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Eleventh U.S. National Conference on Earthquake Engineering
Integrating Science, Engineering & Policy
June 25-29, 2018
Los Angeles, California
SAFETY FACTORS OF BURIED STEEL
NATURAL GAS PIPELINES UNDER
SPATIALLY VARIABLE EARTHQUAKE
GROUND MOTION
N. Psyrras
1
, A. Sextos
2
, O.-S. Kwon
3
and S. Gerasimidis
4
ABSTRACT
The damaging potential of spatial variability in seismic ground motion on the integrity of buried
pipelines is demonstrated in this paper. A numerical analysis methodology is developed first to
determine the seismic demand of a typical straight steel natural gas pipeline running through a site
composed of two different media with an impedance ratio of 2 and swept by vertically propagating
SV-waves. The analysis follows a sub-structured, two-phase approach involving the computation
of pipeline input excitation from 2D linear viscoelastic and linear-equivalent seismic site response
models and the quasi-static application of the derived critical motion profiles on a near-surface 3D
continuum soil model surrounding an extended inelastic shell model of the pipeline. The focus is
then placed on identifying the ground and exciting conditions bearing adverse effects on the peak
pipeline response. By comparing the pipeline demand in terms of stress and strain to capacity
metrics prescribed in present seismic codes, the importance of the local site response is gauged.
Results show that low-frequency ground vibrations produce the most unfavorable demand on the
pipe for the set of cases examined. More importantly, even though pipeline axial strain demand-
to-capacity ratios for elastic local site response under weak excitation imply a large safety margin,
pipeline demand can exceed capacity near the site boundary under strong excitations and
subsequent nonlinear soil response. Plastic local buckling may also develop in the pipeline under
high-intensity input motions, thus highlighting the necessity to account for non-synchronous
earthquake ground motion in case of horizontally nonhomogeneous sites.
1 PhD researcher, Dept. of Civil Engineering, University of Bristol, UK (e-mail: n.psyrras@bristol.ac.uk)
2
Assoc. Professor, Dept. of Civil Engineering, University of Bristol, UK
3
Assoc. Professor, Dept. of Civil Engineering, University of Toronto, Canada
4
Ass. Professor, Dept. of Civil Engineering, University of Massachusetts at Amherst, USA
Psyrras N., Sextos A., Kwon O.-S., Gerasimidis S. On the safety factors of buried steel natural gas pipelines under
spatially variable earthquake ground motion. Proceedings of the 11th National Conference in Earthquake
Engineering, Earthquake Engineering Research Institute, Los Angeles, CA. 2018.
Eleventh U.S. National Conference on Earthquake Engineering
Integrating Science, Engineering & Policy
June 25-29, 2018
Los Angeles, California
Safety factors of buried steel natural gas pipelines under
spatially variable earthquake ground motion
N. Psyrras
1
, A. Sextos
2
, O.-S. Kwon
3
, S. Gerasimidis
4
ABSTRACT
The damaging potential of spatial variability in seismic ground motion on the integrity of buried
pipelines is demonstrated in this paper. A numerical analysis methodology is developed first to
determine the seismic demand of a typical straight steel natural gas pipeline running through a site
composed of two different media with an impedance ratio of 2 and swept by vertically propagating
SV-waves. The analysis follows a sub-structured, two-phase approach involving the computation of
pipeline input excitation from 2D linear viscoelastic and linear-equivalent seismic site response
models and the quasi-static application of the derived critical motion profiles on a near-surface 3D
continuum soil model surrounding an extended inelastic shell model of the pipeline. The focus is
then placed on identifying the ground and exciting conditions bearing adverse effects on the peak
pipeline response. By comparing the pipeline demand in terms of stress and strain to capacity
metrics prescribed in present seismic codes, the importance of the local site response is gauged.
Results show that low-frequency ground vibrations produce the most unfavorable demand on the
pipe for the set of cases examined. More importantly, even though pipeline axial strain demand-to-
capacity ratios for elastic local site response under weak excitation imply a large safety margin,
pipeline demand can exceed capacity near the site boundary under strong excitations and subsequent
nonlinear soil response. Plastic local buckling may also develop in the pipeline under high-intensity
input motions, thus highlighting the necessity to account for non-synchronous earthquake ground
motion in case of horizontally nonhomogeneous sites.
Introduction
The ever-growing need for environmentally friendly energy sources has established natural gas
(NG) as a norm in the energy market. It becomes hence apparent that the associated infrastructure
must be protected against natural and man-made hazards. Onshore long-distance transportation of
natural gas is typically performed by large-diameter, high-pressure, shallow-buried steel pipelines
(transmission system). Although the design of such structures is not earthquake-driven, they still
1
PhD researcher, Dept. of Civil Engineering, University of Bristol, UK (e-mail: n.psyrras@bristol.ac.uk)
2
Assoc. Professor, Dept. of Civil Engineering, University of Bristol, UK
3
Assoc. Professor, Dept. of Civil Engineering, University of Toronto, Canada
4
Ass. Professor, Dept. of Civil Engineering, University of Massachusetts at Amherst, USA
Psyrras N., Sextos A., Kwon O.-S., Gerasimidis S. On the safety factors of buried steel natural gas pipelines under
spatially variable earthquake ground motion. Proceedings of the 11th National Conference in Earthquake
Engineering, Earthquake Engineering Research Institute, Los Angeles, CA. 2018.
have to meet certain code-specified performance criteria. When crossing earthquake-prone areas,
the transmission lines may be exposed to significant seismic risk, thus leading to several cases of
reported damage [1–5]. An issue that has not yet been investigated in adequate depth is that, due
to their extended length, NG pipelines may be subjected to ground motions that considerably differ
spatially in terms of their amplitude, phase and frequency content. This is especially true when
seismic waves propagate through ground with non-uniform properties, giving rise to local site
effects. Local site response results from material stiffness gradients (i.e., inhomogeneity),
topographic features at the surface (e.g., hills and canyons) or special subsurface morphologic
conditions, such as sediment-filled valleys and cavities. The combination of any of these local
features with a suitably oriented oncoming seismic wavefield may cause ground motion
amplification, modify the frequency content and induce normal ground strains and curvatures (e.g.,
[6–9]), which are known to govern the earthquake behavior of buried pipelines [10–12].
The study of the effects of spatially varying earthquake ground motion (SVEGM) on the
seismic behavior of buried pipelines has been driven by different considerations, most notably
regarding the representation of the pipeline as a beam on elastic foundation or shell, the properties
of the surrounding soil (i.e., homogeneous or nonhomogeneous) and the inclusion or not of contact
effects at the soil-pipe interface. Solutions appeared early in the literature for the peak elastic
ground strains in homogeneous soil due to wave arrival delay [13,14], which, by extension, apply
also to the pipeline if interaction is ignored. Sakurai and Takanashi [15] observed experimentally
that limited axial soil-pipe interaction occurs for low-intensity excitations, while Shinozuka and
Koike [16] consolidated analytically that pipeline inertia is negligible. Hindy and Novak [17]
developed a matrix formulation of the full dynamic problem for elastic pipelines under P- or S-
waves both in homogeneous sites and in sites made up of two discrete media. It was found that the
peak axial and bending stresses due to body waves propagating parallel to the pipeline occur near
the boundary of the two media, and are larger than the ones in the homogeneous case. Wong et al.
[18,19] derived analytical descriptions of the coupled soil-pipeline motion under various
wavefronts using the theory of elastodynamics along with shell equations for the pipeline. Ignoring
soil-pipe interaction, Kouretzis et al. [20] presented elastic solutions for the axial and hoop strain
fields of long cylindrical structures due to travelling harmonic waves in elastic halfspace and
uniform soil over bedrock. Furthermore, stochastic analysis has been employed to quantify the
effect of seismic motion incoherence on the pipeline response [21,22].
A loading scenario briefly described in Hindy and Novak [17] is examined herein: a
pipeline crossing at right angles the interface between two vertically adjacent soil strata with
distinctly different shear wave velocities. The seismic excitation is assumed to be in the form of
vertically propagating plane S-waves, resulting principally in alternating axial compression-
extension of the pipeline. The problem is solved numerically by the finite element method using
non-trivial techniques and large-scale modelling of a long soil domain. The objective is to quantify
the influence of the linear and nonlinear local ground response of this particular site on the
predicted seismic demand of the pipeline and to compare the demand with relevant performance
limits available in the latest seismic and pipeline-specific standards.
Generation of the pipeline excitation
To estimate the pipeline stresses and deformations, the complete dynamic soil-pipeline interaction
problem is treated in two phases in order to reduce some of the involved complexities. First, the
time-variant local ground response to SV-wave patterns is obtained by performing 2D seismic site
response analysis. One major limitation in almost of the previous wave propagation studies, that
is, the linearity of the soil, is lifted in this study, as both linear viscoelastic and linear-equivalent
soil models are analyzed here. From the computed response histories at soil points at the level of
the pipeline (assumed to be buried at a depth of 1m from the crown), the critical spatial profile of
displacements is extracted corresponding to the maximum and minimum axial strain. Because the
seismic response of buried pipelines is not inertia-governed, the dynamic terms in the coupled
governing equations of motion can be dropped and a quasi-static analysis may be deemed a
reasonable approximation. If we further invoke the observation that inertial and kinematic
interaction between the pipeline and the soil is in most cases insignificant [12,16,23], the soil
displacements corresponding to the critical timeframe can be applied as static boundary conditions
on a near-field soil model in contact with a pipeline model after due consideration of the sliding
and separation potential between pipe and soil. An outline of this approach is given in Fig. 1.
Figure 1. (a) The problem at hand; (b) flowchart of the proposed methodology: (1) 2D seismic
site response analysis and extraction of the critical differential displacement profile of
the soil; (2) application of the critical soil displacement profile on the near-field soil-
pipeline system and evaluation of the pipeline demand.
Finite element model of the soil
A composite 30m-deep sandy site resting on elastic rock is considered with low-strain shear
modulus Go increasing with depth as described by the empirical formula of Eq. 1 [24]:
Go=1000·K2,max(σm
')0.5 (1)
where σm
' is the average effective confinement stress and K2,max a constant with values that can be
found in the literature [25] as a function of the relative density Dr. A dense (Dr = 90%) and loose
(Dr = 30%) deposit are assumed in contact, with mass densities ρ1=2 Mg/m3 and ρ2=1.4 Mg/m3
and average S-wave velocities of 280 and 200 m/s, respectively, giving an impedance contrast of
2. Fig. 2a illustrates the physical problem and identifies its basic parameters. The generated
discrete S-wave velocity profiles are plotted in Fig. 3a. The nonlinearity of the soil under strong
input motions is accounted for in an approximate way using 2D equivalent-linear soil models,
where the element-specific shear moduli and critical damping ratios are independently adjusted at
the end of each linear dynamic analysis to match shear strain-compatible values. For this iterative
scheme, the strain measure used is the maximum shear strain. The dynamic soil properties are
represented by the analytical Darendeli curve set [26]. Because this model is pressure-dependent,
a different G-D-γ curve is assigned to sublayers partitioned at every 10m depth, based on an
averaged effective confinement stress (Fig. 3b). The initial critical damping ratio is taken ξin=2%
and the Poisson ratio is 0.33. Damping is of the Rayleigh type.
Figure 2. Identification of the significant parameters of the mathematical idealization of the
problem (left) and spatial discretization and layering of the domain (right).
The domain discretization in the vertical sense was carried out in a way to ensure adequate
resolution for exciting frequencies of up to 15 Hz in the range of wave velocities examined in this
study (Fig 2b). The horizontally unbounded medium was rendered finite for the purposes of the
FE analysis by truncating it at a distance of L=150m (half-length) from both sides of the vertical
boundary. This choice was based on a convergence study of the induced axial ground strain
distributions. Standard viscous boundaries [27] were placed at the base of the deposits to absorb
the scattered seismic waves, while horizontal rollers were assigned to the lateral boundaries.
Typical values were assumed for the bedrock properties, namely Vs=1000 m/sec and ρ=2.4 Mg/m3.
Figure 3. (a) The generated shear wave velocity profiles for the two deposits of the site under
consideration; (b) calculated shear moduli degradation and damping curves.
To investigate the effect of the frequency content of the excitation on the ground
deformation, Ricker wavelets with different predominant frequencies fp of 0.5, 1 and 5 Hz were
used to represent input acceleration pulses at the bedrock. Excitations as weak as 0.05g were
assumed at the bedrock propagating vertically. Bedrock motions were further scaled to 0.2g and
0.3g to trigger nonlinear soil response. Their waveforms for bedrock peak ground acceleration
PGA=0.2g are shown in Fig. 4. Site response analysis was performed using the computer code
QUAD4M [28].
Figure 4. Acceleration time-series of Ricker wavelets with varying fp and amplitude 0.2g.
Verification
The finite element modeling was verified against closed-form 1D wave propagation solutions
computed by an alternative computer code, DeepSoil [29]. A uniform, damped soil on elastic rock
was considered with equivalent-linear properties described by the Seed and Idriss curves [24]
(mean limit). The Friuli earthquake record (Tolmezzo station, 1976) was applied as a sample
horizontal base excitation. The obtained transfer functions for the 2D and 1D representations are
plotted in Fig. 5, providing a satisfactory match. Minor differences are mainly attributed to the
different damping formulations used by the two codes in terms of frequency dependence.
Figure 5. Comparison of surface-to-bedrock motion amplification factors between 1D and 2D
equivalent-linear site response models.
Critical deformation profiles
Due to length limitations, only results for strong excitation of 0.3g amplitude are presented here.
The ground axial strain, horizontal displacement, axial curvature and vertical displacement are
plotted in Fig. 5 against the normalized horizontal coordinate. The maximum compressive strains
are marked as well. It is seen that the peak deformation occurs for the 1 Hz pulse, causing a sharp
strain peak with magnitude 12.2% and a marked ‘parasitic’ downward movement of 0.14m. Of
note, the results are quite sensitive to the type and number of G-D-γ curves employed in the model.
Figure 6. Critical spatial profiles of ground response quantities parallel to the pipeline axis for
acceleration Ricker pulses of 0.3g amplitude.
Soil-pipeline interaction analysis
In phase 2, the critical linear and nonlinear in-plane soil deformation in terms of axial strains and
curvatures obtained from phase 1 for fp=1 Hz are prescribed as an external load on the 300m-long
soil-pipe system. Next, an incremental static nonlinear analysis is carried out in Abaqus. Notably,
the imposed displacements only vary in the horizontal dimension; they are invariant with depth
because the depth of the simulated domain is small compared to the longest wavelength of the
impinging waves examined (3D/λmax<0.10), therefore the in-plane motion of the soil particles does
not change much in this dimension.
Finite element model of the soil-pipe system
We chose to model the pipeline as a shell and the near-field soil as a 3D continuum to capture the
actual gravity- and pressure-induced stress field in the pipeline. In this manner, we also tackled
the uncertainty of using soil-pipe springs to model the soil restraint. A pipeline with R=500mm,
t=12mm, σy=450 MPa, σy/σult=0.85, εult=4% and P/Py=0.63, where Py is the yield pressure, is
considered. The cross-section of the system is sketched in Fig. 7a, where the dashed lines show
the truncation of the half-plane. Plastic behavior is considered for steel through classical flow
plasticity and a von Mises criterion. The uniaxial tensile behaviour is described by a Ramberg-
Osgood fit to an elastoplastic curve with isotropic hardening. The soil medium is assumed linear
elastic based on the converged G at the end of iterations as presented in phase 1.
Figure 7. (a) The truncated cross-section of the soil-pipeline system used in the 3D model; (b)
view of the pipeline mesh with progressive refinement towards the site boundary.
The interface frictional behavior is dictated by a Coulomb friction law to allow sliding,
while separation between the soil and the pipe walls is possible. The normal and tangential
interface behaviors are coupled. Assuming an angle of frictional resistance equal to 30° for the
soil, an average interface friction coefficient of 0.4 is used [12]. Boundary conditions for the
pipeline shell are assumed completely free at its end sections. Four-node Abaqus S4R elements
are used for the pipeline and eight-node C3D8R for the soil. The element discretization of the
pipeline is shown in Fig. 7b.
Results
The response of the pipeline is presented in the form of demand-to-capacity ratios (equivalent to
the reciprocal of factor of safety) along a straight line of points. The following strain and stress
limits are used to define pipeline capacity:
the allowable compressive strain
ε
c under wave propagation as defined by:
̶ Eurocode 8 (EC8) [30]: min{1, 20 t R
⁄ } (%)
̶ American Lifeline Alliance (ALA) [31]: 0.75[0.25 t R–0.0025+3000(PR Et
⁄ )2
⁄ ] (%)
̶ Japan Gas Association (JGA) [32]: 3%
the allowable axial stress σ
xx
as specified by ASME [33]: 0.9σy
the Mises yield criterion: σVM < σy
Compression limits were chosen over tension ones because they are more conservative. Results
are shown in Fig. 8. For the low intensity pulse, the axial strain demand in the mid-section was
found, as anticipated, negligible (0.005%), with the pipeline responding in the elastic range. The
increased strains close to the pipe ends arise artificially as a result of the pressure-induced Poisson
deformation effect and the loosely restrained pipe ends. The appreciable level of stress developed
in the pipeline is also a mere result of the internal pressure. On the contrary, for the high intensity
pulse, the peak produced axial strain occurs in the plastic range and is 2 and 1.5 times larger than
the conservative non-buckling limits of EC8 and ALA, respectively. In terms of stresses, the
maximum von Mises value was found to be 97% of the ultimate strength. The ASME axial stress
limit is satisfied, but it is the strain demand that is more of interest in this type of buried
infrastructure. As a last remark not illustrated here, at a certain point after yield, wrinkling appears
in the perfect pipe and gradually localized bulges start to form, denoting shell buckling failure.
Figure 8. Pipeline demand-to-capacity ratios along the crown line in terms of (a) compressive
axial strains and (b) stresses, for 0.05g (top) and 0.3g (bottom), 1 Hz Ricker
acceleration pulse.
Conclusions
A numerical analysis methodology is introduced in this paper with the aim to assess the seismic
performance of transmission natural gas steel pipelines buried in nonhomogeneous sites under
high-intensity excitations, considering the strong soil nonlinearity of local ground response. The
scenario examined involves a straight pipeline laid through a dry cohesionless site consisting of
two deposits of different stiffness, with their interface perpendicular to the pipe section, and
excited by pulse-like SV-waves. To the degree that the dynamic response of the pipeline and the
inertial-kinematic interactions are negligible, the most important findings of this study are
summarized below:
Out of phase vibrations of the adjacent soil deposits generate axial normal strains and
curvatures, the magnitude of which depends heavily on the exciting frequency. Their
dependence on other factors, such as depth to bedrock and 1D/2D soil structure, remains to be
investigated.
Pipeline axial strain demand for elastic local site response under weak excitation is found to
be at least two orders of magnitude lower than the code-specified capacities. The presence of
considerable stresses is attributed to the in-situ state of the pipeline.
When the soil profiles respond asynchronously under stronger earthquake intensity and within
the nonlinear range, the peak demand exceeds capacity even for conservative code limits.
In the worst-case scenario examined, the pipeline starts manifesting deformation localization
in the vicinity of the ground strain peak, which is an early indication of instability collapse.
Overall, this study, even though by no means exhaustive, demonstrates that conventionally
designed NG transmission pipelines crossing soft sites with varying stiffness may experience
remarkably high axial distress under strong seismic input motions, with demand measures
exceeding by a large margin the limits established in the current state-of-practice. This calls for
further investigation of the critical combination of conditions that can lead to ultimate limit states
such as local buckling and reconsideration of the existing allowances.
Acknowledgements
The authors would like to acknowledge the financial support of the Horizon 2020 Programme of
the European Commission through grant MSCA-RISE-2015-691213-EXCHANGE-Risk
(www.exchange-risk.eu). The first author would also like to express his gratitude to the UK
Engineering and Physical Sciences Research Council for sponsoring his doctoral studies.
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