The purpose of this work is to provide response spectra and time histories for use in topical investigations, case studies, and trial applications in the SAC Phase 2 Steel Project. Ground motion estimates are provided in three locations of the United States (Boston, Seattle, and Los Angeles) corresponding to seismic zones 2, 3 and 4 respectively. Suites of time histories are provided at two probabilities of occurrence (2% in 50 years and 10% in 50 years) in each of these three locations for firm soil conditions. Time histories are also provided for 50% in 50 years for Los Angeles. Time histories for soft soil profiles are provided for 10% in 50 years in all three locations. Near fault time histories are also provided for seismic zone 4 conditions.
The NEHRP probabilistic ground motions (Frankel et al., 1997) formed the basis for deriving target response spectra. These ground motions, which are for soft rock conditions (the boundary between site categories SB and SC) were mapped throughout the conterminous United States for a set of response spectral periods from 0.1 to 2.0 seconds at 5% damping. The mapped ground motion values are listed in Table 1 for four return periods:
Maximum Considered ground motion maps were developed by the Building Seismic Safety Council and the USGS. In Boston and Seattle, these ground motions are identical to those for 2% in 50 years. In Los Angeles, the Maximum Considered ground motions are so close to the 2% in 50 year values that the difference between them (less than 10%) is not significant. Accordingly, the time histories for 2% in 50 years can be used to represent the Maximum Considered ground motions for all three cities.
The target response spectra for this study are for NEHRP site category SD, firm soil. The spectra provided by NEHRP and listed in Table 1, which are for the SB/SC boundary, were modified to represent site category SD. The scale factor used was a factor of 1.78 at periods of 1.0, 2.0, and 4.0 seconds. For the period of 0.3 seconds, the scale factor was the ratio of Fa for SD to the Fa for the SB/SC boundary for the appropriate peak acceleration value at the SB/SC boundary. The scale factor ranged from a maximum of 1.45 for the lowest ground motion levels to 1.0 for the highest ground motion levels. The resulting target response spectra are listed in Table 2 and shown in Figure 1 (not currently available). To extend the response spectra to a period of 4.0 seconds, probabilistic hazard calculations were done by Norm Abrahamson at periods of 0.3, 1.0, 2.0 and 4.0 seconds. These calculations were used to extrapolate the NEHRP values to 4.0 second period. The target response spectra are listed in Table 2.
|Return Period||Location||Period (5% damped)|
|Return Period||Location||Period (5% damping)|
The equal hazard response spectral ordinates in the NEHRP maps represent the aggregated contribution of a range of earthquake magnitudes occurring at various rates on each of several discrete faults or seismic source zones located at various distances from the site, and include the effect of random variability in the ground motions for a given magnitude and distance. However, in order to provide ground motion time histories, we must choose one or more discrete combinations of magnitude, distance and epsilon to represent the probabilistic ground motion. The parameter epsilon is defined as the number of standard deviations above or below the median ground motion level for that magnitude and distance that is required to match the probabilistic spectrum. The magnitude, distance, and epsilon values are estimated through deaggregation of the probabilistic seismic hazard using the procedure described by McGuire (1995). When the ground motion time histories were selected, these deaggregations were not available. Accordingly, experience from the deaggregation of seismic hazards in the three locations in other projects was used to select approximate ranges of magnitudes and distance, which are listed in Table 3.
The USGS is now doing deaggregations at 100 sites. Those for Seattle and Los Angeles have not yet been done, but that for Boston (at a slightly different location from that for which ground motion values were supplied for Table 1 is now available. The results for two probabilities of exceedance: 10% in 50 years and 2% in 50 years, and for two ground motion periods: 1 and 2 seconds, are shown in Figures 2 through 5. The contributions by eta value, shown by different shading from bottom to top, are -1 to 0; 0 to 1, 1 to 2, and >2. The median and mode values of magnitude and distance are listed on the plots. These deaggregations indicate that for 10% in 50 years, the hazard at long periods is dominated by ground motions from large distant events having epsilon values larger than 1. For 2% in 50 years, the hazard is dominated by closer but not significantly larger events. The large magnitudes of these events cause the response spectral shapes for Boston to be similar to those for Seattle and Los Angeles for long periods.
In the Los Angeles basin, the joint magnitude-distance mode for 10% probability of exceedance in 50 years is a magnitude 6.75 to 7.0 earthquake at a closest distance of 0 to 5 km Cramer and Peterson (1995). The joint magnitude-distance probability for downtown Los Angeles shown in Figure 6 (not available currently) indicates that, in addition to the magnitude 7 earthquake at less than 5 km that forms the mode of the probability distribution, a magnitude 7.5 to 8 earthquake at a distance of 50 km on the San Andreas fault also makes a significant contribution to the hazard at 2 seconds period (although it is not significant at periods shorter than 1 second). This deaggregation did not include the parameter epsilon which is needed to match the probabilistic ground motions.
In Seattle, the seismic hazard is influenced by three different categories of seismic sources. These are faults in the shallow crust such as the recently identified Seattle fault (at closest distances less than 10 km); earthquakes occurring at depths of about 60 km within the subducted Juan de Fuca plate; and earthquakes occurring on the plate interface of the Cascadia subduction zone about 100 km west of Seattle. Deaggregation of probabilistic seismic hazard analyses indicate that ground motions having 10% probability of exceedance in 50 years are dominated by earthquakes of about magnitude 7 in the subducted plate beneath the region, with the plate interface zone contributing at the longer ground motion periods. We have provided time histories of earthquakes belonging to all three categories of seismic sources.
|Location||2% in 50 years||10% in 50 years||50% in 50 years|
|Boston||6 - 7||5 - 150||5 - 7||5 - 200|
|Seattle||6.5 - 8||8 - 80||6 - 8||15 - 80|
|Los Angeles||6.75 - 7.5||2 - 20||6.5 - 7.25||5 - 40||5 - 7||5 - 15|
We selected time histories for each location based on the approximate deaggregation of the hazard described above for each probability of exceedance. Preference was given to time histories recorded in the region, but it was necessary to also include recordings from analogous source categories and seismic regions, such as recordings of subduction earthquakes from Chile and Japan for use in Seattle and recordings of crustal earthquakes in eastern Canada for use in Boston. Preference was given to time histories recorded on site category SD, but it was necessary to also include recordings from rock conditions. These rock site recordings were modified for site conditions using the procedure described below. Where sufficient recorded time histories were not available, we included broadband strong motion simulations generated using procedures described below.
The broadband procedure that we used has a rigorous basis in theoretical and computational seismology. The earthquake source is represented as a shear dislocation. The radiation pattern of the shear dislocation, and its tendency to become subdued at periods shorter than about 0.5 sec, are accurately represented. This is important for the realistic representation of ground motions at intermediate and long periods, especially for near-fault ground motions in which the large pulse of motion ("fling") oriented perpendicular to the fault strike is due to rupture directivity and radiation pattern effects. Wave propagation is represented rigorously by Green's functions computed for the seismic velocity structure which contains the fault and the site. These Green's functions contain both body waves and surface waves. We calculate the ground motion time history in the time domain using the elastodynamic respresentation theorem by the integration over the fault surface of the convolution of the slip time function on the fault with the Green's function for the appropriate depth and distance. The physical basis of time histories simulated using seismologically based methods makes them superior to time histories generated by purely numerical FFT and ARMA synthesis procedures.
Through extensive testing of this procedure against recorded strong ground motions, we have demonstrated its validity for modeling strong ground motions in the magnitude range of 5 to 8, distance range of 0 to 300 km, and period range of 0.01 to 10 seconds for crustal earthquakes in both the eastern and western United States, as well as for subduction earthquakes in Seattle, Mexico, Chile and Japan. The broadband time history simulation procedure has been used in numerous enginering projects, including Phase 1 of the SAC Steel Building Project (Somerville et al., 1995). The procedure is described in more detail in Appendix 1 (not available currently).
For near-fault time histories from large magnitudes, the ratio of soil to rock is less than unity at short periods and greater than unity at intermediate and short periods. The peak acceleration is controlled by the intermediate periods contained in the directivity pulse, not by the short periods. In this situation, it is not feasible to increase the intermediate and long periods and reduce the short periods. This implies that the response spectral model of Abrahamson and Silva (1997) may not be valid for near-fault ground motions from large earthquakes. For these cases, the spectral matching was done only for periods longer than 0.3 seconds, as shown in Figure 7 (not available currently).
There are large differences between the strike-normal and strike-parallel components of near fault ground motions at periods longer than about 0.5 second (Somerville et al., 1997). These differences may have an important impact on the response of structures, as indicated by preferred failure orientations of structures in both the 1994 Northridge and 1995 Kobe earthquakes (north and northwest respectively). To enable analyses of these effects, the horizontal components of all of the time histories provided in this study have been rotated into the strike-normal and strike-parallel components. They have also been provided after rotation by 45 degrees from strike-normal and strike-parallel, which minimizes the difference between the two components.
The rotation of the two recorded components North (N) and East (E) into strike-parallel and strike-normal components SP and SN was accomplished using the following equations:
where theta is the strike of the fault measured clockwise from North. If the recording orientation is not North and East but rotated clockwise by the angle phi, then theta would be reduced by phi. These equations can be used to rotate the components back into the recorded orientation or into any other desired orientation such as a random orientation. However, if these rotations are done for the soft soil time histories, the resulting time histories will not correspond to those that would be obtained using the rotated time histories for site category SD as inputs into the soil, due to the non-linear nature of the soil response.
Near-fault time histories are included to some extent in all time history sets, as well as in the set of 20 near-fault records. In all near-fault time histories there should be static displacements due to the static dislocation field of the earthquake. However, most recording systems do not adequately record the permanent displacements, and they are filtered out of the recordings in the course of processing. We have not attempted to retain the static displacement field in any of the recorded or simulated time histories, with the exception of the Lucerne recording of the 1992 Landers earthquake. This time history is a modification by Graves (1996) of the version of Iwan and Chen (1994) to include geodetically defined static displacements, documented following the time history plots of near-fault time histories. The rotated time histories were processed by lowpass filtering and baseline removal to ensure that they do not produce large permanent displacements when integrated twice to displacement. The degree of each process was minimized for each three-component time history. The processes were done in the following sequence: lowpass filtering (either none, at 10 seconds, or at 5 seconds period), followed by baseline removal (either none, second, or fourth order polynomial).
The nonlinear response of structures is strongly dependent on the phasing of the input ground motion and on the detailed structure of its spectrum. Unlike the case of linear response, which can often be obtained from a single time history matched to a target spectrum, an appropriate measure of nonlinear response requires the use of multiple realistic time histories having phasing and response spectral peaks and troughs that are appropriate for the magnitude, distance, site conditions, and wave propagation characteristics of the region. The purpose of providing suites of time histories is to provide a statistical sample of this variability in phasing and spectra through a set of time histories that are realistic not only in their average properties but in their individual characteristics.
To be consistent with this approach, the shapes of the response spectra of individual time histories were not modified in the scaling procedure. Instead, a single scaling factor was found which minimized the squared error between the target spectrum and the average response spectrum of the two horizontal components of the time history assuming lognormal distribution of amplitudes. The scale factor that minimized the weighted sum of the squared error between the target values and the average of the two horizontal components was calculated. The weights used were 0.1, 0.3, 0.3, and 0.3 for periods of 0.3, 1, 2, and 4 seconds respectively. The scale factor was then applied to all three components of the time history. This procedure retained the ratios between the three components at all periods.
In many cases, the time histories for Seattle and Boston have response spectra that are lower than the target spectrum at 4 seconds period. We calculated another scale factor that is required to match the time histories, scaled as described above, so that the average of the two horizontal components matches the target spectrum at 4 seconds period. The scaled time histories should be further scaled by this factor if it is desired to match them to the target at 4 seconds period. The response spectra of these rescaled time histories will in many cases exceed the target spectrum at periods shorter than 4 seconds.
Time histories were selected to represent near-fault ground motions from earthquakes having a variety of faulting mechanisms (strike-slip, oblique, and thrust) in the magnitude range of 6 3/4 to 7 1/2. The closest distances for shallow crustal faults lie in the range of 0 to 10 km, and the closest distances for blind thrust faults lie in the distance range of 6 to 18 km. These magnitudes and distance ranges dominate the seismic hazard in Zone 4 for return periods of 10% in 50 years. The time histories do not represent a statistical sample of such ground motion conditions, and were not scaled to represent a target spectrum. However, the variability among these 20 time histories is representative of the variability in recorded data for a given magnitude, distance and site condition in empirical ground motion models, as described below.
Time histories for soft soil sites were derived using the time histories for 10% in 50 years for site category SD described above as the input motions. Two different soil profiles that are broadly representative of soft soil conditions were developed, and three thicknesses of each profile (surface to 50, 100, and 200 feet) were taken for analysis to provide three different predominant periods for each profile. Time histories generated for stiff soil conditions were used as input into equivalent linear calculations (Woodward-Clyde update of SHAKE91; Idriss and Sun, 1992) to produce time histories for soft soil conditions. Selected time histories were also generated using nonlinear soil response analyses (SUMDES; Li et al., 1992) to produce time histories for soft soil conditions. For each input time history, there are six soft soil time histories (one for each combination of soil profile and depth) from the equivalent linear analyses, and for selected time histories, corresponding time histories using nonlinear analyses.
While the spectra of ground motions on stiff soil sites are relatively well constrained by recorded data, limited information is available for recorded ground motions on soft soil sites. To evaluate the effects of soft soil conditions on ground motions, site response analyses were performed for six soil profiles that were representative of Type E and Type F soil conditions (NEHRP 1994). The site response analyses were performed using the well-established equivalent linear computer code SHAKE91.
The six soil profiles were developed to represent a broad range of soft soil conditions encountered in the Boston, Los Angeles, and Seattle. These profiles were represented by shear wave velocities as a function of depth. The variations of shear wave velocity with depth for the selected soil profiles are presented in Figure 1 (not available currently). Soil profiles shown in Figure 1 (not available currently) represent the lower and upper value of soft soil shear wave velocities typically encountered in the three areas.
A plasticity index of 30 was assigned to the soil profiles. Curves for modulus reduction and material damping, as a function of shearing strain amplitude, were developed using the plasticity index value in empirical curves presented by Vucetic and Dobry 1991. The shear modulus reduction and material damping ratios used in the equivalent-linear analysis are presented in Figures 2 and 3 (not available currently).
Three different depths to stiff soil (namely 50 ft, 100 ft and 150 ft) were considered in the analyses to account for possible variations in the thickness of soft soil layers in the three areas. Table 4 lists the characteristics of the six different soft soil profiles used in the site response analyses.
|Profile No.||Soil Type||Depth to Firm Ground
|Average Shear Wave Velocity (fps)||NEHRP|
One of the main concerns in performing ground response analyses of soft sites using the SHAKE program is the validity of the equivalent linear procedure used by SHAKE to model soil response at high shearing strains. In anticipation of the high design ground motions developed for this study coupled with the soft soil profiles, a number of non-linear site response analyses were performed using the computer code SUMDES developed by University of California, Davis (Li et. al. 1992)
The purpose of the non-linear analyses was to provide a comparison of the ground motion computed using the standard-of-practice procedure (i.e. SHAKE) with the more advanced state- of-the-art non-linear approach at levels of shearing strain beyond which the SHAKE approach may be inappropriate. From these comparisons, a determination could be made of the level of ground motion beyond which results from SHAKE analyses may be inappropriate.
The non-linear site response analyses were performed with records from all three locations. Each of the six soil profiles was analyzed with four horizontal components (two stations) using the three depths (i.e., 50 ft, 100 ft, and 150 ft) and two profile stiffness (S1 and S2). The four components used in the non-linear analyses were selected based on the time history's duration and amplitude. Each was representative of a freefield motion. The selected records are listed below.
The soil properties used in SUMDES were kept the same as those used in the corresponding SHAKE analyses. The only additional information needed by SUMDES were the strengths for the soft clay layers. The range of undrained shear strengths used for the S1 and S2 profiles are listed in Table 6.
In addition to performing the non-linear analysis using the selected motions identified above, a limited number of analyses were also performed with motions scaled to a peak ground motion of about 0.05g. The purpose of these low level acceleration analyses was to calibrate and check the SUMDES results against SHAKE results under similar conditions (i.e., when non-linear effects are small). At low levels of acceleration, the SHAKE and SUMDES models should respond in the near elastic range and thus should produce very similar results, which they did.
This section describes each set of ground motion time histories. For each set, the following documentation of the time histories is provided:
1. A table listing and describing the time histories, including the factor by which the time history was scaled, and for Boston and Seattle, the further scale factor needed to match the response spectrum of the scaled time histories to the target spectrum at 4 seconds period. The 2% in 50 years, 10% in 50 years, 50% in 50 years, and near-fault time histories are listed in Tables 7 through 10 respectively (not available currently).
2. Acceleration response spectra at 5% and 2% damping of individual time histories. For the probabilistic time history sets (2% in 50 years; 10% in 50 years; 50% in 50 years), the spectra are shown with the target values for site category SD for 5% damping.
3. Summary acceleration response spectrum at 5% damping showing all horizontal components, their median, 84th and 16th percentile spectra, and the target values where relevant. A similar plot is shown for the vertical component, which was also scaled by the horizontal scale factor.
4. Summary displacement response spectra at 5% and 2% damping for all horizontal components.
5. Acceleration, velocity and displacement time histories
6. Acceleration, velocity and displacement Arias intensity plots
Ten time histories each for Boston, Seattle and Los Angeles for 10% in 50 years are provided. The time histories for Los Angeles are all derived from recordings of crustal earthquakes on soil category SD. Most of the recorded time histories were scaled up by factors between 1 and 3 to match the target values. Two recordings of the magnitude 7.3 Landers earthquake of 1992 at distances of about 40 km are included to represent large earthquakes on the San Andreas fault at a comparable distance from Los Angeles. The other eight time histories are near-fault recordings of strike-slip, oblique and thrust earthquakes in the magnitude range 6 to 7.
The time histories for Seattle are all derived from recordings on soil category SD. Two recordings from the magnitude 8 Valparaiso earthquake of 1985 are included to represent large subduction earthquakes on the Cascadia plate interface. Two recordings of the magnitude 6.5 Olympia earthquake of 1949 and three recordings of the magnitude 7.1 Seattle earthquake of 1965 are included to represent earthquakes within the Wadachi-Benioff zone beneath the Puget Trough. Although the scale factors for these five recordings ranged as high as 9, the shapes of the response spectra of the individual records are a good match to the target shape. The three recordings from crustal earthquakes in the magnitude range 6.2 to 6.5 are included to represent crustal faults such as the Seattle fault.
The time histories for Boston are derived from both recorded and simulated time histories. The set includes one soil site recording and three modified rock site recordings of the magnitude 5.9 Saguenay earthquake of 1988. The three rock site recordings have spectral shapes at short periods that resemble soft rock more closely than hard rock, so no additional adjustment at short periods was necessary. All four recordings required scaling up. The only available closer recording of an earthquake in eastern North America was from the magnitude 4.3 New Hampshire of 1982, which required a scale factor of about 10. All five of these scaled recordings have unrealistically high short perod spectra. To augment the sparse recordings available from eastern North America, we used three recordings of the magnitude 6.9 Nahanni, Northwest Territories, earthquake of December 1985, which occurred near the boundary between the tectonically stable and active regions of North America. These recordings, which are from rock sites, are from a larger magnitude and from closer distances than those that dominate the hazard at Boston at 10% in 50 years, and required scaling down. To augment these recordings, we included two broadband simulations of a magnitude 6.5 earthquake at a distance of 30 km. A wide range of scaling factors was needed to scale the selected time histories to the target spectrum. The shapes of the response spectra of the individual records do not closely match the target shape, which is controlled by large magnitudes at large distances.
The time histories for each location include both recorded and simulated time histories, and in each location some of the time histories have been derived from recordings on rock sites. For the Los Angeles set, all of the time histories are from near-fault recordings or simulations, and the scale factors required to match the response spectra to the target spectra for 2% in 50 years are relatively close to unity. The recorded time histories are from the 1974 Tabas, 1989 Loma Prieta, 1994 Northridge and 1995 Kobe earthquakes. The simulated time histories are for magnitude 7.1 earthquakes on the Palos Verdes fault (a strike-slip fault), and on the Elysian Park fault (a blind thrust fault).
The time histories for Seattle are all derived from recordings on soil category SD. Two recordings from the magnitude 8 Valparaiso earthquake of 1985 are included to represent large subduction earthquakes on the Cascadia plate interface. These are augmented by simulations of magnitude 8 earthquakes occurring having both shallow and deep depth ranges on the plate interface. The Olympia recordings of the magnitude 6.5 Olympia earthquake of 1949 and the magnitude 7.1 Seattle earthquake of 1965 are included to represent earthquakes within the Wadachi-Benioff zone beneath the Puget Trough. Although these two records required large scale factors, the shapes of the response spectra of the individual records are a good match to the target shape. The Petrolia recording of the magnitude 7.1 Cape Mendocino earthquake of 1992 and the Erzincan record of the magnitude 6.7 Erzincan earthquake of 1992 are included to represent crustal faults such as the Seattle fault.
The time histories for Boston are derived from both recorded and simulated time histories. The set includes one soil site recording and three modified rock site recordings of the magnitude 5.9 Saguenay earthquake of 1988. The three rock site recordings have spectral shapes at short periods that resemble soft rock more closely than hard rock, so no additional adjustment at short periods was necessary. All four recordings required large scaling factors, producing unrealistically large short period motions. To augment the sparse recordings available from eastern North America, we used three recordings of the magnitude 6.9 Nahanni, Northwest Territories, earthquake of December 1985, which occurred near the boundary between the tectonically stable and active regions of North America. These recordings, which are from rock sites, are from a larger magnitude and from closer distances than those that dominate the hazard at Boston at 10% in 50 years, and required scaling down. To augment these recordings, we included two broadband simulations of a magnitude 6.5 earthquake at a distance of 30 km. A wide range of scaling factors was needed to scale the selected time histories to the target spectrum. The shapes of the response spectra of the individual records do not closely match the target shape, which is controlled by large magnitudes at large distances.
The time histories for Los Angeles are all derived from recordings of crustal earthquakes on soil category SD. The time histories are derived from earthuakes in the magnitude range 5.7 to 7.7, and the distance range of about 5 to 100 km. With the exception of the Downey recording of the 1987 Whittier Narrows earthquake, which was scaled up by a factor of about 3.6, none of the recordings required scaling by more than a factor of 3.
A set of 20 ground motion time histories (and elastic response spectra) corresponding to near-source motion on firm ground for strike slip and reverse thrust ruptures was developed for major crustal earthquakes in UBC Seismic Zone 4. Ten of the time histories are recorded ones and ten are simulated ones. The ten recorded ones include some that were recorded on soil conditions different from SD; these were adjusted to SD. These were used in order to include a balance of earthquake faulting mechanisms (strike-slip, oblique and dip-slip) among the strongest near-fault recordings that are available at intermediate and long periods. The simulated time histories are for magnitude 7.1 earthquakes on the Palos Verdes fault (a strike-slip fault), and on the Elysian Park fault (a blind thrust fault whose shallowest depth is 10 km).
The 20 time histories were selected to represent near-fault ground motions from earthquakes having a variety of faulting mechanisms (strike-slip, oblique, and thrust) in the magnitude range of 6 3/4 to 7 1/2. The closest distances for shallow crustal faults lie in the range of 0 to 10 km, and the closest distances for blind thrust faults lie in the distance range of 6 to 18 km. These magnitudes and distance ranges dominate the seismic hazard in Zone 4 for return periods of 10% in 50 years.
The time histories do not represent a statistical sample of such ground motion conditions, and were not scaled to represent a target spectrum. However, the variability among these 20 time histories is representative of the variability in recorded data for a given magnitude, distance and site condition in empirical ground motion models. This is shown in Figure 8, which compares the variability among response spectra of the 20 selected time histories with that of the empirical model of Abrahamson and Silva (1997) for magnitude 7, closest distance 5 km, and soil conditions. The comparison is made separately for the strike-normal, strike-parallel, and average horizontal components, and is also shown separately for the the subsets of recorded and simulated time histories. Although the 20 selected time histories are for a range of magnitudes and distances, they form a set that provides a reasonable representation of the median and variability of the ground motions that a given site may experience from a nearby earthquake of magnitude about 7 and distance about 5 km. As shown in Figure 6, this magnitude-distance pair is representative of that which controls the 10% in 50 year ground motions in many large urban regions of California.
Time histories for soft soil sites were derived from the time histories for 10% in 50 years, site category SD, described in item a. Two different soil profiles that are broadly representative of soft soil conditions were developed, and three thicknesses of each profile (surface to 50, 100, and 200 feet) were taken for analysis to provide three different predominant periods for each profile. Time histories generated for stiff soil conditions were used as input into equivalent linear (Woodward-Clyde's update of SHAKE91; Idriss and Sun, 1992). For each input time history, there are six soft soil time histories (one for each combination of soil profile and depth) from the equivalent linear analyses. The same figure was used for the six profiles to facilitate easy comparison of the results for different soft soil profiles for the same earthquake record.
Selected time histories are also being generated using nonlinear (SUMDES; Li et al., 1992) soil response analyses to produce time histories for soft soil conditions. The soft soil time histories and response spectra generated using nonlinear analyses will be described in an addendum to this report.
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Graves, R.W. (1996). Modification of the Lucerne time history of the 1992 Landers earthquake to include geodetically defined static displacements. Unpublished manuscript reproduced following near-fault time history plots.
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