Development of Design Spectra for Deep and Soft Soil Sites

Steven F. Bartlett,a) M.EERI, Farhang Ostadan,b) M.EERI, Abbas Abghari,c) Clifton Farnsworthd)

Deep, unconsolidated, lacustrine and alluvial sediments underlie significant

portions of the urban Wasatch Front in Utah. Deep and/or soft soil profiles can

significantly modify the characteristics of earthquake shaking and often require

site-specific analyses to capture important soil and shallow crustal effects. This

paper summarizes guidance developed for the Utah Department of Transportation

to perform site-specific ground response analyses and developing design spectra

for deep and/or soft soil sites (Site Class D and E) near active faults. The method

includes hanging wall, fault directivity and long period effects resulting from the

deep soil and sedimentary basin. The proposed analyses and spectrum

development are consistent with site-specific ground response analyses and

spectra outlined by MCEER/ATC-49 for highway bridge design, but the methods

are general enough so that can also be applied to building design according to

ASCE 7-05.

INTRODUCTION

Current seismic guidance (MCEER/ATC-49a, b and ASCE 7-05) requires the use of

dynamic response analyses to calculate design response spectra for bridge and building

design on Site Class F soils. However, MCEER/ATC-49a allows the site-specific response

analysis for any site class, as long as the evaluation has the following items: (1)

characterization of seismic sources, (2) ground motion attenuation incorporating current

scientific interpretations, including uncertainties in seismic source and ground motion model

and parameters values, (3) detailed documentation and peer review. Appendix C of

MCEER/ATC-49b “Guidelines for Conducting Site-Specific Geotechnical Investigations and

Dynamic Site Response Analyses” provides the framework for performing such analyses.

This paper summarizes guidance developed for the Utah Department of Transportation

(UDOT) for performing ground response analyses and developing site-specific response

spectra for bridge design at deep and/or soft soil sites (i.e., Site Class D and E). The

proposed methods are also general enough that they can also be applied to performing

response and analyses and developing site-specific design response spectra for building

design using ASCE 7-05.

UDOT has encouraged the use of site-specific seismic hazard studies for major highway

projects. A probabilistic seismic hazard analysis (PSHA) was used to define the highway

bridge design spectra for the $1.5 billion I-15 Reconstruction Project in Salt Lake City, Utah

which was constructed during 1998 to 2002, just prior to the 2002 Winter Olympics. A

2500-year return period design-basis event was used for the 144 overpass structures. The

developed design spectra were uniform hazard spectra with spectral values that varied along

the I-15 alignment according to location and soil type (Dames and Moore, 1996).

After the completion of the I-15 Reconstruction Project, UDOT has continued to design

its interstate bridges using 2500-year return period event. These bridges are considered

lifeline bridges, due to their operational and recovery importance. This paper summarizes

design guidance developed for the UDOT for performing site-specific response analyses and

calculating design spectra for bridge sites on soft and/or deep soil profiles (i.e., Site Class D

and E soils). The methods discussed herein are consistent with MCEER/ATC-49a, which has

not been adopted by UDOT, but its adoption is anticipated.

CALTRNS guidance (CALTRANS, 1996a, b, c) and other sources were also reviewed

and incorporated, as applicable. The guidance does not include Site Class F soils for the case

of liquefaction. Guidance for developing design response spectra at potentially liquefiable

sites has been developed for UDOT by Youd and Carter (2003).

SOFT SOIL EFFECTS

Research from past earthquakes and ground response modeling studies suggest that at

high levels of ground motion, soft soils will yield and behave plastically. This yielding

produces a strong nonlinear soil response that affects the amplitude and frequency content of

the recorded motion. Response spectra for soft/deep soil sites show a deamplification at

higher frequencies and a shift of the predominate response to longer periods, when compared

with adjacent rocks sites at similar earthquake distances (Seed et al., 1976; Idriss, 1990; Seed

et al., 1992; Chang et al. 1997; Seed et al. 1997).

The behavior of soft and deep soil profiles at higher levels of strong ground motion is of

particular interest to Utah, because much of its urban population and infrastructure is located

within 10 km of the Wasatch Fault, where pga rock values are expected to be 0.3 g, or higher.

Undoubtedly, soil effects will play a significant role in modifying the characteristics of the

earthquake shaking in the deep alluvial valleys found in Utah. These valleys are found along

the western edge of the densely populated Wasatch Front are filled with interbedded alluvium

and lacustrine deposits that extend to considerable depths. Arnow et al. (1970) estimate that

the thickness of unconsolidated Quaternary sediments is about 300 m near downtown Salt

Lake City. Furthermore, the upper 20 meters of these sediments in the central part of the

valley are commonly soft to medium stiff clayey layers deposited by Pleistocene-age Lake

Bonneville. Figure 1 shows shear wave velocity profiles for the I-15 alignments near the

downtown area (600 South Street interchange), the I-15/I-80 interchange and for comparison

the San Francisco Bay mud. It is interesting to note that the Lake Bonneville sediments have

shear wave velocities that are very similar to the Bay mud in the upper 50 m of the profile.

Near downtown Salt Lake City, the Lake Bonneville deposits are especially soft between

depths of about 5 to 10 meters and have moisture contents ranging from 35 to 70 percent and

plasticity index (PI) values ranging from 30 to 40 percent. Laboratory shear strength testing

show that the undrained shear strength of this softer layer is about 20 to 30 kPa. Thus, the

600 S. Street interchange and the I-15/I-80 interchange soil profiles are Site Class E is a Site

Class D, respectively.

CODE BASED SPECTRA AND SITE FACTORS

MCEER/ATC-49a defines two design events that are linked to performance objectives.

The expected earthquake has a 50 percent probability of exceedance in 75 years, which will

not be considered further by this paper. The operational design earthquake is a larger event

that has a 3 percent probability of exceedance in 75 years that is equivalent to a 2 percent

probability of exceedance in 50 years event (approximate 2500-year return period). This

larger event is used by UDOT for the seismic design of all of its lifeline bridges. The

performance goals for this earthquake are that the bridge will incur minimum damage and

traffic will have full access to the bridge following an inspection.

MCEER/ATC-49a and ASCE 7-05 uses site coefficients to adjust rock spectra for soil

effects. The current method is based on recommendations developed by the

NCEER/SEAOC/BSSC Site Response Workshop (Rinne and Dobry, 1992; Borcherdt, 1994.)

and uses a two-factor approach. The short period acceleration (0.2 s) rock spectral value, Ss,

is multiplied by a short-period site coefficient Fa. The longer period spectral values are

represented by a curve that is equal to the one-second period rock acceleration value, S1,

divided by the period (i.e., S1/T) and multiplied by the long-period site coefficient, Fv.

The site coefficients published in current bridge and building codes represent soil effects

in a general way and are simplifications and/or extrapolations of the strong motion records

available at the time of their development. Extrapolations were made based on amplification

estimates at the 0.1 g level and extrapolated to higher ground motion levels using laboratory

and theoretical modeling (NEHRP, 2000). However, because considerable uncertainty still

exists in applying these site coefficients to soft/deep soil sites at high levels of ground

motion, we recommend that consideration be given to performing site-specific response

analyses for soft/deep soil sites (Site Class D and E). Site-specific response analyses are

required for all Site Class F soils (MCEER/ATC-49a, b and ASCE 7-05).

OTHER EFFECTS

Near fault effects and basin effects may also influence strong motion at some bridge sites

in urban Utah. For example much of the I-15 alignment parallels the Wasatch Fault zone and

is located within 10 to 15 km of the fault, or less, within a relatively deep sedimentary basin.

This guidance considered fault directivity, hanging wall and long period effects resulting

from the deep unconsolidated and semi-consolidated soil profile found in the Salt Lake

Valley.

Fault directivity effects are not included in the national ground motion maps

(MCEER/ATC-49b). This guidance uses the model of Somerville et al. (1997) to adjust the

input response spectrum for fault directivity. Fault directivity is a pulse or series of pulses of

seismic energy that are preferentially generated in the direction of fault rupture. Shear

dislocation from fault rupture nucleates in a small area and spreads with a rupture velocity

that is almost equal to the velocity of shear wave propagation. This can cause much of the

seismic energy to arrive in a single, long-period pulse or pulses of motion that occur near the

beginning of the record. Such pulses can increase the spectral acceleration values, starting at

a period of approximately 0.5 seconds (Somerville et al., 1997). The radiation pattern of

fault dislocation causes the largest pulses to be oriented in a strike parallel direction for strike

slip faults and strike normal direction for normal and reverse faults.

In addition to fault directivity, a "fling" effect may be present in the strong motion record.

Fault fling results from elastic rebound of the crust resulting from seismic deformation and

can produce similar long-period pulses in the record. Fault directivity and fling effects may

be difficult to distinguish without detailed seismological studies. This study does not

consider increases in spectral acceleration values from fault fling.

For dip-slip faults, such as the Wasatch Fault, the intensity of strong motion may be

greater over the hanging wall portion of the fault. These effects were incorporated in the

guidance by using the Abrahamson and Silva (1996) attenuation relation that includes this

effect as part of the empirical relation.

GROUND RESPONSE METHODOLOGY

We fully recognize the challenge in developing an engineering description of strong

motion that captures all relevant features. The generation of seismic waves and their

propagation and interaction with near surface conditions are complex phenomena. This

complexity, which includes source, path and site effects, introduces large, systematic and

random spatial variations into the ground motion. Although the importance of these effects

has been recognized for some time, it is not a simple matter to incorporate their influence a

comprehensive model. The following guidance was written for design engineers and can be

reasonably implemented in practice; thus it is more pragmatic than theoretical in its approach.

In developing the guidance, UDOT gave us direction that the methods must be implemented

within the framework of MCEER/ATC-49 and be user friendly to its geotechnical

consultants.

In short the recommended steps needed to develop a site-specific spectrum consist of: (1)

performing site-specific geotechnical characterization to define the dynamic properties at a

candidate bridge site, (2) determining the controlling fault and its distance from a seismic

hazard deaggregation published by the U.S.G.S, (3) developing a target rock spectrum for the

controlling earthquake using appropriate attenuation relations, (4) adjusting the target rock

spectrum for fault directivity, as appropriate, (5) performing spectral matching of candidate

earthquake records to the target rock spectrum, (6) inspecting and adjusting the spectrally-

matched records, (7) deconvolving the rock motion to a depth of 5 km using a generic

western U.S. rock Vs profile, (8) convolving the motion obtained in step 7 to the surface

using the site-specific Vs profile to predict the free-field response of the soft/deep soil profile,

(9) interpreting the results and developing the final design spectra.

MCEER/ATC-49b allows the use of equivalent linear (EQL) or nonlinear methods to

perform ground response analyses of the site-specific soil profile. EQL methods can produce

reasonable estimates of soil response with appropriate modulus reduction and damping

relations (CALTRANS, 1996b). In addition, they should be applied to cases where the soil’s

peak shear strain is limited to about 2 percent, or less, to produce reliable results

(CALTRANS, 1996b). (However, this is still uncertainty and discussion about the

appropriateness of EQL methods at this high strain level.) Nonetheless, our response

analyses for the Salt Lake Valley profiles suggest that peak shear strains are about 2 percent

or less, thus we have used EQL methods because of their simplicity and widespread

engineering use. Our ground response analyses were completed using a commercial version

of SHAKE (Schnabel et al. 1972; Idriss and Sun, 1992).

For high levels of strong motion that produce large shear strains, nonlinear analyses are

more appropriate. Nonlinear models use advanced constitutive relations to define the soil’s

complex, nonlinear stress-strain behavior in both loading and unloading; thus these methods

can more realistically model shear strain, permanent deformation and pore pressure

generation, when dynamic effective stress analyses are required. However, the constitutive

relation parameters are often poorly defined or unknown for many soils and must often be

determined by specialized soil testing. Such parameters were not available for the soil

investigations completed in the Salt Lake Valley and further research is needed to develop

such parameters before nonlinear models can be implemented.

SITE CHARACTERIZATION AND UNCERTANTIES

The purpose of site characterization is to obtain an adequate description of the subsurface

soils and their variability so that engineering analyses can be completed to ensure adequate

structural and foundation performance. The first step in a ground response analysis is the

development of a site-specific geotechnical profile of the soil column for ground response

analyses. Typically, a 1-D soil column extending from the ground surface to bedrock, or to a

very dense material, is adequate to capture first-order site response characteristics. However,

2-D or 3-D models may be considered for critical projects where 2-D and 3-D wave

propagation effects are deemed to be significant.

The soil data required for the ground response analyses are: soil description, soil type or

classification, Atterberg limits, thickness of soil layers, depth to groundwater, depth to

bedrock, soil unit weights, Vs measurements for major changes in soil type, density or soil

stiffness. Laboratory testing of undisturbed samples is sometimes necessary to obtain the

applicable dynamic soil properties for numerical modeling.

Estimates of Vs versus depth for the shallow soil profile can be obtained from geophysical

surveys or down-hole or cross-hole techniques. For deep (i.e., greater than 30 meters)

profiles, CALTRANS (1996b) recommends that downhole Vs suspension logging be used.

CALTRANS (1996b) also recommends that the depth of Vs profiles at bridge sites extend at

least 15 m into competent rock or rock-like material at shallow soil sites. However,

MCEER/ATC-49b allows the depth of the soil column analyses to cease when a Site Class C

soil is encountered for soil profiles having great depths. This allowance has important

ramifications for parts of the Salt Lake Valley, where the depth to bedrock is generally

several hundred meters and the depth to Site Class C soils is generally greater than 100 m.

One of the issues addressed by this paper is how the depth of the soil model affects the

predicted ground response, as discussed later.

Our response analyses (see deconvolution analyses) required that we obtain estimates of

Vs to considerable depths (i.e., 5 km). These deeper estimates can be obtained from regional

studies, seismological reports and geophysical surveys, when deep Vs measurements are not

available at the candidate bridge site. For the Salt Lake Valley studies by Wong et al., 2002;

Wong and Silva, 1993; Murphy, 1989; Hill, 1988 are important studies that we used to

develop the deep Vs profiles for the Salt Lake Valley. Because large uncertainty exists in the

deep Vs profile in the Salt Lake Valley, we used two equally-likely possibilities for the I-15/I-

80 and 600 South Interchanges (Figure 2). These are labeled “Deep Vs Profile I” and Deep

Vs Profile II.” The Vs values for “Deep Vs Profile I” were obtained from Hill et al. (1990) for

the Salt Lake Valley and were adjusted for the appropriate depths to the major lithological

boundaries. The Vs values for “Deep Vs Profile II” were obtained from Wong et al. (2002).

We also considered the potential variability of Vs measurements in the shallow soil

profile (i.e., depths less than 200 m). ASCE 4-98 recommends that a 50 percent variation in

the maximum shear modulus (Gmax) be considered for ground response analyses. (Note that a

50 percent variation in Gmax, corresponds to a 22.5 percent variation in Vs). Thus, we

performed analyses that increased the Vs values correspondingly and this increase was

applied to all layers having Vs values less than 1220 m/s. These profiles are labeled “upper

bound” profiles in the subsequent response analyses. We do not recommend that the shear

modulus be decreased by 50 percent and used as a candidate profile in the EQL analysis. Our

experience with ground response analyses at soft soil sites has shown that such an

excessively softened Vs profile will cause convergence and other numerical run-time

problems. Furthermore, an excessively softened profile will cause additional deamplification

of the high frequency spectral accelerations predicted by the EQL method. This is an

outcome that we wish to avoid because of the potential for markedly underestimating the

spectral accelerations at frequencies that are important for bridge design. Thus, only best-

estimate and upper bound Vs profiles were used in the subsequent analyses for the shallow

soil profile.

The EQL method requires shear modulus reduction and damping curves for each soil

layer. We used previously published curves appropriate for each soil type, because no site-

specific curves were available. We used the Vucetic and Dobry (1991) curves for the soft

and medium stiff clayey soils and the Seed and Sun (1989) and Sun et al. (1988) curves for

overconsolidated or stiff clayey soils. For the granular and/or deeper sediments (60 to 220

m), we used Electric Power Research Institute (EPRI, 1993) curves for saturated sands.

CONTROLLING EARTHQUAKE AND SOURCE DISTANCE

The controlling earthquake, its magnitude and source distance are required to develop the

target rock spectrum. The seismic hazard deaggregation from the U.S.G.S. national seismic

hazard website (http://earthquake.usgs.gov/hazmaps/products_data/48_States/index.htm) can

be used to determine these factors. The controlling earthquake is that fault and its associated

source distance that produces the highest spectral accelerations at the frequencies of interest

to the bridge design. The deaggregated hazard for the 600 South and I-15/I-80 interchanges,

respectively obtained from the U.S.G.S. website showed that a M=7.2 earthquake on the Salt

Lake City segment of the Wasatch Fault is the primary contributor to the seismic hazard at

both sites for the 0.2 and 1.0 s periods.

However for more complex situations, determining the controlling earthquake and its

source distance requires knowledge about the nearby faults and their relationships. For

example, it is possible that more than one nearby fault may be the primary contributor to the

seismic hazard, depending on the frequency or period. Often, moderate-sized, nearby

earthquakes control the short period (0.2 s) spectral acceleration values; whereas the long

period (1.0 s and greater) spectral acceleration values are dominated by a more distance, large

earthquake. If the deaggregated hazard plots of magnitude and distance suggest a bimodal or

multimodal hazard distribution, then we recommend using more than one design basis

earthquake (DBEs) to fully represent the earthquake hazard for all frequencies of interest.

However, this was not the case for the sites selected in Salt Lake Valley, where the Wasatch

Fault dominates the seismic hazard for at the 2 percent in 50-year exceedance probability

event for all frequencies.

We found that care must also be exercised in interpreting the earthquake source distance

given in the U.S.G.S. deaggregation tables. It is not apparent which source distance

definition is represented in these tables. (The source distance appears to be an average of the

different source definitions used in the various attenuation relations used to develop the

hazard maps; hence it may not used directly to develop the target rock spectrum as discussed

in the next section.) Therefore, once the controlling fault is identified for the deaggregation

table, we recommend calculating the appropriate site to source distance using the method

appropriate for the attenuation relations selected.

DEVELOPMENT OF TARGET ROCK SPECTRUM

In our initial evaluations, we spectrally matched candidate time histories to a generic

MCEER/ATC-49 Site Class B probabilistic response spectrum developed from the general

procedures and used these time histories in our subsequent soil column response analyses.

However, these initial analyses yielded long period spectral accelerations values that were

unreasonably high. Thus, we caution against using spectrally matched time histories that

have been matched to a “flat topped” uniform hazard spectrum developed from the general

procedures of MCEER/ATC-49a. Instead, we recommend the development of a more

realistic deterministic spectral shape for spectral matching and the subsequent ground

response analyses. This approach is recognized by MCEER/ATC-49a (p. 27), which allows

for the use of a deterministic spectrum:

“Alternatively, deterministic spectra may be defined for each fault, and each spectrum, or the spectrum that governs bridge response, may be used for the analysis of the bridge.”

To develop the target rock spectrum for the controlling earthquake, we selected the Abrahamson and Silva (1996) attenuation relation for the following reasons: (1) it provided the most conservative (i.e., highest) estimate of spectral accelerations in the frequencies of interest to bridge design for the design earthquake, (2) a method has been developed to adjust this attenuation relation for fault directivity, (3) regression coefficients have been developed for deep soil sites, (4) a response spectrum for the vertical component can be developed, if needed. Figure 3 shows a mean deterministic rock spectrum for the I-15/I-80 interchange from the Abrahamson and Silva (1996) attenuation relation using regression coefficients appropriate for hanging wall effects. This spectrum was developed using M = 7.2 and a source distance of R = 2.5 km, which is the closest distance from the site to the rupture plane of the Wasatch Fault, consistent with the source distance used by Abrahamson and Silva (1996). For comparison, a probabilistic spectrum for site Class B conditions has been developed for the same site using the general procedures of MCEER/ATC-49 (Figure 3).

ADJUSTMENT OF TARGET SPECTRUM FOR FAULT DIRECTIVITY EFFECTS

MCEER/ATC-49a requires that near fault effects be considered for sites located within

10 km of an active fault, if these effects could significantly influence bridge response.

Because fault directivity effects were possible at the candidate site, we adjusted the target

rock spectrum to incorporate the increased spectral accelerations. The Abrahamson and Silva

(1996) attenuation relation does not include fault directivity effects, nor does the national

strong motion hazard maps. Because the seismic hazard in Utah is largely dominated by

normal faulting, the directivity effect for normal (i.e., dip-slip) faults was important. For

normal faults, the alignment of both the rupture direction and the slip direction in a direction

that propagates up the fault plane produces rupture directivity effects at sites located near the

surface exposure of the fault (or its updip projection, if the fault does not break the surface)

(Somerville et al., 1997). Because most large normal faults initiate their rupture near the base

of the seismogenic crust, sites on or near the fault trace will experience the maximum effect

of both directivity and systematic fault-normal-to-fault-parallel differences in ground motion.

Forward directivity effects begin to be apparent at a spectral period of about 0.5 seconds and

increase with increasing period. For normal faulting, the maximum amplification effect is

the range of about a 20 percent increase for sites that are within 15 km of the causative fault.

Somerville et al. (1997) provides a method to adjust the Abrahamson and Silva (1996)

attenuation relation for fault directivity effects. This model assumes that amplitude

variations in the spectrum from rupture directivity are dependent upon geometrical

parameters such as: angle between the dip of the fault and the line that connects the site with

the hypocenter, the fault width and depth to the hypocenter, as measured down the dip of the

fault. We applied the Somerville et al. (1997) directivity model to adjust the target spectrum

to include directivity effects (Figure 3). However, the spectral values were reduced by 25

percent to account for differences between normal and reverse faulting (Somerville, 1998a).

SPECTRAL MATCHING

Most acceleration records do not provide an adequate match to the target spectrum

without some modification. They must be scaled, adjusted or matched to the target design

spectrum. CALTRANS (1996a) allows four methods to modify time histories that are

commonly used in engineering practice: (1) Response-Spectrum Compatibility Time History

Adjustment Method, (2) Source-to-Site Numerical Model Time History Simulation Method,

(3) Multiple Actual Recorded Time-History Scaling method, (4) Connecting Accelerogram

Segments Method. Spectrum compatible time histories are acceleration time histories that

have been matched to a target acceleration response spectrum using numerical techniques.

We do not recommend that synthetically generated time histories not be used for ground

response analyses. Such time histories do not have near field and other effects, which may be

important for non-linear time domain analyses.

MCEER/ATC-49b recommends the selection of at least 4 records for the ground response

analyses. We recommend the use of records obtained from rock or very stiff soil sites,

whenever possible. Records from deep or soft soil sites should not be used for the spectral

matching. In addition, the candidate records should be independent motions (i.e., should

have no statistical or spatial correlation).

For our analyses, we have used method 1 and perform spectral matching using the

computer program RSPMATCH (Abrahamson, 1992). The general objective of spectral

matching is to generate a design acceleration time history that approximately achieves a

mean-based fit to the target spectrum (NUREG CR-6728). That is, the average ratio of the

spectral acceleration calculated from the accelerogram to the target spectrum as a function of

frequency is only slightly greater than 1. An additional aim is to achieve an acceleration time

history that does not have significant gaps in the Fourier amplitude spectrum, but is not

biased too high with respect to the target spectrum. An accelerogram that exceeds the target

spectrum at most frequencies may overdrive a site soil column or structure where nonlinear

response is of interest (NUREG CR-6728). It is also important to use a spectral matching

technique that retains the phase characteristics of the ground motion time history that is to be

modified (Somerville, 1998b). Preservation of the phase characteristics is important for non-

linear time domain analyses, because the solution for such analyses can be sensitive to the

phasing of the individual time history.

The candidate acceleration time histories should be rotated to find their principal

components and the principal components should be used for spectral matching. Because the

candidate records for our site were selected to represent near-field motions having strong

velocity pulses in the fault-normal component, it is important the horizontal components of

the candidate records be transformed into their principal components, so that these can be

align with the direction of fault directivity. The major and minor principal components are

the directions that best correlate with the fault-normal and fault-parallel directions.

Because the I-15/I-80 target response spectrum was adjusted for forward rupture

directivity, it is also important to select candidate records that have this effect. (This is true

even if the target spectrum explicitly incorporates directivity effects, because the spectrally

matching process cannot build a forward rupture directivity pulse into a record where none is

present in the first place (Somerville, 1998b).) Because of this consideration, we selected

records that have a forward directivity effects already present. Most of the selected records

have moderate to large vmax to v ratios, which is the ratio of the peak velocity, vmax, compared

to the peak velocity measured in the orthogonal direction, v. A high vmax to v ratio suggests a

velocity pulse is present in the record. Further, CALTRANS (1996a) recommends that the

candidate records have peak ground acceleration (PGA), peak ground velocity (PGV) and

peak ground displacement (PGD) with minus 25 percent and plus 50 percent of the target

spectral values. This guideline will allow the spectral matching process to be completed with

less difficulty and will not introduce as large of change in the spectral content of the matched

time history.

In addition to including velocity pulses from fault directivity, one of the primary goals of

spectral matching is to generate a set of realistic time histories that satisfy other seismological

and geological conditions. Other considerations include: appropriate earthquake magnitude,

faulting mechanism, source-to-site distance and geological structure. The candidate records

should be selected from earthquake events that have similar seismic and site conditions,

whenever possible.

Filtering and baseline correction of the input time history may also be required prior to

performing spectral matching. This filtering step is necessary because the ground response

analyses assume that surface rock motion is a result of vertically propagating shear waves.

However, Silva (1988) and Kramer (1996) have noted that some recorded surface motions

may consists of higher mode surface waves. Thus to remove these unwanted waves, we

recommend that the candidate time histories be filtered to remove frequencies above 15 Hz.

Generally it is recommended that an anti-aliasing filter, such as a Butterworth filter, be used

rather than an abrupt cut-off frequency that is employed by SHAKE. We used a low pass

Butterworth filter to remove frequencies greater than 15 Hz from the rotated acceleration

time histories during spectral matching. We also used a high pass Butterworth filter for

frequencies less than 0.14 Hz (T = 7.0s). The high and low pass filters are included within

the RSPMATCH program and are done during the spectral matching process using a 4-pole

Butterworth filter. However, filtering of the record may not always be necessary, depending

upon the source of the original record. Some databases, like the PEER database, have

earthquake records that have been pre-processed and filtered. We also recommend that a

baseline correction be performed on the candidate record before performing spectral

matching. This step is required to remove any spurious low frequency motions prior to the

filtering and spectral matching.

Lastly, we have not modified the duration of our candidate time histories. We do not

believe that this is necessary because we have selected records that have approximately the

same earthquake magnitude and distance from the seismic source as the controlling fault for

our selected bridge sites. Thus in doing so, we believe that the selected time histories will

have approximately the appropriate duration.

The spectral matching process may also introduce drift into the record, which must be

corrected. If drift is present, a plotting of the displacement time history will show the amount

of drift because the double integration process employed accentuates errors. Correction of

this drift is important if the spectrally matched record is to be used in analyses where

displacement is to be predicted from the analysis of the record (e.g., ground deformation

analysis). It is less important if only the accelerations or forces are to be obtained from the

analysis. We note that some displacement histories from actual earthquakes have a “real”

drift” as opposed to a “processed drift.” Real drift can be a result of permanent tectonic or

ground displacement after the earthquake and is may not be an artifact of the record

processing. However, because our analyses are not interested in estimating this part of drift

and we recommend that all records be baseline corrected, even if they contain real drift.

Another detail that should be considered involves the number of trailing zeros that should

be present in the record to create a “quiet zone.” Because the Fourier series used in EQL

analyses implies periodicity (it is assumed that the total time history repeats itself

indefinitely), there should be enough trailing zeros at the end of the acceleration time history

to form a “quiet zone.” This zone should have sufficient duration to allow the periodic

response to die out before the next motion begins. We recommend that the last third of the

spectrally matched time history contain a quiet zone.

DECONVOLUTION ANALYSIS

MCEER/ATC-49b allows the acceleration time histories to be input into the site-specific

soil column at a depth with the Vs measurements are equal to a Site Class C soil.

“For profiles having great depths of soil above Site Class A or B rock, consideration can

be given to defining the base of the soil profile and the input rock motions at a depth at which

soft rock or very stiff soil of Site Class C is encountered.”

The candidate records are then assigned to this layer as outcropping rock motions and

these motions are convolved to the surface to predict the surface soil response. It one were to

use this approach, then for the I-15/I-80 interchange, the soil model would end at a depth of

about 200 m. However, at the I-15/I-80 site, the Vs profile (both soil and rock) below 200 m

may significantly affect the surface soil response and the simple convolution analysis

suggested by MCEER/ATC-49b may not adequately capture this response, especially at

longer periods.

To better model the deep sedimentary basin, we chose to do a deconvolution analysis to a

significant depth (5 km), followed by a deep convolution analysis (5 km) to incorporate the

affect of the deeper sediments and shallow, crustal rock. To this end, we deconvolved the

spectrally-matched records to depth of 5 km to a point where the generic western U.S. Vs

profile and the Salt Lake Valley Vs profiles are reasonably matched (Figure 2). For the

deconvolution analysis, we recommend that an average western U.S. rock Vs profile of Boore

and Joyner (1997) be used in the deconvolution analysis (Figure 2). This shear wave velocity

profile reasonably represents the average crustal Vs values for the western U.S. and is

appropriate for the attenuation relations used in developing the national seismic hazard maps.

Deconvolution analysis in SHAKE is performed by assigning the spectrally matched

input rock motion to the surface layer (i.e., layer 1) as an “outcropping” motion in SHAKE.

The output object motion at a depth of 5 km should be requested as an “outcropping rock” for

the subsequent convolution analysis (see next section). In essence, the deconvolution results

represents what the surface motion would be, if the rock at a depth of 5 km were outcropping

at the site. This analysis and the subsequent convolution analysis remove any bias in the

strong motion resulting from differences between the generic western U.S. rock Vs profile

and the site-specific Salt Lake Valley profile.

Shear modulus reduction (i.e., G/Gmax) curves appropriate for the generic western U.S.

rock profile are also needed for the deconvolution analysis. We have used the rock G/Gmax

and damping curves used by Geomatrix (1999), which are appropriate for weathered and

fractured rock for shallow depths. For depths below 70 m, where Vs values are equal to or

greater than 4000 ft/s, we assumed that the rock behaves linearly (i.e., no shear modulus

reduction is used).

In addition to G/Gmax curves, estimates of material damping as a function of strain are

also required to complete the deconvolution analysis. For the profile less than 70 m, we used

the damping curves used by Geomatrix (1999). For the linear rock layers between depths of

70 m to 1.5 km, damping for each sub layer was calculated using seismic attenuation

parameter kappa, κ, which is related to the near surface shear wave velocity quality factor,

Qs:

κ = H / (Qs Vs) (1)

where H is the total thickness of the crust over which the energy loss occurs (e.g., 1.5 km)

and Vs is the average shear wave velocity over H. For our calculations, we used H equal to

1.5 km and a κ value for this zone of approximately equal to 0.04 s for western U.S. rock

conditions (Geomatrix, 1999; Boore and Joyner, 1997). Damping, λ, is related to Qs by:

λ = 1/ (2 Qs) (2)

The kappa for each sublayer, κi, in the SHAKE model is calculated from:

κi = 1/ γ ∗ Hi/Vsi2 (3)

where γ is a weighting factor and Hi and Vsi are the thickness and shear wave velocity of the

sublayer, respectively. The value of γ is calculated from:

γ = Σ Hi/(Vsi2) (4)

The portion of Qs for each sublayer, Qsi is calculated from:

Qsi = Hi / (Vsi * κi) (5)

and the damping for each sublayer is calculated from Equation (2).

It is important to note that a κ value of 0.04 s includes the total damping in the upper

portion of the crust (i.e., 0 to 1.5 km). Because we have used rock damping curves for the

upper 70 m of the profile, it is important to account for the portion of κ associated with this

portion of the profile. Once this part of κ is calculated, it must be subtracted from the total κ

of 0.04 s in order to calculate the remaining κ to be distributed to the layers found between

70 m and 1.5 km.

Below a depth of 1.5 km, damping is constant and is calculated from Equation (2) using a

crustal quality factor, Q that is approximately 290 (unitless) (Geomatrix, 1999). This Q

yields a damping of 0.0017 or 0.17 percent for each of the rock sublayers below 1.5 km to a

depth of 5 km.

Our preliminary convolution results showed spurious high frequency spikes in some of

the response spectra of the 5 km deconvolved motion. We also found that if not removed, the

spikes will adversely affect the subsequent convolution analyses. Silva (1988) recommends a

deconvolution procedure that uses pre-filtering of the input motion by applying a 15 Hz low-

pass filter to eliminate the tendency of the deconvolution analysis to develop unrealistically

large accelerations at depth. Thus, we recommend the following additional steps, if spurious

high frequency spikes are present in the deconvolution results.

We recommend a Butterworth filter be used to filter the input time histories spikes after

spectral matching has been performed, but prior to the convolution analysis. We used a 4th

order, low-pass Butterworth filter starting at 15 Hz to filter the spectrally matched time

histories using SeismosignalTM. Figure 4 shows the response spectra for the filtered time

histories used as input to the deconvolution analysis. We also note that 15 Hz Butterworth

filtering does have the slightly undesirable consequence of decreasing the high frequency

spectral acceleration values near pga (Figure 4). This means that the subsequent

deconvolution analysis results will be slightly deficient in the high frequency portion of the

spectrum.

After filtering, we performed the deconvolution analysis by setting the cutoff frequency

in SHAKE to 25 Hz and by using a strain ratio of 0.60. The maximum number of iterations

was set to 10 and an error tolerance of 5 percent was used for all deconvolution analyses.

The results of the deconvolution analysis are shown in Figure 5. These response spectra

represent outcropping rock spectra for the 5 km deep infinite elastic half-space in SHAKE.

These outcropping rock motions will be used as input in the subsequent convolution analysis.

CONVOLUTION ANALYSIS

A convolution analysis is used to predict the surface soil response using a site-specific Vs

profile for the sedimentary basin and surficial soils. However, to complete the convolution

analysis, site-specific estimates of Vs are required to the same depth of the deconvolution

analysis (i.e., 5 km). The depth of the unconsolidated Quaternary sediments in the Salt Lake

Valley extends to depths of about 300 to 400 m in parts of the valley. At the I-15/I-80 Vs

measurements were not available for depths below about 60 m. Thus, for the depth interval

between 60 m to 152 m, we used the median Vs profile for the lacustrine/alluvial silts and

clays unit from the study of Wong et al. (2002). For depths between 152 and about 300 m,

we used an unpublished Vs profile used by Wong et al. (2002).

Below a depth of about 300 m, semi-consolidated sediments with much higher Vs values

are found. Then, at a depth of about 1000 m, the semi-consolidated sediments change to

consolidated sediments as seen by another marked increase in the Vs profile (Figure 2).

Consolidated sediments are found to a depth of about 2.6 km. Below this depth, bedrock is

encountered with Vs values of about 3400 m/s.

Damping values for the linear rock part of the profile (i.e., depths 300 m to 1.5 km) were

calculated in the same manner as the deconvolution analysis. The seismic attenuation

parameter kappa, κ, for the upper 1.5 km of the profile was estimated to be 0.05 s (J.

Pechmann, personal communication). The κ value is slightly higher than the 0.04 s used for

the generic western U.S. rock profile. It was increased to account for the higher attenuation

that is expected in the shallow crust beneath the Salt Lake Valley. Below a depth of 1.5 km,

values of damping were calculated from the crustal quality factor, Q for Utah. Geomatrix

(1999) used the following formula to calculate the Q below 1.5 km:

Q = 500f 0.2 (2)

where f is the frequency in Hz. Using f = 3 Hz, the Q factor below 1.5 km is approximately

623 (unitless). Damping below 1.5 km is not thickness or shear wave velocity dependent,

thus the damping for each layer is the same and calculated Equation (2), which yields a

damping of 0.0008 or 0.08 percent for each sublayer. Also, the deep (5 km) convolution

analyses were completed using a best-estimate and upper-bound shallow (depths between 0

to 300 m) soil profile in combination with two deep Vs models (depths between 300 m to 5

km) for a total of 20 analyses for the case with fault directivity (Figures 6 and 7).

COMPARISON OF THE RESULTS

The ground response results in Figures 6 and 7 represent our best prediction of the deep

basin and soil effects for the Salt Lake Valley at the I-15/I-80 interchange. However, as

previously discussed MCEER/ATC-49b allows the use of a simple convolution analysis for

sites with deep soil profiles. In this approach, the spectrally matched time histories are to be

assigned as outcropping rock motions in SHAKE at a depth where site class C soils are

encountered.

Site Class C soils have Vs values ranging from 360 m/s to 760 m/s. However, as a more

refined estimate, Boore and Joyner (1997) have calculated a generic rock Vs profile for the

western U.S. Their average Vs profile has Vs30 values of 618 m/s, where Vs30 is the average

shear wave velocity in the upper 30 m of the profile. The Vs value of 618 m/s is considered

to be the mean value for rock sites in western North America and is a better estimate of the

average rock Vs value used in the current empirical attenuation relations. Thus, we

recommend that if one is to perform simple convolution analysis using MCEER/ATC-49b

guidance, the SHAKE model should extend to a depth where a Vs value of about 600 m/s is

first encountered. For the I-15/I-80 site, this corresponds to a depth of about 200 m.

Figure 8 shows average, 5 percent damped surface acceleration response spectra for the

200-m convolution case for the best estimate soil profile and the case with fault directivity.

(Note that some of the time histories used in this analysis differ from those used in Figures 6

and 7. The results shown in Figure 8 were done at an earlier time and some of the time

histories were later replaced with different time histories as our analyses evolved and were

reviewed.)

Our SHAKE results show that a simple 200-m convolution analyses, as allowed by

MCEER/ATC-49b may significantly underestimate the long period ground motion for deep

sedimentary basins. Figure 9 compares the mean spectra obtained from the 5 km

deconvolution / convolution analysis with those obtained from the 200-m convolution

analysis. The spectral acceleration values for the 5 km deconvolution / convolution analysis

are significantly higher at a period beginning at about 0.75 s. Thus, for the site we analyzed,

it appears that the 200-m convolution analysis is somewhat conservative for short periods and

is potentially unconservative at longer periods. However, we caution about over-generalizing

these results to other sites and differing earthquake conditions.

Other ground motion studies for the Salt Lake Valley provide a comparison for our

results. Figure 10 shows amplification factors for the 5 km deconvolution / convolution

results compared with amplification factors published by Wong et al. 2002. Wong et al. 2002

factors are for a M6.5 earthquake having an input pga of 0.75 g for a lacustrine-alluvial silt

and clay unit in the Salt Lake Valley. Figure 10 shows that the median SHAKE soil

amplification factors calculated for our site are relatively similar to those calculated by Wong

et al. (2002) for frequencies between about 1 and 100 Hz. At frequencies less than 1 Hz, our

analyses show more amplification. However, it is important to keep these differences in

context. The analysis of Wong et al. (2002) were median estimates from a large statistical

sampling of lacustrine-alluvial silt and clay units from northern California sites, whereas our

estimates are from site-specific analyses of one site with much less statistical support. Thus,

our results probably fall within the uncertainty ranges of the Wong et al. (2002) results. In

addition, the amplification factors calculated by the Wong et al. (2002) study did not include

fault directivity effects, whereas our results did.

However, it is also possible that the SHAKE analyses are artificially overestimating the

amplification at long period (i.e., greater than 1 s) and underestimating the amplification at

mid-range to short periods. If true, the latter underestimation would be unconservative (i.e.,

unsafe) from an engineering standpoint. Thus, we believe that it is potentially

unconservative to accept the SHAKE results at face value and rely solely on them for

developing the design spectra. The next section describes the enveloping process that we

recommend for developing the final design spectrum.

DEVELOPMENT OF FINAL SPECTRUM

It is important to note that MCEER/ATC-49a requires that when response spectra are

calculated from a site-specific studies, the final design spectra shall not be less than two

thirds of the response spectra developed using the generalized procedures of MCEER/ATC-

49a. For this reason, and to guard against potential unconservatism in the SHAKE analyses,

we recommend that a “smoothed” enveloping design spectrum be developed (Figure 11). We

recommend that the enveloping design spectrum bound the following spectra: (1) mean

spectral values calculated from a site-specific SHAKE deconvolution / convolution analyses

for the best-estimate and upper bound soil profiles averaged together, (2) MCEER/ATC-49a

spectrum for soil type E scaled to two-thirds of the spectral acceleration values for the

maximum considered earthquake (i.e., 2500 return period event) and (3) spectral acceleration

values obtained from the Abrahamson and Silva (1996) attenuation relation for a deep soil

site using the appropriate magnitude and source distance for the controlling earthquake.

We recommend the following steps for constructing the enveloping design spectrum:

1. Make a composite plot of the above 5 percent damped spectra as a function of period.

2. The above step should be done for cases with and without fault directivity and these

cases plotted and bounded separately. Separate design spectra should be constructed

for cases without and with fault directivity.

3. From the composite plots, construct a smoothed, enveloping spectrum that bounds all

of the plotted spectra plotted. (Figure 11).

SUMMARY

The methods and analyses presented in the paper show that ground response analyses for

deep and/or soft soil sites found in sedimentary basins require special considerations to

adequately capture long period effects. Deep, unconsolidated, lacustrine and alluvial

sediments underlie significant portions of the urban Wasatch Front in Utah and these

conditions can significantly modify the characteristics of earthquake shaking. This paper

recommends performing site-specific ground response analyses that include deconvolution

and convolution analyses to capture these effects for deep and/or soft soil sites (Site Class D

and E) near active faults. The method for developing the final design spectrum uses an

enveloping spectrum that envelopes the: (1) mean spectral values calculated from a site-

specific SHAKE deconvolution / convolution analyses for the best-estimate and upper bound

soil profiles averaged together, (2) MCEER/ATC-49a spectrum for soil type E scaled to two-

thirds of the spectral acceleration values for the maximum considered earthquake (i.e., 2500

return period event) and (3) spectral acceleration values obtained from the Abrahamson and

Silva (1996) attenuation relation for a deep soil site using the appropriate magnitude and

source distance for the controlling earthquake.

The proposed analyses and spectrum development are consistent with site-specific

ground response analyses and spectra outlined by MCEER/ATC-49 for highway bridge

design, but the methods are general enough so that can also be applied to building design

according to ASCE 7-05.

REFERENCES

Abrahamson, N. A., 1992. Non-Stationary Spectral Matching, Seismological Research Letter, Vol.

63, No. 1.

Abrahamson, N. A., and Silva, W. J., 1996. Empirical Response Spectral Attenuation Relations for

Shallow Crustal Earthquakes, Seismological Research Letters, 68, 94-109.

Arnow, T., Van Horn, R., and LaPray, R., 1970. The pre-Quaternary surface in the Jordan Valley,

Utah, U.S. Geological Survey Professional Paper 700, p. D257-D261.

ASCE 4-98, Seismic Analysis of Safety-Related Nuclear Structures, American Society of Civil

Engineers.

ASCE 7-05, Minimum Design Loads for Buildings and Other Structures, American Society of Civil

Engineers.

Boore, D. M. and Joyner, W. B., 1997. Site amplification for generic rock sites, Bulletin of the

Seismological Society of America, Vol. 87, No. 2, pp. 327-341, April 2997.

Borcherdt, R. D. 1994. Simplified site classes and empirical amplification factors for site-dependent

code provisions, Proceedings of the NCEER/SEAOC/BSSC Workshop on Site Response During

Earthquakes and Seismic Code Provisions, University of Southern California, Los Angeles,

November 18-20.

CALTRANS, 1996a. Guidelines for generation of response-spectrum-compatible rock motion time

histories for application to CALTRANS toll bridge seismic retrofit projects,” Report to Caltrans

Seismic Advisory Board, Ad Hoc Committee on Soil-Foundation-Structure Interaction,

November, 25, 1996.

CALTRANS, 1996b. “Guidelines for performing site response analysis to develop seismic ground

motions for application to CALTRANS toll bridge seismic retrofit projects,” Report to Caltrans

Seismic Advisory Board, Ad Hoc Committee on Soil-Foundation-Structure Interaction, Revised

November, 25, 1996.

CALTRANS, 1996c. Caltrans procedures for development of site-specific acceleration response

spectra,” Caltrans, DNTMR, Office of Geotechnical Engineering.

Chang, W. S., Bray, J. D., Gookin, W. B., and Riemer, M. F. 1997. Seismic response of deep stiff soil

deposits in the Los Angeles, California area during the 1994 Northridge Earthquake,

Geotechnical Research Report No. UCB/GT/97-01, University of California, Berkeley.

Dames and Moore, 1996. Seismic hazard Analysis for the I-15 corridor,” final report submitted to the

Utah Department of Transportation for the I-15 Reconstruction Project, Salt Lake City, Utah.

Electric Power Research Institute, 1993. Guidelines for Determining Design Basis Ground Motions,

Report EPRI TR-102293. Palo Alto, California.

Geomatrix, 1999, Fault evaluation study and seismic hazard assessment, Private Fuel Storage Facility,

Skull Valley Utah, Volume III, Appendix F, Prepared by Geomatrix Consultants, Inc., February

1999.

Hill, J. A., 1988. A finite difference simulation of seismic wave propagation and resonance in Salt

Lake Valley, Utah, M.S. Thesis, Dept. Of Geology and Geophysics, University of Utah.

Idriss, I. M. and Sun, J. I., 1992. User’s Manual for SHAKE91, Center for Geotechnical Modeling,

Department of Civil and Environmental Engineering, University of California, Davis, California.

Idriss, I. M., 1990. Response of soft soil sites during earthquakes,” A memorial Symposium to Honor

Professor Harry Bolton Seed, Department of Civil Engineering, University of California, Davis,

CA.

Joyner, W. B., 2000. Strong motion from surface waves in deep sedimentary basins, Bulletin of the

Seismological Society of America, 90, 6B, pp. S95-S112, December 2000.

Kramer, S. L., 1996. Geotechnical Earthquake Engineering, Prentice-Hall Inc.

MCEER/ATC-49a, Recommended LRFD guidelines for the seismic design of highway bridges, Part

I: Specifications, Applied Technology Council.

MCEER/ATC-49b, Recommended LRFD guidelines for the seismic design of highway bridges, Part

II: Commentary and Appnedicies, Applied Technology Council.

Murphy, M., 1989. Finite difference simulation of seismic P- and SV-wave amplification in Salt Lake

Valley, Utah, Master of Science Thesis, University of Utah, Salt Lake City, Utah.

NEHRP, 2000. NEHRP recommended provisions for seismic regulations for new buildings and other

structures, Part 2:Commentary (FEMA 369), Building Seismic Safety Council.

NUREG/CR-6728, Technical basis for revision of regulatory guidance on design ground motions:

hazard- and risk-consistent ground motion spectra guidelines, U.S. Nuclear Regulatory

Commission, Office of Nuclear Regulatory Research, Washington D.C.

Rinne, E., and R. Dobry. 1992. Preliminary site recommendations, Memorandum to Roland Sharpe,

Chairman TS 2, Building Seismic Safety Council, December 11.

Schnabel, P. B., Lysmer, J. and Seed H. B., 1972. SHAKE - A computer program for earthquake

analysis of horizontally layered sites, Earthquake Engineering Research Center, University of

California, Berkeley, Report No. EERC 72-12.

Seed, R. B., Chang, S. W., Dickenson, S. E., and Bray, J. D., 1997. Site-dependent seismic response

including recent strong motion data, Proceedings Special Session on Earthquake Geotechnical

Engineering, XIV International Conference on Soil Mechanics and Foundation Engineering,

Hamburg, Germany, A. A. Balkema Publication, September 6-12, pp. 125-134.

Seed, R. B., Dickenson, S.E., and Mok, C. M., 1992. Recent lessons regarding seismic response

analyses of soft and deep clay sites,” Seminar proceedings - Seismic Design and Retrofit of

Bridges, University of California at Berkeley, Department of Civil Engineering and California

Department of Transportation, Berkeley, California, June 8 and 9, 1996.

Seed, H. B., and Sun, J. I., 1989. Implications of site effects in the Mexico City earthquake of Sept.

19, 1985 for earthquake-resistant design criteria in the San Francisco Bay Area of California,”

Earthquake Engineering Research Center, College of Engineering, University of California at

Berkeley, Report No. UCB/EERC-89/03, March 1989, 124 p.

Seed, H. B., C. Ugas, and J. Lysmer, 1976. Site dependent spectra for earthquake-resistant design,

Bulletin of the Seismological Society of America 66 (1):221-244.

Silva, W. J., 1988. Soil response to earthquake ground motion, EPRI Report NP-5747, Electric Power

Research Institute, Palo Alto, California.

Somerville, P. G., 1998a, The characterization and quantification of near-fault ground motion with

implications for the Basin and Range province, Proceedings Volume Basin and Range Province

Seismic-Hazards Summit, Western States Seismic Policy Council, Utah Geological Survey

Publication 98-2, pp. 96-109.

Somerville, P. G., 1998b, Emerging art: earthquake ground motion, Geotechnical Earthquake

Engineering and Soil Dynamics III, American Society of Civil Engineers Geotechnical Special

Publication No. 75, Vol. 1, pp 1-38.

Somerville, P. G., Smith, N. F., Graves, R. W., and Abrahamson, N. A., 1997, Modification of

empirical strong ground motion attenuations relations to include the amplitude and duration

effects of rupture directivity, Seismological Research Letters, v. 68, p. 199-222.

Sun, J. I., R. Golesorkhi, and H. B. Seed. 1988. Dynamic Moduli and Damping Ratios for Cohesive

Soils, Report UBC/EERC-88/15, Berkeley: University of California, Earthquake Engineering

Research Center.

Vucetic, M., and R. Dobry. 1991. Effect of Soil Plasticity on Cyclic Response, Journal of

Geotechnical Engineering, ASCE, Vol. 117, No. 1: 89-107.

Wong, I. G., Silva, W., Olig, S., Thomas, P., Wright, D., Ashland, F., Gregor, N., Pechmann, J.,

Dober, M., Christenson, G., and Gerth, R., 2002. Earthquake scenario and probabilistic ground

shaking maps for the Salt Lake City, Utah, metropolitan area, Utah Geological Survey

Miscellaneous Publication 02-5.

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Valley, Utah,” Utah Geological Survey Miscellaneous Publication 93-9.

Youd T. L. and B. Carter, 2003. Influence of soil softening and liquefaction on response spectra for

bridge design, Report No. UT-03.07, Utah Department of Transportation, Research.

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

0 100 200 300 400 500

Shear Wave Velocity, Vs, (m/s)

Dep

th (m

)

600 South Street

I-15/I-80 Interchange

San Francisco BayMud

Figure 1. Comparison of shear wave velocity profiles in Salt Lake City, Utah (600 South Street and I-15/I-80 interchanges) with the San Francisco Bay Mud.

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

0 500 1000 1500 2000 2500 3000 3500 4000Vs (m/s)

dept

h (m

)

SLC Airport East, Wong & Silva(1993)

Lacustrine-alluvial silt and clay(Northern CA Bay Mud), Wong etal. (2002, published)Interpreted cross section, distance= 15.5km, Hill et al. (1990)

Generic U.S. Rock, Boore & Joyner(1997)

Deep Profile I, this study

Deep Profile II, Wong et al. (2002,unpublished)

End, Wong and Silva 1993 (>2600m)

Semi-consolidated

Consolidated

Unconsolidated

Bedrock

End, Wong et al. 2002, published (152m)

Figure 2. Comparison of estimates of the deep Vs profiles for the Salt Lake Valley with the generic western U.S. rock profile from Boore and Joyner (1997).

0

0.5

1

1.5

2

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Period (s)

Spec

tral

Acc

eler

atio

n (g

)

Abrahamson and Silva (1996) attenuation relation

Abrahamson and Silva (1996) adjuste for fault directivity

MCEER/ATC-49 Site Class B

Figure 3. Comparison of response spectra for the I-15/I-80 interchange from Abrahamson and Silva (1997) attenuation relation for M = 7.2, R = 2.5 km. Heavy solid line is for the case with fault directivity.

Figure 4. Response spectra for 5 spectrally matched times histories for the I-15/I-80 interchange for the case with fault directivity. Spectrally matched time histories have been filtered at 15 Hz using a low pass 4th order Butterworth filter.

Figure 2. Results of 5 km deconvolution analysis using I-15/I-80 target spectrum for case with fault directivity.

0

0.5

1

1.5

2

0 1 2 3 4

Period (s)

Acc

eler

atio

n (g

)Cape Mendocino (I)

Erzican Turkey (I)

Superstition Hills (I)

UCLA (I)

Average (I)

Figure 3a. Predicted surface response spectra from the 5 km deconvolution/convolution analysis for the I-15/I-80 interchange for the case with fault directivity and using best-estimate soil properties and deep Vs profile I.

0

0.5

1

1.5

2

0 1 2 3 4

Period (s)

Acc

eler

atio

n (g

)

Cape Mendocino (II)Erzican Turkey (II)Imperial Valley (II)Superstition Hills (II)UCLA (II)Average (II)

Figure 6b. Predicted surface response spectra from the 5 km deconvolution/convolution analysis for the I-15/I-80 interchange for the case with fault directivity and using best-estimate soil properties and deep Vs profile II.

0

0.5

1

1.5

2

0 1 2 3 4Period (s)

Acc

eler

atio

n (g

)Cape Mendocino (I)Erzican Turkey (I)Imperial Valley (I)Superstition Hills (I)UCLA (I)Average (I)

Figure 7a. Predicted surface response spectra from the 5 km deconvolution/convolution analysis for the I-15/I-80 interchange for the case with fault directivity and using upper bound soil properties and deep Vs profile I.

0

0.5

1

1.5

2

0 1 2 3 4Period (s)

Acc

eler

atio

n (g

)

Cape Mendocino (II)Erzican Turkey (II)Imperial Valley (II)Superstition Hills (II)UCLA (II)Average

Figure 7b. Predicted surface response spectra from the 5 km deconvolution/convolution analysis for the I-15/I-80 interchange for the case with fault directivity and using upper bound soil properties and deep Vs profile II.

0

0.5

1

1.5

2

0 1 2 3 4

Period (s)

Acc

eler

atio

n (g

)Pacoima Dam - Best Estimate Vs

Imperial Valley - Best Estimate Vs

Erzican, Turkey - Best Estimate Vs

Calitri, Italy - Best Estimate Vs

Lucerne - Best Estimate Vs

Average - Best Estimate Vs

Figure 8. Results of the 200-m convolution analysis for the I-15/I-80 interchange for the best estimate soil profile and the case with fault directivity.

0

0.5

1

1.5

2

0 1 2 3 4

Period (s)

Acc

eler

atio

n (g

)Average of 5 km Deconvolution / Convolution Analysis

Average of 200 m Convolution Analysis

Figure 9. Comparison of the 5 km deconvolution/convolution analysis with the 200-m convolution analysis for the I-15/I-80 interchange for the case with fault directivity.

0.1

1

10

0.1 1 10 100

Frequency (Hz)

ampl

ifica

tion

Wong et al. (2002) (0.75 g w/o faultdirectivity"

Median with directivity I-15/I-80interchange from SHAKE

Figure 10. Comparison of median amplification factors for the Salt Lake Valley for deep, lacustrine soil sites

0

0.5

1

1.5

2

0 1 2 3 4Period (s)

Acc

eler

atio

n (g

)

A&S Deep Soil M = 7.2, R = 2.5 km

Avg. ProShake Results

MCEER/ATC Site Class E

2/3 MCEER/ATC-49

Recommended Design Spectrum

Figure 11. Recommended enveloping design spectrum for the I-15/I-80 interchange for the case with

fault directivity.