Geotech Geol Eng (2011) 29:463–475
DOI 10.1007/s10706-011-9396-y
ORIGINAL PAPER
Nonlinear Site Response and Liquefaction Analysis
in the New Madrid Seismic Zone
Wei Zheng • Ronaldo Luna
Received: 30 January 2009 / Accepted: 6 February 2011 / Published online: 22 February 2011
Ó Springer Science+Business Media B.V. 2011
Abstract Many existing highway bridges in the
New Madrid Seismic Zone are located in the
Mississippi Embayment, consisting of deep soil
deposits and liquefaction susceptible near surface
soils. It is important to understand the comprehensive
impact of deep soil deposits and liquefaction on the
response of the bridge foundations under seismic
loading. A nonlinear soil model is then presented to
study the impacts of the deep soil deposit and
liquefaction on response analysis. The soil model has
the advantage of using input parameters that can be
obtained from conventional field and laboratory
testing methods, which makes it attractive to engineering practice. The model calibrations used field
recorded motions and laboratory test data, which
indicate that the model provides an acceptable
outcome based on simple input parameters. The
model is implemented into the site response analysis
for a typical Missouri highway bridge site in this
seismic zone. The effect of the deep soil deposit and
liquefaction on the site response analyses is
discussed.
W. Zheng
Black & Veatch Corporation, 11401 Lamar Avenue,
Overland Park, KS 66211, USA
R. Luna (&)
Department of Civil, Architectural and Environmental
Engineering, Missouri University of Science
and Technology, Rolla, MO 65409, USA
e-mail: [email protected]
Keywords Non-linear site response Liquefaction Earthquakes
1 Introduction
The New Madrid Seismic Zone (NMSZ) has experienced some of the largest magnitude (estimated
8.0–8.3) earthquake events in North American history
(1811–1812). Experts agree that similar or greater
magnitude earthquakes will strike this region again.
The geological structure of the NMSZ is composed of
very old rock formed 500 million years ago, which
includes a strike slip fault system overlaid with deep
soil deposits (up to 1,000 m near Memphis). The deep
soil deposit has a long fundamental period and may
amplify more long period components when the
seismic wave is transmitted from rock to ground
surface. This may lead to extensive damage of long
period infrastructure, such as highway bridges. The
effect of high confining stresses on the propagation of
seismic waves in the NMSZ has been found to be
important for site response analysis in the region.
(Hashash and Park 2001; Zheng and Luna 2004). At
the same time, shallow sediments in this area consist of
silts, sands and low plastic soil that have high potential
for liquefaction. Lots of liquefaction vestige, such as
paleoseismic features of sand boils and landslides, can
be still found today for 1811–1812 earthquakes and
older events. The soil liquefaction may damage the
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464
foundations (usually pile foundation) of the highway
bridges in this area. The recent assessment of two river
crossing sites in the NMSZ (Anderson et al. 2001) also
shows that the bridge foundation soils for these sites
are very likely to experience liquefaction for a
2,475 year return earthquake. Liquefaction was evaluated using the simplified liquefaction method (Youd
et al. 2001) with in situ test data including Standard
Penetration Test (SPT) and Cone Penetration Test
(CPT). The peak ground acceleration used in the
liquefaction analysis is developed based on the USGS
seismic map and the ASCE-7-05 site coefficients. The
impact of the deep soil deposit on the site response is
not considered. Park and Hashash (2005) indicated
that the deep soil profile at the NMSZ could make the
site coefficients lower at short period and higher at
long period than the ASCE-7-05 site coefficients,
which suggests the need of a soil model that can
simulate the comprehensive impacts of deep soil
deposits and liquefaction on the site response analysis.
A rational numerical model is presented to consider
the effects of the deep soil deposit and the liquefaction
to the wave propagation in the NMSZ. The constitutive
stress–strain relationship of the model is described by
the empirical unified formulas (Ishibashi and Zhang
1993), which incorporate the influence of the confining
pressure to the shear modulus degradation curve and
the damping curve. Extended Masing (1926) criteria
are applied to represent hysteretic loading and unloading of soils in the model. Then a two-parameter pore
water pressure generation model, based on the widely
used Byrne model (1991), is loosely coupled into the
model to study possible liquefaction of the surface
sediments. The model is incorporated into a twodimensional finite element code of Open System for
Earthquake Engineering Simulation (OpenSEES).
With available interface and structure elements in
OpenSEES, the proposed soil model can be used for
fully-coupled soil-structure interaction for the bridge
foundations under earthquake load. The soil model is
presented for the engineering practice with input
parameters that can be obtained from conventional
field and laboratory testing, such as SPT, geophysical
shear velocity survey, and Atterberg limits. The
calibrations with the field recorded motions and lab
test data indicate that the model provides an acceptable
outcome with simple inputs. Finally, the new model is
applied to a typical Missouri highway bridge site,
located in the New Madrid rift complex, to study the
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Geotech Geol Eng (2011) 29:463–475
effects of the deep soil deposit and the liquefaction to
site response analysis in this area.
2 Soil Model for Deep Deposits
The stress–strain relationship in soil is quite nonlinear
under cyclic loading. Even at small shear strain level
(10-4) soils show shear modulus reduction. At the
same time, the material damping is developed and
increases with the cyclic shear strain. Numerous
researchers (e.g. Hardin and Drnevich 1972; Seed and
Idriss 1970; Vucetic and Dobry 1991) have performed the characterization of shear modulus degradation and damping curves for many soil types and
provide a very valuable database for dynamic analyses. Vucetic and Dobry (1991) summarized that the
plasticity index (PI) is the main factor to control these
relationships. However, Ishibashi (1992) pointed out
that the method of Vucetic and Dobry did not include
one significant parameter, the effective mean normal
00 , particularly for soils of low plasticity.
stress r
Figure 1a shows that increase in G/Gmax for the same
level of strain at different effective mean normal
00 , the material
stress for sands. At higher level of r
shows less degradation and will tend to propagate the
ground motion with less energy dissipation. The
effective mean normal stress can be a significant
factor that influences wave propagation through the
deep soil deposits in the NMSZ.
The effect of confining pressure on the dynamic soil
properties, the shear modulus and the soil damping, has
been recognized by several researchers (e.g. Iwasaki
et al. 1978; Hardin et al. 1994). When this effect is not
considered in the site response analysis of a deep soil
column, the ground surface response could be significantly underestimated (Hashash and Park 2001;
Zheng and Luna 2004). Ishibashi and Zhang (1993)
presented unified formulas to take into account the
effect of the effective confining pressure on the shear
modulus degradation curve and the damping curve.
The normalized shear modulus degradation curves
calculated from these formulas are shown in Fig. 1. For
sand material, Fig. 1a shows that increase in G/Gmax
for the same level of strain at different effective mean
normal stress. At higher level of the effective mean
00 , the material shows less degradation
normal stress r
and will tend to propagate the ground motion with less
energy dissipation. As anticipated, the effect of
Geotech Geol Eng (2011) 29:463–475
(a)
465
(
" #)
0:000556 0:4
mðc; PIÞ ¼ 0:272 1 tan h ln
c
1.0
σ 0' = 1000kPa
0.8
expð0:0145PI 1:3 Þ
σ 0' = 800kPa
G/Gmax
σ 0' = 200kPa
σ 0' = 400kPa
0.6
σ 0' = 50kPa
0.4
σ 0' = 1kPa
0.2
PI=0
0.0
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
Cyclic Shear Strain
(b) 1.0
σ = 1000 kPa
σ 0' = 800kPa
G/Gmax
σ 0' = 400kPa
σ 0' = 200kPa
0.6
σ 0' = 50kPa
σ 0' = 1kPa
0.4
0.2
PI=50
0.0
1.0E-06
1.0E-05
1.0E-04
1.0E-03
where, n is a coefficient to consider the influence of
the plasticity index to the degradation curve, which
can be determined by:
9
8
0:0
for PI ¼ 0
>
>
>
>
=
<
3:37 106 PI 1:404 for 0\PI 15
nðPIÞ ¼
7 1:976
7:0 10 PI
for 15\PI 70 >
>
>
>
;
:
2:7 105 PI 1:115 for PI [ 70
ð4Þ
'
0
0.8
ð3Þ
1.0E-02
1.0E-01
Cyclic Shear Strain
Fig. 1 Influence of mean effective confining pressure on
modulus reduction curves for a non-plastic (PI = 0) soil, and
b plastic (PI = 50) soil (Ishibashi 1992)
confinement is less pronounced for soils with higher
PI, as shown in Fig. 1b. The expression of the formula
for the normalized shear modulus degradation curve
can be expressed in the following form:
0 mðc;PIÞ
0
G=Gmax ¼ Kðc; PIÞ r
ð1Þ
where, Gmax is the initial shear modulus; c is the
shear strain; G is the shear modulus at the shear strain
00 is the
c; PI is the plasticity index of the soil; r
effective mean normal stress. K and m are two
functions used to control the shape of the shear
modulus degradation curve, which can be written as:
Kðc; PIÞ
(
" #)
0:000101 þ nðPIÞ 0:492
¼ 0:5 1 þ tan h ln
c
ð2Þ
The shear modulus degradation curve presented
from Eq. (1) can be described as the backbone curve
in stress–strain field. An example is shown in Fig. 2.
Figure 2a shows the modulus degradation curve for
00 equal to 100 kPa. Figure 2b shows the
sand at r
corresponding backbone curve when the maximum
shear modulus Gmax is 20 MPa. The nonlinear stress–
strain relationship is approximated by the successive
incremental steps in the finite element analysis. At the
beginning of each increment of loading, the modulus
of previous load step is used. Then the iteration is
performed until the appropriate modulus value is
selected for each element on the basis of the values of
the strain in that element.
Based on the backbone curve, the extended
Masing (1926) criteria were implemented to govern
the unloading–reloading behavior of soil. Damping of
soil in seismic loading can be computed based on the
shear modulus ratio G/Gmax. Ishibashi and Zhang
(1993) also developed an empirical formula Eq. (5)
for calculating the damping ratio k of plastic and nonplastic soils. For the unloading or reloading, the
modulus ratio G/Gmax is calculated by the strain
(c - cr)/2.
k¼
0:333ð1 þ expð0:0145PI 1:3 ÞÞ
2
(
)
G 2
G
0:586
1:547
þ1 x
Gmax
Gmax
ð5Þ
The constitutive laws presented above are implemented into a 2-dimensional 4-node plane strain
element. The element was coded by C?? language
and added into the system of OpenSEES developed
by PEER (2000). OpenSEES is a software framework
for creating models and analysis methods to simulate
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466
1.0
0.8
G/Gmax
σ 0' = 100kPa
0.6
0.4
0.2
0.0
1.00E-06
1.00E-05
1.00E-04
1.00E-03
1.00E-02
1.00E-01
Strain
(b)
25
τmax (kpa)
20
σ 0' = 100kPa
Gmax = 20MPa
15
10
Successive
time step
5
0
0
0.005
0.01
Strain
Fig. 2 a Modulus degradation curve for sand. b Corresponding
backbone curve
structural and geotechnical systems in earthquake
loading. Wave propagation equations are solved in
discrete time increments in the time domain. Rayleigh damping scheme is used to determine the soil
element damping. A two mode damping scheme
proposed by Hudson et al. (1994) are used to develop
the global damping matrix. Even though the expression of the model above is complex, only the initial
shear modulus Gmax and the plastic index PI are
needed as the inputs. The simplicity of the inputs
makes this proposed model attractive for engineering
application.
were obtained at ground surface on fill material
underlain by San Francisco Bay sediments and at the
rock outcrop of the adjacent Yerba Buena Island
(YBI), which is located about 1.5 km south of the
TRI. Both islands are located in the center of the San
Francisco Bay, approximately 70–75 km northwest
of the epicenter. Since the locations of TRI and YBI
are close by, the records in YBI can be used as the
input motions at rock base of TRI for the site
response study (Matasovic 1993; Finn et al. 1993).
The peak ground acceleration (PGA) of the strong
motion records ranged from 0.067 g at the rock
outcrop to 0.16 g at the soil surface (90° component)
and from 0.029 g at the rock outcrop to 0.1 g at the
soil surface (00° component).
The soil profile at the Treasure Island site is shown
in Fig. 5. The measured and estimated soil properties
are based on Matasovic (1993). The initial tangent
shear modulus is determined from the average shear
wave velocity profiles and estimated mass density of
the soils. The PI of Young Bay Mud is assumed as 45
and that of Old Bay mud is assumed as 60 based on
the reported PI range for these soils (Pestana et al.
2002; Kwok and Stewart 2006) (Fig. 3).
Both the 90° and 00° component recorded motions
at Yerba Buena Island are used as the input motion at
the base of the soil column. The calculated surface
motions are compared with the recorded surface
motion at Treasure Island site. The comparisons of
response spectra, time history and Fourier spectra are
Shear Wave Velocity (m/s)
0
0
20
Depth (meter)
(a)
Geotech Geol Eng (2011) 29:463–475
200
400
600
800
Gravelly Sand (Artificial fill)
Fine Sand Loam
Holocene Bay Mud
Sand Loam and Loamy Fine
Sand
40
Pleistocene Bay Mud
60
80
3 Validation of the Soil Model
Fine Gravelly Sand
Pleistocene Bay Mud
Sandstone
A case study was used to analyze the ground response
of the Treasure Island (TRI) site for the 1989 Loma
Prieta earthquake (M 7.1). The earthquake records
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100
Fig. 3 Soil profile and shear wave velocity measured at
Treasure Island
467
shown in Figs. 4, 5 and 6, respectively. The results
indicate that the new soil model can provide reasonable predictions to the measure data with simple
input—initial shear modulus and the plastic index of
the soil.
Spectrum Amplitude (g)
(a)
0.8
5% Damping
Fourier Amplitude Spectrum
Geotech Geol Eng (2011) 29:463–475
0.15
Measured
Predicted
0.10
0.05
0.00
0
2
4
6
8
10
Frequency (HZ)
0.6
Fig. 6 Comparisons of recorded Fourier spectra at Treasure
Island with computed Fourier spectra for the 90° component
0.4
0.2
4 Pore Water Pressure Generation Model
0.0
0.0
0.1
1.0
10.0
Period (s)
Spectrum Amplitude (g)
(b)
0.8
5% Damping
0.6
0.4
0.2
0.0
0.0
0.1
1.0
10.0
Period (s)
du ¼ Mdev
Recorded Input at Rock (YBI)
Recorded at Surface (TRI)
Computed at Surface (New Model)
Fig. 4 Comparisons of recorded motions at Treasure Island
with computed response spectra (a) the 90° Component (b) the
00° component
0.3
Acceleration (g)
0.2
Calculated
Measured
0.1
0
0
5
10
15 M 20
25
In order to consider the effect of liquefaction on the
site response analysis, a simple pore water pressure
generation model is loosely coupled into the nonlinear soil model. The pore water pressure is related to
the change of the volumetric strain of granular
material during cyclic shear loading, such as earthquake loading (Martin et al. 1975, 1978; Byrne 1991)
and the model is presented as follows (Byrne and
McIntyre 1995):
ev
dev ¼ 0:25C1 dc exp C2
ð6Þ
c
30
35
40
-0.1
-0.2
-0.3
Time (s)
Fig. 5 Comparisons of recorded time history at Treasure
Island with computed time history for the 90° component
ð7Þ
where, ev is the volumetric strain; c is the shear strain,
which can be assumed as the largest strain in the current
or previous cycle, whichever is larger. C1 and C2 are
constants that control the amount of volumetric strain.
The value of these constants can be empirically
determined from the relative density Dr or the normalized penetration value (N1)60 (Byrne 1991), which
makes the model good for engineering practice. u is the
pore water pressure. M is the constrained rebound
effective stress tangent modulus of the soil skeleton. At
the end of each load step, the pore water pressure is
updated based on the increment of shear strain of this
step. The soil modulus is also updated to consider the
effect of the increase of the pore water pressure.
The pore water pressure generation model was
compared to results using DESRA-MUSC (Qiu 1998),
which has a same two-parameter model. The idealized
soil profile and the shear wave velocity profile are
shown in Fig. 7. The input parameters for the soil
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Geotech Geol Eng (2011) 29:463–475
Acceleration (g) Acceleration (g) Acceleration (g)
(a)
0.2
Input Motion
0.1
0.0
0
10
20
30
40
50
-0.1
60
Time (s)
-0.2
0.2
Ground Surface Motion from DESRA-MUSC
0.1
0.0
0
10
20
30
40
50
-0.1
60
Time (s)
-0.2
0.2
Ground Surface Motion from New Model
0.1
0.0
0
10
20
30
40
50
-0.1
60
Time (s)
-0.2
(b) 1.2
properties and the pore water pressure generation
model are also the same as those used by Qiu 1998. The
1992 Landers earthquake Amboy record (Mw = 6.7) is
selected as the input motion. The peak ground acceleration is scaled to 0.2 g. The analysis results are
compared using the ground surface time history, the
pore water pressure time history and the response
spectra, as shown in Fig. 8. The results indicate that the
proposed soil model and the liquefaction model are in
reasonable agreement with DESRA-MUSC results.
5 Response Analysis in the NMSZ Deep Deposits
The proposed soil model is then applied for a site
response analysis study conducted for a highway
bridge site near Hayti, Missouri, located immediately
northwest of the New Madrid Fault System. The
thickness of the sediment at the study site is estimated
at about 600 m based on geological interpretations
and drill logs of the New Madrid test well 1-X (Crone
1981). Since the fundamental frequency of the soil
column is determined by the thickness of the soil
column, it is important to include all layers in the
analysis. Hashash and Park (2001) have also found
that the use of an arbitrary cut-off depth may lead to
incorrect results. Therefore, it is necessary and also
important to study the dynamic soil properties of the
entire depth of the soil column for any site response
analysis. This is an ongoing challenge for researchers
123
Loose Sand
DESRA-MUSC
0.8
0.6
0.4
Medium Dense Sand
0.2
Dense Sand
0.0
0
10
20
30
40
50
60
Time (second)
(c) 1.0
5% Damping
Input Motion
New Model
Acceleration Response Spectral
Fig. 7 Idealized soil profile and shear wave velocity (Qiu
1998)
Pore Pressure Ratio
New Model
1.0
0.8
DESRA-MUSC
0.6
0.4
0.2
0.0
0.01
0.1
1
10
Period (Second)
Fig. 8 Comparison results: a Ground surface motion, b Pore
water pressure ratio, c Response spectra
in the NMSZ. The soils are too deep (up to 1,000 m)
for adequate subsurface characterization using traditional drilling, soil sampling, and geophysical techniques. Estimates based on correlations and
synthetics are often required in the Mississippi
embayment deep soil deposits.
The shallow shear wave velocity (Vs) profile used
was based on cross-hole geophysical testing data
measured (max. depth of 50 m) at the study site
Geotech Geol Eng (2011) 29:463–475
469
(Chen et al. 2007). One of the challenges in ground
response analyses of deep soil sites is to directly
measure the Vs at greater depths. Since the soil
extends to depths of about 600 m at this site, it is
practically impossible to obtain direct measurements.
For the Hayti site, the portion of the Vs profile deeper
than 50 m was adopted from the work by Romero and
Rix (2001), where several deep wells in the Mississippi Embayment area (near Memphis) were compiled for the same soil formations. The composite Vs
profile used in the ground response analysis is shown
in Fig. 9 including the soil formations. The gradually
increasing Vs profile, shown in Fig. 9 in a dashed line,
was used in the analysis to prevent numerical
problems.
Due to the lack of strong motion records in the
NMSZ, the composite source model program (Zeng
et al. 1994) was used to develop the synthetic ground
motions at the study site. It takes into account near
field effects that are not possible with other point
source models, such as, directivity, near fault, and
fling effect. The composite source model generates
the input rock motion at the rock surface, 600 m
below the soil ground surface (El-Engebawy et al.
2004). A synthetic ground motion with a magnitude
6.5 and PGA 0.148 g was initially used as the input
motion at the rock base. Then, other higher magnitude earthquakes were used to examine the site
response and liquefaction effect in the next section of
Shear Wave Velocity (m/s) vs. Depth (m)
0
200
400
600
800
1000
0
Quaternary
Clay and sandy
SILT over SANDS
100
ALLUVIUM:
saturated silty
sand and sandy
silt.
200
Wilcox Group:
Tertiary
300
400
thick series of
non-marine sands,
silty sands, clays,
and gravels with
some thick
deposits of
lignite.
this paper. The site response analysis was performed
using both the new soil model and SHAKE program
(Schnabel et al. 1972) for comparison. SHAKE is
one-dimensional equivalent linear site response program. Even though the equivalent linear approach has
some limitations to simulate the soil nonlinearity, it
remains more popular than the nonlinear approach in
engineering practice for site response analysis
because of the relatively straightforward input
parameters. The equivalent linear site response
programs, such as SHAKE, are usually used as
benchmark to calibrate the nonlinear soil models for
response analysis (Kwok et al. 2007, Park and
Hashash 2005). Two different cases in SHAKE were
studied for comparison. In the first case—SHAKE1,
Vucetic and Dobry’s modulus degradation curves and
damping curves developed in the database of SHAKE
are used for the whole soil profile. Those curves are
usually obtained at low confining pressure
(100–200 kPa). Therefore, this analysis represents
the simulation without considering the effect of the
confining pressure. In the second case—SHAKE2,
the modulus degradation curve and the damping
curves are calculated using Eq. (3) depending on the
location of the soil layer. The effect of the confining
pressure on the site response analysis is considered in
this analysis. The characteristic period of this site is
approximate 3.8 s. The comparison for the three
cases described is shown in Table 1; Fig. 10.
Figure 10 also includes the synthetic input rock
motion and the resulting spectra with different
degrees of amplification around the 1.5 s period.
The results of the SHAKE2 and the new model also
indicate significant amplification around the 3.3 s
period, corresponding to the characteristic site period.
However, this phenomenon is not presented in the
SHAKE1 case, which generally has lower response in
all ranges of frequency. Figure 11 shows three soil
response profiles for three different cases—the maximum shear strain versus depth, the minimum G/Gmax
Table 1 Comparison of PGA
Motions
PGA (g)
Shear wave velocity profile
Synthetic input motion
0.148
Profile used in the analysis
Computed at surface (new model)
0.259
Computed at surface (SHAKE1)
0.133
Computed at surface (SHAKE2)
0.374
500
600
Fig. 9 Shear wave velocity profile used in the NMSZ analysis
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Geotech Geol Eng (2011) 29:463–475
5% Damping
1.0
0.8
0.6
0.4
0.2
0.0
0.01
0.1
1
10
Period (s)
Synthetic Input Motion
Computed at Surface (SHAKE1)
Computed at Surface (New Model)
Computed at Surface (SHAKE2)
Fig. 10 Comparison of the computed response spectra
versus depth and the maximum damping versus depth
in the analysis. Figure 11a shows the maximum shear
strain versus depth profile for three different cases.
Even though the effect of the confining pressure is
ignored in the case SHAKE1, it shows the similar
shear strain profile, especially at depths greater than
100 m. The confining pressure is at least 1,000 kPa
below this depth. Based on Fig. 1, the sandy soil at
this strain level (less than 6 9 10-4) does not show
(a)
Maximum Shear Strain
(b)
1.00E-04 1.00E-03 1.00E-02 1.00E-01
Minimum G/Gmax
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0
(c)
Maximum Damping
0.0
0
100
100
100
200
200
200
300
Depth (m)
Depth (m)
0
much modulus degradation and is still in the elastic
range (Fig. 11b) and small damping shall be used in
the analysis as indicated in case SHAKE2 (Fig. 11c).
However, when the confining pressure independent
curves are used, the soils at this strain level still have
large modulus degradation and corresponding larger
damping as indicated in case SHAKE1 (Fig. 11c).
Therefore, ignoring the influence of confining
pressure on site response analysis will significantly
underestimate the ground response in deep soil sites.
The difference between SHAKE2 and the proposed model can be explained in Fig. 11. Figure 11a
shows a similar maximum shear strain profile
between SHAKE2 and the proposed model. However, the equivalent linear analysis applies a reduction factor (Kramer 1996) to the maximum shear
strain and uses this shear strain to calculate the
degradation ratio and the damping. The reduction
factor is calculated as (M - 1)/10, where M is the
magnitude. The reduction factor 0.55 for a Magnitude
6.5 earthquake is used for this SHAKE analysis. The
uniform 0.55 reduction factor may be arbitrary for the
deep soil deposit since the surface 60 m soil shows
significant nonlinearity and the soil below remains
elastic. Different reduction factors may be more
appropriate for surface and deep soil elements. When
Depth (m)
Spectrum Acceleration (g)
1.2
300
300
400
400
400
500
500
500
600
600
600
LEGEND
Proposed Model
SHAKE1
Fig. 11 Soil response profiles. a max. Shear strain. b Min. G/Gmax. c Max. Damping
123
SHAKE2
0.1
0.2
0.3
Geotech Geol Eng (2011) 29:463–475
471
Table 2 Summary of the synthetic motions
Magnitude
M = 6.5
M = 7.0
M = 7.5
Series No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
amax (g) FP
0.18
0.27
0.23
0.18
0.13
0.45
0.54
0.39
0.47
0.31
0.78
0.55
0.85
1.03
0.68
amax (g) FN
0.15
0.24
0.27
0.20
0.12
0.42
0.47
0.32
0.41
0.35
1.10
0.73
0.94
1.02
0.79
3
4
5
FP fault parallel, FN fault normal
Table 3 Liquefaction analysis for M = 6.5 earthquake
Layer No.
Depth (m)
Soil type
Max pore water pressure ratio
FP direction
Series No. ?
1
2
FN direction
3
4
5
1
2
1
5.5–7.4
Sandy silt
0.18
0.56
0.16
0.15
0.13
0.18
0.63
0.84
0.96
0.19
2
7.4–11.8
Loose sandy silt
0.30
0.68
0.24
0.25
0.22
0.37
0.76
1.00
1.00
0.31
3
11.8–18.2
Medium dense sand
0.13
0.27
0.11
0.11
0.10
0.13
0.30
0.40
0.46
0.13
4
18.2–22.5
Dense sand
0.05
0.16
0.06
0.07
0.06
0.10
0.18
0.23
0.27
0.08
5
22.5–39.3
Dense sand
0.03
0.06
0.02
0.03
0.02
0.04
0.07
0.09
0.09
0.03
8
9
10
FP fault parallel, FN fault normal
Table 4 Liquefaction analysis for M = 7.0 earthquake
Layer no.
Depth (m)
Soil type
Max pore water pressure ratio
FP direction
Series No. ?
6
7
FN direction
8
9
10
6
7
1
5.5–7.4
Sandy silt
0.93
0.98
0.87
1.00
0.38
0.98
0.84
0.97
0.92
1.00
2
7.4–11.8
Loose sandy silt
1.00
1.00
1.00
1.00
0.49
1.00
1.00
1.00
1.00
1.00
3
11.8–18.2
Medium dense sand
0.50
0.56
0.42
0.64
0.21
0.48
0.41
0.49
0.50
0.55
4
18.2–22.5
Dense sand
0.33
0.37
0.26
0.48
0.14
0.31
0.26
0.32
0.31
0.38
5
22.5–39.3
Dense sand
0.14
0.17
0.10
0.20
0.06
0.13
0.12
0.13
0.12
0.14
FP fault parallel, FN fault normal
using higher reduction factor, such as 0.65, the
difference between the SHAKE2 and proposed model
results shall be less.
6 Liquefaction Analysis
The soil and pore pressure generation model was used
to examine the liquefaction performance at the same
study site. A summary of the amax for a series of
synthetic ground motions at three different magnitudes are shown in Table 2. Five motions of each
magnitude were selected by best fitting the average
response spectra of one hundred seed motions and
also considering the fling and velocity pulse effects
(El-Engebawy et al. 2004). The pore pressure generation model was only applied to the near surface soil
layers (upper 60 m). The nonlinear soil model was
then applied to the soil elements below 60 m. This
assumption is based on the strain levels obtained from
previous analysis without liquefaction consideration.
Also, the bridge pile foundations are typically
installed within these relatively shallow soil layers.
Based on the boring logs, the subsurface layers for
the shallow soils consists of: 5.45 m medium plastic
inorganic clay underlain by 6.35 m sandy silt and
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Geotech Geol Eng (2011) 29:463–475
Table 5 Liquefaction analysis for M = 7.5 earthquake
Layer No.
Depth (m)
Soil type
Max pore water pressure ratio
FP direction
Series No. ?
11
12
FN direction
13
14
15
11
12
13
14
15
1
5.5–7.4
Sandy silt
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
2
7.4–11.8
Loose sandy silt
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
3
11.8–18.2
Medium dense sand
0.85
0.50
0.59
0.55
0.66
1.00
0.60
0.93
0.92
0.66
4
18.2–22.5
Dense sand
0.64
0.36
0.44
0.39
0.48
0.84
0.64
0.67
0.65
0.48
5
22.5–39.3
Dense sand
0.28
0.19
0.21
0.20
0.22
0.36
0.33
0.32
0.21
0.24
FP fault parallel, FN fault normal
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(a) 3.5
Acceleration Spectrum (g)
without liquefaction
3.0
with liquefaction
2.5
2.0
1.5
1.0
0.5
0.0
0.01
1
0.1
10
Period (s)
(b) 3.5
without liquefaction
Acceleration Spectrum (g)
6.4 m medium dense sand, underlain by very dense
sand layers. The ground water table is located within
the clay layer at a depth of about 3 m. The parameters
for the pore water pressure generation model are
estimated from the SPT N-value, which were corrected and normalized (N1)60. The pore water
pressure ratios are then calculated and recorded for
all the earthquake simulations and summarized in
Tables 3, 4 and 5.
The results in Table 3 indicate that the liquefaction
could happen for two of the ten M = 6.5 earthquake
simulations. The soil layer from depths 7.4–11.8 m is
loose sandy silt, which is prone to liquefy as reported
by several researchers (Prakash and Sandoval 1992;
Bray and Sancio 2006; Idriss and Boulanger 2008).
The results also indicate the fault-normal (FN)
component is more severe than the fault-parallel
(FP) component since the liquefied earthquake scenarios in the magnitude 6.5 are all in FN direction.
This trend can be also found in the earthquake
scenarios in the magnitudes 7.0 and 7.5. Tables 4 and
5 indicate that thickness of the liquefaction zone
tends to increase with the increase of the earthquake
magnitude. The liquefaction zone for some M = 7.5
scenarios (column FN 11) extends to 18.2 m deep,
which exceeds the 15 m upper bound thickness for
liquefaction consideration recommended by the simplified liquefaction method (Youd et al. 2001). The
analyses also indicate that high pore pressure could
happen in a dense sand layer for very strong
earthquake shaking, such as M = 7.5 earthquakes.
However, the current pore pressure generation model
does not consider soil dilation that may occur in
dense sand during earthquake loading, which requires
a more complex soil model. The response spectra
comparison in Fig. 12 indicates that more energy is
3.0
with liquefaction
2.5
2.0
1.5
1.0
0.5
0.0
0.01
0.1
1
10
Period (s)
Fig. 12 Comparisons of the computed response spectra for
motion No. 11. a In parallel direction. b In normal direction
absorbed when liquefaction is considered, which is
associated with a lower acceleration response at the
ground surface. This is due to the increased damping
and energy loss in the large strain range. Figure 13
indicates more soil displacement at the ground
Geotech Geol Eng (2011) 29:463–475
Fig. 13 Comparison of the
site response at ground
surface—without and with
liquefaction for motion No.
11 normal direction
(a) response spectra
(b) displacement time
history
473
(a) 3.5
Acceleration Spectrum (g)
without liquefaction
3.0
with liquefaction
2.5
2.0
1.5
1.0
0.5
0.0
0.01
0.1
1
10
Period (s)
(b)
surface induced during liquefaction. Since the nonliquefied clay layer above the liquefiable zone
(5.45 m thick) may apply large force to the bridge
foundation during the liquefaction. More in-depth
soil-pile-structure interaction analysis should be performed in the case of oscillation and lateral spreads
that may impart large lateral loads to the highway
bridge foundations.
7 Conclusion
Many existing highway bridges in the NMSZ were
constructed before 1970s without any seismic design,
which are vulnerable for the next strong earthquake in
this region. Most of the bridges are located in the
Mississippi Embayment associated with deep soil
deposit and liquefiable soils near surface. It is critical
to understand how the deep soil deposit and liquefaction may impact the bridge response under earthquake
loading. A numerical model has been presented herein
to consider these effects. The backbone curve of the
proposed model is developed from empirical formulas
and a two-parameter incremental liquefaction model
is loosely coupled to simulate the pore water pressure
generation of the shallow sediments. The model is
advantageous for engineering practice since all inputs
can be obtained from conventional field and laboratory testing methods. The calibrations with the field
recorded motion and lab test data indicate that the
model provides an acceptable outcome with simple
inputs, such as initial shear modulus, plasticity index,
and (N1)60. The model is implemented into a twodimensional finite element code into OpenSEES,
which can be used for the site response analysis and
further coupled with soil-structure interaction analysis
for bridge foundations with available interface element and structure elements in OpenSEES.
The proposed soil model was applied at a site
response analysis study at a typical Missouri highway
bridge site in the NMSZ rift complex. Synthetic
ground motions created by the composite source
model are used for the input motions at rock base.
The results of the analyses indicate that the confining
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474
pressure has significant influence on the site response
of the deep soil deposit. When the confining pressure
is considered, less damping is involved in the
analyses and more response amplification is expected
at the ground surface. The deep soil deposit corresponds to a long characteristic period, which contributes a significant amplification for the long period
components in the NMSZ. Liquefaction could happen
for earthquakes of magnitude 6.5 or larger at this site
and the depth of the liquefied zone increases with
increased magnitude. The liquefiable zone may not be
limited to the upper 15 m as recommended by
simplified engineering practices. Comparisons of the
analyses with and without liquefaction consideration
indicate that more earthquake energy is absorbed
during the liquefaction and the lower response spectra
at the ground surface. However, the liquefaction
induces large displacements near the head of the
bridge foundation. Bridge foundations could be
damaged due to the large force and moment created
by the displacement at the foundation head. The
effect of liquefaction in the foundation soils of
bridges at these sites should incorporate these deformations and modes of failure.
Acknowledgments Financial support for this research was
provided by the Federal Highway Administration (Cooperative
Agreement DTFH61-02-X-00009). The writers would also like
to acknowledge the contributions of Dr. S. Prakash, Dr. G. Chen
and Dr. M. El-Engebawy, of the Missouri University of Science
and Technology and Dr. R. Herrmann, of St. Louis University,
and Dr. B. Jeremic, of the University of California, Davis.
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