Integration of Probabilistic Seismic Hazard Analysis with Nonlinear Site Effects and Application to the Mississippi Embayment

Integration of Probabilistic Seismic Hazard Analysis with Nonlinear Site Effects and Application to the Mississippi Embayment Duhee Park and Youssef M.A. Hashash ABSTRACT An integrated probabilistic seismic hazard analysis procedure that incorporates non-linear site effects, PSHA-NL, is developed. PSHA-NL follows the methodology of the USGS hazard maps and generates a compatible set of ground motion records. The site effects are directly accounted for by propagating the motions using nonlinear and equivalent linear site response analyses. The procedure fully preserves the probabilistic nature of the USGS hazard maps and can be applied to any geologic setting. The procedure is applied to characterizing the influence of thick deposits of the upper Mississippi embayment. A set of generic site coefficients are derived from the probabilistic surface uniform hazard response spectra. The site coefficients are summarized in a format similar to NEHRP site coefficients, with an added dimension of the embayment deposits thickness. The coefficients compare well with NEHRP site coefficients for 3 m profiles. For thicker soil profiles, developed site coefficients are lower at short periods and higher at long periods than NEHRP site coefficients. Duhee Park, Post-doctoral Research Associate, Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 68, USA Youssef M.A. Hashash, Assistant Professor, Department of Civil and Environmental Engineering; University of Illinois, Urbana at Urbana-Champaign, IL, 68, USA

INTRODUCTION Probabilistic seismic hazard analysis (PSHA), first developed by Cornell (968), accounts for the uncertainties in the size, location, rate of recurrence of earthquakes, and the variation of resulting ground motion characteristics in estimation of the seismic hazard. PSHA computes the mean annual rate of exceedance of a ground motion parameter at a particular site from the aggregate risk of potential earthquakes of many different magnitudes occurring at a range of source-site distances. The output of a PSHA is amplitudes of ground motion parameters at selected annual probabilities of exceedance, such as presented in United States Geological Survey (USGS) hazard maps. USGS hazard maps depict geographic distribution of amplitudes of four ground motion parameters, which are peak ground acceleration (PGA) and spectral accelerations at.,.3 and. sec periods at three probabilities of exceedance (%, 5%, and % in 5 years) throughout the United States (Frankel et al. ). The ground motion amplitude is that which would be expected at a weak rock site, with near surface shear velocity of 76 m/sec (Site class B/C ary according to National Earthquake Hazard Reduction Program, NEHRP, Provisions). Since USGS maps do not represent an actual site condition, mapped spectral accelerations are used with site coefficients proposed in 997 NEHRP Provisions to account for the site effects. NEHRP site coefficients are functions of the seismic hazard level and stiffness of the site. The site coefficients, Fa and Fv, are multiplied to the mapped spectral acceleration at. sec, Ss, and at second, S, respectively. The resulting spectral accelerations are used to develop the surface design response spectrum, as shown in Figure. Although the NHERP-997 site coefficients are useful in better defining the site-specific hazards, it has some major limitations. The NEHRP-997 site coefficients are based on site classes identified by the properties of the top 3 m. In the Mississippi embayment (ME), which is the focus of this study, the unconsolidated deposits are as thick as m near Memphis, Figure. The ME overlies the New Madrid Seismic Zone (NMSZ), considered to be the most seismically active zone in the Central and Eastern US (Ng et al. 989; Shedlock and Johnston 994). Using site coefficients of NEHRP-997 may not be appropriate for thick sediments of the ME. Another limitation of the NEHRP Provisions is that the site coefficients, developed deterministically, are used with the probabilistically derived spectral accelerations from the USGS hazard maps. Spectral Acceleration (g) S Ms S M S Ms =F a x S s S M =F v x S T T. s Period (sec) Figure. The 997 NEHRP recommended response spectrum.

9 9 88 KILOMETERS MISSOURI ILLINOIS KENTUCKY 37 New Madrid Seismic Zone 36 ARKANSAS TENNESSEE Memphis E-W section, see Figure b Boundary of the Reeelfoot Rift Edge of the Mississippi Embayment Recent earthquake epicenters Figure. Plan view of the Mississippi embayment and major structures within it. Circles denote the clustered pattern of earthquake epicenters that define the New Madrid Seismic Zone Mississippi flood plain Memphis m Sea level Recent and Plio-pleistocene Middle and upper Eocene Lower Eocene 5 km m Paleocene Cretaceous Paleozoic rock b. E-W section through Memphis. Note: Vertical dimension is highly exaggerated, and the embayment trough has a shallow slope of less than /5. Figure 3. The Mississippi embayment (after Park and Hashash 4a). PROBABILISTIC SEISMIC HAZARD ANALYSIS WITH NONLINEAR SITE EFFECTS (PSHA-NL) A novel PSHA framework that integrates the site effects, PSHA-NL, has been developed (Park 3; Park and Hashash 4b). The procedure is composed of three main steps: ) source characterization, ) ground motion time history generation, and 3) site response. Steps and, modified from Wen and Wu () s procedure, closely approximate the calculated seismic hazard from a conventional PSHA. The main difference from a conventional PSHA is that actual seismic motion time histories are generated at an equivalent hard rock site. Step 3 is performed to characterize the site effects. The output of PSHA-NL is a suite of surface ground motions and uniform hazard response spectra.

The developed procedure is applied to the ME to quantify the seismic effects of the thick deposits. Step and are performed to reproduce the USGS hazard maps. Step 3 is performed to develop ME specific site coefficients and evaluate the NEHRP site coefficients. The details of each steps of the PSHA-NL applied to the ME are discussed in detail the following sections. Step : Source Characterization The USGS hazard maps define two types of seismic sources, which are a) characteristic and b) gridded seismic sources (Frankel et al. ). The characteristic sources represent sources at which the recurrence interval and magnitude can be estimated based on geologic evidence. The gridded seismic sources are intended to cover the historical seismicity and large background source zones. The background source zones are used to assign hazard in areas with little historical seismicity but with the potential to generate damaging earthquakes. The characteristic and gridded sources are treated separately and added to the final seismic hazard. The proposed procedure utilizes the seismicity information, for both characteristic and gridded seismic sources, from USGS hazard maps, but develops actual sources that occur within a finite number of simulation years. The characteristic source that has the highest contribution to the seismic hazard in the upper ME is the New Madrid seismic zone (NMSZ). USGS uses three fictitious NMSZ faults. A logic tree is used to assign characteristic earthquake moment magnitudes (M) ranging from 7.3 to 8., but the calculated hazard is equivalent to using a single M = 7.7 event. In development of the USGS hazard maps, it is assumed that future characteristic earthquakes at NMSZ faults occur at closest distances from the site to each of the three faults (Frankel 3). The recurrence rate of the NMSZ faults is fixed at /5 years. The contribution of the characteristic faults, NMSZ faults, is very significant in the upper ME. However, the contribution of the gridded seismic sources cannot be ignored, since the contribution can be higher than 3% depending on the location within the ME. The recurrence rates proposed in the USGS hazard maps (Frankel et al. ) are used to characterize the seismicity of the gridded seismic sources. The occurrence in time during a selected simulation years is calculated according to a Poisson process, using the USGS defined recurrence rate. The magnitude, given the occurrence of an earthquake, is then assigned according to the magnitude distribution for gridded seismic events proposed by USGS. Step Ground motion time history generation USGS hazard maps use attenuation relationships to estimate ground motion parameters from the characterized sources. The main difference between PSHA-NL and USGS hazard maps is that instead of using the attenuation relationships, actual ground motion time histories are developed from the sets of magnitude and source-to-site distance information obtained from the source characterization process. The generation of actual ground motion time histories eliminates the need to use attenuation relationships, provided that the characteristics of the ground motion approximate the attenuation relationships. The USGS maps incorporate five attenuation relationships in estimation of the ground motion parameters which include single-corner and double-corner point source models, broadband model, and hybrid model using both empirical data and stochastic model (Frankel et al. ). Only the point source stochastic model is used, due to the lower contributions and difficulties in incorporating the broadband and hybrid models in the simulation. Both single corner and double corner point source models will be used, whereby single corner and double corner models are assigned the same weight, for both gridded and characteristic seismic sources.

Spectral acceleration (g).5.5.5 NEHRP Site Class B USGS Hazard map Simulated UHRS.. Period (sec) Figure 4. Comparison between USGS mapped spectral acceleration, NEHRP Site Class B design response spectrum, and the uniform hazard response spectrum of the proposed simulation procedure (after Park and Hashash 4b). The stochastic model SMSIM version. (Boore ), which has been used in development of the point source model based attenuation relationships, is used to develop ground motion time histories using the USGS defined input parameters (Frankel et al. ). The motions are generated at hard rock (Site Class A according to NEHRP Provisions) representing the Paleozoic bedrock. Comparison with USGS hazard maps The attenuation relationships incorporated in the USGS hazard maps use a Fourier amplification function to represent amplification at B/C ary (Frankel et al. 996). The ground motions generated (hard rock motions at Palezoic bedrock) are converted to B/C ary motions to compare with USGS hazard maps. A maximum cap is imposed on the converted ground motions, as in the USGS hazard maps. Figure 4 shows % in 5 years UHRS from the proposed simulation (Step and ) and the USGS hazard mapped hazard for a selected site (Latitude = 36.N, Longitude = 9.9W) in the ME. The simulated UHRS is in excellent agreement with USGS hazard mapped ground motion parameters (PGA,., and. sec spectral acceleration) and clearly demonstrates that the proposed procedure is able to reproduce seismic hazard levels of USGS maps, while generating the set of ground motions contributing cumulatively to the hazard. Note that the motions are converted to B/C ary and UHRS computed only for the purpose of comparison with the USGS hazard maps. The hard rock motions are used to perform site response analysis, described in the following section. Step 3 Site response analysis The generated ground motions at hard rock (Site Class A) are propagated to the ground surface to account for the effects of embayment deposits.

V (m/sec) s 4 6 8 Sand & gravel Clay & silty sand V (m/sec) s 4 6 8 Memphis sand 3 Depth (m) 4 5 6 Flour Island formation (clay) Fort Pillow sand Old Breastworks formation (clay) Sand & gravel 3 4 Depth (m) 7 Shale and clay Clay & silty sand 5 8 9 Uplands profile Lowlands profile (a) (b) 6 7 Figure 5. Simplified Mississippi embayment stratigraphy and generic shear wave velocity profiles (Uplands and Lowlands) a) up to m and b) up to 7m (Romero and Rix ). The profiles are the same below the depth of 7m. The ground motions are imposed at the bottom of the profiles as rock outcrop motions and then propagated using DEEPSOIL (Hashash and Park, ; Park and Hashash 4c). DEEPSOIL is a one-dimensional nonlinear site response analysis model. Various enhancements have been made over a conventional nonlinear code to simulate wave propagation through deep deposits, which include (a) confining pressure dependent nonlinear constitutive soil model (Hashash and Park ), (b) increased numerical accuracy in propagation of strong ground motions by implementing a flexible strain sub-incrementation scheme (Hashash and Park ), and (c) new viscous damping formulation to reduce artificial damping introduced at deep profiles (Hashash and Park ). Generic shear wave profiles developed for the two geologic categories (Romero et al. ), Uplands and Lowlands, of the ME are used (Figure 5).

Shear strain, γ (%).....9 (a) G/G max.8.7.6.5.4 ME EPRI : m : m 3: 5m 4: m 5: m 6: 3m 7: 4m 8: 5m 9: m 4 9 4 9 3 5 (b) G/G max 5 4 4 9 5 9.... Shear strain, γ (%) Figure 6. Comparison of the proposed Mississippi embayment properties (solid lines and termed ME) with the modified hyperbolic curves to fit EPRI (993) curves (dashed lines and termed EPRI) (Park and Hashash 4a). Lowlands profile represents Holocene-age deposits found along the floodplains of the Mississippi River and its tributaries whereas Uplands represent Pleistocene-age deposits located in the interfluve, terrace regions. The Lowlands profile has lower shear velocity in the upper 7 m compared to the Uplands profile due to loose Holocene-age deposits found in the alluvial plains, but identical below 7 m. The underlying Palezoic bedrock is assumed to have a shear velocity of 3 m/sec (Ou and Herrmann 99; Nicholson et al. 984). These shear wave velocity profiles are used throughout this and the companion paper. Two sets of dynamic soil properties are used in the study to account for the uncertainty in the material properties; a) the generic dynamic soil properties developed by EPRI (993) and b) the ME specific dynamic soil properties (Park and Hashash 4a). Both properties are shown in Figure 6. The ME specific dynamic properties are constrained through weak motions recorded during the Enola Earthquake, and laboratory test data of ME soils at low confining pressures (Park and Hashash 4a). The Enola Earthquake recordings are used to back-calculate the small strain damping properties. The back-calculated small strain damping is much higher than the generic damping profile by EPRI. Overall, the confining pressure

dependency of the ME specific properties is higher than EPRI curves, the ME curves becoming stiffer than the EPRI curves with increase in confining pressure. EVALUATION OF UHRS FOR SELECTED ANALYSIS Various sites are selected in the upper ME to cover the range of the spectral accelerations encountered in the embayment. The thicknesses of the selected sites are also hypothetically varied from 3 m to m to represent the full range of embayment thicknesses. Figure 7 shows UHRS for a selected site (S s =.66g, S =.g), for depths from 3 m to m. The Uplands profile and ME properties are used to develop the UHRS. The 3 m UHRS compares well with the NEHRP design response spectrum (F a =.8, and F v = ). However, the UHRS continuously decreases with increasing deposit thickness at short periods (approximately up to.5 sec). The rate of reduction is quite pronounced up to a thickness of 3 m, but very subtle at higher thickness. This is due to low strain levels and viscous damping at higher thickness. The amplification at long periods, on the other hand, increases significantly. The amplification shifts to longer periods due to a shift to higher resonant periods with increase in column thickness. The UHRS plots demonstrate the need to incorporate soil profile thickness dependent design site coefficients. The short period site coefficient decreases, whereas the long period site coefficient increases with soil column thickness. Spectral Acceleration (g)..8.4 (a) UH R S N EH RP Site D Design response spectrum 3m m m 3m 5m m Figure 7. UHRS at a selected site using Uplands profile / ME properties and six profiles ranging in thickness from 3 m to m. NEHRP Site class D Design response spectrum is shown in thick gray line in plot (after Park 3). COMPUTED UHRS BASED SITE COEFFICIENTS Soil profile thickness dependent site coefficients for the ME are developed based on the UHRS. The site coefficients are chosen such that a reasonable envelope of the UHRS is obtained. Design spectra using the proposed site coefficients and the computed UHRS for a selected site are shown in Figure 8. The site coefficients are developed for Uplands/Lowlands shear wave velocity profiles and

ME/EPRI dynamic soil properties. One set of the developed site coefficients, using Uplands profile, is shown in Figure 9 and also summarized in Table. The proposed coefficients are summarized in a similar format to NEHRP Provisions, with the addition of dependency on the embayment thickness. Decrease in F a for m profile is approximately 3%, but F v increases by approximately %. The probabilistically derived site coefficients clearly demonstrate the importance of sediment thickness dependency on site coefficients. More details on the proposed site coefficients are discussed in (Park 3) (Park and Hashash 4b), in which the upper and lower are developed for both Uplands and Lowlands of the ME. Spectral Acceleration (g) Spectral Acceleration (g) Spectral Acceleration (g)..8.4 (a) 3m. (c) m.8.4..8.4 (e) 5m NEHRPSite D UHRS Proposed design spectrum (b) m (d) 3m (f) m.... Period (sec) Period (sec) Figure 8. UHRS (% in 5 years) and design spectra with soil profile thickness dependent site coefficients for Site using Uplands profile and ME dynamic properties (after Park 3).

Table. Recommended site coefficients of the Mississippi embayment for Uplands (after Park and Hashash 4b). a) Fa as a function of soil profile thickness and mapped. second period spectral acceleration USGS hazard maps. Thick Mapped. sec spectral acceleration from USGS hazard maps ness Ss =.5g Ss =.5g Ss =.75g Ss =.g Ss.5g (m) NEHRP Upper Lower NEHRP Upper Lower NEHRP Upper Lower NEHRP Upper Lower NEHRP Upper Lower 3 3 5.6.6.5.4.5.6.54.6.48.6.4.6.37.6.3.4..35.3..5....5.4.4.44.3..9...9...4.5.3.4.38...3...3...8.95..4.3...7...7.9...85.5.4.7.5...95...85..97.8..4....7.9..97.8..9.78 b) Fv as a function of soil profile thickness and mapped. second period spectral acceleration from USGS hazard maps. Thick Mapped. sec spectral acceleration from USGS hazard maps ness S =.g S =.g S=.3g S=.4g S.5g (m) NEHRP Upper Lower NEHRP Upper Lower NEHRP Upper Lower NEHRP Upper Lower NEHRP Upper Lower 3.4.4.4....8.8.8.6.7.7.5.6.6.4.7.5..3..8..9.6.8.5.9.7.4.8.6..4..8..6..9.5.8 3.4.9.7..5.3.8.3..6..5..9 5.4.95.75..55.35.8.35.5.6.5.5.5.5.95.4 3..8..6.4.8.4..6.3..5. and denote results using ME properties and EPRI properties, respectively. Note: Use straight-line interpolation for intermediate values of SS and S.

Depth (m).5.5 (a) 5 4 3 4 6 8 Proposed 5 4 3 F a NEHRP : Ss=.5g : Ss=.5g 3: Ss=.75g 4: Ss=.g 5: Ss=.5g Depth (m).5.5 3 (b) 4 6 8 5 4 Proposed 3 F v 54 3 NEHRP : S=.g : S=.g 3: S=.3g 4: S=.4g 5: S=.5g Figure 9. Recommended site coefficients for Uplands using ME properties: (a) Fa and (b) Fv (after Park and Hashash 4b). The proposed site coefficients are for the Mississippi embayment and Site Class D only. However, the PSHA-NL methodology is general and can be applied to any sites in the US, provided that the site dynamic properties are available. It should be recognized that the proposed design spectra do not envelope the peaks of the UHRS. Therefore, site-specific analysis is recommended in design of critical structures to avoid the resonant periods at which the hazard is the highest. Site-specific analysis is also warranted in design of long period longitudinal structures in deep embayment deposits, since the design spectrum will underestimate very long period amplification. SUMMARY AND CONCLUSION A novel framework for integrating the probabilistic seismic hazard analysis with nonlinear site effects is developed and applied to the Mississippi embayment. Initially, PSHA is performed to reproduce the USGS hazard maps, but at the same time generates a compatible set of ground motion time histories. The generated motions are propagated through generic profiles of the Mississippi embayment, taking into account non-linear site effects of individual motions. Two generic shear velocity profiles (Uplands and Lowlands) and two sets of dynamic properties (ME specific properties and generic EPRI properties) are used to account for the uncertainty in the soil properties. Surface UHRS are computed and used to develop site coefficients. The coefficients show a strong dependence on Mississippi embayment deposit thickness to the Paleozoic rock, a physically meaningful impedance ary. The proposed site coefficients are presented in NEHRP style with the added dimension of embayment thickness. Results indicate that proposed coefficient for embayment thickness of 3m compare well with NEHRP site coefficients. However, for deep soil

profiles of the ME, the proposed site coefficients are lower at short periods and higher at long periods than the 997 NEHRP site coefficients. ACKNOWLEDGEMENT This work was supported primarily by the Earthquake Engineering Research Centers Program of the National Science Foundation under Award Number EEC-97785; the Mid-America Earthquake Center. The authors gratefully acknowledge this support. The authors would like to thank Dr. David Boore for providing the executable version of the program SMSIM, Dr. Roy Van Arsdale for providing the embayment thickness contour map, and Dr. Mitchel Withers for the earthquake data recorded in the embayment. All opinions expressed in this paper are solely those of the authors. REFERENCES Boore, D. M.,, "SMSIM Fortran programs for simulating ground motions from earthquakes: Version.6. A revision of OFR 96-8-A." US Geological Survey, Menlo Park. Cornell, C. A., 968, "Engineering seismic risk analysis." Bulletin of Seismological Society of America, 58, 583-66. EPRI, 993, "Guidelines for determining design basis ground motions." EPRI Tr-93, Electric Power Research Institute, Palo Alto, CA. Frankel, A., 3, "Personal Communications." Frankel, A., Mueller, C., Perkins, D., Barnhard, T., Leyendecker, E., Safak, E., Hanson, S., Dickman, N., and Hopper, M., 996, "National seismic hazard maps: Documentation June 996." OFR 9653, US Geological Survey. Frankel, A., Pertersen, M. D., Mueller, C. S., Haller, K. M., Wheeer, R. L., Leyendecker, E. V., Wesson, R. L., Harmsen, S. C., Cramer, C. H., Perkins, D. M., and Rukstales, K. S.,, "Documentation for the update of the national seismic hazard maps." OFR -4, US Geological Survey. Hashash, Y. M. A., and Park, D.,, "Non-linear one-dimensional seismic ground motion propagation in the Mississippi embayment." Engineering Geology, 6(-3), 85-6. Hashash, Y. M. A., and Park, D.,, "Viscous damping formulation and high frequency motion propagation in nonlinear site response analysis." Soil Dynamics and Earthquake Engineering, (7), pp. 6-64. Ng, K. W., Chang, T. S., and Hwang, H., 989, "Subsurface Conditions of Memphis and Shelby County." Technical Report NCEER-89-, National Center for Earthquake Engineering Research, State University of New York at Buffalo, Buffalo, N.Y. Nicholson, C., Simpson, D. W., Singh, S., and Zollweg, J. E., 984, "Crustal studies, velocity inversions, and fault tectonics: results from a microearthquake survey in the New Madrid Seismic Zone." Journal of Geophysical Research, 89(B6), 4545-4558. Ou, G. B., and Herrmann, R. B., 99, "A statistical model for ground motion produced by earthquakes at local and regional distances." Bulletin of the Seismological Society of America, 8(6), 397-47. Park, D., 3, "Estimation of non-linear seismic site effects for deep deposits of the Mississippi Embayment," Ph.D. Dissertation, University of Illinois, Urbana. Park, D., and Hashash, Y. M. A., 4a, "Estimation of seismic factors in the Mississippi Embayment: I. Estimation of dynamic properties." Soil Dynamics and Earthquake Engineering, Submitted for review.

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