A PARAMETRIC STUDY ON THE EFFECT OF SOIL-STRUCTURE INTERACTION ON SEISMIC RESPONSE OF MDOF AND EQUIVALENT SDOF SYSTEMS

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1 A PARAMETRIC STUDY ON THE EFFECT OF SOIL-STRUCTURE INTERACTION ON SEISMIC RESPONSE OF MDOF AND EQUIVALENT SDOF SYSTEMS by BEHNOUD GANJAVI B.Sc., M.Sc. THIS THESIS IS PRESENTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY OF THE UNIVERSITY OF WESTERN AUSTRALIA Structural and Earthquake Engneerng School of Cvl and Resource Engneerng June

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3 DECLARATION FOR THESIS CONTAINING PUBLISHED WORK AND/OR WORK PREPARED FOR PUBLICATION The thess contans publshed work and/or work prepared for publcaton, whch has been co-authored. The bographcal of the work and where t appears n the thess are outlned below. Ganjav B., and Hao, H. (). A parametrc nvestgaton of the nfluence of sol-structure nteracton on sesmc response of MDOF and equvalent SDOF systems Advances n Structural Engneerng, under revew. (Chapter 3) The estmated percentage contrbuton of the canddate s 8%. Ganjav B., and Hao, H. (). Effect of structural characterstcs dstrbuton on strength demand and ductlty reducton factor of MDOF systems consderng sol-structure nteracton Earthquake Engneerng and Engneerng Vbraton; (); 5-. (Chapter 4) The estmated percentage contrbuton of the canddate s 8%. Ganjav B., and Hao, H. (). Strength reducton factor for MDOF sol-structure systems The Structural Desgn of Tall and Specal Buldngs, DOI:./tal.; avalable onlne at: (Chapter 5) The estmated percentage contrbuton of the canddate s 8%. Ganjav B., and Hao, H. (). A parametrc study on evaluaton of ductlty demand dstrbuton n Mult-Degree-of-Freedom systems consderng sol-structure nteracton effects Engneerng Structures, 43; (Chapter 6) The estmated percentage contrbuton of the canddate s 8%. Ganjav B., and Hao, H. (). Optmum lateral load pattern for elastc sesmc desgn of buldngs ncorporatng sol-structure nteracton effects Earthquake Engneerng and Structural Dynamcs, (In Press), DOI:./eqe.5. (Chapter 7) The estmated percentage contrbuton of the canddate s 7%. Ganjav B., and Hao, H., and Bolourch, S. A. (). Optmum sesmc-resstant desgn of shear buldngs consderng sol-structure nteracton effects and nelastc behavor Engneerng Structures, to be Submtted. (Chapter 8) The estmated percentage contrbuton of the canddate s 8%. Behnoud Ganjav 6//3 Prnt Name Sgnature Date Hong Hao Prnt Name Sgnature Date

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5 Abstract ABSTRACT Even though extensve researches have been conducted on Sol-Structure Interacton (SSI) snce 96s, there are several aspects of the complex phenomenon of SSI that have not been addressed thoroughly. The complex behavor of SSI together wth uncertantes n sol and structure parameters, and n ground motons result n a sgnfcant controversy over the effect of SSI on structural response n both elastc and nelastc states. Recent studes consdered SSI n nelastc response analyss are manly based on dealzed structural models of sngle-degree-of-freedom (SDOF) systems. However, due to neglectng the effects of hgher modes, the number of buldng stores and lateral strength and stffness dstrbutons along the heght of structures, an SDOF system mght not be able to realstcally capture the SSI effects on the nelastc responses of real buldngs. The prmary objectve of ths research s to advance, through extensve parametrc study and analytcal research, knowledge on the effects of SSI on elastc and nelastc responses of Mult-Degree-Of-Freedom (MDOF) systems, and to develop optmzaton technques for optmum sesmc desgn of elastc and nelastc shear buldngs takng nto consderaton the SSI effects. Frstly, the study addresses the effect of SSI on elastc and nelastc response of MDOF and ts equvalent SDOF systems. The adequacy of equvalent SDOF model to estmate strength and ductlty demand of mult-storey sol-structure systems are ntensvely nvestgated. It s concluded that usng the common E-SDOF systems for estmatng the strength demands of average and slender MDOF systems when SSI effect s sgnfcant can lead to very un-conservatve results. Secondly, the effect of structural property dstrbuton on strength demand and ductlty (strength) reducton factor of MDOF fxed-base and sol-structure systems has been nvestgated. It has been done through ntensve parametrc analyses of numerous lnear and nonlnear MDOF systems and consderng fve dfferent shear strength and stffness dstrbuton patterns ncludng 3 code-specfed patterns as well as unform and concentrc patterns subjected to a group of earthquakes recorded on alluvum and soft sols. Results ndcate that for both fxed-base and flexble-base models, wth excepton of those wth very short perods, the averaged total strength demand values of structures desgned based on unform story strength and stffness dstrbuton pattern along the

6 Abstract heght of the structures are sgnfcantly greater than those of the other patterns such as code-complant patterns. Ths phenomenon s even more pronounced by ncreasng the number of stores. It s concluded that, therefore, usng the results of the unform story strength and stffness dstrbuton pattern whch has been the assumpton of many prevous research works would result n a sgnfcant overestmaton of the strength demands, generally from to 4 tmes, for MDOF systems desgned n accordance to the code-complant desgn patterns. Moreover, through a comprehensve parametrc study of numerous MDOF and ts equvalent SDOF systems subjected to a large number of earthquake ground motons effects of SSI on strength reducton factor of MDOF and equvalent SDOF systems have been ntensvely nvestgated. Based on the numercal results of nonlnear dynamc analyses and statstcal regresson analyses, a new smplfed equaton s proposed to estmate strength reducton factors of MDOF solstructure systems. Subsequently, after extensve parametrc studes on the effect of SSI on global (total) strength and ductlty demand of MDOF and the correspondng E-SDOF systems carred out n Chapters 3 to 5 as the frst part of the thess, the second part of ths research focuses on the effect of SSI on local ductlty (damage) demand dstrbuton along the heght of the structures. It s demonstrated that although the structures desgned accordng to some of the recently proposed optmum load patterns for fxed-base systems may have generally better sesmc performance when compared to those desgned by code-specfed load patterns, ther sesmc performance are far from deal f the SSI effects are consdered. Therefore, more adequate load patterns ncorporatng SSI effects for performance-based sesmc desgn needs to be proposed. Fnally, optmzaton technques have been developed for optmum desgn of elastc and nelastc shear buldngs takng nto consderaton the SSI effects. An teratve analyss procedure s ntroduced to estmate the optmum story shear strength dstrbutons for a gven structure, a gven ground moton and sol-structure key parameters, and an nelastc target level of nterest. Based on numercal analyses and statstcal regresson analyses new smplfed equatons are proposed for estmaton of lateral load patterns of elastc and nelastc sol-structure systems. It s shown that the structures desgned based on the proposed pattern, on average, dsplay remarkably better sesmc performance (.e., less structural weght and more unform damage dstrbuton over heght) than the codecomplant and recently proposed patterns by researchers for fxed-base structures.

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8 Lst of Publcatons LIST OF PUBLICATIONS REFEREED JOURNAL PAPERS: ) Ganjav B., and Hao, H. (). A parametrc nvestgaton of the nfluence of sol-structure nteracton on sesmc response of MDOF and equvalent SDOF systems Advances n Structural Engneerng, (Under revew). ) Ganjav B., and Hao, H. (). A parametrc Study on Evaluaton of Ductlty Demand Dstrbuton n Mult-Degree-of-Freedom Systems Consderng Sol- Structure Interacton Effects Engneerng Structures, 43; 88-4, October. 3) Ganjav B., and Hao, H. (). Effect of Structural Characterstcs Dstrbuton on Strength Demand and Ductlty Reducton Factor of MDOF Systems Consderng Sol-Structure Interacton Earthquake Engneerng and Engneerng Vbraton, (); 5-. 4) Ganjav B., and Hao, H. (). Strength Reducton Factor for MDOF Sol- Structure Systems The Structural desgn of Tall and Specal Buldngs, (DOI:./tal.; 5) Ganjav B., and Hao, H. (). Optmum lateral load pattern for Elastc Sesmc Desgn of Buldngs Incorporatng Sol-Structure Interacton Effects Earthquake Engneerng and Structural Dynamcs, (n Press). DOI:./eqe.5 6) Ganjav B., and Hao, H., and Bolourch, S.A. (). Optmum Sesmc- Resstant Desgn of Shear Buldngs Consderng Sol-Structure Interacton Effects and Inelastc Behavor Engneerng Structures, (To be Submtted). v

9 Lst of Publcatons REFEREED CONFERENCE PAPERS: ) Ganjav B., and Hao, H. (). Elastc and Inelastc Response of Sngle- and Mult-Degree-of-Freedom Systems Consderng Sol Structure Interacton Effects Australan Earthquake Engneerng Socety Conference. Barossa Valley, South Australa, 8- November. ) Ganjav B., and Hao, H. (). Evaluaton of the Adequacy of Code Equvalent Lateral Load Pattern and Ductlty Demand Dstrbuton for Sol-Structure Systems Australan Earthquake Engneerng Socety Conference. Barossa Valley, South Australa, 8- November. 3) Ganjav B., and Hao, H. (). Influence of Structural Property Dstrbuton on Elastc and Inelastc Strength Demand of Shear Buldngs wth Sol-Structure Interacton, Australasan Structural Engneerng Conference. Perth, Western Australa.-3 July. Paper N: 6. 4) Ganjav B., and Hao, H. (). New lateral Force Dstrbuton for Elastc Sesmc Desgn of Shear Buldngs Incorporatng SSI Effects, Australasan Structural Engneerng Conference. Perth, Western Australa.-3 July. Paper N: 3. 5) Ganjav B., and Hao, H. (). An Optmzaton Technque for Unform Damage Dstrbuton n Inelastc Shear Buldng Incorporaton Sol-Structure Interacton Effects, 5 World Conference on Earthquake Engneerng. Lsbon, Portugal, 4-8 September. 6) Ganjav B., and Hao, H. (). Ductlty Reducton Factor for Mult-Degreeof-Freedom Systems wth Sol-Structure Interacton, 5 World Conference on Earthquake Engneerng. Lsbon, Portugal, 4-8 September. v

10 Table of contents TABLE OF CONTENTS ABSTRACT... LIST OF PUBLICATIONS...v LIST OF CONTENTS...v LIST OF FIGURES..x LIST OF TABLES xv ACKNOWLEDGEMENTS.xx CHAPTER INTRODUCTION.... Background and Motvaton.... Research Goals Outlnes..7.4 References..9 CHAPTER MODELING AND ANALYSIS PROCEDURES...4. Introducton...4. Sol-Foundaton- Structure Model 5.. Sol-Foundaton Model.5.. Superstructure Models.8. 3 Key Parameters Methodology and Procedures for Analyss....5 OPTSSI Computer Program...5. Sol and Structural Modellng and Assumpton.5. Structural Dampng Modellng Earthquake Ground Moton Parameters Story Shear Strength and Stffness Dstrbuton Pattern..5.6 Computatonal Features of OPTSSI.5.7 Evaluaton of MDOF Sol-Structure Systems Desgned Based on Fxed-Base Assumptons Database for Parametrc Analyss 8.9 References 3 v

11 Table of contents CHAPTER 3 EFFECT OF SOIL-STRUCTURE INTERACTION ON ELASTIC AND INELASTIC RESPONSE OF MDOF AND EQUIVALENT SDOF SYSTEMS Introducton Methodology and Procedures for Analyss General Procedure Proposed Iteratve Procedure Step-by-Step Procedure for Parametrc Study Effect of SSI on Strength Demands of MDOF and E-SDOF Systems Strength Demands for E-SDOF Systems Correspondng to Dfferent Number of Stores Strength Demands for MDOF and E-SDOF Sol-Structure Systems Adequacy of E-SDOF systems n estmatng strength demands for MDOF fxed-base and sol-structure systems Effect of SSI on Ductlty Demand of MDOF and E-SDOF Systems CONCLUSION References.55 CHAPTER 4 Effect of Structural Characterstcs Dstrbuton on Strength Demand and Ductlty Reducton Factor of MDOF Systems Consderng Sol- Structure Interacton Introducton Selected Story Strength and Stffness Dstrbuton Patterns Analyss Procedure Effect of Structural Characterstcs Dstrbuton on Strength Demand of MDOF Systems Comparson between Strength Demands of Fxed-Base and Flexble-base MDOF Systems Valdaton of the Numercal Results Effect of Structural Characterstcs Dstrbuton on Ductlty Reducton Factor of MDOF Systems Effect of Structural Characterstcs Dstrbuton Effect of Sol Flexblty Summary and Conclusons References 76 v

12 Table of contents CHAPTER 5 Strength Reducton Factor for Mult-Degree-Of-Freedom Systems Consderng Sol-Structure Interacton Effects Introducton Selected Earthquake Ground Motons Procedure for Analyss Effect of SSI on Strength Reducton Factor of E-SDOF Systems Strength Reducton Factors of E-SDOF Systems for Structures wth Dfferent Number of Stores Effect of Ductlty Rato Effect of Dmensonless Frequency Effect of Aspect Rato Usng R of E-SDOF Fxed-base Systems for Sol-Structure Systems Effect of SSI on Strength Reducton Factor of MDOF Systems Effect of Number of Stores Effect of Dmensonless Frequency Effect of Aspect Rato Estmaton of the Strength Reducton Factors of MDOF Sol-Structure Systems Summary and Conclusons 5.8 References... CHAPTER 6 A Paramterc Study on Evaluaton of Ductlty Demand Dstrbuton n MDOF Shear Buldngs Consderng SSI Effects Introducton.5 6. Lateral Loadng Patterns Code-Specfed Sesmc Desgn Lateral Load Patterns Lateral Load Pattern Proposed by Mohammad et al. (4) Lateral Load Pattern Proposed by Park and Medna (7) Lateral Load Pattern Proposed by Hajrasoulha and Moghaddam (9) Analyss Procedure Evaluaton of Ductlty Demand Dstrbuton n Shear-Buldng Structures Consderng SSI Effect 6.4. Effect of Number of Stores... v

13 Table of contents 6.4. Effect of Fundamental Perod Effect of Aspect Rato and Dmensonless Frequency Effect of Dampng Model Effect of Structural Dampng Rato Effect of Structural Stran Hardenng Effect of Earthquake Exctaton Valdaton of the Numercal Results Adequacy of IBC-9 Code-Specfed Lateral Loadng Pattern Effect of Number of Stores and Target Ductlty Demand Effect of Dmensonless Frequency and Aspect Rato Adequacy of Conventonal Code-Complant and Recently Proposed Load Patterns for Sol-Structure Systems Weght-Based Method COV-Based Method Summary and Conclusons References...34 CHAPTER 7 Optmum Lateral Load Pattern for Elastc Sesmc Desgn of Buldngs Incorporaton Sol-Structure Interacton Effects Introducton Selected Earthquake Ground Motons Optmum Dstrbuton of Elastc Desgn Lateral Force for Sol-Structure Systems Effect of Structural Dynamc Characterstcs and SSI Key Parameters on Optmum Lateral Force Pattern Effect of Convergence Parameter Effect of Earthquake Exctaton Effect of Intal Load Pattern Effect of Fundamental Perod Effect of Number of Stores Effect of Dmensonless Frequency Effect of Aspect Rato Effect of Structural Dampng Rato Effect of Structural Dampng Model New Lateral Load Pattern for Elastc Sol-Structure Systems Monte Carlo Smulaton..59 x

14 Table of contents 7. 7 Conclusons References.64 CHAPTER 8 Optmum Sesmc Desgn of Shear Buldngs Consderng Sol- Structure Interacton and Inelastc Behavor Introducton Estmaton of Optmum Inelastc Lateral Force Dstrbuton for Sol-Structure Systems Effect of Structural Dynamc Characterstcs and SSI Key Parameters on Optmum Inelastc Lateral Force Pattern Effect of Fundamental Perod Effect of Target Ductlty Demand Effect of Number of Stores Effect of Dmensonless Frequency Effect of Aspect Rato Effect of Structural Dampng Rato and Dampng Model Effect of Structural Stran Hardenng Effect of Sol Posson s Rato Effect of Earthquake Exctaton New Sesmc Load Pattern for Sol-Structure Systems wth Inelastc Behavor Adequacy of Proposed Optmum Inelastc Lateral Load Pattern Conclusons References...93 CHAPTER 9 Concludng Remarks Man Fndngs Effect of Sol-Structure Interacton on Elastc and Inelastc Response of Equvalent SDOF and MDOF Systems Effect of Structural Charactrastcs Dstrbuton on Strength Demand and Ductlty Reducton Factor of MDOF Systems Consderng Sol-Structure Interacton Strength Reducton Factor For MDOF Systems Consderng Sol- Structure Interacton A Paramterc Study on Evaluaton of Ductlty Demand Dstrbuton n MDOF Shear Buldngs Consderng SSI Effects..97 x

15 Table of contents 9..5 Optmum Lateral Load Pattern for Elastc Sesmc Desgn of Buldngs Incorporaton Sol-Structure Interacton Effects Optmum Lateral Load Pattern for Sesmc Desgn of Inelastc Shear- Buldngs Consderng Sol-Structure Interacton Effects Recommendatons for Future Works x

16 Lst of Fgures LIST OF FIGURES Fgure -: Typcal -storty shear buldng models (a) fxed-base model and (b) flexblebase model... Fgure -: Typcal MDOF and E-SDOF sol-structure systems (a) MDOF system (b) E- SDOF system... Fgure -3: A part of the SSIOPT menu.7 Fgure -4: Typcal database output for SSIOPT (Strength Demand) 9 Fgure -5: Typcal database output for SSIOPT (Strength Reducton Factor).3 Fgure 3-: Comparson of the averaged elastc and nelastc strength demand for dfferent E- SDOF system wth sol-structure nteracton ( a = ).4 Fgure 3- Comparson between frst-mode shape for dfferent number of stores: (a) T fx = and (b) T fx =3..4 Fgure 3-3: Comparson of the averaged elastc strength demand for ESDOF and MDOF sol-structure systems..43 Fgure 3-4: Comparson of the averaged nelastc strength demand for ESDOF and MDOF sol-structure systems for µ = 43 Fgure 3-5: Comparson of the averaged nelastc strength demand for ESDOF and MDOF sol-structure systems for µ =6 44 Fgure 3-6: Effect of number of stores on the averaged elastc and nelastc strength demand of fxed-base and sol-structure systems for H r = 3.45 Fgure 3-7: The rato of elastc and nelastc strength demands n -story buldng to those n the correspondng E-SDOF system.48 Fgure 3-8: COV of story ductlty demand for dfferent MDOF sol-structure systems 48 Fgure 3-9: Heght-wse dstrbuton of averaged ductlty demand for systems wth T fx =.5 and μ= Fgure 3-. Averaged ductlty demand for dfferent E-SDOF and MDOF sol-structure systems for H r= 3 5 Fgure 3-: Averaged ductlty demand for dfferent E-SDOF and MDOF sol-structure systems for µ=..5 Fgure 3-: Averaged ductlty demand for dfferent E-SDOF and MDOF sol-structure systems for µ= x

17 Lst of Fgures Fgure 4-: Dfferent Lateral force and normalzed shear strength patterns for the-story buldng wth T fx =.5 sec.6 Fgure 4-: Effect of structural characterstcs dstrbuton on strength demand for MDOF systems wth N = 5 and H r = Fgure 4-3: Effect of structural characterstcs dstrbuton on strength demand for MDOF systems wth N = 5 and H r = Fgure 4-4: Averaged rato of strength demand n unform pattern to that of the IBC-9 pattern for systems wth H r = Fgure 4-5: Averaged ratos of strength demands of sol-structures systems wth respect to the fxed-base systems n dfferent story strength and stffness patterns ( a = 3, N= ). 67 Fgure 4-6: Effect of structural characterstcs dstrbuton on averaged ratos of strength demands of sol-structures systems to the fxed-base systems (N = ; a = 3; H r =5).67 Fgure 4-7: Comparsons of the averaged strength demands resulted from ths study and OPENSEES for the 5-story buldng wth a = 3 ( earthquakes)..68 Fgure 4-8: Effect of structural characterstcs dstrbuton on averaged ductlty reducton factor of MDOF fxed-base and sol-structure systems (N = and H r = 3).7 Fgure 4-9: Comparson of averaged ratos of ductlty reducton factor n dfferent load patterns to the IBC-9 pattern for systems wth N = and H r = 3 7 Fgure 4-: Effect of sol flexblty on averaged ductlty reducton factor of MDOF systems ( H r = 3)..73 Fgure 4-: Averaged ductlty demand spectra of MDOF sol-structure systems desgned based on fxed-base ductlty reducton factor ( H r = 3 and µ = 6).73 Fgure 5-: Comparson of the averaged strength reducton factor for dfferent E-SDOF systems (µ = 4) 83 Fgure 5-: Averaged strength reducton factor spectra for E-SDOF systems wth dfferent ranges of nonlnearty ( H r = 3)...84 Fgure 5-3: Effect of dmensonless frequency on Averaged strength reducton factor spectra of E-SDOF sol-structure systems..85 Fgure 5-4: Effect of aspect rato on Averaged strength reducton factor spectra of E-SDOF sol-structure systems.86 x

18 Lst of Fgures Fgure 5-5: Averaged ductlty demand spectra of E-SDOF sol-structure systems desgned based on fxed-base strength reducton factors..87 Fgure 5-6: Effect of the number of stores on averaged strength reducton factor spectra of fxed-base and sol-structure systems ( H r = 3)...9 Fgure 5-7: Averaged ratos of shear strength demands on MDOF systems to those on E- SDOF systems for dfferent ranges of nonlnearty (-story buldng; H r = 3) 9 Fgure 5-8: Averaged modfyng factor for MDOF fxed-base and sol-structure systems (- story buldng; H r = 3) 9 Fgure 5-9: Effect of dmensonless frequency on averaged strength reducton factor spectra of MDOF sol-structure systems ( H r = ) Fgure 5-: Effect of dmensonless frequency on averaged strength reducton factor spectra of MDOF sol-structure systems ( H r = 5) Fgure 5-: Effect of aspect rato on averaged strength reducton factor spectra of MDOF sol-structure systems (-story buldng)..95 Fgure 5-: Correlaton between Eq. (5-5) and averaged numercal results for strength reducton factors of MDOF sol-structure systems ( H r = 3) Fgure 6-: Dfferent Lateral force and normalzed shear strength patterns for -story buldng wth T fx =.5 sec and μ= 4.9 Fgure 6-: Effect of number of stores on heght-wse dstrbuton of averaged ductlty demand for systems wth T fx = and H r =3. Fgure 6-3: Effect of fundamental perod on heght-wse dstrbuton of averaged ductlty demand for systems wth N= and H r =3...3 Fgure 6-4: Effect of aspect rato and dmensonless frequency on heght-wse dstrbuton of averaged ductlty demand for systems wth N= and T fx xv =... 4 Fgure 6-5: Effect of dampng model on heght-wse dstrbuton of ductlty demand for systems wth N=, µ = 4 and H r =3subjected to Loma Preta earthquake (APEEL - Redwood Cty).6 Fgure 6-6: Effect of dampng rato on heght-wse dstrbuton of ductlty demand for systems wth N=, T fx =.5, µ = 4 and H r =3 subjected to Loma Preta earthquake (APEEL - Redwood Cty). 6 Fgure 6-7: Effect of stran hardenng on heght-wse dstrbuton of ductlty demand for systems wth N=, T fx =.5, µ = 4 and H r =3 subjected to Loma Preta earthquake (APEEL - Redwood Cty). 8

19 Lst of Fgures Fgure 6-8: Heght-wse dstrbuton of ndvdual and averaged ductlty demand for systems wth N= 5, H r =3, T fx =.5 and µ = 6. 8 Fgure 6-9: Calbratng the stffness of the elastc lnear sprngs presented by Grange et al., ()... Fgure 6-: Comparsons of the ductlty demand dstrbutons resulted from nonlnear macro-element and equvalent lnear elastc (cone) models for two levels of nonlnearty (µ=, 6); -story buldng wth T fx = sec, H r =5 (Average of earthquake records).... Fgure 6-: Effect of number of stores on averaged COV of story ductlty demands for systems wth H r =3 desgned accordng to IBC-9 load pattern Fgure 6-: Effect of maxmum ductlty on averaged COV of story ductlty demands for systems wth H r =3 desgned accordng to IBC-9 load pattern Fgure 6-3: Effect of sol flexblty on averaged COV of story ductlty demands for systems wth N=5 and H r =3 desgned accordng to IBC-9 load pattern 6 Fgure 6-4: Effect of aspect rato on averaged COV of story ductlty demands for systems wth N=5 and a =3 desgned accordng to IBC-9 load pattern. 6 Fgure 6-5: Averaged Weght Index of -story sol-structure system wth H r =3 desgned accordng to dfferent load patterns...3 Fgure 6-6: Averaged COV of -story sol-structure system wth H r =3 desgned accordng to dfferent load patterns.. 3 Fgure 7-: IBC-9 (ASCE/SEI 7-5) desgn spectrum for sol type E and response spectra of adjusted earthquakes (5% dampng) for selected ground motons..4 Fgure 7-: Comparson of IBC-9 wth optmum desgned models of fxed-base and solstructure system: (a) lateral force dstrbuton; (b) story ductlty pattern, -story shear buldng wth T fx =.5 sec, H r =3, Kobe (Shn Osaka) smulated earthquake.45 Fgure 7-3: Varaton of structural weght ndex for dfferent values of convergence powers; -story sol-structure system wth T fx =.5 sec, H r = 3, a =, Kobe (Shn Osaka) smulated earthquake 46 Fgure 7-4: Optmum lateral force dstrbuton for dfferent earthquake exctatons, -story buldng wth T fx =.5 sec: (a) Fxed-base model; (b) Sol-structure model wth H r =3 and a =...48 xv

20 Lst of Fgures Fgure 7-5: Effect of (a) ground moton ntensty and (b) ntal load pattern on optmum lateral force profle for sol-structure systems wth T fx =.5 sec, H r =3 and a = ; Kobe (Shn Osaka) smulated earthquake...48 Fgure 7-6: Effect of ntal load pattern on optmzaton teraton steps; -story shear buldng; (a) Fxed-base systems (b) sol-structure system wth T fx =.5 sec, H r = 3, a, Kobe (Shn Osaka) smulated earthquake Fgure 7-7: Effect of fundamental perod (a) and the number of stores (b) on averaged optmum lateral force profle for sol-structure systems wth H r =3 and a = : T fx =.5 sec....5 Fgure 7-8: Effect of dmensonless frequency on averaged optmum lateral force profle for -story sol-structure systems wth H r =3: (a) T fx = sec.: (b) T fx = sec..5 Fgure 7-9: Effect of aspect rato on averaged optmum lateral force profle for a -story sol-structure system wth T fx =.5 sec...5 Fgure 7-: Effect of structural dampng rato (a) and dampng model (b) on optmum lateral force profle; -story sol-structure system wth H r =3, a = and T fx =.5 sec; Loma Preta (APEEL - Redwood Cty) earthquake...53 Fgure 7-: The spectra of rato of requred to optmum structural weght for the -story sol-structure systems desgned accordng to dfferent load patterns; average of earthquakes...57 Fgure 7-: The spectra of COV for the -story sol-structure systems desgned accordng to dfferent load patterns; average of earthquakes; a = Fgure 7-3: Comparson of dfferent load patterns for -story sol-structure systems wth T fx =.5 sec, H r =3 and a = 3: (a) lateral force dstrbuton; (b) story ductlty pattern; average of earthquakes.58 Fgure 7-4. Correlaton between Eq. (7-4) and numercal results..58 Fgure 7-5: Comparsons of the COV of story ductlty demand dstrbuton of the -story buldng desgned based on the proposed optmum pattern and IBC-9 pattern; ( T fx =.5 sec, H r=3, Kobe (Shn Osaka) smulated earthquake)..6 Fgure 8-: Comparson of IBC-9 and fxed-base optmum load patterns wth optmum desgned models of sol-structure system: (a) lateral force dstrbuton; (b) story ductlty pattern, -story shear buldng wth T fx =.5 sec, H r =3, Kobe (Shn Osaka) smulated earthquake 7 xv

21 Lst of Fgures Fgure 8-: Effect of fundamental perod on averaged optmum lateral force profle for solstructure systems wth H r =3 and a = : -story buldng (average of earthquakes)...74 Fgure 8-3: Effect of target ductlty demand on averaged optmum lateral force profle for sol-structure systems wth H r =3 and a = : -story buldng (average of earthquakes) Fgure 8-4: Effect of the number of stores on averaged optmum lateral force profle for solstructure systems wth H r =3 and a = : T fx =.5 sec. (average of earthquakes)..74 Fgure 8-5: Effect of dmensonless frequency on averaged optmum lateral force profle for -story sol-structure systems wth H r =3, µ= 6: (a) T fx =.5 sec.: (b) T fx = sec..77 Fgure 8-6: Effect of aspect rato on averaged optmum lateral force profle for a -story sol-structure system wth T fx =.5 sec, µ= Fgure 8-7: Optmum lateral force profle for a -story sol-structure system wth H r =3, a =, T fx =.5 sec and µ= 6: (a) Effect of structural dampng rato; (b) Effect of structural dampng model, Loma Preta (APEEL - Redwood Cty) smulated earthquake...79 Fgure 8-8: Effect of structural post yeld behavor on Optmum lateral force profle for a - story sol-structure system wth H r =3, a =, T fx =.5 sec; Loma Preta (APEEL - Redwood Cty) smulated earthquake...8 Fgure 8-9: Effect of sol Posson rato on Optmum lateral force profle for a -story solstructure system wth H r =3, a = 3, T fx =.5 sec; Loma Preta (APEEL - Redwood Cty) smulated earthquake.8 Fgure 8-: Effect of (a) Earthquake exctaton and (b) ground moton ntensty on optmum lateral force profle for sol-structure systems wth H r =3 and a =, µ= 4; Kobe (Shn Osaka) smulated earthquake.8 Fgure 8-: Correlaton between Eq. (8-5) and numercal results..87 Fgure 8-: The spectra of rato of requred to optmum structural weght for the -story sol-structure systems desgned accordng to dfferent load patterns; average of earthquakes (µ= )...9 Fgure 8-3: The spectra of rato of requred to optmum structural weght for the -story sol-structure systems desgned accordng to dfferent load patterns; average of earthquakes (µ= 6)...9 xv

22 Lst of Tables LIST OF TABLES Table -: Propertes of a sol foundaton element based on the cone model concept.. 7 Table 3-: Selected ground motons recorded on alluvum and soft stes based on USGS ste classfcaton 36 Table 5-: Selected ground motons recorded at alluvum and soft stes based on USGS ste classfcaton...8 Table 5-: Constant coeffcent a and b of Eq. (5-5).. 97 Table 5-3: Constant coeffcent a of Eq. (5-5). 97 Table 5-4: Constant coeffcent b of Eq. (5-5). 97 Table 5-5: Constant coeffcent a of Eq. (5-5). 98 Table 5-6: Constant coeffcent b of Eq. (5-5). 98 Table 5-7: Constant coeffcent a of Eq. (5-5). 98 Table 5-8: Constant coeffcent b of Eq. (5-5). 99 Table 7-: Selected ground motons recorded at alluvum and soft stes based on USGS ste classfcaton..39 Table 7-: Constant coeffcent a of Eq. (7-4) as functon of relatve heght. 63 Table 7-3: Constant coeffcent b of Eq. (7-4) as functon of relatve heght. 63 Table 7-4: Constant coeffcent c of Eq. (7-4) as functon of relatve heght. 64 Table 8-: Constant coeffcents of Eq. (8-5) as functon of relatve heght (µ= ). 84 Table 8-: Constant coeffcents of Eq. (8-5) as functon of relatve heght (µ= 4). 85 Table 8-3: Constant coeffcents of Eq. (8-5) as functon of relatve heght (µ= 6). 85 xv

23 Acknowledgments ACKNOWLEDGEMENTS I would lke to express my deep apprecaton to my advsor, Wnthrop Professor Hong Hao, for hs encouragement and support durng the three-year PhD program and for gvng me the opportunty to work under hs supervson. Workng under hs supervson was always an nspraton and honor. I am ndebted to the staff and postgraduate students from School of Cvl and Resource Engneerng and Centre for Offshore Foundaton Systems (COFS) for ther dverse help durng my PhD study n. My specal thanks to Dr. Kamng B for hs nvaluable suggestons and dscusson on varous aspects of the thess. Great apprecaton s dedcated to, School of Cvl and Resource Engneerng and Professor Hong Hao, for the fnancal supports I receved durng my canddature, whch conssted of an Internatonal Postgraduate Research Award (IPRS) through Australan Government, Unversty Postgraduate Award (U.P.A) through UWA, a postgraduate top-up scholarshp and an AD-Hoc scholarshp through School of Cvl and Resource Engneerng and Prof. Hong Hao, respectvely. Fnally, my boundless and sncere thanks to my wfe for all the sacrfces she has endured and never complaned about defcences; to my parents for ther contnual sprtual and fnancal supports durng my PhD and not only years. xx

24 Chapter Chapter INTRODUCTION. BACKGROUND AND MOTIVATION The nescapable reoccurrence of severe earthquakes around the world has emphaszed the necessty of better understandng of the structural responses subjected to earthquake ground motons to reduce ther vulnerablty through better desgn and retrofttng. As ponted out by Krawnkler et al., (6), n performance-based earthquake engneerng framework, a good desgn s generally based on the phlosophy of ncorporatng performance target up front n the desgn process, so that followng performance assessment becomes more of a verfcaton process rather than a desgn mprovement process. Moreover, a poor ntal conceptual desgn lkely wll never lead to a good desgn even though the ntal desgn to some extent satsfes the performance targets (Krawnkler et al., 6).The successful ncorporaton of performance-based earthquake engneerng n the desgn process necesstates accurate evaluaton of the sesmc demands on structures at dfferent hazard levels to compare wth correspondng capacty crtera. Sesmc demands of buldng structures are known to be dependent on many factors such as structural propertes, ground moton characterstcs, ste condtons as well as solstructure nteracton (SSI). SSI s one of the mportant factors that can sgnfcantly affect the sesmc responses of structures located on soft sols by alterng the overall stffness and energy dsspaton mechansm of the systems. In fact, a sol-structure system behaves as a new system havng longer perod and generally hgher dampng due to energy dsspaton by hysteretc behavour and wave radaton n the sol. SSI usually s not an attractve subject for cvl engneerng communty due to ts complex behavour. The complex behavour of SSI together wth uncertantes n sol and structure parameters, and n earthquake ground moton result n a sgnfcant controversy over the effect of SSI on structural response n both elastc and nelastc states.

25 Chapter The general effects of SSI on elastc response of sngle-degree-of freedom (SDOF) and mult-degree-of freedom (MDOF) systems wth an emphass on the former were the subject of many studes n the 97s (Perelman et al., 968; Sarrazn et al., 97; Jennngs and Belak, 973; Chopra and Guterrez, 974; Veletsos and Meek, 974; Veletsos and Nar, 975; Veletsos, 978). In poneerng studes, extensve efforts made by Jennngs and Belak (973), Veletsos and Meek (974) and Veletsos and Nar (975) were led to ntroducng the modfcaton of the sesmc demand of elastc SDOF structures. They found that the effect of nertal nteracton on the structural response can smply be predcted from the response of an equvalent SDOF system through an ncrease n the fundamental natural perod and a change n the assocated dampng of a fxed-base structure. They also concluded that SSI can ether ncrease or decrease the sesmc demand of the structures dependng on the system parameters and the characterstcs of the earthquake ground moton. These works led to provdng tentatve provsons n ATC3-6 (ATC, 978), whch s actually the foundaton of new provsons on earthquake-resstant desgn of sol-structure systems (BSSC, ; FEMA-44, 5). Code-complant sesmc desgns for SSI systems are, conventonally, based on the approxmaton n whch the predomnant perod and assocated dampng of the correspondng fxed-base system are modfed (Jennngs and Belak, 973; Veletsos and Meek, 974). In fact, the current sesmc provsons consder SSI, generally, as a benefcal effect on sesmc response of structures snce SSI usually causes a reducton of total shear strength of buldng structures (BSSC, ; ASCE, 5). However, the nelastc behavour of the superstructure wth the nfluence of SSI, nevtable durng severe earthquakes, has not been well nvestgated. On the other hand, the current sesmc desgn phlosophy s based on elastc behavour of structures wth SSI effect when subjected to moderate and severe earthquakes. Hence, there s a necessty to nvestgate the effect of SSI on nelastc response of buldng structures. One of the poneerng works on nelastc sol-structure systems were made by Veletsos and Verbc (974) and Belak (978). Utlzng the method of equvalent lnearzaton to solve the equatons of moton Belak (978) proposed a smplfed approxmate formula for estmaton of the fundamental resonant frequency of the system and for an effectve crtcal dampng rato. They recognzed that for non-lnear hysteretc structures complance of the sol foundaton may lead to larger dsplacements wth respect to the correspondng fxed-base structure. They also ponted out that ths behavour dffers from that generally observed for lnear systems, for whch the effect of sol-structure nteracton s to reduce the rgd-base response. Muller and Kentzel (98) subsequently

26 Chapter nvestgated the ductlty demands of SDOF sol-structure systems. They showed that the ductlty demand of structures, when consderng sol beneath them, could be dfferent from that of the equvalent SDOF systems wthout consderng SSI. In another study, Campol and Pnto (995) have concluded that the nelastc sesmc demand of SDOF systems essentally remans unaffected by SSI n general, and n some cases SSI results n a decrease n the response. Ths concluson, however, contradcts wth the results of Belak (978). Rodrguez and Montez () nvestgated the response and damage of buldngs located on flexble sol and concluded that nelastc dsplacement demand n sol-structure system can be approxmated by usng an equvalent fxed-base system havng an elongated perod. The effects of SSI n yeldng systems, ncludng both knematc and nertal nteracton, were nvestgated by Avles and Perez-Rocha (3). They developed the concepts of equvalent elastc sol-structure system to nclude the nonlnear behavour of the structure by means of a nonlnear replacement SDOF oscllator defned by an effectve ductlty together wth the effectve perod and dampng of the system for the elastc condton. In further works, consderng aforementoned nonlnear replacement SDOF oscllator, they also studed the effect of SSI on strength-reducton and dsplacementmodfcaton factors as well as damage ndex of structures (Avles and Perez-Rocha, 5; Avles and Perez-Rocha, 7). Ghannad and Ahmadna (6) assessed the adequacy of ATC3-6 (978) regulaton when consderng the SSI effect on nelastc response of structures usng smplfed SDOF system wth elastc-perfectly plastc behavour. They concluded that usng ths provson leads to hgher ductlty demands n the structure, especally for the case of short perod buldngs located on soft sols. In more recent years, more studes have been reported by researchers to nvestgate the SSI effect on nelastc behavour of SDOF systems (Mahsul and Ghannad, 9; Moghaddas et al., ; Avles and Perez-Rocha, ). As mentoned n the lterature, almost all researches made on nonlnear sol-structure systems focused on SDOF systems whle the SSI effect on nelastc response of MDOF systems due ts more complexty has not been nvestgated n detal. A few studes of SSI effects on MDOF systems are those conducted by Dutta et al. (4), Barcena and Steva (7), Chouw and Hao (8a, 8b), Raychowdhury () and Tang and Zhang (). These studes concentrated on nvestgatng the SSI effects on specfc structures. Systematc studes of SSI effects on sesmc demands of MDOF systems cannot be found n the lterature yet. Current practce and research often adopt the studes based on 3

27 Chapter SDOF systems to model the performance of MDOF system. However, SDOF systems havng only one DOF may not be able to correctly reflect the realstc behavour of common buldng structures nteractng wth sol beneath them when subjected to earthquake ground motons. Ths can be due to the lack of ncorporatng the effects of number of stores and hgher modes as well as, more mportantly the effect of heghtwse dstrbuton of lateral strength and stffness on nelastc response of real solstructure systems. In the frst part of ths dssertaton (Chapters 3-5), an ntensve parametrc study s performed to nvestgate the effect of nertal SSI on both elastc and nelastc sesmc strength and ductlty demands of MDOF and ts equvalent SDOF (E-SDOF) systems usng smplfed sol-structure model for surface (shallow) foundaton n whch the knematc nteracton s zero. Ths s carred out for a wde range of non-dmensonal parameters to nvestgate the adequacy of E-SDOF systems on estmaton of sesmc strength and ductlty demand of MDOF sol-structure systems (Chapter 3). Moreover, n Chapter 4 takng nto consderaton the dfferent shear strength and stffness dstrbuton patterns for MDOF systems subjected to a group of earthquake ground motons recorded on alluvum and soft sols, the effect of structural property dstrbutng on strength demand and strength (ductlty) reducton factor of MDOF fxed-base and sol-structure systems are parametrcally nvestgated. Chapter 5 parametrcally study the effects of SSI on strength reducton factor of MDOF and ts equvalent SDOF systems. A new smplfed equaton s proposed to estmate the strength reducton factors of MDOF solstructure systems. In almost all current sesmc desgn codes n the world, lateral-load resstng systems for regular structures are prmarly desgned based on the equvalent statc lateral force procedure. Ths procedure s generally regardng the sesmc effects as lateral nerta forces, whch s called force-based desgn procedure. Therefore, the dstrbuton of story stffness and strength along the heght of the structures are desgned prmarly based on these statc forces that are manly derved accordng to elastc structural behavour analyses of fxed-base structures under sesmc loadng. The nelastc behavour s only accounted approxmately n an ndrect manner. The heght-wse dstrbuton of these lateral load patterns from varous standards such as Euro Code 8 (CEN, 3), Mexco Cty Buldng Code (Mexco, 3), Unform Buldng Code (UBC, 997), NEHRP 3 (BSSC, 3), ASCE/SEI 7-5 (ASCE, 5), Australan Sesmc code (AS- 7.4, 7) and Internatonal Buldng Code, IBC 9 (ICC, 9) depends on the 4

28 Chapter fundamental perod of the structures and ther mass. They are derved prmarly based on elastc dynamc analyss of the correspondng fxed-base structures wthout consderng sol-structure nteracton (SSI) effect. In other words, the sesmc lateral load patterns n all aforementoned provsons are based on the assumpton that the sol beneath the structure s rgd, and hence the nfluence of SSI effect on load pattern s not consdered. The effcency of usng the code-specfed lateral load patterns for fxed-base buldng structures have been nvestgated durng the past two decades (Anderson et al., 99; Glmore and Bertero, 993; Chopra, 995, Moghaddam and Mohammad, 6,; Ganjav et al., 8, Hajrasoulha and Moghaddam, 9). Leelatavwat et al. (999) evaluated the sesmc demands of md-rse moment-resstng frames desgned n accordance to UBC 94. They proposed mproved load patterns usng the concept of energy balance appled to moment-resstng frames wth a pre-selected yeld mechansm. Lee and Goel () also proposed new sesmc lateral load patterns for hgh-rse moment-resstng frames up to -story wth the same concept whch Leelatavwat et al. (999) used. However, they used SDOF response modfcaton factor as well as structural ductlty factors and dealt wth a lmted number of ground motons. Ther proposed load pattern fundamentally follows the shape of the lateral load pattern n the code provsons (.e., UBC 994, 997) and s a functon of mass and the fundamental perod of the structure. In a more comprehensve research, Mohammad et al. (4) and Mohammad and Moghaddam (6) nvestgated the effect of lateral load patterns specfed by the Unted States sesmc codes on drft and ductlty demands of fxed-base shear buldng structures under earthquake ground motons, and found that usng the code-specfed desgn load patterns do not lead to a unform dstrbuton and mnmum ductlty demands. Ganjav et.al (8) nvestgated the effect of equvalent statc and spectral dynamc lateral load patterns specfed by the major sesmc codes on heghtwse dstrbuton of drft, hysteretc energy and damage subjected to severe earthquakes n fxed-base renforced concrete buldngs. They concluded that n strong ground motons, none of the lateral load patterns wll lead to unform dstrbuton of drft, hysteretc energy and damage, and an ntense concentraton of the values of these parameters can be observed n one or two stores especally n equvalent statc method. More recently, several studes have been conducted by researchers to evaluate and mprove the code-specfed desgn lateral load patterns based on the nelastc behavour of the structures (Moghaddam and Hajrasoulha, 6; Park and Medna, 7; Hajrasoulha and Moghaddam, 9; Goel et al., ). However, all researches have 5

29 Chapter been concentrated on the dfferent types of structures wth rgd foundaton,.e., wthout consderng SSI effects. In the second part of ths dssertaton (Chapters 6-8), through performng ntensve parametrc analyses of nonlnear mult-degree-of freedom (MDOF) systems wth SSI subjected to a famly of earthquakes recorded on alluvum and soft sols the effect of SSI on heght-wse dstrbuton of ductlty demands are nvestgated (Chapter 6). Effect of many parameters ncludng fundamental perod, level of nelastc behavour, the number of stores, dampng model, dampng rato, structural stran hardenng, earthquake exctaton, level of sol flexblty, and structure slenderness rato on heght-wse dstrbuton of damage (ductlty demand) are ntensvely nvestgated. In addton, the adequacy of three code-complant lateral loadng patterns, namely UBC-97, IBC-9 and EuroCode-8 as well as three recently proposed optmum loadng patterns derved from analysng fxed-base structures are parametrcally nvestgated for sol-structure systems. In further work (Chapter 7), usng the unform dstrbuton of damage over the heght of structures, as the desgn target, an optmzaton algorthm for sesmc desgn of elastc sol-structure systems s developed. Consequently, utlzng the proposed optmzaton approach a new load pattern for elastc sol-structure systems s proposed for practcal purpose. In Chapter 8, Optmzaton algorthm developed n Chapter 7 for elastc sol-structure systems s modfed to ncorporate the nelastc behavour. By performng ntensve numercal smulatons of responses of nelastc sol-structure shear buldngs wth varous dynamc characterstcs and SSI parameters, the effects of fundamental perod of vbraton, ductlty demand, earthquake exctaton, dampng rato, dampng model, structural post yeld behavor, the number of stores, sol flexblty and structure aspect rato (slenderness rato) on the optmal lateral load pattern of solstructure systems are nvestgated. Based on the results of ths study, a new lateral load pattern for sol-structure systems takng nto account for nelastc behavour s proposed. It s shown that the structures desgned based on the proposed pattern, on average, lead to remarkably better sesmc performance (.e., less structural weght and more unform damage dstrbuton over heght) than the code-complant and recently proposed patterns by researchers for fxed-base structures. 6

30 Chapter. REASERCH GOALS The present study has been undertaken wth the specfc ams of:. Developng a comprehensve computer program to perform parametrc studes on MDOF and SDOF systems subjected to earthquake ground motons wth and wthout consderaton of the SSI effects;. Investgatng the effect of nertal SSI on both elastc and nelastc sesmc strength and ductlty demands of MDOF and ts equvalent SDOF (E-SDOF) systems usng smplfed sol-structure model; 3. A comprehensve parametrc study to nvestgate the effect of structural property dstrbuton on strength demand and ductlty reducton factor of MDOF systems consderng sol-structure nteracton; 4. Proposng a new smplfed equaton to estmate strength reducton factors of MDOF sol-structure systems; 5. Performng parametrc study to evaluate the ductlty demand dstrbuton n MDOF shear buldngs wth SSI effects; 6. Developng optmzaton technques for optmum sesmc desgn of elastc and nelastc shear-buldng structures ncorporatng SSI effects; and 7. Proposng new lateral force patterns for sesmc desgn of shear buldngs ncorporatng SSI effects..3 OUTLINE Ths dssertaton s composed of nne chapters. The eght chapters subsequent to ths ntroductory chapter are organzed as follows: Chapter presents a bref classfcaton of sol-structure nteracton analyss methods and then presents the smplfed sol-structure model utlzed n ths study. The superstructure modellng and assumptons as well as sol-structure key parameters and analyss procedure are elaborated and dscussed. An outlne of the comprehensve computer program wrtten and developed for conductng ntensve parametrc studes wth consderaton of SSI effects s presented. 7

31 Chapter Chapter 3 addresses the effect of SSI on elastc and nelastc response of MDOF and ts equvalent SDOF systems. The adequacy of equvalent SDOF model to estmate strength and ductlty demand of mult-storey sol-structure systems are nvestgated. Chapter 4 studes the effect of structural property dstrbutng on strength demand and ductlty (strength) reducton factor for MDOF fxed-base and sol-structure systems. It has been done through ntensve parametrc analyses of numerous lnear and nonlnear MDOF systems and consderng fve dfferent shear strength and stffness dstrbuton patterns ncludng 3 code-specfed patterns as well as unform and concentrc patterns subjected to a group of earthquakes recorded on alluvum and soft sols. Chapter 5 through a comprehensve parametrc study of numerous MDOF and ts equvalent SDOF systems subjected to a large number of earthquake ground motons recorded on alluvum and soft sols, effects of SSI on strength reducton factor of MDOF and equvalent SDOF systems have been ntensvely nvestgated. Based on the numercal results of nonlnear dynamc analyses and statstcal regresson analyses, a new smplfed equaton s proposed to estmate strength reducton factors of MDOF sol-structure systems. Chapter 6 parametrcally studes the ductlty demand dstrbutons n MDOF shearbuldng structures wth SSI effects. Effect of many parameters ncludng fundamental perod, level of nelastc behavour, the number of stores, dampng model, dampng rato, structural stran hardenng, earthquake exctaton, level of sol flexblty, structure aspect rato on heght-wse dstrbuton of damage (ductlty demand) are ntensvely nvestgated. In addton, the adequacy of three dfferent code-complant lateral loadng patterns ncludng UBC-97, IBC-9 and EuroCode-8 as well as three recently proposed optmum loadng patterns for fxed-base structures are parametrcally nvestgated for sol-structure systems by two methods assocated to the economy of the sesmc-resstant system. Chapter 7 and 8 develop optmzaton technques for optmum desgn of elastc and nelastc shear buldngs takng nto consderaton the SSI effects. An teratve analyss procedure s ntroduced to estmate the optmum story shear strength dstrbutons for a gven structure, a gven ground moton and sol-structure key parameters, and an nelastc target level of nterest. Based on numercal analyses and statstcal regresson 8

32 Chapter analyses new smplfed equatons are proposed for estmaton of lateral load patterns of elastc and nelastc sol-structure systems. Fnally, the man outcomes of ths research are summarzed n Chapter 9. The major research fndngs are hghlghted and dscussed. Suggestons are ncluded for ssues requrng further nvestgaton..4 REFERENCES Anderson JC, Mranda E and Bertero VV (99). Evaluaton of the sesmc performance of a thrty-story RC buldng, UCB/EERC-9/6, Earthquake Engneerng Research Centre, Unv. of Calforna, Berkeley. Appled Technology Councl. (978). Tentatve provsons for the development of sesmc regulatons for buldngs, ATC-3-6, Calforna. AS-7.4. (7). Structural desgn actons: Earthquake actons n Australa. ASCE/SEI 7-5 (5). Mnmum Desgn Loads for Buldngs and Other Structures. Amercan Socety of Cvl Engneers: Reston, VA. Avles J. and Perez-Rocha L. (3) Sol structure nteracton n yeldng systems, Earthquake Engneerng and Structural Dynamcs, 3(): Avles J. and Perez-Rocha JL. (5) Influence of foundaton flexblty on R μ and C μ factors Journal of Structural Engneerng (ASCE) 3(); 3. Avles J. and Perez-Rocha J. L. (7) Damage analyss of structures on elastc foundaton, Journal of Structural Engneerng (ASCE) 33(); Avles J. and Perez-Rocha J. L. () Use of global ductlty for desgn of structure foundaton systems, Sol Dynamcs and Earthquake Engneerng 3(7): 8 6. Barcena A. and Esteva L. (7) Influence of dynamc sol structure nteracton on the nonlnear response and sesmc relablty of multstorey systems, Earthquake Engneerng and Structural Dynamcs 36(3): Belak J. (978) Dynamc response of non-lnear buldng foundaton systems, Earthquake Engneerng and Structural Dynamcs, 6(): 7 3. Buldng Sesmc Safety Councl (BSSC). () NEHRP Recommended Provsons for Sesmc Regulatons for New Buldngs and Other Structures, Federal Emergency Management Agency, Washngton, DC. 9

33 Chapter CEN (3). EuroCode 8: Fnal draft of EuroCode 8: Desgn of structure for earthquake resstance Part : General rules for buldngs: European Commttee for Standardzaton. Chopra A. K. and Guterrez J. A. (974) Earthquake response analyss of multstory buldngs ncludng foundaton nteracton, Earthquake Engneerng and Structural Dynamcs 3(): Chouw N and Hao H. (8a). Sgnfcance of SSI and non-unform near-fault ground motons n brdge response I: effect on response wth conventonal expanson jont. Engneerng Structures 3(): Chouw N and Hao H. (8a). Sgnfcance of SSI and non-unform near-fault ground motons n brdge response II: effect on response wth modular expanson jont. Engneerng Structures 3(): Campol, M., and Pnto, P. E. (995). Effects of sol-structure nteracton on nelastc sesmc response of brdge pers. Journal of Structural Engneerng, (5): Daz O., Mendoza E, and Esteva L. Sesmc ductlty demands predcted by alternate models of buldng frames. Earthquake Spectra 994 (3): Dutta, C. D., Bhattacharya K. and Roy R. (4) Response of low-rse buldngs under sesmc ground exctaton ncorporatng sol structure nteracton, Sol Dynamcs and Earthquake Engneerng 4(): Ganjav, B Vasegh Amr, J., Ghodrat Amr, G and Yahyazadeh Ahmad, Q., (8). Dstrbuton of Drft, Hysteretc Energy and Damage n Renforced Concrete Buldngs wth Unform Strength Rato. The 4th World Conf. on Earthquake Engneerng, Bejng, Chna, October -7. Ghannad, M. A. and Ahmadna A. (6) The effect of sol structure nteracton on nelastc structural demands, European Earthquake Engneerng (): Glmore, T. A, and Bertero, V.V. (993). Sesmc performance of a 3-story buldng located on soft sol and desgned accordng to UBC 99. UCB/EERC-93/4. Earthquake Engneerng Research Center, nversty of Calforna, Berkeley. Goel, S. C., Lao, W.-C., Bayat, M. R., and Chao, S.H. (). Performance-Based Plastc Desgn (PBPD) Method for Earthquake-Resstant Structures: An Overvew. Structural Desgn of Tall Specal Buldngs, (9): Hajrasoulha, I., and Moghaddam, H. (9). New lateral force dstrbuton for sesmc desgn of structures. (ASCE) Journal of Structural Engneerng, 35(8):

34 Chapter Internatonal Code Councl (ICC) (9), Internatonal Buldng Code, ICC, Brmngham, AL. FEMA 44. (5) Improvement of nonlnear statc sesmc analyss procedures, Report No. FEMA 44, Federal Emergency Management Agency, prepared by Appled Technology Councl. Jennngs, P. C. and Belak, J. (973) Dynamcs of buldngs sol nteracton, Bulletn of Sesmologcal Socety of Amerca 63(): Karam Mohammad, R., ElNaggar, M. H. and Moghaddam, H. (4) Optmum strength dstrbuton for sesmc resstant shear buldngs, Internatonal Journal of Solds and Structures 4(): Krawnkler, H., Zarean, F., Medna, R. A. and Ibarra, L. F. (6), Decson support for conceptual performance-based desgn. Earthquake Engneerng & Structural Dynamcs, 35: Leelatavwat, S., Goel, S. C., and Stojadnovc, B. (999). Toward performance-based sesmc desgn of structures. Earthquake Spectra. 5(3): Mahsul, M., and Ghannad. M. A., (9). The effect of foundaton embedment on nelastc response of structures Earthquake Engneerng & Structural Dynamcs., 38(4): Mexco Cty Buldng Code (3). Moghaddam, H., and Mohammad, R. K. (6). More effcent sesmc loadng for multdegrees of freedom structures. (ASCE) Journal of Structural Engneerng, 3(): Moghaddas, M., Cubrnovsk, M., Chase, J. G., Pampann, S., and Carr, A. (). Probablstc evaluaton of sol foundaton structure nteracton effects on sesmc structural response Earthquake Engneerng & Structural Dynamcs., 4(): Park, K., and Medna, R. A. (7). Conceptual sesmc desgn of regular frames based on the concept of unform damage (ASCE) Journal of Structural Engneerng 33(7): Moghaddas, M., Cubrnovsk, M., Chase, J. G., Pampann, S. and Carr, A. () Probablstc evaluaton of sol foundaton structure nteracton effects on sesmc structural response, Earthquake Engneerng and Structural Dynamcs 4(): Muller, F. P. and Kentzel, E. (98) Ductlty requrements for flexbly supported antsesmc structures, Proceedngs of the Seventh European Conference on Earthquake Engneerng, Athens, Greece, vol. 3, 5 September, 7 34.

35 Chapter Nassar, A. and Krawnkler, K. (99) Sesmc Demands for SDOF and MDOF Systems,. Report No.95, Department of Cvl Engneerng, Stanford Unversty, Stanford, Calforna. Perelman, D. S., Parmelee, R. A. and Lee, S. L. (968) Sesmc response of sngle-story nteracton system, Journal of the Structural Dvson (ASCE) 94(ST): Raychowdhury P. (). Sesmc response of low-rse steel moment-resstng frame (SMRF) buldngs ncorporatng nonlnear sol structure nteracton (SSI). Engneerng Structures 33(3): Rodrguez, M. E. and Montes, R. () Sesmc response and damage analyss of buldngs supported on flexble sols, Earthquake Engneerng and Structural Dynamcs 9(5): Santa-Ana, P. R. and Mranda, E. () Strength reducton factors for mult-degree of freedom systems, Proceedngs of the th world conference on Earthquake Engneerng: Auckland, Paper No.446. Sarrazn, M. A., Roesset, J. M. and Whttman, R. V. (97) Dynamc sol structure nteracton, Journal of the Structural Dvson (ASCE) 98(ST7): Senevratna, G. D. and Krawnkler, H. (997) Evaluaton of nelastc MDOF effects for sesmc desgn, Report No., Department of Cvl Engneerng, Stanford Unversty, Stanford, Calforna. Tang, Y. and Zhang, J. () Probablstc sesmc demand analyss of a slender RC shear wall consderng sol structure nteracton effects, Engneerng Structure 33(): 8 9. Unform Buldng Code (UBC). (994). Int. Conf. of Buldng Offcals, Vol., Calf. Unform Buldng Code (UBC). (997). Int. Conf. of Buldng Offcals, Vol., Calf. Veletsos, A. S. and Vann, P. (97) Response of ground-excted elastoplastc systems, Journal of the Structural Dvson, (ASCE), 97(4): Veletsos A. S. and Meek, J. W. (974) Dynamc behavor of buldng foundaton system, Earthquake Engneerng and Structural Dynamcs 3(): 38. Veletsos, A.S. and Verbc, B. (974) Dynamc of elastc and yeldng structurefoundaton systems, Proceedngs of the 5 th world conference on Earthquake Engneerng Rome. Veletsos, A. S. and Nar V.V. D. (975) Sesmc nteracton of structures on hysteretc foundatons, Journal of the Structural Dvson (ASCE) (): 9 9.

36 Chapter Veletsos, A. S. (977) Dynamcs of structure foundaton systems, In Structural and Geotechncal Mechancs, Hall WJ (ed.), A Volume Honorng N.M. Newmark. Prentce-Hall: Englewood Clffs, NJ; Wolf, J. P. (994) Foundaton Vbraton Analyss usng Smple Physcal Models, Prentce-Hall: Englewood Clffs, NJ. 3

37 Chapter Chapter MODELLING AND ANALYSIS PROCEDURE. INTRODUCTION How to treat the behavour at nfnty of the unbounded sol computatonally s the man and mportant subject n modellng sol-structure nteracton problems. It s known that the emtted wave from the vbraton structure-sol nterface wll fnally propagate n the sol towards nfnty, and at a suffcent dstance from the structure only outgong waves exst n the real radaton problem (Wolf, 994). Ths prevents an nfnte energy accumulaton. In fact, no energy assocated wth the waves may radate from nfnty towards the sol-structure system. Ths radaton condton wll lead to a boundary-value problem formulated n the frequency doman for an unbounded doman wth a unque soluton (Wolf, 994). Generally two analyss methods are avalable to solve solstructure problem: the drect method and the substructure method. In the drect method, the regon of the sol adjacent to the sol-structure nterface s explctly modelled wth sophstcated fnte element method n the same way as the structure (Wolf, 994). The artfcal boundary needs to be ntroduced, as there s no possblty to model the unbounded sol doman wth a fnte number of elements wth bounded dmensons. The transent equlbrum equatons are solved smultaneously for both structure and contnuum elements that model surroundng sol. The boundary condtons should be employed for boundares, such that they should be able to dsspate energy of ncdent waves. Owng to the dscretzaton of the sol regon adjacent to the structure, a large number of degrees of freedom appear, leadng to a sgnfcant computatonal effort. In fact, although the drect method s analytcally straghtforward, t s computatonally expensve and not feasble for parametrc studes. In order to utlze such models, one needs excessve data preparaton tme, and experence, to evaluate the results. It s beleved that ths rgorous method should be only used for specal or mportant structures such as nuclear power plants or dams. 4

38 Chapter In the substructure method, the sol-structure system wll be dvded n two parts: the frst part s the structure restng on the foundaton, and s usually modelled by masses, dashpots, and possbly nonlnear sprng or equvalently by fnte elements; the second part s the sol-structure nterface. In ths method, frst the nteracton force-dsplacement (dynamc stffness) n the nodes located on the structure-sol nterface s calculated. Ths dynamc stffness representng the rgorous boundary condton wth the unbounded sol can be physcally modelled by some sprngs and dashpots whose coeffcents are dependent on frequency of the exctaton. Then the superstructure restng on these sprngs and dashpots s analysed subjected to a gven earthquake ground moton. In the substructure method, sol and the structure can be separately analyzed wth two dfferent approaches. Therefore, dependng on the specfc case and the mportance of the problem each of them can be consdered more precsely wth respect to another one. Ths method s approprate for parametrc studes as well as for standard projects of moderate and small szes, and hence wll be utlzed n ths dssertaton.. SOIL-FOUNDATION- STRUCTURE MODEL.. Sol-foundaton model In ths study, substructure method s used to model sol-structure systems. As stated n the lterature, usng the sub-structure method, the sol can be modeled separately and then combned to establsh the sol-structure system. There are varous smplfed analyss procedures based on substructure method that can be used to model the solstructure systems. Cone model based on the one-dmensonal wave propagaton theory has been extensvely used by researchers durng the past decade to nvestgate the elastc and nelastc response of sol-structure systems subjected to earthquake ground motons (Ghannad and Ahmadna, 6; Ghannad and Jahankhah, 7, Nakhae and Ghannad, 8; Mahsul, and Ghannad, 9; Khoshnoudan and Behmanesh, ; Moghaddas et al., a and b). Cone models have been developed durng the past four decades, whch can be dvded nto three stages (Wolf and Deeks, 4): The frst stage ncluded the poneer work untl the md-97s. In ths stage, a surface foundaton restng on a homogenous half-space was analyzed. The second stage was from the 97s untl the md-99s, wth major developments n the md-99s. In that tme, the reflecton and refracton of waves on materal dscontnutes, as exsts n the case of a layer on a half-space, was addressed. Surface and embedded foundatons on a layer restng on a homogenous half-space were 5

39 Chapter modelled. Fnally n the thrd stage that dates back from the md-99s to present, the foundatons restng on mult-layered stes were ntroduced and modelled. A general approach wth suffcent accuracy for a large range of practcal cases was developed. At the ncpent stage, cone model was only used to model a foundaton on the surface of a homogenous half-space for vertcal and horzontal motons. Later, rockng moton was addressed by Meek and Veletsos (974) and, then, torsonal moton was examned by Veletsos and Nar (974). In another development, Meek and Wolf (99, 99) nvestgated the behavour of materal dscontnutes at the nterface of a layer to a halfspace. Reflected and refracted waves at the boundares of layers to a half-space were traced by ther developed cone model wth cross-secton propertes ncreasng n the drecton of the wave propagatons. Further, an embedded foundaton was also treated usng stacks of embedded dsks modelled wth double cones. Owng to many uncertantes n earthquake engneerng such as determnng the dynamc propertes of sol and structures, and earthquake characterstcs the accuracy of any analyss wll always be lmted. A devaton of maxmum % of the results of physcal models from those of the rgorous solutons for one set of nput parameters s, n general, suffcent as engneerng accuracy crteron (Wolf, 994). The Cone model used n the present parametrc study provdes suffcent accuracy for engneerng desgns. In addton to the aforementoned reasons, cone models have some advantages that can be consdered for sol-structure modellng. Cone models satsfy physcal features. For example, for a layer fxed at ts base, no radaton dampng occurs below the cut-off frequency. Cone models can be used for stes wth general layerng (Meek and Wolf, 993). They can also be used for a surface foundaton and an embedded foundaton for all degrees of freedom and for varous foundaton shapes. Cone models n whch wave patterns are clearly postulated utlze smple physcal and exact mathematcal solutons. The wave reflectons and refractons at the materal dscontnutes such as a layer on a half-space are captured usng cone model. The sol-shallow-foundaton element, n whch the knematc nteracton s zero, s modeled by an equvalent lnear dscrete model based on the cone model wth earthquake frequency-ndependent coeffcents and equvalent lnear model (Wolf, 994; Ghannad and Jahankhah, 7, Nakhae and Ghannad). However, to consder the materal dampng vscous sol mpedances,.e., stffness and dampng coeffcents, are dependent on the natural frequency of the system (.e., sol-structure system) through an teratve method. Cone model based on the one-dmensonal wave propagaton theory represents 6

40 Chapter crcular rgd foundaton wth mass m f and mass moment of nerta I f restng on a homogeneous half-space. As mentoned earler, n leu of the rgorous elasto-dynamc approach, the smplfed cone model can be used wth suffcent accuracy n engneerng practce (Wolf, 994). The sway and rockng DOFs are defned as representatves of translatonal and rotatonal motons of the shallow foundaton, respectvely, dsregardng the slght effect of vertcal and torsonal moton. The stffness and energy dsspaton of the supportng sol are represented by sprngs and dashpot, respectvely. In addton, whle beng hysteretc nherently, sol materal dampng s assumed as commonly used vscous dampng so that more ntrcaces n tme-doman analyss are avoded. All coeffcents of sprngs and dashpots for sway and rockng used to defne the sol-shallow foundaton model are summarzed n Table -. Table -: Propertes of a sol foundaton element based on the cone model concept Moton Stffness Vscous Added Mass Dampng Horzontal 8ρv s r ch = ρv sa f k h =, υ cϕ = ρv pi f 3 υ < /3 8ρv s r k ϕ =, 3( υ) cϕ = ρ( v s) If mϕ =.3 πυ ( / 3) ρr /3 υ / Rockng Internal Mass Moment of nerta υ < /3 9 π v p mϕ = ρ If r( υ )( ) 3 v s /3 υ / 9 π mϕ = ρ If r( υ ) 8 Addtonal Parallel Connected Element (= or ϕ ) 5 Materal Dampng Vscous Dampng to Stffness k Vscous Dampng to Mass C C = k ζ ( ) ω m = c ζ ( ) ω The parameters utlzed n Table - defned as k h, c h, k ϕ and c ϕ are sway stffness, sway vscous dampng, rockng stffness, and rockng vscous dampng, respectvely. Equvalent radus and area of cylndrcal foundaton are denoted by r and A f. Besdes, ρ, υ, v p and v s are respectvely the specfc mass densty, Posson s rato, dlatatonal 7

41 Chapter and shear wave velocty of sol. The relatonshp between v p and v s n the above equatons s defned as follows: ( υ) v p = v s f υ < / 3, ( υ) v = v f /3 υ / p s (.) To consder the sol materal dampng, ζ, n the sol-foundaton element, each sprng and dashpot s respectvely augmented wth an addtonal parallel connected dashpot and mass. Also, to modfy the effect of sol ncompressblty, an addtonal mass moment of nerta M ϕ equal to 5.3 πυ ( / 3) ρr can be added to the foundaton for υ greater than /3 (Wolf, 994). It s clear that the shear modulus of the sol wll change wth sol stran such that t decreases as sol stran ncreases. Thus, a reduced shear wave velocty whch s compatble wth the correspondng stran level n sol should be consdered to ncorporate sol nonlnearty. Incorporatng sol nonlnearty to the sol-foundaton element, however, may be approxmated through conventonal equvalent lnear approach n whch a degraded shear wave velocty, compatble wth the estmated stran level n sol, s utlzed for the sol medum (Moghaddas et al., a). Ths s currently used n the modern sesmc provson such as NEHRP (BSSC, ) and FEMA- 44 (5) where the stran level n sol s mplctly related to the peak ground acceleraton (PGA). In the present study, by consderng a range of reasonable values for dmensonless frequency, ths pont has been approxmately ncorporated... Superstructure models MDOF superstructure: To ncorporate the effects of hgher modes, the number of stores and lateral strength and stffness dstrbuton on nelastc response of MDOF buldngs nteractng wth sol beneath them, the well-known shear-beam model s utlzed n ths study. Due to ts smplcty, shear beam s ndeed one of the most frequently used models that facltate performng a comprehensve parametrc study (Daz et al., 994; Moghaddam and Mohammad, ; Mohammad et al., 4; Moghaddam and Mohammad, 6; Hajrasoulha and Moghaddam, 9). In the MDOF shear-buldng models utlzed n the present study, each floor s assumed as a lumped mass to be connected by elasto-plastc sprngs. Story heghts are 3 m and total structural mass s consdered as unformly dstrbuted along the heght of the structure. A 8

42 Chapter blnear elasto-plastc model wth % stran hardenng n the force-dsplacement relatonshp s used to represent the hysteretc response of story lateral stffness. Ths model s selected to represent the behavor of non-deteroratng steel-framed structures of dfferent heghts. In all MDOF models, lateral story stffness s assumed as proportonal to story shear strength dstrbuted over the heght of the structure n accordance wth the 9 IBC load pattern (IBC, 9). Fve percent Raylegh dampng was assgned to the frst mode and the mode n whch the cumulatve mass partcpaton was at least 95%. Equvalent SDOF superstructure: For each MDOF buldng an equvalent SDOF (E- SDOF) system s ntroduced n the analyss for ths study. The propertes of these E- SDOF systems are set such that the mass of the SDOF system s the same as the total mass of the MDOF buldng; smlarly, the perod of vbraton, dampng rato and effectve heght of the E-SDOF systems are the same as the fundamental mode propertes of the MDOF buldng. A typcal MDOF of fxed-base and flexble-base models as well as the correspondng E-SDOF sol-structure system are llustrated n Fgures - and -..3 KEY PARAMETERS It s well known that the response of the sol-structure system essentally depends on the sze of structure, dynamc characterstcs of the sol and structure, the sol profle as well as the appled exctaton. In other words, for a specfc earthquake ground moton, the dynamc response of the structure can be nterpreted based on the propertes of the superstructure relatve to the sol beneath t. It has been shown that the effect of these factors can be best descrbed by the followng dmensonless parameters (Veletsos, 977; Ghannad and Jahankhah, 7; Mahsul and Ghannad, 9):. A dmensonless frequency as an ndex for the structure-to-sol stffness rato defned as: a ω H v fx = (.) s where ω fx s the natural frequency of the correspondng fxed-base structure. It can be shown that the practcal range of a for conventonal buldng structures s from zero for the fxed-base structure to about 3 for the case wth severe SSI effect (Ghannad and Ahmadna, 6). Besdes, H whch s the effectve heght 9

43 Chapter of structure correspondng to the fundamental mode propertes of the MDOF buldng can be obtaned from the followng equaton: H = n m ϕ j j j= = n j = m ϕ j j j h (.3) where m j s the mass of the jth story; h s the heght from the base level to level j; and ϕ j s the ampltude at jth story of the frst mode.. Aspect rato of the buldng defned as H r, where r s the equvalent foundaton radus. 3. Interstory dsplacement ductlty demand of the structure defned as: δ = m µ (.4) δ y where δ m and δ y are the maxmum nterstory dsplacement demand resulted from a specfc earthquake ground moton exctaton and the yeld nterstory dsplacement corresponds to the structural stffness of the same story, respectvely. Note that for the MDOF buldng µ s referred to as the greatest value among all the story ductlty ratos. 4. Structure-to-sol mass rato defned as: m tot m = ρr H (.5) where H and mtot are total heght and mass of the structure, respectvely. 5. Foundaton-to-structure mass rato mf m tot. 6. Posson s rato of the sol denoted by υ. 7. Materal dampng ratos of the sol ζ and the structure ζ S. The frst two factors, affectng the responses more promnently are usually consdered as the key parameters whch defne the man SSI effect. The thrd one controls the nelastc behavor of the structure. The other parameters, havng less mportance, may be set to some typcal values for conventonal buldngs (Veletsos and Meek, 974; Wolf, 994). In the present study, the foundaton mass rato s assumed to be. of the total mass of the MDOF buldngs. However, the effect of ths rato wll be nvestgated n next

44 Chapter chapters. The Posson s rato s consdered to be.4 for the alluvum sol and.45 for the soft sol. Also, a dampng rato of 5% s assgned to the sol materal. (a) (b) Fgure -: Typcal -storty shear buldng models (a) fxed-base model and (b) flexblebase model H (a) (b) Fgure -: Typcal MDOF and E-SDOF sol-structure systems (b) MDOF system (a) E- SDOF system

45 Chapter.4 METHODOLOGY AND PROCEDURE FOR ANALYSIS The adopted sol-foundaton-structure models ntroduced n the prevous sectons are used drectly n the tme doman nonlnear dynamc analyss. Step-by-step soluton scheme n whch dynamc mposed loads are ncrementally appled to the model of the structure s utlzed for all MDOF and E-SDOF models. Varable load ncrements by consderng events wthn steps are defned n order to control the equlbrum errors n each analyss step. An event s consdered as any knd of state change that causes a change n the structural stffness. To conduct parametrc studes for both MDOF and SDOF systems wth consderaton of SSI effects subjected to a gven earthquake ground moton, a comprehensve computer program package, OPTSSI, has been wrtten specfcally for ths thess. The software has the capabltes of performng parametrc analyss automatcally to nvestgate the nfluence of many parameters such as elastc and nelastc strength demand, maxmum drft, resdual drft, strength reducton factors, MDOF modfyng factor as well as optmzaton based on unform damage dstrbuton over the heght of the structure, whch wll be brefly ntroduced n the next part..5 OPTSSI COMPUTER PROGRAM Ths program has been wrtten by FORTRAN and vsual basc programng languages wth more than 7, lnes for E-SDOF and MDOF shear-buldng structures of fxedbase and sol-structure systems. Many verfcaton processes have been conducted, and the results have been compared wth those generated by OPENSEES (). The accuracy of ths program wll be demonstrated n the next chapters. The man features of the software can be summarzed as follows:.5. Sol and structural modellng and assumpton. The structure can be modelled as shear buldng structures wth equal story heght up to 5 stores as descrbed n Secton.. for elastc and nelastc ranges of response. The correspondng E-SDOF structure wll also be created automatcally by the software. Therefore, the user only needs to select the number of stores from the program menu as shown below:

46 Chapter. A blnear elasto-plastc model wth % stran hardenng n the force-dsplacement relatonshp s used to represent the hysteretc response of story lateral stffness. However, the program has the capablty of specfyng dfferent value of stran hardenng. Other types of hysteretc behavor wll be added to the program n the next verson of the software. 3. Sol-foundaton element s modelled by an equvalent lnear dscrete model based on the cone model for an equvalent lnear elastc half space (Wolf, 994) as stated n the prevous secton. Any amount of sol densty, Posson s rato, dmensonless frequency and aspect rato can be selected for a parametrc study. It should be noted that by consderng a very small value for dmensonless frequency (e.g., a =.) the system, n a very good approxmaton, represents a fxed-base structure. 4. Foundaton mas can be consdered (.e., Found. Mass= ) or gnored (.e., Found. Mass= ): 5. Any amount of target ductlty rato and fundamental perod can be specfed for both MDOF and E-SDOF systems wth consderaton of SSI effects. 3

47 Chapter.5. Structural dampng modellng There are three optons to model structural dampng. They are the conventonal vscous dampng models for MDOF systems ncludng stffness-proportonal dampng (ST), mass-proportonal dampng (MA) and Raylegh-type dampng (RA) n whch dampng matrx s composed of the superposton of a mass-proportonal dampng term and a stffness-proportonal dampng term. The E-SDOD systems, havng only one degree-offreedom, are modeled by mass-proportonal dampng (MA). For Raylegh-type dampng model, the program automatcally checks to fnd the mode at whch the cumulatve mass partcpaton exceeds 95%. It wll, then, show the assocated mode number. In addton, any coeffcent of structural dampng (denoted as Str. Damp n the program) can be defned by user..5.3 Earthquake ground moton parameters User can easly defne the earthquake record propertes such as any type of data format (EQ Format), number of acceleraton data (EQ Data), scale factor (EQ S.Fact), acceleraton tme step, tme step for tme hstory analyss. 4

48 Chapter.5.3 Story shear strength and stffness dstrbuton pattern One of the excellent capabltes of the software for research work and parametrc study s that the program has more than optons for story shear strength and stffness dstrbuton pattern. In other word, any knd of the strength and stffness dstrbuton along the heght of structure wll affect the response of the structure such as ductlty reducton factor, dsplacement amplfcaton factor, heght-wse dstrbuton of sesmc demands and etc. Therefore, the program has been wrtten such that user can choose more than dfferent load patterns ncludng unform pattern, concentrc, trangular, trapezod, rectangular, types of parabolc patterns, UBC-97, IBC- 9, Euro-Code 8 and those optmum patterns recently proposed by researches for fxed-base buldngs. All patterns have been predefned n the software and the user just need to choose the specfc load pattern:.6 COMPUTATIONAL FEATURES OF OPTSSI The program has varous computatonal features for both fxed-base and sol-structure systems wth elastc and nelastc behavour. The man features can be descrbed as follows:. OPTSSI can optmze dfferent shear buldngs rangng from to 5 stores for both fxed-base and sol-structure systems for any specfed values of ductlty rato, fundamental perod, aspect rato, and dmensonless frequency. Optmzaton s based on the unform dstrbuton of damage (ductlty or drft) along the heght of the structure subjected to a gven earthquake ground moton. It wll be shown that the structure wll have the least structural weght at ths state. In ths approach, the structural propertes are automatcally modfed through an teratve process so that neffcent materal s gradually shfted from strong to weak parts of the structure. Ths process s contnued untl a state of unform deformaton s acheved. Ths optmzaton technque wll be dscussed n Chapters 7 and 8 of ths thess n detal. 5

49 Chapter. Coeffcent of varaton (COV) for dfferent parameters such as story ductlty demand, maxmum drft, resdual drft are calculated n each step as well as n the fnal step of analyss. 3. The absolute values and the dstrbuton patterns of elastc drft, maxmum drft n nelastc state, and resdual drft and ductlty demands along the heght of the structures are computed. 4. Effectve mass, effectve heght and structural weght ndex are computed. In addton, perods and dampng ratos of the sol-structure system n the frst 5 modes are calculated by the program. The mode number and the total cumulatve effectve mass for Raylegh-type dampng are computed as well. 5. Base shear coeffcent for both E-SDOF and MDOF systems are computed for fxed-base and sol-structure systems n elastc and nelastc ranges of response. The effects of SSI and number of degrees of freedom can be easly nvestgated by comparng the results. 6. In most of the sesmc desgn provsons, the concept of strength reducton factor has been developed to account for nelastc behavour of structures under sesmc exctatons. Most recent studes consdered sol-structure nteracton (SSI) n nelastc response analyss are manly based on dealzed structural models of SDOF systems. However, an SDOF system mght not be able to well capture the structural response characterstcs of real MDOF systems. Another feature of OPTSSI s that the program can compute strength reducton factors of MDOF and E-SDOF systems for both fxed-base and sol-structure systems. MDOF modfyng factor for strength reducton factor are also computed for both fxedbase and sol-structure systems. A part of SSIOPT menu s shown n Fgure -3. 6

50 Chapter Fgure -3: A part of the SSIOPT menu.7 EVALUATION OF MDOF SOIL-STRUCTURE SYSTEMS DESIGNED BASED ON FIXED-BASE ASSUPMTION There s another purpose for the nvestgaton of the effect of SSI on the sesmc demands of structures. Usually structures are desgned wthout consderng SSI effects. Therefore, t s necessary to evaluate the nfluence of SSI on these structures that were already desgned based on fxed-base assumpton wth consderng the effect of sol flexblty. A separate computer programs has been wrtten such that the structure that frst desgned based on the fxed-based assumpton are agan analyzed wth consderaton of the underlyng sol flexblty for the dfferent target perods, ductlty ratos and SSI key parameters for both MDOF and E-SDOF systems. At ths state, the maxmum ductlty demand, heght wse dstrbuton of the ductlty demand and ts COV wll be 7

51 Chapter calculated for the SSI system. Four dfferent analyses are consdered for ths nvestgaton as follows:. Use of base shear of fxed-base system (strength demand) for SSI system.. Use of strength reducton factor of MDOF fxed-base systems for MDOF solstructure systems 3. Use of strength reducton factor of SDOF fxed-base System for MDOF fxedbase System 4. Use of strength reducton factor of SDOF sol-structure systems for MDOF solstructure system.8 DATABASE FOR PARAMETRIC ANALYSIS Although all the aforementoned parameters can be calculated by the software, processng the large numbers of the output data for dfferent earthquakes and structural parameters are really dffcult and maybe mpossble for an ntensve parametrc study. Therefore, a database program has been wrtten to transfer all the completed data to the predesgned spread sheet fles. A database s a collecton of nformaton that s organzed so that t can be easly accessed, managed, and updated. Ths wll act as a database such that after each analyss the results wll be transferred to the specfc place of the spread sheet. Two examples of ths database are shown n Fgures -4 and -5 for strength demands and strength reducton factors of MDOF and E-SDOF systems, respectvely. 8

52 Chapter Fgure -4: Typcal database output for SSIOPT (Strength Demand) 9

53 Chapter Fgure -5: Typcal database output for SSIOPT (Strength Reducton Factor) 3