
Brillouin sensors to measure both tension and compression at the same time, in order to detect the
starting point of buckling in a steel pipe under axial compressive load. To ensure prior knowledge of
the location of buckling initiation, weakening of the specimen wall was performed at a specific region.
Comparison between the measurements from the distributed Brillouin sensor and installed strain gauges
along the pipe body showed good agreement, and tensile strains were successfully detected by the
distributed Brillouin sensor, signifying the initiation of the buckling process. Glisic and Yao [157] put
extensive efforts in developing an integrated damage monitoring method of buried concrete segmented
pipelines exposed to seismic effects, using distributed Brillouin scattering-based fiber optic sensors. In
validating the method with large-scale testing, PGD was simulated to act on a 13 m-long pipeline
assembled inside a test basin and covered with soil, while strain readings obtained from the fiber optic
sensors were verified against data from conventional strain gauges (Figure 14). Damage accumulation
in the joints was mainly observed, as expected, and the sensing system achieved to identify these
patterns as strain peaks in the strain profiles. The applicability of the method can be safely extended to
continuous steel pipelines according to the authors.
5.3 Critical summary and SHM issues to be addressed
The aforementioned pipeline inspection techniques are not universally applicable in industrial practice,
as they present specific drawbacks that limit their implementation. A crucial factor that determines the
suitability of in-line inspection tools is the potential of the pipeline to permit passage of the ‘pig’ unit
through its body (known as ‘pigability’), which depends on a number of pipeline attributes, such as the
size of the pipe section, the operational pressure and the flow conditions [163]. Besides, in-line
inspection requires some degree of manual operation, as well as efficient energy management of the
wireless sensors. More importantly, in-line inspection techniques are considered less suitable than
distributed fiber optic sensing for emergency-state rapid damage detection following an earthquake, as
they require longer operating times. On the other hand, fiber optic solutions are particularly expensive,
and their cost tends to increase dramatically with higher measurement accuracy. Distributed fiber
sensors also require more intricate installation procedures and ensuring of good bonding with the pipe
wall is a prerequisite for accurate sensor readings; further to this, optimized placement of the distributed
sensors on the pipe circumference is another concern for reliable integrity monitoring [164].
As a general remark concerning the full spectrum of available inspection technologies, it should first be
underlined that, like above-ground structures, there is great computational demand in handling
effectively the vast amount of data that are acquired from long-term pipeline monitoring facilities. To
this end, efforts should be made towards the development of efficient data processing tools that
incorporate sophisticated threshold-based algorithms of deterministic or statistical background, to
reliably interpret captured metrics variations on the basis of previous samples. Second, the major
challenge is to take advantage of the existing pipeline SHM technologies in a holistic approach
involving rapid post-rupture health assessment, fast repair actions and decision-making in the direction
of network resilience. Such considerations should not ignore the fact that, during a post-earthquake
crisis period, power supply and wireless communications networks may experience long-lasting outages,
hence hindering any integrity assessment works. The same applies to accessibility issues attributed to
landslides and road network disruption.
Resilience is a rapidly-developing concept in the domain of lifeline engineering that can be understood
in the context of emergency situations caused by natural (e.g. earthquakes, floods, hurricanes) or man-
made (e.g. vehicle collisions, bomb explosions) extreme events that induce abrupt variations in the
performance of lifelines. Even though there is a breadth of different definitions spreading along different
disciplines, in an earthquake engineering context resilience denotes the highly desirable property of
either a physical infrastructure or a social (community) system that relies on engineering works to adapt
to and recover fast from a disruptive or disastrous event. Naturally, it requires multidisciplinary
considerations for its quantification as it draws knowledge from seismology, earthquake (geotechnical
and structural) engineering, economics, social and management sciences, among others.
6.1 Analytical treatment of resilience
In a pioneer work, Bruneau et al. [165] set the foundations for the quantitative assessment of seismic
resilience. They define a resilient system as one that obeys to three basic rules:
It is characterized by enhanced reliability.
It generates tolerable levels of losses when experiencing failure.
It can return quickly to a previous performance standard after failure.
The preliminary identification of these core features of resilience are a prerequisite to its quantification.
Drawing upon a study by Cimellaro et al. [166], seismic resilience is expressed as an index that
represents the capacity of an infrastructure system or community to withstand earthquake effects by
retaining an acceptable level of performance over a given post-earthquake time period, through a
process involving loss estimation, collection of resources, relief strategy planning and restoration
actions. The time-dependent performance of the system is measured in terms of functionality , a
 
Q t
dimensionless function of time, denoting the service quality of an infrastructure system at any time
instant as a proportion of the full functionality corresponding to the initial, intact state of the system,
assumed to be equal to 100% (Figure 15). A mathematical definition of seismic resilience under the
consideration of a single seismic event is possible:
 
R Q t dt
t t
where is the time of the occurrence of the seismic event and is the investigated time horizon.
Graphically, eq. (24) represents the shaded area underneath over the time interval ,
 
Q t
t t
normalized with respect to this interval, as illustrated in Figure 15. The mathematical definition of
functionality involved in Eq. (24) may vary depending on the system examined. In general, it can be
based on qualitative or ranking measures, which provide the means to represent the consequences of
some specific damage level (input) on the functionality of the system (output). Alternatively, it can be
modelled as a non-stationary stochastic process [166].
Fig. 15. Graphical illustration of time-varying functionality, resilience, rapidity and robustness; R: resilience;
: average rapidity; : recovery time
6.2 Dimensions of resilience
Establishing a quantitative definition of resilience is not straightforward, while its evaluation and
enhancement pose an additional challenge, given the various sources of uncertainty that arise and the
subjectivity of the problem. As Bruneau et al. [167] propose, this task can be facilitated if the idea of
resilience is broken down into simpler descriptors: (a) rapidity, (b) robustness, (c) redundancy and (d)
resourcefulness. Detailed descriptions of these quantities are available in Refs. [167,168]. Rapidity and
robustness are quantifiable (refer to Figure 16), while redundancy and resourcefulness are more abstract
qualities of an infrastructure system, difficult to quantify and also interlinked with each other. To make
a distinction from rapidity and robustness, redundancy and resourcefulness provide the means to achieve
resilience, whereas rapidity and robustness are descriptors of the final outcome.
6.3 Seismic resilience assessment of buried NG networks
Some key considerations and existing research on seismic resilience of buried NG networks are
discussed in this section.
Seismic hazard analysis
Similar to seismic risk assessment, seismic hazard analysis forms an integral part of seismic resilience
assessment, as it provides essential input (i.e., IM distribution) to the loss estimation process. Because
of the spatial correlation of the ground motion across different network stations [169], it would be
irrational to construct regional seismic hazard maps based on methods that account for the seismicity of
multiple sources. In this case, the problem is usually addressed by considering single seismic scenarios
derived deterministically or from disaggregation of PSHA-generated seismic hazard maps. Another
approach is proposed by Sextos et al. [170], where seismic scenarios associated with specific return
periods are produced by PSHA for each seismic source independently. Appropriate IMs for assessing
pipeline network loss are discussed in Section 4.
Loss estimation
In loss estimation, a major difficulty is that there is correlation between direct and indirect loss in NG
networks because flow disruption in one network component effectively impedes the functionality of
all downstream components. NG pipeline networks are generally not characterized redundant, hence
flow redistribution is usually impossible. More importantly, given that NG networks also supply energy
to power plants, the indirect losses stemming from a potential general power outage can be elusively
high. This implication may severely slow down the emergency response, the recovery activities and the
rehabilitation process of the damaged network component, and consequently lead to a costly vicious
circle. The strong interdependence between modern life aspects and the uncertainty in identifying and
quantifying losses relating to different domains (e.g. economy, society, and environment) adds to the
complexity of the indirect loss estimation, which is still hard to perform in a reliable quantitative manner.
Moreover, in contrast to the immediate direct loss, indirect loss can grow or shrink during the gradual
restoration of pre-event functionality. Ageing effects, such as corrosion, and previous undetected
structural defects or damage can further impact resilience levels by downgrading the initial state of
functionality and also increasing the immediate functionality drop down to the residual level right after
the natural disaster, a fact that most often goes unnoticed. For these reasons, only a wider network
analysis of the consecutive recovery phases can capture the time evolution of the indirect losses and
give a reliable estimate overall.
Risk mitigation strategies
Another consideration with elevated meaning to resilience enhancement is the risk mitigation strategies.
A distinction between pre- and post-earthquake mitigation measures is meaningful here. Pre-earthquake
measures are usually implemented in the design phase of a pipeline network and aim to either reduce
the friction at the soil-pipe interface, hence eliminate pipe axial stress development, increase pipe
stiffness or strength, hence reduce deformation, or increase flexibility, hence accommodate deformation.
Some common ‘mild’ measures of this type applied in practice to minimize PGD effects in critical
regions are the following: wrapping of the pipeline with geotextiles, use of low-friction coatings,
encasement of pipeline into isolation concrete culverts, backfilling with loose material, trench widening.
These can prove to be effective also when TGD is the main geohazard, particularly in regions of sharp
changes in the ground stiffness or topography. Other more drastic preventative measures include use of
flexible joints and above-ground elevation or re-routing of a pipeline portion to avoid hazardous land
zones, the latter rarely being an option due to right-of-way permissions. A more comprehensive list of
such measures can be found, among others, in [126,171,172]. In [171], a comparative quantitative
evaluation of alternative measures is also presented, and it is found that geotextile fabrics, pipe wall
thickness increase and trench backfilling with loose soil provide rather low to moderate protection,
while concrete culverts appear more effective. The effectiveness of each preventative measure reflects
directly on the residual functionality following a seismic event (i.e., robustness), and implicitly has
effect on the recovery time.
Post-earthquake measures refer to rapid repair actions taken just after the event and long-term
rehabilitation strategies to restore near-initial functionality of the network. For instance, the currently
operating NG network rapid response and risk mitigation system in Istanbul [173] will interrupt NG
flow if threshold IM values are exceeded upon reception of early-warning system signals. Subsequently,
the deployed array of strong motion recording instruments generates real-time regional hazard maps,
and the distribution of damage in the pipeline network is estimated using fragility relations soon after
the earthquake strikes. Based on these, decision-makers are ready to prioritize rapid repair where
necessary. Cimelarro et al. [174] test a NG network retrofit system consisting of automatic seismic gas
shutoff valves, flow dividers and valves located in compressor stations. Analysis for different seismic
scenarios show that it augments resilience by an average of 78%. The effect of each remediation measure
on the recovery time of the network remains to be investigated, so that designers and stakeholders gain
understanding into the techno-economic trade-off of each measure. Distributed fiber optic sensors
(Section 5.2) appear a promising solution for rapid health screening of a NG network and their efficiency
should be evaluated for resilience enhancement purposes.
Latest research
Only a handful of studies on quantitative evaluation of seismic risk and resilience are on record, since
it is a topic that has gained scientific interest quite recently [175]. Esposito et al. [12] analyzed the time-
evolution of network functionality described in terms of the ratio of reconnected customers over total
customers after the shock, showing that only 40% of the customers were reconnected to gas supply after
two months. The low restoration level achieved is attributed to the fact that reconnection was permitted
only to buildings that received a green-tag during post-earthquake inspection. More recently, Cimelarro
et al. [174] developed and applied to a case study a comprehensive quantitative framework for the
seismic risk analysis of gas distribution networks considering the impacted network functionality and
the ensuing recovery process. Network functionality defined as a function of the time-variant gas flow
and total operating pipe length was computed with numerical modeling using SynerGEE software. A
single seismic scenario was extracted by de-aggregating local hazard maps corresponding to 22%
probability of exceedance in 50 years and median PGV maps were calculated using attenuation
relationships. Only PGD-induced pipe damage was considered and the ALA fragility relations were
exploited to express pipe damage distribution in a repair rate format. The study resulted in the estimation
of resilience indices of the gas network for all damage scenarios, before and after the application of a
retrofit alternative, including emergency shutoff valves and flow dividers.
In the same spirit, but for different network type, Dong and Frangopol [176] presented a resilience
assessment methodology for highway bridge networks under mainshock and aftershock effects,
introducing a probabilistic post-event functionality metric that is a function of damage state indices and
bridge fragility. Resilience is estimated from Eq. (24) by using appropriate normal CDFs to model the
recovery phase, depending on the damage state. In Sextos et al. [170], where intercity networks are
addressed, resilience-centered time-dependent qualitative loss indicators of binary form are introduced
to track the over-time variation of direct and indirect losses not easily quantifiable in monetary terms
(here: connectivity, accessibility, environment), and their effect on the functionality metric. The
previous two approaches are examples of transportation networks linking structural, geotechnical with
network and consequence analysis that can be potentially adapted to the case of pipeline networks after
appropriate modifications.
Presently, few modern codes and standards worldwide dictate requirements for the protection of
underground NG pipelines against seismic risk, the most notable being Eurocode 8 - Part 4 [38] in the
European Union, the American Lifeline Alliance guideline [66] in the U.S. and the design
recommendations by Japan Gas Association [37]. In this section, the key points in each normative
document are discussed. It should be made clear that seismic loading is not a primary consideration in
design of pipeline sections, rather it is the flow capacity and the internal pressure that dictate the
selection of diameter, thickness and steel grade.
7.1 Eurocode 8 provisions (2006)
Part 4 of Eurocode 8 [38] provides a broad regulatory framework for the seismic design of pipelines,
inter alias. According to it, the ultimate limit state of a pipeline is associated with structural collapse.
Yet, it is implied that certain critical components of the system susceptible to brittle failure may be
checked for a state prior to total failure. A two-level serviceability limit state hierarchy is prescribed;
the lower one requires that the system remains fully operational and leak-proof and the higher one that
it undergoes some level of damage without losing its whole supplying capacity. Another secondary
safety hazard that should be taken into consideration in ultimate limit state (ULS) design is explosion
and fire in the event of an earthquake-induced breakage and the potential consequences on people and
the environment. The determination of the seismic actions should be based on the two principal sources
of damage, i.e., TGD and PGD.
Further, Eurocode 8 states that pipe inertial forces related to ground acceleration are of minor
significance in comparison with the forces caused by ground deformation, thus they may be neglected;
this simplifies the nature of the problem, converting it to a static one. With regard to wave propagation
effects, Annex B of Eurocode 8 recommends the conservative method developed by Newmark [52] to
determine the induced pipe strains and curvatures, as long as the soil is stable and homogeneous. As for
the spatial variability in ground motion, no particular guideline is provided; however, in the chapter
concerning above-ground pipelines, it is suggested that spatial variability is accounted for when the
pipeline length analyzed is over 600 m or the ground is characterized by longitudinal non-uniformities.
It is also noted that pipelines buried in dense soil are allowed to be designed solely for the effects of
wave propagation.
For steel welded pipelines, Eurocode 8 specifies that the maximum ductility of steel is not exceeded and
buckling modes are not observed. For the first condition, ultimate steel tensile strain is set to 3%; for
the second, the allowable steel compressive strain is proposed as the smaller value between 1% and
, where t is the thickness and r the radius of the pipe.
 
20 t r
7.2 American Lifelines Alliance guidelines (2001)
The report prepared by American Lifelines Alliance (ALA) [66] focuses on roughly the same points
with Eurocode 8. In addition, it suggests performing three-dimensional nonlinear quasi-static FE
analysis for investigating PGD effects, considering soil-pipeline interaction. The mechanical behavior
of both the steel pipe and the soil should be modeled as inelastic. The length of the pipeline model
should be carefully selected in a way that the imposed constraints at the ends do not produce unrealistic
local axial deformations. The need to ensure a more refined mesh in the proximity of the PGD region is
also highlighted.
In terms of modeling of wave propagation effects, it is stressed that flexural strains may be neglected,
due to being much smaller than axial ones. Moreover, the conservative assumption that soil strains are
caused by surface waves can be adopted, since this results in larger strains. Wave propagation-induced
soil strains are usually expected to be lower than 0.3%.
A list of performance criteria are proposed, which, however, are not universally applicable; different
permissible values may be set for each specific case. For PGD-induced axial strains, two performance
states are suggested: operable state and pressure integrity state. For the first, non-exceedance is dictated
of a 2% tensile strain and a limit compressive strain defined as
,0.50 0.0025 3000
' 2
c cr
t pD
D Et
 
 
 
 
where and is the minimum measured diameter due to ovalization.
 
' 1 3D D D D D  
 
Eq. (25) was proposed by Gresnigt [41]. The corresponding limits for the second are and
t cr
. Concerning the effects of wave propagation, the resulting bending stress must not
,1.76 /
c cr t D
exceed the yield strength of steel. The allowable tensile strain is set to 0.5%, while the allowable
compressive strain is defined as 3/4 of the limit specified in Eq. (25). All above limits are in force only
on the condition that strict welding procedures are adopted during construction of the pipeline. The soil
spring relationships discussed in Section 3.1.2 are proposed. It is noted that the calculation of axial
springs must be performed considering backfill soil properties.
7.3 Recommended practice by Japan Gas Association (2000)
The ‘Recommended practice for earthquake-resistant design of gas pipelines’ developed by Japan Gas
Association (JGA) [37] constitutes a revised version of the initial guideline, issued in 1982. It features
a strict methodology for designing high-pressure transmission pipelines to Level 2 seismic motions.
Design seismic motions are specified based on two performance levels similar to Eurocode 8: Level 1
states that ‘operation can be resumed immediately without any repair’, while Level 2 states that ‘the
pipeline does not leak, though deformed’. The design flow comprises two phases. In the first phase, the
design seismic motion is determined considering the potential existence of active faults near the pipeline
route, which may require a fault analysis. The second phase consists of a sequence of simplified
formulas that estimate wave propagation-induced pipe strains. Specifically, the natural period of
vibration of the surface soil layer and then the apparent wavelength of the assumed seismic motion
are calculated first:
where H is the thickness of the layer and the weighted S-wave velocity,
where is the apparent wave propagation velocity of the motion. Following is the calculation of the
axial ground displacement at the depth of the pipe axis as
2cos 2
h V
U c T S H
 
   
 
where is the seismic zone coefficient, the spectral velocity of the soil layer and z the pipe burial
depth. The peak ground strain of uniform, regular ground can then be estimated:
g h
 
The last step involves extraction of the pipe strain from the ground strain using a strain transfer
a q
 
 
 
where q is a coefficient accounting for soil-pipe sliding and is the axial soil spring stiffness. Finally,
pipe strain is calculated as
 
 
and checked against an allowable strain of 3%. The previous procedure applies to straight pipe segments,
provided that no fault affects the pipeline; a slightly different last step is proposed for pipe elbows and
7.4 Other design guidelines
Other standards and regulations provide hardly any additional useful information on the issue. The B31
Code for Pressure Piping by the ASME [177,178] highlights that the maximum axial stress for a
restrained pipeline should be constrained up to a level that no buckling is caused; the permissible value
for the sum of all the longitudinal stresses is established as
,max 0.90 y
 
Axial strain should not develop further than 2%. Furthermore, design against for soil liquefaction and
landslides should be performed based on the operability performance level.
A relevant report by FEMA [21] states among others that, unless previously corroded or poorly
assembled, buried pipeline systems are quite unlikely to get largely affected by traveling seismic waves;
on the other hand, permanent ground deformations are considered to have a higher damaging potential.
Increasing the ductility capacity of the pipeline and ensuring protection against corrosion and high
quality welding are qualified as capable measures to improve the performance of the pipeline even under
large permanent ground movements.
7.5 Observations
Except for JGA guidelines, existing codes are not seen to provide a concrete framework for earthquake-
resistant design or seismic performance assessment of buried steel pipelines, rather their utility is limited
to coarse tips and recommendations on construction practices and simplifying assumptions. Eurocode
8 insists on the conditionally reliable but outdated method by Newmark, disregarding the long
recognized SPI influence on pipe response. ALA goes one step further by proposing soil spring
relationships; their applicability, however, has limitations as discussed previously. On the other hand,
JGA does define a specific methodology for design of buried pipes solely against wave propagation, but
this considers only axial response and homogeneous soil; in addition, it does not address the question
of what soil spring constants should be used.
Overall, the previous guidelines are far from comprehensive and do not yet make use of the breadth of
research observations, methods and data reported in the literature. More importantly, striking is the total
absence of any reference to vulnerability assessment and seismic risk or resilience of gas networks.
Focus is made on the component level instead of the network level. Similarly, no information is provided
on SVEGM and SHM techniques.
This review study provides a critical discussion on the state-of-the-art in seismic analysis, safety
verifications and resilience assessment of buried steel NG pipelines through an integrated treatment of
the most significant relevant aspects. Conclusions and challenges can be summarized as follows:
Current performance criteria for TGD actions, especially those for more complex damage modes,
such as buckling, seem to lack concrete support by experimental findings. Efforts should be
directed towards dynamic SPI tests to develop more reliable limit state parameters, considering
all important factors controlling the dominant damage modes. Criteria for potential interaction of
different damage modes would be valuable as well, as a combined damage mechanism might be
more detrimental.
The true cyclic pattern of TGD has been mostly overlooked in previous SPI analyses. It should be
verified whether experiment-validated cyclic spring models displaying hysteretic loops offer
advantage over the commonly used elastic-perfectly plastic ones in dynamic BNWF model
simulations. Coupling between different SPI directions is generally not considered in current
equivalent spring models. 3D continuum models, although computationally expensive, are
essential to explore the buckling capacity of buried pipelines, and to further our understanding into
the influence of various parameters, such as the contact models, pre-load conditions, initial
imperfections and internal pressure. Pipe axial trains only due to wave passage are usually found
to be way below the 0.5% yield limit of API 5L steel. In light of this, site-specific analyses,
considering the most unfavourable ground conditions (horizontal variation of soil
stiffness/irregular topography) crossed by the pipeline, are deemed necessary to obtain the most
critical pipe demand under local site effects. This approach should be reflected in the relevant
codes. Physical testing would be of value in order to verify and extend analytical findings.
Current knowledge on seismic fragility of buried steel pipelines need be expanded beyond the
simplified expressions of repair rates based on both computational and experimental investigation
of the limit states for the various modes of failure relating to the integrity of a pipeline. This will
also allow the examination of the effect of SPI and SVEGM on pipeline damage rates.
Two are the predominant pipeline SHM methods used in practice today: in-line inspection and
distributed fiber sensors. Both exhibit benefits and drawbacks in different perspectives, though
fiber-based monitoring appears to be a more attractive option in the long term. The challenge here
is to efficiently utilize them in post-earthquake health screening to maximize rapidity of recovery
and consequently resilience levels.
Seismic resilience of buried NG networks is still an open issue. Resilience levels depend on
pipeline robustness, which in turn depends on the network vulnerability; the latter exhibits
dependence on various factors, such as seismic hazard definition, pipeline demand and earthquake
protection measures. Resilience is also affected by rapidity in post-disaster response, which can be
improved through better SHM and emergency preparedness, and redundancy, which is generally
not an inherent property of NG networks. All these interdependencies need to be scrutinized in
order to proceed to the development of reliable seismic resilience assessment methodologies.
These methodologies shall arrive at specific indices that can support the informed decision-making
of the stakeholders. The effect of pre- and post-event mitigation measures on the resilience levels
of the network must be comparatively assessed.
Modern seismic standards and guidelines do not yet reflect important findings of the latest state-
of-the-art in research. The existing provisions for TGD actions mainly concern the wave passage
effect, which however is rarely critical to the pipeline integrity. There is also a general lack of a
detailed step-by-step design methodology that will guide the practicing engineer throughout the
process of seismic design. In contrast, a set of empirical recommendations are mainly provided,
which however are sometimes incomplete or outdated. Last but not least, there is a lack of a holistic
strategy for the resilience-based management of a NG pipeline network towards disaster risk
mitigation at large.
This work was supported by the Horizon 2020 Programme of the European Commission under the
MSCA-RISE-2015-691213-EXCHANGE-Risk grant (Experimental & Computational Hybrid
Assessment of NG Pipelines Exposed to Seismic Risk, This support is
gratefully acknowledged. The first author would also like to express his gratitude to the Engineering
and Physical Sciences Research Council (EPSRC) for financially supporting his doctoral studies. We
are also thankful to the anonymous reviewers whose constructive comments helped towards the
improvement of this manuscript.
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... Most of the pipeline damage reported is attributed to PGD, but there is also strong evidence that wave propagation has contributed to pipe damage, especially TGD in nonuniform sites and undesirable deformations in the pipe, which is overlooked in the present standards of practice [16]. e effect of inhomogeneous soil on pipeline seismic demand was first studied by Hindy and Novak [17] using the dynamic equilibrium of an elastic lumped-mass beam model of the pipeline and appropriate soil springs and dashpots. ...
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The deformation and residual strength of the buried pipeline caused by the earthquake in nonuniform sites has an important influence on the safety of the pipeline. Most of the previous research focuses on the permanent ground deformation (PGD) caused by fault or transient ground deformation (TGD) due to seismic wave propagation independently. The mechanical character of buried pipelines crossing nonuniform sites during seismic sequence after ground settlement has not been studied. This article carried out a dynamic centrifuge experiment to simulate the seismic response of buried pipelines of polyvinyl chloride (PVC) and aluminum alloy (AL) horizontally crossing the loose and dense site and study the residual strength of pipelines after an earthquake. Two simulated seismic waves with 0.6 g and 0.3 g of input peak ground accelerations (PGAs) were inputted in sequence to simulate the strong and weak earthquakes. The deformations of ground and pipelines were obtained during and after seismic. The numerical model consistent with the experiment was established and compared with test, and it was found that the strain of pipeline caused by TGD was different between numerical and experimental results, especially in the loose site. The mechanical model of the pipeline by earthquake indicated that the total strain of the pipeline was composed of bending deformation by PGD and axial deformation by TGD. PGD caused by a strong earthquake had great effects on the deformation and residual strength of the pipeline. The strain of pipeline by TGD was compressive-extensional alternating mode between the loose and dense site and the strain amplitude reached peaks near the block interface in the loose site. The residual strain of pipeline in the dense site was a compressive strain, while in the loose site, it was compressive-extensional alternating mode and varied with the stiffness of the pipeline.
... Έχει αποδειχθεί (Mohammadi 1985) οτι οι βλάβες στα δίκτυα ενδέχεται να προκληθούν από την διάρρηξη του ρήγματος, καθώς και από καταπόνηση οφειλόμενη στην διαφορετική απόκριση τμημάτων του δικτύου. Αυτή η διαφορετική απόκριση αποδίδεται στην μεταβαλλόμενη στον χώρο εδαφική διέγερση, καθώς και σε γεωτεχνικές ή γεωλογικές ασυνέχειες (Psyrras and Sextos 2018;Psyrras et al. 2019). Δεδομένου οτι οι βλάβες ενός δικτύου εξαρτώνται και από τα χαρακτηριστικά της σεισμικής δράσης και από εκείνα του δικτύου, κατά τα τελευταία έτη καταβάλλεται προσπάθεια να προσδοθεί χαμηλή τρωτότητα έναντι σεισμού στα δίκτυα που κατασκευάζονται σε σεισμογενείς περιοχές, μέσω ειδικών μελετών που γίνονται για τον σκοπό αυτό (Menoni et al. 2002). ...