an implementation of numerical analysis in …
TRANSCRIPT
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AN IMPLEMENTATION OF NUMERICAL ANALYSIS IN PREDICTING THE
LIQUEFACTION POTENTIAL ON SOIL SITES IN UNIVERSITY OF
BENGKULU, INDONESIA
Lindung Zalbuin Mase1)
, Hardiansyah2)
1),2)
Department of Civil Engineering, Faculty of Engineering,
University of Bengkulu, Indonesia.
e-mail: [email protected], [email protected]
Abstract
This paper presents an implementation of numerical analysis using pressure dependent
hyperbolic model to estimate liquefaction potential on sandy layers in University of Bengkulu’s
sites. Two sites located at the embankment area and the swamp area are studied. Furthermore,
non-linear one-dimensional seismic response analysis is performed to investigate the soil
behaviours, such as the excess pore pressure, the hysteresis loop, and effective stress path. In
this study, the ground motion of Elcentro is used as the input motion at the base of investigated
sites. In general, this study could recommend the practical analytical method in seismic
response analysis to consider the liquefaction effect before constructing. The results show that
the investigated sites are vulnerable to undergo liquefaction, especially for layers dominated by
loose to medium sandy soils. It can be therefore concluded if a strong earthquake with the peak
ground acceleration similar with the input motion happens near the location, the liquefaction
damage will be possible to occur.
Keywords: hyperbolic model, seismic response analysis, excess pore pressure, liquefaction
INTRODUCTION
Bengkulu is one of provinces in Indonesia, which has the high seismic activity. This is due to
fact that seismotectonic settings of Bengkulu City is relatively complex. It also means that
several earthquake sources exist in Bengkulu. Mase (2018) mentioned that there are three major
earthquake sources existing in Bengkulu City. The first source is subduction zone which is
located at the border of Eurasian Plate and Indo-Australian Plate. Within last two decades, this
subduction zone had triggered two major earthquakes which occurred on 4 June 2000 (the
Bengkulu-Enggano Earthquake) and 12 September 2007 (the Bengkulu-Mentawai Earthquake),
with the magnitude more than 7 Mw. The second source is Mentawai Fault, which is located on
the west of Sumatra Island. Similar with Subduction Zone, the Mentawai Fault has also ever
triggered the destructive earthquake along coastal area of Sumatra Island, such as the great
Padang Earthquake occurred on 30 September 2009 (Hakam, 2009). The last major earthquake
source in Bengkulu City is Sumatra Fault crossing the Sumatra Island. This fault is also
recognised as the main earthquake source during the Liwa Earthquake in 15 February 1994
(Widiwijayanti et al., 1996). Referring to the seismotectonic settings of Bengkulu Province in
general, the intensive earthquake studies have been started since several years ago, especially
related to the two major earthquakes occurred on June 2000 and September 2007.
Several local researchers had studied the earthquake impacts during the Bengkulu-Enggano
Earthquake and the Bengkulu-Mentawai Earthquake. Mase (2015) studied the characteristic of
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earthquake in Bengkulu City. Generally, based on Mase (2015), both earthquakes could trigger
the extensive damage with the Modified Mercalli Intensity (MMI) scale up to XI. Mase (2017
and 2018) studied the liquefaction potential along coastal area of Bengkulu City. The results of
those studies show that along coastal area of Bengkulu City is very vulnerable to undergo
liquefaction at shallow depth. Mase (2018) studied the seismic ground response analysis and the
reliability of spectral acceleration design to the earthquakes for Bengkulu City. The results of
those study reached a conclusion that the concern to designed spectral acceleration before
construction should be firstly considered. In general, the previous studies have reached a
conclusion that the general site of Bengkulu City is very vulnerable to undergo the earthquakes
and liquefactions impacts. The previous studies also considered the site-specific analysis for the
construction in Bengkulu City. However, the detail investigation to the specific site is still rarely
found. Mase et al. (2018) performed a study of site specific during the earthquake in University
Bengkulu, a centre of high education in Bengkulu City. The results of this recent study show
that the studied sites are necessary to be seriously investigated to observe the soil behaviours
during the earthquake. Mase et al. (2018) also recommend to study the soil behaviour of sandy
layers at the studied area, which were suspected to undergo liquefaction during the strong
earthquakes. Learning from Mase et al. (2018), an extended study of seismic response analysis
to observe the soil behaviour related to the liquefaction is performed. Elcentro ground motion is
applied at the bottom of investigated sites. The excess pore water pressure (u), the acceleration
(amax), and the relative displacement () profiles are presented. The time histories responses
including excess pore pressure ratio (ru), hysteretic loop (-), and effective stress path (c-) are
observed. This study also exhibits the comparison of spectral acceleration for the sites. In
general, this study could give a better understanding in the implementation of seismic response
analysis for liquefaction study. This study also would like to recommend the stake holder to
reconsider earthquake and liquefaction for the construction design.
STUDY AREA
Two sites in Bengkulu City Area are investigated in this study (Figure 1). The locations are
referring to Mase et al. (2018) study. The first site is located at the integrated engineering
laboratory, whereas the second site is located at science laboratory. The cone penetration test
(CPT) and geophysical survey using microtremor are performed in the site by Mase et al.
(2018). The CPT data is furthermore analysed to obtain the information of soil profile or soil
type by using Robertson and Cabal (2015) method. In Figure 2, the first site is noted as S-1,
whereas the second one is noted as S-2. The first location is located at the embankment area in
the University of Bengkulu, whereas the second one is located at swamp area.
The results of site investigation data for S-1 and S-2 are presented in Figure 2 and Figure 3,
respectively. In Figure 2, S-1 site is dominated by clayey sands at shallow depth (0 to 3 m
depth). At this depth range, the clays with organic contain and high plasticity (OH and CH) and
silty clay (CM) exist. The average cone resistance or qc for this depth range is about 20 kg/cm2,
whereas the shear wave velocity (Vs) is about 270 m/s. Another CM layer is also found at 4.2 to
6.2 m below the ground surface. The average qc for this layer is about 20 kg/cm2 and the Vs of
about 270 m/s. The silty sand (SM) layers are found at 3 to 4.2 m depth and 6.2 to 7.4 m depth,
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respectively. These layers have the average qc of about 20 to 50 kg/cm2 with Vs of 27 m/s. The
well graded sand (SW) layer is found at depth range of 7.4 to 14.4 m. This layer has qs average
of 120 kg/cm2 and Vs of about 400 m/s. The gravelly sand (GS) is found at the depth of 14.4 to
15.2 m depth, with qc average of 220 kg/cm2 and Vs of 420 m/s.
Figure 1. Site investigation data (modified from Mase et al (2018) and Google Earth (2018))
Figure 3 presents the site investigation data in S-2. Similar with S-1 site, the clay layers
including OH and CM also exist at shallow depth, i.e. up to 2.6 m depth. Another CM layer is
also found at 6.8 to 7.6 m. This layer has the average qc of about 20 kg/cm2 and Vs of 320 m/s.
These layers have the average qc of about 20 kg/cm2 and Vs of 230 m/s. SM layers are also
found at several depth ranges, i.e. at 2.6 to 3.2, 6.2 to 6.8, and 7.6 to 8.4 m. These layers have
the average qc of about 20 to 80 kg/cm2 and Vs of about 320 m/s. SW layer is found at depth of
8.4 to 11.4 m depth, with Vs of about 400 m/s and qc of about 200 kg/cm2. In general, based on
site investigation result, it can be concluded that the geological conditions of S-1 and S-2 are
relatively similar. According to Mase et al. (2018), the seismic ground response analysis is
necessary to perform. In this study, the main focus is to investigate the liquefaction potential on
the sandy layers. A further analysis to the existing sandy layers at the investigated sites is
therefore performed.
THEORY
Non-linear pressure dependent hyperbolic model
Several models for seismic ground response analysis have introduced by several researchers.
One of those models is Non-linear pressure dependent hyperbolic model, which is proposed by
Elgamal et al. (2006). This model is originally developed by Matasovic (1993). This model
emphasises on the implementation of hyperbolic function to simulate the non-linearity of soil
behaviour during cyclic (Elgamal et al., 2006). The model simultaneously models the increment
of plasticity to simulate the permanent deformation for hysteretic damping. Therefore, a number
of yield surface is implemented in this model.
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Mase et al. (2017) mentioned that the importance of this model is on the controlling the
permanent shear mechanism is soil types. This is due to fact that during the earthquake, there
are the decrease of stiffness on sandy soil. This model implements the evaluation of stiffness on
each step as. In another word, the model applies a number of yield surface to model the cyclic
behaviour. Hence, the evaluation of the stiffness on each stage of cyclic loading is relatively
relevant with real condition. For the implementation of the model, several studies have applied
this model to model the non-linear seismic ground response analysis problem, such as Pender et
al. (2016) and Mase et al. (2017). Generally, this model has successful to model the liquefaction
problem for those cases.
0.0 m
0.2 m
1.6 m
3.0 m
4.2 m
6.2 m
7.4 m
14.4 m
15.2 m
OH
CH
CM
SM
CM
SM
SW
GS
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
0 200 400 600
Dep
th (
m)
Vs (m/s)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
0 1 2 3 4 5
Dep
th (
m)
fs (kg/cm2)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
0 100 200 300
qc (kg/cm2)
S-1
Figure 2. Site investigation data at S-1 (modified from Mase et al. (2018)
Finite element method for one dimensional seismic response analysis
One of analytical methods implemented for seismic ground response analysis is the finite
element method. For non-linear seismic ground response analysis, such as liquefaction cases,
the finite element model is common to be implemented, Mase et al. (2017) presented the
procedure to use the finite element method for one-dimensional seismic response analysis to
solve the liquefaction problem during the 6.8 Mw Tarlay Earthquake in Northern Thailand, as
described in Figure 4. In Figure 4, the soil column is initially presented. Furthermore, the
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wavelength analysis is performed to generate the mesh size. In the application, Mase et al. (2016
and 2017) suggested that mesh maximum size of 0.5 m should be used. Figure 4 also
recommended several criteria for seismic ground response analysis using finite element method.
For soil column model, the drainage is assumed only on vertical direction. There is no drainage
path on both vertical and bottom sides or in another word, the bottom of soil column is assumed
as the impermeable layer. The deformation is allowable on vertical direction, whereas the
horizontal displacements on both sides are the same. In the analysis, the lateral normal stress on
both sides are able to be generated. The soil behaviours such as the excess pore pressure, the
effective stress path, and the hysteresis loop can be generated for the selected elements. In
general, the procedure to use the finite element method for one dimensional seismic ground
response analysis is relatively similar with other simulation methods. However, the main factor
in determining the reliable results on the simulation is selection of the appropriate model.
Therefore, Mase et al. (2017) suggested that for liquefaction problem, the effective stress model,
as proposed by Elgamal et al. (2006) can be the alternative.
0
1
2
3
4
5
6
7
8
9
10
11
0 100 200 300
qc (kg/cm2)
0.0 m
0.4 m
0.8 m
1.8 m
2.6 m
5.2 m
6.2 m
6.8 m
7.6 m
8.4 m
11.4 m
SW
SM
CM
SM
SP
SM
CM
OH
OH
CM0
1
2
3
4
5
6
7
8
9
10
11
0 200 400 600
Vs (m/s)
0
1
2
3
4
5
6
7
8
9
10
11
0 1 2 3 4 5
fs (kg/cm2)
S-2
Figure 3. Site investigation data at S-2 (modified from Mase et al. (2018)
METHODOLOGY
In general, the method implemented in this study is relatively similar with several studies which
also investigated the soil behaviour during the earthquake. This study is initially conducted by
collecting the site investigation data at S-1 and S-2. As elaborated in the previous section, the
site investigation data used in this study are the secondary data obtained from Mase et al.
(2018). Based on the site investigation data, the soil column model on each site is generated by
following the procedure suggested by Mase et al. (2017). Furthermore, the non-linear pressure
dependent hyperbolic model is applied for the soil layers. The ground water is assumed at
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ground surface. To simulate the earthquake response, the input motion is applied at the bottom
of boreholes. Since there is no the recorded ground motion in the studied area, the Elcentro
ground motion recorded in 1940 (Figure 5) is applied in this study. This ground motion is
obtained from Pacific Earthquake Engineering Research or PEER (2019) Institute. The
maximum recorded acceleration in Figure 5 is about 0.349g. It is still larger than the predicted
ground motion of the 8.6 Mw Bengkulu Earthquake predicted by Mase (2018) i.e. 0.212g. The
applied ground motion of Elcentro can be therefore roughly describing an impact resulted from
a larger earthquake than the largest earthquake had ever occurred in Bengkulu City. In this
study, the assumption of rigid surface at the bottom of boreholes is implemented since there is
no information where the engineering bedrock exists. During the simulation, soil behaviours
including time history of excess pore pressure, hysteresis loop, and effective stress path are
observed. In addition, the profiles of maximum acceleration (a max) on each depth, the maximum
relative displacement on vertical direction (), and the excess pore pressure as well as the
effective confining pressure (c) are presented. In general, this study is expected to provide a
better understanding in implementing of non-linear seismic response analysis to investigate
liquefaction in sandy soils.
Figure 4. Soil column model for one-dimensional seismic ground response analysis
(Mase et al., 2016)
-0.4
-0.2
0
0.2
0.4
0 10 20 30 40 50 60
Accele
ra
tio
n (g
)
Time (sec)
0.349g
Figure 5. The Elcentro ground motion (PEER, 2019)
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RESULTS AND DISCUSSION
Soil responses profiles
Figure 6 presents the responses profiles during the simulation of Elcentro ground motion at S-1.
In Figure 6, the responses including the relative displacement, the acceleration, and the
comparison of effective stress (v) and the excess pore pressure (u). For relative displacement,
it can be observed that during the cyclic loading, there are the soil deformation resulted during
the simulation. At ground surface, the relative displacement () of about 0.036 m or about 3.6
cm. For acceleration, there is de-amplification of acceleration at ground surface. This is
indicating that the soil is already failure. There is no elastic response resulted; therefore, at the
ground surface the acceleration tends to decrease. For effective stress and excess pore pressure,
it can be observed that the excess pore pressure exceeds the initial effective stress at depth of 3
to 4.2 m, at depth of 6 to 10.5 m depth. Theoretically, liquefaction has happened at those ranges,
since the bearing capacity of those depths has unavailable after the excess pore pressure builds
up. In general, it can be roughly estimated that liquefaction could be possible to happen at first
sand layer (SM), second sand layer (SM), and half of third sand layer (SW). Figure 7 presents
the responses profiles at S-2. The relative displacement at ground surface is about 0.038 m or
3.8 cm. The similar phenomenon, i.e. de-amplification of acceleration is also observed at S-2.
At ground surface, the maximum acceleration during the cyclic loading is about 0.08g. The
liquefied layers are also observed at S-2, especially at depth of 3 to 6.4 m depth. The effective
stress at those depths is exceeded by the excess pore pressure.
-15
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
0 30 60 90 120
Dep
th (
m)
Pressure (kPa)
Effective stress
Excess pore pressure
-15
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
0 0.1 0.2 0.3 0.4 0.5 0.6
Dep
th (
m)
Acceleration (g)
-15
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
0 0.01 0.02 0.03 0.04
Dep
th (
m)
Relative Displacement (m)
Figure 6. The soil responses profiled at S-1
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-11.2
-10.2
-9.2
-8.2
-7.2
-6.2
-5.2
-4.2
-3.2
-2.2
-1.2
-0.2
0 30 60 90
Dep
th (
m)
Pressure (kPa)
Effective stress
Excess pore pressure
-11.2
-10.2
-9.2
-8.2
-7.2
-6.2
-5.2
-4.2
-3.2
-2.2
-1.2
-0.2
0 0.1 0.2 0.3 0.4 0.5 0.6
Dep
th (
m)
Acceleration (g)
-11.5
-10.5
-9.5
-8.5
-7.5
-6.5
-5.5
-4.5
-3.5
-2.5
-1.5
-0.5
0 0.02 0.04 0.06
Dep
th (
m)
Relative Displacement (m)
Figure 7. The soil responses profiled at S-2
Spectral acceleration comparison
Figure 8 shows the spectral accelerations at selected layers at both S-1 and S-2. In Figure 8,
only spectral accelerations at sand layers on each site are presented in this study. The
comparison to the seismic design code of Indonesia (SNI 03-1726-2012) is also performed in
Figure 8. From Figure 8a (S-1), it can be seen that in general at sandy layers the spectral
acceleration exceeds the designed spectral acceleration. Similar tendency is also exhibited by
Figure 8b (S-2). Referring to the results of spectral comparison, the structural design in the
study area should consider the earthquake design for the construction plan in the study area.
Soil behaviour during the cyclic loading
Figure 9 presents the liquefied soil behaviours at S-1. In Figure 9, the selected depths are 3.5 m,
7 m, those selected depths represent the sand layers at S-1. For 3.5 m, i.e. SM layer (Figure 9a),
it can be seen that the excess pore water pressure ratio has reached the liquefaction threshold i.e.
ru >1. It indicated that liquefaction has occurred at this depth. The hysteresis loop comparison
also shows that the response is totally non-linear, which indicates that there is the reduction of
shear modulus during dynamic loading. The effective stress path also indicates that the
liquefaction is able to occur on this layer. It is exhibited by the reduction of effective confining
pressure until zero which indicates that the layer has undergone the loss of bearing capacity.
Similar to first sand layer, the second sand layer (SM) represented at depth of 7 m also shows
the similar tendency, as presented in Figure 9b. In Figure 9b, the excess pore pressure ratio has
exceeded the liquefaction threshold. It indicates that liquefaction occurred at this depth. Other
facts are presented by the hysteresis loop and the effective stress. The hysteresis loop shows the
tendency of shear modulus reduction by the flattered hysteresis loop. It might present that the
soil layer could be failure due to loss of bearing capacity caused by excess pore pressure.
Effective stress path exhibits the reduction of effective confining pressure significantly during
the dynamic loading. The effective stress path also shows that the effective confining pressure
has reached zero. It means that liquefaction could happen in this depth.
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0.01
0.1
1
0.01 0.1 1 10
Sp
ectr
al A
ccel
erat
ion
(g)
Period (sec)
S-2
Input Motion
At 4 m depth (SM)
At 5.5 m depth (SP)
At 6.5 m depth (SM)
At 8 m depth (SM)
At 10 m depth (SW)
SNI 03-1726-2012 (SE)
SNI 03-1726-2012 (SD)
SNI 03-1726-2012 (SC)0.01
0.1
1
0.01 0.1 1 10
Sp
ectr
al A
ccel
erat
ion
(g)
Period (sec)
S-1
Input Motion
At 3.5 m depth (SM)
At 7 m depth (SM)
At 10.5 m depth (SW)
At 15 m depth (GS)
SNI 03-1726-2012 (SE)
SNI 03-1726-2012 (SD)
SNI 03-1726-2012 (SC)
Figure 8. The soil responses profiled at S-2
Figure 10 presents soil behaviour resulted from one dimensional seismic ground response
analysis at S-2. Figure 10a presents the soil behaviour for depth of 4.0 m (SM layer). For excess
pore pressure ratio, it can be seen that the liquefaction threshold has been exceeded by the
excess pore pressure ratio. For the hysteresis loop, the flattered curve indicates that there is the
significant reduction of shear modulus due to the excess pore pressure. The excess pore pressure
also gives the impact to decrease of effective confining pressure as presented in Figure 03a. The
similar tendency is also presented in Figure 10b (SP layer) for depth of 5.5 m. The excess pore
pressure ratio has exceeded the liquefaction threshold. It indicates that liquefaction can be
potentially occurred at this depth. During the loading, the reduction of shear modulus happened.
It is exhibited by the flattered curve of hysteresis loop. The excess pore pressure also tends to
reduce the effective confining pressure. It is presented by the significant reduction of effective
confining pressure.
-4
-3
-2
-1
0
1
2
3
4
-6 -4 -2 0 2 4 6
Sh
ea
r S
tress
()
(kP
a)
Shear Strain () (%)
SM (At 3.5 m depth)
0
0.2
0.4
0.6
0.8
1
1.2
0 10 20 30 40
Excess
Po
re P
ress
ure
Ra
tio
(r u
)
Time (sec)
SM (At 3.5 m depth)
Liquefaction threshold
-4
-3
-2
-1
0
1
2
3
4
0 2 4 6 8
Sh
ea
r S
tress
() (k
Pa
)
Effective Confining Pressure (v)
SM (At 3.5 m depth)
(a)
-20
-15
-10
-5
0
5
10
15
20
-6 -4 -2 0 2 4 6
Sh
ea
r S
tress
()
(kP
a)
Shear Strain () (%)
SM (At 7 m depth)
0
0.2
0.4
0.6
0.8
1
1.2
0 10 20 30 40
Excess
Po
re P
ress
ure
Ra
tio
(r u
)
Time (sec)
SM (At 7 m depth)
Liquefaction threshold
-20
-15
-10
-5
0
5
10
15
20
0 5 10 15 20 25 30
Sh
ea
r S
tress
()
(kP
a)
Effective Confining Pressure (v)
SM (At 7 m depth)
(b)
Figure 9. The soil behaviour at S-1 (a) at depth of 3.5 m and (b) at depth 7 m
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0
0.2
0.4
0.6
0.8
1
1.2
0 10 20 30 40
Ex
cess
Po
re P
ress
ure
Ra
tio
(r
u)
Time (sec)
SM (At 4 m depth)
Liquefaction threshold
-6
-4
-2
0
2
4
6
-6 -4 -2 0 2 4 6
Sh
ear
Str
ess
()
(kP
a)
Shear Strain () (%)
SM (At 4 m depth)
-6
-4
-2
0
2
4
6
0 3 6 9 12 15
Sh
ear
Str
ess
()
(kP
a)
Effective Confining Pressure (v)
SM (At 4 m depth)
(a)
0
0.2
0.4
0.6
0.8
1
1.2
0 10 20 30 40
Exc
ess
Po
re P
ress
ure
Ra
tio
(r u
)
Time (sec)
SP (At 5.5 m depth)
Liquefaction threshold
-8
-6
-4
-2
0
2
4
6
8
-6 -4 -2 0 2 4 6
Sh
ear
Str
ess
()
(kP
a)
Shear Strain () (%)
SP (At 5.5 m depth)
-8
-6
-4
-2
0
2
4
6
8
0 3 6 9 12 15 18
Sh
ear
Str
ess
()
(kP
a)
Effective Confining Pressure (v)
SP (At 5.5 m depth)
(b)
Figure 10. The soil behaviour at S-2 (a) at depth of 4 m and (b) at depth of 5.5
CONCLUDING REMARKS
Implementation of non-linear seismic ground response analysis has been successful to observe
liquefaction potential in study area. An attention to liquefaction countermeasures to minimise
the possible effect of liquefaction in the study area should be a priority before construction.
ACKNOWLEDGEMENT
This research was supported by the Mandatory Research from the University of Bengkulu
Research Fund Grant No. 3968/UN30.15/LT/2018.
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Indonesian
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Sciences, 49(6), 721-736.
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