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Evaluation of non-structural earthquake damage to buildings in southwestern B.C. Cook, Shane Edmond 1999

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E V A L U A T I O N OF NON-STRUCTURAL E A R T H Q U A K E D A M A G E TO BUILDINGS IN SOUTHWESTERN B.C. by SHANE E D M O N D COOK B . A . S c , The University of British Columbia, 1996 A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T OF THE REQUIREMENTS FOR THE DEGREE OF M A S T E R OF APPLIED SCIENCE in T H E F A C U L T Y OF G R A D U A T E STUDIES (Department of Civil Engineering) We accept this thesis as conforming to the reouirj^^tandard^--'-' THE UNIVERSITY OF BRITISH C O L U M B I A April 1999 © Shane Edmond Cook, 1999 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of C / t / J EA^ The University of British Columbia Vancouver, Canada Date Af>*\ 3?jmy DE-6 (2/88) A B S T R A C T The damage to non-structural building components and contents can constitute a significant portion of the total damage and risk to life due to an earthquake. Despite this, structural effects have been the measure of risk in the majority of regional damage assessment studies. It is the purpose of this thesis to develop a methodology for the evaluation of damages to non-structural building components and contents, that is applicable to southwestern British Columbia, and apply this methodology to a case study region. Existing methodologies that have been developed for use in other regions are reviewed and the methodology to be used in this study is outlined. A classification scheme for non-structural components and building contents is presented as well as damage functions for each non-structural component class. The damage functions used to perform the assessment are Damage Probability Matrices that relate non-structural damages to earthquake intensities. The non-structural damages are presented as percentages replacement costs and ground motion intensities are measured in the Modified Mercalli Intensity scale. Lastly, a case study is performed on a building inventory consisting of over 8000 buildings located in the City of New Westminster. n TABLE OF CONTENT ABSTRACT II TABLE OF CONTENTS Ill LIST OF FIGURES V LIST OF TABLES Vll ACKNOWLEDGEMENTS X CHAPTER 1 INTRODUCTION 1 1.1 Background 1 1.2 Objectives 2 1.3 Scope 3 1.4 Organization of Thesis 3 CHAPTER 2 BACKGROUND 5 2.1 Overview 5 2.2 Regional Hazard and Risk Assessment 6 2.3 Non-Structural Components 10 CHAPTER 3 INVENTORY COLLECTION 12 3.1 Introduction 12 3.2 Inventory Information 12 3.3 Data Collection 21 3.4 Summary 25 CHAPTER 4 NON-STRUCTURAL COMPONENTS 26 4.1 Introduction 26 4.2 Classification of Non-Structural Systems 27 4.3 Summary 31 in Chapter CHAPTER 5 NON-STRUCTURAL DAMAGE ASSESSMENT METHODOLOGY 32 5.1 Introduction 32 5.2 ATC 13 33 5.3 FEMA-NIBS (HAZUS) 36 5.4 Proposed Methodology for this Study 43 5.5 Summary 46 CHAPTER 6 DAMAGE PROBABILITY MATRICES 48 6.1 Introduction 48 6.2 MMI Associated Response Spectra 48 6.3 Capacity and Fragility Curves 51 6.4 Damage States 58 6.5 Damage Probability Matrices 59 6.6 Summary 78 CHAPTER 7 CASE STUDY: CITY OF NEW WESTMINSTER 79 7.1 Introduction 79 7.2 Building Inventory 81 7.3 Earthquake Damage Estimation 88 7.4 Summary 99 CHAPTER 8 CONCLUSION AND SUMMARY 100 8.1 Summary 100 8.2 Conclusion 102 8.3 Suggested Future Work 105 CHAPTER 9 REFERENCES 107 APPENDIX A DAMAGE PROBABILITY MATRIX WORKSHEET 110 APPENDIX B CAPACITY VS. DEMAND CURVES 114 APPENDIX C NON-STRUCTURAL DAMAGE PROBABILITY MATRICES . . . 121 IV LIST OF FIGURE Figure 2 . 1 : Regional Seismic Hazard & Risk Analysis 7 Figure 3 . 1 : Sample Building Inventory Form 24 Figure 5 . 1 : Sample DPM for Facility Class 1 - W o o d Frame (Low Rise) 35 Figure 6 . 1 : M e a n Horizontal Spectra for Modif ied Merchall i Intensity V, V I , and Vl l - 5% Damping 49 Figure 6.2: Typical Spectra for M M Intensity Vl l and Greater 51 Figure 6.3: Mean Damage Factors for Wood Light Frame Residential 62 Figure 6.4: Mean Damage Factors for W o o d Light Frame Commercial / Inst i tut ional 63 Figure 6.5: Mean Damage Factors for W o o d Light Frame Low Rise 63 Figure 6.6: Mean Damage Factors for W o o d Post and Beam 64 Figure 6.7: Mean Damage Factors for Light Metal Frame 64 Figure 6.8: Mean Damage Factors for Steel Moment Frame Low Rise 65 Figure 6.9: Mean Damage Factors for Steel Moment Frame Med ium Rise 65 Figure 6.10: Mean Damage Factors for Steel Moment Frame High Rise 66 Figure 6 . 1 1 : Mean Damage Factors for Steel Braced Frame Low Rise 66 Figure 6.12: Mean Damage Factors for Steel Braced Frame Medium Rise 67 Figure 6.13: Mean Damage Factors for Steel Braced Frame High Rise 67 Figure 6.14: M e a n Damage Factors for Steel Frame Concrete Wal ls Low Rise 68 Figure 6.15: Mean Damage Factors for Steel Frame Concrete Wal ls Medium Rise 68 Figure 6.16: Mean Damage Factors for Steel Frame Concrete Wal ls High Rise 69 Figure 6.17: Mean Damage Factors for Steel Frame Concrete Infill 69 Chapter Figure 6.18: Mean Damage Factors for Steel Frame Masonry Infill 70 Figure 6.19: Mean Damage Factors for Concrete Frame Low Rise 70 Figure 6.20: Mean Damage Factors for Concrete Frame Medium Rise 71 Figure 6 .21 : Mean Damage Factors for Concrete Frame High Rise 71 Figure 6.22: Mean Damage Factors for Reinforced Concrete Moment Frame Low Rise . 72 Figure 6.23: Mean Damage Factors for Reinforced Concrete Moment Frame Med ium Rise 72 Figure 6.24: Mean Damage Factors for Reinforced Concrete Moment Frame High Rise . 73 Figure 6.25: Mean Damage Factors for Reinforced Concrete Reinforced Infill Wal l 73 Figure 6.26: Mean Damage Factors for Reinforced Masonry Low Rise 74 Figure 6.27: Mean Damage Factors for Reinforced Masonry Med ium Rise 74 Figure 6.28: Mean Damage Factors for Unreinforced Masonry Low Rise 75 Figure 6.29: Mean Damage Factors for Unreinforced Masonry Medium Rise 75 Figure 6.30: Mean Damage Factors for Tilt Up 76 Figure 6 .31 : Mean Damage Factors for Precast Low Rise 76 Figure 6.32: Mean Damage Factors for Precast Medium Rise 77 Figure 6.33: Mean Damage Factors for Mobile Home 77 Figure 7 . 1 : Map of New Westminster 81 Figure 7.2: Prevalent Material Types 87 Figure 7.3: Prevalent Building Types 88 Figure 7.4: Drift Sensit ive Damage MMI VII 91 Figure 7.5: Drift Sensit ive Damage MMI VIII 92 Figure 7.6: Accelerat ion Sensit ive Damage MMI VII 94 Figure 7.7: Accelerat ion Sensit ive Damage MMI VIII 95 Figure 7.8: Building Content Damage MMI VII 97 Figure 7.9: Building Content Damage MMI VIII 98 Figure A . 1 : Damage Probability Matrix Worksheet with Formulas Revealed 112 Figure A.2: Damage Probability Matrix Worksheet 113 Figure B.1 : Capaci ty vs. Demand Plots 114 vi Table 2.1: Modified Mercalli Intensity 10 Table 3.1: BC-31 Building Classifications 17 Table 3.2: Comparison of Building Type Classifications 18 Table 3.3: Occupancy Classes Describing B C Inventory 20 Table 4.1: List of Typical Nonstructural Components and Contents of Buildings - (From FEMA, 1997) 29 Table 5.1: Percent Contents Damage for each Damage State 42 Table 6.1: Moderate-Code Seismic Design Level - Capacity Curve Parameters 55 Table 6.2: Drift Sensitive Fragility Curve Parameters - Moderate-Code Seismic Design Level 56 Table 6.3: Acceleration Sensitive Fragility Curve Parameters - Moderate-Code Seismic Design Level 57 Table 6.4: Central Damage Factors by Damage Type 60 Table 7.1: Sample Building Inventory Database Attributes 86 Table C. 1: Wood Light Frame Residential Damage Probability Matrices 122 Table C.2: Wood Light Frame Commercial/InstitiutionalDamage Probability Matrices . 123 Table C.3: Wood Light Frame Low Rise Damage Probability Matrices 124 Table C.4: Wood Post and Beam Damage Probability Matrices 125 Table C.5: Light Metal Frame Damage Probability Matrices 126 Table C.6: Steel Moment Frame Low Rise Damage Probability Matrices 127 Table C.7: Steel Moment Frame Medium Rise Damage Probability Matrices 128 vii Chapter Table C.8: Steel Moment Frame High Rise Damage Probability Matrices 129 Table C.9: Steel Braced Frame Low Rise Damage Probability Matrices 130 Table C. 10: Steel Braced Frame Medium Rise Damage Probability Matrices 131 Table C. 11: Steel Braced Frame High Rise Damage Probability Matrices 132 Table C. 12: Steel frame with Concrete Walls Low Rise Damage Probability Matrices . 1 3 3 Table C. 13: Steel frame with Concrete Walls Medium Rise Damage Probability Matrices 134 Table C. 14: Steel frame with Concrete Walls High Rise Damage Probability Matrices .135 Table C. 15. Steel Frame with Concrete Infdl Walls Damage Probability Matrices 136 Table C. 16: Steel Frame with Masonry Infill Walls Damage Probability Matrices 137 Table C. 17: Concrete Frame with Concrete Walls Low Rise Damage Probability Matrices 138 Table C. 18: Concrete Frame with Concrete Walls Medium Rise Damage Probability Matrices 139 Table C. 19: Concrete Frame with Concrete Walls High Rise Damage Probability Matrices 140 Table C.20: Reinforced Concrete Moment Frame Low Rise Damage Probability Matrices 141 Table C.21: Reinforced Concrete Moment Frame Medium Rise Damage Probability Matrices 142 Table C.22: Reinforced Concrete Moment Frame High Rise Damage Probability Matrices 143 Table C.23: Reinforced Concrete Frame with Infill Walls Damage Probability Matrices 144 Table C.24: Reinforced Masonry Shear Wall Low Rise Damage Probability Matrices . . 145 Table C.25: Reinforced Masonry Shear Wall Medium Rise Damage Probability Matrices 146 Table C.26: Unreinforced Masonry Shear Wall Low Rise Damage Probability Matrices 147 Table C.27: Unreinfroced Masonry Shear Wall Medium Rise Damage Probability Matrices 148 viii Chapter Table C.28: Tilt Up Damage Probability Matrices 149 Table C.29: Precast Concrete Low Rise Damage Probability Matrices 150 Table C.30: Precast Concrete Medium Rise Damage Probability Matrices 151 Table C.31: Mobile Home Damage Probability Matrices 152 IX A C K N O W L E D G E M E N T First I would like to thank my partner Laura for her support, patience, and love, without which I could not have reached this point. I also must thank my mother, Lynn, my father, Ed, my sister, Cheryl, and my niece, Brenna, for their support and love during my studies and the rest of my life. The support of my supervisor and mentor, Dr. Carlos Ventura, is gratefully acknowledged. His experience and guidance in the field of seismic risk assessment and earthquake engineering has made this work possible. His encouragement, support, and patience is greatly appreciated. I would like to thank Dr. Liam Finn for being the second reader of this thesis. He has provided me with an abundance of technical support and direction while completing this thesis. I would like to thank several of.my fellow students of the University of British Columbia for their assistance throughout my studies with special thanks to Ms. Ardel Blanquera, Ms. Tuna Onur, Mr. Ding Yuming, Ms. Haidon Wong, Mr. Marc Gerin, Mr. Jachym Rudolf, Mr. Cameron Black and Dr. Vincent Lattendresse. Funding for this project was provided by the Natural Sciences and Engineering Research Council of Canada. The financial support of the British Columbia Insurance Industry is appreciated. I would like to thank Mr. Leon Bell for his valuable advice and training in assessing and compiling an inventory of the local building stock. C H A P T E R 1 Introduction 1.1 Background Non-Structural damage has, until recently, has not received the same attention as structural damage in regional earthquake damage assessment studies. This is because earthquake hazards and damages have often been equated with mainly structural failure. While the effects of structural failure can be catastrophic the effects of non-structural failure are important and in many cases are of greater significance than structural effects. The hazards that arise from the failure of non-structural elements and the potential economic impact arising from non-structural damages need to be assessed in order to better understand and possibly reduce the effects of an earthquake on a region. Developing damage functions is a critical step in performing a regional risk analysis. The damage relations need to be as representative as possible of local conditions as well as usable within the scheme of the risk analysis study. It is also important that the damage functions developed accurately represent the regional building inventory. This holds true for any type of damage functions whether they are structural, non-structural, or component specific. How shaking intensity is represented will affect the type of damage relation as well as the form of the hazards that the building inventory will be subjected to. l Chapter 1 Introduction The use of a Geographic Information System (GIS) is an integral part a the regional risk assessment project. A GIS allows for spatial data, i.e. maps, and tabular data, i.e. a building inventory, to be manipulated and an results can be presented in either a spatial or tabular format. A GIS program is capable of performing the many calculations required in a regional hazard analysis as well as presenting the results in a desirable format. The results from a GIS analysis can be presented as thematic maps. A thematic map presents spacial distributions on a map by demarcating regions of similar scale, in much the same was a topographic map represents elevations with contour lines. The thematic damage maps that are produced as the result of a regional damage assessment analysis can be used by the insurance industry, regional planners, and emergency preparedness groups in order to prepare for and reduce the risks from future earthquakes. 1.2 Objectives The objective of this research is the development of a methodology by which the risk, due to earthquake hazards, to the non-structural building inventory of southwestern British Columbia may be assessed. Three non-structural damage matrices will be developed for each building class that is present in the general building stock of southwestern British Columbia. For each building class the damage matrices developed will represent damage to one of three types of components that are at risk. The three classifications are damage to displacement sensitive components, damage to acceleration sensitive components, and damage to building contents. Risk analysis calculations will be performed for the case study region, New Westminster, with the use of the GIS package Mapinfo (Maplnfo Corporation 1997). Maps describing the regional inventory will be presented as well as regional damage maps. The maps representing 2 Chapter 1 Introduction the regional inventory and the distribution of damages will be compared. The results from this study can be beneficial to many different sectors of society. Insurance groups, Regional Authorities, Local Engineer, and Emergency Preparedness Groups can all benefit from the results of a regional damage assessment study. The insurance industry can use the predicted damage levels to better understand the economic consequences of a major earthquake. Regional authorities can use the results of the study to isolate regions where detailed assessment of the building stock may be required. Local engineers can gain a better understanding of areas that require more attention during design, as well as areas local design practices that my require attention. The damage maps can also be used by regional emergency preparedness organizations to assist in preparing for a major earthquake. 1.3 Scope The objective of this thesis is the development of a locally applicable methodology for assessing the probable non-structural damage resulting from a significant earthquake event, i.e. earthquakes with an intensity of M M I VI or greater. The non-structural systems encompassed by this methodology are the components of the buildings that are not designed as part of either the vertical or lateral load carrying system, such as partition walls and mechanical equipment, as well as the contents of the building. The methodology is applicable to the general building stock and does not include critical facilities which should receive a detailed review on a building by building basis. 1.4 Organization of Thesis An introduction to this study is contained in Chapter 1. The objectives of this study are 3 Chapter 1 Introduction outlined as well as the scope of the study and the methodology to be followed. Chapter 2 contains a review of literature relevant to non-structural hazard assessment and related topics. Regional earthquake hazard assessment, non-structural systems, damage functions, and the application of GIS systems in regional hazard assessment are covered. Chapter 3 outline the information needed in order to implement a regional earthquake hazard assessment as well as methods to collect the information. A summary and classification of non-structural systems and building contents that will be covered within the scope of this thesis is presented in Chapter 4. Chapter 5 presents a review of existing methodologies for performing a regional hazard assessment and gives a detailed account of the methodology used in this thesis. The development of non-structural damage matrices is covered in Chapter 6. This includes the development of response spectra for individual Modified Merchalli Intensity levels and a correlation between the HAZUS (FEMA, 1997) structural classification and the structural classes developed for Southwest British Columbia. Chapter 7 presents a case study of the methodology that is proposed in this thesis. The case study region is the City of New Westminster. The conclusions and a summary of this thesis is presented in Chapter 8. C H A P T E R 2 Background 2.1 Overview Since the early 1970s regional many regional hazard and loss studies have been conducted. These studies vary a great deal in scope and primary areas of emphasis. The majority of studies conducted have been sponsored by either government agencies or the insurance industry (FEMA 249, 1994). Regardless of the specific directives of each study the common theme is an attempt to understand the potential for risk and loss due to a major earthquake in an urban or industrial region. The demand for the information provided by regional risk and damage assessment studies is well demonstrated by the more than 30 major studies conducted in the United States over the last 25 years (FEMA-249, 1994). Regional damage assessment studies have not been limited to the United States, work has also been conducted in other countries of the world (Munich Re-Insurance Company of Canada (1993); Ventura C.E., 1996; Ventura C.E. andRezai, M., 1997). The need for a comprehensive regional damage assessment study conducted in Southwestern B.C. has been demonstrated by the insurance industry and local government officials (Morfitt, G. 1997). 5 Chapter 2 Background 2.2 Regional Hazard and Risk Assessment Seismic risk assessment studies attempt to quantify the probable damages due to a significant earthquake near an urban area to the local building stock. In order to perform this task an assessment of the potential ground motions that can be expected in the region under consideration must be calculated. This assessment of the potential ground motions is referred to as the seismic hazard for the region. The next task in a risk assessment study is to identify the buildings present in the region. This involves compiling an inventory of the building stock of interest to the study. Once the seismic hazard is known and the building stock has been identified motion damage relationships are applied in order to estimate the potential damages to each facility within the region being considered. The individual building damage estimates are then compiled to form a regional damage distribution. It is important to assess the results on a regional basis not a building by building basis since the motion damage relationships are based on statistical models and do not accurately represent the damages to individual structures. A repair and replacement cost model can be applied to the regional damage distributions in order to obtain the regional loss distribution. Figure 2.1, taken from Blanquera (1999) outlines the steps in a regional risk assessment study. 6 Chapter 2 Background Seismic Hazard Analysis Structural Inventory Data Ground Motion Local Site Effects Motion Damage Relationships Regional Damage Distribution Repair and Replacement Cost Model Regional Loss Distribution Figure 2.1: Regional Seismic Hazard & Risk Analysis 2.2.1 Building Damage Functions Among the defining characteristics of a earthquake damage or loss study is the method of describing the relationship between ground motion and damage. The form of the motion damage relationships wil l influence a variety of other input parameters necessary to a study. The description of ground motions, the inventory information required, and the representation of the results will all be directed by the motion damage relationship or can inversely direct the 7 Chapter 2 Background form of the motion damage relationship. The existing motion damage relationships that have been used in regional hazard assessment studies can be separated into two categories. The two categories are empirical/heuristic models and engineering parameter models. Empirical/heuristic models related damages to building stocks to parameters that cannot be directly measured but can only be assessed subjectively. Mean damage factor curves and damage probability matrices are examples of empirical/heuristic models. Engineering parameter models attempt to relate damages to building stocks to specific engineering parameters. The fragility curves used by the HAZUS methodology are examples of engineering parameter models. For a detailed discussion of building damage functions see Chapter 5. 2.2.2 Ground Motion Intensity Measures There is a wide variety of scales used by geoscientists and engineers to describe and measure the ground motions cause by an earthquake. These scales can be grouped into two major categories, engineering parameter scales, and subjective scales. Engineering parameters scales represent the ground motions based on measurable quantities, for example peak ground acceleration, peak spectral response velocity, or the richter scale. Subjective scales measure the intensity of ground motions based on the visible effects of an earthquake. Among these scales are the Modified Mercalli Intensity Scale (MMI), the Japan Meteorological Agency Scale (JMA), and the Rossi-Forrell Scale (RF). The advantage of an engineering parameter scale is that ground motions are directly measured and are not subject to human interpretations. The disadvantage is that in many areas where earthquakes occur there is no 8 Chapter 2 Background instrumentation in place to record the ground motions. This is the primary advantage of a subjective scale, in areas where instrumentation is not in place engineers can visit the site following an earthquake and develop a reasonable understanding of the shaking intensity caused by the earthquake. When a ground motion scale is selected for a regional damage assessment study several factors are important to consider. The predominant scale used to measure existing ground motion data for the region should be considered. When estimates of ground motions are calculated it is convenient to be able to compare with existing data. Local expertise is another important factor to consider when selecting the intensity scale to be used. Input from local experts can be a great asset to a study but if local engineers are not familiar with the methods and measures being implemented then the effectiveness of their input will be reduced. As well as local availability of data and expertise the selection of a ground motion intensity measure must also consider existing sources of data and the preferred form of the damage functions. For this study the Modified Mercalli Intensity (MMI) scale was selected as the measure of ground motions. This scale was selected because local engineers were familiar with the scale and existing studies existed for Southwestern British Columbia that used the M M I scale (Blanquera, A., 1999, Bell, L., 1998, Ventura C.E. andRezai, M., 1997). Table 2.1 is a verbal description of the portion of the M M I scale that is of importance to this damage assessment study (ATC, 1985). 9 Chapter 2 Background Table 2.1: Modified Mercalli Intensity M M I Description of Effects VI Felt by all, many frightened. Some heavy furniture moved. A few instances of fallen plaster. Damage slight. Vll Damage negligible in buildings of good design and construction; slight to moderate in well-built ordinary structures; considerable damage in poorly built structures. Some chimneys broken. VIII Damage slight in specially-designed structures; considerable damage in ordinary substantial buildings with partial collapse. Damage great in poorly-built structures. Fall of chimneys, factory stacks, columns, monuments, walls. Heavy furniture over-turned. IX Damage considerable in specially-designed structures; well-designed frame struc-tures thrown out of plumb. Damage great in substantial buildings, with partial col-lapse. Buildings shifted off foundations. X Some well-built wooden structures destroyed; most masonry and frame structures with foundations destroyed. Rails bent. XI Few, if any masonry structures remain standing. Bridges destroyed. Rails bent greatly. j XII Damage total. Lines of sight and level are distorted. Objects thrown into air. | 2.3 Non-Structural Components Until recently Non-structural components have not received the detailed consideration, under seismic effects, that the primary structural systems receive. In the last decade engineers have released the need for refined methodologies by which non-structural components can be assessed. The result is that codes are being drafted and implemented that provide guidelines for engineers when considering non-structural components (SEAOC, J996, CSA, 1998). The trend by engineers towards improve understanding of non-structural components has carried over to the area of seismic risk assessment. Early seismic risk studied did not directly consider non-structural components in their assessment of potential damages. The ATC-13 report (ATC-1986) released in 1985 was the first major study to directly consider non-structural components (FEMA, 1994). The ATC-13 10 Chapter 2 Background methodology identified six facility classes that are related to mechanical and electrical equipment. More recently the Federal Emergency Management Agency of the United States released a comprehensive regional earthquake risk assessment methodology contained in the HAZUS software package (FEMA, 1998). The HAZUS methodology 'represents the current state of the art in the assessment of non-structural hazards. Non-structural systems are separated into three distinct categories and each category is considered separately. The three divisions that are formed are displacement sensitive components, acceleration sensitive components and building contents. For a detailed review on non-structural components see Chapter 4 of this thesis. 11 C H A P T E R 3 Inventory Collection 3.1 Introduction The collection of a complete and accurate building inventory is an important step in performing a regional earthquake damage study. The inventory process can be very time consuming and is often the most difficult step of a damage estimation study (Applied Technology Council, 1985). It is necessary to collect geographic, structural and occupancy information as well as other less important information for every building within the inventory region. This chapter describes the information required for a complete inventory and methods by which the inventory can be collected. 3.2 Inventory Information Prior to assessing a regions risk due to an earthquake an inventory of including any buildings and facilities that are to be considered is required. The information that is required for an earthquake damage assessment study is usually not available in any individual database that has been collected previous to the study. The inventory database must include sufficient information to identify the buildings as well as make an assessment of the vulnerability of each facility. The report titled Earthquake Damage Evaluation Data for California, ATC-13 12 Chapter 3 Inventory Collection (Applied Technology Council, 1985) identifies five categories of information that are required to determine the economic impact of an earthquake, including loss of function and deaths and injuries. The five categories of information are: • The Earthquake Engineering Facility Classification of the facilities, • The replacement value of the facilities, • The location of the facilities, • The type and value of facilities contents, • The number of occupants or users of the facilities. For the purposes of this study the information regarding replacement value of the facility and the value of facility contents is not required. The replacement values of the facilities and contents can be used in a study to estimate the dollar loss due to an earthquake event. Estimating the dollar loss due to the earthquake is beyond the scope of the study due to time and funding limitations. Therefore the following categories of information are proposed as being necessary in the inventory: • Geographic Information, • Structural Information, • Occupancy Information, • Other Building Information (not necessary but beneficial). Each category is described below. 3.2.1 Geographic Information Information regarding the location of each building is necessary in order to present the result of the study on a geographic basis. Geographic information can be in many forms representing many levels of detail. Examples of geographic location information are listed below: 13 Chapter 3 Inventory Collection • Street Address • Latitude and Longitude • Legal Roll Number, as defined by regional authorities, • Census Tract, as defined by the Federal Census Bureau, • Postal Code, as defined by Canada Post for mail distribution, • Zoning Region, as defined by municipal planning departments. It is necessary to locate (geocode) each building by one identifier within the GIS. The size of the region that will be used to locate each building will determine the maximum detail that results can represent. If the street address is selected or the legal roll number then each building can be located to an specific site. With this level of precision results can be presented to any large level. If the census tract is used to locate the building within the GIS that is the smallest region that can be used to present the results as the GIS will locate each site within the census tract at the centroid of the census region. It can be beneficial to have more than one means of identifying the location of each site within the database. With multiple location identifiers it is possible to geocode each site to a small region an then present the results based on any region that has been identified. 3.2.2 Structural Information In order to perform a regional earthquake damage assessment it is necessary to obtain basic structural information regarding each building within the study region. This information must describe the size of the building as well as identify the structural type especially the lateral load resisting system. The following is a list of the structural information that is required: 14 Chapter 3 Inventory Collection • Height, • Footprint Area, • Footprint Shape, • Building Age. • Structure Type, The building height and footprint serve to identify the size of the building. This information can be used to assess the value of the losses due to earthquake damage. The size information can also be used to weight the damages when represented on a percent of replacement value basis. The shape of the building and the age can have an impact on the expected performance of a building. If the building has and irregular shape or is quite old its performance may be adversely affected. Damage modifiers can be applied based on the footprint shape and building age. The last piece of information is a description of the structure type. The structure type is the primary basis for estimating damages due to earthquakes. It would be ideal to perform a detailed analysis of every building within the study region, but that would be beyond the scope of any project. A detailed analysis would enable the damage assessment to consider specific design details of each building, the age of the building, the condition of the building, the site soil conditions, as well as the specific loading of the building. Unfortunately, the resources required to do a detailed review of every structure as well as a detailed seismic analysis of every structure are prohibitive. In order to reduce the magnitude of the problem buildings within an inventory region are reduced into groups of structural classes. These classes group building into specific categories based on their size, material type, and lateral load resisting system. It is important for the classification system used to 15 Chapter 3 Inventory Collection represent the local building inventory while remaining manageable within the scheme of the study. For this study a classification system has been developed that includes thirty-one building types. The thirty-one classes represent the common structural types that are present in Southwestern British Columbia. The thirty-one building types are listed in Table 3.1. This classification system is specific to Southwestern British Columbia construction but it can be related to classification schemes developed for other studies. Table 3.2 compares the thirty-one building classes with the facility classes defined by the ATC-13 study for California as well as the Building Types defined in the HAZUS software package. For a detailed description of the building classification system employed for this study refer to the report titled Southwestern British Columbia Seismic Fragility Study (Blanquera, 1999). 16 Chapter 3 Inventory Collection Table 3.1: BC-31 Building Classifications Mater ia l Structural Class A c r o n y m Wood Wood Light Frame, Residential WLFR Wood Light Frame, Commercial/Institutional WLFCI Wood Light Frame Low Rise WLFLR Wood Post and Beam WPB Steel Light Metal Frame LMF Steel Moment Frame Low Rise SMFLR Steel Moment Frame Medium Rise SMFMR Steel Moment Frame High Rise SMFHR Steel Braced Frame Low Rise SBFLR Steel Braced Frame Medium Rise SBFMR Steel Braced Frame High Rise SBFHR Steel Frame Concrete Walls Low Rise SFCWLR Steel Frame Concrete Walls Medium Rise SFCWMR Steel Frame Concrete Walls High Rise SFCWHR Steel Frame with Concrete Infill Walls SFCI Steel Frame with Masonry Infill Walls SFMI Concrete Concrete Frame with Concrete Walls Low Rise CFLR Concrete Frame with Concrete Walls Medium Rise CFMR Concrete Frame with Concrete Walls High Rise CFHR Reinforced Concrete Moment Frame Low Rise RCMFLR Reinforced Concrete Moment Frame Medium Rise RCMFMR Reinforced Concrete Moment Frame High Rise RCMFHR Reinforced Concrete Frame with Infill Walls RCFIW Masonry Reinforced Masonry Shear Wall Low Rise RMLR Reinforced Masonry Shear Wall Medium Rise RMMR Unreinforced Masonry Bearing Walls Low Rise URMLR Unreinforced Masonry Bearing Walls Medium Rise URMMR Tilt Up Tilt Up TU Precast Precast Concrete Low Rise PCLR Precast Concrete Medium Rise PCMR Mobile Mobile Homes MH 17 Chapter 3 Inventory Collection Table 3.2: Comparison of Building Type Classifications BC Study Building Type HAZUS Building Type ATC-13 Facility Class BC Study Building Type HAZUS Building Type ATC-13 Facility Class WLFR W1 1 CFLR C2L 6 WLFCI W2 1 CFMR C2M 7 WLFLR W1 1 CFHR C2H 8 WPB W1 N/A RCMFLR C1L 18, 87 LMF S3 2 RCMFMR C1M 19, 88 SMFLR S1L 15, 72 RCMFHR C1H 19, 89 SMFMR S1M 16, 73 RCRIW C3L 79 SMFHR S1H 17, 74 RMLR RM1L 9, 84 SBFLR S2L 12 RMMR RM1M 10, 85 SBFMR S2M 13 URMLR URML 78 SBFHR S2H 14 URMMR URMM 79 SFCWLR S4L 6 TU PC1 21 SFCWMR S4M 7 PCLR PC2L 81 SFCWHR S4H 8 PCMR PC2M 82 SFCI S4L N/A MH MH 23 SFMI S4L N/A 3.2.3 Occupancy Information Occupancy information is necessary in order to assess extend of the losses to non-structural building components and building contents due to earthquake damages. The type of occupancy is used as an indicator of the value of building contents and non-structural systems, as well as estimating the number of occupants that are exposed to injury or possibly death. The classification scheme used for this study describes the primary use of each building in three classes, primary use 1 to 3 with increasing detail in each subsequent category. Table 3.3 shows the primary use classification scheme used for this study. Each increase in primary use level indicates an increase in the detail level of classification. For example describing a building as a Commercial facility is a generic classification. A classification of Financial 18 Chapter 3 Inventory Collection Service Commercial facility provides an increase in detail to the classification of the facility. Primary Use 3 one step more accurate, i.e. the same facility described above could be a Bank or an Office facility, this level of detail provides the most accurate classification of the facility. Depending on the methods used to gather the inventory it is not always possible to describe the occupancy to the level of detail of Primary Use 3. When a sidewalk survey is performed then the specific occupancy can be classified but i f existing databases are being interpreted to inventory a region it is difficult to classify the facilities to a level greater than Primary Use 2 and often Primary Use 1. 19 Chapter 3 Inventory Collection Table 3.3: Occupancy Classes Describing BC Inventory Primary Use 1 Primary Use 2 Primary Use 3 Residential Permanent Dwelling Houses/Apts. Mobile Homes Temporary Lodging Group Institutional Housing Hotels/Motels Dormitories Commercial Retail Wholesale Financial Services Personal Services Professional Services Entertainment & Recreation Parking Stores Warehouses Banks Service Station/Shops Offices Rests ./Bars/Theater Garages Industrial Manufacturing Factories Agriculture Farm buildings Mining Mine buildings Religion/Non-Profit Churches/Offices Government General Services Offices Police Stations Fire Stations Medical Facilities Hospitals Hospitals Ambulance Services Garages Nursing Homes Conv. Centers Health Care Services Clinics Education Elementary Schools Secondary & Jr. Colleges Schools Colleges & Universities Schools Transportation Freight & Passenger Terminals 3.2.4 Other Inventory Information A building inventory containing the information described above would contain sufficient data with which to perform a regional damage assessment. The collection of additional information is not necessary but it will improve the usefulness of the database. The primary 20 Chapter 3 Inventory Collection difficulty when collecting an inventory is the lack of an existing comprehensive database. The inventory collection process is an opportunity to develop just such a cohesive database. Existing databases are often used as a basis for the regional inventory. Examples of existing databases that can be useful for a damage assessment study are census data, assessment authority data, and planning department databases. These databases will likely contain fields that are not directly applicable to the study and in an effort to streamline the inventory they are often discarded. If the fields are not discarded they can make the complete inventory a greater asset by being applicable to multiple users, not just for the purposes of a damage study. Information that identifies regions that are not used for the study may be of use to city planners, or other government officials. Essentially any field may allow future users to link existing data with the gathered inventory. As well as providing benefits for other users many fields may be of use when trying to complete or verify the database. Information such as building names or zoning type can assist in identifying the structural type or the occupancy. Buildings that have names ending in apartment, court, or manor are probably apartments, names ending in Centre are likely have a commercial occupancy. The heritage status of a building can assist in identifying possibly unique structures that may have some value beyond the typical dollars per square foot. These additional "unnecessary fields" can actually be very useful when performing the study as well as benefit future users. 3.3 Data Collection The collection of the building data is a critical step in a damage assessment project. It is 21 Chapter 3 Inventory Collection important that the data is collected quickly and efficiently but it is also crucial that the inventory is as accurate and complete as possible. It is difficult to perform a field survey of every building in a study area with the resources typically available. It is therefore necessary to utilize existing data that may contain much of the information that is needed for the inventory. For the purposes of this study data from the Municipalities in the study area was utilized. This data is then augmented with field verification and reviews of portions of the database. There are many sources of data that are available to engineers compiling a regional study. Statistics Canada or the local assessment authorities are possible sources of information on building locations, values, and occupancies. Many local municipalities will also be receptive when approached for assistance. Planning departments often have digital databases of the buildings in the municipality that contain much of the needed information. These information obtained from one or more of the possible sources must then be processed and augmented to include all of the required information. Inferences can be made based on the zoning, building size, or any structural information that is included in the original database. These inferences serve to complete the existing data to meet the needs of the study. When inferences are made it is important to perform field reviews of a portion of the inventory to verify the inference schemes. The case study described in Chapter 7 contains an example of the methods that can be used to compile a database as well as describing the verification process. If it is not possible to obtain a partial database to be used as a basis for a building inventory 22 Chapter 3 Inventory Collection then it is necessary to compile all of the data manually. A "sidewalk survey" can be performed where trained individuals perform a survey of buildings in the region by reviewing each building from the street. Since this process is very time and manpower intensive it may be necessary to only inventory a portion of the buildings in the study region by this method. In order to utilize resources commercial and industrial areas can be reviewed by means of a sidewalk survey and alternative methods can be used to complete the inventory for residential areas. The commercial and industrial areas should be reviewed by the most detailed method that resources permit due to the large variability of construction types and occupancies. Residential areas can be completed by utilizing aerial photos and inference schemes since residential construction contains less variability. A sidewalk survey can be very resource intensive, therefore it is important to have a data collection framework in place that promotes efficiency and consistency. A building inventory form is used that is organized such that all of the required data can be quickly recorded on the form. The form ensures that the data is collected in a standardized format and promotes efficient information management. Figure 3.1 shows a sample inventory form. A l l of the building information can be either circled or checked and there are spaces for information regarding the surveyor as well as the date of the survey. There is also a spot for a photo of the building, this can be used to review the data as well as when information is missed. With the use of a well organized form the rapid visual screening process should take approximately 5 to 10 minutes per building for trained personnel. 23 Chapter 3 Inventory Collection Figure 3.1: Sample Building Inventory Form Building Inventory Form Reviewer Address: Postal Code: Date: Building Name: Zone: Primary Use: Photo: No. of Storeys: Year Built: Footprint Area: Shape: Rect_ Other Storefront: Y Wood WLFR WLFCI WLFLR WPB Wood Light Frame, Residential Wood Light Frame, Commercial/lnst. Wood Light Frame Low Rise Wood Post and Beam Pounding: Y_ Retrofit: Y N Adjacent Building Types: Soil Type Steel Cone. Masonr Tilt Up Precast Mobile LMF SMFLR SMFMR SMFHR SBFLR SBFMR SBFHR SFCWLR SFCWMR SFCWHR SFCI SFMI Light Metal Frame Steel Moment Frame Low Rise Steel Moment Frame Mid Rise Steel Moment Frame High Rise Steel Braced Frame Low Rise Steel Braced Frame Mid Rise Steel Braced Frame High Rise Steel Frame Concrete Walls Low Rise Steel Frame Concrete Walls Mid Rise Steel Frame Concrete Walls High Rise Steel Frame with Concrete Infill Walls Steel Frame with Masonry Infill Walls CFLR CFMR CFHR RCMFLR RCMFMR RCMFHR RCFIW Concrete Frame with Concrete Walls Low Rise Concrete Frame with Concrete Walls Mid Rise Concrete Frame with Concrete Walls High Rise Reinforced Concrete Moment Frame Low Rise Reinforced Concrete Moment Frame Mid Rise Reinforced Concrete Moment Frame High Rise Reinforced Concrete Frame with Infill Walls RMLR RMMR URMLR URMMR Reinforced Masonry Shear Wall Low Rise Reinforced Masonry Shear Wall Mid Rise Unreinforced Masonry Shear Wall Low Rise Unreinforced Masonry Shear Wall Mid Rise TU Tilt Up PCLR PCMR Precast Concrete Low Rise Precast Concrete Mid Rise MH Mobile Homes Photo/Sketch: Comments: 24 Chapter 3 Inventory Collection When resources do not allow for an inventory to be collected entirely by a field survey some areas will have to be completed through alternative methods. One alternative method is the use of aerial photos. High quality aerial photos are available, for most urban areas, that contain sufficient detail to be used as an inventory tool. While it is difficult or impossible to accurately identify buildings in a diverse structural region areas that are predominantly residential can completed. The number and approximate size of buildings can be assessed from an aerial photo and in residential areas it is possible to separate single family homes from multi-family apartments. Once blanks in the inventory have been filled through the use of aerial photos a "windshield survey" is required to verify the assumptions made in reviewing the photos. 3.4 Summary The collection of the regional building inventory is a critical stage of a regional damage assessment study. The information collected is the basis for damage calculation and the accuracy of the inventory will directly influence the accuracy of the results. The inventory collection process can be very time and resource consuming. The use of existing data, be it from government agencies or private industry, will greatly increase the efficiency of the collection process as well as reducing the resources necessary to complete the inventory. It is important to perform field verification of existing data as well as the inference schemes used to complete the data. Where existing data is not available a field survey must be performed to the extent that resources allow. C H A P T E R 4 Non-Structural Components 4.1 Introduction Historically non-structural systems have received little attention from engineers when earthquake effects were considered. This is due to non-structural components in a building being perceived to be less of a threat than the structural systems of the building. If a building fails and collapses then there is an obvious danger to the occupants as well as a total loss of the building. The economic and social impact of a collapsed structure can not be understated but that does not remove the impacts and dangers of non-structural failures. Damage due to non-structural failure can result in casualties, building function impairment, and major economic losses even when the structural damage is not significant (Building Seismic Safety Council, 1997). The perception of risk due to non-structural failure is starting to change. The Structural Engineers Association of California (SEAOC) has released its Vision 2000 (SEAOC, 1996) which outline the direction that future codes will take. Non-structural components receive much attention in this future vision. The Canadian Standards Association (CSA) has also started to focus more attention on non-structural components and are preparing guidelines for the seismic consideration of functional and operational components of buildings. With the release of guidelines for non-structural systems areas of concern are 26 Chapter 4 Non-Structural Components being identified and the non-structural components are being better classified by engineers. 4.2 Classification of Non-Structural Systems Non-Structural components can be loosely defined as any component of a building or structure that does not comprise part of the structural skeleton. These components include architectural, mechanical, and electrical components. Building contents are treated as a separate category from the permanent non-structural components of buildings. It would be beyond the scope of a regional hazard assessment methodology to develop damage functions for every non-structural component and all building contents. In order to reduce the scope of the problem non-structural components can be separated into categories, drift sensitive and acceleration sensitive (FEMA, 1997). Building contents are separated from non-structural components but damage to contents can be attributed to floor accelerations and thus related to acceleration sensitive component damage. Drift sensitive components are those components damaged due to interstory drift while acceleration sensitive components are those components damaged due to floor accelerations. Table 4.1, based on a table from the HAZUS technical manuals, is a summary showing typical non-structural components and the categories which best describe them, included are many of the components that are identified in the proposed non-structural guidelines for Canadian engineers. The solid bullets indicate the category that the component is evaluated as and the hollow bullets indicate while the response of the system is not dominated by the category it is still largely influenced by the category. Many components are affected by both interstory drift and floor accelerations but damage to each component will be dominated by one or the other and this dominance allows for the components to be effectively categorized. It is important to note that non-structural 27 Chapter 4 Non-Structural Components components, although not a part of the structural system, need to be evaluated based on the seismic performance of the structural system. For instance, the interstory drift and floor accelerations will be very different when a wood light frame low-rise structure in considered than when a steel braced frame high-rise is considered. Due to this difference damage functions will be presented for each structural type in Chapter 6. Many factors affect the extent of damage to non-structural systems other than the magnitude of the ground motions. Anchorage and bracing as well as special detailing can greatly influence the extent that components are damaged. Special consideration is given when detailing components for essential and high potential loss facilities such as hospitals and schools. It is assumed typical buildings will not have specially detailed anchorage and bracing or other special details for non-structural components. 4.2.1 Drift Sensitive Components During an earthquake structures will be shaken and thus will deform due to the ground motion. The deformations that occur between stories of a building will cause nonstructural components that are connected to both stories or secured between columns and walls to deform along with the structure. These deformations will cause the nonstructural component to be damaged. It is easy to see that nonhealing walls or architectural cladding will be subjected to deformations due to interstory drift and subsequently could be damaged. It is also apparent that a boiler sitting on the floor of a structure will not be affected by interstory drift. Typical nonstructural components falling within the category of drift sensitive are nonbearing wall and partition wall, exterior wall panels, veneer, architectural finishes and penthouses. 28 Chapter 4 Non-Structural Components Type Item Drift Sensitive Acceleration Sensitive Architectural Nonbearing Walls/Partition Stud Walls • o Cantilever Elements and Parapets • Exterior Walls • o Veneer and Finishes • o Mechanical Penthouses • Access Floors • Appendages and Ornaments • Mechanical General Mechanical (boilers, etc.) • and Manufacturing and process machinery • Electrical Piping Systems o • Storage Tanks and Spheres • Racks and Cabinets • HVAC Systems o • Elevators o • Ductwork o Tanks • Pumps • Trussed Towers • Cable Trays/Racks o • Lighting fixtures • Panel Boards o • Switchboards/MCC Units • Emergency Generators • • Contents File Cabinets, Bookcases, etc. • Office Equipment and Furnishings • Demountable Partitions • Computer/Communication Equipment • Nonpermanent Manufacturing Equipment • Manufacturing/Storage Inventory • Food Services Equipment • Art and other Valuable Objects • Table 4.1: List of Typical Nonstructural Components and Contents of Buildings - (From FEMA, 1997) 29 Chapter 4 Non-Structural Components 4.2.2 Acceleration Sensitive Components The accelerations that occur at each floor level within a building will transfer through to any component that is attached on that floor. As a result the non-structural components will be excited and will begin to vibrate. The response of the object, assume a boiler, being excited will be governed by the principles of dynamic motion that govern the response of a building. If the boiler is not securely anchored to the floor it may start to slide and shift on its base. As the boiler moves any connecting piping or electrical cables that are attached to it will be deformed and likely will either fail or become disconnected from the boiler. Even if the boiler is securely anchored to the floor it will start to vibrate. If the excitation is near the fundamental frequency of the boiler the response will be large enough to cause damage to occur to the boiler itself as well as the possibility of failure of connecting piping and electrical cables. The effects of the floor accelerations will occur regardless of the component that is considered. Typical components that are affected by floor accelerations are racks and cabinets, mechanical and electrical equipment and parapet walls. For a more detailed list of components that are acceleration sensitive see Table 4.1. 4.2.3 Building Contents Building contents are defined as furniture, equipment that is not integral with the structure, computers, and supplies (FEMA, 1997). Non-structural components that are permanently affixed to a structure are not included in this category building contents. Although building contents are treated separately from acceleration sensitive components the damages to building contents are attributed primarily to floor accelerations. Typical damages to building contents are overturned equipment, computers sliding off of tables, and toppled shelves. 30 Chapter 4 Non-Structural Components 4.3 Summary Until recently structural engineers have focused less attention, during the design process, on non-structural components than may be required to ensure adequate performance during an earthquake event. Significant damage to non-structural components during past earthquakes has shown that while non-structural failures will not cause failure of a building they can result in life safety hazards as well as major economic expenses to repair. This has prompted the development of guidelines to direct engineers design where non-structural components are considered. The extent of non-structural damages in past earthquakes has also prompted regional damage assessment studies to consider non-structural components. When non-structural components are considered in a regional damage assessment study it is necessary to classify the components into categories that will be damaged in similar fashion. The classification method in this study separates components into three categories. The first category is displacement sensitive components. These components are damages due to interstory drift. The next category is acceleration sensitive components. The accelerations occurring at each floor of a structure cause the damages to acceleration sensitive components. The last category is building contents. It is important to separate building contents from other non-structural components. Although the damage mechanism is similar to that of acceleration sensitive components the extent of damages is different. Also, it is possible to salvage building contents after an earthquake. 31 C H A P T E R Non-Structural Damage Assessment Methodology 5.1 Introduction In 1972 Algermissen et al. conducted what was one of the first major studies intended to evaluate the effects of earthquakes on a major metropolitan area (Algermissen et al, 1972). Since then many studies have been completed that present several different damage estimation methodologies and apply the methodologies to metropolitan areas. In 1985 the report ATC-13 was released by the Applied Technology Council in California. It presented the most comprehensive earthquake damage estimation methodology available at the time. The ATC-13 methodology remains one of the most recognized and accepted methodologies to date. In 1997 the National Institute of Building Sciences (NIBS) presented a new methodology to assess the possible damage due to earthquakes in the form of a computer software package called H A Z U S (FEMA, 1997). The FEMA-NIBS methodology utilizes the increased computing power available to todays engineers and planners as well as modem damage functions. A description of these two major methodologies is presented here as well as the proposed methodology for this study. L/fiapter 5 Non-Structural Damage Assessment Methodology 5.2 ATC 13 In 1985 the Applied Technology Council released its report "Earthquake Damage Evaluation Data for California" (ATC-13). This study was the first to compile a methodology that would cover an extensive range of hazards and damages. Included within the scope of the methodology are ground failure hazards (liquefaction, landslide, fault rupture), induced damages (fire, flooding), social impacts (casualties), as well as direct physical damages (buildings, lifelines, large loss facilities, critical facilities). Another important aspect of the study is the inclusion of a methodology for compiling an inventory of facilities within the study region. 5.2.1 Damage Estimation The proposed methodology for assessing the direct damage due to an earthquake was based on developing Damage Probability Matrices (DPMs) for ninety-one proposed earthquake engineering facility classes. Prior to the ATC-13 study, data on the damagability of many of the proposed facility types was limited and in many cases non-existent. In order to better estimate the effects of a large earthquake expert opinions were sought. The expert opinions were solicited based on the Delphi procedure for soliciting expert opinion. This procedure consisted of several rounds of questionnaire in which participants were allowed to view controlled portions of the responses from the previous round of questionnaires. Once the questionnaires were completed statistical methods were used to compile the results. It is noteworthy that "the most frequent comment from the experts was that data and knowledge on the performance of various facilities under earthquake ground motion are very limited and damage assessment is particularly difficult at the high intensity levels" (ATC, 1985). For a 33 Chapter 5 Non-Structural Damage Assessment Methodology more detailed account of the method used to gather the expert opinions see the report ATC-13. The results of the expert survey were damage probability matrices for the seventy-eight proposed facility classes, forty building structures and thirty-eight other structure types. Each row of the DPMs represents the probability of a facility being in a specified damage state for each specified intensity of ground motion. The damage states are summarized by the Central Damage Factor (CDF). The CDF is the midpoint of the probable damage range represented by each damage state; i.e., for a slight damage state the range of probable damages is from 0% to 1% and the CDF is 0.5% of replacement cost. The columns of the DPMs represent the probability of a facility being in each damage state for a given intensity level. The intensity measure used within the ATC-13 study is the Modified Mercalli Intensity (MMI). The M M I is an intensity scale ranging from one to twelve, usually represented as roman numerals, that is based on observed damage. For detailed review of the Modified Mercalli Intensity scale see Section 2.2.2 of this thesis. Figure 5.1 shows a sample D P M for ATC-13 facility class 1, wood frame (low rise). A brief description of each of the damage states is follows: 1 - None No Damage. 2 - Slight Limited localized minor damage not requiring repair. 3 - Light Significant localized damage of some components generally not requiring repair. 4 - Moderate Significant localized damage of many components warranting repair. 5 - Heavy Extensive damage requiring major repairs. 6 - Major Major widespread damage that may result in facility being razed, demolished or repaired. 7 - Destroyed Total Destruction of the majority of the facility. 34 Chapter 5 Non-Structural Damage Assessment Methodology Central Damage Factor Modified Mercalli Intensity Facility Class= 1 0.00% 0.50% 5.00% 20.00% 45.00% 80.00 100.00 VI 3.7% 68.5% 27.8% vn 26.8% 73.2% VIII 1.6% 94.9% 3.5% IX X XI xn 62.4% 37.6% 11.5% 76.0% 12.5% 1.8% 75.1% 23.1% 24.8% 73.1% 1.7 Figure 5.1: Sample DPM for Facility Class 1 - Wood Frame (Low Rise) 5.2.2 Non-Structural Components and Building Contents Within the scope of the ATC-13 report six Facility Classes were developed that applied to non-structural building components and contents. A l l of the non-structural facility classes represented different types of equipment. The six equipment classes were Facility Class 64 -Residential, Facility Class 65 - Office, Facility Class 66 - Electrical, Facility Class 68 -Mechanical, Facility Class 70 - High Technology and Laboratory, Facility Class 90 - Trains, Trucks, Airplanes, and other Vehicles. Detailed information is required in order to effectively use the information from an analysis using the six ATC-13 equipment facility classes. An office building may contain equipment that is within the scope of two or more of the classes described above, i.e. an office will contain office equipment (Facility Class 65) and electrical equipment (Facility Class 66) and mechanical equipment (Facility Class 68). The possibility of several facility classes being 35 Chapter 5 Non-Structural Damage Assessment Methodology represented within a single building will require detailed inventory information in order to properly apply the correct facility classes to each building as well as requiring an increase in computations for additional facility classes being applied to individual structures. The increase in required information is beyond the scope of many damage studies. 5.3 FEMA-NIBS (HAZUS) The American National Institute of Building Sciences (NIBS), under a cooperative agreement with the Federal Emergency Management Agency (FEMA), undertook the task of developing a "nationally applicable standardized methodology for estimating potential earthquake losses on a regional basis" (NIBS, 1997) in October 1992. It was desired that the methodology developed would be applicable to any part of the United States of America and was intended for use by local, state, and regional officials. In 1997 the methodology was released in the form of a GIS based software package called HAZUS. Included within the scope of the H A Z U S methodology are ground failure hazards, induced damages, social impact, functionality losses (loss of function and restoration time), as well as direct physical damage. Recommended inventory methods are described within the methodology but an important aspect of the H A Z U S package is the ability to perform analyses with varying degrees of detail depending on the completeness of the inventory data. This flexibility allows for a preliminary analysis to be performed without any external data being supplied to the system. 5.3.1 Damage Estimation The damage functions that are used by HAZUS to assess direct physical damage to the general building stock due to earthquakes are in the form of Fragility Curves and the ground 36 Chapter 5 Non-Structural Damage Assessment Methodology motions are described by demand spectra. In order to determine the peak building response building capacity (push over) curves are compared to demand spectra for the specified ground motion. The specified ground motion intensities are derived, from user inputs, by the Potential Earth Science Hazards module. The user must input earthquake intensity that will be the basis for the ground motion, the ground motion attenuation relationships that are to be used, and a soil map that wil l be used to determine local site effects. The user supplied information are then used to define a basis for ground shaking, and then a standard shape of response spectra. Attenuation relations are applied to the identified ground motion to attenuate the motions to the entire study region. The final step is to apply amplifications to the ground motions due to the local site conditions. For each site, the demand spectrum is related to a capacity curve, for the facility type located on the site, and the peak spectral demands are identified. Figure 5.2 shows a sample capacity curve and demand spectrum. The critical spectral values are the locations of intersection 37 Chapter 5 Non-Structural Damage Assessment Methodology between the demand spectra and the capacity curve. The probability of the damage to a 38 Chapter 5 Non-Structural Damage Assessment Methodology 1.0 S l i g h t " — " >» / M o d e r a t e ,- , — - — ~~ / / E x t e n s i v e ^ - . - - - - — !B CO / / C o m p l e t e o Q_ 0) > 0.5 TO E o 0.0 0 1 2 3 4 5 6 7 8 9 10 Spectral Displacement (cm) Figure 5.2: Sample Capacity, Demand, Fragility Curves facility being less than the damage indicated by a damage state is the value of the fragility curve for the damage state at the critical spectral values. The fragility curves, shown in Figure 5.2, are cumulative distribution functions that describe the probability of reaching or exceeding specified damage states given peak building response. The equation that describes the fragility curve for a given damage state is (FEMA, 1997): P[ds\Sd] where: P[ds/Sd] Sd,ds Pds 39 is the probability of damage state ds given the spectral displacement Sj. is the median value of spectral displacement at which the building reaches the threshold damage state is the standard deviation of the natural logarithm of spectral displacement for damage state, ds, Uhapter 5 Non-Structural Damage Assessment Methodology O is the standard normal cumulative distribution function. The difference between the fragility curves for each damage state is the probability of being in the higher damage state for the given spectral value. The expected damage for the facility is calculated from the probability levels given by the fragility curves. The process is repeated for every facility within the study region and the results are aggregated to provide a regional damage assessment. This methodology requires greater computational power than the method outlined in ATC-13. The advantage is that any intensity of ground motion can be specified, not just the discrete values identified by the M M I scale, and the building damage functions are continuous curves not discrete systems. The advantage of a continuous damage function is that the continuous functions can define damages of any level, not just the discrete values identified by a DPM. With the currently available technology fragility curves may not improve the accuracy of a damage assessment but the framework is in place for improved accuracy as researchers develop improved parameters to define the fragility curves. 5.3.2 Non-Structural Components Fragility curve parameters are defined for two different classes of non-structural components within the scope of the FEMA-NIBS methodology. The two classes of non-structural building components are Displacement Sensitive components and Acceleration Sensitive components. Chapter 4 provides a detailed description of the two different classes of non-structural components. The fragility curves parameters, S^ d s and P d s for displacement and acceleration sensitive non-structural components are defined separately for each structural building type. The expected damages are computed separately for displacement sensitive and acceleration 40 Uliapter 5 Non-Structural Damage Assessment Methodology sensitive components. The non-structural damages are converted to dollar values based on typical dollar/sq. ft. values for the individual occupancy classes. The total non-structural damage is the sum of the damage due to the displacement and acceleration sensitive components. This total damage can only be assessed on a dollar value basis, not on a percent replacement cost basis. 5.3.3 Building Contents Building content damage is assumed to be a closely related to the acceleration sensitive non-structural damage by the FEMA-NIBS methodology. This is because content damage, such as overturned cabinets, is assumed to be a function of building acceleration. By accepting this assumption it becomes apparent that i f there is no acceleration sensitive non-structural damage there should be no content damage. When assessing the extent of content damage by the FEMA-NIBS methodology the calculations result in dollar values. The dollar values are based on dollar/sq. ft. values given for each occupancy class. The occupancy classes are used because the value of typical building contents will depend greatly on the occupancy of the building. For example, the value of the contents of a high-tech research facility will be extremely different from that of a low rise apartment and yet they both could be concrete frame low rise buildings. The cost of content damage is calculated by the FEMA-NIBS methodology as (FEMA, 1997): 5 CCD, = CICVr £ CDds>i • RCds>i (5.2) ds = 2 41 Chapter 5 Non-Structural Damage Assessment Methodology 36 RCd,ti = £ PMBRNSAdsJ • FAU • (RCA5ti + RCDs<i + RCMBTSiU) where: CCD^ cost of contents damage for occupancy i , CI regional cost index multiplier, C V i contents value for occupancy i (expressed as percent of replacement value), CDds i percent contents damage for occupancy i in damage state ds, R C d s i replacement costs (dollars) for occupancy i in damage state ds, P M B T N S A d s j the probability of model building types j being in non-structural acceleration sensitive damage state ds, FA; j floor area of model building type j in occupancy group i (in square feet), R C A 5 i acceleration sensitive non-structural repair (per square foot) for occupancy i in damage state 5, R C D 5 j drift sensitive non-structural repair (per square foot) for occupancy i in damage state 5, R C M B T 5 y structural repair cost (per square foot) for model building type j in occupancy i in damage state 5. The value of the percent contents damage, C D d s i 9 at the complete damage state assumes that some salvage of contents will take place. The salvageable value is set at 15% of the total value of the contents. Due to a lack of existing data the percent contents damage, C D d s ^ for each damage state is the same for every occupancy. The values of the variable C D d s for each damage state are shown in Table 5.1. Damage State Percent Contents Damage None 0% Slight 1% Moderate 5% Extensive 25% Complete 50% Table 5.1: Percent Contents Damage for each Damage State 42 Chapter 5 Non-Structural Damage Assessment Methodology Damage States: 1 - None No Damage. 2 - Slight Limited localized minor damage not requiring repair. 3 - LightSignificant localized damage of some components generally not requiring repair. 4 - ModerateSignificant localized damage of many components warranting repair. 6 - MajorMajor widespread damage that may result in facility being razed, demolished or repaired. When developing a locally applicable methodology for assessing the risk due to earthquakes it is important to utilize existing data and local expertise. For the study encompassing southwestern British Columbia, local predictions of probable intensity are measured using the M M I scale. Also, local experts and officials are more familiar with the ATC-13 methodology than with the FEMA-NLBS methodology. Due to these factors it was decided that the damage functions for this study should be in the form of damage probability matrices and shaking intensity would be specified according to the M M I scale. Prior to this study DPMs 5 - Heavy Extensive damage requiring major repairs. 7 - Destroyed Total Destruction of the majority of the facility. 5.4 Proposed Methodology for this Study 43 Ufiapter 5 Non-Structural Damage Assessment Methodology representing non-structural damage had not been developed for southwestern British Columbia. The DPMs developed are based on the non-structural fragility curves used by the FEMA-NIBS methodology. 5.4.1 Damage Estimation Motion-damage relationships for this study are in the form of DPMs. The significant difference between the methods used in this study and the methods outlined by the ATC-13 study is the DPMs. The DPMs for this study were developed for thirty-one building types that represent the local building inventory. The structural DPMs for this study were developed through local expert opinion. For a comparison of the structural DPMs for this study with previously defined methods see the thesis entitled "Evaluation of Structural Earthquake Damage to Buildings in Southwestern B.C." (Blanquera, 1999). As with the ATC-13 methodology the ground motion intensities are represented by the M M I scale. Contour maps of ground motion intensity can be created based on either deterministic or probabilistic earthquake ground shaking. For the purposes of this thesis the ground motions are not modified to consider local site effects. GIS systems have been established as an effective tool to evaluate regional damage due to earthquakes (King et al, 1994, FEMA, 1997). The evaluation of earthquake damages for this study are performed through the use of the Maplnfo (Mapinfo Corporation, 1997) GIS program. The GIS program allows for spacial and tabular data to be jointly manipulated which enables all of the calculations required for the damage assessment to be performed in one platform. As well as performing the necessary calculations for an assessment the GIS can 44 Chapter 5 Non-Structural Damage Assessment Methodology display the results either in a tabular form or a spacial form. It is not necessary to enter the complete DPMs into the GIS system. A value called the Mean Damage Factor (MDF) can be calculated for each intensity level, column, of the DPMs. The MDF represents the mean damage that can be expected to occur when all buildings of a single type are considered. The mean damage factor for a given intensity level is calculated as: M D F , = £ CDFj • P(dSj) (5.3) ; = i where: MDFj mean damage factor for intensity level i , CDFj central damage factor for damage state j P(dsj) probability of the building type being in damage state j When the damage analysis is performed the MDFs for each building type are applied to each structure in the local inventory. 5.4.2 Non-Structural Components and Building Contents Within the scope of this study, damage to displacement sensitive components, acceleration sensitive components, and building contents are considered. For displacement sensitive and acceleration sensitive non-structural systems DPMs are developed based on the fragility curve parameters provided in the HAZUS Technical Manuals (FEMA, 1997). The fragility curves are interrogated at representative spectral demand levels for each M M intensity level and the resulting values are compiled to form non-structural DPMs. Fragility curves are not implicitly defined for building contents by the FEMA-NIBS methodology, but damage to building contents can be directly related to damage to acceleration sensitive components. Typical damage levels are defined, in terms of percent replacement value, for each damage state. The 45 U f i a p t e r ^ Non-Structural Damage Assessment Methodology typical damage values represent CDFs for building contents and thus the acceleration sensitive DPMs can be modified to represent building content damage. For a thorough description of the development of the non-structural DPMs see Chapter 6. 5.5 Summary Several methodologies have been developed for assessing the damage due to earthquakes. The primary differences between the different methodologies available are the form of the motion-damage relationships and the intensity measures. The Applied Technology Council report ATC-13 (ATC, 1985) outlines a methodology developed in 1984 for assessing earthquake damage in California. The methodology used in the ATC-13 represents the motion-damage relations in the form of damage probability matrices and measured the ground motion intensity on the Modified Mercalli Intensity scale. More recently the Federal Emergency Management Association released a methodology for assessing the damage due to earthquakes in the form of a software package called HAZUS (FEMA, 1997). This methodology is applicable to any region within the United States of America. The damage functions are in the form of fragility curves and the ground motion intensities are measured by response spectra. While the continuous fragility curves offer the potential for improved accuracy the curves that are available today do not provide an increase in accuracy over the discrete damage functions available. For this study motion damage relationships are in the form of damage matrices and the Modified Mercalli Intensity scale is used to represent ground motions. These were selected because local expertise was available regarding damage matrices and the M M I scale. Damage relations have been developed for both drift sensitive and acceleration sensitive non-structural 46 L/ l iap ter D Non-Structural Damage Assessment Methodology components as well as building contents. In order to develop the damage matrices the fragility and capacity curve parameters from FEMA-NIBS study were related to local building types. Ground motion spectra were developed by averaging the response spectra that have been recorded during past earthquakes for each intensity level. The damage matrices that were developed are described in the next chapter. 47 C H A P T E R 6 Damage Probability Matrices 6.1 Introduction This chapter describe the method used to develop Damage Probability Matrices (DPMs) for this study. It was decided that the damage functions for this project would be DPMs in order to utilize existing work and local expertise as well as to maintain a consistent approach between the methods used for Structural and Non-Structural damage assessment. As there were no applicable DPMs available for non-structural systems, DPMs were developed for drift sensitive components, acceleration sensitive components, and building contents. Fragility curve and capacity curve parameters from HAZUS were used and associated demand spectra were developed for M M I intensity VI and greater. 6.2 MMI Associated Response Spectra Representative response spectra associated with each M M I level were required in order to utilize the fragility curves defined in the HAZUS (FEMA 1997) program. Correlations of M M I and response spectra have previously been drawn for M M I values of V, VI, and VII (Scholl, 1980). These typical response spectra, shown in Figure 6.1, were used for the calculation of the non-structural DPMs for intensity levels less than VIII. For M M I levels VIII 48 Chapter 6 Damage Probability Matrices and greater it was necessary to develop new correlations. Response spectra data from the National Geophysical Data Centre (1996) for earthquakes prior to 1994 was utilised. One hundred thirty-nine horizontal displacement response spectra were available for M M I VIII and one hundred forty-eight pseudo velocity response spectra, S v, were available for M M I IX. The spectra used were all for earthquake records recorded at ground level and were calculated > M 0 19 0 UJUUL±~J-„J 1 U . U . . I , . , i . . , J — ( 1 1 * , . . » , U „ > „ , 1 , »0 .» 4 . . . . ( . . / * , < % ) . > / 4 0 5 0 * «.« I * P J H I O O - S I C « , » 7.0 ( » . » Figure 6.1: Mean Horizontal Spectra for Modified Merchalli Intensity V, VI, and VII 5% Damping 49 Chapter 6 Damage Probability Matrices with 5% damping. Mean velocity response spectra were calculated assuming a lognormal distribution for each intensity level. This method is consistent with previous studies (Scholl, 1981, Agbabian Associates, 1977). The spectral displacement, S d , and the pseudo absolute acceleration spectra, S a, were then calculated, for each intensity level, as shown in equations Equation (6.1) and Equation (6.2). For M M I levels greater than IX there is insufficient horizontal spectra data available to effectively apply statistical calculations. The difference between the velocity spectra for intensity VII and VIII was used to extrapolate spectral values for the higher intensity levels. The difference between the M M I VII and the M M I VIII spectra was added to the M M I VIII spectra to obtain the M M I IX spectra and the same was repeated for each higher intensity level. The spectra obtained from this procedure, shown in Figure 6.2, are representative response spectra for the M M I levels of interest in this study. 2n-f (6.1) Sa = 27i • / • Sv (6.2) 50 Chapter 6 Damage Probability Matrices MMI XII MMI XI. _ . MMIX_. .. MMI IX. . MMI VIII o TO s CD O O < 1.0 0.9 0.8 0.7 0.6 0.5 0.4 o 0.3 CD Q . CO 0.2 0.1 0.0 1 » 1 1 1 ". 1 1 V MMI VII MMI IX 1 1 . 1 1 • 1 1 l« 1 \ ""\ \ \ IVMVM s\ MMI XI i '. ! i MMI XII * i •. i \ \ ^ \ ~~* - r . r i - : - • 10 20 30 Spectral Displacement (cm) 40 50 Figure 6.2: Typical Spectra for M M Intensity VII and Greater 6.3 Capacity and Fragility Curves Buildings capacity curves (or push-over curves) are essentially force-displacement curves calculated for an entire building. A building's lateral load resistance is plotted as a function of its characteristic lateral displacement. To facilitate the necessary comparison with earthquake demand spectra the force axis is converted to the equivalent spectral accelerations and the 51 Chapter 6 Damage Probability Matrices displacement axis is converted to spectral displacement. The building capacity curves used for this study were developed for the FEMA-NIBS methodology, and are based on engineering design parameters and judgment. The building capacity curves applied by this methodology are identified by two control points which define critical points on each capacity curve. The two control points are: • Yield Capacity • Ultimate Capacity These points represent critical locations on the capacity curve. The 1994 NEHRP Provisions were used as the model code for the calculation of the design capacity. The true lateral strength of the building, considering redundancies and true material strengths, is represented by the yield capacity. From the zero load point through to the yield point the capacity curve is assumed to be linear with stiffness based on the true period of the building. Between the yield capacity and the ultimate capacity the capacity curve undergoes a transition from a purely elastic state to a fully plastic state. The ultimate capacity represents the plastic limit of force that can be resisted by the structure. The HAZUS Technical Manual Volume I (FEMA 1997) provides a more detailed review of capacity curves and the parameters used to describe the curves. Fragility curves for each damage state are modeled as a cumulative lognormal distribution functions. In order to define the fragility curves two parameters are required. The two parameters are: • Median, • Beta. 52 Chapter 6 Damage Probability Matrices The Median is the median value of spectral displacement (or acceleration) at which the building reaches the threshold of the damage state. The Beta is the standard deviation of the natural logarithm of spectral displacement (or acceleration) of the damage state. The two parameters are applied to Equation (5.1) which represents the fragility curves. Fragility curves for slight, moderate, extensive and complete non-structural damage states are defined for each building type. Capacity curve and fragility curve parameters are available for four different code design levels: • High-Code, • Moderate-Code • Low-Code • Pre-Code South-Western British Columbia typically falls within the moderate-code seismic design level according to the 1994 NEHRP Provisions. As a result the moderate-code parameters were used to define the capacity and fragility curves with three exceptions. The three exceptions are Reinforced Concrete Frames with Infill Walls (RCFIW), and Unreinforced Masonry buildings both Low Rise and Medium Rise (URMLR, URMMR) . For these three cases the low-code parameters were used because these building types are not allowed to be constructed in areas of moderate seismicity under current codes. Although these building types can no longer be built in zones on moderate seismicity they were not prohibited until after 1973. In a study region there can be many buildings that were built prior to the introduction of the 1973 seismic codes and as such will be best described by these Low code categories. The capacity curve parameters used for building types present in the southwestern British Columbia 53 Chapter 6 Damage Probability Matrices inventory are shown in Tables 6.1 and parameters used to define the displacement sensitive and acceleration sensitive fragility curve parameters are shown in Tables 6.2 and Tables 6.3 respectively. 54 Chapter 6 Damage Probability Matrices Table 6.1: Moderate-Code Seismic Design Level - Capacity Curve Parameters Building Type SWBC Study Building Type FEMA-NIBS Yield Capacity Point Ultimate Capacity Point D y (cm) A y ( g ) D u (cm) A u ( g ) WLFR W1 0.91 0.300 16.46 0.900 WLFCI W2 0.79 0.200 11.94 0.500 WLFLR W1 0.91 0.300 16.46 0.900 WPB W1 0.91 0.300 16.46 0.900 LMF S3 0.79 0.200 9.55 0.400 SMFLR S1L 0.79 0.200 13.97 0.375 SMFMR S1M 2.26 0.078 27.05 0.234 SMFHR S1H 5.92 0.049 53.24 0.147 SBFLR S2L 0.79 0.200 9.55 0.400 | SBFMR S2M 3.07 0.167 24.64 .0333 SBFHR S2H 9.83 0.127 59.03 0.254 SFCWLR S4L 0.48 0.160 6.58 0.360 SFCWMR S4M 1.40 0.133 12.47 0.300 SFCWHR S4H 4.42 0.102 29.87 0.228 SFCI S4L 0.48 0.160 6.58 0.360 SFMI S4L 0.48 0.160 6.58 0.360 CFLR C2L 0.61 0.200 9.14 0.500 CFMR C2M 1.32 0.167 13.19 0.417 CFHR C2H 3.73 0.127 27.99 0.317 RCMFLR C1L 0.51 0.125 8.94 0.375 RCMFMR C1M 1.47 0.104 17.55 0.312 RCMFHR C1H 2.57 0.049 22.99 0.147 RCFIW* C3L 0.30 0.100 3.43 0.225 RMLR RM1L 0.81 0.267 9.75 0.533 RMMR RM1M 1.75 0.222 14.07 0.444 URMLR * URML 0.61 0.200 6.10 0.400 URMMR * URMM 0.69 0.111 4.60 0.222 TU PC1 0.91 0.300 10.97 0.600 PCLR PC2L 0.61 0.200 7.32 0.400 PCMR PC2M 1.32 0.167 10.54 0.333 MH MH 0.46 0.150 5.49 0.300 *. Low-Code Seismic Design Level Parameters 55 Chapter 6 Damage Probability Matrices Table 6.2: Drift Sensitive Fragility Curve Parameters - Moderate-Code Seismic Design Level Building Building Median Spectral Displacement (cm) and Logstandard Deviation (Beta) Type Type Slight Moderate Extensive Complete SWBC Study FEMA-NIBS Median Beta Median Beta Median Beta Median Beta WLFR W1 1.27 2.26 2.57 2.31 8.00 22.86 16.00 2.64 WLFCI W2 2.26 2.39 4.39 2.51 13.72 2.54 27.43 2.29 WLFLR W1 1.27 2.26 2.57 2.31 8.00 22.86 16.00 2.64 WPB W1 1.27 2.26 2.57 2.31 8.00 22.86 16.00 2.64 LMF S3 1.37 2.36 2.74 2.49 8.59 2.57 17.15 2.39 SMFLR S1L 2.18 2.13 4.39 2.11 13.72 2.01 27.43 2.21 SMFMR S1M 5.49 1.80 10.97 1.88 34.29 2.16 68.58 2.41 SMFHR S1H 11.40 1.80 22.83 1.88 71.32 2.13 142.65 2.41 SBFLR S2L 2.18 2.36 4.39 2.11 13.72 2.01 27.43 2.21 SBFMR S2M 5.49 1.88 10.97 1.88 34.29 2.16 68.58 2.44 SBFHR S2H 11.40 1.83 22.83 1.85 71.32 2.03 142.65 2.39 SFCWLR S4L 2.18 2;54 4.39 2.69 13.72 2.51 27.43 2.44 SFCWMR S4M 5.49 1.96 10.97 2.03 34.29 2.41 68.58 2.64 SFCWHR S4H 11.40 1.85 22.83 2.08 71.32 2.36 142.65 2.57 SFCI S4L 2.18 2.54 4.39 2.69 13.72 2.51 27.43 2.44 SFMI S4L 2.18 2.54 4.39 2.69 13.72 2.51 27.43 2.44 CFLR C2L 1.83 2.44 3.66 2.54 11.43 2.69 22.86 2.41 CFMR C2M 4.57 2.13 9.14 2.06 28.58 2.11 57.15 2.49 CFHR C2H 8.79 1.85 17.55 1.93 54.86 2.26 109.73 2.51 RCMFLR C1L 1.83 2.36 3.66 2.44 11.43 2.39 22.86 2.24 RCMFMR C1M 4.57 1.96 9.14 1.93 28.58 2.21 57.15 2.49 RCMFHR C1H 8.79 1.88 17.55 2.03 54.86 2.39 109.73 2.62 RCFIW* C3L 1.83 2.87 3.66 2.74 11.43 2.41 22.86 2.54 RMLR RM1L 1.83 2.54 3.66 2.69 11.43 2.84 22.86 2.57 RMMR RM1M 4.57 2.24 9.14 2.16 28.58 2.13 57.15 2.49 URMLR * URML 1.37 2.72 2.74 2.87 8.59 2.95 17.15 2.57 URMMR * URMM 3.20 2.46 6.40 2.31 20.02 2.49 40.01 2.64 TU PC1 1.37 2.39 2.74 2.51 8.59 2.67 17.15 2.74 PCLR PC2L 1.83 2.54 3.66 2.69 11.43 2.72 22.86 2.36 PCMR PC2M 4.57 2.16 9.14 2.11 28.58 2.34 57.15 2.54 MH MH 1.22 2.44 2.44 2.67 7.62 2.72 15.24 2.36 *. Low-Code Seismic Design Level Parameters 56 Chapter 6 Damage Probability Matrices Table 6.3: Acceleration Sensitive Fragility Curve Parameters - Moderate-Code Seismic Design Level Building Building Median Spectral Acceleration (cm 2) and Logstandard Deviation (Beta) Type Type Slight Moderate Extensive Complete SWBC Study FEMA-NIBS Median Beta Median Beta Median Beta Median Beta WLFR W1 0.25 0.73 0.50 0.68 1.00 0.67 2.00 0.64 WLFCI W2 0.25 0.68 0.50 0.67 1.00 0.68 2.00 0.68 WLFLR W1 0.25 0.73 0.50 0.68 1.00 0.67 2.00 0.64 WPB W1 0.25 0.73 0.50 0.68 1.00 0.67 2.00 0.64 LMF S3 0.25 0.67 0.50 0.66 1.00 0.65 2.00 0.65 SMFLR S1L 0.25 0.67 0.50 0.66 1.00 0.67 2.00 0.67 SMFMR S1M 0.25 0.66 0.50 0.67 1.00 0.67 2.00 0.67 SMFHR S1H 0.25 0.66 0.50 0.68 1.00 0.68 2.00 0.68 SBFLR S2L 0.25 0.66 0.50 0.66 1.00 0.68 2.00 0.68 SBFMR S2M 0.25 0.66 0.50 0.65 1.00 0.65 2.00 0.65 SBFHR S2H 0.25 0.65 0.50 0.65 1.00 0.65 2.00 0.65 SFCWLR S4L 0.25 0.66 0.50 0.66 1.00 0.66 2.00 0.66 SFCWMR S4M 0.25 0.65 0.50 0.65 1.00 0.65 2.00 0.65 SFCWHR S4H 0.25 0.65 0.50 0.66 1.00 0.66 2.00 0.66 SFCI S4L 0.25 0.66 0.50 0.66 1.00 0.66 2.00 0.66 SFMI S4L 0.25 0.66 0.50 0.66 1.00 0.66 2.00 0.66 CFLR C2L 0.25 0.68 0.50 0.66 1.00 0.68 2.00 0.68 CFMR C2M 0.25 0.67 0.50 0.64 1.00 0.67 2.00 0.67 CFHR C2H 0.25 0.66 0.50 0.65 1.00 0.65 2.00 0.65 RCMFLR C1L 0.25 0.67 0.50 0.66 1.00 0.66 2.00 0.66 RCMFMR C1M 0.25 0.66 0.50 0.65 1.00 0.63 2.00 0.63 RCMFHR C1H 0.25 0.65 0.50 0.67 1.00 0.67 2.00 0.67 RCFIW* C3L 0.20 0.65 0.40 0.67 0.80 0.66 1.60 0.66 RMLR RM1L 0.25 0.68 0.50 0.67 1.00 0.67 2.00 0.67 RMMR RM1M 0.25 0.67 0.50 0.64 1.00 0.67 2.00 0.67 URMLR * URML 0.20 0.68 0.40 0.65 0.80 0.65 1.60 0.65 URMMR * URMM 0.20 0.64 0.40 0.66 0:80 0.66 1.60 0.66 TU PC1 0.25 0.68 0.50 0.67 1.00 0.66 2.00 0.66 PCLR PC2L 0.25 0.66 0.50 0.66 1.00 0.65 2.00 0.65 PCMR PC2M 0.25 0.65 0.50 0.65 1.00 0.65 2.00 0.65 MH MH 0.25 0.65 0.50 0.67 1.00 0.67 2.00 0.67 *. Low-Code Seismic Design Level Parameters 57 Chapter 6 Damage Probability Matrices 6.4 Damage States The FEMA-NIBS methodology describes four damage states for non-structural components. The damage states are Slight, Moderate, Extensive, and Complete. These damage states will be used for this study. General damage state descriptions are defined for typical non-structural components, not for individual building types. Building type specific damage state descriptions are not meaningful because non-structural damage is independent of the structural model (i.e. non-structural damages depend on interstory drift and floor accelerations not on whether the structure is a wood frame building or a steel frame building). Typical descriptions of the damage states for a drift sensitive component (partition wall) and an acceleration sensitive component (Electrical-Mechanical Equipment, Piping, Ducts) are shown below (from the HAZUS Technical Manual I (FEMA, 1997)): Partition Walls Slight Non-structural Damage: A few cracks are observed at intersections of walls and ceilings and at corners of door openings. Moderate Nonstructural Damage: Larger and more extensive cracks requiring repair and repainting; some partitions may require replacement of gypsum board or other finishes. Extensive Non-structural Damage: Most of the partitions are cracked and a significant portion may require replacement of finishes; some door frames in the partitions are also damaged and require re-setting. Complete Nonstructural Damage: Most partition finish materials and framing may have to be removed and replaced; damaged studs repaired, and walls be refinished. Most door frames may also have to be repaired and replaced. Electrical-Mechanical Equipment, Piping, Ducts Slight Non-structural Damage: The most vulnerable equipment (e.g. unanchored or on spring isolators) moves and damages attached piping or ducts. Moderate Non-structural Damage: Movements are larger and damage is 58 Chapter 6 Damage Probability Matrices more extensive; piping leaks at few locations; elevator machinery and rails may require realignment. Extensive Non-structural Damage: Equipment on spring isolators topples and falls; other unanchored equipment slides or falls breaking connections to piping and ducts; leaks develop at many locations; anchored equipment indicate stretched bolts or strain at anchorage. Complete Non-structural Damage: Equipment is damaged by sliding, overturning or failure of their supports and is not operable; piping is leaking at many locations; some pipe and duct supports have failed causing pipes and ducts to fall or hang down; elevator rails are buckled or have broken supports and/or counterweights have derailed. 6.5 Damage Probability Matrices Through the application of the information above it is possible to develop non-structural DPMs for each building type. Developing the non-structural DPMs for a given building type is a five step process. The steps are: 1.overlay the capacity curve for the desired building type with the set of demand spectra representing each M M I level, 2. find the values of S d and S a at the intersections of the capacity curve with the demand spectra, 3. for each intensity level i , calculate the values of the fragility curves at the spectral demand (S d for drift sensitive components, S a for acceleration sensitive components and building contents) for intensity i , P [ d s > d S j ] = P[ds\Sd] = O d,ds (6.3) 4.calculate the probability of being in damage state, dsj, for each damage state j and for each intensity level i , MML;, P[dsj\MMIi]= P[ds < dsj]-P[ds < d s j ^ ] (6.4) 5.compile the probability levels given in step 4 into the non-structural DPMs. 59 Chapter 6 Damage Probability Matrices The result from this process is three DPMs that can be used to assess the extent of probable damage to the non-structural inventory. It is important to note that the same parameters and curves are used for the DPMs for acceleration sensitive components as are used for the DPMs for building contents. The result of this is that the probability of being in a given damage state for a given ground motion intensity will be the same for both acceleration sensitive components and building contents. There is an important difference between the DPMs for the two classes. The difference is the value of the CDF. The HAZUS software package defines the damage states for acceleration sensitive components and thus the CDFs for each damage state. When considering building contents, by the FEMA-NH3S methodology, the damage is related to the acceleration sensitive damage but the definitions of the acceleration sensitive damage states do not apply. The damage states for building contents are related to occupancy class, but due to a lack of data with which to correlate damage to each occupancy the CDFs given are the same for every occupancy. Thus the DPMs for acceleration sensitive and building contents have the same probability of reaching a given damage state but different CDFs for each damage state. The CDFs for drift-sensitive components, acceleration sensitive components, and building contents are shown in Tables 6.4. Table 6.4: Central Damage Factors by Damage Type Damage Central Damage Factors State Drift-Sensitive Accelerat ion Sensit ive Building Contents None 0% 0% 0% Slight 2 % 2 % 1 % Moderate 10% 10% 5% Extensive 5 0 % 5 0 % 2 5 % Comple te 8 0 % 8 0 % 4 0 % 60 Chapter 6 Damage Probability Matrices Shown below in Figure 6.3 to Figure 6.33 are plots of the M D F for each building type and damage category versus ground motion intensity. It can be seen from the plots that the displacement sensitive MDFs correspond well with what can be expected for each intensity level. At the lower M M I levels the damages are in the 10% - 20% range and as the intensity increases the M D F increases to the 40% - 50% range. These values are consistent with the description given for each M M I level. When the acceleration sensitive MDFs are considered it is seen that the values do not correspond as well with the descriptions for M M I . When acceleration sensitive components are considered it is expected that the direct cost of damages will not be as great as for displacement sensitive components. Damage to acceleration sensitive components is predominantly due to sliding or tipping of the objects. After an earthquake a significant portion of the acceleration sensitive components do not have to be replaced but can be reused with some minor repairs. The major impact of the dislocation of acceleration sensitive components is to loss of function time. This trend for the direct costs of damages being less for acceleration sensitive components does not justify the extent of differences between the values shown in the figures below. The cause of this discrepancy can be found by reviewing the parameters describing the capacity curves and the fragility curves, from HAZUS. For example consider the parameters for the structure type Concrete Frame High-Rise (CFHR). The ultimate capacity point is given as Au=0.317g and the median spectral acceleration describing the CFHR fragility curve is 2g with a logstandard deviation of 0.65. This indicates that when the capacity curve for a CFHR building is interrogated with respect to the demand spectra the maximum possible acceleration at the working point is 0:317g. When this value is 61 Chapter 6 Damage Probability Matrices compared with the median value of spectral acceleration for the extensive damage state the peak spectral acceleration is over to standard deviation removed from the mean. By applying these values the probability of being in an extensive damage state is very small, even given the maximum spectral acceleration that will can attained at a working point by the structure. Although the values for acceleration sensitive components seem to be unrealistic they will be used for the purposes of this thesis. The non-structural DPMs that were developed and are used in this study are presented Appendix C in Tables C.2 to Tables C.31. Mean Damage Factor vs MMI ( 5 s 60 50 o o ro LL <u TO E CO Q c co 0 ) ~ 40 30 20 10 Displacement Sensitive Acceleration Sensitive Building Contents VI Vll VIII IX MMI Intensity XI XII Figure 6.3: Mean Damage Factors for Wood Light Frame Residential 62 Chapter 6 Damage Probability Matrices Mean Damage Factor vs MMI 60 „ 50 o 4 0 co LL CD D ) CD 3 0 £ CO Q co 2 0 CD 10 . • • ' J . . - - -VI VII VIII IX XI MMI Intensity 60 5 0 4 0 3 0 2 0 1 0 XII Figure 6.4: Mean Damage Factors for Wood Light Frame Commercial/Institutional Mean Damage Factor vs MMI 6 0 — 5 0 o CD LL 0) D ) CO E CD Q sz CD CD 2 4 0 3 0 2 0 1 0 VI VII VIII IX X MMI Intensity Displacement Sensitive • — • — • Building Contents . . . • _ • XI 6 0 5 0 4 0 3 0 2 0 1 0 XII Figure 6.5: Mean Damage Factors for Wood Light Frame Low Rise 63 Chapter 6 Damage Probability Matrices Mean Damage Factor vs MMI o CD U_ CD D ) CO E CO Q c CO CD 60 50 40 30 20 10 VI Displacement Sensitive _ . . • • • A 50 60 40 30 20 10 Vll VIII IX XI XII MMI Intensity Figure 6.6: Mean Damage Factors for Wood Post and Beam Mean Damage Factor vs MMI 60 50 o CO o 40 Displacement Sensitive Acceleration Sensitive Building Contents VI Vll VIII IX MMI Intensity XI XII Figure 6.7: Mean Damage Factors for Light Metal Frame 64 Chapter 6 Damage Probability Matrices Mean Damage Factor vs MMI 60 50 o 40 o 30 co u. CD O ) CO E CO Q CD 10 Displacement Sensitive d 50 60 40 30 20 10 VI Vll VIII IX XI XII MMI Intensity Figure 6.8: Mean Damage Factors for Steel Moment Frame Low Rise Mean Damage Factor vs MMI 60 50 o 40 o CO L L CD g> 30 E co Q 20 10 VI k i l • I I I 1 T 1 " d 50 60 40 30 20 10 Vll VIII IX MMI Intensity XI XII Figure 6.9: Mean Damage Factors for Steel Moment Frame Medium Rise 65 Chapter 6 Damage Probability Matrices Mean Damage Factor vs MMI 60 50 ° 40 o to LL <D CD CO E CO Q c: CO CD 30 20 10 VI VII VIII IX X MMI Intensity xi Displacement Sensitive 60 d 50 40 30 20 10 XII Figure 6.10: Mean Damage Factors for Steel Moment Frame High Rise Mean Damage Factor vs MMI 60 50 ° 40 o CO LL CD CD CO E CO Q c CO CD 30 20 10 VI VII VIII IX X MMI Intensity XI d 50 60 40 30 20 10 XII Figure 6.11: Mean Damage Factors for Steel Braced Frame Low Rise 66 Chapter 6 Damage Probability Matrices Mean Damage Factor vs MMI 60 50 2 40 o CO CD O ) CO E CO Q c CO CD 30 20 10 VI Displacement Sensitive 60 d 50 40 30 20 10 Vll VIII IX MMI Intensity XI xii Figure 6.12: Mean Damage Factors for Steel Braced Frame Medium Rise Mean Damage Factor vs MMI 60 50 o 40 o CO LL CD c? 30 E co Q ra 2 0 CD 10 VI Vll Building Contents d 50 60 40 30 20 10 VIII IX MMI Intensity XI xii Figure 6.13: Mean Damage Factors for Steel Braced Frame High Rise 67 Chapter 6 Damage Probability Matrices Mean Damage Factor vs MMI 60 50 ° 40 o CD L L CD O ) CD E CO Q o5 20 CD 30 10 | Displacement Sensitive d 50 60 40 30 20 10 VI VII VIII IX MMI Intensity XI XII Figure 6.14: Mean Damage Factors for Steel Frame Concrete Walls Low Rise Mean Damage Factor vs MMI 60 50 o 40 o CO CD O ) CD E CD Q c CD CD 30 20 10 Displacement Sensitive Building Contents d 50 60 40 30 20 10 VI VII VIII IX MMI Intensity XI XII Figure 6.15: Mean Damage Factors for Steel Frame Concrete Walls Medium Rise 68 Chapter 6 Damage Probability Matrices 60 50 ° 40 o CO CD O) CO E CO Q c CO CD 30 20 10 VI Mean Damage Factor vs MMI VII Displacement Sensitive Building Contents 60 50 40 30 20 10 VIII IX MMI Intensity XI xii Figure 6.16: Mean Damage Factors for Steel Frame Concrete "Walls High Rise Mean Damage Factor vs MMI 60 50 o 40 o CO CD O ) CO E CO Q c CO CD 30 VI 60 Displacement Sensitive Acceleration Sensitive Building Contents -d 50 40 30 20 10 Vll VIII IX X MMI Intensity XI XII Figure 6.17: Mean Damage Factors for Steel Frame Concrete Infill 69 Chapter 6 Damage Probability Matrices Mean Damage Factor vs MMI 60 50 o 40 o ro LL <u O) ro E TO Q c CO CD 30 20 10 Displacement Sensitive _ 1 . ' -VI VII VIII IX MMI Intensity XI XII Figure 6.18: Mean Damage Factors for Steel Frame Masonry Infill 60 50 2 40 o CO CD D) CO E CO Q c CO CD 30 20 10 VI Mean Damage Factor vs MMI Acceleration Sensitive Building Contents VII VIII IX XI MMI Intensity XII Figure 6.19: Mean Damage Factors for Concrete Frame Low Rise 70 Chapter 6 Damage Probability Matrices 60 50 o 40 o CD CD G) CD E CD Q d CD CD 30 20 VI Mean Damage Factor vs MMI Displacement Sensitive Acceleration Sensitive Building Contents 60 50 40 30 20 10 Vll VIII IX X MMI Intensity XI XII Figure 6.20: Mean Damage Factors for Concrete Frame Medium Rise Mean Damage Factor vs MMI 60 50 ° 40 o CO LL CD c? 30 E co Q 20 VI Displacement Sensitive Acceleration Sensitive Building Contents •-• '-' ^ ' d 50 60 40 30 10 Vll VIII IX X MMI Intensity XI XII Figure 6.21: Mean Damage Factors for Concrete Frame High Rise 71 Chapter 6 Damage Probability Matrices 60 50 2 40 o CD L L CD g> 30 E co Q CO CD 20 10 VI Mean Damage Factor vs MMI Displacement Sensitive =J 50 60 40 30 20 10 VII VIII IX XI XII MMI Intensity Figure 6.22: Mean Damage Factors for Reinforced Concrete Moment Frame Low Rise 60 50 2 40 o CD L L CD O ) CD E CD Q c CD CD 30 20 10 VI Mean Damage Factor vs MMI Acceleration Sensitive Building Contents 60 50 40 30 20 10 VII VIII IX X MMI Intensity XI XII Figure 6.23: Mean Damage Factors for Reinforced Concrete Moment Frame Medium Rise 72 Chapter 6 Damage Probability Matrices Mean Damage Factor vs MMI Displacement Sensitive Acceleration Sensitive ^ . - - i . • I VI Vll VIII IX MMI Intensity XI XII Figure 6.24: Mean Damage Factors for Reinforced Concrete Moment Frame High Rise 60 50 o 40 o CD L L CD g> 30 E CD Q c CD CD 20 10 Mean Damage Factor vs MMI Displacement Sensitive Acceleration Sensitive Building Contents 60 50 40 30 20 10 VI Vll VIII IX MMI Intensity XI XII Figure 6.25: Mean Damage Factors for Reinforced Concrete Reinforced Infill Wall 73 Chapter 6 Damage Probability Matrices Mean Damage Factor vs MMI 60 50 o 40 o 0> C D CD E CO Q c CO CU 30 20 10 Displacement Sensitive Acceleration Sensitive Building Contents 60 50 40 30 20 10 VI VII VIII IX X MMI Intensity XI XII Figure 6.26: Mean Damage Factors for Reinforced Masonry Low Rise Mean Damage Factor vs MMI 60 50 ° 40 o a> C D co E co a c CO CD 30 20 10 Acceleration Sensitive Building Contents /_ 60 4 50 40 30 20 10 VI VII VIII IX XI XII MMI Intensity Figure 6.27: Mean Damage Factors for Reinforced Masonry Medium Rise 74 Chapter 6 Damage Probability Matrices Mean Damage Factor vs MMI 60 50 10 Displacement Sensitive Acceleration Sensitive Building Contents d 50 60 30 20 10 VI Vll VIII IX X MMI Intensity XI XII Figure 6.28: Mean Damage Factors for Unreinforced Masonry Low Rise 60 50 o 40 o CO LL CD CD CO E CO Q c CO CD 30 20 VI Mean Damage Factor vs MMI Displacement Sensitive Acceleration Sensitive Building Contents Vll VIII IX X MMI Intensity XI XII Figure 6.29: Mean Damage Factors for Unreinforced Masonry Medium Rise 75 Chapter 6 Damage Probability Matrices Mean Damage Factor vs MMI 60 50 S 40 o CO LL CD CD CO E CO Q c CO CD 30 20 10 Displacement Sensitive VI VII VIII IX XI XII MMI Intensity Figure 6.30: Mean Damage Factors for Tilt Up 60 50 o 40 o CO CD CD CO E CO Q c CO CD 30 20 10 VI Mean Damage Factor vs MMI Building Contents •-VII VIII IX XI MMI Intensity XII Figure 6.31: Mean Damage Factors for Precast Low Rise 76 Chapter 6 Damage Probability Matrices Mean Damage Factor vs MMI 60 50 o CO LL CU CO CO E CO Q c CO CU ° 40 30 20 VI ' — - * • Displacement Sensitive Acceleration Sensitive Building Contents VII VIII IX XI XII MMI Intensity Figure 6.32: Mean Damage Factors for Precast Medium Rise 77 Chapter 6 Damage Probability Matrices 6.6 Summary The development of damage probability matrices for non-structural components and building contents was a major step in this study. It was beyond the scope of this study to develop entirely new DPMs or fragility curve parameters for the local building types. By utilizing the capacity and fragility curve parameters developed for building types in the United States of America and relating them to the Canadian building types that are used in this study it was possible to develop DPMs. In order to do this demand spectra were calculated by averaging 5% response spectra from many earthquakes of varying M M I . These spectra were related to the capacity curves for each building type and the spectral demands were found for each building class. The spectral demands were used to interrogate the fragility curves for each damage state and for each building type. The results are three DPMs for each building type, displacement sensitive, acceleration sensitive, and building contents. The DPMs for displacement sensitive components appear to be as expected. The DPMs for acceleration sensitive components and building contents seem to be lower than expected. These DPMs can be used to calculate the expected damages to any region in South-Western British Columbia. A case study applying the DPMs developed here is presented in the next chapter. 78 C H A P T E R 7 Case Study: City of New Westminster 7.1 Introduction Overlooking the Fraser River, the City of New Westminster, shown in Figure 7.1, has an area of approximately 15 square kilometers that contains approximately 8000 buildings and is home to 49,350 people (1996 statistics). Due to several factors the City of New Westminster was selected as the location for a case study to be performed. It is a very diverse community, both socially and geographically with a large range building types and a variety of building ages, from the late 1800s to modem construction. New Westminster is very suitable as case study location because it has a good variety of building types and occupancies. There is an extensive commercial district along Columbia St. which contains a varied cross section of modern concrete and wood commercial buildings along with many older unreinforced masonry buildings. The Sixth St. corridor is comprised of many medium and high-rise retail and office facilities. Along the Fraser River there are industrial sectors that are comprised of many steel frames was well as concrete and wood buildings. The remainder of the community is mostly residential buildings, including single family homes, wood frame apartments and high rise condos. 79 Chapter 7 Case Study: City of New Westminster The geophysical diversity is another asset of the City of New Westminster when considering it as a case study region. Although not considered in this portion of the study, the effects of soil types and ground slopes are important when considering the effects of earthquakes on a region. An important expansion of this study will be to include the effects of soil types and landslide on the region. The city is situated along the Fraser River and as a result many of the building sites are located on river sediments with the potential for liquefaction. Away from the river the soil conditions vary from silts to clays to firm soils and rock. As well as a variety of soil types New Westminster also contains many areas with steep slopes that may have a potential for landslides. As additional effects are included within the scope of this study the City of New Westminster will remain an effective area on which to evaluate the proposed methodologies. 80 Chapter 7 Case Study: City of New Westminster Figure 7.1: Map of New Westminster 7.2 Building Inventory The inventory process was completed very efficiently due to the cooperation of the City of New Westminster's Emergency Preparedness and Planning Departments. The Emergency Preparedness group arranged for the planning department to provided their database of building information. This database included basic building information including roll number, address, census tract, building footprint, number of floors, building age and structure type as well as many other fields that were not required for the purposes of this study. This database became the starting point for the building inventory that was completed for the City of New Westminster. 81 Chapter 7 Case Study: City of New Westminster In order for the inventory to be completed three groups of information are required. The first type of information required is the geographic location of the building. The second type of information that is required are structural properties of the building. The last area of information needed is a description of the occupancy of the building. Some of this information was included in the planning department database. The missing information had to be completed by the application of inference schemes and field surveys. Information describing the geographic location each building site was available in several forms from the original New Westminster database. Included in the database were the site roll number, block number, census tract, neighborhood, and street address. The three digit postal code was added to the database based on the site address. Any of the aforementioned fields would be acceptable to locate the data within the GIS system. The block number, a identifier used by the New Westminster planning department was selected for several reasons. The block number will locate the site with a fair degree of accuracy and is also the highest resolution that will be used for presentation of results. If a larger identifier were used to locate the building, such as three digit postal code, results could not be presented to a higher resolution than the three digit postal code. By geocoding the data to the block scale all of the fields that identify regions can be subsequently used to present results. It is not desirable to present the results on a building by building basis because the methods use by this study are not accurate to that level of detail. The results of an analysis are regionally based and to not accurately represent individual buildings. It is also important not to identify individual buildings within a regional study without a performing a detailed analysis of each building. Some of the structural properties required for each building were included within the New 82 Chapter 7 Case Study: City of New Westminster Westminster database. These properties included footprint, total number of floors, floors above ground, and building age. Also included within the original database was a field named structure type. This field described the structural system each building but not in terms of the building types that are used in this study. In order to classify each building by the building types used in this study inferences were developed that would assist in identifying the structural type of each building. The inferences made are described below: Structure Types Concrete... A l l Concrete structure types, i f > 9 floors CFHR if < 9; > 4 floors C F M R if< 5 floors CFLR. Concrete Block.. . A l l Concrete Block structure types, i f newer than 1973 R M L R or R M M R dependent on height i f older than 1973 U R M L R or U R M M R dependent on height. Brick. . . A l l brick structure types U R M L R or U R M H R dependent on height. Metal . . . Metal structure types, SBFLR, SBFMR, SBFHR dependent on # of floor. Most metal structures were in commercial and industrial areas and were field checked. Tall metal buildings, > 9 floors, the drawings on file at N W City Hall were checked. Heavy Timber... A l l heavy timber structure types, WPB prototype. Laminated... A l l Laminated structure types, N W City Hall files were checked for structural drawings to pick prototype. 83 Chapter 7 Case Study: City of New Westminster Frame... Frame structure types > 5 floors, either spot checked or drawings were checked from NW City Hall files, Frame structure types < 5 floors, Building Names were checked: any apartment, court, or manor building names were assumed to be W L F L R ; any church names or other obvious commercial names were assumed to be WLFCI. Building sizes were checked: any building less than 1500 sq. ft. was assumed to be WLFR; any building greater that 1500 sq. ft. were assumed to be W L F L R ; most commercial areas and industrial areas were then spot checked to locate WLFCI buildings. The last area of information required for the study is the occupancy of the buildings. As with the building type the occupancy class for each site was not included in the original New Westminster database. It was necessary to apply inference schemes to the database in order to assume the occupancy of the buildings. The inferences that were used are listed below. Primary Use If Structure type = WLFCI primary use 1 = Commercial If Structure type = WLFR; W L F L R primary use 1 = Residential, PU2 = Permanent Dwellings, PU3 = Homes and Apartments respectively. Building Names were used to develop some Primary Uses, i.e. any churches, apartments, or named garages could be identified i f the building name included this information. The inference described above were not sufficient to complete every building in the database, therefore many building sites had to be field checked in order to identify the occupancy. Through the use of inference schemes 8,113 individual buildings were identified and 84 Chapter 7 Case Study: City of New Westminster classified. Although most necessary fields in the database were completed at this point it was important to perform field checks to verify the inferences used to complete the database. The city zoning map was used as a guide to target commercial and industrial areas for field verification. Large buildings, higher than 5 floors, and buildings with missing information were also targeted for field verification. In total 1030 buildings were checked during the field review. Once field verification of the inference process was completed the inventory was also complete. Table 7.1 is a sample of the attributes that are identified in the New Westminster building inventory database, the Street Number and Roll Number are not given in an attempt to avoid identifying specific buildings. Figure 7.2 shows a map indicating the prevalent material type present in each block and Figure 7.3 shows a map indicating the prevalent building type in each block. It can be seen from Figure 7.2 and Figure 7.3 that the dominant construction type in the study region is wood residential buildings. It is also apparent that there is a variety of construction types along the Fraser River and in the primary commercial areas of Columbia Avenue and Sixth Street. 85 Chapter 7 Case Study: City of New Westminster Field Entry ID 7148 ROLL NUMBER XXXXXXXX BLOCK U-038 CENSUS 933205 NEIGHBORHOOD C STREET NUMBER XXXX STREET NAME Eighth Avenue POSTAL CODE V3M FOOTPRINT 2991 NUMBER OF FLOORS 1 NUMBER OF FLOORS ABOVE GROUND 1 BUILDING AGE 1968 HERITAGE N STRUCTURE TYPE Concrete Block BUILDING TYPE URMLR PRIMARY USE 1 Commercial PRIMARY USE 2 Retail PRIMARY USE 3 Stores BUILDING NAME N/A CHECKED Yes Table 7.1: Sample Building Inventory Database Attributes 86 Chapter 7 Case Study: City of New Westminster Figure 7.2: Prevalent Material Types 87 Chapter 7 Case Study: City of New Westminster • WLFR Figure 7.3: Prevalent Building Types 7.3 Earthquake Damage Estimation Damage estimations are performed in this study by the methodology outlines in Chapter 5. The regional building inventory is assessed for bases on motion damage relationships in the form of damage matrices. The damage matrices used are described in Chapter 6 and represent damage to displacement sensitive and acceleration sensitive components as well as building Chapter 7 Case Study: City of New Westminster contents. The damage levels are represented for each discrete intensity measured by the Modified Mercalli Intensity scale. Potential earthquake damages were assessed for ground motion intensities of M M I VII and M M I VIII. These intensity levels are the ground motions that are arrived at when two different hazard levels are considered. A intensities were calculated for the peak ground accelerations of an event with a return period of 475 years. This return period represents a 10% chance of exceedence in 50 years. This is the probability level used to establish the peak ground accelerations (PGA) that are used in the National Building Code of Canada (1995). The peak ground acceleration calculated for an event with a 475 year return period is 0.196g. The Geological Survey of Canada (1996) developed a relationship between P G A and M M I and this shows that a P G A of 0.196g relates to an M M I of 7.5. Since relations have not been developed for non-integer values of M M I damage estimates were calculated for M M I VII and VIII in an effort to represent the damages that can be expected from the National Building Code of Canada design earthquake. Once the intensity levels are calculated all of the preliminary information for an earthquake damage assessment is compiled. The necessary data, building inventory, damage relations, base maps, and intensity maps, are then combined within the Geographic Information System, Map Info (Mapinfo Corporation, 1997). The GIS assigns the appropriate MDF to each building in the inventory and displays the results in the manor specified by the user. For the purposes of this study it was decided that the results would be presented in the form of average M D F per region. The city of New Westminster planning department has divided the 89 Chapter 7 Case Study: City of New Westminster city into 378 blocks. These block units were selected as the region for presenting results. The large number of blocks allows for a high degree of detail to be presented without identifying individual buildings. 7.3.1 Displacement Sensitive Displacement Sensitive damage is the result of deformation within the structures. Displacement sensitive components, i.e. partition walls and architectural cladding, are typically quite brittle and can be damaged even at small deformation level. As a result even when the ground motions are not sufficient to cause significant structural damage there can often be significant displacement sensitive damages. Figure 7.4 and Figure 7.5 are maps showing the distribution of displacement sensitive damage for M M I VII and M M I V I E respectively. The displacement sensitive damages that have been calculate for New Westminster are predominantly in the range of 15-20% for M M I VII and M M I VIII. There are fourteen blocks that have expected damages in the 20-30% range. By comparing the damage maps and the maps showing the predominant building types it can be seen that the areas of highest damages correspond to the blocks that are predominantly unreinforced masonry. Whereas the areas of the city that are predominately residential wood construction have a lower mean damage factor. This correlation between average damages and building types is expected and serves to confirm that the software package is aggregating the data correctly. 90 Chapter 7 Case Study: City of New Westminster Figure 7.4: Drift Sensitive Damage MMI VII 91 Chapter 7 Case Study: City of New Westminster Figure 7.5: Drift Sensitive Damage MMI VDI 92 Chapter 7 Case Study: City of New Westminster 7.3.2 Acceleration Sensitive Acceleration sensitive damage describes the damage to non-structural components that are resting on or are suspended from the floors of a building. When the floors start to accelerate during an earthquake this motion is transferred to the components and they in turn will be excited. Typical acceleration sensitive components are electrical and mechanical equipment as well as piping and suspended duct work. Figure 7.6 and Figure 7.7 are maps showing the distribution of acceleration sensitive damage for M M I VII and M M I VIII respectively. The acceleration sensitive damages that have been calculate for New Westminster are predominantly in the range of 2-5% for M M I VII and M M I VOL The small level of acceleration sensitive damages is expected considering the inconsistencies in the DPMs discussed in Section 6.5. 93 Chapter 7 Case Study: City of New Westminster Figure 7.6: Acceleration Sensitive Damage MMI VII 94 Chapter 7 Case Study: City of New Westminster Figure 7.7: Acceleration Sensitive Damage MMI VIII 95 Chapter 7 Case Study: City of New Westminster 7.3.3 Building Contents Damage to building contents can be directly related to acceleration sensitive damages. The damaging mechanisms are the same for acceleration sensitive contents as for building contents. The significant difference occurs in the extent of the damages for a given level of shaking. Building contents can include any non-permanent item stored within a building. It is necessary to consider the occupancy of a building when trying to assess the loss due to building content damages. Figure 7.8 and Figure 7.9 are maps showing the distribution of damage to building contents for M M I VII and M M I VIII respectively. The building content damages that have been calculate for New Westminster are predominantly in the range of 0-2% for M M I VII and the dominant damage level remains 0-2% for M M I VIII but a significant number of blocks, 84 of 378, increase to the 2-5% damage range. 96 Chapter 7 Case Study: City of New Westminster Figure 7.8: Building Content Damage M M I VII 97 Chapter 7 Case Study: City of New Westminster Figure 7.9: Building Content Damage MMI VIII 98 Chapter 7 Case Study: City of New Westminster 7.4 Summary Due to its large diversity of building types and geographic conditions the City of New Westminster is a good location for a case study to demonstrate the application of the Non-structural damage assessment methodology developed for this study. A regional building inventory containing more than 8000 buildings was collected. This inventory identifies building type and occupancies of the buildings was well as identifying the location of each building. Damage assessments were performed for the earthquake hazards represented by the design earthquake used hy the National Building Code of Canada. It was found that displacement sensitive damage was typically in the range of 15-20%, acceleration sensitive damage was typically in the range of 2-5%, and building content damage was typically in the range of 0-2%. The level of damages that were estimated by the methodology were consistent with what was expected for the displacement sensitive damages but the estimated damage values were low for the acceleration sensitive damages and damages to building contents. It is important to note that regardless of the non-structural damage state identified for the buildings if there is a total structural failure the content damage states will be complete. 99 C H A P T E R Conclusion and Summary 8.1 Summary In order to accurately assess the potential damages due to an earthquake it is necessary to consider non-structural components. Often overlooked in risk studies and in the design of buildings, the damage to non-structural systems can surpass the effects of structural damages due to an earthquake. This study has reviewed the different non-structural systems and developed a methodology by which non-structural components can be assessed for earthquake damages. The results of this study provide an insight into the response of non-structural systems and can be an asset to many users. The insurance industry can gain a better understanding of the possible losses that can be expected, engineers can gain an insight into areas that deserve further attention during design, and local officials can use the results to assist in the mitigation of the effect of a damaging earthquake. Chapter 2 presents a review of the literature that pertains to the work in this study. A general review of the literature pertaining to earthquake hazard and damage assessment is presented. Intensity measures, non-structural systems and the use of GIS software in the assessment of earthquake damages are review in more detail. 100 Chapter 8 Conclusion and Summary In Chapter 3 methods of collecting an inventory of the regional building stock is discussed. The inventory collection process is one of the most resource intensive steps in a regional damage assessment project and as such must be completed in an accurate and efficient manor. Information describing the geographic location, structure type, and occupancy is required in order to perform the damage assessment. Methods of classifying the buildings in an inventory are presented as well as methods of data collection. A review of non-structural systems is presented in Chapter 4 as well as a method by which these systems can be classified. The non-structural systems are separated into three distinct categories. The first two categories are Displacement Sensitive non-structural components and Acceleration Sensitive non-structural components. The last category is Building Contents which describes non-permanent contents such as furniture or retail stock. It is important to separate permanent non-structural components from building contents as the permanent systems will receive some attention during the design stage and are necessary in the operations of a building. Chapter 5 reviews existing methods of evaluating damage due to an earthquake as well as presenting a summary of the method to be used in this study. The ATC-13 methodology and the FEMA-NIBS methodology are reviewed. The methodology proposed in very similar to the ATC-13 methodology in the form of the motion-damage relations and the measures of intensity. The primary difference is that new motion-damage relations are developed for non-structural systems and building contents. The development of motion-damage relations is presented in Chapter 6. The damage relations 101 Chapter 8 Conclusion and Summary developed are in the form of Damage Probability Matrices. These matrices were developed based on the non-structural fragility curves that have been proposed for the FEMA-NIBS methodology in the HAZUS software package. Typical response spectra were developed for each M M I level of interest, and the capacity and fragility curve parameters presented in the HAZUS technical manuals were utilized. Three non-structural DPMs were developed for each building type. Chapter 7 presents a case study performed in order to test and demonstrate the methodology developed in this study. Non-structural damages were calculated for the City of New Westminster. A review of the inventory collection process is presented as well as a summary of the building stock. Non-structural damage estimates were performed for two intensity levels. Results are presented for displacement sensitive and acceleration sensitive components as well as building contents. 8.2 Conclusion The development of a methodology by which non-structural damages can be evaluated on a regional basis was the purpose of this thesis. It was important that the methodology developed be applicable to the construction in southwestern British Columbia. Included within the scope of the methodology are displacement sensitive and acceleration sensitive non-structural components as well as building contents. Prior to developing DPMs building types had to be identified. The building classifications group buildings of similar construction that are expected to experience similar damage characteristics during an earthquake. Thirty-one building type classifications were identified 102 Chapter 8 Conclusion and Summary that can be used to identify the building stock of south-western British Columbia. The building types represent differences in material type and lateral load resisting system as well as variations of building height. These building types are similar to the classification system used by both the ATC-13 methodology and the HAZUS methodology. While the descriptions of the building types are similar the expected performance of local construction is expected to be different than that of construction elsewhere due to differences in engineering preferences and construction techniques. The only significantly unique building category is the Wood Post and Beam (WPB) building type. This type was not directly represented previously but the frequent use of this construction type in the region for residential building necessitated the inclusion of this classification. A review of existing methodologies revealed that two methodology frameworks are used in the majority of regional earthquake damage assessment studies. The two methodologies are from the ATC-13 study and a study by FEMA-NEBS that has been incorporated into the H A Z U S software package. The major differences between the two methodologies are the form of the motion-damage relations and the intensity scale used to represent ground motions. The ATC-13 methodology uses a subjective ground motion intensity scale, M M I , and the motion-damage relations are damage probability matrices. In the FEMA-NIBS methodology fragility curves are used to represent the motion damage relationships and ground motion response spectra represent the earthquake shaking intensity. The use of continuous fragility curves and actual ground motion intensities by the FEMA-NIBS methodology could be a great advance in earthquake damage estimation. The limitation currently is that the methodology is capable of estimating damages at a level significantly greater than engineers 103 Chapter 8 Conclusion and Summary and researchers understanding of earthquake induced damages. In the future, as our understanding improves, this methodology will be capable of producing far more accurate results than is possible with a methodology using DPMs but with todays technology the increase in accuracy is not realized. It was decided for the purposes of this study that the methodology used be based on the ATC-13 framework. The motion-damage relations are represented by DPMs and the ground motion intensity is measured by the M M I scale. The primary reason for this was the unavailability of existing locally applicable data. Since there was a lack of data it was deemed necessary to utilize local expertise to assist in developing the methodology. It was found that local engineers were more familiar with the ATC-13 methodology than with the FEMA-NIBS methodology. The DPMs developed are representative of the displacement sensitive damages expected. The DPMs representing acceleration sensitive damages and damages to building contents produce results that are significantly lower than can be realistically expected. This underestimation is produced by the parameters provided in the HAZUS methodology. It was decided that even with the observed deficiencies the DPMs developed in Chapter 6 would be used to demonstrate the methodology for calculating damages in southwest British Columbia. The case study performed served to demonstrate the methodology developed for this study. An inventory of over 8000 buildings was collected in the City of New Westminster. The GIS system was used to analyze the building inventory in order to assess the distribution of building material and types through the city. The GIS was also used to perform an assessment of expected damages to the region. It was found that the expected damages for displacement sensitive components was predominantly in the range of 15-20%. In the blocks where the 104 Chapter 8 Conclusion and Summary predominant building type was unreinforced masonry the average damage was slightly higher and in blocks were the predominant building type was concrete frame the average damage was found to be slightly lower. When acceleration sensitive components and building contents were considered the predicted damages were significantly lower. This can be attributed to the initial parameters used to represent the building capacity curves and the fragility curves. 8.3 Suggested Future Work A study that developed improved motion damage relationships for non-structural components would be a very important work. Improved understanding of the relationship between ground motion intensity and non-structural damages could increase the reliability of future damage studies. This work should focus particularly on developing improved non-structural fragility curves. A project that expanded upon the GIS system used in this study to include additional parameters that affect damages would be an asset. The addition of site soil conditions, building age, and the effect of slope failure would greatly increase the understanding of the risk to much of Southwestern British Columbia, particularly areas along the Fraser River delta and on the slopes of the local mountains. This work would hot need to develop a new methodology but could modify the existing damage estimation framework. In order to better understand the overall effects of an earthquake on the region a study that converted the damages identified herein to dollar values is required. This work should convert the damages from a percentage of replacement cost to a direct dollar value. This conversion of the units used to measure damages would facilitate the combining of structural effects with 105 Chapter 8 Conclusion and Summary non-structural effects. In addition to addressing only the dollar values of damages the costs due to loss of function should be addressed. While many non-structural components may not be totally destroyed it may require extensive work and money to return facilities to an operating conditions. 106 C H A P T E R 9 References [1] Ad Hoc Earthquake Reconnaissance Committee (1991) "Reflections on the October 17, 1989 Loma Prieta Earthquake" SEAOC, Structural Engineers Association of California, California. [2] Agbabian Associates, Correlation of Ground Response Spectra with Modified Mercalli Site Intensity, Energy Research and Development Administration, Washington, 1977. [3] Algermissen, S.T., Rinehart, W.A., Dewey, J., Steinbrugge, K.V. , Degenkolb, H.J.,Guff, L.S., McClure, F.E., Gordon, R.F., Scott, S., and Lagorio, H.J. (1972) " A Study of Earthquake Losses in the San Francisco Bay Area: Data and Analysis." Office of Emergency Preparedness, National Oceanic and Atmospheric Administration, Washington, D.C. [4] Applied Technology Council (1985). Earthquake Damage Evaluation Data for California, ATC-13. Redwood City, California. [5] Applied Technology Council (1988). Rapid Visual Screening of Buildings for Potential Seismic Hazards, ATC-21. Federal Emergency Management Agency (FEMA) Publication 154. Washington, D.C. [6] Applied Technology Council (1989). A Handbook for Seismic Evaluation of Existing Buildings, ATC-22. Redwood City, California. [7] Applied Technology Council (1989). Seismic Evaluation of Existing Buildings: Supporting Documentation, ATC-22-1. Redwood City, California. [8] Blanquera, A . (1999) "Evaluation of Structural Earthquake Damage to Buildings in Southwestern B.C." Masters Thesis, Department of Civil Engineering, U B C , Vancouver, British Columbia. [9] Bell, L . (1998). Southwestern British Columbia Seismic Fragility Study. University of British Columbia, B.C. 107 Chapter 9 References [10] BSCC (1997). NEHRP Guidelines for the Seismic Rehabilitation of Buildings ATC-33. by the Applied Technology Council, for the Building Seismic Safety Council and F E M A , . FEMA-273, Washington D.C. [11] Canadian Standards Association (1998). Draft 1 - Guideline for Seismic Considerations of Functional and Operational Components of Buildings. Canadian Standards Association, Ontaria, Canada [12] King, S.A. and A.S. Kiremidjian (1994) "Regional Seismic Hazard and Risk Analysis Through Geographic Information Systems" The John A. Blume Earthquake Engineering Center Report No. 111. Department of Civil Engineering, Stanford University, Stanford, California. [13] F E M A (1997) "HAZUS - Technical Manual Volume I" National Institute of Building Sciences Document Number 5201. Federal Emergency Management Agency. Washington, D.C. [14] F E M A (1997) " H A Z U S - Technical Manual Volume IF National Institute of Building Sciences Document Number 5201. Federal Emergency Management Agency. Washington, D.C. [15] F E M A (1997) "HAZUS - Technical Manual Volume III" National Institute of Building Sciences Document Number 5201. Federal Emergency Management Agency. Washington, D.C. [16] F E M A (1997) "HAZUS - Users Manual" National Institute of Building Sciences Document Number 5201. Federal Emergency Management Agency. Washington, D.C [17] Maplnfo Corporation (1997) "Mapinfo Professional GIS Software" [18] Morfitt, G. (1997) Office of the Auditor General of British Columbia Earthquake Preparedness Performance Audit. Report 1997/1998:1 Office of the Auditor General of British Columbia, Victoria, B.C. [19] Munich Re-Insurance Company of Canada and Rescan Consultants, Inc. (1993). "A Study of the Economic Impact of a Severe Earthquake in the Lower Mainland of British Columbia" [20] Naeim, F., Anderson, J .C , (1996) "Design Classification of Horizontal and Vertical Earthquake Ground Motions (1933-1994)" USGS Award No. 1434-95-G-2596, John A. Martin & Associates, Inc. Research and Development Department, Los Angeles, CA. [21] National Geophysical Data Center (1996) "The Earthquake Strong Motion CD R O M Collection" US Department of Commerce, National Oceanic and Atmospheric Administration, National Geophysical Data Center, Boulder, Colorado. 108 Chapter 9 References [22] National Institute of Building Sciences (1997) "Earthquake Loss Estimation Methodology Study" National Institute of Building Sciences, Washington, D.C. [23] Risk Management Software, Inc., California Universities for Research in Earthquake Engineering (1994) Assessment of the State-of-the-Art Earthquake Loss Estimation Methodologies, FEMA-249 National Institute of Building Sciences, Earthquake Hazards Reduction Series 70, National Institute of Building Sciences, Washington D.C. [24] SEAOC (1996) Recommended Lateral Force Requirements and Commentary, Seismology Committee, Structural Engineers Association of California, Sacramento California. [25] Scholl, R.E. (1980) "Seismic Damage Assessment for High-Rise Buildings" Open File Report 81-381. United States Geological Survey. Menlo Park, California. [26] Tiedemann, H (1992) "Earthquakes and Volcanic Eruptions - A Handbook on Risk Assessment" Swiss Reinsurance Company, Zurich, Switzerland. [27] Ventura C.E. and Rezai, M . (1997). "Classification and Damage Estimation of Buildings in British Columbia." Report to IRAS Insurance Users Group, Dept. of Civil Engineering, University of British Columbia, Vancouver, B.C. 109 A P P E N D I X A Damage Probability Matrix Worksheet This section contain a description of the worksheet used calculate the non-structural DPMs for this study. Figure A . 1 contains a sample of the worksheet used with the formulas revealed and Figure A.2 contains a sample of the worksheet showing the values that were calculated. The descriptions below describe the columns and rows as shown in Figure A. 1: Column C: contains the performance point values that were found when the spectral demand curves were compared with the capacity curves for each building type. See Appendix B. Column G: contains the displacement sensitive fragility curve parameters found in section 5.4.3.5 of the HAZUS Tech Manual I (FEMA, 1998), Moderate Code, Column I: contains the drift sensitive fragility curve parameters converted from imperial to metric, Column N : contains the acceleration sensitive fragility curve parameters found in section 5.4.3.6 of the HAZUS Tech. Manual I, Moderate Code, Appendix A Damage Probability Matrix Worksheet Column S: contains the central damage factors for each damage matrix. The factors can be found on page 15-11 of the H A Z U S Tech. Manual III, Column T: contains the formulas for calculating the probability of a building being in each damage state, based on equation 6.4 in this thesis, Rows 10,19,28 The last line in each matrix is the M D F as shown in equation 5.3 in this thesis. The worksheet shown can be used to calculate DPMs for any building type or intensity levels provided the capacity curves, demand spectra, and fragility curve parameters are available. i l l Appendix A Damage Probability Matrix Worksheet 1 y 3 H 1 $1 is DC U U w 3i3 3 2 8 j j r o : o > o - c z J ; — : o : o : * * i O : C 0 l B ay 1 B 13 19 Pi 3 1— : 3: C: : *>: OJ: : Q.: to: : 8 ^ x; ;E:.p;g: : w: w: *>v VI'- v>: : c; c; C: c! c; c; j i^ }: njj i ^ : o^:'^;^_: : o : o : o o- o : o:^--; o : o : o : o : o : o : l — : " g E g S E E : «: b: fa: fa: E; E: E: J-gj^j 3; 3- 3: 3:"jji. ;3i3i3i T~>L 3 H N I | **|! s i s o. V o s c <-Hp; ,T| #1 Figure A . l : Damage Probability Matrix Worksheet with Formulas Revealed 112 Appendix A Damage Probability Matrix Worksheet m x 1 m 1*1 * i f f ; : 1 a a ssss a: 1^  fit L 1_ ID-S' O (7) i n : n : O : 0 D ; O : f ^ - : O ; ^ M CNJ: 1- ;^ IT): UD: O : t U > CD : U51 O : O : O : 0 : — : 0 : r g : O I - 0 i * : t 5 i U : t > : V*>:TI 0):aj;4>:1B; «i: W «>. £1 Si I?: !2 c 9-•e £ X o :LU U ml 2 Q:U1 r - - c o : r * ~ - . — : o ; c o > o : ^ • c\J ;c^J:^^>:<T>:o:c^J::o:co —'; c\ i : (sj: <\i • CO: Cvi \ cb: <N o ; C 0 : ~ ^ : L 0 : o > O : * r i n : CO; o : CO;.—: O l i d : a 0 : 0 - — : o ; c r > : o ; c o T J : <0:"d- «J:T> ; *0:"d u : ^ ; a>: u i « : ai; °>. IUI •fiv | 5 E Ul: U : 01 o : rjf IL3 SIS uiicn tn;tn CM' O X): *0 cn in : D | o : 01 o : CT| t o o Cfi f3:r^ "U: : <0 IflilM X i * « * CA t» <r> t xi x X X : X'; X X X X. Xi XI X x x U l XI O : 0 : O : O | — > 0 : C N ; 0 0J| aj: <u: 03; aj: a?: ai : a: ; Ei Jill i l l Figure A.2: Damage Probability Matrix Worksheet 113 A P P E N D I X B Capacity vs. Demand Curves This section contains the plots of the capacity curves for each building type versus the repre-sentative demand spectra for each M M I intenstity level. Increasing demand curves represent increasing values of Modified Merchalli Intensity. The curves plotted are described in sections 6.2 and 6.3. •i n 1 . u -50.9 50.8 0 wo.7 O 0.6 O <0.5 CO •fcO.4 0 a> Q.0.3 C/5 o0.2 T J 3 0.1 Q-0.0 C 1 | 0 1.0 0)0-9 C 0 . 8 0 ra0.7 g0.6 0 <0.5 CO .fco.4 0 a> Q.0.3 c/> 00.2 "O </> Q-0.0 C • 1 0 1 • 1 1 A 1 : 1 1 ' \ 1 1 ' • • • 1 • * " \ 1 . 1 i ' i i \ ' i \ v« • » * • i 1 v • > 1 .. " 1 .. I 1 \ '•'\ \ • 1 1 ' 1 • \ '• >** / ' 1 * A \ t. - -{. * V — — . • . ^ \j • \ " - - - * * ^ . . l \ - N-- • • . . ^ 1 A'-.— - "* ""• - . I T — * *. ^ — • • . . . . _ - • - » -) 1 0 2 Spectra I 0 3 Displacer LFR D 4 nent (cm 0 5 ) 1 0 2 Spectra [ \A 0 3 Displacer /LFCI 0 4 nent (cm 0 5 )-. Figure B . l : Capacity vs. Demand Plots 114 Appendix B Capacity vs. Demand Curves 1 . 0 0 ) 0 . 9 J 0 . 8 2 0 . 7 CD gO.6 5 0.5 CO - 0 . 4 <D Q.0.3 W o 0 . 2 "O § 0 . 1 co Q - 0 . 0 • 1 s 1 : » : > ' \ i ? i \ ' \ v> i * V .. * i \ i - ' / 1 % ' — • * • • — . ' . • N K. * ^. ^ " " — — -iV-f l " -— k z : .' 10 20 30 40 Spec t ra D i s p l a c e m e n t ( c m ) W L F L R 50 1 . 0 0 ) 0 . 9 | 0 . 8 20.7 CD O 0 . 6 o f 0.5 2 £ 0 . 4 CD Q.0.3 W o 0 . 2 T3 §0.1 CO Q-o.o —1—1— •v 1 : \ : 1 ' -\ i r i X i • \ \ v- -i « V '.. ' 1 . :i\ 1 * V / • 1 i " \ . i i ' ' - - . — -• 10 20 30 40 Spec t ra D i s p l a c e m e n t ( c m ) W P B 50 1.0 ^ 0 . 9 O) 0.8 10.7 CD 0 )0 .6 o ^ 0 . 5 2 0.4 o 2.0.3 CO o 0 . 2 7 3 0.1 Q-o.o 1 1 1 \ 1 •• • 1 1 1 1 1 ', i . 1 \ 1 ' • i 1 I ' I ' • 1 / • * ' **» TS - v . 1 V. • «« — * V ^ f I b*J 1.0 ^ 0 . 9 O —0.8 10.7 CO "50.6 O ^ 0 . 5 2 0.4 "G g.0.3 CO o 0 2 73 ^0.1 en 0-0.0 1 1 1 A 1 : I ' l l 1 1 1 '. i . 1 I 1 \ • i > V .. 1 1 \ • 1 1 1 1 - 1 * : = = • ^ T : — . A • • " *» - ^ „ I 1 10 20 30 40 S p e c t r a D i s p l a c e m e n t ( c m ) L M F 50 10 20 30 40 Spec t ra D i s p l a c e m e n t ( c m ) S M F L R 50 1.0 ^ 0 . 9 O) —0.8 10.7 CO 0)0.6 o ^ 0 . 5 S 0.4 o g.03 w o 0 . 2 T 3 * 0.1 CO Q-0.0 ! 1 1 1 \ 1 1I ' l l t t 1 '. i . 1 1 | 1 • " 1 1 \ '.. ' 1 . •. 1 1 1 1 " 1 \ " ^ . — \ * "• - » . y-r-.T.-—--1.0 ^ 0 . 9 O) —0.8 10.7 CO 0)0.6 o ^ 0 . 5 2 0.4 "G g.0.3 CO o 0 . 2 T 3 ^0.1 v> 0-0.0 1 1 1 \ 1 : • l l 1 ', 1 . 1 I 1 1 . • i 1 \ .. \ i \ • 1 '. 1 i • 1 \ -^ . ' ' -s. A \ • — . L -— 10 20 30 40 S p e c t r a D i s p l a c e m e n t ( c m ) S M F M R 50 10 20 30 40 S p e c t r a D i s p l a c e m e n t ( c m ) S M F H R 50 Figure B.l: Capacity vs. Demand Plots 115 Appendix B Capacity vs. Demand Curves 1.0 0.9 CD ^-0.8 2 150.6 o 3 0.5 20.4 "G S.0-3 CO o 0 . 2 "O ^0.1 in 0-0.0 f 1 1 ^ > • l i i i . ' i ! • \ '. • i 1 I .. 1 i \ • 1 1 1 1 / • » </' V TV* V "• > ». ' 1 ..».-=- r. -=-r.-r.-—--. — 10 20 30 40 S p e c t r a D i s p l a c e m e n t ( c m ) SBFLR 50 1.0 ^ 0 . 9 CD 10.7 CO L. 0)0.6 o ^ 0 . 5 2 0.4 t> S.0.3 CO o 0 . 2 "O ^ 0.1 in Q-0.0 1 1 1 • < » i ; i . * i » \ • i 1 V '.. » i \ • I • • 1 - 1 \ N — — — — - - _ _ • i\'' \ '' - ^  . i 1 — 10 20 30 40 Spec t ra D i s p l a c e m e n t ( c m ) SBFMR 50 1.0 ^ 0 . 9 CD *-0.8 10.7 co "50.6 o ^ 0 . 5 5 0.4 "C 2.0-3 W o 0 . 2 20.1 Q-o.o 1 1 1 1 ^ 1 : i i i i i i '. \ . 1 l . i \ '. • i * V .. 1 i \ " ' 1 • t \ *. - ^ — — — — \ " . * — ' • ~ •» * — . 1.0 ^_0.9 CD — 0 . 8 10.7 CO "5)0.6 o ^ 0 . 5 £0.4 S.0-3 to o 0 . 2 T 3 ^0.1 in D-0.0 1 1 1 1 ^ 1 "• • 1 1 \ i 1 '. i . 1 1 i 1 '. • i * I '.. ' 1 . ' \ ' • 1 . J - V • — • • • s- • v» </* V — ^ « . TV- v -• •—i i - - - . 1 -• . » - • = - - f -•z-r.r.-—-- . . — - • 10 20 30 40 S p e c t r a D i s p l a c e m e n t ( c m ) SBFHR 50 10 20 30 40 Spec t ra D i s p l a c e m e n t ( c m ) SFCWLR 50 Figure B . l : Capacity vs. Demand Plots 116 Appendix B Capacity vs. Demand Curves 1 . 0 ^ 0 . 9 O) — 0 . 8 10.7 2 0 ) 0 . 6 o ^ 0 . 5 2 0.4 o £ . 0 . 3 CO o 0 . 2 T J § 0 . 1 (/) 0 - 0 . 0 1 1 1 1 1 1 t 1 1 '. 1 . 1 1 1 _ \ . • i 1 \ .. * 1 \ • 1 1 1 1 - 1 \ • > • V • • — t 1 " - - „ / 1 - - r • — • • • — 10 20 30 40 S p e c t r a D i s p l a c e m e n t ( c m ) S F C W M R 50 1.0 __0.9 CD — 0 . 8 10.7 2 0)0.6 o £ 0.5 0.4 £0.3 CO o 0 . 2 •a §0.1 U) 0-0.0 1 1 1 •11 1 1 1 ', 1 . 1 1 1 \ '. •• i 1 V '.. ' 1 . • 1 1 • i - V -/•• •« <./• V T V - v f !*• ' — . t — ^ - ^ - ^ ' 1 ^ • • " • • ^ • • • — . . . — 10 20 30 40 S p e c t r a D i s p l a c e m e n t ( c m ) S F C I 50 1.0 ^0.9 O) — 0 . 8 10.7 2 "5)0.6 o ^ 0 . 5 2 0.4 o g.0-3 co o 0 . 2 X J §0.1 </) D-0.0 1 1 1 1 ^ 1 : i • i i \ i i '. i . 1 I * i . » ' • i > V .. \ i \ '• i '. • i — • \ ^ ' • - - . / ' I • v 10 20 30 40 S p e c t r a D i s p l a c e m e n t ( c m ) S F C W H R 50 1.0 •So.8 10.7 2 0)0.6 o ^ 0 . 5 0.4 o £0.3 CO o 0 . 2 "a §0.1 V) 0-0.0 ! 1 1 1 \ 1 "• 1 1 1 1 1 1 ', i . 1 1 i \ '. • "l 1 I .. > 1 \ • 1 1 1 | 1 — T— TS • v " •»» •* i V \ • •«. —** v ^ I bJ 10 20 30 40 Spec t ra D i s p l a c e m e n t ( c m ) S F M I 50 1.0 ^ 0 . 9 O) — 0 . 8 10.7 0)0.6 o ^ 0 . 5 2 0.4 "G 2.0-3 CO o 0 . 2 T > 2o.i u) 0-0.0 ! 1 1 1 • \ 1 '• •11 1 1 I ' : . 1 l — . — i \ '. • i 1 V .. > i \ • / • ' 1 1 s ii ' V TV ^. f 1 ' * 1.0 ^ 0 . 9 o> — 0 . 8 |o.7 2 "5)0.6 o ^ 0 . 5 2 0.4 -t-» o 2.0.3 CO o 0 . 2 "O §0.1 in 0-0.0 ! 1 1 1 \ 1 "• • 1 1 1 1 1 '. "l . 1 1 1 . \ • i 1 I .. > 1 \ " 1 1 • ' 1 . . -. \ K — . • /. * ^*, A • V ' . , \ - . • — - _ i ' •• •» ^ / 1 . *** t>--= — f, -----— 10 20 30 40 S p e c t r a D i s p l a c e m e n t ( c m ) C F L R 50 10 20 30 40 Spec t ra D i s p l a c e m e n t ( c m ) C F M R 50 Figure B.l: Capacity vs. Demand Plots 117 Appendix B Capacity vs. Demand Curves 1.0 ^ 0 . 9 co — 0 . 8 10.7 CD "c|0.6 o ^ 0 . 5 2 0.4 "o • 0 . 3 CO o 0 . 2 ~a !»0.1 co Q-0.0 1 1 1 \ 1 : • 1 1 1 I 1 I 1 . 1 1 I \ '. •• i 1 V ' . . > I \ • I 1 ' • ^ 1 1 * • *-, " t \ ' — • • • — > . ______ * V * *• - - . / I V. U.w-g • - - r. • a - r . ' - " ^ • • 10 20 30 40 S p e c t r a D i s p l a c e m e n t ( c m ) CFHR 50 1.0 ^ 0 . 9 ft* 10.7 TO 0)0.6 o ^ 0 . 5 2 0.4 o g.0-3 CO 0°-2 "a S^ O.1 ca 0-0.0 1 1 1 1 \ 1 '• I I I 1 1 1; \ . * 1 : 1 _ i 1 V 1 1 . • 1 • 1 1 • 1 L -•< ^ *« K- • / V ' — » t N [ \ • «» ^ •» ' I __d . -** " - L - . T . * - ^ . - — 10 20 30 40 Spec t ra D i s p l a c e m e n t ( c m ) RCMFLR 50 1.0 __0.9 D) — 0 . 8 10.7 co "0)0.6 o ^ 0 . 5 2 0.4 o 2.0.3 CO o 0 . 2 T 3 ^0.1 CO Q-0.0 1 1 \ 1 M - i -\ t '. 1 ', 1 . 1 \ \ \ • i 1 V • 1 \ * — . , , > l i i ^ -V • X ' . • •— _ • •> ~" - _ , / 1 ,. ^ - - r. 1.0 — ° ' 9 cn — 0 . 8 10.7 2 "5)0.6 o 3 0.5 2 0.4 o 2.03 w c.0.2 •o ^O. l CO Q-0.0 1 1 1 > 1 : r- 1 1 1 1 1 1 1 . ' 1 ! 1 . \ '. • i 1 I 1 1 . • 1 1 • | • 1 \ • V ~«• . \ ' . - * 1 — ' " 10 20 30 40 S p e c t r a D i s p l a c e m e n t ( c m ) RCMFMR 50 10 20 30 40 Spec t ra D i s p l a c e m e n t ( c m ) RCMFHR 50 1.0 ^ 0 . 9 co — 0 . 8 J 0.7 2 "5)0.6 o £ 0 . 5 2 0.4 -•—' O CO o 0 . 2 T3 ^0.1 CO Q-0.0 • 1 1 I \ 1 : 1 • I I 1 1 I 1 : . 1 1 I \ '. • i 1 V .. 1 1 \ • 1 1 1 | • 1 \ . , - — — • "—. ( \ • 1 * , *• 1.0 _ 0 - 9 CO 0.8 10.7 2 "5)0.6 o ^ 0 . 5 2 0.4 • o 2.0.3 CO o 0 . 2 2o.i co Q-0.0 1 1 1 \ ' : I I I \ 1 1 ', i . ' 1 1 \ '. •  "1 1 V — ' — — — — — — -" f' • / • 1 / 1 • £ ' ^ . I V v. - - ^  . * - - " — 10 20 30 40 S p e c t r a D i s p l a c e m e n t ( c m ) RCFIW 50 10 20 30 40 Spec t ra D i s p l a c e m e n t ( c m ) RMLR 50 Figure B.l: Capacity vs. Demand Plots 118 Appendix B Capacity vs. Demand Curves 1.0 ^ 0 . 9 O) —0.8 10.7 to "5)0.6 o ^ 0 . 5 2 0.4 o £0.3 CO o l T 3 §0.1 U) O-O.O >0.2 1 1 1 \ 1 "• 1 1 ' 1 1 1 1 '. 1 . 1 1 \ '. •• i 1 V .. 1 1 \ • I > . 1 ' ^  l A ./• -^ N - - - - - -. \ " . • •— _ - * i ' / I •.*.-=:- - r * 10 20 30 40 S p e c t r a D i s p l a c e m e n t ( c m ) RMMR 50 1.0 ^ 0 . 9 f o . 8 10.7 2 "5)0.6 o $0.5 20.4 "G 2.03 CO o 0 2 73 §0 .1 in 0L0.0 1 1 1 1 \ » '• 1 1 ' 1 \ 1 1 '• i . 1 1 | \ • • i 1 \ .. 1 i \ r, . > \[ * V ~ - - - . T V v ~* ^ - > | \ " • j .--=•---'- •c_r.T."^ • • 10 20 30 40 Spec t ra D i s p l a c e m e n t ( c m ) URMLR 50 1.0 ^ 0 . 9 O ) — 0 . 8 10.7 2 "5)0.6 o ^ 0 . 5 20.4 "G 2.0.3 CO o 0 . 2 73 §0.1 in 0-0.0 • 1 1 1 ^ 1 "• 1 \ ' 1 \ i i \ i . ' i » * • i 1 V .. » i \ — M — *-•* ^ _ "" * i • . / 1 . «*"" *-*-=• - - 1". 1.0 ^ 0 . 9 cn —0.8 10.7 2 "550 .6 o £ 0 . 5 2 0 . 4 o CO o 0 . 2 73 § 0 . 1 in 0 - 0 . 0 1 1 1 \ 1 "• 1 1 • 1 1 1 1 '. 1 . 1 1 - 1 \ . • .. \ft \ V - ' ' . > i. • V "•» iS • v. 1 1 " " * — . ' L U * S — — rJ 10 20 30 40 S p e c t r a D i s p l a c e m e n t ( c m ) URMMR 50 10 20 30 40 S p e c t r a D i s p l a c e m e n t ( c m ) TU 50 1.0 ^_0.9 • ) — 0 . 8 J 0.7 2 "5)0.6 o £ 0.5 2 0.4 O CO O 0 . 2 •o §0.1 in O-O.O 1 1 1 1 ^ 1 : i - i i \ t . i \ \ . 1 i * i \ '. •• i 1 \ i i . " i > '. • -T V v ( •i-r. 1.0 ^ 0 . 9 CT) 0.8 J 0.7 2 "5)0.6 o ^ 0 . 5 2 0.4 "G CO o 0 . 2 T3 §0.1 in O-O.O • 1 1 \ 1 "• 1 1 1 1 \ 1 1 i i * | \ I i » V \ i \ ' i 1 'v 1 i . \ \ ~ ^ , X * • •* / 1 * 1 " "* - » . / 1 1.*--=:- - r, 10 20 30 40 S p e c t r a D i s p l a c e m e n t ( c m ) PCLR 50 10 20 30 40 Spec t ra D i s p l a c e m e n t ( c m ) PCMR 50 Figure B.l: Capacity vs. Demand Plots 119 Appendix B Capacity vs. Demand Curves 1.0 ^ 0 . 9 o> — 0 . 8 10.7 CO "550 .6 o ^ 0 . 5 2 0.4 o 2.0-3 CO o 0 . 2 " O § 0 . 1 U) 0 - 0 . 0 1 1 1 1 \ 1 • • I 1 1 t | 1 •, . 1 1 I '. • i 1 \ .. » 1 \ " 1 1 i | • 1 \ > A • v . 1 i ' • — r i i ' ' "* ~ _ . 1 10 20 30 40 Spectra Displacement (cm) MH 50 Figure B.l: Capacity vs. Demand Plots 120 A P P E N D I X C Non-Structural Damage Probability Matrices The non-structural damage probability matrices developed for the purposes of this study are listed on the following pages. For each building type the DPMs are listed for displacement sensitive components, acceleration sensitive components and building contents. These DPMs were developed through the application of the methodology described in Chapter 6. 121 Appendix C Non-Structural Damage Probability Matrices Table C. l : Wood Light Frame Residential Damage Probability Matrices Wood Light Frame Residential (WLFR) Displacement Sensit ive Damage State CDF(%) VI Vl l VIII IX X XI XII None 0 66 .0% 54 .2% 51.0% 41 .2% 32 .7% 2 8 . 1 % 24 .2% Slight 2 10.0% 11.6% 11.9% 12.3% 12.0% 11.5% 11.0% Moderate 10 12.7% 16.0% 16.8% 18.6% 19.5% 19.5% 19.3% Extensive 50 1.8% 3.5% 4.0% 5.8% 7.6% 8.7% 9.6% Complete 80 9.5% 14.7% 16.3% 2 2 . 1 % 28 .3% 3 2 . 1 % 36.0% Accelerat ion Sensit ive Damage State CDF VI Vll VIII IX X XI XII None 0 73 .0% 47 .9% 35.2% 23 .9% 14.0% 9.9% 7.9% Slight 2 22 .4% 35.3% 37.8% 36.3% 30 .4% 25 .9% 2 3 . 1 % Moderate 10 4 .4% 14.6% 22 .2% 3 0 . 1 % 37 .0% 38.9% 39.2% Extensive 50 0.3% 2 . 1 % 4 .7% 9.0% 16.4% 21 .5% 24 .7% Complete 80 0.0% 0 . 1 % 0.2% 0.7% 2 .2% 3.8% 5.0% Contents Damage State CDF VI Vl l VIII IX X XI XII None 0 73 .0% 47 .9% 35.2% 23 .9% 14.0% 9.9% 7.9% Slight 1 22 .4% 35 .3% 37 .8% 36 .3% 30 .4% 25 .9% 2 3 . 1 % Moderate 5 4 .4% 14.6% 22 .2% 3 0 . 1 % 37 .0% 38 .9% 39.2% Extensive 25 0.3% 2 . 1 % 4 .7% 9.0% 16.4% 21 .5% 24 .7% Complete 40 0.0% 0 . 1 % 0.2% 0.7% 2 .2% 3.8% 5.0% 122 Appendix C Non-Structural Damage Probability Matrices Table C.2: Wood Light Frame Commercial/InstitiutionalDamage Probability Matrices Wood Light Frame Commercial/Institutional (WLFCI) Displacement Sensitive Damage State CDF(%) VI Vll VIII IX X XI XII None 0 70.6% 55.2% 53.2% 45.3% 38.8% 34.7% 30.7% Slight 2 8.0% 10.4% 10.6% 11.3% 11.5% 11.5% 11.3% Moderate 10 10.5% 14.5% 14.9% 16.4% 17.3% 17.6% 17.8% Extensive 50 6.2% 9.2% 9.5% 10.8% 11.5% 11.9% 12.1% 1 Complete 80 4.7% 10.7% 11.7% 16.3% 20.9% 24.4% 28.1% Acceleration Sensitive Damage State CDF VI Vll VIII IX X XI XII None 0 77.4% 50.0% 47.7% 31.8% 24.5% 20.3% 18.5% Slight 2 19.0% 35.0% 35.8% 39.2% 38.6% 37.3% 36.5% Moderate 10 3.4% 13.0% 14.1% 23.1% 28.1% 31.1% 32.4% Extensive 50 0.3% 2.0% 2.2% 5.4% 8.0% 10.1% 11.1% Complete 80 0.0% 0.1% 0.1% 0.5% 0.9% 1.3% 1.5% Contents Damage State CDF VI Vll VIII IX X XI XII None 0 77.4% 50.0% 47.7% 31.8% 24.5% 20.3% 18.5% Slight 1 19.0% 35.0% 35.8% 39.2% 38.6% 37.3% 36.5% Moderate 5 3.4% 13.0% 14.1% 23.1% 28.1% 31.1% 32.4% Extensive 25 0.3% 2.0% 2.2% 5.4% 8.0% 10.1% 11.1% Complete 40 0.0% 0.1% 0.1% 0.5% 0.9% 1.3% 1.5% 123 Appendix C Non-Structural Damage Probability Matrices Table C.3: Wood Light Frame Low Rise Damage Probability Matrices Wood Light Frame Low Rise (WLFLR) Displacement Sensitive Damage State CDF(%) VI Vll VIII IX X XI XII None 0 66.0% 54.2% 51.0% 41.2% 32.7% 28.1% 24.2% Slight 2 10.0% 11.6% 11.9% 12.3% 12.0% 11.5% 11.0% Moderate 10 12.7% 16.0% 16.8% 18.6% 19.5% 19.5% 19.3% Extensive 50 1.8% 3.5% 4.0% 5.8% 7.6% 8.7% 9.6% Complete 80 9.5% 14.7% 16.3% 22.1% 28.3% 32.1% 36.0% Acceleration Sensitive Damage State CDF VI Vll VIII IX X XI XII None 0 73.0% 50.0% 38.4% 23.9% 14.0% 9.9% 7.9% Slight 2 22.4% 34.6% 37.5% 36.3% 30.4% 25.9% 23.1% Moderate 10 4.4% 13.5% 20.1% 30.1% 37.0% 38.9% 39.2% Extensive 50 0.3% 1.9% 3.8% 9.0% 16.4% 21.5% 24.7% Complete 80 0.0% 0.1% 0.2% 0.7% 2.2% 3.8% 5.0% Contents Damage State CDF VI Vll VIII IX X XI XII None 0 73.0% 50.0% 38.4% 23.9% 14.0% 9.9% 7.9% Slight 1 22.4% 34.6% 37.5% 36.3% 30.4% 25.9% 23.1% Moderate 5 4.4% 13.5% 20.1% 30.1% 37.0% 38.9% 39.2% Extensive 25 0.3% 1.9% 3.8% 9.0% 16.4% 21.5% 24.7% Complete 40 0.0% 0.1% 0.2% 0.7% 2.2% 3.8% 5.0% 124 Appendix C Non-Structural Damage Probability Matrices Table C.4: Wood Post and Beam Damage Probability Matrices Wood Post and Beam (WPB) Displacement Sensit ive Damage State CDF(%) VI VII VIII IX X XI XII None 0 66 .0% 54.2% 51.0% 41 .2% 32 .7% 2 8 . 1 % 24 .2% Slight 2 10.0% 11.6% 11.9% 12.3% 12.0% 11.5% 11.0% Moderate 10 12.7% 16.0% 16.8% 18.6% 19.5% 19.5% 19.3% Extensive 50 1.8% 3.5% 4.0% 5.8% 7.6% 8.7% 9.6% Complete 80 9.5% 14.7% 16.3% 2 2 . 1 % 28 .3% 3 2 . 1 % 36.0% Accelerat ion Sensit ive Damage State CDF VI VII VIII IX X XI XII None 0 73 .0% 47 .9% 35.2% 23 .9% 14.0% 9.9% 7.9% Slight 2 22 .4% 35.3% 37.8% 36.3% 30 .4% 25 .9% 2 3 . 1 % Moderate 10 4 .4% 14.6% 22 .2% 3 0 . 1 % 37 .0% 38 .9% 39.2% Extensive 50 0.3% 2 . 1 % 4 .7% 9.0% 16.4% 21 .5% 24 .7% Complete 80 0.0% 0 . 1 % 0.2% 0.7% 2 .2% 3.8% 5.0% Contents Damage State CDF VI VII VIII IX X XI XII None 0 73 .0% 47 .9% 35.2% 23 .9% 14.0% 9.9% 7.9% Slight 1 22 .4% 35.3% 37.8% 36.3% 30 .4% 25 .9% 2 3 . 1 % Moderate 5 4 .4% 14.6% 22 .2% 3 0 . 1 % 37.0% 38 .9% 39.2% Extensive 25 0.3% 2 . 1 % 4 .7% 9.0% 16.4% 21 .5% 24 .7% Complete 40 0.0% 0 . 1 % 0.2% 0.7% 2 .2% 3.8% 5.0% 125 Appendix C Non-Structural Damage Probability Matrices Table C.5: Light Metal Frame Damage Probability Matrices 1 Light Metal Frame (LMF) Displacement Sensitive Damage State CDF(%) VI Vll VIII IX X XI XII None 0 65.1% 49.7% 48.5% 36.5% 30.4% 25.9% 22.9% Slight 2 9.0% 11.0% 11.1% 11.5% 11.4% 11.0% 10.6% Moderate 10 11.7% 15.4% 15.6% 17.4% 17.8% 17.9% 17.7% Extensive 50 6.7% 9.3% 9.4% 10.9% 11.3% 11.4% 11.4% Complete 80 7.5% 14.7% 15.4% 23.7% 29.1% 33.7% 37.3% Acceleration Sensitive Damage State CDF VI Vll VIII IX X XI XII None 0 80.7% 55.0% 52.4% 35.6% 29.3% 27.9% 25.3% Slight 2 16.7% 33.1% 34.3% 39.4% 39.8% 39.7% 39.3% Moderate 10 2.6% 10.8% 11.9% 21.0% 25.1% 26.1% 28.0% Extensive 50 0.1% 1.1% 1.4% 3.7% 5.4% 5.8% 6.8% Complete 80 0.0% 0.0% 0.1% 0.2% 0.4% 0.5% 0.6% Contents Damage State CDF VI Vll VIII IX X XI XII None 0 80.7% 55.0% 52.4% 35.6% 29.3% 27.9% 25.3% Slight 1 16.7% 33.1% 34.3% 39.4% 39.8% 39.7% 39.3% Moderate 5 2.6% 10.8% 11.9% 21.0% 25.1% 26.1% 28.0% Extensive 25 0.1% 1.1% 1.4% 3.7% 5.4% 5.8% 6.8% Complete 40 0.0% 0.0% 0.1% 0.2% 0.4% 0.5% 0.6% 126 Appendix C Non-Structural Damage Probability Matrices Table C.6: Steel Moment Frame Low Rise Damage Probability Matrices Steel Moment Frame Low Rise (SMFLR) Displacement Sensit ive Damage State CDF(%) VI VII VIII IX X XI XII None 0 6 8 . 1 % 48 .2% 46 .7% 40 .2% 33 .6% 29 .7% 25 .3% Slight 2 10.9% 13.0% 1 3 . 1 % 13.0% 12.5% 1 2 . 1 % 11.3% Moderate 10 1 3 . 1 % 19.5% 19.8% 2 1 . 1 % 21 .8% 21 .9% 21 .6% Extensive 50 2 .4% 5.7% 6.0% 7.5% 9.0% 9.9% 11.0% Complete 80 5.5% 13.5% 14.3% 18.2% 2 3 . 1 % 26 .4% 30.7% Accelerat ion Sensit ive Damage State CDF VI VII VIII IX X XI XII None 0 89 .0% 63 .0% 57.6% 47 .7% 41 .2% 35 .6% 32.3% Slight 2 9.9% 28 .7% 31.8% 36.2% 38 .3% 39.4% 39.7% Moderate 10 1.0% 7.4% 9.5% 13.9% 17.2% 20 .5% 22 .6% Extensive 50 0.0% 0.8% 1.1% 2 . 1 % 3.0% 4 . 1 % 5.0% Complete 80 0.0% 0.0% 0.0% 0 . 1 % 0.2% 0.3% 0.4% Contents Damage State C D F VI VII VIII IX X XI XII None 0 89 .0% 63 .0% 57.6% 47 .7% 41 .2% 35 .6% 32.3% Slight 1 9.9% 28 .7% 31 .8% 36 .2% 38 .3% 39 .4% 39.7% Moderate 5 1.0% 7.4% 9.5% 13.9% 17.2% 20 .5% 22 .6% Extensive 25 0.0% 0.8% 1 .1% 2 . 1 % 3.0% 4 . 1 % 5.0% Complete 40 0.0% 0.0% 0.0% 0 . 1 % 0.2% 0.3% 0.4% 127 Appendix C Non-Structural Damage Probability Matrices Table C.7: Steel Moment Frame Medium Rise Damage Probability Matrices Steel Moment Frame Medium Rise (SMFMR) Displacement Sensitive Damage State CDF(%) VI Vll VIII IX X XI XII None 0 73.2% 49.9% 48.8% 45.9% 37.8% 33.9% 19.4% Slight 2 10.0% 14.4% 14.5% 14.7% 15.0% 14.9% 12.9% Moderate 10 8.2% 15.8% 16.2% 17.1% 19.4% 20.4% 22.8% Extensive 50 2.0% 5.0% 5.2% 5.7% 7.0% 7.7% 10.5% Complete 80 6.6% 14.8% 15.3% 16.6% 20.8% 23.1% 34.4% Acceleration Sensitive Damage State CDF VI Vll VIII IX X XI XII None 0 98.5% 86.7% 89.3% 81.0% 72.1% 55.0% 52.5% Slight 2 1.5% 11.6% 9.5% 16.1% 22.6% 32.7% 33.9% Moderate 10 0.1% 1.6% 1.1% 2.7% 5.0% 10.9% 12.0% Extensive 50 0.0% 0.1% 0.0% 0.2% 0.4% 1.4% 1.6% Complete 80 0.0% 0.0% 0.0% 0.0% 0.0% 0.1% 0.1% Contents Damage State CDF VI Vll VIII IX X XI XII None 0 98.5% 86.7% 89.3% 81.0% 72.1% 55.0% 52.5% Slight 1 1.5% 11.6% 9.5% 16.1% 22.6% 32.7% 33.9% Moderate 5 0.1% 1.6% 1.1% 2.7% 5.0% 10.9% 12.0% Extensive 25 0.0% 0.1% 0.0% 0.2% 0.4% 1.4% 1.6% Complete 40 0.0% 0.0% 0.0% 0.0% 0.0% 0.1% 0.1% 128 Appendix C Non-Structural Damage Probability Matrices Table C.8: Steel Moment Frame High Rise Damage Probability Matrices Steel Moment Frame High Rise (SMFHR) Displacement Sensit ive Damage State CDF(%) VI VII VIII IX X XI XII None 0 73 .9% 72 .4% 69 .3% 50 .8% 4 1 . 2 % 33 .2% 27 .0% Slight 2 9.8% 10.2% 11.0% 14.3% 15.0% 14.9% 14.3% Moderate 10 8.2% 8.7% 9.8% 15.8% 18.7% 2 0 . 8 % 22 .0% Extensive 50 1.7% 1.9% 2.2% 4 .6% 6.2% 7.6% 8.9% Complete 80 6 .4% 6.8% 7.7% 14.4% 18.9% 2 3 . 5 % 27 .8% Accelerat ion Sensit ive Damage State CDF VI VII VIII IX X XI XII None 0 99 .9% 99.3% 98.5% 97.3% 89 .3% 86.7% 83.9% Slight 2 0 . 1 % 0.7% 1.4% 2.5% 9.4% 11.5% 13.7% Moderate 10 0.0% 0.0% 0 . 1 % 0.2% 1.2% 1.7% 2.2% Extensive 50 0.0% 0.0% 0.0% 0.0% 0 . 1 % 0 . 1 % 0 . 1 % Complete 80 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% Contents Damage State C D F VI VII VIII IX X XI XII None 0 99 .9% 99.3% 98.5% 97.3% 89 .3% 86 .7% 83.9% Slight 1 0 . 1 % 0.7% 1.4% 2.5% 9.4% 11.5% 13.7% Moderate 5 0.0% 0.0% 0 . 1 % 0.2% 1.2% 1.7% 2.2% Extensive 25 0.0% 0.0% 0.0% 0.0% 0 . 1 % 0 . 1 % 0 . 1 % Complete 40 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 129 Appendix C Non-Structural Damage Probability Matrices Table C.9: Steel Braced Frame Low Rise Damage Probability Matrices Steel Braced Frame Low Rise (SBFLR) j Displacement Sensitive Damage State CDF(%) VI Vll VIII IX X XI XII None 0 72.0% 56.3% 53.3% 43.6% 37.6% 32.7% 29.3% Slight 2 7.5% 10.2% 10.6% 11.4% 11.6% 11.6% 11.5% Moderate 10 11.1% 15.2% 15.9% 17.5% 18.0% 18.2% 18.2% Extensive 50 4.6% 7.5% 8.1% 9.6% 10.5% 11.0% 11.3% Complete 80 4.7% 10.7% 12.2% 17.9% 22.2% 26.4% 29.7% Acceleration Sensitive Damage State CDF VI Vll VIII IX X XI XII None 0 81.0% 50.0% 45.4% 35.4% 29.0% 27.6% 25.0% Slight 2 16.3% 35.3% 37.1% 39.6% 40.0% 40.0% 39.6% Moderate 10 2.5% 12.6% 14.8% 20.3% 24.3% 25.2% 27.0% Extensive 50 0.2% 2.0% 2.5% 4.3% 6.1% 6.5% 7.5% Complete 80 0.0% 0.1% 0.2% 0.4% 0.6% 0.7% 0.8% Contents Damage State CDF VI Vll VIII IX X XI XII None 0 81.0% 50.0% 45.4% 35.4% 29.0% 27.6% 25.0% Slight 1 16.3% 35.3% 37.1% 39.6% 40.0% 40.0% 39.6% Moderate 5 2.5% 12.6% 14.8% 20.3% 24.3% 25.2% 27.0% Extensive 25 0.2% 2.0% 2.5% 4.3% 6.1% 6.5% 7.5% Complete 40 0.0% 0.1% 0.2% 0.4% 0.6% 0.7% 0.8% 130 Appendix C Non-Structural Damage Probability Matrices Table C.10: Steel Braced Frame Medium Rise Damage Probability Matrices Steel Braced Frame Medium Rise (SBFMR) Displacement Sensit ive Damage State CDF(%) VI VII VIII IX X XI XII None 0 73 .3% 56.7% 53.7% 52.0% 45 .8% 39 .4% 34.7% Slight 2 10.6% 13.8% 1 4 . 1 % 14.2% 14.6% 14.6% 14.3% Moderate 10 7.9% 13.6% 14.6% 15.2% 17.2% 1 9 . 1 % 20 .4% Extensive 50 1.7% 3.8% 4 .2% 4 .5% 5.5% 6.6% 7.4% Complete 80 6.5% 12.2% 13.4% 1 4 . 1 % 17.0% 20 .4% 23 .2% Accelerat ion Sensit ive Damage State CDF VI VII VIII IX X XI XII None 0 95 .8% 86 .7% 7 2 . 1 % 63 .2% 52 .5% 47 .6% 43 .2% Slight 2 4 .0% 11.9% 2 3 . 1 % 28 .8% 34 .6% 36.6% 38.2% Moderate 10 0.2% 1.4% 4.5% 7.3% 11.5% 13.8% 1 6 . 1 % Extensive 50 0.0% 0 . 1 % 0.3% 0.6% 1.4% 1.8% 2.4% Complete 80 0.0% 0.0% 0.0% 0.0% 0 . 1 % 0 . 1 % 0 . 1 % Contents Damage State CDF VI VII VIII IX X XI XII None 0 95 .8% 86.7% 7 2 . 1 % 63 .2% 52 .5% 47 .6% 43 .2% Slight 1 4 .0% 11.9% 2 3 . 1 % 28 .8% 34 .6% 36 .6% 38.2% Moderate 5 0.2% 1.4% 4.5% 7.3% 11.5% 13.8% 1 6 . 1 % Extensive 25 0.0% 0 . 1 % 0.3% 0.6% 1.4% 1.8% 2.4% Complete 40 0.0% 0.0% 0.0% 0.0% 0 . 1 % 0 . 1 % 0 . 1 % 131 Appendix C Non-Structural Damage Probability Matrices Table C . l l : Steel Braced Frame High Rise Damage Probability Matrices Steel Braced Frame High Rise (SBFHR) Displacement Sensitive Damage State CDF(%) VI Vll VIII IX X XI XII None 0 77.3% 63.7% 60.5% 55.2% 44.5% 37.6% 31.9% Slight 2 9.4% 12.7% 13.3% 14.1% 14.9% 14.9% 14.5% Moderate B 10 7.5% 12.4% 13.5% 15.4% 18.8% 20.7% 22.0% 1 Extensive 50 0.6% 1.9% 2.3% 3.1% 4.8% 6.1% 7.3% Complete 80 5.1% 9.2% 10.3% 12.4% 17.1% 20.7% 24.3% Acceleration Sensitive Damage State CDF VI Vll VIII IX X XI XII None 0 99.9% 92.1% 89.7% 87.1% 75.4% 66.4% 57.8% Slight 2 0.1% 7.3% 9.3% 11.5% 20.6% 26.8% 31.9% Moderate 10 0.0% 0.6% 1.0% 1.4% 3.7% 6.3% 9.3% Extensive 50 0.0% 0.0% 0.0% 0.1% 0.2% 0.5% 1.0% Complete 80 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% Contents Damage State CDF VI Vll VIII IX X XI XII None 0 99.9% 92.1% 89.7% 87.1% 75.4% 66.4% 57.8% Slight 1 0.1% 7.3% 9.3% 11.5% 20.6% 26.8% 31.9% Moderate 5 0.0% 0.6% 1.0% 1.4% 3.7% 6.3% 9.3% Extensive 25 0.0% 0.0% 0.0% 0.1% 0.2% 0.5% 1.0% Complete 40 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 132 Appendix C Non-Structural Damage Probability Matrices Table C.12: Steel frame with Concrete Walls Low Rise Damage Probability Matrices Steel frame with Concrete Walls Low Rise (SFCWLR) Displacement Sensit ive Damage State CDF(%) VI VII VIII IX X XI XII None 0 70 .6% 51 .8% 51.4% 44 .0% 37 .8% 33 .4% 30.5% Slight 2 7.3% 1 0 . 1 % 1 0 . 1 % 10.7% 10.9% 10.8% 10.7% Moderate 10 12.0% 16.2% 16.3% 17.2% 17.5% 17.5% 17.3% Extensive 50 4 .6% 8.0% 8.0% 9.2% 1 0 . 1 % 10.6% 10.8% Complete 80 5.4% 13.9% 1 4 . 1 % 18.9% 23 .7% 2 7 . 7 % 30.7% Accelerat ion Sensit ive Damage State C D F VI VII VIII IX X XI XII None 0 67 .7% 55.5% 47 .4% 30.8% 27 .7% 24 .9% 24 .9% Slight 2 27 .2% 3 5 . 1 % 39.3% 44 .2% 44 .4% 44 .2% 44 .2% Moderate 10 4 .7% 8.5% 11.8% 20 .7% 22 .8% 24 .9% 24 .9% Extensive 50 0.4% 0.9% 1.5% 3.9% 4 .7% 5.6% 5.6% Complete 80 0.0% 0.0% 0 . 1 % 0.3% 0.4% 0.5% 0.5% Contents Damage State CDF VI VII VIII IX X XI XII None 0 67 .7% 55.5% 47 .4% 30 .8% 27 .7% 24 .9% 24 .9% Slight 1 27 .2% 3 5 . 1 % 39.3% 44 .2% 4 4 . 4 % 44 .2% 44 .2% Moderate 5 4 .7% 8.5% 11.8% 20 .7% 22 .8% 24 .9% 24 .9% Extensive 25 0.4% 0.9% 1.5% 3.9% 4 .7% 5.6% 5.6% Complete 40 0.0% 0.0% 0 . 1 % 0.3% 0.4% 0.5% 0.5% 133 Appendix C Non-Structural Damage Probability Matrices Table C.13: Steel frame with Concrete Walls Medium Rise Damage Probability Matrices Steel frame with Concrete Walls Medium Rise (SFCWMR) Displacement Sensitive Damage State CDF(%) VI Vll VIII IX X XI XII None 0 80.1% 57.4% 56.4% 55.0% 48.9% 41.1% 35.4% Slight 2 7.5% 12.5% 12.6% 12.8% 13.4% 13.9% 13.8% Moderate 10 5.0% 12.0% 12.-3% 12.8% 14.6% 16.8% 18.3% Extensive 50 1.7% 4.4% 4.6% 4.8% 5.6% 6.7% 7.6% Complete 80 5.7% 13.7% 14.1% 14.7% 17.5% 21.5% 24.8% Acceleration Sensitive Damage State CDF VI Vll VIII IX X XI XII None 0 94.2% 66.4% 69.3% 55.1% 47.6% 43.1% 41.0% Slight 2 5.4% 26.8% 24.9% 33.3% 36.7% 38.3% 38.9% Moderate 10 0.4% 6.3% . 5.4% 10.4% 13.8% 16.1% 17.3% Extensive 50 0.0% 0.5% 0.4% 1.1% 1.8% 2.4% 2.7% Complete 80 0.0% 0.0% 0.0% 0.0% 0.1% 0.1% 0.1% Contents Damage State CDF VI Vll VIII IX X XI XII None 0 94.2% 66.4% 69.3% 55.1% 47.6% 43.1% 41.0% Slight 1 5.4% 26.8% 24.9% 33.3% 36.7% 38.3% 38.9% Moderate 5 0.4% 6.3% 5.4% 10.4% 13.8% 16.1% 17.3% Extensive 25 0.0% 0.5% 0.4% 1.1% 1.8% 2.4% 2.7% Complete 40 0.0% 0.0% 0.0% 0.0% 0.1% 0.1% 0.1% 134 Appendix C Non-Structural Damage Probability Matrices Table C.14: Steel frame with Concrete Walls High Rise Damage Probability Matrices Steel frame with Concrete Walls High Rise (SFCWHR) Displacement Sensit ive Damage State CDF(%) VI Vll VIII IX X XI XII None 0 81.9% 65.3% 64.2% 60.7% 50.0% 38.3% 32.5% Slight 2 5.5% 10.0% 10.2% 11.0% 13.1% 14.4% 14.7% Moderate 10 5.8% 10.8% 11.1% 12.1% 15.1% 17.9% 19.1% Extensive 50 1.8% 3.7% 3.8% 4.3% 5.6% 7.3% 8.2% Complete 80 5.0% 10.2% 10.6% 11.9% 16.2% 22.1% 25.6% Accelerat ion Sensit ive Damage State CDF VI Vl l VIII IX X XI XII None 0 99.6% 89.7% 87.1% 84.3% 69.3% 57.8% 55.1% Slight 2 0.4% 9.2% 11.4% 13.7% 24.6% 31.5% 32.9% Moderate 10 0.0% 1.0% 1.5% 2.0% 5.6% 9.6% 10.7% Extensive 50 0.0% 0.0% 0.1% 0.1% 0.5% 1.0% 1.2% Complete 80 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.1% Contents Damage State C D F VI Vl l VIII IX X XI XII None 0 99.6% 89.7% 87.1% 84.3% 69.3% 57.8% 55.1% Slight 1 0.4% 9.2% 11.4% 13.7% 24.6% 31.5% 32.9% Moderate 5 0.0% 1.0% 1.5% 2.0% 5.6% 9.6% 10.7% Extensive 25 0.0% 0.0% 0.1% 0.1% 0.5% 1.0% 1.2% Complete 40 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.1% 135 Appendix C Non-Structural Damage Probability Matrices Table C.15: Steel Frame with Concrete Infill Walls Damage Probability Matrices | Steel Frame with Concrete Infill Walls (SFCI) j Displacement Sensit ive Damage State CDF(%) VI VII VIII IX X XI XII None 0 70.6% 53.0% 51.4% 44.0% 37.8% 33.4% 30.5% | Slight 2 7.3% 9.9% 10.1% 10.7% 10.9% 10.8% 10.7% Moderate 10 12.0% 16.0% 16.3% 17.2% 17.5% 17.5% 17.3% Extensive 50 4.6% 7.8% 8.0% 9.2% 10.1% 10.6% 10.8% Complete 80 5.4% 13.2% 14.1% 18.9% 23.7% 27.7% 30.7% Accelerat ion Sensit ive Damage State CDF VI VII VIII IX X XI XII None 0 72.1% 60.4% 52.5% 35.4% 32.1% 29.0% 29.0% Slight 2 22.8% 30.1% 34.2% 39.6% 40.0% 40.0% 40.0% Moderate 10 4.7% 8.5% 11.8% 20.7% 22.8% 24.9% 24.9% Extensive 50 0.4% 0.9% 1.5% 3.9% 4.7% 5.6% 5.6% Complete 80 0.0% 0.0% 0.1% 0.3% 0.4% 0.5% 0.5% Contents Damage State CDF VI VII VIII IX X XI XII None 0 72.1% 60.4% 52.5% 35.4% 32.1% 29.0% 29.0% Slight 1 22.8% 30.1% 34.2% 39.6% 40.0% 40.0% 40.0% Moderate 5 4.7% 8.5% 11.8% 20.7% 22.8% 24.9% 24.9% Extensive 25 0.4% 0.9% 1.5% 3.9% 4.7% 5.6% 5.6% Complete 40 0.0% 0.0% 0.1% 0.3% 0.4% 0.5% 0.5% 136 Appendix C Non-Structural Damage Probability Matrices Table C.16: Steel Frame with Masonry Infill Walls Damage Probability Matrices |Steel Frame with Masonry Infill Walls (SFMI) j Displacement Sensitive Damage State CDF(%) VI VII VIII IX X XI XII None 0 70.6% 53.0% 52.2% 44.0% 37.8% 33.4% 30.5% Slight 2 7.3% 9.9% 10.0% 10.7% 10.9% 10.8% 10.7% Moderate 10 12.0% 16.0% 16.2% 17.2% 17.5% 17.5% 17.3% Extensive 50 4.6% 7.8% 7.9% 9.2% 10.1% 10.6% 10.8% Complete 80 5.4% 13.2% 13.7% 18.9% 23.7% 27.7% 30.7% Acceleration Sensitive Damage State CDF VI VII VIII IX X XI XII None 0 72.4% 60.6% 52.5% 35.2% 31.8% 28.7% 28.7% Slight 2 22.8% 30.3% 34.6% 40.2% 40.5% 40.6% 40.6% Moderate 10 4.5% 8.3% 11.5% 20.6% 22.8% 24.9% 24.9% Extensive 50 0.3% 0.8% 1.4% 3.7% 4.5% 5.4% 5.4% Complete 80 0.0% 0.0% 0.1% 0.2% 0.3% 0.4% 0.4% Contents Damage State CDF VI VII VIII IX X XI XII None 0 72.4% 60.6% 52.5% 35.2% 31.8% 28.7% 28.7% Slight 1 22.8% 30.3% 34.6% 40.2% 40.5% 40.6% 40.6% Moderate 5 4.5% 8.3% 11.5% 20.6% 22.8% 24.9% 24.9% Extensive 25 0.3% 0.8% 1.4% 3.7% 4.5% 5.4% 5.4% Complete 40 0.0% 0.0% 0.1% 0.2% 0.3% 0.4% 0.4% 137 Appendix C Non-Structural Damage Probability Matrices Table C.17: Concrete Frame with Concrete Walls Low Rise Damage Probability Matrices Concrete Frame with Concrete Walls Low Rise (CFLR) Displacement Sensit ive Damage State CDF(%) VI Vl l VIII IX X XI XII None 0 70.3% 53.2% 52.2% 44.3% 36.7% 32.6% 28.7% Slight 2 8.1% 10.5% 10.6% 11.1% 11.2% 11.0% 10.8% Moderate 10 9.4% 13.7% 14.0% 15.5% 16.7% 17.1% 17.3% Extensive 50 6.6% 9.6% 9.7% 10.7% 11.4% 11.5% 11.6% Complete 80 5.7% 12.9% 13.5% 18.4% 24.1% 27.7% 31.6% Accelerat ion Sensit ive Damage State CDF VI Vl l VIII IX X XI XII None 0 80.3% 47.7% 45.5% 28.2% 21.3% 18.5% 16.9% Slight 2 17.0% 36.2% 37.0% 39.4% 37.8% 36.5% 35.6% Moderate 10 2.5% 13.7% 14.8% 25.2% 30.2% 32.3% 33.5% Extensive 50 0.2% 2.2% 2.5% 6.5% 9.5% 11.1% 12.2% Complete 80 0.0% 0.1% 0.2% 0.7% 1.2% 1.5% 1.8% Contents Damage State C D F VI Vl l VIII IX X XI XII None 0 80.3% 47.7% 45.5% 28.2% 21.3% 18.5% 16.9% Slight 1 17.0% 36.2% 37.0% 39.4% 37.8% 36.5% 35.6% Moderate 5 2.5% 13.7% 14.8% 25.2% 30.2% 32.3% 33.5% Extensive 25 0.2% 2.2% 2.5% 6.5% 9.5% 11.1% 12.2% Complete 40 0.0% 0.1% 0.2% 0.7% 1.2% 1.5% 1.8% 138 Appendix C Non-Structural Damage Probability Matrices Table C.18: Concrete Frame with Concrete Walls Medium Rise Damage Probability Matrices Concrete Frame with Concrete Walls Medium Rise (CFMR) Displacement Sensitive Damage State CDF(%) VI Vll VIII IX X XI XII None 0 77.7% 61.1% 60.4% 55.0% 48.3% 43.5% 39.9% Slight 2 9.3% 12.4% 12.5% 13.0% 13.2% 13.1% 12.9% Moderate 10 7.9% 14.0% 14.3% 16.1% 18.0% 19.3% 20.1% Extensive 50 0.3% 2.0% 2.1% 2.9% 4.0% 5.0% 5.8% Complete 80 4.8% 10.4% 10.7% 13.1% 16.4% 19.1% 21.3% -Acceleration Sensitive Damage State CDF VI Vll VIII IX X XI XII None 0 90.2% 63.0% 57.6% 43.3% 35.6% 29.3% 26.6% Slight 2 9.0% 29.3% 32.5% 38.5% 40.1% 40.3% 40.0% Moderate 10 0.7% 6.8% 8.8% 15.4% 19.8% 24.0% 26.0% Extensive 50 0.0% 0.8% 1.1% 2.7% 4.1% 5.8% 6.8% Complete 80 0.0% 0.0% 0.0% 0.2% 0.3% 0.5% 0.7% Contents Damage State CDF VI Vll VIII IX X XI XII None 0 90.2% 63.0% 57.6% 43.3% 35.6% 29.3% 26.6% Slight 1 9.0% 29.3% 32.5% 38.5% 40.1% 40.3% 40.0% Moderate 5 0.7% 6.8% 8.8% 15.4% 19.8% 24.0% 26.0% Extensive 25 0.0% 0.8% 1.1% 2.7% 4.1% 5.8% 6.8% Complete 40 0.0% 0.0% 0.0% 0.2% 0.3% 0.5% 0.7% 139 Appendix C Non-Structural Damage Probability Matrices Table C.19: Concrete Frame with Concrete Walls High Rise Damage Probability Matrices Concrete Frame with Concrete Walls High Rise (CFHR) Displacement Sensit ive Damage State CDF(%) VI VII VIII IX X XI XII None 0 79 .2% 65 .0% 6 4 . 1 % 58 .9% 52.6% 47 .2% 41 .5% Slight 2 8 . 1 % 11.7% 11.9% 12.8% 13.7% 14.2% 14.5% Moderate 10 5.8% 10.3% 10.6% 12.3% 14.3% 16.0% 17.7% Extensive 50 1.5% 3 . 1 % 3.2% 3.9% 4 .8% 5.5% 6.4% Complete 80 5.4% 9.9% 10.2% 1 2 . 1 % 14.7% 17.0% 19.9% Accelerat ion Sensit ive Damage State CDF VI VII VIII IX X XI XII None 0 98 .9% 83.9% 7 8 . 1 % 7 5 . 1 % 60 .4% 55.0% 45 .4% Slight 2 1 .1% 14.2% 18.7% 21 .0% 30 .5% 33 .4% 37.5% Moderate 10 0.0% 1.8% 3.0% 3.7% 8.3% 10.4% 15.0% Extensive 50 0.0% 0 . 1 % 0.2% 0.2% 0.8% 1 .1% 2 . 1 % Complete 80 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0 . 1 % Contents Damage State CDF VI VII VIII IX X XI XII None 0 98 .9% 83.9% 7 8 . 1 % 7 5 . 1 % 60 .4% 55 .0% 45 .4% Slight 1 1 .1% 14.2% 18.7% 21 .0% 30 .5% 33 .4% 37.5% Moderate 5 0.0% 1.8% 3.0% 3.7% 8.3% 10.4% 15.0% Extensive 25 0.0% 0 . 1 % 0.2% 0.2% 0.8% 1 .1% 2 . 1 % Complete 40 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0 . 1 % 140 Appendix C Non-Structural Damage Probability Matrices Table C.20: Reinforced Concrete Moment Frame Low Rise Damage Probability Matrices Reinforced Concrete Moment Frame Low Rise (RCMFLR) Displacement Sensitive Damage State CDF(%) VI Vll VIII IX X XI XII None 0 68.1% 49.4% 48.5% 39.6% 33.8% 29.3% 26.6% Slight 2 8.9% 11.2% 11.3% 11.5% 11.4% 11.1% 10.8% Moderate 10 12.1% 16.8% 17.0% 18.2% 18.6% 18.7% 18.5% Extensive 50 5.7% 9.3% 9.5% 10.9% 11.6% 12.0% 12.1% Complete 80 5.2% 13.3% 13.8% 19.7% 24.5% 28.9% 31.9% Acceleration Sensitive Damage State CDF VI Vll VIII IX X XI XII None 0 86.3% 60.3% 57.6% 41.2% 33.9% 30.8% 27.9% Slight 2 12.1% 30.3% 31.8% 38.3% 39.6% 39.8% 39.7% Moderate 10 1.5% 8.5% 9.6% 17.4% 21.8% 23.9% 25.8% Extensive 50 0.1% 0.9% 1.0% 2.9% 4.3% 5.2% 6.1% Complete 80 0.0% 0.0% 0.0% 0.2% 0.3% 0.4% 0.5% Contents Damage State CDF VI Vll VIII IX X XI XII None 0 86.3% 60.3% 57.6% 41.2% 33.9% 30.8% 27.9% Slight 1 12.1% 30.3% 31.8% 38.3% 39.6% 39.8% 39.7% Moderate 5 1.5% 8.5% 9.6% 17.4% 21.8% 23.9% 25.8% Extensive 25 0.1% 0.9% 1.0% 2.9% 4.3% 5.2% 6.1% Complete 40 0.0% 0.0% 0.0% 0.2% 0.3% 0.4% 0.5% 141 Appendix C Non-Structural Damage Probability Matrices Table C.21: Reinforced Concrete Moment Frame Medium Rise Damage Probability Matrices Reinforced Concrete Moment Frame Medium Rise (RCMFMR) Displacement Sensit ive Damage State CDF(%) VI VII VIII IX X XI XII None 0 74 .0% 52.7% 51.7% 48 .6% 42 .6% 36 .7% 31.9% Slight 2 10.4% 13.9% 13.9% 1 4 . 1 % 14.2% 13.9% 13.4% Moderate 10 7.5% 14.7% 1 5 . 1 % 1 6 . 1 % 17.9% 19.6% 20.7% Extensive 50 1.7% 4 .4% 4.6% 5 . 1 % 6 . 1 % 7 . 1 % 8.0% Complete 80 6 .4% 14.3% 14.7% 16.2% 19.3% 22 .8% 26 .0% 1 Accelerat ion Sensit ive Damage State C D F VI VII VIII IX X XI XII None 0 95.8% 7 8 . 1 % 7 5 . 1 % 60 .4% 52 .5% 45 .4% 4 1 . 1 % Slight 2 4 .0% 18.7% 21 .0% 30.5% 34 .6% 37 .5% 38.8% Moderate 10 0.2% 3 . 1 % 3.8% 8.4% 11.8% 15.3% 17.6% Extensive 50 0.0% 0 . 1 % 0.2% 0.6% 1 . 1 % 1.8% 2.4% Complete 80 0.0% 0.0% 0.0% 0.0% 0.0% 0 . 1 % 0 . 1 % Contents Damage State C D F VI VII VIII IX X XI XII None 0 95 .8% 7.8.1% 7 5 . 1 % 60 .4% 52 .5% 45 .4% 4 1 . 1 % Slight 1 4 .0% 18.7% 21 .0% 30.5% 34 .6% 37 .5% 38.8% Moderate 5 0.2% 3 . 1 % 3.8% 8.4% 11.8% 15.3% 17.6% Extensive 25 0.0% 0 . 1 % 0.2% 0.6% 1 .1% 1.8% 2.4% Complete 40 0.0% 0.0% 0.0% 0.0% 0.0% 0 . 1 % 0 . 1 % 142 Appendix C Non-Structural Damage Probability Matrices Table C.22: Reinforced Concrete Moment Frame High Rise Damage Probability Matrices Reinforced Concrete Moment Frame High Rise (RCMFHR) Displacement Sensitive Damage State CDF(%) VI Vll VIII IX X XI XII None 0 76.2% 56.4% 54.8% 48.8% 38.1% 30.7% 24.9% Slight 2 7.9% 12.4% 12.6% 13.5% 14.3% 14.3% 13.8% Moderate 10 6.7% 12.7% 13.1% 14.9% 17.7% 19.5% 20.5% Extensive 50 2.2% 4.6% 4.8% 5.6% 7.1% 8.2% 9.1% Complete 80 7.0% 14.0% 14.6% 17.3% 22.7% 27.3% 31.7% Acceleration Sensitive Damage State CDF VI Vll VIII IX X XI XII None 0 99.6% 96.0% 94.2% 87.1% 84.3% 79.9% 78.4% Slight 2 0.4% 3.7% 5.3% 11.3% 13.5% 16.9% 18.0% Moderate 10 0.0% 0.3% 0.5% 1.6% 2.1% 3.0% 3.4% Extensive 50 0.0% 0.0% 0.0% 0.1% 0.1% 0.2% 0.2% Complete 80 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% Contents Damage State CDF VI Vll VIII IX X XI XII None 0 99.6% 96.0% 94.2% 87.1% 84.3% 79.9% 78.4% Slight 1 0.4% 3.7% 5.3% 11.3% 13.5% 16.9% 18.0% Moderate 5 0.0% 0.3% 0.5% 1.6% 2.1% 3.0% 3.4% Extensive 25 0.0% 0.0% 0.0% 0.1% 0.1% 0.2% 0.2% Complete 40 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 143 Appendix C Non-Structural Damage Probability Matrices Table C.23: Reinforced Concrete Frame with Infill Walls Damage Probability Matrices Reinforced Concrete Frame with Infill Walls (RCFIW) Displacement Sensit ive Damage State CDF(%) VI VII VIII IX X XI XII None 0 67.4% 45.7% 44.9% 34.0% 26.0% 19.9% 10.5% Slight 2 9.7% 12.5% 12.5% 12.7% 12.1% 11.1% 8.3% Moderate 10 11.9% 17.6% 17.8% 19.5% 19.9% 19.5% 16.9% Extensive 50 5.1% 8.9% 9.1% 10.8% 11.7% 12.2% 11.7% Complete 80 5.9% 15.2% 15.7% 23.1% 30.3% 37.3% 52.6% Accelerat ion Sensit ive Damage State C D F VI VII VIII IX X XI XII None 0 82.1% 50.0% 47.0% 44.2% 44.2% 44.2% 44.2% Slight 2 15.2% 35.0% 36.2% 37.2% 37.2% 37.2% 37.2% Moderate 10 2.6% 13.3% 14.7% 16.1% 16.1% 16.1% 16.1% Extensive 50 0.1% 1.7% 2.0% 2.4% 2.4% 2.4% 2.4% Complete 80 0.0% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% Contents Damage State CDF VI VII VIII IX X XI XII None 0 82.1% 50.0% 47.0% 44.2% 44.2% 44.2% 44.2% Slight 1 15.2% 35.0% 36.2% 37.2% 37.2% 37.2% 37.2% Moderate 5 2.6% 13.3% 14.7% 16.1% 16.1% 16.1% 16.1% Extensive 25 0.1% 1.7% 2.0% 2.4% 2.4% 2.4% 2.4% Complete 40 0.0% 0.1% 0.1% 0.1% 0.1% 0.1% 0.1% 144 Appendix C Non-Structural Damage Probability Matrices Table C.24: Reinforced Masonry Shear Wall Low Rise Damage Probability Matrices Reinforced Masonry Shear Wall Low Rise (RMLR) Displacement Sensitive Damage State CDF(%) VI Vll VIII IX X XI XII None 0 68.2% 61.0% 59.4% 45.1% 37.9% 33.8% 30.1% Slight 2 7.7% 8.9% 9.1% 10.5% 10.8% 10.8% 10.6% Moderate 10 9.8% 11.5% 11.9% 14.7% 15.7% 16.1% 16.4% Extensive 50 7.0% 8.2% 8.5% 10.2% 10.8% 10.9% 10.9% Complete 80 7.3% 10.4% 11.1% 19.4% 24.8% 28.4% 32.0% Acceleration Sensitive Damage State CDF VI Vll VIII IX X XI XII None 0 74.4% 43.4% 41.4% 25.7% 19.4% 16.9% 14.7% Slight 2 21.1% 37.3% 37.8% 38.8% 36.9% 35.6% 34.1% Moderate 10 4.1% 16.5% 17.6% 27.5% 32.1% 33.9% 35.4% Extensive 50 0.3% 2.7% 3.0% 7.3% 10.4% 12.0% 13.7% Complete 80 0.0% 0.2% 0.2% 0.7% 1.3% 1.7% 2.1% Contents Damage State CDF VI Vll VIII IX X XI XII None 0 74.4% 43.4% 41.4% 25.7% 19.4% 16.9% 14.7% Slight 1 21.1% 37.3% 37.8% 38.8% 36.9% 35.6% 34.1% Moderate 5 4.1% 16.5% 17.6% 27.5% 32.1% 33.9% 35.4% Extensive 25 0.3% 2.7% 3.0% 7.3% 10.4% 12.0% 13.7% Complete 40 0.0% 0.2% 0.2% 0.7% 1.3% 1.7% 2.1% 145 Appendix C Non-Structural Damage Probability Matrices Table C.25: Reinforced Masonry Shear Wall Medium Rise Damage Probability Matrices Reinforced Masonry Shear Wall Medium Rise (RMMR) 1 Displacement Sensitive I Damage State CDF(%) VI VII VIII IX X XI XII None 0 76.6% 66.2% 65.3% 55.3% 49.1% 44.3% 40.6% Slight 2 9.2% 11.3% 11.4% 12.4% 12.6% 12.6% 12.4% Moderate 10 8.9% 12.8% 13.1% 16.4% 18.1% 19.2% 19.9% Extensive 50 0.5% 1.5% 1.6% 3.1% 4.2% 5.1% 6.0% Complete 80 4.8% 8.2% 8.6% 12.8% 16.0% 18.8% 21.2% Acceleration Sensitive Damage State CDF VI VII VIII IX X XI XII None 0 90.2% 60.3% 55.0% 41.2% 32.3% 26.6% 23.0% Slight 2 9.0% 31.0% 33.8% 39.0% 40.3% 40.0% 39.2% Moderate 10 0.7% 7.8% 9.8% 16.5% 22.0% 26.0% 28.7% Extensive 50 0.0% 1.0% 1.4% 3.0% 5.0% 6.8% 8.3% Complete 80 0.0% 0.0% 0.1% 0.2% 0.4% 0.7% 0.9% Contents Damage State CDF VI VII VIII IX X XI XII None 0 90.2% 60.3% 55.0% 41.2% 32.3% 26.6% 23.0% Slight 1 9.0% 31.0% 33.8% 39.0% 40.3% 40.0% 39.2% Moderate 5 0.7% 7.8% 9.8% 16.5% 22.0% 26.0% 28.7% Extensive 25 0.0% 1.0% 1.4% 3.0% 5.0% 6.8% 8.3% Complete 40 0.0% 0.0% 0.1% 0.2% 0.4% 0.7% 0.9% 146 Appendix C Non-Structural Damage Probability Matrices Table C.26: Unreinforced Masonry Shear Wall Low Rise Damage Probability Matrices Unreinforced Masonry Shear Wall Low Rise (URMLR) Displacement Sensitive Damage State CDF(%) VI Vll VIII IX X XI XII None 0 64.5% 47.7% 45.2% 32.2% 33.7% 29.1% 26.1% Slight 2 7.9% 9.7% 9.9% 10.0% 10.1% 9.9% 9.7% Moderate 10 10.9% 14.1% 14.5% 15.5% 15.5% 15.6% 15.5% Extensive 50 8.3% 10.7% 10.9% 11.2% 11.2% 11.0% 10.8% Complete 80 8.4% 17.8% 19.6% 31.0% 29.5% 34.4% 37.9% Acceleration Sensitive Damage State CDF VI Vll VIII IX X XI XII None 0 56.2% 32.9% 3T.0% 20.5% 17.3% 15.4% 15.4% Slight 2 32.9% 39.8% 39.8% 37.6% 35.9% 34.6% 34.6% Moderate 10 9.9% 22.5% 23.8% 31.7% 34.3% 35.7% 35.7% Extensive 50 1.0% 4.4% 4.9% 9.2% 11.3% 12.7% 12.7% Complete 80 0.0% 0.3% 0.4% 1.0% 1.3% 1.6% 1.6% Contents Damage State CDF VI Vll VIII IX X XI XII None 0 56.2% 32.9% 31.0% 20.5% 17.3% 15.4% 15.4% Slight 1 32.9% 39.8% 39.8% 37.6% 35.9% 34.6% 34.6% Moderate 5 9.9% 22.5% 23.8% 31.7% 34.3% 35.7% 35.7% Extensive 25 1.0% 4.4% 4.9% 9.2% 11.3% 12.7% 12.7% Complete 40 0.0% 0.3% 0.4% 1.0% 1.3% 1.6% 1.6% 147 Appendix C Non-Structural Damage Probability Matrices Table C.27: Unreinfroced Masonry Shear Wall Medium Rise Damage Probability Matrices Unreinfroced Masonry Shear Wall Medium Rise (URMMR) Displacement Sensit ive Damage State CDF(%) VI VII VIII IX X XI XII None 0 72 .2% 58.4% 57.6% 52.2% 45 .2% 39 .7% 35.9% Slight 2 1 0 . 1 % 11.7% 11.7% 11.8% 11.6% 11.2% 10.7% Moderate 10 8.3% 12.8% 13.0% 14.6% 16.3% 17.5% 18.2% Extensive 50 2 .7% 4 .8% 4 .9% 5.8% 6.9% 7.8% 8.5% Complete 80 6.6% 12.4% 12.8% 15.7% 19.9% 23 .8% 26 .8% Accelerat ion Sensit ive Damage State C D F VI VII VIII IX X XI XII None 0 82 .5% 50 .0% 36.4% 1 9 . 1 % 15.8% 13.9% 13.9% Slight 2 15.0% 35 .3% 39 .8% 38.9% 37 .3% 3 6 . 1 % 3 6 . 1 % Moderate 10 2 .4% 12.9% 19.9% 31 .5% 33 .9% 35 .3% 35.3% Extensive 50 0 . 1 % 1.7% 3.7% 9.5% 11.5% 12.9% 12.9% Complete 80 0.0% 0 . 1 % 0.2% 1 .1% 1.5% 1.8% 1.8% Contents Damage State CDF VI VII VIII IX X XI XII None 0 82 .5% 50.0% 36.4% 1 9 . 1 % 15.8% 13.9% 13.9% Slight 1 15.0% 35.3% 39.8% 38.9% 37 .3% 3 6 . 1 % 3 6 . 1 % Moderate 5 2 .4% 12.9% 19.9% 31.5% 33 .9% 35 .3% 35.3% Extensive 25 0 . 1 % 1.7% 3.7% 9.5% 11.5% 12.9% 12.9% Complete 40 0.0% 0 . 1 % 0.2% 1 .1% 1.5% 1.8% 1.8% 148 Appendix C Non-Structural Damage Probability Matrices Table C.28: Tilt Up Damage Probability Matrices Tilt Up (TU) I Displacement Sensitive j Damage State CDF(%) VI Vll VIII IX X XI XII None 0 66.4% 57.0% 55.3% 41.4% 33.5% 28.8% 25.9% Slight 2 8.7% 10.1% 10.3% 11.4% 11.4% 11.1% 10.9% Moderate 10 10.6% 13.0% 13.4% 16.1% 17.2% 17.5% 17.6% Extensive 50 4.4% 5.8% 6.0% 7.9% 8.9% 9.4% 9.6% Complete 80 9.9% 14.1% 15.0% 23.2% 29.1% 33.2% 36.0% -Acceleration Sensitive Damage State CDF VI Vll VIII IX X XI XII None 0 68.5% 50.0% 43.4% 24.5% 16.9% 12.9% 12.3% Slight 2 25.1% 35.0% 37.3% 38.6% 35.6% 32.6% 32.0% Moderate 10 5.9% 13.3% 16.7% 28.7% 34.3% 37.0% 37.4% Extensive 50 0.5% 1.7% 2.5% 7.5% 11.8% 15.2% 15.7% Complete 80 0.0% 0.1% 0.1% 0.7% 1.5% 2.4% 2.5% Contents Damage State CDF VI Vll VIII IX X XI XII None 0 68.5% 50.0% 43.4% 24.5% 16.9% 12.9% 12.3% Slight 1 25.1% 35.0% 37.3% 38.6% 35.6% 32.6% 32.0% Moderate 5 5.9% 13.3% 16.7% 28.7% 34.3% 37.0% 37.4% Extensive 25 0.5% 1.7% 2.5% 7.5% 11.8% 15.2% 15.7% Complete 40 0.0% 0.1% 0.1% 0.7% 1.5% 2.4% 2.5% 149 Appendix C Non-Structural Damage Probability Matrices Table C.29: Precast Concrete Low Rise Damage Probability Matrices Precast Concrete Low Rise (PCLR) Displacement Sensit ive Damage State CDF(%) VI VII VIII IX X XI XII None 0 69.5% 53.1% 52.1% 42.8% 36.5% 31.8% 28.4% Slight 2 7.5% 9.9% 10.0% 10.6% 10.8% 10.7% 10.5% Moderate 10 10.5% 14.3% 14.5% 15.9% 16.5% 16.7% 16.7% Extensive 50 7.2% 10.3% 10.5% 11.6% 12.0% 12.1% 12.0% Complete 80 5.3% 12.4% 13.0% 19.1% 24.3% 28.8% 32.4% Accelerat ion Sensit ive Damage State CDF VI VII VIII IX X XI XII None 0 72.1% 55.0% 52.5% 32.1% 27.6% 26.3% 23.8% Slight 2 22.8% 33.0% 34.2% 40.0% 40.0% 39.8% 39.4% Moderate 10 4.8% 10.8% 11.9% 23.1% 26.1% 27.0% 28.8% Extensive 50 0.3% 1.1% 1.4% 4.5% 5.8% 6.3% 7.3% Complete 80 0.0% 0.0% 0.1% 0.3% 0.5% 0.5% 0.7% Contents Damage State CDF VI VII VIII IX X XI XII None 0 72.1% 55.0% 52.5% 32.1% 27.6% 26.3% 23.8% Slight 1 22.8% 33.0% 34.2% 40.0% 40.0% 39.8% 39.4% Moderate 5 4.8% 10.8% 11.9% 23.1% 26.1% 27.0% 28.8% Extensive 25 0.3% 1.1% 1.4% 4.5% 5.8% 6.3% 7.3% Complete 40 0.0% 0.0% 0.1% 0.3% 0.5% 0.5% 0.7% 150 Appendix C Non-Structural Damage Probability Matrices Table C.30: Precast Concrete Medium Rise Damage Probability Matrices Precast Concrete Medium Rise (PCMR) Displacement Sensitive Damage State CDF(%) VI Vll VIII IX X XI XII None 0 78.2% 63.3% 62.5% 53.9% 46.9% 42.4% 36.2% Slight 2 8.8% 11.8% 11.9% 12.7% 12.9% 12.9% 12.5% Moderate 10 6.4% 11.3% 11.6% 14.3% 16.3% 17.5% 19.0% Extensive 50 1.7% 3.6% 3.8% 5.0% 6.1% 6.9% 8.0% Complete 80 4.9% 10.0% 10.3% 14.1% 17.6% 20.3% 24.4% Acceleration Sensitive Damage State CDF VI Vll VIII IX X XI XII None 0 89.7% 63.4% 60.6% 47.6% 41.0% 37.0% 33.5% Slight 2 9.3% 28.6% 30.3% 36.7% 38.9% 39.9% 40.4% Moderate 10 1.0% 7.3% 8.3% 13.8% 17.3% 19.5% 21.7% Extensive 50 0.0% 0.6% 0.8% 1.8% 2.7% 3.4% 4.1% Complete 80 0.0% 0.0% 0.0% 0.1% 0.1% 0.2% 0.3% Contents Damage State CDF VI Vll VIII IX X XI XII None 0 89.7% 63.4% 60.6% 47.6% 41.0% 37.0% 33.5% Slight 1 9.3% 28.6% 30.3% 36.7% 38.9% 39.9% 40.4% Moderate 5 1.0% 7.3% 8.3% 13.8% 17.3% 19.5% 21.7% Extensive 25 0.0% 0.6% 0.8% 1.8% 2.7% 3.4% 4.1% Complete 40 0.0% 0.0% 0.0% 0.1% 0.1% 0.2% 0.3% 151 Appendix C Non-Structural Damage Probability Matrices Table C.31: Mobile Home Damage Probability Matrices Mobile Home (MH) 1 Displacement Sensit ive j Damage State CDF(%) VI VII VIII IX X XI XII None 0 62 .5% 44 .6% 43 .7% 33.3% 2 7 . 1 % 2 3 . 5 % 17.6% Slight 2 8.4% 10.8% 10.9% 11.3% 11.2% 10.9% 1 0 . 1 % Moderate 10 12.2% 15.6% 15.7% 16.7% 16.8% 16.6% 15.9% Extensive 50 8.7% 11.4% 11.5% 1 2 . 1 % 11.9% 11.6% 10.7% Complete 80 8 . 1 % 17.7% 18.3% 26 .7% 33 .0% 37 .3% 45 .7% Accelerat ion Sensit ive Damage State C D F VI VII VIII IX X XI XII None 0 75 .4% 57.8% 5 5 . 1 % 4 3 . 1 % 4 1 . 0 % 39 .0% 39.0% Slight 2 20 .2% 31 .2% 32.6% 37 .6% 38 .2% 38 .8% 38.8% Moderate 10 4 . 1 % 9.8% 10.9% 16.5% 17.6% 18.7% 18.7% Extensive 50 0.3% 1 .1% 1.4% 2.7% 3.0% 3.4% 3.4% Complete 80 0.0% 0.0% 0 . 1 % 0.2% 0.2% 0.2% 0.2% Contents Damage State C D F VI VII VIII IX X XI XII None 0 75 .4% 57.8% 5 5 . 1 % 4 3 . 1 % 41 .0% 39.0% 39.0% Slight 1 20 .2% 31 .2% 32.6% 37.6% 38 .2% 38 .8% 38.8% Moderate 5 4 . 1 % 9.8% 10.9% 16.5% 17.6% 18.7% 18.7% Extensive 25 0.3% 1 .1% 1.4% 2 .7% 3.0% 3.4% 3.4% Complete 40 0.0% 0.0% 0 . 1 % 0.2% 0.2% 0.2% 0.2% 152 

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