Debra G. Murphy 1, John A. Egan 2, Donald L. Wells 3 ABSTRACT

Transcription

1 EXAMINATION OF CHARACTERISTICS OF GROUND SHAKING EXPERIENCED DURING THE MINERAL EARTHQUAKE, INCLUDING CONTRIBUTIONS OF LOCAL SITE RESPONSE EFFECTS ON OBSERVED DAMAGE Debra G. Murphy 1, John A. Egan 2, Donald L. Wells 3 ABSTRACT The August 23, 2011, moment magnitude (M w ) 5.8 Mineral, Virginia, earthquake is one of the strongest seismic events to occur in the Eastern United States since the M 5.9 Giles County, Virginia, earthquake in The earthquake, centered approximately 130 km south-southwest of Washington, D.C., caused significant damage in the epicentral region and widespread minor damage in Virginia and the Washington metropolitan area. Minor damage occurred to such notable Washington buildings as the National Cathedral, the Washington Monument, and the Smithsonian Castle, as well as to other buildings in their vicinities. The recorded motions experienced throughout the felt region of the Mineral earthquake, including the Washington, D.C., area, were generally lower than maximum considered earthquake (MCE) ground-motion hazard levels as mapped by the National Seismic Hazard Mapping Project. However, local geologic/geotechnical conditions at some locations produced significant amplification of ground shaking within relatively narrow period ranges that exceeded the MCE level and this ground shaking appears to have contributed to the observed damage. Ground motions likely to have been experienced at sites along and near the National Mall during the Mineral earthquake were estimated based on recent Central and Eastern United States ground motion prediction equations and site response analyses for representative subsurface conditions underlying the mall area. The results of these analyses indicate that the ground shaking was tuned to the site period of the soil column. These estimated ground shaking characteristics compare favorably to those of recordings of the event that we received for a nearby building site after performing our analyses. Site-specific probabilistic analyses were also performed to characterize MCE and design-level 1 Engineer, AMEC Environment & Infrastructure, Oakland, CA 94612, USA 2 Principal Engineer, Environment & Infrastructure, Oakland, CA 94612, USA 3 Geologist, AMEC Environment & Infrastructure, Oakland, CA 94612, USA Murphy DG, Egan JA, Wells DL. Examination of characteristics of ground shaking experienced during the Mineral earthquake, including contributions of local site response effects on observed damage. Proceedings of the 10 th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

2 ground motions that could be expected for future earthquakes, and these ground shaking conditions were compared to design response spectra as defined by ASCE The results of this comparison highlight the importance of performing site-specific analysis. Following the Mineral, Virginia, earthquake, a team of USGS personnel developed shearwave-velocity profiles for the recording stations that captured the event. Using this information, we developed comparisons between code-based response spectra for those sites and the response spectra of the ground shaking from the Mineral, Virginia, earthquake recorded at several sites in the Eastern United States that experienced stronger levels of ground shaking from the event. The comparison between as-recorded motions and code-based response spectra emphasizes the importance of performing site-specific analysis of ground motions for design. The damage experienced by structures along and in the general vicinity of the National Mall in Washington, D.C., shows how code-based response spectra may not adequately capture the response effects of local geologic/geotechnical conditions and may have an adverse effect on the performance of a structure.

3 EXAMINATION OF CHARACTERISTICS OF GROUND SHAKING EXPERIENCED DURING THE MINERAL EARTHQUAKE, INCLUDING CONTRIBUTIONS OF LOCAL SITE RESPONSE EFFECTS ON OBSERVED DAMAGE Debra G. Murphy 4, John A. Egan 5, Donald L. Wells 6 ABSTRACT The August 23, 2011, moment magnitude (M w ) 5.8 Mineral, Virginia, earthquake is one of the strongest seismic events to occur in the Eastern United States since the M 5.9 Giles County, Virginia, earthquake in The earthquake, centered approximately 130 km south-southwest of Washington, D.C., caused significant damage in the epicentral region and widespread minor damage in Virginia and the Washington metropolitan area. Minor damage occurred to such notable Washington buildings as the National Cathedral, the Washington Monument, and the Smithsonian Castle, as well as to other buildings in their vicinities. The recorded motions experienced throughout the felt region of the Mineral earthquake, including the Washington, D.C., area, were generally lower than maximum considered earthquake (MCE) ground-motion hazard levels as mapped by the National Seismic Hazard Mapping Project. However, local geologic/geotechnical conditions at some locations produced significant amplification of ground shaking within relatively narrow period ranges that exceeded the MCE level and this ground shaking appears to have contributed to the observed damage. Ground motions likely to have been experienced at sites along and near the National Mall during the Mineral earthquake were estimated based on recent Central and Eastern United States ground motion prediction equations and site response analyses for representative subsurface conditions underlying the mall area. The results of these analyses indicate that the ground shaking was tuned to the site period of the soil column. These estimated ground shaking characteristics compare favorably to those of recordings of the event that we received for a nearby building site after performing our analyses. Site-specific probabilistic analyses were also performed to characterize MCE and design-level ground motions that could be expected for future earthquakes, and these ground shaking conditions were compared to design response spectra as defined by ASCE The results of this comparison highlight the importance of performing site-specific analysis. Following the Mineral, Virginia, earthquake, a team of USGS personnel developed shearwave-velocity profiles for the recording stations that captured the event. Using this information, we developed comparisons between code-based response spectra for those sites and the response spectra of the ground shaking from the Mineral, Virginia, earthquake recorded at several sites in the Eastern United States that experienced stronger levels of ground shaking from the event. The 1 Engineer, AMEC Environment & Infrastructure, Oakland, CA 94612, USA 5 Principal Engineer, AMEC Environment & Infrastructure, Oakland, CA 94612, USA 6 Geologist, AMEC Environment & Infrastructure, Oakland, CA 94612, USA Murphy DG, Egan JA, Wells DL. Examination of characteristics of ground shaking experienced during the Mineral earthquake, including contributions of local site response effects on observed damage. Proceedings of the 10 th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

4 comparison between as-recorded motions and code-based response spectra emphasizes the importance of performing site-specific analysis of ground motions for design. The damage experienced by structures along and in the general vicinity of the National Mall in Washington, D.C., shows how code-based response spectra may not adequately capture the response effects of local geologic/geotechnical conditions and may have an adverse effect on the performance of a structure. Introduction On August 23, 2011, a moment magnitude (M W ) 5.8 earthquake occurred that was centered near Mineral, Virginia, about 130 km south-southwest of Washington, D.C. The earthquake caused significant damage in the immediate epicentral area and widespread minor damage in Virginia and the Washington metropolitan area; it was felt from Georgia to Maine along the Atlantic seaboard of the United States, as well as inland to Detroit and Chicago and in southeastern Canada to Montreal and Windsor. The purpose of this paper is to present a comparison between code-based response spectra as defined by ASCE 41-06, actual strong motion recordings, and response spectra developed using site-response methods. Seismotectonic Setting and Historical Ground Shaking Virginia and Washington, D.C., are located in the eastern part of the Central and Eastern United States (CEUS), which is a stable continental region (SCR). Although SCRs characteristically have low rates of seismic activity, localized areas within the CEUS are characterized by elevated rates of seismic activity. Examples of such areas are Eastern Tennessee; the Charlevoix region of Quebec, Canada; the Wabash Valley of Illinois and Indiana; Charleston, South Carolina; and New Madrid, Missouri (including adjoining areas of Arkansas, Kentucky, and Tennessee). The first three areas are characterized by ongoing small- to moderatemagnitude earthquakes (magnitudes of less than about 6½), whereas the latter two areas are characterized as sources of repeated large-magnitude earthquakes (magnitudes greater than or equal to 6½) [1]. The Washington, D.C., area is characterized by a low level of seismic activity (Fig. 1). However, the area has experienced strong ground shaking several times historically as a result of moderate-magnitude earthquakes occurring in Virginia and large-magnitude earthquakes occurring in the New Madrid, Missouri, and Charleston, South Carolina, regions. Despite extensive research over the past 30 years, including geologic, geophysical, and paleoseismic investigations, there remain significant uncertainties regarding the sources and mechanisms that generate the larger earthquakes in Central and Eastern United States [1].

5 Figure 1. Historical ground shaking in the Washington, D.C., region Historical Ground Shaking in Washington, D.C. The four most significant historical earthquakes to cause moderate-to-strong ground shaking and damage in Washington, D.C., are the New Madrid, Missouri, earthquakes; the 1886 Charleston, South Carolina, earthquake; the 1897 Giles County, Virginia, earthquake; and the 2011 Mineral, Virginia, earthquake. As there have been are relatively few instruments to record ground shaking levels, particularly in the Eastern United States, ground shaking levels are often interpreted using reported shaking effects and observed damage. The most widely used scale in the United States to describe ground shaking levels is the Modified Mercalli Intensity (MMI) scale; for reference, the intensity values and effects for levels MMI IV to VIII (moderate to destructive) reported for Washington, D.C., and the Virginia epicentral areas for these historical earthquakes are described below in Table 1. As may be noted, slight damage to structures typically is associated with MMI shaking levels of VI or higher, depending on the nature and quality of construction.

6 Table 1. Description of Modified Mercalli Intensity (MMI) levels IV through VIII Intensity Value IV V VI VII VIII Description During the day felt indoors by many, outdoors by few. At night some awakened. Dishes, windows, doors disturbed; walls make creaking sound. Sensation like heavy truck striking building. Standing automobiles rocked noticeably. Felt by nearly everyone, many awakened. Some dishes, windows, and so on broken; cracked plaster in a few places; unstable objects overturned. Disturbances of trees, poles, and other tall objects sometimes noticed. Pendulum clocks may stop. Felt by all, many frightened and run outdoors. Some heavy furniture moved; a few instances of fallen plaster and damaged chimneys. Damage slight. Everybody runs outdoors. Damage negligible in buildings of good design and construction; slight to moderate in well-built ordinary structures; considerable in poorly built or badly designed structures; some chimneys broken. Noticed by persons driving cars. Damage slight in specially designed structures; considerable in ordinary substantial buildings with partial collapse; great in poorly built structures. Panel walls thrown out of frame structures. Fall of chimneys, factory stack, columns, monuments, walls. Heavy furniture overturned. Sand and mud ejected in small amounts. Changes in well water. Persons driving cars disturbed New Madrid, Missouri, Earthquakes The largest earthquakes to occur in the CEUS were the four large earthquakes occurring in the area of New Madrid, Missouri, in December 1811 and January and February The magnitudes of these earthquakes are estimated to be between 7.5 and 7.7 [2]. All four earthquakes were felt in Washington, D.C., with MMI shaking effects of IV to V reported by Bakun et al. [3]. Based on detailed studies of the earthquake sequence and anecdotal accounts in contemporary newspapers compiled by Nuttli [4], Stover and Coffman [5] show Washington as within the isoseismal area of MMI V Charleston, South Carolina, Earthquake The September 1, 1886, Charleston earthquake is the largest historical event in the Eastern United States, with an estimated magnitude of 7.3. The earthquake resulted in widespread damage and ground failure (liquefaction) in the Charleston region, with ground shaking effects of MMI X in the meizoseismal area (area of maximum damage). This earthquake was felt as gentle swaying in upper levels of the Opera House in Washington, D.C., causing some patrons to rush outside, and as shaking of furniture in a three-story building [6] in the city. In nearby Alexandria, Virginia, it was reported that people were alarmed by the shaking, and many rushed into the streets. The effects in Washington, D.C., were reported as MMI IV by Bollinger [7]; however, Stover and Coffman [4] show Washington as within the isoseismal area of MMI V.

7 1897 Giles County, Virginia, Earthquake The May 31, 1897, estimated magnitude 5.9 earthquake in Giles County is the largest to occur in Virginia and the Washington, D.C., area. The earthquake resulted in moderate damage and MMI shaking effects of about VIII in Giles County. The earthquake was felt as gentle shaking in Washington, D.C., approximately 370 km northeast of the epicenter, with MMI effects assigned as IV to V and no reports of damage [8]. Stover and Coffman [4] show Washington as just outside the isoseismal area of MMI V, which is consistent with the MMI assigned by Virginia Tech [8] Mineral, Virginia, Earthquake The August 23, 2011, magnitude (M w ) 5.8 earthquake near Mineral, Virginia, was one of the largest earthquakes to occur in the Eastern United States since the 1897 Giles County, Virginia, earthquake. The 2011 Mineral earthquake was centered approximately 130 km southsouthwest of Washington, D.C., and is the largest known earthquake associated with the Central Virginia seismic zone. (The Giles County, Virginia, earthquake occurred in the Giles County, Virginia, seismic zone.) The U.S. Geological Survey (USGS) [9] reports that the earthquake rupture was characterized by reverse slip at shallow depth on a north- or northeast-trending fault. Field investigations show that the fault rupture did not extend to the ground surface [10]. As mentioned previously, ground shaking from the earthquake was felt widely throughout the Eastern United States and in southeastern Canada and resulted in moderate damage (MMI VII effects) in the epicentral region and slight damage over a wider area in Virginia and adjoining states. The damage and ground shaking effects of the earthquake are described in detail in a report published by the Geotechnical Extreme Events Reconnaissance [10]. In addition, the USGS, which compiles reports of felt ground shaking through the online Did You Feel It questionnaire ( indicates that reported MMI shaking effects in Washington ranged from IV to VI, with most reports in the vicinity of the National Mall indicating MMI V effects [11]. Minor damage in the Washington area included cracking and spalling of exterior panels and interior ribbing of the Washington Monument, minor exterior and interior damage to the National Cathedral as a result of the ground shaking, and minor damage to the Smithsonian Castle and contents in the National Museum of Natural History. The reported MMI IV to V ground shaking effects in Washington, D.C., for these four historic earthquakes are consistent with the general absence of reported damage to structures. These shaking levels are typically associated with peak ground acceleration (PGA) of approximately 0.07 g, based on relationships presented by Ebel and Wald (2003) [12]. Recorded Ground Motions for the 2011 Mineral Earthquake The Mineral earthquake was recorded at USGS National Strong Motion Program (NSMP) station sites along the East Coast of the United States from South Carolina to Vermont. Because there were few operating strong motion stations in the Eastern United States at the time,

8 however, only four NSMP recordings were obtained at epicentral distances of less than 300 km. It is estimated that PGAs greater than 0.25 g were experienced in the epicentral area. The station most comparable to the azimuth and epicentral distance to Washington, D.C. ( 130 km), is at Reston, Virginia, a distance of 124 km from the epicenter of the earthquake, and located about 26.5 km west-northwest of Washington, D.C.. PGA recorded at the Reston station was 0.11 g, which is somewhat higher than the PGA inferred from the ground shaking effects reported near the National Mall (less than 0.10 g). The site conditions at the Reston station are characterized as a deeply weathered soil profile over bedrock, with an average shear-wave velocity for the upper 30 m (V S30 ) reported as 364 m/s by the USGS [13]. This corresponds approximately to the boundary for Site Classes C and D (360 m/s) as specified in the International Building Code [14], ASCE 7 [15, 16], and ASCE 41 [17]. The Reston shear-wave-velocity profile is generally similar to the range of the shear-wave-velocity characteristics for subsurface profiles along and in the vicinity of the National Mall. In addition to the NSMP recordings, eight strong ground shaking recordings for the 2011 Mineral earthquake were obtained from instruments at a site in Washington. The site is located near the National Mall in a similar geologic and subsurface setting. The geometric mean of these eight recordings had a peak horizontal ground acceleration of g. Subsurface Characterization Following the 2011, Mineral, Virginia, earthquake, a team from the USGS collected data to develop shear-wave-velocity profiles for 24 sites along the eastern seaboard. As mentioned previously, among these sites was the Reston Fire Station strong-motion station; other sites were located near the Washington Monument and the National Cathedral in Washington (Fig. 2). The shear-wave-velocity profiles were used to characterize the subsurface conditions at the stations where strong motion recordings were obtained from the event and at the locations of several national historic buildings that incurred minor shaking damage. In addition to obtaining the 24 USGS shear-wave-velocity profiles, AMEC collected velocity information to assess ground shaking effects at several other sites in the vicinity of the National Mall.

9 (a) RFS (b) WNC (c) WM Figure 2. Shear-wave-velocity profiles for (a) Reston Fire Station, (b) Washington National Cathedral, and (c) Washington Monument from USGS [13] Seismic Hazard Analysis A deterministic seismic hazard analysis (DSHA) was conducted to develop the 84 th percentile response spectra for a scenario earthquake representing the 2011 Mineral, Virginia, earthquake at an estimated magnitude of M w 5.8. The DSHA was performed using the most current stable continental region ground-motion-prediction equations: the 2006 Atkinson and Boore [18] model as updated in 2011 Atkinson and Boore [19]; the 2008 Atkinson [20] model as updated in 2011 Atkinson and Boore [19]; the 2003 Silva et al. [21] model, and the 2011 Pezeshk et al. [22] model. The deterministic response spectra were developed at rock levels for each of 26 sites from which strong motion recordings and/or shear-wave-velocity profiles were available. Site Response Analysis Equivalent-linear free-field site response analysis was performed for the 26 sites where shear-wave-velocity profiles were available. The site response analysis was performed using the site response computer program STRATA (Version alpha, Revision 327) [23]. STRATA is a frequency-domain equivalent-linear program that uses random vibration theory (RVT) methods to compute the expected maximum site response of a layered site subjected to one-dimensional (vertical) propagation of earthquake ground motions. The input parameters for performing RVT site response analysis include a layered soil system with shear-wave velocity, shear modulus reduction and damping values defined by specified strain-dependent relationships, and an input motion represented by a Fourier amplitude spectrum (FAS) and ground motion duration [24]. The input FAS is back-calculated from an input acceleration response spectrum using the RVT inversion technique developed by Vucetic and Dobry [25].

10 For each of the 26 sites, the soil units were modeled using equivalent-linear material properties for both sands and clays, as the material types at each of the locations is unknown. The granular model used the Seed and Idriss mean modulus reduction curves and mean damping curves for sand [26]. Clay layers were modeled using the Vucetic and Dobry modulus reduction curves and damping curves for cohesive materials with a plasticity index of 15 [25]. The input acceleration response spectrum applied to the bottom of the model was based on the deterministic analysis performed at each site for the 2011 Mineral, Virginia, earthquake. The shear-wave-velocity profiles were input into the model for each of the sites. A total of 52 cases were run, 26 sites each with a sand profile and a clay profile. The ground surface response spectra developed based on the described analysis are plotted on Fig. 3. Because the present evaluation is focused primarily on ground shaking and effects in Washington and its immediate vicinity, the results are illustrated herein for only a few sites in that area. Comparison of Response Spectra We compared the actual strong motion recordings obtained at Reston and the building site near the National Mall with the estimated Mineral, Virginia, earthquake ground motions as calculated using the above-mentioned site response methods; these comparisons are shown on Fig. 3. Fig. 3 illustrates the effects that various site conditions of even similar V S30 characteristics can have in producing significantly different site amplification effects on the response of the soil at a given site. We note that in this comparison, short-period soil amplification ratios are in the range of about 2 to 3 for the Reston Fire Station site, about 2½ to 4 for the Washington National Cathedral site, and about 3½ to nearly 5 for the Washington Monument site. We also note that these observed and calculated amplification ratios associated with local site response effects are substantially greater than would be implied by site coefficients of 1.2 (Site Class C) to 1.6 (Site Class D) given in code documents. Figure 3 illustrates that the fundamental period of the soil column for the sites within the Washington, D.C. area of approximately 0.3 seconds. The damage experienced by the Washington National Cathedral and the Washington Monument are likely the result of tuning of the fundamental period of both soil column and each of the building. Spectral Acceleration (g) Mineral EQ Rock (estimated) Reston Recording (geomean) RFS - Site Response Analysis (STRATA) Mineral EQ Rock (estimated) National Mall Recording (geomean) WNC - Site Response Analysis (STRATA) Mineral EQ Rock (estimated) National Mall Recording (geomean) WM foundation - Site Response Analysis (STRATA) Period (seconds) Period (seconds) Period (seconds) (a) RFS (b) WNC (c) WM Figure 3. Ground surface response spectra results for (a) Reston Fire Station, (b) Washington

11 National Cathedral, and (c) Washington Monument. Conclusions The results shown on Figs. 3a, 3b and 3c illustrate the importance of understanding the detailed characteristics of the subsurface conditions at a site and the importance of considering the potential effects that those conditions may have beyond an assessment based simply on V S30 or site class. The comparisons presented herein between recorded motions and site-specific response analyses demonstrate the nuances of stratigraphic and shear-wave-velocity variations within subsurface profiles. These variations in stratigraphy can be seen at sites within the same site class. Sites with similar V S30 characterizations can also produce significantly different site amplification effects relative to one another. These amplifications effects due to local subsurface conditions may also be significantly different than those implied by the site response coefficients in building codes (e.g., F a and F v ) and can be important to the performance of existing structures and/or design of new structures. Site-specific ground response analyses performed to estimate the potential effects of local geology on ground shaking conditions produced by the 2011 Mineral earthquake suggest that the damage experienced in the Washington, D.C., area occurred in a large part because of the relative tuning of the ground shaking by local subsurface conditions to the fundamental response periods of the structures supported in/on those subsurface conditions. References 1. Electric Power Research Institute, U.S. DOE, and U.S. NRC. Technical Report: Central and Eastern United States Seismic Source Characterization for Nuclear Facilities, 2012; Palo Alto, Calif.; 2. Hough SE. Cataloging the New Madrid, Central U.S., earthquake sequence. Seismological Research Letters 2009; 80 (6): Bakun WH, Johnston AC, Hopper MG. Modified Mercalli Intensities (MMI) for Large Earthquakes near New Madrid, Missouri, in and near Charleston, South Carolina, in 1886: U.S. Geological Survey Open- File Report , 2002; 31 pp. 4. Nuttli OW. The Mississippi Valley earthquakes of 1811 and 1812: Intensities, ground motion, and magnitudes. Bulletin of the Seismological Society of America 1973; 63: Stover CW, Coffman JL. Seismicity of the United States, (Revised), U.S. Geological Survey Professional Paper 1527, 1993; 418 pp. 6. Dutton CE. The Charleston Earthquake of August 31, 1886: U.S. Geological Survey Ninth Annual Report , 1889; pp Bollinger GA. Reinterpretation of the intensity data for the 1886 Charleston, South Carolina, Earthquake. In Studies Related to the Charleston, South Carolina, Earthquake of 1886: A Preliminary Report, Rankin DW, ed., U.S. Geological Survey Professional Paper 1028B, 1977; 17 pp. 8. Virginia Polytechnic Institute. Giles County Earthquake of May 31, 1897 News Reports, 2012; 9. U.S. Geological Survey. Magnitude 5.8 Virginia. Significant EQ Archive, 2011; Geotechnical Extreme Events Reconnaissance Central Virginia Earthquake, GEER Association Report

12 No. GEER-026, 2011; /index.html. 11. U.S. Geological Survey. Shakemap us a, 2012; global/shake/082311a/. 12. Ebel JE, Wald DJ. Bayesian estimations of peak ground acceleration and 5% damped spectral acceleration from Modified Mercalli Intensity data. Earthquake Spectra 2003; 19: Kayen R. Personal communication regarding U.S. Geological Survey shear wave velocity result for Reston, Virginia, Fire Station No. 25, Strong motion station No. 2555; March 30, International Code Council, Inc International Building Code, 2009; Falls Church, Virginia. 15. American Society of Civil Engineers. ASCE/SEI 7-05: Minimum Design Loads for Buildings and Other Structures, 2006; Reston, Va. 16. American Society of Civil Engineers. ASCE/SEI 7-10, Minimum Design Loads for Buildings and Other Structures, 2010; Reston, Va. 17. American Society of Civil Engineers. ASCE/SEI 41-06, Seismic Rehabilitation of Existing Buildings, 2007; Reston, Va, 411 pp. 18. Atkinson GM, Boore, DM. Earthquake ground-motion prediction equations for Eastern North America. Bulletin of the Seismological Society of America 2006; 96 (6): Atkinson GM, Boore DM. Modifications to existing ground-motion prediction equations in light of new data. Bulletin of the Seismological Society of America 2011; 101 (3): Atkinson GM. Ground motion prediction for Eastern North America from a referenced empirical approach: Implications for epistemic uncertainty. Bulletin of the Seismological Society of America 2008; 98 (3): Pezeshk S, Zandieh A, Tavakoli B. Hybrid empirical ground-motion prediction equations for eastern North America using NGA models and updated seismological parameters. Bulletin of the Seismological Society of America 2011; 101 (4): Silva W, Gregor N, Darragh R. Development of regional hard rock attenuation relations for Central and Eastern North America, mid-continent and Gulf Coast areas, 2003; Pacific Engineering and Analysis, El Cerrito, CA. 23. Kottke AR, Rathje EM. Technical Manual for STRATA, prepared for the Pacific Earthquake Engineering Research (PEER) Center at the College of Engineering, University of California, Berkeley, PEER Report 2008/10, February Rathje EM, Kottke AR, Ozbey CM. Using inverse random vibration theory to develop input Fourier amplitude spectra for use in site response. Prepared for the 16 th International Conference on Soil Mechanics and Geotechnical Engineering Osaka, Japan, September Vucetic M, Dobry R. Effect of soil plasticity on cyclic response. ASCE, Journal of Geotechnical Engineering 1991; 117, Paper No Seed HB, Idriss IM. Soil Moduli and Damping Factors for Dynamic Response Analysis, Report No. UCB/EERC-70/10, Earthquake Engineering Research Center, University of California, Berkeley, December 1970; 48 pp.