Technical Note
Numerical Study of Liquefaction-Induced Uplift of
Underground Structure
Downloaded from ascelibrary.org by Indian Institute of Technology Madras on 12/03/19. Copyright ASCE. For personal use only; all rights reserved.
Priya Beena Sudevan, S.M.ASCE 1; A. Boominathan, Ph.D., A.M.ASCE 2; and Subhadeep Banerjee, Ph.D. 3
Abstract: A finite-difference modeling was performed to investigate the liquefaction-induced uplift of an underground structure. The
liquefaction-induced uplift of a 5 m diameter underground structure buried at a depth of 5.5 m was analyzed. The soil was modeled using
the elastic-perfectly plastic Mohr–Coulomb model by incorporating the Finn–Byrne pore-pressure formulation. The pore pressure and uplift
response of the underground structure obtained using sinusoidal input motion were validated by comparing centrifuge tests and numerical
analysis results reported in the literature. The responses obtained using a scaled-up 2015 Nepal-Gorkha earthquake accelerogram and equivalent sinusoidal motion were compared and were found to be similar. Further parametric analysis was carried out to study the effect of the
characteristics of the input motion on the uplift of the structure. The numerical results revealed that the primary reason for the uplift of the
underground structure was the generation of pore pressure at the invert of the structure. It also was found that significant liquefaction-induced
uplift displacement of the underground structure occurred for input motion with a peak input acceleration more than 0.22g and a frequency
less than 0.75 Hz. DOI: 10.1061/(ASCE)GM.1943-5622.0001578. © 2019 American Society of Civil Engineers.
Author keywords: Underground structure; Liquefaction-induced uplift; Pore-pressure build up; Peak input acceleration; Frequency.
Introduction
Underground structures such as utility pipes, sewerage pipes, manholes, metro tunnels, and so forth are used worldwide for transportation, conveyance of water, sewage and natural gas, and so forth. In
general, these structures are exposed to various natural or artificial
challenges such as failure due to earthquake (Koseki et al. 1997a;
Chou et al. 2011), fault movement (Robert et al. 2016), frost action
(Foriero and Ladanyi 1994; Nobahar et al. 2007), constructionrelated failure of underground structures (Abolmaali and Kararam
2013; Huange et al. 2013), and so forth. The majority of failures
occur due to the liquefaction of the soil (Kiku and Tsujino 1996;
Koseki et al. 1997b; Chou et al. 2011). Such failure of various
underground structures was observed during past seismic events
such as the 1964 Niigata earthquake (Koseki et al. 1997b), 2004
Niigataken-Chuestsu earthquake (Yasuda and Kiku 2006), 2010
Chile earthquake (Kang et al. 2014), 2011 Great East Japan earthquake (Bhattacharya et al. 2011; Tokimatsu and Katsumata 2012),
and 2011 Christchurch earthquake (Sherson et al. 2015). Currently,
southeast Asia operates more than 25,000 km of oil and natural gas
product pipelines (Chenna et al. 2014), which is expected to double
in the coming years. Most of these structures run through seismically active regions. Hence it is necessary to ensure the proper functioning of the structures even after an earthquake.
1
Research Scholar, Dept. of Civil Engineering, Indian Institute of
Technology Madras, Chennai, Tamil Nadu 600036, India. Email:
priyabeenasudevan@gmail.com
2
Professor, Dept. of Civil Engineering, Indian Institute of Technology
Madras, Chennai, Tamil Nadu 600036, India (corresponding author).
Email: boomi@iitm.ac.in
3
Associate Professor, Dept. of Civil Engineering, Indian Institute
of Technology Madras, Chennai, Tamil Nadu 600036, India. Email:
subhadeep@iitm.ac.in
Note. This manuscript was submitted on September 18, 2018; approved
on July 13, 2019; published online on December 2, 2019. Discussion period open until May 2, 2020; separate discussions must be submitted for
individual papers. This technical note is part of the International Journal
of Geomechanics, © ASCE, ISSN 1532-3641.
© ASCE
The uplift of underground structures triggered by various factors
has been studied in recent years (Koseki et al. 1997a; Yang et al.
2004; Stringer and Madabhushi 2007; Cheuk et al. 2008; Jiang
et al. 2015; Roy et al. 2018). From a series of model tests, Koseki
et al. (1997a) determined that the liquefaction-induced uplift of
underground structures occurs mainly due to three phenomena:
lateral deformation of the surrounding soil below the structure, followed by the movement of pore fluid to the bottom of the structure,
and finally the reconsolidation of the liquefied soil. Furthermore,
Chian et al. (2014), in a finite-difference (FD) study, were able to
obtain similar soil deformation patterns around the structure as that
observed by Koseki et al. (1997a).
A few researchers, such as Azadi and Hosseini (2010), Chian
and Madabhushi (2012), and Kang et al. (2013), studied the effect
of various factors on the liquefaction-induced uplift of structures.
Liu and Song (2005), in a study of the behavior of a large underground structure in liquefiable soil subjected to horizontal and vertical excitation, pointed out that the overall uplift observed using
the vertical excitation was similar to that observed using horizontal
excitation. Azadi and Hosseini (2010) in a FD study, noticed a considerable reduction in the uplift in the presence of a nonliquefiable
layer around the underground structure. Tobita et al. (2011), in a
series of model tests, determined that the liquefaction-induced
uplift of an underground structure depends on the nature of the
contact between the structure and the soil. Based on the centrifuge
study by Chian and Madabhushi (2012), it can be concluded that
there is a considerable reduction in the uplift with the increase in
depth of embedment and diameter of a structure. Liu (2012) determined that the behavior of an underground structure depends on the
input motion frequency and the ground characteristics such as the
thickness and the soil stiffness. The effect of various factors such as
the presence of a nonliquefiable layer above the groundwater, unit
weight of the backfill material, and the size of underground structures on the uplift of the underground structure was studied by
Tobita et al. (2012). Watanabe et al. (2016), using shake table tests,
pointed out that the uplift of a tunnel decreased with increasing
thickness of liquefiable soil below the tunnel. Hu and Liu (2017)
captured the response of a subway station subjected to a moderate
06019020-1
Int. J. Geomech., 2020, 20(2): 06019020
Int. J. Geomech.
Downloaded from ascelibrary.org by Indian Institute of Technology Madras on 12/03/19. Copyright ASCE. For personal use only; all rights reserved.
earthquake. The study showed a gradual uplift until initial liquefaction; thereafter, it showed a rapid uplift in the case of loose sand
and a significant settlement for medium dense sand. It was postulated that the primary reason for the liquefaction-induced uplift of a
structure is the accumulation of pore water at the bottom of the
structure (Kang et al. 2014; Sudevan et al. 2018).
The preceding discussion indicated a limited number of experimental studies, from which the effect of various factors affecting the
liquefaction-induced uplift of underground structures cannot be inferred properly. Further numerical study of the liquefaction-induced
uplift of underground structures whose parameters can be easily
obtained is required. Additionally, it remains unknown how the
characteristics of the input motion, in tandem, influence the uplift
displacement of the underground structure. Therefore, in the present
study, a numerical analysis was carried out to understand the uplift
mechanism of a structure embedded in liquefiable soil. The study
was further extended to investigate the effect of various input motion
characteristics on the uplift displacement of the structure.
Details of Problem Studied
The experimental data from a large-scale centrifuge study of the
uplift response of an underground structure buried within a liquefiable soil conducted by Chian et al. (2014) was chosen for the
numerical simulation. The soil medium in the study consisted of a
40-m-wide and 16-m-deep liquefiable Houston sand (emax ¼ 1.01,
emin ¼ 0.555). The effective size (D10 ) and mean particle size (D50 )
of the Houston sand considered in the study was 0.209 and
0.335 mm (Chian et al. 2014). A circular underground structure
5 m in diameter was buried at a depth of 5.5 m (depth of embedment h ¼ 1.1D) from the ground surface. The schematic view of
the model used for the study is shown in Fig. 1.
Finite-Difference Modeling
A numerical analysis was carried out to study the response of an
underground structure buried in liquefiable soil subjected to dynamic loading. A loosely coupled fluid flow analysis was carried
out using a FD code, FLAC3D version 5.0 (Itasca Consulting
Group 2012). The method was loosely coupled because the pore
pressures were computed only after each 1/2 cycle of stress as
the analysis proceeded (Byrne 1991). The Cauchy’s equation of
motion was solved to obtain the velocity and displacement due
to the dynamic loading
∂σij
∂v
þ ρbi ¼ ρ i
∂xi
∂t
ð1Þ
where σij = stress tensor; bi = body force per unit mass; ρ = mass
density; and vi = grid point velocity. These nodal velocities then
were used to obtain new strain rates, Δεij as
1
Δεij ¼ ðvi;j þ vj;i Þ
ð2Þ
2
Finally, the constitutive equations were invoked to calculate the
new stresses using the incremental form Hij from the strain rate and
the stresses from the previous time and were solved iteratively to
reach the final solution
σˇij ¼ Hij ðσij ; Δεij ; kÞ
ð3Þ
where σˇij = corotational stress rate tensor; and k = parameter which
takes into account the loading history.
One of the most important aspects of finite-difference modeling
is choosing the correct mesh and boundary conditions. The dimensions for the present study model were chosen the same as the
dimensions of the centrifuge study by Chian et al. (2014). The soil
medium was considered as a continuum element 40 m long, 1 m
wide, and 16 m deep. In the present study, the mesh size was chosen
based on Lysmer and Kuhlemeyer (1969), such that the spatial
element size, Δl, must be smaller than 1/10 or 1/8 the wavelength
associated with the highest frequency of the input wave
Δl ≤
λ
10
to
λ
8
ð4Þ
where λ = wavelength associated with the highest frequency component. The highest frequency motion used in the present study was
1.5 Hz, which gave a maximum mesh size of 8.3 m for reasonable
accuracy. Based on the criteria, the backfill soil was discretized into
720 zones connected by 1,568 grid points using eight-noded brick
elements 0.5 m in size and radcylinder elements of finer mesh size
near the structure. The circular 500-mm-thick structure was discretized using 80 primitive shell elements.
During the static analysis, the whole model was modeled using
gravity loading. The base of the model was fixed in all the three
directions whereas the vertical boundaries were fixed in x- and
y- direction. During the dynamic analysis, to eliminate the reflection of the outward propagating wave, vertical boundaries
were placed at a sufficient distance to minimize wave reflections
Fig. 1. Schematic model used in the study.
© ASCE
06019020-2
Int. J. Geomech., 2020, 20(2): 06019020
Int. J. Geomech.
and achieve a free-field condition. Additionally, the whole model
was fully saturated with an impermeable boundary at the base.
pore water pressure, Δu, at every half cycle of stress can be obtained
using (Byrne 1991)
ð8Þ
Δu ¼ MΔεvd
The behavior of the geomaterial in the present numerical study was
defined using the elastic-perfectly plastic Mohr–Coulomb model.
The pore-pressure buildup within the saturated soil medium during
cyclic loading under an undrained condition was computed using a
Finn–Byrne formulation (Finn 1981; Byrne 1991). The Finn–Byrne
formulation was incorporated with the Mohr–Coulomb plasticity
model in which the incremental volumetric strain, ðΔεvd Þ1=2 cycle ,
was obtained at every half cycle of stress using the two-parameter
equation (Byrne 1991) [Eq. (5)]. The irrecoverable volume contraction within a fully saturated soil medium that leads to the increase in
pore pressure in the undrained condition can be represented using
C1 and C2 parameters (Byrne 1991; Azadi and Hosseini 2010)
which can be determined based on the relative density (Dr ) of the
soil being studied [Eqs. (6) and (7)]
Δϵθd
ϵ
¼ C1 exp −C2 θd
ð5Þ
γ
γ
C2 ¼
0.4
C1
ð6Þ
C1 ¼ 7600ðDr Þ−2.5
where M = rebound tangent modulus of sand skeleton, which
mainly depends on effective stress and can be obtained from
0 0.5
σ
ð9Þ
M ¼ 1600Pa v
Pa
where Pa = atmospheric pressure; and σv0 = effective stress. The
calculation sequence within an element is shown in Fig. 2.
The backfill soil considered in the present study was loose sand
(dry density ¼ 1,450 kg=m3, friction angle = 33°, permeability ¼
10−3 m=s, bulk modulus = 15 MPa, and shear modulus = 5.5 MPa)
whose general properties were similar to those adopted by Chian
et al. (2014). From the relative density, the dynamic soil properties
representing the cyclic behavior of the sand, C1 and C2 , were
obtained as 0.56 and 0.72 from Eqs. (6) and (7), respectively.
A concrete underground structure (υ ¼ 0.33) of 5 m diameter
was considered in the present study. The interface between the soil
and the underground structure whose shear strength was defined
by the Mohr–Coulomb failure criterion was characterized by a frictional angle of 21.8° (Chian et al. 2014). A very low Rayleigh
damping of about 2% (Ma et al. 2008) was used to reduce the
numerical instability that arises during a dynamic analysis involving large strain problems.
ð7Þ
where C1 = amount of volume change; and C2 controls the shape of
the variation of volume change with progressive number of cycles.
From the measured volumetric strain increment, the incremental
Fig. 2. Calculation sequence within an element.
Input Motion
In the present study, a sinusoidal input acceleration with a peak
input acceleration of 0.22g and frequency of 0.75 Hz for a total
duration of 27 s was applied at the base of the numerical model.
The time step used for the dynamic analysis was calculated internally by considering the stiffness of the soil and the p-wave velocity
(Itasca Consulting Group 2012).
Additionally, numerical analysis was performed on the same
model to compare the response of the underground structure subjected to the 2015 Nepal-Gorkha earthquake [Mw ¼ 7.8, peak
ground acceleration ðPGAÞ ¼ 0.155g, and f ¼ 0.23 Hz] recorded
at the Kanti Path station in Nepal (Center for Engineering Strong
Motion Data 2016). To compare the results of the equivalent sinusoidal motion with peak input acceleration of 0.3g, the amplitude of
Nepal-Gorkha earthquake input motion was scaled up by a factor of
2 to adjust the peak ground acceleration to 0.3g with the frequency
content unchanged. Fig. 3. shows the earthquake motion and the
equivalent sinusoidal motion for a total duration of 35 s considered
in the present study.
4
4
Acceleration (m/s2)
Acceleration (m/s2)
Downloaded from ascelibrary.org by Indian Institute of Technology Madras on 12/03/19. Copyright ASCE. For personal use only; all rights reserved.
Material Characterization
2
0
-2
2
0
-2
Sinusoidal motion
2015 Nepal-Gorkha Earthquake (scaled up by 2)
-4
-4
0
5
10
15
20
25
30
35
0
5
Time (s)
10
15
20
25
30
35
Time (s)
Fig. 3. 2015 Nepal-Gorkha Earthquake and equivalent sinusoidal input motion.
© ASCE
06019020-3
Int. J. Geomech., 2020, 20(2): 06019020
Int. J. Geomech.
Pore-Pressure Response
The pore-pressure response observed away from and near the
underground structure buried at a depth of 5.5 m in saturated sand
was studied. The results then werecompared with those obtained by
Chian et al. (2014) in their experimental and numerical studies.
The pore-pressure response in terms of the pore-pressure ratio, ru
(excess pore pressure normalized by the initial effective stress of the
soil), developed at depths of 16.0, 8.0, and 5.5 m at a point away
from the underground structure is shown in Fig. 4. The pore pressure
Pore pressure ratio, ru
1.0
0.8
0.6
0.4
Chian et al. (2014)., Experimental
Chian et al. (2014)., Numerical
Sudevan et al. (2018)
Present study
At a depth of 8.0 m
0.2
0.0
0
5
10
15
20
25
30
35
20
25
30
35
20
25
30
35
Time (s)
Pore pressure ratio, ru
1.0
0.8
0.6
0.4
0.2
At a depth of 5.5 m
0.0
0
5
10
15
Time (s)
1.4
1.2
Pore pressure ratio, ru
Downloaded from ascelibrary.org by Indian Institute of Technology Madras on 12/03/19. Copyright ASCE. For personal use only; all rights reserved.
Away from Underground Structure Surface
increased rapidly as soon as the shaking started and after 2–3 s
reached a maximum (ru ¼ 1.0), which remained constant throughout the entire duration of shaking. A maximum pore-pressure ratio
of about 1.0 was observed in the present study and in the centrifuge
and numerical study by Chian et al. (2014). When soil undergoes a
large cyclic shear strain, there is a possibility that the soil will dilate.
Due to the dilation of the soil during cyclic loading, additional pore
spaces will be created. In the saturated state, due to the relatively fast
rate of loading, water migration will be hindered and the additional
pore space created will be filled by the pore water. This results in the
immediate reduction of the pore-water pressure and an associated
increase in the effective confinement (Elgamal et al. 1998). Due
to this, small spikes in the form of small cycles were observed
1.0
0.8
0.6
0.4
0.2
At a depth of 2.5 m
0.0
0
5
10
15
Time (s)
Fig. 4. Far-field pore-pressure response of the saturated soil deposit (0.22g, 0.75 Hz).
© ASCE
06019020-4
Int. J. Geomech., 2020, 20(2): 06019020
Int. J. Geomech.
in the pore pressure response. Similar observations were reported by
Madabhushi and Madabhushi (2015) in their finite-element (FE)
study of a buried tunnel subjected to seismic input motion. However, neither Chian et al. (2014) and Sudevan et al. (2018) were able
to capture these dilation spikes in their numerical models.
The pore-pressure response observed near the underground structure buried at a depth of 5.5 m in saturated sand was studied. The
excess pore-water pressure generated at three levels, i.e., at the invert, springing, and crown of the underground structure (BTC
2004), due to the shaking is shown in Fig. 5. Compared with that
Crown
Excess Pore pressure (kPa)
30
Springing
20
Invert
10
0
-10
-20
Chian et al. (2014)., Experimental
Chian et al. (2014)., Numerical
Sudevan et al. (2018)
Present study
-30
-40
0
5
10
15
(a)
20
25
30
35
20
25
30
35
20
25
30
35
Time (s)
Excess pore pressure (kPa)
50
40
30
20
10
0
0
5
10
15
(b)
Time (s)
70
Excess pore pressure (kPa)
Downloaded from ascelibrary.org by Indian Institute of Technology Madras on 12/03/19. Copyright ASCE. For personal use only; all rights reserved.
Near Underground Structure Surface
at the invert and the springing, the pore-pressure response near the
crown was found to be different due to the deformation of the soil
structure. Near the crown of the underground structure [Fig. 5(a)],
the pore pressure initially increased to a low value, and thereafter
decreased to reach a negative value. A similar observation was
reported by Ling et al. (2003) from their centrifuge study and by
Sudevan et al. (2018) from their numerical study. The excess porepressure response near the springing level [Fig. 5(b)] had a large
peak-to-peak amplitudes due to the soil-structure displacement.
A gradual buildup of pore-water pressure was observed near the
invert [Fig. 5(c)] until it became a constant value. Higher pore pressure accumulation of about 40 kPa was observed near the invert
of the structure. A negative pore pressure of about −10 kPa was
60
50
40
30
20
10
0
0
(c)
5
10
15
Time (s)
Fig. 5. Variation of excess pore pressure around the underground structure: (a) at the crown of the structure; (b) at the springing of the structure; and
(c) at the invert of the structure.
© ASCE
06019020-5
Int. J. Geomech., 2020, 20(2): 06019020
Int. J. Geomech.
ratio remained more or less the same. The maximum pore-pressure
ratio near the structure will not be close to unity due to the shear
deformation of the soil, as reported by Bao et al. (2017) in their
FE-FD study.
Uplift Response of Underground Structure
The vertical displacement of the underground structure embedded
at a depth of 5.5 m from the ground surface due to the dynamic
motion was analyzed. Fig. 7 shows the displacement of the underground structure at 0, 10, 20, and 30 s. As the time elapsed, the
underground structure was lifted from its mean position to a maximum of 1 m by the end of 30 s. The uplift response of the underground structure subjected to a dynamic motion is shown in Fig. 8.
The present study results are compared with those obtained by
Chian et al. (2014) in their centrifuge and numerical study. The
dynamic motion initiated the uplift of the structure due to the rapid
accumulation of pore water in the vicinity of the structure. As the
Pore pressure ratio, ru
1.0
0.8
0.6
0.4
0.2
2015 Nepal-Gorkha Earthquake (scaled up by 2)
Sinusoidal motion
0.0
0
5
10
15
20
25
30
Time (s)
Fig. 6. Comparison of pore-pressure ratio at the invert of the underground structure subjected to 2015 Nepal-Gorkha Earthquake and sinusoidal input
motion (0.3g, 0.23 Hz).
Time= 0 s
Time= 10 s
Time= 20 s
Time= 30 s
Fig. 7. Uplift of the structure at different times.
1.2
Uplift Displacement (m)
Downloaded from ascelibrary.org by Indian Institute of Technology Madras on 12/03/19. Copyright ASCE. For personal use only; all rights reserved.
observed near the crown, and matched quite well with that observed
by Chian et al. (2014) in their experimental studies and by Sudevan
et al. (2018) in their FD study. In contrast, a positive pore pressure
of about 10 kPa was observed near the crown by Chian et al. (2014)
in their numerical study. The ability of the present study model
to estimate the additional pore space developed due to the soilstructure deformation led to the drastic reduction of the pore pressure observed in the region above the structure. The present study
resulted in a maximum pore pressure of 40 and 35 kPa near the invert
and the springing level, which matched quite well with the results of
the experimental and numerical study by Chian et al. (2014).
A similar study was done by comparing the response of the soil
subjected to 2015 Nepal-Gorkha earthquake and an equivalent
sinusoidal input motion. The pattern of the pore-pressure response
developed at the invert of the structure by two types of input motion
is presented in Fig. 6. For both sinusoidal motion and earthquake
motion, the pattern of pore pressure obtained was similar. The porepressure ratio started to increase as the shaking started, and reached
a maximum of 0.6. When the shaking ceased, the pore-pressure
1.0
0.8
0.6
Chian et al. (2014)., Experimental
Chian et al. (2014)., Numerical
Sudevan et al. (2018)
Present Study
0.4
0.2
0.0
0
5
10
15
20
25
30
35
Time (s)
Fig. 8. Uplift displacement of the underground structure (0.22g, 0.75 Hz).
© ASCE
06019020-6
Int. J. Geomech., 2020, 20(2): 06019020
Int. J. Geomech.
Uplift displacement (m)
0.8
0.6
0.4
0.2
2015 Nepal-Gorkha Earthquake (scaled up by 2)
Sinusoidal input motion
0.0
-0.2
Downloaded from ascelibrary.org by Indian Institute of Technology Madras on 12/03/19. Copyright ASCE. For personal use only; all rights reserved.
0
5
10
15
20
25
30
35
Time (s)
Fig. 9. Comparison of uplift response of the underground structure subjected to 2015 Nepal-Gorkha earthquake and sinusoidal input motion
(0.3g, 0.23 Hz).
structure was uplifted, the soil above the structure was pushed
away, thus reducing the resistance of the soil. The primary reason
for the liquefaction-induced uplift of underground structure was development of the pore pressure at the invert of the structure. In the
present constitutive model, the pore pressure developed was directly proportional to the volumetric strains incremental measured
at every half cycle of loading. A linear increase in the volumetric
strain was observed near the structure. This might be the reason for
the linear variation in the uplift of the underground structure. Additionally, when the pore pressure started to rise, the soil started to
behave like a viscous fluid, which caused the buried structure to be
uplifted rather than flowing. The general trend of present results
was found to be comparable with experimental results by Chian
et al. (2014), although the experimental results by Chian et al.
(2014) lagged the uplift obtained from the present study by 25%.
However, Sudevan et al. (2018) in their numerical study, observed
the same uplift of the structure, 1.0 m.
Fig. 9 compares the uplift of the structure caused by the sinusoidal motion and a real earthquake motion. The primary focus of
this study was to understand the liquefaction-induced uplift of the
underground structure. Therefore, the other forces acting on the
underground structure are not presented in this study. Moreover,
the primary reason for the liquefaction-induced uplift was the pore
pressure developed near the invert of the structure. Figs. 6 and 9
show that the pore pressure developed and the resulting uplift
for both cases was similar. Furthermore, because the vertical component of the input acceleration was absent, there was no direct
effect of the input acceleration on the forces leading to the uplift
of the underground structure (Liu and Song 2005). The sinusoidal
motion decreased suddenly to zero, whereas the earthquake motion
had a gradual reduction in the acceleration time history; the authors
suspect that this might be responsible for difference in the uplift
response observed after the peak. However, the rate of decrease
in 20–30 s was not as significant as the rate of uplift. Moreover,
the total uplift and the period of maximum uplift were the main
observations inferred from the results. In both cases, a maximum
uplift of about 0.6 m was observed at around 7 s. After the shaking
ceased, the underground structure remained at the same level because the pore water accumulated did not dissipate.
Effect of Peak Acceleration and Frequency of
Input Motion
After the numerical model was verified, the effect of the peak acceleration and frequency of the input motion on the development of
pore pressure at the invert of the structure and the resulting uplift of
© ASCE
the underground structure were studied. The response due to a
sinusoidal input motion with peak input accelerations of 0.1g,
0.22g, 0.3g and frequencies of 0.4, 0.75, and 1.5 Hz was studied
for eight cycles of loading.
Pore-Pressure Response
The pore-pressure ratio of different peak input accelerations and
frequencies to the number of cycles of loading is shown in Fig. 10.
When the peak input acceleration was 0.1g [Fig. 10(a)], a maximum pore pressure ratio of 0.4 was obtained, which was less than
that obtained using 0.22g and 0.3g peak accelerations. This clearly
showed that the soil did not liquefy for the peak input acceleration
of 0.1g. For the given problem, a significant increase in the pore
pressure at the invert of the structure was observed within the first
cycle for a peak input acceleration higher than 0.22g [Figs. 10(b
and c)] whereas a 0.1g peak amplitude input motion took almost
2 cycles to reach the maximum pore pressure. A pore-pressure ratio
less than 0.1 was observed when the frequency was 1.5 Hz, indicating that the soil did not liquefy [Fig. 10(a)]. For a low-frequency
motion i.e., 0.4 Hz, a steep rise in the pore pressure accumulation
occurred at the invert of the structure and reached the maximum
pore pressure within 1 cycle [Figs. 10(b and c)], whereas 0.75- and
1.5-Hz motions required at least 2 cycles to reach the maximum
pore pressure.
Uplift of Structure
The final uplift of the underground structure at different frequencies
and peak input accelerations is shown in Fig. 11. An input acceleration of 0.1g led to a negligible uplift of the structure due to low
pore pressure accumulated at the invert. When the peak input acceleration was 0.22g and 0.3g, the soil liquefied and a significant
structural uplift was observed at the end of eight cycle of loading.
However, the maximum uplift of about 1.1 m was observed when
the peak input acceleration was 0.3g and the frequency was 0.4 Hz.
As the frequency of the excitation increased to 0.75 and 1.5 Hz, the
magnitude of final uplift displacement of the structure decreased.
The uplift occurred due to the development of the pore pressure
at the invert of the structure. Reducing the frequency of the input
motion increased the pore water accumulated near the structure
(Azadi and Hosseini 2010; Jiang et al. 2010; Mortezaie and Vucetic
2013; Jin et al. 2018). With decreasing input frequency, the duration of the input motion increased for a specific number of cycles
(Subramaniam and Banerjee 2014). Thus input motion remained in
the soil model for more time, resulting in larger accumulation of
06019020-7
Int. J. Geomech., 2020, 20(2): 06019020
Int. J. Geomech.
Pore pressure ratio, ru
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.4 Hz
0.75 Hz
1.5 Hz
0
2
4
Pore pressure ratio, ru
8
10
1.0
0.8
0.6
0.4 Hz
0.75 Hz
1.5 Hz
0.4
0.2
0.0
0
Pore pressure ratio, ru
6
No of cycles
2
4
(b)
6
8
10
No of cycles
1.0
0.8
0.6
0.4 Hz
0.75 Hz
1.5 Hz
0.4
0.2
0.0
0
2
4
6
8
10
No of cycles
(c)
Fig. 10. Effect of the input motion characteristics on the pore-pressure response of the structure: (a) peak input acceleration ¼ 0.1g; (b) peak input
acceleration ¼ 0.22g; and (c) peak input acceleration ¼ 0.3g.
Uplift displacement (m)
Downloaded from ascelibrary.org by Indian Institute of Technology Madras on 12/03/19. Copyright ASCE. For personal use only; all rights reserved.
(a)
1.2
1.0
0.8
0.6
0.4 Hz
0.75 Hz
1.5 Hz
0.4
0.2
0.0
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Peak input acceleration (g)
Fig. 11. Effect of the input motion characteristics on the uplift of the structure.
pore water near the structure. For this reason, larger liquefactioninduced uplift was observed for lower-frequency input motions.
Conclusions
A numerical simulation of the uplift of an underground structure
buried within a saturated sandy soil layer was carried out using
the Finn–Byrne formulation and its results were compared with
those of a centrifuge test and two-dimensional numerical results
reported by Chian et al. (2014). The pore-pressure responses and
the uplift of the underground structure were investigated. Some of
the major findings from the present study are as follows:
• A comprehensive numerical model with a simple constitutive
relationship is proposed to capture the liquefaction-induced
© ASCE
uplift of underground structures. The results obtained from the
proposed numerical model compared favorably with those observed in a previously published centrifuge test and numerical
analysis. Furthermore, the proposed model is able to capture the
dilating nature of the soil during full liquefaction as observed by
Madabhushi and Madabhushi (2015).
• The excess pore pressure observed near the invert of the underground structure is significantly higher than that near the springing and the crown. This phenomenon is primarily responsible
for the uplift of the underground structure.
• The pore pressure response and the resulting uplift displacement of the structure obtained for sinusoidal input motion
and 2015 Nepal-Gorkha earthquake accelerogram with identical
peak ground acceleration and frequency content were found to
be similar. Considering the large computational cost involved in
06019020-8
Int. J. Geomech., 2020, 20(2): 06019020
Int. J. Geomech.
Downloaded from ascelibrary.org by Indian Institute of Technology Madras on 12/03/19. Copyright ASCE. For personal use only; all rights reserved.
three-dimensional dynamic analysis, a sinusoidal input motion
in place of an actual earthquake accelerogram can be adopted
for estimation of liquefaction-induced uplift of an underground
structure with reasonable accuracy.
• Significant uplift of the underground structure occurred for a
peak input acceleration higher than 0.22g after the first cycle of
loading. When the frequency of the input motion was less than
0.75 Hz, a maximum uplift of the underground structure occurred as excess pore pressure buildup occurred within the first
cycle of loading. Hence it can be concluded that the significant
liquefaction-induced uplift of the underground structures can
occur for input motion with the high peak input acceleration
above 0.22g but low frequency less than 0.75 Hz.
Notation
The following symbols are used in this paper:
bi = body force per unit mass;
D = diameter of underground structure;
D10 = effective size;
D50 = mean particle size;
Dr = relative density;
emax = maximum void ratio;
emin = minimum void ratio;
f = predominant frequency of input motion;
g = gravity acceleration;
h = depth of embedment;
k = parameter which takes into account loading
history;
M = rebound tangent modulus of sand skeleton;
Mw = moment magnitude;
Pa = atmospheric pressure;
ru = pore pressure ratio;
t = time;
vi = grid point velocity;
xi = x-coordinate vector;
ϒ = cyclic shear strain;
σˇij = corotational stress rate tensor;
ρ = mass density;
υ = Poisson’s ratio;
Δl = spatial element size;
Δt = time step;
Δu = increment in pore pressure;
Δεvd = volumetric strain increment;
εij = strain rate tensor;
σij = stress tensor; and
λ = wavelength.
References
Abolmaali, A., and A. Kararam. 2013. “Nonlinear finite-element modeling
analysis of soil-pipe interaction.” Int. J. Geomech. 13 (3): 197–204.
https://doi.org/10.1061/(ASCE)GM.1943-5622.0000196.
Azadi, M., and S. M. M. M. Hosseini. 2010. “The uplifting behavior
of shallow tunnels within the liquefiable soils under cyclic loadings.”
Tunnelling Underground Space Technol. 25 (2): 158–167. https://doi
.org/10.1016/j.tust.2009.10.004.
Bao, X., Z. Xia, G. Ye, Y. Fu, and D. Su. 2017. “Numerical analysis on the
seismic behavior of a large metro subway tunnel in liquefiable ground.”
Tunnelling Underground Space Technol. 66 (Jun): 91–106. https://doi
.org/10.1016/j.tust.2017.04.005.
© ASCE
Bhattacharya, S., M. Hyodo, K. Goda, T. Tazoh, and C. A. Taylor. 2011.
“Liquefaction of soil in the Tokyo Bay area from the 2011 Tohoku
(Japan) earthquake.” Soil Dyn. Earthquake Eng. 31 (11): 1618–1628.
https://doi.org/10.1016/j.soildyn.2011.06.006.
BTC (British Tunnelling Society). 2004. Tunnel lining design guide.
London: Thomas Telford.
Byrne, P. M. 1991. “A cyclic shear-volume coupling and pore pressure
model for sand.” In Proc., 2nd Int. Conf. on Recent Advances in
Geotechnical Earthquake Engineering and Soil Dynamics, 47–55.
Columbia, MO: Univ. of Missouri.
Center for Engineering Strong Motion Data. 2016. “Lamjung, Nepal earthquake of 25 April 2015.” Accessed December 1, 2017. https://
strongmotioncenter.org/.
Chenna, R., S. Terala, A. P. Singh, K. Mohan, B. K. Rastogi, and P. K.
Ramancharla. 2014. “Vulnerability assessment of buried pipelines:
A case study.” Front. Geotech. Eng. 3 (1): 24–33.
Cheuk, C. Y., D. J. White, and M. D. Bolton. 2008. “Uplift mechanism of
pipes buried in sand.” J. Geotech. Geoenviron. Eng. 134 (2): 154–163.
https://doi.org/10.1061/(ASCE)1090-0241(2008)134:2(154).
Chian, S. C., and S. P. G. Madabhushi. 2012. “Effect of buried depth and
diameter on uplift of underground structures in liquefied soils.” Soil
Dyn. Earthquake Eng. 41 (Oct): 181–190. https://doi.org/10.1016/j
.soildyn.2012.05.020.
Chian, S. C., K. Tokimatsu, and S. P. G. Madabhushi. 2014. “Soil
liquefaction-induced uplift of underground structures: Physical and numerical modeling.” J. Geotech. Geoenviron. Eng. 140 (10): 04014057.
https://doi.org/10.1061/(ASCE)GT.1943-5606.0001159.
Chou, J. C., B. L. Kutter, T. Travasarou, and J. M. Chacko. 2011. “Centrifuge modeling of seismically induced uplift for the BART transbay
tube.” J. Geotech. Geoenviron. Eng. 137 (8): 754–765. https://doi.org
/10.1061/(ASCE)GT.1943-5606.0000489.
Elgamal, A. W., R. Dobry, E. Parra, and Z. Yang. 1998. “Soil dilation and
shear deformation during liquefaction.” In Proc., 4th Int. Conf. on Case
Histories in Geotechnical Engineering, 1238–1259. Columbia, MO:
Univ. of Missouri.
Finn, W. D. L. 1981. “Liquefaction potential: Developments since 1976.” In
Proc., 1st Int. Conf. on Recent Advances in Geotechnical Earthquake
Engineering and Soil Dynamics, edited by S. Prakash, 655–681.
Columbia, MO: Univ. of Missouri-Rolla.
Foriero, A., and B. Ladanyi. 1994. “Pipe uplift resistance in frozen soil and
comparison with measurements.” J. Cold Reg. Eng. 8 (3): 93–111.
https://doi.org/10.1061/(ASCE)0887-381X(1994)8:3(93).
Hu, J. L., and H. B. Liu. 2017. “The uplift behavior of a subway station
during different degree of soil liquefaction.” Procedia Eng. 189: 18–24.
https://doi.org/10.1016/j.proeng.2017.05.004.
Huange, X., H. F. Schweiger, and H. Huang. 2013. “Influence of deep excavations on nearby existing tunnels.” Int. J. Geomech. 13 (2): 170–180.
https://doi.org/10.1061/(ASCE)GM.1943-5622.0000188.
Itasca Consulting Group. 2012. FLAC3D 5.0 manual. Minneapolis: Itasca
Consulting Group.
Jiang, M., Z. Cai, P. Cao, and D. Liu. 2010. “Effect of cyclic loading frequency on dynamic properties of marine clay.” In Proc., Geoshanghai
Int. Conf., Soil Dynamics and Earthquake Engineering, 240–245.
Reston, VA: ASCE.
Jiang, M., W. Zhang, J. Wang, and H. Zhu. 2015. “DEM analyses of an
uplift failure mechanism with pipe buried in cemented granular
ground.” Int. J. Geomech. 15 (5): 04014083. https://doi.org/10.1061
/(ASCE)GM.1943-5622.0000430.
Jin, J. X., H. Z. Cui, L. Liang, S. W. Li, and P. Y. Zhang. 2018. “Variation of
pore water pressure in tailing sand under dynamic loading.” Shock Vibr.
2018: 1921057.
Kang, G. C., T. Tobita, and S. Iai. 2014. “Seismic simulation of
liquefaction-induced uplift behavior of a hollow cylindrical structure
buried in shallow ground.” Soil Dyn. Earthquake Eng. 64 (Sep): 85–94.
https://doi.org/10.1016/j.soildyn.2014.05.006.
Kang, G. C., T. Tobita, S. Iai, and L. Ge. 2013. “Centrifuge modeling and
mitigation of manhole uplift due to liquefaction.” J. Geotech. Geoenviron. 139 (3): 458–469. https://doi.org/10.1061/(ASCE)GT.1943-5606
.0000769.
06019020-9
Int. J. Geomech., 2020, 20(2): 06019020
Int. J. Geomech.
Downloaded from ascelibrary.org by Indian Institute of Technology Madras on 12/03/19. Copyright ASCE. For personal use only; all rights reserved.
Kiku, H., and S. Tsujino. 1996. “Post liquefaction characteristics of sand.”
In Proc., 11th World Conf. on Earthquake Engineering, 1088. Oxford,
UK: Pergamon.
Koseki, J., O. Matsuo, and Y. Koga. 1997a. “Uplift behaviour of underground structures caused by liquefaction of surrounding soil during
earthquake.” Soils Found. 37 (1): 97–108. https://doi.org/10.3208/sandf
.37.97.
Koseki, J., O. Matsuo, Y. Ninomiya, and T. Yoshida. 1997b. “Uplift of
sewer manholes during 1993 Kushiro-Oki earthquake.” Soils Found.
37 (1): 109–121. https://doi.org/10.3208/sandf.37.109.
Ling, H. I., L. Sun, H. Liu, T. Kawabata, and Y. Mohri. 2003. “Centrifuge
modeling of seismic behavior of large-diameter pipe in liquefiable soil.”
J. Geotech. Geoenviron. Eng. 129 (12): 1092–1101. https://doi.org/10
.1061/(ASCE)1090-0241(2003)129:12(1092).
Liu, H. 2012. “Three-dimensional analysis of underground tunnels in liquefiable soil subject to earthquake loading.” In Proc., GeoCongress 2012:
State of the Art and Practice in Geotechnical Engineering, 1819–1823.
Reston, VA: ASCE.
Liu, H., and E. Song. 2005. “Seismic response of large underground structures in liquefiable soils subjected to horizontal and vertical earthquake
excitations.” Comput. Geotech. 32 (4): 223–244. https://doi.org/10.1016
/j.compgeo.2005.02.002.
Lysmer, J., and R. L. Kuhlemeyer. 1969. “Finite dynamic model for infinite
media.” J. Eng. Mech. Div. 95 (4): 859–877.
Ma, F. G., J. LaVassar, and Z. L. Wang. 2008. “Three dimensional versus
two dimensional liquefaction analyses of a hydraulic fill earth dam.” In
Proc., 14th World Conf. on Earthquake Engineering. Beijing: Chinese
Association of Earthquake Engineering.
Madabhushi, S. S. C., and S. P. G. Madabhushi. 2015. “Finite element
analysis of floatation of rectangular tunnels following earthquake induced liquefaction.” Indian Geotech. J. 45 (3): 233–242. https://doi
.org/10.1007/s40098-014-0133-3.
Mortezaie, A. R., and M. Vucetic. 2013. “Effect of frequency and vertical
stress on cyclic degradation and pore water pressure in clay in the
NGI simple shear device.” J. Geotech. Geoenviron. Eng. 139 (10):
1727–1737. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000922.
Nobahar, A., S. Kenny, and R. Phillips. 2007. “Buried pipelines subjected
to subgouge deformations.” Int. J. Geomech. 7 (3): 206–216. https://doi
.org/10.1061/(ASCE)1532-3641(2007)7:3(206).
Robert, D. J., K. Soga, and T. D. O’Rourke. 2016. “Pipelines subjected to
fault movement in dry and unsaturated soils.” Int. J. Geomech. 16 (5):
C4016001. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000548.
© ASCE
Roy, K., B. Hawlader, S. Kenny, and I. Moore. 2018. “Uplift failure
mechanisms of pipes buried in dense sand.” Int. J. Geomech. 18 (8):
04018087. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001226.
Sherson, A. K., M. Nayyerloo, and N. A. Horspool. 2015. “Seismic
performance of underground pipes during the Canterbury earthquake
sequence.” In Proc., 10th Pacific Conf. on Earthquake Engineering.
Sydney, Australia: Building an Earthquake Resilient Pacific.
Stringer, M., and G. Madabhushi. 2007. “Modelling of liquefaction around
tunnels.” In Proc., 4th Int. Conf. on Earthquake Geotechnical Engineering. Dordrecht, Netherlands: Springer.
Subramaniam, P., and S. Banerjee. 2014. “Factors affecting shear
modulus degradation of cement treated clay.” Soil Dyn. Earthquake
Eng. 65 (Oct): 181–188. https://doi.org/10.1016/j.soildyn.2014.06
.013.
Sudevan, P. B., A. Boominathan, and S. Banerjee. 2018. “Uplift analysis of
an underground structure in a liquefiable soil subjected to dynamic
loading.” In Proc., 5th Geotechnical Earthquake Engineering and Soil
Dynamics, 464–472. Reston, VA: ASCE.
Tobita, T., G. C. Kang, and S. Lai. 2011. “Centrifuge modeling on manhole
uplift in a liquefiable trench.” Soils Found. 51 (6): 1091–1102. https://
doi.org/10.3208/sandf.51.1091.
Tobita, T., G. C. Kang, and S. Lai. 2012. “Estimation of liquefactioninduced manhole uplift displacements and trench-backfill settlements.”
J. Geotech. Geoenviron. Eng. 138 (4): 491–499. https://doi.org/10.1061
/(ASCE)GT.1943-5606.0000615.
Tokimatsu, K., and K. Katsumata. 2012. “Liquefaction-induced damage to
building in Urayasu City during the 2011 Tohoku Pacific earthquake.”
In Proc., Int. Symp. on Engineering Lessons Learned from the 2011
Great East Japan Earthquake, 665–674. Tokyo: Japanese Association
of Earthquake Engineering.
Watanabe, K., R. Sawada, and J. Koseki. 2016. “Uplift mechanism of opencut tunnel in liquefied ground and simplified method to evaluate the
stability against uplifting.” Soils Found. 56 (3): 412–426. https://doi
.org/10.1016/j.sandf.2016.04.008.
Yang, D., E. Naesgaard, P. M. Byrne, K. Adalier, and T. Abdoun. 2004.
“Numerical model verification and calibration of George Massey
Tunnel using centrifuge models.” Can. Geotech. J. 41 (5): 921–942.
https://doi.org/10.1139/t04-039.
Yasuda, S., and H. Kiku. 2006. “Uplift of sewage manholes and pipes during the 2004 Niigataken-Chustsu earthquake.” Soils Found. 46 (6):
885–894. https://doi.org/10.3208/sandf.46.885.
06019020-10
Int. J. Geomech., 2020, 20(2): 06019020
Int. J. Geomech.