Download Observations from Nonlinear, Effective Stress Ground Motion

 Title
Observations from Nonlinear, Effective-Stress Ground Motion Response Analyses following
the AASHTO Guide Specifications for LRFD Seismic Bridge Design
Authors
Donald G. Anderson, PE, PhD – Corresponding Author
CH2M HILL
1100 112th Avenue NE
Bellevue, WA 98004
Phone: 425-233-3418
Fax: 425-468-3100
[email protected]
Seungcheol Shin, PE, PhD
CH2M HILL
1100 112th Avenue NE
Bellevue, WA 98004
Phone: 425-233-3189
Fax: 425-468-3100
[email protected]
Steven L. Kramer, PhD
University of Washington
Department of Civil Engineering
More Hall Rm 201
Seattle, WA 98195
Phone: 206-836-5252
[email protected]
Submission Date: November 15, 2010
Word Count: 5,337 words in text (including captions) plus 10 figures = 7,837
TRB 2011 Annual Meeting
Paper revised from original submittal.
ABSTRACT
Nonlinear, effective-stress ground motion response analyses were conducted for a bridge site
located north of Seattle, Washington. This site was characterized by silt and sand layers in the upper 90
feet (27.4 meters) of the soil profile that were expected to liquefy during a 975-year seismic event.
Procedures described in the 2009 AASHTO Guide Specifications for LRFD Seismic Bridge Design were
followed when conducting site-specific, ground motion response analyses. Two one-dimensional,
nonlinear effective-stress computer programs, D-MOD2000 and PSNL, were used to perform the
analyses. Field and laboratory tests were conducted to define soil parameters for the nonlinear soil
models. Results of the analyses were used to identify soil layers that were likely to liquefy, as well as
changes in design response spectra that could result from liquefaction. These results demonstrated
important differences in site-response prediction from subtle changes in soil modeling, including the
potential for shielding of upper liquefiable soil layers and the importance of soil dilation when lower
layers liquefy. This paper provides a summary of the analyses and discusses observations made from
comparison of the two sets of analyses. The paper also highlights uncertainties that can occur when
conducting nonlinear, effective-stress ground motion response analyses.
TRB 2011 Annual Meeting
Paper revised from original submittal.
INTRODUCTION
The 2009 AASHTO Guide Specifications for LRFD Seismic Bridge Design (1) describes methods
for conducting site-specific ground motion response studies. These methods, described in Section 3.4 of
the Guide Specifications, are required for Site Class F soils and are allowed for other soil conditions,
including sites where liquefaction could occur. The Guide Specifications provide commentary on
developing the model for the soil profile, selecting input earthquake motions, and interpreting results of
the analyses. Included in the Guide Specifications are restrictions on the maximum reduction in the
spectral accelerations relative to the response spectrum determined by the general procedure in the Guide
Specifications.
Procedures for conducting site-specific ground response studies were developed for the Guide
Specifications in recognition that the general procedure for developing site soil factors to correct firmground spectral values given in the AASHTO seismic hazard maps are not suitable for some site
conditions, such as Site Class F, and that site-specific ground response analyses can be conducted with
limited effort using commercially available software. Though the software makes the determination of
site effects fairly easy, results of the site response studies can be sensitive to development of the soil
model, selection of earthquake records, and interpretation of results. The Guide Specifications are
intended to provide more consistency in the methodology used to perform these analyses, and include a
one-third maximum reduction in the spectrum obtained by the general procedure to avoid excessive
reductions in design ground motions.
The methodology described in the Guide Specifications provides direction and warnings
regarding use of site-specific ground response analyses. The importance of these warnings became
apparent in the work described in this paper. In this work site-specific ground motion studies were
conducted for a project site north of Seattle, Washington. The site is characterized by deposits of
potentially liquefiable soils. In view of the site conditions, nonlinear, effective-stress ground response
studies were conducted to develop a design spectrum. Procedures described in the Guide Specifications
were followed during the analyses. Also, as required by the Washington State Department of
Transportation (WSDOT) and advised within the Guide Specifications, an independent reviewer was
used. As part of this review, the independent reviewer conducted a set of independent analyses using a
separate software package. The supplemental analyses were also performed with a nonlinear, effectivestress-based computer model, but it had subtle differences in the soil model used to estimate porewater
pressure. The results of these independent analyses showed important differences in the ground motions
at the site. These differences led to considerable concern on the part of the design team on the “correct”
ground motion to use in design and, perhaps as important, it pointed out the epistemic uncertainty that
comes from different results provided by different models.
This paper describes the results of these site response analyses. Procedures that were used to
characterize the site are summarized, and the differences between the two sets of analyses are discussed.
The paper concludes with observations on the need for further study of the procedures used to conduct
nonlinear, effective-stress ground response analyses.
PROJECT SITE CHARACTERIZATION
The project site is located approximately 40 miles (67 kilometers) north of Seattle at the SR 532
General Mark W. Clark Memorial Bridge (Figure 1). This bridge crosses the Stillaguamish River between
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Paper revised from original submittal.
a) Location of SR 532 General Mark W. Clark Memorial Bridge
b) Locations of Supplemental Field Investigations
FIGURE 1 Project location and location of supplemental explorations.
the city of Stanwood and Camano Island. WSDOT is upgrading the bridge to increase traffic capacity and
to provide greater life safety during seismic loading. The 975-year earthquake, as required by the then
current 2009 Interim of the AASHTO LRFD Bridge Design Specifications (2) was used as a basis of
design.
Field Investigations
A number of field investigations had been carried out by WSDOT in the vicinity of the bridge.
These explorations involved drilling and sampling to depths in excess of 140 feet (42.7 meters). Standard
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Paper revised from original submittal.
penetration test (SPT) blowcounts were available at 5- to 10-foot (1.5- to 3-meter) intervals. Results of
these explorations revealed that the soil profile consisted of very soft or loose alluvial and estuarine
deposits to depths of 80 feet (24.4 meters) or more, underlain by medium dense to dense alluvial deposits.
Uncorrected SPT blowcounts ranged from 1 to 20 blows per foot (bpf) in the upper soft soil unit to 30 bpf
or higher in the deeper soil unit. Groundwater was generally located within 10 feet (3.3 meters) of the
ground surface, and was affected somewhat by tidal action within the Stillaguamish River.
As part of the site-specific ground response analyses, supplemental field investigations comprised
of a cone penetrometer test (CPT) sounding, soil drilling and sampling, and a downhole geophysical test
were conducted. The locations of the supplemental explorations are shown in Figure 1. The purpose of the
CPT sounding was to identify locations for high-quality soil sampling. A seismic downhole test was also
conducted as part of the CPT sounding. Drilling and sampling were performed to obtain samples for
laboratory testing and to install a casing for the downhole geophysical test. Additional SPT blowcounts
were also obtained during the drilling and sampling program using an auto-hammer system. Drilling,
sampling, and the CPT sounding were conducted by WSDOT.
The CPT sounding met refusal at the top of the dense alluvium deposit at approximately 90 feet
(27.4 meters) below the ground surface (bgs). The sounding confirmed the presence of loose silts and
sands throughout the soil profile, and particularly between 55 and 80 feet (16.7 and 24.4 meters) bgs.
Figure 2 shows a soil profile developed from the soil sample descriptions, CPT sounding, and blowcount
information.
The downhole geophysical test was conducted to obtain compression- and shear-wave velocities
to depths of 140 feet (42.7 meters). The velocity information was required for the site-specific ground
response analyses. Northwest Geophysical Inc. of Corvallis, Oregon conducted this test. An observation
from the downhole survey was that the compression-wave velocity did not reach 4,800 feet per second
(fps) [1,463 meters per second (mps)] until about 18 feet (5.5 meters) bgs, whereas piezometer
measurements identified groundwater at 10 feet (3.3 meters) bgs. This difference could have indicated a
slightly lower degree of soil saturation between 10 and 18 feet (3.3 and 5.5 meters). For design purposes
the higher elevation was assumed.
Laboratory Investigation
A series of classification tests had been performed during previous exploration programs. These
tests provided moisture content, organic content, specific gravity, fines content, grain-size distribution,
and Atterberg limit information. This existing information was augmented with additional classification
testing during the supplemental testing program. Generally the results of the different test programs
showed that soils are primarily sands and low plasticity or non-plastic silts.
The focus of the supplemental testing program was on the cyclic behavior of potentially
liquefiable soils. Both field SPT and CPT methods were used to estimate the liquefaction potential in the
sands. This approach was taken because of inherent difficulties in obtaining high quality, intact samples
of sands using conventional sampling methods. However experience has been that high quality samples of
low plasticity and non-plastic silts can be obtained by Shelby tube sampling methods, and therefore the
field program was focused on obtaining samples of silt that would be suitable for laboratory testing. Six
full-length Shelby tube samples of silt and silty sand were obtained from the field program.
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Paper revised from original submittal.
Vs (ft/sec)
0
500
0
1000
CPT Tip Resistance (TSF)
1500
0
0
100
200
SPT N (field)
Pore Water Pressure (psi)
300
0
50
100
0
150
0
10
20
30
40
0
SM
20
20
40
20
20
40
40
40
60
60
60
60
80
80
80
80
SP-SM / SP
Depth (ft)
ML
SP-SM / SM
ML
SP-SM / SP
ML
SP-SM / SM
ML
100
100
100
100
SP / SP-SM
120
140
120
120
120
140
140
140
160
160
160
Dow nHole Test
Seismic CPT
Best Estiamte Vs
160
FIGURE 2 Results of supplemental field explorations.
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Cyclic direct simple shear (CyDSS) tests were conducted on four intact samples of silt and silty sand.
Gamma ray photographs of the tubes were obtained to identify the most suitable sample increments for
testing. The intact silt samples had from 60 to 90% passing the No. 200 sieve, liquid limits from 31 to 32,
plastic indices from 8 to 10, and were essentially normally consolidated. Cyclic tests were conducted by
MEG Technical Services of Richmond, British Columbia using a constant volume CyDSS testing
apparatus. Wire-reinforced membranes were used to constrain the samples; normal stresses were applied
to replicate overburden stress conditions. Cyclic loads were imposed under both strain- and stresscontrolled conditions.
Following cyclic loading, either residual strength or volumetric strain tests were conducted. These
tests were accomplished by either shearing the sample at constant volume after cyclic loading or
monitoring sample consolidation when volume change was allowed. Static simple shear tests were also
conducted on two specimens to define the static undrained strength. Bender element tests were conducted
on all cyclic test specimens to evaluate the shear wave velocity of test specimens at various stages of
confinement and cyclic loading.
Results of the CyDSS tests were used to define porewater pressure buildup, post-cyclic residual
strength, and post-cyclic volumetric strain for the test specimens. The porewater pressure information was
used to calibrate the porewater pressure models for the nonlinear, effective-stress analyses. Results of the
CyDSS showed that the silt samples were dilative at strains exceeding approximately 1.5%.
SITE RESPONSE MODELING
Significant advances in nonlinear site response modeling have occurred in recent years, and userfriendly computer programs are now readily available. These programs are seeing increasingly
widespread use for total stress analyses, and are beginning to be applied to the more complex problem of
effective-stress analysis. Two general approaches to effective-stress modeling have developed – one in
which porewater pressures increase monotonically with increasing numbers of loading cycles, and
another based on constitutive models capable of representing the contraction/dilation behavior seen in
laboratory tests and field records. Two codes representative of the two approaches to porewater pressure
modeling were used in this project. A soil profile model was developed using the previously described
field and laboratory results, and used as the basis for a series of nonlinear, effective-stress analyses. Most
of the analyses were conducted using the commercially available computer software, D-MOD2000
Version 1.03 (3) and referred to as D-MOD in this paper. D-MOD accounts for the strain-dependent
modulus and material damping of the soil, as well as the porewater pressure buildup that can occur in
cyclic loading. D-MOD models the monotonic buildup of porewater pressure and reduces the soil
stiffness accordingly. Independent nonlinear, effective-stress analyses using a research code, PSNL (S.L.
Kramer, unpublished data), that accounts for contraction/dilation behavior were conducted as part of the
independent review process.
Earthquake Records
Earthquake records were determined following the methodology in the Guide Specifications.
Firm-ground response spectra were obtained from the AASHTO seismic hazard map CD for the bridge
location based on latitude and longitude. Deaggregation of the response spectra (based on the USGS
website for a 5% hazard in 50 years) showed that three sources of motion contributed to the uniform
hazard: shallow crustal sources (55% contribution), intraplate subduction zone sources (30%), and
interplate subduction zone sources (15%). These earthquakes all have the potential of causing a design
TRB 2011 Annual Meeting
Paper revised from original submittal.
basis earthquake at the site, though their likelihood of occurrence differs. The peak ground acceleration
(PGA) for firm-ground motions was estimated from the AASHTO CD to be 0.37g.
A suite of seven earthquake records was selected to model ground motions. These records
included four crustal events (1978 Tabas, 1984 Morgan Hill, 1984 Northridge, and 1989 Loma Prieta),
two records from a local intraplate event (orthogonal components from 1949 Olympia), and one interface
event (1985 Valparaiso). These records were scaled so that the average of the seven records generally
matched the firm-ground response spectrum over the period range of 0.2 to 2 seconds, as shown in Figure
3, following recommendations in the 2009 AASHTO LRFD Bridge Design Specifications. This approach
to scaling – rather than spectral matching – was done to preserve the features of actual earthquake
records.
Site Response Modeling with D-MOD
D-MOD represents the soil profile as a single column comprised of layers that are characterized
by a nonlinear, inelastic soil model. The low-strain shear moduli used in the soil model were computed
from the shear wave velocities measured at the site. A visco-elastic halfspace with a shear wave velocity
of 2,500 fps (762 mps) was used to characterize the soil below the base of the model. Geologic reports for
the area suggest that bedrock is located at least 500 feet (152 meters) bgs; the depth to the 2,500 fps (762
1.60
1.40
Spectral Acceleration (g)
1.20
1.00
0.80
0.60
0.40
0.20
0.00
0.01
0.10
Period (seconds)
1.00
10.00
84 Morgan Hill, Anderson Dam, DS, 250
89 Loma Prieta, Anderson Dam, DS, 270
94 Northridge, Pacoima Dam, DS, 265
49 Olympia, HMTL, 086
49 Olympia, HMTL, 356
85 Valparaiso, Chile, UFSM, 070
78 Tabas, Iran, Dayhook, 190
Average of 7 Scaled Input Ground Motions
Site Class B Design Response Spectrum (AASHTO 3.10.4.1 2008)
FIGURE 3 Firm-ground response spectrum and scaled motions for site response analyses.
TRB 2011 Annual Meeting
Paper revised from original submittal.
mps) velocity was estimated to be from 600 feet (183 meters) to 800 feet (244 meters) bgs based on an
extrapolation of measured velocities for the site.
D-MOD uses a modified Kondner and Zelasko hyperbolic (MKZ) model (4) to characterize the
nonlinear, inelastic stress-strain behavior of the soil. Backbone curve parameters were selected to produce
behavior consistent with published modulus reduction and damping curves for sands and silts. Model
parameters for the silty soils were determined using published relationships by Vucetic and Dobry (5); the
EPRI sand model (6) was used to characterize the behavior of the sand layers.
Porewater pressure generation in D-MOD is computed using the Dobry et al. (7) model, as
modified by Vucetic and Dobry (8) and Matsovic (9) and referred herein as the modified Dobry model.
The modified Dobry model estimates incremental porewater pressure generation at the end of each
“cycle” of loading in an earthquake motion. The total porewater pressure at a particular time, taken as the
sum of all of the porewater pressure increments up to that time, increases monotonically over the duration
of motion. The strength and stiffness of the sand are reduced in proportion to generated excess porewater
pressures based on two functions: G = (1-u*)0.5 and  = 1 - (u*), where G and  are degradation index
functions for modulus and strength, respectively, u* is the porewater pressure ratio, and  is a material
parameter. Note that different degradation index functions are used for soft clays versus cohesionless
soils. With this model the shear strength and stiffness both decrease monotonically and, under strong
shaking, can become very low.
Parameters for the modified Dobry model in silts were developed by fitting porewater pressures
produced by D-MOD to the porewater pressures recorded in the CyDSS tests, as shown in Figure 4. For
sandy soils, the porewater generation model parameters were developed by calibrating the model
parameters to give liquefaction curves consistent with those developed by Idriss and Boulanger (10) and
Youd et al. (11). The calibration approach for sands involved defining a two-layer model in D-MOD. The
dry upper layer was assigned a unit weight that would produce the desired initial effective stress at the
center of the saturated lower layer. Sinusoidal loading (at a frequency of 1 Hz) was applied to the base of
the model. The porewater pressure parameters were then modified until the lower layer in the model
liquefied at 15 cycles of loading with the cyclic stress ratio (CSR) corresponding to the measured SPT
blowcounts, similar to the cyclic resistance ratio (CRR) curve shown by Idriss and Boulanger (10). For
layers below 50 feet (15.2 meters) the CRR curve was modified by a depth adjustment factor (Kσ). A
threshold strain of 0.02% was used in the model.
Other modeling considerations during the D-MOD analyses included specification of Rayleigh
damping parameters required by D-MOD for numerical stability considerations and representation of lowstrain damping which is not accounted for in the MKZ model. A sensitivity analysis was conducted to
define a minimum damping ratio that would provide stable results. A full Rayleigh damping scheme with
two target frequencies (fsite and 5fsite, where fsite is the site natural frequency) was applied as suggested by
Kwok et al. (12). The porewater pressure dissipation model within D-MOD was not activated for most
analyses because porewater pressure dissipation in the silty soils during shaking was anticipated to be
minimal.
Alternate Modeling Using PSNL
Independent evaluations using the computer program PSNL were performed with the same soil
profile and earthquake records as described above. PSNL uses a one-dimensional, constitutive model to
describe nonlinear, inelastic soil behavior. The PSNL soil model has a hardening law that explicitly
matches a selected modulus reduction curve, as well as unloading-reloading rules that allow simultaneous
TRB 2011 Annual Meeting
Paper revised from original submittal.
1
0.9
0.8
0.7
V&D PWP Parameters
P = 1.05
f=2
F = 0.3
s = 1.5
th = 0.02%
20
10
5
2
Ncyc=1
30
Ru (--)
0.6
0.5
0.4
0.3
0.2
0.1
0
0.01
0.1
1
10
Shear Strain (%)
GMWC-1A-08 ST-5 (Sample Depth = 87 ft)
GMWC-1C-08 ST-2 (Sample Depth = 34 ft)
Modified Dobry model
FIGURE 4 Calibrated porewater pressure generation model for silt.
matching of a corresponding damping curve. Because PSNL models the soil profile as a continuum
(rather than a lumped-mass model as used in D-MOD), Rayleigh damping is not required. The PSNL
model accounts for non-zero, low-strain damping by hysteretic means. The PSNL soil model accounts for
porewater pressure generation and contractive/dilative phase transformation behavior using a nonassociative flow rule.
For saturated granular soils, zero-volume change (i.e., undrained) conditions are ensured by
matching volumetric strain of the soil skeleton to volumetric strain of the porewater (using the bulk
modulus of water). This procedure allows the tendencies for volumetric strain under drained conditions to
produce excess porewater pressures under undrained conditions. The explicit modeling of phase
transformation behavior allows the effective-stress level (and, hence, stiffness) in the soil to decrease and
increase during individual loading cycles as the soil exhibits contractive and dilative behavior. For cyclic
loading beyond the occurrence of initial liquefaction (i.e., 100% excess porewater pressure ratio [Ru]), the
PSNL soil model further softens the soil using a function of dissipated energy to simulate soil fabric
degradation. The PSNL soil model has also been calibrated to published field liquefaction data using
(N1)60 blowcount values.
PSNL and D-MOD have been found to agree closely for total stress analyses and effective stress
analyses when porewater pressure ratios are less than about 0.5. A key difference between D-MOD and
PSNL is that the soil model in PSNL can account for soil dilation associated with phase transformation
TRB 2011 Annual Meeting
Paper revised from original submittal.
behavior of liquefied soil. This feature was found to produce some significant differences in the computed
soil response.
PREDICTED GROUND RESPONSE FROM SITE RESPONSE ANALYSES
The initial phase of the site response analyses focused on evaluation of results from D-MOD.
These evaluations included comparisons to results of total stress analyses using the computer program
SHAKE2000 and assessments of the sensitivity to assumptions made on the depth below the ground
surface of the input motions. Once the D-MOD results for total stress analyses were consistent with the
SHAKE results, effective-stress analyses were performed to evaluate the porewater pressure buildup and
the effect of this buildup on predicted ground surface motions. Finally, the independent comparison was
made between the D-MOD and PSNL results.
Preliminary Studies
The first set of analyses compared results of D-MOD and SHAKE2000 analyses for total stress
conditions. In these analyses the porewater pressure model within D-MOD was deactivated. Comparison
of peak horizontal accelerations and maximum shear strains were relatively similar, giving confidence in
the D-MOD model.
The sensitivity of the analysis to different depths of earthquake input (i.e., halfspace location) was
performed for depths of 300, 600, and 800 feet (91.4, 182.9, and 243.9 meters). This comparison was
conducted in the effective-stress mode (i.e., porewater pressure model activated) within D-MOD. Results
of the comparisons are shown in Figure 5 in terms of spectral amplification ratios (SARs), where the SAR
is the ratio between the ground surface spectral acceleration and the input spectral acceleration at each
frequency. The conclusion from this evaluation was that an input depth of 600 feet (182.9 meters)
provided reasonable ground surface motions.
D-MOD Effective-Stress Results
Nonlinear effective-stress analyses were conducted with D-MOD to evaluate the effects of
porewater pressure buildup on ground response. For these analyses porewater pressure dissipation
features within D-MOD were deactivated in the first two analyses (Runs 1 and 2) and activated in the last
run (Run 3) to consider the effect of porewater pressure dissipation. For Run 3 hydraulic conductivity
values of 10-3 cm/sec and 10-5 cm/sec were assigned for sand and silt, respectively. As shown in the
Figure 6, the overall responses with the dissipation are slightly higher than those without the dissipation.
Results of nonlinear, effective-stress analyses using D-MOD confirmed expectations that
liquefaction would develop in sand and silt layers that had low SPT blowcounts. The two cases in Figure
6 illustrate the effects of changing the silt model to a sand model between 30 to 50 feet (9.1 to 15.2
meters). This alternative was evaluated to determine whether the silty sand layer within this depth interval
would be dominated by silt- or sand-like behavior. Results clearly show a significant difference in the
porewater pressure response, depending on the model that is used. This illustrates one of the key
observations from these analyses and emphasizes the importance of accurate modeling of the soil profile.
The SARs for the case noted above are plotted in Figure 7. These results show that ground
motions with periods less than approximately 0.5 to 0.7 seconds were de-amplified, while longer period
motions were amplified. These observations are consistent with comments made within the commentary
of the Guide Specifications, and are similar to observations made by Youd and Carter (13). Relative to the
total stress results, the effective-stress analyses gave lower SAR values to periods of 2.5 seconds.
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Paper revised from original submittal.
Spectral Amplification Ratio (SAR)
2.5
2
1.5
1
SAR (Effective Stress Analysis, Vs=2500 fps @ 600 ft deep)
SAR (Effective Stress Analysis, Vs=2500 fps @ 800 ft deep)
SAR (Effective Stress Analysis, Vs=2500 fps @ 300 ft deep)
0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
Period (s)
FIGURE 5 Effects of input motion depth on spectral amplification factors.
p
p
Spectral Amplification Ratio (SAR)
3
2.5
2
1.5
DMOD Effective Stress Analysis Run 1
1
DMOD Effective Stress Analysis Run 2
DMOD Effective Stress Analysis Run 3
DMOD Total Stress Analysis
0.5
PSNL
0
0
0.5
1
1.5
2
2.5
3
3.5
4
Period (s)
FIGURE 7 Spectral amplification ratios from D-MOD analyses.
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Paper revised from original submittal.
1 PHA (g)
0
0.1
0.2
Peak Shear Strain (%)
0.3
0.4
0
1
2
Peak CSR
3
0
0.1
0.2
Ru
0.3
0.4
0
0
0
0
0
10
10
10
10
20
20
20
20
30
30
30
30
0.5
1
Silt
40
50
50
40
Depth (ft)
50
40
Depth (ft)
Depth (ft)
Depth (ft)
40
Silt
50
60
60
60
60
70
70
70
70
Silt
80
80
80
80
90
90
90
100
100
100
DMOD Eff. Stress Analysis Run 1 (average)
90
DMOD Eff. Stress Analysis Run 2 (average)
Silt
DMOD Eff. Stress Analysis Run 3 (average)
100
FIGURE 6 Results of D-MOD analyses showing porewater pressure development (Run 1 with silt model from 30 to 50 feet and 40 to 50
feet; Run 2 with sand model from 30 to 35 feet and 40 to 50 feet; Run 3 is same as Run 1 except PWP was allowed to dissipate during the
analysis; 1 foot = 0.305 meters).
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Paper revised from original submittal.
Figure 8 illustrates the ground surface spectra obtained by multiplying the SAR and the spectra
obtained from the AASHTO seismic hazard map. The resulting spectra are significantly lower than the
spectrum defined by the general procedure. These results illustrate the benefits of the site-specific
analyses compared to using the site factors in the general procedure. Further, the comparison of the total
stress to the effective-stress analyses shows that liquefaction suppressed the level of spectral accelerations
at periods less than approximately 2.5 seconds. This difference demonstrates how the generation of
porewater pressure, as accounted for in an effective-stress program (e.g., D-MOD and PNSL), compares
to a total stress program (e.g., SHAKE). Again, the benefits to the designer are significant with spectral
accelerations decreasing by a factor of nearly two within the period range of interest. The reduction in
spectral acceleration leads directly to lower design inertial forces and, consequently, reduced construction
costs.
Results of Independent Peer Review
Results from the D-MOD analyses were compared against results obtained from PSNL as part of
the independent peer review process. As noted before, the PSNL program has many of the same features
as D-MOD. However, the sand model in PSNL is fit to the field liquefaction strength based on the (N1)60
values from the SPT blowcount, and the potential effects of dilation at large strains are considered.
Close review of the PSNL results revealed high frequency pulses that propagated upward through
the soil profile after the development of high porewater pressures. The colormap plots of porewater
pressure ratios in Figure 9 show representative results. The vertical “stripes” of yellow color indicate that
dilation occurs periodically in the lower layers after liquefaction has occurred. The dilation produces
(
y
)
1.2
DMOD Effective Stress Analysis Run 1
DMOD Effective Stress Analysis Run 2
1
DMOD Effective Stress Analysis Run 3
Spectral Acceleration (g)
DMOD Total Stress Analysis
PSNL
0.8
2008 AASHTO Site Class E General Design Response Spectrum
2/3 x 2008 AASHTO Site Class E General Design Response Spectrum
0.6
0.4
0.2
0
0
0.5
1
1.5
2
2.5
3
3.5
4
Period (s)
FIGURE 8 Site-specific ground surface response spectra (5% damped, 975-year return period).
TRB 2011 Annual Meeting
Paper revised from original submittal.
FIGURE 9 Colormap plots from PSNL showing dilation effects on porewater pressure for two
earthquake records (see Figure 3 for record information. Lower record for each set is input; upper record
is response at ground surface).
TRB 2011 Annual Meeting
Paper revised from original submittal.
temporary stiffening of the lower layers, which allows higher shear stresses to be transmitted upward to
shallower, overlying layers. These higher shear stresses induced very high porewater pressures in loose,
saturated sand layers at depths shallower than 50 feet (15.2 meters). They also led to relatively strong
acceleration spikes at the ground surface, even after liquefaction has occurred at depth. These high stress
pulses have been observed in ground motion recordings (14) and during centrifuge testing (15).
The SAR and response spectrum from the PSNL analyses are shown in Figures 7 and 8 relative to
results of D-MOD analyses. While overall the comparison between D-MOD and PSNL results appears to
be generally similar, there are some subtle but important differences in these results. The PSNL results
indicate that liquefaction could occur between 10 and 20 feet (3.3 and 6.1 meters) and between 30 and 35
feet (9.1 and 10.7 meters), whereas the D-MOD results suggest that only the 30- to 35-foot (9.1 to 10.7
meter) layer would liquefy – and then only when the soil was modeled as a sand. This difference is
believed to be due in part to the dilation feature within PSNL which allows more energy to propagate
through the liquefied soil between 50 to 70 feet (15.2 to 21.3 meters).
OBSERVATIONS FROM SITE-SPECIFIC GROUND RESPONSE ANALYSES
The difference in results between the two nonlinear, effective-stress models, particularly
relatively to the potential for liquefaction in the upper soil layers, led to some important observations:

Despite the apparent ease in use of new Window-based software such as D-MOD, liquefaction is
an extremely complicated, highly nonlinear process. A number of aspects of its modeling, not all
of which are well understood, can lead to significant differences in computed site response. In
practice, these can contribute to uncertainty in the profession’s ability to accurately replicate the
wave propagation process. As illustrated by the comparison of results from the D-MOD and
PSNL analyses, what might appear to be subtle differences in soil models can lead to significantly
different site response mechanisms (e.g., differences in the locations of liquefaction) and can
result in different response spectra used in design. There is little question for this project that
different conclusions would have been reached if the second, independent analysis using a
completely separate software package had not been performed.

Liquefaction of deeper soil layers can lead to apparent “shielding” of upper loose soil layers
during ground shaking, particularly when phase transformation behavior is considered. In this
case the extreme and persistent softening of a deeper, liquefied soil layer can allow it to act
essentially as a base isolator, suppressing energy transmission through the liquefied layer and into
overlying layers. While this mechanism seems plausible, it can suffer from two key limitations.
First, soil profiles are rarely uniform and therefore the one-dimensional representation is often an
approximation. The layering within a normal soil profile can disrupt vertical propagation of shear
waves, resulting in surface waves and non-vertically incident waves reaching shallower soil
layers, causing transient loads that no standard one-dimensional model can predict. Second, the
dilation within the liquefied soil layer at larger strains can result in pulses of energy passing
through the liquefied soil, again resulting in more energy in the overlying layers. These
mechanisms can result in inaccurate prediction of ground response.
TRB 2011 Annual Meeting
Paper revised from original submittal.
For the SR 532 General Mark W. Clark Memorial Bridge Project, these modeling uncertainties
were discussed during meetings with WSDOT staff and the independent peer reviewer. In view of the
uncertainties in the wave propagation process for this particular site, it was decided to use a combination
of results from the total stress and general procedure to define the design spectra, as shown in Figure 10.
1.2
DMOD Total Stress Analysis
2008 AASHTO Site Class E General Design Response Spectrum
Spectral Acceleration (g)
1
2/3 x 2008 AASHTO Site Class E General Design Response Spectrum
Recommended Site Specific Ground Surface Design Spectrum
0.8
0.6
0.4
0.2
0
0
0.5
1
1.5
2
2.5
3
3.5
4
Period (s)
FIGURE 10 Site-specific response spectra selected for final design (5% damped, 975-year return period).
While this decision was clearly conservative based on results of the effective-stress analyses
shown in Figure 8, it provided a margin of additional safety on design that WSDOT felt was important for
this project.
OBSERVATIONS REGARDING USE OF THE AASHTO GUIDE SPECIFICATIONS
Section 3.4 of the Guide Specifications provides useful direction regarding requirements for
conducting site-specific, ground response analyses. These requirements identify key considerations in
conducting the analyses. However, it was apparent from the analyses described above that a number of
other factors – ranging from field and laboratory testing methods to the type of soil model – must be
appropriately considered during the site-specific, ground response analyses. Often these requirements are
overlooked during the modeling process, or do not become evident until separate analyses are conducted.
A significant need exists within the profession to develop further guidance on the factors
affecting site-specific nonlinear, effective-stress response analyses. This guidance needs to provide
specific direction on the selection and scaling of earthquake records, including near-fault effects; the
requirements for field and laboratory testing; and the features of the soil models used in the site modeling.
These modeling features include the appropriate depth of the input motions, the robustness of the soil
model used to predict porewater pressure buildup, and methods of model calibration. Guidance also needs
to be provided on appropriate sensitivity and calibration studies, and the confidence that can be assigned
to these analyses.
TRB 2011 Annual Meeting
Paper revised from original submittal.
ACKNOWLEDGMENTS
The authors would like to thank WSDOT’s Geotechnical and Regional staff for allowing publications of
the information described in this paper and the TRB viewers for their helpful suggestions. The authors
also note that the views expressed in this paper are those of the authors and not necessarily those of
WSDOT.
REFERENCES
(1) American Association of State Highway and Transportation Officials. AASHTO Guide Specifications
for LRFD Seismic Bridge Design, 1st Edition, 2009.
(2) American Association of State Highway and Transportation Officials. AASHTO LRFD Bridge Design
Manual. 4th Edition, 2009.
(3) D-MOD2000 User’s Manual. Geomotion, LLC. 2007.
(4) Matosovic, N. and M. Vucetic. Cyclic Characterization of Liquefiable Sands. Journal of Geotechnical
Engineering, ASCE, Vol. 119, No. 11, 1991, pp. 1805-1822.
(5) Vucetic, M. and R. Dobry. Effect of Soil Plasticity on Cyclic Response. Journal of Geotechnical
Engineering, ASCE, Vol. 117, No. 1, 1991, pp. 89-107.
(6) Electric Power Research Institute. Guidelines for Site Specific Ground Motion. Palo Alto, California,
November, TR-102293, 1993.
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Straining of Sand. Research Report, Civil Engineering Department, Rensselaer Polytechnic Institute,
Troy, New York, 1985, 56 p.
(8) Vucetic, R. and R, Dobry. Cyclic Triaxial Strain-Controlled Testing of Liquefiable Sands. Advanced
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Philadelphia, 1988, pp. 475-485.
(9) Matasovic, N. Seismic Response of Composite Horizontally-Layered Soil Deposits. Ph.D.
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(10) Idriss, I.M. and R.W. Boulanger. Semi-Empirical Procedures for Evaluating Liquefaction Potential
during Earthquakes. Proceeding of 11th International Conference on Soil Dynamics and Earthquake
Engineering (ICSDEE), and 3rd International Conference of Earthquake Geotechnical Engineering
(ICEGE), 2004. pp. 32-56.
(11) Youd, T.L. et al. Liquefaction Resistance of Soils: Summary Report from the 1996 NCEER and
1998 NCEER/NSF Workshops on Evaluation of Liquefaction Resistance of Soils. Journal of
Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 127, No. 10, 2001, pp. 817-833.
(12) Kwok, A.O.L., Stewart, J.P., Hashhash, Y.M.A., Matasovic, N., Pyke, R., Wang, Z., and. Z. Yang.
Use of Exact Solutions of Wave Propagation Problems to Guide Implementation of Nonlinear Seismic
Ground Response Analysis Procedures. Journal of Geotechnical and Geoenvironmental Engineering,
ASCE, Vol. 133, No. 11, 2007, pp. 1385-1398.
TRB 2011 Annual Meeting
Paper revised from original submittal.
(13) Youd, T.L. and B.L. Carter. Influence of Soil Softening and Liquefaction on Spectral Acceleration.
Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 131, No. 7, 2005, pp. 811-825.
(14) Zeghal, M. and A.-W. Elgamal. Analysis of Site Liquefaction using Earthquake Records. Journal of
Geotechnical Engineering, ASCE, Vol. 12, No. 6, 1994, pp. 996-1017.
(15) Elgamal, A.-W., Yang, Z., Lai, T.L., Kutter, B.L., and D. Wilson. Dynamic Response of Saturated
Dense Sand in Laminated Centrifuge Container. Journal of Geotechnical and Geoenvironmental
Engineering, ASCE, Vol. 131, No. 5, 2005, pp. 598-609.
TRB 2011 Annual Meeting
Paper revised from original submittal.