Japanese Geotechnical Society Special Publication
8th International Conference on
Earthquake Geotechnical Engineering
Influence of ground motion characteristics on liquefaction-induced pipe uplift
Devdeep Basu i) and Dharma Wijewickreme ii)
i) Postdoctoral Research Fellow, Department of Civil Engineering, University of British Columbia, Vancouver, BC V6M 2L8, Canada.
ii) Professor, Department of Civil Engineering, University of British Columbia, Vancouver, BC V6M 2L8, Canada.
ABSTRACT
Soil liquefaction occurring due to earthquakes poses severe risk to both above-ground structures as well as buried
structures such as pipes, manholes etc. During liquefaction, the shear strength of the soil above and around the pipeline
could decrease due to build-up of excess pore pressures and, subsequently, resulting in buoyancy forces that could
cause the pipelines to displace and potentially “float up” towards the ground surface. Limit-equilibrium based
procedures allow for prediction of uplift occurrence, but predicting the magnitude of uplift is a complex task with a
number of components such as soil type, pipe diameter (D) and burial depth (H), pipe boundary constraints, and
earthquake motion contributing to this mechanism. This study utilizes a well-calibrated and validated 2D numerical
model to investigate the effects of input motion characteristics on pipe uplift for a steel pipe buried in a saturated,
loose, and homogeneous deposit of Fraser River sand. The commercially available finite difference FLAC software
and soil constitutive model PM4Sand were utilized. The influence of input motion amplitude and duration on uplift
behavior of pipe was examined and discussed.
Keywords: liquefaction, earthquake, pipe uplift, numerical modeling
1 INTRODUCTION
duration (TD) and significant duration (TSD) on pipe uplift
for shallow-buried pipes in loose, saturated sand deposit
subjected to both synthetic, harmonic and recorded
earthquake input motions. A well-calibrated 2D
numerical framework is developed employing the
numerical platform FLAC v8.1 (Itasca 2016) and the
constitutive model PM4Sand v3.1 (Boulanger and
Ziotopoulou 2017) considering Fraser River sand (called
FRS hereafter), abundantly found in the Lower Mainland
region of British Columbia, Canada, as the soil material
for the study. BC Lower Mainland is situated in an
active seismic zone underlain by soils that are
susceptible to liquefaction, and many buried pipelines
traverse the region. It is recognized that the response of
pipelines subject to lateral (uplift or otherwise)
movements is a complex 3-D soil-pipe interaction (SPI)
problem with several soil, pipe cross-sectional properties
and boundary conditions, as well as seismic loading
parameters serving as contributing factors. As such, the
2-dimensional analysis presented herein is mainly aimed
towards
understanding
the
basic
SPI
response/mechanisms involved, and thereby providing
input and insights with respect to assessing the risk of
liquefaction-induced damage to existing pipelines as
well as during the design of new pipelines.
Earthquake-induced
soil
liquefaction
poses
vulnerability to not only above-ground infrastructure but
also to buried structures such as manholes, pipelines,
tunnels, shafts, etc. (Okamoto 1984; O’Rourke et al.
1991; Sitar et al. 1995; MCEER 1999). Buried pipelines
are considered effective in the transportation of fluids
such as water and liquid hydrocarbons safely over long
distances. During liquefaction, the shear strength of the
soil above and around the pipeline could decrease due to
build-up of excess pore pressures and, subsequently,
resulting in potential buoyancy forces that could cause
the pipelines to displace and “float up” towards the
ground surface. Limit-equilibrium based analytical
formulations (Koseki et al. 1997) have been developed
to predict the occurrence of uplift. Moreover, several
experimental studies in the form of shake table and
centrifuge tests have been performed to study
liquefaction-induced responses of geotechnical systems
with structures buried in untreated or mitigated soil
deposits (Yasuda et al. 1995; Ling et al. 2003). Similarly,
numerical modeling has also been undertaken to
investigate liquefaction-induced uplift of buried
structures (Azadi and Mir Mohammad Hosseini 2010;
Mahmoud et al. 2020).
This study aims to numerically investigate the
influence of ground motion parameters such as peak
ground acceleration (PGA), Arias intensity (Ia), total
https://doi.org/10.3208/jgssp.v10.OS-11-06
838
2 NUMERICAL MODELING
by simulating the centrifuge experiment modeling
liquefaction-induced uplift of a pipe buried in a uniform,
loose deposit of clean Nevada sand (Sun 2001). A
reasonable agreement to the experimentally observed
excess pore pressures and uplift had been noted (Basu
and Wijewickreme 2023), and therefore, the numerical
framework was deemed to be suitable for analysis of
liquefaction-induced uplift of pipes buried in other clean
sands having similar relative densities.
2.1 Simulation approach
The two-dimensional (2D) numerical model used in
this study replicated a uniform deposit of FRS having a
width of 18 m and a thickness of 12 m and it comprised
of square zones with each side having a dimension of 0.3
m (Fig. 1). This mesh size was chosen by optimizing the
solution time and accuracy for each simulation.
Additional soil columns were also used on either side of
the region-of-interest (ROI) to isolate it (separation
distance, W = 80 m used herein) from any lateral
boundary effects such as wave reflections back into the
ROI (Chian et al. 2014) to represent the free-field
scenario of a semi-infinite lateral extent. A steel pipe
having a diameter, D = 1.5 m and with a burial depth to
the centerline of pipe, H = 1.5 m in the FRS mass was
assumed for the analysis as shown in Figure 1. The pipe
was modeled using elastic beam elements, and the
density and Young’s modulus of steel was assumed to be
7850 kg/m3 and 200 GPa, respectively. The pipe wall
thickness was considered as 10 mm based on the pipe
diameter considering guidelines from CSA Z662:19
(2019). The pipe was connected to the soil using
unbonded interfaces to simulate a frictional interface
between these two materials while separation and
slippage was accounted for. A soil-pipe interface friction
′
angle of 23º (2/3rd of the critical state friction angle, 𝜑𝑐𝑣
)
was used that was similar to what Chian et al. (2014)
used in their pipe uplift study. The normal and shear
stiffnesses for the interface were set to 3.1 GPa, which
was approximately equal to 10 times the stiffness of the
neighboring soil, as recommended in the FLAC User
Manual (Itasca 2016).
There were two stages in each simulation. In the first
stage, the model geometry, soil properties and boundary
conditions were defined, and the geostatic stress state
(static equilibrium) was achieved. Hydrostatic pore
pressure conditions were established across the model to
match the depth of the ground water table which was
assumed to be at the ground surface. The base of the
model was fixed against movement. Only vertical
movements along the sides of the model were allowed in
both stages which is similar to the lateral boundary
condition enforced by Azadi and Mir Mohammad
Hosseini (2010) in their numerical modeling study on
pipe uplift. In the second stage of the analysis,
earthquake shaking was applied to the base of the model
as a horizontal acceleration time history. Drainage could
take place from the model top, but the sides of the model
were considered as no flow boundaries for both stages.
To mitigate numerical noise, a Rayleigh damping of
0.5% centered at the predominant frequency of the soil
deposit was used based on recommendations by
Boulanger and Ziotopoulou (2017). In the absence of
available experimental data on liquefaction-induced pipe
uplift for FRS, the numerical framework described
herein was validated by Basu and Wijewickreme (2023)
Fig. 1. Numerical model of the FRS deposit with a buried pipe
simulated in FLAC.
2.2 PM4Sand calibration
The nonlinear constitutive model PM4Sand v3.1
requires soil-specific calibration of three primary input
parameters: relative density (𝐷𝑟 ), shear modulus
coefficient (𝐺𝑜 ), and contraction rate parameter (ℎ𝑝𝑜 )
whereas all secondary parameters have been precalibrated by the developers to a broader body of clean
sand data to reasonably approximate the general range of
sand behavior. 𝐷𝑟 controls the relative state of soil, 𝐺𝑜 is
related to the shear wave velocity (𝑉𝑠 ) and controls the
small-strain shear stiffness (𝐺𝑚𝑎𝑥 ), and ℎ𝑝𝑜 controls the
soil’s contractiveness and, therefore, its cyclic strength.
The maximum void ratio (𝑒𝑚𝑎𝑥 ), minimum void ratio
′
(𝑒𝑚𝑖𝑛 ), and 𝜑𝑐𝑣
were assigned values based on relevant
FRS data (Chillarige et al. 1997; Sivathayalan and Vaid
2002; Sriskandakumar 2004; Dabeet 2008). Default
values of all the other PM4Sand parameters as described
in Boulanger and Ziotopoulou (2017) were used.
Fig. 2. Laboratory DSS test results on FRS from Sivathayalan
(1994) and calibrated DSS simulations corresponding to a Dr =
40% and at a confinement of 100 kPa.
For the current study, a 𝐷𝑟 value of 40% was used for
all the simulations to evaluate liquefaction-induced
uplift in a relatively loose deposit. Equations 1 and 2
were used to estimate 𝐺𝑜 for the selected 𝐷𝑟 of 40% that
839
was used in this study, wherein, the shear wave velocity
measurements reported by Chillarige et al. (1997) were
utilized.
𝐺𝑚𝑎𝑥 = 𝜌 𝑉𝑠2
𝐺𝑜 =
𝐺𝑚𝑎𝑥
𝑃𝑎
𝑃
( 𝑎′ )
increase from 13.2 to 24.3 cm with an increase in PGA
(or Ia) of the input motions from 0.15g to 0.45g (Fig. 4)
when the duration and frequency characteristics of the
motions were the same, as also noted in past literature
(Chian et al. 2014). It must be noted that Ia has been well
noted to encompass the effects of motion amplitude,
frequency content and duration simultaneously, and it
has a strong correlation with various metrics of seismic
response such as slope stability and landslides (Harp and
Wilson 1995) and soil liquefaction (Kayen and Mitchell
1997); therefore, making Ia a useful parameter to define
motion characteristics for such studies.
(1)
0.5
(2)
𝑝
where, 𝜌 is the soil density, 𝑝′ is the mean effective
confining pressure, and Pa is the atmospheric pressure
used for normalizing. Laboratory data on liquefaction
triggering was available for FRS (Sivathayalan 1994) at
a 𝐷𝑟 of 40% and was used to calibrate ℎ𝑝𝑜 . This
calibration was performed using single element cyclic
direct simple shear (DSS) simulations to approximately
match the cyclic stress ratio (i.e., the soil’s cyclic
resistance) to reach 3% single amplitude shear strain in
15 cycles (Fig. 2). Table 1 outlines some of the key
PM4Sand calibration parameters and soil properties used
in this study.
Table 1. PM4Sand calibration parameters and FRS properties.
𝑫𝒓
(%)
40
𝑮𝒐
𝒉𝒑𝒐
457
0.7
𝒌1
(cm/s)
0.042
𝑮𝒔 2
𝒆𝒎𝒂𝒙
𝒆𝒎𝒊𝒏
𝝋′𝒄𝒗
2.71
0.95
0.62
35 º
1Hydraulic conductivity, 𝑘 based on Tsaparli et al. (2017).
2Specific
gravity of solids, 𝐺𝒔 based on Northcutt and
Wijewickreme (2013).
2.3 Input motion
Five synthetic, harmonic motions having PGAs
ranging from 0.15g to 0.45g were used for the
simulations. Each of these motions had a frequency of 1
Hz with the first and last cycles having an amplitude
equal to 1/3rd of the peak acceleration as shown in Fig.
3. One recorded earthquake motion (shown in Fig. 3)
corresponding to the 1986 Taiwan (Mw = 7.3) earthquake
was also used. Table 2 outlines some of the properties of
the selected input motions. The PGAs of the motions
selected for this study are representative of the expected
seismic hazard in Fraser River Basin near Vancouver,
British Columbia, Canada as per NBC (2020).
Fig. 3. Acceleration time histories corresponding to some of the
input motions considered in this study.
Table 2. Characteristics of the input motions used in this study.
Motion
No.
S-1
S-2
S-3
S-4
S-5
R-1
3
Type
Cycles
Synthetic
Synthetic
Synthetic
Synthetic
Synthetic
Recorded
6
12
12
12
24
-
PGA
(g)
0.45
0.15
0.3
0.45
0.2
0.6
Ia
(m/s)
6.59
1.77
7.09
15.94
6.85
7.41
TD
(s)
6
12
12
12
24
32.9
TSD
(s)
3.7
9.3
9.3
9.3
20
12.2
Fig. 4. Uplift time histories illustrating the effect of input motion
amplitude on end-of-shaking uplift magnitude.
RESULTS
3.2 Effect of motion duration
End-of-shaking uplift movement was observed to
increase with an increase in TSD (time duration between
5% and 95% of the Ia buildup) of input motion when the
Ia of the motions were similar, as outlined in Figure 5 for
3.1 Effect of motion amplitude
Figure 4 shows the uplift movement of the pipe
versus time for simulations using the input motions S-2,
S-3 and S-4. The end-of-shaking uplift was observed to
840
simulations using the synthetic motions S-1, S-3 and S5. The simulation using the recorded earthquake motion
R-1 showed that significant uplift of pipe might occur
before and after the TSD time bracket (Fig. 6), with the
rate of uplift decreasing in the post- TSD time bracket.
This is because excess pore pressure difference might
build up between the pipe invert and crown prior to Ia
reaching a value of 5% of its maximum value and
thereby initiating uplift. Furthermore, some uplift might
occur in the post- TSD bracket on account of inertia. This
implies that the effects of both TSD and TD should be
accounted for individually while assessing uplift
behavior.
4
CONCLUSIONS
The present study utilized a well-calibrated and
validated 2D numerical model to investigate the effects
of input motion characteristics on pipe uplift for a steel
pipe buried in a saturated, loose and homogeneous
deposit of Fraser River sand. The commercially
available finite difference software FLAC v8.1 and the
constitutive model PM4Sand v3.1 were utilized. A 1.5 m
diameter (D) pipe was considered and burial depth (H)
of 1.5 m was assumed. Simulations used five synthetic
harmonic motions and one recorded earthquake motion
with each having a different combination of amplitude
and duration characteristics.
End-of-shaking uplift movement increased with an
increase in shaking intensity, characterized through peak
ground acceleration (PGA) or Arias intensity (Ia), when
the duration and frequency characteristics of the motions
were the same. It also increased with an increase in the
significant duration (TSD) of the input motions when the
Ia of the motions were similar. Significant uplift of pipe
was also observed to occur before and after the TSD time
bracket, implying that the effects of both TSD and total
duration (TD) should be accounted for individually while
assessing uplift behavior.
As mentioned earlier, this is a complex 3dimensional SPI problem with several factors such as
soil conditions, pipe geometry and stiffness, and
boundary conditions/constraint, as well as seismic
loading parameters contributing to the overall real-life
response of pipelines subject to lateral movements. The
2-dimensional analysis results presented herein is
intended to provide input and insights with respect to
assessing the risk of liquefaction-induced damage to
pipelines.
Fig. 5. Uplift time histories illustrating the effect of input motion
TSD on end-of-shaking uplift magnitude.
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Fig. 6. Normalized Ia and uplift time history obtained from
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