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The seismic response of natural gas pipelines buried in discontinuous permafrost under vertically propagating shear waves: parametric analysis

Conference Paper

The seismic response of natural gas pipelines buried in discontinuous permafrost under vertically propagating shear waves: parametric analysis

Abstract

Buried natural gas pipelines are important infrastructure to connect areas of gas exploration to areas of use. In many parts of the world, pipelines cross seismic regions and varieties of soil strata, including regions of discontinuous permafrost in the Northern hemisphere. Initial studies find that the seismic response of soils can be strongly influenced by changes in underlying soil strata, hence potentially leading to greater seismic demands on buried infrastructure such as pipelines. Frozen soil deposits, in particular, can lead to a significant change in dynamic soil response to seismic excitation. To study the effect of crossing discontinuous permafrost zones on the seismic behaviour of buried natural gas pipelines, a combined modelling approach is proposed: (1) dynamic site response analysis to determine the load conditions and (2) quasi-static finite-element analysis on the pipeline and surrounding soil. In this paper, results from one-dimensional equivalent linear soil response analyses for a site of dis-continuous permafrost is presented. Despite the frozen soil stratum lying at a depth of 40 m, the response of the soil at the depth of the buried pipeline is found to be significantly affected. A parametric numerical validation study on a finite element model of a typical buried natural gas pipeline is then presented to assess the influence of geometrical and mechanical parameters on the response of pipeline and surrounding soil by means of a series of incremental dynamic analyses. Outcomes of this study highlights the strong effect of the soil properties on the strain in buried pipelines.
COMPDYN 2019
7th ECCOMAS Thematic Conference on
Computational Methods in Structural Dynamics and Earthquake Engineering
M. Papadrakakis, M. Fragiadakis (eds.)
Crete, Greece, 2426 June 2019
THE SEISMIC RESPONSE OF NATURAL GAS PIPELINES BURIED IN
DISCONTINUOUS PERMAFROST UNDER VERTICALLY
PROPAGATING SHEAR WAVES: PARAMETRIC ANALYSIS
Daniel A. Pohoryles1, Luigi Di Sarno2, Oh-Sung Kwon3, Marianna Ercolino4and Ana-
stasios Sextos5
1European Commission, Joint Research Centre (JRC), Ispra, Italy; University of Sannio, Italy
e-mail: daniel.pohoryles@ec.europa.eu
2University of Sannio, Italy and University of Liverpool, UK
3University of Toronto, Canada;
4University of Greenwich, UK;
5University of Bristol, UK;
Abstract
Buried natural gas pipelines are important infrastructure to connect areas of gas exploration
to areas of use. In many parts of the world, pipelines cross seismic regions and varieties of
soil strata, including regions of discontinuous permafrost in the Northern hemisphere. Initial
studies find that the seismic response of soils can be strongly influenced by changes in under-
lying soil strata, hence potentially leading to greater seismic demands on buried infrastruc-
ture such as pipelines. Frozen soil deposits, in particular, can lead to a significant change in
dynamic soil response to seismic excitation. To study the effect of crossing discontinuous
permafrost zones on the seismic behaviour of buried natural gas pipelines, a combined mod-
elling approach is proposed: (1) dynamic site response analysis to determine the load condi-
tions and (2) quasi-static finite-element analysis on the pipeline and surrounding soil. In this
paper, results from one-dimensional equivalent linear soil response analyses for a site of dis-
continuous permafrost is presented. Despite the frozen soil stratum lying at a depth of 40 m,
the response of the soil at the depth of the buried pipeline is found to be significantly affected.
A parametric numerical validation study on a finite element model of a typical buried natural
gas pipeline is then presented to assess the influence of geometrical and mechanical parame-
ters on the response of pipeline and surrounding soil by means of a series of incremental dy-
namic analyses. Outcomes of this study highlights the strong effect of the soil properties on
the strain in buried pipelines.
Keywords: Pipelines, Seismic behaviour, Structural Dynamics, Earthquake Engineering, Fro-
zen Soil, Discontinuous Permafrost.
Daniel A. Pohoryles, Luigi Di Sarno, Oh-Sung Kwon, Marianna Ercolino and Anastasios Sextos
1 INTRODUCTION
Long-distance buried pipelines often unavoidably cross terrain with different soil types as
well as with variation of surface-level built-environment. For instance, the pipeline can cross
highways or railways that may induce additional settlement under static loading [1]; moreover,
they may also concern the boundaries between soil strata causing local stress concentrations un-
der vertically propagating seismic waves [2].
The effect of local site conditions on the ground motions is a known phenomenon and ground
response analyses are common practice in geotechnical earthquake engineering [3]. Changes in
soil properties along the length of a pipeline are still considered to be an under-examined issue of
importance. A variation in the seismic behaviour of soils and, hence, a variation in local stress in
pipelines can be caused by discontinuous permafrost, which occurs in regions with mean annual
soil surface temperature of -2 to -4°C, causing partial freezing of soil layers below ground. In the
Northern Hemisphere, 24% of the ice-free land area is affected by permafrost, i.e. soil that con-
tinuously has a ground temperature below 0 °C for at least two consecutive years [4]. Still, its
effect on the seismic site response for buried infrastructure has not yet been studied extensively,
and in current design practice, it is ignored. As the exploration of natural resources in seismically
active regions, such as Alaska, U.S., or Canada, that are also permafrost regions, is expanding, it
is critical to further explore this topic [5].
Frozen soil deposits can lead to a significant change in dynamic soil response to seismic exci-
tation. In particular, geotechnical properties, such as soil stiffness and shear wave velocities, in-
crease in frozen soils. In a discontinuous permafrost zone, only some parts of the soil mass are in
frozen conditions. This can lead to a stark contrast in soil response at their boundaries, in both
lateral and vertical directions. The effect of permafrost on the ground response to transient
ground motions has only sparked interest in the last decade. Some examples are given in north-
ern Canada [6], Alaska [5], as well as in Tibetan regions of China [7], where critical infrastruc-
ture, such as railways or buried pipelines, cross seismically active zones and permafrost sites.
To study the effect of crossing discontinuous permafrost zones on the seismic behaviour of
buried natural gas pipelines, a combined modelling approach is proposed: (1) dynamic site re-
sponse analysis to determine the load conditions and (2) quasi-static finite-element analysis on
the pipeline and surrounding soil.
In this paper, the results from one-dimensional equivalent linear analyses for soil strata in dis-
continuous permafrost at a site in Alaska are presented. Despite the frozen soil stratum lying at a
depth of 40 m, the response of the soil at the assumed depth of the buried pipeline (5 m) is found
to be significantly affected due to the large change in shear wave velocities in the frozen layer.
This paper also presents the outcomes of a preliminary numerical validation study to define the
influence of some geometrical and mechanical parameters on the response of pipeline and sur-
rounding soil. A 3D finite element model of a typical buried natural gas pipeline is developed,
including the soil surrounding it. By means of a series of incremental dynamic analyses (IDA),
parameters, such as mesh size and geometry of the surrounding soil, are investigated to assess
their effect on the response of the pipeline in soils with different geotechnical properties. Out-
comes of this study highlight the significant effect of the surrounding soil properties on the strain
in buried pipelines. Moreover, the study validates the use of both coarse mesh and smaller geom-
etry of the surrounding soil to allow a computationally efficient model.
2 BACKGROUND
2.1The effect of vertical components of ground motions
A majority of studies on the seismic resilience of buried steel pipelines considers seismic
loading in the horizontal plane of the pipeline, be it in lateral or axial directions [8]. The effect of
the vertical component of ground motions is not well-studied. Vertical loading is mainly consid-
ered in the case of static loading or permanent ground deformations caused by earthquakes, such
as fault movements or landslides.
Lee [9] undertook a series of finite-element analyses on the combined vertical static (traffic
and soil weight) and vertical seismic loading. The soil is modelled homogenously along its depth
and length and traffic load is spread evenly across the surface of the soil and is not considered in
the dynamic load. A number of different, albeit homogenous, soil conditions are investigated, as
well as the effect of boundary conditions, corresponding to continuous and segmented pipelines.
It is found that continuous pipelines behave better, and that sandy soils increase the stress in the
pipelines compared to clay under static loading conditions, however only to a level that may lead
to temporary serviceability issues. While no specific limit states are specified, under vertical
seismic loading, it is found that for continuous boundary conditions, acceptable stress levels are
obtained, while stress increases for segmented boundary conditions. A deeper analysis of the lo-
cal effect of variation in soil type or built-environment is however needed.
Jeon [10] carried out incremental dynamic analyses (IDAs) to investigate the relative behav-
iour of buried pipelines designed to Korean and US guidelines under vertical seismic excitation.
A two-dimensional model along the length of the pipeline is created, with the soil considered
homogenous throughout. Maximum strains along the pipelines of up to 0.6% are observed. The
range of peak ground accelerations (pga) in the study is limited to up to 1.2g and no internal
pipeline pressure is assumed in the analysis.
2.2Variations in vertical load conditions along pipelines
The effect of different vertical surface load conditions on buried high-pressure gas pipelines is
the topic of a finite element study by Brückner et al [11], who applied a modular approach to
look at traffic loading, water loading and railway crossings.
Manna and Duari [12] investigated the local effect of pipeline-road crossings in terms of cy-
clic traffic load and find that corrosion and damage is more likely underneath road-crossings.
Zhou et al [1] assessed the uneven static loading conditions on a buried pipeline using finite ele-
ment analysis. The authors determined that local stress concentrations in the pipeline are ob-
served when a gas pipeline crosses a high-filling road, which may affect its operational safety.
The effect of pipeline internal pressure, as well as pipeline wall-thickness are found to be signifi-
cantly affecting local stress in pipeline elements under static vertical loading.
The combined effect of seismic and traffic loading has been studied by Kokavessis and Anag-
nostidis [2], which however focused on the soil-structure interaction in the case of soil-
liquefaction.
2.3Variations in soil conditions along pipelines
Changes in soil properties along the length of a pipeline are still considered to be an under-
examined issue of importance. Local site conditions can significantly influence the response of
soil to ground motions [3], [6]. A variation in soil properties may be a case of two horizontally
Daniel A. Pohoryles, Luigi Di Sarno, Oh-Sung Kwon, Marianna Ercolino and Anastasios Sextos
adjacent soil strata of different stiffness, but also the case of a pipeline crossing a soft alluvial
valley [3].
In the case of pipelines crossing soil strata characterized by large temperature differences in
soil layers, such as discontinuous permafrost regions, a multitude of potential issues have been
studied in the literature, including uplift of the pipeline due to frozen soil around pipelines under
static loading conditions [13], but also the effect of thawed layers in frozen soil on soil liquefac-
tion [14].
However, also the dynamic properties of frozen soil are significantly different, for instance,
the Young´s modulus of frozen soils can be magnitudes of 10s or 100s times larger than for the
same soil in unfrozen state [4]. As ground temperatures can increase with depth below the per-
mafrost, its stiffness will hence also decrease with depth. Similarly, the shear wave velocities are
lower for unfrozen soil.
Wang et al [7] compiled wave velocities obtained from field tests along the Quinghai-Tibet
railway in China for different soil types (silty clay, mudstone, marl, fine sandy soil) under frozen
and unfrozen conditions. This zone is very seismically active and constitutes the largest area of
permafrost at high elevations in the world. The data from ten boreholes was then used to carry
out site response analyses and obtain ground motion acceleration spectra. Wave velocities are 1.2
- 1.6 times and 1.4 - 1.7 times larger in frozen soils for S-wave and P-waves, respectively.
Yang et al. [5] looked at another seismically active permafrost region, namely Alaska. One-
dimensional equivalent linear analysis was carried out looking at the vertically propagating hori-
zontal shear waves. The aim was to investigate the effect of permafrost on the seismic response
of bridges in Alaska, hence looking at the response at ground level in soils with and without
permafrost. Variations in permafrost depth, thickness as well as depth to bedrock were the main
parameters studied.
The parametric study showed that a soil profile with a permafrost table at -20 m and the bed-
rock table at -66 m produces the largest surface response spectrum. This particular soil profile
may produce a site response that is larger than anticipated by design codes. The authors hence
concluded that the seismic design of structures should consider the presence of continuous per-
mafrost, as it influences the site response significantly.
Dadfar et al [6] investigated the effects of discontinuous permafrost on the seismic behaviour
of pipelines by modelling the 2D response of a pipeline that is crossing alternating regions of
frozen and unfrozen soil. The frozen and unfrozen free-field responses in the horizontal direction
of the soil are determined to be significantly different due to a large change in seismic shear
wave velocities. The results from the soil free-field response study is then used as input motion
along the length of the pipeline and compared to a uniform support excitation case. It is found
that considering regions of frozen soils leads to a large induced moment and plastic deformation
in the pipeline, which is not observed in the uniform case. Ovalisation is not found to be critical,
but the pipeline is instead found to yield in bending.
In discontinuous permafrost, frozen soil deposits can lead to a significant change in soil re-
sponse. In particular, the stiffness of the soil and shear wave velocities are increased in the frozen
soil [15]. In a discontinuous permafrost zone, parts of the soil mass are frozen conditions while
others are not. This can lead to a stark contrast in soil response at their boundaries, in both lateral
and vertical directions, as frozen soils have different geotechnical properties and shear-wave ve-
locities than unfrozen soils.
Dadfar et al [15] conducted a combined experimental and numerical study on the seismic site
response of alternate blocks of frozen and unfrozen soil. Free-field spectral accelerations were
found to be larger for the frozen soil, but the increase is affected significantly by the spacing and
geometry of the frozen soil blocks.
3 METHODOLOGY
An intensive study of available literature on modelling the effect of transient seismic ground
motions on pipelines [3] found that the inertial soil-pipeline interaction is negligible and that the
fully dynamic problem of buried pipelines can be split into a dynamic soil analysis and a quasi-
static analysis of the pipeline behaviour.
In the case of vertical loading with variation in soil properties in the soil model, ovalisation of
the pipeline cross-section, as well as bending failure of the pipeline are assumed the only poten-
tial failure mechanisms, the latter being less realistic due to the high ductility of steel pipelines
used for natural gas transportation [8]. Excessive ovalisation of the cross-section can lead to loss
of pipeline integrity or serviceability and is limited to 15% by most guidelines [6]. Buckling or
fracture of the pipeline are only observed under axial loading [3].
It is hence proposed to use a similar two step approach to modelling as proposed by Psyrras
and Sextos [3]. First, one-dimensional equivalent linear analysis on two different sets of soil stra-
ta, with and without permafrost layer at 40 m depth, is performed to obtain soil response spectra
at different depths of the soil. Initial results from the ground response analysis step are presented
in the next section, highlighting the effect of permafrost layers on the soil response at ground
level.
Next, the pipeline and surrounding soil are modelled in a three-dimensional finite element
model, with vertical displacement applied to the top of the soil, according to the obtained accel-
eration histories obtained from the ground response analysis. In this study, a parametric analysis
on the various parameters affecting the finite element modelling of the pipeline-surrounding soil
model is presented. The effects of different soil materials around the pipeline, different pipeline
diameter and thickness of the pipeline-wall, as well as geometric parameters of the surrounding
soil model, including mesh-size and depth of modelled soil stratum are assessed.
The results obtained in this study can then be used for future modelling of pipelines crossing
two different soil strata, by applying two different loading histories along the length of the pipe-
line, obtained from ground response analyses.
4 GROUND RESPONSE ANALYSIS WITH AND WITHOUT PERMAFROST
In this section, an initial response analysis of potential vertical soil strata with and without
permafrost layer is presented. Two soil profile are constructed for a site in Alaska [5], with the
mechanical properties of the different layers provided in Table 1 and Table 2.
A one-dimensional equivalent linear analysis is then performed in the DEEPSOIL software
[16], with two low velocity transition layers with thickness of 1.5 m assigned on the top and bot-
tom of permafrost layer to account for the surface condition and the partially frozen layer be-
tween frozen and unfrozen soils.
Daniel A. Pohoryles, Luigi Di Sarno, Oh-Sung Kwon, Marianna Ercolino and Anastasios Sextos
Layer name
Thickness
(m)
Unit
weight
(kN/m3)
Shear wave
velocity
(m/s)
Damping
ratio
(%)
Sandy Silt 1
14.00
20.00
200.00
0.48
Sandy Silt 2
23.00
20.00
300.00
0.48
Sandy Silt 3
14.00
20.00
400.00
0.48
Gravel
6.00
20.40
450.00
0.50
Weathered
Rock (Clay)
9.00
20.40
550.00
2.60
Table 1. Soil characteristics for the stratum without permafrost
Layer name
Thickness
(m)
Unit
weight
(kN/m3)
Shear wave
velocity
(m/s)
Damping
ratio
(%)
Sandy Silt 1
10.00
20.00
200.00
0.48
Sandy Silt 2
20.00
20.00
300.00
0.48
Sandy Silt 3
10.00
20.00
400.00
0.48
Frozen Soil
11.00
20.00
1500.00
2.20
Gravel
6.00
20.40
450.00
0.50
Weathered
Rock (Clay)
9.00
20.40
550.00
2.60
Table 2. Soil characteristics for the stratum without permafrost
A dynamic analysis was performed using twelve earthquake records (Chi Chi, Coyote, Impe-
rial Valley, Kocaeli, Loma Gilroy, Loma Gilroy (2), Mammoth Lake, Nahanni, Northridge,
Northridge(2), Parkfield and Whittier Narrows). For details of the records, the reader is directed
to the documentation of DEEPSOIL[16].
A comparison of the two soil profiles is hence made based on this analysis. In a first stage, the
response of the soil at 5 m depth, i.e. in the first soil layer of sandy silt, is analysed. This corre-
sponds to the buried depth of the pipeline assumed in the initial finite element analysis [9]. The
results are hence compared for strain, acceleration and displacement for this depth in the pres-
ence or absence of a layer of frozen soil below.
Looking at soil acceleration at 5 m depth for soil with and without permafrost layer below, re-
spectively, an increase between 2.7% and 22.0% with a mean of 9.2% (standard deviation = 0.08)
is recorded over the twelve applied ground motions. This difference in soil acceleration at a
boundary between two soil profiles could lead to a highly localised difference in demand on a
buried pipeline. In Figure 1, an example of the effect of a permafrost layer at 40 m depth on the
acceleration time history in the top soil layer for the Parkfield ground motion record is displayed.
The figure highlights the effect on the peak acceleration in the top layer of soil due to the pres-
ence of permafrost.
Daniel A. Pohoryles, Luigi Di Sarno, Oh-Sung Kwon, Marianna Ercolino and Anastasios Sextos
Figure 1. Acceleration - time history at 5m depth for both soil profiles for the Parkfield record
Obtained maximum strain in the top layer of soil and recorded peak ground acceleration
for the soil strata are shown in Figure 2. It indicates that higher levels of strain are reached in
the soil without permafrost in the strata below. It would hence seem that the presence of per-
mafrost attenuates the strain in the top layer of soil. A similar trend, albeit with more disper-
sion, can be seen for the maximum soil displacements, shown in Figure 3.
Figure 2. Strain in the first soil layer against pga for all records
Soil Acceleration (g)
Strain (%)
Daniel A. Pohoryles, Luigi Di Sarno, Oh-Sung Kwon, Marianna Ercolino and Anastasios Sextos
Figure 3. Maximum displacement in the first soil layer against pga for all records
To further investigate of the results, the maximum soil strain and displacement throughout
the depth of the two soil profiles is analysed. The results displayed in Figure 4 highlight that
in the frozen soil, due to the strong increase in stiffness, a very low maximum strain is ob-
tained, compared to the unfrozen soil. This reduction in strain for the same ground motions is
then transferred to the layers, leading to the attenuation in soil strain observed at 5 m depth.
Figure 4. Maximum strain versus depth in the soil profile for all ground motions
For soil displacement, a similar observation can be made, with reduced values observed in
the permafrost layer and the layers above it (Figure 5). In both cases, below the frozen soil
depth (m)
Daniel A. Pohoryles, Luigi Di Sarno, Oh-Sung Kwon, Marianna Ercolino and Anastasios Sextos
layer, the response of gravel and weathered bedrock are not affected by the presence of per-
mafrost. In the top soil layer, i.e. where the pipeline is buried, a reduction of 21% in soil dis-
placement and 31% in soil strain are observed on average for the profile including a layer of
permafrost.
Figure 5. Maximum displacement versus depth in the soil profile for all ground motions
Overall, the results from this initial soil response study are in line with previous studies
([15], [17]) and highlight the difference in behaviour between the two soil profiles under the
same earthquake loading. It is important to note, however, that the response is highly depend-
ent on the selection of ground motions and that larger spectral acceleration will amplify this
difference.
5 PARAMETRIC FINITE ELEMENT ANALYSIS
In the literature, finite element studies on the seismic behaviour of buried pipelines that as-
sess the relative influence of modelling parameters are rare. Lee [9] undertook a parametric
study concentrating on the influence of buried depth, mesh size and pipeline length. In this
study, the influence of four model parameters (soil type, soil depth below pipeline, pipeline
diameter and mesh size) are assessed individually. These parameters are summarised in Table
3 and are described in more detail in the following section.
Soil Type
Soil depth
below pipe-
line, h’
(m)
Pipeline
diameter
(m)
Mesh
size
(m)
Saturated sand /
10 - 30
0.2 0.4
124
Silty sand
Table 3. Assessed parameters in the finite element model
depth (m)
Daniel A. Pohoryles, Luigi Di Sarno, Oh-Sung Kwon, Marianna Ercolino and Anastasios Sextos
A finite element model of a buried pipeline is created in ABAQUS [18]. The pipeline has a
diameter of 0.4 m and a wall thickness of 10 mm for all models except for the parametric
study of pipeline diameter for which a smaller diameter of 0.2 m and thickness of 5 mm are
tested. For all models, this pipeline is buried at a depth of 5 m and has a length of 15 m. The
soil surrounding the pipeline is modelled with a width of 10 m and a length of 15 m. The
model dimensions are summarized and illustrated in Table 4 and Figure 6, respectively.
Figure 6. Finite element model dimensions
Dimension
Symbol
Value (m)
Length
L
15
Width
W
10
Total depth
H
15.4 35.4
Buried depth
h
5
Depth below
h’
10 30
Pipeline diameter
D
0.2 0.4
Pipeline wall thickness
t
510 (mm)
Table 4. Model dimensions summary
The material properties of the pipeline are constant in all models and represent a ductile
steel pipeline. The elasto-plastic material properties [9] are shown in Table 5. To model the
pipeline, second order reduced integration shell element with eight nodes (S8R) are chosen.
The elements have a thickness corresponding to the pipeline wall thickness and a mesh size of
1 m for all models in the parametric study (Figure 7).
Mechanical property
Symbol
Value
Density (kg/m3)
ρ
7850
Young’s modulus (GPa)
E
210.7
Poisson’s ratio
ν
0.3
Shear modulus (GPa)
G
81.0
Yield strength (MPa)
fy
490
Yield strain (%)
εy
0.23
Table 5. Pipeline elasto-plastic material properties
L
H
D
t
h
W
h’
Daniel A. Pohoryles, Luigi Di Sarno, Oh-Sung Kwon, Marianna Ercolino and Anastasios Sextos
Figure 7. Pipeline finite element model and meshing.
The effect of two different soil types on the seismic performance of the pipeline is assessed.
As shown in Table 6, a flexible silty sand material [5], as well as a stiffer saturated sandy ma-
terial [9] are defined. The materials aim to reflect the material in the top layer of the soil strata
defined in the ground response study, as well as a stiffer variant of it. The soil is considered as
elasto-plastic material with Mohr-Coulomb plastic properties and is modelled using three-
dimensional second order reduced integration brick elements with 20 nodes (C3D20R). The
material properties for the soil types are summarised in Table 6.
Type of property
Mechanical property
Symbol
Saturated
sandy soil
Silty sand
Elastic
Density (kg/m3)
ρ
2160
2160
Young’s modulus
(MPa)
E
96.00
5.00
Poisson’s ratio
ν
0.25
0.35
Mohr-Coulomb
Friction angle (°)
φ
40.00
20.00
Dilation angle (°)
ψ
2.00
2.00
Cohesion
Cohesive strength
(kPa)
c
17.00
10.00
Table 6. Soil properties in finite element model
The influence of soil depth below the pipeline is assessed in the parametric study for a con-
stant mesh size (4 m), for a pipeline buried at 5 m in sandy silt, for one earthquake record.
The comparison is performed on two soil depths representative of values found in the litera-
ture. As shown in Figure 8, these correspond to 15 and 35 m total depth, for the shallow [9]
and deep [10] soil models, respectively.
Daniel A. Pohoryles, Luigi Di Sarno, Oh-Sung Kwon, Marianna Ercolino and Anastasios Sextos
Shallow soil (15m total depth)
Deep soil (35 m total depth)
Figure 8. Model geometry with different soil depths
While the mesh size of the pipeline is kept constant at 1 m, a mesh size sensitivity study
for the soil surrounding it is conducted, testing the effect of mesh size varying from 1 m to 4
m. The mesh obtained for the three sizes, varying from fine to coarse, for the soil elements are
shown for the deeper soil model in Figure 9.
Fine mesh (1 m)
Medium coarse (2 m)
Coarse mesh (4 m)
Figure 9. Mesh sizes for sensitivity study
The boundary conditions for the model are shown in Figure 10. The base of the soil is fully
restrained, while roller supports are put on the side faces (Y-Z planes) of the soil model. The
ends (Y-X planes) of the pipeline are also modelled as rollers. The nodes at the interface be-
tween soil and pipeline are fully tied.
Daniel A. Pohoryles, Luigi Di Sarno, Oh-Sung Kwon, Marianna Ercolino and Anastasios Sextos
Figure 10. Boundary conditions in finite element model.
For the parametric analysis, an IDA is performed scaling the six sample records for values
of pga up to 2.0 g. While this value of pga is large, it is consistent with other studies in the
field (e.g.: [19]). The reader is reminded that the purpose of this initial study is the investiga-
tion of modelling parameters´ influence, rather than a vulnerability assessment of pipelines.
The details of each analysis are reported within the sections focusing on the individual param-
eters. The seismic load is applied as body force in Abaqus [18]. Before applying the seismic
load, a realistic static load is applied in the first step of the analysis. This includes the gravity
load and an additional load due to traffic loading applied on the ground surface as a uniformly
distributed pressure of 1100 kPa. This corresponds to a total load of 165 000 kN applied on
the soil with dimensions of 10 by 15 m.
The seismic behaviour of the pipeline is then assessed by comparing the maximum abso-
lute strain and stress in the longitudinal direction along the axis of the pipeline and the vertical
displacement in the pipeline elements at midspan at each step in the IDA.
6 RESULTS
6.1Mesh sensitivity
As an initial assessment, sensitivity to the mesh size is analysed using the larger diameter
pipeline and saturated sandy soil properties. The deeper soil geometry is chosen as the differ-
ence in mesh size would be more pronounced for it. The pipeline material and pipeline ele-
ment mesh size are kept constant. An IDA with pga intensities of 0.25 up to 2.0 g with a step
size of 0.25 g are ran and the differences in results for the three mesh sizes are compared.
In particular, mean differences in terms of longitudinal strain (Δε) and vertical displace-
ment (Δδ) to the fine mesh for the coarser mesh sizes are reported in Table 7. The differences
to the fine meshed model in terms of strain are below 1.7% on average and around 1.0% in
terms of displacement.
Medium mesh
Coarse mesh
Δε
1.68 %
0.21%
Δδ
1.04%
1.09%
Table 7. Mesh size sensitivity in terms of strain and vertical displacement
Daniel A. Pohoryles, Luigi Di Sarno, Oh-Sung Kwon, Marianna Ercolino and Anastasios Sextos
These minor differences in results combined with the reduced computational time for the
coarse mesh. On average, one step in the IDA for the coarse mesh size (ca. 1 h per run) is
about four times lower than the fine mesh (ca. 4 h). The heavily reduced computational cost
hence justifies the use of a 4 m mesh size.
6.2Influence of pipeline diameter
As a parameter of pipeline geometry, the influence of the pipeline diameter is assessed.
Two different diameters (0.4 m and 0.2 m) with different wall thicknesses (10 mm and 5 mm,
respectively) are modelled. Note that for both geometries the diameter to thickness ratio (D/t)
is kept constant at 40. The ground motions selected for the IDA are scaled with pga intensities
ranging from 0.25 to 2.0 g with a step size of 0.25 g. For this comparison, the total soil depth
used is 15 m (shallow soil) and the soil material corresponds to the saturated sandy soil.
The results for the applied ground motion records and the average are plotted in Figure 11.
It can be observed that for the pipeline with larger diameter, the average longitudinal strain at
mid-span is up to 10.8% higher. The average strain values obtained reach 0.13 % for the small
diameter pipeline and 0.11% for the larger diameter. In both cases this is below the yield
strain of 0.23%.
Figure 11. pga against strain comparing the influence of pipeline geometry.
Figure 12. pga against total vertical displacement for two pipeline geometries.
Daniel A. Pohoryles, Luigi Di Sarno, Oh-Sung Kwon, Marianna Ercolino and Anastasios Sextos
In terms of maximum vertical displacement, for both relatively low values up to -0.22 m
are obtained due to the stiffness of the soil (Figure 12). As it would be expected, the pipeline
properties do not influence the response of the soil, instead it is expected that the soil geome-
try and properties, assessed in the next section, are critical parameters.
6.3Influence of soil depth
Another important point in terms of computational cost is the total model size. This can be
heavily reduced by reducing the depth of soil layers below the pipeline. In the literature for
similar pipeline dimensions, 10 m to 30 m of soil below the pipeline can be found. To test the
influence of this parameter, a constant mesh size of 4 m is selected. The silty soil material de-
posit of the site response analysis is chosen as soil material, as the influence of soil depth is
expected to be highest for softer soils.
In terms of vertical displacement, large displacements for the deep soil model are observed,
resulting from the significantly larger accumulated settlement under the imposed traffic load.
Removing this contribution, an average difference of 14.2% is obtained between the two
models, with the deeper soil presenting larger vertical displacements.
Looking at the maximum strain at mid span in Figure 13, on average there is a 20.2%
higher strain in the bottom elements of the pipeline for the shallow soil model. The maximum
values of strain obtained exceed the yield strain in the case of the shallow soil at 1.4 g of pga.
For analysing the seismic behaviour and fragility of buried pipelines, using the shallower soil
geometry seems hence appropriate as it gives more conservative results with higher strain,
while simultaneously requiring less computational time (50 mins compared to 90 mins on av-
erage).
Figure 13. pga against strain comparing the influence of soil depth
6.4Effect of soil material properties
As the model with shallow soil is deemed most appropriate and coarse mesh size is
deemed appropriate for analysis, giving more conservative results and computational efficien-
cy, the influence of material properties is also tested for the shallow geometry. The results for
the same pipeline buried in soft silty soil are compared to the saturated sandy soil model.
As shown in Figure 14, the difference in strain is pronounced, with the pipeline reaching
yield in the case of the soft silty sand only. The longitudinal strain is more than double the
value for the pipeline buried in silty sand compared to saturated sandy soil at the extreme val-
Daniel A. Pohoryles, Luigi Di Sarno, Oh-Sung Kwon, Marianna Ercolino and Anastasios Sextos
ue of pga of 2.0 g. Strain is increased from maximum values of 0.12% to up to 0.27% in the
silty sand (+125%).
Figure 14. pga against strain comparing the influence of soil stiffness
This observation can be explained by the much larger vertical displacements observed for
the softer soil. Even when the settlement under gravity loading is excluded (Figure 15), the
vertical displacement is 81% lower for the saturated sand compared to soft silty sand.
Figure 15. pga vs vertical displacement without gravity load contribution for the comparison of soil types.
Overall it can be concluded that the case of softer soils leads to higher values of strain. The
sandy silt material deposit studied in the ground response study hence constitutes an im-
portant case study.
6.5IDA of a pipeline buried in a layer of silty sand
After assessing the influence of different parameters on the behaviour of the model, an in-
cremental dynamic analysis with six records scaled to pga values of 0.25 to 2.0 g in steps of
0.25g is undertaken for a pipeline buried in the soft silty material. This constitutes a case
Daniel A. Pohoryles, Luigi Di Sarno, Oh-Sung Kwon, Marianna Ercolino and Anastasios Sextos
study of a pipeline buried in a similar soil to the one at the location of ground response study.
The effect of underlying permafrost is however not yet considered in this study.
The material properties for silty sand in Table 6 are used for the IDA. The model soil ge-
ometry is chosen to be of 15 m total depth (shallow soil), with 10 m of soil beneath pipeline
and 5 m buried depth, similar to the model geometry used by Lee [9]. Based on the mesh size
sensitivity analysis presented in the previous section, a 4 m mesh for the soil elements is
deemed appropriate.
As shown in Figure 16, values of strain up 0.3% are reached, with an average of 0.27% at
the highest pga of 2.0 g. On average, plastic strain is reached in the pipelines at a pga of 1.4 g.
Plastic behaviour is hence observed for the pipeline after this level of pga, as shown in Figure
17.
Figure 16. pga against strain for the case study pipeline buried in layer of silty sand
Figure 17. pga against strain for the case study pipeline buried in layer of silty sand
It is worth noting that the ground response study on the soil strata with and without under-
lying permafrost suggests a differential acceleration history along the length of the pipeline,
which is not investigated here. Larger values of strain at the interface of the two soil strata
Daniel A. Pohoryles, Luigi Di Sarno, Oh-Sung Kwon, Marianna Ercolino and Anastasios Sextos
would be expected. In this case, which may lead to reaching yield at lower values of pga then
the ones reported here. This constitutes an important factor to be analysed in future studies.
7 CONCLUSIONS
This paper discussed the modelling parameters of influence for buried natural gas pipelines
crossing seismic regions with underlying irregular permafrost soil layers. An initial soil re-
sponse study for a site in Alaska shows results in line with previous studies ([15], [17]). The
study highlights the difference in behaviour between two soil profiles, with and without un-
derlying permafrost, under the same earthquake records applied. The soil acceleration at 5 m
depth is increased by up to 22%, resulting in a change in response of the buried pipeline. This
is particularly remarkable given the depth of the permafrost layer, still influencing the rela-
tively shallow depth of the buried pipeline. These findings are however not general and are
highly dependent on the spectral accelerations of the selected ground motion at the natural
frequencies of the soil strata.
A parametric finite element study is then conducted to assess the influence of various
modelling parameters on the results of incremental dynamic analyses carried out on a model
of the buried pipeline and the surrounding soil layer.
It is found that parameters such as mesh size and soil geometry selected to render the
most computationally efficient models will render more conservative results. An increase in
soil element mesh size from 1 m to 4 m is only found to affect the results in terms of maxi-
mum strain in the pipeline by 1.7%. A larger depth of surrounding soil in the model has a
more pronounced effect, increasing the relative displacement in the pipeline soil layer by an
average of 14.7%. The increased strain in the pipeline for the smaller soil depth, however, jus-
tifies the conservative use of the more computationally efficient parameters. The results are
most influenced by the type of soil in which the pipeline is buried, as reduced stiffness of the
soil will enhance the strain in the pipeline, with maximum strain results for a softer silty sand
more than double of the ones obtained for a pipeline buried in a stiffer material.
The next steps of the study could hence bring interesting results when looking at the re-
sponse of pipelines to vertically propagating waves at the boundary of two different soil pro-
files, such as the ones investigated in the ground response analysis. It is anticipated that the
different soil response along the length of the pipeline would lead to higher strains in the pipe-
line than anticipated when only assessing the pipeline for the two soil strata individually, as it
is usually done at the design stage.
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