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Seismic risk assessment in southwestern British Columbia Onur, Tuna 2002

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SEISMIC RISK ASSESSMENT IN SOUTHWESTERN BRITISH C O L U M B I A by TUNA ONUR B.Sc , Bogazici University, Istanbul, Turkey, 1994 M.Sc., Bogazici University, Istanbul, Turkey, 1997 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE F A C U L T Y OF G R A D U A T E STUDIES DEPARTMENT OF CIVIL ENGINEERING We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH C O L U M B I A November 2001 ©TunaOnur, 2001 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada Date DE-6 (2/88) A B S T R A C T Southwestern British Columbia is exposed to the highest seismic risk in Canada. Estimation of the damage to structures as a consequence of a major earthquake is essential for emergency and risk management. In this thesis, first the probability and distribution of seismic damage to structural and non-structural components of buildings were calculated for three cities in southwestern BC, Vancouver, Victoria and New Westminster, using conventional damage estimation procedures. This involved estimation of the seismic hazard in the area, compilation of building databases for these cities, and the calculation and mapping of the damage distribution using Geographic Information Systems. The building classification scheme with 31 prototypes and the damage matrices relating the expected level of damage for each of these prototypes at different levels of ground shaking were available to be used in these analyses. Among the three case studies, the highest risk was observed in the City of Victoria, in which about 35% of the blocks within the study area were estimated to have damage levels between 10% and 30% of the replacement cost. The estimated damage level in Vancouver stayed generally in the 5% to 10% range, however, it went up to the 10%-20% range in quite a few number of blocks. About half of Victoria lies on relatively soft soil that is expected to amplify the peak ground accelerations by about 1.5 (if the earthquake dominantly contains low frequencies), which in turn increases the expected damage up to higher than 30% in many blocks. Direct monetary losses due to structural and non-structural damage to buildings were also estimated following the damage assessment. Next, an alternative damage estimation method was investigated and the necessary parameters to apply this method to buildings constructed in B C were developed for three sample building types. The damage levels obtained from the two methods were compared and differences were discussed. ii TABLE OF CONTENTS Abstract » Table of Contents iii List of Tables v List of Figures x Acknowledgements xiii Dedication xiv 1. Introduction l 1.1. Background 3 1.2. Objectives 5 1.3. Scope 6 1.4. Organization of the Thesis 7 2. Literature Review 9 3. Seismic Hazard Assessment 15 3.1. Overview 15 3.2. Tectonics and Seismicity of Southwestern BC 21 3.3. Seismic Source Zones 25 3.4. Attenuation Relationships 27 3.5. Seismic Hazard in the Region 30 4. Site Amplification 33 5. Assessment of Structural Damage: MMI-Based 38 5.1. Overview 38 iii 5.2. Classification of BC Buildings 42 5.3. Damage Matrices for BC Building Prototypes 44 6. Assessment of Non-Structural Damage 47 7. Monetary Losses 55 8. Case Study: New Westminster 57 9. Case Study: Victoria 69 10. Case Study: Vancouver 85 11. Alternative Damage Estimation Method: SD-Based 99 11.1. Capacity Curves 103 11.2. Demand Spectrum 119 11.3. Fragility Curves 125 12. Results and Discussion 130 13. Conclusions and Recommendations 141 13.1. Summary 141 13.2. Conclusions 142 13.3. Recommendations for Future Research 143 Appendix A. Modified Mercalli Intensity (MMI) Scale 147 Appendix B. Description of BC Building Prototypes 148 Appendix C. Damage Matrices for BC Building Prototypes 160 Appendix D. Damage Matrices for Non-Structural Components 171 Appendix E. Building Inventory Forms 187 References 190 iv LIST OF TABLES Table 3.1. Seismic source zone parameters 27 Table 3.2. Expected PGA and M M I levels 31 Table 3.3. Spectral acceleration levels expected in Vancouver and Victoria 32 Table 4.1. NEHRP site classes 35 Table 4.2. NEHRP site coefficients, F a 36 Table 4.3. NEHRP site coefficients, F v 36 Table 4.4. NEHRP site classes corresponding to geological units in Victoria 37 Table 5.1. Damage states in terms of damage factors (DF) 41 Table 5.2. Damage Probability Matrix (DPM) for Wood Frame - Low Rise 42 Table 5.3. B C building classification 43 Table 5.4. Damage probabilities (MMI-based) 44 Table 5.5. Mean Damage Factors (MDFs) 46 Table 6.1. Non-structural damage states in terms of central damage factors 5 0 Table 6.2. Building prototypes of BC versus FEMA/NIBS study 51 Table 6.3. MDFs for displacement sensitive components 52 Table 6.4. MDFs for acceleration sensitive components 53 Table 6.5. MDFs for building contents 54 Table 7.1. BC building costs 56 Table 8.1. Example inference schemes for New Westminster building database 59 Table 11.1. Building capacity curve control points (U.S. prototypes) 104 V Table 11.2. Fundamental period for engineered WLFR buildings 109 Table 11.3. Building capacity parameters i n Table 11.4. Building capacity curve control points (BC prototypes) 119 Table 11.5. Damping parameters and spectrum reduction factors 122 Table 11.6. Fragility curve parameters 127 Table 11.7. Discrete probabilities of structural damage 129 Table 12.1. Damage states in two methodologies 136 Table 12.2. Comparison of MDFs 137 Table 12.3. Effect of period and ductility on MDF for CFHR 139 Table A . l . Modified Mercalli Intensity (MMI) Scale 147 T a b l e d . D P M for WLFR (Wood Light Frame Residential) 160 Table C.2. D P M for WLFCI (Wood Light Frame Commercial/Institutional) 161 Table C.3. D P M for W L F L R (Wood Light Frame Low Rise Residential) 161 Table C.4. D P M for WPB (Wood Post and Beam) 161 Table C.5. D P M for L M F (Light Metal Frame) 162 Table C.6. D P M for S M F L R (Steel Moment Frame Low Rise) 162 Table C.7. D P M for S M F M R (Steel Moment Frame Medium Rise) 162 Table C.8. D P M for SMFHR (Steel Moment Frame High Rise) 163 Table C.9. D P M for SBFLR (Steel Braced Frame Low Rise) 163 Table CIO. D P M for SBFMR (Steel Braced Frame Medium Rise) 163 Table C. 11. D P M for SBFHR (Steel Braced Frame High Rise) 164 Table C.12. D P M for SFCWLR (Steel Frame with Concrete Walls Low Rise) 164 vi Table C.13. D P M for SFCWMR (Steel Frame with Concrete Walls Medium Rise) .... 164 Table C.14. D P M for SFCWHR (Steel Frame with Concrete Walls High Rise) 165 Table C.15. D P M for SFCI (Steel Frame with Concrete Infill Walls) 165 Table C.16. D P M for SFMI (Steel Frame with Masonry Infill Walls) 165 Table C.17. D P M for C F L R (Concrete Frame with Concrete Walls Low Rise) 166 T a b l e d 8. D P M for C F M R (Concrete Frame with Concrete Walls Medium Rise) ... 166 Table C.19. D P M for CFHR (Concrete Frame with Concrete Walls High Rise) 166 Table C.20. D P M for R C M F L R (Reinforced Concrete Moment Frame Low Rise) 167 Table C.21. D P M for R C M F M R (Reinforced Concrete Moment Frame Medium Rise) 167 Table C.22. D P M for R C M F H R (Reinforced Concrete Moment Frame High Rise) .... 167 Table C.23. D P M for RCFIW (Reinforced Concrete Frame with Infill Walls) 168 Table C.24. D P M for R M L R (Reinforced Masonry Shear Wall Low Rise) 168 Table C.25. D P M for R M M R (Reinforced Masonry Shear Wall Medium Rise) 168 Table C.26. D P M for U R M L R (Unreinforced Masonry Bearing Wall Low Rise) 169 Table C.27. D P M for U R M M R (Unreinforced Masonry Bearing Wall Medium Rise) 169 Table C.28. D P M for T U (Tilt Up) 169 Table C.29. D P M for PCLR (Precast Concrete Low Rise) no Table C.30. D P M for P C M R (Precast Concrete Medium Rise) no Table C.31. D P M for M H (Mobile Homes) no Table D . l . Non-structural damage probability matrices for WLFR 171 Table D.2. Non-structural damage probability matrices for WLFCI 172 Table D.3. Non-structural damage probability matrices for W L F L R 172 vii Table D.4. Non-structural damage probability matrices for WPB 173 Table D.5. Non-structural damage probability matrices for L M F 173 Table D.6. Non-structural damage probability matrices for S M F L R 174 Table D.7. Non-structural damage probability matrices for S M F M R 174 Table D.8. Non-structural damage probability matrices for SMFHR 175 Table D.9. Non-structural damage probability matrices for SBFLR 175 Table D.10. Non-structural damage probability matrices for SBFMR 176 Table D . l 1. Non-structural damage probability matrices for SBFHR 176 Table D.12. Non-structural damage probability matrices for SFCWLR 177 Table D.13. Non-structural damage probability matrices for SFCWMR 177 Table D.14. Non-structural damage probability matrices for SFCWHR 178 Table D.15. Non-structural damage probability matrices for SFCI 178 Table D. 16. Non-structural damage probability matrices for SFMI 179 Table D.17. Non-structural damage probability matrices for C F L R 179 Table D. l8 . Non-structural damage probability matrices for C F M R 180 Table D. 19. Non-structural damage probability matrices for CFHR 180 Table D.20. Non-structural damage probability matrices for R C M F L R 181 Table D.21. Non-structural damage probability matrices for R C M F M R 181 Table D.22. Non-structural damage probability matrices for R C M F H R 182 Table D.23. Non-structural damage probability matrices for RCFIW 182 Table D.24. Non-structural damage probability matrices for R M L R 183 Table D.25. Non-structural damage probability matrices for R M M R 183 viii Table D.26. Non-structural damage probability matrices for U R M L R 184 Table D.27. Non-structural damage probability matrices for U R M M R 184 Table D.28. Non-structural damage probability matrices for T U 185 Table D.29. Non-structural damage probability matrices for P C L R 185 Table D.30. Non-structural damage probability matrices for P C M R 186 Table D.31. Non-structural damage probability matrices for M H 186 Table E . l . Sample building inventory form 188 Table E.2. Sample compact building inventory form 189 ix LIST OF FIGURES Figure 3.1. Tectonic setting of southwestern BC 21 Figure 3.2. Seismicity in southwestern BC 23 Figure 3.3. Seismic source zones 25 Figure 3.4. Comparison of P G A - M M I relationships 30 Figure 3.5. Uniform hazard spectra for Vancouver and Victoria 32 Figure 8.1. City of New Westminster in G V R D 58 Figure 8.2. Prevalent material type by block 60 Figure 8.3. Prevalent prototype by block 61 Figure 8.4. Structural damage distribution (average MDF) 63 Figure 8.5. Structural damage distribution (average MDF weighted by floor area) 64 Figure 8.6. Non-structural damage distribution (displacement-sensitive components).. 65 Figure 8.7. Non-structural damage distribution (acceleration-sensitive components) ... 66 Figure 8.8. Non-structural damage distribution (building contents) 67 Figure 8.9. Distribution of total monetary loss by block 68 Figure 9.1. City of Victoria in CRD 70 Figure 9.2. Study area in City of Victoria 70 Figure 9.3. Prevalent material type by block 72 Figure 9.4. Prevalent prototype by block 73 Figure 9.5. Structural damage distribution (average MDF) 75 Figure 9.6. Structural damage distribution (average M D F weighted by floor area) 76 Figure 9.7. Non-structural damage distribution (displacement-sensitive components).. 77 Figure 9.8. Non-structural damage distribution (acceleration-sensitive components) ... 78 Figure 9.9. Non-structural damage distribution (building contents) 79 Figure 9.10. Geological units in Victoria 81 Figure 9.11. Structural damage in Victoria with site amplification 82 Figure 9.12. Total monetary losses In Victoria (no site amplification) 83 Figure 9.13. Total monetary losses In Victoria (with site amplification) 84 Figure 10.1. City of Vancouver in G V R D 86 Figure 10.2. Study area in City of Vancouver 86 Figure 10.3. Prevalent building material type by block 88 Figure 10.4. Prevalent building prototype by block 89 Figure 10.5. Structural damage distribution (average MDF) 91 Figure 10.6. Structural damage distribution (average MDF weighted by footprint area) 92 Figure 10.7. Structural damage distribution (average M D F weighted by total area) 93 Figure 10.8. Non-structural damage distribution (displacement-sensitive components) 94 Figure 10.9. Non-structural damage distribution (acceleration-sensitive components) . 95 Figure 10.10. Non-structural damage distribution (building contents) 96 Figure 10.11. Geological units in Vancouver 97 Figure 10.12. Distribution of total monetary losses by block 98 Figure 11.1. Example building capacity curve ioo Figure 11.2. Example demand spectrum 101 Figure 11.3. Example fragility curves for different damage states 102 xi Figure 11.4. Capacity curve for U R M L R i n Figure 11.5. Capacity curve for WLFR 118 Figure 11.6. Capacity curve for CFHR 118 Figure 11.7. Construction of a standard-shaped input spectrum 120 Figure 11.8. Intersection of demand spectrum and capacity curve (URMLR) 123 Figure 11.9. Intersection of demand spectrum and capacity curve (WLFR) 124 Figure 11.10. Intersection of demand spectrum and capacity curve (CFHR) 124 Figure 11.11. Fragility curve for U R M L R 128 Figure 11.12. Fragility curve for WLFR 128 Figure 11.13. Fragility curve for CFHR 129 Figure 12.1. Comparison of averaging schemes 133 Figure 12.2. Effect of site amplification (for long period ground motion) 135 Figure 12.3. CFHR capacity curves for periods: T e = 1.20, 1.40, 1.65 and 1.80 138 Figure 12.4. CFHR capacity curves for ductilities: u = 2.0, 3.0, and 4.0 139 xii A C K N O W L E D G E M E N T S Getting through this degree was not easy. What I accomplished at the end of the four years would not have been possible without the support and help from many people. I would like to express my gratitude to my research supervisors, Dr. Liam Finn and Dr. Carlos Ventura, for their continuous support and guidance throughout my studies. There were trying times for me during this degree when I fell into despair. I would like to extend my special thanks to Dr. Ventura for being there for me at those times and not letting me give up. I would also like to acknowledge the contributions from my supervisory committee. Dr. Atkinson provided valuable comments starting from the earliest versions of the thesis. Dr. Ulrych was very supportive throughout. And I am grateful for the enthusiasm, support, and stimulating discussions that Dr. Cassidy has provided. I have to thank my family for having unfaltering faith in me. I have been blessed by their unbounded support all through my life and maybe most of all during this degree. Finally, without my friends it would not have been possible to go through it all. I would like to thank Oemer Kutbay, Georgia Lysay, Judith Cneac, Cheryl Sewell, Marc Gerin and Jachym Rudolf for being so patient with me right from the beginning, being there for me at hard times and sharing my happy moments. I would also like to thank Rozlyn Bubela, Houman Ghalibafian, Martin Turek, Jean-Francois Lord, Terrence Davies and Canisius Chan for their support and warm friendship during my last year, giving me the energy I needed to complete my degree. xiii This thesis is dedicated to the memory of my grandfather, whom Istrived to make proud since I was four years old. xiv 1. I N T R O D U C T I O N Southwestern British Columbia with a population of 1.5 million people is exposed to the highest seismic risk in Canada. Assessment of seismic hazard in the area and estimation of potential damage and loss from future earthquakes are essential to reduce the risk. These estimates can be utilized by municipal and/or governmental organizations for earthquake preparedness, emergency response planning and risk mitigation. They can also be used by insurance and reinsurance companies for premium assessment and risk management. Although the seismic hazard in this region is well studied, there has been a need for rational studies of its effects on the existing structures. Apart from a few evaluations mainly based on extrapolations from limited data, construction of detailed building databases and prediction of damage based on these data have not been undertaken until recently. As a result of these concerns, the insurance industry in British Columbia initiated a study, which was earned out by the University of British Columbia (UBC) and Carleton University in partnership with Geological Survey of British Columbia, Financial Institutions Commission of the Ministry of Finance and Corporate Relations, and British Columbia Ministry of Transportation and Highways. The project aims to estimate damage distribution and mitigate the seismic risk in the area. It is financed by the Natural Sciences and Engineering Research Council of Canada as well as the insurance l industry. Local governments of City of New Westminster, City of Victoria and City of Vancouver also contributed by providing their building databases for the study. Within the research framework, Carleton University focused on the seismological aspects of the project and U B C provided geotechnical evaluations as well as structural damage and loss estimations. In response to the needs of the insurance industry and the local governments, an estimation of the damage distribution due to probable earthquakes was carried out using the best currently available methodology. This methodology is mainly based on expert opinion and it uses Modified Mercalli Intensity (MMI) as the ground motion parameter. In addition, future trends in estimating the damage and alternative methodologies using spectral displacement (SD) as the ground motion parameter were investigated. A software program developed in the U.S., HAZUS (FEMA/NIBS, 1997), is capable of carrying out SD-based damage and risk assessments. However, this program is specifically designed for the U.S. and in order to adapt it for use in Canada, modifications in the program code are required. Therefore, instead of using HAZUS, a similar SD-based methodology suitable for Canadian construction practices was developed. The proposed method was applied to three building prototypes, and the damage levels obtained from MMI-based and SD-based methods were compared to each other for these prototypes. 2 1.1. BACKGROUND Seismic risk analysis involves determining the adverse consequences that people and society might suffer as a result of future earthquakes (EERI Committee on Seismic Risk, 1989). There are three main elements of seismic risk: seismic hazard, vulnerability of the structures exposed to the hazard, and loss (often in form of monetary losses or loss of life). In order to estimate the seismic risk in an urban area, first the intensity of ground shaking is determined through a seismic hazard analysis for reference ground conditions, usually stiff soil. For sites that differ from the reference condition, the effects of local soil deposits are evaluated and reflected upon the level of ground shaking obtained from the hazard analysis. Next, a building inventory is constructed, which typically contains the following information: street address, primary use, construction material, lateral load bearing system, age, height (number of stories), and footprint area for each building in the study area. The amount of information collected may be enormous depending on the size of the urban area under study. Geographic Information Systems (GIS) provide a convenient platform for storage, administration and exchange of these data. A GIS integrates graphical data management capabilities of a computer aided design ( C A D ) or a digital cartographic environment with non-graphical data management capabilities of a relational database management system, providing a link between the two types of data. 3 Since it is not feasible to develop motion-damage relationships for every individual building, the buildings in the database are classified into groups of similar structural characteristics. Then, the probability and amount of structural damage is estimated using the motion-damage relationships developed for these building classes. A similar methodology is employed to calculate non-structural damage. Finally, based on the output from the damage assessment, loss estimation techniques are used to estimate the monetary losses. Damage to non-structural building components and contents constitute a major portion of the total economic losses. Therefore, estimation of the non-structural • damage has recently become an important component of loss assessment. Current damage estimation methodologies can roughly be grouped in two categories according to the parameter used to characterize the ground motion intensity. These are Modified Mercalli Intensity (MMI) based and engineering parameter based methodologies. M M I based methodologies, which are mainly based on expert opinion, have been the most common means of estimating damage until recently. They define in damage matrices for each building type the probability of being in specific damage states at different levels of ground shaking intensities. Methodologies based on engineering parameters are currently evolving. The parameters used in these methods include peak ground acceleration (PGA) or velocity (PGV), spectral acceleration (SA), and spectral displacement (SD). Peak values of ground parameters do not correlate as well with the amount of damage to structures as the spectral parameters do, since peak values do not take into account the effect of the frequency content of ground motion. Therefore, 4 spectral parameters are usually preferred. The level of motion that the building will experience is determined not only by the characteristics of input ground motion, but also the strength, stiffness and ductility of the building. In spectral parameter based methods, the building properties affecting the level of motion in the structure are usually represented by capacity curves. The input motion is commonly expressed by demand spectra and the vulnerability of the buildings is described by fragility curves. Construction of these curves requires determination of several structural parameters for each type of building. These parameters include elastic fundamental period, design strength, overstrength ratios, ductility, elastic and hysteretic damping, and the levels of SD at which each building type reaches certain damage states. 1.2. O B J E C T I V E S The objectives of this thesis are: 1) to calculate the level of ground motion expected in southwestern British Columbia for a certain return period, 2) to estimate the probability and distribution of seismic damage due to the calculated ground motion level using current best damage estimation methods, 3) to estimate monetary losses in the area resulting from the calculated damage, 4) to investigate an alternative SD-based damage estimation methodology and to develop structural parameters required for this methodology with regard to Canadian building codes/practices, and 5) to compare damage levels obtained from the two analyses for three sample prototypes of buildings. 1.3. SCOPE A series of seismic hazard analyses were carried out to determine the level of ground motion expected in the study area in terms of PGA, M M I and SA. Comprehensive information on the building stock in the City of Victoria and the City of Vancouver was compiled, primarily by sidewalk surveys, and detailed building inventory databases were constructed for these cities. The MMI-based ground motion-damage relationships available for Canadian building types were utilized to produce maps of structural damage distribution. Non-structural damage was also mapped using similar methodologies. Monetary losses resulting from direct damage to structural and non-structural components of buildings were estimated. Next, an alternative, SD-based method was investigated. The parameters to be used in this method needed to be developed for Canadian building types. Three sample prototypes of buildings were selected for this purpose based on their prevalence and risk level. These are unreinforced masonry buildings, reinforced concrete frame high rises with concrete shear walls and wood light frame single-family houses. The structural parameters required to develop SD-based ground motion-damage relationships for these three types of buildings were determined. The inelastic demand spectra were constructed by reducing the uniform hazard spectrum calculated for Vancouver by the amount of damping expected in each type of building. Damage estimation was carried out and probabilities of damage in the three prototypes of buildings for the expected ground motion levels were determined. The results were then compared to those obtained from the MMI-based methodology. 1.4. O R G A N I Z A T I O N O F T H E T H E S I S In this thesis, the following topics are discussed in the order they are listed. In Chapter 2, past research on seismic damage estimation in southwestern BC is reviewed. Chapter 3 summarizes the fundamentals of seismic hazard assessment, presents an overview of the tectonic setting and seismicity of southwestern BC, describes the seismic source zones used in the hazard assessments as well as the attenuation laws, which carry the ground motion from the source location to the site of interest. In the last section of this chapter, the results of the probabilistic seismic hazard analyses carried out for the study area in terms of various ground motion parameters are presented. Chapter 4 discusses the effect of local soil conditions on the ground shaking intensity. Chapter 5 includes the building classification for southwestern B C and MMI-based damage assessment methodology. Non-structural damage estimation methodologies are presented in Chapter 6 and loss estimation is discussed in Chapter 7. In the next three chapters, Chapters 8, 9 and 10, three case studies are described: the Cities of New Westminster, Victoria and Vancouver, respectively. These cities were selected based on data availability and cooperation of the city planning departments. In these chapters, the building inventory databases constructed for the three cities are described and damage distribution maps calculated using a GIS platform are presented for each of the cities. These maps were used to identify the highest risk areas, to determine the prevalence of building classes in these cities, exploring ways of displaying information and effects of soil amplification. Next, the alternative, SD-based damage estimation method is described in Chapter 11, which requires the development of capacity curves, inelastic demand spectra and fragility 7 curves. The capacity curves were developed for three sample building classes using the proposed values of the required structural parameters. These structural parameters and the rationale behind the proposed values are also discussed in this chapter. Finally, damage levels are derived using the fragility curves and they are compared to those obtained from the MMI-based methods in Chapter 5. In Chapter 12, results displayed in damage and loss distribution maps are discussed and the comparison of the damage levels calculated using MMI-based and SD-based methods for three building classes is presented. The possible reasons behind the differences are also discussed. Finally, Chapter 13 presents the conclusions drawn from all the aspects of the seismic risk assessments and recommendations for further research. 8 2. LITERATURE REVIEW In this chapter, a summary of seismic risk assessment studies carried out in southwestern British Columbia is presented. A l l past studies acknowledge the lack of comprehensive building databases and detailed analysis of the seismic risk in the area. An overview of the seismic risk and hazard reduction programs in the Greater Vancouver Regional District (GVRD) is given by Ventura and Schuster (1993). It includes information on demographics, seismic hazard, earthquake awareness, emergency response, construction practice and research on seismic risk in the area. It investigates the distribution as well as budgets and sizes of several response organizations in the area such as hospitals, fire and police stations. An interesting note indicates that only about 25% to 30% of all buildings constructed in the area are designed by professional engineers and architects. Also some key facilities for emergency response such as the City Hall and several fire and police stations were noted to be incapable of sustaining even half the current design load specifications. A review of the condition of schools, which are expected to act as post-disaster emergency shelters, indicated that it would take more than 20 years to upgrade these buildings to the current code requirements. A study to identify the seismic sources and possible earthquake related hazards in the area was conducted by Association of Professional Engineers of British Columbia (1988) and was presented to the British Columbia Government. It includes remarks on how different types of buildings are expected to perform in case of an earthquake, however a 9 quantitative estimation of the damage is not attempted. It also discusses the expected performance of lifelines and emergency response preparedness. Recommendations on how to reduce the risk and minimize loss of life and injury are provided. Canada Mortgage and Housing Corporation (CMHC, 1989) carried out a study on the assessment of earthquake effects on buildings and lifelines in the Greater Vancouver area. This study considered a design level earthquake based on the 1985 National Building Code of Canada and a major subduction earthquake off the coast of British Columbia. It grouped the buildings into five broad categories and estimated the damage based on the performance of similar structures in past earthquakes in California, Alaska and Washington. Results were presented in terms of loss ratio for major structural damage, based on the best estimate of the authors and do not reflect a statistical analysis of vulnerability of the regional building or lifeline inventory. Shortly after the Loma Prieta earthquake in the San Francisco Bay area, a group of researchers from Canada visited the area (Rainer et al., 1990). Their objective was to determine the nature and extent of the damage to buildings and lifelines in the Bay area in order to predict the impact of a similar magnitude earthquake in the Greater Vancouver area. They examined the effects of ground conditions and level of emergency preparedness as well as performance of different types of buildings and lifelines such as transportation, water, sewage, gas, power, and communication systems. When they applied the Bay area experience to Greater Vancouver, they considered earthquake characteristics, geology and soil conditions, codes and standards, type of construction and 10 level of earthquake resistant design. Extending the Loma Prieta earthquake to ground motions that correspond to the design earthquake for Vancouver with a number of assumptions and extrapolations, they estimate the percentage of damaged buildings within each building category. They predict serious damage in about 2% to 5% of the low rise residential/commercial buildings, 20% to 50% of the unreinforced masonry buildings, 5% to 10% of the high-rise residential buildings, and 10% to 30% of the schools and hospitals. Serious damage is defined as a level that would prevent safe occupancy of the building immediately after the earthquake. They also estimate that about 5% to 10% of the Greater Vancouver area will experience disconnection of services and utilities, such as transportation, water and power. Munich Re (1990) conducted a study on the economic impact of a scenario earthquake of magnitude 6.5 in the Strait of Georgia on the area. This study selected M M I as the ground motion parameter to represent the severity of the shaking and used loss ratios provided by Munich Re to calculate the losses. In the study report, it was pointed out that reliable estimates would only be possible with an inventory methodology that assembled a database of all buildings within the study area. Nevertheless, this study did not attempt to construct such a database arguing that gathering of such data was an undertaking of immense proportions. It adopted instead, a procedure to estimate the number and type of building stock on an aggregate basis and two complementary methodologies: 1) aggregating square footage data multiplied by appropriate replacement costs on a square footage basis to yield total replacement costs; and 2) examining in detail every structure n within the downtown core of Vancouver and using the data derived from there to extrapolate loss estimates for the rest of the metropolitan area. The downtown core of Vancouver represents the highest density of commercial and residential properties, majority of which are concrete high-rises. The rest of the city mainly consists of wood residential buildings including single family 1 or 2-storey houses and 4-storey apartments and wood or reinforced masonry low-rise commercial buildings. An exception is the older parts of the city that consist of many old unreinforced masonry buildings. Although in the absence of larger amount of information an extrapolation from downtown core was necessary in the Munich Re study, such an extrapolation appears to be inappropriate considering the large differences between the building types in downtown area and elsewhere in the city. Consequently, there is an obvious need for a more comprehensive database encompassing a larger portion of the city and representing all the building types that exist in the region. The data on the buildings in downtown Vancouver for the Munich Re study were gathered from numerous data sources as follows: Use information from City directory, height from assessment rolls and real estate listings, square footage and date of construction from City Hall files and real estate listings, type of construction from Fire Marshall's office, assessed values from B.C. Assessment Authority, and the replacement values from a local architectural firm. Despite the large number of data sources, the most critical input to the damage estimation, building material information was available for 12 only 47% of the buildings in the database and had to be deduced for the rest using inference schemes. This confirms the need for a more accurate database for the area. In response to the need of rational damage estimations in the region, researchers in University of British Columbia (UBC) undertook an extensive investigation of seismic damage assessment methodologies. In coordination with U B C , Bell (1998) developed a building classification and MMI-based damage matrices based on ATC-13 (1985). The classification consisted of 31 building prototypes reflective of the construction practice in southwestern BC. The damage matrices were obtained by modifying the ATC-13 matrices to take into account the differences between the construction practice in BC and California. Subsequently, Blanquera (1999) used these damage matrices to estimate the structural damage distribution in the City of New Westminster due to the ground motion levels consistent with those suggested in the 1995 National Building Code of Canada. A comprehensive database of the city was assembled supplementing the building database provided by city with inference schemes and onsite building surveys. The amount of damage was represented by damage factors (DF), which are described by ratio of the repair cost to the replacement cost. Damage distribution was calculated and mapped on a block by block basis making use of GIS. In an accompanying study by Cook (1999), damage to non-structural components and building contents was investigated. In this study, a damage estimation methodology that is a combination of MMI-based damage matrices and spectral parameter based fragility curves was proposed and applied to the City of New Westminster. The fragility curves 13 proposed by FEMA/NIBS (1997) for non-structural components and building contents were converted to MMI-based damage matrices, which were then used to estimate the non-structural damage. The building classification and the rest of the methodology are the same as those used by Blanquera (1999). Office of the Auditor General of British Columbia (1997) conducted a performance audit for the province to assess the degree to which governments in British Columbia were prepared for a major earthquake in high hazard areas of the province. Their assessment was that governments in British Columbia were not yet adequately prepared for a major earthquake. The report provides a comprehensive list of recommendations, including development of planning scenarios. It is pointed out that credible information is available on the seismic hazard in the area, yet there is a need for a tool that can, from the identified hazards, project the potential impact that a major earthquake is likely to have on structures and lifelines. 14 3. SEISMIC HAZARD ASSESSMENT In this chapter, an overview of seismic hazard assessment is given and the tectonic setting and seismicity of southwestern BC is discussed. Then, the seismic source zones and the attenuation relationships used in the hazard assessments are described. Finally, the results from the seismic hazard analyses in terms of PGA, M M I and SA are presented. 3.1 O V E R V I E W The term "seismic hazard" describes the likelihood of earthquakes occurring at a location of interest. Alternatively, seismic hazard may be defined as the level of ground shaking at a specified location due to future earthquakes. Seismic hazard may be calculated either deterministically or probabilistically. Deterministic Seismic Hazard Analysis (DSHA) deals with discrete events with a specific magnitude and distance to the site of interest. The controlling event can be the maximum probable earthquake, a design basis earthquake, a seismic safety evaluation earthquake, etc., depending on the nature and requirements of the problem at hand. The ground motion due to this earthquake is carried to the site using an appropriate attenuation relationship, which defines how the motion travels and attenuates with distance, depending on the source characteristics and ground conditions between the source and the site of interest. DSHA is performed when a scenario earthquake is of interest and the 15 level of ground motion needs to be estimated due this earthquake. It has the advantage of being simple to perform and clear to understand as it utilizes two well-recognized parameters: magnitude and distance. In southwestern B C , seismicity is diffuse with no distinct alignment with specific faults, therefore it is difficult to define a scenario event. Probabilistic Seismic Hazard Analysis (PSHA) groups events with similar characteristics into so-called "seismic source zones" within which seismicity is relatively uniform. The total seismic hazard is given by the integration of the contributions from each possible combination of source-to-site distance and magnitude in all different seismic source zones at different probabilities of occurrence. As in the DSHA, an appropriate attenuation relationship is used to carry the ground motion from the source to the site. The calculation process and the parameters used are more complicated in this type of analysis compared to DSHA, since PSHA takes into account all the earthquakes of different sizes that had occurred in the region. In this thesis, the seismic hazard in southwestern BC is determined probabilistically, therefore, a summary of the PSHA procedure is presented. The main input for the seismic hazard analyses is the seismicity in the region, that is the occurrence of earthquakes in time and their location. Since the late 1890s, it has been possible to record earthquakes and a few decades later their location and magnitude could be determined instrumentally. A seismicity database for a region can be built by compiling these instrumental records. However, the return period of large earthquakes, in many cases, is longer than 120 years. Hence, a database containing instrumental seismicity alone is 16 incomplete, missing the infrequent, large events that may have occurred in the area before the installation of the recording instruments (Rogers, 1992). The next source of seismicity information is historical records, consisting of written evidence of the effects of earthquakes on humans. Records of historical seismicity can extend back several thousand of years in the birthplace of ancient civilizations such as Mediterranean Basin, while in North America historical records rarely go back more than a few hundred years. An equally important input to seismic hazard analyses is the tectonic setting of the region, which includes the geometry, mechanism and activity rate of the faults in the area as well as the rate and direction of the motion of tectonic plates. Geological evidence of prehistoric seismicity may also be possible to obtain from some faults. Based on the knowledge of tectonic setting and the seismicity of the region under study, seismic source zones are defined, within which seismicity is assumed to be uniform. Well-delineated faults may be regarded as linear source zones. In the absence of such distinct features, areal source zones are preferred. Following the determination of the spatial layout and geometrical properties of the seismic source zones, the recurrence relationships need to be developed to describe the distribution of earthquake sizes within a given period of time inside each source zone. Gutenberg and Richter (1954) proposed a widely used recurrence relationship of the form: \ogXm= a-b-m (Eq. 3.1) 17 where Xm is the mean annual rate of exceedance of magnitude m, \0a is the mean yearly number of earthquakes of magnitude greater than or equal to zero, and b value describes the relative likelihood of large and small earthquakes. The a and b parameters are determined for each source zone generally by regression on a database of seismicity within that source zone. In general, PSHA is intended to evaluate hazard from discrete, independent seismic events. Therefore, dependent events such as aftershocks need to be removed from the seismicity database. In addition, the seismicity database should be as complete as possible to produce reliable recurrence relationships. The standard Gutenberg-Richter recurrence law (Equation 3.1) can also be expressed as: ^ , = 1 0 " - " " or X„,= e a - p " ' (Eq.3.2) where a = 2.303a and p = 2.3036. The standard Gutenberg-Richter law covers an infinite range of magnitudes, with no lower or upper bounds. However, for engineering purposes, the effects of small earthquakes that seldom cause significant damage are of little interest and a maximum magnitude m m a x is associated with all seismic source zones. Earthquakes smaller than a lower threshold magnitude m0 and larger than mmax can be eliminated to obtain truncated Gutenberg-Richter recurrence laws. The lower threshold magnitude is often set as values from about 4.0 to 5.0 and the upper bound depends on the source zone characteristics. To further improve the recurrence laws, especially for data sets that are not well defined, Weichert (1980) proposes a maximum likelihood method, addressing the issues of unequal periods of observation and the use of maximum magnitude. 18 Following an earthquake, seismic waves travel through the ground medium to reach the site of interest. The propagation and attenuation of the ground motion is usually defined by an attenuation relationship, which is established by regression on a set of ground motion data from past events. It commonly relates the ground motion amplitude at the site of interest to the earthquake size (usually magnitude) and the distance of the site to the source for various site conditions and fault mechanisms. The general functional form of the attenuation relationships is: InY = C, + C 2 • M + C 3 • \n(R) + C4-R + /(source) + /(site) (Eq. 3.3) where Y is the ground motion parameter, M is the magnitude and R is the distance between the site and the source. C\ are coefficients obtained from the regression analysis. Generally, attenuation relationships also include variables that are functions of the source characteristics (fault mechanism such as normal faulting, strike-slip, subduction, etc.) and site conditions (soft soil, firm soil, rock, etc.). An extensive number of attenuation relationships have been proposed for different tectonic systems and various ground motion parameters (Hasegawa et al., 1981; Campbell, 1985; Crouse, 1991; Abrahamson and Silva, 1997; Boore et al., 1993; Atkinson, 1995; Campbell, 1997; Youngs et al., 1997; Atkinson, 1997; Sadigh et a l , 1997). Appropriate attenuation relationships should be selected based on the characteristics of the source zones in the region under study. Once the recurrence relationships and the attenuation equations to be used in conjunction with the source zones are selected, seismic hazard at the site can be calculated: H{a) = £ v, • Jj> [A > a | m, r] • fMi (m) • fRi{Mi (r;m)-dr-dm , (Eq. 3.4) 19 where H(a) is the annual frequency of earthquakes that produce a ground-motion amplitude A higher than a. A may represent peak ground acceleration, velocity or displacement, or it may represent spectral pseudo-acceleration for a given frequency or period. The summation in Equation 3.4 extends over all source zones, v, is the annual rate of earthquakes with magnitudes higher than a threshold, m0 in source and /MI (m) and f^Mi (r ; m) are the probability density functions on magnitude and distance, respectively. P [A > a \ m, r] is the probability that an earthquake of magnitude m at distance r produces a ground motion amplitude A at the site that is greater than a (Risk Engineering, Inc., 1997). The fundamentals of the PSHA calculations were developed by Cornell (1968) and it has been subsequently investigated and applied by many researchers in the U.S. (Algermissen et al., 1982; EPRI, 1986; McGuire and Arabasz, 1989; Coppersmith and Youngs, 1990; Algermissen et al., 1991; McGuire, 1993; Jacob et al., 1994; WGCEP, 1995; Hanson and Perkins, 1995; Leyendecker et al., 1995; Frankel, 1995; Frankel et a l , 1996). In Canada also, extensive research on seismicity and tectonics of the country has been carried out as well as on the calculation of seismic hazard (Milne and Davenport, 1969; Rogers, 1983; Weichert, 1994; Atwater et al., 1995; Adams et al., 1995; Basham, 1995; Clague, 1996; Adams et al., 1996; Rogers, 1998; Adams et a l , 1999, Halchuk and Adams, 1999). Several computer software such as SEISRISK III (Bender and Perkins, 1987) and EZ-FRisk ™ (Risk Engineering, Inc., 1997) are available to carry out seismic hazard analyses. 20 3 . 2 T E C T O N I C S A N D S E I S M I C I T Y O F S O U T H W E S T E R N B C Southwestern British Columbia is situated over the active Cascadia subduction zone. Here, the oceanic Juan de Fuca and Explorer plates are being subducted beneath the continental North American plate, at rates of about 45 mm per year (Monger and Journeay, 1994). The motion of Juan de Fuca and Explorer plates is primarily towards east with some component towards north and the North American Plate is currently moving westward, overriding the oceanic plates. The tectonic setting of the area is displayed in Figure 3.1 (adopted from Cannings and Cannings, 1999). Figure 3.1. Tectonic setting of southwestern BC Earthquakes in southwestern British Columbia generally occur in three distinct source groups located in this tectonic setting. These are shallow earthquakes within the continental crust overlying the North American plate, deep earthquakes within the subducting oceanic (Juan de Fuca) plate, and earthquakes at the interface between the two 21 plates. The seismicity observed between 1980 to 1991 is presented in Figure 3.2. The size of the circles is proportional to the earthquake magnitude, from the smallest of magnitude 1 to the largest of 5.2. The stars indicate the location of Quaternary volcanoes of the Cascade magmatic arc. Also shown in Figure 3.2 is a cross-section showing the depths of the seismic events occurred in the area. The majority of the small earthquakes in the region occur in the continental crust of the North American plate. They are a mixture of strike-slip and thrust events with a dominant north-northwest orientation of the principal stress suggesting north-northwest compression. These crustal earthquakes do not seem to have distinct alignments to indicate the locations of active faults. Most of these earthquakes occur at depths of about 20 km, therefore do not create surface faulting and have fewer aftershocks than shallower earthquakes such as those in California, which occur typically within the top 10 km of the crust. Examples of large crustal earthquakes are 1918 Vancouver Island (M 7), 1946 central Vancouver Island (M 7.3), and 1872 northern Washington State (M 7.4). Sometimes crustal earthquakes occur in the upper 10 km of the crust. Examples are 1975 Strait of Georgia (M 4.9), 1990 Deming, Washington (M 4.8). These shallow events are rare, but they constitute high uncertainty in the hazard calculations, because their distribution and maximum magnitude are hard to assess. 22 Seismicity of Southwestern British Columbia (all earthquakes between 1980 and 1991) Seismicity of SW British Columbia (subcrustal earthquakes only) Vancouver Island Distance (km) Earthquakes in the 100 km wide corridor shown above on the left, projected onto a cross-section through Vancouver Figure 3.2. Seismicity in southwestern B C (after Rogers, 1998) Subcrustal earthquakes are those that occur within the subducting Juan de Fuca plate. Normal faulting predominates in this plate, however considerable variability is observed in the focal mechanisms of small earthquakes in Puget Sound (Rogers and Horner, 1991). The position of this plate is well defined with microearthquake activity. The maximum size of earthquakes in this zone is constrained to magnitude 7 range because the brittle portion of the subducting plate is very thin, less than 10 km, which induces an upper limit to the rupture area for typical rupture lengths of less than 100 km. An important area of concentrated seismicity is at about 45 to 65 km depth below the Strait of Georgia and 23 Puget Sound. Large subcrustal earthquakes are 1949 (M 7.0) and 1965 (M 6.5) southern Puget Sound earthquakes, 1864, 1904, 1909, 1920 and 1976 Gulf Islands / San Juan Islands region earthquakes (M 5 to 6 range), and 2001 Nisqually earthquake (M 6.8). Subduction earthquakes are rare events that occur on the subduction interface between the Juan de Fuca and North American plates. The position of the interface is known from microearthquake activity, seismic reflection and refraction surveys. The thermal models show that the depth of the seismogenic region does not extend further than 30 km. Although no subduction earthquakes had occurred in the written history of this area, there is abundant evidence suggesting great subduction earthquakes in the past. In tidal marshes, repeating sediment sequences of peat overlain with mud, often with a sand layer at the interface, are interpreted to result from abrupt subsidence events and tsunamis accompanying great earthquakes. Layers of coarse sediments in deep-sea mud deposits are attributed to turbidity currents originating from periodic strong shaking on the continental margin. Trees killed suddenly by salt water influx due to coastal subsidence and a legend of Cowichan people of the southern Vancouver island indicate the last great earthquake to occur around 1700 A D (Rogers, 1994), which is also confirmed by a tsunami in Japan that occurred at the same date (Satake et al., 1996). The return period of a subduction event cannot be estimated from observed seismicity using a recurrence relationship since there are no historical records of subduction earthquakes of any magnitude in this region from which to draw a statistical sample (Rogers, 1988). 24 3.3 SEISMIC S O U R C E ZONES Based on these seismicity patterns, Geological Survey of Canada (GSC) defined seismic source zones (Adams et al., 1999) in this region as well as the rest of Canada. These seismic source zones as defined by GSC are adopted in this thesis for the estimation of probabilistic seismic hazard in southwestern British Columbia. The four source zones that affect the area of study are "Cascade Mountains (CAS)", "Southern Coast Mountains (SCM)", "Georgia Strait (GEO)", and "Puget Sound (PUG)" (Figure 3.3). Contributions from the rest of the source zones are negligible in the study areas. . ^ 1 h 1 i 1 1 1 126" 125" 124" 123" 12?' 121" 120' Figure 3.3. Seismic source zones The first two, CAS and S C M are shallow source zones with an assigned "pseudo-depth" of 2.9 km. This value has no physical meaning in the hazard calculations since depth is a 25 regression parameter in the attenuation relationship used for these source zones as discussed in the following section (Adams et al., 1999). The GEO and PUG are deep source zones that represent the subcrustal earthquakes under Georgia Strait and Puget Sound. Hence, they are assigned a depth of 50 km. Further parameters for these source zones are summarized in Table 3.1 (Adams et al., 1999). Minimum and maximum magnitudes define the lower and upper bound for the earthquakes in each source zone. The lower bound is set since magnitudes smaller than that seldom cause significant damage. The upper bound is usually determined based on the highest observed or expected magnitude in a specific source zone. Activity rate and p are parameters of the Gutenberg-Richter recurrence relationship (Equations 3.1 and 3.2). Activity rate represents (when raised to the power of e, the base of the natural logarithm) the mean yearly number of earthquakes of magnitude greater than or equal to the minimum magnitude. The P value describes the likelihood of large and small earthquakes. As the p value increases, the number of larger magnitude earthquakes decreases compared to those of smaller magnitudes. The reason for dividing the CAS and S C M source zones into two sections (greater than and smaller than 100km) is the nature of the attenuation relationship used in conjunction with these source zones. This issue is further discussed in the following section. 26 Table 3.1. Seismic source zone parameters Source Zone Parameters CAS (<100km) SCM (<100km) CAS (>100km) SCM (>100km) GEO PUG Depth (km) 2.9 2.9 2.9 2.9 50.0 50.0 Min. M 4.75 4.75 4.75 4.75 4.75 4.75 Max. M 7.3 7.0 7.3 7.0 7.0 7.3 Activity Rate 0.01477 0.005913 0.0853 0.03423 0.00137 0.1485 P 2.01 1.7 2.01 1.7 2.27 1.01 3.4 A T T E N U A T I O N R E L A T I O N S H I P S Peak ground acceleration (PGA) is the most widely used ground motion parameter in attenuation relationships, and hence in seismic hazard analyses. The parameters used in this thesis were PGA, M M I and spectral acceleration (SA). In the analyses based on PGA and SA, two separate attenuation relationships were used for shallow and deep source zones. In the M M I based analyses, the same attenuation relationship was used for all source zones. For the shallow source zones in southwestern B C , GSC adapted the ground motion attenuation relationships from Boore et al. (1993). However, this attenuation relationship is derived based on data for distances less than 80-100 km. Therefore, GSC adaptation included the addition of a period-dependent anelastic attenuation term (Atkinson, 1997) applied to distances larger than 100 km. This adapted version of the relationship was 27 used in the hazard calculations in terms of PGA and SA. The basic relationship is of the form: log7 = Z>, + b2-(M-6) + b3 - (M-6) 2 + b4 • r + b5-logr + b6-GB +b7 Gc +er +ee (Eq. 3.5) where r = 4d2+h2 (Eq. 3.6) In these equations, Y is the ground motion parameter (in cm/s for spectral velocity and g for PGA), M is moment magnitude, d is the closest horizontal distance (in km) from the station to the point on the earth's surface that lies directly above the rupture. GB and Gc are site classification factors (GB = 1 for class B and zero otherwise, Gc = 1 for class C and zero otherwise). Site classes are defined according to the average shear wave velocity in the upper 30 m. Class B corresponds to shear wave velocity range of 360-750 m/s and class C corresponds to 180-360 m/s. A reference ground condition corresponding to site class B was assumed for Vancouver, Victoria and New Westminster in the seismic hazard calculations. The independent variables, e r and ee take on a specific value for each record and for each earthquake, respectively. The coefficients bj through 67, and the variance of zr and et, (a2, and a], respectively) are determined by the regression and are available for PGA as well as SA at several periods. The coefficient h is a fictitious depth that is also determined by the regression (Boore et al., 1993). 28 For the deeper subcrustal source zones under Georgia Strait and Puget Sound, the attenuation relationship developed by Youngs et al. (1997) was used in the PGA and SA calculations. The general form of the relationship is given below (for rock): InOO = 0.2418 + 1 . 4 1 4 - M + C, +C 2 - ( 1 0 - M ) 3 + C 3 • ln(rnip +1 .7818 . E ° - 5 5 4 M ) + 0.00607-H + 0.3846• ZT (Eq. 3.7) Standard Deviation = C 4 + C 5 • M (Eq. 3.8) In these equations, y is the ground motion parameter (SA or PGA in g), M is moment magnitude, rrup is the closest distance to rupture in km, H is depth in km, and Z r is source type factor {ZT - 0 for interface, Z r = 1 for intraslab). Interface events are mega earthquakes at a subduction interface. Intraslab earthquakes are those occur within overriding or subducting plates. For the two deep source zones, GEO and PUG, H is 50 km and the source type is intraslab ( Z r = 1 ) . The coefficients C/ through C 5 are regression coefficients that are available for PGA as well as SA at several periods (Youngs et al., 1997). Conversion of PGA to M M I is necessary in order to use the output from the hazard analyses in M M I based damage estimation methods. The relationship proposed by Neumann (1954) to convert PGA (in cm/sec) to M M I is presented below: MMI= '°g(POA) + 0.041 0.308 V 4 ' This equation was compared to more recent relationships (Trifunac and Brady, 1975; McCormack and Rad, 1997; Wald et al., 1999; Atkinson and Sonley, 2000) and at the ground motion levels considered for southwestern BC, all but Wald et al. (1999) relationship yield similar values (Figure 3.4). 29 In addition to PGA and SA, seismic hazard was calculated in terms of M M I using an MMI attenuation relationship developed by Atkinson (1999) for southwestern BC (Equation 3.10). Whereas in the PGA/SA calculations different attenuation relationships were utilized for shallow and deep zones, in M M I calculations the same attenuation relationship was used for all source zones. MMI = 1.6 • M - 0 . 5 log(/?)-0.0135/?-2.0 (Eq. 3.10) where M is local magnitude and R is hypocentral distance in km. 3.5 SEISMIC H A Z A R D IN T H E R E G I O N The seismic hazard analyses were carried out using the software EZ-FRisk (Risk Engineering Inc., 1997). It calculates the seismic hazard using the standard methodologies (Cornell, 1968; McGuire, 1974, 1976). It requires a set of user defined 30 databases describing site location and source parameters. Attenuation equations can be selected from the inbuilt database or can be added by the user. The probability level used was 10% chance of exceedance in 50 years, which corresponds to a return period of 475 years. Firm ground was assumed as reference ground condition for all hazard calculations. The ground motion parameters used in the analyses were PGA, SA and M M I . Results in terms of SA were used in the damage estimation by fragility curves. Results in terms of PGA and M M I on the other hand were used in damage calculations by damage probability matrices, which are given in terms of M M I . For this purpose, PGA values were converted to M M I using an empirical relationship (Equation 3.9). The resulting seismic hazard levels in terms of PGA and M M I for New Westminster, Victoria and Vancouver are summarized in Table 3.2. " M M I from P G A " refers to the M M I converted from the PGA values given in the same table, and " M M I " values are those calculated directly by a separate hazard analysis using an M M I attenuation relationship (Equation 3.10). It should be noted that although the P G A varies, the corresponding M M I remains uniform throughout the study areas. Table 3.2. Expected PGA and M M I levels New Westminster Victoria Vancouver PGA 0.24g 0.31g 0.23g M M I from PGA 7.8 (rounded to VIII) 8.2 (rounded to VIII) 7.8 (rounded to VIII) M M I 8.2 (rounded to VIII) 8.5 (rounded to VIII) 8.2 (rounded to VIII) 31 The hazard was also calculated in terms of spectral acceleration (SA) for several periods (T) ranging from 0.1 to 2.0 seconds. The periods and the corresponding SA for Vancouver and Victoria are presented in Table 3.3. Since the SA values at each period were calculated with the same level of probability (10% chance of exceedance in 50 years), the spectrum plotted using these SA values is called a uniform hazard spectrum (UHS). The UHS calculated for Vancouver and Victoria are plotted in Figure 3.5. Table 3.3. Spectral acceleration levels expected in Vancouver and Victoria Period, T (sec) SA (g) in Vancouver SA (g) in Victoria 0.1 0.489 0.665 0.2 0.529 0.713 0.4 0.394 0.529 0.5 0.353 0.474 0.75 0.230 0.309 1.0 0.159 0.215 2.0 0.0692 0.0914 Uniform Hazard Spectra for Vancouver and Victoria (10% in 50 years) Vancouver Victoria Period (s) Figure 3.5. Uniform hazard spectra for Vancouver and Victoria 32 4. SITE AMPLIFICATION The ground motion levels obtained from seismic hazard analyses are generally for a reference ground condition such as firm soil or rock. Many past earthquakes demonstrated that local site conditions have significant effect on seismic response of the ground. Therefore, following the estimation of ground motion on rock, the effects of the local soil conditions need to be evaluated. Major causes of damage apart from strong ground shaking are soil amplification, liquefaction and landslides. Usually, a separate analysis is performed to evaluate the landslide and liquefaction potentials. The effect of soil amplification on the other hand is directly reflected onto the resulting ground motion level from the seismic hazard assessment. Soil amplification is caused by the difference in the impedances of two subsequent layers of soil and/or rock. Impedance is defined as the product of the density and the shear wave velocity of the medium. Amplification can be estimated by numerically modelling the soil properties and wave-propagation, or alternatively by using empirical relations derived from observed data. The simplest wave propagation model has a single uniform soil layer resting on rigid rock. The amplification is described by the transfer function, which is defined as the ratio of the ground motion amplitude at the top of the layer to the amplitude at the bottom of the layer. A more comprehensive model can take into account the elasticity of the rock, and include multiple layers instead of just one. The computer program, S H A K E 33 (Schnabel et al., 1972) performs such a multi-layer analysis and takes into account the non-linearity of the soil by equivalent linear approximation. This type of detailed analysis requires knowledge of the soil profile, and extensive geotechnical information on each layer of soil. An alternative approach for quantifying the effect of soil amplification is making use of empirical multiplication factors (Aki, 1988). These factors are typically developed by comparing measured ground motions (usually peak ground acceleration, PGA) on rock outcrops and soil sites from past earthquakes (Seed et al., 1976; Idriss, 1990; Seed et a l , 1997). Due to the non-linearity of the soil, amplification decreases as the ground shaking gets stronger. Sugito et al. (1991) developed a ground motion amplification factor based on the ground motion records from the Loma Prieta earthquake of 1989, which takes into account the nonlinear effects of the soil. It is modeled as a function of local soil parameters such as shear wave velocity, depth to bedrock and the intensity of ground motion, which is needed to determine the extent of nonlinear effects. In addition to the amplitude, local site conditions also influence the frequency content of the ground motions and hence the response spectra they produce. NEHRP (BSSC, 1994) uses the site geology classification scheme shown in Table 4.1, where V s is the average shear wave velocity in the upper 30 metres. NEHRP site classes range from A (hard rock) to E (soft soil). Site class F indicates areas with peat layers deeper than 3 metres, susceptible to very high amplification and requiring detailed site-specific analysis to estimate the amount of amplification. Based on these site classes and ground shaking 34 intensity, two separate amplification factors are provided for the low-period and one high-period portions of the response spectrum. By providing two separate factors, it takes into account the frequency content of the ground motion in an approximate way. It should be noted that NEHRP site classes B and C do not have the same definition as the Boore et al. (1993) site classes B and C discussed in Chapter 3. Table 4.1 NEHRP site classes Soil Class Description Properties A Hard rock Vs> 1500 m/sec B Rock 760 m/sec < Vs < 1500 m/sec C Very dense soil and soft rock 360 m/sec < Vs < 760 m/sec N>50, su> 100 kPa D Stiff soil 180 m/sec < Vs < 360 m/sec 15 < N < 50, 50 kPa < su < 100 kPa E Soil Vs< 180 m/sec > 3m of soft clay (PI > 20, w > 40% and su < 25 kPa) The NEHRP Provisions describe the ground motion level by effective peak acceleration and effective peak velocity. Effective peak acceleration is proportional to the average spectral acceleration at low periods (near 0.2 sec), and effective peak velocity is proportional to the spectral velocity at longer periods (above 1.0 sec). The dimensionless coefficient, A a is obtained by dividing the effective peak acceleration by g, and A v is obtained by dividing effective peak velocity by g/2u. Once A a and A v are determined through seismic hazard analyses, the amplification factors F a and F v can be obtained from Tables 4.2 and 4.3. Table 4.2 NEHRP site coefficients, F, Site Class Shaking Intensity A. = 0.1 A a = 0.2 A a = 0.3 A a = 0.4 A a = 0.5 A 0.8 0.8 0.8 0.8 0.8 B 1.0 1.0 1.0 1.0 1.0 C 1.2 1.2 1.1 1.0 1.0 D 1.6 1.4 1.2 1.1 1.0 E 2.5 1.7 1.2 0.9 -Table 4.3 NEHRP site coefficients, F v Site Class Shaking Intensity A v = 0.1 A v = 0.2 A v = 0.3 A v = 0.4 A v = 0.5 A 0.8 0.8 0.8 0.8 0.8 B 1.0 1.0 1.0 1.0 1.0 C 1.7 1.6 1.5 1.4 1.3 D 2.4 2.0 1.8 1.6 1.5 E 3.5 3.2 2.8 2.4 -For the regional risk assessment in southwestern B C , site amplification factors were preferred since the regional study covers a large area and it would not be feasible to conduct a detailed amplification study. Geology of Victoria was mapped and the geological units were roughly matched to NEHRP site classes (Monahan et a l , 2000). In Victoria for stiff soil, the coefficient A a is 0.5 and A v is 0.4. 36 Table 4.4 NEHRP site classes corresponding to geological units in Victoria Geologic Unit Description NEHRP Site Class Range Fa F v R 2 Thin soil cover over bedrock with scattered outcrops; generally < 5 m of Victoria clay over < 10 m of older Pleistocene A t o C 1.0 1.0 C 2 > 3 m of the grey clay fades of the Victoria clay, under the brown clay facies and over thin (< 10 m) older Pleistocene deposits D to E 1.0 2.0 C l Areas where units R2 & C2 cannot be differentiated; also areas with > 5 m of the Victoria clay but < 3 m of grey clay facies C toE 1.0 1.5 F Anthropogenic fill with variable amplification C toE 1.0 1.5 OI Holocene peat over the grey clay facies of the Victoria clay Eto F 1.0 2.5 The amount of amplification depends on the surface geology, thickness of the upper layer, level of ground shaking and period of the ground motion. For the ground shaking level estimated for Victoria (PGA ~ 0.35g), short-period ground motions are not expected to be amplified. Long-period ground motions, on the other hand, are expected to be amplified roughly by 1.5 for landfill, 2.0 for grey clay facies of the Victoria clay thicker than 3 m, and 2.5 for Holocene peat over clay. The effect of this amplification is especially critical for tall structures with long fundamental periods coinciding with the amplified portion of the response spectrum. 37 5. ASSESSMENT OF T H E S T R U C T U R A L D A M A G E : M M I - B A S E D Structural damage assessment methodologies are discussed in two parts, MMI-based "damage probability matrices" (ATC-13, 1985 approach) and SD-based "fragility curves" (FEMA/NIBS, 1997 approach). An overview of the MMI-based damage estimation methodology, the building classification used for BC, damage state descriptions and the mean damage factors for buildings in southwestern BC are presented in the following sections. SD-based damage estimation methodology is discussed in Chapter 11. 5.1. O V E R V I E W The basics of seismic risk and damage assessments are given by the EERI Committee on Seismic Risk (1989) and Kiremidjian (1992). In order to carry out a risk analysis in an area, information on the building stock is required. In general, collection of this data is the most time consuming and resource extensive part of any damage estimation study. The accuracy of a building inventory is determined by the amount of available time and resources as well as the requirements of the study. A typical inventory contains the following information: street address, primary use, material, structural load bearing system, age, height (number of stories), and footprint area. The first step in collecting this information is to identify existing data sources including provincial/local government databases and private sector databases, and to acquire the available data from these sources. Next step is to integrate the data obtained into a uniform and complete database. 38 This is usually achieved by using classification and inference schemes where appropriate or by field surveys where data is insufficient to build inference schemes. Vasudevan et al. (1992) and King et al. (1994) address the need to integrate information from several data sources in order to obtain an inventory of buildings as accurate and complete as possible. The estimation of seismic damage on the existing building stock requires the development of relationships correlating the ground motion at the site to the damage in the buildings. A number of damage estimation methods have been proposed since early 1970s using various ground motion parameters, and with different levels of detail and coverage (Reithermann, 1985). Common ground motion parameters related to damage are PGA (Petrovski et al., 1992; Hwang et al., 1997), MMI , SA and SD. Since it is not feasible to develop a separate relationship for each individual building, a classification scheme suitable to the region under study is usually developed based on building material, height, age, etc. These ground motion parameters and classification of building types will be further discussed in the following paragraphs. Despite its disadvantages, such as being a subjective scale and lacking a good correlation with recorded parameters such as PGA and SA, Modified Mercalli Intensity (MMI) has been commonly used as the key ground motion parameter in the damage estimation methodologies (ATC-13, 1985; Cochrane and Schaad, 1992; Emmi and Horton, 1993; King and Kiremidjian, 1994; McCormack and Rad, 1997, Rojahn et al., 1997; Dowrick and Rhoades, 1997; Blanquera, 1999). It is a simple scale known to engineers and most of the reported damage from past earthquakes is in terms of M M I . It is also directly 39 related to description of the damage experienced in an earthquake. Detectable damage to the structures is observed starting at an M M I level of VI . The M M I scale for intensities VI and up is presented in Appendix A. A widely used classification scheme is proposed by Applied Technology Council within their damage estimation methodology (ATC-13, 1985). It was originally developed for buildings in California, however it has become a basis for classification schemes elsewhere and has been frequently used in other regions with adjustments for the area under study. In ATC-13, expected damage was related to ground motion intensity through the Damage Probability Matrices (DPMs), which have been widely used in California and with some adjustments in other regions. They describe for each building class, the probability that a building is in a specified damage state given the level of ground shaking intensity (MMI). The seven discrete damage states are: 1. None: No damage. 2. Slight: Limited localized minor damage not requiring repair. 3. Light: Significant localized damage of some components generally not requiring repair. 4. Moderate: Significant localized damage of many components warranting repair. 5. Heavy: Extensive damage requiring major repairs. 6. Major: Major widespread damage that may result in facility being demolished or repaired. 7. Destroyed: Total destruction of the majority of the facility. Each of these damage states is associated with a range of damage factors (DF), which are defined as the ratio of dollar loss to the replacement value. These ranges and the corresponding central damage factors are given in Table 5.1. 40 Table 5.1. Damage states in terms of damage factors (DF) D A M A G E STATE DF RANGE (%) CENTRAL DF (%) 1. None 0 0 2. Slight 0 - 1 0.5 3. Light 1 - 10 5 4. Moderate 1 0 - 3 0 20 5. Heavy 3 0 - 6 0 45 6. Major 6 0 - 1 0 0 80 7. Destroyed 100 100 A n example Damage Probability Matrix (DPM) for one of the building classes (Wood Frame - Low Rise) defined in ATC-13 (1985) is shown in Table 5.2. Damage matrices were originally developed by A T C (1985) for 40 different building classes based on expert opinion through a multiple questionnaire process. A group of 71 earthquake engineering experts were asked to provide best, low and high estimates of the damage factor to selected building classes for M M I levels VI through XII. After the three-round questionnaire, a Beta probability distribution was fitted to the data to develop the DPMs. 41 Table 5.2. Damage Probability Matrix (DPM) for Wood Frame - Low Rise Central DF Modified Mercalli Intensity VI VII VIII IX X XI XII Wood Frame - Low Rise 0 3.7 * * * *** *** *** *** *** 0.5 68.5 26.8 1.6 * * * *** *** *** 5 27.8 73.2 94.9 62.4 11.5 1.8 *** 20 *** *** 3.5 37.6 76.0 75.1 24.8 45 *** *** *** *** 12.5 23.1 73.5 80 *** *** *** *** *** *** 1.7 100 *** *** *** *** *** ** * *** 5.2. C L A S S I F I C A T I O N OF B C BUILDINGS A classification scheme based on ATC-13 (ATC, 1985), modified for the construction practice in southwestern BC was used for the BC buildings. They were first grouped in terms of materials and then further divided into 31 prototypes based on their heights, ages and structural systems (Table 5.3). These building prototypes are described in detail in Appendix B. 42 Table 5.3. BC building classification Material Building Prototype Code 1 Wood Wood Light Frame Residential WLFR 2 Wood Light Frame Low Rise Commercial/Institutional WLFCI 3 Wood Light Frame Low Rise Residential WLFLR 4 Wood Post and Beam WPB 5 Steel Light Metal Frame LMF 6 Steel Moment Frame Low Rise SMFLR 7 Steel Moment Frame Medium Rise SMFMR 8 Steel Moment Frame High Rise SMFHR 9 Steel Braced Frame Low Rise SBFLR 10 Steel Braced Frame Medium Rise SBFMR 11 Steel Braced Frame High Rise SBFHR 12 Steel Frame with Concrete Walls Low Rise SFCWLR 13 Steel Frame with Concrete Walls Medium Rise SFCWMR 14 Steel Frame with Concrete Walls High Rise S F C W H R 15 Steel Frame with Concrete Infill Walls SFCI 16 Steel Frame with Masonry Infill Walls SFMI 17 Concrete Concrete Frame with Concrete Walls Low Rise CFLR 18 Concrete Frame with Concrete Walls Medium Rise CFMR 19 Concrete Frame with Concrete Walls High Rise CFHR 20 Reinforced Concrete Moment Frame Low Rise RCMFLR 21 Reinforced Concrete Moment Frame Medium Rise RCMFMR 22 Reinforced Concrete Moment Frame High Rise RCMFHR 23 Reinforced Concrete Frame with Infill Walls RCFIW 24 Masonry Reinforced Masonry Shear Wall Low Rise RMLR 25 Reinforced Masonry Shear Wall Medium Rise RMMR 26 Unreinforced Masonry Bearing Wall Low Rise URMLR 27 Unreinforced Masonry Bearing Wall Medium Rise URMMR 28 Tilt Up Tilt Up TU 29 Precast Precast Concrete Low Rise PCLR 30 Precast Concrete Medium Rise PCMR 31 Mobile Mobile Homes MH 43 5.3. D A M A G E M A T R I C E S F O R B C B U I L D I N G P R O T O T Y P E S Damage matrices describe, for each building prototype and M M I level, the probability of reaching a particular damage state. The seven discrete damage states used in the M M I -based methodology are: None, Slight, Light, Moderate, Heavy, Major and Destroyed as described in Section 5.1. The damage matrices were developed for the 31 building prototypes of B C , with the assumptions that the buildings are very nearly regular in shape, founded on firm ground and designed to a code prior to 1990. Collateral hazards such as ground failure and fire were not considered (Bell, 1998). Discrete probabilities for three sample prototypes are presented in Table 5.4 for an M M I level of VIII. The complete damage matrices for 31 prototypes are presented in Appendix C. Table 5.4. Damage probabilities (MMI-based) Building Prototype M M I Discrete Probabilities (%) for Damage States None Slight Light Moderate Heavy Major Destroyed U R M L R VIII 0.0 0.0 21.0 60.0 15.0 2.0 2.0 WLFR VIII 1.0 6.0 86.0 5.0 2.0 0.0 0.0 CFHR VIII 0.0 2.0 57.0 40.0 1.0 0.0 0.0 The total level of damage in a building is described by the mean damage factors (MDF), in terms of the ratio of dollar loss to replacement cost. To calculate the MDFs for each M M I level, the product of the CDFs and their corresponding probabilities for all discrete damage states (Table 5.1) are added up as follows: 44 , 7 jyjjjpMMi _ — i — y CDF. • P{ds .) prototype j QQ Z - I 7 K J' 7=1 where CDF, is the central damage factor for damage state j and P(dsj) is the probability of the prototype being in damage state j. As an example, for U R M L R at an M M I level of VIII, the M D F can be calculated as: n ^ T ^ v m 0.0 0.0 + 0.5 0.0 + 5.0-21.0 + 20.0-60.0 + 45.0 15.0 + 80.0-2.0 + 100.0-2.0 „ „ A n , M D F U R M L R = — = 23.4% 100 where the bold numbers indicate the CDF (%) and the regular ones indicate the probabilities (%) corresponding to each CDF. A summary of MDFs calculated similarly for the 31 prototypes at M M I levels of interest is presented in Table 5.5. 45 Table 5.5. Mean Damage Factors (MDFs) Material Prototype Mean Damage Factor (%) for MMI VI VII VIII IX X XI XII Wood WLFR 1.2 4.4 7.4 12.0 25.4 29.9 37.7 WLFCI 1.2 5.5 9.1 14.5 27.4 36.9 44.1 WLFLR 1.0 3.8 4.9 11.6 18.9 28.1 37.4 WPB 1.4 6.4 11.8 18.9 31.6 39.1 45.9 Steel LMF 0.5 2.7 4.1 7.0 18.8 23.9 36.7 SMFLR 0.6 3.2 5.0 6.3 17.3 23.4 36.1 SMFMR 0.7 3.7 5.1 8.7 20.6 31.7 42.8 SMFHR 0.7 4.5 5.8 17.2 23.6 37.4 44.8 SBFLR 0.9 2.6 6.9 12.3 22.4 31.4 40.8 SBFMR 1.6 4.5 10.1 14.8 22.1 32.5 38.3 SBFHR 1.6 5.9 10.5 16.0 23.8 39.6 48.4 SFCWLR 0.9 4.5 6.2 15.6 22.2 36.0 46.5 SFCWMR 1.3 4.7 7.7 19.3 29.1 42.2 51.1 SFCWHR 1.3 4.7 9.3 22.8 32.8 49.3 57.0 SFCI 0.9 3.6 7.9 16.8 23.8 39.1 51.2 SFMI 3.1 7.5 16.5 36.2 45.8 64.0 69.2 Concrete CFLR 0.9 4.7 5.0 13.9 21.0 36.9 49.4 CFMR 0.9 3.6 7.9 16.8 23.8 39.1 51.2 CFHR 1.1 4.0 11.3 22.9 30.4 43.2 54.2 RCMFLR 3.0 5.5 13.8 21.0 37.9 49.9 54.5 RCMFMR 3.0 5.8 13.6 22.3 41.0 55.3 60.3 RCMFHR 3.4 4.9 15.7 25.5 41.6 60.1 67.4 RCFIW 2.9 7.7 15.6 30.4 39.6 60.6 67.5 Masonry RMLR 0.7 4.0 5.9 16.6 31.5 43.4 58.3 RMMR 0.9 4.6 8.0 26.7 35.3 47.8 67.3 URMLR 2.8 10.2 23.4 34.9 51.7 65.8 80.0 URMMR 4.3 12.2 26.9 38.2 53.8 70.0 83.7 Tilt Up TU 0.8 3.7 9.0 18.8 34.0 50.5 65.6 Precast PCLR 2.3 4.9 11.3 25.0 39.2 51.7 66.6 PCMR 2.7 6.1 13.0 28.4 38.0 53.0 69.0 Mobile Home MH 1.8 5.6 13.5 18.8 31.8 45.0 56.7 46 6. ASSESSMENT OF THE NON-STRUCTURAL DAMAGE In the early seismic damage and loss estimation practices, non-structural damage was usually not considered, since the damage affecting casualties and catastrophic loss of function were attributed to structural failure. However, in a number of recent earthquakes it has been observed that non-structural damage tends to dominate the economic loss. Therefore, estimation of non-structural damage has become of great importance. The first comprehensive study to address estimation of damage to non-structural components was the ATC-13 (1985). It grouped the non-structural components into six facility classes (residential equipment, office equipment and furniture, electrical equipment, mechanical equipment, high technology and laboratory equipment, and vehicles). The expected damage to each of the six facility classes were estimated through damage matrices that described the probability of being in a certain damage state in terms of MMI . The ATC-13 damage states are presented in Chapter 5 and the description of the M M I scale is given in Appendix A . In the more recent damage estimation methodologies, non-structural components are typically separated into two categories, drift-sensitive and acceleration-sensitive. Drift-sensitive components include non-load-bearing partition walls, exterior wall panels, architectural finishes, veneer, cladding and penthouses. Acceleration-sensitive components include cantilever elements, parapets, mechanical and electrical equipment, suspended ceilings, elevators, tanks, pumps, piping systems, racks and cabinets. Building 47 contents such as bookcases, office equipment and furnishings are also considered acceleration sensitive. A recent methodology proposed by FEMA/NIBS (1997) takes into account the difference in behaviour of these two groups of components. In this methodology, fragility of the drift-sensitive components is defined in terms of the interstorey drift and fragility of the acceleration-sensitive components is depicted in terms of the peak floor acceleration. The damage states used in this methodology differ from those in the ATC-13 (1985) methodology. They are defined for each type of non-structural component, not for the structural prototype of the building that contains these components. The reason is that the levels of interstorey drift and floor acceleration are the primary determinants of damage and whether these levels are reached in a wood or a steel frame building is inconsequential. Typical description of the damage states for a sample drift-sensitive component (partition walls) and a sample acceleration-sensitive component (electrical-mechanical equipment) are presented in the following paragraphs. Partition Walls 1. None: No damage. 2. Slight: A few cracks are observed at intersections of walls and ceilings, also at corners of door openings. 3. Moderate: Larger and more extensive cracks requiring repair and repainting are observed. Some partitions may require replacement of gypsum board or other finishes. 4. Extensive: Most of the partitions are cracked and a significant portion may require replacement of finishes. Some door frames in the partitions are also damaged and require re-setting. 48 5. Complete: Most partition finish materials and framing may have to be removed and replaced; damaged studs repaired, and walls refinished. Most door frames may also have to be repaired and replaced. Electrical-Mechanical Equipment, Piping, Ducts 1. None: No damage. 2. Slight: The most vulnerable equipment (e.g. unanchored or on spring isolators) moves and damages attached piping or ducts. 3. Moderate: Movements are larger and damage is more extensive; piping leaks at few locations. Elevator machinery and rails may require realignment. 4. Extensive: Equipment on spring isolators topples and falls; other unanchored equipment slides or falls breaking connections to piping and ducts; leaks develop at many locations; anchored equipment indicate stretched bolts or strain at anchorage. 5. Complete: Equipment is damaged by sliding, overturning or failure of their supports and is not operable. Piping is leaking at many locations; some pipe and duct supports have failed causing pipes and ducts to fall or hang down. Elevator rails are buckled or have broken supports and/or counterweights have derailed. Each of these damage states is associated with a range of damage factors (DF), which are defined as the ratio of dollar loss to the replacement value. These ranges together with the central damage factors (CDFs) associated with the damage states are presented in Table 6.1 for acceleration-sensitive components, displacement-sensitive components and building contents. Although the building contents are considered acceleration sensitive, their CDFs differ from those of acceleration-sensitive components. 49 Table 6.1. Non-structural damage states in terms of central damage factors Damage State Central Damage Factor (%) Displacement-sensitive Acceleration-sensitive Building contents 1. None 0 0 0 2. Slight 2 2 1 3. Moderate 10 10 5 4. Extensive 50 50 25 5. Complete 80 80 40 For each damage state, the fragility curves describe the probability of reaching or exceeding that damage state given the level of spectral displacement or acceleration. Fragility curves are cumulative lognormal distribution functions defined by two parameters, a median and a beta value, for each damage state. Median is the median value of the spectral displacement or acceleration at which the non-structural component reaches the threshold of a certain damage state. Beta is the standard deviation of natural logarithm of the spectral displacement or acceleration at that damage state. For the estimation of non-structural damage in BC, damage matrices in terms of M M I were developed by Cook (1999) based on the fragility curve parameters for non-structural components and the capacity curve parameters for structures, provided by the FEMA/NIBS (1997). Developing the damage matrices in terms of M M I involved the conversion of spectral displacement/acceleration to MMI , details of which can be found in Cook (1999). In addition, the building prototypes in BC were matched to those in FEMA/NIBS study (Table 6.2). The resulting non-structural damage matrices are presented in Appendix D. 50 Table 6.2. Building prototypes of BC versus FEMA/NIBS study (after Cook, 1999) Material BC prototype FEMA/NIBS prototype Wood W L F R W l WLFCI W2 W L F L R W l WPB W l Steel L M F S3 S M F L R S1L S M F M R S I M SMFHR S1H SBFLR S2L SBFMR S2M SBFHR S2H SFCWLR S4L SFCWMR S4M SFCWHR S4H SFCI S4L SFMI S4L Concrete C F L R C2L C F M R C 2 M CFHR C2H R C M F L R C1L R C M F M R C 1 M R C M F H R C1H RCFIW C3L Masonry R M L R R M 1 L R M M R R M 1 M U R M L R U R M L U R M M R U R M M Tilt Up TU PCI Precast Concrete PCLR PC2L P C M R PC2M Mobile Homes M H M H The total damage can be expressed by the mean damage factors (MDFs) as described in Chapter 5. A summary of MDFs calculated for the 31 prototypes and three groups of non-structural components at M M I levels of interest is presented in Tables 6.3, 6.4 and 6.5. The reason for having same MDFs for some prototypes, e.g. WLFR, W L F L R and WPB, is the correspondence of these prototypes with the same FEMA/NIBS prototype, in this case W l , as displayed in Table 6.2. Table 6.3. MDFs for displacement-sensitive components Material Prototype Mean Damage Factor (%) for MMI VI VII VIII IX X XI XII Wood WLFR 10.0 15.3 17.0 22.7 27.6 32.2 35.8 WLFCI 8.1 14.8 15.8 20.3 24.4 27.5 30.5 W L F L R 10.0 15.3 17.0 22.7 28.3 32.2 35.8 WPB 10.0 15.3 17.0 22.7 28.6 32.2 35.8 Steel L M F 10.7 18.2 18.8 26.4 30.9 34.7 37.5 SMFLR 7.1 15.9 16.7 20.7 25.4 28.5 32.4 SMFMR 7.3 16.2 16.8 18.1 22.4 24.7 35.3 SMFHR 7.0 7.5 8.5 15.7 20.4 25.0 29.2 SBFLR 7.3 14.0 15.6 21.1 25.0 28.7 31.5 SBFMR 7.1 13.3 14.6 15.3 18.4 21.8 24.6 SBFHR 5.3 9.8 11.0 13.3 18.3 22.0 25.6 SFCWLR 8.0 16.9 17.1 21.7 26.0 29.4 31.9 SFCWMR 6.1 14.6 15.1 15.7 18.5 22.5 25.7 SFCWHR 5.6 11.3 11.7 13.1 17.5 23.4 26.8 SFCI 8.0 16.3 17.1 21.7 26.0 29.4 31.9 SFMI 8.0 16.3 17.1 21.7 26.0 29.4 31.9 Concrete CFLR 9.0 16.7 17.3 21.8 26.9 29.8 33.0 CFMR 5.0 11.0 11.3 13.8 17.2 20.0 22.2 CFHR 5.8 10.7 11.1 13.1 15.9 18.2 21.2 R C M F L R 8.4 17.2 17.7 23.3 27.5 31.2 33.6 R C M F M R 6.9 15.4 15.8 17.4 20.6 24.0 27.1 RCMFHR 7.5 15.0 15.6 18.4 23.8 28.2 32.2 RCFIW 8.7 18.6 19.1 26.1 32.3 38.1 49.8 Masonry R M L R 10.5 13.7 14.5 22.3 27.0 30.0 32.9 R M M R 5.2 8.8 9.2 13.7 17.0 19.8 22.2 U R M L R 12.1 21.2 22.8 32.2 31.0 34.8 37.5 U R M M R 7.7 13.8 14.2 17.2 21.2 24.9 27.7 Tilt Up T U 11.4 15.7 16.5 24.3 29.7 33.2 35.6 Precast P C L R 9.0 16.7 17.3 22.9 27.3 31.0 33.8 P C M R 5.6 11.2 11.5 15.5 19.0 21.7 25.7 Mobile Home MH 12.2 21.6 22.2 29.3 34.3 37.5 43.7 52 Table 6.4. MDFs for acceleration-sensitive components Material Prototype Mean Damage Factor (%) for MMI VI VII VIII IX X XI XII Wood WLFR 1.0 3.3 5.5 8.8 14.3 18.2 20.7 WLFCI 0.9 3.1 3.3 6.2 8.3 9.9 10.7 WLFLR 1.0 3.3 5.5 8.8 14.3 18.2 20.7 WPB 1.0 3.3 5.5 8.8 14.3 18.2 20.7 Steel L M F 0.6 2.3 2.7 4.9 6.3 6.7 7.5 SMFLR 0.3 1.7 2.1 3.2 4.1 5.1 5.9 SMFMR 0.0 0.4 0.3 0.7 1.2 2.4 2.8 SMFHR 0.0 0.0 0.0 0.1 0.4 0.5 0.5 SBFLR 0.7 3.0 3.6 5.3 6.8 7.1 7.9 SBFMR 0.1 0.4 1.1 1.6 2.6 3.1 3.7 SBFHR 0.0 0.2 0.3 0.5 0.9 1.6 2.4 SFCWLR 1.2 2.0 2.8 5.1 5.8 6.6 6.6 SFCWMR 0.1 1.4 1.2 2.3 3.1 3.7 3.9 SFCWHR 0.0 0.3 0.4 0.5 1.3 2.1 2.4 SFCI 1.2 2.0 2.8 5.1 5.8 6.6 6.6 SFMI 1.2 2.0 2.8 5.1 5.8 6.6 6.6 Concrete CFLR 0.7 3.3 3.6 7.1 9.5 10.7 11.6 CFMR 0.3 1.7 2.1 3.8 5.1 6.5 7.4 CFHR 0.0 0.5 0.8 0.9 1.8 2.3 3.4 RCMFLR 0.4 1.9 2.1 4.1 5.4 6.1 6.8 RCMFMR 0.1 0.7 0.9 1.8 2.4 3.3 3.8 RCMFHR 0.0 0.1 0.2 0.4 0.5 0.7 0.8 RCFIW 0.6 3.0 3.3 3.6 3.6 3.6 3.6 Masonry RMLR 1.0 3.9 4.2 7.7 10.2 11.5 12.8 RMMR 0.3 1.9 2.4 4.1 5.8 7.4 8.5 URMLR 2.1 5.5 5.9 9.3 10.8 11.9 11.9 URMMR 0.6 2.9 4.8 9.6 11.1 12.1 12.1 Tilt Up TU 1.3 3.0 3.7 8.0 11.2 13.9 14.2 Precast PCLR 1.1 2.3 2.7 5.6 6.7 7.0 7.9 PCMR 0.3 1.6 1.8 3.1 3.9 4.6 5.3 Mobile Home MH 1.0 2.2 2.5 3.9 4.2 4.5 4.5 Table 6.5. MDFs for building contents Material Prototype Mean Damage Factor (%) for M M I VI VII VIII IX X XI XII Wood WLFR 0.5 1.6 2.7 4.4 7.1 9.1 10.4 WLFCI 0.4 1.5 1.7 3.1 4.2 5.0 5.4 W L F L R 0.5 1.6 2.7 4.4 7.1 9.1 10.4 WPB 0.5 1.6 2.7 4.4 7.1 9.1 10.4 Steel L M F 0.3 1.1 1.3 2.4 3.2 3.4 3.7 SMFLR 0.1 0.9 1.1 1.6 2.1 2.6 2.9 SMFMR 0.0 0.2 0.2 0.3 0.6 1.2 1.4 SMFHR 0.0 0.0 0.0 0.0 0.2 0.2 0.3 SBFLR 0.3 1.5 1.8 2.6 3.4 3.6 3.9 SBFMR 0.1 0.2 0.5 0.8 1.3 1.5 1.8 SBFHR 0.0 0.1 0.1 0.2 0.5 0.8 1.2 SFCWLR 0.6 1.0 1.4 2.6 2.9 3.3 3.3 SFCWMR 0.1 0.7 0.6 1.1 1.5 1.8 2.0 SFCWHR 0.0 0.1 0.2 0.3 0.7 1.0 1.2 SFCI 0.6 1.0 1.4 2.6 2.9 3.3 3.3 SFMI 0.6 1.0 1.4 2.6 2.9 3.3 3.3 Concrete CFLR 0.3 1.6 1.8 3.6 4.7 5.4 5.8 CFMR 0.1 0.8 1.0 1.9 2.5 3.3 3.7 CFHR 0.0 0.3 0.4 0.4 0.9 1.1 1.7 R C M F L R 0.2 1.0 1.0 2.1 2.7 3.1 3.4 R C M F M R 0.1 0.4 0.5 0.9 1.2 1.6 1.9 RCMFHR 0.0 0.1 0.1 0.2 0.3 0.4 0.4 RCFIW 0.3 1.5 1.6 1.8 1.8 1.8 1.8 Masonry R M L R 0.5 2.0 2.1 3.9 5.1 5.7 6.4 K M M R 0.1 1.0 1.2 2.0 2.9 3.7 4.3 U R M L R 1.1 2.7 3.0 4.7 5.4 5.9 5.9 U R M M R 0.3 1.5 2.4 4.8 5.5 6.1 6.1 Tilt Up T U 0.7 1.5 1.9 4.0 5.6 6.9 7.1 Precast P C L R 0.5 1.1 1.3 2.8 3.4 3.5 3.9 P C M R 0.1 0.8 0.9 1.5 2.0 2.3 2.6 Mobile Home M H 0.5 1.1 1.3 2.0 2.1 2.3 2.3 7. M O N E T A R Y L O S S E S The final step in a seismic risk assessment is the estimation of losses. Losses can be divided into monetary and non-monetary. Financial losses resulting from damage to structural and non-structural components are examples of monetary losses, and fatalities and injuries are examples of non-monetary losses. Losses can also be divided into direct and indirect losses depending on the cause. Direct losses result from damage due to strong shaking, whereas indirect losses result from damage associated with collateral hazards like fire caused by the earthquake or tsunami. In this thesis, only the direct monetary losses resulting from damage to structural and non-structural components of buildings due to strong shaking will be considered and these losses will be referred to as "monetary losses" in general. The monetary losses in the study areas in southwestern BC were calculated by adding up the losses resulting from damage to structural, displacement-sensitive non-structural and acceleration-sensitive non-structural components. The amount of damage estimated for these three components of buildings were expressed by Mean Damage Factor (MDF) which is the ratio of dollar loss to replacement cost. Therefore, the monetary losses resulting from damage to these components were simply calculated by multiplying the MDFs by replacement costs. Construction costs for the 31 B C building prototypes obtained from a local construction company are presented in Table 7.1 in terms of Canadian dollars (CAD). Based on the 55 judgement of the local engineers, about 25% of these costs were considered to be for the structural components and 75% for the non-structural components. The acceleration- and displacement-sensitive non-structural components were assumed to have equal costs. Table 7.1. BC building costs Prototype Construction cost (CAD per square foot) WLFR $90 WLFCI $50 WLFLR $75 WPB $125 LMF $85 SMF (LR, MR and HR) $65 SBF (LR, MR and HR) $65 SFCW (LR, MR and HR) $80 SFCI $80 SFMI $70 CF (LR, MR and HR) $110 RCMF (LR, MR and HR) $135 RCFIW $135 RM (LR and MR) $60 URM (LR and MR) $40 TU $50 PC (LR and MR) $120 MH $70 The distribution and amount of monetary losses estimated for New Westminster, Victoria and Vancouver on a block by block basis are given in Chapters 8, 9 and 10, respectively. 8. CASE STUDY: NEW WESTMINSTER In this chapter, damage and loss estimations carried out for the City of New Westminster is described. It involved construction of a comprehensive building database, estimating structural and non-structural damage using MMI-based damage probability matrices, estimating monetary losses due to calculated damage, and mapping the damage and loss distributions within the city on a block-by-block basis. The City of New Westminster is located along the north banks of the Fraser River, in the centre of the Greater Vancouver Regional District (GVRD), which is a partnership of the 21 municipalities and one electoral area that make up the metropolitan area of Greater Vancouver (Figure 8.1). The City of New Westminster was incorporated in 1860 and was the first capital of British Columbia. It has a population over 50,000 people as of 1999 and rests on roughly 15.5 square kilometre area. The building inventory within the city boundaries consists of over 8,000 structures, including buildings that date back to the late 1800's and turn of the century, as well as modern high-rise structures. A probabilistic seismic hazard analysis for New Westminster (49.2° N , 122.9° W) was carried out for firm ground conditions to yield a PGA level of 0.24g (Table 3.2), which corresponds to M M I VIII (Equation 3.9). An alternative hazard analysis was performed by directly using an M M I attenuation relationship (Atkinson, 1999), which also yielded an M M I value of VIII. The probability level in both analyses was 10% chance of exceedance in 50 years, which is equivalent to a return period of 475 years. 57 Figure 8.1. City of New Westminster in G V R D Inventory collection comprises of identifying existing sources of data, acquiring the available information from them, cross checking and supplementing the database when necessary, and integrating them into a uniform database. For this study, the Planning Department of the City of New Westminster provided their substantial building database, which includes location, zoning and land use information as well as structural properties of every building in the municipality. However, the structural classification scheme the City used had to be converted to the 31 building prototypes used in this study (Table 5.3). This was achieved by making spot checks 58 using building plans on file with the city as well as using inference schemes developed by expert opinion. Some example inference schemes in terms of structure type, age, number of stories and area are presented in Table 8.1. Other fields such as building name were also used in some cases. "Frame" buildings with apartment, court or manor names were assumed to be WLFLR, and those with religious or commercial names were classified as WLFCI (Blanquera, 1999). When inference schemes were insufficient, building plans on file with City Hall were reviewed to determine the building prototype. When all resources at hand were exhausted, field surveys were carried out to complete the rest of the missing information and to check the inferred building prototypes. The survey form used in the sidewalk surveys is presented in Appendix E. Table 8.1. Example inference schemes for New Westminster building database "IF" S T R U C T U R E T Y P E ( S T ) A N D O T H E R A R G U M E N T S " T H E N " P R O T O T Y P E IF (ST = Concrete) and (number of stories > 9) THEN C F H R IF (ST = Concrete Block) and (number of stories = 1) and (age <1973) THEN U R M L R IF (ST = Brick) and (number of stories = 5) THEN U R M M R IF (ST = Heavy timber) THEN W P B IF (ST = Frame) and (number of stories < 5) and (area < 1500 sq. ft.) THEN W L F R IF (ST = Frame) and (number of stories < 5) and (area > 1500 sq. ft.) THEN W L F L R Once the database was ready, the damage estimation was carried out using the GIS software, Maplnfo (Maplnfo Co., 1997). The geographical unit selected for the damage estimation was "block", which is typically rectangular and is bounded by streets on four sides. It is suitable in size and convenient for the GIS database, since the planning department numbers the blocks and uses them as a reference for each building in the database. 59 Discrete classification attributes (e.g. material type and prototype) for buildings within a block were counted to yield the attribute with most number of occurrences in each block. The prevalent material type and building prototype in the City of New Westminster determined this way are presented on a block-by-block basis in Figures 8.2 and 8.3, respectively. 0 OS 1 Figure 8.2. Prevalent material type by block 60 The majority (94%) of the buildings in New Westminster are wood structures and it is the prevalent material in 90% of the blocks. Concrete and masonry buildings constitute about 3% of the building stock each and they each are the prevalent material type in about 4% of the blocks. In about 2% of the blocks in the city, the prevalent material type is steel or tilt up. 0 05 1 Figure 8.3. Prevalent prototype by block 61 The most common prototype is W L F R , which constitutes about 86% of all the buildings in the city and about 91% of all the wood buildings. Two other wood prototypes, W L F L R and W L F C I make up about 8% of the buildings. About 2% of all the buildings and 79%) of the masonry buildings are U R M L R . About 1% of all buildings and 59% of concrete buildings are C F L R . Among the few steel structures in the city, most are braced frame low rise buildings ( S B F L R ) . The damage estimation was carried out using the MMI-based damage matrices, which describe, for each building prototype, the probability of being in a certain damage state for a particular M M I level. Total damage levels as a percentage of replacement cost (mean damage factors, M D F s ) for different M M I levels are given in Table 5.5 for each building prototype. The mean M D F for each block was calculated by averaging (either straight average or weighted by a parameter such as "footprint area") the M D F s of the buildings within that block. The estimated structural damage distributions on a block-by-block basis are presented in Figures 8.4 and 8.5, with straight average and weighted average (weighted by "footprint area"), respectively. About 93% of the blocks in N e w Westminster are expected to have M D F s between 5% and 10%o, and 6% have M D F s between 10% and 20%. Only a few blocks have M D F s as high as 20%> to 30%. When the M D F s are averaged over the blocks weighted by footprint area, changes are observed in a few blocks. These blocks are those within which there are buildings with high differences in footprint area. 62 0 OS 1 Figure 8.4. Structural damage distribution (average MDF) 63 OS Kilometers Non-structural damage distribution was calculated in a similar manner using the MDFs presented in Tables 6.3, 6.4 and 6.5, respectively for displacement-sensitive components, acceleration-sensitive components and building contents. Resulting non-structural damage distribution maps are presented in Figures 8.6, 8.7 and 8.8 for displacement-64 sensitive components, acceleration-sensitive components and building contents, respectively. Figure 8.6. Non-structural damage distribution (displacement-sensitive components) About 80% of the blocks are expected to have MDFs between 20% and 30%, and the rest between 15% and 20% for displacement sensitive components. 65 Figure 8.7. Non-structural damage distribution (acceleration-sensitive components) For acceleration-sensitive components, about 80% of the blocks in New Westminster are expected to have MDFs in the range of 5% to 10%, and the rest are expected to have MDFs between 0% and 5%. 66 Figure 8.8. Non-structural damage distribution (building contents) Damage to building contents stay below 5% in all the blocks in New Westminster. Monetary losses resulting from damage to structural and non-structural components of buildings were also estimated for New Westminster. Distribution of total dollar loss by block is given in Figure 8.9. 67 0 OS 1 Figure 8.9. Distribution of total monetary loss by block 68 9. CASE STUDY: VICTORIA In this chapter, damage and loss estimations carried out for the City of Victoria is described. It includes building inventory collection, estimation of structural and non-structural damage using MMI-based damage matrices, and assessment of monetary losses resulting from the estimated damage. City of Victoria is located on the Southern tip of Vancouver Island on the West Coast of Canada and is a part of the Capital Regional District, CRD (Figure 9.1). Victoria is Western Canada's oldest city, started in 1843 as a Hudson Bay Company trading post, named in honour of Queen Victoria. It was incorporated as a City in 1862 and was proclaimed the capital of British Columbia in 1871. It has a population of over 77,000 people as of 1999 and rests on roughly 23.5 square kilometre area. The building inventory of the City consists of over 13,000 structures, out of which, about 2,500 are in the study area, which consists of downtown and near vicinity (Figure 9.2). A probabilistic seismic hazard analysis for Victoria (48.5° N , 123.3° W) was carried out for firm ground conditions to yield a PGA level of 0.3lg (Table 3.2), which corresponds to M M I VIII. A n alternative hazard analysis performed directly in terms of M M I also yielded an M M I value of VIII. The probability level considered for the hazard calculations is 10% chance of exceedance in 50 years, which is equivalent to a return period of 475 years. 69 Capital Regional District Figure 9.1. City of Victoria in CRD Figure 9.2. Study area in City of Victoria 70 Inventory collection involved identifying existing sources of data, supplementing them with field surveys when necessary, and integrating all the information into a uniform database. For this study, the Planning Department of the City of Victoria provided their building database, which included location (street address), zoning and land use information on every structure in the municipality. However, there was no information available on structural properties of the buildings, such as building material, construction date, load bearing system, height (or number of stories), and footprint area. These were collected by sidewalk surveys covering about 2,500 buildings in and around the downtown core of the city. A sample survey sheet used in Victoria for this purpose is presented in Appendix E, Table E.2. Damage estimation was carried out using the GIS software, Maplnfo (Maplnfo Co., 1997). The geographical unit selected for the damage estimation was "block". It is suitable in size for the scale of the study and convenient for the GIS database, since the planning departments number the blocks and it is possible to use them as a reference for each building in the database. Discrete classification attributes (e.g. material type and prototype) for buildings within a block were counted to yield the attribute with most number of occurrences in each block. The prevalent material types and building prototypes in the City of Victoria are presented on a block-by-block basis in Figures 9.3 and 9.4, respectively. 71 Figure 9.3. Prevalent material type by block Wood is the most common material in Victoria. About 65% of the buildings surveyed in Victoria are wood and it is the prevalent material in about 51% of the blocks studied. Since the study area covers downtown Victoria where most of the historical buildings are located, the number of masonry buildings is also quite high. About 28% of the buildings are masonry, and it is the prevalent material type in about 42% of the blocks. Concrete 72 buildings constitute about 7% of the buildings in the study area. There are a few steel buildings in the study area but steel is not the prevalent material type in any of the blocks. Figure 9.4. Prevalent prototype by block The most common prototype is WLFR, which constitutes about 45% of all the buildings in the study area and about 67% of the wood buildings. The second most common 73 building prototype is U R M L R . About 20% of all buildings and 57% of the masonry buildings in the study area are of this prototype. Among the concrete buildings, C F M R is the most common prototype, which makes up about 3% of all buildings and 41%> of concrete buildings in the study area. Damage estimation was carried out using the MMI-based damage matrices, which describe, for each building prototype, the probability of being in a certain damage state for a particular M M I level. Total damage levels as a percentage of replacement cost (mean damage factors, MDFs) for different M M I levels are given in Table 5.5 for each building prototype. The mean MDF for each block was calculated by averaging (either straight average or weighted by a parameter such as "footprint area") the MDFs of the buildings within that block. The estimated structural damage distributions on a block-by-block basis are presented in Figures 9.5 and 9.6, with straight average and weighted average (weighted by "footprint area"), respectively. The majority of the buildings in downtown Victoria have MDFs between 10%> and 30%, which constitutes about 35%> of all the blocks in the study area. The surrounding neighbourhoods however have lower MDFs, in the range of 5% to 10%. The averaging scheme weighted by floor area made a difference in a few blocks only, where there were large differences in floor areas of buildings within the same block. 74 Figure 9.5. Structural damage distribution (average MDF) 75 Figure 9.6. Structural damage distribution (average M D F weighted by floor area) Non-structural damage distribution was calculated in a similar manner using the MDFs presented in Tables 6.3, 6.4 and 6.5, respectively for displacement-sensitive components, acceleration-sensitive components and building contents. The resulting non-structural damage distribution maps are presented in Figures 9.7, 9.8 and 9.9 for displacement-76 sensitive components, acceleration-sensitive components and building contents, respectively. Figure 9.7. Non-structural damage distribution (displacement-sensitive components) About half the blocks are expected to have MDFs in the 20%-30% range and the other half in the 15%-20% range for displacement-sensitive components. Figure 9.8. Non-structural damage distribution (acceleration-sensitive components) About half the blocks are estimated to have MDFs between 5% and 10%, and the rest between 0% and 5% for acceleration-sensitive components. 78 Figure 9.9. Non-structural damage distribution (building contents) Damage to building components remains below 5% in all the blocks. In Victoria, the effect of geology was considered important because half the city rests on softer material than the "firm soil" assumed in the hazard calculations. Therefore, the effects of possible soil amplification were investigated. The geological units that appear in the study area (Monahan et al., 2000) are described below and presented in Figure 9.10. R2: Thin soil cover over bedrock with scattered outcrops; generally < 5 m of Victoria clay over < 10 m of older Pleistocene (corresponds to NEHRP site classes B or C). C2: > 3 m of the grey clay facies of the Victoria clay, under the brown clay facies and over thin (< 10 m) older Pleistocene deposits (corresponds to NEHRP site classes D or E). C l : Areas where units R2 and C2 cannot be differentiated with data available; also includes areas with > 5 m of the Victoria clay but < 3 m of the grey clay facies (corresponds to NEHRP site classes C, D or E). F: Anthropogenic fill with variable amplification (corresponds to NEHRP site classes C, D or E). O l : Holocene peat over the grey clay facies of the Victoria clay (corresponds to NEHRP site classes E or F). The amplification depends on the geological unit, level of ground shaking and the period of ground motion. In Victoria, relatively strong level of shaking (PGA of 0.3 lg) is expected for the probability level of 10% in 50 years. For this level of shaking, short-period ground motions are not amplified considerably, however long-period ground motions are amplified roughly by 1.5 for C l and F, 2.0 for C2 and 2.5 for O l (Monahan et al., 2000). The geological unit R2 is not expected to amplify the ground motion. 80 Figure 9.10. Geological units in Victoria The PGA expected in Victoria was multiplied with the amplification factors corresponding to each geological unit and the resulting PGA values were converted into M M I to interrogate the damage probability matrices. The resulting damage distribution map calculated using these M M I levels is presented in Figure 9.11. Figure 9.11. Structural damage in Victoria with site amplification Monetary losses resulting from the estimated structural and non-structural damage were calculated for Victoria for M M I VIEt (no site amplification at short periods) and summed over each block to display total loss in each block (Figure 9.12). 82 Figure 9.12. Total monetary losses in Victoria (no site amplification) Monetary losses corresponding to amplified long period ground motions are calculated and displayed in Figure 9.13. 83 Figure 9.13. Total monetary losses in Victoria (with site amplification) 84 10. CASE STUDY: VANCOUVER In this chapter, damage and loss estimations carried out for the City of Vancouver are described. They involved compilation of a comprehensive building database, estimation of structural and non-structural damage, and assessment of the monetary losses resulting from the estimated damage. The City of Vancouver is located on the western end of the Greater Vancouver Regional District (GVRD), which is a partnership of the 21 municipalities and one electoral area that make up the metropolitan area of Greater Vancouver (Figure 10.1). The City of Vancouver was incorporated in 1886. It is currently the largest city in British Columbia with a population of over 550,000 people as of 1999. It rests on roughly 113 square kilometres of land. The building inventory within the city boundaries consists of over 95,000 structures, out of which, about 20,000 buildings were included in this study (Figure 10.2). A probabilistic seismic hazard analysis for Vancouver (49.2° N , 123.2° W) yielded a PGA level of 0.23g (Table 3.2) for firm ground, which corresponds to M M I VIII. An alternative hazard analysis performed directly in terms of M M I also yielded an M M I value of VIII. The probability level considered for the hazard calculations is 10% chance of exceedance in 50 years, which is equivalent to a return period of 475 years. 85 Figure 10.1. City of Vancouver in G V R D Figure 10.2. Study Area in City of Vancouver 86 The next step in damage estimation is inventory collection, which comprises of identifying existing sources of data, supplementing them with field surveys when necessary, and integrating them into a uniform database. For this study, the Planning Department of the City of Vancouver provided part of their building database, which merely included location (street address) information. The scarcity of data made inference schemes inapplicable. Therefore, sidewalk surveys were conducted to collect data on structural properties of the buildings. The survey forms used in the sidewalk surveys are presented in Appendix E, Tables E . l and E.2. For about 10,000 buildings that were surveyed, the survey form shown in Table E. 1 was used and photographs of the buildings were attached to the forms. For the rest of buildings surveyed, the survey form shown in Table E.2 was used without the photographs. Damage estimation was carried out using the GIS software, Maplnfo (Maplnfo Co., 1997). The geographical unit selected for the damage estimation was "block", which is typically rectangular and is bounded by streets on four sides. It is suitable in size for the scale of the study and convenient for the GIS database. Discrete classification attributes (e.g. material type and prototype) for buildings within a block were counted to yield the attribute with most number of occurrences in each block. The prevalent material type and building prototype in the City of Vancouver are presented on a block-by-block basis in Figures 10.3 and 10.4, respectively. 87 Prevalent Material Figure 10.3. Prevalent building material type by block 88 Figure 10.4. Prevalent building prototype by block In Vancouver, out of the 20,000 buildings surveyed, about 15,000 (75%) are wood buildings (WLFR, WLFLR, WLFCI or WPB) and out of the 15,000 wood buildings, about 11,500 (77%) are single family wood houses (WLFR), making it the most prevalent building prototype in the city. Large areas of residential neighbourhoods outside the core downtown area are mainly comprised of WLFR buildings. There are about 1660 U R M L R buildings in the study area, which approximately corresponds to 88% of the unreinforced masonry buildings and 8% of all the buildings surveyed in Vancouver. Majority of the high-rise buildings in Vancouver have concrete frames to carry the vertical static loads and concrete core walls to carry the lateral seismic loads (CFHR). They make up less than 3% of the total building inventory in the study area, 89 however, out of 600 high-rise buildings, about 565 (94%) are CFHR. They are mainly concentrated in downtown core as commercial office towers and residential high-rises, but also appear as residential high-rises in other parts of the city. Damage estimation was carried out using the MMI-based damage matrices, which describe, for each building prototype, the probability of being in a certain damage state for a particular M M I level. Total damage levels as a percentage of replacement cost (mean damage factors, MDFs) for different M M I levels are given in Table 5.5 for each building prototype. The mean MDF for each block was calculated by averaging the MDFs of the buildings within that block (either straight average or weighted by a parameter such as "footprint area" or "total area = [footprint area] x [the number of stories]"). The estimated structural damage distributions on a block-by-block basis are presented in Figures 10.5, 10.6 and 10.7, with straight average, weighted average by "footprint area", and weighted average by "total area", respectively. 90 MMI Vlll Figure 10.5. Structural damage distribution (average MDF) 91 MMI VIII Weighted Avg MDF (%) by Block • X to 100 | 20to 30 ISto 20 10to 15 5to 10 Oto 5 no data 92 MMI VIII-Average MDF (%) Figure 10.7. Structural damage distribution (average M D F weighted by total area) About 68% of the blocks in Vancouver study area have average MDFs between 5% and 10%. Considerable number of blocks have higher MDFs, between 10% and 20%. Only 4% have MDFs higher than 20%. The high damage concentrations are at the east side of downtown, which has a high number of unreinforced masonry buildings. Non-structural damage distribution was calculated in a similar manner using the MDFs presented in Tables 6.3, 6.4 and 6.5, respectively for displacement-sensitive components, acceleration-sensitive components and building contents. The resulting non-structural damage distribution maps are presented in Figures 10.8,10.9 and 10.10 for displacement-93 sensitive components, acceleration-sensitive components and building contents, respectively. M M I V l l l Figure 10.8. Non-structural damage distribution (displacement-sensitive components) In Vancouver, about half the blocks are expected to have MDFs in the 20%-30% range and the other half in the 15%-20% range for displacement-sensitive components. For acceleration-sensitive components, about half the blocks are estimated to have MDFs between 5% and 10%, and the other half between 0% and 5%. Damage to building components stays below 5% in all the blocks in the study area. 94 MMI VIII Figure 10.9. Non-structural damage distribution (acceleration-sensitive components) 95 MMI Vlll Figure 10.10. Non-structural damage distribution (building contents) Most of the City of Vancouver rests on till, which does not expect to amplify the ground motions. Of particular interest is the False Creek area, which sits on landfill. About 20 blocks out of 1420 that were included in this study are on this filled land (Figure 10.11). Landfill has the potential of amplifying the ground motion, however due to the low number of buildings resting on this type of soil and limitations in time, the amplification potential of this area was not studied in detail. The description of the geological units that appear in Figure 10.11 are given below (Armstrong, 1984): 96 VC: Glacial drift including: lodgment and minor flow till, lenses and interbeds of substrafied glaciofluvial sand to gravel, and lenses and interbeds of glaciolacustrine laminated stony silt; up to 25 m thick. PVa: Quadra fluvial channel fill and floodplain deposits, crossbedded sand containing minor silt and gravel lenses and interbeds. T: Tertiary bedrock including sandstone, siltstone, shale, conglomerate, and minor volcanic rocks. C: Raised marine, deltaic and fluvial deposits. SAa: Landfill including sand, gravel, till, crushed stone and refuse. SAe: Upland peat up to 8 m or more thick overlying VC units. Figure 10.11. Geological units in Vancouver 97 The economic losses were also estimated for the study area in City of Vancouver. The procedures used to calculate losses as well as the building costs used in this analysis are described in Chapter 7. Direct monetary losses resulting from structural and non-structural damage were calculated for each building in a block and then summed over the block to display the distribution of losses in the city (Figure 10.12). MMI VIII Figure 10.12. Distribution of total monetary losses by block 98 1 1 . ASSESSMENT OF THE STRUCTURAL DAMAGE: SD-BASED Damage estimation methodologies are discussed in two parts, MMI-based damage probability matrices and SD-based fragility curves. Damage probability matrices are described in Chapter 5, and the estimates of the damage distribution using this method are presented in Chapters 8, 9 and 10 for the Cities of New Westminster, Victoria and Vancouver, respectively. In this chapter, the SD-based methodology is presented and applied to three sample BC prototypes (URMLR, WLFR and CFHR). Until recently, the most widely used damage estimation method was the MMI-based damage probability matrices. An alternative methodology was proposed as a result of a cooperative effort by the U.S. Federal Emergency Management Agency (FEMA) and National Institute of Building Science (NIBS). It was implemented in the earthquake loss estimation software HAZUS and documented in its technical manuals (FEMA/NIBS, 1997). This methodology relates expected damage to engineering parameters (spectral acceleration and displacement) instead of M M I . It involves construction of capacity curves, demand spectra and fragility curves. The spectral displacement level that the building will experience is determined by intersecting the capacity curve by the demand spectrum. Five damage states are defined (none, slight, moderate, extensive and complete) and they are described separately for each building class. Fragility curves describe the probability of being in or exceeding each damage state at the spectral displacement level determined from the previous step. 99 Capacity curve estimates the response of a specific class of buildings for a given level of spectral demand. It is defined by two key points: the yield capacity point and the ultimate capacity point. The curve is assumed to remain linear up to the yield point. The slope of this portion of the curve represents the stiffness of the building in the elastic range. The stiffness is estimated from the expected fundamental vibration period of the building, which is calculated using formulas provided in building codes. From the yield point to the ultimate point, the curve has a variable slope, starting with the slope of the elastic state to the fully plastic state. Past the ultimate point, the building is assumed to remain fully plastic. An example capacity curve is presented in Figure 11.1. Spectral Displacement Figure 11.1. Example building capacity curve The inelastic demand spectrum is constructed by reducing the 5%-damped site response spectrum for effective damping when effective damping exceeds 5% level. This is achieved by dividing the elastic response spectrum by two different damping reduction factors for constant-acceleration and constant-velocity regions of the spectrum. Both ioo reduction factors are functions of the effective damping of the building. A n example inelastic demand spectrum is given in Figure 11.2. Spectra l Displacement Figure 11.2. Example demand spectrum Fragility curves were developed for each building class using a lognormal probability distribution (FEMA/NIBS, 1997). They describe the probability of being in or exceeding a specific damage state as a function of spectral displacement (Figure 11.3). The value of the spectral displacement at the intersection of the capacity curve and demand spectrum is used to interrogate the fragility curves for damage probabilities. 101 Spectral Displacement Figure 11.3. Example fragility curves for different damage states In the following sections this methodology is demonstrated on three sample BC building prototypes, U R M L R (Unreinforced Masonry Bearing Wall Low Rise), W L F R (Wood Light Frame Residential), and CFHR (Concrete Frame with Concrete Walls High Rise). The demand spectrum is calculated for Vancouver and Victoria using the uniform hazard spectra obtained from hazard analyses as described in Chapter 3. The fragility curves are adopted from those developed for the U.S. building prototypes (FEMA/NIBS, 1997) due to lack of observed damage data in BC. The capacity curve parameters for U.S. prototypes are presented, and then parameters based on Canadian building code and practice are proposed. The damage probabilities for these three prototypes of buildings are calculated using the proposed B C capacity curves. The results are then compared to those obtained from the MMI-based damage matrices. 102 11.1. CAPACITY CURVES Capacity curves estimate peak displacement response of buildings for a given level of spectral demand. These curves are analogous to pushover curves of individual buildings and are based on engineering parameters, yield and ultimate strength, of the structural system that characterizes the nonlinear behaviour of different building prototypes (Kircher et al., 1997). Until yield, the building capacity curve is assumed to stay linear with stiffness based on an estimate of the expected elastic period of the building. From yield to the ultimate point, the capacity curve changes in slope from an essentially elastic state to a fully plastic state. The capacity curve is assumed to remain plastic past the ultimate point. The yield point is defined by A y and D y : A y = - ^ L (Eq. 11.1) a i where C s is the design strength approximately corresponding to the lateral-force design requirements of current seismic codes, y is the ratio of yield to design strength (overstrength ratio - yield) and a i is the fraction of building weight effective in the pushover mode. D y =9.8A y T e 2 (Eq. 11.2) where T e is the expected "elastic" fundamental-mode period of the building. 103 The ultimate point is defined by A u and D u : A u =x-A y (Eq. 11.3) where X is the ratio of ultimate to yield strength (overstrength ratio - ultimate). D u=^-D y (Eq. 11.4) where \x is the ductility ratio. The values of these parameters for the U.S. building prototypes corresponding to the three sample BC prototypes under study are given in Table 11.1. Table 11.1. Building capacity curve control points (U.S. prototypes) Building Type D y (inches) Ay(g) D u (inches) Au(g) URML (URMLR) 0.24 0.200 2.40 0.400 Wl (WLFR) 0.24 0.200 4.32 0.600 C 2 H (CFHR) 1.47 0.127 11.02 0.317 The construction practices for unreinforced masonry in the U.S. and Canada were considered similar enough to permit the use of the parameters developed for U.S. low-rise U R M buildings to be used for Canadian ones (URMLR) without any modification. However, single family wood houses have slight differences and concrete wall buildings have even more pronounced differences between the U.S. and Canadian construction practice. Capacity curve parameters based on Canadian code and practice were determined for W L F R and CFHR prototypes. 104 Effective periods (Te) and design strengths (C s) were calculated using the National Building Code of Canada, N B C C (NRC, 1995). Overstrength ratios (y and X) and ductility ratios (u.) were determined by modifying the FEMA/NIBS overstrength factors to reflect the differences in building practice between the U.S. and B C , Canada. In N B C C (NRC, 1995) the minimum lateral seismic force, Vis calculated by the formula: V.*-S-FR'-W -V (Eq.H.5) where U is a factor representing level of protection based on experience (takes a value of 0.6); v is the zonal velocity ratio, which is equal to the specified zonal horizontal ground velocity expressed as a ratio to 1 m/s; S is the seismic response factor for unit value of zonal velocity ratio; F is the foundation factor, I is the seismic importance factor of the structure, R is the force modification factor that reflects the capability of a structure to dissipate energy through inelastic behaviour, and W represents the weight of the building. Capacity Curve Parameters for WLFR The effective period of a wood frame house varies considerably depending on whether or not it was engineered. Both engineered wood frame houses with plywood or OSB shear wall panels and non-engineered ones with horizontal boards are considered in this thesis. In addition to the N B C C period formula, experimental studies on wood frame houses or sub-systems are examined to obtain the elastic fundamental period to be used for WLFR prototype. 105 According to the N B C C (NRC, 1995), the fundamental period of buildings that have a lateral force resisting system other than concrete or steel moment resisting frame is determined by the formula: where hn and Ds are in metres; h„ is the height of the building and Ds is the length of the wall that constitutes the main lateral-force-resisting system in the direction parallel to the applied forces. A typical two-storey WLFR building with a height of 6 m and a wall length of 5 m has a fundamental period of 0.241 seconds based on the N B C C formula. Results from dynamic tests on full-scale wood structures or on subsystems were also reviewed to estimate the effective period. Dolan (1989) conducted full-scale shake table tests on 2.4 x 2.4 m model walls and measured the fundamental period of these walls. A seismic mass of 5.4 N-s2/mm was attached at the top of the frame to simulate the contribution of the top two stories to the tributary area of the wall. Free-vibration impact tests were conducted on plywood sheathed walls prior to earthquake tests in order to determine the initial fundamental periods of the wall specimens when coupled with the mass attached. The periods measured were consistently around 0.29 seconds. The same walls were modeled by Filiatrault (1990) and a linear free-vibration analysis was performed on the models to yield fundamental periods around 0.31 seconds. In order to compare these periods to h r = 0.09- (Eq. 11.6) 106 those obtained by the N B C C formula for a building with a 5 m wall length, the stiffness of these 2.4 x 2.4 m specimen should be multiplied by approximately 2. This increase in the following relationship between stiffness and fundamental period (assuming the first mode dominates the response): By this argument, the period reduces from 0.29 seconds to 0.21 seconds. Tarabia and Itani (1997) modeled single-storey light-frame wood buildings and calibrated their model with two experiments (Dolan, 1989; Kamiya, 1988). To evaluate the seismic response of light-frame wood buildings with different configurations, they used two earthquake time-history records. The results from the dynamic analyses of a single storey building with two 2.4 x 2.4 exterior walls indicated a fundamental period of 0.21 seconds. Note that this period is obtained for a single storey building, and for a two-storey structure, it would be higher. In a paper emphasizing the importance of ductile connections, Buchanan and Dean (1988) propose a relatively simple design methodology. This method suggests the expected stiffness to be calculated by multiplying the theoretical stiffness by a factor of 0.5 or less to reduce the stiffness for the effects of connection flexibility. Applying this concept to the calculation of the fundamental period, expected fundamental period can be obtained as follows: the stiffness causes a decrease in the fundamental period by a factor of because of (Eq.11.7) 107 I f Tlha)nlical=2-n-jr^ and Texpecleii=2-n-jZ^T ; then Texvecled=lA\4-Tlheorelical Using this factor of 1.414 to calibrate the fundamental period calculated by the N B C C formula (0.24 seconds) yields Texpected= 0.34 seconds. A comprehensive study reported by Stewart et al. (1988) investigates damping as well as the fundamental period of plywood sheathed shear walls both in elastic and inelastic range. They conducted shake table tests and subjected the test specimens to a series of sinusoidal input motions. The recorded fundamental periods increased from 0.35 seconds during elastic behaviour up to 0.9 seconds during nonlinear behaviour. The damping ratio started in the range of 10% (elastic) and increased to as high as 40% (non-linear) including hysteretic damping. It is also noted that the wall damping observed during elastic response appears to reduce with wall age. Dynamic testing of different configurations of wood frame buildings was recently undertaken by the Earthquake Research Laboratory of the University of British Columbia (UBC). The testing program included a full-scale two-storey engineered wood house with OSB panels. Preliminary unpublished results indicate a fundamental period of 0.29 seconds for this type of construction. The fundamental period values from the discussion above are presented in Table 11.2. These values are based on wood structures with shear wall panels designed by engineers. 108 Table 11.2. Fundamental period for engineered WLFR buildings Method Code (NBCC) Dolan (1989) Filiatrault (1990) UBC (2000) unpublished Stewart et al. (1988) Period (sec) 0.24 -0.21 -0.22 0.29 0.35 The behaviour of non-engineered wood frame houses with horizontal boards has not been studied as extensively as the timber shear wall buildings. The recent testing program at U B C included B C type buildings with horizontal board sheathing as external walls, for which the elastic fundamental period was determined to be between 0.30 seconds and 0.55 seconds, depending on detailing. These tests were performed on a single storey subsystem, however the second storey was simulated by an equivalent mass at the top of the subsystem. These tests are currently ongoing and the results have not been published yet. Considering that a considerable portion of the WLFR buildings in BC are not engineered, an elastic fundamental period of 0.40 seconds was selected to represent these buildings in southwestern BC. The design strength coefficient, C s , approximately represents the lateral force design requirements of the seismic codes (Kircher et al., 1997), and is defined as a fraction of the building weight, V - C s • W, C S = V ' S R F ' 1 -U (Eq. 11.8) 109 Zonal velocity ratios (v) for major Canadian cities are given in Appendix C of the N B C C (NRC, 1995). For Vancouver, it is given as: v., = 0.20 Vancouver For 0.25 < T < 0.50 seconds, and when Z a = Z v , which are acceleration-related and velocity-related seismic zones, respectively (Z a = Z v = 4 for Vancouver), N B C C gives the following expression to calculate the seismic response factor, S: S =3.0 - 3 . 6 (T - 0 .25 ) which yields: 5 = 2.46 The seismic importance factor of the structure, /, is equal to 1.0 for all structures that are not post-disaster buildings or schools. Since WLFR buildings are single family houses, the importance factor is 1.0. 7 = 1.0 The values of R for different lateral force resisting systems are given in Table 4.1.9. L B of the N B C C (NRC, 1995). N B C C assigns an R value of 3.0 for timber structures with "nailed shear panel with plywood, waferboard or OSB", and 1.5 for wood buildings that "do not have shear panels, concentrically braced timber frames or moment resisting wood frames with ductile connections". For non-engineered structures, an R value of 1.5 was selected. R = l.5 n o The foundation factor, F is listed in Table 4.1.9. l .C of the N B C C (NRC, 1995), based on the description of the ground conditions. Til l up to 25 m thick is the dominant surface and near-surface material over much of the Vancouver upland, where it is overlain by patchy marine silt and sand. It is a heterogeneous glacial deposit consisting of clay, silt, sand and stones ranging from pebble to boulder size. Til l commonly has a high bearing capacity and thus is an excellent foundation material (Turner et al., 1998). Based on this information, a foundation factor of 1.0 is selected for Vancouver, which is described in N B C C as to include rock, dense and very dense coarse-grained soils, very stiff and hard fine-grained soils, compact coarse-grained soils and firm and stiff fine-grained soils from 0 to 15 m deep. F = 1.0 Substituting the above parameters in Equation 11.8, the design strength coefficient, C s can be calculated. However, since these buildings do not comply with the current codes, C s calculated by this equation is halved. C =0.08 s The overstrength ratio - ultimate (A,) was reduced from a value of 3.00 that was suggested for wood frame houses by FEMA/NIBS (1997) to a value of 2.00 for their BC counterparts. The reason for this reduction is based on the fact that many BC wood frame buildings do not have timber shear walls, which reduces the expected performance i l l of these buildings after yield. The values of the rest of the parameters (p., y, and cti) are adopted from the FEMA/NIBS (1997) study. A l l the capacity curve parameters selected for the WLFR prototype are summarized in Table 11.3 together with those for the CFHR prototype, which is discussed in detail in the following section. Capacity Curve Parameters for CFHR A major difference between the construction practices of concrete shear walls in Canada and in the U.S. is the use of coupled shear walls without moment resisting frames in Canada versus isolated cantilever shear walls in the U.S. Coupled shear walls are formed usually by two walls interconnected or coupled to each other by beams. The connecting beams are substantially weaker than the walls and when suitably detailed, they sustain large rotations that make them yield, dissipating energy over the entire height of the structure. A 15 storey high building is selected to be representative of the CFHR prototype and a wall length of 8 m is considered. Substituting these values into Equation 11.6, the fundamental period can be calculated as 1.432 seconds. In addition to the N B C C formula for estimation of the fundamental period, other expressions have also been explored for concrete shear wall systems (Syngellakis and Papoulia, 1987; Syngellakis and Chan, 1992; Chaallal et a l , 1996; Wallace and Moehle, 112 1992; L i and Choo, 1995; Cheung et al., 1977; Mukherjee and Coull, 1973; Rutenberg, 1975; Goel and Chopra, 1998). Among these, the expression proposed by Chaallal et al. (1996) is based on a statistical regression correlation between fundamental periods of coupled shear walls and their elastic and geometric properties: s0.19 rr, Chaallal ~ T =3-n-V Hb J s0.76 J w (Eq. 11.9) g-Ec-t where HH is the coupling beam height, Lb is the coupling beam length, hw is the coupled shear wall height, Dw is the wall length, n is the number of stories, W is the average storey seismic weight, Ec is the concrete modulus of elasticity and t is the wall thickness. The 15-storey building whose period was calculated using N B C C formula is considered again. A mean storey height of 3 m is selected, in which case the building height, and the wall height are 45 m. The floor weight was assumed 7500 kN approximately. The length of the walls is 8 m and the thickness is 0.4 m. The modulus of elasticity of concrete is obtained by the formula: £c=4500--//f (Eq. 11.10) which yields Ec = 2.5-104 MPa or Ec =2.5-107kN/m2 for normal density concrete with fc = 30 MPa (CPCA, 1995). The additional parameters are selected as: Hh = 0.6 m and Lb = 2 m. Substituting these values, the period can be obtained as T- 1.838 seconds. Based on this period value (1.838 sec) and the code value (1.432 sec) an elastic period of 1.65 seconds was selected for CFHR buildings in southwestern BC. This is higher than the period used for 12-storey U.S. buildings with concrete shear walls in the FEMA/NIBS (1997) calculations, however the number of stories in each prototype is different. When the fundamental period is greater than 0.5 seconds, the seismic response factor, S is determined by the formula: (Eq. 11.11) which, for the fundamental period of 1.65 seconds, results in: 5 = 1.17 The values of R for different lateral force resisting systems are given in Table 4.1.9.1.B of the N B C C (NRC, 1995). The two alternatives tabulated in N B C C for coupled wall systems are "wall with nominal ductility" with an R of 2.0 and "ductile couple wall" with an R of 4.0. An R value between these two cases was selected to represent in average the ductility of CFHR buildings in Vancouver: R = 3.0 Then using U = 0.6 and v = 0.20 for Vancouver, the design strength coefficient, C s , can be calculated as: C =0.05 s 114 In terms of ductility, the coupled shear walls are reported to behave better than isolated cantilever shear walls i f they are designed properly (Paulay and Santhakumar, 1976; Pekau and Gocevski, 1978; Abrams, 1991; Mutrie et al., 2000). Coupled shear walls are very efficient structural systems, particularly suited for ductile response with very good energy dissipation characteristics if openings are arranged in a regular pattern. When suitably detailed, connecting beams can dissipate energy over the entire height of the structure (Paulay, 1986). The collapse mechanism of a coupled wall consists of two plastic hinges in the coupling beams and when those are exhausted, one plastic hinge at the bottom of each wall. Hence, in coupled walls, several lines of defense may be mobilized when extreme displacements are imposed upon a building, as opposed to a single cantilever wall, which has only one plastic hinge location in the collapse mechanism (Paulay, 1975). Therefore, larger ductility and higher overstrength factor (ratio of ultimate strength to yield strength) is assumed for coupled shear wall systems compared to cantilever shear wall systems. The proposed value of ductility is 3.1 and overstrength factor (ultimate) is 3.0 for the "Canadian type" high-rise concrete buildings with walls (CFHR). The same parameters for the "U.S. type" shear wall structures are 3.0 and 2.5, respectively (FEMA/NIBS, 1997). The proposed ductility level is not much different from its U.S. counterpart, because the ductility of the coupled shear walls is highly sensitive to detailing of the coupling beams and the walls. Therefore, in the absence of extensive information on the detailing of about 600 CFHR buildings surveyed, it was preferred to stay on the conservative side. The force reduction factor in N B C C aims to reflect the capability of a structure to dissipate energy through inelastic behaviour. Therefore, the selection of the force reduction factor and the ductility are closely related to each other. The relations between these two parameters are explored in detail by Miranda and Bertero (1994) and by Rainer (1987) in relation to N B C C . The relationship suggested by Miranda and Bertero (1994) describes the strength reduction factor, R ^ , in terms of ductility (u), period (T) and soil conditions at the site: where O is defined separately for rock, alluvium and soft soil sites. For rock sites, which is the case assumed for Vancouver: For the ductility level (u. = 3.1) and period (T = 1.65 sec) selected for CFHR in Vancouver: 0CFHR = 0 ? 9 A N D R = 3 6 6 rack ^ which confirms that the selection of an R value between 2.0 and 4.0 is consistent with the level of ductility assumed in the system. A summary of all the building parameters proposed for the selected three building prototypes is given in Table 11.3. R =1 + u -1 cD (Eq. 11.12) (Eq. 11.13) 116 Table 11.3. Building capacity parameters Building Prototype Te(sec) cs a. y URMLR 0.35 0.067 0.50 1.5 2.0 5.0 WLFR 0.40 0.08 0.75 1.5 2.0 6.0 CFHR 1.65 0.047 0.65 1.1 3.0 3.1 The capacity curve coordinates for the yield point (D y , A y ) and the ultimate point (D u , A u ) calculated using these relationships (Equations 11.1 through 11.4) and parameters are presented in Table 11.4. The corresponding capacity curves for each of the three prototypes are plotted in Figures 11.4 through 11.6. Capacity curve (URMLR) Spectral Displacement (inches) Figure 11.4. Capacity Curve for U R M L R 117 Capacity curve (WLFR) cn c o o 0.4 0.3 o 0.2 o o < u Q. Ui 0.1 0.0 /i Jmmate Point (Du, A u ) -(3.01, 0.32) V i olrl D • II -> A \ (0.25, 0.16) 0.0 0.6 1.2 1.8 2.4 3.0 Spectral Displacement (inches) 3.6 Figure 11.5. Capacity Curve for WLFR 0.3 ., 3 c o o.: *J ra 0) 0) u u < S o u V a. CO 0.0 0.0 Capacity curve (CFHR) Ultimate Point (Du, A H9.65. 0.23m j) I Yield Point (Dy, A,) (2.11, 0.079) j I y 5.0 10.0 15.0 20.0 Spectral Displacement (inches) 25.0 Figure 11.6. Capacity Curve for CFHR 118 Table 11.4. Building capacity curve control points (BC prototypes) Building Type D y (inches) Ay(g) D u (inches) A u (g) U R M L R 0.24 0.201 2.41 0.402 W L F R 0.25 0.160 3.01 0.320 C F H R 2.11 0.079 19.65 0.238 These values can be compared to those in Table 11.1, which shows the same parameters for the U.S. prototypes. Ultimate displacement for BC wood homes is lower than that of U.S. ones. On the other hand, BC concrete high-rises with shear walls are able to sustain higher ultimate displacements than their U.S. counterparts. 11.2. D E M A N D S P E C T R U M The standard shape of the input spectrum consists of a region of constant spectral acceleration (SA) at short periods and a region of constant spectral velocity at long periods. Short-period SA is defined by the value of SA at a period of 0.3 seconds. The constant spectral velocity region has SA proportional to 1/T and is anchored to the value of SA at 1 second period (Kircher et al., 1997) The uniform hazard spectrum for Vancouver was calculated using the seismic hazard assessment software EZ-FRISK (Risk Engineering, Inc., 1997). The attenuation relationship developed by Boore et al. (1993) was used for shallow source zones and the relationship by Youngs et al. (1997) was used for deep zones. Spectral acceleration values were calculated for periods of 0.1, 0.2, 0.4, 0.5, 0.75,1 and 2 seconds (Chapter 3). 119 The input spectrum calculated by EZ-FRISK was modified to obtain a standard-shape response spectrum. The SA at 0.3-second period was determined from the input spectrum as 0.45g and the short period section of the spectrum was fixed at this value of SA. The SA at 1-second was 0.16g as obtained from the input spectrum. The long period section of the spectrum was anchored to this point and was constructed as proportional to 1/T. This standard-shape input spectrum is plotted versus SD in Figure 11.7. The x-axis was changed from period (T) to SD making use of the following relationship between SA and SD: (Eq. 11.14) The x-axis was also changed from logarithmic to linear. Vancouver Input Spectrum 0.6 f « 0.2 ~ 0.3 sec —e— E Z - F R I S K Standard Shape / \ ^ . 1 sec - 1 1 I 1 1 1 1 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Spectral Displacement (inches) Figure 11.7. Construction of standard-shaped input spectrum 120 The input spectrum was then modified to reflect the effect of damping when the damping is higher than 5 % . This was achieved by using spectrum reduction factors, which are functions of effective damping, peff, of the building. Effective damping is defined as the total energy dissipated by the building during peak earthquake response and is the sum of an elastic damping term (P E ) and a hysteretic damping term (P H ) associated with post-yield, inelastic response: P ^ P E + P H (Eq. 1 1 . 1 5 ) The elastic damping term (pE) is assumed to be amplitude independent and is derived from the recommendations of Newmark and Hall ( 1 9 8 2 ) for materials at or just below their yield points. The hysteretic damping term (pH) is dependent on the amplitude of the post-yield response. It is based on the area enclosed by the hysteresis loop, as defined by a symmetrical push-pull of the building capacity curve up to peak positive and negative displacements, ±D and accelerations, ±A. Area ( B H = K (Eq. 1 1 . 1 6 ) , 2 - T t - D - A , where Area is the area enclosed by the hysteresis loop, D is the peak displacement response, A is the peak acceleration response at D, and K is a degradation factor that defines the fraction of the Area used to determine hysteretic damping. For a value of K = 1.0, Equation 1 1 . 1 6 yields the definition of equivalent viscous damping. The K factor 121 reduces the amount of hysteretic damping depending on the building prototype and seismic design level. The expected values of elastic damping (PE) and degradation factors (K) for three sample prototypes are given in Table 11.5. Seismic design level was assumed low for U R M L R and W L F R , and moderate for C F H R buildings. A moderate duration of earthquake exposure was considered. The hysteretic (PH) and effective damping (J3eff) values calculated (Equations 11.15 and 11.16) for each of the prototypes based on these parameters are also presented in Table 11.5. The spectrum reduction factors for the constant acceleration (RA) and constant velocity (Rv) parts of the spectra are functions of the effective damping (Newmark and Hal l , 1982): R * ° 3 . 2 , - 0 ^ ^ , ) < ^ 1 1 - 1 7 ) R " ° 2 , l - , ' 4 | 5 | n ( , , „ ) ^ » - 1 8 > These factors were calculated for the three sample building prototypes, U R M L R , W L F R and C F H R as presented in Table 11.5. Table 11.5. Damping parameters and spectrum reduction factors Building Type PE K PH Peff RA Rv URMLR 10% 0.3 6% 16% 1.600 1.406 WLFR 15% 0.4 8% 23% 1.967 1.611 CFHR 7% 0.4 9% 16% 1.600 1.406 122 The demand spectrum was constructed dividing the input spectrum by R A at the constant acceleration region and by Rv at the constant velocity region. The resulting demand spectra for each prototype were intersected with the capacity curve of the corresponding prototype to determine the spectral displacement level at the intersection. These curves and the intersection points are displayed in Figures 1 1 . 8 , 11.9 and 1 1 . 1 0 for the prototypes, U R M L R , W L F R and CFHR, respectively. The resulting spectral displacement levels for the three building prototypes are presented in Table 1 1 . 7 . Capacity Curve & Demand Spectrum (URMLR) 0.5 , 3 0.4 c o 2 0.3 1 S h X S, s. s -1 0.0 D = 0 .50 in 1.0 1.5 2 Spectral Displacement (inches) D e m a n d S p e c t r u m (16%) — I n p u t S p e c t r u m C a p a c i t y C u r v e Figure 1 1 . 8 . Intersection of demand spectrum and capacity curve (URMLR) 123 06 Capacity curve & Demand Spectrum (WLFR) O) c o ra u 8 0.3 u < ra o u CL CO 1 0.0 - T 0.0 0.3 D = D.50 in 0.9 1.2 1.5 1.8 2.1 Spectral Displacement (inches) _ B — D e m a n d S p e c t r u m (23%) Input S p e c t r u m - C a p a c i t y C u r v e Figure 11.9. Intersection of demand spectrum and capacity curve (WLFR) Capacity curve (CFHR) 0.5 . _ 0.4 c o ra 0.3 i_ CD d> O < 0.2 ro u .P- 0.1 CO 1 0.0 . 4 0.0 1.0 2.0 D = 2.2 in 3.0 Spectral Displacement (inches) j D e m a n d S p e c t r u m (16%) Input S p e c t r u m • C a p a c i t y C u r v e Figure 11.10. Intersection of demand spectrum and capacity curve (CFHR) 124 11.3. F R A G I L I T Y C U R V E S Building fragility curves are lognormal functions that describe the probability of reaching or exceeding a damage state given the level of spectral displacement. Five damage states are defined (none, slight, moderate, extensive and complete) for each building class based on material and structural system. The description of the damage states for U R M L R , WLFR and CFHR are presented in the following paragraphs. U R M L R 1. None: No damage. 2. Slight: Diagonal, stair-step hairline cracks on masonry wall surfaces; larger cracks around door and window openings, in walls with large proportion of openings; movement of lintels; cracks at the base of parapets. 3. Moderate: Most wall surfaces exhibit diagonal cracks; some of the walls exhibit larger diagonal cracks; masonry walls may have visible separation from diaphragms; significant cracking of parapets; some masonry may fall from walls or parapets. 4. Extensive: In buildings with relatively large area of wall openings, most walls have suffered extensive cracking. Some parapets and gable end walls have fallen. 5. Complete: Structure has collapsed or is in imminent danger of collapse due to in-plane or out-of-plane failure of the walls. W L F R 1. None: No damage. 2. Slight: Small plaster or gypsum-board cracks at corners of door and window openings and wall-ceiling intersections; small cracks in masonry chimneys and masonry veneer. 125 3. Moderate: Large plaster or gypsum-board cracks at corners of door window openings; small diagonal cracks across shear wall panels exhibited by small cracks in stucco and gypsum wall panels; large cracks in brick chimneys; toppling of tall masonry chimneys. 4. Extensive: Large diagonal cracks across shear wall panels or large cracks at plywood joints; permanent lateral movement of floors and roof; toppling of most brick chimneys; cracks in foundations; splitting of wood sill plates and/or slippage of structure over foundations; partial collapse of soft-story configurations. 5. Complete: Large permanent lateral displacement, collapse, or imminent danger of collapse; slippage and falling off the foundations; large foundation cracks. CFHR 1. None: No damage. 2. Slight: Diagonal hairline cracks on most concrete shear wall surfaces; minor concrete spalling at few locations. 3. Moderate: Most shear wall surfaces exhibit diagonal cracks; some shear walls have exceeded yield capacity indicated by larger diagonal cracks and concrete spalling at wall ends. 4. Extensive: Most concrete shear walls have exceeded their yield capacities; some walls have exceeded their ultimate capacities indicated by large, through-the-wall diagonal cracks, extensive spalling around the cracks and visibly buckled reinforcement or rotation of narrow walls with inadequate foundations. Partial collapse may occur due to failure of non-ductile columns not designed to resist lateral loads. 5. Complete: Collapse or imminent danger of collapse due to failure of most shear walls. 126 Each fragility curve is defined by a median value of the spectral displacement that corresponds to the threshold of that damage state and by the variability associated with that damage state. The conditional probability of being in or exceeding a particular damage state, ds, given the spectral displacement, SD, is defined by the following relationship: p[ds |SD]= P •In ds '_sp N SE>ds (Eq. 11.19) where SDdsis the median value of spectral displacement at which the building reaches the threshold of damage state, ds; Pds is the standard deviation of the natural logarithm of spectral displacement for damage state, ds; and O is the standard normal cumulative distribution function. The median and beta values used in developing the fragility curves the three sample prototypes U R M L R , WLFR and CFHR are given in Table 11.6. Table 11.6. Fragility curve parameters Building Prototype Slight Moderate Extensive Complete Median Beta Median Beta Median Beta Median Beta U R M L R 0.41 0.99 0.81 1.05 2.03 1.10 4.73 1.08 WLFR 0.50 0.93 1.25 0.98 3.86 1.02 9.45 0.99 CFHR 1.73 0.66 3.64 0.68 10.00 0.70 25.92 0.87 The fragility curves calculated and plotted using the parameters above are given in Figures 11.11, 11.12 and 11.13 for the prototypes, U R M L R , WLFR, and CFHR, respectively. The spectral displacement (SD) levels associated with each of these prototypes are marked on these plots. 127 Fragility Curve (URMLR) Spectral Displacement (in) Figure 11.11. Fragility curve for U R M L R Fragility Curve (WLFR) Spectral Displacement (in) Figure 11.12. Fragility curve for WLFR 128 Fragility Curve (CFHR) Spectra l Displacement (in) Figure 11.13. Fragility curve for CFHR For any given value of spectral response, discrete probability of being in a certain damage state can be calculated as the difference of the cumulative probabilities of reaching or exceeding successive damage states. The discrete probabilities at each of the five damage states for the three prototypes (URMLR, WLFR and CFHR) are calculated and presented in Table 11.7. Table 11.7. Discrete probabilities of structural damage Building Prototype SD (in) Discrete Probabilities (%) for Damage States None Slight Moderate Extensive Complete U R M L R 0.5 42.1 25.6 22.2 8.3 1.9 W L F R 0.5 50.0 32.5 15.2 2.1 0.1 C F H R 2.2 35.8 41.3 21.4 1.3 0.2 129 12. R E S U L T S A N D DISCUSSION The results from the case studies are summarized and discussed in the first part of this chapter. Then, the damage probabilities obtained from SD-based methods are compared to those obtained from MMI-based methods, and possible reasons and implications of the differences are discussed. Probabilistic seismic hazard analyses were carried out to determine the level of ground motion expected for a reference ground condition with a probability of 10% of exceedance in 50 years, which corresponds to a return period of 475 years. The peak ground accelerations calculated for firm ground in New Westminster, Victoria and Vancouver are 0.24g, 0.3 lg and 0.23g, respectively. The M M I level estimated for all three cities is VIII. The distribution of the structural damage (average MDF) at M M I VIII is presented in Figures 8.5, 9.5 and 10.5 for the City of New Westminster, City of Victoria and City of Vancouver, respectively. In New Westminster, the damage distribution is fairly uniform among the blocks and 93% of the blocks are expected to have MDFs between 5% and 10%). In Victoria, there is more spread in the damage values. The majority of the buildings in downtown Victoria have MDFs between 10% and 30%>. The surrounding neighbourhoods however have lower MDFs, in the range of 5%> to 10%>. About 68%> of the blocks in Vancouver study area have average MDFs between 5%> and 10%>. Considerable number of blocks have higher MDFs, between 10%) and 20%. Only 4%> 130 have MDFs higher than 20%. The high damage concentrations are at the eastern side of downtown, which has a high number of unreinforced masonry buildings. The distribution of non-structural damage to displacement-sensitive components, acceleration-sensitive components and building contents at M M I VIII is presented in Figures 8.6 through 8.8, 9.7 through 9.9 and 10.8 through 10.10 for Cities of New Westminster, Victoria and Vancouver, respectively. In New Westminster, about 80% of the blocks are expected to have MDFs between 20% and 30%. In Victoria and Vancouver, about half the blocks are expected to have MDFs in the 20%-30% range and the other half in the 15%-20% range for displacement-sensitive components. For acceleration-sensitive components, about 80% of the blocks in New Westminster are expected to have MDFs in the range of 5% to 10%. In Victoria and Vancouver, about half the blocks are estimated to have MDFs between 5% and 10%, and the other half between 0% and 5% for acceleration-sensitive components. In summary, the damage to displacement-sensitive components in all cities generally stays between 15% and 30%, the acceleration-sensitive between 0% and 10%. Damage to building components does not exceed 5% in any of the cities. Damage distribution maps obtained by three different averaging schemes over the blocks are presented in Chapters 8, 9 and 10 for three case studies, New Westminster, Victoria and Vancouver, respectively. The effect of the averaging scheme on the damage distribution in Vancouver is presented in Figure 12.1. 131 Majority of the blocks remain in the same range of mean damage factors (MDFs), however there are a few blocks that experience a large enough change to move them to a different range in M D F . A sample block containing 12 buildings had a jump in average M D F (%) from 15-20 range to 20-30 range by changing the averaging scheme from straight average to weighted average (either by footprint area or total area). The footprint areas of these buildings showed large variances, from 350 square metres to 3000 square metres, which caused the change in estimated damage for this block. In downtown core, it is common to see a high-rise building next to a two-storey store, and the affect of the averaging scheme that uses the height of the building is evident in those areas. Therefore, the use of weighted averaging scheme is especially advised when there are buildings with very different footprint areas and/or heights within a particular block. In those cases, taking into consideration the footprint area and/or height of the buildings in the averaging scheme provides a more proper estimation of the amount of damage in that block. 132 Figure 12.1. Comparison of averaging schemes 133 The effect of site amplification on the ground motion levels and consequently on the amount of damage to the buildings needs to be taken into account when the study area contains regions of soft soil deposits. The amplification depends on the geology, level of ground shaking and the period of ground motion. At high levels of ground shaking, amplification is not as pronounced as it is at low levels of shaking, especially for low periods (high frequencies). At higher periods on the other hand, considerable amplification may be expected. A peak ground acceleration (PGA) of 0.3 lg was estimated for Victoria with 10% chance of exceedance in 50 years, which is fairly high and the low periods of ground motion are not expected to be amplified at this level of ground shaking. However, high period ground motions are expected to be amplified depending on the geology. Surface geology of the study area in Victoria is presented in Figure 9.10. About half the study area rests on relatively firm ground (R2), which does not amplify the ground motion. The rest of the city however lies on softer material (Cl and C2) and experiences some amount of amplification. The geological unit C l amplifies the peak ground acceleration by a factor of 1.5 and C2 by a factor of 2.0. The PGA calculated for firm ground (0.3lg) was multiplied by these factors, resulting in PGA values of 0.3lg (no amplification) on R2, 0.47g on C l , and 0.62g on C2. These PGA levels were converted to M M I using Equation 3.9. The expected M M I levels are VIII on R2 and IX on C l and C2. The damage distribution due to these M M I levels is presented in Figure 12.2 together with the damage distribution with no site effects. There is considerable difference in the amount of expected damage. About 13% of the blocks now have a M D F higher than 30%. However, it should be noted that these amplification 134 values are valid for high period ground motions only. Low period motions are not expected to be amplified at the level of shaking estimated for Victoria. Figure 12.2. Effect of site amplification (for long period ground motion) The distribution of the economic losses was estimated for the three cities resulting from direct damage to structures and non-structural components. Although highest amount of structural damage is expected to occur in Victoria, Vancouver is expected to suffer most in terms of monetary losses. Almost all blocks in downtown Vancouver are expected to experience losses higher than 1 million C A D . Other commercial parts of Vancouver and the downtown and commercial areas in Victoria and New Westminster are expected to have losses as high as 500,000 C A D . In the residential neighbourhoods, economic loss usually stays below 50,000 C A D . 135 It should be noted that the MMI-based damage matrices that were used in estimating damage to structural components are based on expert opinion and may inherently include damage to some non-structural components as well. However, it was not possible to distinguish which non-structural components were included in these structural damage matrices. Hence, they were assumed to represent structural damage only. This may cause the overall damage and loss estimations to be slightly conservative. The differences in the damage estimations from the two methods, MMI-based and SD-based, will be discussed next. The discrete damage probabilities in Table 5.4 (MMI-based) and Table 11.7 (SD-based) can not be compared directly, because the damage states are defined with different ranges of Central Damage Factors, CDF (Table 12.1). Table 12.1. Damage states in two methodologies MMI-based SD-based Damage State Central Damage Factor Damage State Central Damage Factor None 0% None 0% Slight 0.5% Slight 2% Light 5% Moderate 10% Moderate 20% Extensive 50% Heavy 45% Complete 100% Major 80% Destroyed 100% Therefore, Mean Damage Factors (MDF) will be compared instead of the discrete probabilities. M D F is calculated for each ground motion level by adding up the products of the CDFs with the discrete probabilities of being in the corresponding damage state, 136 maintaining the damage state definitions of each method. The comparison of MDFs obtained for three sample prototypes in Vancouver and Victoria is given in Table 12.2. Table 12.2. Comparison of MDFs Prototype MMI-based (VII) MMI-based (VIII) SD-based Vancouver Victoria URMLR 10.2 23.4 8.8 16.5 WLFR 4.4 7.4 3.3 7.3 CFHR 4.0 11.3 3.6 4.7 The results from the MMI-based method are presented for both M M I VII and VIII since the M M I level in Vancouver (converted from PGA) is between the two, 7.8 (Table 3.2). The large discrete steps of M M I create difficulties in making a precise comparison with the SD-based method, which uses a continuous ground motion parameter. A possible approach is interpolation of the MDF values for intermediate M M I values such as 7.8. This was not attempted in this study, however the effects of a linear interpolation on the results were explored for three types of buildings, U R M L R , WLFR and CFHR. When the MDF values were interpolated for M M I 7.8 in Vancouver and 8.2 in Victoria, it was observed that the results differ by -11%, -10%>, and -13%> in Vancouver and +10%>, +18%o, and +20% in Victoria for U R M L R , WLFR and CFHR buildings, respectively. Another factor that makes the comparison hard is the selection of particular structural properties in the SD-based method such as fundamental period and ductility. These parameters may vary considerably within the same prototype, yet a single value needs to be selected to represent the prototype. The effect of these parameters on the capacity 137 curve for CFHR prototype in Vancouver is presented in Figures 12.3 and 12.4. The resulting spectral displacement levels and MDFs are given in Table 12.3. CFHR prototype includes buildings from 8 stories up to about 30 stories high. The average number of stories for this prototype in the Vancouver building database is 14. According to the Canadian building code, these structures can have force reduction factors (reflecting ductility) from 2 for nominally ductile systems up to 4 for ductile structures. 0.5 Capacity curve (CFHR) — 0.4 5 c o 2 0.3 5% Spectrum 16% Spectrum _ _ _ T e = 1.2 s e c Te = 1.4 s e c Te = 1.65 s e c Te = 1.8 s e c cu cu o o "* 0.2 Spectral o o Spectral o o v Spectral o o >' Spectral o o > 0.0 1.0 2 Spectral Displa 0 3 cement (inches) 0 4.0 Figure 12.3. CFHR capacity curves for periods: T e = 1.20, 1.40, 1.65, and 1.80 138 Capacity curve (CFHR) 0.5 , . , . , , . . , . Spectral Displacement (inches) Figure 12.4. CFHR capacity curves for ductilities: p = 2.0, 3.0, and 4.0 Table 12.3. Effect of period and ductility on MDF for CFHR Fundamental Period (sec) Ductility 1.20 1.40 1.65 1.80 2.0 3.1 4.0 SD (in) 1.4 1.7 2.2 2.4 2.5 2.2 1.8 MDF 1.47 2.21 3.62 4.22 4.52 3.62 2.48 Note that as the ductility decreases the code requirement on the strength of the building increases and the building yields later. When the building has not yielded the intersection of the capacity curve with the 5% damped response spectrum is used instead of the 16% damped spectrum since the extra damping is utilized only after yield occurs. In general, SD-based method predicts less damage in the three prototypes that were studied. The definition of M M I VIII reads: "Damage slight in specially-designed structures; considerable in ordinary substantial buildings with partial collapse; great in 139 poorly-built structures". CFHR buildings can generally be considered as "specially-designed", assuming the building codes were followed in the design of these concrete high-rise structures. WLFR buildings are "ordinary substantial buildings", since many of these buildings were not designed according to a seismic code, however they conventionally have some lateral resistance. U R M L R falls in "poorly-built structures" category. Based on the rough definitions of M M I VIII, CFHR structures should not receive more than "slight" damage, hence MMI-based method seems to be over-estimating the damage to these structures. Again, based on the M M I VIII description, WLFR buildings are expected to have "considerable" damage, hence SD-based method is under-estimating the damage to these buildings. Finally, according to M M I VIII definition, U R M L R buildings receive "great" damage, hence the SD-based method seems to be under-estimating the damage to these structures also. It should be noted that the fragility curves used in this study (FEMA/NIBS, 1997) have large uncertainties associated with them as well as the damage probability matrices. Although several earthquakes occurred in different regions of the world since the development of these methods, it has not been possible to compare the damage estimations from these methods to damage data from real earthquakes. The reason is the non-standard definition of damage states and structural prototypes as well as lack of one or more of the critical components of data necessary to make the comparison. The required data includes location, severity of ground shaking (preferably PGA), structural prototype and damage state the building is in (as defined in the damage estimation methods). 140 13. CONCLUSIONS A N D R E C O M M E N D A T I O N S A clear need for rational damage estimation and risk assessment methods in southwestern British Columbia was identified. The seismic hazard level is considerable and it has been well studied, however the consequences of an expected ground shaking in the area required more research. This thesis attempted to answer these needs and offer a reliable methodology to estimate the distribution of seismic damage and loss in southwestern BC caused by design level earthquake ground motions. 13.1. SUMMARY An assessment of the seismic risk in southwestern BC was carried out. First, the seismic hazard in the area was evaluated. This included the estimation of P G A and M M I in the area as well as the calculation of uniform hazard spectra. Then, damage to structures and non-structural components were estimated based on the expected ground motions in three major cities in B C , New Westminster, Victoria and Vancouver. Distribution of the structural and non-structural damage was mapped and high-risk areas and building types were identified. Effect of geology was studied and different averaging schemes for the damage distribution within each block were introduced. Economic losses resulting from damage to structural and non-structural components of buildings were also estimated. Next, an alternative approach to the conventional MMI-based method was investigated, which involved calculation of damage based on spectral displacement (SD). Structural 141 parameters needed in the SD-based method were developed for three sample prototypes. The resulting damage levels were compared to those obtained from the MMI-based method. Damage distribution was mapped using Geographic Information Systems (GIS) software. The GIS provided a very convenient platform to store the data such as building inventory, the damage-motion relationships and geology maps; to run analyses and to draw thematic maps of the estimated damage and loss distributions. It should be noted that the methods used in this thesis are applicable for a regional study with a large number of buildings. They can be modified to incorporate for more detailed information to some extent. However, they are not suited for a site-specific study on a particular building since in these methods buildings and site conditions are grouped into categories, and the estimations are based on the general average characteristics of each category. 13.2. C O N C L U S I O N S Seismic risk is a combination of seismic hazard and the vulnerability of the buildings. Among the three case studies, the highest damage is expected in the City of Victoria. It has a high seismic hazard due to its location, about half the city lies on soil that may amplify the ground motion, and the building stock includes a high number of very vulnerable (unreinforced masonry) buildings. Vancouver and New Westminster are also 142 expected to experience considerable damage. In terms of economic losses, Vancouver is expected to suffer most, especially the downtown area of the city. The most vulnerable buildings are unreinforced masonry buildings, especially those that are higher than three stories. About 2% of the buildings in New Westminster, 8% of those surveyed in Vancouver and 17% of those surveyed in Victoria are unreinforced masonry buildings. Considerable differences were observed in the damage levels estimated by MMI-based and SD-based methodologies. These differences were discussed in Chapter 12. M M I -based method predicts higher damage in general compared to SD-based method. For engineered structures such as CFHR, SD-based method is expected to give more reliable damage estimates since it is based on the code parameters. For buildings that were not built according to code requirements however (such as U R M L R ) , the damage levels appear to be underestimated by SD-based method. 13.3. R E C O M M E N D A T I O N S F O R F U T U R E R E S E A R C H There are many cities and districts exposed to seismic risk in southwestern BC. This study estimated damage and loss distribution for three case studies, cities of Vancouver, Victoria and New Westminster. The rest of the cities require similar assessments of the seismic risk for emergency planning and management. Cities of Vancouver and Victoria were represented with "study areas", which were selected to include the parts of the cities 143 with the most diversity in terms of building types. The building inventories in the regions outside the study areas need to be completed. MMI-based damage matrices provide values of MDF for discrete steps of M M I , i.e. M M I VI, VII, VIII, IX, X , XI and XII. Although in this study, the M M I levels were rounded to these discrete steps when necessary, an alternative approach is the interpolation of MDF for intermediate values of MMI . A linear interpolation was performed for three building types, U R M L R , W L F R and CFHR to determine the effect in the results and the difference was less than 20% for Vancouver and Victoria. However, such an interpolation can be performed for the rest of the building types and the damage distribution maps can be updated with the interpolated values of M D F . Many key structural parameters were used in the calculation of the damage probabilities. However, additional structural information such as shape, soft-storey and pounding effects can also be included in the methodology. These attributes may highly change the outcome and they are available for cities of Vancouver and Victoria as part of the information collected in the building surveys. Therefore, improvement of the current procedures to take into account these building properties is recommended. Among the site effects, only amplification was taken into account in one case study (Victoria). Effect of site amplification in other cities, particularly in certain areas such as False Creek in Vancouver and Queensborough area in New Westminster needs to be evaluated. In addition, determination of other site effects such as liquefaction and 144 landslide potentials is recommended to be integrated into the methodology. Site amplification in Victoria was estimated using a broad site classification scheme. An in depth study on the effects of site amplification in Victoria using a more refined site classification scheme is recommended. This study was restricted to building type structures due to the availability of information. Seismic damage to lifelines and non-building structures should be estimated for a more complete picture of the seismic risk in the area. This requires construction of appropriate structural databases and development of a methodology that is suitable to the special aspects of these structures. This study considered direct damage only. The effects of secondary causes of damage, such as fire following earthquake can be included in future studies. In addition, non-monetary losses such as casualties can also be estimated i f occupancy information on the buildings can be compiled, which was out of the scope of this study. MMI-based and SD-based methodologies were compared in this thesis and the differences in the results are significant. The SD-based method was applied to only three sample prototypes due to the constraints in time and resources. Development of the capacity curves for the rest of the building prototypes is recommended so that damage distribution can be mapped using SD-based methods also. Both methods have weak and strong points, which are discussed in Chapter 12. The strengths of the two methods can be combined to make estimates that are more rational. 145 Some of the parameters needed in constructing the capacity curves of the SD-based method such as strength and fundamental period, were derived mainly based on the building code. The capacity curves for each building type in fact are equivalent to the pushover curves for individual buildings. For each prototype, a representative building can be selected and modelled by a structural analysis program. Elastic models can be calibrated by microtremor measurements, which provide valuable information on the dynamic characteristics of the buildings in the elastic range. Pushover analyses can then be carried out on inelastic models to determine the capacity curves for each building prototype. This procedure is very time-consuming and detailed. However, over a course of time, a valuable database would build up and the behaviour of different building prototypes can be analyzed using various building configurations and properties. In addition, effects of many variables such as building period, shape, size, structural irregularities and construction quality can be studied in a detailed and rational manner. The best way to determine the reliability of damage estimation methods is to compare their results with observed damage data from real earthquakes. As discussed in Chapter 12, abundant post-earthquake data collections efforts exist, however unfortunately not much of it is suitable for the purpose of damage estimation because of incompleteness or differences in definitions and formats. Therefore, it is of utmost importance to gather damage information after a major earthquake in an urban area using the damage state and building type descriptions consistent with the methodologies used in damage estimations. The data needed includes location (address or geographical coordinates), ground motion level at that location (preferably SA or PGA), building type, and the damage state. 146 A P P E N D I X A . M O D I F I E D M E R C A L L I INTENSITY S C A L E The Modified Mercalli Intensity (MMI) scale for the intensity levels that can cause damage is presented below. Table A. 1. Modified Mercalli Intensity (MMI) Scale M M I DESCRIPTION OF EFFECTS VI Felt by all, many frightened. Some heavy furniture moved. A few instances of fallen plaster. Damage slight. VII Damage negligible in buildings of good design and construction; slight to moderate in well-built ordinary structures; considerable in poorly-built structures. Some chimneys broken. VIII Damage slight in specially-designed structures; considerable in ordinary substantial buildings with partial collapse; great in poorly-built structures. Fall of chimneys, factory stacks, columns, walls. Heavy furniture overturned. IX Damage considerable in specially-designed structures; well-designed frame structures thrown out of plumb. Damage great in substantial buildings, with partial collapse. Buildings shifted off foundations. X Some well-built wooden structures destroyed; most masonry and frame structures with foundations destroyed. Rails bent. XI Few, if any masonry structures remain standing. Bridges destroyed. Rails bent greatly. XII Damage total. Lines of sight and level are distorted. Objects thrown into air. 147 A P P E N D I X B. DESCRIPTION OF B C B U I L D I N G P R O T O T Y P E S Descriptions of the building prototypes listed in Chapter 5, Table 5.3 are given in the following paragraphs. 1. WLFR (Wood Light Frame Residential): This prototype includes single family detached homes and attached town houses. They are generally one or two stories high with a foot print area in the range of 70 to 350 square meters. The vast majority of buildings in southwestern BC are of this prototype, usually located in the residential or suburban areas. These buildings usually behave very well (lightweight, low rise, many walls) except when a parking garage is built into the structure creating an equivalent of a weak storefront. 2. WLFCI (Wood Light Frame Low Rise Commercial/Institutional): This prototype includes one or two storey commercial and institutional buildings varying in size from 80 to 600 square meters in footprint area. The ground floor usually has extensive areas of glazing creating a storefront. This prototype makes up about 10% of the commercial/institutional building stock. These buildings behave well i f there are less window openings than half the area of the perimeter wall. Commercial buildings with storefronts are subject to extensive damage if they are stand-alone structures. 148 3. WLFLR (Wood Light Frame Low Rise Residential): This prototype includes wood frame structures up to four stories in height principally for residential use. The footprint area can be as large as 1500 square meters. They usually have considerable interior load bearing walls and no extensive glazing. Exterior walls may be clad in a variety of materials including wood or vinyl siding, stucco, brick veneer, and metal. About 90% of all low-rise residential buildings are of this prototype. These structures generally behave well if they do not have a ground level parking area, or i f they have concrete underground parking levels. 4. WPB (Wood Post and Beam): This prototype includes some one or two storey commercial and institutional structures. Old high-rise structures (industrial, storage, manufacturing) are also classified as post and beam if the perimeter columns are load bearing and the masonry part is not load bearing. This prototype can be found in "Westcoast Style" post and beam homes of the 1950's and 1960's; one or two storey industrial facilities of the 1920's to 1950's; schools, gymnasiums, churches, warehouses as well as some commercial structures of the 1950's and 1960's. These buildings generally behave poorly. 5. LMF (Light Metal Frame): This prototype includes lightweight pre-engineering "Butler" type industrial and agricultural buildings (usually used as warehouses or industrial shops) with rigid frames in the short direction and cross bracing in the other direction. About 5% of the inventory 149 of industrial warehouse type buildings are of this prototype. These buildings are expected to behave well. 6. SMFLR (Steel Moment Frame Low Rise): This prototype includes steel moment framed structures of one to three stories in height, generally used for institutional facilities or office structures. Moment frames transfer lateral forces from the floors to the foundations in one or both directions. These structures are extremely rare in southwestern BC and are extremely hard to identify unless portions of the structure are exposed. These are very flexible buildings and will cause extensive non-structural damage due to the flexibility and torsional effects (rigid floor diaphragms with flexible frame). 7. SMFMR (Steel Moment Frame Medium Rise): This prototype includes steel moment framed structures of four to seven stories in height, generally used for institutional facilities or office structures. These structures are very rare in southwestern BC and are extremely hard to identify unless portions of the structure are exposed. These are very flexible buildings and will cause extensive non-structural damage due to the flexibility and torsional effects (rigid floor diaphragms with flexible frame). 8. SMFHR (Steel Moment Frame High Rise): This prototype includes steel moment framed structures of over eight stories in height, generally used for institutional facilities or office structures. These structures are very 150 rare in southwestern BC and are extremely hard to identify unless portions of the structure are exposed. These are very flexible buildings and will cause extensive non-structural damage due to the flexibility and torsional effects (rigid floor diaphragms with flexible frame). 9. SBFLR (Steel Braced Frame Low Rise): This prototype includes structures with steel braced frames in both directions, one to three stories in height, generally used for one or two storey commercial and institutional buildings as well as many low-rise industrial facilities. About one third of older industrial facilities and 5% of the commercial and institutional buildings are of this prototype. They are hard to identify unless the bracing is exposed. These structures usually have storefronts and flexible diaphragms, which may cause problems as well as connections of the bracing system. 10. SBFMR (Steel Braced Frame Medium Rise): This prototype includes structures with steel braced frames in both directions, four to seven stories in height, generally found in older office buildings as well as in older light manufacturing facilities. Many multi-storey industrial facilities such as pulp and paper mill boiler plants are also of this prototype. However, other than these structures, this prototype is very rare in southwestern BC. They are also hard to identify unless the bracing is exposed. These structures are in high risk because of their flexibility coupled with the attachment of a heavy perimeter cladding. They behave poorly usually because of poor connections in the bracing system. 151 11. SBFHR (Steel Braced Frame High Rise): This prototype includes structures with steel braced frames in both directions, over eight stories in height, generally used for office buildings and some very tall industrial buildings such as grain elevators. These structures are very rare in southwestern BC and hard to identify unless the bracing is exposed. These structures are in high risk because of their flexibility coupled with the attachment of a heavy perimeter cladding. They behave poorly usually because of poor connections in the bracing system. 12. SFCWLR (Steel Frame with Concrete Walls Low Rise): This prototype includes one and two-storey steel framed structures that use concrete shear walls as their vertical elements to transfer seismic forces from roof and floors to the foundations. It is one of the most common forms of steel construction for commercial and institutional buildings, particularly those constructed after 1970's. The steel frame may be hard to identify unless drawings or access is available. These buildings generally behave well, particularly i f the walls are well distributed, although structures with storefronts will experience damage. 13. SFCWMR (Steel Frame with Concrete Walls Medium Rise): This prototype includes steel frame structures with concrete shear walls from three to seven stories in height, generally used for commercial and institutional buildings. It is a fairly common form of steel construction for commercial and institutional buildings, making up about 30% of the inventory of medium rise buildings. The steel frame may be 152 hard to identify unless drawings or access to the structure is available. These buildings generally behave well, particularly i f the walls are well distributed to minimize torsional effects. 14. SFCWHR (Steel Frame with Concrete Walls High Rise): This prototype includes steel frame structures with concrete shear walls over eight stories in height, used for commercial and institutional buildings. It was fairly common prior to 1985, however, is now being superceded by concrete frame with concrete shear wall structures (CFHR). About 15% of the pre-1985 office towers and probably less than 10% of the post-1985 towers are of this prototype. The steel frame may be hard to identify unless drawings or access to the structure is available. These buildings generally behave well, particularly i f the concrete shear walls are well distributed to minimize torsional effects and have well-detailed connections to the steel frames. 15. SFCIW (Steel Frame with Concrete Infill Walls): This prototype includes steel framed buildings with concrete infill walls, which were usually built along the sides of the building and used as a fire separation between the buildings (not considered as shear walls). This was a common form of construction prior to the 1950's, when offices and some light industrial buildings (up to seven stories) were constructed in this manner. These buildings are hard to identify unless the adjacent building has been torn down. They are expected to behave reasonably well although extensive damage and partial collapses can be expected if storefronts exist. 153 16. SFMIW (Steel Frame with Masonry Infill Walls): This prototype includes steel framed buildings with masonry infill walls, which were usually built along the sides of the building and used as a fire separation between the buildings (not considered as shear walls). This was a common form of construction prior to the 1950's, when offices and some light industrial buildings (up to seven stories) were constructed in this manner. These buildings are hard to identify unless the adjacent building has been torn down. They were generally not designed for seismic forces, hence they will not behave well and extensive damage and partial collapse can be expected. 17. CFLR (Concrete Frame with Concrete Walls Low Rise): This prototype includes one to three-storey concrete framed structures that use concrete shear walls (in one or both directions) as their vertical elements to transfer seismic forces from the roof and floors to the foundations. It is commonly used for commercial and even more commonly for institutional buildings. These buildings generally behave well, particularly i f the footprint is rectangular unless the footprint is large enough to cause torsional problems together with inappropriately located shear walls. 18. CFMR (Concrete Frame with Concrete Walls Medium Rise): This prototype includes concrete framed structures with concrete shear walls from four to seven stories in height. It is a very common form of construction for medium rise residential, commercial and institutional buildings, making up more than 50% of the inventory of medium rise buildings. These buildings are usually easy to identify and they 154 generally behave well, particularly if the walls are well distributed to minimize torsional effects. 19. CFHR (Concrete Frame with Concrete Walls High Rise): This prototype includes concrete framed structures with concrete shear walls over eight stories in height. It is an extremely common form of construction for commercial and residential high rises, making up over 90% of the inventory of high rise buildings. These buildings are usually easy to identify and they generally behave well, particularly those built after 1985. 20. RCMFLR (Reinforced Concrete Moment Frame Low Rise): This prototype includes reinforces concrete moment frame structures of one to three stories in height, generally used for institutional facilities or office structures. The moment frames are used in one or both directions and they replace the shear walls to transfer lateral forces from the floors to the foundation. This form of construction is very rare in southwestern BC and is extremely hard to identify without drawings. Inadequate detailing of the joints may cause extensive damage in these structures. 21. RCMFMR (Reinforced Concrete Moment Frame Medium Rise): This prototype includes reinforces concrete moment frame structures of four to seven stories in height, generally used for office structures. This form of construction is extremely rare in southwestern B C and is very difficult to identify without drawings. Inadequate detailing of the joints may cause extensive damage in these structures. 155 22. RCMFHR (Reinforced Concrete Moment Frame High Rise): This prototype includes reinforces concrete moment frame structures of over eight stories in height, generally used for office structures. This form of construction is extremely rare in southwestern BC and is very difficult to identify without drawings. Inadequate detailing of the joints may cause extensive damage in these structures. 23. RCFIW (Reinforced Concrete Frame with Infill Walls): This prototype includes reinforced concrete frame buildings with masonry infill walls, which were usually built along the sides of the building and used as a fire separation between the buildings (not considered as shear walls). This was a common form of construction prior to the 1950's, when offices and some light industrial buildings (up to seven stories) were constructed in this manner. These buildings are difficult to identify unless the adjacent building has been torn down. They were generally not designed for seismic forces, hence they are expected to behave poorly and experience extensive damage. 24. RMLR (Reinforced Masonry Shear Wall Low Rise): This prototype includes one to three stories high buildings with perimeter load bearing walls of reinforced masonry. Since 1973, when the National Building Code of Canada required that all masonry be reinforced, this has become a very common form of construction for low rise commercial, institutional and industrial buildings. These buildings are usually easy to identify. The walls generally behave well, however, 156 whether or not the roof diaphragm connection to the walls will function adequately is a major concern for these buildings. 25. RMMR (Reinforced Masonry Shear Wall Medium Rise): This prototype includes buildings with perimeter load bearing walls of reinforced masonry, over three stories in height. In the mid-1970's, these buildings were constructed to compete with reinforced concrete structures, however, after a small number were built, they were found noncompetitive. Therefore, they are very rare in southwestern BC. Extensive damage is anticipated in these types of buildings. 26. URMLR (Unreinforced Masonry Bearing Wall Low Rise): This prototype includes buildings up to three stories in height with perimeter load bearing walls of clay brick, concrete block and hollow clay. This was a very common form of low-rise construction for commercial, institutional and industrial buildings until 1973, when the National Building Code of Canada required that all masonry be reinforced. These buildings are easy to identify, usually showing extensive areas of red clay brick. They behave very poorly and are considered the most hazardous form of construction in seismic areas. 27. URMMR (Unreinforced Masonry Bearing Wall Medium Rise): This prototype includes three to six storey high buildings with perimeter load bearing walls of mainly clay brick with thickness reaching 750 mm. This form of construction was used for commercial and light industrial buildings prior to 1940. These buildings are 157 easy to identify with thick walls and usually extensive areas of red or orange clay brick exposed, often in poor condition. They behave very poorly and are considered as the most hazardous form of construction in seismic areas. 28. T U (Tilt Up): This prototype includes low-rise structures with walls that are constructed of reinforced concrete panels, which have been cast on site on top of the concrete slab on grade and then tilted into position. It is commonly used since late 1970's for warehouses, light manufacturing and research facilities. These buildings are expected to behave reasonably well in BC because of the use of steel roof systems and their superior connections. 29. P C L R (Precast Concrete Low Rise): This prototype includes one to three stories high buildings that are constructed of concrete components that have been manufactured off site in a plant and transported to the construction site for installation. Installation consists of lifting and connecting the members together and then pouring a topping over the floors to create a level surface. This form of construction was quite common during the 1960's and 1970's for institutional buildings as well as for parking structures. These structures make up a very small portion of the southwestern BC inventory and behave poorly, primarily due to the connection failures. 158 30. P C M R (Precast Concrete Medium Rise): This prototype includes over four stories high buildings that are constructed of concrete components that have been manufactured off site in a plant and transported to the construction site for installation. Although this form of construction is common in Canada for commercial and institutional buildings, it has been seldom used in southwestern BC. These structures make up a very small portion of the southwestern BC inventory and behave poorly, primarily due to the connection failures. 31. M H (Mobile Homes): This prototype includes single storey wood framed factory manufactured buildings and school potables. They are generally not more than 33 square meters in area. Individual units behave well i f adequately skirted and anchored to a foundation. 159 A P P E N D I X C. D A M A G E M A T R I C E S F O R B C B U I L D I N G P R O T O T Y P E S Buildings located in southwestern BC were classified into 31 prototypes and damage probability matrices were developed for each of these prototypes. These matrices were developed assuming that the buildings are very nearly regular in shape and they are founded on firm ground, designed to a code prior to 1990. Collateral hazards such as ground failure and fire were not considered (Bell, 1998). The damage probability matrices (DPMs) for each of the 31 prototypes of buildings are presented below. In these tables, CDF is the Central Damage Factor as defined in Chapter 5, and *** indicates very small probability. Table C l . D P M for WLFR (Wood Light Frame Residential) Description This prototype includes one or two-storey single family detached homes and attached townhouses. The vast majority of the buildings in southwestern BC are of this prototype. C D F V I VI I VIII I X X X I XI I 0.0 8.0 4.0 1.0 *** *** *** *** 0.5 75.0 28.0 6.0 1.0 *** *** *** 5.0 17.0 64.0 86.0 69.0 10.0 2.0 *** 20.0 *** 4.0 5.0 20.0 76.0 69.0 42.0 45.0 *## *** 2.0 10.0 12.0 25.0 50.0 80.0 *** *** *** *** 2.0 4.0 6.0 100.0 *** *** *** *** *** *** 2.0 160 Table C.2. D P M for WLFCI (Wood Light Frame Commercial/Institutional) Description This prototype includes one or two-storey C/I buildings. This prototype makes up about 10% of the C/I building stock. They often have "storefronts", extensive areas of glazing. C D F VI VII VIII LX X XI XII 0.0 7.0 1.0 *** *** *** *** *** 0.5 77.0 23.0 3.0 1.0 *** *** *** 5.0 16.0 69.0 77.0 55.0 9.0 1.0 *** 20.0 * * * 5.0 15.0 35.0 66.0 57.0 40.0 45.0 * ** 2.0 5.0 7.0 18.0 25.0 37.0 80.0 *** *** *** 2.0 7.0 14.0 18.0 100.0 * * * *** *** *** 3.0 5.0 Table C.3. D P M for W L F L R (Wood Light Frame Low Rise Residential) Description This prototype includes residential apartment buildings usually up to four storeys high. About 90% of all low-rise (multi-family) residential buildings are expected to be of this form. C D F VI VII VIII IX X XI XII 0.0 7.0 4.0 *** *** *** *** *** 0.5 81.0 30.0 12.0 1.0 *** ** * *** 5.0 12.0 64.0 85.0 65.0 20.0 2.0 *** 20.0 *** 2.0 3.0 28.0 73.0 70.0 44.0 45.0 * * * *** *** 6.0 7.0 24.0 47.0 80.0 *** *** *** *** *** 4.0 8.0 100.0 *** * * * *** *** *** *** 1.0 Table C.4. D P M for WPB (Wood Post and Beam) Description This prototype includes one or two-storey C/I structures (making up 20% of C/I building stock). Also, industrial plants built between 1920-1950 were commonly of this prototype. C D F VI VII VIII IX X XI XII 0.0 2.0 1.0 *** *** *** *** *** 0.5 77.0 12.0 2.0 *** *** *** *** 5.0 21.0 77.0 72.0 60.0 6.0 1.0 *** 20.0 *** 8.0 17.0 22.0 64.0 54.0 40.0 45.0 * * * 2.0 7.0 10.0 18.0 25.0 33.0 80.0 *** *** 2.0 5.0 8.0 15.0 20.0 100.0 *** *** *** 3.0 4.0 5.0 7.0 161 Table C.5. D P M for L M F (Light Metal Frame) Description This prototype includes lightweight pre-engineering industrial and agricultural buildings. It makes up about 5% of the inventory of industrial warehouse type buildings. CDF VI VII VIII IX X XI XII 0.0 40.0 10.0 2.0 *** *** *** *** 0.5 55.0 40.0 17.0 5.0 1.0 *** *** 5.0 5.0 50.0 81.0 80.0 15.0 3.0 *** 20.0 * * * *** *** 15.0 79.0 81.0 43.0 45.0 ** * *** *** *** 5.0 15.0 50.0 80.0 * ** * * * *** *** *** 1.0 7.0 100.0 *** * * * *** *** *** *** *** Table C.6. D P M for S M F L R (Steel Moment Frame Low Rise) Description This prototype includes SMF structures of one to three stories in height. Extremely rare in BC and hard to identify without drawings, unless portions of the structure are exposed. CDF VI VII VIII IX X XI XII 0.0 30.0 10.0 2.0 *** *** *** *** 0.5 65.0 30.0 5.0 2.0 *** *** *** 5.0 5.0 60.0 91.0 89.0 20.0 1.0 *** 20.0 * * * *** 2.0 9.0 79.0 85.0 40.0 45.0 * * * * * * * * * *** 1.0 14.0 57.0 80.0 * * * * * * *** * * * *** * * * 3.0 100.0 *** *** *** *** *** *** *** Table C.7. D P M for S M F M R (Steel Moment Frame Medium Rise) Description This prototype includes SMF structures of four to seven stories in height. Extremely rare in BC and difficult to identify without drawings, unless portions of the structure are exposed. CDF VI VII VIII IX X XI XII 0.0 25.0 8.0 1.0 *** *** *** *** 0.5 68.0 20.0 6.0 2.0 *** *** *** 5.0 7.0 72.0 90.0 76.0 8.0 1.0 *** 20.0 *** *** 3.0 20.0 85.0 56.0 20.0 45.0 * * * *** *** 2.0 7.0 40.0 72.0 80.0 * * * * * * *** *** *** 3.0 8.0 100.0 * * * * * * * * * *** *** *** *** 162 Table C.8. D P M for SMFHR (Steel Moment Frame High Rise) Description This prototype includes SMF structures over eight stories in height. Extremely rare in BC and difficult to identify without drawings, unless portions of the structure are exposed. CDF VI VII VIII IX X XI XII 0.0 20.0 5.0 *** *** *** *** *** 0.5 73.0 13.0 12.0 *** *** ** * *** 5.0 7.0 80.0 79.0 32.0 1.0 *** *** 20.0 * * * 2.0 9.0 60.0 84.0 36.0 12.0 45.0 * * * *** * * * 8.0 15.0 60.0 80.0 80.0 *** * * * *** *** *** 4.0 8.0 100.0 *** *** *** *** *** *** *** Table C.9. D P M for SBFLR (Steel Braced Frame Low Rise) Description This prototype includes SBF C/I and industrial structures of one to three stories in height. It is hard to identify. About 33% of older industrial facilities and 5% of C/I buildings are SBFLR. CDF VI VII VIII IX X XI XII 0.0 20.0 8.0 *** *** *** *** *** 0.5 70.0 45.0 5.0 *** *** * * * *** 5.0 10.0 47.0 81.0 60.0 6.0 1.0 * * * 20.0 *** *** 14.0 35.0 85.0 60.0 31.0 45.0 * * * *** *** 5.0 6.0 34.0 60.0 80.0 * * * ** * *** *** 3.0 5.0 7.0 100.0 * ** *** *** *** *** *** 2.0 Table CIO. D P M for SBFMR (Steel Braced Frame Medium Rise) Description This prototype includes SBF C/I and industrial structures of four to seven stories in height. It is very rare except some pulp and paper mills, and extremely difficult to identify. CDF VI VII VIII IX X XI XII 0.0 15.0 2.0 *** *** *** *** *** 0.5 60.0 10.0 1.0 • ** *** *** *** 5.0 25.0 88.0 65.0 40.0 6.0 1.0 *** 20.0 *** *** 34.0 57.0 82.0 50.0 32.0 45.0 *** *** *** 3.0 12.0 48.0 65.0 80.0 *** *** *** *** *** 1.0 2.0 100.0 *** *** *** *** *** *** 1.0 163 Table C l 1. D P M for SBFHR (Steel Braced Frame High Rise) Description This prototype includes SBF structures above eight stories in height. It is very rare and extremely difficult to identify without drawings unless portions of the system are exposed. CDF VI VII VIII IX X XI XII 0.0 15.0 2.0 *** *** *** *** *** 0.5 60.0 2.0 *** *** *** *** *** 5.0 25.0 89.0 65.0 32.0 3.0 1.0 *** 20.0 *** 7.0 34.0 65.0 80.0 27.0 10.0 45.0 *** *** 1.0 3.0 17.0 67.0 75.0 80.0 *** *** *** *** *** 5.0 12.0 100.0 * * * *** *** *** *** *** 3.0 Table C. 12. D P M for SFCWLR (Steel Frame with Concrete Walls Low Rise) Description This prototype includes one or two-storey SF buildings with concrete shear walls in one or both directions. It is very common in C/I buildings but may be hard to identify. CDF VI VII VIII LX X XI XII 0.0 20.0 3.0 1.0 *** *** *** *** 0.5 67.0 15.0 5.0 2.0 *** *** *** 5.0 12.0 80.0 84.0 30.0 15.0 1.0 *** 20.0 *** *** 10.0 66.0 70.0 40.0 15.0 45.0 *** *** *** 2.0 13.0 55.0 70.0 80.0 *** *** *** *** 2.0 4.0 15.0 100.0 *** *** *** *** #** *** *** Table C.13. D P M for SFCWMR (Steel Frame with Concrete Walls Medium Rise) Description This prototype includes three to seven-storey SF buildings with concrete shear walls. It makes up about 30% of the inventory of medium rise C/I buildings. It may be hard to identify. CDF VI VII VIII IX X XI XII 0.0 15.0 2.0 1.0 *** *** *** *** 0.5 65.0 15.0 5.0 1.0 *** *** *** 5.0 20.0 80.0 74.0 10.0 2.0 1.0 *** 20.0 *** 3.0 20.0 85.0 62.0 18.0 5.0 45.0 * * * *** * #* 4.0 35.0 75.0 74.0 80.0 *** *** *** *** 1.0 6.0 21.0 100.0 *** *** *** *** *** *** *** 164 Table C.14. D P M for SFCWHR (Steel Frame with Concrete Walls High Rise) Description This prototype includes SF C/I buildings higher than 8 stories. About 15% of the pre-1985 office towers and <10% of the post-1985 towers are of this prototype, but hard to identify. CDF VI VII VIII IX X XI XII 0.0 20.0 3.0 1.0 * * * *** *** *** 0.5 67.0 15.0 5.0 2.0 *** *** *** 5.0 12.0 80.0 84.0 30.0 15.0 1.0 *** 20.0 * * * *** 10.0 66.0 70.0 40.0 15.0 45.0 *** * * * *** 2.0 13.0 55.0 70.0 80.0 *** * * * *** *** 2.0 4.0 15.0 100.0 *** *** *** *** *** *** *** Table C.15. D P M for SFCI (Steel Frame with Concrete Infill Walls) Description This prototype is a common form of construction for buildings constructed prior to the 1950's (offices and some light industrial buildings up to seven stories). It is very hard to identify. CDF VI VII VIII IX X XI XII 0.0 10.0 2.0 *** *** *** *** *** 0.5 75.0 14.0 3.0 *** *** *** *** 5.0 15.0 82.0 73.0 25.0 2.0 *** *** 20.0 *** 2.0 24.0 68.0 60.0 16.0 3.0 45.0 * * * * * * *** 6.0 35.0 65.0 72.0 80.0 * * * * * * * * * 1.0 3.0 18.0 23.0 100.0 ** * *** *** *** 1.0 2.0 Table C.16. D P M for SFMI (Steel Frame with Masonry Infill Walls) Description This prototype is a common form of construction for buildings constructed prior to the 1950's (offices and some light industrial buildings up to seven stories). It is very hard to identify. CDF VI VII VIII IX X XI XII 0.0 6.0 1.0 *** *** *** *** *** 0.5 40.0 3.0 *** *** *** *** *** 5.0 53.0 80.0 37.0 3.0 *** *** *** 20.0 1.0 15.0 55.0 39.0 25.0 3.0 1.0 45.0 *** 1.0 8.0 52.0 55.0 43.0 40.0 80.0 *** *** *** 6.0 20.0 50.0 45.0 100.0 * * * *** *** *** *** 4.0 15.0 165 Table C.17. D P M for C F L R (Concrete Frame with Concrete Walls Low Rise) Description This prototype includes one to three-storey CF structures with concrete shear walls. It is common in commercial and institutional buildings and is generally easy to identify. CDF VI VII VIII IX X XI XII 0.0 20.0 5.0 1.0 *** *** *** *** 0.5 70.0 12.0 8.0 2.0 *** *** * * * 5.0 10.0 80.0 88.0 40.0 15.0 1.0 *** 20.0 * * * 3.0 3.0 57.0 75.0 40.0 10.0 45.0 *** *** *** 1.0 8.0 53.0 72.0 80.0 * * * *** *** * * * 2.0 5.0 15.0 100.0 * ** *** *** *** *** 1.0 3.0 Table C.18. D P M for C F M R (Concrete Frame with Concrete Walls Medium Rise) Description This prototype includes CF structures from four to seven stories in height. It is very common for medium rise residential and C/I buildings, and is relatively easy to identify. CDF VI VII VIII IX X XI XII 0.0 15.0 2.0 # * * *** *** *** *** 0.5 75.0 40.0 2.0 * * * *** *** *** 5.0 10.0 55.0 78.0 33.0 8.0 1.0 *** 20.0 * * * 3.0 20.0 60.0 72.0 29.0 5.0 45.0 *** *** *** 7.0 20.0 65.0 75.0 80.0 *** *** *** *** *** 5.0 18.0 100.0 *** *** *** *** *** *** 2.0 Table C.19. D P M for CFHR (Concrete Frame with Concrete Walls High Rise) Description This prototype is very common (over 90% of the inventory of high rise structures - virtually every residential tower and majority of the recent commercial towers). It is easy to identify. CDF VI VII VIII IX X XI XII 0.0 12.0 2.0 *** *** *** *** *** 0.5 73.0 30.0 2.0 *** *** *** *** 5.0 15.0 65.0 57.0 15.0 1.0 1.0 *** 20.0 * * * 3.0 40.0 66.0 61.0 28.0 5.0 45.0 *** *** 1.0 18.0 35.0 55.0 67.0 80.0 *** *** *** 1.0 3.0 16.0 25.0 100.0 *** *** *** *** *** *** 3.0 166 Table C.20. D P M for R C M F L R (Reinforced Concrete Moment Frame Low Rise) Description This prototype includes one to three-storey RCMF structures, generally used for institutional facilities or office structures. It is very rare in BC and extremely hard to identify. C D F VI VII VIII IX X XI XII 0.0 5.0 1.0 *** *** *** *** ** * 0.5 40.0 5.0 1.0 *** *** *** *** 5.0 55.0 89.0 45.0 10.0 1.0 *** *** 20.0 *** 5.0 51.0 80.0 34.0 10.0 1.0 45.0 *** *** 3.0 10.0 60.0 73.0 74.0 80.0 *** * * * *** * * * 5.0 15.0 20.0 100.0 *** * * * *** *** *** 2.0 5.0 Table C.21. D P M for R C M F M R (Reinforced Concrete Moment Frame Medium Rise) Description This prototype includes four to seven-storey RCMF structures, generally used for office structures. It is extremely rare in BC and is extremely hard to identify without drawings. C D F VI VII VIII IX X XI XII 0.0 5.0 1.0 *** *** *** *** 0.5 40.0 5.0 1.0 *** *** *** *** 5.0 55.0 87.0 43.0 5.0 1.0 *** *** 20.0 *** 7.0 55.0 83.0 23.0 5.0 1.0 45.0 * * * *** 1.0 12.0 70.0 65.0 58.0 80.0 * * * *** *** *** 6.0 25.0 35.0 100.0 * * * *** *** *** *** 5.0 6.0 Table C.22. D P M for R C M F H R (Reinforced Concrete Moment Frame High Rise) Description This prototype includes RCMF structures higher than eight-storey, generally used for office structures. It is extremely rare in BC and is extremely hard to identify without drawings. C D F VI VII VIII IX X XI XII 0.0 2.0 1.0 *** *** *** *** *** 0.5 33.0 7.0 *** *** *** ** * *** 5.0 65.0 90.0 39.0 5.0 1.0 *** *** 20.0 *** 2.0 55.0 70.0 22.0 2.0 1.0 45.0 * * * *** 6.0 25.0 70.0 57.0 39.0 80.0 *** *** *** *** 7.0 35.0 52.0 100.0 *** *** *** *** *** 6.0 8.0 167 Table C.23. D P M for RCFIW (Reinforced Concrete Frame with Infill Walls) Description This prototype is common in buildings (offices and some light industrial buildings up to 7 stories) constructed prior to 1950's. Masonry infill walls are not considered as shear walls. CDF VI VII VIII IX X XI XII 0.0 6.0 1.0 *** *** *** *** *** 0.5 40.0 5.0 ** * *** *** *** *** 5.0 54.0 76.0 38.0 5.0 2.0 *** *** 20.0 * * * 17.0 57.0 56.0 38.0 5.0 1.0 45.0 * * * 1.0 5.0 35.0 46.0 48.0 42.0 80.0 * ** *** ## * 4.0 14.0 45.0 43.0 100.0 * * * *** * * * *** *** 2.0 14.0 Table C.24. D P M for R M L R (Reinforced Masonry Shear Wall Low Rise) Description This prototype is very common in post-1973 low-rise C/I and industrial buildings. Distinctive pattern of masonry makes it easy to identify. CDF VI VII VIII IX X XI XII 0.0 30.0 15.0 1.0 *** *** *** * *# 0.5 63.0 13.0 10.0 2.0 *** *** *** 5.0 7.0 70.0 80.0 30.0 2.0 *** *** 20.0 ** * 2.0 9.0 62.0 62.0 25.0 5.0 45.0 * ** * * * *** 6.0 28.0 63.0 57.0 80.0 * * * *** *** *** 8.0 10.0 32.0 100.0 *** *** *** *** *** 2.0 6.0 Table C.25. D P M for R M M R (Reinforced Masonry Shear Wall Medium Rise) Description This prototype constitutes an insignificant component of the southwestern BC inventory of buildings. They look very similar to concrete buildings with masonry/glazing cladding. CDF VI VII VIII IX X XI XII 0.0 15.0 3.0 *** *** *** *** *** 0.5 75.0 22.0 *** *** * * * * * * *** 5.0 10.0 70.0 80.0 2.0 *** *** *** 20.0 *** 5.0 20.0 70.0 60.0 10.0 1.0 45.0 * * * *** *** 28.0 25.0 75.0 38.0 80.0 * * * *** *** *** 15.0 15.0 55.0 100.0 *** * * * * * * *** *** *** 6.0 168 Table C.26. D P M for U R M L R (Unreinforced Masonry Bearing Wall Low Rise) Description This prototype was a very common form of low-rise construction until 1973 for C/I and industrial buildings. Easy to identify with extensive areas of red clay brick showing. CDF VI VII VIII IX X XI XII 0.0 10.0 * * * *** *## *** *** *** 0.5 55.0 3.0 *** *** *** *** *** 5.0 30.0 65.0 21.0 5.0 1.0 *** ** * 20.0 5.0 30.0 60.0 47.0 20.0 6.0 2.0 45.0 #** 2.0 15.0 40.0 48.0 35.0 8.0 80.0 *** *** 2.0 4.0 25.0 51.0 70.0 100.0 *** *** 2.0 4.0 6.0 8.0 20.0 Table C.27. D P M for U R M M R (Unreinforced Masonry Bearing Wall Medium Rise) Description This prototype was used for commercial and light industrial buildings up to six stories in height, constructed principally prior to 1940. It is commonly seen in the older parts of cities. CDF VI VII VIII IX X XI XII 0.0 2.0 *** * * * *** * * * *** 0.5 30.0 2.0 *** * * * * * * * * * * * * 5.0 63.0 58.0 6.0 *** *** *** *** 20.0 5.0 35.0 70.0 43.0 15.0 2.0 *** 45.0 *** 5.0 20.0 48.0 52.0 28.0 1.0 80.0 * * * *** 2.0 5.0 28.0 65.0 79.0 100.0 *** *** 2.0 4.0 5.0 5.0 20.0 Table C.28. D P M for TU (Tilt Up) Description This prototype is commonly used for the construction of warehouses (seldom over 2 stories). RC panel walls are cast on site on top of the concrete slab and then tilted into position. CDF VI VII VIII IX X XI XII 0.0 30.0 10.0 *** *** *** *** *** 0.5 60.0 35.0 12.0 2.0 *** *** *** 5.0 10.0 50.0 58.0 12.0 2.0 *** * * * 20.0 *** 5.0 30.0 82.0 48.0 10.0 1.0 45.0 *** *** *** 4.0 45.0 70.0 43.0 80.0 *** *** *** *** 5.0 15.0 50.0 100.0 *** *** *** *** *** 5.0 6.0 169 Table C.29. D P M for P C L R (Precast Concrete Low Rise) Description This prototype was common during 1960's and 1970's for institutional buildings. It has been common for parking structures, but rare otherwise. Easily identified with exposed concrete. CDF VI VII VIII IX X XI XII 0.0 10.0 3.0 *** *** *** *** *** 0.5 50.0 17.0 5.0 *** *** *** *** 5.0 40.0 75.0 60.0 5.0 1.0 *** *** 20.0 * * * 5.0 30.0 77.0 38.0 10.0 4.0 45.0 *** *** 5.0 15.0 51.0 66.0 35.0 80.0 *** *** *** 2.0 7.0 20.0 55.0 100.0 *** *** *** 1.0 3.0 4.0 6.0 Table C.30. D P M for P C M R (Precast Concrete Medium Rise) Description This prototype is very rare in southwestern BC although it is common in the rest of Canada for commercial and institutional buildings. CDF VI VII VIII LX X XI XII 0.0 10.0 1.0 *** *** *** *** *** 0.5 40.0 5.0 1.0 *** *** *** *** 5.0 50.0 85.0 54.0 1.0 ** * *** *** 20.0 *** 9.0 40.0 65.0 35.0 10.0 1.0 45.0 *** *** 5.0 34.0 60.0 60.0 33.0 80.0 * * * *** *** *** 5.0 30.0 60.0 100.0 *** *** *** *** *** *** 6.0 Table C.31. D P M for M H (Mobile Homes) Description This prototype includes single storey wood framed factory-manufactured buildings and school portables consisting of a number of factory-manufactured modules joined on site. CDF VI VII VIII IX X XI XII 0.0 25.0 10.0 *** *** *** *** *** 0.5 55.0 10.0 5.0 *** *** *** *** 5.0 30.0 70.0 40.0 25.0 *** *** *** 20.0 *** 10.0 53.0 65.0 60.0 10.0 1.0 45.0 *** *** 2.0 10.0 35.0 83.0 65.0 80.0 *** *** ** * *** 5.0 7.0 34.0 100.0 *** *** *** *** *** *** *** 170 A P P E N D I X D. D A M A G E M A T R I C E S F O R N O N - S T R U C T U R A L C O M P O N E N T S For the estimation of non-structural damage in BC, damage matrices were developed in terms of M M I (Cook, 1999). These non-structural damage matrices are given for each of the 31 building prototypes of southwestern BC. In these tables, CDF is the Central Damage Factor as defined in Chapter 5. It can be noted that the damage probabilities of the building contents are the same as those of acceleration-sensitive components. The only difference between the two is their central damage factors. Table D . l . Non-Structural Damage Probability Matrices for W L F R CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 66.0 54.2 51.0 41.2 32.7 28.1 24.2 2.0 10.0 11.6 11.9 12.3 12.3 11.5 11.0 10.0 12.7 16.0 16.8 18.6 18.6 19.5 19.3 50.0 1.8 3.5 4.0 5.8 5.8 8.7 9.6 80.0 9.5 14.7 16.3 22.1 28.3 32.1 36.0 Acceleration-sensitive components 0.0 73.0 47.9 35.2 23.9 14.0 9.9 7.9 2.0 22.4 35.3 37.8 36.3 30.4 25.9 23.1 10.0 4.4 14.6 22.2 30.1 37.0 38.9 39.2 50.0 0.3 2.1 4.7 9.0 16.4 21.5 24.7 80.0 0.0 0.1 0.2 0.7 2.2 3.8 5.0 Building Contents 0.0 73.0 47.9 35.2 23.9 14.0 9.9 7.9 1.0 22.4 35.3 37.8 36.3 30.4 25.9 23.1 5.0 4.4 14.6 22.2 30.1 37.0 38.9 39.2 25.0 0.3 2.1 4.7 9.0 16.4 21.5 24.7 40.0 0.0 0.1 0.2 0.7 2.2 3.8 5.0 171 Table D.2. Non-Structural Damage Probability Matrices for WLFCI CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 70.6 55.2 53.2 45.3 38.8 34.7 30.7 2.0 8.0 10.4 10.6 11.3 11.5 11.5 11.3 10.0 10.5 14.5 14.9 16.4 17.3 17.6 17.8 50.0 6.2 9.2 9.5 10.8 11.5 11.9 12.1 80.0 4.7 10.7 11.7 16.3 20.9 24.4 28.1 Acceleration-sensitive components 0.0 77.4 50.0 47.7 31.8 24.5 20.3 18.5 2.0 19.0 35.0 35.8 39.2 38.6 37.3 36.5 10.0 3.4 13.0 14.1 23.1 28.1 31.1 32.4 50.0 0.3 2.0 2.2 5.4 8.0 10.1 11.1 80.0 0.0 0.1 0.1 0.5 0.9 1.3 1.5 Building Contents 0.0 77.4 50.0 47.7 31.8 24.5 20.3 18.5 1.0 19.0 35.0 35.8 39.2 38.6 37.3 36.5 5.0 3.4 13.0 14.1 23.1 28.1 31.1 32.4 25.0 0.3 2.0 2.2 5.4 8.0 10.1 11.1 40.0 0.0 0.1 0.1 0.5 0.9 1.3 1.5 Table D.3. Non-Structural Damage Probability Matrices for W L F L R CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 66.0 54.2 51.0 41.2 32.7 28.1 24.2 2.0 10.0 11.6 11.9 12.3 12.0 11.5 11.0 10.0 12.7 16.0 16.8 18.6 16.5 19.5 19.3 50.0 1.8 3.5 4.0 5.8 7.6 8.7 9.6 80.0 9.5 14.7 16.3 22.1 28.3 32.1 36.0 Acceleration-sensitive components 0.0 73.0 50.0 38.4 23.9 14.0 9.9 7.9 2.0 22.4 34.6 37.5 36.3 30.4 25.9 23.1 10.0 4.4 13.5 20.1 30.1 37.0 38.9 39.2 50.0 0.3 1.9 3.8 9.0 16.4 21.5 24.7 80.0 0.0 0.1 0.2 0.7 2.2 3.8 5.0 Building Contents 0.0 73.0 50.0 38.4 23.9 14.0 9.9 7.9 1.0 22.4 34.6 37.5 : 36.3 30.4 25.9 23.1 5.0 4.4 13.5 20.1 30.1 37.0 38.9 39.2 25.0 0.3 1.9 3.8 9.0 16.4 21.5 24.7 40.0 0.0 0.1 0.2 0.7 2.2 3.8 5.0 172 Table D.4. Non-Structural Damage Probability Matrices for WPB CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 66.0 54.2 51.0 41.2 32.7 28.1 24.2 2.0 10.0 11.6 11.9 12.3 12.0 11.5 11.0 10.0 12.7 16.0 16.8 18.6 19.5 19.5 19.3 50.0 1.8 3.5 4.0 5.8 7.6 8.7 9.6 80.0 9.5 14.7 16.3 22.1 28.3 32.1 36.0 Acceleration-sensitive components 0.0 73.0 47.9 35.2 23.9 14.0 9.9 7.9 2.0 22.4 35.3 37.8 36.3 30.4 25.9 23.1 10.0 4.4 14.6 22.2 30.1 37.0 38.9 39.2 50.0 0.3 2.1 4.7 9.0 16.4 21.5 24.7 80.0 0.0 0.1 0.2 0.7 2.2 3.8 5.0 Building Contents 0.0 73.0 47.9 35.2 23.9 14.0 9.9 7.9 1.0 22.4 35.3 37.8 36.3 30.4 25.9 23.1 5.0 4.4 14.6 22.2 30.1 37.0 38.9 39.2 25.0 0.3 2.1 4.7 9.0 16.4 21.5 24.7 40.0 0.0 0.1 0.2 0.7 2.2 3.8 5.0 Table D.5. Non-Structural Damage Probability Matrices for L M F CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 65.1 49.7 48.5 36.5 30.4 25.9 22.9 2.0 9.0 11.0 11.1 11.5 11.4 11.0 10.6 10.0 11.7 15.4 15.6 17.4 17.8 17.9 17.7 50.0 6.7 9.3 9.4 10.9 11.3 11.4 11.4 80.0 7.5 14.7 15.4 23.7 29.1 33.7 37.3 Acceleration-sensitive components 0.0 80.7 55.0 52.4 35.6 29.3 27.9 25.3 2.0 16.7 33.1 34.3 39.4 39.8 39.7 39.3 10.0 2.6 10.8 11.9 21.0 25.1 26.1 28.0 50.0 0.1 1.1 1.4 3.7 5.4 5.8 6.8 80.0 0.0 0.0 0.1 0.2 0.4 0.5 0.6 Building Contents 0.0 80.7 55.0 52.4 35.6 29.3 27.9 25.3 1.0 16.7 33.1 34.3 39.4 39.8 39.7 39.3 5.0 2.6 10.8 11.9 21.0 25.1 26.1 28.0 25.0 0.1 1.1 1.4 3.7 5.4 5.8 6.8 40.0 0.0 0.0 0.1 0.2 0.4 0.5 0.6 173 Table D.6. Non-Structural Damage Probability Matrices for S M F L R CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 68.1 48.2 46.7 40.2 33.6 29.7 25.3 2.0 10.9 13.0 13.1 13.0 12.5 12.1 11.3 10.0 13.1 19.5 19.8 21.1 21.8 21.9 21.6 50.0 2.4 5.7 6.0 7.5 9.0 9.9 11.0 80.0 5.5 13.5 14.3 18.2 23.1 26.4 30.7 Acceleration-sensitive components 0.0 89.0 63.0 57.6 47.7 41.2 35.6 32.3 2.0 9.9 28.7 31.8 36.2 38.3 39.4 39.7 10.0 1.0 7.4 9.5 13.9 17.2 20.5 22.6 50.0 0.0 0.8 1.1 2.1 3.0 4.1 5.0 80.0 0.0 0.0 0.0 0.1 0.2 0.3 0.4 Building Contents 0.0 89.0 63.0 57.6 47.7 41.2 35.6 32.3 1.0 9.9 28.7 31.8 36.2 38.3 39.4 39.7 5.0 1.0 7.4 9.5 13.9 17.2 20.5 22.6 25.0 0.0 0.8 1.1 2.1 3.0 4.1 5.0 40.0 0.0 0.0 0.0 0.1 0.2 0.3 0.4 Table D.7. Non-Structural Damage Probability Matrices for S M F M R CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 73.2 49.9 48.8 45.9 37.8 33.9 19.4 2.0 10.0 14.4 14.5 14.7 15.0 14.9 12.9 10.0 8.2 15.8 16.2 17.1 19.4 20.4 22.8 50.0 2.0 5.0 5.2 5.7 7.0 7.7 10.5 80.0 6.6 14.8 15.3 16.6 20.8 23.1 34.4 Acceleration-sensitive com ponents 0.0 98.5 86.7 89.3 81.0 72.1 55.0 52.5 2.0 1.5 11.6 9.5 16.1 22.6 32.7 33.9 10.0 0.1 1.6 1.1 2.7 5.0 10.9 12.0 50.0 0.0 0.1 0.0 0.2 0.4 1.4 1.6 80.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1 Building Contents 0.0 98.5 86.7 89.3 81.0 72.1 55.0 52.5 1.0 1.5 11.6 9.5 16.1 22.6 32.7 33.9 5.0 0.1 1.6 1.1 2.7 5.0 10.9 12.0 25.0 0.0 0.1 0.0 0.2 0.4 1.4 1.6 40.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1 174 Table D.8. Non-Structural Damage Probability Matrices for SMFHR CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 73.9 72.4 69.3 50.8 41.2 33.2 27.0 2.0 9.8 10.2 11.0 14.3 15.0 14.9 14.3 10.0 8.2 8.7 9.8 15.8 18.7 20.8 22.0 50.0 1.7 1.9 2.2 4.6 6.2 7.6 8.9 80.0 6.4 6.8 7.7 14.4 18.9 23.5 27.8 Acceleration-sensitive components 0.0 99.9 99.3 98.5 97.3 89.3 86.7 83.9 2.0 0.1 0.7 1.4 2.5 9.4 11.5 13.7 10.0 0.0 0.0 0.1 0.2 1.2 1.7 2.2 50.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 80.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Building Contents 0.0 99.9 99.3 98.5 97.3 89.3 86.7 83.9 1.0 0.1 0.7 1.4 2.5 9.4 11.5 13.7 5.0 0.0 0.0 0.1 0.2 1.2 1.7 2.2 25.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 40.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Table D.9. Non-Structural Damage Probability Matrices for SBFLR CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 72.0 56.3 53.3 43.6 37.6 32.7 29.3 2.0 7.5 10.2 10.6 11.4 11.6 11.6 11.5 10.0 11.1 15.2 15.9 17.5 18.0 18.2 18.2 50.0 4.6 7.5 8.1 9.6 10.5 11.0 11.3 80.0 4.7 10.7 12.2 17.9 22.2 26.4 29.7 Acceleration-sensitive components 0.0 81.0 50.0 45.4 35.4 29.0 27.6 25.0 2.0 16.3 35.3 37.1 39.6 40.0 40.0 39.6 10.0 2.5 12.6 14.8 20.3 24.3 25.2 27.0 50.0 0.2 2.0 2.5 4.3 6.1 6.5 7.5 80.0 0.0 0.1 0.2 0.4 0.6 0.7 0.8 Building Contents 0.0 81.0 50.0 45.4 35.4 29.0 27.6 25.0 1.0 16.3 35.3 37.1 39.6 40.0 40.0 39.6 5.0 2.5 12.6 14.8 20.3 24.3 25.2 27.0 25.0 0.2 2.0 2.5 4.3 6.1 6.5 7.5 40.0 0.0 0.1 0.2 0.4 0.6 0.7 0.8 175 Table D.10. Non-Structural Damage Probability Matrices for SBFMR CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 73.3 56.7 53.7 52.0 45.8 39.4 34.7 2.0 10.6 13.8 14.1 14.2 14.6 14.6 14.3 10.0 7.9 13.6 14.6 15.2 17.2 19.1 20.4 50.0 1.7 3.8 4.2 4.5 5.5 6.6 7.4 80.0 6.5 12.2 13.4 14.1 17.0 20.4 23.2 Acceleration-sensitive components 0.0 95.8 86.7 72.1 63.2 52.5 47.6 43.2 2.0 4.0 11.9 23.1 28.8 34.6 36.6 38.2 10.0 0.2 1.4 4.5 7.3 11.5 13.8 16.1 50.0 0.0 0.1 0.3 0.6 1.4 1.8 2.4 80.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 Building Contents 0.0 95.8 86.7 72.1 63.2 52.5 47.6 43.2 1.0 4.0 11.9 23.1 28.8 34.6 36.6 38.2 5.0 0.2 1.4 4.5 7.3 11.5 13.8 16.1 25.0 0.0 0.1 0.3 0.6 1.4 1.8 2.4 40.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 Table D. 11. Non-Structural Damage Probability Matrices for SBFHR CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 77.3 63.7 60.5 55.2 44.5 37.6 31.9 2.0 9.4 12.7 13.3 14.1 14.9 14.9 14.5 10.0 7.5 12.4 13.5 15.4 18.8 20.7 22.0 50.0 0.6 1.9 2.3 3.1 4.8 6.1 7.3 80.0 5.1 9.2 10.3 12.4 17.1 20.7 24.3 Acceleration-sensitive components 0.0 99.9 92.1 89.7 87.1 75.4 66.4 57.8 2.0 0.1 7.3 9.3 11.5 20.6 26.8 31.9 10.0 0.0 0.6 1.0 1.4 3.7 6.3 9.3 50.0 0.0 0.0 0.0 0.1 0.2 0.5 1.0 80.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Building Contents 0.0 99.9 92.1 89.7 87.1 75.4 66.4 57.8 1.0 0.1 7.3 9.3 11.5 20.6 26.8 31.9 5.0 0.0 0.6 1.0 1.4 3.7 6.3 9.3 25.0 0.0 0.0 0.0 0.1 0.2 0.5 1.0 40.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 176 Table D.12. Non-Structural Damage Probability Matrices for SFCWLR CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 70.6 51.8 51.4 44.0 37.8 33.4 30.5 2.0 7.3 10.1 10.1 10.7 10.9 10.8 10.7 10.0 12.0 16.2 16.3 17.2 17.5 17.5 17.3 50.0 4.6 8.0 8.0 9.2 10.1 10.6 10.8 80.0 5.4 13.9 14.1 18.9 23.7 27.7 30.7 Acceleration-sensitive components 0.0 67.7 55.5 47.4 30.8 27.7 24.9 24.9 2.0 27.2 35.1 39.3 44.2 44.4 44.2 44.2 10.0 4.7 8.5 11.8 20.7 22.8 24.9 24.9 50.0 0.4 0.9 1.5 3.9 4.7 5.6 5.6 80.0 0.0 0.0 0.1 0.3 0.4 0.5 0.5 Building Contents 0.0 67.7 55.5 47.4 30.8 27.7 24.9 24.9 1.0 27.2 35.1 39.3 44.2 44.4 44.2 44.2 5.0 4.7 8.5 11.8 20.7 22.8 24.9 24.9 25.0 0.4 0.9 1.5 3.9 4.7 5.6 5.6 40.0 0.0 0.0 0.1 0.3 0.4 0.5 0.5 Table D. l3 . Non-Structural Damage Probability Matrices for SFCWMR CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 80.1 57.4 56.4 55.0 48.9 41.1 35.4 2.0 7.5 12.5 12.6 12.8 13.4 13.9 13.8 10.0 5.0 12.0 12.3 12.8 14.6 16.8 18.3 50.0 1.7 4.4 4.6 4.8 5.6 6.7 7.6 80.0 5.7 13.7 14.1 14.7 17.5 21.5 24.8 Acceleration-sensitive components 0.0 94.2 66.4 69.3 55.1 47.6 43.1 41.0 2.0 5.4 26.8 24.9 33.3 36.7 38.3 38.9 10.0 0.4 6.3 5.4 10.4 13.8 16.1 17.3 50.0 0.0 0.5 0.4 1.1 1.8 2.4 2.7 80.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 Building Contents 0.0 94.2 66.4 69.3 55.1 47.6 43.1 41.0 1.0 5.4 26.8 24.9 33.3 36.7 38.3 38.9 5.0 0.4 6.3 5.4 10.4 13.8 16.1 17.3 25.0 0.0 0.5 0.4 1.1 1.8 2.4 2.7 40.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 177 Table D.14. Non-Structural Damage Probability Matrices for SFCWHR CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 81.9 65.3 64.2 60.7 50.0 38.3 32.5 2.0 5.5 10.0 10.2 11.0 13.1 14.4 14.7 10.0 5.8 10.8 11.1 12.1 15.1 17.9 19.1 50.0 1.8 3.7 3.8 4.3 5.6 7.3 8.2 80.0 5.0 10.2 10.6 11.9 16.2 22.1 25.6 Acceleration-sensitive components 0.0 99.6 89.7 87.1 84.3 69.3 57.8 55.1 2.0 0.4 9.2 11.4 13.7 24.6 31.5 32.9 10.0 0.0 1.0 1.5 2.0 5.6 9.6 10.7 50.0 0.0 0.0 0.1 0.1 0.5 1.0 1.2 80.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1 Building Contents 0.0 99.6 89.7 87.1 84.3 69.3 57.8 55.1 1.0 0.4 9.2 11.4 13.7 24.6 31.5 32.9 5.0 0.0 1.0 1.5 2.0 5.6 9.6 10.7 25.0 0.0 0.0 0.1 0.1 0.5 1.0 1.2 40.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1 Table D.15. Non-Structural Damage Probability Matrices for SFCI CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 70.6 53.0 51.4 44.0 37.8 33.4 30.5 2.0 7.3 9.9 10.1 10.7 10.9 10.8 10.7 10.0 12.0 16.0 16.3 17.2 17.5 17.5 17.3 50.0 4.6 7.8 8.0 9.2 10.1 10.6 10.8 80.0 5.4 13.2 14.1 18.9 23.7 27.7 30.7 Acceleration-sensitive components 0.0 72.1 60.4 52.5 35.4 32.1 29.0 29.0 2.0 22.8 30.1 34.2 39.6 40.0 40.0 40.0 10.0 4.7 8.5 11.8 20.7 22.8 24.9 24.9 50.0 0.4 0.9 1.5 3.9 4.7 5.6 5.6 80.0 0.0 0.0 0.1 0.3 0.4 0.5 0.5 Building Contents 0.0 72.1 60.4 52.5 35.4 32.1 29.0 29.0 1.0 22.8 30.1 34.2 39.6 40.0 40.0 40.0 5.0 4.7 8.5 11.8 20.7 22.8 24.9 24.9 25.0 0.4 0.9 1.5 3.9 4.7 5.6 5.6 40.0 0.0 0.0 0.1 0.3 0.4 0.5 0.5 178 Table D. l6 . Non-Structural Damage Probability Matrices for SFMI CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 70.6 53.0 52.2 44.0 37.8 33.4 30.5 2.0 7.3 9.9 10.0 10.7 10.9 10.8 10.7 10.0 12.0 16.0 16.2 17.2 17.5 17.5 17.3 50.0 4.6 7.8 7.9 9.2 10.1 10.6 10.8 80.0 5.4 13.2 13.7 18.9 23.7 27.7 30.7 Acceleration-sensitive components 0.0 72.4 60.6 52.5 35.2 31.8 28.7 28.7 2.0 22.8 30.3 34.6 40.2 40.5 40.6 40.6 10.0 4.5 8.3 11.5 20.6 22.8 24.9 24.9 50.0 0.3 0.8 1.4 3.7 4.5 5.4 5.4 80.0 0.0 0.0 0.1 0.2 0.3 0.4 0.4 Building Contents 0.0 72.4 60.6 52.5 35.2 31.8 28.7 28.7 1.0 22.8 30.3 34.6 40.2 40.5 40.6 40.6 5.0 4.5 8.3 11.5 20.6 22.8 24.9 24.9 25.0 0.3 0.8 1.4 3.7 4.5 5.4 5.4 40.0 0.0 0.0 0.1 0.2 0.3 0.4 0.4 Table D.17. Non-Structural Damage Probability Matrices for C F L R CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 70.3 53.2 52.2 44.3 36.7 32.6 28.7 2.0 8.1 10.5 10.6 11.1 11.2 11.0 10.8 10.0 9.4 13.7 14.0 15.5 16.7 17.1 17.3 50.0 6.6 9.6 9.7 10.7 11.4 11.5 11.6 80.0 5.7 12.9 13.5 18.4 24.1 27.7 31.6 Acceleration-sensitive components 0.0 80.3 47.7 45.5 28.2 21.3 18.5 16.9 2.0 17.0 36.2 37.0 39.4 37.8 36.5 35.6 10.0 2.5 13.7 14.8 25.2 30.2 32.3 33.5 50.0 0.2 2.2 2.5 6.5 9.5 11.1 12.2 80.0 0.0 0.1 0.2 0.7 1.2 1.5 1.8 Building Contents 0.0 80.3 47.7 45.5 28.2 21.3 18.5 16.9 1.0 17.0 36.2 37.0 39.4 37.8 36.5 35.6 5.0 2.5 13.7 14.8 25.2 30.2 32.3 33.5 25.0 0.2 2.2 2.5 6.5 9.5 11.1 12.2 40.0 0.0 0.1 0.2 0.7 1.2 1.5 1.8 179 Table D . l 8 . Non-Structural Damage Probability Matrices for C F M R CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 77.7 61.1 60.4 55.0 48.3 43.5 39.9 2.0 9.3 12.4 12.5 13.0 13.2 13.1 12.9 10.0 7.9 14.0 14.3 16.1 18.0 19.3 20.1 50.0 0.3 2.0 2.1 2.9 4.0 5.0 5.8 80.0 4.8 10.4 10.7 13.1 16.4 19.1 21.3 Acceleration-sensitive components 0.0 90.2 63.0 57.6 43.3 35.6 29.3 26.6 2.0 9.0 29.3 32.5 38.5 40.1 40.3 40.0 10.0 0.7 6.8 8.8 15.4 19.8 24.0 26.0 50.0 0.0 0.8 1.1 2.7 4.1 5.8 6.8 80.0 0.0 0.0 0.0 0.2 0.3 0.5 0.7 Building Contents 0.0 90.2 63.0 57.6 43.3 35.6 29.3 26.6 1.0 9.0 29.3 32.5 38.5 40.1 40.3 40.0 5.0 0.7 6.8 8.8 15.4 19.8 24.0 26.0 25.0 0.0 0.8 1.1 2.7 4.1 5.8 6.8 40.0 0.0 0.0 0.0 0.2 0.3 0.5 0.7 Table D. l9 . Non-Structural Damage Probability Matrices for CFHR CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 79.2 65.0 64.1 58.9 52.6 47.2 41.5 2.0 8.1 11.7 11.9 12.8 13.7 14.2 14.5 10.0 5.8 10.3 10.6 12.3 14.3 16.0 17.7 50.0 1.5 3.1 3.2 3.9 4.8 5.5 6.4 80.0 5.4 9.9 10.2 12.1 14.7 17.0 19.9 Acceleration-sensitive components 0.0 98.9 83.9 78.1 75.1 60.4 55.0 45.4 2.0 1.1 14.2 18.7 21.0 30.5 33.4 37.5 10.0 0.0 1.8 3.0 3.7 8.3 10.4 15.0 50.0 0.0 0.1 0.2 0.2 0.8 1.1 2.1 80.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1 Building Contents 0.0 98.9 83.9 78.1 75.1 60.4 55.0 45.4 1.0 1.1 14.2 18.7 21.0 30.5 33.4 37.5 5.0 0.0 1.8 3.0 3.7 8.3 10.4 15.0 25.0 0.0 0.1 0.2 0.2 0.8 1.1 2.1 40.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1 180 Table D.20. Non-Structural Damage Probability Matrices for R C M F L R CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 68.1 49.4 48.5 39.6 33.8 29.3 26.6 2.0 8.9 11.2 11.3 11.5 11.4 11.1 10.8 10.0 12.1 16.8 17.0 18.2 18.6 18.7 18.5 50.0 5.7 9.3 9.5 10.9 11.6 12.0 12.1 80.0 5.2 13.3 13.8 19.7 24.5 28.9 31.9 Acceleration-sensitive components 0.0 86.3 60.3 57.6 41.2 33.9 30.8 27.9 2.0 12.1 30.3 31.8 38.3 39.6 39.8 39.7 10.0 1.5 8.5 9.6 17.4 21.8 23.9 25.8 50.0 0.1 0.9 1.0 2.9 4.3 5.2 6.1 80.0 0.0 0.0 0.0 0.2 0.3 0.4 0.5 Building Contents 0.0 86.3 60.3 57.6 41.2 33.9 30.8 27.9 1.0 12.1 30.3 31.8 38.3 39.6 39.8 39.7 5.0 1.5 8.5 9.6 17.4 21.8 23.9 25.8 25.0 0.1 0.9 1.0 2.9 4.3 5.2 6.1 40.0 0.0 0.0 0.0 0.2 0.3 0.4 0.5 Table D.21. Non-Structural Damage Probability Matrices for R C M F M R CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 74.0 52.7 51.7 48.6 42.6 36.7 31.9 2.0 10.4 13.9 13.9 14.1 14.2 13.9 13.4 10.0 7.5 14.7 15.1 16.1 17.9 19.6 20.7 50.0 1.7 4.4 4.6 5.1 6.1 7.1 8.0 80.0 6.4 14.3 14.7 16.2 19.3 22.8 26.0 Acceleration-sensitive components 0.0 95.8 78.1 75.1 60.4 52.5 45.4 41.1 2.0 4.0 18.7 21.0 30.5 34.6 37.5 38.8 10.0 0.2 3.1 3.8 8.4 11.8 15.3 17.6 50.0 0.0 0.1 0.2 0.6 1.1 1.8 2.4 80.0 0.0 0.0 0.0 0.0 0.0 0.1 0.1 Building Contents 0.0 95.8 78.1 75.1 60.4 52.5 45.4 41.1 1.0 4.0 18.7 21.0 30.5 34.6 37.5 38.8 5.0 0.2 3.1 3.8 8.4 11.8 15.3 17.6 25.0 0.0 0.1 0.2 0.6 1.1 1.8 2.4 40.0 0.0 0.0 0.0 0.0 0.0 0.1 0.1 181 Table D.22. Non-Structural Damage Probability Matrices for R C M F H R CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 76.2 56.4 54.8 48.8 38.1 30.7 24.9 2.0 7.9 12.4 12.6 13.5 14.3 14.3 13.8 10.0 6.7 12.7 13.1 14.9 17.7 19.5 20.5 50.0 2.2 4.6 4.8 • 5.6 7.1 8.2 9.1 80.0 7.0 14.0 14.6 17.3 22.7 27.3 31.7 Acceleration-sensitive components 0.0 99.6 96.0 94.2 87.1 84.3 79.9 78.4 2.0 0.4 3.7 5.3 11.3 13.5 16.9 18.0 10.0 0.0 0.3 0.5 1.6 2.1 3.0 3.4 50.0 0.0 0.0 0.0 0.1 0.1 0.2 0.2 80.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Building Contents 0.0 99.6 96.0 94.2 87.1 84.3 79.9 78.4 1.0 0.4 3.7 5.3 11.3 13.5 16.9 18.0 5.0 0.0 0.3 0.5 1.6 2.1 3.0 3.4 25.0 0.0 0.0 0.0 0.1 0.1 0.2 0.2 40.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Table D.23. Non-Structural Damage Probability Matrices for RCFIW CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 67.4 45.7 44.9 34.0 26.0 19.9 10.5 2.0 9.7 12.5 12.5 12.7 12.1 11.1 8.3 10.0 11.9 17.6 17.8 19.5 19.9 19.5 16.9 50.0 5.1 8.9 9.1 10.8 11.7 12.2 11.7 80.0 5.9 15.2 15.7 23.1 30.3 37.3 52.6 Acceleration-sensitive components 0.0 82.1 50.0 47.0 44.2 44.2 44.2 44.2 2.0 15.2 35.0 36.2 37.2 37.2 37.2 37.2 10.0 2.6 13.3 14.7 16.1 16.1 16.1 16.1 50.0 0.1 1.7 2.0 2.4 2.4 2.4 2.4 80.0 0.0 0.1 0.1 0.1 0.1 0.1 0.1 Building Contents 0.0 82.1 50.0 47.0 44.2 44.2 44.2 44.2 1.0 15.2 35.0 36.2 37.2 37.2 37.2 37.2 5.0 2.6 13.3 14.7 16.1 16.1 16.1 16.1 25.0 0.1 1.7 2.0 2.4 2.4 2.4 2.4 40.0 0.0 0.1 0.1 0.1 0.1 0.1 0.1 182 Table D.24. Non-Structural Damage Probability Matrices for R M L R CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 68.2 61.0 59.4 45.1 37.9 33.8 30.1 2.0 7.7 8.9 9.1 10.5 10.8 10.8 10.6 10.0 9.8 11.5 11.9 14.7 15.7 16.1 16.4 50.0 7.0 8.2 8.5 10.2 10.8 10.9 10.9 80.0 7.3 10.4 11.1 19.4 24.8 28.4 32.0 Acceleration-sensitive components 0.0 74.4 43.4 41.4 25.7 19.4 16.9 14.7 2.0 21.1 37.3 37.8 38.8 36.9 35.6 34.1 10.0 4.1 16.5 17.6 27.5 32.1 33.9 35.4 50.0 0.3 2.7 3.0 7.3 10.4 12.0 13.7 80.0 0.0 0.2 0.2 0.7 1.3 1.7 2.1 Building Contents 0.0 74.4 43.4 41.4 25.7 19.4 16.9 14.7 1.0 21.1 37.3 37.8 38.8 36.9 35.6 34.1 5.0 4.1 16.5 17.6 27.5 32.1 33.9 35.4 25.0 0.3 2.7 3.0 7.3 10.4 12.0 13.7 40.0 0.0 0.2 0.2 0.7 1.3 1.7 2.1 Table D.25. Non-Structural Damage Probability Matrices for R M M R CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 76.6 66.2 65.3 55.3 49.1 44.3 40.6 2.0 9.2 11.3 11.4 12.4 12.6 12.6 12.4 10.0 8.9 12.8 13.1 16.4 18.1 19.2 19.9 50.0 0.5 1.5 1.6 3.1 4.2 5.1 6.0 80.0 4.8 8.2 8.6 12.8 16.0 18.8 21.2 Acceleration-sensitive components 0.0 90.2 60.3 55.0 41.2 32.3 26.6 23.0 2.0 9.0 31.0 33.8 39.0 40.3 40.0 39.2 10.0 0.7 7.8 9.8 16.5 22.0 26.0 28.7 50.0 0.0 1.0 1.4 3.0 5.0 6.8 8,3 80.0 0.0 0.0 0.1 0.2 0.4 0.7 0.9 Building Contents 0.0 90.2 60.3 55.0 41.2 32.3 26.6 23.0 1.0 9.0 31.0 33.8 39.0 40.3 40.0 39.2 5.0 0.7 7.8 9.8 16.5 22.0 26.0 28.7 25.0 0.0 1.0 1.4 3.0 5.0 6.8 8.3 40.0 0.0 0.0 0.1 0.2 0.4 0.7 0.9 183 Table D.26. Non-Structural Damage Probability Matrices for U R M L R CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 64.5 47.7 45.2 32.2 33.7 29.1 26.1 2.0 7.9 9.7 9.9 10.0 10.1 9.9 9.7 10.0 10.9 14.1 14.5 15.5 15.5 15.6 15.5 50.0 8.3 10.7 10.9 11.2 11.2 11.0 10.8 80.0 8.4 17.8 19.6 31.0 29.5 34.4 37.9 Acceleration-sensitive components 0.0 56.2 32.9 31.0 20.5 17.3 15.4 15.4 2.0 32.9 39.8 39.8 37.6 35.9 34.6 34.6 10.0 9.9 22.5 23.8 31.7 34.3 35.7 35.7 50.0 1.0 4.4 4.9 9.2 11.3 12.7 12.7 80.0 0.0 0.3 0.4 1.0 1.3 1.6 1.6 Building Contents 0.0 56.2 32.9 31.0 20.5 17.3 15.4 15.4 1.0 32.9 39.8 39.8 37.6 35.9 34.6 34.6 5.0 9.9 22.5 23.8 31.7 34.3 35.7 35.7 25.0 1.0 4.4 4.9 9.2 11.3 12.7 12.7 40.0 0.0 0.3 0.4 1.0 1.3 1.6 1.6 Table D.27. Non-Structural Damage Probability Matrices for U R M M R CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 72.2 58.4 57.6 52.2 45.2 39.7 35.9 2.0 10.1 11.7 11.7 11.8 11.6 11.2 10.7 10.0 8.3 12.8 13.0 14.6 16.3 17.5 18.2 50.0 2.7 4.8 4.9 5.8 6.9 7.8 8.5 80.0 6.6 12.4 12.8 15.7 19.9 23.8 26.8 Acceleration-sensitive components 0.0 82.5 50.0 36.4 19.1 15.8 13.9 13.9 2.0 15.0 35.3 39.8 38.9 37.3 36.1 36.1 10.0 2.4 12.9 19.9 31.5 33.9 35.3 35.3 50.0 0.1 1.7 3.7 9.5 11.5 12.9 12.9 80.0 0.0 0.1 0.2 1.1 1.5 1.8 1.8 Building Contents 0.0 82.5 50.0 36.4 19.1 15.8 13.9 13.9 1.0 15.0 35.3 39.8 38.9 37.3 36.1 36.1 5.0 2.4 12.9 19.9 31.5 33.9 35.3 35.3 25.0 0.1 1.7 3.7 9.5 11.5 12.9 12.9 40.0 0.0 0.1 0.2 1.1 1.5 1.8 1.8 184 Table D.28. Non-Structural Damage Probability Matrices for T U CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 66.4 57.0 55.3 41.4 33.5 28.8 25.9 2.0 8.7 10.1 10.3 11.4 11.4 11.1 10.9 10.0 10.6 13.0 13.4 16.1 17.2 17.5 17.6 50.0 4.4 5.8 6.0 7.9 8.9 9.4 9.6 80.0 9.9 14.1 15.0 23.2 29.1 33.2 36.0 Acceleration-sensitive components 0.0 68.5 50.0 43.4 24.5 16.9 12.9 12.3 2.0 25.1 35.0 37.3 38.6 35.6 32.6 32.0 10.0 5.9 13.3 16.7 28.7 34.3 37.0 37.4 50.0 0.5 1.7 2.5 7.5 11.8 15.2 15.7 80.0 0.0 0.1 0.1 0.7 1.5 2.4 2.5 Building Contents 0.0 68.5 50.0 43.4 24.5 16.9 12.9 12.3 1.0 25.1 35.0 37.3 38.6 35.6 32.6 32.0 5.0 5.9 13.3 16.7 28.7 34.3 37.0 37.4 25.0 0.5 1.7 2.5 7.5 11.8 15.2 15.7 40.0 0.0 0.1 0.1 0.7 1.5 2.4 2.5 Table D.29. Non-Structural Damage Probability Matrices for P C L R CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 69.5 53.1 52.1 42.8 36.5 31.8 28.4 2.0 7.5 9.9 10.0 10.6 10.8 10.7 10.5 10.0 10.5 14.3 14.5 15.9 16.5 16.7 16.7 50.0 7.2 10.3 10.5 11.6 12.0 12.1 12.0 80.0 5.3 12.4 13.0 19.1 24.3 28.8 32.4 Acceleration-sensitive components 0.0 72.1 55.0 52.5 32.1 27.6 26.3 23.8 2.0 22.8 33.0 34.2 40.0 40.0 39.8 39.4 10.0 4.8 10.8 11.9 23.1 26.1 27.0 28.8 50.0 0.3 1.1 1.4 4.5 5.8 6.3 7.3 80.0 0.0 0.0 0.1 0.3 0.5 0.5 0.7 Building Contents 0.0 72.1 55.0 52.5 32.1 27.6 26.3 23.8 1.0 22.8 33.0 34.2 40.0 40.0 39.8 39.4 5.0 4.8 10.8 11.9 23.1 26.1 27.0 28.8 25.0 0.3 1.1 1.4 4.5 5.8 6.3 7.3 40.0 0.0 0.0 0.1 0.3 0.5 0.5 0.7 185 Table D.30. Non-Structural Damage Probability Matrices for P C M R CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 78.2 63.3 62.5 53.9 46.9 42.4 36.2 2.0 8.8 11.8 11.9 12.7 12.9 12.9 12.5 10.0 6.4 11.3 11.6 14.3 16.3 17.5 19.0 50.0 1.7 3.6 3.8 5.0 6.1 6.9 8.0 80.0 4.9 10.0 10.3 14.1 17.6 20.3 24.4 Acceleration-sensitive components 0.0 89.7 63.4 60.6 47.6 41.0 37.0 33.5 2.0 9.3 28.6 30.3 36.7 38.9 39.9 40.4 10.0 1.0 7.3 8.3 13.8 17.3 19.5 21.7 50.0 0.0 0.6 0.8 1.8 2.7 3.4 4.1 80.0 0.0 0.0 0.0 0.1 0.1 0.2 0.3 Building Contents 0.0 89.7 63.4 60.6 47.6 41.0 37.0 33.5 1.0 9.3 28.6 30.3 36.7 38.9 39.9 40.4 5.0 1.0 7.3 8.3 13.8 17.3 19.5 21.7 25.0 0.0 0.6 0.8 1.8 2.7 3.4 4.1 40.0 0.0 0.0 0.0 0.1 0.1 0.2 0.3 Table D.31. Non-Structural Damage Probability Matrices for M H CDF (%) Damage Probability (%) at MMI: VI VII VIII IX X XI XII Displacement-sensitive components 0.0 62.5 44.6 43.7 33.3 27.1 23.5 17.6 2.0 8.4 10.8 10.9 11.3 11.2 10.9 10.1 10.0 12.2 15.6 15.7 16.7 16.8 16.6 15.9 50.0 8.7 11.4 11.5 12.1 11.9 11.6 10.7 80.0 8.1 17.7 18.3 26.7 33.0 37.3 45.7 Acceleration-sensitive components 0.0 75.4 57.8 55.1 43.1 41.0 39.0 39.0 2.0 20.2 31.2 32.6 37.6 38.2 38.8 38.8 10.0 4.1 9.8 10.9 16.5 17.6 18.7 18.7 50.0 0.3 1.1 1.4 2.7 3.0 3.4 3.4 80.0 0.0 0.0 0.1 0.2 0.2 0.2 0.2 Building Contents 0.0 75.4 57.8 55.1 43.1 41.0 39.0 39.0 1.0 20.2 31.2 32.6 37.6 38.2 38.8 38.8 5.0 4.1 9.8 10.9 16.5 17.6 18.7 18.7 25.0 0.3 1.1 1.4 2.7 3.0 3.4 3.4 40.0 0.0 0.0 0.1 0.2 0.2 0.2 0.2 186 A P P E N D I X E . B U I L D I N G I N V E N T O R Y F O R M S The building inventory form used in the sidewalk surveys is presented in Table E. 1. The critical information that needs to be filled in includes the street address, primary use, the age of building (the year it was built), footprint area, number of stories, and the building prototype. Other useful information also queried in the inventory form includes shape, primary use, presence of storefront and retrofit, possibility of pounding, adjacent building prototypes, soil type. There is further space for a photo to be attached and additional comments to be filled in. A large portion of the commercial areas and downtown area in Vancouver were surveyed using this form including photographs in most cases. These forms were individually scanned and stored on CD-ROMs. To compile data on structural types in Victoria and the mainly residential areas of Vancouver, a more compact version of this sheet was used without the photograph section and the list of prototypes (Table E.2). This way, information on five buildings could fit on one page. In Vancouver and Victoria, some single-family houses were merely marked on the map as WLFR without filling out these forms, in order to speed up the data collection in the predominantly residential areas. 187 Table E. 1. Sample Building Inventory Form Building Inventory Form Reviewer Adress: Postal Code: Date: Building Name: Zone: Primary Use: Photo: Number of Stories: Year Built: Footprint Area: Shape: Rect L T E C Z Other Storefront: Y N Wood WLFR Wood Light Frame Residential Pounding: Y N WLFCI Wood Light Frame Commercial/Inst. Retrofit: Y N WLFLR Wood Light Frame Low Rise Adjacent Building Types: WPB Wood Post and Beam Soil Type: Steel LMF Light Metal Frame Photo/Sketch: SMFLR Steel Moment Frame Low Rise SMFMR Steel Moment Frame Mid Rise SMFHR Steel Moment Frame High Rise SBFLR Steel Braced Frame Low Rise SBFMR Steel Braced Frame Mid Rise SBFHR Steel Braced Frame High Rise SFCWLR Steel Frame Concrete Walls Low Rise SFCWMR Steel Frame Concrete Walls Mid Rise SFCWHR Steel Frame Concrete Walls High Rise SFCI Steel Frame Concrete Infdl Walls SFMI Steel Frame Masonry Infdl Walls Concrete CFLR Concrete Frame Concrete Walls Low Rise CFMR Concrete Frame Concrete Walls Mid Rise CFHR Concrete Frame Concrete Walls High Rise RCMFLR Reinf. Concrete Moment Frame Low Rise RCMFM Reinf. Concrete Moment Frame Mid Rise RCMFHR Reinf. Concrete Moment Frame High Rise RCFIW Reinf. Concrete Frame with Infdl Walls Masonry RMLR Reinforced Masonry Shear Wall Low Rise RMMR Reinforced Masonry Shear Wall Mid Rise URMLR Unreinf. 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