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Estimation of Non-Linear Seismic Site Effects for Deep Deposits of the Mississippi Embayment

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Estimation of Non-Linear Seismic Site Effects for Deep Deposits of the Mississippi Embayment Estimation of Non-linear Seismic Site Effects for Deep Deposits of the Mississippi Embayment Duhee Park, Ph.D. Post Doctoral Researcher Department of Civil & Environmental Engineering University of Illinois at Urbana Champaign Room 2216 NCEL 205 N. Mathews Avenue e-mail: [email protected] Youssef M.A. Hashash, Ph.D., PE Associate Professor Department of Civil & Environmental Engineering University of Illinois at Urbana Champaign Room 2230C NCEL 205 N. Mathews Avenue e-mail: [email protected] National Science Foundation Mid America Earthquake Center October 2004 ABSTRACT This report describes the development of a new one-dimensional nonlinear site response model and application of the model in probabilistic hazard analysis of the Mississippi embayment (ME) for estimation of depth dependent site coefficients. The first part of the report describes the development of a new one-dimensional nonlinear site response model, DEESPOIL, to simulate seismic wave propagation through deep deposits. DEEPSOIL incorporates several enhancements over currently available non-linear models. A confining pressure dependent non-linear constitutive soil model is developed. Full and extended Rayleigh viscous damping formulations have been incorporated in the site response analysis code to increase the accuracy of the solution. Current formulations of non-linear site response analysis contain a frequency dependent viscous damping term that often artificially filters out high frequency components of ground motion. The proposed formulations preserve most of these components. The second part of the report describes the probabilistic seismic hazard analysis with non-linear site effect performed in the ME to develop site coefficients. Current site coefficients, proposed in National Earthquake Hazard Reduction Program (NEHRP), are used with USGS hazard maps to develop site specific recommended response spectrum. The coefficients are developed for 30 m thick soil profile and do not account for the depth of the soil column. A suite of ground motion time histories are developed that in sum result in the same hazard level as USGS hazard maps. The generated motions are propagated through the generic profiles of the ME using DEEPSOIL. The results of the analyses are presented in the form of site coefficient as functions of a) depth of the soil profile and b) level of shaking (spectral accelerations at 0.2 and 1.0 sec, both at B/C boundary). The site coefficients are comparable to NEHRP coefficients for 30 m thick profiles, but they show significant depth dependence for thicker soil profiles. A wide range of depth dependent site coefficients is developed for the ME. ii ACKNOWLEDGEMENTS This project was funded by the Mid America Earthquake Center under grant EEC- 9701785. The authors would like to acknowledge Dr. David M. Boore for his helpful advice, as well as the SMSIM code. Dr. Mitchell M. Withers for providing the earthquake data. Dr. Chiun- Lin Wu for his code. Dr. Glen Rix, Dr. Shahram Pezeshk, and Dr. Roy Van Arsdale for their data. The authors would also like to thank Dr. Chris Cramer, Dr. Robert B. Herrmann, Dr. James H. Long, Dr. Gholamreza Mesri, Dr. Timothy D. Stark, and Dr. Yi-Kwei Wen for their valuable comments. iii TABLE OF CONTENTS LIST OF TABLES.......................................................................................................................viii LIST OF FIGURES ....................................................................................................................... ix LIST OF SYMBOLS .................................................................................................................. xvii LIST OF ABBREVIATIONS...................................................................................................... xxi CHAPTER 1 INTRODUCTION .............................................................................................. 1 1.1 Non-linear site response analysis model......................................................................... 2 1.2 Dynamic soil properties for Mississippi embayment...................................................... 2 1.3 Probabilistic seismic hazard analysis for the Mississippi embayment with nonlinear site effects ....................................................................................................... 3 CHAPTER 2 ONE DIMENSIONAL SITE RESPONSE ANALYSIS .................................... 6 2.1 Evidence of local site effects .......................................................................................... 6 2.2 Empirical procedures for characterizing site effects....................................................... 7 2.3 Simulation of local site effects........................................................................................ 8 2.4 Cyclic soil behavior ...................................................................................................... 10 2.4.1 Factors affecting cyclic soil behavior ................................................................... 11 2.4.2 Influence of confining pressure on cyclic soil behavior ....................................... 11 2.5 Material constitutive model representation of cyclic soil behavior.............................. 12 2.5.1 Linear viscoelastic model ..................................................................................... 13 2.5.2 Non-linear simple-shear model............................................................................. 15 2.5.3 Plasticity based models......................................................................................... 17 2.6 Numerical formulation for one-dimensional site response analysis............................. 18 2.7 Frequency domain solution for one-dimensional site response analysis...................... 19 2.7.1 Equivalent linear analysis for one-dimensional site response analysis ................ 20 2.7.2 Quarter wavelength method.................................................................................. 21 2.8 Time domain solution ................................................................................................... 23 2.9 Summary....................................................................................................................... 24 CHAPTER 3 ONE DIMENSIONAL NONLINEAR SITE RESPONSE ANALYSIS MODEL DEVELOPMENT .............................................................................. 36 3.1 Introduction................................................................................................................... 36 3.2 Viscous damping formulation....................................................................................... 36 3.2.1 Simplified Rayleigh damping formulation ........................................................... 36 3.2.2 Full Rayleigh damping formulation...................................................................... 39 3.2.3 Extended Rayleigh viscous damping formulation ................................................ 40 3.2.4 Selection of frequencies/modes for the Rayleigh damping formulations............. 42 3.2.5 Update of the viscous damping matrix ................................................................. 47 3.3 Confining pressure dependent constitutive model........................................................ 48 3.4 Numerical implementation of non-linear site response analysis model: DEEPSOIL .. 49 3.4.1 Numerical integration ........................................................................................... 49 3.4.2 Viscous damping formulation............................................................................... 49 3.4.3 Flexible incrementation scheme ........................................................................... 50 3.4.4 Implementation of equivalent linear frequency domain analysis ......................... 50 iv 3.4.5 User interface........................................................................................................ 50 3.4.6 Guidelines for performing a nonlinear analysis with viscous damping................ 52 3.5 Evaluation of DEEPSOIL............................................................................................. 53 3.5.1 Significance of Rayleigh damping formulation.................................................... 53 3.5.2 Significance of variable [C] matrix....................................................................... 55 3.5.3 Significance of confining pressure dependent soil model .................................... 55 3.5.4 Significance of complex modulus......................................................................... 56 3.6 Evaluation of DEEPSOIL using recordings at Treasure Island.................................... 57 3.7 Summary....................................................................................................................... 58 CHAPTER 4 ESTIMATION OF DYNAMIC PROPERTIES OF THE MISSISSIPPI EMBAYMENT ................................................................................................. 93 4.1 Introduction................................................................................................................... 93 4.2 Geology and seismicity in the Mississippi embayment................................................ 93 4.3 Shear wave velocity profiles......................................................................................... 95 4.4 Available dynamic soil properties for deep deposits .................................................... 96 4.5 Estimation of small
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