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Development of site-specific design ground motions in Western and Eastern North America
Soil Dynamics and Earthquake Engineering 22 (2002) 755–764 www.elsevier.com/locate/soildyn
Development of site-specific design ground motions in Western and Eastern North America Walter Silvaa,*, Carl Costantinob a
Pacific Engineering Analysis, El Cerrito, CA, USA City University of New York, New York, NY, USA
b
Abstract This paper presents results recently obtained for generating site-specific ground motions needed for design of critical facilities. The general approach followed in developing these ground motions using either deterministic or probabilistic criteria is specification of motions for rock outcrop or very firm soil conditions followed by adjustments for site-specific conditions. Central issues in this process include development of appropriate attenuation relations and their uncertainties, differences in expected motions between Western and Eastern North America, and incorporation of site-specific adjustments that maintain the same hazard level as the control motions, while incorporating uncertainties in local dynamic material properties. For tectonically active regions, such as the Western United States (WUS), sufficient strong motion data exist to constrain empirical attenuation relations for M up to about 7 and for distances greater than about 10 – 15 km. Motions for larger magnitudes and closer distances are largely driven by extrapolations of empirical relations and uncertainties need to be substantially increased for these cases. For the Eastern United States (CEUS), due to the paucity of strong motion data for cratonic regions worldwide, estimation of strong ground motions for engineering design is based entirely on calibrated models. The models are usually calibrated and validated in the WUS where sufficient strong motion data are available and then recalibrated for applications to the CEUS. Recalibration generally entails revising parameters based on available CEUS ground motion data as well as indirect inferences through intensity observations. Known differences in model parameters such as crustal structure between WUS and CEUS are generally accommodated as well. These procedures are examined and discussed. q 2002 Elsevier Science Ltd. All rights reserved. Keywords: Site response; Soil Hazards; Soil nonlinear properties; Point source rock motions
1. Introduction Due to the low rates of seismicity, a significant and currently unresolvable issue exists in the estimation of strong ground motion for given magnitude, distance and site conditions in Central and Eastern United States (CEUS). In general, the preferred approach to estimating ground motion is through the use of empirical attenuation relations, perhaps augmented with model based relations to capture regional influences. For Western United States (WUS), particularly California, seismicity rates are such that sufficient strong motion recordings are generally available to properly constrain regression analyses, except at close distances (, 10 km) for large magnitude events (M . 6.75). For CEUS, however, very little data is available and most are for relatively small events (M , 5.8) at relatively long * Corresponding author. E-mail addresses: [email protected] (W. Silva), [email protected] (C. Costantino).
distances exceeding 50 km. This may be fortunate in terms of seismic hazard but, since the potential exists for large though infrequent earthquakes to occur in CEUS, the risk to life and structures (particularly critical facilities) may be comparable to that which exists in the more seismically active WUS. As a result, significant effort has been directed to developing attenuation relations for CEUS conditions using numerical simulations to attempt to characterize these relations. Essential elements in this approach include using a physically realistic and well-validated model, selection of appropriate parameter values and their distributions and using a statistically stable estimate of model variability to account for uncertainty effects. This paper is intended to summarize this process and the results generated recently for the Nuclear Regulatory Commission to estimate ground motions considered appropriate for use in design of critical facilities in both WUS and CEUS. Recent observations of both small and intermediate magnitude earthquakes which have occurred in CEUS have shown larger peak accelerations as well as high frequency
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spectral content (5 – 10 Hz) than would be expected based on recordings available from WUS events [1]. In addition to these observations at high frequencies, intermediate magnitude (M , 6.2) earthquakes have shown an opposite trend at intermediate and low frequencies (below about 2 Hz), having lower motions than comparable WUS recordings would suggest [2]. This latter observation, in terms of strong ground motions, is principally limited to the 1988 M5.8 Saguenay, Canada earthquake but is supported by inferences from intensity data [3], regional seismograms (D , 1000 km) of early instrumental recordings in ENA and teleseismic data of worldwide intraplate earthquakes [4]. The following discussion is intended to illustrate the differences between WUS and CEUS rock site motions and to suggest the physical bases for the differences.
2. CEUS and WUS strong ground motions at rock sites Observations of strong ground motion due to small magnitude earthquakes occurring in ENA, although not causing damage to reasonably engineered structures, have shown considerably higher peak accelerations than would have been expected based upon WUS experience [5]. In addition to the relatively higher peak accelerations associated with these CEUS events, response spectral ordinates appear richer in high frequency energy, particularly for frequencies exceeding about 10 Hz [6]. It has been known for some time that ground motion for CEUS attenuate less rapidly with distance than ground motion in WUS for events of similar moment magnitudes and source depths [7]. The difference in attenuation rate has been attributed to the higher absorptive characteristics generally present in the crust and upper mantle beneath WUS as compared to CEUS [8]. Other sources of data also indicate that CEUS ground motions, recorded at rock or very shallow soil sites, are richer in high frequency energy relative to analogous WUS ground motions. These include aftershocks of the 1982 Miramichi, New Brunswick earthquake, the 1982 Enola, Arkansas swarm, aftershocks of the 1986 Painesville, Ohio event, the 1985 Nahanni earthquakes, the 1982 New Hampshire earthquake, and the M5.8 1988 Saguenay earthquakes. The trends shown in these CEUS data indicate significantly higher spectral content at high frequencies compared to WUS rock motion of comparable magnitudes and distances. 2.1. Effects of shallow crustal damping and site amplification The difference in spectral content can perhaps be most easily seen in spectral amplifications (Sa/a) computed from recordings typical of WUS and CEUS tectonic environments. Fig. 1 shows average spectral shapes (Sa/a)
Fig. 1. Comparison of response spectral shapes (Sa/amax at 5% damping) between WUS (solid lines) and CEUS (dashed lines) crustal conditions for earthquakes recorded at rock sites: M6.75 (a) and M5.25 (b).
computed on rock at relatively close distances (, 25 km) for magnitudes of approximately 6.75 and 5.25 for WUS and CEUS. The differences are significant and indicate that CEUS spectral content is higher than that in WUS for frequencies greater than approximately 10 Hz. The controlling mechanism for the differences in high frequency spectral content (at close distances) between WUS and CEUS ground motions is thought to be due to differences in damping in the shallow (1 – 2 km) part of the crust [1]. The parameter which controls the shallow damping is
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termed kappa ( ¼ H/VsQs where H is the thickness of the zone over which the damping is taking place, Vs the average shear wave velocity and Qs the average quality factor over the depth H ). In a recent study, kappa values were estimated by fitting spectral shapes computed from the stochastic ground motion model to shapes computed from motions recorded at rock sites in the CEUS, WUS, Mexico, Italy (Friuli), USSR (Gazli), and Taiwan (SMART1). Rock sites characterized as soft, such as sedimentary, showed significantly higher kappa values than those characterized as hard, e.g. crystalline basement. Hard and soft rock sites may exist in either WUS or CEUS. However, on the average, sites in stable cratonic regions are more likely to be classified as hard while those associated with active tectonic regions are more likely to be soft. An example of generic crustal models reflecting typical WUS soft rock and CEUS hard rock crustal conditions is shown in Fig. 2 for both P and S wave velocities. The CEUS model is the midcontinent structure from Ref. [8] and is considered appropriate for strong ground motion propagation in CEUS except for the Gulf Coast region. The WUS model reflects an average of several California crustal models [9] representing the most seismically active regions, the north coast and peninsular range areas. The shallow portion of the WUS crustal model structure is based on velocities measured at strong motion rock sites and shows low near surface P and S wave velocities [1]. The differences in the shallow crustal velocities between the WUS and CEUS models are striking, particularly over the top 2– 3 km, and its effects on strong ground motions are
Fig. 2. Comparison of generic rock velocity profiles for WUS [9] and CEUS [8] crustal conditions.
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profound. In terms of amplification from source regions below about 5 km to the surface, the differences between hard (CEUS) and soft (WUS) crustal conditions results in a difference of a factor close to 3 in amplification for frequencies exceeding about 5 Hz. All else being equal, WUS high frequency ( f . 5 Hz) ground motions would then be expected to be nearly three times larger than corresponding CEUS motions. As suggested earlier however, pervasive observations reflect the converse; that is, high frequency CEUS motions generally exceed comparable WUS motions. Damping in the shallow crust, parameterized through kappa, is much greater in soft crustal rocks resulting in a dramatic loss in high frequency energy content compared to hard rock conditions. On average, kappa values for the WUS are about five times large than the CEUS (0.037 and 0.008 s). Soft rock conditions are reflected in higher kappa values and corresponding lower P and S wave velocities. The lower velocities result in larger amplification, counteracting the effects of increased damping resulting from larger kappa values. 2.2. Effects of source processes Another issue of consideration regarding the differences in spectral composition between WUS and CEUS strong ground motions at rock sites is the probable differences in earthquake source processes. Prior to the occurrence of the 1998 M5.8 Saguenay earthquake, there was thought to be a difference of about two in stress drop between WUS and CEUS sources with the CEUS having larger values, about 100 bar compared to about 50 bar [10]. These measures of stress drop are primarily based on high frequency ground motion levels assuming a single-corner frequency source model. Apart from the differences in stress drop, the overall source processes were thought to be similar in both tectonic regimes. The stochastic single-corner-frequency pointsource model [11], provides accurate predictions of WUS strong ground motions using a stress drop of about 50 bar [1] although with a tendency to overpredict low frequency (, 1 Hz) motions for large magnitude earthquakes. For the CEUS, the simple point-source model with a stress drop of about 100 bar, about double that of the WUS, provided good agreement with existing data until the occurrence of the 1988 M5.8 Saguenay earthquake. Strong ground motions from this earthquake, the largest to have occurred in the CEUS in over 50 years, depart significantly from predictions of the simple 100 bar stress drop model. The stress drop required to match high frequency strong ground motions for this earthquake exceed 500 bar, while the intermediate frequency spectral levels are overestimated by a factor of two or more, requiring a significantly lower stress drop. Concurrently, using low frequency teleseismic data (, 2 Hz), it was shown [4] that the source spectra of large intraplate earthquakes differ in general from the simple single-corner-frequency omega-square model, showing the presence of a second corner frequency.
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Based on the limited ground motion data in the CEUS as well as inferences on intensity observations developed an empirical two-corner source model for CEUS earthquakes [3]. This two-corner model currently provides unbiased estimates of recorded CEUS ground motions over the frequency range of the majority of the data, about 10.0 – 0.1 Hz, while the single-corner-frequency model, with stress drops ranging from about 120– 150 bar, overpredicts low frequency ground motions in the frequency range of about 1– 0.1 Hz but is unbiased in the 2 –10 Hz frequency range. Both the double and single corner source models, with actual or implied stress drops below 200 bar, underpredict the high frequency (. 2 Hz) ground motions for the Saguenay earthquake by factors of 2 –3 suggesting anomalous high frequency levels for this event. While it currently appears that a two-corner source model may be the more appropriate model for CEUS strong ground motions, it is evident that in predicting strong ground motions for engineering design, significantly more variability should be accommodated in applications to the CEUS than to the WUS. This increased variability should accommodate both randomness (aleatory variability) in stress drop above that for the WUS as well as uncertainty (epistemic variability) in the source model.
3. Comparisons of WUS and CEUS spectral shapes at rock sites Comparisons of WUS to CEUS response spectra are shown in Fig. 3 for shapes and absolute spectra, respectively. Also illustrated in the figure are the differences between the single and double corner source spectral models. For the shapes, the difference in spectral composition between the WUS and CEUS single corner models (solid lines) is clearly illustrated in the maximum spectral amplifications: about 5 Hz for WUS and 40 Hz for CEUS. The difference between the single and double corner source models (solid verses dashed lines) is also clearly illustrated. For the WUS, the difference is mainly at low frequency and is not large, about 20% near 0.3 Hz. For the CEUS, the single corner source model significantly exceeds the double corner below about 2 Hz. The largest difference occurs near 0.4 Hz and is a factor of over 3 in 5% damped spectral acceleration. Choices between the two shapes for the CEUS, single or double corner, clearly have major impacts on design motions. Considering absolute spectra, the WUS and CEUS single corner spectral estimates are nearly the same for frequencies up to about 5 Hz. This is the result of compensating effects previously discussed, that is, higher stress drop for CEUS and larger amplification factors for WUS. Beyond about 5 Hz, the differences in kappa values (0.04 s as compared to 0.006 s) result in the differences in high frequency spectral estimates. To see how well the simple point-source models (single and double corner frequency) capture the differences in
Fig. 3. Response spectra and spectral shapes (for 5% damping) computed for M6.5 at R ¼ 25 km using both single and double corner source spectra for WUS and CEUS parameters.
shapes between WUS and CEUS rock motions, comparison of predictions with statistical shapes generated from recorded data are shown in Fig. 4. For WUS sites, both models capture the overall shape reasonably well but
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spectral models capture the difference in shape between WUS and CEUS equally well with the single corner frequency model showing an overprediction at low frequency (, 1 Hz) similar to the WUS. Interestingly, the double corner model shows an underprediction for frequencies below about 2 Hz. Since this is only a single earthquake and variability is large in CEUS strong ground motions, these results may not reflect a potential bias in the model for spectral shapes but do suggest the spectral sag may be too extreme and emphasize the current state of uncertainty regarding CEUS strong ground motions. These comparisons to CEUS statistical shapes point out the quandary in estimating strong ground motions in the CEUS. Sufficient recordings at close distances (, 50 km) for earthquakes of engineering significance (M . 5) are not available to unequivocally distinguish between plausible models.
4. Site-specific soil motions incorporating profile uncertainties
Fig. 4. Comparison of 5% damped statistical spectral shapes for M6.75 on rock at 30.8 km for WUS (a) and CEUS (b) single and double corner predictions.
overpredict at low frequency (below 1 – 2 Hz). The double corner model provides a better fit but still shows overprediction in this magnitude range. For the CEUS, there is only one earthquake, 1985 Nahanni, with hard rock site recordings (three stations) in this distance range. Both
The conventional approach to developing site-specific soil motions involves convolution analysis, either equivalent-linear or fully nonlinear, using rock outcrop control motions at the soil/rock transition zone. For bottomless profiles the rock control motions may be input at a sufficiently deep location such that soil amplification extends to the lowest frequency of interest, about 0.5 Hz (generally about 500 ft for motions adequate to a lowfrequency limits of about 0.5 Hz [12]. In the convolutional analyses, uncertainty in dynamic material properties is generally accommodated through parametric variations, either deterministically with upper-, mid-, and lower-range moduli or through a Monte Carlo approach using randomly generated properties using statistically based distributions. Uncertainties in soil properties and in model deficiencies (in the convolutional formulation) are accommodated by either smoothly enveloping the deterministic variations or selecting a fractile level, generally the mean, for the Monte Carlo approach. Both these procedures appear to result in conservative spectral estimates since site variability is already accommodated in the variability associated with the attenuation relations used in developing the control (rock) motions. The approach which uses randomized material properties is preferred since the conservatism is quantified, provided the parameter distributions reflect a realistic assessment of how well the base case profile and nonlinear properties are known (epistemic uncertainty) as well as the variability over the site or footprint of the structure (aleatory uncertainty). A motivation for using the more conservative mean rather than median spectral estimates, which acknowledges double counting site variability to some extent, is to accommodate a degree of model uncertainty [9] (vertically propagating shear-waves and equivalent-linear approximation) in the convolutional
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formulation. Since this component of model uncertainty is currently unquantified, it is not possible to add it explicitly. It is however, thought to be relatively small, based on validation exercises of a complete model. As a result, the possible double counting of site variability may be largely offset by neglecting the deficiencies in the convolutional formulation. For attenuation relations based solely on validated stochastic point- or finite-source models the inclusion of model uncertainty accommodates the site model deficiencies for the vertically propagating shearwave model using the equivalent-linear approximation. The various approaches to developing hazard-consistent site-specific soil spectra in increasing order of accuracy are shown in Table 1. Approach 1 involves driving the soil column with the broad rock UHS spectrum (control motions) and may result in unconservative high frequency motions, particularly when using equivalent-linear site response analyses. Additionally, the appropriate magnitude and time history duration are ambiguous using Approach 1 for hazard environments which do not result in strongly unimodal M and R disaggregations. Approach 2A recognizes that different earthquakes may dominate the high and low frequencies, and uses separate transfer functions for these events. The use of multiple rock shapes scaled to the UHS at high and low frequencies is consistent with Regulatory Guide 1.165 [13] although not explicitly stated. In Approach 2B, mean, high and low percentile magnitudes from disaggregations for each design earthquake (e.g. 1 and 10 Hz) are used to scale spectral shapes to the 1 and 10 Hz rock UHS, and the resulting control motions are used to develop weighted mean transfer functions for Table 1 Approaches for developing hazard consistent soil motions Approach 1
Rock UHS used as control motions Approach 2A Use scaled 1 and 10 Hz design earthquakes as control motions to develop 1 and 10 Hz soil motions (R.G. 1.165 approach) or develop transfer function for 1 and 10 Hz design earthquakes, using a single control motion (scaled shape) for each frequency, the envelope of the two transfer functions is then used to scale the rock UHS Approach 2B Develop weighted mean transfer functions for 1 and 10 Hz design earthquakes accommodating magnitude distributions, the envelope of the two mean transfer functions is then used to scale the rock UH Approach 3 Approximations to UHS integrations Approach 4 UHS computed using site-specific soil attenuation relations
each design earthquake. The transfer functions are then used to scale each design earthquake or are combined to scale the rock UHS. The use of a three-point magnitude distribution for each design earthquake better accounts for nonlinear effects that may be caused by a wide range of earthquake magnitudes contributing to the hazard. Approach 3 involves approximations to the hazard integration using suites of transfer functions based on randomized soil profiles. Its development is recent [14] and it has been implemented at the DOE Savannah River Site [15]. In this approach, complete hazard curves may be generated as it is a direct approximation to Approach 4, essentially substituting suites of transfer functions in place of the site-specific soil attenuation relation. The approach is attractive, although requiring significant computations in site response and hazard disaggregation and necessarily counts the site uncertainty twice, once in the aleatory variability about the rock attenuation relations and again in the randomized site-specific dynamic material properties. The approximations implemented in the hazard integrations have been evaluated for a limited number of profiles and loading conditions and further evaluations are needed for ranges in site conditions, hazard environments, and nonlinear dynamic material properties before it can be implemented in practice. In Approach 4, a site-specific soil attenuation relation is used in the hazard analysis. This approach assumes that appropriate parametric variations are incorporated in the development of the attenuation relation and that they are also reflected in the uncertainty about the median ground motions [12]. 4.1. Approaches for vertical motions Assessment of site-specific soil vertical motions to accompany corresponding horizontal motions is a perplexing issue, particularly if it is desirable to maintain hazard consistency with the horizontal motions. Rarely are separate hazard analyses performed for horizontal and vertical control or rock outcrop motions (currently no vertical relations are available for the CEUS) and there are no widely accepted site response methodologies currently available to accommodate vertical analyses. Commonly, equivalent-linear site response analyses for vertical motions have used strain iterated shear moduli from a horizontal motion analysis to adjust the compression-wave velocities assuming either a strain independent Poisson’s ratio or bulk modulus. Some fraction (generally 30 – 100%) of the strain iterated shear-wave damping is used to model the compression-wave damping and a linear analyses is performed for vertically propagating compression waves using the horizontal control motions scaled by some factor near 2/3. Alternatively, fully nonlinear analyses can be made using two- or three-component control motions [8,16]. These nonlinear analyses require two- or three-dimensional soil models which describe plastic flow and
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yielding and the accompanying volume changes as well as coupling between vertical and horizontal motions through Poisson’s effect. While these analyses are important to examine expected dependencies of computed motions on material properties and may have applications to the study of soil compaction, deformation, slope stability, and component coupling, the models are very sophisticated and require specification of many parameters, at least some of which are difficult to measure both in mean or central values as well as expected ranges (uncertainties). The approach recommended here makes use of generic soil V/H ratios to scale the site-specific horizontal soil motions. It is intended to maintain as many site-specific attributes as possible through the use of the horizontal soil motions (soil column) and generic soil V/H ratios (controlling magnitudes and distances) while avoiding the currently inherent ambiguity in vertical site response analyses.
5. Example results for WUS and CEUS soil sites Section 4 presents a number of approaches to estimating site-specific soil spectra that are consistent with a specified hazard level that accommodate uncertainties in soil properties. In this section, comparisons are made among several of these approaches, and site-specific soil UHS are computed for a soft (Imperial Valley, California) soil profile located in the WUS (Mojave, California) and a relatively stiff soil profiles located in the CEUS (Charleston) tectonic environments. The site-specific soil UHS reflect the desired hazard level with which to evaluate the various degrees of approximations using rock outcrop UHS and site response analyses. However, an issue exists in the soil UHS calculated with Approach 4 involving long return periods where the hazard may result from motions that significantly exceed the median ground shaking during earthquakes contributing to the hazard. Under these conditions for highly nonlinear profiles, the site-specific UHS may overestimate the hazard at high frequency, as the residual dispersion in the site-specific attenuation relation(s) does not reflect the soils limited capacity to transmit high levels of motion (i.e. its nonlinearity). This is an important issue and requires further elaboration. 5.1. Horizontal motions The scaled (and corrected WUS) bedrock outcrop earthquake spectra are shown in Fig. 5 for the WUS and CEUS, respectively. The difference in the hazard environments between the WUS and CEUS is evident in the large differences in 1 and 10 Hz magnitude distributions. The difference in magnitudes for the 1 and 10 Hz design earthquakes is 1.3 units for the CEUS and only 0.6 units for the WUS. The potential effects of magnitude distribution in the rock UHS on nonlinear soil
Fig. 5. Rock outcrop spectra (uniform hazard, 1 and 10 Hz) for WUS (a) and CEUS (b) for example soil site response analyses.
response are much less an issue for WUS conditions than CEUS, at least for these example sites. The Imperial Valley Meloland profile is considered a soft profile and has a column frequency of about 0.5 Hz. While it is considered ‘bottomless’ and extends kilometers in depth,
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it was truncated at a depth of 1000 ft for these analyses. It is the location of a recently installed (Caltrans/CDMG) vertical strong motion array and the nearby CDMG strong motion site recorded the M6.5 1979 Imperial Valley earthquake at a rupture distance of 0.5 km (average horizontal component peak acceleration of about 0.3 g). The soil modulus reduction and damping curves used for site convolutions are based on modeling strong motions from the 1979 Imperial Valley earthquake recorded at Meloland and nearby sites and reflect relatively weak strain dependencies. The profile is considered nonlinear to a depth of 500 ft. The Savannah River generic profile was adopted from measured shear-wave velocity profiles at the DOE Savannah River site. The profile is generally stiff but does have a broad soft zone at intermediate depths (around 25 m) with a steep gradient thereafter. The low-strain column resonance is near 0.8 Hz. G/Gmax and hysteretic damping curves based on modeling strong ground motions in the Los Angeles area recorded at cohesionless soil sites from the M6.7 1994 Northridge earthquake are used for this site. Fig. 6 shows the soil UHS computed using Approaches 1, 2A, 2B, and 4. For the WUS soil site, similar results are obtained for Approaches 2A and 2B, both of which show higher motions than Approach 1 for frequencies above about 1 Hz. The soil column is being softened more by the rock UHS (Approach 1) than by either of the scaled design spectra. In general either Approach 2A or 2B adequately reflects the motions of Approach 4 (soil UHS) from about 0.3– 100 Hz (PGA). In this case, little difference is seen in Approaches 2A and 2B and either may be used. Approach 1 is not recommended. For the CEUS (Savannah River generic profile), Approach 1 again underestimates the soil UHS at the higher frequencies while Approaches 2A and 2B are generally slightly above the UHS, except at very low frequency. Approaches 2A and 2B are nearly identical and both are conservative (above 10 Hz) while Approach 2B remains closer to the soil UHS at very low frequency (, 0.4 Hz). Cyclic shear strain (effective) levels are much lower for the CEUS site than the corresponding WUS site. Maximum median strains developed in the soft zone have values near 2 £ 1022% compared to about 0.3% for the WUS Meloland profile. The loading levels are much lower and the profile is significantly stiffer. 5.2. Vertical motions To estimate vertical soil motions consistent with the horizontal soil motions, a WUS empirical generic soil V/H ratio was developed for M ¼ 6.7 and D ¼ 18 km, based on the rock UHS disaggregation at 1 Hz. The empirical V/H ratio is an average of ratios from empirical WUS data [17,18]. A comparison of the resulting vertical spectrum with the horizontal spectrum is shown in Fig. 7(a). The vertical motions exceed the horizontal between 10 and
Fig. 6. Comparison of soil surface spectra using Approaches 1, 2A, 2B and 4 for WUS (a) and CEUS (b) for example soil sites.
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soil applied to a WUS empirical deep soil V/H ratio. This process results in a generic soil CEUS V/H ratio which is applied to the site-specific horizontal design spectrum. The resulting vertical (unsmoothed) soil design spectrum is shown in Fig. 7(b) along with the horizontal. The exceedance of the vertical spectrum over the horizontal at high frequency ( f . 10 Hz) at this site is larger than normally recommended and indicates the greater uncertainty in predicting vertical responses.
Acknowledgments Support for this work was provided by Nuclear Regulatory Commission under the direction of Roger Kenneally. Careful reviews by Dave Boore, Nilesh Chokshi, Allin Cornell, I.M. Idriss, Robert Rothman, Robert Kennedy, Carl Stepp, Roger Kenneally, Buck Ibraham, and Robert Darragh contributed substantially to the quality of the work and are gratefully acknowledged. References
Fig. 7. Horizontal and vertical soil design spectra corresponding to 1024 per exceedance probability rock outcrop UHS for WUS (a) and CEUS (b) example soil sites.
20 Hz due to the close distance (18 km) and large magnitude (M6.7) [8]. The approach used to develop site-specific vertical motions for the CEUS site relies on modeling results to produce WUS-to-CEUS V/H scale factors for deep
[1] Silva WJ, Darragh R. Engineering characterization of earthquake strong ground motion recorded at rock sites. Report TR-102261. Electric Power Research Institute, Palo Alto, CA, 1995. [2] Boore DM, Atkinson GM. Source spectra for the 1988 Saguenay, Quebec earthquakes. Bull SSA 1992;82(2):683–719. [3] Atkinson GM. Source spectra for earthquakes in eastern North America. Bull SSA 1993;83(6):1778 –98. [4] Boatwright J, Choy G. Acceleration source spectra anticipated for large earthquakes in Northeastern North America. Bull SSA 1992;82: 660–82. [5] Munro PS, Weichert D. The Saguenay earthquake of November 25, 1988. Processed strong motion records, Geological Survey of Canada Open File/Dossier Public 1996, 1989. [6] Borcherdt RD. Preliminary report on aftershock sequence for earthquake of January 31, 1986 near Painesville, Ohio. US Geological Survey Open File Report 86-181, 1986. [7] Atkinson GM, Boore DM. Ground motion relations for eastern North America. Bull SSA 1995;85(1):17– 30. [8] Electric Power Research Institute. Guidelines for determining design basis ground motions. EPRI TR-102293. Electric Power Research Institute, Palo Alto, CA, 1993, vol. 1– 5. [9] Silva WJ, Abrahamson N, Toro G, Costantino CJ. Description and validation of the stochastic ground motion model, Nuclear Energy Department Brookhaven National Laboratory, Associated Universities, Inc. Upton, New York, 1997. [10] Atkinson GM. Attenuation of strong ground motion in Canada from a random vibrations approach. Bull SSA 1984;74(5):2629–53. [11] Schneider JF, Silva WJ, Stark CL. Ground motion model for the 1989 M6.9 Loma Prieta earthquake including effects of source, path and site. Earthquake Spectra 1993;9(2):251– 87. [12] Silva WJ, McGuire R, Costantino CJ. A comparison of site specific soil UHS to soil motions computed with rock UHS. Proceedings of OECD-NEA Workshop on Engineering Characterization of Seismic Input, November 15–17, NEA/CSNI/R, 2000, 2, vol. 2, 1999. p. 397 –504. [13] USNRC. Identification and characterization of seismic sources and determination of safe shutdown earthquake ground motion. US Nuclear Regulatory Commission, Regulatory Guide 1.165, March 1997.
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[14] Bazzurro P, Cornell CA, Pelli F. A site- and soil-specific PSHA for nonlinear soil sites. Proceedings of the 4th EQ. Resist. Design Structures Conference (ERES99). Catania, Italy, June 15– 17, 1999. [15] Lee R. Personal communication, 1998. [16] Costantino CJ. Two dimensional wave propagation through nonlinear media. J Comput Phys 1969;4:2.
[17] Abrahamson NA, Silva WJ. Empirical response spectral attenuation relations for shallow crustal earthquakes. Seismol Res Lett 1997; 68(1):94–127. [18] Campbell KW. Empirical nearsource attenuation relationships for horizontal and vertical components of peak ground acceleration, peak ground velocity, and pseudoabsolute acceleration response spectra. Seismol Res Lett 1997;68(1):154 –79.
Development of site-specific design ground motions in Western and Eastern North America Walter Silvaa,*, Carl Costantinob a
Pacific Engineering Analysis, El Cerrito, CA, USA City University of New York, New York, NY, USA
b
Abstract This paper presents results recently obtained for generating site-specific ground motions needed for design of critical facilities. The general approach followed in developing these ground motions using either deterministic or probabilistic criteria is specification of motions for rock outcrop or very firm soil conditions followed by adjustments for site-specific conditions. Central issues in this process include development of appropriate attenuation relations and their uncertainties, differences in expected motions between Western and Eastern North America, and incorporation of site-specific adjustments that maintain the same hazard level as the control motions, while incorporating uncertainties in local dynamic material properties. For tectonically active regions, such as the Western United States (WUS), sufficient strong motion data exist to constrain empirical attenuation relations for M up to about 7 and for distances greater than about 10 – 15 km. Motions for larger magnitudes and closer distances are largely driven by extrapolations of empirical relations and uncertainties need to be substantially increased for these cases. For the Eastern United States (CEUS), due to the paucity of strong motion data for cratonic regions worldwide, estimation of strong ground motions for engineering design is based entirely on calibrated models. The models are usually calibrated and validated in the WUS where sufficient strong motion data are available and then recalibrated for applications to the CEUS. Recalibration generally entails revising parameters based on available CEUS ground motion data as well as indirect inferences through intensity observations. Known differences in model parameters such as crustal structure between WUS and CEUS are generally accommodated as well. These procedures are examined and discussed. q 2002 Elsevier Science Ltd. All rights reserved. Keywords: Site response; Soil Hazards; Soil nonlinear properties; Point source rock motions
1. Introduction Due to the low rates of seismicity, a significant and currently unresolvable issue exists in the estimation of strong ground motion for given magnitude, distance and site conditions in Central and Eastern United States (CEUS). In general, the preferred approach to estimating ground motion is through the use of empirical attenuation relations, perhaps augmented with model based relations to capture regional influences. For Western United States (WUS), particularly California, seismicity rates are such that sufficient strong motion recordings are generally available to properly constrain regression analyses, except at close distances (, 10 km) for large magnitude events (M . 6.75). For CEUS, however, very little data is available and most are for relatively small events (M , 5.8) at relatively long * Corresponding author. E-mail addresses: [email protected] (W. Silva), [email protected] (C. Costantino).
distances exceeding 50 km. This may be fortunate in terms of seismic hazard but, since the potential exists for large though infrequent earthquakes to occur in CEUS, the risk to life and structures (particularly critical facilities) may be comparable to that which exists in the more seismically active WUS. As a result, significant effort has been directed to developing attenuation relations for CEUS conditions using numerical simulations to attempt to characterize these relations. Essential elements in this approach include using a physically realistic and well-validated model, selection of appropriate parameter values and their distributions and using a statistically stable estimate of model variability to account for uncertainty effects. This paper is intended to summarize this process and the results generated recently for the Nuclear Regulatory Commission to estimate ground motions considered appropriate for use in design of critical facilities in both WUS and CEUS. Recent observations of both small and intermediate magnitude earthquakes which have occurred in CEUS have shown larger peak accelerations as well as high frequency
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spectral content (5 – 10 Hz) than would be expected based on recordings available from WUS events [1]. In addition to these observations at high frequencies, intermediate magnitude (M , 6.2) earthquakes have shown an opposite trend at intermediate and low frequencies (below about 2 Hz), having lower motions than comparable WUS recordings would suggest [2]. This latter observation, in terms of strong ground motions, is principally limited to the 1988 M5.8 Saguenay, Canada earthquake but is supported by inferences from intensity data [3], regional seismograms (D , 1000 km) of early instrumental recordings in ENA and teleseismic data of worldwide intraplate earthquakes [4]. The following discussion is intended to illustrate the differences between WUS and CEUS rock site motions and to suggest the physical bases for the differences.
2. CEUS and WUS strong ground motions at rock sites Observations of strong ground motion due to small magnitude earthquakes occurring in ENA, although not causing damage to reasonably engineered structures, have shown considerably higher peak accelerations than would have been expected based upon WUS experience [5]. In addition to the relatively higher peak accelerations associated with these CEUS events, response spectral ordinates appear richer in high frequency energy, particularly for frequencies exceeding about 10 Hz [6]. It has been known for some time that ground motion for CEUS attenuate less rapidly with distance than ground motion in WUS for events of similar moment magnitudes and source depths [7]. The difference in attenuation rate has been attributed to the higher absorptive characteristics generally present in the crust and upper mantle beneath WUS as compared to CEUS [8]. Other sources of data also indicate that CEUS ground motions, recorded at rock or very shallow soil sites, are richer in high frequency energy relative to analogous WUS ground motions. These include aftershocks of the 1982 Miramichi, New Brunswick earthquake, the 1982 Enola, Arkansas swarm, aftershocks of the 1986 Painesville, Ohio event, the 1985 Nahanni earthquakes, the 1982 New Hampshire earthquake, and the M5.8 1988 Saguenay earthquakes. The trends shown in these CEUS data indicate significantly higher spectral content at high frequencies compared to WUS rock motion of comparable magnitudes and distances. 2.1. Effects of shallow crustal damping and site amplification The difference in spectral content can perhaps be most easily seen in spectral amplifications (Sa/a) computed from recordings typical of WUS and CEUS tectonic environments. Fig. 1 shows average spectral shapes (Sa/a)
Fig. 1. Comparison of response spectral shapes (Sa/amax at 5% damping) between WUS (solid lines) and CEUS (dashed lines) crustal conditions for earthquakes recorded at rock sites: M6.75 (a) and M5.25 (b).
computed on rock at relatively close distances (, 25 km) for magnitudes of approximately 6.75 and 5.25 for WUS and CEUS. The differences are significant and indicate that CEUS spectral content is higher than that in WUS for frequencies greater than approximately 10 Hz. The controlling mechanism for the differences in high frequency spectral content (at close distances) between WUS and CEUS ground motions is thought to be due to differences in damping in the shallow (1 – 2 km) part of the crust [1]. The parameter which controls the shallow damping is
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termed kappa ( ¼ H/VsQs where H is the thickness of the zone over which the damping is taking place, Vs the average shear wave velocity and Qs the average quality factor over the depth H ). In a recent study, kappa values were estimated by fitting spectral shapes computed from the stochastic ground motion model to shapes computed from motions recorded at rock sites in the CEUS, WUS, Mexico, Italy (Friuli), USSR (Gazli), and Taiwan (SMART1). Rock sites characterized as soft, such as sedimentary, showed significantly higher kappa values than those characterized as hard, e.g. crystalline basement. Hard and soft rock sites may exist in either WUS or CEUS. However, on the average, sites in stable cratonic regions are more likely to be classified as hard while those associated with active tectonic regions are more likely to be soft. An example of generic crustal models reflecting typical WUS soft rock and CEUS hard rock crustal conditions is shown in Fig. 2 for both P and S wave velocities. The CEUS model is the midcontinent structure from Ref. [8] and is considered appropriate for strong ground motion propagation in CEUS except for the Gulf Coast region. The WUS model reflects an average of several California crustal models [9] representing the most seismically active regions, the north coast and peninsular range areas. The shallow portion of the WUS crustal model structure is based on velocities measured at strong motion rock sites and shows low near surface P and S wave velocities [1]. The differences in the shallow crustal velocities between the WUS and CEUS models are striking, particularly over the top 2– 3 km, and its effects on strong ground motions are
Fig. 2. Comparison of generic rock velocity profiles for WUS [9] and CEUS [8] crustal conditions.
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profound. In terms of amplification from source regions below about 5 km to the surface, the differences between hard (CEUS) and soft (WUS) crustal conditions results in a difference of a factor close to 3 in amplification for frequencies exceeding about 5 Hz. All else being equal, WUS high frequency ( f . 5 Hz) ground motions would then be expected to be nearly three times larger than corresponding CEUS motions. As suggested earlier however, pervasive observations reflect the converse; that is, high frequency CEUS motions generally exceed comparable WUS motions. Damping in the shallow crust, parameterized through kappa, is much greater in soft crustal rocks resulting in a dramatic loss in high frequency energy content compared to hard rock conditions. On average, kappa values for the WUS are about five times large than the CEUS (0.037 and 0.008 s). Soft rock conditions are reflected in higher kappa values and corresponding lower P and S wave velocities. The lower velocities result in larger amplification, counteracting the effects of increased damping resulting from larger kappa values. 2.2. Effects of source processes Another issue of consideration regarding the differences in spectral composition between WUS and CEUS strong ground motions at rock sites is the probable differences in earthquake source processes. Prior to the occurrence of the 1998 M5.8 Saguenay earthquake, there was thought to be a difference of about two in stress drop between WUS and CEUS sources with the CEUS having larger values, about 100 bar compared to about 50 bar [10]. These measures of stress drop are primarily based on high frequency ground motion levels assuming a single-corner frequency source model. Apart from the differences in stress drop, the overall source processes were thought to be similar in both tectonic regimes. The stochastic single-corner-frequency pointsource model [11], provides accurate predictions of WUS strong ground motions using a stress drop of about 50 bar [1] although with a tendency to overpredict low frequency (, 1 Hz) motions for large magnitude earthquakes. For the CEUS, the simple point-source model with a stress drop of about 100 bar, about double that of the WUS, provided good agreement with existing data until the occurrence of the 1988 M5.8 Saguenay earthquake. Strong ground motions from this earthquake, the largest to have occurred in the CEUS in over 50 years, depart significantly from predictions of the simple 100 bar stress drop model. The stress drop required to match high frequency strong ground motions for this earthquake exceed 500 bar, while the intermediate frequency spectral levels are overestimated by a factor of two or more, requiring a significantly lower stress drop. Concurrently, using low frequency teleseismic data (, 2 Hz), it was shown [4] that the source spectra of large intraplate earthquakes differ in general from the simple single-corner-frequency omega-square model, showing the presence of a second corner frequency.
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Based on the limited ground motion data in the CEUS as well as inferences on intensity observations developed an empirical two-corner source model for CEUS earthquakes [3]. This two-corner model currently provides unbiased estimates of recorded CEUS ground motions over the frequency range of the majority of the data, about 10.0 – 0.1 Hz, while the single-corner-frequency model, with stress drops ranging from about 120– 150 bar, overpredicts low frequency ground motions in the frequency range of about 1– 0.1 Hz but is unbiased in the 2 –10 Hz frequency range. Both the double and single corner source models, with actual or implied stress drops below 200 bar, underpredict the high frequency (. 2 Hz) ground motions for the Saguenay earthquake by factors of 2 –3 suggesting anomalous high frequency levels for this event. While it currently appears that a two-corner source model may be the more appropriate model for CEUS strong ground motions, it is evident that in predicting strong ground motions for engineering design, significantly more variability should be accommodated in applications to the CEUS than to the WUS. This increased variability should accommodate both randomness (aleatory variability) in stress drop above that for the WUS as well as uncertainty (epistemic variability) in the source model.
3. Comparisons of WUS and CEUS spectral shapes at rock sites Comparisons of WUS to CEUS response spectra are shown in Fig. 3 for shapes and absolute spectra, respectively. Also illustrated in the figure are the differences between the single and double corner source spectral models. For the shapes, the difference in spectral composition between the WUS and CEUS single corner models (solid lines) is clearly illustrated in the maximum spectral amplifications: about 5 Hz for WUS and 40 Hz for CEUS. The difference between the single and double corner source models (solid verses dashed lines) is also clearly illustrated. For the WUS, the difference is mainly at low frequency and is not large, about 20% near 0.3 Hz. For the CEUS, the single corner source model significantly exceeds the double corner below about 2 Hz. The largest difference occurs near 0.4 Hz and is a factor of over 3 in 5% damped spectral acceleration. Choices between the two shapes for the CEUS, single or double corner, clearly have major impacts on design motions. Considering absolute spectra, the WUS and CEUS single corner spectral estimates are nearly the same for frequencies up to about 5 Hz. This is the result of compensating effects previously discussed, that is, higher stress drop for CEUS and larger amplification factors for WUS. Beyond about 5 Hz, the differences in kappa values (0.04 s as compared to 0.006 s) result in the differences in high frequency spectral estimates. To see how well the simple point-source models (single and double corner frequency) capture the differences in
Fig. 3. Response spectra and spectral shapes (for 5% damping) computed for M6.5 at R ¼ 25 km using both single and double corner source spectra for WUS and CEUS parameters.
shapes between WUS and CEUS rock motions, comparison of predictions with statistical shapes generated from recorded data are shown in Fig. 4. For WUS sites, both models capture the overall shape reasonably well but
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spectral models capture the difference in shape between WUS and CEUS equally well with the single corner frequency model showing an overprediction at low frequency (, 1 Hz) similar to the WUS. Interestingly, the double corner model shows an underprediction for frequencies below about 2 Hz. Since this is only a single earthquake and variability is large in CEUS strong ground motions, these results may not reflect a potential bias in the model for spectral shapes but do suggest the spectral sag may be too extreme and emphasize the current state of uncertainty regarding CEUS strong ground motions. These comparisons to CEUS statistical shapes point out the quandary in estimating strong ground motions in the CEUS. Sufficient recordings at close distances (, 50 km) for earthquakes of engineering significance (M . 5) are not available to unequivocally distinguish between plausible models.
4. Site-specific soil motions incorporating profile uncertainties
Fig. 4. Comparison of 5% damped statistical spectral shapes for M6.75 on rock at 30.8 km for WUS (a) and CEUS (b) single and double corner predictions.
overpredict at low frequency (below 1 – 2 Hz). The double corner model provides a better fit but still shows overprediction in this magnitude range. For the CEUS, there is only one earthquake, 1985 Nahanni, with hard rock site recordings (three stations) in this distance range. Both
The conventional approach to developing site-specific soil motions involves convolution analysis, either equivalent-linear or fully nonlinear, using rock outcrop control motions at the soil/rock transition zone. For bottomless profiles the rock control motions may be input at a sufficiently deep location such that soil amplification extends to the lowest frequency of interest, about 0.5 Hz (generally about 500 ft for motions adequate to a lowfrequency limits of about 0.5 Hz [12]. In the convolutional analyses, uncertainty in dynamic material properties is generally accommodated through parametric variations, either deterministically with upper-, mid-, and lower-range moduli or through a Monte Carlo approach using randomly generated properties using statistically based distributions. Uncertainties in soil properties and in model deficiencies (in the convolutional formulation) are accommodated by either smoothly enveloping the deterministic variations or selecting a fractile level, generally the mean, for the Monte Carlo approach. Both these procedures appear to result in conservative spectral estimates since site variability is already accommodated in the variability associated with the attenuation relations used in developing the control (rock) motions. The approach which uses randomized material properties is preferred since the conservatism is quantified, provided the parameter distributions reflect a realistic assessment of how well the base case profile and nonlinear properties are known (epistemic uncertainty) as well as the variability over the site or footprint of the structure (aleatory uncertainty). A motivation for using the more conservative mean rather than median spectral estimates, which acknowledges double counting site variability to some extent, is to accommodate a degree of model uncertainty [9] (vertically propagating shear-waves and equivalent-linear approximation) in the convolutional
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formulation. Since this component of model uncertainty is currently unquantified, it is not possible to add it explicitly. It is however, thought to be relatively small, based on validation exercises of a complete model. As a result, the possible double counting of site variability may be largely offset by neglecting the deficiencies in the convolutional formulation. For attenuation relations based solely on validated stochastic point- or finite-source models the inclusion of model uncertainty accommodates the site model deficiencies for the vertically propagating shearwave model using the equivalent-linear approximation. The various approaches to developing hazard-consistent site-specific soil spectra in increasing order of accuracy are shown in Table 1. Approach 1 involves driving the soil column with the broad rock UHS spectrum (control motions) and may result in unconservative high frequency motions, particularly when using equivalent-linear site response analyses. Additionally, the appropriate magnitude and time history duration are ambiguous using Approach 1 for hazard environments which do not result in strongly unimodal M and R disaggregations. Approach 2A recognizes that different earthquakes may dominate the high and low frequencies, and uses separate transfer functions for these events. The use of multiple rock shapes scaled to the UHS at high and low frequencies is consistent with Regulatory Guide 1.165 [13] although not explicitly stated. In Approach 2B, mean, high and low percentile magnitudes from disaggregations for each design earthquake (e.g. 1 and 10 Hz) are used to scale spectral shapes to the 1 and 10 Hz rock UHS, and the resulting control motions are used to develop weighted mean transfer functions for Table 1 Approaches for developing hazard consistent soil motions Approach 1
Rock UHS used as control motions Approach 2A Use scaled 1 and 10 Hz design earthquakes as control motions to develop 1 and 10 Hz soil motions (R.G. 1.165 approach) or develop transfer function for 1 and 10 Hz design earthquakes, using a single control motion (scaled shape) for each frequency, the envelope of the two transfer functions is then used to scale the rock UHS Approach 2B Develop weighted mean transfer functions for 1 and 10 Hz design earthquakes accommodating magnitude distributions, the envelope of the two mean transfer functions is then used to scale the rock UH Approach 3 Approximations to UHS integrations Approach 4 UHS computed using site-specific soil attenuation relations
each design earthquake. The transfer functions are then used to scale each design earthquake or are combined to scale the rock UHS. The use of a three-point magnitude distribution for each design earthquake better accounts for nonlinear effects that may be caused by a wide range of earthquake magnitudes contributing to the hazard. Approach 3 involves approximations to the hazard integration using suites of transfer functions based on randomized soil profiles. Its development is recent [14] and it has been implemented at the DOE Savannah River Site [15]. In this approach, complete hazard curves may be generated as it is a direct approximation to Approach 4, essentially substituting suites of transfer functions in place of the site-specific soil attenuation relation. The approach is attractive, although requiring significant computations in site response and hazard disaggregation and necessarily counts the site uncertainty twice, once in the aleatory variability about the rock attenuation relations and again in the randomized site-specific dynamic material properties. The approximations implemented in the hazard integrations have been evaluated for a limited number of profiles and loading conditions and further evaluations are needed for ranges in site conditions, hazard environments, and nonlinear dynamic material properties before it can be implemented in practice. In Approach 4, a site-specific soil attenuation relation is used in the hazard analysis. This approach assumes that appropriate parametric variations are incorporated in the development of the attenuation relation and that they are also reflected in the uncertainty about the median ground motions [12]. 4.1. Approaches for vertical motions Assessment of site-specific soil vertical motions to accompany corresponding horizontal motions is a perplexing issue, particularly if it is desirable to maintain hazard consistency with the horizontal motions. Rarely are separate hazard analyses performed for horizontal and vertical control or rock outcrop motions (currently no vertical relations are available for the CEUS) and there are no widely accepted site response methodologies currently available to accommodate vertical analyses. Commonly, equivalent-linear site response analyses for vertical motions have used strain iterated shear moduli from a horizontal motion analysis to adjust the compression-wave velocities assuming either a strain independent Poisson’s ratio or bulk modulus. Some fraction (generally 30 – 100%) of the strain iterated shear-wave damping is used to model the compression-wave damping and a linear analyses is performed for vertically propagating compression waves using the horizontal control motions scaled by some factor near 2/3. Alternatively, fully nonlinear analyses can be made using two- or three-component control motions [8,16]. These nonlinear analyses require two- or three-dimensional soil models which describe plastic flow and
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yielding and the accompanying volume changes as well as coupling between vertical and horizontal motions through Poisson’s effect. While these analyses are important to examine expected dependencies of computed motions on material properties and may have applications to the study of soil compaction, deformation, slope stability, and component coupling, the models are very sophisticated and require specification of many parameters, at least some of which are difficult to measure both in mean or central values as well as expected ranges (uncertainties). The approach recommended here makes use of generic soil V/H ratios to scale the site-specific horizontal soil motions. It is intended to maintain as many site-specific attributes as possible through the use of the horizontal soil motions (soil column) and generic soil V/H ratios (controlling magnitudes and distances) while avoiding the currently inherent ambiguity in vertical site response analyses.
5. Example results for WUS and CEUS soil sites Section 4 presents a number of approaches to estimating site-specific soil spectra that are consistent with a specified hazard level that accommodate uncertainties in soil properties. In this section, comparisons are made among several of these approaches, and site-specific soil UHS are computed for a soft (Imperial Valley, California) soil profile located in the WUS (Mojave, California) and a relatively stiff soil profiles located in the CEUS (Charleston) tectonic environments. The site-specific soil UHS reflect the desired hazard level with which to evaluate the various degrees of approximations using rock outcrop UHS and site response analyses. However, an issue exists in the soil UHS calculated with Approach 4 involving long return periods where the hazard may result from motions that significantly exceed the median ground shaking during earthquakes contributing to the hazard. Under these conditions for highly nonlinear profiles, the site-specific UHS may overestimate the hazard at high frequency, as the residual dispersion in the site-specific attenuation relation(s) does not reflect the soils limited capacity to transmit high levels of motion (i.e. its nonlinearity). This is an important issue and requires further elaboration. 5.1. Horizontal motions The scaled (and corrected WUS) bedrock outcrop earthquake spectra are shown in Fig. 5 for the WUS and CEUS, respectively. The difference in the hazard environments between the WUS and CEUS is evident in the large differences in 1 and 10 Hz magnitude distributions. The difference in magnitudes for the 1 and 10 Hz design earthquakes is 1.3 units for the CEUS and only 0.6 units for the WUS. The potential effects of magnitude distribution in the rock UHS on nonlinear soil
Fig. 5. Rock outcrop spectra (uniform hazard, 1 and 10 Hz) for WUS (a) and CEUS (b) for example soil site response analyses.
response are much less an issue for WUS conditions than CEUS, at least for these example sites. The Imperial Valley Meloland profile is considered a soft profile and has a column frequency of about 0.5 Hz. While it is considered ‘bottomless’ and extends kilometers in depth,
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it was truncated at a depth of 1000 ft for these analyses. It is the location of a recently installed (Caltrans/CDMG) vertical strong motion array and the nearby CDMG strong motion site recorded the M6.5 1979 Imperial Valley earthquake at a rupture distance of 0.5 km (average horizontal component peak acceleration of about 0.3 g). The soil modulus reduction and damping curves used for site convolutions are based on modeling strong motions from the 1979 Imperial Valley earthquake recorded at Meloland and nearby sites and reflect relatively weak strain dependencies. The profile is considered nonlinear to a depth of 500 ft. The Savannah River generic profile was adopted from measured shear-wave velocity profiles at the DOE Savannah River site. The profile is generally stiff but does have a broad soft zone at intermediate depths (around 25 m) with a steep gradient thereafter. The low-strain column resonance is near 0.8 Hz. G/Gmax and hysteretic damping curves based on modeling strong ground motions in the Los Angeles area recorded at cohesionless soil sites from the M6.7 1994 Northridge earthquake are used for this site. Fig. 6 shows the soil UHS computed using Approaches 1, 2A, 2B, and 4. For the WUS soil site, similar results are obtained for Approaches 2A and 2B, both of which show higher motions than Approach 1 for frequencies above about 1 Hz. The soil column is being softened more by the rock UHS (Approach 1) than by either of the scaled design spectra. In general either Approach 2A or 2B adequately reflects the motions of Approach 4 (soil UHS) from about 0.3– 100 Hz (PGA). In this case, little difference is seen in Approaches 2A and 2B and either may be used. Approach 1 is not recommended. For the CEUS (Savannah River generic profile), Approach 1 again underestimates the soil UHS at the higher frequencies while Approaches 2A and 2B are generally slightly above the UHS, except at very low frequency. Approaches 2A and 2B are nearly identical and both are conservative (above 10 Hz) while Approach 2B remains closer to the soil UHS at very low frequency (, 0.4 Hz). Cyclic shear strain (effective) levels are much lower for the CEUS site than the corresponding WUS site. Maximum median strains developed in the soft zone have values near 2 £ 1022% compared to about 0.3% for the WUS Meloland profile. The loading levels are much lower and the profile is significantly stiffer. 5.2. Vertical motions To estimate vertical soil motions consistent with the horizontal soil motions, a WUS empirical generic soil V/H ratio was developed for M ¼ 6.7 and D ¼ 18 km, based on the rock UHS disaggregation at 1 Hz. The empirical V/H ratio is an average of ratios from empirical WUS data [17,18]. A comparison of the resulting vertical spectrum with the horizontal spectrum is shown in Fig. 7(a). The vertical motions exceed the horizontal between 10 and
Fig. 6. Comparison of soil surface spectra using Approaches 1, 2A, 2B and 4 for WUS (a) and CEUS (b) for example soil sites.
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soil applied to a WUS empirical deep soil V/H ratio. This process results in a generic soil CEUS V/H ratio which is applied to the site-specific horizontal design spectrum. The resulting vertical (unsmoothed) soil design spectrum is shown in Fig. 7(b) along with the horizontal. The exceedance of the vertical spectrum over the horizontal at high frequency ( f . 10 Hz) at this site is larger than normally recommended and indicates the greater uncertainty in predicting vertical responses.
Acknowledgments Support for this work was provided by Nuclear Regulatory Commission under the direction of Roger Kenneally. Careful reviews by Dave Boore, Nilesh Chokshi, Allin Cornell, I.M. Idriss, Robert Rothman, Robert Kennedy, Carl Stepp, Roger Kenneally, Buck Ibraham, and Robert Darragh contributed substantially to the quality of the work and are gratefully acknowledged. References
Fig. 7. Horizontal and vertical soil design spectra corresponding to 1024 per exceedance probability rock outcrop UHS for WUS (a) and CEUS (b) example soil sites.
20 Hz due to the close distance (18 km) and large magnitude (M6.7) [8]. The approach used to develop site-specific vertical motions for the CEUS site relies on modeling results to produce WUS-to-CEUS V/H scale factors for deep
[1] Silva WJ, Darragh R. Engineering characterization of earthquake strong ground motion recorded at rock sites. Report TR-102261. Electric Power Research Institute, Palo Alto, CA, 1995. [2] Boore DM, Atkinson GM. Source spectra for the 1988 Saguenay, Quebec earthquakes. Bull SSA 1992;82(2):683–719. [3] Atkinson GM. Source spectra for earthquakes in eastern North America. Bull SSA 1993;83(6):1778 –98. [4] Boatwright J, Choy G. Acceleration source spectra anticipated for large earthquakes in Northeastern North America. Bull SSA 1992;82: 660–82. [5] Munro PS, Weichert D. The Saguenay earthquake of November 25, 1988. Processed strong motion records, Geological Survey of Canada Open File/Dossier Public 1996, 1989. [6] Borcherdt RD. Preliminary report on aftershock sequence for earthquake of January 31, 1986 near Painesville, Ohio. US Geological Survey Open File Report 86-181, 1986. [7] Atkinson GM, Boore DM. Ground motion relations for eastern North America. Bull SSA 1995;85(1):17– 30. [8] Electric Power Research Institute. Guidelines for determining design basis ground motions. EPRI TR-102293. Electric Power Research Institute, Palo Alto, CA, 1993, vol. 1– 5. [9] Silva WJ, Abrahamson N, Toro G, Costantino CJ. Description and validation of the stochastic ground motion model, Nuclear Energy Department Brookhaven National Laboratory, Associated Universities, Inc. Upton, New York, 1997. [10] Atkinson GM. Attenuation of strong ground motion in Canada from a random vibrations approach. Bull SSA 1984;74(5):2629–53. [11] Schneider JF, Silva WJ, Stark CL. Ground motion model for the 1989 M6.9 Loma Prieta earthquake including effects of source, path and site. Earthquake Spectra 1993;9(2):251– 87. [12] Silva WJ, McGuire R, Costantino CJ. A comparison of site specific soil UHS to soil motions computed with rock UHS. Proceedings of OECD-NEA Workshop on Engineering Characterization of Seismic Input, November 15–17, NEA/CSNI/R, 2000, 2, vol. 2, 1999. p. 397 –504. [13] USNRC. Identification and characterization of seismic sources and determination of safe shutdown earthquake ground motion. US Nuclear Regulatory Commission, Regulatory Guide 1.165, March 1997.
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[14] Bazzurro P, Cornell CA, Pelli F. A site- and soil-specific PSHA for nonlinear soil sites. Proceedings of the 4th EQ. Resist. Design Structures Conference (ERES99). Catania, Italy, June 15– 17, 1999. [15] Lee R. Personal communication, 1998. [16] Costantino CJ. Two dimensional wave propagation through nonlinear media. J Comput Phys 1969;4:2.
[17] Abrahamson NA, Silva WJ. Empirical response spectral attenuation relations for shallow crustal earthquakes. Seismol Res Lett 1997; 68(1):94–127. [18] Campbell KW. Empirical nearsource attenuation relationships for horizontal and vertical components of peak ground acceleration, peak ground velocity, and pseudoabsolute acceleration response spectra. Seismol Res Lett 1997;68(1):154 –79.