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Life safety modelling framework and performance measures to assess community protection systems : application… Johnstone, William McAdam 2012

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LIFE SAFETY MODELLING FRAMEWORK AND PERFORMANCE MEASURES TO ASSESS COMMUNITY PROTECTION SYSTEMS: APPLICATION TO TSUNAMI EMERGENCY PREPAREDNESS AND DAM SAFETY MANAGEMENT  by WILLIAM MCADAM JOHNSTONE M.A.Sc., University of Waterloo, 1985 B.A.Sc., University of Waterloo, 1983  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES  (Civil Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) October 2012 © William McAdam Johnstone, 2012  Abstract  Abstract Rapid-Onset, High-Intensity hazards such as dam failures, tsunami, flash floods, volcanic lahars, urban-wildland interface fires and industrial accidents can produce catastrophic mortality for Populations at Risk (PAR). Governments, local communities and other stakeholders can use risk management, sustainable hazards mitigation and emergency/disaster management processes before an event to establish a Community Protection System (CPS) to protect the PAR. A CPS is a system-of-systems that combines the capabilities of the natural, critical infrastructure and social infrastructure environments. Since a CPS can be expensive to establish and maintain, and since there can be many uncertainties associated with system performance, there is a need to develop reliability-based Life Safety Measures that can be used to analyse and rank alternatives, to optimize designs and to inform stakeholders. Forensic datasets that describe historic disaster outcomes generally cannot support the process of loss and survival estimation; therefore, analytical and simulation-based methods must be used to develop synthetic CPS performance data. Life Safety can be assessed using two limit state equations that assess the sufficiency of time and the sufficiency of protection offered to individuals in the hazard impact zone. These equations consider causal event chains, spatial pathways, network interdependencies, management decisions, differential vulnerabilities, individual decisions and emergent/non-linear systems behaviours. The performance estimates can be estimated and visualized using a Life Safety Performance Space and a time-dependent Life Safety State Space. A Systems Modelling Framework is developed to guide the integration of the analytical and systems simulation models used to estimate mortality and survival. The framework combines concepts from systems engineering, systems safety, Geographic Information Systems, systems simulation, critical infrastructure modelling, hazards research and disaster research. The resulting probabilistic-causal-quantitative framework provides a basis for developing estimates that are transparent and defensible. Detailed theoretical formulations of the Systems Modelling Framework and the Life Safety Measures are developed. A series of hypothetical examples are used to demonstrate the methods. Applications are developed for tsunami preparedness and dam safety at the macro-, meso- and microresolutions. The tsunami example considers the Cascadia Subduction Zone tsunami hazard. The dam safety examples consider the St. Francis and Malpasset Dam Failures.  ii  Preface  Preface Some of the materials presented in this dissertation have been published. Materials presented in parts of Sections 6.2, 6.3, 6.4 and 6.5 have been published in: Johnstone, W.M., and Lence, B.J. (2012). "Use of Flood, Loss and Evacuation Models to Assess Exposure and Improve a Community Tsunami Response Plan: Vancouver Island." ASCE Natural Hazards Review, 13(2), 162-171. Materials presented in Sections 7.2, 7.3 and Appendix B have been published in two forms: 1) Johnstone, W.M. and B.J. Lence (2010), "Assessing the Life Safety Performance of Emergency Action Plans," ASDSO Dam Safety 2010, Association of State Dam Safety Officials (ASDSO): Seattle, WA. Sept 19-23, 2010 and 2) as an invited paper, Johnstone, W.M., and Lence, B.J. (2011). "Assessing the Life Safety Performance of Integrated Emergency Action Plans." ASDSO Journal of Dam Safety, 9(1), 29-37. Materials presented in Appendix C.1 have been published in: Johnstone, W. M., and Lence, B. J. (2009). "Assessing the Value of Mitigation Strategies on Reducing the Impacts of Rapid-Onset, Catastrophic Floods." Journal of Flood Risk Management, 2(3), 209-221. Materials presented in Appendix D.1 that describe the BC Hydro Life Safety Model have been published in: Johnstone, W. M., Sakamoto, D., Assaf, H., and Bourban, S. (2005). "Architecture, Modelling Framework and Validation of BC Hydro's Virtual Reality Life Safety Model." Ninth International Symposium on Stochastic Hydraulics, 23 and 24 May, 2005, International Association of Hydraulic Research (IAHR), Nijmegen, Netherlands. The opinions presented in this dissertation are the author's and do not reflect the opinions or policies of the funding, supporting or collaborating organizations or their staff. No warranties are expressed or implied by this dissertation.  iii  Table of Contents  Table of Contents Abstract ........................................................................................................................................................................ii Preface ........................................................................................................................................................................ iii Table of Contents........................................................................................................................................................ iv List of Tables..............................................................................................................................................................vii List of Figures ............................................................................................................................................................. ix List of Acronyms and Symbols ................................................................................................................................. xv Acknowledgements ..................................................................................................................................................xxii Dedication................................................................................................................................................................ xxiv 1  Introduction ........................................................................................................................................................ 1  2  Literature Review and Synthesis ....................................................................................................................... 6 2.1 Systems Theory, Engineering, Analysis and Modelling .............................................................................. 6 2.2 Hazards and Vulnerabilities ....................................................................................................................... 13 2.3 Emergencies, Disasters and Consequences ................................................................................................ 17 2.4 Stakeholder Processes and Systems ........................................................................................................... 19 2.4.1 General Processes .............................................................................................................................. 20 2.4.2 Lifecycle Asset Management of Critical and Social Infrastructures ................................................. 22 2.4.3 Risk Management.............................................................................................................................. 25 2.4.4 Emergency Management and Disaster Management ........................................................................ 30 2.4.5 Stakeholder Questions ....................................................................................................................... 34 2.4.6 Discussion ......................................................................................................................................... 35 2.5 Concepts for Development of the Systems Modelling Framework ........................................................... 38 2.5.1 Observation of ROHI Hazard Events and Consequences.................................................................. 41 2.5.2 Drills, Exercises and Experiments..................................................................................................... 45 2.5.3 Systems Data Models ........................................................................................................................ 46 2.5.4 Systems Process and Functional Models ........................................................................................... 50 2.5.5 Analytical, Simulation and Integrated Models .................................................................................. 58 2.6 Concepts for the Development of the Life Safety Measures ...................................................................... 64 2.6.1 Decision Context and Measures of Merit .......................................................................................... 64 2.6.2 Reliability, Time-Dependent Reliability and Uncertainty ................................................................. 65  3  Development of a Systems Modelling Framework for Life Safety Estimation .............................................. 72 3.1 World Systems, Performance Modelling Systems and Systems Behaviours ............................................. 72 3.2 Development of System-Level Functional Models .................................................................................... 76 3.3 Supporting Systems Modelling Using Available Data Models and Datasets............................................. 81 3.4 Description of the Integrated Systems Modelling Framework................................................................... 84 3.5 Summary and Discussion ........................................................................................................................... 89  4  Formulation of the Life Safety Measures ....................................................................................................... 90 4.1 Problem Definition..................................................................................................................................... 90 4.2 General Process to Estimate the Life Safety Measures .............................................................................. 92 4.3 Formulation of the Life Safety MOPs and MOE ....................................................................................... 97 4.3.1 General Framework and Reliability-Based Formulation ................................................................... 97 4.3.2 Identification of the Measures of Performance ............................................................................... 100 4.3.3 Development of the Life Safety Limit State Equations ................................................................... 101 4.3.4 Incorporation of Spatial and Temporal Factors ............................................................................... 104 4.3.5 Visualization and Estimation of the Life Safety MOE .................................................................... 109 4.3.6 Time-Dependent CPS Reliability and Formulation of the Life Safety State Space ........................ 114 4.3.7 Exploration of Different Forms of the Life Safety Assessment Function ....................................... 118  iv  Table of Contents 4.4  Summary and Discussion ......................................................................................................................... 124  5  Interpretations, Extensions and Examples of the Life Safety Measures.................................................... 126 5.1 Estimation of CPS Effectiveness Using the Safety Margin Method ........................................................ 127 5.2 Estimation of CPS Effectiveness for a Single-Leg Journey Using Monte Carlo Simulation ................... 128 5.3 Estimation of Safelines and MaxF Isochrones ......................................................................................... 131 5.3.1 Estimation of Safeline Extents ........................................................................................................ 131 5.3.2 Estimation of Timeline Extents (MaxF Isochrones)........................................................................ 133 5.3.3 Development of a Composite Spatio-Temporal Analysis of the Hazard ......................................... 133 5.4 Estimation of GP, FLOL and FOK Using Fixed HAZ_I(x) and Varying CPS_P(x) ..................................... 134 5.4.1 Formulation for the Linear Cross-Section ....................................................................................... 135 5.4.2 Formulations for a General Cross-Section ...................................................................................... 138 5.5 Estimation of GP, FLOL and FOK Using Varying HAZ_I(x) and Varying CPS_P(x) ................................. 140 5.6 Consideration of the Influence of Time-Dependent HAZ_I and CPS_P on Outcomes ............................ 143 5.7 Accounting for Multiple Loss Mechanisms for CPS Components and People ........................................ 145 5.8 Assessment of the Influence of Individual Decisions on Outcomes ........................................................ 148 5.9 Development of Life Safety State Space Plots......................................................................................... 154 5.10 Assessment of CPS Alternatives Using MACES and Systems Architecture Concepts ........................... 157 5.11 Time-Dependent Decision-Making Using the Life Safety Measures ...................................................... 160 5.12 Summary and Discussion ......................................................................................................................... 162  6  Application of CPS and Life Safety Concepts to Tsunami Preparedness .................................................. 163 6.1 Systems Analysis of the General Problem Using CPS and Life Safety Concepts ................................... 163 6.2 Overview of Tsunami Life Safety Analyses for Ucluelet and Tofino, BC .............................................. 171 6.3 Development of the CSZ Hazard Model .................................................................................................. 175 6.4 Development of Benchmark Loss Estimates for Ucluelet ....................................................................... 178 6.5 Development of Mitigation Estimates for Ucluelet ................................................................................. 182 6.6 Assessment of Ucluelet's Single Haven Evacuation Plan (Micro-Resolution) ........................................ 184 6.7 Comparison of Single and Multi-Haven Evacuation Plans for Ucluelet (Meso-Resolution) ................... 192 6.8 Assessment of Evacuability and Shelterability for Ucluelet and Tofino (Macro-Resolution) ................. 197 6.9 Summary .................................................................................................................................................. 202  7  Application of CPS and Life Safety Concepts to Dam Safety ..................................................................... 204 7.1 Systems Analysis of the General Problem Using CPS and Life Safety Concepts ................................... 204 7.2 Analysis of the St. Francis Dam Failure Using the Life Safety Performance Space................................ 211 7.3 Estimation of the Life Safety Performance of a Dam Safety EAP........................................................... 215 7.4 Life Safety State Space Analysis of the Malpasset Dam Failure ............................................................. 222 7.4.1 Background ..................................................................................................................................... 222 7.4.2 Simulation of Benchmark and Mitigation Scenarios ....................................................................... 223 7.4.3 Estimation of CPS Performance as a Function of Control Parameter TSMM .................................... 230 7.5 Summary and Discussion ......................................................................................................................... 232  8  Summary, Contributions and Future Directions ......................................................................................... 234 8.1 Contributions............................................................................................................................................ 235 8.1.1 Characterization of the Problem Space ........................................................................................... 235 8.1.2 Development of the Systems Modelling Framework ...................................................................... 236 8.1.3 Formulation of the Life Safety Measures ........................................................................................ 237 8.1.4 Application of the Measures and Framework to Tsunami Preparedness and Dam Safety .............. 238 8.2 Recommendations for Future Research ................................................................................................... 240  References ................................................................................................................................................................ 243 Appendix A. Profiles of Tsunami and Dam Failure ROHI Hazards .................................................................. 272 A.1 Tsunami Hazard Events ........................................................................................................................... 272 A.2 Dam Failure Hazard Events ..................................................................................................................... 273 Appendix B. Examples of CPS ............................................................................................................................... 275 Appendix C. Identification of the Life Safety Measures of Performance ........................................................... 278 C.1 Survey of Models and Methods for Flood Loss Estimation ..................................................................... 278  v  Table of Contents C.2 C.3 C.4  Survey of Models and Methods for Estimating Systems Behaviour and Performance ............................ 282 Conclusion ............................................................................................................................................... 286 Discussion ................................................................................................................................................ 287  Appendix D. Models, Tools and Data for Estimating Life Safety ....................................................................... 289 D.1 Software Tools and System Simulation Models ...................................................................................... 289 D.2 Primary Data Sources............................................................................................................................... 295 Appendix E. Estimation of CPS Performance for Different Cross-Sections ...................................................... 297 E.1 Curved-Down Cross-Section ................................................................................................................... 299 E.2 Ramp Cross-Section................................................................................................................................. 303 E.3 Flat-Then-Ramp Cross-Section ................................................................................................................ 303 E.4 Detailed Calculations of Evacuability and Shelterability for Tofino and Ucluelet .................................. 306 Appendix F. Examples of Input Files for Simulation of the Malpasset Dam Failure ........................................ 310  vi  List of Tables  List of Tables Table 1 – Examples of Methods to Qualify, Verify, Validate, Calibrate and Certify System Models ........................ 12 Table 2 - Examples of Combined Human Mortality/Morbidity Scales ....................................................................... 18 Table 3 - Examples of Quantitative Consequences Scales .......................................................................................... 19 Table 4 - Typical Stakeholder Groups, Organizations and Roles ................................................................................ 20 Table 5 –CI Sectors and Subsectors (from Johnstone and Clark 2009)....................................................................... 24 Table 6 - Emergency Response Functions (Lindell et al. 2007) .................................................................................. 32 Table 7 - Emergency Support Functions (FEMA 2008b) ............................................................................................ 32 Table 8 - Examples of Stakeholder Questions ............................................................................................................. 35 Table 9 - Risk and Emergency Management Questions of Interest to this Dissertation .............................................. 37 Table 10 - Statistics of Reported Mortality for the Selected Hazard Types (1900-2009) (Johnstone 2012a) ............. 43 Table 11 - Systems Modelling Detail .......................................................................................................................... 50 Table 12 - Examples of Models That Could be Integrated Using a Systems Modelling Framework .......................... 60 Table 13 - Examples of Primary Systems.................................................................................................................... 75 Table 14 - HAZ-CPS-PAR Systems Combinations .................................................................................................... 75 Table 15 - Examples of CI System Objects for Selected Subsectors (from Johnstone and Clark 2009) ..................... 82 Table 16 - Examples of Tasks for Estimating the Life Safety Effectiveness of a CPS ............................................... 93 Table 17 - Examples of Quantities for Scenarios and Outcomes ................................................................................ 96 Table 18 - Time-Dependent Outcome Variables for a Composite Scenario ............................................................. 117 Table 19 - Summary of Life Safety Assessment Methods ........................................................................................ 119 Table 20 - Number of Random Variables in the Limit State Equations .................................................................... 122 Table 21 - Parameters for the Input Random Variables ............................................................................................ 129 Table 22 - Summary of Outcomes for One Thousand Realizations .......................................................................... 130 Table 23 - Assumptions and Performance Estimates for the Time-Independent Example........................................ 141 Table 24 - Examples of Multiple Loss Mechanisms for a Two-Storey Building ...................................................... 146 Table 25 - Point Estimates of Variables Used to Estimate CPS Performance ........................................................... 150 Table 26 - Calculations of CPS Performance On Route and At Haven Given an Individual's Choices .................... 152 Table 27 - Input Parameters for Scenarios A1 to D5 ................................................................................................. 154 Table 28 - Examples of Pre-Impact MAPP Functions Provided by a CPS for Tsunami ........................................... 163 Table 29 - Examples of Trans-Impact MACES Functions Provided by a CPS for Tsunami .................................... 165 Table 30 - Summary of Benchmark, Mitigation and Life Safety Performance Analyses and Simulations ............... 173 Table 31 - Ucluelet's Buildings at Risk and Estimated Losses by Hazard Zone (Johnstone and Lence 2012). ©2012 ASCE - With permission from ASCE. ................................................................................................. 180 Table 32 - Ucluelet's Population at Risk and Estimated Losses by Hazard Zone (Johnstone and Lence 2012). ©2012 ASCE - With permission from ASCE. ................................................................................................. 181 Table 33 - Composite Evacuation Input Scenarios and Estimated Societal Life Safety Measures ........................... 188 Table 34 - Examples of Pre-Impact MAPP Functions Provided by a CPS for Dam Safety ...................................... 205 Table 35 - Examples of Trans-Impact MACES Functions Provided by a CPS for Dam Safety ............................... 206  vii  List of Tables Table 36 - Time of Key Hazard Events for the St. Francis Dam Failure (developed from Outland 2002). ©2011 ASDSO. This table appeared in the Journal of Dam Safety Issue 9.1 and is reprinted with permission from ASDSO ........................................................................................................................................ 213 Table 37 - Time and Location of Vulnerabilities, Warnings, Evacuations and Losses (from Outland 2002). ©2011 ASDSO. This table appeared in the Journal of Dam Safety Issue 9.1 and is reprinted with permission from ASDSO ........................................................................................................................................ 213 Table 38 - Model Parameters Used for Analysis©2011 - ASDSO. This table appeared in the Journal of Dam Safety Issue 9.1 and is reprinted with permission from ASDSO .................................................................... 216 Table 39 - Assessment of Mitigation Scenarios for the Failure of Malpasset Dam................................................... 228 Table 40 - Examples of Tsunami Hazard Events That Informed the Research ......................................................... 273 Table 41 - Examples of Dam Failures and Incidents That Informed the Research ................................................... 274 Table 42 - Assessment of Selected Flood Loss Estimation Methods (from Johnstone and Lence 2009). ©2009 Blackwell Publishing. Used with permission. ...................................................................................... 279 Table 43 - Survey of Methods and Models for Estimating System Behaviours and Performance ............................ 284 Table 44 - Software Tools and System Simulation Models Used to Support the Research ...................................... 289 Table 45 - Selected LSM Objects (Johnstone et al. 2005). ©2005 International Association for Hydro-Environment Engineering and Research (IAHR). Used with permission. ................................................................. 291 Table 46 - Primary Data Sources ............................................................................................................................... 295 Table 47 - Example of a Set of Inputs to a Life Safety Analysis............................................................................... 299 Table 48 - Example of a Life Safety Cross-Section Analysis and Outcomes Summary Table ................................. 300 Table 49 - Example Scenario Input File for a Malpasset Evacuation Simulation ..................................................... 310 Table 50 - Example of a Road Network File for a Malpasset Evacuation Simulation .............................................. 312 Table 51 - Example of a Building Input File for a Malpasset Evacuation Simulation .............................................. 313 Table 52 - Example of a PARU Input File for a Malpasset Evacuation Simulation.................................................. 314 Table 53 - Example of a Detailed PARU Snapshot File for a Malpasset Evacuation Simulation ............................. 315 Table 54 - Example of an Output Summary File for a Malpasset Evacuation Simulation ........................................ 316  viii  List of Figures  List of Figures Figure 1 - Hazard, Community Protection System, Vulnerabilities and Consequences ................................................ 2 Figure 2 - Conceptual Views of a System: a) System Hierarchy, b) System Functions and Processes, c) System Dynamics and Feedback .......................................................................................................................... 8 Figure 3 - Simulation Model Verification and Validation (adapted from Schlesinger et al. 1979). ©1979 - Sage Science Press - UK. Used with permission. ........................................................................................... 12 Figure 4 - Research Focus: Rapid-Onset, High-Intensity Hazards .............................................................................. 16 Figure 5 - The Disaster Cycle ...................................................................................................................................... 20 Figure 6 - Disaster Phases (adapted from NRC 2006). ©2006 The National Academies Press. Used with permission. ............................................................................................................................................................... 21 Figure 7 - Ways to Study Systems, Behaviours, Interactions and Outcomes .............................................................. 40 Figure 8 - Example of a Bow Tie Risk Analysis Model (after Hartford (2009)). ©2009 - Elsevier. Adapted from Structural Safety, 31(2), D.N.D. Hartford, "Legal Framework Considerations in the Development of Risk Acceptance Criteria" with permission from Elsevier. .................................................................... 52 Figure 9 - Hybrid Causal Logic (HCL) Model (modified from Groen et al. 2006). ©2006 - Elsevier. Adapted from Reliability Engineering and System Safety, 91(3), Groen, F. J., Smidts, C., and Mosleh, A, "QRAS The Quantitative Risk Assessment System" with permission from Elsevier. ........................................ 53 Figure 10 - Fault Tree (FT) Diagram: a) Fault Tree and Symbols, b) Dam Safety Example ...................................... 54 Figure 11 - Initiating Events (IE) Diagram: a) Tree Structure and Symbols, b) Tsunami Example ............................ 55 Figure 12 - Event Sequence (ES) Diagram.................................................................................................................. 55 Figure 13 - Event-Activity Sequence (EAS) Diagram ................................................................................................ 56 Figure 14 - Event Tree (ET) Diagram ......................................................................................................................... 57 Figure 15 - Decision Tree (DT) Diagram .................................................................................................................... 58 Figure 16 - System Simulation Notations: Systems States, Observer and Controller Processes ................................. 62 Figure 17 - Decision Context, Measures of Merit and Systems Models ..................................................................... 64 Figure 18 - Uncertainty Categories (Hartford and Baecher 2004). ©2004 - Thomas Telford. Used with permission. ............................................................................................................................................................... 69 Figure 19 - Mapping of Objects Between World Systems and Performance Modelling Systems............................... 73 Figure 20 - Systems States, Interactions, Behaviours and Outcomes .......................................................................... 74 Figure 21 - HAZ and PAR System Functional Models ............................................................................................... 77 Figure 22 - Integrated Model of Stakeholder Processes .............................................................................................. 78 Figure 23 - Proposed CPS Functional Model .............................................................................................................. 80 Figure 24 - Concept of Object Types and Linkages Between Objects ........................................................................ 82 Figure 25 - Concept of Using Systems Data and Systems Models to Support Life Safety Estimation ....................... 83 Figure 26 - Integrated Systems Modelling Framework for Life Safety Estimation..................................................... 84 Figure 27 - HAZ, CPS and PAR EAS Diagrams for One Composite scenario ........................................................... 85 Figure 28 - One Triplet of Hazard, Protection and Response Chains .......................................................................... 86 Figure 29 - Integrated Framework for Estimating Life Safety Using Systems Simulation Models ............................ 87  ix  List of Figures Figure 30 - Simplified Problem Representation .......................................................................................................... 91 Figure 31 - Schema for Performance Estimates, Life Safety Input Scenarios and Outcomes ..................................... 94 Figure 32 - Process for Simulating Life Safety Outcomes .......................................................................................... 95 Figure 33 - Visualization of Mortality and Survival Outcomes for Passengers of RMS Titanic................................. 97 Figure 34 - Resulting Framework for Estimating the Life Safety MOE.................................................................... 103 Figure 35 - Plan and Cross-Section Views of a Route, Hazard Intensity and Protection for an Individual .............. 104 Figure 36 - Hazard Formation and Propagation Distances and Times ...................................................................... 106 Figure 37 - Individual Journeys: Travel Times and Distances from Route Origin to Destination ............................ 107 Figure 38 - Encounters Between a Person and the Propagating Hazard Plume......................................................... 108 Figure 39 - Hazard Intensity, Individual Strength and CPS Protection During a Journey Along a Route ................ 109 Figure 40 - Life Safety Performance Space and One Person's Journey Line............................................................. 110 Figure 41 - Examples of Effects of Uncertainties and Emergent Effects on Life Safety Performance: a) Influence of Uncertainties, b) Delays, c) Road Congestion ..................................................................................... 112 Figure 42 - Life Safety Performance Space, Outcomes and Performance Distribution for all Individuals ............... 113 Figure 43 - Life Safety Performance Distributions for Several Individuals .............................................................. 114 Figure 44 - Time-Dependent CPS Performance (Time-Dependent Reliability) for a Population at Risk ................. 115 Figure 45 - Time-Series View of Events, Outcomes and Derived Performance Variables ....................................... 117 Figure 46 - Life Safety State Space Plot.................................................................................................................... 118 Figure 47 - Event Tree Diagram for Assessing CPS Performance ............................................................................ 120 Figure 48 - Extended Framework and Event Tree Diagram for Assessing CPS Performance .................................. 121 Figure 49 - Representations of the Simplified Life Safety Assessment Method: a) System Reliability Diagram, b) Event Tree Diagram, c) Life Safety Performance Space ..................................................................... 123 Figure 50 - Hazard Scenarios, CPS and Community Layout .................................................................................... 127 Figure 51 - Triplet of Hazard, Protection and Response Chains for One Person at Risk .......................................... 129 Figure 52 - Probabilistic Assessment of Life Safety Effectiveness for One Person at Risk ...................................... 130 Figure 53 - Maximum Intensity Safelines as a Function of Maximum Allowable Failure Probability ..................... 132 Figure 54 - Determination of Isochrones as a Function of Maximum Allowable Failure Probability ...................... 133 Figure 55 - Visualizations of Space-Time Benchmark Analysis and Life Safety Performance Space...................... 134 Figure 56 - General Community Layouts: a) Plan view, b) Cross-Section View with Three Different Community Shapes .................................................................................................................................................. 135 Figure 57 - Geometric Representation of Limit State Calculations for GP: a) Ramp Cross-Section, b) Geometric Ratios ................................................................................................................................................... 138 Figure 58 - Calculations of FLOL for Values of HAZ_I, PAR_S, BLDG_S and the Cross-Section Shape Parameter (N) ............................................................................................................................................................. 139 Figure 59 - HAZ_I(x) and CPS_P(x) for Assumed Values of Protection Shape Parameter (NP) and Hazard Shape Parameter (NH), and CPS_PMAX=2xHAZ_IMAX ..................................................................................... 142 Figure 60 - Families of GP(x) Curves for Protection Shape Parameter NP = 0.25 and 4.0, and Varying Values of Hazard Shape Parameter NH ................................................................................................................ 142  x  List of Figures Figure 61 - Composite Community Cross-Sections: a) Functional Building Blocks, b) Examples Developed from Functional Building Blocks.................................................................................................................. 143 Figure 62 - Time-Dependent Changes in HAZ_I(x) and the Protection offered to a Person [CPS_P(x)] .................. 144 Figure 63 - Map Representation of Protective Action Alternatives........................................................................... 148 Figure 64 - Decision Tree Representation of One Individual's Protective Action Alternatives ................................ 150 Figure 65 - Operational Life Safety Performance "On Route" or "At Destination": a) Outcomes Symbolized by Hazard Scenario, b) Outcomes Symbolized by Target Safe Haven ..................................................... 151 Figure 66 - State-Time Plots: a) Time-Dependent Change