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Methodology for the seismic risk assessment of low-rise school buildings in British Columbia Pina, Freddy E. 2010

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  METHODOLOGY  FOR  THE  SEISMIC  RISK ASSESSMENT  OF  LOW-RISE  SCHOOL BUILDINGS IN  BRITISH  COLUMBIA  by FREDDY E. PINA B.Sc. (Civil Engineering), Universidad de Santiago de Chile, 2000 M.A.Sc. (Civil Engineering/Structural Engineering), Carleton University, 2006    A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF   DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Civil Engineering)    The University of British Columbia (Vancouver) December 2010 © Freddy E. Pina, 2010 - ii - ABSTRACT This thesis presents a methodology for the seismic risk assessment and risk reduction of schools in British Columbia.  The methodology permits school buildings to be ranked by risk levels, and includes information that allows designers to establish the seismic capacity of school buildings and to select appropriate retrofit options.  This research includes the treatment of seismic hazard in the province by reference to different types of earthquakes that affect the region, and the development of an extensive database of structural performance of typical school buildings for different types of earthquakes and levels of shaking.  The seismic hazard in the province is due to crustal, subcrustal and subduction earthquakes.  The ground motion characteristics and the rates of occurrences of these different types of earthquakes are sufficiently different that it justifies assessing their effects separately in the risk calculations. The results of probabilistic seismic hazard analyses have been combined with incremental nonlinear dynamic analyses of a variety of structural systems subjected to the three earthquake types.  A suite of thirty ground motions representative of these earthquakes has been used for the calculation of seismic risk.  This process resulted in a large database of response of structural systems on different types of soils.  The database was developed first for systems on firm soils (Site Class C).  To account for soft soils (Site Class D) a simplified procedure was developed to convert structural performance on Class C sites to that on Class D sites. This thesis presents information that contributes to the state of knowledge in seismic risk in two forms: research and engineering practice.  It provides a better understanding of - iii - how the risk in a region can be deaggregated according to the earthquake types, how representative ground motions for each earthquake type can be selected, and how the site conditions can be incorporated in probabilistic risk assessment.  The contribution to engineering practice is the development of a ready-to-use methodology for risk assessment and for determining whether or not a retrofit is required for a giving type of structure on a certain type of soil and in a given seismic region.   Table of Contents - iv - TABLE OF CONTENTS Abstract.................................................................................................................................... ii Table of Contents ................................................................................................................... iv List of Tables ........................................................................................................................ viii List of Figures......................................................................................................................... ix List of Programs.................................................................................................................... xii Acknowledgements .............................................................................................................. xiii Dedication ............................................................................................................................ xvii Co-Authorship Statement ................................................................................................. xviii Chapter 1. Introduction......................................................................................................1 1.1. The Seismic Risk Of British Columbia Schools Under Earthquakes........................1 1.1.1 Worldwide context .................................................................................................1 1.1.2 Potential seismic risk of damage to British Columbia schools .............................2 1.1.3 Community motivated action .................................................................................3 1.2. Background................................................................................................................5 1.2.1 Worldwide seismic risk mitigation programs in schools .......................................5 1.2.2 Methodologies for seismic risk assessment ...........................................................9 1.2.3 Current researches ..............................................................................................14 1.3. A Method Suitable for BC Schools .........................................................................17 1.3.1 Deaggregated hazard by earthquake type ...........................................................17 1.3.2 Site conditions......................................................................................................20 1.3.3 Practical implementation of the methodology .....................................................21 1.4. Objectives and Scope...............................................................................................22 1.4.1 Research objective ...............................................................................................23 1.4.2 Engineering practice objective ............................................................................23 1.4.3 Scope....................................................................................................................23 1.5. Organization of Thesis.............................................................................................24 1.5.1 Chapter 2 .............................................................................................................24 1.5.2 Chapter 3 .............................................................................................................25 1.5.3 Chapter 4 .............................................................................................................25 1.5.4 Appendices ...........................................................................................................25 1.6. References................................................................................................................30 Chapter 2. Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia.................................................................................................36  Table of Contents - v - 2.1. Introduction..............................................................................................................36 2.2. Risk of Damage .......................................................................................................37 2.2.1 Damage for BC school buildings.........................................................................37 2.2.2 Risk formulation...................................................................................................38 2.3. Risk of Damage Calculation Procedure...................................................................40 2.3.1 Step 1 – Buildings ................................................................................................41 2.3.2 Step 2 – Seismic hazard calculations...................................................................43 2.3.3 Step 3 – Ground motion records..........................................................................44 2.3.4 Step 4 – Incremental dynamic analyses...............................................................45 2.3.5 Step 5 – Conditional probabilities .......................................................................46 2.3.6 Step 6 – Probability of drift exceedance, PDE ....................................................46 2.4. PDE Calculation for a School Building System ......................................................47 2.4.1 Step 1 – Buildings ................................................................................................47 2.4.2 Step 2 – Seismic hazard calculations...................................................................51 2.4.3 Step 3 - Ground motion records ..........................................................................54 2.4.4 Step 4 – Incremental dynamic analyses...............................................................58 2.4.5 Step 5 – Conditional probabilities .......................................................................59 2.4.6 Step 6 – PDE........................................................................................................60 2.5. Considerations for the School Project .....................................................................62 2.5.1 Limits on PDE......................................................................................................62 2.5.2 Required lateral resistance..................................................................................63 2.5.3 Deaggregated risk per earthquake type...............................................................65 2.5.4 Site conditions......................................................................................................66 2.5.5 Generation of database........................................................................................66 2.5.6 User interface ......................................................................................................67 2.6. Conclusions..............................................................................................................69 2.7. References................................................................................................................86 Chapter 3. Seismic Risk Assessment Methodology for British Columbia Schools Located on Site Class D Soils ................................................................................................90 3.1. Introduction..............................................................................................................90 3.2. SRA Procedure for Site Class C ..............................................................................92 3.3. Equivalent Intensity Factor......................................................................................93 3.4. Site Response Analysis............................................................................................94 3.4.1 Site description ....................................................................................................94 3.4.2 Modeling and numerical processing....................................................................94 3.4.3 Results..................................................................................................................95 3.4.4 Observations ........................................................................................................95 3.5. Structural Analysis...................................................................................................96 3.6. EIF Calculation ........................................................................................................97 3.6.1 EIF Results...........................................................................................................98 3.6.2 Recommended EIFs .............................................................................................99 3.6.3 Proposed EIF equation........................................................................................99 3.7. Application.............................................................................................................101  Table of Contents - vi - 3.8. Summary and Conclusions ....................................................................................102 3.9. References..............................................................................................................116 Chapter 4. Conclusions and Future Work....................................................................118 4.1. Summary of Contributions.....................................................................................118 4.1.1 Research contributions ......................................................................................118 4.1.2 Engineering practice contributions ...................................................................120 4.2. Future Work...........................................................................................................122 4.3. References..............................................................................................................125 Appendix A. The Batching Process in the School Project ..........................................126 A.1. Background............................................................................................................126 A.2. The Need for a Batching Process...........................................................................128 A.3. What’s a Batching Process?...................................................................................129 A.4. Basic Tools for an Efficient Batching Process ......................................................130 A.5. Automatic Process for Calculating Risk................................................................131 A.5.1 Multiple input files .............................................................................................131 A.5.2 Batch process.....................................................................................................133 A.5.3 Post-processing..................................................................................................133 A.6. References..............................................................................................................146 Appendix B. The Parameters Involved in the School Project....................................147 B.1. Summary of Parameters.........................................................................................147 B.2. Prototypes ..............................................................................................................147 B.2.1 Lateral deformation resistance systems, LDRSs................................................147 B.2.2 Walls rocking out-of-plane ................................................................................149 B.2.3 Diaphragms .......................................................................................................150 B.3. Inter-Storey Height ................................................................................................150 B.4. Type of Earthquake................................................................................................150 B.5. Seismic Source Models..........................................................................................150 B.6. Location .................................................................................................................151 B.7. Seismicity Level ....................................................................................................151 B.8. Resistance Values ..................................................................................................152 B.9. Intensities or Levels of Shaking.............................................................................153 B.10. Rigidity ..................................................................................................................153 B.11. Site Condition ........................................................................................................154 B.12. References..............................................................................................................157 Appendix C. Detailed Information of Selected Records .............................................158 C.1. Crustal Earthquake Records...................................................................................158 C.1.1 Time histories.....................................................................................................159 C.1.2 Spectra (5% damping) .......................................................................................163 C.1.3 Scaled spectra (5% damping) ............................................................................171 C.2. Subcrustal Earthquake Records .............................................................................172  Table of Contents - vii - C.2.1 Time histories.....................................................................................................173 C.2.2 Spectra (5% damping) .......................................................................................177 C.2.3 Scaled spectra (5% damping) ............................................................................183 C.3. Subduction Earthquake Records............................................................................184 C.3.1 Time histories.....................................................................................................185 C.3.2 Spectra (5% damping) .......................................................................................189 C.3.3 Scaled spectra (5% damping) ............................................................................196 C.4. References..............................................................................................................197 Appendix D. Description of Sites and Soil Columns ...................................................198 D.1. Site 1 - Mount Douglas Secondary School............................................................198 D.1.1 Soil column A:....................................................................................................199 D.1.2 Soil column B .....................................................................................................199 D.2. Site 2 - Margaret Jenkins Elementary School........................................................200 D.2.1 Soil column A .....................................................................................................201 D.2.2 Soil column B .....................................................................................................201 D.3. Site 3 - Lincoln Park Elementary School...............................................................202 D.3.1 Soil column A .....................................................................................................203 D.3.2 Soil column B .....................................................................................................204 D.4. Site 4 - Langley Fine Arts School..........................................................................205 D.4.1 Soil column A .....................................................................................................206 D.4.2 Soil column B .....................................................................................................207 D.5. Site 5 - James Park Elementary School .................................................................208 D.5.1 Soil column A .....................................................................................................209 D.5.2 Soil column B .....................................................................................................209 D.5.3 Soil Column C....................................................................................................210 D.6. References..............................................................................................................211   List of Tables - viii - LIST OF TABLES Table 2.1:  Ranges of moment magnitude, depth and hypocentral distance for the preliminary selection of recording stations of crustal, subcrustal and subduction earthquakes..........71 Table 2.2:  Summary of earthquakes and number of stations searched for the selection of records..............................................................................................................................72 Table 2.3:  Summary of selected records for Vancouver in Site Class C soils grouped by earthquake type ................................................................................................................73 Table 2.4:  Results of calculation process of seismic risk to the W2-10%W prototype for the crustal earthquake suite of motions .................................................................................74 Table 3.1:  Coefficients for calculating EIF with Equation (3.1) ..........................................104 Table B.1: Seismicity given by the PSV*ratio of BC communities included in the seismic risk assessment program for BC schools classified by type of earthquake and seismic source model ..................................................................................................................155   List of Figures - ix - LIST OF FIGURES Figure 1.1: Distribution of earthquakes that occurred in the last 50 years associated with extensive damage in school building grouped by the time of occurrence, during or outside school sessions.  Selected facts from some earthquakes are also displayed .......27 Figure 1.2: Magnitude-recurrence curves for the GSC (shallow) earthquakes, the PUG (deep) earthquakes and the USGS deep earthquakes (Natural Resources Canada, available at: http://earthquakescanada.nrcan.gc.ca/hazard/inslab2000/)..............................................28 Figure 1.3: Seismic hazard curves deaggregated per earthquake type (Crustal, Subcrustal and Subduction) prorated in 50 years for the cities of Vancouver and Victoria (reproduced from Ventura et al. 2010). Design refers to the Uniform Hazard Spectrum in the NBCC 2005. ................................................................................................................................29 Figure 2.1:  Cascadia Subduction Zone showing crustal earthquakes in North America plate; subcrustal earthquakes in Juan de Fuca plate and subduction earthquakes. (Cascadia_earthquake.jpeg is a courtesy of the U.S. Geological Survey. The USGS home page is http://www.usgs.gov).................................................................................75 Figure 2.2:  Generic IDA curves for four earthquake records and the distribution of drift dr at a given intensity ...............................................................................................................75 Figure 2.3:  Proposed calculation procedure of the probability of drift exceedance, PDE......76 Figure 2.4:  Lay-out and details of plan and elevation of an unblocked plywood shearwall in the classroom section of an existing BC school building ................................................77 Figure 2.5:  (a) Representation of the 2-storey example school building and (b) modeling for nonlinear dynamic analysis including the (c) backbone curve and (d) hysteretic rule of the unblocked plywood shearwall system .......................................................................78 Figure 2.6:  Distribution of elastic and effective (equivalent inelastic) periods of a representative sample of low-rise wood-frame school building systems in BC..............79 Figure 2.7:  Annual frequencies of level of shaking (a) exceedance and (b) occurrence of crustal subcrustal and subduction earthquakes for Vancouver........................................80 Figure 2.8:  Spectral pseudo-velocities for each earthquake type and for the UHS of a Site Class C in Vancouver (5%-damping) ..............................................................................81 Figure 2.9:  Spectral 5%-damping pseudo-velocities of selected/modified records and target hazard spectra for crustal, subcrustal and subduction earthquakes .................................82  List of Figures - x - Figure 2.10:  Median IDA curves for a plywood shear-wall 2-storey building with a lateral resistance of 10%W, W2-10%W, located in Vancouver..................................................83 Figure 2.11:  Distribution of probabilities of 4% drift exceedance of the W2-10%W system located in Vancouver for crustal, subcrustal and subduction earthquake motions for a range of incremental intensities .......................................................................................83 Figure 2.12:  Annual frequencies of drift exceedance of a plywood shear wall system, W2, located in Vancouver .......................................................................................................84 Figure 2.13:  (a) Hysteretic rule and (b) annual frequencies of drift exceedance of a reinforced concrete shear wall system, C1, located in Vancouver ..................................84 Figure 2.14:  Preliminary seismic performance calculator snapshots of 4 options for LDRSs: a) Basic Risk Assessment, b) Detailed Risk Assessment, c) Basic Retrofit and d) Detailed Retrofit ..............................................................................................................85 Figure 3.1: Calculation process of the Equivalent Intensity Factor, EIF, for a Site Class D site, for a given i-th intensity of the j-th record .............................................................105 Figure 3.2: Distribution of shear wave velocities in the 11 soil columns of school sites......106 Figure 3.3: Distribution of the amplification of median maximum accelerations of 11 soil columns for the 100% motion intensity of crustal, subcrustal and subduction earthquakes ....................................................................................................................107 Figure 3.4: Distribution of the median pseudo-velocity spectra of 11 soil columns for the 100% motion intensity of crustal, subcrustal and subduction earthquakes ...................108 Figure 3.5: Amplification factor of the average pseudo-velocity spectra in the 1 to 2 second period, PSV*1-2, range for 11 soil columns of crustal, subcrustal and subduction earthquake motions ........................................................................................................109 Figure 3.6: (a) Representation of a 2-storey building, (b) corresponding model for NDA and (c) hysteretic rules of 3 systems (W2, C1 and R1) ........................................................110 Figure 3.7: 84-th percentile of log-normally distributed median EIFs for the W2, C1 and R1 systems, for different drift values and for the crustal, subcrustal and subduction earthquake motions ........................................................................................................111 Figure 3.8:  Calculated (Calc) and predicted (Pred) EIF values for the W2 structural systems, for different drift values and for the crustal (CR), subcrustal (SCR) and subduction (SD) earthquakes ....................................................................................................................112  List of Figures - xi - Figure 3.9:  Calculated (Calc) and predicted (Pred) EIF values for the C1 structural systems, for different drift values and for the crustal (CR), subcrustal (SCR) and subduction (SD) earthquakes ....................................................................................................................113 Figure 3.10:  Calculated (Calc) and predicted (Pred) EIF values for the R1 structural systems, for different drift values and for the crustal (CR), subcrustal (SCR) and subduction (SD) earthquakes ....................................................................................................................114 Figure 3.11: Site Class D IDA curves calculated from existing Site Class C IDA curves using the proposed EIF values of the W2 system for crustal, subcrustal and subduction earthquakes ....................................................................................................................115 Figure A.1: Example of a Resistance Table extracted from the Second Editions of the BG (APEGBC 2006) for an unblocked plywood system located in Vancouver, BC. .........135 Figure A.2:  Overall automatic process for calculating the risk in the Schools Project. .......136  List of Programs - xii - LIST OF PROGRAMS Program A.1:  WinBatch program that automatize the process of opening CANNY, opening an input file, running and closing CANNY. ..................................................................137 Program A.2:  MATLAB program for the multiple creations of CANNY input files. .........138 Program A.3:  WinBatch program that automatize the process of running CANNY multiple times and storing massive output data. ..........................................................................142 Program A.4:  MATLAB program for extracting drift information from CANNY output data. .......................................................................................................................................145   Acknowledgements - xiii - ACKNOWLEDGEMENTS The first person that I would like to express my deepest gratitude to is my supervisor, Professor Carlos E. Ventura.  His support, not only on technical aspects, but also in personal and family matters, makes Dr. Ventura a great professional and a wonderful person.  I was fortunate to work with him and acquire relevant experience that he is always willing to offer to both his colleagues and his students.  Dr. Ventura is passionate about the beautiful science and related fields of Earthquake Engineering.  His enthusiasm for researching and teaching radiates to everyone and makes the learning journey just fascinating.  I hope to keep working with Dr. Ventura for many years to come and pass to my future students the knowledge with the same energy that he displays in his daily work. Gracias Professor! I want to take this opportunity to also express my sincere words of respect and appreciation to Dr. Graham Taylor, a great mentor on the practice of Structural Engineering. We may have some differences on the way we look at some issues within this engineering specialty, but I’m absolutely convinced that from every meeting, argument and talk I got new and thoughtful ideas from him.  The way he sees the engineering practice goes beyond my capabilities and how he transforms research into an efficient tool for engineers is masterful.  I am very thankful to Graham for all his technical support, his politeness, his generosity on sharing his precious ideas and for the motivation on many research aspects that pushed me always to the limit of my knowledge.  Thank you Graham! There is another great figure from the Department of Civil Engineering at UBC that I would like to thank.  He is not only a well-known and distinguished researcher and professor,  Acknowledgements - xiv - but for those of you that have not had the chance to share meetings and time with him I have to tell you that he is also a great human being.  I’m really thankful to Professor Liam Finn for spending precious time from his daily tasks to give me advice, allowing me to participate in his classes, on sharing his knowledge on seismology and on geotechnical engineering with me, and caring many times about me and my family.  I thank Dr. Finn for helping me on improving my writing skills, for assisting me on getting my papers ready for submission, and for his insightful feedback on this research work. Special thanks are due to Professors Ricardo Foschi, Ken Elwood and Steven Kuan for their guidance on technical aspects they provided me during my research work at UBC.  I would like also to thank Dr. Armin Bebamzadeh, Juan Carlos Carvajal, Bishnu Pandey, Jose Centeno and Manuel Archila for helping me on key aspects and tasks during the time I was directly involved in the school project.  Many thanks also to Mr. Felix Yao for his technical support in this project. My research work was in partly funded by the Natural Sciences and Engineering Research Council of Canada, NSERC, and the Ministry of Education of British Columbia through the Association of Professional Engineers and Geoscientists of British Columbia, APEGBC, and the Department of Civil Engineering at UBC.  I would like to thank these institutions for their valuable economic support. I am very thankful to my employer, the University of Santiago of Chile (USACH), who gave me the opportunity to study in a multi-cultural country, such as Canada, and at a prestigious institution, such as The University of British Columbia.  My sincere thanks for  Acknowledgements - xv - the financial and logistic support that many faculty and staff members at the USACH gave me during my studies in Canada. Special thanks are due to these wonderful persons that my family and I have had the chance to meet in our lives, Elsa Pelcastre, Hugon Juarez and Mike Bodnar. I wish them all the best in their lives.  I could repeat myself here from other acknowledgements, but these words truly reflect my feelings of gratitude to them: I think that there are some people for whom we do not have enough words to define “acknowledgements” or to express our gratitude.  These types of persons are Elsa, Hugon and Mike. “Gracias por todo Elsa y Hugon” and “Thanks for everything Mike”. Several other friends have joined me in academic and social activities during these last four years in Vancouver.  They have made myself and my family feel at home and enjoy every single day in Canada.  Among many of them I would like to particularly thank: Joanne, Jose, Juan Carlos, Otton, Kate, Bishnu, Indira, Pascale, Manuel, Seku and the extended latin- american community at Acadia Park in UBC.  I thank them all and many others not-listed here for being such a wonderful people and for sharing their precious time with Claudia, Matias and myself.  My sincere apologies to those of you that I could not include in these acknowledgements.  I truly believe that another document would be needed to thank properly everyone that has supported me and joined me in this journey. I wish to express my deepest appreciation to my parents and sisters for their unconditional love, patience, support and for demonstrating all the virtues that one can find in a “perfect” family.  The logistic support of my family in Chile was invaluable during my  Acknowledgements - xvi - long stay in Canada.  I am counting the days for our reunion in Chile to reciprocate all that they have given me. Written words would never be enough to express my gratitude to my partner, Claudia. Claudia and I have been beautifully rewarded during our stay in Vancouver with the coming of the most precious treasure that we could have asked for, our son Matias.  Certainly, the PhD and my research work had to be placed in a different level of my priorities, but that change was totally worth it.  It focused me on my work and on getting things done with a different perspective.  The school project all of a sudden became a personal issue and earthquake tragedies around the world were observed from rather a social than a technical point of view.  Claudia and Matias have motivated me to keep working on spreading the word on making buildings safer from earthquakes and to make people aware of the effects of earthquakes on society, which I think, is the basic motivation for any research work in this field.  I’m deeply thankful to Claudia and Matias for sharing and sacrificing their precious time with me and for being part of this marvelous learning process.    Dedication - xvii - DEDICATION This work was intended to be solely dedicated to Claudia and Matías, but I hope that they agree upon sharing this dedication with all of our countrymen and countrywomen who struggled with the February 27, 2010, earthquake in Chile, and who are now suffering the post-earthquake consequences of such a devastating event.  I do not expect to alleviate any suffering of this terrible event in Chile, but I wish that this document serves to help us build a more prepared and resilient society in the near future. To all of you who were in Chile during that earthquake, who had to run to the hills, are now sleeping in tents, are struggling with the rain and cold weather, do not have proper shelter, are thinking about the future, are afraid of more shakings, are psychologically affected and are feeling helpless…I dedicate my research work. FUERZA CHILE!    Co-Authorship Statement - xviii - CO-AUTHORSHIP STATEMENT The main body of this thesis consists of two papers that will be submitted for journal revision that are described in chapters 2 and 3 each.  These two papers present an innovative methodology for assessing the risk of school buildings in British Columbia to seismic damage.  All of this was in close collaboration with my co-authors: Dr. Carlos Ventura, Dr. Graham Taylor and Dr. Liam Finn.  I conducted all the studies related to selection of ground motions, developed and implemented the methodology, carried out all the analyses, and prepared all the basic routines for risk calculations.  I drafted the initial versions of the papers and finalized them in an iterative process with inputs from my co-authors.  Chapters 1 and 4, and the appendices of this thesis were written in their entirety by me.   Chapter 1: Introduction - 1 - Chapter 1. INTRODUCTION 1.1. THE SEISMIC RISK OF BRITISH COLUMBIA SCHOOLS UNDER EARTHQUAKES 1.1.1 Worldwide context For many years earthquakes have caused extensive damage or collapse of school buildings, which in many cases have resulted in severe injuries and deaths of thousands of children around the globe.  At least 40 of these earthquakes have occurred during the last 50 years.  Figure 1.1 shows the distribution of some of the most destructive earthquakes that have affected school buildings grouped by the time of occurrence (during or outside school session).  The figure includes earthquakes since the 1930s.  The number of casualties in school buildings is always associated with whether or not the schools were in session.  But, regardless of this, the number of schools heavily damaged or collapsed was very high.  These numbers are still unacceptable by society at large, and many communities are now expressing concerns that governments and institutions are not doing enough to protect the occupants of schools buildings.  Some of these questions are: why have so many schools (and why schools?) collapsed during earthquakes?; how safe are schools in our communities?; and what risk will our children and teachers be exposed to in schools regarding future earthquakes?  To provide the answer to these questions, authorities, engineers and research communities of many earthquake prone regions need to work together in order to develop  Chapter 1: Introduction - 2 - technology and policies for the construction of new school buildings, and for the evaluation and retrofit of existing school buildings. 1.1.2 Potential seismic risk of damage to British Columbia schools More than 70% of schools in British Columbia (BC) are located within or very close to the Cascadia subduction zone in the southwest corner of the province.  The seismic hazard in this part of BC is mainly dominated by shallow continental, deep continental and subduction earthquakes (Ristau 2004).  These three types of earthquakes can potentially trigger excessive deformations in school buildings, leading to excessive structural and non-structural damage or collapse. School buildings in BC are generally one to three story buildings sectioned in blocks, e.g., classrooms, gymnasiums and offices.  The main structure of most schools consists of wood shear walls with plywood sheathing or reinforced concrete walls and columns connected by either wood or reinforced concrete diaphragms.  Many non-structural elements, such as heavy partition walls of concrete masonry and shelves, are also common inside schools.  Unfortunately, most of these schools were built when requirements for earthquake loading on structural and non-structural elements were minimal or non-existent. More than 30% of BC schools in high-to-moderate seismicity zones were built on soft soil sites.  These soils can amplify earthquake shaking and consequently increase the damage to school buildings.  These schools are certainly at more risk to earthquake damage than those at firm soil sites and may require particular attention.  Chapter 1: Introduction - 3 - Seismic hazard, old construction and soft soil site conditions are clear indications of observing extreme damage or collapse of many school buildings in BC in the event of an earthquake.  The occurrence of an earthquake in British Columbia within school hours could claim the lives of hundreds of children and teachers.  Repair and reconstruction processes can be painful and costly to many communities, having a devastating effect on both local (provincial) and national (federal) economies. 1.1.3 Community motivated action In 1989, a consulting structural engineer assessed the structural integrity of each school building in Vancouver and implemented a ranking system to identify the most vulnerable school buildings to earthquakes.  Around 290 schools (30% of buildings assessed) were classified as high and moderate risk buildings respectively (Angel 1992, TBG 1989).  A cost of CAD$402 million was estimated for the seismic upgrade of Vancouver schools.  After this assessment, the Vancouver School Board received CAD $67.7 million from the provincial government for seismic upgrades.  By 2003, only 10 schools (out of the 290 at-high-risk schools) had been seismically upgraded, due to organizational problems and uncoordinated plans. In 2004, a group of parents in BC concerned about the slow rate of schools upgraded per year, and the potential risk of schools being excessively damaged or collapsing and its consequent effects on children, pushed for more efficient and effective action from the provincial government to assess and retrofit the schools in BC that are most vulnerable to earthquakes (Wisner and Monk, 2005).  In response to this concern, the Ministry of  Chapter 1: Introduction - 4 - Education of British Columbia (MoEBC) carried out a short and general seismic assessment program of the 800 schools (out of 1500 schools) that lie within the high seismic hazard zones to estimate the cost and time for a major upgrade program of schools in the province. As a result of this assessment program, the MoEBC announced a 1.5 billion dollar plan to identify the most at-risk schools in British Columbia and make them earthquake safe by 2020 (Auditor General of British Columbia 2008). One crucial component of the assessment/retrofit program of BC schools was a multi- year development of policies and technical standards for guiding the mitigation program. The objective of these standards was the development of performance-based cost-effective retrofit strategies that reflect life-safety standards. Given the need to commence retrofit construction prior to the completion of the multi- year standards development, a document called the Bridging Guidelines (BG) was developed in 2005 and further improved with a second edition in 2006 (APEGBC 2006).  These guidelines have assisted local engineers more efficiently with their assessment/retrofit projects.  By 2010, more than 100 schools have been seismically upgraded by implementing these guidelines.  Although the rate of retrofitted schools has increased, the associated retrofit costs are still high and, therefore, there was a need to further refine the methodology so that budget can be met.  The methodology presented in this thesis is in response to that need.  Chapter 1: Introduction - 5 - 1.2. BACKGROUND Worldwide programs on seismic risk reduction of schools have been carried out using well developed methodologies for the seismic risk assessment of buildings.  Some of these worldwide programs and methodologies are briefly discussed in the following sections, as well as some recent research on seismic risk assessment methodologies.  The review of these programs and methodologies places this thesis in a global context of the seismic risk assessment field.  The review of recent research sets the body of knowledge for this thesis and the basis for achieving a consistent seismic risk assessment methodology for BC schools. 1.2.1 Worldwide seismic risk mitigation programs in schools There are several seismic risk mitigation programs that are currently being implemented around the world.  Several of the publicly known programs for the seismic risk reduction in schools located in high-to-moderate seismic regions are summarized in this section. Japan After the Kobe earthquake in 1995, the Japanese government, with the support of the engineering community, promulgated the Special Measures Law on Earthquake Disaster Prevention, and commenced a 10 year program for the seismic assessment and/or upgrading of the existing infrastructure throughout the country (Nakano 2004, Nakano and Teshigawara 2007).  This law and other measures have allowed the local governments to increase the number of research programs and to raise the subsidy on seismic mitigation programs. However, surveys conducted in 2002 showed that only 30% of the building inventory had  Chapter 1: Introduction - 6 - been inspected and assessed, and that only 40% of school buildings had been actually upgraded (out of 120,000 schools, approximately).  To overcome this concern, the Japanese government developed a set of guidelines, during 2002 and 2003, for the efficient assessment and upgrading of elementary and secondary schools.  Since then, the guidelines were distributed and a considerable increase in the annual budget was prepared (around CAD$1.2 billion per year).  As a result, 96% of the building inventory was assessed and 62% of the schools were actually upgraded in the next 4 years (during 2003 to 2007).  Currently, the Japanese government is conducting the upgrading of 10,000 at-high-risk schools and has tripled the annual budget to accelerate the seismic risk mitigation program. Venezuela Schools have also been the main attention of both academia and government institutions in Venezuela (Lopez et al. 2007).  After the Cariaco earthquake in 1997, a series of studies on the performance of school buildings was conducted.  A nationwide program was developed in 2006 to both reduce the risk of damage in school buildings and to raise awareness of students and teachers in a future earthquake event.  The program involves the inspection of a sample of 28,000 schools, and was started with a pilot assessment/retrofit program of 10 at- high-risk schools. United States of America The Seattle’s Project Impact (Seattle Office of Emergency Management 2009) was initially implemented in the city of Seattle, Washington, in 1995.  The Department of Planning and Development helped the city developed the standards for this program and is now responsible for executing and expediting services for retrofit projects in the city.  This mitigation  Chapter 1: Introduction - 7 - program was primarily intended for strengthening 125,000 existing wood-frame houses, and its success has permitted other districts to be included, with a current inventory of 250,000 houses.  An extension of this program also allowed non-structural retrofit and overhead hazard removal from schools, and is currently developing and implementing awareness programs in these communities. In 2005, the state of Oregon commenced a seismic mitigation program to make all the emergency facilities and the high-occupancy public schools safe from future earthquakes, such as the likely magnitude 9 Cascadia earthquake in the Pacific Northwest shoreline.  The Oregon Department of Geology and Mineral Industries, in the first stage of this program, reported more than 3,000 facilities at seismic risk (Lewis 2007) where 1,300 of them have high to very high seismic collapse potential.  In 2008, the Oregon Department of Education created the “Quake Safe Schools” program to share information on the program updates and on earthquake preparedness information with the public.  The actual rehabilitation program started in 2009 with a Seismic Rehabilitation Grant Program of $30 million, and with a $1.2 billion grant to be released in the future, to begin the seismic mitigation program.  It is expected that emergency facilities and schools be seismically retrofitted by 2022 and 2032, respectively (McConnell 2010). Public schools in the state of Washington will be part of a regional seismic risk assessment project funded by the federal government, commencing in 2010 with a pilot project (Washington Military Department 2009). In this pilot project, two existing schools will be assessed, based on the ASCE-31 (ASCE 2003) methodology, to provide a list of  Chapter 1: Introduction - 8 - structures that should be targeted for seismic retrofit and to assist with grant applications to seismically retrofit deficient structures. Southern Europe Seismic risk mitigation programs in schools have also been developed in some European countries, such as Greece and Italy (OECD 2004), where many old school buildings are still at high risk of earthquake damage or collapse.  In Greece, a 10-year pre- earthquake evaluation/retrofit program for school buildings was put into practice by the School Building Organization of the Ministry of Public Works of Greece right after the Attica earthquake on September of 1999 (Penelis 2001).  At first, a rapid visual screening of school buildings and selection of the most vulnerable school buildings were conducted. Then, the high risk scored schools were evaluated in more detail using state-of-the-art techniques to bring them to a percentage of the current seismic design requirements in Greece.  This program was applied in its first stage to 500 schools located in the city of Thessaloniki, with an estimated 10.5% of the replacement cost. In Italy, the tragic consequences after the 31 October 2002 Molise earthquake provided a large stimulus to earthquake risk mitigation programs with important implications for older school buildings stock.  In fact, a new earthquake code was drafted after that earthquake, setting out detailed procedures for evaluating and strengthening existing structures.  In 2004, the Italian government allocated 460 million euros for the seismic assessment and retrofit of the most-at-risk schools.  By 2007, 150 schools had been retrofitted as part of these programs, 590 had received funding approval for seismic upgrading, and 560 had been classified as in need of structural intervention (Grant et al. 2007).  Chapter 1: Introduction - 9 - Turkey Since 2006, the government of Turkey has being implementing and financing a major seismic risk mitigation program in Istanbul (Elgin 2009), the Istanbul Seismic Risk Mitigation Project (ISMEP).  This major regional project is divided into three components that deal with preparedness, mitigation, and building code enforcement.  In the mitigation part of this program, 2,473 public buildings, where more than 70% correspond to school buildings, have been prioritized for retrofitting or reconstruction (if needed).  Due to budget restrictions, the ISMEP has focused on only 800 buildings that are at higher risk. By 2008, after two years of commencing this program, 310 buildings had been retrofitted (Elgin 2009). 1.2.2 Methodologies for seismic risk assessment A basic step towards assessing the seismic risk of schools in BC is to search for available methodologies, guidelines or techniques on the risk assessment of buildings that could be potentially used and/or adapted.  These methodologies are described in this section. Japan The seismic evaluation guidelines of existing buildings in Japan (Otani 2000) consist of three levels of screening.  The first level evaluates the lateral strength of the structural system considering variables such as geometry, materials, system configuration and existing damage. In the second level, the deformation capacity of the system is estimated depending on the predominant failure mode (shear or flexure).  These two levels are based on approximations where the structural damage is correlated with previous earthquakes in Japan through seismic capacity indices.  If the building is found deficient in the first or second levels, then a third level is required. This third level requires the evaluation of the strength and the ductility  Chapter 1: Introduction - 10 - capacities of the structure by using either a nonlinear static procedure or a time history analysis. USA HAZUS-MH (FEMA 2003), a free risk assessment software package for analyzing potential damage losses from earthquakes, uses nonlinear static analysis procedures to define the level of damage of the structure and subsequently to estimate seismic risk.  Four different damage states, from slight damage at small deformations to complete damage at large deformations, are defined for associated spectral demands for a certain location.  This package includes a large database of both structural prototypes (36 structural prototypes are grouped into 33 building classes depending on the occupancy of the building) and most locations within the United States. ASCE 41 (ASCE 2007) is the new standard for assessing and upgrading buildings in the USA.  This standard superseded the guidelines provided in FEMA 356 (BSCC 2000).  It begins with the definition of seismic hazard and the selection of a target performance level for the building.  The performance level under the defined seismic hazard can be evaluated at four levels of assessment.  The first two levels are merely code-based procedures similar to the coefficient method and to the modal spectral methods. The next two levels correspond to nonlinear analysis tools. The third method is the nonlinear static analysis, which is the same as included in FEMA 356. The fourth method is the nonlinear dynamic analysis, that uses several ground motions to describe the most likely response of the building under dynamic loading.  Chapter 1: Introduction - 11 - An in-progress research that also deals with structural assessment is being undertaken by the ATC-58 Project team.  The team has released a 50% technical draft report (ATC 2009) that includes a comprehensive methodology for the seismic performance assessment of structures in terms of casualties, repair costs and downtime.  The assessment is based on nonlinear analyses of structural systems to compute the probability of losses given a certain earthquake condition: intensity-based, scenario-based, and time-based.  An intensity-based condition is the intensity of the shaking (e.g., peak ground response).  Scenario-based condition is a specific earthquake defined by its magnitude and its closest distance of the fault.  A time- based condition is the time period of assessment and the mean frequency of occurrence of the earthquake.  In terms of analysis, the main difference between these three conditions comes from the selection of input ground motions and from the calculation of losses. Assessments based on both intensity-based and scenario-based conditions require a reliability analysis to prepare fragility curves and subsequent calculation of losses.  The assessment for a time- based condition uses the intensity-based assessment to compute losses at different intensity levels, which are combined with the occurrences of these intensity levels derived from a seismic hazard curve. Taiwan In Taiwan, the National Center for Research on Earthquake Engineering developed an application based on HAZUS methodology with modifications in the analysis models and seismic hazard parameters to accommodate the special environment and engineering practices in Taiwan (Yeh et al. 2003).  This application has an advanced built-in probabilistic hazard analysis tool to determine ground motion intensity parameters for different site  Chapter 1: Introduction - 12 - conditions.  The calculation of the performance of the buildings is based on the same static analysis adopted in HAZUS. New Zealand The study group from the New Zealand Society for Earthquake Engineering, NZSEE, has released guidelines for the structural assessment of buildings for earthquakes in New Zealand (NZSEE 2006).  These guidelines include a two-stage assessment procedure plus one document for the improvement of the structural performance. The first stage considers just an initial evaluation of buildings using a scoring process which includes variables such as age, soil type, structural system, importance, location and an overall ductility of the structure. In a following step, the overall score is modified by structural weakness factors such as plan/vertical irregularities, short columns and pounding effect. Factors for all of these variables can be read from tables whose values were based on both reviews of design codes and professional experience. The second evaluation is based almost on the same procedures defined in the assessment procedures of FEMA 356 (BSCC 2000) with slight differences on the rational methods to be adopted.  This evaluation is similar to code requirements and it looks into more detailed characteristics of the building and its structural response to earthquakes using nonlinear static analyses.  Time history analysis is also proposed at this stage of the assessment, but guidelines clearly state that methods based on static nonlinear analyses are more applicable alternatives for the seismic assessment of structural systems. Italy A detailed evaluation/retrofit methodology has been developed to reduce the risk of earthquake damage in school buildings in Italy (Grant et al. 2007).  Due to the large number  Chapter 1: Introduction - 13 - of schools to be assessed, a complete framework with three levels of assessment had to be defined in order to reduce the size of school inventory.  The first two levels are based on simple risk-assessment methods that do not require inspection and specific studies of the various buildings under consideration; the first level requires knowledge of the construction year and geographical location alone, while the second level makes use of previously collected building data, assembled in a national database.  A third (last) level estimates the performance of structures in terms of displacement ductility.  This method is based on a simplified structural analysis using assumed failure mechanisms and equivalent linearization of structural response. Seismic demand is represented by the spectral displacement modified by the effective period and the equivalent viscous damping of the structure. A capacity ratio, the displacement capacity of the seismic displacement demand, and the gradient of the hazard curves are combined to estimate the annual probability of collapse. Greece Seismic assessment/rehabilitation techniques have also been developed for buildings in Greece.  Kappos et al. (2008) have built a family of fragility curves (conditional cumulative probability in exceedance of the damage state) of most characteristics structural systems in Greece.  The seismic performance of these systems is estimated based on the age of the building and consequently on the respective code-based seismic forces.  In some cases, “local experience” from past-earthquakes allowed for defining these curves at different earthquake scenarios by following the same approach as adopted in ATC-13 (ATC 1985).  In many other cases limited information from past events was available.  Thus, nonlinear dynamic analyses of building models were carried out to build the fragility curves.  The calculated fragility  Chapter 1: Introduction - 14 - curves for the existing buildings were compared to those for the same systems designed with the current seismic design code.  A ratio between these two curves was proposed for assessment and retrofit decision purposes. Europe – Eurocode 8 Part 3 Part 3 of Eurocode 8 (CEN 2005) is the new European code for the seismic assessment and retrofit of existing structures and is representative of 23 countries.  This document addresses modeling, analysis and verification procedures more detailed than those needed for the design of new structures.  This code uses a displacement-based approach to assess the performance of buildings.  Three performance requirements (near-collapse, significant damage, and damage limitation) are defined in this code associated to three seismic hazard levels (2475-yr, 475-yr, and 225-yr return period earthquakes).  The structural performance is evaluated by means of linear or non-linear analyses.  The verification of structural elements varies depending on the type of failure: ductile or brittle.  Elements with ductile behaviour are checked by limiting a permissible deformation, while those with brittle behaviour are checked by limiting a maximum strength or force.  The uncertainties on the properties of the structural elements are given by a “confidence factor”.  This factor will modify the responses obtained from the structural analyses afterwards.  The modification of structural responses will depend on the type of structural analysis techniques adopted by the engineer. 1.2.3 Current research About two decades ago, many efforts were made for estimating the seismic risk of damage to buildings accounting for the uncertainties both of the input ground motions and of  Chapter 1: Introduction - 15 - the structural response of buildings to earthquakes.  Many procedures were developed to calculate the probability of exceeding a damage level of any damage measure for a given earthquake (e.g., Collins et al. 1996, Han and Wen 1997, Shome 1999).  The calculation of this probability was based on the same principles of the probabilistic seismic hazard analysis, PSHA (Kramer 1996), which is nowadays widely used to define the uniform hazard spectra of many assessment/retrofit/design guidelines or codes.  Most of the original approaches required simplified models of the ground motions or the structure to avoid a long calculation process because of the technology limitations at that time. During the last decade, seismic risk assessment procedures based on probabilistic approaches started to gain more attention due to advances in technology.  Ellingwood et al. (2001) studied the use of uncertainties of earthquake demand and structural behaviour by reviewing several reliability methods for practical assessment of the structural conditions of buildings.  A step-by-step method was developed to calculate the probability of exceeding a certain building drift ratio.  The method combines fragility curves calculated from nonlinear dynamic analyses with seismic hazard curves calculated from a probabilistic seismic hazard analysis, PSHA.  Although the incremental dynamic analysis, IDA, technique (Vamvatsikos and Cornell 2004) was not coined at that time, this method had already been used to obtain fragility curves for a suite of selected motions.  The method was applied to an existing moment-frame steel building in Los Angeles and later (Ellingwood et al. 2008) to wood buildings located in moderate seismic regions of USA. The PEER research group (e.g., Cornell and Krawinkler 2000, Porter 2003, Deierlein 2004, Krawinkler et al. 2006) expanded the probabilistic approach to involve the  Chapter 1: Introduction - 16 - participation of several disciplines and actors in the seismic risk assessment/retrofit of engineered structures, e.g., seismology engineers, geotechnical engineers, structural engineers, owners, insurance companies, etc.  The PEER approach assumes that the adequacy of the structure can be only predicted probabilistically based on a decision variable, DV, such as the earthquake loss and/or the exceedance of a limit state.  The adequacy of the structure can be quantified by the mean annual frequency of the decision variable, λDV, or in other words by the number of times that the earthquake loss exceeds a certain amount of money, or the structural response exceeds a certain threshold, in one year.  The mean annual frequency depends on two quantities: the structural Damage Measure, DM, and the ground motion Intensity Measure, IM, which is expressed by: IMDV dIMDMPdDMDVP λλ )|()|(∫∫= 1 (1.1) in which P(DV|DM) is the conditional probability that the DV exceeds a certain threshold given that DM is equal to a specific value, P(DM|IM) is the conditional probability that the DM exceeds limiting damage values given that the IM is equal to a particular value, and λDV is the mean annual frequency of the IM (conventionally known as the seismic hazard curve). Many researchers in New Zealand have developed methodologies to quantify seismic risk of engineered structures using the PEER approach (Mander et al. 2007, Solberg et al. 2008 and Bradley et al. 2009). The decision variable, DV, in all these cases was measured in terms of earthquake losses exceeding a certain monetary threshold.  These methodologies have used IDA (or an adapted version of IDA in the case of Solberg et al. 2008) to estimate  1 This is the basic PEER integral proposed by Cornell and Krawinkler 2000 that has been described here for reference purposes with the methodology developed in this thesis.  Chapter 1: Introduction - 17 - the damage measure, DM, in structures.  PSHA was conducted to obtain seismic hazard curves, λDV. Other researchers have developed simplified versions of the aforementioned methodologies based on the basic concepts of the PEER approach.  Dolsek and Fajfar (2007) developed a technique that keeps the basic idea of PEER but replaces IDA by an incremental static analysis method named as the Incremental N2, IN2, method for estimating fragility curves.  The uncertainties of the earthquake demand and of the structural behaviour are included in the elastic spectra and in the capacity curves obtained through the IN2 method, respectively.  Augusti and Ciampioli (2008) presented an efficient simulation technique compared to traditional Monte-Carlo techniques to estimate the mean annual frequency from the PEER approach.  This method adopted an analytical expression to the probability functions of the PEER integral, based on spectral values for the IM and on IDA results for the DM.  Other authors (Yin and Li 2010, Vamvatisikos and Fragiadakis 2010, Koduru and Haukaas 2010) have also investigated and postulated methods based on reliability analysis for estimating seismic risk by adopting simplifications to the PEER equation and using results of techniques such as IDA, selection/modification of ground motions and probabilistic seismic hazard analysis. 1.3. A METHOD SUITABLE FOR BC SCHOOLS 1.3.1 Deaggregated hazard by earthquake type Most applications of the methodologies described in the previous section base the risk assessment of existing buildings on a unique seismic hazard that is contributed by different  Chapter 1: Introduction - 18 - earthquake types2.  The use of a unique seismic hazard can not properly account for the contribution of the earthquake type to the total risk of seismic damage to buildings because of the different occurrences of these earthquakes.  Schools in British Columbia are located in a unique tectonic setting where at least three different earthquake types occur: crustal, subcrustal and subduction.  The rate of occurrence of crustal, subcrustal and subduction earthquakes are different and so are their effects on seismic hazard.  Figure 1.2 shows the magnitude-recurrence curves between Cascade Mountains (shallow) for crustal earthquakes and the Puget Sound (deep) for subcrustal earthquakes used to compute the hazard data for BC (Adams and Halchuk 2000).  It is clear from the magnitude-recurrence curves of Figure 1.2 that subcrustal earthquakes are more recurrent than crustal earthquakes for a wide range of earthquake magnitudes in one-year period. Many authors have reported important differences in the ground motions recorded from crustal, subcrustal and subduction earthquakes (e.g., Abrahamson and Silva 1997, Young et al. 1997, Bolt and Abrahamson 2003, Kawaga et al. 2004, Lin and Li 2008).  These differences can be also observed in the attenuation relationship of ground motion parameters developed for subduction zone earthquakes (e.g., Youngs et al. 1997, Atkinson and Boore 2003, Lin and Li 2008). Different equations have been used to attenuate ground motions of crustal and subcrustal earthquakes for calculating the seismic hazard of BC, as well as different earthquake sources and magnitude-recurrence relationships (Ventura et al. 2010).  Figure 1.3  2 Although there are some cases were a deaggregated hazard has been adopted to assess the performance of some structural systems, there is no clear guidance on how to assess the seismic risk for structures under different earthquake types in the same region.  Chapter 1: Introduction - 19 - shows hazard curves of crustal, subcrustal and subduction earthquakes for the cities of Victoria and Vancouver.  Hazard values are given by the probability of exceeding the spectral acceleration at selected periods calculated in 50 years.  Spectral accelerations of each earthquake type are different.  If a uniform probability is assigned to define earthquake demand for buildings, then the acceleration spectra will clearly differ by earthquake type. The fragility of earthquake damage (probability of exceeding a damage level) for these buildings will also differ by earthquake type. The slope of distributed probabilities3 (Figure 1.3) defines the occurrence of the spectral accelerations which, combined with the fragility curves, gives the total risk of damage to buildings (e.g., PEER approach).  The distributions of probabilities exceeding spectral accelerations of the three earthquakes are different and so are the slopes.  The individual risks calculated for each earthquake type will therefore be different.  Even in the cases where fragilities were similar for the three earthquake types, each earthquake will contribute differently to the total risk of damage to BC schools. A suitable method for assessing the seismic risk of BC schools should capture the inherent characteristics of crustal, subcrustal and subduction earthquakes explicitly.  The method should consider a deaggregated seismic demand (one spectrum for each earthquake) and a deaggregated hazard occurrence for each earthquake.  A method that accounts for the contribution of all these three earthquakes in one uniform hazard spectrum will not capture  3 The slope of the curve refers to the derivative of the mean annual frequency dλDV of Equation (1.1).  Chapter 1: Introduction - 20 - properly the individual characteristics of these earthquake and their effects on the school buildings, and neither will it give a reliable estimate of seismic risk. 1.3.2 Site conditions Most schools in BC are located in Site Class C sites – defined in the national building code, NBCC 2005 (Canadian Commission on Building and Fire Codes 2005), as soft rock or firm soil with an average shear wave velocity between 360 m/s and 760 m/s in the upper 30 meters– but many others are located in softer soils, especially in Site Class D sites – defined in the NBCC 2005 as soft soil with an average shear wave velocity between 180 m/s and 360 m/s in the upper 30 meters.  Class D4 soils amplify the sites and increase the risk of damage to BC school buildings. Many studies have addressed the seismic risk assessment of buildings located on soft soils.  Some of these studies have included the effects of soft soils in the hazard spectrum modified with code-based site factors (e.g., ATC-58, ASCE 2005, Dolce et al. 2003, Pergalani et al. 2008).  Other studies have developed site-specific hazard spectra calculated from PSHA that considered site effects (e.g., Romeo et al. 2000, Wen et al. 2006).  There are also some studies that have adopted free-surface motions calculated from non-linear response analyses of many characteristic soft soils to estimate the risk of damage to buildings (e.g., Zaslavsky 2006, Bala et al. 2009).  4 As a reference, the ASCE 7-05 (ASCE 2005) adopted Class D soils as the default site when the site soil condition is unknown.  Chapter 1: Introduction - 21 - It is evident that a suitable seismic risk assessment procedure should take into account the amplification of soft soils for measuring the seismic risk of damage of BC school buildings located on these soil types.  The site effect of soft soils should also be investigated within the context of a seismic hazard dominated by crustal, subcrustal and subduction earthquakes in BC.  The possible relation between the site effect and the type of earthquake is an aspect that is relevant for developing a risk assessment procedure for BC schools located on soft soils, which has not been addressed in past studies. 1.3.3 Practical implementation of the methodology A suitable seismic risk assessment methodology should merge most recent research work with tools that are familiar to practicing engineers who will conduct the assessment/retrofit of BC schools.  There is sufficient research work related to advanced procedures for the seismic risk assessment of structures that still need to be brought to a level that is feasible to be adopted by local engineers.  A procedure needs to be presented in a way that is easily digested by experience practicing engineers to receive feedback on how the results of applying the procedure can be better and more efficiently delivered to local practice. In the development of a tool for practice engineering, elements and concepts that are familiar to local engineers must be kept in mind.  Some of these elements can be: materiality (e.g., plywood, steel, masonry), conventional construction systems (e.g., shear walls, moment frames, partition walls, diaphragms), maximum capacity or resistance force of structural systems (e.g., ultimate capacity, yielding force), maximum deformations (e.g., inter-storey  Chapter 1: Introduction - 22 - drift deformations), code-based site classification and structural performance objectives (e.g., life safety). A seismic risk assessment procedure should include the aforementioned elements to generate results that can be implemented in a database that is accessible by local engineers. This database should give immediate information regarding both risk assessment and retrofit design of school buildings.  Engineers accessing this database will not need to perform seismic hazard analyses, define input ground motions, conduct numerous nonlinear dynamic analyses and perform site-specific site response analyses.  Engineers, instead, can dedicate their time to defining the structural systems from the existing schools, calculating or estimating the capacity of the existing systems, ranking schools for retrofit programs and/or defining retrofit solutions. 1.4. OBJECTIVES AND SCOPE The goal of this thesis is to develop a methodology for the seismic risk assessment of BC schools that incorporates the latest knowledge in seismic risk assessment and at the same time can be easily implemented in practice.  The results of this methodology should assist engineers and local authorities in prioritizing the at-risk schools and in defining cost-effective seismic retrofit solutions.  In order to achieve this goal, this thesis has two main objectives: one related to research and one related to engineering practice.  Chapter 1: Introduction - 23 - 1.4.1 Research objective Development of a methodology for estimating the seismic risk of school buildings in BC accounting both for the hazard of crustal, subcrustal and subduction earthquakes and for the effects of soft soils. 1.4.2 Engineering practice objective Development of a practical tool that assists local engineers in the assessment of risk of earthquake damage to existing school buildings in BC and in the design of seismic retrofit solutions. 1.4.3 Scope The concepts and information presented in this thesis are for the BC schools retrofit program. Therefore, the scope is limited to the risk of damage assessment to low-rise school buildings in BC.  Risk is calculated for crustal, subcrustal and subduction earthquakes.  The site conditions investigated in this study correspond to soft rock and soft soil sites that are characteristics of the Greater Vancouver and the Greater Victoria areas.  This thesis addressed code-based site class D sites only.  Schools located on much softer soils, such as those built on potentially liquefiable soils, are out of the scope of this thesis.  The application example of the proposed methodologies is limited to a characteristic plywood shear-wall building located in Vancouver.  Chapter 1: Introduction - 24 - 1.5. ORGANIZATION OF THESIS This thesis is delivered in a manuscript-based format.  Each of the main chapters (excluding this and the last chapters) are produced as stand-alone manuscripts for journal publication.  Due to the nature of this format, the content of each chapter is delivered independently to other chapters which may yield to repeated information.  Chapter 2, details the proposed seismic risk assessment methodology for BC schools.  Chapter 3 introduces a procedure for estimating seismic risk for schools located in softer soils, as a complement to the methodology presented in Chapter 2.  A summary, list of contributions, and further research studies are included in Chapter 4.  Four appendices summarize additional and relevant information for this thesis. A synopsis of each chapter and appendices is as follows. 1.5.1 Chapter 2 Chapter 2 describes the proposed procedure for estimating the risk of damage of schools in British Columbia.  It introduces the idea of a deaggregated risk for each earthquake type expected in BC.  The seismic risk assessment methodology is formulated and applied to a characteristic structural system of school buildings in BC.  The definition of ground motions and their use in the methodology are an essential part of this chapter.  This chapter also describes other important aspects of the methodology within the context of the BC school assessment/retrofit program.  Chapter 1: Introduction - 25 - 1.5.2 Chapter 3 Chapter 3 describes a procedure that is complimentary to the overall seismic risk assessment methodology presented in Chapter 2.  The procedure takes into account the effects of softer soils through an introduced Equivalent Intensity Factor, EIF.  The EIF modifies the existing results calculated with the methodology presented in Chapter 2, without incurring further analyses.  This chapter presents the results, the formulation and application of these EIFs for the same school structural system described in Chapter 2. 1.5.3 Chapter 4 Chapter 4 presents a summary of this thesis and a summary of contributions for both research and engineering practice within the field of seismic risk assessment.  Limitations and further research directions to complement or improve this research work are also listed in this chapter. 1.5.4 Appendices Appendix A summarizes the automatic process developed and implemented for the BC school project to speed up the risk calculations. Routines developed for the various programs used in this process are also shown in this appendix. Appendix B describes each parameter and variable involved in the BC school project in more detail.  The description of each of these parameters given within the context of the BC school assessment/retrofit program.  Chapter 1: Introduction - 26 - Appendix C shows some additional information of the selected input ground motions, such as time histories and response spectra of each record. Appendix D gives additional information regarding the location of school sites studied in Chapter 3. Soil columns are graphically depicted in this appendix.  Chapter 1: Introduction - 27 -  0 2 4 6 8 10 12 19 80 - 19 99  - 1 98 1 20 03  - 2 00 0 20 05  - 2 00 4 20 07  - 2 00 6 20 09  - 2 00 8  -2 01 0 Time Interval (years) N um be r o f E ar th qu ak es In school session Ouside school session 1933 Long Beach Several schools collapsed, 5 children died in a collapsed gym 1985 Mexico More than 100 schools collapsed. About 10,000 people died. No school- related casualties 2002 Molise, Italy Moderate earthquake, but 56 casualties, mostly in a school that collapsed killing 26 children 2005 Kashmir 17,000 children were killed when 7,000 schools collapsed 2006 Java 148 schools collapsed and 537 were severely damaged 2008 Sichuan 10,000 students died in the collapse of 7,000 classrooms and dormitory rooms 2010 Chile More than 2000 schools were damaged and left unusable. More than 600000 students affected  Figure 1.1: Distribution of earthquakes that occurred in the last 50 years associated with extensive damage in school building grouped by the time of occurrence, during or outside school sessions.  Selected facts from some earthquakes are also displayed5   5 Data collected from the USGS website: http://earthquake.usgs.gov/earthquakes/world/historical.php, the Family for School Seismic Safety website: http://fsssbc.org/, the GeoHazards International website: http://www.geohaz.org/index.html, and the National Information Service for Earthquake Engineering website: http://nisee.berkeley.edu/  Chapter 1: Introduction - 28 -  Figure 1.2: Magnitude-recurrence curves for the GSC (shallow) earthquakes, the PUG (deep) earthquakes and the USGS deep earthquakes (Natural Resources Canada, available at: http://earthquakescanada.nrcan.gc.ca/hazard/inslab2000/)  Chapter 1: Introduction - 29 -      Figure 1.3: Seismic hazard curves deaggregated per earthquake type (Crustal, Subcrustal and Subduction) prorated in 50 years for the cities of Vancouver and Victoria (reproduced from Ventura et al. 2010). Design refers to the Uniform Hazard Spectrum in the NBCC 2005.  Chapter 1: Introduction - 30 - 1.6. REFERENCES Abrahamson, N.A., and Silva, W.J., 1997. Empirical response spectral attenuation relations for shallow crustal earthquakes, Seismological Research Letters, 68, 94–127. Adams, J., and Halchuk, S., 2000. Knowledge of in-slab earthquakes needed to improve seismic hazard estimates for southwestern British Columbia, Intraslab Earthquakes in the Cascadia Subduction System: Science and Hazards workshop, Victoria, British Columbia, Canada. American Society of Civil Engineers (ASCE), 2003. Seismic Evaluation of Existing Buildings (ASCE/SEI 31-03), Reston, VA, USA. American Society of Civil Engineers (ASCE), 2005. Minimum design loads for buildings and other structures, SEI/ASCE 7-05, Reston, Va, USA. American Society of Civil Engineers (ASCE), 2007. Seismic Rehabilitation of Existing Buildings (ASCE/SEI 41-06), Reston, VA, USA. Angel, B.A., 1992. Report on Seismic Evaluation and Upgrading of Schools in Vancouver, BC, EERI Conference, San Francisco, CA, USA. Applied Technology Council (ATC), 1985.  ATC-13: Earthquake Damage Evaluation Data for California, Redwood City, CA, USA. Applied Technology Council (ATC), 2009.  ATC-58 50% Draft: Guidelines for Seismic Performance Assessment of Buildings, Department of Homeland Security, Federal Emergency Management Agency, Washington, D.C., USA. Association of Professional Engineers and Geoscientists of British Columbia (APEGBC), 2006. Bridging Guidelines for the Performance-based Seismic Retrofit of BC Schools, Second Edition, Burnaby, B.C., Canada. Atkinson, G.M., and Boore, D.M., 2003. Empirical ground-motion relations for subduction- zone earthquakes and their application to Cascadia and other regions, Bulletin of the Seismological Society of America, 93, 1703–1729. Auditor General of British Columbia, 2008.  Planning for School Seismic Safety, Office of the Auditor General of British Columbia, Report 2008/2009: 12, Victoria, BC, Canada, http://www.bced.gov.bc.ca/capitalplanning/seismic/ Augusti, G., and Ciampoli, M., 2008.  Performance-Based Design in risk assessment and reduction, Probabilistic Engineering Mechanics, 23, 496–508.  Chapter 1: Introduction - 31 - Bala, A., Ritter, J. R. R., Hannich, D., and Balan, S. F., 2009. Seismic site effect modeling based on in-situ borehole measurements in Bucharest, Romania. T. Schanz and R. Iankov (eds.), Coupled Site and Soil-Structure Interaction Effects 101 with Application to Seismic Risk Mitigation, NATO Science for Peace and Security Series C: Environmental Security, Springer Science+Business Media B.V. Bolt, B.A., and Abrahamson, N.A., 2003. Estimation of strong seismic ground motions. In: Lee W, Kanamori H, Jennings CP, Kisslinger C, editors. International handbook of earthquake and engineering seismology – Part B. Academic Press, 2003, Chapter VII. Bradley, B.A., Dhakal, R.P., Cubrinovski, M., MacRae, G.A., Lee, D.S., 2009. Seismic loss estimation for efficient decision making. Bulletin of the New Zealand Society of Earthquake Engineering, 42, 96–110. Building Seismic Safety Council (BSSC), 2000. Prestandard and Commentary for the Seismic Rehabilitation of Buildings, FEMA-356, Federal Emergency Management Agency, Washington, D.C., USA. Canadian Commission on Building and Fire Codes, 2005.  National Building Code of Canada, National Research Council of Canada, Ottawa, ON, Canada. CEN, 2005.  Eurocode 8: Design of structures for earthquake resistance. Part 3: Assessment and retrofitting of buildings. March 2005, Ref.No EN 1998-3: 2005. Comité Européen de Normalisation, Brussel, Belgium. Collins, K.R, Wen, Y.K., and Foutch, D.A., 1996.  Dual-level design: a reliability-based methodology, Earthquake Engineering and Structural Dynamics, 25, 1433–1467. Cornell, C.A., and Krawinkler, H., 2000. Progress and challenges in seismic performance assessment, PEER Center News, Spring 2000, 3, available at <http://peer.berkeley.edu/news/2000spring/> Deierlein, G., 2004. Overview of a comprehensive framework for earthquake performance assessment. In: Fajfar P, Krawinkler H (eds) Proceedings of the international workshop on performance-based seismic design–concepts and implementation, Bled, Slovenia, PEER Report 2004/05:15–26, Berkeley, USA. Dolce, M., Masi, A., Marino, M., and Vona, M., 2003. Earthquake damage scenarios of the building stock of Potenza (Southern Italy) including site effects, Bulletin of Earthquake Engineering, 1, 115–140. Dolsek, M., and Fajfar, P., 2007. Simplified probabilistic seismic performance assessment of plan-asymmetric buildings, Earthquake Engineering and Structural Dynamics, 36, 2021– 2041.  Chapter 1: Introduction - 32 - Elgin, K.G., 2009. Istanbul Seismic Risk Mitigation and Emergency Preparedness Project (ISMEP), Proceedings of the ATC & SEI 2009 Conference on Improving the Seismic Performance of Existing Buildings and Other Structures, San Francisco, CA, USA, 1129–1140. Ellingwood, B.R., 2001. Earthquake risk assessment of building structures, Reliability Engineering & System Safety, 74, 251–262. Ellingwood, B.R., Rosowsky, D.V., and Pang, W., 2008. Performance of light-frame wood residential construction subjected to earthquakes in regions of moderate seismicity, Journal of Structural Engineering, 134, 1353–1363. Federal Emergency Management Agency (FEMA), 2003. Multi-hazard Loss Estimation Methodology: Earthquake Model, HAZUS-MH MR3, Technical Manual, Department of Homeland Security Emergency Preparedness and Response Directorate FEMA, Mitigation Division, Washington D.C., USA. Grant, D., Bommer, J., Pinho, R., Calvi, G., Goretti, A., and Meroni, F., 2007. A prioritisation scheme for Seismic intervention in school buildings in Italy. Earthquake Spectra, 23, 291–314. Han, S.W., and Wen, Y.K., 1997.  Method of reliability-based seismic design. I: Equivalent nonlinear systems. II: Calibration of code parameters, Journal of Structural Engineering, ASCE, 123, 256–270. Kappos, A., and Dimitrakopoulos, E., 2008. Feasibility of pre-earthquake strengthening of buildings based on cost-benefit and life-cycle cost analysis, with aid of fragility curves, Nat. Hazards, 45, 33–54. Kawaga, T., Irikura, K., Somerville, G.P., 2004. Differences in ground motion and fault process between the surface and buried rupture earthquakes. Earth Planets and Space, 56, 3–14. Koduru, S.D., and Haukaas, T., 2010. Probabilistic seismic loss assessment of a Vancouver high-rise building, Struct. Engrg., 136, 235–245. Kramer, S., 1996. Geotechnical Earthquake Engineering 1st edition, Pearson Education, Singapore. Krawinkler, H., Zareian, F., Medina, R.A., and Ibarra, L., 2006. Decision support for conceptual performance-based design, Earthquake Engineering and Structural Dynamics, 35, 115–133. Lewis, D., 2007. Statewide Seismic Needs Assessment: Implementation of Oregon 2005 Senate Bill 2 relating to Public Safety, Earthquakes, and Seismic Rehabilitation of Public  Chapter 1: Introduction - 33 - Buildings, Report to the 74th Oregon Legislative Assembly, Open-File Report O-07-02, State of Oregon, Department of Geology and Mineral Industries, Portland, OR, USA, http://www.oregongeology.com/sub/projects/rvs/OFR-O-07-02-SNAA-onscreen.pdf Lin, P.-S., and Lee, C.-T., 2008.  Ground-motion attenuation relationships for subduction- zone earthquakes in Northeastern Taiwan, Bulletin of the Seismological Society of America, 98, 220–240. Lopez, O.A., Hernandez, J.J., Del Re, G., Puig, J., and Espinosa, L., 2007.  Reducing Seismic Risk of School Buildings in Venezuela, Earthquake Spectra, 23, 771–790. Mander, J.B., Dhakal, R. P., Mashikoa, N., and Solberga, K.M., 2007. Incremental dynamic analysis applied to seismic financial risk assessment of bridges, Engineering Structures, 29, 2662–2672. McConnell, V., 2010.  Notes from your State Geologist - Oregon’s take away question: time or money?, Cascadia, Winter 2010, Oregon Department of Geology and Mineral Industries, Portland, OR, USA, http://www.oregongeology.com/sub/quarpub/CascadiaWinter2010.pdf Nakano Y., 2004. Seismic Rehabilitation of School Buildings in Japan, Special Issue / Recent Development of Research and Practice on Earthquake Engineering in Japan, Journal of Japan Association for Earthquake Engineering, 4, 218–229. Nakano, Y., and Teshigawara, M., 2007. Seismic evaluation and rehabilitation of vulnerable RC buildings, -Experiences and lessons in Japan.  Indonesia-Japan Joint Seminar on Mapping-out Strategies for Better Seismic Disaster Mitigation. 12 February, 2007, Jakarta, Indonesia. New Zealand Society for Earthquake Engineering (NZSEE), 2006.  Assessment and Improvement of the Structural Performance of Buildings in Earthquake, Wellington, New Zealand. Organisation for Economic Co-operation and Development (OECD), 2004. Keeping Schools Safe in Earthquakes, Programme on Educational Building (PEB), Proceedings of the ad- hoc Experts’ Group Meeting on Earthquake Safety in Schools, Paris, France, 218–228. Otani, S., 2000. Seismic vulnerability assessment method for buildings in Japan, Earthquake Engineering and Engineering Seismology, 2, 47–56. Penelis, G., 2001. Pre-Earthquake Assessment of Public Buildings in Greece, International Workshop on Seismic Assessment and Rehabilitation of Structures, Athens, Greece.  Chapter 1: Introduction - 34 - Pergalani, F., Compagnonia, M., and Petrinia, V., 2008. Evaluation of site effects using numerical analyses in Celano (Italy) finalized to seismic risk assessment, Soil Dynamics and Earthquake Engineering, 28, 964–977. Porter, K.A., 2003. An overview of PEER’s performance-based engineering methodology. In: A. Der Kiureghian, S. Madanat and J.M. Pestana, Editors, Proceedings of the ninth international conference on applications of statistics and probability in civil engineering, Civil Engineering and Reliability Association (CERRA), Millpress, Rotterdam. Ristau, J.P., 2004. Seismotectonics of Western Canada from Regional Moment Tensor Analysis, Ph.D. Thesis, University of Victoria, Victoria, B.C., Canada. Romeo, R.W., Paciello, A., and Rinaldis, D., 2000. Seismic hazard maps of Italy including site effects, Soil Dynamics and Earthquake Engineering, 20, 85–92. Seattle Office of Emergency Management, 2009.  Seattle All-Hazards Mitigation Plan.  City of Seattle, Seattle Police Department, Emergency Preparedness Bureau, Emergency Management Section, July 2009 Edition, Seattle, WA, USA, <http://www.seattle.gov/emergency/library/SeattleMitigationPlan.pdf> Shome, N., 1999. Probabilistic Seismic Demand Analysis of Nonlinear Structures, Ph.D. Thesis, Stanford University, California, USA. Solberg, K.M., Dhakal, R.P., Mander, J.B., and Bradley, B.A., 2008. Computational and rapid expected annual loss estimation methodologies for structures, Earthquake Engineering and Structural Dynamics, 37, 81–101. Transit Bridge Group (TBG), 1989. Seismic Assessment of Vancouver School Buildings - Executive Summary, available at <http://fsssbc.org/> in Background Information section. Vamvatsikos, D., and Cornell, C.A., 2004. Applied incremental dynamic analysis, Earthquake Spectra, 20, 523–553. Vamvatsikos, D., and Fragiadakis, M., 2010. Incremental dynamic analysis for estimating seismic performance sensitivity and uncertainty, Earthquake Engineering and Structural Dynamics, 39, 141–163. Ventura, C.E., Archila, M., Pina, F.P., and Centeno, J., 2010.  Sensitivity of design spectrum for British Columbia to different levels of probability of exceedance, Proceedings of the 9th US national and 10th Canadian conference on earthquake engineering: reaching beyond borders, Paper 1129, Toronto, Ontario, Canada. Washington Military Department, 2009. A Pilot Project: Washington State School Seismic Needs Assessment, Emergency Management Division, available at <http://www.emd.wa.gov/hazards/haz_natural.shtml> in the Earthquake section.  Chapter 1: Introduction - 35 - Wen, Z.-P., Gao, M.-T., Zhao, F.-X., Li, X.-J., Lü, H.-S., and He, S.-L. 2006. Seismic vulnerability estimation of the building considering seismic environment and local site condition, Acta Seismologica Sinica, 19, 292–298. Wisner, B. and Monk, T., 2005. Prioritizing Schools and Hospitals: Good Intentions But Miles To Go, United Nations World Conference on Disaster Reduction, Kobe, Japan, <http://www.unisdr.org/wcdr/thematic-sessions/presentations/session5-1/fsss-mr- wisner.pdf> Yeh, C. H., Loh, C. H., and Tsai, K. C., 2003, Development of Earthquake Assessment Methodology in NCREE, Proceedings of Joint NCREE/JRC Workshop, International Collaboration on Earthquake Disaster Mitigation Research, NCREE-03-029, Taipei, Taiwan. Yin, Y.J., and Li, Y., 2010. Seismic collapse risk of light-frame wood construction considering aleatoric and epistemic uncertainties, Structural Safety, 32, 250–261. Youngs, R.R., Chiou, S.-J., Silva, W.J., and Humphrey, J.R., 1997. Strong ground motion attenuation relationships for subduction zone earthquakes, Seismological Research Letters, 68, 94–127. Zaslavsky, Y., 2006. Empirical determinations of local site effect using ambient vibration measurements for the earthquake hazard and risk assessment to Qrayot-Haifa Bay areas, Report No 595/064/06, The Steering Committee for National Earthquake Preparedness and Mitigation, Israel.    Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 36 - Chapter 2. SEISMIC RISK ASSESSMENT PROCEDURE FOR LOW-RISE SCHOOL BUILDINGS LOCATED IN BRITISH COLUMBIA6 2.1. INTRODUCTION The province of British Columbia, BC, is undertaking major seismic risk mitigation for all at-risk school buildings (herein refered to as the Schools Project).  The seismicity of the west coast of BC, where most of these schools are located, is dominated by crustal (shallow in the continental plate), subcrustal (deep in the oceanic subducting plate) and subduction earthquakes driven by geologic processes occurring at the Cascadia Subduction Zone (Figure 2.1).  The rate of occurrences of these three earthquake types in BC are different and ground motions recorded in similar tectonic settings to that in BC from these earthquake types have shown distinctive patterns.  It is therefore expected that both hazard in BC and risks to BC schools is substantially different for these three earthquake types. Many tools for assessing damage states, and consequently for estimating the risk to damage in buildings, have been developed in the last years (e.g., ATC 2009, FEMA 2003, NZSEE 2006, Otani 2000) based on a single set of hazard data.  So far, there are no guidelines or procedures on how to deal with these different earthquake types at the seismic risk level.  6 A version of this chapter will be submitted for a peer-reviewed journal publication. Pina, F.E., Ventura, C.E., Taylor, G., and Finn, W.D.L., “Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia.”  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 37 - This chapter presents a procedure for estimating the risk of damage to existing BC school buildings taking into account the actions of multiple earthquake types in the risk calculation process explicitly.  The procedure is applied to characteristic structural systems typical of BC schools.  The generalization of the methodology to a large inventory of schools and sites, the generation of a massive database and the access to this extensive database in a user-friendly interface are also described in this chapter. 2.2. RISK OF DAMAGE 2.2.1 Damage for BC school buildings In this study, damage is related to the inter-storey drift deformation of school buildings (herein referred to as drift).  Drift is a physical response of building structures that is widely accepted by engineers for estimating damage in buildings, which can be measured from tests and obtained from structural analyses7. An excessive drift can cause buildings to loose the capacity of taking vertical loads and cause part or a section of the building to collapse.  Lower drifts can avoid excessive both structural and non-structural damage in the building, thus ensuring life-safety to its occupants.  Much lower drifts can cause minor damage in buildings and allowing the continuity of the service immediately or few days after the earthquake.  7 There are a number of other measurements that can be adopted to define the performance of structures.  Most of these measurements will depend largely on the type of elements studied within a building, e.g. diaphragms, partition walls, non-structural walls, non-structural components, piping, etc.  The scope of this thesis is the application of the methodology to lateral deformation resistance systems, in which the inter-storey drift is one the best measurements of damage in buildings.  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 38 - 2.2.2 Risk formulation The risk of any damage states can be measured by calculating the probability of exceeding a drift deformation in the building.  The probability of drift exceedance, PDE, of a structural system subjected to earthquake shaking is done in a similar way to the estimation of seismic hazard using probabilistic seismic hazard analysis (PSHA), in which earthquakes arrive according to a temporal probabilistic model.  Using a Poisson model, the PDE is given by: )exp(1 1 ∑ = ⋅⋅−−= n i ii tPPDE ν  (2.1) in which i is the type of earthquake mechanism (crustal, subcrustal and subduction in this case), n is the number of earthquake mechanisms (n = 3 in the Schools Project), the parameter νi is the mean arrival rate of the i-th earthquake type, Pi is the probability of damage exceedance if the earthquake is type i, and t is the time interval8.  In Equation (2.1) one has to calculate first the probability of exceedence for each earthquake as it occurs, individually, and then weight these probabilities with the arrival rates to calculate the compound total probability over t. Since Poisson model has been used, Equation (2.1) is only valid if the occurrence of the i-th earthquake does not affect the occurrences of the other n-i earthquakes, i.e., there is no interaction between earthquakes and their occurrences.  In the Schools Project, it is assumed that there is no relationship between the three types of earthquakes considered in the risk calculation.  8 This t time interval refers to the period of time adopted to assess the buildings, which is different to the time period T used to describe dynamic properties of structures.  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 39 - The calculation of Pi in Equation (2.1) should consider all the possible earthquakes of the i-th type that trigger all the possible damage scenarios in the building.  In other words, the compound probability of earthquake occurrence should add to unity.  This requirement can be satisfied by capturing all possible damage states in the building through nonlinear dynamic analyses using incremented intensities, I, of the earthquake motion.  This technique has been coined as Incremental Dynamic Analysis, IDA (Vamvatsikos and Cornell, 2004) and is now being used to assess seismic risk of buildings and to estimate building collapse. The characteristic result of IDA is a plot that relates the damage measure (the maximum drift during the earthquake) of the building model in the abscissa with the intensity increment of the input motion in the ordinates.  A family of IDA curves is shown in Figure 2.2 for many input records.  From these plots, it is possible to collect the maximum drifts (indicated with dots in Figure 2.2) produced at a given intensity I, over the input records.  These points are represented with a lognormal distribution, from which one calculates the probability that the drift Dr exceeds a target dr conditional on the intensity level I, P(Dr > dr | I).  The total exceedance probability P(Dr > dr) for a given earthquake type (Pi in Equation 2.1) is then obtained, using the marginal distribution of intensities, according to: dIIfIdrDrPdrDrPP I I i )()()( max min >=>= ∫  (2.2) in which f(I) is the probability density for the intensities corresponding to the i-th earthquake type of interest.  This probability density comes from a probabilistic hazard analysis and is given in terms of the annual frequency of hazard intensity exceedance (the hazard curve).  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 40 - The product of Equation (2.2) with the parameter νi yields to the mean annual frequency of drift exceedance, λi , as follows: dIIfIdrDrPP I I iiii )()( max min >== ∫νλν  (2.3) If a discrete number of intensities over a finite range are considered, then Equation (2.3) can be expressed as: )()|( 1 j nI j ji IHIdrDrP λλ ∆⋅>≈ ∑ =  (2.4) in which j is the j-th intensity increment, nI is the number of intensity increments, and ∆λH(Ij) is the annual frequency of intensity occurrence given by the difference between the annual frequencies of hazard exceedance at the increment points j–1 and j, λH(Ij-1) – λH(Ij). Finally, the discrete version of Equation (2.1) can be written as: )exp(1)( 1 ∑ = ⋅−−=>= n i iT tdrDrPPDE λ  (2.5) in which λi is given by Equation (2.4).  In the Schools Project, the drift limit, dr, will depend on the level of damage accepted for BC school buildings, n =3 and t = 50 years. 2.3. RISK OF DAMAGE CALCULATION PROCEDURE The calculation of risk of damage, PDE from Equation (2.5), requires the interaction of different disciplines, e.g. seismology, seismology engineering, structural engineering, decision makers, etc.  Gathering all the tasks performed by each discipline in a single procedure can be challenging.  A single procedure should not only include current research  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 41 - work, but also delivers a useful and attractive tool for practicing engineering to make the assessment/retrofit of BC schools more efficiently. Specific tasks of the many disciplines are gathered and combined in a systematic procedure for calculating the seismic risk of damage to BC school buildings.  This procedure computes the probability of drift exceedance, PDE, of any drift limit (to any damage state) for structural systems of existing BC school buildings.  The procedure can be also used to estimate the resistance required of a retrofit system to limit the risk of a given damage state, which is further explained in the following section. The proposed procedure for calculating PDE, shown in Figure 2.3, has been divided into six general steps: Buildings, Seismic Hazard Calculations, Ground Motion Records, Incremental Dynamic Analysis, Conditional Probabilities and Probability of Drift Exceedance.  These steps are described in the following section. 2.3.1 Step 1 – Buildings The objective of this step is to identify in the school building all the existing earthquake-resistance systems and their characteristics. Step 1.1. Overall geometry of school building.  Identify school blocks or individual buildings within the school, overall dimensions and number of storeys. Step 1.2. Structural systems.  Identify building components that have significant influence on the seismic performance and group them by the following categories: (1)  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 42 - gravity columns, (2) lateral deformation resistance systems (LDRS), (3) out-of- plane behaviour systems, (4) diaphragms, and (5) connections. Step 1.3. Modeling.  Create a mathematical representation of each structural system. Identify nonlinearities of the systems from test results: backbone curves and hysteretic rules from cyclic or dynamic tests.  From the test results, identify inherent effects of the cyclic loading to the performance of the structure such as P-Delta, stiffness degradation, strength decay, and/or pinching. Step 1.4. Required performance.  Define the drift limit to achieve the required performance to earthquake shaking for each structural system.  Some guidelines for seismic upgrading of existing buildings, such as the ASCE 41 (ASCE 2007), suggest drift limits for different performance objectives, e.g., serviceability, life-safety and near collapse.  Design codes usually prescribed drift limits for a single performance objective. Step 1.5. Period range of interest. Estimate the range of building periods of the structural systems identified in Step 1.2 at the first yielding and at drift limit defined in Step 1.4.  Calculate these periods using the secant stiffness at the yielding drift and at the drift limit from the backbone curves defined in Step 1.3.  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 43 - 2.3.2 Step 2 – Seismic hazard calculations The objectives of this step are (1) to obtain the annual frequencies of intensity occurrences, ∆λHj of Equation (2.4), and (2) to define the target spectrum demand for the selection of input ground motions. Step 2.1. Identification of earthquake types.  Gather the following information from the seismic history of the site:  sources of earthquakes, magnitude-recurrence relationships and ground motion attenuation/prediction relationships. Step 2.2. Hazard analysis.  Compute the annual frequencies of exceeding the ground motion shaking from the attenuation/prediction relationship by means of a Probabilistic Seismic Hazard Analysis, PSHA (Kramer 1996).  Transform the ground motion shaking parameter to intensity increments by defining the 100% intensity at a given annual frequency of occurrence, e.g., at 4×10-4 annual frequency that is equivalent to a probability of 2% being exceeded in 50 years. Step 2.3. Annual frequency of intensity occurrence.  Compute the annual frequencies of occurrences from the slope between two consecutive intensity increments. Step 2.4. Target spectra.  Define the target spectra at the annual frequency of exceedance of the reference motion intensity (100% intensity).  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 44 - 2.3.3 Step 3 – Ground motion records. The objective of this step is the selection of ground motion records representative of the 100% intensity grouped by earthquake type. Step 3.1. Basic search.  Define a reference site and identify from the seismic hazard data the magnitudes and source-to-site distances that contribute mostly to the hazard. Use magnitudes for searching earthquakes, and source-to-site distances and the reference site for searching recording stations.  Obtain the records from selected stations. Step 3.2. Signal processing.  Review the recording file for errors.  If required, process the data using the instrument specifications, correct the base-line of records and remove frequencies outside the scope of structures under assessment (signal filtering). Step 3.3. Record modification.  Adopt a record modification procedure that keeps most of the original information of the record intact and ensures also that does not bias the structural response.  Single scaling factors applied to the records ensure at least to keep information regarding frequency and phase-angle content intact, which are crucial in nonlinear dynamic analyses.  However, some scaling techniques could bias the structural response to the scaling factor.  To avoid this, many researchers (e.g., Shome et al. 1998, Iervolino and Cornell 2005, Watson-Lamprey and Abrahamson 2005) have proposed different scaling techniques that accounts for  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 45 - structural characteristics, e.g., scaling records to a target spectrum at the first- mode period. Step 3.4. Selection criteria.  Define a set of criteria for selecting a representative sample of records from the pool of modified records.  A minimum number of records must be selected to ensure a reliable fitting of the resulting damage estimates (maximum drifts) to a probability distribution. 2.3.4 Step 4 – Incremental dynamic analyses The objective of this step is to estimate the maximum drift of the system through nonlinear dynamic analysis using a wide range of earthquake motions.  Incremental Dynamic Analysis, IDA, technique is used to capture these drifts for a wide range of intensity increments of the selected motions (Vamvatsikos and Cornell 2004). Step 4.1. Range of intensities.  Set a wide range of intensities to capture all possible drift deformations that can be expected from a wide range of possible earthquake motion intensities. Step 4.2. Analyses.  Run IDA of system models defined in Step 1.3 using the selected records of Step 3.4 for the range of intensities defined in Step 4.1. Step 4.3. Responses.  Extract the maximum drift deformations from the analysis results for each increment and for each record.  Gather the information in an m×n matrix, the drift matrix; being m the number of records and n the number of intensity increments.  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 46 - 2.3.5 Step 5 – Conditional probabilities The objective of this step is to calculate the probability of exceeding the drift limit at each increment. Step 5.1. Probability function.  Fit a probability function to the set of drifts obtained at each increment (each column of the drift matrix). Step 5.2. Conditional probability.  Compute the probability of exceeding the drift limit, P(Dr>dr|Ij), defined in Step 1.4 at each intensity increment from the fitted probability function of Step 5.1. 2.3.6 Step 6 – Probability of drift exceedance, PDE The objective of this step is to calculate the total probability of exceeding the drift limit. Step 6.1. Total probability.  As per Equation (2.4), multiply the conditional probabilities calculated in Step 5.2 with the annual frequencies of intensity occurrences obtained in Step 1.3.  Add the resulting values for all the intensity increments to obtain the mean annual frequency of drift exceedance. Step 6.2. Calculation for other earthquake types.  Repeat all the steps from Step 2 to obtain the mean annual frequency of drift exceedance for the other earthquake types. Step 6.3. PDE.  Replace the mean annual frequencies of drift exceedance of each earthquake type and time t in Equation (2.5) to compute the PDE.  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 47 - 2.4. PDE CALCULATION FOR A SCHOOL BUILDING SYSTEM The proposed procedure is used to estimate the seismic risk of damage of most structural systems and components of BC school buildings.  More than 30 different structural systems and components have been identified from existing buildings.  Predominant systems in BC school buildings are plywood or reinforced concrete shearwalls, unreinforced masonry wall, reinforced concrete moment frames, reinforced concrete columns, and both flexible plywood and rigid reinforced concrete diaphragms. A characteristic school building of BC has been selected to illustrate the calculation of seismic risk of damage with the proposed procedure.  The school has a conventional lay-out and is located in Vancouver in a Site Class C soil (soft rock).  For completeness, this illustration example follows all the steps and sub-steps described in previous section. 2.4.1 Step 1 – Buildings Step 1.1. Overall geometry of school systems The lay-out and overall dimensions of the typical building are shown in Figure 2.4. The building has 2 storeys with inter-storey heights of 3 meters.  The gymnasium, offices and lobby, and classrooms are distinctive individual sections of this school building, which can be evaluated separately.  This example focuses only on the classroom section of the building.  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 48 - Step 1.2. Structural systems Both gravity and lateral loads are transferred to the foundation through the unblocked plywood shearwalls, which are identify as the lateral deformation resistance system, LDRS, of this building section.  Out-of-plane rocking behaviour is likely to be observed in the heavy partition unreinforced masonry, URM, walls that divide some of the classrooms. Diaphragms are comprised by wood panels supported to joists and beams that are connected to the plywood shearwalls with nails.  The LDRSs are connected to the foundation with anchor bolts. PDE calculations are shown here for the unblocked plywood shearwalls, W2 system (see Appendix B), which is the main LDRS of the classroom section of the building.  The evaluation of PDE for W2 is critical and can govern the risk of damage to the whole building section if sufficient strength and deformation capacity is provided to diaphragms and connections, and a controlled out-of-plane failure control system is implemented to the URM walls. Step 1.3. Modeling It is assumed that all LDRSs of the building can be modeled by a 2-D representation of a single LDRS (Figure 2.5a).  The regular plan of the LDRSs in the classroom section of the building allows for the implementation of this assumption.  To define this plan regularity, current guidelines in the School Project (APEGBC 2006) suggest a maximum plan  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 49 - eccentricity of buildings of 20% in the direction of the earthquake shaking and 10% in the orthogonal direction.  These eccentricity limits are being reviewed in a parallel study. The 2-storey plywood shearwall, W2, is modeled with a two-degree-of-freedom system with lumped masses at each floor simulating the dynamic contribution of the slab and the roof (Figure 2.5b).  Shear spring elements have being placed at each storey to represent the nonlinear behaviour of the LDRS under dynamic loading.  Figure 2.5c shows the nonlinear backbone curve and the hysteretic rule of shear springs representing W2.  The hysteretic rule follows the backbone curve, which loops have strength degradation (C to D), stiffness deterioration (D to E) at many loading cycles and it is heavily pinched during the reloading (E to F to G)9. A constant damping of 3% was adopted and agreed amongst many experienced engineers and researchers within the project for the W2 model.  The 3% damping was based mainly on the expected energy released by the interaction between the foundation and the soil or nonstructural components during shaking.  It was assumed that a small contribution to the total energy dissipated be represented by this value and that most energy be dissipated by large nonlinear deformations in the structure during earthquake shaking.  More detailed information regarding this model and its nonlinear behaviour under earthquake loading has been published elsewhere (Hanson et al. 2009).  9 It must be mentioned at this point that the parameters that define the hysteretic rule were fixed to deterministic values observed from tests.  Thus, the randomness of these parameters was not considered in this project. Nevertheless, the use of more than one parameter to describe the hysteretic rule can still be included in this methodology with a more intense calculation process.  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 50 - Step 1.4. Required performance In the school project the required performance of at-risk schools is life-safety, i.e., excessive damage in the building with a very low probability of collapse under the actions of very large earthquakes (a 2475-yr return period earthquake).  For a W2 system, the excessive damage is limited to a 4% maximum inter-storey drift (APEGBC 2006).  Recent tests of W2 systems conducted for the Schools Project (EERF 2009) have shown large drift deformations under different loading protocols (earthquake motions).  All tested specimens showed that the capacity of systems was dropped in 50% the maximum lateral force capacity at around 4% drift and that the failure or collapse of the specimens was observed at around 10% drift.  In view of these results, the 4% drift was considered a reasonable limit of damage to define the life-safety performance objective of a W2 system for the Schools Project. Step 1.5. Period range of interest. The period range of interest was determined by conducting a statistical analysis of the characteristic range of periods for typical wood-frame BC school buildings undergoing nonlinear response.  Figure 2.6 shows the distribution of two defining periods; the period at yielding (T1) and the period at an inter-storey drift limit of 4% (Teff).  The period at yielding may be an approximation to the fundamental period, while Teff is a reference parameter of these systems deforming nonlinearly.  On the basis of the Teff results, the period range of interest for wood-frame buildings was selected to be 1.0s to 2.0s.  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 51 - 2.4.2 Step 2 – Seismic hazard calculations Step 2.1. Identification of earthquake types The tectonic setting of South-western British Columbia (Figure 2.1) is influenced mainly by the subduction of the oceanic Juan de Fuca plate beneath the North America continental plate occurring about 100 km west of Southern Vancouver Island (Ristau 2004). Mega-thrust earthquakes may occur at the interface of these two plates (Atwater et al. 2005). There are other two types of earthquakes that may occur at either of these two plates as well. Crustal or shallow earthquakes have been recorded at depth not longer than 20km in the continental North America plate.  Subcrustal or deep earthquakes have been also recorded in this region at depth longer than 50km in the subducting Juan de Fuca plate.  There is no clear understanding about the type of faulting of these types of events, but there is solid evidence that either of them may occur. Basic information for calculating the seismic hazard data of BC, such as magnitude- recurrence relationships, sources and attenuation relationships was provided by the Geological Survey of Canada; the GSC report (Adams and Halchuk 2003). Step 2.2. Hazard analysis Seismic hazard analyses have been performed using computer program EZ-FRISK (Risk Engineering 2008).  Using the same approach as GSC, crustal and subcrustal data has been treated probabilistically and subduction data deterministically.  Probabilities have been assigned to subduction hazard data to treat the three types of earthquakes uniformly.  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 52 - Regional (R) and historical (H) seismic source models are available in the GSC report to calculate the seismic hazard in this region.  Hazard data was calculated for these two models independently and the robust hazard values between the two were adopted.  Although this procedure has been accepted to compute the total hazard, there is not much theoretical basis to support it.  This chapter does not attempt finding an explanation or studying further this procedure, although it is an open question for a future research on improving the proposed risk calculation methodology.  In the school retrofit project, the risk is calculated based on the same procedure of calculating individual risks for each model and then defining the total risk as the robust combination of both.  In this particular example, the risk is calculated for those models that contribute mostly to seismic hazard, i.e. R model for Crustal earthquakes and H model for Subcrustal earthquakes. The hazard data is given in terms of the spectral acceleration at 1 second period, Sa(T=1s), which is a period of interest in this assessment example (the selection of this period was further explained in Step 1.5). The annual frequency of exceedance of 4.04 × 10-4 (a 2475-yr return period earthquake) is selected for the 100% intensity which occurs at 0.2g for the total or aggregated hazard.  Figure 2.7a shows the distribution of annual frequencies of exceedance over a wide range of motion intensities (from 10% to 250%) for the hazards of crustal, subcrustal and subduction earthquakes.  The value of the aggregated hazard at 100% intensity, f(100%), is displayed in Figure 2.7a for reference purposes only.  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 53 - Step 2.3. Annual frequency of intensity occurrence The annual frequencies of the intensity occurrences – ∆λHi in Equation (2.4) – are calculated in intervals of 10%.  Figure 2.7a shows the calculation of the annual frequency of the 100% intensity occurrence, ∆λH(100%), given by the difference λH(90%) – λH(100%) = 109.2 × 10-6.  The distributions of these frequencies are shown in Figure 2.7b for the 70% to 150% intensity range.  Note that shapes of these curves are quite similar, where the low intensities occur more frequently than the high ones. Step 2.4. Target spectra The spectral velocity derived from the spectral acceleration was chosen as the representative demand parameter in the school project.  This selection was mainly based on the period range of interest of the structural system of 1 to 2 seconds, which indicates velocity-sensitive spectral values. Figure 2.8 shows the pseudo-velocity spectra for crustal, subcrustal and subduction earthquakes in Vancouver with a probability of motion exceedance of 2% in 50 years (2475- year return period earthquake).  The robust spectrum derived from the current hazard data available for Vancouver (UHS-Vancouver) has been included in Figure 2.8 for comparison with the new measures of hazard.  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 54 - 2.4.3 Step 3 - Ground motion records Step 3.1. Basic search Site Class C soils were adopted for selecting motion records in the Schools Project.  A Site Class C is the reference site of the NBCC 2005 (Canadian Commission on Building and Fire Codes 2005) defined as soft rock or firm soil with an average shear wave velocity between 360 m/s and 760 m/s in the upper 30 m. Appropriate ranges of magnitudes and distances to earthquake sources were determined by deaggregating the seismic hazard using EZ-FRISK (Risk Engineering 2008).  We selected modal values to define the ranges of magnitudes and distances of interest.  The range of modal values for the combined magnitude and source-to-site distances are summarized in Table 2.1 for the three types of earthquakes.  These values were defined for the deaggregated 2% in 50year probability of exceedance of the spectral accelerations at periods of 1.0s and 2.0s. Earthquakes that have occurred in a similar tectonic setting to that in BC (at the interface of plates in subduction zones, in the overlaying crust and in the subducting plate) have been mostly searched.  These similar settings were found in Japan (Nakanishi, Kinoshita & Miura 2001), Northern Pacific of USA (Ristau 2004, Seno and Yoshida 2004), the West coasts of Mexico (Seno and Yoshida 2004) and Central America (Bent and Evans 2004), the West coast of South America (Scholl and Thiel 1986, Alvarado et al. 2005 and Araujo et al. 2005), New Zealand (Reyners 1987) and Southern Europe (Selvaggi and Amato 1992, Radulian et al. 2000).  Crustal earthquakes that are in the PEER-NGA database (Chiou  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 55 - et al. 2008) have been also searched.  Many of these crustal earthquakes occurred in different tectonic settings to the one in BC, but records were selected because of the extensive data available. Selected earthquakes and the number of stations selected for each earthquake are listed in Table 2.2.  Most crustal earthquakes were downloaded from the PEER-NGA database (Chiou et al. 2008).  Subcrustal and subduction earthquakes were mostly downloaded from the COSMOS database (Archuleta et al. 2006).  Japanese earthquakes available in COSMOS database were directly downloaded from the K-NET (Kinoshita 1998) and KiK-net (Aoi et al. 2000) databases. Not all the stations of the searched databases had enough information regarding the soil underneath, and estimations of the Vs30 had to be conducted in those cases.  In many Japanese stations, the shear wave velocity was measured in the upper 10m only.  An extrapolation method (Boore 2004) was adopted to estimate the Vs30 of the sites of these stations. Considering that the seismic hazard data was calculated based on aerial seismic sources, earthquakes have been selected regardless the type of faulting.  Besides, near-source events and the direction of shaking were not accounted in this search.  Also, the horizontal components of the records have been extracted from each instrument only (the estimation of risk in BC schools is based on the horizontal response of structural systems and has not made any attempt to include the vertical component of the ground motion records in the analyses).  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 56 - Step 3.2. Signal processing None of the PEER-NGA records required further signal processing and the information regarding site conditions was properly reported.  The majority of subcrustal records and subduction records required the reformatting of the information and signal processing. Records were baseline corrected using a lineal function and then filtered with a 4-th order band-pass Butterworth filter with cut-off frequencies of 0.10 Hz and 25 Hz (cut-off periods of 10s and 0.04s).  In some cases, records were filtered in a wider range of cut-off frequencies and larger filter orders (6-th to 8-th) were used. Step 3.3. Record scaling Records have been linearly scaled to closely match the spectral demand in a period range that is developed by progressive structural softening or the period range of interest (this scaling method has been also proposed by Lestuzzi et al. 2004, Naumoski et al. 2004 and Elenas 2002).  The scaling of records within this period range allows also the use of the same records to many other structural systems. The 5%-damping velocity spectra were obtained and the average spectral pseudo- velocities of the period range 1s to 2s, PSV*1-2, were computed for each record.  The scaling factor was then calculated as the ratio of these average spectral pseudo-velocities to the one for the target demand.  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 57 - Step 3.4. Selection criteria Three suites of records were defined for each earthquake type by following these criteria: • Select 10 records per earthquake type; • All records should be in the scaling range of periods; • Preferably select those records above the 70% of the target in the scaling range of periods; • The average of the spectra of selected records should be above the 90% of the target spectra in the scaling range of periods; • Select one record per station; • Give preference to records of different earthquakes. Table 2.3 shows the final selection of records for Vancouver representing crustal, subcrustal and subduction earthquakes.  This table provides earthquake names, dates, station names, moment magnitudes (Mw), hypocentral distances (D), peak ground accelerations (PGA) of recorded motions, the average spectral velocities in the 1.0s to 2.0s period range (PSV*1-2) and the scaling factors (SF). Figure 2.9 compares the spectral pseudo-velocities of the selected motions and average spectrum with the target spectrum.  Differences amongst these three suites can be observed in terms of spectral shapes or period content.  Crustal earthquakes have a clear short-period spectral content with a progressive decay for periods longer than 2 seconds.  The same is true for the subcrustal suite, but with spectral values dominated at the scaled 1.0s to 2.0s period  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 58 - range only10.  Subduction earthquake records have a better correlation with the target spectral values over most of periods with a clear long-period spectral content. 2.4.4 Step 4 – Incremental dynamic analyses Step 4.1. Range of intensities The range of intensities was selected to be from 0 to 2.5 times (0% to 250%) the base intensity (100%) of selected ground motions in increments of 0.1 (10%). Step 4.2. Analyses Incremental dynamic analysis (IDA) was performed using computer program CANNY (Li 2009) to the wood system model for the selected range of intensity increments.  For illustration purposes, it is assumed that the LDRS has a maximum lateral resistance or capacity (P force in Figure 2.5c) of 10% the total seismic weight, W, of the building (the following results will be referred to the W2-10%W system).  P-Delta effect has inherently included during the nonlinear dynamic analyses performed to this model. Step 4.3. Responses Maximum drift deformations at each increment, Ij, and for each record, GMi, were stored in a drift matrix as per shown in Table 2.4 for crustal earthquake motions.  For illustration purposes, the median IDA curves for W2-10%W are presented in Figure 2.10 for  10 Many subcrustal earthquake records were not selected because of the steep decay of their spectra at periods longer than 0.5 seconds.  These records should be investigated further in order to verify or update existing attenuation relationships of subcrustal earthquakes.  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 59 - the three earthquake types.  From these median IDA curves, slightly different structural responses can be observed between crustal and subcrustal records, but a significant difference is observed in those for subduction records.  Subduction earthquakes trigger the failure (a flat line in the IDA curve) at intensity levels higher than 190% of the base intensity while the crustal and subcrustal earthquakes at intensity levels around the 140% of the base intensity. 2.4.5 Step 5 – Conditional probabilities Step 5.1. Probability function A log-normal distribution is assigned to the computed maximum drifts at each level of intensity for each suite.  The mean and standard deviation of natural logarithms of drifts were calculated and used to build a normal distribution at each intensity level.  These statistical parameters were only computed with actual values.  Infinite values due to excessive deformations in the analyses were considered separately to the actual values to compute probabilities by simple counting11. Step 5.2. Conditional probability Table 2.4 shows the resulting probabilities for a 4% drift exceedance below the IDA results (row A) for the crustal earthquake suite of motions.  Infinite values are shown in this table as “Inf”, which were counted and added to the probability.  The distributions of  11 E.g. if 6 results out of the ten results are very large deformations (with infinite values), then the function is fitted to the other 4 results.  The 6 out of 10 probability was then added to the probability calculated out of the fitted function.  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 60 - resulting probabilities of 4% drift exceedance for the W2-10%W model are shown in Figure 2.11 for the three earthquake types (Crustal, Subcrustal and Subduction). As expected from median IDA results shown in Figure 2.10, the conditional probabilities of drift exceedance differ by the type of earthquake.  It is clear that the probabilities of exceeding the 4% drift with subduction earthquakes are much lower than those with the other earthquake types up to intensities of 180%.  Between 110% and 130% intensities, the contribution from subcrustal earthquakes to this probability is higher than those from crustal earthquakes.  Crustal and subcrustal effects in the structural system are comparable at intensities larger than 140%.  The three earthquakes have similar contribution to this probability at intensities larger than 200%. 2.4.6 Step 6 – PDE Step 6.1. Total probability According to Equation (2.4), the probability of drift exceedance is the multiplication of the conditional probabilities of drift exceedance (row A in Table 2.4) with the frequencies of intensity occurrences (row B in Table 2.4).  The resulting multiplication is shown in row C of Table 2.4.  The addition of individual values in row C yields to a total annual frequency of drift exceedance for crustal earthquakes, λCr, of 1.23×10-4.  In words, the 4% drift of this W2 system will be exceeded once if a crustal earthquake occurs in 8,130 years.  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 61 - Step 6.2. Calculation for other earthquake types By analogy to the calculation process of Table 2.4, annual frequencies of the 4% drift exceedance for subcrustal, λSCr, and subduction, λSd, earthquakes are 1.46×10-4 and 0.47×10-4, respectively, giving a total annual frequency of 3.16×10-4.  This is equivalent to say that the 4% drift will be exceeded for this wood system once if any of the three earthquake types occurred in 3,165 years. Step 6.3. PDE The risk to life-safety or PDE of the W2-10%W system in 50 years is given by Equation (2.5), %6.1)501016.3exp(1%)4( 4 =××−−=>= −DrPPDE T .  In other words, the probability of exceeding 4% drift in this wood system is 1.6% if any of the three earthquake types occurred within the next fifty years.  This can be also expressed in terms of the performance objective adopted for the Schools Project, i.e., there are 1.6% chances of having at least one seriously injured person or casualty in this school building if the any of the three earthquakes occurred within school hours in the next fifty years. By following the same Poisson process for individual earthquakes, then the probabilities of exceeding 4% drift in W2 if crustal, subcrustal and subduction earthquake occurred alone in fifty years will be 0.6%, 0.7% and 0.2%, respectively.  These individual probabilities serve to identify the contribution to the total risk or PDE of each earthquake type.  In this case, crustal and subcrustal earthquakes are predominant with a contribution of more than 80% to the total risk or PDE.  In some sense, this is similar to the seismic hazard  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 62 - defined for Vancouver in the NBCC 2005, which is mainly contributed by subcrustal and crustal earthquakes. A PDE of 1.6% is useful information for the Schools Project in relative terms.  A basic comparison with the 2% probability of ground shaking exceedance in 50 years prescribed in the NBCC 2005 shows that the seismic risk of life-safety damage to a W2 system is lower than the probability of occurrence of the design earthquake prescribed in the code.  This comparison is for reference purposes only and is given to compare or contrast the probability values in fifty years.  Considering the 2% probability of the code as a reference point, then it is possible to say that the PDE of the W2 system is relatively low. More interestingly for the Schools Project is the comparison of the 1.6 % PDE with the PDE values of many other school buildings.  A set of PDE values can be used for ranking the schools and for prioritizing the seismic retrofit of those with the highest PDEs.  The definition of PDE limits for the risk assessment and retrofit prioritization of BC school buildings is further discussed in the next section. 2.5. CONSIDERATIONS FOR THE SCHOOL PROJECT 2.5.1 Limits on PDE A PDE of 2% for all the building prototypes has been initially recommended to the MoEBC for the life-safety performance of BC schools.  The rationale for selecting 2% PDE is that the tolerable risk of death of a person that has been used for risk assessment (Vrijling 2001, Bowles 2007) is 1 in 10,000 per year, which can be shown to be equivalent to 2% in 50  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 63 - years12.  This PDE limit is still been discussed by the project members, but it has been accepted as a reasonable starting point to define an acceptable risk limit for this project. To assist the MoEBC in prioritizing the school buildings that need to be retrofitted, PDE ranges have been used to define levels of risks.  The recommended risk levels were: low, moderate, high, and very-high risk, which correspond to PDE ranges of 0%-2%, 2%- 5%, 5%-10% and 10%-or-higher, respectively. With this information, the MoEBC has been able to identify which schools fall into the high and very high risk categories, and has allocated the necessary financial resources to proceed with the retrofits of the schools in these categories. 2.5.2 Required lateral resistance The 1.6% PDE in the example shown in section 2.4 was calculated for a system exceeding 4% drift with a lateral resistance of 10%W.  The procedure described before can also be adapted to calculate the required lateral resistance of the structural system for a prescribed PDE value.  This information can be compared with the existing capacity of the building in order to determine if strengthening of the structure is required.  In case where strengthening of the structure is not feasible, the engineer can adopt an alternative retrofit solution, such as replacing the existing lateral resisting system with another system that provides the required capacity.  12 Vrijling (2001) provided a base value of tolerable risk of death of 1 in 10,000/year when voluntariness is neutral and there are direct benefits in the activity, such as driving a car.  The tolerable risk of failure then is given by this tolerable risk of death divided by the probability of being killed in the event of an accident.  In the Schools Project, this probability can be estimated by the rate in time spent by the person in a school during one year, i.e., 10hrs in 24hrs/day × 20days in 30days/mth × 10mths in 12 mths/yr = 0.23.  Thus, the acceptable or tolerable risk of failure is around 4 × 10-4 or its Poisson-based equivalent of 2% in 50 years.  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 64 - The calculation of the required resistance unavoidably involves an iterative process until the limiting risk value is reached.  In the Schools Project, several lateral resistance values of the generic structural systems were implemented and the proposed procedure was repeated several times.  A family of resistance-PDE pair values was finally obtained and then used to determine the required resistance by interpolation. It should be clarified that in this iterative process the yield deformation was kept constant and the initial stiffness was modified to obtain corresponding resistance values. Consequently, an increase or decrease in the lateral resistance of the system was directly related to an increase or decrease of the of the initial stiffness of the system To illustrate the calculation process of the required lateral resistance, the procedure was repeated for the W2 system for resistance values of 5%W, 6%W and 20%W.  Figure 2.12 shows the annual frequency of exceeding a 4% drift in the W2 system with the four different resistance values.  Resulting curves are shown for the three earthquake types and for the aggregated or total value.  Considering a PDE limit of 2% (annual frequency of drift exceedance of 4×10-4) for the 4% drift limit, the required resistance for the W2 system will be 9.5%W.  Therefore, the engineer should provide at least a lateral force capacity (base shear) for this system of 9.5%W to ensure a life-safety performance for the classroom section of this school.  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 65 - 2.5.3 Deaggregated risk per earthquake type The curves of Figure 2.12 show the contribution to the total (aggregated) risk of damage by earthquake type for a W2 system with different resistance values.  Clearly, the contribution of each earthquake to the total risk of damage is different for each resistance value.  While the contributions of crustal and subduction earthquakes are similar for systems with lateral resistances lower than 8%W, the contribution of subduction earthquakes is very small for resistances larger than 10%W.  Subcrustal and crustal earthquakes have similar contribution to the risk of damage for systems with a resistance higher than 8%W. The contribution of the earthquake type to the total risk will depend largely on the type of structural system to be assessed.  To illustrate this dependency, the seismic risk to a reinforced concrete shearwall (also common in BC schools) is also calculated.  The nonlinear behaviour of this system is characterized by strength/stiffness-deteriorated loops shown in Figure 2.13a.  The maximum drift deformation for this system has been set to 2% for a life- safety performance.  The resulting annual probabilities of exceeding this 2% drift are shown in Figure 2.13b.  In contrast to that for W2, the relative contribution of each earthquake type to the total risk is the same for all resistance values of C1.  In this case, crustal earthquakes are the most dominant contributors to total risk, while subduction earthquakes are the least dominant contributors to total risk. One common observation from above risk results is that the risk posed by crustal earthquakes is higher than that by subcrustal and subduction earthquakes for W2 and C1 located in Vancouver.  The dominant contribution of crustal earthquakes to total risk is even  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 66 - more evident for buildings systems that experience low levels of deformation, i.e., more rigid systems.  In general, the risk contribution by earthquake type will depend significantly on the type of structural system, location and site conditions. 2.5.4 Site conditions The calculation of risk, based on motions recorded on Site Class C soils, was extended to schools located in Site Class D soils.  An Equivalent Intensity Factor, EIF, was developed to transform the IDA results to Class D-based IDA results.  The use of the EIF is an advantageous tool to account for site effects of Class D soils in the Schools Project that saves running more than a million analyses and conducting expensive site-specific site response studies.  The details and application of the EIF are provided in Chapter 3. 2.5.5 Generation of database A strategy was established in this project to run massive analyses and to manage the results generated by using the proposed procedure.  This project involves many variables or parameters: building typology, site condition, geographical location, lateral resistance, drift value, motion intensity and type of earthquake.  The combination of these variables using the proposed procedure yields to more than a million runs generating a massive database. An automatic process that involves the combination of several computer programs was developed.  Four general stages were defined for this process: (1) the generation of multiple input files for analyses, (2) batch process of multiple analyses, (3) final risk calculations and preparation of database information.  Matlab (The Mathworks 2008) program was used to  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 67 - generate multiple input files, to extract information from output files, to calculate risk and to prepare basic information for the database.  WinBatch (Wilson WindowWare 2008) program was used to batch multiple runs of CANNY (Li 2009), the structural analyses program, in parallel processors.  This automatic process is further explained in Appendix A. 2.5.6 User interface A user-friendly interface program, called the Seismic Performance Calculator13 (SPC), is being developed for this project to provide instant access to required data for assessing the need of retrofit and for running retrofit options.  The SPC is seen as the final analytical tool of the proposed methodology that provides the engineer access to a highly advanced, peer- reviewed analytical database without requiring him/her to be experienced in the use of nonlinear dynamic analysis techniques.  This final analytical program permits the engineer to quickly analyze principal building elements that have analytically complex behaviour. The SPC is still under development with a preliminary layout shown in Figure 2.14 for the LDRS option.  The SPC has two potential options for the estimation of seismic risk and two potential options for running retrofit options of LDRSs: Basic Risk Assessment, Detailed Risk Assessment, Basic Risk Retrofit and Detailed Risk Retrofit (options in the left-side of the four screens shown in Figure 2.14).  Lists of options are displayed for input variables such as Community, Soil Type, Prototype, Resistance, Drift Limit and Drift.  Two action buttons are available for the user: Analysis and Print.  Information stored in the database is instantly displayed by clicking the Analysis button.  A summarized report of the information  13 It is expected that the final version of the Seismic Performance Calculator be released by March 2011.  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 68 - displayed will be printed by clicking the Print button (this summary can be used to support or to complement the engineering calculation report). The information displayed by clicking the Analysis button is different in each screen. The four screens shown in Figure 2.14 correspond to the W2 system located in Vancouver in a Site Class C soil. The first screen (Figure 2.14a) shows the Basic Risk Assessment option that computes the risk of exceeding a tolerable drift limit in the system with a specific maximum lateral resistance.  The tolerable drift is 4% and the system resistance is 10%W yielding to a risk value or PDE of 1.6% with a retrofit priority classified as “Lower”.  This classification is used for prioritizing schools for future retrofit. The second screen (Figure 2.14b) shows the Detailed Risk Assessment option that calculates the required resistance of the system to limit specific risk estimates of exceeding a tolerable drift limit.  The tolerable drift is 4% and the required resistance associated to risks of 2%, 3%, 5% and 10% in 50 years are 9.6%W, 7.5%W, 5.1%W and 2.6%W, respectively. A graph of these values allows the user to inter/extrapolate other resistance values at different risk estimates.  This option shows how sensitive risk estimates are to the resistance values and is useful when the resistance of an existing system can not be defined clearly. The third screen (Figure 2.14c) shows the Basic Retrofit option that computes the required resistance of the system to limit a 2% PDE (risk in 50 years) to a specific range of tolerable drifts.  The resistances are calculated for 2%, 3% and 4% drifts.  A graph showing  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 69 - drifts versus resistances allows the user that other retrofit options (e.g., increasing the resistance with another system) be examined. The fourth screen (Figure 2.14d) shows the Detailed Retrofit option that computes the required resistance to limit different risks to a specific drift.  The drift is 4% and the calculated resistance for a 2% risk in 50 years is 9.6%W.  This option also checks the risk conditioned to a certain intensity level of the total seismic hazard (aggregated to the three earthquake types).  A histogram shows the sensitivity of these conditional risks between 80% and 120% (e.g., 7.1% risk at the 100% intensity).  In this project, a maximum 10% conditional probability has been recommended at the 100% intensity.  This recommendation is consistent with recent guidelines on estimating the seismic performance of existing buildings before collapse (FEMA 2009). 2.6. CONCLUSIONS This chapter described a procedure for estimating the risk of damage of existing low- rise school buildings in British Columbia.  Damage was associated to the maximum drift deformation of the building exceeding a drift limit, which depends on the performance objective defined for the building, e.g., life-safety.  The procedure estimates a deaggregated risk for crustal, subcrustal and subduction earthquakes that occur in British Columbia.  The calculation of risk of damage was based on a deaggregated seismic hazard by earthquake type.  Ground motion records were selected to represent this deaggregated seismic hazard and used to compute the maximum drift deformation of school building components at different intensity increments.  Conditional probabilities of drift exceedance were computed  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 70 - at each increment and convolved with the annual probabilities of occurrences of the intensity increments.  The compound probability of all intensity increments was calculated for each earthquake type and aggregated to obtain a total annual probability of drift exceedance.  The total annual probability was prorated to 50 years to get the total risk.  An example of a characteristic school building in British Columbia was used to illustrate the proposed procedure.  The following features can be highlighted from the proposed seismic risk assessment procedure: • use of incremental non-linear dynamic analysis technique; • full range of ground motion intensity increments considered; • combining structural analysis results with current seismic hazard data; • insight into structural response to different earthquake types; • ability to mitigate earthquake damage to any drift deformation; • rational quantitative method of assigning risk; The application of the proposed procedure in the Schools Project generated a very extensive database that contains risk values and required resistances of more than thirty structural systems, located in more than 50 locations across the province and in two different soil conditions.  This data can be accessed by practicing engineers through a user-friendly interface named as the Seismic Performance Calculator that is still under development.  This interface will be available next year to local engineers for the quick assessment/retrofit of school buildings and for assisting the Ministry of Education of British Columbia to identify the most-at-risk schools in the province.  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 71 - Table 2.1:  Ranges of moment magnitude, depth and hypocentral distance for the preliminary selection of recording stations of crustal, subcrustal and subduction earthquakes   Crustal EQs Subcrustal EQs Subduction EQs Moment Magnitude (Mw) 6.5 – 7.5 6.3 – 7.6 8 – Max Depth (km) 0 – 30 30 – 90 0 – 50 Hypocentral Distance (km) 0 – 80 30 – 100 120 – 250   Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 72 - Table 2.2:  Summary of earthquakes and number of stations searched for the selection of records Crustal Number Earthquake Date Mag. Stations ID Name dd/mm/yy Mw No 1 Kern County 21-Jul-52 7.4 2 2 Parkfield 28-Jun-66 6.2 1 3 San Fernando 09-Feb-71 6.6 4 4 Friuli, Italy-01 06-May-76 6.5 2 5 Gazli, USSR 17-May-76 6.8 1 6 Santa Barbara 13-Aug-78 5.9 1 7 Tabas, Iran 16-Sep-78 7.4 1 8 Imperial Valley-06 15-Oct-79 6.5 2 9 Mammoth Lakes-01 25-May-80 6.1 1 10 Victoria, Mexico 09-Jun-80 6.3 1 11 Irpinia, Italy-01 23-Nov-80 6.9 2 12 Irpinia, Italy-02 23-Nov-80 6.2 2 13 Coalinga-01 02-May-83 6.4 5 14 Morgan Hill 24-Apr-84 6.2 2 15 Nahanni, Canada 23-Dec-85 6.8 2 16 N. Palm Springs 08-Jul-86 6.1 1 17 New Zealand-02 02-Mar-87 6.6 1 18 Whittier Narrows-01 01-Oct-87 6 6 19 Loma Prieta 18-Oct-89 6.9 22 20 Manjil, Iran 20-Jun-90 7.4 1 21 Cape Mendocino 25-Apr-92 7 2 22 Landers 28-Jun-92 7.3 1 23 Landers 28-Jun-92 7.3 1 24 Northridge-01 17-Jan-94 6.7 34 25 Kobe, Japan 16-Jan-95 6.9 2 26 Kocaeli, Turkey 17-Aug-99 7.5 1 27 Chi-Chi, Taiwan-03 20-Sep-99 6.2 7 28 Chi-Chi, Taiwan-04 20-Sep-99 6.2 1 29 Chi-Chi, Taiwan-06 20-Sep-99 6.3 2 30 Hector Mine 16-Oct-99 7.1 1 31 Duzce, Turkey 12-Nov-99 7.1 1 32 E. Honshu, Japan 13-Jun-08 6.8 13 Subcrustal Number Earthquake Date Magnitude Stations ID Name dd/mm/yy Mw No 1 Nisqually, WA 28-Feb-01 6.8 20 2 Guerrero, Mexico 10-Dec-94 6.6 3 3 Michoacan, Mexico 11-Jan-97 7.1 2 4 El Salvador 13-Jan-01 7.6 1 5 S. Honshu, Japan 24-Mar-01 6.4 11 6 Miyagi_Oki, Japan 16-Aug-05 7.2 4 7 Olympia, WA 13-Apr-49 6.9 1 8 Puget Sound, WA 29-Apr-65 6.7 1 Subduction Number Earthquake Date Magnitude Stations ID Name dd/mm/yy Mw No 1 Tokachi_Oki, Japan 25-Sep-03  8 15 2 Valparaiso, Chile  03-Mar-85  8 1 3 Southern Peru  23-Jun-01  8.4 5 4 Tarapaca, Chile  13-Jun-05  8 1 5 Michoacan, Mexico  19-Sep-85  8.1 (Ms) 7  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 73 - Table 2.3:  Summary of selected records for Vancouver in Site Class C soils grouped by earthquake type Crustal Suite - Vancouver - Site Class C Earthquake Date Station Mw1 D2 PGA PSV*1-2 SF3 Name  Name km g cm/sec Kern County 21-Jul-1952 USGS 1095 Taft Lincoln School 7.4 46.2 0.18 30.8 1.38 Tabas, Iran 16-Sep-1978 Stn: 9102 Dayhook 7.4 21.4 0.41 44.5 0.95 Irpinia, Italy-01 23-Nov-1980 ENEL 99999 Calitri 6.9 17.8 0.13 44.0 0.97 Nahanni, Canada 23-Dec-1985 Stn: 6098 Site 2 6.8 10.3 0.32 36.5 1.16 CDMG 57007 Corralitos 6.9 18.9 0.64 51.8 0.82 Loma Prieta 18-Oct-1989 CDMG 57217 Coyote Lake Dam (SW Abut) 6.9 35.4 0.48 54.7 0.78 Cape Mendocino 25-Apr-1992 CDMG 89156 Petrolia 7.0 10.5 0.59 57.0 0.75 Northridge-01 17-Jan-1994 USGS 5108 Santa Susana Ground 6.7 22.8 0.29 33.2 1.28 Kobe, Japan 16-Jan-1995 CUE 99999 Nishi-Akashi 6.9 19.9 0.51 43.0 0.99 E. Honshu, Japan 13-Jun-2008 Ichinoseki (IWT010) 6.8 20.0 0.22 40.4 1.05 Subcrustal Suite - Vancouver - Site Class C Earthquake Date Station Mw D PGA PSV*1-2 SF Name  Name km g cm/sec Renton (RBEN) 6.8 73.1 0.11 21.1 1.94 Seattle (BHD) 6.8 76.8 0.16 40.6 1.01 Seattle (KIMB) 6.8 77.4 0.14 34.2 1.19 Seattle (MAR) 6.8 77.6 0.13 13.2 3.08 Poulsbo (KITP) 6.8 78.9 0.06 21.4 1.91 Seattle (CRO) 6.8 79.4 0.09 18.4 2.22 Nisqually, WA 28-Feb-2001 Seattle (EVA) 6.8 80.7 0.06 22.1 1.84 Guerrero, Mexico 10-Dec-1994 Zihuatanejo (AZIH) 6.6 76.6 0.06 11.3 3.61 Michoacan, Mexico 11-Jan-1997 Villita (VILE) 7.1 71.4 0.10 12.2 3.35 El Salvador 13-Jan-2001 Unidad de Salud, Panchimalco (PA) 7.6 95.7 0.19 17.9 2.28 Subduction Suite - Vancouver - Site Class C Earthquake Date Station Mw D PGA PSV*1-2 SF Name  Name km g cm/sec Meguro (HKD113) 8.0 58.6 0.16 27.2 0.96 Noya (HKD107) 8.0 126.4 0.09 38.0 0.69 Obihiro (HKD095) 8.0 132.2 0.18 51.6 0.51 Hombetsu (HKD090) 8.0 145.8 0.50 26.8 0.97 Futamata (HKD087) 8.0 148.7 0.26 38.9 0.67 Tokachi-oki, Japan 25-Sep-2003 Tsurui (HKD083) 8.0 163.4 0.19 35.8 0.73 Caleta De Campos (CALE) 8.1 38.3 0.15 42.1 0.62 Villita (VILE) 8.1 47.8 0.11 24.0 1.09 La Union (UNIO) 8.1 83.9 0.17 34.3 0.76 Michoacan, Mexico 4 19-Sep-1985 Zihuatanejo (AZIH) 8.1 132.6 0.10 34.9 0.75 1 Moment magnitude 2 Hypocentral distance 3 Scaling factor 4 Local Magnitude was reported for this earthquake only  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 74 - Table 2.4:  Results of calculation process of seismic risk to the W2-10%W prototype for the crustal earthquake suite of motions   Drift (%)  GMi Intensity, Ij (%)  # 10 ··· 100 110 120 130 140 ··· 250  1 0.2 ··· 1.8 2.1 2.3 3.1 Inf ··· Inf  2 0.2 ··· 2.3 2.6 2.9 3.6 4.0 ··· Inf             10 0.2 ··· 1.9 2.2 2.6 2.4 3.3 ··· Inf IDA Results (Drift Matrix) A P(Dr > 4% | Ij) 0.00 ··· 0.00 0.00 0.00 0.23 0.82 ··· 1.00 Conditional Probability B ∆λHj (× 10-6) Inf ··· 109.2 91.3 62.3 47.5 38.1 ··· 2.5 Frequency of Occurrence C A × B (× 10-6) 0.00 ··· 0.00 0.00 0.00 10.9 31.2 ··· 2.5 D λCr = Σ C (× 10-4) 1.23 Annual Frequency of Drift Exceedance - Equation (2.4)     Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 75 -  Figure 2.1:  Cascadia Subduction Zone showing crustal earthquakes in North America plate; subcrustal earthquakes in Juan de Fuca plate and subduction earthquakes. (Cascadia_earthquake.jpeg is a courtesy of the U.S. Geological Survey. The USGS home page is http://www.usgs.gov)  Figure 2.2:  Generic IDA curves for four earthquake records and the distribution of drift dr at a given intensity Drift, Dr Intensity dr I IDA curves Data fitting  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 76 -  Figure 2.3:  Proposed calculation procedure of the probability of drift exceedance, PDE Step 1 - Buildings Step 2 - Seismic Hazard Calculations Step 3 - Ground Motion Records Step 4 - Incremental Dynamic Analysis Step 5 - Conditional Probabilities Step 6 - Probability of Drift Exceedance  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 77 -  Figure 2.4:  Lay-out and details of plan and elevation of an unblocked plywood shearwall in the classroom section of an existing BC school building Gymnasium Classrooms Offices and Lobby 42m 42m 60m 18m 25m 10m URM Walls + Windows Unblocked Plywood Shearwalls 12m 8m 2.4m 3m 3m Elevation  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 78 -  Figure 2.5:  (a) Representation of the 2-storey example school building and (b) modeling for nonlinear dynamic analysis including the (c) backbone curve and (d) hysteretic rule of the unblocked plywood shearwall system  LDRS  LDRS 0.8 m1 m1 k W2 k (a) (b) (c) Fo rc e Drift (%) 1.7 2.5 4.5 10 0.52P P 0.95P B C D E A F G H I F1 F1  2 ∆1 ∆1  2 Fo rc e Drift (d)  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 79 - 0 2 4 6 8 10 0.2 0.6 1.0 1.4 1.8 2.2 2.6 Period (sec) N um be r o f S tr uc tu ra l S ys te m s T1 Teff  Figure 2.6:  Distribution of elastic and effective (equivalent inelastic) periods of a representative sample of low-rise wood-frame school building systems in BC  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 80 - a) 1 10 100 1000 10000 100000 60 80 100 120 140 160 180 200 Intensity, I  (%) A nn ua l F re qu en cy  o f E xc ee da nc e,  f ( I ) (x  1 0- 6 )  Crustal Subcrustal Subduction Total ∆λ H (100%) = λ H (90%) - λΗ (100%) = 109.2 × 10-6 f (100%) = 4 × 10-4  b) 1 10 100 1000 10000 70 80 90 100 110 120 130 140 150 Intensity, I  (%) A nn ua l F re qu en cy  o f O cc ur re nc e,  ∆λ H j (x 10 -6 ) Crustal Subcrustal Subduction Total ∆λ H (100%) = 109.2 × 10-6  Figure 2.7:  Annual frequencies of level of shaking (a) exceedance and (b) occurrence of crustal subcrustal and subduction earthquakes for Vancouver  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 81 - PSV Spectra - Vancouver - Site Class C 0 20 40 60 0.0 0.5 1.0 1.5 2.0 Period (sec) PS V (c m /s ec ) Crustal - R Subcrustal - H Subduction UHS - Vancouver  Figure 2.8:  Spectral pseudo-velocities for each earthquake type and for the UHS of a Site Class C in Vancouver (5%-damping)  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 82 - Crustal Earthquakes 0 20 40 60 80 100 0 1 2 3 4 Period (sec) PS V (c m /s ec ) Records Records Average Target Target x 0.7  Subcrustal Earthquakes 0 20 40 60 80 100 0 1 2 3 4 Period (sec) PS V (c m /s ec ) Records Records Average Target Target x 0.7  Subduction Earthquakes 0 20 40 60 80 100 0 1 2 3 4 Period (sec) PS V (c m /s ec ) Records Records Average Target Target x 0.7  Figure 2.9:  Spectral 5%-damping pseudo-velocities of selected/modified records and target hazard spectra for crustal, subcrustal and subduction earthquakes14  14 PSV spectra of crustal earthquakes have been limited to 100 cm/sec for convenience.  The full-scale plot of these spectra can be found in Appendix C.  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 83 - Median IDA Curves W2-10%W  - Vancouver 0 50 100 150 200 250 0 1 2 3 4 5 6 Inter-storey Drift, Dr  (%) In te ns ity , I  (% ) Crustal Subcrustal Subduction  Figure 2.10:  Median IDA curves for a plywood shear-wall 2-storey building with a lateral resistance of 10%W, W2-10%W, located in Vancouver W2-10%W  - Vancouver 0.0 0.2 0.4 0.6 0.8 1.0 1.2 100 110 120 130 140 150 160 170 180 190 200 Intensity, I  (%) Pr ob ab ili ty  o f E xc ee da nc e,  P ( D r > dr  | I) Crustal Subcrustal Subduction  Figure 2.11:  Distribution of probabilities of 4% drift exceedance of the W2-10%W system located in Vancouver for crustal, subcrustal and subduction earthquake motions for a range of incremental intensities  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 84 - W2 - 4% drift - Vancouver 9.5%W at 4 x 10-4 1 10 100 1000 10000 0 5 10 15 20 25 Resistance (%W ) A nn ua l F re qu en cy  o f D rif t Ex ce ed an ce , λ  (x  1 0- 6 )  Total Crustal Subcrustal Subduction  Figure 2.12:  Annual frequencies of drift exceedance of a plywood shear wall system, W2, located in Vancouver  C1 - 2% drift - Vancouver 1 10 100 1000 10000 0 5 10 15 20 25 Resistance (%W ) A nn ua l F re qu en cy  o f D rif t Ex ce ed an ce , λ  (x  1 0- 6 )  Total Crustal Subcrustal Subduction    Figure 2.13:  (a) Hysteretic rule and (b) annual frequencies of drift exceedance of a reinforced concrete shear wall system, C1, located in Vancouver                    a)                                                                                      b)  Drift Force  A B E C D F G  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 85 -   Figure 2.14:  Preliminary seismic performance calculator snapshots of 4 options for LDRSs: a) Basic Risk Assessment, b) Detailed Risk Assessment, c) Basic Retrofit and d) Detailed Retrofit Community Vancouver Soil Type Site Class C Prototype W2 Resistance 10%W Drift Limit 4% Analysis PDE = 1.6% Retrofit Priority Lower Seismic Performance Calculator Print Basic Risk Assessment Detailed Risk Assessment Basic Risk Retrofit Detailed Risk Retrofit Community Vancouver Soil Type Site Class C Prototype W2 Analysis Seismic Performance Calculator Print Basic Risk Assessment Detailed Risk Assessment Basic Risk Retrofit Detailed Risk Retrofit Analysis Results Drift (%) Resistance (%W) 2 43 21 1014 Drift (%) R es is ta n ce  ( % W ) 2 3 4 10 20 Community Vancouver Soil Type Site Class C Prototype W2 Drift 4% Analysis Seismic Performance Calculator Print Basic Risk Assessment Detailed Risk Assessment Basic Risk Retrofit Detailed Risk Retrofit Resistance (%W) 4 8 12 4 12 P D E (% ) Analysis Results PDE (%) Resistance (%W) 2 53 9.6 5.17.5 10 2.6 8 Community Vancouver Soil Type Site Class C Prototype W2 Drift 4% Analysis Seismic Performance Calculator Print Basic Risk Assessment Detailed Risk Assessment Basic Risk Retrofit Detailed Risk Retrofit Resistance (%W) 4 8 12 4 12 8 P D E (% ) Analysis Results Resistance = 9.6%W Level of Shaking (%) 80 5 15 10 P (D r> dr ) (% ) 90 100 110 120 2.5 5.5 7.1 8.1 14.2 2 a) b) c) d)  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 86 - 2.7. REFERENCES Adams, J., and Halchuk, S., 2003. Fourth generation seismic hazard maps of Canada: values for over 650 Canadian localities intended for the 2005 National Building Code of Canada, Open file 4459, Geological Survey of Canada, Ottawa, ON, Canada. Alvarado, P., Beck S., Zandt, G., Araujo, M., and Triep, E., 2005. Crustal deformation in the south-central Andes backarc terranes as viewed from regional broad-band seismic waveform modeling, Geophysical Journal International, 163, 580–598. American Society of Civil Engineers (ASCE), 2007. Seismic Rehabilitation of Existing Buildings (ASCE/SEI 41-06), Reston, VA, USA. Aoi, S., Obara, K., Hori, S., Kasahara, K., and Okada, Y., 2000. New Japanese uphole/downhole strong-motion observation network: KiK-net, Seismological Research Letters, 72, 239. Applied Technology Council (ATC), 2009.  ATC-58 50% Draft: Guidelines for Seismic Performance Assessment of Buildings, Department of Homeland Security, Federal Emergency Management Agency, Washington, D.C., USA. Araujo, M., Pérez A., and Millán, M., 2005.  The last destructive earthquakes occurred in La Rioja (05-28-2002) and Catamarca (09-07-2004), northwestern Pampean ranges, Argentina, 6th International Symposium on Andean Geodynamics (ISAG 2005, Barcelona), extended abstracts, 53–56. Archuleta, R.J., Steidl, J., and Squibb, M., 2006.  The COSMOS virtual data center: a web portal for strong motion data dissemination, Seismological Research Letters, 77, 651– 658. Association of Professional Engineers and Geoscientists of British Columbia (APEGBC), 2006. Bridging Guidelines for the Performance-based Seismic Retrofit of BC Schools, Second Edition, Burnaby, B.C., Canada. Atwater, B.F., Satoko, M.-R., Satake, K., Yoshinobu, T., Kazue, U., and Yamaguchi, D.K., 2005. 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Subduction of young plates: A case of the Philippine Sea plate beneath the Chugoku region, Japan, Earth Planets Space, 54, 3–8.  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 88 - Naumosky, N., Saatcioglu, M., and Amiri-Hormozaki, K., 2004. Effects of scaling of earthquake excitations on the dynamic response of reinforced concrete frame buildings, Proceedings of the13th world conference on earthquake engineering, Paper 2917, Vancouver, BC, Canada. New Zealand Society for Earthquake Engineering (NZSEE), 2006.  Assessment and Improvement of the Structural Performance of Buildings in Earthquake, Wellington, New Zealand. Otani, S., 2000. Seismic vulnerability assessment method for buildings in Japan, Earthquake Engineering and Engineering Seismology, 2, 47–56. Radulian, M., Vaccari, F., Mandrescu, N., Panza, G. F., Moldoveanu, C. L., 2000. Deterministic Hazard computation for Vrancea (Romania) subcrustal earthquakes, Proceedings of the 3rd EU-Japan Workshop on Seismic Risk, Kyoto, Japan, 61–67. Reyners, M., 1987. Subcrustal earthquakes in the central south island, New Zealand, and the root of the Southern Alps, Geology, 15, 1168–1171. Risk Engineering, 2008.  EZ-FRISK version 7.33 Software for Earthquake Ground Motion Estimation. User’s Manual, Risk Engineering Inc., Golden, CO, USA. Ristau, J.P., 2004. Seismotectonics of Western Canada from Regional Moment Tensor Analysis, Ph.D. Thesis, University of Victoria, Victoria, B.C., Canada. Scholl, R., and Thiel, Jr. C., 1986. The Chile Earthquake of March 3, 1985. Earthquake Spectra, 2, 249–508. Selvaggi, G., and Amato, A., 1992. Subcrustal earthquakes in the northern Apennines (Italy): evidence for a still active subduction? Geophysical Research Letters, 19, 2127–2130. Seno, T., and Yoshida, M., 2004. Where and why do large shallow intraslab earthquakes occur? Physics of the Earth and Planetary Interiors, 141, 183–206. Shome, N., Cornell, C. A., Bazzurro, P., and Carballo, J. E., 1998. Earthquakes, records and nonlinear responses, Earthquake Spectra, 14, 469–500. The Mathworks, 2008. MATLAB – The Language of Technical Computing, Natick, MA, USA, http://www.mathworks.com/products/matlab/ Vamvatsikos, D., and Cornell, C.A., 2004. Applied incremental dynamic analysis, Earthquake Spectra, 20, 523–553. Vrijling, J.K., 2001. Probabilistic design of water defense systems in the Netherlands, Reliability Engineering and System Safety, 74, 337–344.  Chapter 2: Seismic Risk Assessment Procedure for Low-rise School Buildings Located in British Columbia - 89 - Watson-Lamprey, J.., and Abrahamson, N., 2005. Selection of ground motion time series and limits on scaling, Soil Dynamics and Earthquake Engineering, 26, 477–482. Wilson WindowWare, 2008. WINBATCH 2008B, Wilson WindowWare, Inc., Seattle, WA, USA, http://www.winbatch.com   Chapter 3:   Seismic Risk Assessment Methodology for British Columbia Schools Located in Site Class D Soils - 90 - Chapter 3. SEISMIC RISK ASSESSMENT METHODOLOGY FOR BRITISH COLUMBIA SCHOOLS LOCATED ON SITE CLASS D SOILS15 3.1. INTRODUCTION A major seismic risk mitigation program is being conducted for schools in British Columbia, BC.  A probabilistic seismic risk assessment, SRA, procedure was developed for assessing the seismic risk to BC school buildings and for defining minimum requirements of seismic upgrading considering the three earthquake types (crustal, subcrustal and subduction) that contribute to BC seismicity.  This tool was based on multiple analyses of school structural systems using selected earthquake motions recorded on Site Class C sites – defined in the national building code, NBCC 2005 (Canadian Commission on Building and Fire Codes 2005), as soft rock or firm soil with an average shear wave velocity between 360 m/s and 760 m/s in the upper 30 meters.  These risk estimates are, therefore, valid only for schools located on Class C sites. More than a million analyses were conducted to cover the entire database for the risk assessment and seismic retrofit of schools in Class C soils.  Building a database for schools located on other classes of sites would require another million runs.  This was not feasible given the time constraints and the budget limitations on the project.  Therefore, a procedure was developed for converting Site Class C data to be applicable to other sites.  15 A version of this chapter will be submitted for a peer-reviewed journal publication. Pina, F.E., Ventura, C.E., Finn, W.D.L., and Taylor, G., “Seismic Risk Assessment Methodology for British Columbia Schools Located in Softer Soils.”  Chapter 3:   Seismic Risk Assessment Methodology for British Columbia Schools Located in Site Class D Soils - 91 - Many schools in BC are located on Site Class D sites (Taylor et al. 2006).  These sites are defined in the NBCC 2005 as soft soils with average shear wave velocities between 180 m/s and 360 m/s in the upper 30 meters.  Class D soils amplify the site response with respect to Class C soils and increase the risk of damage in school buildings.  So far, specific site response analyses have been undertaken for all schools founded on Site Class E soils (Vs30 ≤ 180 m/s), and school buildings on these sites are in the stage of retrofit design or construction.  For schools located on Site Class D soils, a code-based approach was momentarily implemented till information from these sites was gathered (APEGBC 2006). Ground surface motions were obtained by site response analyses for a range of Class D sites (APEGBC 2007), using the program SHAKE based on equivalent linear dynamic analyses (Idriss and Sun 1992).  However, the earthquake demands on the structure due to these free-surface motions were even larger than those given by the current building code, NBCC 2005, for Class D sites.  It was found in many cases that the free-surface motions were highly amplified at high-to-moderate intensities of the outcrop motions.  This response is associated with high strain levels, as has been reported in many other studies (e.g., Martin and Lew 1999, Silva et al. 2000, Stewart et al. 2008).  Current practice considers nonlinear dynamic analysis to be more appropriate for estimating soft-soil surface motions at these high strain levels.  The nonlinear dynamic analyses were conducted using computer program DESRA-2D (Lee and Finn 1978). In this study, the results of nonlinear dynamic response of different site profiles characteristic of Class D soils of BC schools are investigated.  The concept of Equivalent  Chapter 3:   Seismic Risk Assessment Methodology for British Columbia Schools Located in Site Class D Soils - 92 - Intensity Factor, EIF, was developed to transform Class C data to Class D data.  This transformation makes it unnecessary to carry out again the many analyses conducted to get Class C data.  In particular, this study focuses on the effect of sites to typical structural systems of schools using motions recorded from three different earthquake types (crustal, subcrustal and subduction).  Earthquake types were treated separately because there is a possibility that site/structural responses be very different. 3.2. SRA PROCEDURE FOR SITE CLASS C In order to understand the transformation of data for Site Class C to Site Class D, it is necessary to describe in general terms the procedure adopted for calculating the seismic risk of schools in Class C soils.  A detailed description has been given in Chapter 2. The SRA procedure uses incremental dynamic analyses, IDA (Vamvatsikos and Cornell 2004), to estimate the incremental inter-storey deformation drifts of 36 generic types of school building systems (Appendix B) under 3 sets of 10 motions each recorded from crustal, subcrustal and subduction earthquakes on Site Class C sites.  These motions were selected to represent their corresponding 2%-in-50yr-exceedance uniform hazard spectra. The records were scaled to match the average spectral velocity in the 1 to 2 seconds period of interest for all school buildings.  The intensities of the input motions range from 10% to 250% the design motion intensity given by the NBCC 2005.  This level of shaking is called the 100% intensity level.  Conditional probabilities of drift exceedance were calculated for each intensity increment of the 100% motion level.  The conditional probabilities were convoluted with the annual frequency of the intensity increment to give the total probability  Chapter 3:   Seismic Risk Assessment Methodology for British Columbia Schools Located in Site Class D Soils - 93 - of drift limit being exceeded, PDE, for all earthquake types.  The PDE can be calculated in this way for any damage level specified by the appropriate drift ratio.  For the school project, the drift ratio of interest for each generic school type is the one corresponding to a retrofit objective of life-safety. 3.3. EQUIVALENT INTENSITY FACTOR The equivalent intensity factor, EIF, is the ratio of the intensity in the Site Class D site to the intensity in the Site Class C site that yields the same drift ratio.  This definition is illustrated in Figure 3.1 in a typical plot of IDA results showing the variation of the drift ratio with the intensity increment of the j-th input record.  The calculation process of EIFs is as follows: 1. The i-th intensity level of the j-th motion record is defined for the Site Class D site, IDi,j; 2. The drift ratio, dri, is computed; 3. The intensity level, ICi,j, associated with dri is read from the Site Class C IDA curve; 4. The equivalent intensity factor for the j-th record and for the i-th intensity level is then given by the ratio of the two intensities, ICi,j / IDi,j; This process is repeated for all the records with the same i-th intensity level and the median value is calculated, which is considered here as the characteristic EIF value for Site Class D.  Chapter 3:   Seismic Risk Assessment Methodology for British Columbia Schools Located in Site Class D Soils - 94 - 3.4. SITE RESPONSE ANALYSIS This section describes some generalities about the site response analyses conducted in this study.  Particular emphasis is made on the results obtained from these analyses for the three earthquake types adopted in the Schools Project. 3.4.1 Site description Site response analyses were conducted for 11 soil columns on Site Class D sites in the Greater Vancouver and Greater Victoria areas.  The columns were selected to cover a relatively broad range of properties and depths.  Figure 3.2 shows the distribution of shear wave velocities of the 11 different sites.  Graphic details of each site are given in Appendix D. Detailed information of each site was provided by local geotechnical consultants responsible for each site (APEGBC 2006). 3.4.2 Modeling and numerical processing The three suites of scaled 10 Class-C site ground motions (for crustal, subcrustal and subduction earthquakes) were used as the outcrop ground motions for site response analyses. Detailed information on the selection and modification of these records is provided in Chapter 2.  The nonlinear program DESRA (Lee and Finn 1978) was used to generate free- surface motions for the 11 sites.  Chapter 3:   Seismic Risk Assessment Methodology for British Columbia Schools Located in Site Class D Soils - 95 - 3.4.3 Results The results of the site response analyses are shown in Figure 3.3 in non-dimensional form. These plots show the variation of the amplification of median maximum accelerations with depth.  The accelerations correspond to the 100% intensity input motion for crustal, subcrustal and subduction earthquakes.  The effects of site amplification in terms of spectral values are shown in Figure 3.4.  In this figure the median pseudo-velocity spectra16 of the Class C motions and the Class D motions are presented. Additional calculations were carried out for ground motion intensities of 50%, 75%, 150% and 200%.  The median amplification of 10 ground motions per earthquake type was considered to be the characteristic value of each site.  These characteristic values were logarithmically distributed and then used to compute the median and the 84-th percentile of the 11 sites per earthquake type.  The results of these analyses in terms of the average spectral velocity for each of the five intensities in the 1 to 2 second period range17 are shown in Figure 3.5. 3.4.4 Observations The amplification of peak accelerations in Figure 3.3 is evident for all earthquake motions but the magnitude of amplifications differ by earthquake type.  Crustal motions are less amplified with depth than subcrustal and subduction motions.  Although these are only median results, we can observe some different patterns of results for each type of earthquake.  16 Spectral pseudo-velocities were used to calculate the earthquake demand for BC schools 17 The PSV*1-2 is the earthquake demand that defines the seismicity of BC locations in the Schools Project.  All records have been scaled to match this demand for each BC location.  Chapter 3:   Seismic Risk Assessment Methodology for British Columbia Schools Located in Site Class D Soils - 96 - Although distinctive patterns are observed in peak accelerations, they are not clearly identified in terms of the amplification of the spectral velocities (Figure 3.4).  Furthermore, the medians and 84-th percentiles of the amplification factors of Figure 3.518 are relatively similar for the three earthquake types for the entire range of intensities.  Only at the 50% intensity of the motions, clear differences by earthquake type are observed.  At 75% or larger intensities, where larger strains develop at the site, a constant amplification is observed regardless of the earthquake type.  These observations suggest that the assessment of Class D amplification in schools for each earthquake type individually is unnecessary.  However, it is important to confirm these observations by including in the site response analysis the response of the structural system.  A discussion of this is presented in the following section. 3.5. STRUCTURAL ANALYSIS The resulting surface acceleration time histories are applied to a set of structures using nonlinear dynamic analysis (NDA).  The NDA are repeated for the three suites of the 11 sites for the five outcrop motion intensities: 50%, 75%, 100%, 150% and 200% of the reference intensity defined in the code.  NDA was conducted using computer program CANNY (Li 2008).  An in-house software program was developed for data post-processing. NDA is illustrated for a regular 2-story building model (Figure 3.6a).  The earthquake demand is resisted by lateral deformation resistance systems (LDRS) located in each floor.  18 Note the large scale of the ordinates, which has been purposely fixed this way to be later compared with the EIF (this one considering the results of structural analyses).  Chapter 3:   Seismic Risk Assessment Methodology for British Columbia Schools Located in Site Class D Soils - 97 - Mass of second floor, “m2”, has been assigned as 80% of the mass of the first floor, “m1”.  A lumped mass system with nonlinear shear springs models the system (Figure 3.6b). To check the sensitivity of the EIF to the type of structure, we have purposely selected three different nonlinear behaviours of the springs, “k” (Figure 3.6c).  The first case, W2, corresponds to a very flexible unblocked plywood shear-wall. The hysteretic loops have strength degradation (D to E), stiffness deterioration (F to G) at many loading cycles and it is heavily pinched during the reloading (C to D to E).  The second case, C1, is a rigid reinforced concrete shear-wall with strength/stiffness-deteriorated loops.  The third case, R1, is a rigid rocking masonry wall with negligible hysteretic dissipative energy. 3.6. EIF CALCULATION EIFs are calculated using the procedure summarized in Figure 3.1.  Four drift performance criteria were selected for the structural systems as follows: 1.5%, 2%, 3% and 4% drift for the W2 and R1, and 0.75%, 1%, 1.5% and 2% for C1.  At each of the five intensity levels, the maximum resistance force of each system was iteratively reduced till these drifts were reached.  The maximum resistance and the drift were used to extract the intensity level form the Site Class C database.  The EIF is then given by the ratio of the defined Site Class D intensity to the extracted Site Class C intensity.  This exercise was repeated for the three systems, the four drift values, the ten ground motions of the three earthquake types.  Chapter 3:   Seismic Risk Assessment Methodology for British Columbia Schools Located in Site Class D Soils - 98 - 3.6.1 EIF Results Ten EIF values were calculated for each site.  The median of the ten EIFs was determined for each site and log-normally distributed for all 11 sites.  The 84-th percentile for the log-normally distributed median values was adopted as the deterministic EIF value for Class D sites19.  Figure 3.7 shows the distribution of the calculated 84-th percentile EIF with the motion intensity, I, for each type of earthquake, for each structural system and for each level of deformation. The trends on both magnitude and shape of the EIFs clearly differ by type of earthquake, but they are somehow similar amongst the three structural systems.  Except for the 1.5% drift in W2, crustal EIFs vary linearly from approximately 1.6 at the 50% intensity to 1.2 at the 200% intensity for most drift ratios of the three systems.  Subcrustal and subduction EIFs have approximately a quadratic variation with the intensity level for the three systems.  This variation is highly dependent on the drift value, especially at the lower intensity levels.  Subduction EIFs differ significantly by drift ratio at intensities lower than and equal to 75%. EIF results shown in Figure 3.7 are also compared to the 84-th percentile amplification factors shown in Figure 3.5 to see how the levels of deformation of the structural systems and the type of earthquake impact the actions of softer soils on the building response.  Site amplification factors closely agree with the EIFs for all the levels of deformations of the  19 Considering the limited number of sites studied, the authors considered prudent to adopt the 84-th percentile as the representative amplification factor for site response and also for calculating the EIFs.  As more sites become available from this project, the EIF values will be updated.  The EIF resulting from this study are preliminary recommendations for the Schools Project only.  Chapter 3:   Seismic Risk Assessment Methodology for British Columbia Schools Located in Site Class D Soils - 99 - three systems for crustal motions.  However, EIFs do not follow the same trend to that for site amplification for the other two earthquake types.  The 84-th percentile site amplification factors for subcrustal and subduction motions are around a constant value of 1.4, which is rather a lower bound of EIFs for all drifts of the three systems.  It can be deduced that site factors are good indicators of amplification by Class D sites for crustal motions only, and that they do not represent the amplification for subcrustal and subduction motions.  Site factors or code-based factors are, therefore, not suitable to account for amplification by Class D sites in BC schools and hence for the subsequent calculation of risk. 3.6.2 Recommended EIFs For the school project, a preliminary constant value of EIF can be recommended per earthquake type: 1.4 for crustal and 1.6 for both subcrustal and subduction.  Although not reflecting the variation by drift ratios at different intensity levels observed in this study, the recommended EIFs are practical estimates to modify Site Class C results to Site Class D and to subsequently measure the risk to schools located on Class D sites.  These are conservative estimates of EIFs based on the 84-th percentile of results for all sites.  These recommended values could change as more sites are available for future studies. 3.6.3 Proposed EIF equation An equation for EIF was developed to account for all the variables involved in this study, such as earthquake type, structural system, drift deformation, and motion intensity. For each earthquake type, each structural system and each drift value, the variation of the EIFs with respect to the intensity level was determined by curve fitting the data with a simple  Chapter 3:   Seismic Risk Assessment Methodology for British Columbia Schools Located in Site Class D Soils - 100 - linear regression.  Then, the variation of the regression coefficients with respect to the drift values was determined by curve fitting the values with a nonlinear regression.  This procedure permitted to develop an equation to determine the EIFs as a function of the drift, motion intensity, structural system and type of earthquake. A convenient form of this equation is: 86 753 2 2 2 1 ]4)ln()ln([),( CC IcdratcIcIdratcIcIdratcIdratEIF ++++=  (3.1) in which drat is the ratio of a specified drift to maximum tolerable drift of the system, the variable I is the corresponding motion intensity as a percentage of the reference 100% intensity, and the coefficients c1 to c7 are given in Table 3.1 for each type of earthquake and for each system.  The drat variable is a normalized way to express the drift of the system as a function of the tolerable drift.  For example, the maximum tolerable drift for the W2 system is 4% and for a specified drift of 1.5%, drat = 1.5/4 = 0.375. The application of EIF values calculated from Equation 3.1 is valid only in the range of 50% to 200% of the 100% intensity of input motions.  A constant value given by the respective extreme value is recommended for those cases outside the range, i.e., use the EIF at 50% intensity for EIFs < 50% and the EIF at 200% intensity for EIFs > 200%.  This recommendation over predicts EIF values at intensities larger than 200% and under predicts EIF values at intensities lower than 50%.  Considering that the contributions to total risk of  Chapter 3:   Seismic Risk Assessment Methodology for British Columbia Schools Located in Site Class D Soils - 101 - extreme motion intensities are negligible20, this recommendation can be considered as reasonable. Figures 3.9 to 3.11 shows the proposed EIF equation (in solid lines) compared to observed EIF values (with markers) in the 50% to 200% intensity range for the three earthquake types and for the four drift levels of the W2, C1 and R1 systems, respectively. Good correlation is observed between the proposed EIFs and the observed values.  The only exception to this good correlation is observed at low drift values in the W2 system.  An effort has been made in this case to represent conservatively with Equation (3.1) the values for crustal earthquakes in a W2 system. 3.7. APPLICATION The use of EIFs is illustrated here by application to a wood structural system, W2, located in Vancouver on a Site Class D site.  The model of the system is the same as the one described in Figure 3.6 assuming a maximum resistance of 10% the total seismic weight of the structure, W.  The calculated EIF values are used to transform the Site-Class-C-based IDA curves of each ground motion to equivalent Site-Class-D IDA curves. Figure 3.11 shows the IDA curves of a W2 system for a Site Class C ground motion and its corresponding EIF-modified IDA curve for a Site Class D ground motion of each type of earthquake.  The intensity values (in the ordinates) of Class C curves were divided by EIFs  20 The contribution to total risk from each motion intensity refers to the multiplication of the probability of drift exceedance for the motion intensity times the probability of occurrence of the motion intensity.  In this context, contributions at extreme motion intensities are almost negligible.  The probabilities of drift exceedance for very low motion intensities are very small, while the probabilities of occurrences of very high motion intensities are close to zero.  Chapter 3:   Seismic Risk Assessment Methodology for British Columbia Schools Located in Site Class D Soils - 102 - calculated from Equation 3.1.  For illustration purposes, the calculations at the 100% level of shaking are shown in each case.  For a W2 system subjected to a site-class-C crustal ground motion, the maximum drift at the 100% intensity level is 1.84% resulting in a drat = 1.84/4 = 0.46.  Replacing the intensity, I, of 100% and the drat = 0.46 in Equation (3.1), the EIF value gives 1.46.  Thus, the motion intensity in a Site Class D site associated to a 1.84% drift is 100/1.46 = 68.3%.  The same exercise was repeated for the subcrustal and subduction motions at the 100% intensity; EIF values being 1.63 and 1.50, respectively. This application of the EIF in the Class C IDA curves is only performed to one ground motion of each earthquake type.  This exercise is repeated to modify all the Class C IDA curves to Class D IDA curves.  In this case, both site response and structural analyses are avoided.  The risk can now be calculated by using only the last step of the SRA procedure presented in Chapter 2. 3.8. SUMMARY AND CONCLUSIONS An equivalent intensity factor, EIF, was developed to transform seismic risk and retrofit demand data from Class C sites to Class D sites.  This study was based on five intensity levels, thirty input motions, eleven sites and three structural systems, which makes a total of 4,950 analyses.  The number of analyses for estimating the risk of BC schools in Class C soils was more than a million.  The main advantages of using the EIFs are: (a) avoids the need of costly site-specific response analyses for Class D soils; (b) avoids the need to run a large number of additional structural analyses of the prototypes considered for the Schools Project; and (c) allows for a quick estimation of risk to BC schools located on Class D sites.  Chapter 3:   Seismic Risk Assessment Methodology for British Columbia Schools Located in Site Class D Soils - 103 - From the EIF values and their calculation process presented in this study, the following conclusions can be drawn: • The use of EIF values is a new and better method than code-based approaches to capture the effects of Class D sites to schools in British Columbia.  EIF values recognize the different types of earthquakes of British Columbia seismicity, which is fundamental for the estimation of seismic risk of damage to BC schools.  The usual code-based amplification factors are based only on site response analyses, while EIFs are based on combined site/structure analyses; • There are significant differences in EIF for the different earthquake types, crustal, subcrustal and subduction. • The observed EIF values can be described with a single equation considering type of earthquake, structural system, intensity of the ground motion and the level of deformation in the structural system. • The method for calculating EIF is general and can be extended for estimating the structural responses and subsequently the risk of damage to BC school buildings located in other soil types as the necessary data becomes available. The results of this study were based on specific ground motion intensities and on limited numbers of sites.  Future studies should be focused on updating the proposed EIF values by refining the intensity levels and including more sites.  Chapter 3:   Seismic Risk Assessment Methodology for British Columbia Schools Located in Site Class D Soils - 104 - Table 3.1:  Coefficients for calculating EIF with Equation (3.1) Earthquake Prototype c1 c2 c3 c4 c5 c6 c7 c8 Type   x 10-5 x 10-5 x 10-3 x 10-3 W2 C1 Crustal R1 0 0 0 -2.67 1.73 0 1.00 0 W2 1.01 -0.01 C1 1.00 0 Subcrustal R1 -2.0 -2.2 7.35 5.75 1.26 -0.45 0.75 0.05 W2 0.54 0.11 C1 1.00 0 Subduction R1 -2.0 -3.1 8.20 8.9 1.05 -0.62 0.82 0.03   Chapter 3:   Seismic Risk Assessment Methodology for British Columbia Schools Located in Site Class D Soils - 105 -  Site Class C Site Class D Site Class C Site Class D IDi,j ICi,j dri Drift Ratio Intensity EIFi,j = ICi,j / IDi,j EIFi = Median (EIFi,j) j-th record j-th record  Figure 3.1: Calculation process of the Equivalent Intensity Factor, EIF, for a Site Class D site, for a given i-th intensity of the j-th record    Chapter 3:   Seismic Risk Assessment Methodology for British Columbia Schools Located in Site Class D Soils - 106 - 100 200 300 400 500 600 700 8000 10 20 30 40 Shear Wave Velocity (m/s) D ep th  (m )   Li m it D  / E Li m it C  / D  Figure 3.2: Distribution of shear wave velocities in the 11 soil columns of school sites  Chapter 3:   Seismic Risk Assessment Methodology for British Columbia Schools Located in Site Class D Soils - 107 - 0 0.5 1 1.5 20 10 20 30 40 Median Max. Accn. Amplification Factor - Crustal D ep th  (m )   A F  =  1 Site 1-A Site 1-B Site 2-A Site 2-B Site 3-A Site 3-B Site 4-A Site 4-B Site 5-A Site 5-B Site 5-C 0 0.5 1 1.5 20 10 20 30 40 Median Max. Accn. Amplification Factor - Subcrustal D ep th  (m )   A F  =  1 Site 1-A Site 1-B Site 2-A Site 2-B Site 3-A Site 3-B Site 4-A Site 4-B Site 5-A Site 5-B Site 5-C 0 0.5 1 1.5 20 10 20 30 40 Median Max. Accn. Amplification Factor - Subduction D ep th  (m )   A F  =  1 Site 1-A Site 1-B Site 2-A Site 2-B Site 3-A Site 3-B Site 4-A Site 4-B Site 5-A Site 5-B Site 5-C  Figure 3.3: Distribution of the amplification of median maximum accelerations of 11 soil columns for the 100% motion intensity of crustal, subcrustal and subduction earthquakes  Chapter 3:   Seismic Risk Assessment Methodology for British Columbia Schools Located in Site Class D Soils - 108 - 0 0.5 1 1.5 2 2.5 3 3.5 4 0 20 40 60 80 100 Pseudo-velocity spectra - Crustal Period (s) S p ec tr al  P se u d o -v el o ci ty  ( cm /s )   C-sites Median D-sites Median Median of D-sites Median  0 0.5 1 1.5 2 2.5 3 3.5 4 0 20 40 60 80 100 Pseudo-velocity spectra - Subcrustal Period (s) S p ec tr al  P se u d o -v el o ci ty  ( cm /s )   C-sites Median D-sites Median Median of D-sites Median  0 0.5 1 1.5 2 2.5 3 3.5 4 0 20 40 60 80 100 Pseudo-velocity spectra - Subduction Period (s) S p ec tr al  P se u d o -v el o ci ty  ( cm /s )   C-sites Median D-sites Median Median of D-sites Median  Figure 3.4: Distribution of the median pseudo-velocity spectra of 11 soil columns for the 100% motion intensity of crustal, subcrustal and subduction earthquakes  Chapter 3:   Seismic Risk Assessment Methodology for British Columbia Schools Located in Site Class D Soils - 109 - Site Amplification of PSV* 1-2 1 1.2 1.4 1.6 0 50 100 150 200 250 Intensity, I  (%) PS V* 1- 2 i n Si te  C la ss  D  / PS V* 1- 2 in  S ite  C la ss  C Crustal Subcrustal Subduction 84-th Percentile Medians 75  Figure 3.5: Amplification factor of the average pseudo-velocity spectra in the 1 to 2 second period, PSV*1-2, range for 11 soil columns of crustal, subcrustal and subduction earthquake motions  Chapter 3:   Seismic Risk Assessment Methodology for British Columbia Schools Located in Site Class D Soils - 110 -  Figure 3.6: (a) Representation of a 2-storey building, (b) corresponding model for NDA and (c) hysteretic rules of 3 systems (W2, C1 and R1)   Drift Fo rc e A B E C D F G  LDRS  LDRS m2 = 0.8 m1 m1 k Drift Fo rc e A B E C D F G Drift Fo rc e A B C W2 C1 R1 k (a) (b) (c)  Chapter 3:   Seismic Risk Assessment Methodology for British Columbia Schools Located in Site Class D Soils - 111 - 50 100 150 20050 100 150 200 Intensity (%) 50 100 150 200 0.8 1.2 1.6 2 R1  - EI F   1.5% drift 2.0% drift 3.0% drift 4.0% drift 0.8 1.2 1.6 2 C1  - EI F   0.75% drift 1.0% drift 1.5% drift 2.0% drift SubductionSubcrustal 0.8 1.2 1.6 2 W 2 - E IF Crustal   1.5% drift 2.0% drift 3.0% drift 4.0% drift  Figure 3.7: 84-th percentile of log-normally distributed median EIFs for the W2, C1 and R1 systems, for different drift values and for the crustal, subcrustal and subduction earthquake motions  Chapter 3:   Seismic Risk Assessment Methodology for British Columbia Schools Located in Site Class D Soils - 112 - 50 100 150 200 Intensity (%) 50 100 150 200 0.8 1.2 1.6 2 Intensity (%) W 2  -  E IF   Calc-CR Calc-SCR Calc-SD Pred-CR Pred-SC Pred-SD 0.8 1.2 1.6 2 W 2  -  E IF 4% drift3% drift 2% drift1.5% drift  Figure 3.8:  Calculated (Calc) and predicted (Pred) EIF values for the W2 structural systems, for different drift values and for the crustal (CR), subcrustal (SCR) and subduction (SD) earthquakes     Chapter 3:   Seismic Risk Assessment Methodology for British Columbia Schools Located in Site Class D Soils - 113 - 50 100 150 200 Intensity (%) 50 100 150 200 0.8 1.2 1.6 2 Intensity (%) C 1  -  E IF   Calc-CR Calc-SCR Calc-SD Pred-CR Pred-SC Pred-SD 0.8 1.2 1.6 2 C 1  -  E IF 0.75% drift 1% drift 1.5% drift 2% drift  Figure 3.9:  Calculated (Calc) and predicted (Pred) EIF values for the C1 structural systems, for different drift values and for the crustal (CR), subcrustal (SCR) and subduction (SD) earthquakes   Chapter 3:   Seismic Risk Assessment Methodology for British Columbia Schools Located in Site Class D Soils - 114 - 50 100 150 200 Intensity (%) 50 100 150 200 0.8 1.2 1.6 2 Intensity (%) R 1  -  E IF   Calc-CR Calc-SCR Calc-SD Pred-CR Pred-SC Pred-SD 0.8 1.2 1.6 2 R 1  -  E IF 4% drift3% drift 2% drift1.5% drift  Figure 3.10:  Calculated (Calc) and predicted (Pred) EIF values for the R1 structural systems, for different drift values and for the crustal (CR), subcrustal (SCR) and subduction (SD) earthquakes  Chapter 3:   Seismic Risk Assessment Methodology for British Columbia Schools Located in Site Class D Soils - 115 - W2 - 1 Crustal Ground Motion 0 20 40 60 80 100 120 140 160 180 0 1 2 3 4 5 Maximum Inter-storey Drift (%) In te ns ity  (% ) Site Class C Site Class D EIF = 1.46 Drift       = 1.84 % Intensity = 100 % Drift       = 1.84 % Intensity = 100 % / 1.46 Intensity = 68.3 % W2 - 1 Subrustal Ground Motion 0 20 40 60 80 100 120 140 160 180 0 1 2 3 4 5 Maximum Inter-storey Drift (%) In te ns ity  (% ) Site Class C Site Class D EIF = 1.63 Drift       = 2.12 % Intensity = 100 % Drift       = 2.12 % Intensity = 100 % / 1.63 Intensity = 61.4 % W2 - 1 Subduction Ground Motion 0 20 40 60 80 100 120 140 160 180 0 1 2 3 4 5 Maximum Inter-storey Drift (%) In te ns ity  (% ) Site Class C Site Class D EIF = 1.50 Drift       = 2.42 % Intensity = 100 % Drift       = 2.42 % Intensity = 100 % / 1.50 Intensity = 66.7 %  Figure 3.11: Site Class D IDA curves calculated from existing Site Class C IDA curves using the proposed EIF values of the W2 system for crustal, subcrustal and subduction earthquakes  Chapter 3:   Seismic Risk Assessment Methodology for British Columbia Schools Located in Site Class D Soils - 116 - 3.9. REFERENCES Association of Professional Engineers and Geoscientists of British Columbia (APEGBC), 2007. Preliminary Site Response Analysis for Bridging Guidelines - Second Edition, presented at the Ninth Canadian Conference on Earthquake Engineering Ottawa, Ontario, Canada, Ottawa, Canada. Association of Professional Engineers and Geoscientists of British Columbia (APEGBC), 2006. Bridging Guidelines for the Performance-based Seismic Retrofit of BC Schools, Second Edition, Burnaby, B.C., Canada. Canadian Commission on Building and Fire Codes, 2005. National Building Code of Canada 12th Ed., National Research Council of Canada, Ottawa, ON, Canada. Idriss, I.M., and Sun, J.I., 1992.  User’s Manual for SHAKE91, Center for Geotechnical Modeling, Department of Civil and Environmental Engineering, University of California, Davis, CA, USA. Lee, M. K., and Finn, W. D. L., 1978.  DESRA 2C-Dynamic effective stress response analysis of soil deposits with energy transmitting boundary including assessment of liquefaction potential,  Soil Mechanics Series, 38, Dept. of Civil Engineering, Univ. of British Columbia, Vancouver, B.C., Canada. Li, K., 2008. CANNY Technical Manual, CANNY Consultant PTE Ltd., Singapore. Martin, G. R., and Lew, M., 1999.  Recommended procedures for implementation of DMG Special Publication 117—Guidelines for analyzing and mitigating liquefaction hazards in California, Southern California Earthquake Center, Los Angeles, CA, USA. Silva, W.J., Darragh, R.B., Gregor, N., Martin, G., Abrahamson, N.A., and Kircher, C., 2000. Reassessment of site coefficients and near-fault factors for building code provisions, Report to U.S. Geological Survey, National Earthquake Hazards Reduction Program, Award No. 98-HQGR-10-10, USA. Stewart, J. P., Kwok, A. O., Hashash, Y. M. A., Matasovic, N., Pyke, R. M., Wang, Z. L. and Z. Yang, 2008.  Benchmarking of nonlinear geotechnical ground response analysis procedures, PEER-2008/04, Pacific Earthquake Engineering Research Center (PEER), University of California, Berkeley, CA, USA. Taylor, G., Monahan, P., White, T., and Ventura, C., 2006. British Columbia schools seismic mitigation program: Dominant influence of soil type on life safety of Greater Vancouver and Lower Mainland schools of British Columbia, 8th US National Conference on Earthquake Engineering, EERI, San Francisco, CA, USA.  Chapter 3:   Seismic Risk Assessment Methodology for British Columbia Schools Located in Site Class D Soils - 117 - Vamvatsikos, D., and Cornell, C.A., 2004. Applied incremental dynamic analysis, Earthquake Spectra, 20, 523–553.    Chapter 4: Conclusions and Future Work - 118 - Chapter 4. CONCLUSIONS AND FUTURE WORK 4.1. SUMMARY OF CONTRIBUTIONS The methodology presented in this thesis is the fundamental basis of the seismic risk assessment/retrofit of BC schools that has had a high impact in both research and engineering practice at both the local and the international levels.  Besides, this thesis is part of an evolving process.  Many aspects of this thesis have been the results of extensive discussions amongst local and international experts. This thesis presented information that contributes knowledge to the seismic risk assessment in two forms: research and engineering practice.  A list of specific contributions in these two forms is summarized in this section.  Each item in the following list is contrasted with past studies or previous work to emphasize the contributions of this thesis.  The previous works or studies mentioned in this list have already been discussed throughout the thesis. 4.1.1 Research contributions The main research contributions of this thesis are: 1. Deaggregated seismic risk by earthquake type.  Most applications of risk assessment methodologies were focused on calculating risk due to a single seismic hazard contributed by either one or more earthquake types.  In contrast, the proposed  Chapter 4: Conclusions and Future Work - 119 - methodology allows that the contributions of crustal, subcrustal and subduction earthquakes to the total seismic risk of BC schools be determined. 2. A formulation and procedure for combining the deaggregated risk.  Previously, there were no studies or guidelines for combining individual risk estimates per earthquake type.  The contribution of earthquake type to total risk was only reflected in an aggregated seismic hazard. The proposed methodology combines the individual risks calculated per earthquake type to get a total estimate of seismic risk. This is valuable information for risk ranking purposes and retrofit decisions. 3. Procedure for selecting input ground motions in a seismic risk assessment program. Most existing procedures for selecting input records are intended for the assessment of specific structures or for the design of new buildings, but they are not intended to cover a large number of structural systems or buildings in a major seismic risk assessment program. The proposed procedure presents a method for the selection of suites of records that can be used for the risk assessment of a large number of structural systems. 4. Available input motions selected per earthquake type.  Public databases include many records of crustal earthquakes, some of subduction earthquakes, and few of subcrustal earthquakes, which makes the searching/selection task very time consuming for a seismic risk assessment project.  This thesis includes a database of selected ground motion records representative of the seismicity of British Columbia grouped by earthquake type.  These records can be used to investigate the effect of the earthquake type in a large variety of structures.  Chapter 4: Conclusions and Future Work - 120 - 5. A procedure for modifying IDA curves per soil conditions.  Past studies considered the site effect for the seismic risk assessment of structures at the seismic hazard level only and did not account for site effects at the seismic risk level explicitly.  The thesis introduces the concept of the Equivalent Intensity Factor that transform IDA results calculated for buildings on Site Class C sites to make them applicable for Site Class D sites.  The calculation of EIF values was based on these two particular sites, but the methodology presented in this thesis also holds for any other combination of sites. 6. Site effect depending on earthquake type.  The site effects of softer soils as a function of the earthquake type have not been adequately considered in past works of seismic risk assessment.  This thesis provides a solution to evaluate site effects taking into account soil and earthquake types.  The EIF values of this thesis were calculated for crustal, subcrustal and subduction earthquakes. 4.1.2 Engineering practice contributions The main contributions of this thesis to engineering practice are: 7. A feasible methodology for risk calculations.  The previous methodology developed in the Schools Project was deterministic and was not based on current probabilistic seismic risk assessment approaches, i.e., it did not account for the inherent uncertainty of the earthquake demand in the risk calculations.  The thesis presents a step-by-step procedure specifically developed for the BC schools assessment/retrofit program.  The  Chapter 4: Conclusions and Future Work - 121 - procedure has been automatized and used to provide engineers with risk estimates for the most prevalent structural systems in the BC schools. 8. A versatile methodology for assessment and retrofit.  The proposed procedure calculates both the risk of existing BC school buildings and also the required resistance of a structural system for limiting the risk to a user-defined deformation.  While the risk estimate is useful to identify at-risk school buildings, the required resistance is useful information for defining a retrofit solution for the building. 9. Efficient calculation of risk for soft soils. In the previous editions of the Schools Project, the site conditions were accounted for at the hazard level only.  In the previously adopted procedure the spectral demands were modified by code-based site factors and then input records were matched to them accordingly.  Preliminary studies based on several site response analyses were conducted at that stage of the project, but they did not generate any procedure for assessing/retrofitting schools in other site conditions. The use of the EIF values does not require performing specific site response analyses and conducting repetitive structural analyses.  Using EIFs avoid the preparation of new input data and the extraction of new output data, making it a very advantageous feature for the Schools Project in terms of time and costs. 10. An automatic process for speeding up calculations for the school project.  Extensive data for assessment/retrofit in previous stages of this project was not generated automatically.  Therefore, a calculation process for generating a massive amount of risk estimates for the Schools Project was not a feasible task at that time.  The automation  Chapter 4: Conclusions and Future Work - 122 - process of the overall seismic risk methodology saves thousands of man-power hours and reduces the costs involved in the calculation processes. It also removes the likely errors involved during data processing. 11. An accessible database tool.  The results obtained from the application of this methodology to school buildings in BC are gathered in a database that is accessible to local engineers through an online interface.  This program displays risk estimates and required resistances instantly for a number of variables involved in this project, such as location, structural system, level of deformation and soil type.  This tool is new for local practitioners and is a complement to technical guidelines to be released early next year (2011). 4.2. FUTURE WORK This work requires the study of many topics in the areas of seismology, structural engineering and geotechnical engineering.  Many individual components in the proposed methodology that were outside the scope of this thesis require further investigation.  Some of these investigations can be summarized as follows: 1. Probabilistic seismic hazard analysis for the Cascadia subduction earthquakes in BC. There is very limited information about the Cascadia subduction earthquake, but this requires more research to improve develop more reliable probabilistic seismic hazard from probable subduction earthquakes.  The need for this research is also recognized by the Geological Survey of Canada (Adams and Halchuk 2003).  Chapter 4: Conclusions and Future Work - 123 - 2. Updating the sample of selected records.  Ten records were selected for each earthquake type.  More records are available as more earthquakes occur, and that are instrumentally captured.  New records could potentially modify the probabilistic seismic hazard of BC.  In view of this, the selected records for this study may have to be revisited in the future and certainly be increased with the most current seismic data to make more reliable estimates of risk. 3. Evaluation of other techniques for scaling/modifying records.  Records in this study were linearly scaled to match part of the elastic hazard spectrum.  The impact to be fully comparable to fully response spectra can be also explored.  Exploring other techniques, such as the Conditional Mean Spectrum, is also legitimate. 4. Refined deaggregation of seismic risk. Suites of records were only separated by earthquake type.  Within one particular type of earthquake, there are many seismic sources with different earthquake recurrence rates.  Records and earthquakes can be also grouped by these seismic sources so that more bins or suites of motions can be defined.  The effect of grouping ground motions per seismic sources should be investigated in order to determine how risk estimates are affected. 5. Adaptation of the methodology to other types of buildings.  The procedure is only for the assessment of existing low-rise building structures.  The adaptation of the proposed methodology to taller buildings can be also explored.  Chapter 4: Conclusions and Future Work - 124 - 6. Flexibility on selecting different damage states for the building.  The proposed methodology was used to assess the risk to school buildings in BC for a damage state associated to a life-safety performance.  Seismic risk of damage associated to different performances can be also explored using the proposed methodology.  Chapter 4: Conclusions and Future Work - 125 - 4.3. REFERENCES Adams, J. and Halchuk, S., 2003. Fourth generation seismic hazard maps of Canada: values for over 650 Canadian localities intended for the 2005 National Building Code of Canada, Open file 4459, Geological Survey of Canada, Ottawa, ON, Canada.    Appendix A: The Batching Process in the School Project - 126 - Appendix A. THE BATCHING PROCESS IN THE SCHOOL PROJECT A.1. BACKGROUND The first set of guidelines, the Bridging Guidelines or BG herein (APEGBC 2006), required of an important number of analysis and of a coordinated process amongst different software programs of structural analysis and post-processing.  A tedious and time-consuming work was performed at that time to collect all the information required to build the basic data adopted in the BG.  A description of this previous work will help the reader on getting a better picture of the batching process described in this appendix. The resulting data from analyses was graphically delivered in the so-called Resistance Tables, which are familiar to and widely used by local engineers.  A Resistance Table shows a unique relationship between the maximum inter-storey drift and the minimum required capacity of a building structural model or prototype.  The drift is given as a percentage of the inter-storey height (%h) of the building and the required capacity is given in terms of the minimum required lateral resistance, Rm, of the system as a percentage of the total seismic weight of the structure (%W).  An example of these tables is shown in Figure A.1.  The name and seismic zone are shown at the top of the table.  This table corresponds to a W-2 prototype or an unblocked plywood structural system located in the Seismic Zone 4 defined in the BG (Vancouver is the reference city of this zone).  Detailed information about the structural system is given at the bottom of the table.  Three curves are shown for three site casses: C, D and E according to the site classification of the NBCC 2005 (Canadian Commission on  Appendix A: The Batching Process in the School Project - 127 - Building and Fire Codes, 2005).  Values of Rm (%W) at selected drift values (%h) are given at the bottom of the Resistance Tables for completeness. An important number of steps had to be performed in order to get these Resistance Tables.  They can be summarized as follows: Step 1. Define the structural model.  A two dimensional model of a two-story building with a 3-meter inter-storey height and lumped masses at each floor was adopted. Step 2. Select proper input ground motions.  Ground motion records from severe crustal earthquakes of California were adopted in this project and scaled to match the Uniform Hazard Spectra of five seismic zones in BC. Step 3. Define material and geometry parameters for the system.  Each storey of the structural system was modeled by a non-linear shear spring that was defined by a backbone curve and a characteristic hysteretic rule. Step 4. Prepare input files for structural analyses.  Two computer programs were used to capture the nonlinear response of each structural system: Quake-soft (Taylor 2006) – an in-house program, and CANNY (Li 2008) – a commercial nonlinear analysis program. Step 5. Run analysis for a system with very high lateral resistance, say 60%W, and get the maximum inter-storey drift from the output files of each analysis.  Appendix A: The Batching Process in the School Project - 128 - Step 6. Repeat Steps 3 to 5 for a lower resistance value till selected drift values are reached.  E.g. The Resistance Table of Figure A.1 shows drifts of 1.5%, 2%, 3% and 4%. An unknown number of runs needed to be performed in order to reach the selected drifts.  This task required the preparation of input files for different resistance values, i.e. different backbone curve parameters.  On top of that, this procedure had to be repeated for each input motion (10 in each case), for each site condition (3 in this case) and for each seismic zone (4 in this case).  In the fortunate, but unlikely, scenario where at the first resistance-value trial the selected drifts were reached, 480 runs were required for this particular structural system.  The BG had 17 systems, meaning that a minimum 8160 runs were required.  Of course, more than 8160 runs were needed for preparing the final Resistance Tables in the BG.  This significant number of analyses and manual post- processing were very time-consuming tasks at that stage of the project.  An automatic process could have certainly reduced the preparation of the Resistance Tables and consequently reduced the error involved in a manual data processing. A.2. THE NEED FOR A BATCHING PROCESS Currently, the First Edition of Technical Guidelines is under preparation to be released late summer of 2010.  In this new set of guidelines, a more complex and comprehensive procedure than the one presented in the BG is developed.  The new procedure estimates the risk to damage by following the procedure presented in this thesis for a large number of parameters.  This procedure now uses three suites of 10 motions representatives of the three  Appendix A: The Batching Process in the School Project - 129 - different types of earthquakes likely to occur in BC and it is repeated for several ground motion intensities, from 0 to 2.5 times the original intensity of selected motions in increments of 0.1.  Thus, a minimum of 36,000 runs are required for one structural system to determine the risk to damage.  This new set of guidelines also increases the number of structural systems to more than 30, thus increasing the computational process to a minimum of 1,080,000 runs.  Therefore, an automatic process is mandatory for this project. A.3. WHAT’S A BATCHING PROCESS? The reader may find better explanations of the batching process on-line by just web- browsing the word “batch file”.  As per the author’s experience, a definition for a batch file is: “a ‘very simple’ program that allows us focusing on other important matters.  The preparation of this ‘very simple’ program can sometimes yield to unexpected delays at the beginning of the overall work, but the results will make life much easier than neglecting or avoiding it”.  The reader must be aware that this is not an expert’s definition neither an advocacy message to automatize everything in our regular tasks.  However, it is certainly recommended that these “batch files” be codified and used for numerous repetitive tasks, such as the case for calculating risk in the school project. In technical terms, a batch file is a series of instructions in a text file to run many applications automatically.  A batch process, then, is the execution of a series of programs on a computer without human interaction.  A common example of a batch process in Civil Engineering is the modification of few parameters in an input data file many times, running the files, and extracting just few data from the output files.  Many researchers could find this  Appendix A: The Batching Process in the School Project - 130 - process familiar and sometimes, when doing this by hand, associated to frustrated results or delays on his projects or research work.  Automatizing this process is totally recommended, but it’s not an easy task. At the beginning this could be a frustrating experience as well. To help on understanding and applying more satisfactory this process, the following sections will deliver the batching process established, developed and adopted for the risk calculation of BC schools.  This process makes use of familiar and available tools to engineers and researchers that can be readily used in other projects or research areas. A.4. BASIC TOOLS FOR AN EFFICIENT BATCHING PROCESS Many script-based programs, such as Mathcad, Matlab, Python, etc., have built-in functions or procedures that deal with automatic processes.  These programs can call other applications from their scripts or can create executable files that can be run from other environments.  There are many programs that can be easily called or run from the DOS command prompt.  This is probably the most efficient and easiest way to batch a process for those that are familiar with basic command functions and script-based languages. One of the main problems with script-based languages (or DOS commands) is that they are not always able to open external applications.  It will require extensive knowledge on these languages to really call those applications and start working in a batch environment. This situation happens often with commercial software programs of structural engineering, such as SAP2000, ETABS, PERFORM, and even with CANNY.  In these cases, it is totally recommended that languages that are mainly intended for batching processes be used.  One  Appendix A: The Batching Process in the School Project - 131 - very powerful and easy to handle language is WINBATCH (Wilson WindowWare 2008). This software program allows for programming automatic processes by following exactly the human-based approach (e.g. open – edit – save – close) with very simple instructions.  The instructions for automatizing the process of opening CANNY – opening an input file – running – closing CANNY is shown in Program A.1. A.5. AUTOMATIC PROCESS FOR CALCULATING RISK Figure A.2 shows a scheme of the programs used to batch the risk calculations in the school project. A.5.1 Multiple input files A.5.1.1 Multiple variables/parameters There are several parameters involved in this project which combined yield to multiple input files for subsequent structural analyses.  Details on each of these parameters are given in Appendix B.  A list of these parameters is as follows: 1. Prototypes. 36 systems: 26 Lateral Deformation Resistance Sytems (LDRSs), 4 out- of-plane (OOP) systems, and 4 diaphragm (Diaph) systems; 2. Inter-storey height. Variable number of options depending on each prototype, e.g. 4 options for wood prototypes: H1=2.5m, H2=3.0m, H3=3.5m and H4=4.0m; 3. Type of Earthquake. 3 types with 10 scaled ground motions per suite: Crustal (Cr), Subcrustal (SCr) and Subduction (Sd); 4. Seismic Source Models. 2 models for crustal and subcrustal earthquakes, only: Historical (H) and Regional (R); 5. Seismic Level. 3 levels: High, Moderate (Mod) or Low; 6. Intensities or levels of shaking. 25 levels (in percentages) with increments of 10%;  Appendix A: The Batching Process in the School Project - 132 - 7. Resistance values. 42 values (as percentages of seismic weight W): 1 to 20%W in increments of 1%W; 22 to 40%W in increments of 2%W; 45 to 100%W in increments of 5%W; 8. Location. 58 communities of BC; 9. Rigidity. 2 cases: Flexible or Rigid; 10. Site Condition. 2 sites: Site Class C and Site Class D as per NBCC 2005 classification. A.5.1.2 Organizing input data CANNY has a feature that allows running of a limited number of input files in series. To take advantage of this feature in CANNY, all the input files were stored in single folders to be called and run from CANNY program automatically. Multiple input files were stored in single folders for a combination of prototypes, inter- storey height and type of earthquake.  For example, “W1H1_Cr” folder stored input files for wood prototypes W-1 with an inter-storey height H1=2.5m using Crustal earthquake motions. The naming format of the stored files was defined as follows:   “prototype – suite – ground motion # – resistance value – level of shaking. dat”.  The name of the prototype follows the same format as that in the folder name. The suite name includes information about the type of earthquake, source model and seismic level. The six suite names are as follows: (1) Cr_R_High; (2) Cr_R_Mod; (3) Scr_H_High; (4) Scr_H_Mod; (5) Sd_High; (6) Sd_High.  The ground motion # goes from 01 to 10.  The resistance value goes from 1 to 42.  And, the level of shaking goes from 010 to 250.  E.g. a file in the “W1H1_Cr” folder named as “W1-Cr_R_High-01-1-010.dat” corresponds to a W1 prototype with a 10%W resistance run for the first ground motion of the Cr_R_High list  Appendix A: The Batching Process in the School Project - 133 - scaled to 10% of the base intensity.  The extended information in each file name allows that a particular CANNY result be easily spot checked. A.5.1.3 Creation of multiple input files A MATLAB (The Mathworks 2008) routine (Program A.2) was developed to create the multiple input files using the naming process described above.  This routine creates thousands of input files in a matter of minutes.  These files are ready to be called from CANNY using the multiple run option. A.5.2 Batch process A batch code was created to automatize the multiple run option of CANNY.  The result of running this code is a set of multiple output files stored in the same input file folder.  The complete coding of the batch file is detailed in Program A.3 (Note that a semicolon “;” indicates that a comment has been placed). WINBATCH compiler was used to create an executable version of this batch file and distributed to many processors to run them in parallel.  In terms of speed using this executable files, all the analyses were completed with a 2GHz CPU in about two hours for one prototype and for all the parameter combinations. A.5.3 Post-processing The post-processing reads the files from the output file folders based on exactly the same name format described in the previous section.  A MATLAB routine allows for the extraction of the maximum inter-storey drift of each output file and store them in a 250×42 drift matrix for a given prototype, inter-storey height, seismic level and type of earthquake.  Appendix A: The Batching Process in the School Project - 134 - Drift values are organized in 10 rows for each ground motion and repeated 25 times for all the motion intensities, with a total of 250 rows.  The 42 columns correspond to drifts calculated for each resistance value.  The MATLAB code for extracting the drifts from output files and then storing them in the drift matrix is given in Program A.4.  Appendix A: The Batching Process in the School Project - 135 - Site Class 1.0% 1.5% 2.0% 2.5% 3.0% 4.0% C NR 35% 18% 14% 12% 9% D NR 44% 31% 19% 17% 12% E NR 54% 36% 28% 21% 17% Minimum Required Lateral Factored Resistance R m  (%W) Wood Prototype W-2 Unblocked OSB/Plywood Seismic Zone 4 (Vancouver) W-2   Zone 4 Figure 3-2(c) 0% 10% 20% 30% 40% 50% 60% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% Maximum Interstorey Drift (%h) M in im um  R eq ui re d La te ra l F ac to re d R es is ta nc e R m  (% W ) Site Class C Site Class D Site Class E  Figure A.1: Example of a Resistance Table extracted from the Second Editions of the BG (APEGBC 2006) for an unblocked plywood system located in Vancouver, BC.  Appendix A: The Batching Process in the School Project - 136 -  Figure A.2:  Overall automatic process for calculating the risk in the Schools Project.  Multiple input files Batch Process Matlab CANNY & Winbatch Post- processing Matlab Risk Calculations Matlab  Appendix A: The Batching Process in the School Project - 137 - Program A.1:  WinBatch program that automatize the process of opening CANNY, opening an input file, running and closing CANNY. ;--------- ;Run CANNY ;--------- Run("C:\Users\User\CANNY\canny.exe","") SendKey( "{~ 4}") ; Press enter 4 times SendKey("^o") ; Press Control + o (Open-file window) ;----------------------- ;Open and run input file ;----------------------- SendKey("C:\Users\User\CANNY\Examples\ex1.dat") ; Type path and file name Sendkey("~") ; Enter Timedelay(1) ; Wait for 1 second Sendkey("{RIGHT}") ; Press right arrow Sendkey("~") ; Enter ;----------- ;Close CANNY ;----------- Sendkey("!f") ; Press Alt + f (File menu window) Sendkey("x") ; Press x (close option) Sendkey("~") ; Enter ; End of batch file ;--------------------    Appendix A: The Batching Process in the School Project - 138 - Program A.2:  MATLAB program for the multiple creations of CANNY input files. function multi_input(N,Nesp,data,rootEQ,orig_input,folder) % MULTI_INPUT (N,Nesp,data,rootEQ,orig_input,folder) % Generate multiple input data files for CANNY program % Input data: %  N: number of increments for each record in increments of 10% %     e.g. N=25 implies 20 files: 10%, 20%, 30%,...250% %  Nesp: specific increment to create multi-input %        Nesp == 0 creates all the N increment files %  data: text file name including list of records %        and scaling factors %  rootEQ: directory path of records %  orig_input: original input file name %  folder: where the input files be stored % % Output data: N times number of records included in data file  fid1 = fopen(data , 'r+'); indpoint = strfind(data , '.'); site = data(1:indpoint(1)-1);  i = 1; while 1     tline =fgetl(fid1);     if ~ischar(tline), break, end      indE = strfind(tline , blanks(1));     record = tline(1 : indE(1)-1);      % get record name     sfactor = tline(indE(1)+1 : end);   % get scaling factor     sfactor = str2double(sfactor);     Nres    = 41;  % resistance levels     %------------------------------------     % Read only one increment file?     if Nesp == 0         ko = 1;         flag1 = 0;     else         ko = Nesp/10; %Increments of 10 by-default         N  = ko;         flag1 = ko;     end     %-------------------------------------     for k=ko:N         for j = 1:Nres             gen_input(record, sfactor, site, i, j, k, rootEQ,…                        orig_input,flag1);         end     end      i = i + 1; %Next record end  fclose(fid1);  Appendix A: The Batching Process in the School Project - 139 - %Move .dat files to "type" folder indEs = strfind(orig_input,'-'); indEs1 = indEs(1); type = [orig_input(1:indEs1-1)]; destination = [pwd '\' folder]; movefile([type '-' site '*'], destination);  return % End of Function  ------------------------------------------------------  function inputfile = gen_input (record, sfactor,...     site, i,j, k, rootEQ, orig_input, flag1) % GEN_INPUT(RECORD, SFACTOR, SITE, I, K, ROOTEQ, ORIG_INPUT) % Generate input file for CANNY program % input: %       record: record name %       sfactor: scaling factor associated to the record %       site: place or site class of the project e.g. C or PG %       i: record number %       j: file number per record (from 1 to 10 due to a CANNY lim.) %       k: inputfile number depending on how many %levels are required %       rootEQ: directory path of records %       orig_input: original input file name %       flag1: number due to a single run and affect the record scaling %              factor sf (for site response only) % output: name of modified input file  %inc_Rm = 2;  %2%W increments of Rm (by default) %Rm    = inc_Rm * j;%Current Rm (increments of 2% by default) Rmb = [(2:1:20) (22:2:40) (45:5:100)]; Rm = Rmb(j); sf = 10*k;   %10% increments of shaking level (by default) fid1 = fopen(orig_input,'r+'); % read and write the open file indline = strfind(orig_input,'-'); % find position of this string "-" indpoint = strfind(orig_input,'.'); common_name = [orig_input(1:indline(1)) site '-0' num2str(i) '-' num2str(j) '-']; common_ext = orig_input( indpoint : end);  % create name to input file if sf<=9     inputfile = [common_name '00' num2str(sf) common_ext]; elseif sf>9 && sf<=99     inputfile = [common_name '0' num2str(sf) common_ext]; else     inputfile = [common_name num2str(sf) common_ext]; end fid2 = fopen(inputfile,'w');  % Weight per floor Mass1 = 100; Mass2 = 80;  Appendix A: The Batching Process in the School Project - 140 - m1 = 100*Mass1/(Mass1+Mass2); m2 = 100*Mass2/(Mass1+Mass2);  %Inter-storey height in meters h_bdg   = 3; while 1     tline = fgetl(fid1);     if ~ischar(tline), break, end     fprintf(fid2,'%s\n',tline);     %disp(tline)     if strcmp(tline, '/*Site Class C Zone 4')         fgetl(fid1);         if flag1 == 0 % FLAG1 for site reponse analysis ONLY             factor = sfactor*sf/100;         else             factor = sfactor;             record = [record '_' num2str(sf)];         end         tline = ['factor ' num2str(factor) ' TX file = ' ...             rootEQ record '.txt'];         fprintf(fid2,'%s\n',tline);     end      if strcmp(tline, '//floor, unit (kN, m)')         fgetl(fid1);         %Writing this format: 3F Z=6         tline = ['3F Z=' num2str(2*h_bdg)];         fprintf(fid2,'%s\n',tline);         tline = ['2F Z=' num2str(1*h_bdg)];         fprintf(fid2,'%s\n',tline);         tline = ['1F Z=' num2str(0*h_bdg)];         fprintf(fid2,'%s\n',tline);     end      if strcmp(tline, '//node weight, unit (kN, m)')         fgetl(fid1);         % Writing this format:         % X1 Y1 3F W=44.4         % X1 Y1 2F W=55.6         tline = ['X1 Y1 3F W=' num2str(m2)];         fprintf(fid2,'%s\n',tline);         tline = ['X1 Y1 2F W=' num2str(m1)];         fprintf(fid2,'%s\n',tline);     end      if strcmp(tline, '//spring, unit (kN, m)')         fgetl(fid1);         % Writing this format:         % X1 Y1 2F-3F TX U100         % X1 Y1 1F-2F TX U100         elnum1 = 100;         tline = ['X1 Y1 1F-2F TX U' num2str(elnum1)];         fprintf(fid2,'%s\n',tline);  Appendix A: The Batching Process in the School Project - 141 -         tline = ['X1 Y1 2F-3F TX U' num2str(elnum1)];         fprintf(fid2,'%s\n',tline);     end      if strcmp(tline,'/*5%W')         if strncmp(common_name,'C1',2)==1 %DONE             [tline] = get_tline_C1(h_bdg,Rm);         elseif strncmp(common_name,'M1',2)==1 %DONE             [tline] = get_tline_M1(h_bdg,Rm);         elseif strncmp(common_name,'R1',2)==1 %DONE             [tline] = get_tline_R1(h_bdg,Rm);         elseif strncmp(common_name,'R2',2)==1 %DONE             [tline] = get_tline_R2(h_bdg,Rm);         elseif strncmp(common_name,'R3',2)==1 %DONE             [tline] = get_tline_R3(h_bdg,Rm);         elseif strncmp(common_name,'S1',2)==1 %DONE             [tline] = get_tline_S1(h_bdg,Rm);         elseif strncmp(common_name,'W1',2)==1 %DONE             [tline] = get_tline_W1(h_bdg,Rm);         elseif strncmp(common_name,'W2',2)==1 %DONE             [tline] = get_tline_W2(h_bdg,Rm);         end         fgetl(fid1);         fprintf(fid2,'%s\n',tline);     end     if strcmp(tline, 'load factor 1.0')     tline = ['spring X1 Y1 1F-2F TZ F0=' num2str(m1+m2)];     fgetl(fid1);     fprintf(fid2,'%s\n',tline);     tline = ['spring X1 Y1 2F-3F TZ F0=' num2str(m2)];     fgetl(fid1);     fprintf(fid2,'%s\n',tline);     end end fclose(fid1); fclose(fid2);  return    Appendix A: The Batching Process in the School Project - 142 - Program A.3:  WinBatch program that automatize the process of running CANNY multiple times and storing massive output data. ;=====HEADER================================================== ; ;MCANNY.WBT ;Runs multiple input DAT files in CANNY & ;Generates multiple output TRF files from the CA2 CANNY option ; ;The User must select: ; 1st. The directory where CANNY.EXE is ; 2nd. The directory where sub-dierctories are; ; 3rd. The sub-directory(ies) where input DAT files are (many folders can ; be selected); ; ;TRF files will be stored in the same sub-directories where DAT files are. ; ;September 2, 2009 ;Copyright - Freddy Pina ;----------------------  ;=============INPUT DIRECTORIES========================================== ;ASK DIRECTORY OF CANNY.EXE default_dir = "D:\SERIAS-Tool" dir1=AskDirectory("Select CANNY.EXE Directory","",default_dir, "Are you sure?",1|4) Message("Directory Path selected was", dir1) ;Create "Temp" folder in CANNY directory wpdir = StrCat(dir1,"Temp") If !DirExist(wpdir) Then DirMake(wpdir) temp_dir = StrCat(wpdir,'\')  ;ASK DIRECTORY OF ANALYSES ;Note that inputdir must be one single string, i.e. no spaces in between dir2=AskDirectory("Select ANALYSES Directory","",default_dir, "Are you sure?",1|4) Message("Directory Path selected was",dir2) list_dir2 = DirItemize(StrCat(dir2,"*.*"))  ;ASK FOLDER TO BE ANALYZED list_an = AskItemlist("Select Folders to be Analyzed",list_dir2,@Tab,@SORTED, @multiple, @FALSE) n_list = ItemCount(list_an, @TAB) ;========================================================================  For xx = 1 To n_list  ; For-loop for Multiple Analyses  folder_or = ItemExtract(xx,list_an,@Tab)  inputdir_or = StrCat(dir2,folder_or,"\")   ;-------------------  ;Open CANNY  program  ;-------------------  Appendix A: The Batching Process in the School Project - 143 -  cannydir = StrCat(dir1,"\CANNY.exe")  Run (cannydir,"")  SendKey( "{~ 5}")  DirGet ( )  DirChange(temp_dir)  TimeDelay(0.2)  FileDelete("*.brf|*.bdf|*.tmf|*.tof|*.trf|*.dat")  TimeDelay(1)   ;GET FILENAMES FROM INPUTDIR  filelist = StrCat(inputdir_or,"*.dat")  file_dat = filelist  Nbin = 50  infoarray = FileInfoToArray(file_dat, 0)  Ninfo = infoarray[0,0]   ; Number of dat files  n = Ninfo/Nbin  filetot = ArrDimension(n)  inputfile = ArrDimension(Nbin)  for j = 0 To n-1   pos_ini = Nbin*j + 1  ; Initial position of file package   pos_fin = pos_ini + Nbin - 1 ; Final position of file package   ; ; Rename input file for i = pos_ini To pos_fin  file1  = infoarray[i,0]    inputfile[i-pos_ini] = "%i%.dat"    file_new = StrCat(temp_dir,"%i%.dat")    Filecopy(StrCat(inputdir_or,file1),temp_dir,@False)    FileRename(StrCat(temp_dir,file1),file_new)   Next   ;   SendKey("!f")   ;Display File menu   SendKey("m")    ;Select Multi-Open option   if j==0    TimeDelay(0.3)   ;Delay of 0.3sec at the beginning only    SendKey(temp_dir) ;Work on default directory    TimeDelay(1)    Sendkey("~")    ;Enter key   endif   ;   ;Select all files in the Multi-open window   TimeDelay(1)   Sendkey("{TAB 8}") ;Tab 8 times   Sendkey("{SP}")  ;Space once   Sendkey("+{END}")   ;Shift + down-arrow   TimeDelay(0.5)   Sendkey("~")   Sendkey("!cc")   ;   ;Set conditions of first window   if j==0    Sendkey("{UP}")    Sendkey("{UP}")  Appendix A: The Batching Process in the School Project - 144 -    Sendkey("{UP}")    Sendkey("{SP}")    Sendkey("{UP}")    Sendkey("{SP}")    Sendkey("{UP}")    Sendkey("{SP}")    TimeDelay(0.5)   endif   Sendkey("~")   TimeDelay(.5)   ;   ;Running all files within 10 seconds   Sendkey("~")   TimeDelay(10)   ;   ;Store trf-file names in a list   destination = temp_dir   filelist_trf = StrCat(destination,"*.trf")   infoarray_trf = FileInfoToArray(filelist_trf, 0)   Ntrf = infoarray_trf[0,0]   TimeDelay(2)   FileDelete("*.dat")  Next   ; -------------------  ; Close CANNY program  ; -------------------  Sendkey("!f")  Sendkey("x")  Sendkey("~")  TimeDelay(10)  ;  for i=1 to Ninfo   file_dat  = infoarray[i,0]   pos_point = StrIndex(file_dat, ".", 1, @FWDSCAN)   f1_name  = StrSub(file_dat, 1, pos_point - 1)   f1_trf_new = StrCat(f1_name,".TRF")   f1_trf_or = "%i%.TRF"   file_trf_or = StrCat(destination,f1_trf_or)   file_trf_new = StrCat(destination,f1_trf_new)   ;;Change name to TRF files to input-file name format   FileRename(file_trf_or,file_trf_new)   ; Move TRF files to input-file directory   FileMove(file_trf_new,inputdir_or,@FALSE)  Next  ;  TimeDelay(8) Next ; Next of Multi Analyses For-loop ;---------------------------------------------- ; END OF CODE   Appendix A: The Batching Process in the School Project - 145 - Program A.4:  MATLAB program for extracting drift information from CANNY output data. function dr = getdrift(input_file) % GETDRIFT reads one value from the CANNY output file % input_file: file name  fid = fopen(input_file,'r'); while 1     tline = fgetl(fid);     if ~ischar(tline);         break;     end     % ***** READ JOINT COORDINATES *************************     if strcmp(tline,'(7) Interstory horizontal displacement')         tline = fgetl(fid);         datos2 = fgetl(fid);         datos3 = fgetl(fid);         esp2 = strfind(datos2,';');         dr2 = datos2((esp2(end)+1):end);         esp3 = strfind(datos3,';');         dr3 = datos3((esp3(end)+1):end);         if strncmp(dr2,' 1.#INFe+',6) == 1             dr2 = '1000';         end         if strncmp(dr3,' 1.#INFe+',6) == 1             dr3 = '1000';         end         dr2 = str2double(dr2);         dr3 = str2double(dr3);         if dr2 >= 1000             dr2 = 1000;         end         if dr3 >= 1000             dr3 = 1000;         end         dr = max(dr2,dr3);     end     if strfind(tline,'Analysis terminated')== 1         dr = 1000;     end end fclose(fid); return   Appendix A: The Batching Process in the School Project - 146 - A.6. REFERENCES Association of Professional Engineers and Geoscientists of British Columbia (APEGBC), 2006. Bridging Guidelines for the Performance-based Seismic Retrofit of BC Schools, Second Edition, Burnaby, B.C., Canada. Canadian Commission on Building and Fire Codes, 2005.  National Building Code of Canada, National Research Council of Canada, Ottawa, ON, Canada. Li, K., 2008. CANNY Technical Manual, CANNY Consultant PTE Ltd., Singapore. Taylor, G., 2006.  Quakesoft, TBG Seismic Consultants, Victoria, BC, Canada. The Mathworks, 2008. MATLAB – The Language of Technical Computing, Natick, MA, USA, http://www.mathworks.com/products/matlab/ Wilson WindowWare, 2008. WINBATCH 2008B, Wilson WindowWare, Inc., Seattle, WA, USA, http://www.winbatch.com    Appendix B: The Parameters Involved in the School Project - 147 - Appendix B. THE PARAMETERS INVOLVED IN THE SCHOOL PROJECT B.1. SUMMARY OF PARAMETERS 1. Prototypes. 36 systems: 26 Lateral Deformation Resistance Sytems (LDRSs), 4 out-of- plane (OOP) systems, and 4 diaphragm (Diaph) systems; 2. Inter-storey height. Variable number of options depending on each prototype, e.g. for concrete prototypes 2.5m, 3.5m and 5.0m; 3. Type of Earthquake. 3 types with 10 scaled ground motions per suite: Crustal (Cr), Subcrustal (SCr) and Subduction (Sd); 4. Seismic Source Models. 2 models for crustal and subcrustal earthquakes, only: Historical (H) and Regional (R); 5. Seismic Level. 3 levels: High, Moderate or Low; 6. Intensities or levels of shaking. 25 levels (in percentages) with increments of 10%; 7. Resistance values. 42 values (as percentages of seismic weight W given as follows): 1 to 20%W in increments of 1% W; 22 to 40% W in increments of 2% W; 45 to 100% W in increments of 5% W; 8. Location. 58 communities of BC; 9. Rigidity. 2 options: Flexible or Rigid; 10. Site Condition. 2 sites: Site Class C and Site Class D as per NBCC 2005 classification. B.2. PROTOTYPES B.2.1 Lateral deformation resistance systems, LDRSs LDRSs are divided by material and type of behaviour.  The following tables show the prototype number adopted in this project, a brief description of the system, the drift limit recommended for a life-safety performance objective, and the over-strength reduction factor, Ro. The Ro values account for other variables that can not be included within the backbone  Appendix B: The Parameters Involved in the School Project - 148 - curves or the hysteretic rules.  Details of many of these structural systems can be found in the Commentary section of the Bridging Guidelines (APEGBC 2006). B.2.1.1 Wood Prototypes Prototype No. Prototype Description Drift Limit Ro W-1 Blocked OSB / plywood 4% 1.7 W-2 Unblocked OSB / plywood 4% 1.7 W-3 Gypsum wallboard 4% 1.7 W-4 Horizontal boards 4% 1.7 B.2.1.2 Steel Prototypes Prototype No. Prototype Description Drift Limit Ro S-1 Concentric braced steel frame (tension only) 4% 1.3 S-2 Concentric braced steel frame (tension / compression) 1% – 3% 1.3 S-3 Eccentric braced steel frame 4% 1.5 S-4 Steel moment frame (moderately ductile) 4% 1.5 S-5 Steel shearwall 4% 1.5 B.2.1.3 Concrete Prototypes Prototype No. Prototype Description Drift Limit Ro C-1 Concrete moment frame #1 4% 1.7 C-2 Concrete moment frame #2 3% 1.4 C-3 Concrete moment frame #3 2% 1.3 C-4 Squat concrete shearwall (shear) 2% 1.3 C-5 Concrete shearwall (shear)  2% 1.3 C-6 Moderately ductile concrete shearwall (flexure) 2% 1.4 C-7 Concrete shearwall (flexure) conventional construction 2% 1.3  Appendix B: The Parameters Involved in the School Project - 149 - B.2.1.4 Concrete Masonry Prototypes Prototype No. Prototype Description Drift Limit Ro M-1 Masonry sliding at base of wall 4% 1.5 M-2 Running bond URM bed joint sliding 2% 1.5 M-3 Running bond reinforced masonry shearwall (shear) 2% 1.5 M-4 Running bond reinforced masonry shearwall (flexure) 4% 1.5 M-5 Stack bond URM 2% 1.5 B.2.1.5 Clay Brick Masonry Prototypes Prototype No. Prototype Description Drift Limit Ro B-1 Clay brick bed joint sliding 2% 1.5 B.2.1.6 Rocking Prototypes Prototype No. Prototype Description Drift Limit Ro R-1 Rocking (low aspect ratio) 4% 1.0 R-2 Rocking (medium aspect ratio) 4% 1.0 R-3 Rocking (high aspect ratio) 4% 1.0 B.2.1.7 Foundation Prototypes Prototype No. Prototype Description Drift Limit Ro F-1 Sliding foundation connected to building 4% 1.0   B.2.2 Walls rocking out-of-plane Prototype No. Prototype Description OP-1 Out-of-plane URM cantilever OP-2 Out-of-plane URM wall (laterally supported top / bottom) OP-3 Out-of-plane cantilever (reinforced masonry)  Appendix B: The Parameters Involved in the School Project - 150 - B.2.3 Diaphragms Prototype No. Prototype Description Inelastic Strain Limit Ro D-1 Diaphragm – blocked OSB / plywood 4% 1.7 D-2 Diaphragm – unblocked OSB / plywood  4% 1.7 D-3 Diaphragm – horizontal boards 4% 1.7 D-3 Diaphragm – steel deck Type A 1% 1.67 D-4 Diaphragm – steel deck Type B 0.5% 1.67   B.3. INTER-STOREY HEIGHT Most prototypes have three storey height choices. These three storey height choices are 2500 mm, 3000 mm and 5000 mm. B.4. TYPE OF EARTHQUAKE Three earthquake types were considered in this project for defining the hazard demand and the hazard data for risk calculations.  The hazard demand was given by the spectral velocity spectrum for each type of earthquake.  Ten ground motions were selected to represent the seismicity of each earthquake type.  Details and results of this selection were explained in Chapter 2 of this thesis. B.5. SEISMIC SOURCE MODELS Historical (H model) and regional (R model) seismic sources were used to define both the hazard demand and the hazard data for risk calculations when dealing with crustal and  Appendix B: The Parameters Involved in the School Project - 151 - subcrustal earthquakes.  Subduction hazard data was calculated deterministically using a single source. The hazard demand was calculated for each earthquake and for each source model separately.  The selection of ground motions was based only on the data that contribute mostly to the seismic hazard.  In this project, the hazard demand of Crustal and Subcrustal earthquakes using the R and H models were adopted, respectively.  The same selected records were scaled to the demands obtained from the combination of other models and earthquake type accordingly. The maximum estimates of risk from all the possible combinations of earthquake type and source model were adopted. B.6. LOCATION This project involves 58 communities that together cover the 100% of school inventory in British Columbia.  A preliminary study was carried out to identify the seismicity level of each community classified by type of earthquake and seismic model as per shown in Table B.1. B.7. SEISMICITY LEVEL Seismicity is defined here in terms of the ratios of the pseudo-velocities in the 1 to 2 sec period range for each community in BC to that for a reference location, PSV*ratio. Vancouver is the reference location for crustal and subcrustal earthquakes and Victoria is the reference location for subduction earthquakes.  Appendix B: The Parameters Involved in the School Project - 152 - The province was divided into three levels of seismicity: High, Moderate and Low.  A High seismicity location is defined by the PSV*ratio larger than 70%. A moderate seismicity is given by a PSV*ratio between 70% and 40%. A low seismicity is given by a PSV*ratio less than 40%.  Table B.1 shows communities with High and Moderate seismicity highlighted.  Locations with Low seismicity were assumed to be dominated by other loading cases, e.g. wind loads, and therefore excluded form this risk assessment project. B.8. RESISTANCE VALUES All the prototypes are characterized by a backbone curve that relates the resistance forces with the inter-storey drift deformations.  It is assumed that the maximum force occurs at the yielding deformation, which is considered constant for a single prototype.  Resistance forces at other points of the backbone curve are proportional to this resistance force. The maximum resistance force of each system is varied till the objective drift is reached.  In this project, a progressive approach was adopted for a wide range of force values.  42 resistance values (give as a percentage of seismic weight W) were adopted as follows: 1 to 20%W in increments of 1%W; 22 to 40%W in increments of 2%W; 45 to 100%W in increments of 5%W. It has been observed in many cases that the relationship between the maximum resistance force and the maximum drift is not a one-on-one relationship.  A system with different resistance values can reach the same drift due to the nature of each earthquake record.  In such as cases, only the maximum value has been adopted here.  Appendix B: The Parameters Involved in the School Project - 153 - B.9. INTENSITIES OR LEVELS OF SHAKING Incremental dynamic analysis has been adopted in this project to capture all the possible outcomes of the system under earthquake motions.  A wide range of intensities of the earthquake motions was used to run these incremental analyses.  Intensities in this project were represented in percentages of the base intensity (100%) of the input motion matched to the target hazard demand.  Twenty five intensities were considered in this study from 10% to 250% the base intensity in increments of 10%. B.10. RIGIDITY Rigidity refers to expected period undergoing inelastic deformations in a structural system.  Prototypes are likely to behave rigid or flexible depending on the following period ranges: 0.5 to 1s or 1 to 2s, respectively.  The period of each system was estimated by an effective period controlled by the level of drift deformation of each prototype.  The following list shows the prototypes for the specified drift limits that were considered as rigid in this project. Prototype1 C-4 C-5 C-6 M-1 M-2 M-3 M-4 M-5 B-1 R-1 R-2 R-3 D-4 D-5 Drift Limit (%) 1 1 1 1 1 1 1 1 1 1 1 1 * * 1 All the other cases (prototypes at other drift limits) were considered to behave flexible. * No limit is provided for diaphragms The scaling of ground motion records was based on a period range of 1 to 2 second period.  To avoid the selection of new ground motions to match at the 0.5 to 1 second period range, a modification procedure of the drift matrix has been adopted.  The values in the drift matrix were interpolated by the ratio of PSV* in the 1-2 sec period range to that in the 0.5-1 sec period range for each earthquake type and for source model.  Appendix B: The Parameters Involved in the School Project - 154 - B.11. SITE CONDITION There are two site conditions adopted in this project: Site Class C and Site Class D as per code classification, NBCC 2005 (Canadian Commission on Building and Fire Codes 2005).  These are the only two sites investigated in this project.  Other site conditions will require a special study and further directions on that particular school from a technical review board assigned by the APEGBC.  The study on the site conditions that is part of this methodology was covered in Chapter 3.  Appendix B: The Parameters Involved in the School Project - 155 - Table B.1: Seismicity given by the PSV*ratio of BC communities included in the seismic risk assessment program for BC schools classified by type of earthquake and seismic source model  Ratios of Average Pseudo-velocities in the 1-2s period range   PSV ratio Crustal PSV ratio Subcrustal PSV ratio Subduction District H model R model H model R model C model Burns Lake 0.08 0.16 0.00 0.17 0.10 Prince George 0.14 0.16 0.00 - 0.09 Quesnel 0.26 0.21 0.00 0.06 0.11 Ocean Falls 0.27 0.49 0.00 0.01 0.21 Revelstoke 0.29 0.21 0.10 0.07 0.10 Nelson 0.29 0.20 0.10 0.08 0.10 Williams Lake 0.29 0.35 0.10 0.08 0.13 Nakusp 0.29 0.21 0.11 0.08 0.10 Port Hardy 0.54 0.66 0.11 0.10 0.56 Port McNeill 0.56 0.67 0.12 0.12 0.64 Trail 0.29 0.22 0.12 0.10 0.12 Salmon Arm 0.29 0.27 0.13 0.10 0.12 Vernon 0.30 0.29 0.15 0.12 0.14 Kamloops 0.30 0.38 0.17 0.13 0.15 Kelowna 0.30 0.35 0.19 0.15 0.16 Ashcroft 0.30 0.59 0.21 0.16 0.18 Penticton 0.30 0.41 0.22 0.17 0.17 Gold River 0.98 0.95 0.22 0.26 1.27 Merritt 0.30 0.57 0.26 0.19 0.19 Campbell River 0.70 0.98 0.28 0.29 0.69 Tofino 0.99 0.82 0.29 0.35 1.91 Princeton 0.31 0.68 0.33 0.25 0.22 Courtenay 0.82 0.99 0.36 0.42 0.78 Powell River 0.58 1.00 0.40 0.44 0.70 Port Alberni 0.94 0.99 0.47 0.60 0.96 Hope 0.37 0.98 0.54 0.40 0.30 Qualicum 0.78 0.99 0.55 0.69 0.80 Squamish 0.45 1.00 0.63 0.56 0.42 Sechelt 0.53 1.00 0.68 0.75 0.58  Appendix B: The Parameters Involved in the School Project - 156 -  Ratios of Average Pseudo-velocities in the 1-2s period range   PSV ratio Crustal PSV ratio Subcrustal PSV ratio Subduction District H model R model H model R model C model Chilliwack 0.49 1.00 0.77 0.55 0.37 Youbou3 0.91 0.99 0.80 0.92 1.02 Nanaimo 0.65 1.00 0.80 0.91 0.74 West Vancouver 0.49 1.00 0.92 0.79 0.51 North Vancouver 0.49 1.00 0.94 0.78 0.50 Abbotsford 0.51 1.00 0.98 0.69 0.44 Mission 0.51 1.00 0.98 0.69 0.44 Coquitlam 0.50 1.00 0.98 0.73 0.46 Burnaby 0.50 1.00 1.00 0.78 0.50 Vancouver 0.50 1.00 1.00 0.83 0.53 Maple Ridge 0.51 1.00 1.01 0.72 0.46 New Westminster 0.51 1.00 1.04 0.81 0.51 Richmond 0.52 1.00 1.07 0.87 0.55 Surrey 0.52 1.00 1.08 0.80 0.50 Duncan 0.72 0.99 1.11 1.03 0.89 Langley 0.52 1.00 1.11 0.81 0.50 Sooke 0.82 0.98 1.15 0.98 1.23 Ladner 0.55 1.00 1.15 0.92 0.58 Ganges 0.64 1.00 1.17 1.03 0.78 Victoria 0.66 0.99 1.31 1.05 1.00 Fort St. John 0.06 0.12 - - 0.04 Dawson Creek 0.06 0.13 - - 0.05 Fort Nelson 0.13 0.11 - - 0.04 Smithers 0.17 0.22 - - 0.08 Kitimat 0.28 0.47 - - 0.10 Kimberley 0.29 0.19 - - 0.08 Cranbrook 0.29 0.19 - - 0.08 Prince Rupert 0.46 0.59 - - 0.08 Masset 1.10 1.17 - - 0.07  Appendix B: The Parameters Involved in the School Project - 157 - B.12. REFERENCES Association of Professional Engineers and Geoscientists of British Columbia (APEGBC), 2006. Bridging Guidelines for the Performance-based Seismic Retrofit of BC Schools, Second Edition, Burnaby, B.C., Canada. Canadian Commission on Building and Fire Codes, 2005.  National Building Code of Canada, National Research Council of Canada, Ottawa, ON, Canada.   Appendix C: Detailed Information of Selected Records - 158 - Appendix C. DETAILED INFORMATION OF SELECTED RECORDS C.1. CRUSTAL EARTHQUAKE RECORDS Crustal Suite - Vancouver - Site Class C - R Model Earthquake Date Station Mw1 D PGA PSV*1-2 SF Name  Name km g cm/sec Kern County 21-Jul-1952 USGS 1095 Taft Lincoln School 7.4 46.2 0.18 30.8 1.38 Tabas, Iran 16-Sep-1978 Stn: 9102 Dayhook 7.4 21.4 0.41 44.5 0.95 Irpinia, Italy-01 23-Nov-1980 ENEL 99999 Calitri 6.9 17.8 0.13 44.0 0.97 Nahanni, Canada 23-Dec-1985 Stn: 6098 Site 2 6.8 10.3 0.32 36.5 1.16 CDMG 57007 Corralitos 6.9 18.9 0.64 51.8 0.82 Loma Prieta 18-Oct-1989 CDMG 57217 Coyote Lake Dam (SW Abut) 6.9 35.4 0.48 54.7 0.78 Cape Mendocino 25-Apr-1992 CDMG 89156 Petrolia 7.0 10.5 0.59 57.0 0.75 Northridge-01 17-Jan-1994 USGS 5108 Santa Susana Ground 6.7 22.8 0.29 33.2 1.28 Kobe, Japan 16-Jan-1995 CUE 99999 Nishi-Akashi 6.9 19.9 0.51 43.0 0.99 E. Honshu, Japan 13-Jun-2008 Ichinoseki (IWT010) 6.8 20.0 0.22 40.4 1.05    Appendix C: Detailed Information of Selected Records - 159 - C.1.1 Time histories Acceleration (g) Velocity (cm/sec) Displacement (cm)   Ap pe nd ix  C : D et ai le d In fo rm at io n of  S el ec te d Re co rd s - 1 60  -  -0.5 0 0.5 Time (Sec) Kern County, USA, 21-Jul-1952, USGS 1095 Taft Lincoln School 111 -0.5 0 0.5 Time (Sec) Tabas, Iran, 16-Sep-1978, Stn: 9102 Dayhook TR -0.5 0 0.5 Time (Sec) Irpinia, Italy-01, 23-Nov-1980, ENEL 99999 Calitri 230 -0.5 0 0.5 Time (Sec) Nahanni, Canada, 23-Dec-1985, Stn: 6098 Site 2 330 -0.5 0 0.5 Time (Sec) Loma Prieta, 18-Oct-1989, CDMG 57007 Corralitos 0 -0.5 0 0.5 Time (Sec) Loma Prieta, 18-Oct-1989, CDMG 57217 Coyote Lake Dam (SW Abut) 285 -0.5 0 0.5 Time (Sec) Cape Mendocino, 25-Apr-1992, CDMG 89156 Petrolia 0 -0.5 0 0.5 Time (Sec) Northridge-01, 17-Jan-1994, USGS 5108 Santa Susana Ground 290 -0.5 0 0.5 Time (Sec) Kobe, Japan, 16-Jan-1995, CUE 99999 Nishi-Akashi 0 0 10 20 30 40 50 60 -0.5 0 0.5 Time (Sec) A cc el er at io n (g ) E. Honshu, Japan, 13-Jun-2008, Ichinoseki (IWT010) NS  Ap pe nd ix  C : D et ai le d In fo rm at io n of  S el ec te d Re co rd s - 1 61  -  -50 0 50 Time (Sec) Kern County, USA, 21-Jul-1952, USGS 1095 Taft Lincoln School 111 -50 0 50 Time (Sec) Tabas, Iran, 16-Sep-1978, Stn: 9102 Dayhook TR -50 0 50 Time (Sec) Irpinia, Italy-01, 23-Nov-1980, ENEL 99999 Calitri 230 -50 0 50 Time (Sec) Nahanni, Canada, 23-Dec-1985, Stn: 6098 Site 2 330 -50 0 50 Time (Sec) Loma Prieta, 18-Oct-1989, CDMG 57007 Corralitos 0 -50 0 50 Time (Sec) Loma Prieta, 18-Oct-1989, CDMG 57217 Coyote Lake Dam (SW Abut) 285 -50 0 50 Time (Sec) Cape Mendocino, 25-Apr-1992, CDMG 89156 Petrolia 0 -50 0 50 Time (Sec) Northridge-01, 17-Jan-1994, USGS 5108 Santa Susana Ground 290 -50 0 50 Time (Sec) Kobe, Japan, 16-Jan-1995, CUE 99999 Nishi-Akashi 0 0 10 20 30 40 50 60 -50 0 50 Time (Sec) V el oc ity  (c m /s ec ) E. Honshu, Japan, 13-Jun-2008, Ichinoseki (IWT010) NS  Ap pe nd ix  C : D et ai le d In fo rm at io n of  S el ec te d Re co rd s - 1 62  -  -20 0 20 Time (Sec) Kern County, USA, 21-Jul-1952, USGS 1095 Taft Lincoln School 111 -20 0 20 Time (Sec) Tabas, Iran, 16-Sep-1978, Stn: 9102 Dayhook TR -20 0 20 Time (Sec) Irpinia, Italy-01, 23-Nov-1980, ENEL 99999 Calitri 230 -20 0 20 Time (Sec) Nahanni, Canada, 23-Dec-1985, Stn: 6098 Site 2 330 -20 0 20 Time (Sec) Loma Prieta, 18-Oct-1989, CDMG 57007 Corralitos 0 -20 0 20 Time (Sec) Loma Prieta, 18-Oct-1989, CDMG 57217 Coyote Lake Dam (SW Abut) 285 -20 0 20 Time (Sec) Cape Mendocino, 25-Apr-1992, CDMG 89156 Petrolia 0 -20 0 20 Time (Sec) Northridge-01, 17-Jan-1994, USGS 5108 Santa Susana Ground 290 -20 0 20 Time (Sec) Kobe, Japan, 16-Jan-1995, CUE 99999 Nishi-Akashi 0 0 10 20 30 40 50 60 -20 0 20 Time (Sec) D is pl ac em en t ( cm ) E. Honshu, Japan, 13-Jun-2008, Ichinoseki (IWT010) NS  Appendix C: Detailed Information of Selected Records - 163 - C.1.2 Spectra (5% damping) The following figures contain four plots per earthquake record: 1. Acceleration time histories; 2. Spectral accelerations, SA; 3. Spectral velocities, SV; 4. Spectral displacements, SD; The scales of the following plots are the same for all the records.  In some cases, the plotted lines are outside the maximum values set for these scales.  Full-scale plots of those records are shown at the end of this section.  Appendix C: Detailed Information of Selected Records - 164 - 0 10 20 30 40 50 60 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.5 1 1.5 2 Period (Sec) S A  ( g ) 0 1 2 3 4 0 20 40 60 80 100 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 10 20 30 40 Period (Sec) S D  ( cm ) Kern County, USA, 21-Jul-1952, USGS 1095 Taft Lincoln School 111  0 10 20 30 40 50 60 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.5 1 1.5 2 Period (Sec) S A  ( g ) 0 1 2 3 4 0 20 40 60 80 100 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 10 20 30 40 Period (Sec) S D  ( cm ) Tabas, Iran, 16-Sep-1978, Stn: 9102 Dayhook TR     Appendix C: Detailed Information of Selected Records - 165 - 0 10 20 30 40 50 60 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.5 1 1.5 2 Period (Sec) S A  ( g ) 0 1 2 3 4 0 20 40 60 80 100 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 10 20 30 40 Period (Sec) S D  ( cm ) Irpinia, Italy-01, 23-Nov-1980, ENEL 99999 Calitri 230  0 10 20 30 40 50 60 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.5 1 1.5 2 Period (Sec) S A  ( g ) 0 1 2 3 4 0 20 40 60 80 100 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 10 20 30 40 Period (Sec) S D  ( cm ) Nahanni, Canada, 23-Dec-1985, Stn: 6098 Site 2 330   Appendix C: Detailed Information of Selected Records - 166 - 0 10 20 30 40 50 60 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.5 1 1.5 2 Period (Sec) S A  ( g ) 0 1 2 3 4 0 20 40 60 80 100 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 10 20 30 40 Period (Sec) S D  ( cm ) Loma Prieta, 18-Oct-1989, CDMG 57007 Corralitos 0  0 10 20 30 40 50 60 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.5 1 1.5 2 Period (Sec) S A  ( g ) 0 1 2 3 4 0 20 40 60 80 100 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 10 20 30 40 Period (Sec) S D  ( cm ) Loma Prieta, 18-Oct-1989, CDMG 57217 Coyote Lake Dam (SW Abut) 285   Appendix C: Detailed Information of Selected Records - 167 - 0 10 20 30 40 50 60 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.5 1 1.5 2 Period (Sec) S A  ( g ) 0 1 2 3 4 0 20 40 60 80 100 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 10 20 30 40 Period (Sec) S D  ( cm ) Cape Mendocino, 25-Apr-1992, CDMG 89156 Petrolia 0  0 10 20 30 40 50 60 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.5 1 1.5 2 Period (Sec) S A  ( g ) 0 1 2 3 4 0 20 40 60 80 100 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 10 20 30 40 Period (Sec) S D  ( cm ) Northridge-01, 17-Jan-1994, USGS 5108 Santa Susana Ground 290   Appendix C: Detailed Information of Selected Records - 168 - 0 10 20 30 40 50 60 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.5 1 1.5 2 Period (Sec) S A  ( g ) 0 1 2 3 4 0 20 40 60 80 100 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 10 20 30 40 Period (Sec) S D  ( cm ) Kobe, Japan, 16-Jan-1995, CUE 99999 Nishi-Akashi 0  0 10 20 30 40 50 60 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.5 1 1.5 2 Period (Sec) S A  ( g ) 0 1 2 3 4 0 20 40 60 80 100 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 10 20 30 40 Period (Sec) S D  ( cm ) E. Honshu, Japan, 13-Jun-2008, Ichinoseki (IWT010) NS   Appendix C: Detailed Information of Selected Records - 169 - C.1.2.1 Selected full-scale plots 0 10 20 30 40 50 60 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.5 1 1.5 2 2.5 Period (Sec) S A  ( g ) 0 1 2 3 4 0 50 100 150 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 10 20 30 40 Period (Sec) S D  ( cm ) Loma Prieta, 18-Oct-1989, CDMG 57007 Corralitos 0  0 10 20 30 40 50 60 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.5 1 1.5 2 Period (Sec) S A  ( g ) 0 1 2 3 4 0 20 40 60 80 100 120 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 10 20 30 40 Period (Sec) S D  ( cm ) Loma Prieta, 18-Oct-1989, CDMG 57217 Coyote Lake Dam (SW Abut) 285   Appendix C: Detailed Information of Selected Records - 170 - 0 10 20 30 40 50 60 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.5 1 1.5 2 Period (Sec) S A  ( g ) 0 1 2 3 4 0 50 100 150 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 10 20 30 40 Period (Sec) S D  ( cm ) Cape Mendocino, 25-Apr-1992, CDMG 89156 Petrolia 0  0 10 20 30 40 50 60 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.5 1 1.5 2 Period (Sec) S A  ( g ) 0 1 2 3 4 0 50 100 150 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 10 20 30 40 Period (Sec) S D  ( cm ) Kobe, Japan, 16-Jan-1995, CUE 99999 Nishi-Akashi 0       Appendix C: Detailed Information of Selected Records - 171 - C.1.3 Scaled spectra (5% damping) Crustal Earthquakes 0 20 40 60 80 100 120 140 160 180 0 1 2 3 4 Period (sec) PS V (c m /s ec ) Records Records Average Target Target x 0.7     Appendix C: Detailed Information of Selected Records - 172 - C.2. SUBCRUSTAL EARTHQUAKE RECORDS SubCrustal Suite - Vancouver - Site Class C - H Model Earthquake Date Station Mw D PGA PSV*1-2 SF Name  Name km g cm/sec Renton (RBEN) 6.8 73.1 0.11 21.1 1.94 Seattle (BHD) 6.8 76.8 0.16 40.6 1.01 Seattle (KIMB) 6.8 77.4 0.14 34.2 1.19 Seattle (MAR) 6.8 77.6 0.13 13.2 3.08 Poulsbo (KITP) 6.8 78.9 0.06 21.4 1.91 Seattle (CRO) 6.8 79.4 0.09 18.4 2.22 Nisqually, WA 28-Feb-2001 Seattle (EVA) 6.8 80.7 0.06 22.1 1.84 Guerrero, Mexico 10-Dec-1994 Zihuatanejo (AZIH) 6.6 76.6 0.06 11.3 3.61 Michoacan, Mexico 11-Jan-1997 Villita (VILE) 7.1 71.4 0.10 12.2 3.35 El Salvador 13-Jan-2001 Unidad de Salud, Panchimalco (PA) 7.6 95.7 0.19 17.9 2.28    Appendix C: Detailed Information of Selected Records - 173 - C.2.1 Time histories Acceleration (g) Velocity (cm/sec) Displacement (cm)   Ap pe nd ix  C : D et ai le d In fo rm at io n of  S el ec te d Re co rd s - 1 74  -  -0.5 0 0.5 Time (Sec) Nisqually, WA, 28-Feb-2001, Renton (RBEN) EW -0.5 0 0.5 Time (Sec) Nisqually, WA, 28-Feb-2001, Seattle (BHD) 90 -0.5 0 0.5 Time (Sec) Nisqually, WA, 28-Feb-2001, Seattle (KIMB) EW -0.5 0 0.5 Time (Sec) Nisqually, WA, 28-Feb-2001, Seattle (MAR) 328 -0.5 0 0.5 Time (Sec) Nisqually, WA, 28-Feb-2001, Poulsbo (KITP) NS -0.5 0 0.5 Time (Sec) Nisqually, WA, 28-Feb-2001, Seattle (CRO) 270 -0.5 0 0.5 Time (Sec) Nisqually, WA, 28-Feb-2001, Seattle (EVA) 90 -0.5 0 0.5 Time (Sec) Guerrero, Mexico, 10-Dec-1994, Zihuatanejo (AZIH) N00W -0.5 0 0.5 Time (Sec) Michoacan, Mexico, 11-Jan-1997, Villita (VILE) S90E 0 10 20 30 40 50 60 -0.5 0 0.5 Time (Sec) A cc el er at io n (g ) El Salvador, 13-Jan-2001, Unidad de Salud, Panchimalco (PA) NS  Ap pe nd ix  C : D et ai le d In fo rm at io n of  S el ec te d Re co rd s - 1 75  -  -50 0 50 Time (Sec) Nisqually, WA, 28-Feb-2001, Renton (RBEN) EW -50 0 50 Time (Sec) Nisqually, WA, 28-Feb-2001, Seattle (BHD) 90 -50 0 50 Time (Sec) Nisqually, WA, 28-Feb-2001, Seattle (KIMB) EW -50 0 50 Time (Sec) Nisqually, WA, 28-Feb-2001, Seattle (MAR) 328 -50 0 50 Time (Sec) Nisqually, WA, 28-Feb-2001, Poulsbo (KITP) NS -50 0 50 Time (Sec) Nisqually, WA, 28-Feb-2001, Seattle (CRO) 270 -50 0 50 Time (Sec) Nisqually, WA, 28-Feb-2001, Seattle (EVA) 90 -50 0 50 Time (Sec) Guerrero, Mexico, 10-Dec-1994, Zihuatanejo (AZIH) N00W -50 0 50 Time (Sec) Michoacan, Mexico, 11-Jan-1997, Villita (VILE) S90E 0 10 20 30 40 50 60 -50 0 50 Time (Sec) V el oc ity  (c m /s ec ) El Salvador, 13-Jan-2001, Unidad de Salud, Panchimalco (PA) NS  Ap pe nd ix  C : D et ai le d In fo rm at io n of  S el ec te d Re co rd s - 1 76  -  -20 0 20 Time (Sec) Nisqually, WA, 28-Feb-2001, Renton (RBEN) EW -20 0 20 Time (Sec) Nisqually, WA, 28-Feb-2001, Seattle (BHD) 90 -20 0 20 Time (Sec) Nisqually, WA, 28-Feb-2001, Seattle (KIMB) EW -20 0 20 Time (Sec) Nisqually, WA, 28-Feb-2001, Seattle (MAR) 328 -20 0 20 Time (Sec) Nisqually, WA, 28-Feb-2001, Poulsbo (KITP) NS -20 0 20 Time (Sec) Nisqually, WA, 28-Feb-2001, Seattle (CRO) 270 -20 0 20 Time (Sec) Nisqually, WA, 28-Feb-2001, Seattle (EVA) 90 -20 0 20 Time (Sec) Guerrero, Mexico, 10-Dec-1994, Zihuatanejo (AZIH) N00W -20 0 20 Time (Sec) Michoacan, Mexico, 11-Jan-1997, Villita (VILE) S90E 0 10 20 30 40 50 60 -20 0 20 Time (Sec) D is pl ac em en t ( cm ) El Salvador, 13-Jan-2001, Unidad de Salud, Panchimalco (PA) NS  Appendix C: Detailed Information of Selected Records - 177 - C.2.2 Spectra (5% damping) The following figures contain four plots per earthquake record: 5. Acceleration time histories; 6. Spectral accelerations, SA; 7. Spectral velocities, SV; 8. Spectral displacements, SD;  Appendix C: Detailed Information of Selected Records - 178 - 0 10 20 30 40 50 60 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.2 0.4 0.6 0.8 1 Period (Sec) S A  ( g ) 0 1 2 3 4 0 10 20 30 40 50 60 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 5 10 15 20 Period (Sec) S D  ( cm ) Nisqually, WA, 28-Feb-2001, Renton (RBEN) EW  0 10 20 30 40 50 60 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.2 0.4 0.6 0.8 1 Period (Sec) S A  ( g ) 0 1 2 3 4 0 10 20 30 40 50 60 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 5 10 15 20 Period (Sec) S D  ( cm ) Nisqually, WA, 28-Feb-2001, Seattle (BHD) 90   Appendix C: Detailed Information of Selected Records - 179 - 0 10 20 30 40 50 60 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.2 0.4 0.6 0.8 1 Period (Sec) S A  ( g ) 0 1 2 3 4 0 10 20 30 40 50 60 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 5 10 15 20 Period (Sec) S D  ( cm ) Nisqually, WA, 28-Feb-2001, Seattle (KIMB) EW  0 10 20 30 40 50 60 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.2 0.4 0.6 0.8 1 Period (Sec) S A  ( g ) 0 1 2 3 4 0 10 20 30 40 50 60 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 5 10 15 20 Period (Sec) S D  ( cm ) Nisqually, WA, 28-Feb-2001, Seattle (MAR) 328   Appendix C: Detailed Information of Selected Records - 180 - 0 10 20 30 40 50 60 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.2 0.4 0.6 0.8 1 Period (Sec) S A  ( g ) 0 1 2 3 4 0 10 20 30 40 50 60 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 5 10 15 20 Period (Sec) S D  ( cm ) Nisqually, WA, 28-Feb-2001, Poulsbo (KITP) NS  0 10 20 30 40 50 60 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.2 0.4 0.6 0.8 1 Period (Sec) S A  ( g ) 0 1 2 3 4 0 10 20 30 40 50 60 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 5 10 15 20 Period (Sec) S D  ( cm ) Nisqually, WA, 28-Feb-2001, Seattle (CRO) 270   Appendix C: Detailed Information of Selected Records - 181 - 0 10 20 30 40 50 60 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.2 0.4 0.6 0.8 1 Period (Sec) S A  ( g ) 0 1 2 3 4 0 10 20 30 40 50 60 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 5 10 15 20 Period (Sec) S D  ( cm ) Nisqually, WA, 28-Feb-2001, Seattle (EVA) 90  0 10 20 30 40 50 60 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.2 0.4 0.6 0.8 1 Period (Sec) S A  ( g ) 0 1 2 3 4 0 10 20 30 40 50 60 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 5 10 15 20 Period (Sec) S D  ( cm ) Guerrero, Mexico, 10-Dec-1994, Zihuatanejo (AZIH) N00W   Appendix C: Detailed Information of Selected Records - 182 - 0 10 20 30 40 50 60 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.2 0.4 0.6 0.8 1 Period (Sec) S A  ( g ) 0 1 2 3 4 0 10 20 30 40 50 60 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 5 10 15 20 Period (Sec) S D  ( cm ) Michoacan, Mexico, 11-Jan-1997, Villita (VILE) S90E  0 10 20 30 40 50 60 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.2 0.4 0.6 0.8 1 Period (Sec) S A  ( g ) 0 1 2 3 4 0 10 20 30 40 50 60 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 5 10 15 20 Period (Sec) S D  ( cm ) El Salvador, 13-Jan-2001, Unidad de Salud, Panchimalco (PA) NS   Appendix C: Detailed Information of Selected Records - 183 - C.2.3 Scaled spectra (5% damping) Subcrustal Earthquakes 0 20 40 60 80 100 0 1 2 3 4 Period (sec) PS V (c m /s ec ) Records Records Average Target Target x 0.7    Appendix C: Detailed Information of Selected Records - 184 - C.3. SUBDUCTION EARTHQUAKE RECORDS Subduction Suite - Vancouver - Site Class C - Deterministic Model Earthquake Date Station Mw D PGA PSV*1-2 SF Name  Name km g cm/sec Meguro (HKD113) 8.0 58.6 0.16 27.2 0.96 Noya (HKD107) 8.0 126.4 0.09 38.0 0.69 Obihiro (HKD095) 8.0 132.2 0.18 51.6 0.50 Hombetsu (HKD090) 8.0 145.8 0.50 26.8 0.97 Futamata (HKD087) 8.0 148.7 0.26 38.9 0.67 Tokachi-oki, Japan 25-Sep-2003 Tsurui (HKD083) 8.0 163.4 0.19 35.8 0.73 Caleta De Campos (CALE) 8.1 38.3 0.15 42.1 0.62 Villita (VILE) 8.1 47.8 0.11 24.0 1.09 La Union (UNIO) 8.1 83.9 0.17 34.3 0.76 Michoacan, Mexico * 19-Sep-1985 Zihuatanejo (AZIH) 8.1 132.6 0.10 34.9 0.75 *Local Magnitude was reported for this earthquake only.   Appendix C: Detailed Information of Selected Records - 185 - C.3.1 Time histories Acceleration (g) Velocity (cm/sec) Displacement (cm)   Ap pe nd ix  C : D et ai le d In fo rm at io n of  S el ec te d Re co rd s - 1 86  -  -0.5 0 0.5 Time (Sec) Tokachi-oki, Japan, 25-Sep-2003, Meguro (HKD113) NS -0.5 0 0.5 Time (Sec) Tokachi-oki, Japan, 25-Sep-2003, Noya (HKD107) EW -0.5 0 0.5 Time (Sec) Tokachi-oki, Japan, 25-Sep-2003, Obihiro (HKD095) NS -0.5 0 0.5 Time (Sec) Tokachi-oki, Japan, 25-Sep-2003, Hombetsu (HKD090) EW -0.5 0 0.5 Time (Sec) Tokachi-oki, Japan, 25-Sep-2003, Futamata (HKD087) EW -0.5 0 0.5 Time (Sec) Tokachi-oki, Japan, 25-Sep-2003, Tsurui (HKD083) EW -0.5 0 0.5 Time (Sec) Michoacan, Mexico, 19-Sep-1985, Caleta De Campos (CALE) N00W -0.5 0 0.5 Time (Sec) Michoacan, Mexico, 19-Sep-1985, Villita (VILE) N00W -0.5 0 0.5 Time (Sec) Michoacan, Mexico, 19-Sep-1985, La Union (UNIO) S00E 0 10 20 30 40 50 60 70 80 90 100 -0.5 0 0.5 Time (Sec) A cc el er at io n (g ) Michoacan, Mexico, 19-Sep-1985, Zihuatanejo (AZIH) S00E  Ap pe nd ix  C : D et ai le d In fo rm at io n of  S el ec te d Re co rd s - 1 87  -  -50 0 50 Time (Sec) Tokachi-oki, Japan, 25-Sep-2003, Meguro (HKD113) NS -50 0 50 Time (Sec) Tokachi-oki, Japan, 25-Sep-2003, Noya (HKD107) EW -50 0 50 Time (Sec) Tokachi-oki, Japan, 25-Sep-2003, Obihiro (HKD095) NS -50 0 50 Time (Sec) Tokachi-oki, Japan, 25-Sep-2003, Hombetsu (HKD090) EW -50 0 50 Time (Sec) Tokachi-oki, Japan, 25-Sep-2003, Futamata (HKD087) EW -50 0 50 Time (Sec) Tokachi-oki, Japan, 25-Sep-2003, Tsurui (HKD083) EW -50 0 50 Time (Sec) Michoacan, Mexico, 19-Sep-1985, Caleta De Campos (CALE) N00W -50 0 50 Time (Sec) Michoacan, Mexico, 19-Sep-1985, Villita (VILE) N00W -50 0 50 Time (Sec) Michoacan, Mexico, 19-Sep-1985, La Union (UNIO) S00E 0 10 20 30 40 50 60 70 80 90 100 -50 0 50 Time (Sec) V el oc ity  (c m /s ec ) Michoacan, Mexico, 19-Sep-1985, Zihuatanejo (AZIH) S00E  Ap pe nd ix  C : D et ai le d In fo rm at io n of  S el ec te d Re co rd s - 1 88  -  -20 0 20 Time (Sec) Tokachi-oki, Japan, 25-Sep-2003, Meguro (HKD113) NS -20 0 20 Time (Sec) Tokachi-oki, Japan, 25-Sep-2003, Noya (HKD107) EW -20 0 20 Time (Sec) Tokachi-oki, Japan, 25-Sep-2003, Obihiro (HKD095) NS -20 0 20 Time (Sec) Tokachi-oki, Japan, 25-Sep-2003, Hombetsu (HKD090) EW -20 0 20 Time (Sec) Tokachi-oki, Japan, 25-Sep-2003, Futamata (HKD087) EW -20 0 20 Time (Sec) Tokachi-oki, Japan, 25-Sep-2003, Tsurui (HKD083) EW -20 0 20 Time (Sec) Michoacan, Mexico, 19-Sep-1985, Caleta De Campos (CALE) N00W -20 0 20 Time (Sec) Michoacan, Mexico, 19-Sep-1985, Villita (VILE) N00W -20 0 20 Time (Sec) Michoacan, Mexico, 19-Sep-1985, La Union (UNIO) S00E 0 10 20 30 40 50 60 70 80 90 100 -20 0 20 Time (Sec) D is pl ac em en t ( cm ) Michoacan, Mexico, 19-Sep-1985, Zihuatanejo (AZIH) S00E  Appendix C: Detailed Information of Selected Records - 189 - C.3.2 Spectra (5% damping) The following figures contain four plots per earthquake record: 9. Acceleration time histories; 10. Spectral accelerations, SA; 11. Spectral velocities, SV; 12. Spectral displacements, SD; The scales of the following plots are the same for all the records.  In some cases, the plotted lines are outside the maximum values set for these scales.  Full-scale plots of those records are shown at the end of this section.  Appendix C: Detailed Information of Selected Records - 190 - 0 20 40 60 80 100 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.5 1 1.5 2 Period (Sec) S A  ( g ) 0 1 2 3 4 0 20 40 60 80 100 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 10 20 30 40 Period (Sec) S D  ( cm ) Tokachi-oki, Japan, 25-Sep-2003, Meguro (HKD113) NS  0 20 40 60 80 100 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.5 1 1.5 2 Period (Sec) S A  ( g ) 0 1 2 3 4 0 20 40 60 80 100 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 10 20 30 40 Period (Sec) S D  ( cm ) Tokachi-oki, Japan, 25-Sep-2003, Noya (HKD107) EW   Appendix C: Detailed Information of Selected Records - 191 - 0 20 40 60 80 100 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.5 1 1.5 2 Period (Sec) S A  ( g ) 0 1 2 3 4 0 20 40 60 80 100 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 10 20 30 40 Period (Sec) S D  ( cm ) Tokachi-oki, Japan, 25-Sep-2003, Obihiro (HKD095) NS  0 20 40 60 80 100 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.5 1 1.5 2 Period (Sec) S A  ( g ) 0 1 2 3 4 0 20 40 60 80 100 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 10 20 30 40 Period (Sec) S D  ( cm ) Tokachi-oki, Japan, 25-Sep-2003, Hombetsu (HKD090) EW   Appendix C: Detailed Information of Selected Records - 192 - 0 20 40 60 80 100 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.5 1 1.5 2 Period (Sec) S A  ( g ) 0 1 2 3 4 0 20 40 60 80 100 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 10 20 30 40 Period (Sec) S D  ( cm ) Tokachi-oki, Japan, 25-Sep-2003, Futamata (HKD087) EW  0 20 40 60 80 100 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.5 1 1.5 2 Period (Sec) S A  ( g ) 0 1 2 3 4 0 20 40 60 80 100 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 10 20 30 40 Period (Sec) S D  ( cm ) Tokachi-oki, Japan, 25-Sep-2003, Tsurui (HKD083) EW   Appendix C: Detailed Information of Selected Records - 193 - 0 20 40 60 80 100 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.5 1 1.5 2 Period (Sec) S A  ( g ) 0 1 2 3 4 0 20 40 60 80 100 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 10 20 30 40 Period (Sec) S D  ( cm ) Michoacan, Mexico, 19-Sep-1985, Caleta De Campos (CALE) N00W  0 20 40 60 80 100 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.5 1 1.5 2 Period (Sec) S A  ( g ) 0 1 2 3 4 0 20 40 60 80 100 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 10 20 30 40 Period (Sec) S D  ( cm ) Michoacan, Mexico, 19-Sep-1985, Villita (VILE) N00W   Appendix C: Detailed Information of Selected Records - 194 - 0 20 40 60 80 100 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.5 1 1.5 2 Period (Sec) S A  ( g ) 0 1 2 3 4 0 20 40 60 80 100 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 10 20 30 40 Period (Sec) S D  ( cm ) Michoacan, Mexico, 19-Sep-1985, La Union (UNIO) S00E  0 20 40 60 80 100 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.5 1 1.5 2 Period (Sec) S A  ( g ) 0 1 2 3 4 0 20 40 60 80 100 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 10 20 30 40 Period (Sec) S D  ( cm ) Michoacan, Mexico, 19-Sep-1985, Zihuatanejo (AZIH) S00E   Appendix C: Detailed Information of Selected Records - 195 - C.3.2.1 Selected full-scale plots 0 20 40 60 80 100 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.5 1 1.5 2 Period (Sec) S A  ( g ) 0 1 2 3 4 0 50 100 150 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 20 40 60 80 Period (Sec) S D  ( cm ) Tokachi-oki, Japan, 25-Sep-2003, Obihiro (HKD095) NS  0 20 40 60 80 100 -0.5 -0.25 0 0.25 0.5 Time (Sec) A cc el er at io n  ( g ) 0 1 2 3 4 0 0.5 1 1.5 2 Period (Sec) S A  ( g ) 0 1 2 3 4 0 20 40 60 80 100 Period (Sec) S V  ( cm /s ec ) 0 1 2 3 4 0 10 20 30 40 50 Period (Sec) S D  ( cm ) Tokachi-oki, Japan, 25-Sep-2003, Tsurui (HKD083) EW   Appendix C: Detailed Information of Selected Records - 196 - C.3.3 Scaled spectra (5% damping) Subduction Earthquakes 0 20 40 60 80 100 0 1 2 3 4 Period (sec) PS V (c m /s ec ) Records Records Average Target Target x 0.7   Appendix C: Detailed Information of Selected Records - 197 - C.4. REFERENCES Records were obtained from the following databases:  PEER-NGA at http://peer.berkeley.edu/nga/index.html COSMOS at http://db.cosmos-eq.org/scripts/earthquakes.plx KiK-Net at http://www.kik.bosai.go.jp/ K-Net at http://www.k-net.bosai.go.jp/  Records were processed with computer programs:  MATLAB version 2008b, and SeismoSignal (free version at http://www.seismosoft.com/en/Download.aspx)      Appendix D: Description of Sites and Soil Columns - 198 - Appendix D. DESCRIPTION OF SITES AND SOIL COLUMNS D.1. SITE 1 - MOUNT DOUGLAS SECONDARY SCHOOL Community: Saanich, BC     Appendix D: Description of Sites and Soil Columns - 199 - D.1.1 Soil column A:  D.1.2 Soil column B  Brown very stiff clay Brown-grey very stiff clay Compact Capilano sand 1.5m 5.5m 9.5m Brown very stiff clay Brown-grey very stiff clay Compact Capilano sand 1.5m 5.5m 9.5m 13.5m 17.5m 21.5m 25.5m Very dense Quadra sand  Appendix D: Description of Sites and Soil Columns - 200 - D.2. SITE 2 - MARGARET JENKINS ELEMENTARY SCHOOL Community: Victoria, BC      Appendix D: Description of Sites and Soil Columns - 201 - D.2.1 Soil column A  D.2.2 Soil column B   Sand Stiff clay Very firm clay 1.0m 2.0m 5.0m 7.0m 3.0m 9.0m 11.0m 13.0m 15.0m 17.0m 19.0m Sand Stiff clay Very firm clay 1.0m 3.5m 7.0m 9.0m 5.0m 11.0m  Appendix D: Description of Sites and Soil Columns - 202 - D.3. SITE 3 - LINCOLN PARK ELEMENTARY SCHOOL Community: Port Coquitlam, BC      Appendix D: Description of Sites and Soil Columns - 203 - D.3.1 Soil column A  Dense sand and gravel (fill) Sensitive organic silt Loose sand 1.2m 3.5m 4.7m 19.9m 26.6m 29.6m 40.1m Sensitive silt Loose to compact sand or sandy gravel 8.9m 10.6m Stiff clayey silt 14.4m Dense sandy gravel Compact to dense sandy with gravel layers Hard silt Compact to dense sandy with some gravel  Appendix D: Description of Sites and Soil Columns - 204 - D.3.2 Soil column B  Dense sand and gravel (fill) Sensitive organic silt Loose sand + Pore Pressure 1.2m 3.5m 4.7m 19.9m 26.6m 29.6m 40.1m Sensitive silt + Pore Pressure Loose to compact sand or sandy gravel + Pore Pressure 8.9m 10.6m Stiff clayey silt + Pore Pressure 14.4m Dense sandy gravel Compact to dense sandy with gravel layers + Pore Pressure Hard silt Compact to dense sandy with some gravel  Appendix D: Description of Sites and Soil Columns - 205 - D.4. SITE 4 - LANGLEY FINE ARTS SCHOOL Community: Langley, BC      Appendix D: Description of Sites and Soil Columns - 206 - D.4.1 Soil column A  Granular fill Brown to grey fine-coarse sand and occasional fine- coarse gravel 1.0m Sand, gravel and some silt Sand Brown to grey fine-coarse sand and occasional fine- coarse gravel Sand 1.8m 3.3m 4.8m 6.3m 7.3m 8.1m 9.6m 12.6m 14.1m 15.6m 33.6 m 17.1m 21.6m 18.6m 24.6m 27.6m 39.9 m 38.4 m Grey fine-coarse sand and occasional fine-coarse gravel  Appendix D: Description of Sites and Soil Columns - 207 - D.4.2 Soil column B  Granular fill Brown to grey fine-coarse sand and occasional fine- coarse gravel 1.0m Sand, gravel and some silt Sand Brown to grey fine-coarse sand and occasional fine- coarse gravel Sand 1.8m 3.3m 4.8m 6.3m 7.3m 8.1m 9.6m 12.6m 14.1m 15.6m 33.6 m 17.1m 21.6m 18.6m 24.6m 27.6m 39.9 m 38.4 m Grey fine-coarse sand and occasional fine-coarse gravel (Saturated) Sand (Saturated)  Appendix D: Description of Sites and Soil Columns - 208 - D.5. SITE 5 - JAMES PARK ELEMENTARY SCHOOL Community: Port Coquitlam, BC      Appendix D: Description of Sites and Soil Columns - 209 - D.5.1 Soil column A  D.5.2 Soil column B  Sand (fill) Silty sand Sand and gravel (Lower bound of Shear Strength) 1.5m 3.0m 5.0m 8.0m 10.0m 12.0m 15.0m 20.0m Sand (fill) Silty sand Sand and gravel (Higher bound of Shear Strength) 1.5m 3.0m 5.0m 8.0m 10.0m 12.0m 15.0m 20.0m  Appendix D: Description of Sites and Soil Columns - 210 - D.5.3 Soil Column C   Sand (fill) Silty sand (Saturated) Sand and gravel (Saturated) 1.5m 3.0m 5.0m 8.0m 10.0m 12.0m 15.0m 20.0m Sand and gravel (Lower bound shear strength) Sand and gravel (Lower bound shear strength)  Appendix D: Description of Sites and Soil Columns - 211 - D.6. REFERENCES Maps of school sites and 3-D views of schools were obtained from Google Maps © on March of 2010.

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