UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Development and application of a computer simulation framework for assessing disaster recovery in urban… Costa, Rodrigo Carneiro da 2019

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Notice for Google Chrome users:
If you are having trouble viewing or searching the PDF with Google Chrome, please download it here instead.

Item Metadata


24-ubc_2020_may_costa_rodrigo.pdf [ 27.77MB ]
JSON: 24-1.0386772.json
JSON-LD: 24-1.0386772-ld.json
RDF/XML (Pretty): 24-1.0386772-rdf.xml
RDF/JSON: 24-1.0386772-rdf.json
Turtle: 24-1.0386772-turtle.txt
N-Triples: 24-1.0386772-rdf-ntriples.txt
Original Record: 24-1.0386772-source.json
Full Text

Full Text

Development and Application of a Computer Simulation Framework forAssessing Disaster Recovery in Urban CommunitiesbyRodrigo Carneiro da CostaB. Eng., Western Parana State University, 2012M.Sc., Federal University of Rio de Janeiro, 2015A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Civil Engineering)The University of British Columbia(Vancouver)December 2019c© Rodrigo Carneiro da Costa, 2019The following individuals certify that they have read, and recommend to the Faculty of Graduate and Post-doctoral Studies for acceptance, the dissertation entitled:Development and Application of a Computer Simulation Framework for Assessing DisasterRecovery in Urban Communitiessubmitted by Rodrigo Carneiro da Costa in partial fulfillment of the requirements for the degree of Doctorof Philosophy in Civil Engineering.Examining Committee:Terje Haukaas, Department of Civil EngineeringCo-supervisorStephanie Chang, School of Community and Regional PlanningCo-supervisorBarbara Lence, Department of Civil EngineeringUniversity ExaminerSara Shneiderman, Department of AnthropologyUniversity ExaminerAdditional Supervisory Committee Members:Jose´ Martı´, Department of Electrical and Computer EngineeringSupervisory Committee MemberiiAbstractIn this dissertation an object-oriented framework of models is developed and applied to study disaster recov-ery in communities in British Columbia, Canada. The impact of earthquakes on communities is quantifiedover months and years, and the focus is on identifying the factors that affect the recovery. Contrasting withthe practice of investigating disaster impacts to infrastructure or societal systems in isolation, an integratedapproach is used in this dissertation. Lifelines, buildings, and persons are modelled in the same compu-tational environment. One contribution of this dissertation is the development of models for infrastructureand social systems of a community. Another contribution is the development of a new approach to simulatethe transportation of goods through a network of models. This new approach allows great flexibility in thecomposition of the transported goods and facilitates the modelling of the competition for resources. Anotherinnovation is the individual modelling of buildings and dwellings, in this work referred to as dwellings, inthe community. The socioeconomic demographics of the dwellings determine their capacity to compete forlimited resources, which affect their recovery capacity. The integration of socioeconomic demographics,infrastructure, and buildings in the same computational environment allows for a broad range of disastermitigation actions to be compared. This dissertation assesses the benefits of improving resource manage-ment, retrofitting physically vulnerable infrastructure, improving access to funds for recovery, among otheractions. The findings in this dissertation can inform pre-disaster plans and help identifying mitigation strate-gies that improve disaster recovery in communities in British Columbia.iiiLay SummaryThis dissertation develops a collection of computer models for studying how to reduce the impact of naturaldisasters to society. Natural disasters pose an increasing threat to urban communities. These events candamage buildings and infrastructure, causing material and life losses. Rebuilding after a natural disaster cantake several years and even be impossible for disadvantaged families. The best way to reduce the impact ofdisasters is to act before they occur. The computer models developed in this dissertation are used to informthese pre-disaster actions. Results show that a large earthquake near Vancouver can displace 70,000 persons.Of those, 19,000 would need public sheltering. Furthermore, it is demonstrated that housing recovery aftera strong earthquake in Vancouver can take more than three years.ivPrefaceI, Rodrigo Carneiro da Costa, confirm that I was responsible for reviewing the literature, deriving equations,developing models, computer programming, data processing, conducting analyses, and interpreting the re-sults in this dissertation. Several manuscripts based on this research were drafted by me and finalised inan iterative process with the dissertation advisor, Dr. Terje Haukaas, in consultation with co-supervisor Dr.Stephanie Chang. The author of this dissertation was responsible for preparing the tables and figures.In the following are listed the chapters of this dissertation that are based on versions of manuscripts thathave been accepted or submitted for publication in peer-reviewed journals or conference proceedings:The content of Chapter 3 has been published in Costa, R., Haukaas, T., Chang, S. and Dowlatabadi,H. (2018) Object-Oriented Model of the Seismic Vulnerability of the Fuel Distribution Network in CoastalBritish Columbia, Reliability Engineering and System Safety. I was the principal investigator, responsiblefor major areas of concept formation, literature analysis, as well as the majority of manuscript composition.Haukaas, T., Chang, S., and Dowlatabadi, H. were the supervisory authors on this manuscript and wereinvolved in concept formation and manuscript edits.Chapter 3 also contains material published in Costa, R., Haukaas, T., Chang, S. and Dowlatabadi, H.(2017) Network Model to Assess the Probability of Fuel Shortage Due to Earthquakes in Coastal BritishColumbia, proceedings of the 12th International Conference on Structural Safety and Reliability, 6-10 Au-gust 2017, Vienna, Austria. I was the principal investigator, responsible for major areas of concept forma-tion, literature analysis, as well as the majority of manuscript composition. Haukaas, T., Chang, S., andDowlatabadi, H. were the supervisory authors on this manuscript and were involved in concept formationand manuscript edits.A version of Chapter 4 has been submitted in September 2019 as Costa, R., Haukaas, T. and Chang,S. (n.d.) Object-Oriented Model for Post-Earthquake Housing Recovery. I was the principal investigator,vresponsible for major areas of concept formation, literature analysis, as well as the majority of manuscriptcomposition. Haukaas, T., and Chang, S., were the supervisory authors on this manuscript and were involvedin concept formation and manuscript edits.A version of Chapter 5 was submitted in November 2019 as Costa, R., Haukaas, T. and Chang, S. (n.d.)Predicting Population Displacements After Earthquakes. I was the principal investigator, responsible formajor areas of concept formation, literature analysis, as well as the majority of manuscript composition.Haukaas, T., and Chang, S., were the supervisory authors on this manuscript and were involved in conceptformation and manuscript edits.viContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vContents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 An Object-Oriented Framework for Disaster Recovery Modelling . . . . . . . . . . . . . . . 112.1 Fundamentals of Object-oriented Programming . . . . . . . . . . . . . . . . . . . . . . . . 112.2 Fundamentals of Rt and Rts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3 Network Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.4 Discrete and Continuous Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.5 Damage and Interruption of Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21vii3 Predicted Fuel Shortages in Coastal British Columbia . . . . . . . . . . . . . . . . . . . . . . 253.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.2 Modelling of Interdependent Infrastructure Systems . . . . . . . . . . . . . . . . . . . . . . 283.3 Description of the Modelling of Fuel Transportation . . . . . . . . . . . . . . . . . . . . . . 313.4 Analyses and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.4.1 Case Study: Fuel Distribution in Coastal British Columbia . . . . . . . . . . . . . . 343.4.2 Case Study: Fuel Distribution to the Powell River Community . . . . . . . . . . . . 393.5 Final Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444 Predicted Housing Recovery in the City of Vancouver . . . . . . . . . . . . . . . . . . . . . . 464.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.2 Factors Affecting Housing Recovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.3 Modelling Housing Recovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.3.1 Model 1: Housing Recovery Model . . . . . . . . . . . . . . . . . . . . . . . . . . 594.3.2 Models 2: Census Information Model . . . . . . . . . . . . . . . . . . . . . . . . . 624.3.3 Models 3-7: Earthquake Hazard and Damage . . . . . . . . . . . . . . . . . . . . . 704.3.4 Model 8: Power Infrastructure Models . . . . . . . . . . . . . . . . . . . . . . . . . 704.3.5 Model 9: Transportation Infrastructure Models . . . . . . . . . . . . . . . . . . . . 714.3.6 Model 10: Materials Supplier Models . . . . . . . . . . . . . . . . . . . . . . . . . 734.3.7 Model 11: Post-earthquake Inspectors . . . . . . . . . . . . . . . . . . . . . . . . . 744.3.8 Model 12: Contractor Firm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 744.3.9 Model 13: Engineering Firm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 764.3.10 Model 14: Insurance Firm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774.3.11 Model 15: Private Lender . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774.3.12 Model 16: Public Lender . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 784.3.13 Model 17: Permit Assessor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 784.4 Analysis and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.4.1 Case Study: M7.3 Earthquake in the Straight of Georgia . . . . . . . . . . . . . . . 814.4.2 Case Study: Earthquake in the Straight of Georgia with Probabilistic Magnitude . . 994.5 Final Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104viii5 Predicted Population Displacements in the City of Vancouver . . . . . . . . . . . . . . . . . . 1065.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1075.2 Modelling Population Displacement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1085.3 Displaced Population Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1105.3.1 The Decision to Leave Home Temporarily . . . . . . . . . . . . . . . . . . . . . . . 1115.3.2 The Decision to Relocate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1145.4 Indoor Fatality Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1185.5 Dwelling Disaster Preparedness Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1195.6 Water Infrastructure Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1225.7 Case study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1265.8 Final Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1366 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1376.1 Overview of Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1396.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166Appendix A Earthquake Hazard and Infrastructure in British Columbia . . . . . . . . . . . . . 167A.1 Seismic Hazard in British Columbia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167A.2 Selected Electric Power Infrastructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170A.3 Selected Water Distribution Infrastructure . . . . . . . . . . . . . . . . . . . . . . . . . . . 173A.4 Selected Transportation Infrastructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177A.5 Selected Fuel Distribution Infrastructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179A.6 Census and Housing Information for the City of Vancouver . . . . . . . . . . . . . . . . . . 181Appendix B Detailed Results From Chapters 4 and 5 . . . . . . . . . . . . . . . . . . . . . . . . 187B.1 Detailed Results From Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187B.2 Detailed Results From Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196ixList of TablesTable 3.1 Estimated demands and fuel delivery information. . . . . . . . . . . . . . . . . . . . . . 32Table 3.2 Simulation parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34Table 3.3 Fragility curves for storage tanks with different fill levels. . . . . . . . . . . . . . . . . . 41Table 4.1 Factors that affect housing recovery accounted for in this study. . . . . . . . . . . . . . . 50Table 4.2 Definition of symbols used in Figure 4.2. . . . . . . . . . . . . . . . . . . . . . . . . . . 52Table 4.3 Examples of Census information objects. . . . . . . . . . . . . . . . . . . . . . . . . . . 63Table 4.4 Socioeconomic demographics categories for instantiated dwellings. . . . . . . . . . . . . 63Table 4.5 Dwelling income by tenure for Metro Vancouver municipalities (MetroVancouver, 2019). 67Table 4.6 Attributes of the Inspector Model class. . . . . . . . . . . . . . . . . . . . . . . . . . . . 75Table 4.7 Housing completions in Vancouver MetroVancouver (2019). . . . . . . . . . . . . . . . . 76Table 4.8 Simulation parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81Table 4.9 Dwellings in need of repairs over time. . . . . . . . . . . . . . . . . . . . . . . . . . . . 88Table 4.10 Housing recovery descriptors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90Table 5.1 Length of distribution pipelines per neighbourhood. . . . . . . . . . . . . . . . . . . . . 125Table 5.2 Simulation parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127Table A.1 Earthquake area sources in Western Canada (Adams and Halchuk, 2003) . . . . . . . . . 169Table A.2 Hydroelectric dams in Lower Mainland. . . . . . . . . . . . . . . . . . . . . . . . . . . 171Table A.3 Power substations in Lower Mainland. . . . . . . . . . . . . . . . . . . . . . . . . . . . 172Table A.4 Water dams in Lower Mainland. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173Table A.5 Water treatment facilities in Lower Mainland. . . . . . . . . . . . . . . . . . . . . . . . 176xTable A.6 Water storage facilities in Lower Mainland. . . . . . . . . . . . . . . . . . . . . . . . . . 176Table A.7 Water pump stations in Lower Mainland. . . . . . . . . . . . . . . . . . . . . . . . . . . 176Table A.8 Bridges in Lower Mainland. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179Table A.9 Ports in Lower Mainland British Columbia . . . . . . . . . . . . . . . . . . . . . . . . . 179Table A.10 Fuel supplier in British Columbia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181Table A.11 Fuel tank farms in British Columbia. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181xiList of FiguresFigure 1.1 Location of British Columbia. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Figure 1.2 Earthquake hazards in Southwest British Columbia. . . . . . . . . . . . . . . . . . . . . 3Figure 1.3 Diagram of dependencies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Figure 2.1 Examples of a classes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Figure 2.2 Example of loss analysis using Rt (Mahsuli, 2012, Figure 2-8, p. 35). . . . . . . . . . . 14Figure 2.3 Community modelling in Rts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Figure 2.4 Class flowchart for network models in Rts. . . . . . . . . . . . . . . . . . . . . . . . . 17Figure 2.5 Flow of supplies under normal conditions. . . . . . . . . . . . . . . . . . . . . . . . . . 18Figure 2.6 Moving packets with commodities from one object to another. . . . . . . . . . . . . . . 19Figure 2.7 Propagation of requests in the framework. . . . . . . . . . . . . . . . . . . . . . . . . . 21Figure 2.8 Seismic fragility curves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Figure 2.9 Object flowchart for fuel deliveries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Figure 2.10 Fuel flow disrupted by an earthquake. . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Figure 3.1 Density of fuel vessel tracks (Tanner et al., 2017). . . . . . . . . . . . . . . . . . . . . . 27Figure 3.2 Connectivities in the fuel distribution network in coastal British Columbia. . . . . . . . 27Figure 3.3 Illustration of the objects used in the network model. . . . . . . . . . . . . . . . . . . . 31Figure 3.4 Probability of experiencing a fuel shortage longer than three days in a period of timeperiod T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Figure 3.5 Probability of losing functionality for longer than three days for different infrastructureelements in a period of time period T. . . . . . . . . . . . . . . . . . . . . . . . . . . . 37xiiFigure 3.6 Likelihood of being the infrastructure element with the longest repair time in the supplychain to Cobble Hill in case of a fuel shortage. . . . . . . . . . . . . . . . . . . . . . . 38Figure 3.7 Probability distribution of the number of tank farms experiencing fuel shortages longerthan three days simultaneously. Zero means no tank farm was affected, while six meansall tanks farms experienced a shortage longer than three days. . . . . . . . . . . . . . . 39Figure 3.8 Fuel distribution to Powell River. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40Figure 3.9 Rate of fuel shortage given a supply-side event. . . . . . . . . . . . . . . . . . . . . . . 42Figure 3.10 Rate of fuel shortage given a demand-side event. . . . . . . . . . . . . . . . . . . . . . 43Figure 3.11 Rate of shortage considering supply-side and demand-side events. . . . . . . . . . . . . 44Figure 4.1 Conceptual map of the City of Vancouver. . . . . . . . . . . . . . . . . . . . . . . . . . 51Figure 4.2 Overview of the objects used in the housing recovery modelling. . . . . . . . . . . . . . 56Figure 4.3 Graphical representation of the recovery process for two buildings. . . . . . . . . . . . . 58Figure 4.4 Flowchart of actions taken by the Neighbourhood Object, i.e., Object 1 in Figure 4.2. . . 61Figure 4.5 Algorithm for homeowner repair financing decisions. . . . . . . . . . . . . . . . . . . . 62Figure 4.6 Relationship between home ownership and income MetroVancouver (2019). . . . . . . . 68Figure 4.7 Relationship between home renting and income MetroVancouver (2019). . . . . . . . . 69Figure 4.8 Statistical equivalence between insurance take-up ratio and median dwelling income. . . 70Figure 4.9 Assumed power grid for the Vancouver case-study. . . . . . . . . . . . . . . . . . . . . 71Figure 4.10 Restoration curves for power network infrastructure. . . . . . . . . . . . . . . . . . . . 72Figure 4.11 Simplified construction materials network for the Vancouver case study. . . . . . . . . . 72Figure 4.12 Restoration curves for bridges. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Figure 4.13 Restoration curves for port waterfront structure and storage facilities. . . . . . . . . . . 74Figure 4.14 Vancouver neighbourhoods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Figure 4.15 Epicentre location and distance to Vancouver city limits. . . . . . . . . . . . . . . . . . 82Figure 4.16 Comparison of spectral acceleration between two neighbourhoods. . . . . . . . . . . . . 82Figure 4.17 Peak ground acceleration for each neighbourhood. . . . . . . . . . . . . . . . . . . . . 83Figure 4.18 Spectral acceleration at the period of 0.3 seconds for each neighbourhood. . . . . . . . . 84Figure 4.19 Spectral acceleration at the period of 1.0 seconds for each neighbourhood. . . . . . . . . 85Figure 4.20 Duration of repairs, in days, to power substations. . . . . . . . . . . . . . . . . . . . . . 86xiiiFigure 4.21 Housing recovery curves for a four-years period. . . . . . . . . . . . . . . . . . . . . . 87Figure 4.22 Dwellings in need of repairs immediately after the earthquake. . . . . . . . . . . . . . . 87Figure 4.23 Dwellings in need of repairs one year after the earthquake. . . . . . . . . . . . . . . . . 89Figure 4.24 Dwellings in need of repairs two years after the earthquake. . . . . . . . . . . . . . . . 89Figure 4.25 Dwellings in need of repairs three years after the earthquake. . . . . . . . . . . . . . . . 90Figure 4.26 Damaged dwellings by structural factors. . . . . . . . . . . . . . . . . . . . . . . . . . 91Figure 4.27 Number of damaged dwellings by socioeconomic factors. . . . . . . . . . . . . . . . . 91Figure 4.28 Recovery curves considering supplies are distributed on a demand basis. . . . . . . . . . 92Figure 4.29 Recovery curves for unlimited resources. . . . . . . . . . . . . . . . . . . . . . . . . . 93Figure 4.30 Impact of availability of inspectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93Figure 4.31 Impact of availability of engineer teams. . . . . . . . . . . . . . . . . . . . . . . . . . . 94Figure 4.32 Impact of availability of permit assessors. . . . . . . . . . . . . . . . . . . . . . . . . . 95Figure 4.33 Impact of availability of work crews. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Figure 4.34 Impact of retrofitting on recovery times. . . . . . . . . . . . . . . . . . . . . . . . . . . 96Figure 4.35 Return on investments as percentage of building value. . . . . . . . . . . . . . . . . . . 97Figure 4.36 Effects of mitigation actions on recovery time. . . . . . . . . . . . . . . . . . . . . . . 99Figure 4.37 Impact of mitigation actions on recovery equity. . . . . . . . . . . . . . . . . . . . . . . 99Figure 4.38 Robustness indexes of neighbourhoods for different moment magnitudes. . . . . . . . . 100Figure 4.39 Rapidity indexes of neighbourhoods for different moment magnitudes. . . . . . . . . . . 101Figure 4.40 Resilience indexes of neighbourhoods for different moment magnitudes. . . . . . . . . . 102Figure 4.41 Probability of observing different ground shaking intensities. . . . . . . . . . . . . . . . 102Figure 4.42 Expected recovery times for probabilistic earthquake magnitude. . . . . . . . . . . . . . 103Figure 4.43 Expect losses for probabilistic earthquake magnitude. . . . . . . . . . . . . . . . . . . . 104Figure 5.1 Overview of the objects used in the modelling of population displacements. . . . . . . . 110Figure 5.2 Factors affecting the decisions of dwellings. . . . . . . . . . . . . . . . . . . . . . . . . 111Figure 5.3 Algorithm for temporary dwelling displacement. . . . . . . . . . . . . . . . . . . . . . 113Figure 5.4 Effect of neighbours housing conditions on dwelling decision. . . . . . . . . . . . . . . 117Figure 5.5 Water distribution grid and pipelines in Vancouver. . . . . . . . . . . . . . . . . . . . . 123Figure 5.6 Restoration curves for water distribution infrastructure. . . . . . . . . . . . . . . . . . . 124xivFigure 5.7 Total number of pipeline breaks (left) and number of breaks per kilometre of pipeline(right) by neighbourhood. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128Figure 5.8 Displaced persons by neighbourhood over time. . . . . . . . . . . . . . . . . . . . . . . 129Figure 5.9 Persons displaced immediately after the earthquake per neighbourhood. . . . . . . . . . 130Figure 5.10 Total persons displaced over time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Figure 5.11 Socioeconomic profile of the displaced dwellings. . . . . . . . . . . . . . . . . . . . . . 132Figure 5.12 Displaced persons seeking rental housing or hotel rooms per neighbourhood. . . . . . . 132Figure 5.13 Socioeconomic profile of the dwellings seeking rental housing or hotel rooms. . . . . . 133Figure 5.14 Displaced persons seeking public shelter per neighbourhood. . . . . . . . . . . . . . . . 133Figure 5.15 Socioeconomic profile of the dwellings seeking public shelter. . . . . . . . . . . . . . . 134Figure 5.16 Persons who decided to relocate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135Figure 5.17 Displaced persons who decided to relocate within one year. . . . . . . . . . . . . . . . . 135Figure 5.18 Socioeconomic profile of the dwellings that decide to relocate. . . . . . . . . . . . . . . 136Figure A.1 Earthquake area sources in Western Canada, adapted from Adams and Halchuk (2003). . 168Figure A.2 Power transmission network to Vancouver - adapted from BC Hydro (2018). . . . . . . 170Figure A.3 Location of power distribution infrastructure in Lower Mainland British Columbia. . . . 171Figure A.4 Water transmission network to Vancouver. . . . . . . . . . . . . . . . . . . . . . . . . . 174Figure A.5 Location of water distribution infrastructure in Lower Mainland British Columbia. . . . 175Figure A.6 Location of bridges around the City of Vancouver. . . . . . . . . . . . . . . . . . . . . 177Figure A.7 Location of selected ports in Coastal British Columbia. . . . . . . . . . . . . . . . . . . 178Figure A.8 Location of selected fuel distribution infrastructure in Coastal British Columbia. . . . . 180Figure A.9 Median dwelling income for Vancouver (Statistics Canada, 2016). . . . . . . . . . . . . 182Figure A.10 Prevalence of dwellings with low income in Vancouver (Statistics Canada, 2016). . . . . 182Figure A.11 Prevalence of dwellings with high income in Vancouver (Statistics Canada, 2016). . . . 183Figure A.12 Prevalence of single-family buildings in Vancouver (Statistics Canada, 2016). . . . . . . 184Figure A.13 Prevalence of multifamily buildings in Vancouver (Statistics Canada, 2016). . . . . . . . 184Figure A.14 Prevalence of buildings built before 1980 in Vancouver (Statistics Canada, 2016). . . . . 185Figure A.15 Renter dwellings in Vancouver (Statistics Canada, 2016). . . . . . . . . . . . . . . . . . 185Figure A.16 Recent immigrant dwellings in Vancouver (Statistics Canada, 2016). . . . . . . . . . . . 186xvFigure B.1 Housing recovery curves for selected neighbourhoods for a four-years period. . . . . . . 187Figure B.2 Housing recovery curves for selected neighbourhoods for a four-years period. . . . . . . 188Figure B.3 Housing recovery curves for selected neighbourhoods for a four-years period. . . . . . . 188Figure B.4 Housing recovery curves for selected neighbourhoods for a four-years period. . . . . . . 189Figure B.5 Robustness indexes of selected neighbourhoods for different moment magnitudes. . . . . 189Figure B.6 Robustness indexes of selected neighbourhoods for different moment magnitudes. . . . . 190Figure B.7 Robustness indexes of selected neighbourhoods for different moment magnitudes. . . . . 190Figure B.8 Robustness indexes of selected neighbourhoods for different moment magnitudes. . . . . 191Figure B.9 Rapidity indexes of selected neighbourhoods for different moment magnitudes. . . . . . 191Figure B.10 Rapidity indexes of selected neighbourhoods for different moment magnitudes. . . . . . 192Figure B.11 Rapidity indexes of selected neighbourhoods for different moment magnitudes. . . . . . 192Figure B.12 Rapidity indexes of selected neighbourhoods for different moment magnitudes. . . . . . 193Figure B.13 Resilience indexes for selected neighbourhoods for different moment magnitudes. . . . . 193Figure B.14 Resilience indexes for selected neighbourhoods for different moment magnitudes. . . . . 194Figure B.15 Resilience indexes for selected neighbourhoods for different moment magnitudes. . . . . 194Figure B.16 Resilience indexes for selected neighbourhoods for different moment magnitudes. . . . . 195Figure B.17 Displaced persons for selected neighbourhoods over time. . . . . . . . . . . . . . . . . 196Figure B.18 Displaced persons for selected neighbourhoods over time. . . . . . . . . . . . . . . . . 197Figure B.19 Displaced persons for selected neighbourhoods over time. . . . . . . . . . . . . . . . . 197Figure B.20 Displaced persons for selected neighbourhoods over time. . . . . . . . . . . . . . . . . 198xviAcknowledgementsForemost, I would like to express my sincere gratitude to my primary supervisor Prof. Terje Haukaas for thecontinuous support of my Ph.D study and research, for his patience, motivation, enthusiasm, and immenseknowledge. His guidance helped me in all the time of research and writing of this thesis.I would also like to thank my co-supersvisor Prof. Stephanie Chang for sharing with me her vast knowl-edge about disasters and communities. Without her support I would have not been able to explore suchcomplex topics in my research.Besides my supervisors, I would like to thank the rest of my thesis committee: Prof. Jos Mart, Prof.Barbara Lence, and Prof. Sara Shneiderman, for their encouragement, insightful comments, and hard ques-tions.I would to thank the people that made Vancouver feel like home over the last four years: Alexa, Brenda,and Laura. Thank you to all the friends I have made here: Filipe, Marco, Cristina, Juuso, Nathalie, Zainaband many others. I would like to also thank my labmates for the stimulating and fun discussions: Steve,Christian, Swanand, Peter.I would like to thank the University of British Columbia for providing me, an international student, atruly inclusive experience.I would like to thank His Noodliness, The Flying Spaghetti Monster, for His spiritual guidance and thewisdom bestowed upon me to finish this research.Last but not the least, I would like to thank my family for supporting me in this journey.xviiChapter 1IntroductionBetween 2005 and 2015, natural disasters claimed the lives of 700,000 persons, injured 1.4 million, andmade 23 million homeless (Aitsi-Selmi et al., 2015). It is estimated that more 1.5 billion persons have beenaffected directly or indirectly by these events, which caused 1.3 trillion in economic losses. In 2016 alone,natural disasters displaced 31 million persons, three times as much as conflicts (Irish Times, 2019), andtwice as many as in the 1970s (Goldenber, 2019). Two of the most devastating natural disasters in Canadianhistory happened recently: the 2016 Fort McMurray fires and the 2013 Calgary floods. These events hadsevere impact on infrastructure. The Calgary floods damaged more than 200 bridges (Ledge, 2014) and theFort McMurray fires damaged more than 2,500 buildings. The impact to livelihoods was also devastating.More than 100,000 residents were evacuated on each of these disasters. Of those, many had not returned totheir homes one year later (Ledge, 2014; Taylor, 2017).Disaster mitigation actions are considered the most cost-effective alternative to reduce the impact ofnatural disasters on society (Aitsi-Selmi et al., 2015). It is generally accepted that predictive models canprovide valuable insights for pre-disaster planning and serve as a platform for evaluating the benefits ofmitigation actions. Nonetheless, to be comprehensive, such models need to go beyond the common practiceof evaluating disaster impacts in terms of immediate losses. It is also fundamental to model how physical,economic, and social infrastructure systems within a real community interact and affect disaster recovery.The long-term goal in this dissertation is to develop a framework of computer models to study disasterrecovery in communities and quantitatively compare the benefits of mitigation measures. To do so, thisdissertation draws knowledge from empirical studies, behavioural and social sciences, and engineering tocreate models that represent entities of a community and their behaviours.1The focus of this dissertation is the province of British Columbia located on the Pacific Coast of Canada.It has borders with Alaska (U.S) and Yukon to the North, Alberta to the East, and Washington State (U.S.)to the South, as shown in Figure 1.1. British Columbia is comprised of a main continental area and severalislands. The largest and most populated is the Vancouver Island. The largest population centre in theprovince is the Lower Mainland, located Southwest on the continental British Columbia. The Strait ofGeorgia separates Lower Mainland from the Vancouver Island. This region is highlighted in Figure 1.1.Figure 1.1: Location of British Columbia.The West coast of Canada lies on the boundaries of the North American plate, the Juan de Fuca plate,and the Pacific plate, exposing the region to significant seismic hazard. The municipalities along the Strait ofGeorgia are susceptible to three types of earthquakes, as shown in Figure 1.2. Crustal intraplate earthquakesmay occur in the Cascade Mountains area source with maximum moment magnitude of 7.7 (Adams andHalchuk, 2003). Subcrustal intraplate earthquakes with maximum magnitude of 7.3 can occur in the sub-ducting Juan the Fuca slab (Adams and Halchuk, 2003). Megathrust earthquakes can also occur along thesubduction interface and can reach magnitude 9.0, with a rupture length of up to 900 kilometres (Hyndmanand Wang, 1995).One specific objective in this dissertation is to better understand how infrastructure in British Columbiamay be impacted by and recover from earthquakes. This dissertation models infrastructure, their depen-2GSPCASR0km200-130 -125 -120  50CSZLowerMainlandFigure 1.2: Earthquake hazards in Southwest British Columbia.dencies, and the impact of their disruptions on communities. Earthquakes can also have large impact onresidential buildings. Housing recovery after recent earthquakes took several years (Olshansky, 2006; Com-erio, 2013). Because a sense of normalcy cannot be restored if persons do not have places to live, anotherspecific objective in this dissertation is to model housing recovery and population displacements in the re-gion. In this dissertation, housing recovery is modelled accounting for the competition for scarce supplies.The speed of recovery is then used to estimate the number of persons displaced from their homes over theyears following an earthquake. Figure 1.3 shows a high-level diagram of the different types of dependencies,indicated by the arrows, accounted for in this dissertation. The thick-line boxes represent the main resultsinvestigated in Chapters 3-5.This dissertation is organised as follows. In Chapter 2, the framework of models is introduced, andconcepts that are fundamental for the analysis in the remaining chapters are discussed. Chapter 3 applies thepresented framework to study disruptions to the fuel transportation in coastal British Columbia caused byearthquakes. In Chapter 4, the recovery of housing following earthquakes near Vancouver is studied using3Figure 1.3: Diagram of dependencies.the developed framework. Chapter 5 employs the framework to investigate population displacements underthe same conditions as are used in Chapter 4. Chapter 6 concludes the dissertation, reviewing contributionsfrom a broader perspective and proposing future research to improve it. Appendix A comprises the datacollected and used in the case studies in this dissertation.1.1 ObjectivesThis dissertation targets the area of disaster risk reduction, with focus on modelling disaster recovery at aregional scale. The objectives in this dissertation are:(1) to develop a framework of computer models to study disaster recovery in communities;(2) to simulate the transportation of resources through a network of models;(3) to investigate the relationship between infrastructure recovery and resource availability;(4) to study the relationship between resource availability and recovery of buildings;(5) to examine how resource constraints to housing recovery impact population displacements;(6) to quantitatively compare disaster mitigation actions.Objective (1) in this dissertation is to evaluate the disaster recovery in communities over weeks, months,and years. This idea goes beyond the predominant focus on quantifying immediate losses present inperformance-based earthquake engineering assessments (Cornell and Krawinkler, 2000; Deierlein et al.,2003; Moehle and Deierlein, 2004; Yang et al., 2009; Mahsuli and Haukaas, 2013b). The recovery fromdisasters is a multifaceted concept with physical, economic, and social dimensions. Only by comprehend-ing how these factors interact and affect recovery efforts can the impact of disasters be properly assessed.4To achieve Objective (1), models for buildings, dwellings, critical infrastructure, and resource suppliersneed to be developed. Furthermore, for the presented framework to be applicable to multiple communities,the models should be developed to only require publicly available information. This allows for high-levelassessments of impacts and recovery to be conducted at reasonable data requirements.Objective (2) is to create a versatile modelling technique to facilitate model communication in orderto simulate the transportation of supplies between models. This technique should allow models to makerequests for specific types and amounts of resources. It should also allow for models that can provideresources to identify and collect these requests. Models collecting requests should also be able to prioritiseresource allocation if resources are scarce. Thus, this should be a demand-based approach where requestsinitiate the delivery of resources.Objective (3) is to use the simulation framework to investigate how seismic damage to infrastructure im-pact the availability of resources in a community. The fuel distribution system in coastal British Columbiais selected for this study. In this system, fuel is transported from refineries in Lower Mainland BritishColumbia to remote communities along the Strait of Georgia, often by water. Thus, the recovery of infras-tructure is directly tied to the occurrence of fuel shortages. Models for refineries, ports, bridges, pipelines,and storage tanks need to be developed. In Objective (3), the technique developed in Object (2) should beused to facilitate the communication between the storage tanks in need of fuel and the refineries. Identifyingthe conditions that lead to fuel shortages, as well as alternative routes for fuel delivery, and the impact of therefilling strategy on risk of fuel shortage are parts of Objective (3).Objective (4) is to employ the simulation framework to study how resource scarcity constrains recoveryof buildings damaged by an earthquake. A case study of the recovery of housing in Vancouver after anearthquake is employed for this purpose. In the aftermath of a large earthquake, it is expected that moreresources for recovery, i.e., work crews and materials, will be needed than available in Vancouver. Thus, thespeed of recovery will be impacted by the capacity of a homeowner to acquire these resources, which in turnis a function of socioeconomic status. This analysis should include all residential buildings in Vancouverand account for their competition for recovery resources. A specific goal is to compare the housing recoveryamongst the neighbourhoods in Vancouver. Thus, a robust integration between engineering and socioeco-nomic metrics is necessary. This assessment should be able to identify the best predictors of successfulhousing recovery.Objective (5) is to investigate population displacements following a large earthquake with epicentre5close to Vancouver. This includes evaluating both temporary and permanent displacements, i.e., relocation.To properly model temporary displacements, the availability of utilities, the dwelling socioeconomic statusand preparedness have to be accounted for. The model for permanent displacements should be influencedby the speed of housing recovery, and therefore restrained by socioeconomic status. Furthermore, the pre-disposition to leave of dwellings, the state of the neighbourhood, and interactions with neighbours need tobe included.Objective (6) is to use the presented framework to quantitatively compare selected mitigation actions,identifying their benefits in terms of reducing risk, reducing recovery times, and improving equity in recov-ery.1.2 ScopeThis dissertation focuses on the impact of earthquakes on communities in British Columbia. AlthoughBritish Columbia is exposed to other natural hazards, e.g., wildfires, floods, or tsunamis, these are notaccounted for in this dissertation.The efforts in this dissertation concentrate in modelling the disaster response and recovery phases, thatis, the earthquake impact over the weeks, months, and years after the event. The modelling of emergencymanagement efforts, i.e., the first hours and days after the earthquake is not the focus of this work.The analyses in Chapter 3 include models for fuel refineries, pipelines, and storage tanks, as well as,bridges, ports, trucks and ships. The fuel replenishment strategies of the communities included in the studyare also accounted for. However, the analyses do not consider that vessels may be rerouted, new vesselsmay be included in the system, and new routes for fuel delivery can be created in response to a disaster.Furthermore, dependencies between the fuel and power infrastructure are outside of the scope of this study,as is the availability of personnel to carry out tasks, such as operating the ships.Chapters 4 and 5 have a common scope because they approach the same problem with different per-spectives. The analysis of housing recovery in these chapters includes models for building damage andreparability, availability of inspectors, financing, permit assessors, contractors, engineers, construction ma-terial, and power/transportation infrastructure. Competition for scarce resources is accounted for and it isaffected by socioeconomic factors. However, in Chapters 4 and 5, the concept of filtering (Peacock et al.,2014), which is the higher tendency of poorer dwellings to unwillingly inhabit older and poorer-qualityhomes is not accounted for. As a result, the correlation between physical and social vulnerabilities is weaker6in the analyses.The analyses in Chapters 4 and 5 study the recovery in Vancouver in relative isolation, while in realityVancouver is part of a metropolitan region. Hence, its recovery is expected to be impacted by the stateof the nearby municipalities. Furthermore, macro economic factors may become significant after a largeearthquake due to Vancouver’s importance in the local economy. The influence of these factors is outside ofthe scope of this dissertation.Lastly, only residential buildings are included in the analyses in Chapters 4 and 5. Thus, impact to indus-trial and commercial buildings and its impact on the availability of jobs is outside of the scope. Furthermore,the recovery of essential community services, e.g., schools, hospitals, and grocery stores, is assumed to oc-cur at the same rate of the recovery of residential buildings. The availability of jobs may influence thedecision of dwellings to leave their homes but these factors are outside of the scope of this work.1.3 BackgroundThis section presents an overview of the literature that is pertinent to the overall research thrust of thisdissertation. The literature that pertains to the specific subject of each chapter is reviewed in the introductionof the respective chapter.To mitigate the impacts of natural disaster on society, the United Nations Office for Disaster Risk Re-duction has been holding the World Conference on Natural Disaster Reduction (WC-NDR) over the last twodecades. These conferences resulted in the creation of the Yokohama Strategy and Plan of Action for a SaferWorld (United Nations Office for Disaster Risk Reduction, 1994), the Hyogo Framework For Action (UnitedNations Office for Disaster Risk Reduction, 2014), and more recently the Sendai Framework (Aitsi-Selmiet al., 2015). For the next decade, the Sendai Framework will be the guideline for the implementation ofdisaster risk reductions across the globe.Over the last two decades a paradigm shift also occurred in the earthquake engineering community.Until the mid 1990s, the main criterion for the design of buildings was life safety. However, this started tochange after the 1994 Northridge earthquake. Although buildings were capable of protecting lives duringthe earthquake, the economic losses observed after the earthquake were too high. It became evident that thebuilt environment should guarantee more than life safety, and that socioeconomic impacts of earthquakesshould be considered. This spurred the development of the Performance-Based Earthquake Engineering(PBEE) (Cornell and Krawinkler, 2000; Deierlein et al., 2003; Moehle and Deierlein, 2004).7The convergence of the interests of governments and earthquake researchers in reducing disaster risk al-lowed for a community of practice to spring around this topic. Three large centres for earthquake engineer-ing research were established in the US in 1997. The PEER Center (National Earthquake Hazard ReductionProgram, 2019c), The Mid-America Earthquake (MAE) Center (National Earthquake Hazard ReductionProgram, 2019a), and The Multidisciplinary Center for Earthquake Engineering Research (MCEER) (Na-tional Earthquake Hazard Reduction Program, 2019b). More recently, in 2015, the Center for Risk-BasedCommunity Resilience Planning funded by the National Institute of Standards and Technology (NIST) waslaunched (National Institute of Standards and Technology, 2019). A year later, the Computational Mod-eling and Simulation Center (SimCenter) within the Natural Hazards Engineering Research Infrastructure(NHERI) was created (SimCenter, 2019). In Europe, in 2009, the Seismic Hazard Harmonization in Eu-rope (SHARE) consortium was established (Giardini et al., 2014). Also in 2009, the Systemic SeismicVulnerability and Risk Analysis for Buildings, Lifeline Networks and Infrastructures Safety Gain (Syner-G)was created (Pitilakis et al., 2014). In 2010, the Network of European Research Infrastructures for Earth-quake Risk Assessment and Mitigation (NERA) was established (Akkar et al., 2014). NERA was succeededin 2017 by the Horizon-2020-funded Seismology and Earthquake Engineering Research Infrastructure Al-liance for Europe (SERA) (SERA, 2019). In Chile, the Centre for Investigation and Integrated Managementof Natural Disasters (CIGIDEN) was established in 2011 (CIGIDEN, 2019). Japan established in 2017 theResilience Research and Education Promotion Consortium.Disaster risk reduction studies within structural engineering have generally focused two topics: risk andresilience. Risk is commonly defined as the product of the hazard intensity, exposure, and vulnerability.In terms of earthquakes, the hazard is characterised by the magnitude and return period, exposure refersto the location and value of the assets that can be impacted by earthquakes, and vulnerability refers to thelikelihood of being negatively impacted. Thus, seismic risk is a measure of immediate impact. Becauseinterventions to reduce intensity and exposure are more challenging, the most feasible alternative to re-duce risk is to mitigate vulnerability. Research on vulnerability has gained emphasis for buildings (DAyalaand Speranza, 2003; Hassan and Sozen, 1997), power networks (Panteli and Mancarella, 2015; Mensahand Duen˜as-Osorio, 2015; Zhang et al., 2014; Ouyang, 2013; Ouyang et al., 2012; Xu et al., 2007), waternetworks (Laucelli and Giustolisi, 2014; Yazdani and Jeffrey, 2010b,a; Tabucchi et al., 2010; Adachi andEllingwood, 2008), transportation network (Costa et al., 2019; Balomenos and Padgett, 2018; Bucher et al.,2017; Ghosh et al., 2013; Padgett, 2007), and other infrastructure. An important aspect of the vulnerabil-8ity of infrastructure systems, e.g., water and power networks, are cascading failures (Rinaldi et al., 2001).Cascading failures can occur between systems, for example, when water distribution is interrupted due toa power outage. Because of this, infrastructure interdependency is an important area of study within thedisaster risk modelling community (Guidotti et al., 2017b; Hasan and Foliente, 2015; Ahmadi et al., 2014;McDaniels et al., 2007; Glass et al., 2003).Several computer simulation models have been developed for assessing earthquake risk. A 2014 reviewby the Global Facility for Disaster Reduction and Recovery (World Bank, 2014) included HAZUS-MH(FEMA, 2015), MAEviz (Elnashai et al., 2008), CAPRA (Cardona et al., 2012), SELENA (Molina et al.,2010), RiskScape (King and Bell, 2005), EQRM (Robinson et al., 2006); InaSAFE (Pranantyo et al., 2015),and OpenQuake (Silva et al., 2014). More recently, the Interdependent Networked Community ResilienceModeling Environment (IN-CORE), has been developed by the Center of Excellence for Risk-Based Com-munity Resilience Planning. IN-CORE 2.0 is expected to launch in 2019.The definition of resilience is not as simple as the definition of risk. The term ”resilient” was firstadopted by Holling (1973) to describe biomes capable of returning to their original state after impacted byexternal changes. As described by Norris et al. (2008), since then the term has been adapted to describeindividuals, infrastructure, and human communities. In this dissertation, a resilient system is assumed to beone with reduced failure probabilities, reduced consequences from failures, and reduced time to recovery, assuggested by Bruneau et al. (2003). Thus, the resilience of a system is tied not only to immediate impacts butalso to its capacity to recover from shocks. Because of this, to assess the resilience of a community one needsto capture how physical, economic, and social infrastructure systems within a real community interact andaffect recovery efforts (Lee et al., 2019; Masoomi and van de Lindt, 2018; Sutley et al., 2017a,b; Davidson,2015). While several models for risk assessment exist, there are currently no models that consider all aspectsof how a natural disaster affects a community or measure its recovery quantitatively.This dissertation contributes to disaster research by developing a collection of simulations models toquantitatively study how communities are impacted by and recover from earthquakes. To develop suchmodels, a versatile modelling approach that can account for the different attributes and behaviours of the in-frastructure and social systems in the community is needed. This dissertation uses an agent-based approach.Agent-based models approximate the behaviour of real-world elements within the software environment(Bucovetchi et al., 2015). They adopt a bottom-up approach and assume the complex behaviours emergefrom relatively simple interactions of autonomous agents (Eusgeld et al., 2009). It is easier to implement9agent-based modelling using object-oriented programming than it would be by using a traditional functionallanguage such as Pascal or FORTRAN (Johnson, 2001). For this reason, an agent-based object-orientedapproach is adopted in this dissertation.10Chapter 2An Object-Oriented Framework forDisaster Recovery ModellingIn this chapter the fundamental concepts of object-oriented programming are presented together with thesoftware infrastructure that underpins the developments in Chapters 3, 4, and 5. Of particular importance isthe concept of models, and how the models communicate with each other. Some of this infrastructure wasdeveloped earlier in the program Rt (Mahsuli and Haukaas, 2013a), including models for the earthquakehazard, residential building damage, and the infrastructure that allows for models to communicate usingbasic data structures. Thus, it is the new models related to network analysis, community modelling, and theimprovement of the model communication to allow for the simulation of goods being transported through anetwork of models that are highlighted in this chapter.2.1 Fundamentals of Object-oriented ProgrammingThe first object-oriented programming language was Smalltalk, developed at the pioneering Xerox PARCresearch laboratories (Goldberg and Robson, 1983). Today the language C++, developed by Bjarne Strous-trup, is the most commonly used object-oriented compiled language (Stroustrup, 2000). There are severaladvantages of this approach compared with the alternative, i.e., procedural programming. One benefit is”encapsulation” of data; all information is stored within ”classes”. An instantiation of a class is called anobject, and many objects can be created from one class (Deitel and Deitel, 2006). Importantly, the datain one object usually cannot be modified by another object. This encapsulation of the data contrasts with11the large data arrays that were passed around in old-fashioned procedural programs, which often causederroneous modification of unprotected data.Another advantage of object-oriented programming is ”inheritance;” a class may inherit functionalityfrom another. For example, a generic network model may have a certain functionality, such as conveyanceof commodities, that is inherited by subclasses, such as ports and power substations. Figure 2.1 illustratesthis inheritance by the triangle symbol. The figure shows that the port model inherits functionality from thenetwork model, which inherits functionality from the generic model.Another aspect of object-oriented programming that is illustrated in Figure 2.1 is ”polymorphism.” Tounderstand this concept, notice in Figure 2.1 that the power substation contains a damage estimator via themechanism called aggregation. Specifically, the power substation has a damage estimator. However, theclass named DamageEstimator is empty. It simply promises a functionality named ”estimateDamage().”The ”=0” that follows the function declaration means it does not contain any code. Instead, the promise”estimateDamage()” made by that base class is implemented in two different ways in the subclasses Re-gressionDamageEstimator and HazusDamageEstimator. The programmer does not need to specify whichmethod will be called; the user decides that later without changing any C++ code. Depending on the user’schoice the correct call from the power substation to one of the two damage estimators will be made. This iscalled polymorphism.In addition to encapsulation, inheritance, and polymorphism it is commonly said that ”abstraction” isthe fourth pillar of object-oriented programming. Abstraction is the task of idealising a real-world probleminto classes. In this dissertation, entities such as ports, refineries, neighbourhoods, and financial institutionsare implemented in classes.12Figure 2.1: Examples of a classes.2.2 Fundamentals of Rt and RtsThe work presented in this dissertation extends the computer program Rt developed earlier at the Universityof British Columbia in Vancouver (Mahsuli and Haukaas, 2013a). The extended program is named Rtsand several concepts from Rt are at the core of the new developments. The most important is the flow ofinformation through models. Figure 2.2, published in Mahsuli’s PhD dissertation Mahsuli (2012), illustrateseveral aspects of Rt that underpin the work in Rts presented in this dissertation. Each box in Figure 2.2 is onemodel. For instance, the box labelled 6 is an earthquake intensity model that takes the magnitude, M, fromModel 3 as input. Model 6 takes five additional variables as input but the model needs not know whetherthose are random variables, constants, or output from upstream models. After completing its calculations,Model 6 gives the ground motion intensity, Sa, as output to Model 12, which is the structural responsemodel.The multi-model analysis framework in Rt, illustrated in Figure 2.2, was originally developed to addressseismic risk analyses. This type of analysis requires the sequential calculation of ground motion intensity,structural response, damage, and loss. However, software architecture behind Rt and Rts allows far moregeneral applications due to the following features: 1) Any model can be replaced by another without any13changes to the underlying framework; 2) There is great flexibility in the input to a model because the modelneed not know whether the input is a random variable, a constant, or a response from another model; 3) Thesoftware architecture auto-detects which models need to be run first; and 4) The framework automaticallypropagates responses and also response sensitivities.Figure 2.2: Example of loss analysis using Rt (Mahsuli, 2012, Figure 2-8, p. 35).In a typical application of Rt and Rts the response from the right-most model, i.e., Model 14 in theexample shown in Figure 2.2, is input into a ”scenario model” whose output is given to a ”sampling model.”The sampling model prompts repeated analyses with different realisations of the random variables, whilethe scenario model conducts an analysis that progresses along a time-line, from a given start time to anend time that is typically a few years after the start time. For example, in several of the analyses presentedin this dissertation the models are evaluated every 24 hours along the time-line. One analysis along thetime-line is called a ”scenario.” A scenario is repeated, with new realisations of the random variables, asmany times as is desired. Within each scenario, an analysis at a particular time is called a ”time step.”The random variables that represent model uncertainty and other random variables that represent epistemicuncertainty should be re-sampled for each scenario, but they should remain constant through all the time14steps within each scenario. Conversely, random variables that represent aleatory uncertainty, such as anearthquake magnitude, should be re-sampled at every time step.2.3 Network ModelsA series of models aimed at representing elements of a community and their interactions are developed inthis dissertation. These models are referred to as network models. Figure 2.3 displays a map of the city ofVancouver, highlighting some of the infrastructure on which the city depends on a daily-basis, e.g, bridges,water and power distribution systems, ports. The models developed for each of these infrastructure ele-ments reside in a C++ class in Rts. For example, as indicated in Figure 2.3, the model for a generic port isdefined in the RPortModel class, whereas, the model for a power substation is defined in the RPowerSub-stationModel class. Thus, to instantiate the Port of Vancouver in the computer environment of Rts, an objectof class RPortModel needs to be created and given the attributes of the Port of Vancouver. This way, theabstract and generic classes can be used to instantiate specific real-world elements of the community. Anadvantage of implementing C++ classes in this work is the superior flexibility offered when selecting theattributes and functionality of each model. Existing commercial computer programs have several built-infeatures that enable certain aspects of the presented analyses. However, certain functionalities of the modelspresented here, and the models that will be implemented in the future, are unavailable without access to thesource code. Moreover, the adopted approach allows the future decomposition of the models into separatestructural, damage, and functionality models.Beyond models for the infrastructure of a community, network models for certain resource suppliersare also developed. The models for the resource suppliers seek to represent behaviours of that sector usingonly one object. For example, the whole insurance sector is represented by an instance of the RInsurance-CompanyModel class, and it mimics the average behaviour of all insurance companies. Modelling the exactbehaviour of each insurance company is outside of the scope of this dissertation, hence this simplified ap-proach is employed. Engineering and contractor firms, private and public money loaners, and constructionmaterials supplier are modelled in this fashion.Lastly, two classes are developed to represent the buildings and the dwellings in one subdivision of thecommunity, e.g., a neighbourhood. The buildings in the neighbourhood are modelled in the RHousingRe-coveryModel class, while the dwellings are modelled in the RDisplacedPopulationModel class. The build-ings and dwellings are simulated from Census data, but there is not a one-to-one correspondence with real-15world buildings. The goal is to approximate the number and characteristics of the buildings and dwellingsin the neighbourhood, and not to precisely model any individual building or dwelling.Figure 2.3: Community modelling in Rts.In Figure 2.4 the class flowchart for network models in Rts is shown. All classes for network models arederived classes of RNetworkModel, a virtual class with the capacity to receive packets and create requests.This means that all network models inherit these capacities from the RNetworkModel class. Packets andrequests are explained later. Furthermore, the RNetworkClass is a subclass of RModel, which in turn is asubclass of RObject, both classes previously discussed. The classes for infrastructure are on the left-handside, whereas the classes for resource suppliers and neighbourhoods on the right-hand side. A namingconvention is adopted so that the class name indicates what are the outputs of that class, e.g., housingrecovery is modelled in the RHousingRecoveryModel class, or that it indicates what the objects of thatclass represent, e.g., power substations are instances of RPowerSubstationModel. Because infrastructureobjects represent physical entities, they require their location to be defined. Location and fragility curves areused to determine the intensity of ground shaking at the location of the object and its seismic vulnerability,respectively. The location parameter is not required to instantiate objects representing the resource suppliers.The values for the attributes of each infrastructure object used in this dissertation are specified Appendix A.16Figure 2.4: Class flowchart for network models in Rts.The framework of models introduced in this chapter and explained in detail in the following chapters isfairly generalisable. As it is demonstrated in Chapter 3, the framework can be used to simulate earthquakeswith varied location and magnitude. The applications in Chapters 4 and 5 focus on a single earthquakescenario in order to reduce computational cost. Using a single scenario earthquake also improves the read-ability of the results, since these do not need to presented as probability distributions. The framework isalso generalisable in terms of the problems that can be modelled. Applications beyond the ones discussedin this dissertation may require the implementation of new models. However, the software infrastructure toallow the communication between the new models and the existing ones is implemented in the RNetwork-Model class. Thus, any new models implemented as derived of RNetworkModel will automatically inheritthe capacity to communicate with any of the existing models. This provides the presented framework greatpotential to be extended.172.4 Discrete and Continuous FlowAn important aspect of the presented approach is that resources can be requested and transported betweennetwork objects. The screen capture of Rts in Figure 2.5 shows the fluctuation of the reserves of a certainsupply at one network object, for example, fuel levels in a storage tank. The figure covers a period of 30days in which supply is requested whenever the reserves drop below 50 percent of the maximum capacity.The delivery of supply is indicated by the recovery of the reserves to full.Figure 2.5: Flow of supplies under normal conditions.To model the flow of supplies in Figure 2.5, this dissertation extends the software architecture of Rtto accommodate flow through a network of objects. A commodity, such as fuel or construction materials,may move from a refinery or hardware store through roads and ports, and ultimately arrive at a tank farmor a building. Figure 2.6 illustrates the movement of a commodity between two ports. The port classesare displayed at the top of Figure 2.6. Each object contains one member function named evaluateModel()which contains code particular to each object. The arrow in Figure 2.6 indicates that the data membercalled response in the port is the same data member called input in the ship. It is such responses thatfacilitate the communication between objects in Rts. The data members input and response in Figure 2.6are instantiations of the class RPacketResponse. It is also shown in Figure 2.6 that the response containsan object of the class RPacket. Packets are objects that have as attributes the content type, such as fuel orconstruction materials, destination, and amount of supply provided. More importantly they contain a list of18other Packets. Those Packets may in turn contain new Packets and so on, yielding great flexibility in thecomposition of transported goods. The Packets in Rts are analogous to containers transported by trucks,which in turn may contain packets that represent the cargo itself. This functionality allows a single truck orship in the network to carry different types of supplies.Figure 2.6: Moving packets with commodities from one object to another.To understand how Packets move around in a network it is useful to be familiar with the concept ofpointers in C++ programming. Simply speaking, a pointer is the address to the computer memory of anobject. It is that address that moves around in the network; the object stays at the same memory address andis neither deleted nor recreated during its movement through the network. To illustrate this with reference toFigure 2.6, consider a port that has received some fuel. The fuel is now stored in the contents of the RPacketthat is marked with a thick line in Figure 2.6. In other words, the fuel is stored in the Packet that is stored inthe packetList of the RPacket contained in the port’s RPacketResponse. Because the response from the portis stored as input in the ship, the ship loads the fuel by first calling getPacket in the input object. Next, it callsgetPacketList in that Packet and determines if it should be loaded. If yes, then the ship removes the name ofthe packet from the packetList and adds it to the packetList of the Packet that sits in its own response object.19At the final destination, e.g., a tank farm, getContents() and setContents() of the moving Packet are calledto unload the fuel. It is observed that the Packet contained in the RPacketResponse never moves because itserves as a container through which content and other Packets move, such as the Packet marked with a thickline in Figure 2.6.Figure 2.6 explains how the packets move from one object to another, but not what triggers the movementof commodities in the network. These triggers are either supply-based or demand-based. An example of asupply-based shipment is a refinery that, on its own accord, ships fuel at regular intervals. A demand-basedexample is a tank farm that sends a request to a refinery that fuel is needed. The demand-based approach isadopted in this dissertation and explained next.To illustrate how demands are communicated in Rts, Figure 2.7 shows the transportation of fuel andconstruction materials in a conceptual community. If during its evaluation the Tank Farm Object identifiesthe need for fuel, i.e., reserves are running low, it communicates this need by creating a Request Object. Thisobject is shown in Figure 2.7 below the Tank Farm Object. Requests have as attributes the content type, thename of the requester object, amount of supply needed, and a preferred supplier list. Thus, Requests canbe understood as the counterpart of Packets. In the next analysis time step, during the evaluation of theRefinery Objects, they check all objects in search of requests. A Refinery Object will only collect a requestif:(i) it can provide the requested supply type;(ii) its reserves are not completely depleted;(iii) it is physically possible to make the delivery;(iv) the refinery is one of the preferred suppliers;Item (i) guarantees that an object will not collect requests for supplies it cannot provide. In Figure 2.7a Neighbourhood Object in need of construction materials is also shown. Because the supply type for thisrequest is not provided by the Refinery Objects this request is not collected by them. Item (ii) checks ifthe available fuel at a refinery is sufficient to provide the requested amount. If there are many Tank FarmObjects requesting fuel, the Refinery Object will prioritise on a first-come-first-serve basis. Other objectsmay have different prioritisation rules, as it will be discussed in Chapter 4. Item (iii) defines that a deliverymay be impossible if, for example, a port that connects the refinery and the tank farm is not functional. InFigure 2.7, the red crosses on the connections to port P1 indicate that it is damaged and cannot receive or20ship packets. Thus, Refinery R1 cannot send a fuel shipment to Tank Farm TF at that time step. In general,objects do not collect requests if they cannot make the delivery. Lastly, in Chapter 3 requests can be directed.That is because tank farms are operated by companies that also operate refineries. One of the attributes ofthe Requests is the list of preferred suppliers. Refineries will only collect fuel requests that lists them as thepreferred supplier. In the cases where the preferred supplier list is not defined, condition (iv) is not checked.This is the case in Chapters 4 and 5.Figure 2.7: Propagation of requests in the framework.2.5 Damage and Interruption of FlowIn the presented framework, the earthquake hazard previously discussed may damage infrastructure anddisrupt their functionality. Damage to infrastructure objects is evaluated using seismic fragility curves.Fragility curves associate a measure of the earthquake intensity to probabilities of no, slight, moderate,severe, or complete damage. These damage states are usually numbered from 0 through 4, with zero meaningno damage and 4 representing complete damage. Fragility curves are commonly defined by lognormallydistributed random variables. To go into more detail on fragility curves, it is useful to remember that if Z isa normally distributed random variable with mean µZ and standard deviation σZ , we call X a lognormallydistributed random variable ifln(X) = Z = N(µZ,σZ) (2.1)21and the cumulative probability distribution of X, F(X), isFX(x) =Φ(ln(x)− ln(µZ)ln(σZ))(2.2)where ln(σZ) is commonly represented as βZ and referred to as the dispersion of Z, and ln(µZ) is alsothe median of X, mX (Porter, 2015). With these substitutions, and remembering that the subtraction of thelogarithms of two terms is also the logarithm of their division, FX(x) can be written asFX(x) =Φ(ln(x)− ln(mX)βX)=Φ[1βX· ln(xmX)](2.3)The notation in Equation 2.3 is widely used to represent fragility curves. Thus, the probability that aninfrastructure experiences damage state ds when exposed to a ground shaking intensity I isP(DS = ds|I)=Φ[1βds· ln(IIds)](2.4)where Ids is the median value of earthquake intensity measure at which the structure reaches the thresholdof damage state ds, and βds is the logarithmic dispersion of the earthquake intensity measure for damagestate ds. For water, power, transportation, and fuel distribution infrastructure the peak ground accelerationis usually the intensity measure of choice because it is not dependent on structural properties. For buildingsthe spectral acceleration is more commonly employed. In Figure 2.8 fragility curves for damage states 1through 4 for a generic infrastructure are presented. Given the intensity of the peak ground acceleration,IPGA, the probability of the infrastructure being in damage state is calculated asP(DS = ds|IPGA)=Φ[1β4 · ln(IPGAIPGA,4)]if DS=41−Φ[1β1 · ln(IPGAIPGA,1)]if DS=0Φ[1βDS · ln(IPGAIPGA,DS)]−Φ[1βDS−1 · ln(IPGAIPGA,DS−1)]otherwise(2.5)The damage state of a structure is used to determine its repair time. Repair time estimates used in thisdissertation are obtained from the HAZUS-MH manual (FEMA, 2015). The repair time increases with thelevel of damage, being zero for no damage, and being equal to the time to rebuild the structure if completedamage is observed. Thus, considering an uncertain damage state defined by the probabilities in Equation2.5, the expected restoration time, E(Tr), is calculated as22Figure 2.8: Seismic fragility curves.E(Tr) =N∑i=1(P(DS = dsi) ·Tdsi)(2.6)where Tds is the restoration time for damage state ds. During the time a structure is being repaired, itsfunctionality is assumed to be limited. With the exception of residential buildings, which are discussed indetail in Chapter 4, all structures are assumed to be fully functional if at least 80 percent of the expectedtime needed to repair them has passed, and to be fully disrupted otherwise. While disrupted, a structure,including residential buildings, can make requests and receive packets, however, it cannot create or shippackets. To exemplify this, Figure 2.9 presents an object flowchart for the transportation of fuel from arefinery, Object 5, to a tank farm, Object 11. Objects 5, 6, 7, 9, and 11 are infrastructure objects and aresubjected to the earthquake hazard represented by objects 1, 2, 3 and 4. Under normal operation, fuel isreceived every three days and the fuel reserves at the tank farm are constantly replenished, as was shown inFigure 2.5. In Figure 2.10 the impact of an earthquake on the fuel reserves at the tank farm is demonstrated.At the time of the event, damage to some of the tanks in the tank farm cause an immediate loss of stored fueland drop in the reserves. In the following days, because some infrastructure is damaged and not operational,new fuel shipments are not received, leading to a fuel shortage. The shortage lasts for approximately one23week, when the damaged infrastructure becomes functional again and new shipments of fuel are delivered.Figure 2.9: Object flowchart for fuel deliveries.Figure 2.10: Fuel flow disrupted by an earthquake.24Chapter 3Predicted Fuel Shortages in Coastal BritishColumbiaIn this chapter, the impact of earthquakes on the availability of fuel at selected coastal communities inBritish Columbia is investigated. An object-oriented model for the fuel distribution network in the region ispresented, and objects representing infrastructure components with varied attributes and behaviours are de-scribed. This chapter offers three key contributions. First, the information gathered from published sourcesprovides new perspectives and understanding of the fuel distribution system in Coastal British Columbia.This information is helpful to the public and private sectors and can be the basis of future studies. Second, anew modelling approach is developed, where the behaviours of agents and connections change dynamically,and heterogeneity exists between agent types. The approach models demand-based flow using requests toinitiate the production of supply and packets to represent real-world deliveries. Finally, this chapter con-tributes with insights on the seismic vulnerability of the fuel distribution system in coastal British Columbia.The study shows that the likelihood of localised fuel shortages due to earthquakes is significant and that sub-duction earthquakes have the potential to cause widespread fuel shortages in the province. The results ofthis assessment can be used to inform emergency response plans.3.1 IntroductionPrevious disruptions around the world have demonstrated how fuel transportation can be disrupted in ex-treme events. Fuel shortages after Hurricane Sandy (Smythe, 2013), after Japan’s 2011 earthquake, tsunami,25and nuclear disaster (Holguin-Veras et al., 2014), and after the unexpected shut down of a marine fuel ter-minal in Nova Scotia (Macneil and Keefe, 2015), are a few examples. These disruptions caused logistical aswell as public relations concerns, compounded emergency response difficulties, and affected public services.Disruptions to the fuel distribution system on the west coast of Canada could have similar consequences.Coastal and island communities in British Columbia are dependent on on-water and on-land transportationto receive fuel. Due to an increasing shift towards just-in-time deliveries, the local reserves of fuel on thesecommunities are limited. Consequently, coastal communities will experience shortages of fuel any timeregular transportation services are disrupted beyond the level that can be met using local caches.The region considered in this study is shown in Figure 3.1. Attention is primarily devoted to the distri-bution of fuel from the Greater Vancouver area to the tank farms at Powell River and Vancouver Island. Asshown in Figure 3.1, the Greater Vancouver area has a hub for fuel distribution consisting of one refineryand four fuel terminals. A fuel terminal is a storage facility without refining capacity. A schematic viewof the fuel distribution network is shown in Figure 3.2. It is observed that most fuel consumed in coastalBritish Columbia originates in the neighbouring provinces of Alberta and Saskatchewan, delivered by railand pipeline to the Lower Mainland British Columbia. Fuel is also provided by a refinery in WashingtonState, USA, which delivers fuel to the aforementioned terminals, as well as directly to Vancouver Island.Figure 3.2 shows how the fuel destined to coastal communities is transported from the refinery andterminals to nearby marine docks and ports by pipelines and trucks. Except the YVR Airport, which receivesaviation fuel directly via pipeline, gasoline and diesel destined for the tank farms that supply the coastalcommunities goes onto barges or roll-on-roll-off ships. Barges, used in the fuel transportation to most of thetank farms in this case study, are loaded at docks connected to the refinery or terminals by pipelines. Theexception is the tank farm at Powell River, which receives fuel by roll-on-roll-off ships. The fuel destined tothis tank farm is transported from the refinery and terminals to the Mitchell Island port, on the Fraser River,using trucks that there enter onto the vessels.Figure 3.2 also shows that some tank farms, e.g., in Powell River and at the YVR Airport, are supplied bymore than one refinery or fuel terminal. In such cases, for lack of more detailed information, it is assumedthat each refinery or terminal contributes with the same amount of fuel. Once fuel is delivered to a tankfarm, the local distribution is unique in each community and involves many stakeholders. Modelling thelocal fuel distribution from the tank farms would require in-depth understanding of each community’s fuelconsumption and is considered outside the scope of this study. In this chapter, the tank farms are the final26Figure 3.1: Density of fuel vessel tracks (Tanner et al., 2017).Figure 3.2: Connectivities in the fuel distribution network in coastal British Columbia.27destination of fuel and the overall fuel demand, i.e., fuel consumption rate, of the community determinesthe rate at which fuel reserves in those tank farms are depleted. Within the scope of this study are four tankfarms on the Vancouver Island, one in Powell River, and one at the YVR Airport. In short, the transportationof fuel addressed in this study involves refineries, fuel terminals, pipelines, roads, ports, as well as tankfarms that store fuel in the communities.As demonstrated in Figures 3.1 and 3.2, the delivery of fuel to remote coastal communities in BritishColumbia involves several infrastructure and transportation modes. Because Canada’s Pacific coastlineis susceptible to megathrust interplate earthquakes and weaker but nonetheless damaging intraplate earth-quakes, these infrastructure are exposed to significant seismic hazard. A disruption to this fuel distributionsystem following an earthquake could limit the emergency response capacity of these communities, whichcan lead to societal and economical losses. To reduce such loss potential, well-informed disaster mitiga-tion actions are needed. These require knowledge about the most common failure patterns and the level ofsystem disruption, i.e., localised vs widespread. The former helps to determine retrofit priorities, while thelatter provides insights on the number of people affected. Since the region has not dealt with any disrup-tive seismic events in the last decades, knowledge from prior events is limited. Thus, the use of computersimulations to assess the impacts of seismic events on the fuel distribution system is a powerful alternative.In the following, a new approach for modelling infrastructure systems that can be employed for assessingseismic vulnerabilities and informing mitigation plans is presented.3.2 Modelling of Interdependent Infrastructure SystemsSince the pioneering work on infrastructure interdependency by Rinaldi et al. (2001), efforts towards in-frastructure modelling have grown and several modelling techniques have been proposed. For example,Pederson et al. (2006) mention seven techniques used to model critical infrastructure systems: Markovchains, Petri Nets, dynamic simulation, agent-based, physics based, ordinary differential equations, andinput-output model. Eusgeld and Kroger (2008) complement this list including hybrid system modelling,hierarchical holographic modelling, the critical path method, and high level architecture. Since these tech-niques all have advantages and limitations, defining which one is the best depends mostly on which aspectsof the system at hand need to be modelled and what outputs are sought.The fuel distribution network in coastal British Columbia is comprised of individual facilities for pro-duction, transportation, and storage, each with unique characteristics. Each facility can also have different28vulnerability to earthquake ground motion and recover at different rates. Another consideration is that sup-ply is delivered in a discrete manner due to it being transported across the Strait of Georgia using marinevessels. Each tank farm has its own storage capacity and top-up strategy based on how fast their stocksare depleted. Modelling approaches that are based on continuous flows, commonly used for representingpower and water networks, cannot appropriately represent this fuel distribution network. What is needed isa modelling approach that can account for the different attributes of the infrastructure elements, behavioursof the fuel flows, and where specific volumes of fuel are delivered after requests are passed by the tank farmsthat are running low on reserves.In a review of almost 100 articles on modelling of interdependent infrastructure systems published be-tween 1987 and 2007, Eusgeld and Kroger (2008) suggest that methods based on high-level architectureand agent-based modelling are two universal modelling approaches. The authors indicate that agent-basedmodelling is the most used technique in the area of interdependency modelling and simulation of critical in-frastructures. The authors review 33 simulation tools for modelling of interdependent infrastructure systems,and nearly one third are agent-based.In a more recent review of nearly 200 articles on modelling of interdependent critical infrastructure sys-tems, Ouyang (2014) reaches similar conclusions. The author suggests that high-level architecture methods,agent-based methods, and methods based on arcs and nodes are the most comprehensive methods to assessinterdependent infrastructure resilience. However, the author emphasises that the high-level architecturemethods need to be better understood before being widely applied.Methodologies based on arcs and nodes are an intuitive approach for modelling networked systems. Inthese, nodes represent the elements of the system, while the arcs connecting the nodes represent interdepen-dence. The simplest approach based on nodes and arcs are topology-based, in which the network is describedby their node degree distribution and are usually developed to be solved analytically. Topological modelsrepresent dynamical processes of the networks under disruptive events without the consideration of particletransportation and redistribution (Ouyang, 2013). Hines et al. (2010) showed that topological measures canindicate some general measure of vulnerability, but that they can also lead to incorrect assessments if usedin isolation. As per the authors, overly-abstracted topological models can result in erroneous conclusions,which could lead to ineffective allocation of risk mitigation resources.A node-arc based methodology that tries to accommodate a better description of the system is Bayesiannetworks (BN). In a BN, if a node ”C” depends on the state of a nodes ”A” and ”B”, it is said that ”A” and29”B” are parents of ”C”, the child node. The interdependence is therefore quantified by conditional proba-bilities for each node given the state of its parents in the network (Khakzad, 2015). Thus, the BN enablesan efficient modelling of joint outcomes by factoring the joint probability distribution into conditional dis-tributions for each variable given its parents (Tien and Der Kiureghian, 2016, 2015). BNs are also efficientat observing the cause and inferring the possible effects, as well as, observing effects and inferring possi-ble causes (Kabir et al., 2016). This represents an improvement when compared to pure topology-basedapproaches.A challenge in using BNs is to define the needed conditional probability tables. This is usually accom-plished using expert judgement or from training algorithms (Siraj et al., 2013; Kabir et al., 2016). Anotherchallenge pointed out by Liu et al. (2016a) is that BN-based approaches assume that the attributes and be-haviours of nodes do not change over time. An approach called Dynamic Bayesian Network (DBN) hasbeen developed to account for the temporal dimension in the behaviour of interdependent systems Zhu andCollette (2015). However, Liu et al. (2016b) mention that learning algorithms for DBN increase exponen-tially in complexity the more elements there are in the model. For this, Cavalieri et al. (2017) suggests thatdespite the recent advances, BNs are still limited for modelling large system composed of elements withunique attributes and dynamic behaviours.A third methodology based on nodes and arcs is obtained combining a topology-based approach forrepresenting the system with augmented adjacency matrices and likelihood tables to model dependencies(Guidotti et al., 2017a,b; Feng et al., 2017; Guidotti et al., 2016). This methodology has been successfullyapplied to model water and power distribution networks. It can capture the damage, loss and recoveryof functionality, and dependencies between infrastructure elements and networks. However, the methodrequires the types and intensities of dependencies be known before-hand, which is difficult for most real-world scenarios. This modelling scheme is also unable to model discrete deliveries of supplies, one of theimportant aspects of the fuel distribution system in British Columbia.The aforementioned methods present limitations in modelling large systems with unique compositionand complex relationships of their individual entities. As mentioned by Glass et al. (2003), using networkmodels having nodes and connections with uniform properties to model complex networked systems ex-cludes important information. From this perspective, the agent-based modelling (ABM) approach is a betteroption for modelling the fuel distribution network in British Columbia. ABM was developed to approximatethe behaviour of real-world elements within the software environment (Bucovetchi et al., 2015). Thus, it fo-30cuses directly on individual objects, their behaviour, and their interaction. ABM adopts a bottom-up methodand assumes the complex behaviours emerge from relatively simple interactions of autonomous agents (Eu-sgeld et al., 2009). As a result, ABM represents a natural step forward in understanding and managingthe complexity of interdependent critical infrastructure systems. ABM excels in modelling heterogeneitywithin agent types, adaptation of agent behaviours, and dynamic changes in connections, while being versa-tile in terms of detailing (Glass et al., 2003). ABM also captures dependencies among critical infrastructuresystems by discrete event simulations, and can be used for scenario-based ”what-if” analysis.Johnson (2001) suggests that it is easier to implement ABM using object-oriented programming thanit would be by using a traditional functional language such as Pascal or FORTRAN. This is because theobject-oriented programming paradigm is based on ”classes” and ”objects,” which are used to representagents. For this reason, an agent-based object-oriented approach is adopted in this paper to model the fuelnetwork in British Columbia.3.3 Description of the Modelling of Fuel TransportationFigure 3.3 illustrates the straightforward concept behind the network modelling approach developed in thischapter. The flow of fuel, emanating from the refinery and fuel terminals on the left-hand side, flows througha series of models to the communities at the right-hand of Figure 3.3. Each model in Rts is implemented ina C++ class from which the objects in Figure 3.3 are instantiated.Figure 3.3: Illustration of the objects used in the network model.Refineries and fuel terminals objects are instantiated from the RRefineryModel and RFuelStorage-TankModel classes. These objects create and ship fuel packets based on requests received from tank farmobjects. Refineries and fuel terminal objects are supplied by pipelines coming from other provinces, andtheir fuel reserves are replenished constantly as long as these pipelines are functional. The pipeline model31is based on FEMA (2015), which characterises damage based on the expected number of leaks and breaks,and implemented in the RFuelPipelineModel class. Pipeline objects recover functionality based on repairrates that depend on the type of repair and available workforce. Models for ports are implemented in theRPortModelClass. Attributes of the ports waterfront structures, fuel storage facilities, and cranes are re-quired to instantiate port objects. Each substructure has an individual fragility curve and the functionalityof a port is determined by the minimum functionality of its substructures. Tank farm objects are instancesof the RFuelTankFarmModel class. These objects can contain one or more individual storage tanks, andtheir storage capacity is given by the sum of the capacity of the tanks that are functional. If a storage tankis severely damaged by ground motion, the reserves and storage capacity of the tank farm are reduced ac-cordingly. The reduced storage capacity is maintained until the storage tank is repaired. In this chapter, itis assumed that tank farms can store enough fuel to miss one delivery without running out of fuel. Thisimplies that storage capacity = 2 × daily demand × days between deliveries. Finally, a model for the fuelconsumption of a community is implemented in the RCommunityModel. Community objects do not havean associated damage model. Their most important property is their fuel demand, shown in Table 3.1, whichthey request from the tank farms on a daily basis. Shortages of fuel are defined as the period of time atwhich communities are unable to have their daily demand supplied. The duration of such shortages are themain results obtained from this chapter.Table 3.1: Estimated demands and fuel delivery information.Tank FarmDaily Deliveries Days BetweenDemand (bbl) per Year DeliveriesPowell River 900 122 3Chemainus Bare Point 2,200 23 18Cobble Hill 7,500 95 4ESSO Nanaimo 14,500 121 3Suncor Nanaimo 16,200 82 4YVR 45,000 – –Beyond the information given in Figures 3.1 and 3.2, the availability of detailed information about fuelflows in terms of quantities, origins, and destinations is difficult to obtain. A large number of stakeholdersare involved and many operators may have privacy concerns about sharing information. The informationused in the analyses was collected by Tanner et al. (2017) through expert interviews, stakeholder workshops,32and surveys. Nineteen interviews with 28 key stakeholders were completed. The interviewees included rep-resentatives from municipalities in the Strait of Georgia region, emergency response organisations, shippingand transportation companies, and port authorities. Publicly available data were also collected to estimatethe flow of fuel within the region. Fuel facility locations, capacities, and fuel transportation operations werefound at websites and in various reports (Pynn, 2013, 2015; Moreau, 2012; Chevron Canada, 2017; OilSands Magazine, 2016; Statistics Canada, 2018; City of Port Moody, 2018).Additional information was obtained from AIS satellite data through the MEOPAR-ExactEarth partner-ship agreement. These data reveal the movement of commercial shipping vessels, tracked over a period ofone year. The coloured lines in Figure 3.1 displays the frequency of shipping vessels travelling to each tankfarm considered in this study. This information was employed to estimate the number of annual deliveries,average number of days between deliveries, and daily demands for fuel summarised in Table 3.1. Since theYVR Airport is supplied via pipelines, only its daily demand is presented in Table 3.1. The table demon-strates the variability in daily demands and refilling strategies, denoting the need for a modelling approachthat can capture these characteristics.3.4 Analyses and ResultsThis section presents the results of different assessments of the vulnerability of the fuel distribution systemin coastal British Columbia. Initially, the effects of the fill level on the seismic fragility of fuel storage tanksis investigated in a case study including only one tank farm and one earthquake hazard. Then, a case studyinvolving the six tank farms in Table 3.1 is presented, where the communities most likely to experience afuel shortage, the most common failure patterns, and the effects of the earthquake source on the magnitudeof the fuel shortage are assessed.In the following case studies, the key assumptions listed below are present. These assumptions reflectdata and scope limitations.• post-disaster fuel demands are equal to pre-disaster demands;• vessels cannot be rerouted;• new vessels are not added to the system during recovery;• tank farms store enough fuel to miss one delivery without running out of fuel;• infrastructure with functionality above 80 percent operate normally;33• no aftershocks occur before infrastructure is repaired to pre-disaster levels;• the seismic fragility of infrastructure does not change over time.In Table 3.2, the number of objects and other information about the simulations conducted in this caseare presented. Note that the simulations in the case study in Section 3.4.2 only include a fraction of theobjects for infrastructure.Table 3.2: Simulation parameters.Hazard objects 5Refineries objects 2Fuel terminals objects 4Ports objects 11Bridges objects 10Pipeline objects 12Tank Farm objects 6Community objects 6Time step [hours] 6Scenarios per hazard 1,0003.4.1 Case Study: Fuel Distribution in Coastal British ColumbiaThe analyses in this case study include all six tank farms and investigate the likelihood and the causes offuel shortages in coastal British Columbia. Tank farms are used as a proxy for communities and the mainvariables analysed here are the probabilities that they will experience fuel shortages longer than three days.The three days period was adopted based on Macneil and Keefe (2015), who described a temporary fuelshortage on Canadian soil. The authors mention that a fuel shortage longer than three days could affectbasic public sectors. Three days is also a commonly used period for emergency response planning.Crustal, subcrustal, and subduction earthquake hazards are considered. The Cascadia Mountains and theGeorgia Strait/Puget Sound area sources (Adams and Halchuk, 2003) are used to represent the crustal andsubcrustal earthquake hazards in the region. For the subduction earthquake hazard, megathrust earthquakescaused by the partial or complete rupture of the Cascadia subduction zone are considered. Thus, fourtypes of events are considered, namely, (i) a crustal earthquake at the Cascade Mountains area source, (ii)a subcrustal earthquake at the Georgia Strait/Puget Sound area source, (iii) a partial , and (iv) a complete34rupture of the Cascadia subducton zone. The parameters that define these earthquake hazards are shown inthe Appendix A. The rate of occurrence of fuel shortages longer than three days at any tank farm given anearthquake of type i {i=1,. . .,4} is defined as λSi . This rate is given byλSi = P(S|Ei) ·λEi (3.1)where P(S|Ei) is the conditional probability of a shortage longer than three days given an earthquake oftype i, obtained from the 1000 scenarios analysis for earthquake type i previously discussed, and λEi is therate of occurrence of earthquakes from source i (Adams and Halchuk, 2003). With this, and consideringthat earthquake occurrences are statistically independent (Cornell and Winterstein, 1988), the compoundprobability of a fuel shortage over a period T considering all Ns sources, P(S), is modelled according to thePoisson process and is given asP(S) = 1− exp(−( Ns∑i=1λSi)T)(3.2)the sum in Equation 3.2 is a direct application of the rule of total probability and considers the occurrenceof one or more earthquakes. From Equation 3.2 the probability of a fuel shortage longer than three days iscalculated for different periods up to T=50 years. This period is chosen to demonstrate how the probability ofdisruption increases as a function of T. Note that the probability in Equation 3.2 tends to unity as the negativeterm on right-hand side tends to zero in an inversely exponential fashion as T increases. The results, shownin Figure 3.4, point to the tank farm in Cobble Hill as the most vulnerable to fuel shortages longer than threedays. The tank farms in Nanaimo, Powell River, and at the YVR airport present similar vulnerabilities tofuel shortages, lower than the tank farm in Cobble Hill. In contrast, the tank farm in Chemainus is the leastvulnerable. As discussed in the following, two reasons explain these results.The first reason is related to direct structural damage. While the crustal earthquake hazard is similarfor all locations, infrastructure located closer to the Cascadia subduction zone are more exposed to damageinduced by subcrustal and subduction earthquakes. Furthermore, the algorithm used to calculate damageinduced by ground displacements (FEMA, 2015) is a function of the earthquake magnitude and epicentredistance, as well as, groundwater level. Since subduction earthquakes tend to have the highest magnitudes,sites closer to the Cascadia subduction zone are also more vulnerable to damage induced by permanentground displacement. Due to the lack of site-specific information, only ports and docks were assumed to35Figure 3.4: Probability of experiencing a fuel shortage longer than three days in a period of time periodT.be susceptible to ground displacements due to these being at sea level, i.e., shallow groundwater level. Thisexplains the higher vulnerability of the ports and docks in Chemainus, Cobble Hill, and Anacortes, shownin Figure 3.5 and explained next.In Figure 3.5, the numbers in parentheses are probabilities of fuel shortages longer than three days overa period of 50 years, the maximum period considered in Figure 3.4. Although Chemainus and CobbleHill are near each other, these tank farms present the lowest and highest vulnerabilities to fuel shortages.Thus, proximity to the Cascadia subduction zone alone cannot explain the results. The other issue is top-upstrategies. In this case study, it was assumed that the storage capacity of a tank farm would allow them tomiss only one delivery without running out of fuel. Since the tank farms in Cobble Hill and Chemainusreceive fuel every four and eighteen days, respectively, the latter is more robust when interruptions occur inthe network. This is an example of how the shift towards ”just-in-time” deliveries can be detrimental to theresilience against fuel shortages.As important as it is to assess vulnerabilities, it is also necessary to be able to identify possible mitigationmeasures. Using the fuel supply to the tank farm in Cobble Hill as an example, this distribution network36Figure 3.5: Probability of losing functionality for longer than three days for different infrastructureelements in a period of time period T.involves a refinery, two docks, and one tank farm. Thus, if actions are to be taken to increase the resilienceof the network, identifying the most vulnerable infrastructure and common failure patterns that lead todisruptions is essential. This framework can also perform such analysis. To do so, for each of the scenariosin which a fuel shortage occurred, the ”bottleneck” object, i.e., infrastructure object with the longest repairtime, was identified. The number of times an infrastructure object was the bottleneck object was stored. Bydividing this number by the total number of times a shortage was identified, the likelihood that this objectwould be the bottleneck is calculated.The results of this analysis for the supply network to Cobble Hill are shown in Figure 3.6. Note that,if two or more objects show the same repair times both are accounted for as bottlenecks. Thus, the sumof the probabilities in Figure 3.6 may be above unity for each hazard. The results indicate that the infras-tructure with the longest repair times changes based on the hazard being considered. When subcrustal andsubduction earthquakes hazards are considered, the tank farm and the docks at Cobble Hill are the most37likely to be the bottlenecks. Both are located on the Vancouver Island, being more exposed to these hazardsdue to proximity to the Cascadia subduction zone. Furthermore, the tank farm and the docks are similarlyvulnerable to ground shaking damage, however, tank farms take longer to be repaired when extensive ormore severe damage is observed (FEMA, 2015). This explains the higher likelihood of tank farm being thebottleneck. Alternatively, for the crustal earthquake hazard, the refinery displays the highest likelihood totake the longest to be repaired. All infrastructure have similar exposure to this hazard. However, given theseismic vulnerability defined by the fragility curves used to model the refinery it presents higher likelihoodbe the bottleneck.Figure 3.6: Likelihood of being the infrastructure element with the longest repair time in the supplychain to Cobble Hill in case of a fuel shortage.38Finally, a proxy measure of the capacity of the system to withstand different types of earthquakes isobtained. This information is important for emergency managers in order to define effective disaster miti-gation actions. Response plans designed for a local event, i.e., small number of tank farms being affected,may be ineffective against a fuel shortage that is wide-spread across the province. Figure 3.7 presents thelikelihood of any number of tank farms to experience a fuel shortage considering the different hazards. It isobserved that only the subduction earthquake hazard presents considerable capacity to cause a wide-spreadfuel shortages. It is noted that there is more than 50 percent chance that after a megathrust earthquake alongthe subduction interface of the Pacific and North American plates, at least one tank farm will experiencea fuel shortage. For a crustal earthquake, on the other hand, this chance is only 10 percent. These resultsexemplify that disaster mitigation plans have to be tailored for specific hazards or be comprehensive andacknowledge the different consequences of different extreme events.Figure 3.7: Probability distribution of the number of tank farms experiencing fuel shortages longerthan three days simultaneously. Zero means no tank farm was affected, while six means all tanksfarms experienced a shortage longer than three days.3.4.2 Case Study: Fuel Distribution to the Powell River CommunityThis case study focuses on the distribution of fuel to the community of Powell River, which is served by twofuel terminals in the Greater Vancouver area. The fuel transportation network to Powell River was previouslyshown in Figure 3.2. Fuel is transported via tanker trucks from the terminals to a single port where they are39loaded onto specialised vessels and shipped to Powell River, and from there the trucks deliver fuel to localstorage facilities. The community receives shipments of 900 bbl every three days and has a maximumstorage capacity 2,700 bbl. In this case study, the storage facilities of Powell River are modelled by a singletank with 2,700 bbl capacity.The Greater Vancouver area and the city of Power River are shown in Figure 3.8. The distance betweenthe supply side, i.e., Greater Vancouver, and the demand side, i.e., Powell River, is about 120km. Thus,a shallow earthquake occurring close enough to cause disruptions at one side is very unlikely to causesignificant damage to the opposite side. Shallow earthquakes occurring in the Cascade Mountain crustalzone (CASR) represent the hazard in this study. The parameters that describe this earthquake hazard arelisted in the Appendix A.Figure 3.8: Fuel distribution to Powell River.The effects of the fill level of the fuel tanks at the time of the earthquake on the likelihood of fuelshortages is investigated in this case study. Comprehensive studies of storage tanks subjected to earthquakeloads have shown that there is correlation between the tank fill level and physical vulnerability (O’Rourkeand So, 2000; Eidinger and Davis, 2012; Cooper and Cooper, 1997). The extensive review presented inEidinger and Davis (2012) analysed data from 532 storage tanks exposed to strong ground accelerations.40Using this database, Eidinger and Davis (2012) determined fragility curves for peak ground acceleration-induced damage for four tank fill levels. Table 3.3 presents these curves, as well as, a fragility curve forground permanent displacement-induced damage provided by FEMA (2015), which are not dependent onthe fill level. The fragility curves for peak ground acceleration show that tanks with fill level < 50 percentare not known to experience damage states 3 or 4, which is associated with rapid loss of all contents orcollapse. Also, the fragility curves for damage states 1 and 2 have little influence from the tank fill level.On the other hand, tanks with fill levels of 90 percent or higher have considerably lower fragility levels fordamage states 3 and 4. Note that, although the median peak ground acceleration associated with damagestate 4 is the same for all fill levels, β is much lower for fill level higher than 90 percent. The smallerdispersion means that peak ground acceleration level associated with certain collapse is lower for near fullcapacity tanks.Table 3.3: Fragility curves for storage tanks with different fill levels.Damage Fill < 50% Fill ≥ 50% Fill ≥ 60% Fill ≥ 90% All fill levelsstate m[g] β m[g] β m[g] β m[g] β m[in] βDS ≥ 1 0.56 0.80 0.18 0.80 0.22 0.80 0.13 0.07 - -DS ≥ 2 >2.00 0.40 0.73 0.80 0.70 0.80 0.67 0.80 - -DS ≥ 3 - - 1.14 0.80 1.09 0.80 1.01 0.80 10.00 1.20DS = 4 - - 1.16 0.40 1.16 0.41 1.15 0.10 - -Two scenarios are considered to investigate the effect of the fill level at the time of earthquake on therate of fuel shortages, i.e., the likelihood of observing a fuel shortage given a fill level at the time of theevent. The two scenarios are (i) a supply-side event, defined by a shallow earthquake in the CASR area withepicentre close to Vancouver and, (ii) a demand-side event, defined as a shallow earthquake in the CASRarea with epicentre close to the Powell River community.For each scenario, a Monte Carlo simulation comprised of 1,000 scenarios is used. Each scenario simu-lates a period of two weeks, starting at the time of the event. Under the demand of 40,000 litres every 3 days,this time-window guarantees that if the community does not run out of fuel it is because the supply chainhas resumed normal operations, i.e., all infrastructure are functional. The speed at which the communitydepletes its reserve is not considered in this study, that is, instant loss of all reserves due to tank failureand consumption of all reserves over a few days are treated equally. To reduce the computational cost, theepicentre location for shallow earthquakes is limited to points inside the dashed areas in Figure 3.8. This41avoids simulations that would represent normal operation conditions.The results shown in Figure 3.9 and Figure 3.10 are given in terms of the same fill levels of the fragilitycurves presented in Table 3.3. While this option is made to minimise assumptions, it also highlights the needfor more detailed fragility curves to allow a more comprehensive study, involving more fill level intervals.The first results in Figure 3.9 refer to supply-side events. The results show that the rate of fuel shortage isinversely proportional to the fill level, i.e., the higher the reserves at the time of the event, the less likely thecommunity is to experience a fuel shortage. In a supply-side event, the community’s storage tank remainsintact while the supply-side infrastructure is expected to be damaged. Thus, the increased fragility of thetank with a higher fill level is not relevant and higher reserve levels allow a longer period without receivingnew shipments of fuel.Figure 3.9: Rate of fuel shortage given a supply-side event.Figure 3.10 presents the results for the demand-side events. In this case, the storage tank is subjected tonon-negligible ground accelerations and, therefore, the fill level increases its tendency to experience moresevere damage. This is demonstrated by the considerable increase in the rate of fuel shortages for the caseswhere the tank is closer to full capacity. However, the big picture remains the same: the higher the fuelreserves at the time of the event, the less likely the community is to experience a fuel shortage. Table 3.3shows that only for damage states 3 and 4, tanks closer to full capacity are considerably more fragile. Sincethese damage states are less likely to be observed, the influence of the fill level to the overall probability of42fuel shortage is limited. An important consideration is that the results for the demand-side are very sensitiveto the fragility curves used for the tanks. The curves given by Eidinger and Davis (2012) present verysimilar median peak ground acceleration values for damage state 4, showing a small correlation between thefill level and the probability of collapse of the tank. If, however, this correlation was stronger, the resultscould be considerably different, which demonstrates the importance of further studies on the relationshipbetween fill level and tank fragility.Figure 3.10: Rate of fuel shortage given a demand-side event.The results presented in Figures 3.9 and 3.10 are associated with earthquakes happening within thedashed lines in Figure 3.8, thus, they are not equally likely, i.e., their likelihood is proportional to theirrespective areas. Thus, to accommodate both results in a single plot, Figure 3.11 shows the sum of the resultspreviously presented, weighted by the size of the respective area sources. It is noticeable that, consideringboth types of events, the likelihood of a fuel shortage is smallest when the reserves are close to full capacityat the time of the earthquake. Ultimately, it means that, under the conditions of this case study, refillingstrategies that seek to keep the tank as full as possible under normal operations are preferred.43Figure 3.11: Rate of shortage considering supply-side and demand-side events.3.5 Final RemarksThis chapter presents an agent-based, object-oriented model for assessing the seismic vulnerability of criticalinfrastructure networks. Models for representing several critical infrastructure elements, e.g., refineries,ports, tank farms, and transportation modes are presented. These models contain parameters that allow eachagent in the network to be represented with its unique characteristics. This is an improvement over othermethodologies that treat infrastructure elements as homogeneous nodes. The use of packets for representingreal-world shipments of goods is also introduced. Packets allow discrete deliveries to be modelled, makingthis a demand-based modelling approach, which is an improvement over flow-based approaches in terms ofmodelling certain networks.This agent-based, object-oriented framework is used to model the fuel distribution network in BritishColumbia, on the West Coast of Canada. This network involves different types of infrastructure and trans-portation modes both on land and on sea, which requires an approach such as the one presented here inorder to be properly modelled. The framework is capable of identifying the vulnerabilities of the system,both in terms of the structural fragility of the infrastructure elements and also in terms of the top-up strate-gies of communities. The framework can be applied to devise better disaster mitigation plans to reduce thevulnerability of the fuel distribution network of British Columbia when earthquake hazards are of concern.44Nonetheless, it should be noted that the results obtained from a framework like this are only as accurateas the information used in the model. Reliable and detailed information about origin and destination ofshipments, frequency of deliveries, amounts and type of fuel being transported in the region would increasethe accuracy of the results obtained. Access to the emergency management plans of suppliers, communities,and government agencies would also improve the capacity of this modelling approach to represent the post-event state of the system. This reinforces the idea that, in order to effectively improve the resilience of thissystem, better communication between the different stakeholders and information sharing are essential.45Chapter 4Predicted Housing Recovery in the City ofVancouverIn this chapter, housing recovery in the City of Vancouver, Canada, is investigated considering resourcesfor repairs are scarce. Building recovery is modelled in the context of a community, contrasting with thepractice of assessing the recovery of buildings in isolation. Thus, the presented approach better capturesthe effect of competition for resources, infrastructure disruptions, and socioeconomic factors on recovery.The analyses include models for damage, inspection, financing, power infrastructure, and labour/materialsfor repairs. The presented approach is applied to simulate the recovery of 114,832 residential buildings in22 neighbourhoods in Vancouver. Results indicate that recovery after a strong earthquake will take morethan three years. The density of old and rented buildings, and the income and immigration status of thehomeowners are shown to be good predictors of the speed of recovery for a neighbourhood. Mitigationmeasures are compared and it is shown that retrofitting the most physically vulnerable buildings or doublingthe available workforce are effective at reducing housing recovery times. It is demonstrated that the equityin recovery between low and high socioeconomic status homeowners is improved if mitigation measures areimplemented. The results presented in this chapter can inform disaster recovery plans and mitigation actionsin Vancouver and similar communities.464.1 IntroductionAn object-oriented model is presented in this chapter to quantify housing recovery times after an earthquake.The impact of damage and disruptions to transportation and power networks is modelled together withsocioeconomic factors and potential scarcity in resources for inspection, financing, and repairs. The goalin this work is to create a robust tool that facilitates quantitative comparisons of different housing recoverystrategies. Such a tool can inform decisions to increase the speed and equity in housing reconstruction. Inthis chapter it is a specific objective to utilise publicly available data, making the approach transferable toother urban communities. To that end, census data for the City of Vancouver (Statistics Canada, 2016) forma basis for the analyses and results presented here.Repairs to residential buildings took between two and ten years after earthquakes in 1989 in Loma Prieta(Comerio, 2006), 1994 in Northridge (Olshansky, 2006), 1995 in Kobe (Comerio, 2014; Olshansky, 2006),2009 in L’Aquila (Di Ludovico et al., 2017a,b), 2010 in Chile (Comerio, 2013), and 2011 in East Japan(Ranghieri and Ishiwatari, 2014). The repairs needed after the 2010 and 2011 Canterbury earthquakes areexpected to extend beyond 2020 (Wood et al., 2016). During recovery, economic growth and quality of lifeare impacted, and socioeconomic inequities can be exacerbated (Wang et al., 2015; Bolin, 1985). The SendaiFramework for Disaster Risk Reduction indicates that pre-disaster actions are the most effective alternativeto shorten recovery times (Aitsi-Selmi et al., 2015, p. 13).It is generally accepted that predictive models of housing recovery can provide valuable insights andserve as a platform for evaluating the benefits of different mitigation actions. Many techniques have beenemployed in developing housing recovery models, such as linear regression (Sutley et al., 2019), systemdynamics (Kumar et al., 2015), discrete event simulation (Lin and Wang, 2019; Huling and Miles, 2015),fuzzy-logic (De Iuliis et al., 2019), Monte Carlo simulation (Zeng and Zhang, 2019; Burton et al., 2017),and agent-based (Grinberger and Felsenstein, 2014; Nejat and Damnjanovic, 2012; Miles and Chang, 2011).Nonetheless, there is growing agreement that housing recovery needs to be modelled in the context of thecommunity, being influenced by infrastructural and socioeconomic factors, and constrained by the availableresources (Lee et al., 2019; Masoomi and van de Lindt, 2018; Ellingwood et al., 2018; Bilau et al., 2018;Sutley et al., 2017a).The aforementioned contributions have brought much-needed attention to the study of housing recoveryafter disasters, and they have substantially improved our knowledge in the field. However, a holistic model47for housing recovery that quantitatively evaluates the benefits of different mitigation actions is still needed.The research presented in this chapter addresses this gap in three ways: First, object-oriented models aredeveloped for building portfolio recovery, inspection, financing, permitting, contractors, engineering firms,construction material suppliers, and power/transportation infrastructure. Second, the presented approachsimulates the recovery of all residential buildings in a community. This addresses the challenge that theavailability of joint but potentially scarce resources in a community is vital to its recovery. As a result, thepresented approach improves the simulation of impacts of mitigation strategies compared to approaches thatinvestigate buildings in isolation. Third, this paper contributes with insights into the future housing recoveryin Vancouver, including the effect of selected mitigation actions.4.2 Factors Affecting Housing RecoveryThe impact of structural damage on the habitability of buildings have been extensively studied (De Iuliiset al., 2019; Foltz and Hueste, 2004; Takahashi and Shiohara, 2004; Hwang and Lignos, 2017; Yang, 2009).Nonetheless, empirical evidence demonstrates that socioeconomic and community factors also play an im-portant role in housing recovery. After the 1989 Loma Prieta earthquake, recovery of housing in the Stanfordcampus was significantly delayed by slow recruitment of engineers and contractors (Comerio, 2006). Fol-lowing the 1994 Northridge earthquake, building type, i.e., single-family or multi-family, ethnicity, hous-ing tenure, income, financing, and language barriers influenced recovery (Lu and Xu, 2014; Kamel andLoukaitou-Sideris, 2004; Loukaitou-Sideris and Kamel, 2004; Wu, 2004; Hirayama, 2000). Lack of inter-organisational coordination affected housing recovery after the 1999 earthquake in Turkey (Ganapati, 2013).After the 2004 Indian Ocean Tsunami, the 2003 earthquake in Iran, and the 2001 earthquake in India ma-terials shortage, and recruitment of skilled workers extended recovery times (Bilau et al., 2015). In China,after the 2008 Wenchuan earthquake, housing recovery for families with low-income, unemployed, or wholost loved ones was more difficult (Wang et al., 2015). Insurance payment delays after the 2010 Canterburyearthquake significantly hindered housing rebuilding (Comerio, 2014; Wood et al., 2016). Additionally, theREDi framework (Almufti and Willford, 2013), based on Comerio (2006), offers a list of factors that in-fluence building recovery, including inspections, financing, engineer and contractor negotiations, materialsand permit acquisition.The factors listed above are compiled in Table 4.1, indicating those accounted for in the presentedapproach. Income, housing tenure, ethnicity, and language barriers are included as properties of objects that48represent buildings, and influence the capacity and willingness to rebuild. The remaining factors accountedfor are resources, which are modelled individually. Employment, inter-organisational coordination, and theloss of loved ones are not accounted for. The modelling of commercial buildings and, in consequence,availability of jobs is deferred to a later study. Housing recovery is assumed to be a responsibility of owners,therefore, inter-organisational coordination is less relevant in the context of the presented research. Finally,the loss of loved ones is not accounted for because fatalities are not estimated.49Table 4.1: Factors that affect housing recovery accounted for in this study.Reference Income TenureImmigrantFinancingWorkInspections Permits MaterialsBuildingstatus crews typeWu (2004)Kamel and Loukaitou-Sideris (2004)Loukaitou-Sideris and Kamel (2004)Bilau et al. (2015)Nejat and Ghosh (2016)Comerio (2014)Comerio (2006)Wood et al. (2016)Lu and Xu (2014)Almufti and Willford (2013)504.3 Modelling Housing RecoveryTo illustrate the basis for the models presented in this paper, a conceptual map of the City of Vancouveris presented in Figure 4.1. The dashed lines represent the city limits, whereas the red lines encompass ageneric neighbourhood in which buildings are damaged by an earthquake. Electrical power is providedby the power substations indicated by orange circles and connected by orange power lines. Constructionmaterials are transported into the community from a port to the neighbourhood by roads indicated by greylines. In addition, the community itself provides other recovery resources, such as inspectors, financing,permits, engineers, and workers. Those are aspects that the presented models aim to capture.Permits EngineersFinancingPortInspectorsPowersubstationNeighbourhoodWatertreatmentstation BridgePowersubstationBridgeDamagedbuildingsBridgeMaterialsPowerWaterWorkersFigure 4.1: Conceptual map of the City of Vancouver.In the object-oriented approach adopted in this paper the entities identified in Figure 4.1 are modelled51by C++ classes. Instances of classes are called objects; for example, only one Contractor class is imple-mented but many contractor objects can be instantiated at run-time. The functionality of objects are definedthrough ”data members,” which store information, and ”member functions,” which carry out operations onthe data (Deitel and Deitel, 2006). Specifically, data members represent attributes of infrastructure objectsand member functions define the actions that an object can perform, such as delivering financing.The classes, i.e., models developed in this paper are enumerated in Figure 4.2 and explained in the sub-sequent sections. In Figure 4.2 the attributes are listed above each object, while the responses are indicatedby solid arrows connecting them to other objects. All the symbols are explained in Table 4.2. Notice that re-quests are employed to communicate resource needs; see the dashed line emanating from Model 1 in Figure4.2. Requests serve as input to models in the same manner as attributes and responses from other models.For example, Model 11 is a material supplier that takes as input material requests, Rm, and the number ofdaily materials deliveries, Nm; it also receives/sends packets of materials, m©.Table 4.2: Definition of symbols used in Figure 4.2.Symbol Description Class/typeBCL Code level StringBn Area source boundaries RLocationBOC Occupancy class StringBt Building type StringdH Earthquake depth Real NumberH Building habitability Real NumberLH Epicentre location RLocationLlc Large claim threshold Real numberLS Site location RLocationLsc Small claim threshold Real numberContinued on next page52Table 4.2 – continued from previous pageSymbol Description Class/typeLsr Small request threshold Real numberM Magnitude RResponsemcm Median contractor mobilisation time Real numberme Median assessment time Real numberm f c Median payment time Real numberm f g Median payments time Real numberm f p Median payments time Real numbermi Mean inspection time Real numbermp Median permit approval time Real numberMlc Delay multiplier for small claims Real numberMmax Maximum magnitude Real numberMmin Minimum magnitude Real numberMsc Delay multiplier for large claims Real numberMsr Delay multiplier for small request Real numberNe Number of engineers Integer numberNi Number of inspectors Integer numberNp Number of permits Integer numberNm f c Multi-family housing crews Integer numberNs f c Single-family housing crews Integer numberPGA Peak ground acceleration RResponseContinued on next page53Table 4.2 – continued from previous pageSymbol Description Class/typeRc Contractor mobilisation request RRequestRe Engineering assessment request RRequestR f∗ Financial request RRequestR f c Insurance request RRequestR f g Public aid request RRequestR f p Private loan request RRequestRi Inspection request RRequestRm Material request RRequestSa Spectral acceleration RResponseTE Occurrence time RResponseTE Time of earthquake Real numberTf g Time for public loans RRandomVariableTr Time for building repairs Real numberVs30 Shear wave velocity RRandomVariableβcm Dispersion of contractor mobilisation time Real numberβe Dispersion of assessment time Real numberβ f c Dispersion of payment time Real numberβ f g Dispersion of payment time Real numberβ f p Dispersion of payment time Real numberβM Dispersion of magnitude Real numberContinued on next page54Table 4.2 – continued from previous pageSymbol Description Class/typeβp Dispersion of permit approval time Real number∆p Peak transient drift RResponse∆r Residual drift RResponseεe GMPE error RRandomVariableλE Occurrence rate Real numberρs structural damage ratio Real numberρd displacement damage ratio Real numberρa acceleration damage ratio Real numberi© Inspection packet RPacketResponsef© Financial packet RPacketResponsem© Materials packet RPacketResponsecn© Contractor negotiation packet RPacketResponsecm© Contractor mobilisation packet RPacketResponsee© Engineering assessment packet RPacketResponsep© Permit packet RPacketResponseIt is important to note that the analyses conducted with the models in Figure 4.2 progress along a time-line, from a given start time to an end time, which is typically a few years after the start time. In the analysespresented in this chapter the models in Figure 4.2 are evaluated every 24 hours along the time-line. Anothersignificant aspect of the analysis is that buildings may have the recovery process delayed while waiting forcertain supplies. The potentially delaying effect of this competition for resources is illustrated in Figure4.3. The solid line in the top graph in Figure 4.3 represents the functionality of Building 1, which drops55Figure 4.2: Overview of the objects used in the housing recovery modelling.at the time of the earthquake, indicating that the building needs repairs. To be repaired, a building needsto (i) be inspect, (ii) be assessed by an engineer, (iii) obtain a permit, (iv) mobilise a contractor, (v) obtainmaterials, and (vi) obtain financial resources. An important observation in Figure 4.3 is that certain actionsmay proceed simultaneously. The horizontal solid bars in Figure 4.3 indicate the time needed to performeach action. If a resource is available when the building needs it then there is no waiting time. That is thecase for the contractor mobilisation for Building 1. At the same time, the power distribution system is beingrestored, independently. Once all resources, including power, are available, the repairs start and the buildingbegins to regain its functionality. A crew of workers is allocated to the building for the duration of therepairs and is dismissed once full functionality is recovered. In the bottom graph of Figure 4.3 the recovery56of Building 2 is illustrated. If the resources needed by Building 2 are currently allocated to Building 1 thenthe recovery of Building 2 is delayed. Such delays due to the competition for limited resources is indicatedby white horizontal bars in Figure 4.3.In summary, the time needed for a building to recover, i.e., the total length of the bars in Figure 4.3,is uncertain. It depends on extent of damage, type of building, socioeconomic factors, and competition forlimited resources. Thus, the total recovery time, T, for a building is given byT = Tr +Tcm+maxTi+TfTi+TcnTi+TmTi+Te+TpTd(4.1)where Tr is the time needed for repairs once all resources are available, Tcm is the time for contractor mobil-isation, Ti is the time needed for inspections, Tf is the time needed to obtain financial resources, Tm is thetime needed for materials to be delivered, Tcn is the time needed for contractor negotiations, Te is the timeneeded for engineering assessment and/or redesign, Tp is the time needed for obtaining a permit, and Td isthe time needed to repair utility disruptions. The time needed to complete each task depends on the availableworkforce in the community in how it is allocated. The development of detailed resource allocation modelsrequires collaboration with public and private sector and are system specific (Wang and Sun, 2018; Tabucchiet al., 2010; Vaziri et al., 2010; Xu et al., 2007). For this reason, a combination of restoration curves (FEMA,2015), and empirical data (Almufti and Willford, 2013), are used as guidelines for the development of themodels in this chapter.The concept of requests and packets are adapted to the application in this chapter. As an example,consider the need for inspectors, provided by Model 12 as described later. Requests are collected by theInspector Model and added to a list that contains all requests for inspections, including requests from otherNeighbourhoods. If enough supplies are available, the Inspector Model creates and ships packets to eachNeighbourhood containing what was requested. These packets have a list of supplied amounts, which hasthe same structure as the list of requests. Thus, when the Neighbourhood receives a packet, it knows exactly57Figure 4.3: Graphical representation of the recovery process for two buildings.what type of supply is being delivered and the amounts destined to each building. A similar approach is usedfor engineering assessments, permits, financing, and workers, but some resources require a processing timebefore being delivered, e.g., financing and permits. This allows for the needs of each building to be treatedindividually and for the buildings to compete for limited resources. If the demand for a certain resourceis higher than the available supply then prioritisation rules are applied to select the buildings to receivesupplies first. Those prioritisation rules are different for each model, but in general they simulate businessesbehaviours, e.g., maximising profits and minimising losses.584.3.1 Model 1: Housing Recovery ModelModel 1 in Figure 4.2 is central in the presented framework. It is the Neighbourhood entity that was iden-tified in Figure 4.1 and it interacts with many of the other models in the framework to obtain financing,supplies, etc. Each Neighbourhood contains many buildings and dwellings, instantiated from informationcontained in the Census Information Model, i.e., Model 2. In the context of this chapter, a dwelling refersto the housing unit, e.g., detached house or apartment, and its occupants. Figure 4.4 presents the decisionsconsidered by the Neighbourhoods at each time step. Decision (1) guarantees that all Nb buildings are eval-uated. In Decision (2), the Neighbourhood checks the response from the hazard objects to determine if anearthquake has occurred in the current time step. If yes, loss and repair times are obtained by the Neighbour-hood via the hazard and building models, which are identified as Models 3-8 in Figure 4.4 and explainedlater. Buildings affected by earthquakes are replaced if repairs are not technically or economically feasible.FEMA P-356 (Federal Emergency Management Agency, 2000) refers to past events where buildings expe-riencing losses beyond 40-50% of their replacement cost were replaced. Buildings that did not meet currentcode before the event are also more likely to be replaced. In addition, the extent of permanent deformationscan make a building irreparable (Ramirez and Miranda, 2012; Ramirez et al., 2012; Hwang and Lignos,2017; Ruiz-Garcia and Miranda, 2006; Ruiz-Garcia and Chora, 2015; Pampanin et al., 2002; Hanson andComartin, 2000). Replacement costs and times are nearly 1.25 times the building construction costs andtimes, due to demolishing and clean-up (Federal Emergency Management Agency, 2012). In this paper, theprobability that a building is irreparable isp =1.0 if ρ ≥ 0.51.0 if ρ ≥ 0.4 and does not meet current codeΦ(β−1 ln(∆r/∆¯))otherwise(4.2)where ρ is the total damage ratio, which takes contributions from structural and non-structural damage, Φ(·)is the standard normal cumulative distribution function, β is the lognormal dispersion parameter, ∆r is thepermanent inter-story drift calculated as in Appendix C of the FEMA-58 (Federal Emergency ManagementAgency, 2012), and ∆¯ is the residual drift associated with a 50% chance of irreparability. The third conditionin Equation 4.2 gives the probability of irreparability of a building based on the permanent deformationdefined in the FEMA-58 (Federal Emergency Management Agency, 2012), ∆r, given as59∆r =0 if ∆< ∆y0.3(∆−∆y) if ∆y ≤ ∆≤ 4∆y∆−3∆y if ∆> 4∆y(4.3)where ∆ and ∆y are the peak inter-story drift and inter-story drift at yield, respectively. Thus, depending onwhether the building is irreparable, the loss isL =1.25 ·Vb if building is irreparableρ ·Vb otherwise(4.4)where Vb is the building value. The repair time, Tr, is similarly calculated as a function of the buildingconstruction time, Tc, asTr =1.25 ·Tc if building is irreparableρ ·Tc otherwise(4.5)If an earthquake is not identified in the current analysis step, the loss and repair assessment are skipped,and Decision (3) checks if the building is still damaged from an earthquake in a previous analysis step. Ifbuilding i is not damaged, or the building is already repaired, then the analysis proceeds to building i + 1.Alternatively, it is checked if the building was already inspected in Decision (4), and if not, a request forinspection is created. Once the building has been inspected, it needs to acquire resources for repairing, i.e.,materials, workers, engineers, permits, and financial resources. This is done in Decision (5) in Figure 4.4.Owner-occupied buildings start securing these resources immediately, whereas renter-occupied buildingswait a 30-days period. The delay in Decision (6) simulates the finding after the 1989 Loma Prieta and 1994Northridge earthquakes that owners of rented buildings did not take action immediately (Comerio et al.,1994). Decision (5) only returns ”yes” when all resources are obtained. Then, the availability of power inthe neighbourhood is checked in Decision (6). If power is available, repairs start.Financial resources may come from three sources, as shown by the symbol f© in Figure 4.2. Somehomeowners can also self-fund repairs. The decision on what type of funding to be used is based on loss andsocioeconomic characteristics of the building owner. The algorithm for this decision is shown in Figure 4.5.The outcome of this decision is the time for obtaining financial resources, Tf . If repairs are self-funded then60Figure 4.4: Flowchart of actions taken by the Neighbourhood Object, i.e., Object 1 in Figure 4.2.Tf = 0. Alternatively, Tf is a lognormal variable that depends on the type of financing, i.e., insurance, privateloan, or public loan. The following assumptions are included in the algorithm: All multi-family buildingsare insured; high income owners with no mortgage can self-fund repairs; insurance deductible is 10 percentof the value of the building; low income owners need loans even if insured to pay for deductible; recentand established immigrants do not have the needed credit history to get loans; moderate income owners canpay deductibles of up to $20,000 out of pocket. Also note that a key assumption in this dissertation is thatbuilding owners have the desire to repair their buildings to pre-disaster conditions.61Figure 4.5: Algorithm for homeowner repair financing decisions.4.3.2 Models 2: Census Information ModelIn Rts, a class named RCensusInformation is created to serve as a repository of data for a community or itssubdivisions, e.g., neighbourhoods, Census tracts. The main function of objects of this class is to instantiatethe buildings and dwellings within a neighbourhood, for example. Examples of Census Information Objectsbased on 2016 data (Statistics Canada, 2016) are shown in Table 4.3. The attributes of these objects canbe separated into building-related and population-related. Building information defines the housing stockof the neighbourhood and is used to instantiate the buildings. Population information is used to instantiatedwellings, and comprises high level socioeconomic data about the neighbourhood.The inputs in Table 4.3 are used to determine the socioeconomic demographics of dwellings. Thesocioeconomic demographics are categorical variables and their categories are listed Table 4.4. Incomecategories are defined as low, i.e., under C$60,000, moderate, i.e., between $60,000 and $100,000, and high,i.e., above $100,000. Immigration status is defined based on when the dwelling settled in Canada. Recentimmigrants settled in the last five years, established immigrants settled in the last ten years but more thanfive years ago, and the remaining are long-term residents (Statistics Canada, 2016). Dwelling size is aninteger number. Age category refers to the presence of children or seniors in the dwelling. The remaining62Table 4.3: Examples of Census information objects.Socioeconomic DemographicShaughnessy Strathconaof the neighbourhood [unit]Median dwelling income[$] 92179 21462Average dwelling size 2.40 1.7Males [%] 46.7 54.8Children [%] 13.9 8.5Seniors [%] 18 22.1Recent immigrants [%] 3.1 2.6Established immigrants [%] 34.9 28.3Occupancy rate 0.99 0.99Rented buildings [%] 25.3 80.8Dwellings with mortgage [%] 36.8 66.7Dwellings with cars [%] 68.3 31.5Pre-code buildings [%] 25.4 15.3Low-code buildings [%] 25.4 15.3Moderate-code buildings [%] 15.4 24.8High-code buildings [%] 33.6 44.4Single-family dwellings 2330 1090Multi-family dwellings 610 4750Median value of dwellings [C$] 3,494,588 799,509variables have self-explanatory categories.Table 4.4: Socioeconomic demographics categories for instantiated dwellings.Socioeconomic demographic CategoriesIncome low, medium, highDwellings tenure owner, renterInsurance coverage insured, not insuredImmigrant status recent immigrant, established immigrant, citizenDwelling size 1, 2, 3, 4, or 5 membersAge category has children, has seniors, has both, has noneMortgage with mortgage, without mortgageCar ownership car owner, non car owner63The Census information objects instantiate buildings and its dwellings following the steps in Algorithm1. For each building type, e.g., wood-frame, concrete moment-frame, the number of buildings to be gener-ated, Nb, is a function of the total number of dwellings for that building type, Nt , defined in the Census data.Buildings instances are generated and randomly assigned a number of storeys, number of dwellings, area,and value of the dwelling. The number of dwellings in each simulated building is subtracted from Nt , andthis process is repeated while Nt is larger than zero. Once the number of building instance is defined, thedwellings in each building have their socioeconomic demographics assigned.Algorithm 1 Building stock simulation for one building typeNumber of simulated building: Nb← 0;n← Ntwhile n > 0 doAssign code level;Assign number of storeys for the building, Ns;Assign number of dwellings for the building, Nd ;Assign floor area for each dwelling, Ad ;Assign value for each dwelling, Vd ;Nb ← Nb + 1;n← n - Nd ;end whilen← Nbwhile n > 0 doAssign tenure status for each dwelling;Assign income level for each dwelling as a function of tenure status;Assign insurance coverage;Assign immigrant status;Assign dwelling size;Assign age category;Assign mortgage status;Assign car ownership;n← n - 1end whileThe code level is the main descriptor of the physical vulnerability of a building. The Canadian buildingcode first included seismic provisions in 1940, and these were upgraded in 1975. It is here assumed thatbuildings built before 1940 are not design to resist seismic loads, and that buildings built between 1940and 1975 have limited seismic capacity (Mitchell et al., 2010). To assign the building code level, a randomnumber between zero and one is generated and compared to a discrete random variable characterised by thenumber of buildings built in each of these periods.The number of storeys, Ns, depends on the type of building, single- or multi-family, and on the if it is a64low-rise building or not, and it is mathematically defined asNs =2 if single-family4 if low-rise multi-family6 if medium-rise multi-family at low density area⌊0.25−(U(0,1)·0.2+0.05)0.02⌉+5 otherwise(4.6)where U(0,1) is a random variable uniformly distributed between 0 and 1. The number of dwellings in abuilding, Nd , is defined in terms of building type and the number of storeys. Single-family buildings containa single dwelling, whereas the number of dwellings for multi-family buildings depend on the number ofstoreys and the number of residential units per floor. Thus, the number of dwellings is a random variabledefined asNd =Ns ·⌊(0.25−(U(0,1) ·0.2+0.05))/0.05⌉+4 if multi-family and Ns < 7Ns ·4 if multi-family and Ns ≥ 71 otherwise(4.7)The area and values of each dwelling are assumed to be uniformly distributed around the median valuesfor the neighbourhood. The dwelling area in ft2, Ad , isAd = mA−500+U(0,1) ·1000 (4.8)and the value of the dwelling in C$, Vd , isVd = mV · (0.75+0.5 ·U(0,1)) (4.9)where mA is the median building area, and mV the median building value for the neighbourhood.Once the buildings are instantiated, the tenure status of the dwellings is defined. Dwellings are randomlycategorised into renter-occupied and owner-occupied based the percentage of rented and owned units in theneighbourhood. The type of building, i.e., single-family of multi-family, is not factored in when assigningdwellings as renters or owners. The dwelling income of each dwelling is assumed to be a function of thetenure status. A correlation between tenure status and dwelling income is observed for the municipalities in65the Metro Vancouver area, as shown in Table 4.5. It is assumed that the same correlation is present in theneighbourhoods in the City of Vancouver. Thus, the data in Table 4.5 is used to calibrate a linear model toestimate the probabilities of a dwelling being at low, moderate, and high income based on its tenure status.The goodness of fit for the models can be observed in Figures 4.6 and 4.7, and the models in Equations 4.10,4.11, and 4.12. With this, once a dwelling is randomly assigned a tenure status, i.e., owner or renter, itsprobabilities of being in low, moderate, or high income are calculated using Equations 4.10, 4.11, and 4.12.A uniformly distributed new random number is then generated to assign the income level of the dwellingbased on the probabilities of being low, moderate, or high income.66Table 4.5: Dwelling income by tenure for Metro Vancouver municipalities (MetroVancouver, 2019).Renter dwellings Owner dwellingsAverage Income Average IncomeMunicipality dwelling income Low Moderate High dwelling income Low Moderate HighAnmore $100760 – – – $153883 14% 24% 62%Belcarra n/a – – – $154863 13% 27% 61%Bowen Island $56791 51% 35% 14% $97444 27% 30% 42%Burnaby $45839 61% 27% 12% $80492 37% 29% 35%Coquitlam $46425 62% 26% 12% $89265 32% 29% 40%Delta $56195 53% 30% 17% $104000 24% 29% 47%Electoral Area A $34294 65% 20% 15% $59956 50% 20% 30%Langley City $38380 69% 24% 7% $73676 38% 34% 27%Langley Township $54761 53% 32% 15% $100065 25% 31% 45%Lions Bay $73116 – – – $130839 17% 28% 55%Maple Ridge $44797 62% 26% 12% $97820 26% 30% 43%New Westminster $44368 63% 27% 10% $86115 32% 33% 36%North Vancouver City $50398 56% 30% 14% $85991 33% 30% 38%North Vancouver District $59344 50% 29% 21% $119465 22% 26% 52%Pitt Meadows $53268 57% 30% 14% $98055 26% 32% 42%Port Coquitlam $49432 58% 28% 14% $95752 26% 32% 42%Port Moody $66690 45% 35% 21% $105118 24% 29% 47%Richmond $48989 58% 27% 15% $71840 42% 29% 30%Surrey $47965 60% 29% 11% $92614 28% 32% 40%Tsawwassen $61101 – – – $96222 35% 25% 40%Vancouver $50251 57% 28% 15% $88427 33% 28% 39%West Vancouver $48392 57% 25% 18% $112697 29% 23% 48%White Rock $41790 64% 24% 12% $73667 40% 30% 30%67Figure 4.6: Relationship between home ownership and income MetroVancouver (2019).P(I = low) =−3.5075 ·10−6 ·mi+0.64113 if owner−7.72 ·10−6 ·mi+0.974837 if renter(4.10)P(I = moderate) =−3.576 ·10−7 ·mi+0.3248 if owner4.50 ·10−6 ·mi+0.0629 if renter(4.11)P(I = high) =3.802 ·10−6 ·mi−0.0489 if owner3.365 ·10−6 ·mi−0.0241 if renter(4.12)Insurance coverage is assumed to be correlated to the median dwelling income in a neighbourhood. In-formation about insurance take-up rates in the City of Vancouver are available at city-level (AIR Worldwide,2013). This insurance take-up rate is transformed from city-level into neighbourhood-level using statisticalequivalence, that is, it is assumed that neighbourhoods with higher income also have a higher insurance68Figure 4.7: Relationship between home renting and income MetroVancouver (2019).take-up rate. The statistical equivalence is graphically demonstrate in Figure 4.8, and it is mathematicallyexpressed asP(In) = exp(( 10.35)· ln( InIc))·0.25+ ln(P(Ic))(4.13)where P(In) is the probability of being insured adjusted by the median dwelling income of the neighbour-hood, In is the median dwelling income of the neighbourhood, Ic and P(Ic) are the median dwelling incomeand the probability of being insured for all dwellings in the City of Vancouver.Finally, dwelling immigration and mortgage status, size, age category, and car ownership, are assigned.For each variable, realisations of a random variable uniformly distributed between zero and one, u∼U(0,1),is generated and used to assign the dwelling into a category based on the Census data. Using car ownershipas an example, if 40 percent of the dwelling have cars according to Census data and u < 0.40, the dwellingis considered to have a car. Otherwise it is considered to not to own a car.69Figure 4.8: Statistical equivalence between insurance take-up ratio and median dwelling income.4.3.3 Models 3-7: Earthquake Hazard and DamageModels 3-7 represent the seismic hazard, ground-motion prediction equations, building response and dam-age. These models, briefly discussed in Section 2.2, were developed earlier at the University of BritishColumbia in Mojitaba Mahsuli’s PhD dissertation Mahsuli (2012). These models are here tailored for thepresent application.4.3.4 Model 8: Power Infrastructure ModelsThe power network in the community is comprised of many substations, and each substation is representedby one object. For clarity, these are represented by a single instantiation of Model 9 in Figure 4.2. Acomprehensive and detailed representation of the power network in Vancouver is outside of the scope of thischapter; hence, a simplified approach where only high voltage, i.e., ≥ 230 kV, substations are included isadopted. The line diagram for the power network used in this chapter is shown in Figure A.2. The simplifiedpower grid in Figure 4.9 is assumed, where seven power substations provide electrical power for the nearbyneighbourhoods. The power network is represented by Substations and Hydroelectric Dams objects. Theresponse from these objects is not a packet; rather, it is a numerical value that indicates if the infrastructureis functional or not, i.e., whether it can provide power. Functionality may be lost due to direct damageor dependencies with other infrastructure, i.e., cascading effects (Rinaldi et al., 2001). During the period70power is unavailable, Td , buildings cannot be repaired. The seismic vulnerability and restoration of powerinfrastructure is modelled using fragility and restoration models in FEMA (2015). Figure 4.10 displaysthe restoration curves for power generation stations and power substations at complete damage. The meanrecovery time for substations is 30 days, and for generation stations 65 days. Power substations and damsare assumed not operational if their functionality is below 80 percent.HPNMANMPTMURCSQSPGCSNFigure 4.9: Assumed power grid for the Vancouver case-study.4.3.5 Model 9: Transportation Infrastructure ModelsFigure 4.11 shows the construction materials network employed in this paper. Construction materials aredelivered to Vancouver from suppliers overseas, in the United States, or in other Canadian provinces. Theoverseas suppliers use ship transportation and are dependent on the functionality of the ports in the region.Conversely, Canadian suppliers can deliver materials by truck or rail. The US suppliers are assumed to usetruck transportation. On-land transportation can be disrupted due to damage to bridges. The main attributesof Bridges are length, width, number of spans, and skew angle, which define the seismic fragility curvesfor each bridge. Twelve bridge objects are included in this study, and their properties are shown in TableA.8. Deliveries by sea may be disrupted due to damage to the Ports. Ports are modelled as not having71Figure 4.10: Restoration curves for power network infrastructure.back-up power and with unanchored components, i.e., no fully retrofitted to resist seismic loads. Damage tobridges and ports is accounted for with fragility curves provided by the HAZUS-MH manual (FEMA, 2015).Damaged bridges and ports regain functionality based on restoration curves provided by the HAZUS-MHmanual. Restoration curves for bridges are shown in Figure 4.12, and for waterfront facilities and storagefacilities in Figure 4.13. It is assumed that bridges and ports that are at least 80 percent functional allownormal traffic, and that traffic is completely disrupted otherwise.Figure 4.11: Simplified construction materials network for the Vancouver case study.72Figure 4.12: Restoration curves for bridges.4.3.6 Model 10: Materials Supplier ModelsOnce delivered to the region, wood materials are stored at a Hardware Store Model and concrete materialsare stored the Concrete Plant Model. The number of daily deliveries that the Material Suppliers can make,Nm, is an input to the model. It is assumed that under normal operations of the transportation network theMaterials Suppliers can make as many deliveries as needed, and that these are made immediately after arequest is received. If the transportation network is disrupted, a delay Tm is incurred. This way, the influenceof the transportation network on the availability of materials is captured but the availability of trucks fortransportation is not accounted for.73Figure 4.13: Restoration curves for port waterfront structure and storage facilities.4.3.7 Model 11: Post-earthquake InspectorsPost-earthquake inspections are processed by the Inspector Model, which collects requests for inspectionsand ships packets that simulate the visit of an inspector to a Neighbourhood. The number of daily inspectionsthat can be performed is a function of the number of available inspectors, Ni, number of daily work hours,Hd , and mean inspection time, mi. The number of inspections to be performed in any evaluation step, Is, iscalculated asIs =Hd ·Nimi· ∆t24(4.14)Thus, if the demand for inspections exceeds the availability of inspectors, some building will experience adelay Ti in their recovery. The attributes of the Inspector Model are the variables in Equation 4.14, and theseare presented in Table 4.6. The numbers in brackets in the following tables indicate assumed values.4.3.8 Model 12: Contractor FirmIn order to hire a contractor, a negotiation is necessary. A building in need of repairs indicates its need tohire a contractor by creating a request for contractor negotiation. The Contractor Firm collects this requestand provides a packet that simulates a contract between the homeowner and the firm. The contract is an74Table 4.6: Attributes of the Inspector Model class.Attribute Value UnitsNumber of inspectors [1200] –Number of daily work hours [12] hours/dayMean inspection time [1] hoursagreement on price and time-line for repairs, and it is a necessary step in order to mobilise workers. TheContractor Firm can start negotiations with all buildings at the same time, and the negotiating time, Tcn, indays, is a lognormal random variable defined asTcn ∼7 if single-familyLN(77,0.43) if repair class = 1 & low riseLN(161,0.41) if repair class = 3 & low riseLN(196,0.30) if repair class = 1 & high riseLN(280,0.31) if repair class = 3 & high rise0 otherwise(4.15)where the repair class is 1 if the structural damage ratio is 10-50 percent, 3 if the structural damage ratio ishigher than 50 percent, and 0 otherwise, and multi-family buildings with less than 20 floors are defined aslow-rise.Requests for contractor mobilisation are also collected by the Contractor Firm. Contractors are mo-bilised by buildings once repairs can start, and are allocated to the building until repairs are finished. Thus,the time for contractor mobilisation is the time needed for a crew of construction workers to be available.This time is dependent on the demand for workers; thus, buildings that request workers earlier tend not tohave to wait. The number of housing completions per year is utilised to indirectly calculate the numberof available crews. This information is publicly available from the Metro Vancouver Housing Data Book(MetroVancouver, 2019), and it is replicated in Table 4.7. A five-year average for the number of single-family and multi-family dwellings completions is computed. Note that multi-family buildings compriseseveral dwellings.From Table 4.7, 1816 single-family dwellings and 3855 multi-family dwellings are completed yearly in75Table 4.7: Housing completions in Vancouver MetroVancouver (2019).Dwelling type 2013 2014 2015 2016 20175 yearaverageSingle detached 1518 1195 1125 1058 1194 1218Accessory suite 378 375 367 349 368 367Semi-detached 126 178 166 120 100 138Row housing 132 95 35 102 99 93Total single-family 2154 1843 1693 1629 1761 1816Multi-family 2575 2444 2443 2151 3318 3855Vancouver. A 50 percent increase in building activity is assumed after an earthquake, similarly to what wasobserved after the 2010 Canterbury earthquake (Wood et al., 2016). According to HAZUS-MH (FEMA,2015) the construction time is 180 days for a single-family unit and 240 days for a multi-family building.Thus, the number of post-earthquake crews specialised on single-family housing, Ws f , is estimated asWs f = 1.5 · 180365 ·1816 = 1343 (4.16)and the number of multi-family specialized crews, Wm f , asWm f = 1.5 · 240365 ·3855 = 3802 (4.17)4.3.9 Model 13: Engineering FirmRequests for engineering services are collected by the Engineering Firm. Packets from this model representan engineering assessment performed by the engineering firm. The attributes of the Engineering Firm are thenumber of engineering assessments that can be performed simultaneously for single-family, Es f , and multi-family, Em f , buildings. These numbers are estimated in the same fashion as the number of constructioncrews. If the demand for assessments exceeds the capacity of the engineering firm, a waiting time, Te1,is needed until an assessment currently under way is completed. The time to complete an assessment ismodelled as a lognormal random variable (Almufti and Willford, 2013). The total time for an engineeringassessment, Te, is thus76Te ∼ Te1+1 if single-familyLN(42,0.40) if repair class = 1LN(84,0.40) if repair class = 3LN(350,0.32) if redesign is necessary0 otherwise(4.18)where Te is given in days. The repair class depends on the level of structural damage, and redesign isnecessary if the building needs to be replaced. The criteria for replacement was defined in Equation 4.2.The number of engineers available for single- and multi-family assessments is the same as the number ofconstructions crews.4.3.10 Model 14: Insurance FirmThe Insurance Company provides financing to insured buildings. Insurance covers up to total building re-placement cost, with a deductible of 10 percent of the building value. It is assumed that the InsuranceCompany expedites the processing of small claims and delays the processing of large claims. These be-haviours simulate empirical findings (Wood et al., 2016; Walker and Crawford, 2017). The threshold forsmall and large claims are defined in terms of the value of the building, Vb, and the changes in the process-ing time are defined by multipliers of the baseline values. The processing time for insurance claims in days,Tf c, is a random variable defined as (Almufti and Willford, 2013)Tf c ∼0.75 ·LN(42,1.11) if claim < 0.25 · Vb1.25 ·LN(42,1.11) if claim > 0.75 · Vb1.00 ·LN(42,1.11) otherwise(4.19)4.3.11 Model 15: Private LenderPrivate loans are provided to building owners who have the necessary credit histories by the Private Lender.The time needed for processing private loan requests in days, Tf p, is (Almufti and Willford, 2013)Tf p ∼ LN(105,0.68) (4.20)774.3.12 Model 16: Public LenderThe Public Lender provides publicly backed loans and expedites the processing of small financial requeststo simulate the willingness of the government to boost early recovery. However, large financial requests arenot delayed; thus, the time needed for processing public loan requests in days, Tf g, isTf g ∼0.75 ·LN(336,0.57) if claim < $20,0001.00 ·LN(336,0.57) otherwise(4.21)4.3.13 Model 17: Permit AssessorBuildings that need to be replaced require a permit. The Permit Assessor processes permit requests andcreates packets that simulate the delivery of a permit. The number of permitting approvals that can beprocessed simultaneously, Np, is limited, an any requests for permits beyond that are delayed by Tp1. Thecommunity’s capacity to process building permits is also calculated based on the number of yearly housingcompletions, but no distinction is made between single- and multi-family, so thatNp = 1.5 · 180365 ·1816+1.5 ·240365·3855 = 5144 (4.22)The processing time for permits, Tp1, for for single-family dwelling is set to one week. For multi-familybuildings this time is defined as a lognormal random variable that depends on the repair class for the building(Almufti and Willford, 2013).Thus, the processing time for permits, Tp2, isTp =[7] if single-familyLN(7,0.86) if repair class = 1LN(56,0.32) if repair class = 30 otherwise(4.23)and the total time for obtaining a permit is Tp = Tp1+Tp2.784.4 Analysis and ResultsIn the following, the housing recovery in Vancouver is investigated, using the models and analysis tech-niques presented earlier. It is assumed that the recovery is independent of the recovery of other municipal-ities in the Metro Vancouver area. The City of Vancouver is subdivided into 22 neighbourhoods, as shownin Figure 4.14. For reference, a baseline scenario is defined where 1,200 inspections, 1,343 engineeringassessments of single-family buildings, 3,082 engineering assessments of multi-family buildings, and 5,145permit assessments can be conducted simultaneously. Furthermore, 1,343 crews of workers specialised insingle-family buildings, and 3,082 crews specialised in multi-family buildings are available. The medianpayment times for insurance, private loans, and public loans are 6 weeks, 15 weeks, and 48 weeks, respec-tively. Power is directly transmitted from four hydroelectric dams by a system comprised of 17 substations.The transportation network comprises twelve bridges which are included in this case study.WestPointGreyKitsilanoKerrisdaleMarpoleOakridgeSunsetVictoria-FraserviewKillarneyRenfrew-CollingwoodHastings-SunriseGrandview-WoodlandStratconaDowntownWestEndFairview MountPleasantKensington-CedarCottageRileyParkSouthCambieShaughnessyArbutus-RidgeDunbar-Southlands0km 2km 4kmNFigure 4.14: Vancouver neighbourhoods.After an earthquake, most buildings are expected to experience some damage. Nonetheless, it is consid-ered that minor damage does not affect habitability. Thus, dwellings are considered damaged if the damage79requires more than 30 days to repair, which is equivalent to moderate damage according to the HAZUS-MHmethodology (FEMA, 2015). Otherwise, they are considered functional; hence, they are not competing forthe same resources as the damaged buildings. To compare the physical vulnerability of the neighbourhoods,a robustness index, Rb, is used. The index is calculated asRb =FD,0ND(4.24)where FD,0 is the number of functional dwellings immediately after the earthquake and ND is the total numberof dwellings. The speed of reconstruction is measured with a rapidity index that defines the percentage ofrepairs completed after a time t, calculated asRp(t) =FD,t −FD,0ND−FD,0 (4.25)where FD,t is the number of functional dwellings at t. Finally, the resilience of the neighbourhoods isassessed using the resilience index (Cimellaro et al., 2010; Bruneau et al., 2003)R =1t1− t0∫ t1t0Q(t)dt (4.26)where the index is defined in the time interval t0 to t1, and Q(t) is housing recovery curve.In the following case studies, the key assumptions listed below are present. These assumptions reflectdata and scope limitations.• all buildings seek repairs to pre-disaster state;• resources are distributed on a first-come-first-serve basis;• only buildings moderately or more damaged compete for resources;• owners of rented buildings do not start repair actions before 30 days of the event;• all multi-family buildings are insured;• high-income owner may pay out-of-pocket for repairs;• private loans are only available for long-term residents;• the recovery of Vancouver is not affected by the recovery of nearby municipalities;• the number of workers in the city increases by 50 percent during recovery;• all detached homes in Vancouver have similar structural properties;• all multi-family buildings with less than 5 storeys in Vancouver have similar structural properties;80• all multi-family buildings with more than 4 storeys in Vancouver have similar structural properties;• buildings built before 1940 are considered pre-code based on (Mitchell et al., 2010);• buildings built between 1940 and 1975 are considered low-code based on (Mitchell et al., 2010);• building built after 1975 are considered moderate-code based on (Mitchell et al., 2010).In Table 4.8, the number of objects and other information about the simulations conducted in this casestudy are presented.Table 4.8: Simulation parameters.Hazard objects 5 Inspector objects 1Ports objects 1 Insurance company objects 1Bridges objects 10 Public lender objects 1Road objects 6 Private lender objects 1Hydroelectric dam objects 4 Engineering firm objects 1Power substation object 17 Permit assessor objects 1Census information objects 22 Contractor firm objects 1Neighbourhood objects 22 Hardware store object 1Number of buildings 114,832 Concrete plant object 1Number of dwellings 283,815Number of dwellings 283,815Analysis time step [hours] 244.4.1 Case Study: M7.3 Earthquake in the Straight of GeorgiaIn this case study, recovery of housing in the City of Vancouver after a M7.3 earthquake in the Strait ofGeorgia is investigated. This a crustal earthquake with 5km assumed epicentre depth, located at 49o16’21”N, 123o24’36” W, 10 km West off the coast of the City of Vancouver, as shown in Figure 4.15.The closest and furthest neighbourhoods in the City of Vancouver are located nearly 14 km and 28km of the epicentre, respectively. Due to this, on-site ground acceleration significantly varies betweenneighbourhoods, as shown in Figure 4.16. Figure 4.16 also highlights the ground shaking intensity at threeperiods. An approximation for the natural period of a building is its number of storeys divided by 10.Thus, a 2 story house has a natural period of around 0.2s, a 4-story building has a natural period of 0.4s,and a 15 story building has a period of nearly 1.5s. Figure 4.16 indicates that the 2-story houses and the 4-81Figure 4.15: Epicentre location and distance to Vancouver city limits.story buildings experience similar spectral acceleration, whereas the taller buildings experience significantlylower intensities. Because wood-frame buildings are better at dissipating the energy from the ground motion,damage to low-rise and medium-rise concrete buildings is expected to be predominant.Figure 4.16: Comparison of spectral acceleration between two neighbourhoods.82In Figures 4.17-4.19 the peak ground acceleration, as well as the spectral acceleration for the period of0.3 seconds and and 1.0 seconds for each neighbourhood is shown. The peak ground acceleration is used tocalculate damage to infrastructure. The spectral accelerations are used to estimate damage to buildings ofdifferent heights. The period of 0.3 seconds approximates the period of a 3 storey building, and the periodof 1.0 seconds is close to a building with 10 storeys. The ground motion is more intense for neighbourhoodscloser to the epicentre of the M7.3 earthquake, that is, on the west side of the city of Vancouver.Figure 4.17: Peak ground acceleration for each neighbourhood.Figure 4.20 displays the duration of repairs in days in each the power substations following the M7.3earthquake. Repair times for the low-voltage substation decreases as distance to epicentre increases. Nonethe-less, the high-voltage substations located West of Vancouver present the higher repair times than most low-voltage substations. The fragility curves employed in modelling the power substations indicate that high-voltage substations are more vulnerable to seismic loads (FEMA, 2015). Due to repairs at the Meridian andIngledow a minimum 6-day long power outage is expected for all neighbourhoods. These results highlightthe importance of system-wide modelling, since these dependencies would not be captured by a model thatfocuses on the power substations within Vancouver limits.In Figure 4.21 the baseline scenario is explored, showing that the recovery for the baseline scenario83Figure 4.18: Spectral acceleration at the period of 0.3 seconds for each neighbourhood.extends over two years for all neighbourhoods, and extending for more than four years in some cases. Theextent of initial damage is higher for neighbourhoods closer to the epicentre and those that containing a largenumber of multi-storey buildings. For the first three months, most neighbourhoods do not experience anysignificant progress in their recoveries. After that, the recovery speed is highest for neighbourhoods withhigher income and lower percentage of renter-occupied homes and recent immigrants. The curves in Figure4.21 are presented separately in Figures B.1-B.4 in Appendix B to provide more detail.Table 4.9 presents the number of damaged dwellings immediately after the earthquake in each neigh-bourhoods, showing that the West End neighbourhood is the most immediately impacted. Table 4.9 alsoshows the progress of repairs after one, two, and three years. Repairs are slowest for West End and Strath-cona, the two poorest neighbourhoods. The results in Table 4.9 are also graphically presented in Figures4.22-4.25 to provide a geographical representation of housing recovery. The model for housing recoveryassumes that the limited resources for repairs are provided on a first-come-first-serve basis, as shown in Fig-ure 4.3. Under these assumptions, homeowner at low income and immigrant dwellings are in disadvantagebecause they have more difficulty securing funding. Furthermore, it is assumed that rented buildings willenter the competition for resources later. West End and Strathcona concentrate a large population of rented84Figure 4.19: Spectral acceleration at the period of 1.0 seconds for each neighbourhood.buildings, and for this reason, these neighbourhoods have a poorer recovery performance. The assumptionthat resources are distributed on a first-come-first-serve basis creates a strong relationship between socioe-conomic status and recovery capacity. Nonetheless, in reality the competition for resources may be betterrepresented by a bidding process. While the modelling of this bidding process is outside of the scope of thisstudy, a scenario where the correlation between socioeconomic status and recovery capacity is minimum isinvestigated in Section 4.4.1.The robustness, rapidity, and resilience indices that are obtained from Figure 4.21 are presented inTable 4.10. In terms of robustness, the Strathcona neighbourhood is the most severely impacted, with33 percent of its dwellings needing repairs that will take longer than 30 days, i.e., Rb=0.77. The leastimpacted neighbourhood is Renfrew-Collingwood, where only 6 percent of the dwellings are damaged,i.e. Rb=0.94. In terms of rapidity, the percentage of repairs completed after one year, Rp(365), determineswhich neighbourhoods are the first to start recovering. Neighbourhoods that primarily contain single-familybuildings present higher levels of recovery in the first year. This is because single-family wood-framebuildings experience less damage and are faster to repair. Neighbourhoods with high-income and low renterpopulation, e.g., Dunbar Southlands and Shaughnessy, fare better in terms of recovery in the first year after85Figure 4.20: Duration of repairs, in days, to power substations.the earthquake. The resilience index is highest for the neighbourhoods with lowest immediate impact andhighest speed of recovery, that is, newer and richer areas comprised mostly of wood-frame buildings.In Figures 4.26 and 4.27, the recovery capacity of Vancouver is investigated in terms of selected struc-tural and socioeconomic factors. The figures display the number of dwellings in need of repair over time.In the left-hand side graph in Figure 4.26 the results are compiled in terms of code level, i.e, pre-code, low-code, moderate-code, and high-code. The code level defines the building vulnerability and, as expected,pre-code and low-code buildings fare the worst, where as damaged to moderate-code and high-code build-ings is minor. Results for building types, i.e., single-family and multi-family, are shown in the right-handside of Figure 4.26. Overall, there are more multi-family dwellings in Vancouver (62 percent) and theseexperience more damage. Thus, nearly three times more multi-family dwellings are damaged immediatelyafter the earthquake.In Figure 4.27, the influence of selected socioeconomic factors is demonstrated. The results include onlysingle-family dwellings because all multi-family dwellings are assumed to be insured and socioeconomicaspects play a smaller role in their recovery. The recovery for single-family buildings is, in general, shorterthan for multi-family buildings and extends for less than three years. The slope of the curves is a measure of86Figure 4.21: Housing recovery curves for a four-years period.Figure 4.22: Dwellings in need of repairs immediately after the earthquake.the speed of recovery. It is shown that recovery is faster for single-family owner-occupied buildings whoseowner has a high income, is insured, and is a long-term resident. Those factors affect the building owner’swillingness and capacity to start repairs. By entering in the competition for recovery resources early, thesebuildings avoid delays related to engineers and workers being unavailable. As a result, the recovery times87Table 4.9: Dwellings in need of repairs over time.NeighbourhoodImmediately 1 year 2 years 3 yearsafter after after afterArbutus Ridge 1066 1066 867 786Downtown 2107 1361 2 0Dunbar Southlands 1187 536 182 0Fairview 3744 2890 113 0Grandview Woodland 2565 1869 120 0Hastings Sunrise 1180 733 156 0Kensington Cedar Cottage 1985 1467 262 0Kerrisdale 920 635 141 0Killarney 640 487 79 0Kitsilano 4967 4761 2874 0Marpole 1479 1406 1257 0Mount Pleasant 3168 3110 3000 104Oakridge 661 593 513 121Renfrew Collingwood 1056 896 688 84Riley Park 1408 1187 880 280Shaughnessy 406 280 154 0South Cambie 293 291 130 20Strathcona 1327 1327 1314 1250Sunset 1025 1025 624 20Victoria Fraserview 698 698 455 156West End 6530 6530 6520 6359West Point Grey 1155 1155 729 478for these buildings are shorter.88Figure 4.23: Dwellings in need of repairs one year after the earthquake.Figure 4.24: Dwellings in need of repairs two years after the earthquake.89Figure 4.25: Dwellings in need of repairs three years after the earthquake.Table 4.10: Housing recovery descriptors.Neighbourhood Rb Rp(365) R Neighborhood Rb Rp(365) RArbutus Ridge 0.82 0.00% 0.85 Mount Pleasant 0.82 1.83% 0.89Downtown 0.94 35.41% 0.98 Oakridge 0.87 10.29% 0.92Dunbar S. 0.84 54.84% 0.96 Renfrew C. 0.94 15.15% 0.97Fairview 0.81 22.81% 0.94 Riley Park 0.84 15.70% 0.91Grandview W. 0.83 27.13% 0.95 Shaughnessy 0.86 31.03% 0.94Hastings Sunrise 0.91 37.88% 0.97 South Cambie 0.91 0.68% 0.96Kensington 0.89 26.10% 0.96 Strathcona 0.77 0.00% 0.79Kerrisdale 0.83 30.98% 0.95 Sunset 0.91 0.00% 0.95Killarney 0.94 23.91% 0.98 Victoria F. 0.93 0.00% 0.96Kitsilano 0.78 4.15% 0.89 West End 0.79 0.00% 0.82Marpole 0.86 4.94% 0.92 West Point Grey 0.79 0.00% 0.8790Figure 4.26: Damaged dwellings by structural factors.Figure 4.27: Number of damaged dwellings by socioeconomic factors.91Parametric AnalysesThe results presented for the M7.3 earthquake considered the baseline scenario. Nonetheless, this scenariocomprises several assumptions on the pre-disaster and post-disaster state of the community. Here, the impactof changes to these assumptions is investigated. The impact of the assumption that resources are distributedon a first-come-first-serve basis is evaluated first. In Figure 4.28, the recovery curves for 22 neighbourhoodsare shown. The results assume that resources are distributed on a demand basis, that is, all things equal,the neighbourhoods most damaged receive supplies first. The results indicate that housing recovery is moreeven across the city under this assumption. Nonetheless, the correlation between the socioeconomic demo-graphics of the homeowners and their recovery capacity is not accounted for if resources are distributed inthis fashion.Figure 4.28: Recovery curves considering supplies are distributed on a demand basis.Figure 4.29 considers a scenario where an infinite number of inspectors, engineers, workers exist in thecommunity. Under these assumptions, there is no competition for resources and the recovery of the buildingsshould be independent. The results in Figure 4.29 demonstrate that in fact this is what happens, indicatingsoftware consistency.In Figures 4.30-4.32 the availability of inspectors, engineer teams, and permits assessors in the commu-nity is investigated. In all cases, the baseline results are compared to a scenario where the availability ofthese resources is doubled. In the three cases, there is no significant improvement over the baseline scenario,92Figure 4.29: Recovery curves for unlimited resources.what denotes that none of these factors is working as a bottleneck for recovery.Figure 4.30: Impact of availability of inspectors.In Figure 4.33, the impact of the availability of work crews on recovery is assessed. Unlike the results forinspectors, engineer teams, and permit assessors, the number of work crews significantly increase the speedof recovery, i.e., the slope of the recovery curve. However, it is noted that there are diminishing returns to93Figure 4.31: Impact of availability of engineer teams.increasing the number of work crews. This demonstrates that as the number of work crews increases, it nolonger acts as the bottleneck for housing recovery.94Figure 4.32: Impact of availability of permit assessors.Figure 4.33: Impact of availability of work crews.95Mitigation measuresBeyond modelling housing recovery, this case study also seeks to identify and quantify the benefits ofmitigation actions. Retrofitting the most vulnerable buildings in the community is an appealing mitigationaction. In Figure 4.34 the effect of retrofitting the pre-code and low-code buildings to moderate-code isshown. Five scenarios are evaluated, where the number of retrofitted buildings varies from zero, i.e., baselinescenario, to a scenario where all pre-code and low-code buildings are retrofitted. Damage and recovery timesare diminished as the percentage of buildings retrofitted is increased, nonetheless, because moderate-codeand high-code buildings still experience damage, not all losses are avoided.Figure 4.34: Impact of retrofitting on recovery times.Retrofitting is a powerful mitigation option, nonetheless it requires an initial investment. It is difficult toestimate this cost for multi-family buildings because each building may require a different intervention. Forsingle-family wood-frame buildings, a common retrofitting measure is to bolt the foundation and brace thecripple walls. Figure 4.35 shows the possible payoffs, as percentage of the building value, from retrofittingall pre-code and low-code buildings. The expected payoff for retrofitting a single-family wood-frame build-ing for each neighbourhood isE(Ph) =1Nr·Nr∑i=1((L0,i−Lr,i))/VB,i (4.27)96where L0,1 and Lr,i are the immediate loss without and with retrofit, respectively, for building i, and Nr is thetotal number of buildings retrofitted. The results indicate that retrofitting provides returns for homeownersin most neighbourhoods. Dunbar Southlands, Kitsilano, and Kerrisdale observe the highest gains, as theseneighbourhoods have a significant percentage of pre-code and low-code highly-valued buildings. The min-imum returns are seen for Killarney and Renfrew Colligwood, the two neighbourhoods furthest away fromthe epicentre. On average, a return of 7.82% of the building value is observed for the city of Vancouverconsidering the M7.3 earthquake. It is highlighted that these results are in terms of the earthquake in thiscase study and will change if other hazards are considered.Figure 4.35: Return on investments as percentage of building value.In terms of recovery times, the results presented in Figure 4.36, consider three mitigation actions: (i)97retrofitting 50 percent of the pre-code and low-code buildings to moderate-code level; (ii) doubling theavailable workforce for recovery through training programs; and (iii) shortening the time for public loansto be paid out, from 48 weeks to 15 weeks. In Figure 4.36 the changes in recovery time as percentagesof the baseline results are shown. It is observed that Action (i) reduces the physical vulnerability of thebuildings and reduces the immediate losses and extent of damage. Conversely, Action (ii) does not affectthe immediate impacts but greatly increases the speed of recovery. Action (iii) reduces the time that thedisadvantaged homeowners (immigrants and low income homeowners) need to wait to start repairs. Theresults in Figure 4.36 are presented as percentages of the recovery times in the baseline scenario. It is shownthat reducing the loan processing time has the least effect on recovery times. This measure helps lowersocioeconomic status homeowners to obtain financing earlier, which increases the demand for workers in thecommunity. Because the number of workers is the same as in the baseline scenario, it becomes a bottleneckfor the housing recovery. Retrofitting 50 percent of the buildings has a more significant impact on therecovery, reducing the mean recovery time in nearly 40 percent. This mitigation action reduces the numberof buildings damaged and the extent of damage, thus reducing initial impacts and causing fewer buildingsto compete for resources. Doubling the number of workers has a slightly higher impact, reducing the meanrecovery time for all neighbourhoods by approximately 45percent. Although increasing the number ofworkers is the most effective measure on average, retrofitting provides more benefits in terms of recoverytimes for the neighbourhoods closer to the epicentre. Because of this, a combination of the consideredactions is likely to be the most effective mitigation plan. In Figure 4.36, the results of the combinationof Actions (i), (ii), and (iii) is also shown, in the right-most columns. The combined effect of the threemitigation measures reduce the average recovery by nearly 60percent.For completeness, the impact of the mitigation measures on the equity of recovery is also investigated. InFigure 4.37, the dashed lines represent the baseline number of damaged dwellings over time based on income(left), and immigrant status (right). The results only include single-family dwellings, since the recoveryof multi-family buildings is not affected by income and immigration status. The results that include themitigation measures are represented by the solid lines. In both cases, the mitigation measures significantlyreduce disparities in the recovery of immigrants and low income homeowners.98Figure 4.36: Effects of mitigation actions on recovery time.Figure 4.37: Impact of mitigation actions on recovery equity.4.4.2 Case Study: Earthquake in the Straight of Georgia with Probabilistic MagnitudeIn this case study, housing recovery in the City of Vancouver is investigated following an earthquake withepicentre 14 kilometres west of Vancouver and with probabilistic moment magnitude. Four moment magni-tudes, M, are investigated, i.e., 5.5, 6.0, 6.5, and 7.0. Figure 4.38 shows the results for the robustness index,Equation 4.24, for the neighbourhoods as the moment magnitude is increased. The robustness index is an99inverse measure of damage, therefore it is inversely proportional to the magnitude of the hazard. Neighbour-hoods with a large number of old multi-storey buildings, e.g., Strathcona, West End, and Kitsilano have thelowest robustness.Figure 4.38: Robustness indexes of neighbourhoods for different moment magnitudes.In Figure 4.39, the time it takes to repair 95 percent of the buildings in each neighbourhood is shown foreach moment magnitude. For M≤6.0 no neighbourhood has more than five percent of its buildings damaged.For M=6.5, the neighbourhoods with a significant number of pre-code and low-code buildings experiencesome damage and repair times up to 800 days are observed in West End, Strathcona, and Arbutus Ridge.At M =7 all neighbourhoods experience some level of damage. The increased damage and competition forresources extend recovery times to more than 1,200 days at the neighbourhoods that fare worse.Lastly, the resilience of the neighbourhoods is investigated for the different moment magnitudes. Theresults in Figure 4.40 show that, in general, resilience decreases as hazard levels increases. Downtownpresents the highest resilience index in all cases. As it was demonstrated in Figures 4.38 and 4.39, Downtownhas the highest robustness and highest recovery capacity, what is translated into the high resilience. Thelowest resilience index is observed for Strathcona.100Figure 4.39: Rapidity indexes of neighbourhoods for different moment magnitudes.The hazard levels investigated in Figures 4.38-4.40 have different probabilities of being experienced.The Gutenberg-Richter law can be used to estimate the likelihood of each observing each moment magni-tude, f (m) (Gutenberg and Richter, 1944)f (m) =b · exp[−b · (m−Mmin)]1− exp[−b · (Mmax−Mmin)] for Mmin ≤ m≤Mmax (4.28)Figure 4.41 presents f (m) considering usual values for the parameters in Equation 4.28, namely Mmin= 5, Mmax = 7.5, and b = 1.0, and the probability that the moment magnitude will exceed the selected M,P(M ≥ m), are listed. Because the selected M do not cover the whole spectrum of possible outcomes, therule of total probability is used to estimate the likelihood of observing the selected moment magnitudesconditional on the occurrence of an earthquake, P˜(M = m|E)P˜(M = mi|E) = P(M = mi|E)∑4i=1 P(M = mi|E)(4.29)Using the probabilities P˜(M = m|E), the expected time to recover from an earthquake in the Strait ofGeorgia with probabilistic magnitude, E(T ), can be calculated101Figure 4.40: Resilience indexes of neighbourhoods for different moment magnitudes.Figure 4.41: Probability of observing different ground shaking intensities.E(T ) =4∑i=1P˜(M = mi|E) ·Ti(95%) (4.30)where mi are the four hazard levels considered, and Ti(95%) is the time to repair 95 percent of the buildings102for a given mi. In Figure 4.42 the expected recovery time for each neighbourhood is presented. The baselinescenario is shown in red, whereas the scenario including retrofitting is shown in green, and the scenario withdouble the workforce is shown in blue. The average baseline recovery time for all neighbourhoods is 28days. This means that if an earthquake moment magnitude between 5 and 7 occurs in the selected location,it is expected that housing recovery in Vancouver will take 28 days on average. The Downtown, HastingsSunrise, Killarney, Renfrew Collingwood, South Cambie, Sunset and Victoria Fraserview neighbourhoodsare expected to not be impacted. Conversely, expected recovery time for West End is greater than 90 days.Doubling the number of workers reduce the mean expected recovery time by nearly one quarter, whereasretrofitting the pre-code and low-code buildings halve the mean expected recovery time.Figure 4.42: Expected recovery times for probabilistic earthquake magnitude.Finally, the results in Figure 4.43 show the expected losses for each neighbourhood for the baseline and103retrofit scenarios. The immediate losses are concentrated in the Downtown, Fairview, Mount Pleasant, andWest End neighbourhoods. These neighbourhoods comprise a large number of multi-family buildings withhigh value. The bars in green show the differential loss between the baseline and the retrofit scenarios, thatis, the savings results from taking this mitigation action. The retrofitting is most effective for the West Endneighbourhood.Figure 4.43: Expect losses for probabilistic earthquake magnitude.4.5 Final RemarksThis chapter presented an object-oriented model framework for assessing the post-earthquake housing re-covery in urban communities. A collection of models were introduced, aiming to improve the modelling ofbuilding recovery compared with methodologies that focus on buildings in isolation. Socioeconomic fac-tors, e.g., building tenure, homeowner’s income and immigration status, were accounted for in the recoverycapacity of the community. In the consideration of the City of Vancouver the neighbourhoods are unique104in terms of their buildings and their socioeconomic demographics. This translated into heterogeneous re-covery capacities. Only an approach that accounts for these two dimensions, i.e., building vulnerability andsocioeconomic demographics, can fully capture the housing recovery trends in a modern community. Theproposed approach is capable of identifying the neighbourhoods most immediately impacted and those thattake the longest to recover. The approach presented in this chapter can quantitatively assess the benefits ofdiverse mitigation measures. It was shown that retrofitting selected buildings and training new workers canreduce recovery times by nearly 40 percent, and that mitigation actions can be ineffective if they are notaccompanied by an increase in the availability of resources in the community. This information is valuablein the designing of disaster recovery plans. It is important to note that the problem at hand is complex.The results presented here are predicated on the aforementioned modelling assumptions and the informationprovided by the census data for the City of Vancouver. The main challenge in using publicly available in-formation is in accurately representing the building stock. Nonetheless, if more detailed information aboutthe building stock is available, this can be incorporated with little changes to the overall analysis due to theobject-oriented nature of the presented framework.105Chapter 5Predicted Population Displacements in theCity of VancouverAn object-oriented model for population displacements is presented and used to analyse the decision-makingfor dwellings after a M7.3 earthquake in the City of Vancouver, Canada. Temporary displacements andpermanent relocation are accounted for in this chapter. The analyses include models for buildings, waterand power infrastructure, and dwellings. In the context of this chapter, a dwelling refers to the housingunit, e.g., detached house or apartment, and its occupants. The models for the decisions dwellings includeconsiderations on socioeconomic demographics, social networks, and disaster preparedness. The decisionof dwellings to relocate accounts for internal and external factors. The analysis results indicate that nearly70,000 persons are expected to be displaced by the M7.3 earthquake. Of those, close to 19,000 will needpublic sheltering. In addition, nearly 40,000 persons are expected to relocate in the two years following theearthquake. Among the displaced, occupants of multi-family pre-code and low-code are over-represented.Among those needing public shelter or relocating, there is a disproportional high number of renters andlow-income persons. The information obtained in this chapter can improve pre-disaster plans by suggestingoptimal location of public shelters and identifying mitigation strategies that reduce the number of personsopting to relocate.1065.1 IntroductionThis chapter presents new object-oriented models for assessing the decisions of dwellings to leave theirhomes temporarily or permanently, i.e., relocate, after an earthquake. Structural damage, availability of wa-ter and power, as well as socioeconomic demographics are assumed to impact temporary displacements.To model the decision of dwellings to relocate, housing recovery speed, neighbourhood recovery, pre-disposition to move out, and psychological trauma are accounted for. The goal in this chapter is to create arobust tool to identify the factors that make dwellings more likely to be displaced, temporarily and perma-nently. Such a tool can inform decisions to be made prior to earthquakes to mitigate the number of displacedpersons and the number of persons relocating.Between 2005 and 2015, natural disaster claimed the lives of 700,000 persons, injured 1.4 million, andmade 23 million homeless (Aitsi-Selmi et al., 2015). It is estimated that more 1.5 billion persons have beenaffected directly or indirectly by these events. Twice as many persons lose their homes to natural disastersnowadays as in the 1970s (Goldenber, 2019). In 2016 alone, natural disasters displaced 31 million persons,three times as much as conflicts (Irish Times, 2019). Estimates of the number of displaced persons and theirneeds are important information for the development of emergency plans and recovery strategies. Severalempirical studies have investigated what conditions lead to population displacement after natural disasters(Hong, 2017; Ahmad et al., 2017; Zhang et al., 2014; Voskanyan and Cahill, 2016), with many focusingspecifically on earthquakes (Vecere et al., 2017; Franchin and Cavalieri, 2015; Giovinazzi et al., 2011;Khazai et al., 2012; Wright and Johnston, 2010). Simulation models for estimating the number of displacedpersons have also been developed. A review of open-access software packages for assessing earthquakeimpacts conducted by the World Bank (World Bank, 2014) identified that dwelling displacement was ametric considered in HAZUS-MH (FEMA, 2015), MAEviz (Elnashai et al., 2008), CAPRA (Cardona et al.,2012), SELENA (Molina et al., 2010), SYNER-G (Pitilakis et al., 2014), RiskScape (King and Bell, 2005),EQRM (Robinson et al., 2006), OpenQuake (Silva et al., 2014), and InaSAFE (Pranantyo et al., 2015).These simulation models have been developed for estimating immediate population displacement, whichis commonly used as proxy for public sheltering demand. Nonetheless, the majority of those seeking tem-porary shelter use public sheltering as a refuge of last resort (Perry and Lindell, 2003; Quarantelli, 1982).Research has found that less than a quarter of those seeking sheltering use large-scale public facilities (Lin-dell et al., 1985), and that dwellings with low income, in rental housing, in unsafe homes (prior to the event),107and with limited social support are more likely to do so (Perry et al., 2001; Elliott and Pais, 2006). Thus,socioeconomic disadvantaged persons are forced into worse housing conditions for longer periods of time,since socioeconomic factors dictate housing recovery rates (Miles and Chang, 2011). The lack of adequatehousing conditions may force disadvantaged persons to relocate. Mass relocation can change the socialfabric, impede recovery, and even lead to the abandonment of certain neighbourhoods (Lawless, 2019).It becomes evident that simulation models that investigate population displacements beyond the responsephase can improve the capacity of communities to prepare for disasters. However, a holistic model forpopulation displacement that can quantitatively compare mitigation actions is still needed. The researchpresented in this chapter addresses this gap in three ways. First, this chapter introduces new object-orientedmodels for dwelling decision making, dwelling disaster preparedness, fatalities caused by earthquakes, andwater distribution infrastructure. Second, the models are used to evaluate the decision of dwellings aftera large earthquake in Vancouver, Canada. In the short-term, dwellings that decide to leave their homestemporarily are assumed to go to hotels, stay with family or friends, or seek public sheltering. In the long-term, displaced persons need to decide to wait for repairs to their homes or to relocate. The destinationof persons that relocate is not modelled in this study. Finally, this chapter contributes with insights intothe factors that lead to temporary and permanent displacements, identifying the socioeconomic groups thatare over-represented among the displaced population. Comparison of the benefits of selected mitigationmeasures are also presented.5.2 Modelling Population DisplacementChapter 4 focuses on the modelling of housing recovery and the aspects that constrain it. In this chapter, thefocus shifts from the buildings to the persons that occupy them. The following questions are investigated inthis chapter: How many persons are expected to be displaced by an earthquake near Vancouver? What are thehousing conditions of displaced populations? What are the best predictors of dwelling displacement? Howmany persons are expected to relocate in each neighbourhood? What are the socioeconomic demographicsof those who decide to leave?The modelling of population displacement presented in this chapter builds upon the modelling of hous-ing recovery in Chapter 4. The state of residential buildings, as well as the recovery speed in each neighbour-hood are important factors in determining population displacements in this chapter. The case study in thischapter employs the assumptions, the scenario earthquake, estimated available workforce, and behaviours of108resource providers used in the case in Section 4.4.1. Thus, the case study in this chapter can be interpretedas an extension of the case study in Section 4.4.1.In Figure 5.1 the models used to evaluate population displacement for one neighbourhood are shown.Many models are used to represent the hazard, the water, power, and transportation infrastructure, as wellas the resource suppliers, e.g., contractor firm and insurance company. However, for clarity, in Figure 5.1these are indicated by only one box. The models for the hazard, the power infrastructure, and resourcesuppliers, as well as the Census Information Model were introduced in Chapter 4. The models developedin this chapter are the Displaced Population Model, the Indoor Fatality Model, the Dwelling PreparednessModel, and the models for water distribution infrastructure. These are discussed in detail in the followingsections.The Displaced Population Model represents all dwellings in one neighbourhood. The dashed line in Fig-ure 5.1 indicates requests for resources coming from the dwellings. The response object from the SupplierModels is indicated by a generic packet response containing supplies, s©. These supplies are transportedthrough the transportation network to the neighbourhood. The response from the power and water infras-tructure models are the time needed to repair these infrastructure, Td and Tw. The response from the BuildingDamage Model is a vector DS containing the damage state of each building in the neighbourhood. Damageto buildings and infrastructure is calculated based on peak and spectral accelerations coming from the haz-ard models, indicated by PGA and Sa in Figure 5.1. The output of the Displaced Population Model is thenumber of persons displaced, Pd .109Figure 5.1: Overview of the objects used in the modelling of population displacements.5.3 Displaced Population ModelThe Displaced Population Model is a key model in the analyses in this chapter. This model estimates thehabitability of buildings in the same fashion as the Housing Recovery Model introduced in Section 4.3.1.Nonetheless, the Displaced Population Model uses the recovery state of the building, alongside other factors,to assess if a dwelling will be displaced in the aftermath of an earthquake. Dwellings may be displacedtemporarily, i.e., while the conditions of the homes are not ideal, or permanently, if they decide to relocate.Temporary displacement is considered to have a positive effect on permanent relocation. The DisplacedPopulation Model contains the algorithms for these two decisions.In this chapter, temporary displacement is assumed to be driven primarily by the building safety, avail-ability of water and power, as well as the perception of livability of the dwelling. Conversely, the decisionof a dwelling to relocate is based on pre-disposition to move out, psychological trauma, housing and neigh-bourhood recovery, and the decisions of neighbours. Figure 5.2 shows a diagram of the factors that affecttemporary and permanent displacements. The arrows indicate the dependencies between factors.110Figure 5.2: Factors affecting the decisions of dwellings.5.3.1 The Decision to Leave Home TemporarilyIn Figure 5.3, the algorithm for temporary dwelling displacement is shown. To model the tendency ofa dwelling to leave its home temporarily, the Displaced Population Model considers that both structuraldamage, availability of water and power, and certain socioeconomic factors are determinant. Decisionsare represented by diamond-shaped boxes, and actions are represented by rectangular boxes. Decision (1)guarantees all NB buildings are evaluated. For each building, the first action is to evaluate the buildinghabitability, i.e., the capacity of the building to provide adequate sheltering. Structural damage, as well as,availability of water and power influence the building habitability. The conditions defined by Chang et al.(2008) are used to define the functional habitability, H f , as111H f =Very low if Ds = 4Low if Ds = 3, or Td > Ap days, or Tw > AwLow if Ds = 2 and Td > Ap and Tw > AwHigh if Ds = 0 or 1 and Td < Ap and Tw < AwModerate otherwise(5.1)where Ap and Aw are the number of days a dwelling is willing to stay at home without power and withoutwater, respectively. These values are discussed in detail in Section 5.5. If H f = very low, all dwellings areforced to leave the building. Conversely, the perception of the dwelling about the living conditions of itshome is evaluated. Decision (2) in Figure 5.3 guarantees that the decisions of all NH dwellings in the buildingare assessed. Decision (3) evaluates the perception of the dwellings about the building in order to determinetheir desire to leave. The perceived habitability depends on the functional habitability, building tenure, ageof the dwelling members, as well as the neighbourhood and weather conditions (Chang et al., 2008). Studiesshown that perceived habitability is also influenced by ethnicity (Peacock et al., 2014; Fothergill et al., 1999;Comerio, 1997). These studies showed that certain ethnic groups who have experienced earthquakes in theircountries of origin are more concerned with the risk of aftershocks, and have a higher tendency to abandontheir homes. Because similar information is not available for Vancouver, this effect is not included in thisdissertation. Thus, the perceived habitability, Hp, can be ”unacceptable”, U, or ”acceptable”, A, and isevaluated asHp =U if H f = ”Very low”U if H f = ”Low” and is a renter and has children or seniorsU if H f = ”Low” and is a renter and neighbourhood condition is ”Bad”U if H f = ”Moderate” and neighbourhood and weather are ”Bad”A otherwise(5.2)where weather conditions are ”Bad” during Winter, and the neighbourhood conditions are ”Bad” if theaverage damage state for the buildings in the neighbourhood is equal or larger than three, i.e., extensivedamage (Chang et al., 2008). Dwellings that find their conditions acceptable choose to remain at home.112Figure 5.3: Algorithm for temporary dwelling displacement.Dwellings that perceive the conditions of their homes to be unacceptable have the desire to leave.The housing conditions of displaced dwellings depends on many factors. If the building is owner-occupied and insured, it is assumed that the cost of temporary alternative housing is covered and they goto rental housing or hotels. If owner-occupied buildings are uninsured, the income of the homeowner ischecked. High income dwellings are assumed to go to rental housing or hotels. For low and moderate113income dwellings, Decision (4) in in Figure 5.3 evaluates if they have support from family or friends in thecommunity. If so, they stay with them, otherwise, they will seek public sheltering. Renter dwellings behavelike uninsured owner dwellings. The access to support from family or friends is determined from the 2014survey on emergency preparedness in Canada (Statistics Canada, 2019) as a function of the dwelling incomeand immigration status. The probability a dwelling will have family or friends to support them given theirincome, P(FF |Ii, j), is (Statistics Canada, 2019)P(FF |Ii, j) =0.20 if low income0.25 if moderate income0.25 if high income(5.3)and the probability of having support from family or friends conditioned on immigration status, P(FF |Si, j),is (Statistics Canada, 2019)P(FF |Si, j) =0.15 if recent immigrant0.16 if established immigrant0.24 if long-term resident(5.4)The conditional probabilities in Equations 5.3 and 5.4 are used to calculate the probability a dwellingwill have support from family or friends asP(FF) = max(P(FF |Ii, j),P(FF |Si, j)) (5.5)the probability P(FF) is used to determine if a dwelling will stay with family or friends or seek publicsheltering.5.3.2 The Decision to RelocateThe spatiotemporal scale of major housing recovery events make longitudinal collection of quantitative datadifficult (Chang, 2010). As a result, the literature on the factors that lead to the relocation of sizeable pop-ulations after natural disasters is limited (Levine et al., 2007). Zhang and Peacock (2009) studied housingrecovery after Hurricane Andrew and identified that dwelling dislocation was driven by damage to the neigh-bourhood, housing tenure, and minority status. Henry (2013) provides a comprehensive study of the factors114that influenced the decisions of dwellings to relocate after Hurricanes Katrina and Rita, in 2005. Three fac-tors were found to be dominating the decisions of dwellings: risk, family, and work. Risk refers to the riskperception of the dwellings after a disaster. Family refers to the decisions, i.e. leave or stay, of their familymembers in other dwellings. Work refers to the availability of jobs, and has been identified as an importantfactor in other studies as well (Nejat, 2011; Zhang and Peacock, 2009). Nejat and Ghosh (2016) used leastabsolute shrinkage and selection operator to investigate the main factors affecting the decisions of dwellingsafter Hurricanes Sandy and Katrina. Availability of insurance, availability of funding from external sources,as well as tenure or place attachment were identified as impacting to the decisions of dwellings. The im-portance of place attachment was also highlighted by Airriess et al. (2008) and Chamlee-Wright and Storr(2009). Nejat and Damnjanovic (2012) also developed a temporospatial agent-based model for decisionsof homeowners in which the main factor accounted for are dynamic interactions of homeowners with theirneighbours. The psychological well-being of the affected dwellings has also been shown to influence thedecisions of dwellings (Rust and Killinger, 2006; Bolin, 1976).In this study, the willingness of a dwelling to relocate is a time-dependent variable, W (t). The short-literature review presented above is used to determine which factors should be considered in estimatingW (t). Because a surrogate measure of risk perception is not easily obtainable, this factor highlighted asimportant by Henry (2013) is not accounted for here. Thus, the following factors are accounted for in thisdissertation:• housing recovery capacity;• current living conditions;• pre-disposition to move out;• loss of loved ones;• state of the neighbourhood;• number of neighbours moving out;• place attachment;• time since the event.The housing recovery capacity is the capacity of a dwelling to repair its buildings in a timely manner. Itis affected by several factors, e.g., dwelling income, tenure, insurance availability, etc and it was discussedin detail in Chapter 4.115Current living conditions are the result of the decision to leave home temporarily, shown in Equation 5.2.Temporary displacements are affected by structural damage, building type, availability of water and power,as well socioeconomic aspects. Current living conditions different from those pre-disaster are assumed toincrease the willingness of a dwelling to relocate, W (t). The multiplier ML is used to capture this effect andis defined asML =1.0 if living in rented housing1.25 if living with family or friends1.5 if living in a public shelter(5.6)Pre-disposition to move out and the loss of loved represent the psychological state of the dwelling. Pre-disposition to move out refers to non-ideal housing conditions before the earthquake and it is determinedin this chapter based on three factors: pre-disaster safety, affordability, and suitability. Pre-disaster safetyreflects the maintenance state of the building prior to the earthquake. Dwellings spending more than 30percent of their combined income with shelter are considered to have an affordability problem (StatisticsCanada, 2016). Finally, suitability refers to whether the dwelling has enough bedrooms for the size andcomposition of the dwelling. The percentage of pre-disaster unsafe, unaffordable, and unsuitable homesis provided from census data. It is also considered that dwellings experiencing post-traumatic stress fromthe loss of a loved one are more likely to relocate. It is assumed that pre-disposition to move out andpost-traumatic stress increase W (t) by a factor MP, given asMP =1.5 if lost loved one or was pre-disposed to move out1.0 otherwise(5.7)The state of the neighborhood is considered to influence the willingness to relocate of a dwelling. Dam-age to school, hospital, grocery store, and other commercial buildings reduce the quality of life of families.Furthermore, the state of these buildings also impact the availability of jobs. The neighbourhood condi-tion at a given time, Cn(t), is calculated as the average structural damage ratio in the neighbourhood. Thewillingness to leave, W (t), is multiplied by 1+Cn(t) to capture the influence of this factor.The decisions of their neighbours is also assumed to influence the decisions of dwellings. It is consideredthat the more dwellings decide to relocate, the more likely the temporarily displaced dwellings are to do the116same. Conversely, the more dwellings have completed repairing their homes and have decided not to stay,the more likely the temporarily displaced dwellings are to wait for their homes to be repaired. To capturethis factor, the function f (Rh,Gh, t) is proposed heref (Rh,Gh, t) =Th(t)−Rh(t)Th(t)−Gh(t) (5.8)where Th(t) is the total number of dwellings in the neighbourhood, Rh(t) is the number of dwellings thatalready completed repairs, and Gh(t) is the number of dwellings who decided to relocate. Note that Equation5.8 only accounts for pre-earthquake residents leaving the neighbourhood, and does not account for newfamilies moving in to the neighbourhood. In Figure 5.4, Equation 5.8 is plotted for a given time t fortwo cases. On the left-hand side it is shown that if few persons leave the neighbourhood that has a smallimpact on f (Rh,Gh, t). Conversely, if the majority of the dwellings leave, there are large incentives for theremaining dwellings to also leave. On the right-hand side, it is shown that f (Rh,Gh, t) decreases linearlywith the increase in the number of dwellings deciding to stay.Figure 5.4: Effect of neighbours housing conditions on dwelling decision.Finally, it is considered that willingness to leave, W (t), grows the longer a dwelling remains displaced.It is assumed that renters are willing to stay 180 days under non-ideal living conditions, i.e., Tthreshold =180, whereas homeowners will stay in such conditions for 365 days, i.e., Tthreshold = 365. With this, theexpression proposed for the willingness of dwellings to leave their homes, W (t), isW (t) = ML ·MP · (1+Cn(t)) · f (Rh,Gh, t) · t− t0Tthreshold (5.9)117where t0 is the time of the earthquake. While the approach in Equation 5.9 simplifies a complex decisionprocess, it shows the potential of the presented framework to incorporate diverse factors into modellingdecisions. With W (t), the decision of dwelling j in building i to leave after t time is calculated asD(t, i, j) =Leave if has no funds to repairLeave if W (t)> 0.5Stay otherwise(5.10)5.4 Indoor Fatality ModelIn the presented approach, dwelling that lose loved ones are considered more willing to relocate due topsychological trauma. The Indoor Fatality Model is used by the Displaced Population Model to determinelikelihood that a dwelling member is killed during the earthquake. It should be noted, however, the totalnumber of persons in the community is not reduced by casualties. Many software for estimating earthquakeimpacts include fatality rates quantification (Elnashai et al., 2008; Cardona et al., 2012; Molina et al., 2010;King and Bell, 2005; Robinson et al., 2006; Silva et al., 2014; Pranantyo et al., 2015). In most of thesesoftware, the HAZUS-MH (FEMA, 2015) approach is employed. The HAZUS-MH methodology for esti-mating indoor fatalities defines that residential building occupancy varies throughout the day, being highestat night when all occupants are assumed to be at home, and lowest during business hours. The occupancy ata given time, O(t), is (FEMA, 2015)O(t) =0.70 ·0.50 if t between 6 a.m. and 9 a.m.0.70 ·0.075 if t between 9 a.m. and 4 p.m.0.70 ·0.50 if t between 4 a.m. and 8 p.m.0.999 ·0.99 if t between 8 p.m. and 6 a.m.(5.11)The probability of fatalities for a dwelling, Pf ,0, is then estimated asPf ,0 = O(t) ·P(F |DS = dsi) ·P(DS = dsi) (5.12)where O(t) is the percentage of occupants indoors at the time of earthquake, and P(F |DS = dsi) is theprobability of fatalities given damage state i, where as P(DS = dsi) is the probability of damage state i.118The HAZUS-MH approach estimates fatalities based on the structural damage. Nonetheless, by review-ing data from several past earthquakes, Sutley et al. (2017a) determined that fatalities are more commonamong certain socioeconomic groups, e.g., low income persons. Sutley et al. (2017a) suggest that the fa-tality rates calculated based on structural damage state should be multiplied by factors that are conditionalon the socioeconomic demographics of the community. In this chapter, the fatality multiplier for incomecalculated by Sutley and her colleagues is applied considering the income of the dwelling. Thus, the fatalitymultiplier for income, Fi, is (Sutley et al., 2017a)Fi =3.485 if low income1.850 if moderate income1.000 if high income(5.13)Thus, the likelihood of fatalities for a dwelling, updated by its socioeconomic demographics, Pf ,SED, isthus obtained asPf ,SED = Fi ·Pf ,0 (5.14)5.5 Dwelling Disaster Preparedness ModelDisaster preparedness activities are defined as actions to ”effectively anticipate, respond to, and recoverfrom, the impacts of likely, imminent, or current hazard events or conditions” (United Nations, 2009, p.21). Disaster preparedness is one of the most effective ways to mitigate potential losses from disasters(Levac et al., 2012). Dwelling disaster preparedness can be measured by the level of material preparedness,i.e., physical items that a ”prepared” dwelling is expected to have, and preparedness activities, i.e., thelevel of disaster planning for a dwelling (Dore, 2000). This chapter focuses on material preparedness, andresults from studies indicate that Canadian dwellings do not have sufficient material preparedness (Lemyreet al., 2007). In order to estimate the disaster preparedness for the dwelling in the city of Vancouver,data from a study on disaster preparedness conducted by Statistics Canada in 2014 are used (StatisticsCanada, 2019). These data indicate that in Vancouver, 15 percent of the dwellings have a back-up generator,and that 44 percent have bottled water at home. For Canada, these values are 23 percent and 43 percent,respectively. The probabilities that a dwelling has a back-up generator, P(Sp), or bottled water at home,P(Sw), are of interest for this dissertation. These probabilities are conditioned on housing tenure (St), income119(I), immigration status (Si), age (A), and dwelling size (Sh) as (Statistics Canada, 2019)P(Sp|St) =0.077 if owner0.048 if renter(5.15)P(Sp|I) =0.024 if low income0.118 if moderate income0.020 if high income(5.16)P(Sp|Si) =0.098 if long-term resident0.030 if established immigrant0.007 if recent immigrant(5.17)P(Sp|A) =0.105 if has children or elders0.040 otherwise(5.18)P(Sp|Sh) =0.038 if one person0.054 if two persons0.019 if three persons0.015 if four persons0.010 if five or more persons(5.19)P(Sw|St) =0.226 if owner0.190 if renter(5.20)120P(Sw|I) =0.072 if low income0.341 if moderate income0.062 if high income(5.21)P(Sw|Si) =0.272 if long-term resident0.127 if established immigrant0.034 if recent immigrant(5.22)P(Sw|A) =0.331 if has children or elders0.119 otherwise(5.23)P(Sw|Sh) =0.151 if one person0.147 if two persons0.061 if three persons0.042 if four persons0.030 if five or more persons(5.24)From Equations 5.15-5.24, the probability of having access to back-up a generator isP(Sp) = max(P(Sp|St),P(Sp|I),P(Sp|Si),P(Sp|A),P(Sp|Sh)) (5.25)and the probability of having bottled water at home isP(Sw) = max(P(Sw|St),P(Sw|I),P(Sw|Si),P(Sw|A),P(Sw|Sh)) (5.26)The probabilities P(Sp) and P(Sw), are used to determine the number of days a dwelling can stay at homewhile electrical power from the community is unavailable, Ap, as121Ap =∞ if has a generator4 otherwise(5.27)note that Equation 5.27 assumes that fuel for the generator is available during the recovery. The number ofdays a dwelling can stay at home if water is unavailable from the community, Aw, isAw =7 if has an alternate water source4 otherwise(5.28)5.6 Water Infrastructure ModelsTo account for the availability of water in Vancouver distribution facilities and pipelines are modelled. Thewater transmission to Vancouver is presented in Figure A.4, in Appendix A. Four water pump stations areassumed to serve Vancouver directly, and the water distribution grid in Figure 5.5 is assumed. Thus, awater shortage is observed if the water pump station is directly damaged, or if there is significant damageother infrastructure on which the pump station depends. Water infrastructure regain functionality basedon restoration curves (FEMA, 2015). Restoration curves for water infrastructure experiencing completedamage are shown in Figure 5.6. It is assumed that facilities that are 80 percent or more functional canoperate normally, and that they are disrupted otherwise. Thus, water lift stations completely damaged takenearly 50 days to be operating again, whereas water tanks take nearly 250 to be operational if damage iscomplete.Water shortages can also occur due to damage to the pipeline system that supplies the residential build-ings. In Figure 5.5, the distribution pipelines in Vancouver are shown. A model for pipeline functionality,based on the algorithm in the HAZUS-MH (FEMA, 2015), is used to estimate damage to pipelines. Thismodel represents all pipeline segments in one neighborhood as a single surrogate pipeline. The length of thesurrogate pipeline is equivalent to the total length of all pipeline segments in the neighborhood, Lp, whichis obtained from publicly available drawings. The surrogate pipeline is assumed to be ductile, and consid-erations about the age of the pipeline system are outside of the scope of this chapter. The surrogate pipelineis exposed to the ground shaking intensities measured at the centroid of the neighborhood, from which theexpected number of leaks and breaks is estimated. Pipelines may suffer damage from transient and perma-122KerslandLittleMountainVancouverHeightsSasamatFigure 5.5: Water distribution grid and pipelines in Vancouver.nent ground deformations. Transient deformations are largely controlled by the peak ground velocity thesoil experiences. Thus, the number of repairs due to peak ground velocity needed after an earthquake, Rt , iscalculated asRt = 0.0001 ·Lp · fµ ·PGV 2.25 (5.29)where Lp is the pipeline length in kilometres, fµ is the ductility factor, and PGV is the peak ground velocitycalculated at the centroid of the neighbourhood. The ductility factor is fµ=1.0 for brittle pipelines, e.g.,asbestos cement, concrete, and cast iron, whereas fµ=0.3 for ductile pipelines, e.g., steel, ductile iron, andPVC. It is noted that all pipelines are considered to be ductile and that the age of the pipeline system123Figure 5.6: Restoration curves for water distribution infrastructure.is not accounted for in this dissertation. Thus, it is expected that the damage to the pipeline system isunderestimated. The number of repairs needed due to permanent ground deformations, Rp, is given byRp = Lp · fµ ·P(L) ·PGD0.56 (5.30)where PGD is the permanent ground deformation, and P(L) is the probability of liquefaction, which is afunction of PGD and the ground settlement susceptibility. It is assumed that Vancouver has low susceptibil-ity to liquefaction.Damage to pipelines can cause leaks or breaks. A leak is a minor damage, associated with a damageratio of 10 percent, and it takes a four-person crew four hours to fix a leak in distribution pipelines. Breaksare associated with a damage ratio of 70 percent, and it takes a four-person crew eight hours to fix a breakin distribution lines. It is assumed that damage due to seismic waves will consist of 80 percent leaks and20 percent breaks, conversely, damage due to ground failure will consist of 20 percent leaks and 80 percentbreaks. Thus, the total number of leaks isNleaks = 0.8 ·Rt +0.2 ·Rp (5.31)and the total number of breaks is124Nbreaks = 0.2 ·Rt +0.8 ·Rp (5.32)The time needed to repair one leak is half the time needed to repair one break. Thus, from a repair-timestandpoint, one break is equal to two leaks. If a four-person crew takes eight hours to fix one break, the totaltime to complete repairs to the distribution, Tw, lines isTw = (Nbreaks+Nleaks ·0.5)/(3 ·Nc) (5.33)where Nc is the number of four-person crews allocated to the job. The functionality of the distributionpipelines is calculated asFw = 1−Φ(10.85· ln(ρr/0.1))(5.34)where ρr is the repair rate given byρr =(Nbreaks+Nleaks ·0.5)−3 ·Nc · (t− t0)Lp(5.35)where t and t0 are the current time and the time of event, respectively. It is considered that if 80 percent of thepipelines are functional then dwelling have access to water. The length of the water distribution pipelines,Lp, for each neighbourhood calculated from publicly available drawings is shown in Table 5.1.Table 5.1: Length of distribution pipelines per neighbourhood.NeighbourhoodLength ofNeighbourhoodLength ofpipelines (km) pipelines (km)Arbutus Ridge 45.55 Mount Pleasant 58.86Downtown 59.20 Oakridge 46.69Dunbar Southlands 84.76 Renfrew Collingwood 106.89Fairview 41.88 Riley Park 65.08Grandview Woodland 66.67 Shaughnessy 62.70Hastings Sunrise 86.39 South Cambie 25.34Kensington-Cedar Cottage 112.17 Strathcona 39.17Kerrisdale 61.56 Sunset 77.80Killarney 57.66 Victoria Fraserview 72.40Kitsilano 79.05 West End 37.92Marpole 62.34 West Point Grey 49.281255.7 Case studyThis case study investigates the impact of the M7.3 earthquake discussed in Section 4.4.1 on the populationof Vancouver. Assessing the number of persons displaced, their housing conditions, and socioeconomicprofile are key goals in this case study. The number of persons leaving is a proxy for changes in the socialfabric of the neighbourhoods in Vancouver, rather than an estimate of population decline. The progress ofhousing recovery is an important indicator of population displacement. In terms of housing recovery, thesame baseline assumptions used in Chapter 4 are employed. Power is directly supplied by seven powersubstations, and water is provided by four water treatment and distribution plants, as shown earlier in Figure5.5. In this case study, the effectiveness of four mitigation measures is evaluated: (i) retrofitting 50 percent ofpre-code and low-code buildings, (ii) doubling the number of work crews in the community, (iii) reducingthe payment time of public loans to 15 weeks, and (iv) creating incentives for homeowners to stay, i.e.,increasing place attachment. Mitigation action (i) is implemented by changing the fragility curve of pre-code and low-code buildings. Mitigation action (ii) is implemented by doubling the number of work crewsavailable to the Contractor Firm Model. Mitigation action (iii) is implemented by reducing the mean of therandom variable that defines the payment time of public loans. Mitigation action (iv) is implemented byincreasing the threshold value in Equation 5.10 from 0.5 to 0.75.In the following case studies, the key assumptions listed in Section 4.4 are complemented by the onespresented below. The only exception is the assumption in Section 4.4 that all buildings are repaired to pre-disaster state. In this chapter, buildings abandoned by their owners are not repaired at all. These assumptionsreflect data and scope limitations.• public shelters are a last resort option for dwellings;• insurance covers the costs of rental housing during recovery;• high income dwellings can afford the costs of rental housing during recovery;• renters are less attached to their homes and neighbourhoods than owners;• injuries do not affect the decisions of dwellings, fatalities do;• once dwellings repair their buildings, they do not consider relocating anymore.In Table 5.2, the number of objects and other information about the simulations conducted in this caseare presented.The first results presented are in terms of the number of effective pipeline breaks, that is, the number126Table 5.2: Simulation parameters.Hazard objects 5 Inspector objects 1Ports objects 1 Insurance company objects 1Bridges objects 10 Public lender objects 1Road objects 6 Private lender objects 1Hydroelectric dam objects 4 Engineering firm objects 1Power substation object 17 Permit assessor objects 1Water treatment facility objects 6 Contractor firm objects 1Water storage tank objects 4 Hardware store object 1Water pump station objects 6 Concrete plant object 1Water pipeline system objects 22 Number of buildings 114,832Census information objects 22 Number of dwellings 283,815Neighbourhood objects 22 Number of dwellings 283,815Analysis time step [hours] 24 Number of persons 606,352of breaks plus half the number of leaks. In Figure 5.7, the results on the left-hand side map show thatthe number is the highest for the Dunbar Southlands and Kesington-Cedar Cottage neighbourhoods. Theseneighbourhoods have some of the longest pipeline grids, and as defined in Equations 5.31 and 5.32, thenumber of breaks and leaks if a function of the length of the pipeline grid. Furthermore, ground accelerationand velocity are highest for Dunbar Southlands due to proximity to the epicentre, as shown in Figures 4.18and 4.19. The map on the right-hand side in Figure 5.7 normalises the number of breaks by the total pipelinelength in each neighbourhood. In this case, the number of breaks per kilometre of pipeline are determinedby the hazard intensity and the neighbourhoods closest to the epicentre fare worse.It is assumed in this case study that one work crew is available to fix pipeline damage on each neigh-bourhood. Under this assumption, the longest repair time for pipelines is nine days for Dunbar Southlands,and the longest water shortage for this neighbourhood is 80 percent of the repair time, that is, nearly sevendays. Moreover, power outages are expected to be shorter than five days, as shown in Figure 4.20. Thus, theavailability of utilities plays a small role in the displacement of dwellings in this case study.In Figure 5.8 the number of person at home over time is presented. Unlike the curves for the number offunctional dwellings shown in Chapter 4, the curves in Figure 5.8 are not monotonically increasing and theydo not return to pre-disaster conditions. This is because dwellings may decide to leave their homes after127Figure 5.7: Total number of pipeline breaks (left) and number of breaks per kilometre of pipeline(right) by neighbourhood.some time and because some dwellings leave their homes permanently. The largest percentage populationdisplacements are observed in West End and Kitsilano. The neighbourhoods to lose the largest percentageof their pre-disaster populations are West End and Strathcona. Renfrew-Collingwood presented the lowestpercentage of displaced persons immediately after the earthquake, and residents of Downtown were thefastest to be able to return to their homes, on average.The number of persons immediately displaced is shown in Figure 5.9 for each neighbourhood. Structuraldamage is an important factor in the results in Figure 5.9. The neighbourhoods comprising significantnumber of pre-code and low-code multi-family buildings, e.g., West End and Kitsilano, have the largestpopulation displacements. Another important factor is population density. In Figure 5.8 it was shown thatnearly 22 percent of the population in West End and 15 percent of the population in West Point Grey areimmediately displaced. Although the percent of the population displaced in West End is nearly 1.5 timesthat of West Point Grey, the number of persons displaced in West End is six times larger.The total number of displaced persons in the Vancouver over time is shown in Figure 5.10. The resultsconsidering the four mitigation measures are also included in the figure. Shortening the payment time forpublic loans are demonstrated to be ineffective at reducing the number of persons displaced. Increasingthe number of work crews speeds up recovery, shortening the time needed for dwellings to return home,particularly early on. Increasing place attachment has a slightly smaller impact on the number of personsdisplaced in the first three years, but significantly reduces the number of persons displaced at the end of thefour-year period studied. Nonetheless, these two alternatives do not reduce the number of persons that areimmediately displaced. Because of that, the alternative that is most effective at reducing displacements is the128Figure 5.8: Displaced persons by neighbourhood over time.retrofitting of the most vulnerable buildings. This mitigation action reduces the number of person leavingthe community over the four years by nearly 50 percent.Beyond the trends in population displacement, the housing conditions and the socioeconomic profile ofthose displaced is investigated. This information is useful in designing pre-disaster mitigation and recov-ery plans. In Figure 5.11, a radar chart containing selected descriptors of housing conditions and selectedsocioeconomic demographics is shown. The curve in black represents the profile of the Vancouver popu-lation. For example, in Vancouver nearly 50 percent of the population have low income, nearly 60 percentare long-term residents, and nearly 20 percent of the buildings are pre-code. The curve in orange representsthe profile of the dwellings that are immediately displaced after the M7.3 earthquake. From Figure 5.11 it isnoted that renter dwellings in multi-family, pre-code or low-code buildings are over-represented among the129Figure 5.9: Persons displaced immediately after the earthquake per neighbourhood.displaced population. Conversely, owner dwellings in single-family, moderate-code or high-code, buildingsare under represented among the displaced population. These results provide insights on what fraction of thepopulation are the most vulnerable to being displaced after the scenario earthquake. Note that the numberof insured dwellings is also larger among the displaced population than in the general population. This isexplained by the assumption that all multi-family buildings are insured, and multi-family buildings are infact more susceptible to seismic damage.In Figure 5.12, the number of displaced persons seeking rental housing or hotel rooms in the baselinescenario is shown. This includes all dwellings displaced from owner-occupied insured buildings and thosewith high income. West End and Kitsilano have the largest demands for rented housing and hotel rooms,6,986 and 6,177 persons, respectively. In total, 43,346 residents of Vancouver are expected to seek rentalhousing or hotels rooms, or approximately 19,702 dwellings. The average occupancy rate in Vancouverin 2016 was 99.3 percent (Statistics Canada, 2016). Thus, it is expected that nearly 2,000 dwellings arevacant. There were 23,000 hotel rooms in Metro Vancouver, and 13,925 hotel rooms within Vancouver(Chan, 2019). If all rental homes and hotel rooms are unoccupied and functional, 15,925 units are availablein Vancouver. This demonstrates that even under unlikely good conditions nearly 8,000 persons would needto seek rental housing or hotel rooms in neighbouring municipalities.In terms of their socioeconomic profile, those seeking rental housing or hotel rooms have higher income130Figure 5.10: Total persons displaced over time.when compared to the displaced population in general, as shown in Figure 5.13. Owners are also over-represented among the population seeking rental housing or hotel rooms.Displaced persons that are uninsured or do not have the funds to seek temporary shelter in rental homesor hotels will seek public sheltering or will stay with family or friends. In Figure 5.14 the number ofdisplaced persons expected to seek public shelters is shown for each neighbourhood. The West End neigh-bourhood presents the largest shelter needs, with nearly 6000 persons in need of public sheltering. Aspreviously shown, a large number of persons is displaced from West End. Because this neighbourhood iscomprised of a large number of low-income renter dwellings, many of its residents are expected to dependon public shelters after the M7.3 earthquake. The number of persons living with family or friends, althoughnot presented, follow the exact same pattern as in Figure 5.14. This is because it is assumed the personsstaying with family or friends are a subgroup of those that will seek shelter.The socioeconomic profile of the dwellings seeking public sheltering is compared to that of the overallpopulation and the displaced population in Figure 5.15. Low-income renter are disproportionately repre-sented in this group in comparison both to the overall population and the displaced population. For othervariables, the profile of those in need of public sheltering is very similar to the profile of the displaced131Figure 5.11: Socioeconomic profile of the displaced dwellings.Figure 5.12: Displaced persons seeking rental housing or hotel rooms per neighbourhood.population.Finally, in Figure 5.16, the number of persons deciding to relocate over time is shown, considering thebaseline scenario, as well, as the four mitigation actions. Speeding up the payment of public loans have132Figure 5.13: Socioeconomic profile of the dwellings seeking rental housing or hotel rooms.Figure 5.14: Displaced persons seeking public shelter per neighbourhood.negligible effect in reducing relocation, as it was previously demonstrated. From Figure 5.16 it is noted thatdoubling the number of work crews reduces the number of persons deciding to relocate by nearly 10,000.However, this mitigation action is not effective to reduce the relocation rates, i.e., the slope of the curve. In133Figure 5.15: Socioeconomic profile of the dwellings seeking public shelter.the aforementioned cases, nearly 30,000 persons leave their homes within one year of the M7.3 earthquakeand this needs to be considered when planning for recovery. Increasing place attachment reduces the numberof persons relocating by nearly 15,000. This alternative also delays the time it takes for the first dwellingsto relocate, compared to the other options. Amongst the ones considered, the best alternative to reduce thenumber of persons leaving the community is to retrofit half of the pre-code and low-code buildings. Thisalternative is the most effective at reducing the relocation rates and the total number of persons who decideto relocate in the four-year period.In terms of the neighbourhoods expected to experience the largest loss of their population in the baselinescenario, West End is again the most critical case, as shown in Figure 5.17. In total, close to 40,000 personsare expected to relocate. Approximately 14,000, or 35 percent of these, are residents of the West Endneighbourhood. The main reasons for these results are the large number of residents of West End temporarilydisplaced and the slow housing recovery presented by this neighbourhood. The slow housing recoverycauses the majority of the temporarily displaced persons to decide to relocate.Figure 5.18 compares the profile of those relocating with those immediately displaced and the populationas a whole. The results indicate that renters and low-income dwellings are over-represented among those134Figure 5.16: Persons who decided to relocate.Figure 5.17: Displaced persons who decided to relocate within one year.who decide to permanently leave their homes.135Figure 5.18: Socioeconomic profile of the dwellings that decide to relocate.5.8 Final RemarksThis chapter presents an object-oriented model framework for assessing population displacements in urbancommunities following earthquakes. A collection of models is introduced, aiming to improve the modellingof long-term population displacements compared with methodologies that focus on population displace-ments during the recovery phase only. Building damage, availability of utilities, socioeconomic factors,pre-disposition to move out, psychological trauma, and dwelling disaster preparedness are accounted for inthe dwellings’ decision leave their homes temporarily or permanently. It is shown that 35 percent of all dis-placed persons are in the West End and Kitsilano neighbourhoods. In addition, the West End and Kitsilanoalso comprise 50 percent the dwellings leaving their homes over a four-year period after the earthquake.This information is valuable in pre-planning the location of post-earthquake public shelters and strategiesto retain residents. It is also shown that low-income renters and those occupying pre-code and low-codebuildings are the most likely to be displaced and to relocate after an earthquake. This provides insights onthe needs of the displaced population and helps design better response and recovery strategies.136Chapter 6ConclusionsAn integrated approach was employed in this dissertation. Power, water, and transportation infrastructure,as well as buildings and dwellings are included in the analyses. This integrated approach provides greatversatility in terms of the mitigation measures that can be studied by the presented framework. More im-portantly, the integrated approach allows for the assessment of the benefits of mitigation measures to onesystem on other systems. For example, with an integrated approach the effects of improvements to the waterpipeline system on the number of persons displaced can be examined. The effectiveness of the followingmitigation actions is assessed in this dissertation:(1) increasing the fullness of fuel storage tanks to reduce the number of persons without fuel in remotecommunities;(2) partially retrofitting the most physically vulnerable buildings to reduce dwelling displacement times;(3) increasing the workforce available in the community to speed up housing recovery;(4) reducing payment times for public loans to reduce socioeconomic disparities in housing recovery;(5) increasing place attachment to reduce the number of persons that will abandon their homes duringrecovery.Action (1) was shown to reduce the probability of fuel shortages for the community investigated. Action(2) reduced immediate losses, recovery times, and was the most effective alternative to reduce the numberof persons permanently relocating after the M7.3 earthquake. Action (3) has shown great potential to speedup recovery in the community, being the most effective alternative to shorten recovery times. Action (4) wasdemonstrated to be beneficial for certain neighbourhoods and detrimental for others, having little capacity to137reduce average housing recovery times. Action (5) was not effective at reducing the the number of personsabandoning their homes during recovery.It was also shown that the presented framework is capable of identifying bottlenecks for disaster recov-ery. In Chapter 3, the framework is used to identify the infrastructure more likely to be the cause a disruptionin the fuel distribution network. The results indicate that tank farms tend to be the infrastructure that takesthe longest to repair, thus, being the cause of fuel shortages in many cases. This provides evidence for thefuel system operators that retrofitting these infrastructures by anchoring them is beneficial. Furthermore,it was shown that tank farms operating under a just-in-time refilling strategy are up to three times morelikely to experience fuel shortages in the aftermath of earthquakes. This demonstrates that non-structuralinterventions are also appealing actions to reduce the risk of fuel shortages.In Chapter 4, the presented framework is used to test the sensitivity of the housing recovery speed to theavailability of inspectors, engineers, and work crews in the city of Vancouver. It was shown that the numberof work crews is the most important resource among the ones investigated. The study of housing recovery inVancouver also shows that recovery after a strong earthquake will take more than three years. The density ofmulti-family old buildings, renters, and the income and immigration status of the homeowners are shown tobe good predictors of the speed of recovery for a neighbourhood. Homeowners at the West End, Strathcona,and Kitsilano neighbourhoods are shown to be last to repair their buildings. These findings can inform plansdeveloped by the Chief Resilience Officer in the City of Vancouver to increase resilience. This informationcan help in the development of disaster mitigation actions that target the most vulnerable buildings andhomeowners, as well as in tailoring housing recovery strategies that lessen disparities during recovery. Twomitigation measures, namely retrofitting the most vulnerable buildings and doubling the workforce in thecity during recovery, were demonstrated to be efficient in reducing housing recovery times and improvingequity in recovery.The analysis results in Chapter 5 indicate that nearly 70,000 persons are expected to be displaced bythe M7.3 earthquake. Of those, close to 19,000 will need public sheltering. The West End and Kitsilanoneighbourhoods comprise the largest portion of the displaced population. These results can help the city ofVancouver to better prepare for such catastrophic event. By preemptively knowing where the high demandsfor public sheltering are, the city can take actions to improve the community centres and schools in theseneighbourhoods, since these are good candidates for the location of post-earthquake public shelters. Theresults also show that among those needing public sheltering, there is a high number of renters and low-138income dwellings. This helps estimating the demand for public sheltering, as well as the needs of thoseseeking public sheltering. If it is demonstrated, for example, that low-income renters in Vancouver tendto be recent immigrants, with a small and also vulnerable social networks, the needs of this group can beanticipated.Chapter 5 also shows that nearly 40,000 persons are expected to relocate in the two years following theM7.3 earthquake investigated. Among those relocating, there is a disproportionally high number of rentersand low-income dwellings. These findings can help planners in the City of Vancouver in identifying mitiga-tion strategies that reduce the number of dwellings relocating. This will reduce the likelihood that sectionsof neighbourhoods will be significantly changed, either in terms of their residents or type of housing.It should be noted that all findings and conclusions obtained in Chapters 4 and 5 are based on an earth-quake with epicentre 14 km west of the City of Vancouver. The spatial distribution of damage to residentialbuildings, as well as critical infrastructure are likely to be significantly different if another earthquake isconsidered. In consequence, demands for resources for recovery are also expected to change.This dissertation demonstrates the value of object-oriented approaches for investigating complex phys-ical and social dependencies. This approach allows for a broad range of mitigation measures to be inves-tigated, and it is specially suited to study recovery processes and outcomes over time. It is important tohighlight that all analyses in this dissertation were performed on a single Intel Coffee Lake i7-8750H CPUwith 2.20 GHz clock speed. The scenario analyses in Chapter 3 took approximately three seconds to run dueto the smaller number of objects and smaller number of time steps, 120. The most CPU-intensity analyseswere the ones in Chapter 5, which contained a large number of objects and comprised a larger number oftime steps, namely 1460. Each scenario analysis in Chapter 5 took up to 600 seconds to run. This demon-strates that the presented computer framework can easily be used by individuals, students or professionals,to investigate new scenarios.6.1 Overview of ContributionsThe contributions of this work include:(1) the compilation of data on seismic hazard and exposure for Lower Mainland Vancouver;(2) the development of a comprehensive simulation framework for studying disaster impacts on commu-nities;139(3) new models for water, power, and transportation infrastructure, resource suppliers, residential build-ings, and dwellings;(4) the development of a new modelling approach to simulate the transportation of discrete shipmentsthrough a network of models;(5) vulnerability assessment of the fuel distribution system in coastal British Columbia;(6) the evaluation of post-earthquake housing recovery in Vancouver;(7) the estimation of the number of displaced persons and the identification of their socioeconomic profile.In Appendix A, data on seismic hazard and exposed assets in Lower Mainland British Columbia fromseveral sources are compiled. Information on the location and seismic vulnerabilities was collected forselected water, power, transportation, and fuel distribution infrastructure. A review of published sourceswas used in compiling these data. They can be used for comprehensive risk assessments and disaster impactevaluations in Lower Mainland British Columbia.Chapters 2-5 introduce several models for representing the entities in a community. These models arebased on empirical studies, public available data, models developed by other researchers, and reasonable as-sumptions. Uncertainty is represented through random variables and treated through Monte Carlo sampling.One innovative aspect of this framework is that it integrates critical infrastructure, buildings, and dwellingsin the same analysis. Thus, a contribution of this dissertation is the better representation of the dependenciesbetween engineering and socioeconomic factors, as well as resource availability.In Chapter 3, the objective of investigating the effect of infrastructure damage on the transportation ofresources is addressed. A new approach is presented for modelling interconnected infrastructure where thebehaviours of agents and connections change dynamically, and heterogeneity exists between agent types.Models for refineries, storage tanks, ports, bridges, fuel pipelines, trucks, and ships are developed. Ademand-based approach is also introduced where ”packets” are used to transport fuel through a networkof models.This dissertation contributes with insights on the seismic vulnerability of the fuel distribution systemin coastal British Columbia. It is shown that the likelihood of localised fuel shortages due to earthquakesis significant and that subduction earthquakes have the potential to cause widespread fuel shortages in theprovince. The influence of the fill level at the time of the earthquake on the vulnerability of storage tanks isinvestigated. It is demonstrated that, although full tanks are more prone to collapse in earthquakes, keeping140the fuel storage tanks as full as possible reduces the chances of experiencing fuel shortages on average.In Chapter 4, the objective of studying housing recovery under limited resources is addressed, and anew simulation framework for housing recovery is developed. Object-oriented models are developed forbuilding portfolio recovery, inspection, financing, permitting, contractors, engineering firms, constructionmaterial suppliers, and power/transportation infrastructure. Building recovery is modelled in the context ofa community, contrasting with the practice of assessing the recovery of buildings in isolation. Thus, thepresented approach better captures the effect of competition for resources, infrastructure disruptions, andsocioeconomic factors on recovery.This dissertation also contributes with insights on housing recovery in the City of Vancouver follow-ing a large earthquake. The density of old and rented buildings, and the income and immigration statusof the homeowners are shown to be good predictors of the speed of recovery for a neighbourhood. Ad-dressing the objective of quantitatively comparing mitigation actions, Chapter 4 shows that retrofitting themost physically vulnerable buildings or doubling the available workforce are effective at reducing housingrecovery times. It is demonstrated that the equity in recovery between low and high socioeconomic statushomeowners is improved if mitigation measures are implemented.The contributions from Chapter 4 extend the work by Mahsuli and Haukaas (2013b), who focus onimmediate losses, by evaluating long-term impacts of earthquakes in Vancouver. The presented work alsoexpands on the research of Miles and Chang (2003, 2006, 2011) by quantitatively evaluating the effective-ness of mitigation actions in a comprehensive model for community recovery.In Chapter 5, the objective of estimating population displacement is addressed through the develop-ment of models for post-earthquake dwelling decision-making. Temporary displacements and relocation ofdwellings are accounted for, contrasting with the practice of assessing population displacements only duringthe disaster response phase. The analyses include models for building damage, housing recovery, water andpower infrastructure, and dwellings. The models for dwellings include considerations on socioeconomicdemographics, social networks, and disaster preparedness. The decision of dwellings to relocate accountsfor inherit and external factors.Another contribution in Chapter 5, are insights on the number of displaced persons after a large earth-quake near the City of Vancouver. The analyses results indicate that nearly 70,000 persons are expected tobe displaced, out of those, close to 19,000 will need public sheltering. In addition, nearly 40,000 personsare expected to relocate in the two years following the earthquake. Amongst the displaced, occupants of141multi-family pre-code and low-code buildings are over represented. Amongst those needing public shelter-ing renters and low-income dwellings are the majority. Renters are the group most likely to permanentlyrelocate during the recovery phase.Chapter 5 accounts for socioeconomic factors in modelling post-disaster dwelling displacement. Thisexpands the scope of previously developed models for post-disaster population displacement based solelyon structural damage (FEMA, 2015; Elnashai et al., 2008; Robinson et al., 2006). Chapter 5 also extends thework of Chang et al. (2008) on post-disater sheltering by including the possibility of dwellings abandoningtheir homes permanently.6.2 Future WorkThe comprehensive nature of the presented framework is perhaps its greatest strength, but it also leaves roomfor improvements to be performed in future work. The behaviour of some agents, and some of the policiesassumed to be in-place during recovery are simplistic and limited in scope. To improve the frameworkand reduce some of its limitations, future research focusing on three key aspects is suggested. First, it issuggested that further research efforts focus on improving the existing models. In particular, the followingimprovements are envisioned for future research:• In this dissertation several models for power, water, and transportation infrastructure were developed.The seismic vulnerability of these infrastructure is modelled according to fragility curves. It is sug-gested that these models are improved with the use finite element models. This will allow morerealistic damage and consequence evaluations.• Similarly, the models for residential buildings can also be improved in one of two ways. Finite elementmodels for the typical residential building archetypes in Vancouver can be developed and included inthe framework. Conversely, the use of fragility curves specific to Vancouver is an appealing andsimpler alternative. The research group lead by Professor Carlos Ventura at the department of CivilEngineering at the University of British Columbia initiated the development of such fragility curves.Future collaborations with Professor Ventura’s group are suggested.• Further research is suggested to improve how the community is represented. The use of neighbour-hoods to represent the community makes it challenging to properly model water and power availabil-ity. That is because there is a mismatch between the boundaries of the neighbourhoods and water and142power distribution grids and the neighbourhoods. The use of a smaller community subdivision, suchas Census Tracts is an appealing alternative, as census information at the Census Tract level is readilyavailable.• Future research should also focus on better representing the correlation between socioeconomic de-mographics. Correlation between housing tenure and income is the only one accounted for in thisdissertation, but other important correlations may exist and need to be accounted for. Furthermore,the correlation between social and physical vulnerabilities also need to be properly accounted for.Empirical evidence shows that dwellings with low socioeconomic status are often residents of lowerquality buildings. Thus, the least resilient families tend to be the most vulnerable, and this factor hasto be accounted for to properly represent the disaster impact.Second, it is suggested that new models are developed, expanding the capabilities of the presentedapproach. The following developments are suggested for future research:• The development of models for schools, hospital, industrial, and commercial buildings is suggested.The benefits of the inclusion of such models is twofold. First, more realistic estimates of losses andrecovery times can be obtained if all buildings in the community are included. Second, damage tothese buildings is directly related to the availability of jobs and services in a community. While notaccounted for in this dissertation, the availability of jobs and services has been shown to be a goodpredictor of community recovery and population retention.• The inclusion of models for other hazards is another alternative to expand the framework. Models forwind and flood hazards can increase the comprehensiveness of the presented approach and allow formulti-hazard analysis to be performed. This is important because disaster mitigation actions that areeffective against one hazard may create vulnerability against another. For example, houses built onstilts are flood-resistant but also more vulnerable to lateral forces from an earthquake. Other mitigationmeasures can be effective against several hazards, e.g., increasing dwelling disaster preparedness. Thetrue benefits of disaster mitigation can only be assessed in multi-hazard analyses.Finally, future work can also focus on conducting new types of analyses, in specific:• It is suggested that analyses that are more comprehensive in terms of the earthquake hazard andresource availability are conducted. The descriptors of the different earthquake hazards in Western143Canada are presented in the Appendix A. Sampling analyses with a large number of earthquakes canbe conducted to better characterise the expected losses and recovery times. Furthermore, uncertaintyin the availability of work crews, engineers, and inspectors discussed in Chapter 4 can also improvethe quality of the analyses. It is suggested that a large number of samples with random earthquakemagnitudes, location, and availability of resources is conducted. The use of parallel computing isstrongly encouraged to conduct this analyses as computational costs can be impeditive otherwise.• The accuracy of the presented framework is unknown, for this reason, efforts to validate it againstpast events are encouraged. An approach named ”hindcast” can be employed for this validation.Hindcasting consists of using a software of unknown accuracy to simulate a specific extreme eventand comparing empirical findings to those obtained from the simulation.A final suggestion for future work is to investigate the value of the analyses and results to decision-makers and planners. Collaborations with these professionals may help highlight improvements to be madeto the framework, as well as new types of analysis that can be included.144BibliographyAdachi, T. and Ellingwood, B. R. Serviceability of earthquake-damaged water systems: Effects ofelectrical power availability and power backup systems on system vulnerability. Reliability engineering& system safety, 93(1):78–88, 2008. → page 8Adams, J. and Halchuk, S. Fourth generation seismic hazard maps of Canada, Geological Survey ofCanada, Open file 4459. Technical report, Geological Survey of Canada, 2003. [Online; accessed15-May-2019]. → pages x, xv, 2, 34, 35, 167, 168, 169Ahmad, J., Ahmad, M. M., Sadia, H., and Ahmad, A. Using selected global health indicators to assesspublic health status of population displaced by natural and man-made disasters. International journal ofdisaster risk reduction, 22:228–237, 2017. → page 107Ahmadi, H., Alsubaie, A., and Martı´, J. R. Distribution system restoration considering criticalinfrastructures interdependencies. In 2014 IEEE PES General Meeting— Conference & Exposition,pages 1–5. IEEE, 2014. → page 9AIR Worldwide. Study of Impact and the Insurance and Economic Cost of a Major Earthquake in BritishColumbia and Ontario/Quebec. Technical report, AIR Worldwide, 2013. [Online; accessed15-May-2019]. → page 68Airriess, C. A., Li, W., Leong, K. J., Chen, A. C.-C., and Keith, V. M. Church-based social capital,networks and geographical scale: Katrina evacuation, relocation, and recovery in a New OrleansVietnamese American community. Geoforum, 39(3):1333–1346, 2008. → page 115Aitsi-Selmi, A., Egawa, S., Sasaki, H., Wannous, C., and Murray, V. The Sendai framework for disaster145risk reduction: Renewing the global commitment to peoples resilience, health, and well-being.International Journal of Disaster Risk Science, 6(2):164–176, 2015. → pages 1, 7, 47, 107Akkar, S., Bossu, R., Cauzzi, C., Clinton, J., Damico, M., Van Eck, T., Frobert, L., Godey, S., Gueguen, P.,Ka¨stli, P., et al. Network of European research infrastructures for earthquake risk assessment andmitigation (NERA)–networking accelerometric networks and Sm Data Users (NA3). In SecondEuropean conference on earthquake engineering and seismology, Istanbul, 2014. → page 8Almufti, I. and Willford, M. REDi Rating System: Resilience Based Earthquake Design Initiative for theNext Generation of Buildings. Version 1.0. Technical report, Arup, 2013. URL https://www.arup.com/-/media/arup/files/publications/r/redi final-version october-2013-arup-website.pdf. →pages 48, 50, 57, 76, 77, 78Balomenos, G. P. and Padgett, J. E. Vulnerability assessment of port structures subjected to storm surgeand waves. In Structures Congress 2018: Buildings and Disaster Management, pages 345–358.American Society of Civil Engineers Reston, VA, 2018. → page 8BC Hydro. Bulk Provincial Transmission System.https://www.bchydro.com/energy-in-bc/operations/transmission/transmission-system/maps.html, 2018.[Online; accessed 15-May-2019]. → pages xv, 170Bilau, A., Witt, E., and Lill, I. Practice Framework for the Management of Post-Disaster HousingReconstruction Programmes. Sustainability, 10(11):3929, 2018. → page 47Bilau, A. A., Witt, E., and Lill, I. A framework for managing post-disaster housing reconstruction.Procedia Economics and Finance, 21:313–320, 2015. → pages 48, 50Bolin, R. Family Recovery from Natural Disaster-Preliminary Model. Mass Emergencies, 1(4):267–277,1976. → page 115Bolin, R. Disasters and long-term recovery policy: a focus on housing and families. Review of PolicyResearch, 4(4):709–715, 1985. → page 47Bruneau, M., Chang, S. E., Eguchi, R. T., Lee, G. C., O’Rourke, T. D., Reinhorn, A. M., Shinozuka, M.,Tierney, K., Wallace, W. A., and Von Winterfeldt, D. A Framework to Quantitatively Assess and146Enhance the Seismic Resilience of Communities. Earthquake Spectra, 19(4):733–752, 2003. ISSN87552930. doi:10.1193/1.1623497. → pages 9, 80Bucher, C., Ellingwood, B. R., and Frangopol, D. M. Towards Resilience Modelling of Railway Networks- A Case Study on Shelby County, Tennessee. 12th International Conference on Structural Safety &Reliability (ICOSSAR2017), 2017. → page 8Bucovetchi, O., Simion, C. P., and Stanciu, R. D. Object-oriented Modelling Applied to Electricity CriticalInfrastructures. Procedia Technology, 19:651–656, 2015. ISSN 22120173.doi:10.1016/j.protcy.2015.02.092. URL http://linkinghub.elsevier.com/retrieve/pii/S2212017315000936.→ pages 9, 30Burton, H. V., Deierlein, G., Lallemant, D., and Singh, Y. Measuring the impact of enhanced buildingperformance on the seismic resilience of a residential community. Earthquake spectra, 33(4):1347–1367, 2017. → page 47Cardona, O. D., Ordaz, M., Reinoso, E., Yamin, L., and Barbat, A. CAPRA–comprehensive approach toprobabilistic risk assessment: international initiative for risk management effectiveness. In Proceedingsof the 15th World Conference on Earthquake Engineering. Lisbon, Portugal, 2012. → pages 9, 107, 118Cavalieri, F., Franchin, P., Gehl, P., and DAyala, D. Bayesian networks and infrastructure systems:Computational and methodological challenges. In Risk and Reliability Analysis: Theory andApplications, pages 385–415. Springer, 2017. → page 30Chamlee-Wright, E. and Storr, V. H. Theres no place like New Orleans: sense of place and communityrecovery in the Ninth Ward after Hurricane Katrina. Journal of Urban Affairs, 31(5):615–634, 2009. →page 115Chan, K. Net loss of over 1,100 hotel rooms in Vancouver due to condo developments, 2019. URLhttps://dailyhive.com/vancouver/interim-hotel-rooms-development-policy-vancouver-shortage. [Online;accessed 15-May-2019]. → page 130Chang, S. E. Urban disaster recovery: a measurement framework and its application to the 1995 Kobeearthquake. Disasters, 34(2):303–327, 2010. → page 114147Chang, S. E., Pasion, C., Tatebe, K., and Ahmad, R. Linking lifeline infrastructure performance andcommunity disaster resilience: models and multi-stakeholder processes. Technical ReportMCEER-08-0004, Multi-disciplinary Center for Earthquake Engineering Research, 2008. → pages111, 112, 142Chevron Canada. Burnaby Refinery — Chevron Canada, 2017. URLhttp://www.chevron.ca/our-businesses/burnaby-refinery. → page 33CIGIDEN. Centro de investigacion para la gestion integrada de desastres naturales, 2019. URLhttps://www.cigiden.cl/en/home/. → page 8Cimellaro, G. P., Reinhorn, A. M., and Bruneau, M. Framework for analytical quantification of disasterresilience. Engineering structures, 32(11):3639–3649, 2010. → page 80City of Port Moody. City of Port Moody : Imperial Oil, 2018. URLhttp://www.portmoody.ca/index.aspx?page=842. → page 33Comerio, M. C. Housing issues after disasters. Journal of Contingencies and Crisis Management, 5(3):166–178, 1997. → page 112Comerio, M. C. Estimating downtime in loss modeling. Earthquake Spectra, 22(2):349–365, 2006. →pages 47, 48, 50Comerio, M. C. Housing recovery in Chile: A qualitative mid-program review. Pacific EarthquakeEngineering Research Center Headquarters at the , 2013. → pages 3, 47Comerio, M. C. Disaster Recovery and Community Renewal: Housing Approaches. Cityscape: A Journalof Policy Development and Research, 16(2):51–68, 2014. ISSN 1936007X. → pages 47, 48, 50Comerio, M. C., Landis, J. D., and Rofe, Y. Post-disaster residential rebuilding. University of California atBerkeley, Institute of Urban and Regional , 1994. → page 60Cooper, T. W. and Cooper, T. W. A study of the performance of petroleum storage tanks duringearthquakes, 1933-1995. US National Institute of Standards and Technology USA, 1997. → page 40Cornell, C. A. and Krawinkler, H. Progress and Challenges in Seismic Performance Assessment, 2000.URL https://peer.berkeley.edu/news/2000spring/performance.html. → pages 4, 7148Cornell, C. A. and Winterstein, S. R. Temporal and magnitude dependence in earthquake recurrencemodels. Bulletin of the Seismological Society of America, 78(4):1522–1537, 1988. → page 35Costa, R., Haukaas, T., Chang, S. E., and Dowlatabadi, H. Object-oriented model of the seismicvulnerability of the fuel distribution network in coastal British Columbia. Reliability Engineering &System Safety, 186:11–23, 2019. → page 8Davidson, R. A. Integrating disciplinary contributions to achieve community resilience to natural disasters.Civil Engineering and Environmental Systems, 32(1-2):55–67, 2015. → page 9De Iuliis, M., Kammouh, O., Cimellaro, G. P., and Tesfamariam, S. Downtime estimation of buildingstructures using fuzzy logic. International journal of disaster risk reduction, 34:196–208, 2019. →pages 47, 48Deierlein, G., Krawinkler, H., and Cornell, C. A. A framework for performance-based earthquakeengineering. In Pacific conference on earthquake engineering, pages 1–8. Citeseer, 2003. → pages 4, 7Deitel, H. M. and Deitel, P. J. C++ How to Program. Prentice Hall, 2006. → pages 11, 52Di Ludovico, M., Prota, A., Moroni, C., Manfredi, G., and Dolce, M. Reconstruction process of damagedresidential buildings outside historical centres after the LAquila earthquake: part I - ” light damage”reconstruction. Bulletin of Earthquake Engineering, 15(2):667–692, 2017a. → page 47Di Ludovico, M., Prota, A., Moroni, C., Manfredi, G., and Dolce, M. Reconstruction process of damagedresidential buildings outside historical centres after the LAquila earthquake: part IIheavy damagereconstruction. Bulletin of Earthquake Engineering, 15(2):693–729, 2017b. → page 47Dore, M. C. Factors affecting household disaster preparedness: a study of the Canadian context. PhDthesis, University of North Texas, United States of America, 2000. → page 119DAyala, D. and Speranza, E. Definition of collapse mechanisms and seismic vulnerability of historicmasonry buildings. Earthquake Spectra, 19(3):479–509, 2003. → page 8Eidinger, J. and Davis, C. A. Recent earthquakes: implications for US water utilities. Water ResearchFoundation, 2012. → pages 40, 41, 43149Ellingwood, B. R., Wang, N., Harris, J. R., and McAllister, T. P. Performance-based engineering to achievecommunity resilience. Routledge Handbook of Sustainable and Resilient Infrastructure, pages 94–112,2018. → page 47Elliott, J. R. and Pais, J. Race, class, and Hurricane Katrina: Social differences in human responses todisaster. Social science research, 35(2):295–321, 2006. → page 108Elnashai, A., Hampton, S., Lee, J. S., McLaren, T., Myers, J. D., Navarro, C., Spencer, B., and Tolbert, N.Architectural overview of MAEviz–HAZTURK. Journal of Earthquake Engineering, 12(S2):92–99,2008. → pages 9, 107, 118, 142Eusgeld, I. and Kroger, W. Comparative evaluation of modeling and simulation techniques forinterdependent critical infrastructures. 9th International Conference on Probabilistic Safety Assessmentand Management 2008, PSAM 2008, 1(August):484–491, 2008. URLhttp://www.scopus.com/inward/record.url?eid=2-s2.0-84876497440{&}partnerID=tZOtx3y1. → pages28, 29Eusgeld, I., Kroger, W., Sansavini, G., Schlapfer, M., and Zio, E. The role of network theory andobject-oriented modeling within a framework for the vulnerability analysis of critical infrastructures.Reliability Engineering & System Safety, 94(5):954–963, 2009. → pages 9, 31Federal Emergency Management Agency. Prestandard and commentary for the seismic rehabilitation ofbuildings. FEMA, 2000. → page 59Federal Emergency Management Agency. Seismic Performance Assessment of Buildings Volume 1 -Methodology. FEMA, 2012. → page 59FEMA. HazusMH 2.1: Technical Manual. Technical report, Federal Emergency Management Agency,2015. URL www.fema.gov/plan/prevent/hazus. → pages9, 22, 32, 35, 38, 41, 57, 71, 72, 76, 80, 83, 107, 118, 122, 142, 170, 173, 174, 175, 177, 178, 179Feng, K., Hou, G., and Li, Q. Evaluating the role of transportation system in community resilienceassessment. In 12th international conference on applications of statistics and probability in civilengineering (ICASP12), Vienna, Austria, pages 6–10, 2017. ISBN 9783903024281. → page 30150Foltz, R. and Hueste, M. B. Estimating seismic damage and repair costs. Not published, 2004. → page 48Fothergill, A., Maestas, E. G., and Darlington, J. D. Race, ethnicity and disasters in the United States: Areview of the literature. Disasters, 23(2):156–173, 1999. → page 112Franchin, P. and Cavalieri, F. Probabilistic assessment of civil infrastructure resilience to earthquakes.Computer-Aided Civil and Infrastructure Engineering, 30(7):583–600, 2015. → page 107Ganapati, N. E. Measuring the processes and outcomes of post-disaster housing recovery: Lessons fromGo¨lcu¨k, Turkey. Natural hazards, 65(3):1783–1799, 2013. → page 48Ghosh, J., Padgett, J. E., and Duen˜as-Osorio, L. Surrogate modeling and failure surface visualization forefficient seismic vulnerability assessment of highway bridges. Probabilistic Engineering Mechanics, 34:189–199, 2013. → page 8Giardini, D., Wo¨ssner, J., and Danciu, L. Mapping Europe’s seismic hazard. Eos, Transactions AmericanGeophysical Union, 95(29):261–262, 2014. → page 8Giovinazzi, S., Stevenson, J., Mason, A., and Mitchell, J. Assessing temporary housing needs and issuesfollowing Christchurch Earthquakes. New Zealand, Christchurch: University of Canterbury, 2011. →page 107Glass, R. J., Beyeler, W. E., Conrad, S. H., Brodsky, N. S., Kaplan, P. G., and Brown, T. J. Definingresearch and development directions for modeling and simulation of complex, interdependent adaptiveinfrastructures. Physical Review Letters, 59(4):381–384, 2003. → pages 9, 30, 31Goldberg, A. and Robson, D. Smalltalk-80: the language and its implementation. Addison-WesleyLongman Publishing Co., Inc., 1983. → page 11Goldenber, S. Natural disasters displaced more people than war in 2013, study finds.https://www.theguardian.com/world/2014/sep/17/natural-disasters-refugee-people-war-2013-study,2019. [Online; accessed 15-May-2019]. → pages 1, 107Grinberger, A. Y. and Felsenstein, D. Bouncing Back or Bouncing Forward? Simulating Urban Resilienceand Policy in the Aftermath of an Earthquake. Proc. Institution of Civil Engineers: Urban Design andPlanning, 167(3), 2014. → page 47151Guidotti, R., Chmielewski, H., Unnikrishnan, V., Gardoni, P., McAllister, T., and van de Lindt, J. Modelingthe resilience of critical infrastructure: the role of network dependencies. Sustainable and ResilientInfrastructure, 1(3-4):153–168, 2016. ISSN 2378-9689. doi:10.1080/23789689.2016.1254999. URLhttps://www.tandfonline.com/doi/full/10.1080/23789689.2016.1254999. → page 30Guidotti, R., Gardoni, P., and Chen, Y. Network reliability analysis with link and nodal weights andauxiliary nodes. Structural Safety, 65:12–26, 2017a. ISSN 01674730.doi:10.1016/j.strusafe.2016.12.001. URL http://dx.doi.org/10.1016/j.strusafe.2016.12.001. → page 30Guidotti, R., Gardoni, P., and Chen, Y. Multi-layer heterogeneous network model for interdependentinfrastructure systems. In Proceedings of the 12th International Conference on Structural Safety andReliability, pages 6–10, 2017b. ISBN 9783903024281. → pages 9, 30Gutenberg, B. and Richter, C. F. Frequency of earthquakes in California. Bulletin of the SeismologicalSociety of America, 34(4):185–188, 1944. → page 101Hanson, R. D. and Comartin, C. D. The Repair of earthquake Damaged Buildings. In 12th WorldConference on Earthquake Engineering, Auckland, New Zealand, 2000. → page 59Hasan, S. and Foliente, G. Modeling infrastructure system interdependencies and socioeconomic impactsof failure in extreme events: emerging R&D challenges. Natural Hazards, 78(3):2143–2168, 2015.ISSN 0921030X. doi:10.1007/s11069-015-1814-7. → page 9Hassan, A. F. and Sozen, M. A. Seismic vulnerability assessment of low-rise buildings in regions withinfrequent earthquakes. ACI Structural Journal, 94(1):31–39, 1997. → page 8Henry, J. Return or relocate? An inductive analysis of decision-making in a disaster. Disasters, 37(2):293–316, 2013. → pages 114, 115Hines, P., Cotilla-Sanchez, E., and Blumsack, S. Do topological models provide good information aboutelectricity infrastructure vulnerability? Chaos, 20(3):1–11, 2010. ISSN 10541500.doi:10.1063/1.3489887. → page 29Hirayama, Y. Collapse and reconstruction: Housing recovery policy in Kobe after the Hanshin GreatEarthquake. Housing Studies, 15(1):111–128, 2000. → page 48152Holguin-Veras, J., Taniguchi, E., Jaller, M., Aros-Vera, F., Ferreira, F., and Thompson, R. G. The Tohokudisasters: Chief lessons concerning the post disaster humanitarian logistics response and policyimplications. Transportation Research Part A: Policy and Practice, 69:86–104, 2014. ISSN 09658564.doi:10.1016/j.tra.2014.08.003. → page 26Holling, C. S. Resilience and stability of ecological systems. Annual review of ecology and systematics, 4(1):1–23, 1973. → page 9Hong, Y. A study on the condition of temporary housing following disasters: Focus on container housing.Frontiers of Architectural Research, 6(3):374–383, 2017. → page 107Huling, D. and Miles, S. B. Simulating disaster recovery as discrete event processes using python. In 2015IEEE Global Humanitarian Technology Conference (GHTC), pages 248–253. IEEE, 2015. → page 47Hwang, S.-H. and Lignos, D. G. Earthquake-induced loss assessment of steel frame buildings with specialmoment frames designed in highly seismic regions. Earthquake Engineering & Structural Dynamics, 46(13):2141–2162, 2017. → pages 48, 59Hyndman, R. D. and Wang, K. The rupture zone of Cascadia great earthquakes from current deformationand the thermal regime. Journal of Geophysical Research, 100154(10):133–22, 1995. ISSN 0148-0227.doi:10.1029/95JB01970. → page 2Irish Times. Natural disasters displace three times more people than conflicts. https://www.irishtimes.com/news/world/natural-disasters-displace-three-times-more-people-than-conflicts-1.3091785, 2019.[Online; accessed 15-May-2019]. → pages 1, 107Johnson, P. E. Economic Simulations in Swarm: Agent-Based Modelling and Object OrientedProgramming. Journal of Artificial Societies and Social Simulation, 4(2), 2001. ISSN 14607425.doi:10.1080/17517570701275390. → pages 10, 31Kabir, G., Sadiq, R., and Tesfamariam, S. A fuzzy Bayesian belief network for safety assessment of oil andgas pipelines. Structure and Infrastructure Engineering, 12(8):874–889, 2016. ISSN 17448980.doi:10.1080/15732479.2015.1053093. URL http://dx.doi.org/10.1080/15732479.2015.1053093. →page 30153Kamel, N. M. and Loukaitou-Sideris, A. Residential assistance and recovery following the Northridgeearthquake. Urban Studies, 41(3):533–562, 2004. → pages 48, 50Khakzad, N. Application of dynamic Bayesian network to risk analysis of domino effects in chemicalinfrastructures. Reliability Engineering & System Safety, 138:263–272, 2015. → page 30Khazai, B., Daniell, J., Franchin, P., Cavalieri, F., Vangelsten, B., Iervolino, I., and Esposito, S. A NewApproach to Modeling Post-Earthquake Shelter Demand: Integrating Social Vulnerability in SystemicSeismic Vulnerability Analysis. In Proceedings of World Conference on Earthquake Engineering, 2012.→ page 107King, A. and Bell, R. RiskScape New Zealand: A multihazard loss modelling tool. In Proceedings ofEarthquake Engineering in the 21st Century (EE-21C) conference, topic, volume 8. Citeseer, 2005. →pages 9, 107, 118Kumar, S., Diaz, R., Behr, J. G., and Toba, A.-L. Modeling the effects of labor on housing reconstruction:A system perspective. International Journal of Disaster Risk Reduction, 12:154–162, 2015. → page 47Laucelli, D. and Giustolisi, O. Vulnerability assessment of water distribution networks under seismicactions. Journal of Water Resources Planning and Management, 141(6):04014082, 2014. → page 8Lawless, S. A tour of abandoned New Orleans 10 years after Katrina. https://www.theguardian.com/cities/gallery/2015/jul/30/abandoned-new-orleans-hurricane-katrina-in-pictures, 2019. [Online; accessed15-May-2019]. → page 108Ledge, A. Calgary’s Flood Recovery Story - The Business Perspective. Technical report, CalgaryChamber, 2014. URLhttps://www.calgarychamber.com/wp-content/uploads/2018/01/Flood-Story-Calgary-Chamber 0.pdf.→ page 1Lee, J. Y., Zhao, J., Li, Y., and Yin, Y.-J. Quantitative Impact of Catastrophe Risk Insurance on CommunityResilience. In 13th International Conference on Applications of Statistics and Probability in CivilEngineering, 2019. → pages 9, 47154Lemyre, L., Lee, J. E., Turner, M. C., and Krewski, D. Terrorism preparedness in Canada: a public surveyon perceived institutional and individual response to terrorism. International Journal of EmergencyManagement, 4(2):296–315, 2007. → page 119Levac, J., Toal-Sullivan, D., and OSullivan, T. L. Household emergency preparedness: a literature review.Journal of community health, 37(3):725–733, 2012. → page 119Levine, J. N., Esnard, A.-M., and Sapat, A. Population displacement and housing dilemmas due tocatastrophic disasters. Journal of planning literature, 22(1):3–15, 2007. → page 114Lin, P. and Wang, N. A Probabilistic Framework for Post-Disaster Functionality Recovery of CommunityBuilding Portfolios. In 13th International Conference on Applications of Statistics and Probability inCivil Engineering, 2019. → page 47Lindell, M. K., Bolton, P. A., Perry, R. W., Stoetzel, G., Martin, J., and Flynn, C. Planning concepts anddecision criteria for sheltering and evacuation in a nuclear power plant emergency. Executive report.Technical report, Battelle Human Affairs Research Center, Seattle, WA (USA); Pacific Northwest , 1985.→ page 107Liu, Q., Peres, F., and Tchangani, A. Object Oriented Bayesian Network for complex system riskassessment. IFAC-PapersOnLine, 49(28):31–36, 2016a. ISSN 24058963.doi:10.1016/j.ifacol.2016.11.006. → page 30Liu, Q., Tchangani, A., and Pe´re`s, F. Modelling complex large scale systems using object orientedBayesian networks (OOBN). IFAC-PapersOnLine, 49(12):127–132, 2016b. ISSN 24058963.doi:10.1016/j.ifacol.2016.07.562. → page 30Loukaitou-Sideris, A. and Kamel, N. M. Residential Recovery from the Northridge Earthquake: AnEvaluation of Federal Assistance Programs. Technical report, CALIFORNIA POLICY RESEARCHCENTER, 2004. [Online; accessed 15-May-2019]. → pages 48, 50Lu, Y. and Xu, J. Comparative study on the key issues of Postearthquake recovery and reconstructionplanning: Lessons from the United States, Japan, Iran, and China. Natural Hazards Review, 16(3):04014033, 2014. → pages 48, 50155Macneil, A. and Keefe, D. J. The Nova Scotia Fuel Shortage: Report of the Independent Review Panel,2015. URL https://novascotia.ca/dma/documents/NovaScotiaFuelShortage.pdf. → pages 26, 34Mahsuli, M. and Haukaas, T. A computer program for multi model reliability and optimization analysis.Journal of Computing in Civil Engineering, 27(1):87–98, 2013a. ISSN 0887-3801.doi:10.1061/(ASCE)CP.1943-5487.0000204. → pages 11, 13Mahsuli, M. Probabilistic Models, Methods, and Software for Evaluating Risk to Civil Infrastructure. PhDthesis, University of British Columbia, 2012. → pages xii, 13, 14, 70Mahsuli, M. and Haukaas, T. Seismic risk analysis with reliability methods, part I: Models. StructuralSafety, 42:54–62, 5 2013b. ISSN 01674730. doi:10.1016/j.strusafe.2013.01.003. URLhttp://linkinghub.elsevier.com/retrieve/pii/S0167473013000040. → pages 4, 141Masoomi, H. and van de Lindt, J. W. Community-Resilience-Based Design of the Built Environment.ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, 5(1):04018044, 2018. → pages 9, 47McDaniels, T., Chang, S. E., Peterson, K., Mikawoz, J., and Reed, D. Empirical Framework forCharacterizing Infrastructure Failure Interdependencies. Journal of Infrastructure Systems, 13(3):175–184, 2007. ISSN 1076-0342. doi:10.1061/(ASCE)1076-0342(2007)13:3(175). URLhttp://ascelibrary.org/doi/10.1061/{%}28ASCE{%}291076-0342{%}282007{%}2913{%}3A3{%}28175{%}29. → page 9Mensah, A. F. and Duen˜as-Osorio, L. Efficient resilience assessment framework for electric power systemsaffected by hurricane events. Journal of Structural Engineering, 142(8):C4015013, 2015. → page 8Metro Vancouver. Metro Vancouver Water Services. https://gis.metrovancouver.org/maps/Water, 2018.[Online; accessed 15-May-2019]. → page 173MetroVancouver. Metro Vancouver Housing Data Book. Technical report, Technical report, 2019. →pages x, xiii, 67, 68, 69, 75, 76Miles, S. B. and Chang, S. E. Urban disaster recovery: A framework and simulation model. TechnicalReport MCEER-03-0005, Multi-disciplinary Center for Earthquaker Engineering Research, 2003. →page 141156Miles, S. B. and Chang, S. E. Modeling community recovery from earthquakes. Earthquake Spectra, 22(2):439–458, 2006. ISSN 87552930. doi:10.1193/1.2192847. → page 141Miles, S. B. and Chang, S. E. ResilUS: A Community Based Disaster Resilience Model. Cartography andGeographic Information Science, 38(1):36–51, 2011. doi:10.1559/1523040638136. URLhttp://www.tandfonline.com/doi/abs/10.1559/1523040638136. → pages 47, 108, 141Mitchell, D., Paultre, P., Tinawi, R., Saatcioglu, M., Tremblay, R., Elwood, K., Adams, J., and DeVall, R.Evolution of seismic design provisions in the National building code of Canada. Canadian Journal ofCivil Engineering, 37(9):1157–1170, 2010. → pages 64, 81Moehle, J. and Deierlein, G. G. A framework methodology for performance-based earthquake engineering.In 13th world conference on earthquake engineering, volume 679, 2004. → pages 4, 7Molina, S., Lang, D. H., and Lindholm, C. D. SELENA - An open-source tool for seismic risk and lossassessment using a logic tree computation procedure. Computers & Geosciences, 36(3):257–269, 2010.→ pages 9, 107, 118Moreau, J. Who’s moving oil on the Burrard Inlet?, 2012. URLhttp://www.burnabynow.com/news/who-s-moving-oil-on-the-burrard-inlet-1.413969. → page 33National Earthquake Hazard Reduction Program. The Mid-America Earthquake Center: ManagingSeismic Risks from Source to Society. https://www.nehrp.gov/pdf/SeismicWavesSep08.pdf, 2019a.[Online; accessed 15-May-2019]. → page 8National Earthquake Hazard Reduction Program. MCEER Research: Enabling Disaster-ResilientCommunities. https://www.nehrp.gov/pdf/SeismicWavesNov08.pdf, 2019b. [Online; accessed15-May-2019]. → page 8National Earthquake Hazard Reduction Program. The Pacific Earthquake Engineering Research Center: ADecade of Achievement. https://www.nehrp.gov/pdf/SeismicWavesFeb08.pdf, 2019c. [Online; accessed15-May-2019]. → page 8National Institute of Standards and Technology. Center for Risk-Based Community Resilience Planning.https://www.nist.gov/el/center-risk-based-community-resilience-planning, 2019. [Online; accessed15-May-2019]. → page 8157Nejat, A. Modeling dynamics of post disaster recovery. PhD thesis, Texas A&M University, CollegeStation, 2011. → page 115Nejat, A. and Damnjanovic, I. Agent-based modeling of behavioral housing recovery following disasters.Computer-Aided Civil and Infrastructure Engineering, 27(10):748–763, 2012. → pages 47, 115Nejat, A. and Ghosh, S. LASSO Model of Postdisaster Housing Recovery: Case Study of HurricaneSandy. Natural Hazards Review, 17(3):1–13, 2016. ISSN 15276988.doi:10.1061/(ASCE)NH.1527-6996.0000223. → pages 50, 115Norris, F. H., Stevens, S. P., Pfefferbaum, B., Wyche, K. F., and Pfefferbaum, R. L. Community resilienceas a metaphor, theory, set of capacities, and strategy for disaster readiness. American journal ofcommunity psychology, 41(1-2):127–150, 2008. → page 9Oil Sands Magazine. Why Vancouver desperately needs a new oil refinery — Oil Sands Magazine, 2016.URL http://www.oilsandsmagazine.com/news/2016/3/03/why-vancouver-desperately-needs-a-new-oil-refinery.→ page 33Olshansky, R. B. Planning After Hurricane Katrina. Journal of the American Planning Association, 72(2):147–153, 2006. doi:10.1080/01944360608976735. URLhttp://www.tandfonline.com/doi/abs/10.1080/01944360608976735. → pages 3, 47O’Rourke, M. J. and So, P. Seismic fragility curves for on-grade steel tanks. Earthquake spectra, 16(4):801–815, 2000. → page 40Ouyang, M. Review on modeling and simulation of interdependent critical infrastructure systems.Reliability Engineering and System Safety, 121:43–60, 2014. ISSN 09518320.doi:10.1016/j.ress.2013.06.040. URL http://dx.doi.org/10.1016/j.ress.2013.06.040. → page 29Ouyang, M. Comparisons of purely topological model, betweenness based model and direct current powerflow model to analyze power grid vulnerability. Chaos: An Interdisciplinary Journal of NonlinearScience, 23(2):023114, 2013. → pages 8, 29Ouyang, M., Duen˜as-Osorio, L., and Min, X. A three-stage resilience analysis framework for urbaninfrastructure systems. Structural safety, 36:23–31, 2012. → page 8158Padgett, J. E. Seismic vulnerability assessment of retrofitted bridges using probabilistic methods. PhDthesis, Georgia Institute of Technology, 2007. → page 8Pampanin, S., Christopoulos, C., and Priestley, M. Residual deformations in the performance-seismicassessment of frame structures. Technical report, Research Report No. ROSE-2002, 2002. → page 59Panteli, M. and Mancarella, P. The grid: Stronger bigger smarter?: Presenting a conceptual framework ofpower system resilience. IEEE Power Energy Mag, 13(3):58–66, 2015. → page 8Peacock, W. G., Van Zandt, S., Zhang, Y., and Highfield, W. E. Inequities in Long-Term Housing RecoveryAfter Disasters. Journal of the American Planning Association, 80(4):356–371, 2014.doi:10.1080/01944363.2014.980440. URLhttp://www.tandfonline.com/doi/abs/10.1080/01944363.2014.980440. → pages 6, 112Pederson, P., Dudenhoeffer, D., Hartley, S., and Permann, M. Critical Infrastructure InterdependencyModeling. Contract, 2006. → page 28Perry, R. W. and Lindell, M. K. Preparedness for emergency response: guidelines for the emergencyplanning process. Disasters, 27(4):336–350, 2003. → page 107Perry, R. W., Lindell, M. K., and Tierney, K. J. Facing the unexpected: Disaster preparedness andresponse in the United States. Joseph Henry Press, 2001. → page 108Pitilakis, K., Franchin, P., Khazai, B., and Wenzel, H. SYNER-G: Systemic seismic vulnerability and riskassessment of complex urban, utility, lifeline systems and critical facilities: Methodology andapplications, volume 31. Springer, 2014. → pages 8, 107Porter, K. Beginners guide to fragility, vulnerability, and risk. Encyclopedia of earthquake engineering,pages 235–260, 2015. → page 22Pranantyo, I. R., Fadmastuti, M., and Chandra, F. InaSAFE applications in disaster preparedness. In AIPConference Proceedings, volume 1658, page 060001. AIP Publishing, 2015. → pages 9, 107, 118Pynn, L. The high stakes of transporting oil by rail. Vancouver Sun, 2013. URLhttp://www.vancouversun.com/technology/high+stakes+transporting+rail/9124923/story.html. → page33159Pynn, L. Rail shipments of crude oil continue to increase in B.C. Vancouver Sun, 2015. URLhttp://www.vancouversun.com/news/Rail+shipments+crude+continue+increase/10733394/story.html.→ page 33Quarantelli, E. L. General and particular observations on sheltering and housing in American disasters.Disasters, 6(4):277–281, 1982. → page 107Ramirez, C., Liel, A., Mitrani-Reiser, J., Haselton, C., Spear, A., Steiner, J., Deierlein, G., and Miranda, E.Expected earthquake damage and repair costs in reinforced concrete frame buildings. EarthquakeEngineering & Structural Dynamics, 41(11):1455–1475, 2012. → page 59Ramirez, M. and Miranda, E. Significance of residual drifts in building earthquake loss estimation.Earthquake Engineering & Structural Dynamics, 41(11):1477–1493, 2012. → page 59Ranghieri, F. and Ishiwatari, M. Learning from megadisasters: lessons from the Great East JapanEarthquake. The World Bank, 2014. → page 47Rinaldi, S. M., Peerenboom, J. P., and Kelly, T. K. Identifying, understanding, and analyzing criticalinfrastructure interdependencies. IEEE Control Systems, 21(6):11–25, 2001. → pages 9, 28, 70Robinson, D., Fulford, G., and Dhu, T. EQRM: Geoscience Australia’s Earthquake Risk Model: TechnicalManual Version 3.0. Geoscience Australia, 2006. → pages 9, 107, 118, 142Ruiz-Garcia, J. and Chora, C. Evaluation of approximate methods to estimate residual drift demands insteel framed buildings. Earthquake Engineering & Structural Dynamics, 44(15):2837–2854, 2015. →page 59Ruiz-Garcia, J. and Miranda, E. Evaluation of residual drift demands in regular multi-storey frames forperformance-based seismic assessment. Earthquake engineering & structural dynamics, 35(13):1609–1629, 2006. → page 59Rust, E. B. and Killinger, K. The Financial Services Roundtable Blue Ribbon Commission onMega-Catastrophes: A Call to Action. Financial Services Roundtable, 2006. → page 115SERA. Seismology and Earthquake Engineering Research Infrastructure Alliance for Europe, 2019. URLhttp://www.sera-eu.org/en/home/. → page 8160Silva, V., Crowley, H., Pagani, M., Monelli, D., and Pinho, R. Development of the OpenQuake engine, theGlobal Earthquake Model’s open-source software for seismic risk assessment. Natural Hazards, 72(3):1409–1427, 2014. → pages 9, 107, 118SimCenter. SimCenter: Computational Modeling and Simulation Center.https://simcenter.designsafe-ci.org/, 2019. [Online; accessed 15-May-2019]. → page 8Siraj, T., Tesfamariam, S., and Duen˜as-Osorio, L. Seismic risk assessment of high-voltage transformersusing Bayesian belief networks. Safety, Reliability, Risk and Life-Cycle Performance of Structures andInfrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability,ICOSSAR 2013, 2479(February):3147–3154, 2013. ISSN 1573-2479.doi:10.1080/15732479.2014.921826. URLhttp://www.scopus.com/inward/record.url?eid=2-s2.0-84892408116{&}partnerID=tZOtx3y1. → page30Smythe, T. C. Assessing the Impacts of Hurricane Sandy on the Port of New York and New Jersey’sMaritime Responders and Response Infrastructure. Technical report, University of Colorado NaturalHazards Center, 2013. → page 25Statistics Canada. Statistics Canada, Census of Population, 2016, 2016. URLhttps://www12.statcan.gc.ca/census-recensement/2016/dp-pd/index-eng.cfm. → pagesxv, 47, 62, 116, 130, 181, 182, 183, 184, 185, 186Statistics Canada. Sales of fuel used for road motor vehicles, by province and territory (Alberta, BritishColumbia, Yukon, Northwest Territories, Nunavut), 2018. URLhttp://www.statcan.gc.ca/tables-tableaux/sum-som/l01/cst01/trade37c-eng.htm. → page 33Statistics Canada. Emergency preparedness in Canada, 2014, 2019. URLhttps://www150.statcan.gc.ca/n1/pub/85-002-x/2015001/article/14234-eng.htm. → pages 114, 119, 120Stroustrup, B. The C++ programming language. Pearson Education India, 2000. → page 11Sutley, E. J., Peek, L., and van de Lindt, J. W. Community-Level Framework for Seismic Resilience. I:Coupling Socioeconomic Characteristics and Engineering Building Systems. Natural Hazards Review,18(3):4016014, 2017a. doi:10.1061/(ASCE)NH.1527-6996.0000239. → pages 9, 47, 119161Sutley, E. J., van de Lindt, J. W., and Peek, L. Community-Level Framework for Seismic Resilience . II :Multiobjective Optimization and Illustrative Examples. Natural Hazards Review, 18(3):1–11, 2017b.doi:10.1061/(ASCE)NH.1527-6996.0000230. → page 9Sutley, E. J., Hamideh, S., Dillard, M. K., Gu, D., Seong, K., and van de Lindt, J. W. Integrative Modelingof Housing Recovery as a Physical, Economic, and Social Process. In 13th International Conference onApplications of Statistics and Probability in Civil Engineering, 2019. → page 47Tabucchi, T., Davidson, R., and Brink, S. Simulation of post-earthquake water supply system restoration.Civil Engineering and Environmental Systems, 27(4):263–279, 2010. → pages 8, 57Takahashi, N. and Shiohara, H. Life Cycle Economic Loss Due to Seismic Damage Of NonstructuralElements. In 13th World Conference on Earthquake Engineering, Vancouver, Canada, 2004. → page 48Tanner, A., Dowlatabadi, H., Chang, S. E., Costa, R., Shen, X., and Brown, A. Resilient Coast: Liquid FuelDelivery to British Columbia Coastal Communities. Technical report, University of British Columbia,2017. URLhttps://open.library.ubc.ca/cIRcle/collections/facultyresearchandpublications/52383/items/1.0360721.→ pages xii, 27, 32Taylor, A. After the Fire: Recovery in Fort McMurray, 2017. URLhttps://www.theatlantic.com/photo/2017/05/after-the-fire-recovery-in-fort-mcmurray/525249/. → page 1Tien, I. and Der Kiureghian, A. Compression and inference algorithms for Bayesian network modeling ofinfrastructure systems. In 12th international conference on applications of statistics and probability incivil engineering (ICASP12), Vancouver, BC, Canada, pages 12–15, 2015. → page 30Tien, I. and Der Kiureghian, A. Algorithms for Bayesian network modeling and reliability assessment ofinfrastructure systems. Reliability Engineering & System Safety, 156:134–147, 2016. → page 30United Nations. UNISDR Terminology on Disaster Risk Reduction. United Nations International Strategyfor Disaster Reduction, 2009. [Online; accessed 15-May-2019]. → page 119United Nations Office for Disaster Risk Reduction. Yokohama Strategy and Plan of Action for a SaferWorld: Guidelines for Natural Disaster Prevention, Preparedness and Mitigation. Technical report,United Nations, 1994. [Online; accessed 15-May-2019]. → page 7162United Nations Office for Disaster Risk Reduction. Hyogo Framework for Action 2005-2015: Building theResilience of Nations and Communities to Disasters. Technical report, United Nations, 2014. [Online;accessed 15-May-2019]. → page 7Vaziri, P., Davidson, R. A., Nozick, L. K., and Hosseini, M. Resource allocation for regional earthquakerisk mitigation: a case study of Tehran, Iran. Natural hazards, 53(3):527–546, 2010. → page 57Vecere, A., Monteiro, R., Ammann, W. J., Giovinazzi, S., and Santos, R. H. M. Predictive models for postdisaster shelter needs assessment. International Journal of Disaster Risk Reduction, 21:44–62, 2017. →page 107Voskanyan, A. and Cahill, J. D. Displaced Populations. In Ciottone’s Disaster Medicine (Second Edition),pages 361–364. Elsevier, 2016. → page 107Walker, J. F. and Crawford, C. A. Cash in a housing context: Transitional shelter and recovery in Japan.International Journal of Disaster Risk Reduction, 24:216–231, 2017. → page 77Wang, Y. and Sun, B. A Multiobjective Allocation Model for Emergency Resources That BalanceEfficiency and Fairness. Mathematical Problems in Engineering, 2018, 2018. → page 57Wang, Y., Zou, Z., and Li, J. Influencing factors of households disadvantaged in post-earthquake liferecovery: a case study of the Wenchuan earthquake in China. Natural Hazards, 75(2):1853–1869, 2015.→ pages 47, 48Wood, A., Now, I., and Parker, M. The Canterbury rebuild five years on from the Christchurch earthquake.Technical Report 3, Bank of New Zealand, 2016. URLhttp://www.rbnz.govt.nz/research-and-publications/reserve-bank-bulletin. → pages 47, 48, 50, 76, 77World Bank. Understanding risk: Review of open source and open access software packages available toquantify risk from natural hazards. Technical report, World Bank, 2014. URLhttp://documents.worldbank.org/. → pages 9, 107Wright, K. and Johnston, D. Post-earthquake sheltering needs: how loss of structures and services affectsdecision making for evacuation. In 2010 New Zealand Society for Earthquake Engineering ConferenceProceedings, pages 21–23, 2010. → page 107163Wu, J. Y. A comparative study of housing reconstruction after two major earthquakes: The 1994Northridge earthquake in the United States and the 1999 Chi-Chi earthquake in Taiwan. PhD thesis,Texas A&M University, 2004. → pages 48, 50Xu, N., Guikema, S. D., Davidson, R. A., Nozick, L. K., C¸ag˘nan, Z., and Vaziri, K. Optimizing schedulingof post-earthquake electric power restoration tasks. Earthquake engineering & structural dynamics, 36(2):265–284, 2007. → pages 8, 57Yang, J. Probabilistic Seismic Damage Assessment and Repair Cost Analysis of Existing Steel MomentFrame Buildings. PhD thesis, Cornell University, United States of America, 2009. → page 48Yang, T., Moehle, J., Stojadinovic, B., and Der Kiureghian, A. Seismic performance evaluation offacilities: methodology and implementation. Journal of Structural Engineering, 135(10):1146–1154,2009. → page 4Yao, X., Elnashai, A., and Jiang, J. Analytical seismic fragility analysis of concrete arch dams. InProceedings of the 15th World Conference on Earthquake Engineering, 2012. → page 173Yazdani, A. and Jeffrey, P. Robustness and vulnerability analysis of water distribution networks usinggraph theoretic and complex network principles. In Water Distribution Systems Analysis 2010, pages933–945. American Society of Civil Engineers, 2010a. → page 8Yazdani, A. and Jeffrey, P. A complex network approach to robustness and vulnerability of spatiallyorganized water distribution networks. arXiv preprint arXiv:1008.1770, 2010b. → page 8Zeng, D. and Zhang, H. Modelling correlated damages of residential building portfolios under tropicalcyclone wind loads. In 13th International Conference on Applications of Statistics and Probability inCivil Engineering, 2019. → page 47Zhang, G., Setunge, S., and van Elmpt, S. Using shipping containers to provide temporary housing inpost-disaster recovery: Social case studies. Procedia Economics and Finance, 18:618–625, 2014. →pages 8, 107Zhang, Y. and Peacock, W. G. Planning for housing recovery? Lessons learned from Hurricane Andrew.Journal of the American Planning Association, 76(1):5–24, 2009. → pages 114, 115164Zhu, J. and Collette, M. A dynamic discretization method for reliability inference in Dynamic BayesianNetworks. Reliability Engineering & System Safety, 138:242–252, 2015. → page 30165Appendices166Appendix AEarthquake Hazard and Infrastructure inBritish ColumbiaA.1 Seismic Hazard in British ColumbiaThe West coast of Canada lies on the boundaries of the North American plate, the Juan de Fuca plate, andthe Pacific plate. The Geological Survey of Canada (Adams and Halchuk, 2003) represent the earthquakehazard using 26 earthquake area sources, as shown in Figure A.1. These area sources are characterised by amaximum magnitude, Mmax, a dispersion parameter, β , and a return period. The values for theseparameters are listed in Table A.1.167ALC - Alaska CoastalALI - Alaska InlandBFT - Beaufort SeaBRO - Brooks PeninsulaCASR - Cascade MountainCST - CoastalDENR - DenaliEXP - Explorer PlateFHL - Flathead LakeGOA - Gulf of AlaskaGSP - Georgia StraitHECR - Hecate StraitJDFF - Juan de Fuca Plate Bending - OffshoreJDFN - Juan de Fuca Plate Bending - OnshoreMMB - Mackenzie MountainsNBC - Northen British ColumbiaNOFR - Nootka FaultNYK - Northern YukonOFS - OffshoreQCFR - Queen Charlotte FaultALCALIYAKGOASOYMMBSBCROCFHLCASRBROJDFFEXPOFSCSTNBCHECRQCFRNYKRMNRMSDENRGSP0km500-140 -135 -130 -125 -120 -115 -110 -105  50  55  60  65   70JDFNNOFRRMN - Richardson Mountains NorthRMS - Richardson Mountains SouthROC - Rocky Mountain Fold and Thrust BeltSBC - Southern BCSOY - Southern YukonYAK - Yakutat Fairweather FaultFigure A.1: Earthquake area sources in Western Canada, adapted from Adams and Halchuk (2003).168Table A.1: Earthquake area sources in Western Canada (Adams and Halchuk, 2003)β Maximum Depth Area mg5 per 106 rate ofEstimate Best Lower Upper Best Lower Upper Best[103 sq km] sq km/year occurrenceWeights 0.68 0.16 0.16 0.6 0.3 0.1 0.5Area sourceALC 1.43 1.51 1.35 8.5 8.2 8.7 5 139 21.6 3.00ALI 1.73 1.84 1.62 8.5 8.2 8.5 5 339 29.5 10.0BFT 1.69 1.86 1.52 7 6.7 7.3 5 65.4 1.93 0.13BRO 1.19 1.46 0.93 7 6.7 7.3 5 65.4 31.5 2.06CASR 0.85 1.88 0.85 7.7 7.7 7.7 5 167 1.12 0.19CST 1.5 1.7 1.29 7.5 7.4 7.6 5 278 0.52 0.14DENR 1.88 1.97 1.78 7.5 7 8 5 73.6 4.48 0.33EXP 1.3 1.45 1.15 7 6.7 7.3 5 12.5 11.4 0.14FHL 2.49 2.93 2.06 7.3 7.1 7.5 5 23.5 2.32 0.05GOA 2.31 2.47 2.15 7.8 7.6 8 5 29.8 15.8 0.47GSP 1.13 1.26 0.99 7.1 6.9 7.3 50 36.1 2.57 0.09HECR 1.9 2.04 1.76 7 6.7 7.3 5 35.4 1.95 0.07JDFF 1.87 2.26 1.48 7 6.7 7.3 5 21.4 0.367 0.01JDFN 2.07 2.58 1.56 7.1 6.7 7.3 5 15.9 0.218 0.00MMB 2.43 2.5 2.35 7.1 6.9 7.3 5 214 1.43 0.31NBC 2 2.2 1.8 7 6 7 5 310 0.024 0.01NOFR 1.57 1.69 1.45 7 6.7 7.3 5 9.12 11.2 0.10NYK 3.75 4.35 3.15 7 6.7 7.3 5 259 0.196 0.05OFS 2.1 2.22 1.98 7.1 6.9 7.3 5 61.8 20.4 1.26QCFR 1.56 1.62 1.49 8.5 8.2 8.5 5 82 8.66 0.71RMN 2 2.14 1.86 7 6.7 7.3 5 19.2 6.8 0.13RMS 1.67 1.78 1.56 7 6.7 7.3 5 20.8 13.8 0.29ROC 2.04 2.25 1.82 7 6.7 7.3 5 231 0.247 0.06SBC 2.21 2.49 1.92 7 6.7 7.3 5 187 0.117 0.02SOY 2.15 2.42 1.87 7 6.7 7.3 5 268 0.135 0.04YAK 2.01 2.07 1.95 8.5 8.2 8.7 5 117 5.98 0.70169A.2 Selected Electric Power InfrastructureElectrical power to the City of Vancouver is primarily supplied by the Mica and Revelstoke dams, locatednearly 400 kilometres Northeast, and the Gordom M. Shrum and Peace Canyon dams, nearly 750kilometres North. A line diagram of the power transmission and distribution systems, from thehydroelectric dams to the local high voltage power substations, i.e., ≥ 200 kV, is shown in Figure A.2.Seven power substations are assumed to directly supply neighbourhoods in Vancouver, with six of thesebeing located in Vancouver and one on the adjacent municipality of Burnaby.Figure A.2: Power transmission network to Vancouver - adapted from BC Hydro (2018).In Figure A.3 the location of the hydroelectric dams and power substations is presented. It is noted that thehydroelectric dams are exposed to a lesser earthquake hazard, since they are far from the Cascadiasubduction zone.In Rts, hydroelectric dams and power substations are instances of the RPowerDamModel andRPowerSubstationModel classes, respectively. The information needed to instantiate the aforementioneddams and substations is listed in Tables A.2 and A.3. The fragility curve is chosen from those provided inthe HAZUS-MH manual (FEMA, 2015) and it defines the seismic vulnerability of the structure. Allstructures are assumed to be anchored, that means that seismic loads were considered in their design, orthat they were retrofitted to resist seismic loads. The modelling of power lines, towers, and poles areconsidered outside of the scope of this dissertation.170Figure A.3: Location of power distribution infrastructure in Lower Mainland British Columbia.Table A.2: Hydroelectric dams in Lower Mainland.Dam LocationCapacity Year Fragility(MW) Built curveGordom M. Shrum Dam 56.017 , -122.207 2876 1968 Large AnchoredRevelstoke Dam 51.051 , -118.195 2480 1984 Large AnchoredMica Dam 52.076 , -118.564 2800 1976 Large AnchoredPeace Cannyon Dam 55.982 , -121.993 694 1980 Large Anchored171Table A.3: Power substations in Lower Mainland.Substation LocationFragilitycurve(1) Ashton Creek 50.561 , -118.993 Medium voltage anchored(2) Cambie 49.190 , -123.062 Medium voltage anchored(3) Camosun 49.249 , -123.197 Medium voltage anchored(4) Cathedral Square 49.282 , -123.113 Medium voltage anchored(5) Cheekeye 49.790 , -123.160 Medium voltage anchored(6) Horne Payne 49.266 , -123.016 Medium voltage anchored(7) Ingledow 49.158 , -122.874 Medium voltage anchored(8) Kelly Lake 51.024 , -121.739 Medium voltage anchored(9) Kennedy 55.068 , -122.783 Medium voltage anchored(10) Kidd 49.199 , -123.115 Medium voltage anchored(11) Mainwaring 49.227 , -123.079 Medium voltage anchored(12) Meridian 49.309 , -122.806 Medium voltage anchored(13) Mount Pleasant 49.266 , -123.112 Medium voltage anchored(14) Murrin 49.280 , -123.1 Medium voltage anchored(15) Nicola 50.180 , -120.390 Medium voltage anchored(16) Sperling 49.250 , -123.152 Medium voltage anchored(17) Willinston 53.851 , -122.611 Medium voltage anchored172A.3 Selected Water Distribution InfrastructureAccording to publicly available information from the Metro Vancouver Water Services (Metro Vancouver,2018), the water consumed in the City of Vancouver comes primarily from the Cleveland dam, in theCapilano Lake, and the Seymour Falls dam, in the Seymour Lake. A large system of water treatmentfacilities, e.g., filtration and re-chlorination plants, pump stations, and storage tanks supply potable water toVancouver dwellings. The case studies in Chapter 5 considers that the availability of water influences adwelling’s likelihood to leave their homes. In order to include the water distribution system in these casestudies, the simplified water distribution system in Figure A.4 is assumed. In the figure are identified thewater infrastructure, as well as, six power substations which are assumed to supply power to water pumpstations and treatment facilities. For clarity, only the substations that directly supply water infrastructureare represented in Figure A.4. However, these power substations are a part of the power distributionnetwork shown in Figure A.2.The general locations of the water distribution infrastructure are presented in Figure A.5. Because someinfrastructure are closely located, the numbers in parenthesis in Figure A.5 are used in Tables A.4-A.7 toidentify the location of each facility.The RWaterDamModel class is used in Rts to create water dam objects, which have their location andseismic fragility as attributes. However, as indicated by Yao et al. (2012), fragility curves for dams aredifficult to obtain due to limited field data and lack of efficient analytical approaches for conductingdynamic response history analyses of these structures. Thus, because fragility curves for dams are notprovided in the HAZUS-MH manual (FEMA, 2015), and because it is outside the scope of this research todevelop them, water dams are assumed to not to be damaged by seismic loads. This assumption reduces thevulnerability to water shortages in the results in Chapter 5. In Table A.4 the location, year built, height, andlength of the dams that supply the City of Vancouver are listed. This information can be useful in obtainingfragility curves for these structures in the future.Table A.4: Water dams in Lower Mainland.Dam LocationYear Height Lengthbuilt (m) (m)Cleveland Dam 49.360 , -123.111 1994 92 195Seymour Falls Dam 49.440 , -122.969 2007 30 235Water treatment facility objects are instances of the RWaterTreatmentFacilityModel class, and their173Figure A.4: Water transmission network to Vancouver.attributes are their location and seismic fragility curve (FEMA, 2015). Nonetheless, the capacity of theplant is also necessary to properly choose the fragility curve for these facilities. Table A.5 lists the values ofthese parameters adopted in the later case studies. Only information about the Seymour-Capilano filtrationplant was obtained, and it is capacity is 480 mgd, making it a large plant. For the remaining plants, it isassumed the they are medium plants, i.e., 50 mgd to 200 mgd. Furthermore, it is assumed that these facilityhave been retrofitted against seismic loads. Thus, the Seymour-Capilano filtration plant is classified as alarge plant with anchored components, ”PTW5” in the HAZUS classification, and the re-chlorinationstations are modelled as medium plants with anchored components, ”PWT3” in the HAZUS classification.In Rts, the RWaterStorageTankModel class is used to instantiate water storage tank farms objects. Thesetank farms can contain one or more individual storage tanks. For the Vancouver case study, it is assumedthat all storage tank farms comprehend a single on-ground anchored concrete tank, classifying them as174Figure A.5: Location of water distribution infrastructure in Lower Mainland British Columbia.”PST1” according to the HAZUS convention. The ”PST1” fragility curves are the least vulnerable toseismic loads. Table A.6 lists the location and seismic parameters of the water storage tank objects.Finally, water pump stations are represented by objects of the RWaterPumpStationModel class, and take asattributes their location and HAZUS fragility curve (FEMA, 2015). Pumping plants are classified as eithersmall pumping stations (less than 10 mgd capacity) or medium/large pumping stations (more than 10 mgdcapacity). Pumping plants are also classified with respect to whether their subcomponents are anchored ornot. Due to lack of more detailed information, all pumping stations are modelled as medium/large plantswith anchored components, i.e., ”PPP3” in the HAZUS convention, because these are the least vulnerableplants.175Table A.5: Water treatment facilities in Lower Mainland.Facility LocationCapacity Fragility(mgd) curve(2) Seymour-Capilano Filtration Plant 49.349 , -123.013 480 PWT5(3) Stanley Park Re-chlorination Station 49.340 , -122.773 - PWT3(4) Vancouver Heights Re-chlorination Station 49.287 , -123.024 - PWT3(6) Little Mountain Re-chlorination Station 49.240 , -123.115 - PWT3(7) Kersland Re-chlorination Station 49.239 , -123.115 - PWT3Table A.6: Water storage facilities in Lower Mainland.Reservoir LocationNumber of Fragilitytanks curve(4) Vancouver Heights 49.289 , -123.019 1 PST1(5) Sasamat 49.258 , -123.209 1 PST1(6) Little Mountain 49.241 , -123.113 1 PST1(7) Kersland 49.238 , -123.112 1 PST1Table A.7: Water pump stations in Lower Mainland.Pump station LocationFragilitycurve(1) Capilano Pump Station 49.358 , -123.112 PPP3(2) Seymour-Capilano 49.348 , -123.020 PPP3(4) Vancouver Heights Pump Station 49.289 , -123.019 PPP3(5) Sasamat Pump Station 49.258 , -123.209 PPP3(6) Little Mountain Pump Station 49.241 , -123.114 PPP3(7) Kersland Pump Station 49.239 , -123.115 PPP3176A.4 Selected Transportation InfrastructureThe Metro Vancouver region is highly dependent on maritime transportation to receive goods.Furthermore, transportation within the region needs to go over several water bodies, such as the Burrardinlet, Fraser and Pitt rivers. Thus, in the aftermath of a catastrophic earthquake, the functionality of thelocal ports and bridges is fundamental for supplies to be delivered to and distributed in the region. InFigure A.6 the locations of the bridges around the City of Vancouver are shown. It is noted that significantredundancy exists in the connections to South and West municipalities, whereas only two bridges connectto the North Shore, as shown in Figure A.6. This lack of redundancy can limit the capacity to transportsupplies from the Port of Vancouver to the City of Vancouver. In Figure A.7 are also highlighted thelocation of ports along the Strait of Georgia which are relevant for the case study in Chapter 3.Figure A.6: Location of bridges around the City of Vancouver.In Rts bridges are objects of the RBridgeModel class, whereas, ports are instances of the RPortModelClass.Twenty-eight fragility curves for bridges are available, based on the HAZUS-MH models (FEMA, 2015).The attributes in Table A.8 are used to determine the most appropriate fragility curve for each bridge. Notesome of these attributes, e.g., angle of skew, number of spans, are approximations. In Rts, Port objects arecomprised of three substructures: (i) waterfront structures, i.e., piers and wharves structures, (ii) fuel177Figure A.7: Location of selected ports in Coastal British Columbia.storage facilities, and (iii) cranes. Each substructure has an individual fragility curve and the functionalityof a port is determined by the minimum functionality of its substructures. Because the transportation offuel discussed in Chapter 3 is done by barges and roll-on-roll-off vessels, the functionality of cranestructures is not included. Considering this, the attributes for the ports modelled in this dissertation arepresented in Table A.9. Note that, due to limited information, only the major ports considered to haveanchored components, i.e., designed to resist seismic loads. Fragility curves for ports are selected fromFEMA (2015).178Table A.8: Bridges in Lower Mainland.Bridge Location Length SpansSpan Angle Fragilitywidth (m) of skew curve(1) Alex Fraser 49.159 , -122.943 931 5 186 0 HWB20(2) Annacis Channel 1 49.176 , -122.956 380 4 95 0 HWB1(3) Annacis Channel 2 49.175 , -122.958 500 10 50 0 HWB1(4) Arthur Laing 49.198 , -123.136 480 6 80 0 HWB1(5) Dinsmore 49.179 , -123.149 416 13 32 0 HWB1(6) Knight Street 49.202 , -123.077 345 3 115 0 HWB20(7) Lions Gate 49.315 , -123.139 840 3 280 0 HWB1(8) Massey Tunnel 49.122 , -123.076 1000 1 1000 0 HWB1(9) No. 2 Road 49.176 , -123.157 700 7 100 0 HWB1(10) Oak Street 49.200 , -123.126 213 3 71 0 HWB16(11) Patullo 49.208 , -122.894 760 8 95 0 HWB15(12) Port Mann 49.220 , -122.813 1890 3 630 0 HWB1(13) Queensborough 49.196 , -122.947 330 3 110 0 HWB15(14) Second Narrows 49.296 , -123.026 1300 4 325 0 HWB1Table A.9: Ports in Lower Mainland British ColumbiaFragility curvePort LocationWaterfrontStorage facilitiesstructureChemainus 49.289 , -122.954 WF1 Unanchored, no back-up powerCobble Hill 48.928 , -123.704 WF1 Unanchored, no back-up powerNanaimo 49.201 , -123.091 WF1 Unanchored, back-up powerPowell River 49.167 , -123.933 WF1 Unanchored, no back-up power(1) Burnaby Chevron 49.290 , -123.003 WF1 Unanchored, no back-up power(2) Burnaby Esso 49.301 , -122.889 WF1 Unanchored, no back-up power(3) Burnaby Shell 49.291 , -122.928 WF1 Unanchored, no back-up power(4) Burnaby Suncor 49.289 , -122.881 WF1 Unanchored, no back-up power(5) Mitchell Island 49.202, -123.090 WF1 Unanchored, no back-up power(6) Port of Vancouver 49.314, -123.086 WF1 Unanchored, no back-up power(7) Westridge Marine 49.283, -122.956 WF1 Unanchored, back-up powerA.5 Selected Fuel Distribution InfrastructureIn Figure A.8 the location of selected fuel refineries, terminals, and tank farms is presented. Refineries andfuel terminals are the departure points of fuel shipments in the fuel distribution system in coastal BritishColumbia. Table A.10 presents the attributes of the refineries and fuel terminals considered in the casestudy in Chapter 3. Their main attributes are their location, storage capacities, and HAZUS classification,which determines the most appropriate fragility curve to represent them (FEMA, 2015). Refineries are179instantiated from the RFuelRefineryModel class in Rts, whereas, fuel terminals are instances of theRFuelStorageTankModel because fuel terminals are modelled as storage facilities. In addition, refineriesand fuel terminals are modelled as having unanchored components due to lack of detailed informationabout their seismic vulnerabilities. Tank farms are the final destination of fuel before being consumed bycommunities. Tank farms can contain a single or multiple storage tanks and the vulnerability of each tankis considered independently. The main attributes of tank farm objects are the number of tanks and the totalstorage capacity, which is assumed to be evenly distributed in the individual tanks.Figure A.8: Location of selected fuel distribution infrastructure in Coastal British Columbia.180Table A.10: Fuel supplier in British ColumbiaFuel supplier LocationStorage Fragilitycapacity (bbl) curveAnacortes Shell Refinery 49.284 , -123.003 4730000 Small unanchoredBurnaby Chevron Refinery 48.466 , -122.560 171000 Small unanchoredBurnaby Esso Terminal 49.261 , -122.928 124500 On-ground steel unanchoredBurnaby Shell Terminal 49.301 , -122.882 199500 On-ground steel unanchoredBurnaby Suncor Terminal 49.279 , -122.881 96000 On-ground steel unanchoredWestridge Marine Terminal 49.286 , -122.954 45000 On-ground steel unanchoredTable A.11: Fuel tank farms in British Columbia.Tank farm LocationCapacity Number HAZUS(bbl/d) of tanks classificationBella Coola 48.695 , -123.545 6720 1 Concrete anchoredChemainus Shell 49.193 , -123.950 80183 5 Concrete anchoredCobble Hill Chevron 49.186 , -123.950 74919 4 Concrete anchoredHartley Bay 48.926 , -123.705 12996 1 Concrete anchoredNanaimo Esso 49.836 , -124.529 58315 4 Steel unanchoredNanaimo Suncor 53.426 , -129.251 64956 4 Steel unanchoredPowell River 52.374 , -126.753 5412 4 Concrete anchoredYVR Airport 49.197 , -123.161 90000 4 Concrete anchoredA.6 Census and Housing Information for the City of VancouverA visual representation of the characteristics of the residential buildings and dwellings used in thisdissertation is presented in the following. The City of Vancouver is divided into 22 neighbourhoods, asshown in Figure 4.14. A Census information object is created for each neighbourhood using data from the2016 Census (Statistics Canada, 2016). The information in these 22 objects is used to create the plots inFigures A.9-A.16, which help understanding the vulnerabilities of the City of Vancouver.In Figure A.9 the median dwelling income for the neighbourhoods is displayed. The Dunbar Southlandsand Shaughnessy neighbourhoods present the highest median dwelling incomes, close to C$90,000,whereas the lowest income is observed in the Strathcona and West End neighbourhoods.Figures A.10 and A.11 present the percentage of low- and high-income dwellings per neighbourhood. TheStrathcona displays the highest number of low-income dwellings, and the lowest number of high-incomedwellings. This indicates that this is an overall poor neighbourhood. Alternatively, the Shaughnessyneighbourhood, for example, presents a high percentage of high-income dwellings and a low percentage oflow-income neighbourhoods, indicating that this is a richer neighbourhood. Lastly, the Arbutus-Ridge, for181Figure A.9: Median dwelling income for Vancouver (Statistics Canada, 2016).example, has a significant number of low- and high-income, indicating a high level of income disparity.Figure A.10: Prevalence of dwellings with low income in Vancouver (Statistics Canada, 2016).182Figure A.11: Prevalence of dwellings with high income in Vancouver (Statistics Canada, 2016).In Figures A.12 and A.13 the building portfolio of the City of Vancouver is explored. It is noted that theDowntown peninsula and the adjacent neighbourhoods concentrate the majority of the multi-familybuildings in the city. The Kensington-Cedar Cottage and Renfrew-Collingwood neighbourhoodsconcentrate the majority of the single-family buildings.The age of the building stock in the City of Vancouver is also important when seismic loads are considered.Figure A.14 indicates that the majority of the buildings in the Shaughnessy and Dunbar-Southlandsneighbourhoods were built before 1980. It is noted that these are the neighbourhoods with the highestincomes. The Downtown neighbourhood presents the smallest percentage of old buildings, this is becausethis neighbourhood is composed primarily of newer multi-family buildings.The tenure status of the building in the City of Vancouver is shown in Figure A.15. A correlation betweenthe median dwelling income and the tenure status is observed, with the neighbourhoods with highestincome, i.e., Dunbar-Southlands and Shaughnessy, presenting the least amount of rented buildings. Theopposite is also true, as the highest number of rented buildings are observed in the Strathcona and WestEnd neighbourhoods.Finally, the percentage of new immigrants, i.e., persons who entered Canada after 2011, per neighbourhood183Figure A.12: Prevalence of single-family buildings in Vancouver (Statistics Canada, 2016).Figure A.13: Prevalence of multifamily buildings in Vancouver (Statistics Canada, 2016).184Figure A.14: Prevalence of buildings built before 1980 in Vancouver (Statistics Canada, 2016).Figure A.15: Renter dwellings in Vancouver (Statistics Canada, 2016).185is shown in Figure A.16. The figure indicates that the neighbourhoods in the South of the City ofVancouver tend to have a higher concentration of recent immigrants.Figure A.16: Recent immigrant dwellings in Vancouver (Statistics Canada, 2016).186Appendix BDetailed Results From Chapters 4 and 5B.1 Detailed Results From Chapter 4Figure B.1: Housing recovery curves for selected neighbourhoods for a four-years period.187Figure B.2: Housing recovery curves for selected neighbourhoods for a four-years period.Figure B.3: Housing recovery curves for selected neighbourhoods for a four-years period.188Figure B.4: Housing recovery curves for selected neighbourhoods for a four-years period.Figure B.5: Robustness indexes of selected neighbourhoods for different moment magnitudes.189Figure B.6: Robustness indexes of selected neighbourhoods for different moment magnitudes.Figure B.7: Robustness indexes of selected neighbourhoods for different moment magnitudes.190Figure B.8: Robustness indexes of selected neighbourhoods for different moment magnitudes.Figure B.9: Rapidity indexes of selected neighbourhoods for different moment magnitudes.191Figure B.10: Rapidity indexes of selected neighbourhoods for different moment magnitudes.Figure B.11: Rapidity indexes of selected neighbourhoods for different moment magnitudes.192Figure B.12: Rapidity indexes of selected neighbourhoods for different moment magnitudes.Figure B.13: Resilience indexes for selected neighbourhoods for different moment magnitudes.193Figure B.14: Resilience indexes for selected neighbourhoods for different moment magnitudes.Figure B.15: Resilience indexes for selected neighbourhoods for different moment magnitudes.194Figure B.16: Resilience indexes for selected neighbourhoods for different moment magnitudes.195B.2 Detailed Results From Chapter 5Figure B.17: Displaced persons for selected neighbourhoods over time.196Figure B.18: Displaced persons for selected neighbourhoods over time.Figure B.19: Displaced persons for selected neighbourhoods over time.197Figure B.20: Displaced persons for selected neighbourhoods over time.198


Citation Scheme:


Citations by CSL (citeproc-js)

Usage Statistics



Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            async >
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:


Related Items