Applied Science, Faculty of
Civil Engineering, Department of
DSpace
UBCV
Blowes, Kristen
Doctor of Philosophy - PhD
University of British Columbia
Past earthquakes have shown that seismic damage may lead to lengthy loss of function and tenant displacement, even in modern buildings. A new generation of computational tools has enabled researchers to assess post-earthquake safety, loss of function, and recovery time. With this development, there is an opportunity to develop new recovery-based seismic design provisions that ensure building recovery performance meets societal expectations. In the first half of this dissertation, methods to evaluate functional recovery risk across a broad range of intensity levels are introduced. These methods are then implemented to evaluate the current functional recovery risk and the variability of risk across cities in the United States. The results show that the risk of exceeding short recovery targets is high (e.g., 50% probability in 50 years of the functional recovery time exceeding 1 month) and is driven by nonstructural damage in frequent events. The risk of exceeding long recovery targets, however, is much lower (e.g., 12% probability in 50 years of the functional recovery time exceeding 1 year). Safety-critical structural damage (i.e., structural damage that must be addressed before tenants can safely reoccupy) in rarer earthquakes has a larger impact on the risk of exceeding longer recovery targets. For recovery time targets under one year, current life-safety design practice in the United States also does not ensure uniform recovery risk across high seismicity cities. In the second half of this dissertation, the efficacy of structural and nonstructural design requirements is assessed to support the 2026 National Earthquake Hazards Reduction Program’s effort to develop the first generation of recovery-based design provisions in the United States. The results of this dissertation include structural design recommendations, such as response modification coefficients, Rfr, and allowable drift limits, Δafr, for functional recovery, for a wide range of lateral force-resisting systems. Nonstructural design recommendations include a component importance factor for functional recovery, Ipfr, and requirements for seismic qualification of equipment. At this moment of renewed focus on post-earthquake recovery, this work provides crucial methods and data to inform this major advance in building code development.
POST-EARTHQUAKE RECOVERY PERFORMANCE OF MODERN BUILDINGS AND DEVELOPMENT OF RECOVERY-BASED SEISMIC DESIGN PROVISIONS by Kristen Blowes B.Eng., McGill University, 2015 M.S., University of California, Berkeley, 2016 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Civil Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) April 2025 © Kristen Blowes, 2025 ii The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the dissertation entitled: Post-earthquake recovery performance of modern buildings and development of recovery-based prescriptive seismic design provisions submitted by Kristen Blowes in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Civil Engineering Examining Committee: Carlos Molina Hutt, Associate Professor, Civil Engineering, UBC Supervisor Carlos Ventura, Professor, Civil Engineering, UBC Supervisory Committee Member Dustin Cook, Research Structural Engineer, National Institute of Standards and Technology Supervisory Committee Member Perry Adebar, Professor, Civil Engineering, UBC University Examiner Ronald Kellett, Professor, School of Architecture + Landscape Architecture, UBC University Examiner iii Abstract Past earthquakes have shown that seismic damage may lead to lengthy loss of function and tenant displacement, even in modern buildings. A new generation of computational tools has enabled researchers to assess post-earthquake safety, loss of function, and recovery time. With this development, there is an opportunity to develop new recovery-based seismic design provisions that ensure building recovery performance meets societal expectations. In the first half of this dissertation, methods to evaluate functional recovery risk across a broad range of intensity levels are introduced. These methods are then implemented to evaluate the current functional recovery risk and the variability of risk across cities in the United States. The results show that the risk of exceeding short recovery targets is high (e.g., 50% probability in 50 years of the functional recovery time exceeding 1 month) and is driven by nonstructural damage in frequent events. The risk of exceeding long recovery targets, however, is much lower (e.g., 12% probability in 50 years of the functional recovery time exceeding 1 year). Safety-critical structural damage (i.e., structural damage that must be addressed before tenants can safely reoccupy) in rarer earthquakes has a larger impact on the risk of exceeding longer recovery targets. For recovery time targets under one year, current life-safety design practice in the United States also does not ensure uniform recovery risk across high seismicity cities. In the second half of this dissertation, the efficacy of structural and nonstructural design requirements is assessed to support the 2026 National Earthquake Hazards Reduction Program’s effort to develop the first generation of recovery-based design provisions in the United States. The results of this dissertation include structural design recommendations, such as response modification coefficients, Rfr, and allowable drift limits, Δafr, for functional recovery, for a wide range of lateral force-resisting systems. Nonstructural design recommendations include iv a component importance factor for functional recovery, Ipfr, and requirements for seismic qualification of equipment. At this moment of renewed focus on post-earthquake recovery, this work provides crucial methods and data to inform this major advance in building code development. v Lay Summary Building codes in North America aim to ensure occupants survive large earthquakes. Building codes do not, however, address whether buildings are safe to reoccupy following an earthquake or the impact of building damage on recovery. There is a new effort in North America to develop the first generation of design requirements that address post-earthquake recovery of buildings. This work supports this development by (1) assessing the current risk of lengthy recovery times and the types of building damage that drive this risk, and (2) developing structural and nonstructural design recommendations that will directly inform the building code. This work critically identifies the types of damage that cause long-term societal impacts and provides data-driven solutions to ensure better recovery outcomes. vi Preface This thesis contains original work that I developed with the support of my research supervisor, Dr. Carlos Molina Hutt. Each chapter is based on manuscripts that have been published or submitted to peer-reviewed journals or international conferences. I conducted several studies in this thesis as part of a consensus-based process to develop building code developments, and as a result, the work was highly collaborative. In each of the studies included, however, I was the primary researcher – I took on the lead role of planning the studies, developing models and performing calculations, analyzing the resulting data, and writing the manuscripts. The role of each collaborator is outlined below. The content in Chapter 2 was published with minor changes in the journal article Blowes, K., Kourehpaz, P., and Molina Hutt, C., 2023. Risk‐targeted seismic evaluation of functional recovery performance in buildings. Earthquake Engineering & Structural Dynamics, 52(13), 4245–4264. DOI: 10.1002/eqe.3984. The journal article was included in the special issue “Risk-targeted seismic design: prospects, applications, and open issues, for the next generation of building codes”. I conducted the analyses, interpreted the results, and wrote the manuscript. P. Kourehpaz wrote the python-based software package, TREADS, that I used to perform the study and provided training and support in using the tool. My supervisor, C. Molina Hutt aided with the formulation of the study, interpretation of results, and reviewing the manuscript. This work uses engineering demand parameters from Marafi (2018) for a suite of archetype buildings. I reran the FEMA P-58 damage assessment using building performance models from Kourehpaz et al. (2021), which evaluated expected damage and loss for this set of archetypes. These damage estimates were then the inputs for the remainder of the study. Attribution is given to these two studies in 2.4.1 to vii 2.4.3, where the models, engineering demand parameters, and losses are discussed and plotted in figures. The content in Chapter 3 was published in the conference paper Blowes, K., Molina Hutt, C., and Cook, D., 2024. Evaluating the variability in functional recovery performance in modern buildings across the United States. Proceedings of the 18th World Conference of Earthquake Engineering. I also presented the work in this paper at the 18th World Conference of Earthquake Engineering, Milan, Italy, in July 2024. D. Cook and I developed the study together. D. Cook performed the initial functional recovery time assessments using the ATC-138 methodology. I then used those as the inputs for the risk-based assessments, which I performed under the supervision of C. Molina Hutt. I conducted the literature review, all calculations apart from the initial ATC-138 assessments, interpretation of results, and all writing. D. Cook and C. Molina Hutt both aided with interpretation of results and reviewing the manuscript. Chapter 4 contains the content of a journal article in review: Blowes, K., Molina Hutt, C., Zimmerman, R., Cook, D., Almeter, E., and Haselton, C., 2025a. Limiting safety-critical structural damage in recovery-based seismic design provisions. Earthquake Spectra. This work was conducted in my role as a corresponding member of the Functional Recovery Task Committee (FRTC), which was tasked with developing prescriptive functional recovery seismic design provisions to be included in the 2026 NEHRP recommendations. I led the design of the research program, with support from my supervisor C. Molina Hutt and committee chair R. Zimmerman. D. Cook provided support with using the functional recovery time assessment tool ATC-138 and the design ground motion. This study involved running approximately 9000 models, each with a design variation and 5000 Monte Carlo simulations. Because of the size of the study, computational support was provided by the Haselton Baker Risk Group (HB-Risk). E. Almeter set viii up the inputs to run the analyses on HB-Risk’s platform. I processed all raw data output and iterated with E. Almeter to make updates to the input file as needed to reflect comments from the FRTC. I performed all calculations, analyses, and wrote the manuscript. C. Molina Hutt, R. Zimmerman, D. Cook, E. Almeter, and C. Haselton all provided feedback throughout the duration of the study, worked together to interpret the results, and reviewed and edited the manuscript included herein. Chapter 5 contains the content of a journal article in review: Blowes, K., Molina Hutt, C., Zimmerman, R., Cook, D., Almeter, E., and Haselton, C., 2025b. Nonstructural component design requirements for functional recovery. Earthquake Spectra. This work was also conducted to support building code development and with the same group roles described above for the work in Chapter 4. Again, the work was highly collaborative. I led the development of the study, processed all results output by the HB-Risk team, performed all calculations and analysis, and wrote the manuscript. All authors provided feedback, helped with interpreting results, and reviewed and edited the manuscript that is included herein. Finally, I wrote the contents of the thesis, with review provided by my supervisor, Dr. C. Molina Hutt, and supervisory committee members, Dr. C. Ventura and Dr. D. Cook. Generative Artificial Intelligence was not used in the development of this work. ix Table of Contents Abstract ......................................................................................................................................... iii Lay Summary .................................................................................................................................v Preface ........................................................................................................................................... vi Table of Contents ......................................................................................................................... ix List of Tables ................................................................................................................................xv List of Figures ............................................................................................................................ xvii Acknowledgements ................................................................................................................... xxii Chapter 1: Introduction ................................................................................................................1 1.1 Background and Motivation ........................................................................................... 1 1.2 Objectives ....................................................................................................................... 4 1.2.1 Objective 1: Establish methods to perform risk-based assessments for functional recovery.. ................................................................................................................................. 4 1.2.2 Objective 2: Evaluate the variability in functional recovery risk achieved using only life-safety design requirements ............................................................................................... 5 1.2.3 Objective 3: Develop methodology to determine structural design requirements that limiting safety-critical structural damage ............................................................................... 6 1.2.4 Objective 4: Propose nonstructural design requirements and explicitly verify efficacy of functional recovery provisions ............................................................................. 7 1.3 Organization .................................................................................................................... 8 1.4 Additional Notes ............................................................................................................. 9 Chapter 2: Risk-Based Seismic Evaluation of Functional Recovery Performance in Buildings........................................................................................................................................................11 x 2.1 Introduction ................................................................................................................... 11 2.2 Literature Review.......................................................................................................... 13 2.3 Probabilistic Evaluation of Functional Recovery Performance .................................... 15 2.3.1 Scenario-based Methodology................................................................................ 17 2.3.2 Intensity-based Methodology................................................................................ 18 2.3.3 Risk-based Methodology ...................................................................................... 19 2.4 Case Study of Modern Reinforced Concrete Shear Wall Buildings ............................. 22 2.4.1 Archetype Reinforced Concrete Shear Wall Buildings ........................................ 22 2.4.2 Seismic Hazard and Engineering Demand Parameters ......................................... 23 2.4.3 Damage and Repair Time Assessment ................................................................. 25 2.4.4 Functional Recovery Time Assessment ................................................................ 27 2.5 Functional Recovery Performance Evaluation ............................................................. 31 2.5.1 Scenario-based Functional Recovery Performance .............................................. 31 2.5.2 Intensity-based Functional Recovery Performance .............................................. 33 2.5.3 Risk-Based Functional Recovery Performance .................................................... 36 2.6 Conclusions, Limitations, and Future Work ................................................................. 43 2.7 Application to Canadian Building Code Development ................................................ 46 Chapter 3: Evaluating the Variability in Functional Recovery Performance with Risk-Targeting for Life-Safety .............................................................................................................48 3.1 Introduction ................................................................................................................... 48 3.2 Literature Review.......................................................................................................... 50 3.3 Methodology ................................................................................................................. 51 3.3.1 Archetype Building ............................................................................................... 51 xi 3.3.2 Structural Response Prediction and Damage Assessment .................................... 52 3.3.3 Recovery Time Assessments ................................................................................ 53 3.3.4 Risk-based Assessment of Functional Recovery Time ......................................... 53 3.3.5 Safety-Critical Structural Damage and Nonstructural Damage ............................ 54 3.4 Functional Recovery Risk ............................................................................................. 55 3.5 Identifying Drivers of Functional Recovery Risk ......................................................... 59 3.6 Partition Damage and Safety-Critical Structural Damage ............................................ 60 3.7 Conclusions, Limitations, and Future Work ................................................................. 64 3.8 Application for Canadian Building Code Development ............................................... 65 Chapter 4: Limiting Safety-Critical Structural Damage in Recovery-Based Seismic Design Provisions ......................................................................................................................................67 4.1 Introduction ................................................................................................................... 67 4.2 Literature Review.......................................................................................................... 69 4.3 Evaluating Safety-Critical Structural Damage .............................................................. 70 4.4 Functional Recovery Earthquake and Performance Targets ......................................... 76 4.5 Functional Recovery Structural Design Requirements ................................................. 79 4.6 Scope of Study .............................................................................................................. 82 4.7 Methodology ................................................................................................................. 83 4.8 Illustrative Example ...................................................................................................... 88 4.9 Limiting Safety-Critical Structural Damage for a Range of Lateral Force-Resisting Systems ..................................................................................................................................... 92 4.9.1 Reinforced Concrete Shear Wall Systems ............................................................ 93 4.9.2 Steel Buckling Restrained Braced Frame Systems ............................................... 95 xii 4.9.3 Moment Frame Systems ....................................................................................... 96 4.10 Conclusions, Limitations, and Future Work ............................................................... 101 4.11 Application to Canadian Building Code Development .............................................. 103 Chapter 5: Nonstructural Design Requirements for Functional Recovery Performance ..104 5.1 Introduction ................................................................................................................. 104 5.2 Literature Review........................................................................................................ 106 5.3 Functional Recovery Categories and Reliability Targets ........................................... 108 5.4 Structural Design for Functional Recovery ................................................................ 109 5.5 Nonstructural Design for Functional Recovery .......................................................... 112 5.6 Implementation of Nonstructural Design Interventions ............................................. 113 5.6.1 Acceleration-Sensitive Components ................................................................... 114 5.6.2 Seismic Qualification .......................................................................................... 116 5.6.3 Drift-Sensitive Components ................................................................................ 117 5.6.4 Components with No Interventions .................................................................... 117 5.7 Methodology to Inform Nonstructural Design Criteria .............................................. 117 5.7.1 Structural Response Prediction ........................................................................... 118 5.7.2 Component Damage Assessment ........................................................................ 119 5.7.3 Functional Recovery Time Assessment .............................................................. 119 5.7.4 Modeling Uncertainty and Truncation ................................................................ 124 5.7.5 Developing Nonstructural Component Design Recommendations .................... 126 5.7.6 Probability of Individual Components Impeding Function ................................ 126 5.8 Illustrative Example: Reinforced Concrete Moment Frame Building ........................ 127 5.8.1 Enhanced Recovery-Based Structural Design and Damage Assessment ........... 127 xiii 5.8.2 Impact of Nonstructural Design Interventions on Functional Recovery Time ... 128 5.8.3 Component Contributions to Function Loss ....................................................... 129 5.9 Impact of Ipfr on Functional Recovery Performance ................................................. 132 5.9.1 Shear-Governed Reinforced Concrete Shear Wall Systems ............................... 132 5.9.2 Flexure-Governed Reinforced Concrete Shear Wall Systems ............................ 132 5.9.3 Steel Buckling Restrained Braced Frames .......................................................... 133 5.9.4 Steel Moment Frames ......................................................................................... 135 5.10 Reinforced Concrete Moment Frames ........................................................................ 135 5.11 Summary of Ipfr Required for All Systems ................................................................. 136 5.12 Nonstructural Components Likely to Impede Function .............................................. 137 5.13 Conclusions ................................................................................................................. 138 5.14 Application to Canadian Building Code Development .............................................. 139 Chapter 6: Conclusions .............................................................................................................140 6.1 Significant and Original Contributions ....................................................................... 140 6.2 Detailed Summary of Key Findings ........................................................................... 141 6.2.1 Finding 1: The risk of exceeding short recovery time targets is high for modern buildings. ............................................................................................................................. 141 6.2.2 Finding 2: Functional recovery risk is highly variable in the United States. ...... 143 6.2.3 Finding 3: Structural design requirements to limit safety-critical structural damage. 165 6.2.4 Finding 4: Nonstructural design requirements and explicit verification of recovery performance. ....................................................................................................................... 144 6.3 Translation to Canadian Building Code Development ............................................... 145 xiv 6.4 Limitations and Future Work ...................................................................................... 146 6.5 Closing Remarks ......................................................................................................... 151 Bibliography ...............................................................................................................................152 Electronic Supplements .............................................................................................................162 Appendix A ............................................................................................................................. 164 A.1 Risk-Based Assessment Results for All RCSW Archetype Heights ...................... 164 Appendix B ............................................................................................................................. 172 B.1 Risk-Based Assessment of Functional Recovery Time for 34 Cities – Fragilities and Disaggregation Plots ........................................................................................................... 172 B.2 Risk-Based Assessment of Severe Partition Damage Time for 34 Cities – Fragilities and Disaggregation Plots .................................................................................................... 184 B.3 Risk-Based Assessment of Safety-Critical Structural Damage Time for 34 Cities – Fragilities and Disaggregation Plots ................................................................................... 195 Appendix C ............................................................................................................................. 203 C.1 Engineering Demand Parameter Plots for All Systems and Heights ...................... 203 C.2 Relationship Between Realized Drift and Safety-Critical Structural Damage for All Heights ................................................................................................................................ 223 C.3 Probability of Safety-Critical Structural Damage Plots .......................................... 231 Appendix D ............................................................................................................................. 260 D.1 Engineering Demand Parameter Plots for All Systems and Heights ...................... 260 D.2 Nonstructural Importance Factor Plots for Other Systems and Heights ................. 274 D.3 Component Disaggregation Plots for All Systems and Heights ............................. 276 xv List of Tables Table 2.1 Spectral accelerations (in units of g) of the intensity levels considered and the simulated M9 earthquake scenario. ............................................................................................................... 24 Table 2.2 Median downtime (in days) to achieve functional recovery (FR) under the intensity levels considered and the simulated M9 earthquake scenario. ..................................................... 30 Table 2.3 Probability of achieving functional recovery (FR) at varying time targets conditioned on the M9 earthquake scenario. ......................................................................................................... 33 Table 2.4 Probability of achieving functional recovery (FR) at varying time targets and intensity levels for the 12-story RCSW archetype. ..................................................................................... 36 Table 2.5 Median and dispersions of downtime fragilities ........................................................... 38 Table 2.6 Expected annual downtime to functional recovery, EADFR.......................................... 43 Table 3.1 Geographic and hazard information for 34 cities in the United States. ........................ 52 Table 3.2 50-year probability of exceeding various recovery targets across the 34 sites in the United States. ............................................................................................................................................ 58 Table 3.3 50-year probability of incurring severe damage to partitions and red tags across the 34 sites in the United States. .............................................................................................................. 61 Table 4.1 Lateral force-resisting systems and building heights evaluated. .................................. 82 Table 4.2 Lateral force-resisting systems and building heights evaluated. .................................. 93 Table 4.3 Recommended functional recovery response modification coefficient, Rfr, and allowable drift limit, Δafr, to achieve 10% or less probability of safety-critical structural damage across the systems considered........................................................................................................................ 99 Table 5.1 Building functional recovery targets for each functional recovery category. ............. 109 Table 5.2 Lateral force resisting systems and building heights evaluated. ................................. 111 xvi Table 5.3 Impeding factors and mitigation strategies. ................................................................ 121 Table 5.4 ATC-138 requirements for function. .......................................................................... 122 Table 5.5 Recommended Ipfr for various recovery categories with qualified equipment. .......... 136 Table 5.6 Components most likely to impede function. ............................................................. 137 xvii List of Figures Figure 2.1 Annualized downtime risk calculation: (a) downtime fragility function, (b) slope of hazard curve and (c) disaggregated downtime risk (modified after Eads et al., 2013). ................ 21 Figure 2.2 Typical floor plan (from Kourehpaz et al., 2021) of the 12-story RCSW archetype. . 23 Figure 2.3 Sample nonlinear analysis results of the 12-story RCSW archetype: (a) story drift ratios (SDR) and (b) peak floor accelerations (PFA) across intensity levels, as well as (c) SDRs and (d) PFAs for all building heights at the 475-year intensity level........................................................ 25 Figure 2.4 (a) Direct economic loss estimates for all archetypes and (b) percent of realizations that result in reparable damage, irreparable damage, or collapse for the 12-story RCSW archetype at intensity levels ranging from 100 to 4975 years and the M9 scenario considered in the assessment........................................................................................................................................................ 27 Figure 2.5 Histogram of downtime and recovery trajectories for the 12-story archetype at the (a) 475-year intensity level and (b) M9 earthquake scenario. ............................................................ 29 Figure 2.6 Disaggregation of mean downtime to functional recovery for repairable realizations for the (a) 475-year intensity level and (b) the M9 earthquake scenario as obtained from TREADS........................................................................................................................................................ 31 Figure 2.7 Probability of achieving downtime to functional recovery of Y days for a range of archetype RCSW buildings of varying height when subjected to M9 CSZ earthquake scenario. 32 Figure 2.8 Probability of achieving a downtime to functional recovery of Y days for a range of RCSW archetype buildings of varying height when subjected to ground motion intensities with varying return periods: (a) 100, (b) 475, (c) 975, (d) 2475, and (e) 4975 years. .......................... 34 Figure 2.9 (a) Seismic hazard curve and (b) downtime fragility to functional recovery at varying targets for 12-story RCSW archetype. .......................................................................................... 37 xviii Figure 2.10 Disaggregated downtime risk for 12-story RCSW archetype for downtime targets of (a) 1 month, (b) 4 months, (c) 6 months, (d) 1 year and (e) one and a half years. ....................... 39 Figure 2.11 50-year probability of downtime to functional recovery exceeding Y days for all building heights considered and target times ranging from 1 month to one and a half years. ..... 41 Figure 3.1 Hazard curve and fragility functions for the probability of exceeding various functional recovery time targets as a function of the spectral acceleration at the first mode period (SA(T1))....................................................................................................................................................... 56 Figure 3.2 Disaggregation by SA(T1) of the risk of exceeding functional recovery time (TFR) targets for a residential 8-story RCSW archetype building in Los Angeles, CA. ........................ 60 Figure 3.3 (a) Hazard curve and fragility functions for the probability of nonstructural component damage as a function of the spectral acceleration at the first mode period (SA(T1)) and (b) disaggregation by SA(T1) of nonstructural component damage for a site in Los Angeles, CA. . 62 Figure 3.4 (a) Hazard curve and fragility functions for the probability of safety-critical structural damage as a function of the spectral acceleration at the first mode period (SA(T1)) and (b) disaggregation by SA(T1) of safety-critical structural damage for a site in Los Angeles, CA. ... 63 Figure 4.1 Fault tree used to determine whether the building has safety-critical structural damage (modified after Cook et al., 2021). ................................................................................................ 74 Figure 4.2 Comparison of the Dmax,DE and Dmax,FRE spectra. ......................................................... 79 Figure 4.3 Methodology to develop design space used to evaluate the probability of safety-critical structural damage associated with various allowable drift limits, Δafr, and functional recovery response modification coefficients, Rfr. ........................................................................................ 84 xix Figure 4.4 Median story drift ratio for a set of 56 design variations of an 8-story reinforced concrete moment frame buildings expressed in terms of (a) design drift limit and (b) response modification coefficient. .................................................................................................................................... 88 Figure 4.5 Median peak floor acceleration for a set of 56 design variations of an 8-story reinforced concrete moment frame building expressed in terms of (a) design drift limit and (b) response modification coefficient. ............................................................................................................... 89 Figure 4.6 Median story drift ratio at the most critical story as a function of drift limit for a set of 56 design variations of an 8-story reinforced concrete moment frame building .......................... 90 Figure 4.7 Relationship between the median story drift ratio at the most critical story and the probability of safety-critical structural damage for a set of 56 design variations of an 8-story reinforced concrete moment frame building. ................................................................................ 90 Figure 4.8 Functional recovery response modification coefficient, Rfr, and allowable drift limit combinations that achieve various safety-critical structural damage probabilities, shown for an example 8-story reinforced moment frame building. ................................................................... 92 Figure 4.9 (a) Probability of safety-critical structural damage as a function of maximum story drift of the median realization and (b) contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for low-rise, shear-governed special RCSWs (bearing) models with post-tensioned slabs. ....................................... 94 Figure 4.10 Probability of safety-critical structural damage as a function of maximum story drift of the median realization for bearing (a) cantilevered RCSWs and (c) ductile coupled RCSWs with post-tensioned slabs and contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for the controlling height xx of the bearing (b) cantilevered RCSWs and (d) ductile coupled RCSWs with post-tensioned slabs........................................................................................................................................................ 95 Figure 4.11 Probability of safety-critical structural damage as a function of maximum story drift of the median realization for BRBFs (a) without a welded backup frame and (c) with a welded backup frame for all building heights and contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for the controlling height of the BRBFs (b) without a welded backup frame and (d) with a welded backup frame. ................................................................................................................................ 96 Figure 4.12 (a) Probability of safety-critical structural damage as a function of maximum story drift of the median realization for all building heights and (b) contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for the controlling height of the SMF models. ...................................................... 97 Figure 4.13 (a) Probability of safety-critical structural damage as a function of maximum story drift of the median realization and (b) contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for controlling height of RCMF models with post-tensioned slabs. ..................................................................... 98 Figure 5.1 Application of component seismic importance factor for functional recovery, Ipfr, for various component types. ............................................................................................................ 114 Figure 5.2 Example fragility function showing the probability of component damage given an engineering demand parameter, with median values increasing proportionally with Ipfr. The dispersion, β, is equal for all fragilities. ...................................................................................... 116 Figure 5.3 Outline of methodology to develop nonstructural design recommendations. ........... 118 Figure 5.4 Illustrative diagram of truncated lognormal and lognormal distributions. ................ 126 xxi Figure 5.5 (a) Median realized inelastic story drift ratios and (b) median realized peak floor accelerations and ASCE 7 design accelerations for the 8-story RCMF archetype. .................... 127 Figure 5.6 Impact of Ipfr on the probability of the functional recovery times exceeding the recovery time target (a) without seismic qualification of equipment and (b) with seismic qualification of equipment. ................................................................................................................................... 129 Figure 5.7 Component disaggregations for RC B, RC C, and RC D, with the seismic qualification of equipment. Disaggregations show the probability that each component impedes function at the specified functional recoverytime target for an 8-story RC moment frame. .............................. 131 Figure 5.8 Impact of Ipfr on the probability of exceeding recovery targets for Recovery Categories B, C, and D, with seismic certification of equipment for shear-governed RCSW bearing wall systems. ....................................................................................................................................... 132 Figure 5.9 Impact of Ipfr on the probability of exceeding recovery targets for Recovery Categories B, C, and D, with seismic certification of equipment for flexure-governed RCSW (a) cantilever systems (bearing wall) and (b) coupled wall systems (bearing wall). ........................................ 133 Figure 5.10 Impact of Ipfr on the probability of exceeding recovery targets for Recovery Categories B, C, and D, with seismic certification of equipment for BRBFs with (a) without and (b) with a welded backup frame. ................................................................................................................. 134 Figure 5.11 Impact of Ipfr on the probability of exceeding recovery targets for Recovery Categories B, C, and D, with seismic certification of equipment for steel moment frames (RBS). ............. 135 Figure 5.12 Impact of Ipfr on the probability of exceeding recovery targets for Recovery Categories B, C, and D, with seismic certification of equipment for RCMFs. ............................................. 136 xxii Acknowledgements First and foremost, I would like to thank my supervisor, Dr. Carlos Molina Hutt, for his guidance and support throughout my PhD. When choosing a supervisor, I was told that it is important to choose someone who is kind and also someone who will say your name in a room full of opportunities. Carlos embodies both qualities. He leads with kindness, offering help and support without hesitation. Throughout my degree, he consistently opened doors into bigger and bigger rooms and gave me the opportunity to grow into the roles. I would like to thank my supervisory committee members, Dustin Cook and Carlos Ventura, for their insightful comments and guidance throughout the development of this work. Dustin was also a collaborator on three of four chapters of this work, and I feel incredibly grateful for this generous commitment of time and his thoughtful and constructive feedback. I also would like to thank my other collaborators, Reid Zimmerman, Ed Almeter, and Curt Haselton, who spent dozens of hours discussing results with me. I was supported by British Columbia Graduate Scholarship (BCGS), the Natural Sciences and Engineering Research Council of Canada (NSERC) Post-graduate Scholarship (PGS-D), and UBC’s Four Year Fellowship through my degree, which allowed me the flexibility to pursue research that built on my professional background and felt both exciting and impactful. I would like to thank the members of the ESR Lab. Thank you Preetish Kakoty, Pouria Kourehpaz, and Kiran Kaur for always taking a coffee walk with me when I needed it. Thank you as well to Carmine Galasso for being a mentor and friend throughout this process. Finally, I would like to thank my husband, sister, and parents for encouraging me to pursue a PhD and for being my biggest supporters throughout my degree. To my family and friends, thank you for all of the airport pickups and for the visits that always feel too short. 1 Chapter 1: Introduction 1.1 Background and Motivation Past earthquakes have demonstrated a clear bifurcation in recovery outcomes depending on the extent of building damage (Comerio and Blecher, 2010; Mitrani-Reiser, 2007; Paul et al., 2023). It has often been observed that when structural damage is extensive, building tenants face prolonged displacement and are unable to return to a sense of normalcy. By contrast, when post-earthquake damage is limited, tenants quickly return to life as usual. This observed divide is exacerbated by access to resources, place attachment, and other socioeconomic factors (Costa et al., 2022). Current seismic design provisions in North American building codes address life-safety by ensuring a low probability of collapse in large earthquakes; however, they do not ensure buildings are (1) safe to reoccupy and (2) functional post-earthquake. This exclusive focus on safety is expected to result in difficulties in recovery. A growing number of studies (e.g., Molina Hutt et al., 2022a, 2022b; Terzic and Kolozvari, 2022) are highlighting this vulnerability in modern building codes. These studies predict recovery times ranging from seven to 13 months for modern buildings in Washington and California at the 475-year intensity level. The primary types of damage that are expected to cause issues in recovery are nonstructural (e.g., elevators and HVAC equipment) but structural component damage, such a slab-column connection damage in modern reinforced concrete buildings is also likely to occur and to lead to loss of building function until repairs can be completed. Opabola and Elwood (2024) also demonstrated that the median recovery time of modern reinforced concrete moment frame buildings exceeds three months at a similar intensity level. Finally, Cook et al. (2024) showed an average recovery time of approximately 4.5 2 months at the 475-year intensity level for both reinforced concrete moment frame and shear wall buildings designed following modern building codes. In addition to analytical studies, past earthquakes have also drawn attention to the potential for lengthy post-earthquake recovery times. The 2001 Nisqually and 2014 Napa earthquakes highlighted the impact of nonstructural component damage on recovery in modern buildings (Filiatrault et al., 2001; Fischer, 2014). Modern buildings experienced damage to ceilings, partitions, and HVAC equipment. Falling glass from exterior glazing (Filiatrault et al., 2001) was also observed, making it unsafe to enter or exit buildings until temporary repairs could take place. While recent earthquakes in North America have not caused significant structural damage in modern buildings, we can look to the performance of modern buildings in New Zealand in the 2010-2011 Canterbury earthquake sequence as a point of reference. In this earthquake sequence, modern code-compliant buildings did not collapse but widespread structural damage was observed in the region (Kam et al., 2011). Kam et al. (2011) showed that nine of 46 (approximately 20%) concrete frame buildings in the Christchurch Central Business District designed between 1990 and 2010 were red tagged during post-earthquake inspections. Eight of 28 (approximately 30%) concrete shear wall buildings constructed during this period were also red tagged. While cost-effective and rapid repair options (e.g., epoxy repair) were available, at the time, there was little confidence in the residual capacity of damaged buildings (Kam et al., 2011). Delays in recovery in damaged buildings were attributed to uncertainty in the post-earthquake safety of buildings (Kim et al., 2017). Further, many buildings experienced significant structural and nonstructural damage, blurring insurance payout decisions. As a result, many buildings were demolished and replaced – an effort that delayed recovery of businesses and housing in the region and was costly 3 both in direct expenses and environmental impacts (Gonzalez et al., 2022; Parker and Steenkamp, 2012). To address these observed deficiencies in modern building codes, there is a new effort in many countries to develop recovery-based design provisions. These provisions aim specifically to address functional recovery time. Functional recovery time is defined as the time required following an earthquake for a building to return to its basic intended function (EERI, 2019). The notion of functional recovery time relates to the performance of the building and the recovery actions related to the structure and its components. Therefore, functional recovery performance excludes externalities, such as restoration of utilities, and the social dimensions of recovery. The intention of these provisions is to provide engineers and owners with guidance on how to design and prepare for an earthquake to ensure post-earthquake functional recovery times meet societal expectations. In Canada, the 2020 National Building Code included its first provisions for recovery (National Research Council of Canada (NRCC), 2020). These provisions aim to ensure that post-disaster and high importance buildings have limited damage by requiring engineers to demonstrate the building remains elastic at lower intensity levels (NRCC, 2025). The provisions also require structural elements that are not part of the lateral force-resisting system to behave elastically in certain types of normal importance buildings. Similarly, in the United States, the Building Seismic Safety Council (BSSC) has outlined steps to develop seismic design provisions for functional recovery (BSSC, 2023). The BSSC is currently developing a first-generation of prescriptive functional recovery design requirements to be included in the 2026 National Earthquake Hazards Reduction Program (NEHRP) recommendations. Finally, following the 2010-2011 Canterbury earthquake sequence, New Zealand also moved towards a recovery-based standard that addresses 4 post-earthquake safety as well as functional recovery (Applied Technology Council (ATC), 2021a; Hulsey et al., 2022). These first-generation provisions vary in terms of their ground motion considerations for the design checks, risk-targeting, and the resulting structural and nonstructural design requirements. The early standards, however, broadly aim to accomplish two goals. The first goal is to limit safety-critical structural damage – that is damage that must be repaired for tenants to reoccupy a building (Blowes et al., 2025; Opabola and Elwood, 2024). The second goal is to limit overall functional recovery time by limiting damage to all components, including nonstructural elements (Hulsey et al., 2022). While these two objectives have been established, few studies have explicitly verified whether the proposed building code requirements meet the intended goals. This dissertation contains four studies that support the development of the 2026 NEHRP recommendations which are also being considered for inclusion in ASCE 7-28. Each of the objectives outlined below aims to inform various clauses in the upcoming provisions – including the return period used for the design checks, risk-targeting, and structural and nonstructural design requirements. Ultimately, the work developed provides methods and findings to ensure the first generation of recovery-based seismic design provisions is data-informed. Finally, efforts are made throughout this dissertation to discuss how methods or findings could be used to expand current efforts to develop recovery-based design provisions in Canada as well. 1.2 Objectives 1.2.1 Objective 1: Establish methods to perform risk-based assessments for functional recovery In the United States, building codes target a 1% probability of collapse in 50 years (e.g., ASCE/SEI, 2022a). This requirement aims to ensure that all buildings, regardless of lateral force-5 resisting system type and location, achieve similar life-safety performance. As a first step in developing recovery-based design provisions, it is necessary to establish methods to develop a similar metric for functional recovery. Chapter 2 adapts current formulations used for collapse to propose a scenario-based, intensity-based, and ultimately, a risk-based assessment of functional recovery performance. Formulations are developed using the probability of the functional recovery time exceeding a given target as the consequence, in place of collapse. For the risk-based assessment, fragilities are fit to data from recovery time assessments that cover a range of intensity levels and then integrated with the hazard curve. Resulting performance metrics include the 50-year probability of the functional recovery time exceeding increasing recovery time targets, from one month to two years. Further, as is common with risk-based assessments for collapse, disaggregations can also be performed to determine the intensity level that drives the risk of exceeding a recovery target. Finally, once the governing intensity level is determined, the corresponding damage assessments can be leveraged to identify the types of damage that most frequently impede function. The methods outlined in Chapter 2 open the discussion of how to use outputs from new functional recovery time estimation frameworks to perform risk-based assessments that may be used to establish risk targets in the development of recovery-based design provisions. 1.2.2 Objective 2: Evaluate the variability in functional recovery risk achieved using only life-safety design requirements The United States building code aims to ensure a uniform 50-year probability of collapse across the country (ASCE/SEI, 2022), which is achieved through risk-targeting (Luco et al., 2017). Risk-targeting is a method used to adjust the Maximum Considered Earthquake (MCE) iteratively 6 such that the resulting probability of collapse is approximately 1% across the country for various levels of seismicity. The goal of this study is to determine whether current life-safety design provisions, including current risk-targeting methods for collapse, ensure a uniform 50-year probability of exceeding various recovery time targets. In Chapter 3, risk-based functional recovery assessments are performed, following methods outlined in Objective 1, for a single reinforced concrete shear wall archetype that has been updated to reflect the seismicity at 34 cities that are commonly used in building code development (Luco et al., 2017, 2007). The risk-based assessments are repeated with recovery targets ranging from two weeks to one year to evaluate the variability in the functional recovery risk. Next, risk-based assessments are also performed at each city for safety-critical structural damage (i.e., red tags) and for severe partition damage. Building on Objective 1, disaggregations are performed for increasing recovery targets to identify the ground motion shaking intensity that drives the risk of exceeding each target. These two measures are also analyzed to identify the ground motion rates of exceedance (i.e., return periods) that drive the risk of safety-critical structural damage and nonstructural damage. The results of this study can inform building code committees determine whether risk-targeting efforts for functional recovery are necessary based on the current uniformity of functional recovery risk, as well as the damage mechanisms and return periods that drive the risk. 1.2.3 Objective 3: Develop methodology to determine structural design requirements that limiting safety-critical structural damage Designing to limit structural damage has been shown to ensure (1) the post-earthquake capacity is not significantly reduced (Opabola et al., 2023) and (2) that there is a much lower probability of lengthy recovery times (ATC, 2021; Opabola and Elwood, 2024). In Chapter 4, a method is 7 proposed that uses the ATC-138 methodology (ATC, 2021b; Cook et al., 2022) to develop strength and stiffness recommendations that limit the probability of safety-critical structural damage at a new risk-targeted Functional Recovery Earthquake (FRER). These strength and stiffness requirements include the response modification coefficient for functional recovery, Rfr, and the allowable drift limit for functional recovery, Δafr. The study is conducted for reinforced concrete shear wall buildings (both cantilever and coupled), steel buckling restrained braced frames (both with and without a welded backup frame), and reinforced concrete and steel special moment frames. Models with heights ranging from 3 to 24 stories are evaluated. The results ultimately can be used to inform system-specific Rfr and Δafr values for inclusion in the prescriptive functional recovery design provisions in the United States. Further, the methods outlined can be used in the future as a qualification procedure for additional lateral force-resisting systems. 1.2.4 Objective 4: Propose nonstructural design requirements and explicitly verify efficacy of functional recovery provisions The final objective of this dissertation is to propose nonstructural design requirements for functional recovery, in combination with the structural requirements determined in Objective 3. In Chapter 5, models from Objective 3 are populated with nonstructural components and then the functional recovery time is evaluated using the ATC-138 framework (ATC, 2021b; Cook et al., 2022). The performance is evaluated at the FRER for a 25% reliability target (i.e., probability of exceeding a given recovery time target), as set by the FRTC. The impact of various nonstructural design requirements is also studied, including seismic qualification and a nonstructural component importance factor for functional recovery, Ipfr. The structural and nonstructural design requirements are evaluated for different recovery categories, which are similar to risk categories 8 in the life-safety provisions (FEMA, 2024). The designs for each recovery category are evaluated for a different recovery time target that was set by the FRTC and with assumptions that aim to reflect quality control and preparedness measures. Ultimately, Chapter 5 aims to propose nonstructural design requirements that, when combined with the previously introduced structural design requirements, produce designs that can reliably meet the corresponding functional recovery time targets. Results may be used to inform nonstructural design provisions in the prescriptive functional recovery design provisions in the United States. 1.3 Organization This dissertation addresses the objectives outlined above in the next five chapters. Chapter 2 outlines methods to perform risk-based assessments of functional recovery performance and presents an example for a modern reinforced concrete shear wall building (Objective 1). Chapter 3 employs methods presented in Chapter 2 to evaluate the variability in functional recovery risk that can be achieved with risk-targeting methods currently used for life-safety performance (Objective 2). Chapter 3 also highlights drivers of recovery risk, by identifying intensity levels and types of damage with the highest contribution for various recovery time targets. Chapter 4 then proposes methods to determine structural design requirements to limit safety-critical structural damage, including response modification coefficients and allowable drift limits. Response modification coefficients and allowable drift limits are then provided for a wide range of lateral force-resisting systems. Chapter 5 explicitly evaluates the functional recovery performance with nonstructural component design strategies, in conjunction with the structural design requirements proposed in Chapter 4. Chapter 6 provides a summary of key conclusions, contributions and future research opportunities. 9 1.4 Additional Notes Each chapter of this dissertation is either a published journal article or is in review; therefore, there is some repetition in the introduction, literature reviews, limitations and suggestions for future work across chapters. Next, the field of recovery-based design is evolving rapidly. The term “downtime” is used interchangeably with “recovery time” in Chapter 2. I adopt the term “recovery time” throughout the remainder of this work to be consistent with vocabulary currently employed by the BSSC (BSSC, 2023). I also switched from using the functional recovery time assessment framework developed by Molina Hutt et al. (2022b) to using the method developed by Cook et al. (2022) after Chapter 2 to be consistent with the FRTC. While the recovery-time estimation frameworks employed in Chapter 2 and Chapter 3 are unique, the two tools provide very similar results. A comparative study of the two, however, is beyond the scope of this dissertation. Finally, the term “red tag” is used in Chapter 3 and the calculations of red tags is considered as a proxy for safety-critical structural damage. As this work developed, through review, the term “red tag” was replaced simply adopted the term “safety-critical structural damage”. The primary reason for this substitution is because the goal is not to simulate placarding decisions by inspectors, but instead the occurrence of the types of damage that make a building unsafe to enter. Chapters 4 and 5 of my dissertation focus on the work I performed to support the development of the 2026 NEHRP Functional Recovery Provisions. During my PhD, I was a member of an FRTC subcomittee that was responsible for writing an entirely new set of provisions for functional recovery. My supervisor, Carlos Molina Hutt, vice-chaired the subcommittee so we formulated the Chapter 4 and 5 studies to support the needs of the FRTC. I evaluated the impact of potential hazard levels, risk and reliability targets, performance objectives, and each design parameters in the design checks outlined in Chapter 4 and 5. As outlined in the Preface, the work 10 was extremely collaborative, bringing in the subcommittee chair (Reid Zimmerman), the chair of an adjacent subcommittee focused on seismic hazard (Dustin Cook), and the support of HB-Risk (Ed Almeter and Curt Haselton) to rapidly update design changes through SP3. Calculations were also updated dozens of times to address comments that arose through BSSC consensus-based process. I ultimately documented this work in two first-authored journal articles, which correspond to Chapters 4 and 5. Drafts of these journal articles were used as a reference to the BSSC as a resource while balloting the provisions. Finally, Chapter 4 and 5 include proposed design recommendations based on draft 2026 NEHRP Functional Recovery Provisions developed by the FRTC in late 2024 (FEMA, 2024). These draft provisions, however, will continue to be updated through a consensus-based process until their final publication. This dissertation therefore may not reflect the final provisions. Furthermore, the journal articles reflecting Chapter 4 and 5 work are still in review and will also be revised as part of the peer review process before their final publication. 11 Chapter 2: Risk-Based Seismic Evaluation of Functional Recovery Performance in Buildings This chapter is based on the following reference: Blowes, K., Kourehpaz, P., and Molina Hutt, C., 2023. Risk‐targeted seismic evaluation of functional recovery performance in buildings. Earthquake Engineering & Structural Dynamics, 52(13), 4245–4264. DOI: 10.1002/eqe.3984 2.1 Introduction Observations from past earthquakes have shown that life-safety performance objectives in modern seismic design standards can result in loss of building function and extensive downtimes after moderate seismic events. These prolonged downtimes have severe economic impacts and can result in permanent population displacement (Chang et al., 2014; Comerio and Blecher, 2010; Olshansky et al., 2005), most often affecting marginalized communities (Chang, 2016). Analytical studies have also estimated prolonged earthquake-induced downtimes in modern buildings. For instance, Molina Hutt et al. (2022a) reported that the expected downtime for tall modern residential reinforced concrete shear wall buildings was expected to exceed seven months at the 10% in 50-ear intensity level and to exceed one year at the 2% in 50-year intensity level. These extensive downtimes highlight the need for building code provisions that go beyond life-safety to, additionally, consider recovery time. The National Institute of Science and Technology (NIST) and the Federal Emergency Management Agency (FEMA) outlined the need to establish new performance objectives for 12 buildings and infrastructure to be expressed in terms of post-earthquake recovery time (FEMA, 2020). Functional recovery is defined as the “post-earthquake state in which capacity is sufficiently maintained or restored to support pre-earthquake functionality” (EERI, 2019). The United States Building Seismic Safety Council (BSSC), by means of the Provisions Update Committee (PUC) has established a Functional Recovery Task Committee intended to develop seismic design provisions for functional recovery performance. Ultimately, the committee intends to integrate such provisions into the 2026 NEHRP Recommended Seismic Provisions for New Buildings and Other Structures. These provisions will inform the development of the 2028 edition of ASCE 7: Minimum Design Loads for Buildings and Other Structures, and ultimately, the 2030 edition of the International Building Code. The work presented in this study provides valuable information in support of this ongoing effort. The development of these new building-level downtime estimation frameworks now allows us to evaluate building performance compliance based on recovery time. This study outlines methods to evaluate the probability of achieving the functional recovery state within a pre-defined period of time. Analogous to collapse-safety metrics used in today’s building codes, we present three assessment methods to evaluate building functional recovery performance: a scenario-based, an intensity-based, and a risk- assessment. The existing formulation is adapted from life-safety to consider recovery-based performance objectives. The work is then illustrated using a series of modern reinforced concrete shear wall buildings ranging in height from eight- to 24-stories in a site in downtown Seattle, WA. These assessment results provide insights into how buildings designed following ASCE 7-16 (ASCE/SEI, 2016) perform in terms of their anticipated recovery time. The goal of this study is not to set functional recovery targets, but rather to present a structure that enables the evaluation of building performance in terms of recovery time using the latest 13 generation of downtime estimation frameworks. Ultimately, the formulations presented permit the explicit evaluation of building performance and support the development of prescriptive design provisions to achieve functional recovery performance. 2.2 Literature Review The development of downtime estimation frameworks is critical for the inclusion of recovery time performance objectives in future building codes. Several recently proposed downtime assessment frameworks build on the well-established FEMA P-58(FEMA, 2018a) methodology. FEMA P-58 uses fragility and consequence functions of different building components to estimate repair times based on expected damage. However, it does not include impeding factors, which may delay the initiation of repairs, or robust repair sequencing methods to evaluate building downtime. REDi (Almufti and Willford, 2013) advanced the FEMA P-58 methodology to estimate recovery time, by introducing impeding factors delays such as time required for engineering, permitting, and contractor mobilization (Almufti and Willford, 2013). REDi also introduced the concept of repair classes, which are used to identify building component damage that hinders achieving different recovery states. Despite these improvements, REDi is expected to overestimate recovery times because the framework employs a repair sequence that requires the completion of all structural repairs before nonstructural component damage repair can commence, whereas data from past earthquakes (e.g., from Terzic et al., 2016) has shown that certain types of nonstructural damage are typically repaired in parallel to structural damage. Building on these efforts to develop downtime estimation methods, Molina Hutt et al. (2022b), Cook et al. (2022), and Terzic et al. (2021) recently presented new building-level frameworks to estimate the downtime to reach functional recovery as well as other key recovery states, such as shelter-in-place or reoccupancy. This study uses the downtime estimation 14 framework developed by Molina Hutt et al. (2022b) and TREADS, an open-source, python-based implementation of the calculation methodology (Kourehpaz and Molina Hutt, 2022). TREADS employs a structure that builds on FEMA P-58 and REDi concepts, to model temporal building recovery trajectories. The framework employs a repair sequencing approach that allows for parallel paths of structural and nonstructural (e.g., exterior, elevator, and staircase) component repair, based on the experience of contractors following the 1994 Northridge earthquake (Terzic et al., 2016), removing some of the conservatism from the REDi framework. The framework also builds on past research to include irreparable and collapse realizations. Downtime associated with irreparable and collapse realizations is based on observations from the 2010-2011 Canterbury earthquake sequence and is included by sampling data from Marquis et al. (2017) for demolition and financing delays. The framework employed leverages findings from historical events, including the 1994 Northridge earthquake (Terzic et al., 2016) to inform the post-earthquake repair sequencing and the 2010-2011 Canterbury earthquake sequence to inform estimates of recovery in the event building damage requiring demolition and reconstruction (Marquis et al., 2017). Other default values reflect construction practices and financing structures on the West Coast of the United States, where the case study building is located. The framework developed by Cook et al. (2022), was adopted by the ATC-138 project (ATC, 2021b) to evaluate functional recovery performance in buildings. Like the framework by Molina Hutt et al. (2022b), the methodology models building recovery trajectories. It employs a ‘tenant unit’ structure wherein recovery is assessed for individual tenant units to model the overall building functionality as it is recovered over time. The framework utilizes explicit fault trees to address the interdependencies and criticality of different building systems. Similarly, the F-REC framework developed by Terzic et al. (2021) uses fault trees to assess building function over time, 15 making use of extensive contractor mobilization and financing data collected by the authors. While modeling assumptions to evaluate functional recovery performance vary across the ATC-138, F-REC and TREADS frameworks, the methods presented in this study can be used by leveraging downtime assessment results of any of these frameworks. While the frameworks outlined above represent a few of the latest generation of building-level functional recovery analysis, other studies have proposed alternate methodologies (De Iuliis et al., 2019; Iervolino and Giorgio, 2015). The building-level frameworks discussed in this study (Almufti and Willford, 2013; Cook et al., 2022; Molina Hutt et al., 2022b; Terzic et al., 2021) do not explicitly model loss of function due to external lifeline systems, nor do they consider cordoning due to red-tagging of neighboring buildings. Impeding factor delay assumptions used in these frameworks also do not account for expected competition for surge demands. Several regional frameworks have been developed to model interdependencies within a region (Blagojević and Stojadinović, 2022; Costa et al., 2021; Mohammadgholibeyki et al., 2023b) as well as the impact of cordons on regional recovery (Hulsey et al., 2022). However, these regional methods often use simplified approaches to model building loss of function. Finally, recovery trajectories developed with this latest generation of frameworks do not consider the impact of aftershocks on recovery. Iervolino and Giorgio (Iervolino and Giorgio, 2015) provide a discussion of how to include the impact on recovery from aftershock events, which has also not been included in this analysis. 2.3 Probabilistic Evaluation of Functional Recovery Performance Due to the large uncertainty in downtime estimation, researchers have highlighted the need to evaluate functional recovery performance probabilistically. Molina Hutt et al. (2022b) introduced methods to use downtime estimates to evaluate the probability of achieving a recovery state by a 16 target time. Similar methods were also presented by Terzic et al. (2021). Here, we extend those formulations and utilize the downtime estimation outputs to probabilistically evaluate functional recovery performance. Three methods are presented: a scenario-based, an intensity-based and a risk-based method. First, the scenario-based assessment is used to evaluate the functional recovery performance of a building given an earthquake with a known magnitude and distance occurs. Second, the intensity-based assessment allows for the prediction of building functional recovery performance given a suite of ground motions scaled to a response spectrum representative of a given intensity level. Finally, a risk-based assessment, also referred to as a time-based assessment, evaluates the functional recovery performance of the building over a given time frame. Risk-based performance metrics include the annualized rate of downtime exceeding a target time, the 50-year probability of downtime exceeding a target time, or the expected annual downtime to functional recovery. While the expected annual downtime is a useful metric to determine insurance premiums, the rates and probabilities of downtime exceedance serve to communicate expected outcomes over the lifetime of a building. Outputs of downtime estimation frameworks include n simulated recovery trajectories that describe the recovery of building function over time. Each recovery trajectory leverages the repair time results of a FEMA P-58 realization. As such, the resulting n recovery trajectories consider uncertainty in hazard (record-to-record variability), building response and repair time (i.e., direct time to repair structural and nonstructural components) through the FEMA P-58 methodology. In this study, the uncertainty in impeding factor delays (i.e., inspection, financing, mobilization) and repair sequencing are considered by propagating the realizations through the downtime assessment framework, TREADS (Kourehpaz and Molina Hutt, 2022). 17 2.3.1 Scenario-based Methodology First, we evaluate the probability of downtime to functional recovery, DTFR, being less than a target time of Y days, following an earthquake. To calculate this probability, we employ a scenario earthquake with a magnitude, M, distance, R, and other source and site characteristics, summarized by variable, θ. This method considers the uncertainty in ground shaking given that an event has occurred and the uncertainty in building performance. For n realizations, the probability of the downtime to functional recovery being less than Y days, P(DTFR < Y), is equal to the number of realizations where the downtime to functional recovery does not exceed the time threshold, nDTFR<Y, divided by the total number of realizations, n, as illustrated in Equation 2.1. P(DTFR<Y |M, R, θ) = nDTFR<Y n (2.1) Repairable, irreparable and collapse cases are all included while calculating the likelihood of downtime non-exceedance. The inclusion of irreparable and collapse cases is necessary to avoid underestimating the downtime probabilities, in line with findings by Molina Hutt et al. (2019). The probability of not achieving functional recovery by Y days in an earthquake scenario with magnitude, M, distance R, and site characteristics, θ, is then the complement of Equation 1, as illustrated in Equation 2.2. P(DTFR>Y |M, R, θ) = 1 − P(DTFR<Y |M, R, θ) (2.2) A cumulative distribution function, CDF, can be developed by incrementing the value of Y days from zero to the maximum downtime to create a functional recovery performance function. A scenario-based method to assess functional recovery performance is used to evaluate building performance under a single earthquake scenario from a specific seismic source. The rupture distance must therefore be known. Scenario-based earthquake assessments are commonly used by 18 planners (e.g., the Haywired Scenario (USGS, 2017)) to understand the distribution of physical damage and its impacts throughout a region. The results of such assessments are generally easier to convey to the general public than intensity- and risk-based assessments. Furthermore, this scenario-based formulation lends itself to the use of physics-based ground motion simulations, which can incorporate effects that are not be explicitly included in seismic hazard models, such as basin amplification, or to recreate historical events for which empirical ground motion recordings are not available (Eksir Monfared et al., 2021; Kakoty et al., 2021; Molina Hutt et al., 2021). 2.3.2 Intensity-based Methodology A similar intensity-based formulation is developed to evaluate the probability of achieving functional recovery within a specified time frame when a building is subjected to a given earthquake ground motion intensity (i.e., the building has X% probability of achieving a functional recovery performance state within Y days following an earthquake of a Z-year ground motion intensity). This approach leverages n downtime realizations at the intensity level considered. P(DTFR<Y | IM) denotes the probability that the downtime to functional recovery is less than Y days, when the building is subjected to a suite of ground motions with a given intensity measure, IM. This probability is calculated by considering the number of realizations from recovery simulations where the time to functional recovery is less than Y days at the intensity level considered as shown in Equation 2.3. P(DTFR<Y | IM) = nDTFR<Y n (2.3) where nDTFR<Y is equal to the number of realizations where the downtime to functional recovery is less than the threshold time of Y days, n is the total number of realizations performed at a given IM, such as the spectral acceleration at the first mode period of the building. The complement 19 represents the likelihood of not achieving functional recovery or, of the downtime exceeding the target time limit of Y days at a given ground motion intensity as shown in Equation 2.4. P(DTFR>Y | IM) = 1 − P(DTFR<Y | IM) (2.4) Intensity measures used for analysis can be derived from probabilistic seismic hazard analysis or represent a code design spectrum. For the intensity-based assessment to be hazard consistent, the suite of ground motions selected and scaled to the desired intensity level must be representative of the hazard in the region. 2.3.3 Risk-based Methodology A risk-based, or time-based assessment, is presented next. The annualized probability of downtime to functional recovery exceeding Y days can be computed by adapting the annualized collapse risk calculation employed in modern seismic design standards (e.g., ASCE/SEI, 2016). The inputs required are a seismic hazard curve and the associated downtime fragility. The seismic hazard curve describes the annual rate of exceedance of the ground motion IM, and the downtime fragility describes the probability of the downtime exceeding Y days as a function of the ground motion IM, P(DTFR > Y | IM), typically expressed in terms of spectral acceleration at fundamental period of vibration. The downtime fragility is comparable to a collapse fragility, P(C | IM), but in lieu of the y-axis representing the probability of collapse, the y-axis represents the probability of not achieving functional recovery within Y days. Because a target time to functional recovery is now embedded within the formulation, this calculation is repeated at each target time considered, i.e., the building has an annual rate of X of the downtime to functional recovery exceeding Y days, where Y days can be taken as different values: one week, one month, four months, one year, etc. The formulations presented above are consistent with formulations presented to date (Molina Hutt et al., 2022b; Terzic et al., 2021), which describe the probability of achieving functional recovery 20 within a certain time frame. By contrast, the downtime fragility describes the probability of not achieving functional recovery within a certain time frame, i.e., the probability of failure, consistent with the formulation employed to develop collapse fragilities. The downtime fragility is generated from exceedance probabilities from the complementary CDF, or CCDF (refer to Equation 2.4) at increasing intensity levels for a target value of Y days. The downtime fragility can then be integrated with the seismic hazard curve to find the annual rate of the downtime exceeding Y days as shown in Equation 2.5. This risk-based procedure can then be repeated for key recovery-time performance objectives, or downtime targets. The numerical integration is presented in Equation 2.6. The annualized risk of not achieving functional recovery by Y days, defined as λ𝐷𝐷𝐷𝐷𝐹𝐹𝐹𝐹>𝑌𝑌, is: λ𝐷𝐷𝐷𝐷𝐹𝐹𝐹𝐹>𝑌𝑌=� P(DTFR>Y | IM) |dλIM(IM)|∞0 (2.5) λ𝐷𝐷𝐷𝐷𝐹𝐹𝐹𝐹>𝑌𝑌=�P(DTFR>Y | IM) �dλIM(IM)dIM �∆IM∞0 (2.6) where P(DTFR>Y | IM) is the downtime fragility and λIM(IM) is the seismic hazard curve. Using an annualized rate allows for the evaluation of the risk posed by different seismic sources or intensity levels. Much like the standard formulation for collapse risk, disaggregation enables the identification of earthquake intensity levels that drive the risk of not recovering within a threshold time. Eads et al. (2013) presented a summary of current methods to calculate collapse risk, which are adapted here to describe downtime risk. Figure 2.1 illustrates the procedure to evaluate the risk of downtime to functional recovery exceeding Y days. Figure 2.1a shows the downtime fragility, developed by performing a series of intensity-based assessments representing a wide range of shaking intensities. The intensity levels should be selected to range from little or no downtime 21 (i.e., 100-year) to intensities that result in building replacement (i.e., 2475- or 4975-year). The derivative of the hazard curve, as shown in Figure 2.1b, is evaluated at each of the intensity levels used to construct the downtime fragility. The downtime fragility is then multiplied with the slope of the hazard curve to calculate the disaggregated risk, as shown Figure 2.1c. Analogous to a disaggregation plot for collapse risk, this plot provides an understanding of the intensity levels that contribute most to the probability of not reaching functional recovery by Y days. This calculation can be repeated for any downtime target, Y. (a) (b) (c) Figure 2.1 Annualized downtime risk calculation: (a) downtime fragility function, (b) slope of hazard curve and (c) disaggregated downtime risk (modified after Eads et al., 2013). Modern design standards (e.g., ASCE/SEI, 2016) currently set target collapse probabilities by considering a 50-year lifespan of a building (i.e., 1% probability of collapse in 50-years). We develop a parallel formulation for the 50-year probability downtime to functional recovery exceeding Y days. This procedure provides an understanding of the risk of not achieving functional recovery within a pre-defined threshold in the lifetime of a building. The probability of not achieving functional recovery by Y days in t years is calculated from the annualized rate as shown in Equation 2.7. This formulation assumes that the occurrence of earthquakes over time follows a Poisson process. 𝑃𝑃𝐷𝐷𝐷𝐷𝐹𝐹𝐹𝐹>𝑌𝑌(𝑖𝑖n t years) = 1 − exp�−λ𝐷𝐷𝐷𝐷𝐹𝐹𝐹𝐹>𝑌𝑌∙t� (2.7) 22 where 𝑃𝑃𝐷𝐷𝐷𝐷𝐹𝐹𝐹𝐹>𝑌𝑌(𝑖𝑖n t years) is the probability over t years of not reaching functional recovery within Y days and λ𝐷𝐷𝐷𝐷𝐹𝐹𝐹𝐹>𝑌𝑌∙is the annual risk of not achieving functional recovery by Y days. The expected annual downtime to functional recovery, or EADFR, can also be estimated following a similar formulation to that of the expected annual loss, EAL, as shown in Equation 2.8. EADFR = � E[DTFR|IM]|dλIM(IM)|∞0 (2.8) where E[DTFR|IM] is the expected downtime to functional recovery, DTFR, given an intensity measure, IM and |dλIM(IM)| represents the annual rate of occurrence of IM. The benefit of using the EADFR to assess functional recovery performance is that downtime fragilities do not have to be developed for different target thresholds (i.e., Y days) and this metric is therefore threshold agnostic. 2.4 Case Study of Modern Reinforced Concrete Shear Wall Buildings 2.4.1 Archetype Reinforced Concrete Shear Wall Buildings To illustrate the proposed performance evaluation methods, we evaluate the functional recovery performance of a series of modern residential reinforced concrete shear wall (RCSW) buildings designed by Marafi et al. (2020a) in Seattle, WA. This study directly uses the nonlinear engineering demand parameters provided by Nasser Marafi as an input, so a discussion of the archetypes, the seismic hazard, and engineering demand parameters is provided for completeness in Sections 2.4.1 and 2.4.2. The archetype buildings range in height from eight to 24 stories and have been used extensively to evaluate collapse risk in the Cascadia region (Marafi et al., 2020a; Marafi et al., 2020b). The floor dimensions of the archetype buildings are 30.5 m × 30.5 m (100 ft × 100 ft) above grade and 48.8 m × 48.8 m (160 ft × 160 ft) below grade. The height of each story is 23 constant up the building, as well as across archetypes, and equal to 3.05 m (10 ft). The eight-story archetype has three basement levels, and all other archetypes have four basement levels. The lateral-resisting structural system consists of coupled walls in one direction and cantilevered walls in the orthogonal direction. The archetype buildings are enclosed by three 9.15 m (30 ft) bays of gravity frames along each side of the floor plate perimeter. A typical floor plan of the archetype buildings is shown in Figure 2.2. Figure 2.2 Typical floor plan (from Kourehpaz et al., 2021) of the 12-story RCSW archetype. Marafi et al. (2020a) designed the archetypes in the cantilevered direction. The archetypes were designed to have a 2% drift limit and a flexural demand-to-capacity ratio equal to 1.0 at grade in compliance with minimum (i.e., ASCE/SEI, 2016) code prescriptive requirements. A seismic force reduction factor (R) of 6 was adopted for all buildings, whose design complied with ACI 318-14 (ACI, 2014) requirements for special reinforced concrete shear walls. More details about the modeling assumptions can be found in Marafi et al. (2020a). 2.4.2 Seismic Hazard and Engineering Demand Parameters Marafi et al. (2020a) also assessed the seismic performance of these archetype buildings at five different intensity levels using a multiple stripe analysis (MSA) procedure (Jalayer and Cornell, 24 2009). The return periods associated with these intensity levels were 100, 475, 975, 2475 and 4975 years. At each return period, 100 ground motion records from crustal, intraslab, and interface sources were selected and scaled to match the target conditional mean spectra (CMS) (Jayaram et al., 2011) consistent with the 2014 National Seismic Hazard Model (NSHM) (Petersen et al., 2014) for a site in downtown Seattle, WA. The spectral accelerations at the fundamental period of vibration of each archetype building, assuming cracked section properties, are summarized in Table 2.1. Table 2.1 Spectral accelerations (in units of g) of the intensity levels considered and the simulated M9 earthquake scenario. Archetype Intensity Level Scenario 100-yr 475-yr 975-yr 2475-yr 4975-yr M9 8-story (T1 = 1.93 s) 0.05 0.15 0.23 0.37 0.48 0.20 12-story (T1 = 2.70 s) 0.03 0.10 0.15 0.25 0.33 0.14 16-story (T1 = 3.53 s) 0.02 0.07 0.11 0.19 0.25 0.09 20-story (T1 = 4.36 s) 0.02 0.05 0.09 0.15 0.20 0.06 24-story (T1 = 5.11 s) 0.01 0.04 0.07 0.12 0.17 0.05 To perform a scenario-based assessment of functional recovery performance, we also employ nonlinear analysis results of these archetype buildings, as generated by Marafi et al. (2020a), under a plausible moment magnitude 9.0 (M9) Cascadia Subduction Zone Earthquake (CSZ), with a return period of approximately 500 years. The ground motions used in this scenario-based assessment were generated by Frankel et al. (2018) by combining synthetic seismograms from three-dimensional finite-difference simulations (for periods greater than 1 s) with finite-source stochastic synthetics (for periods less than 1 s). Past megathrust subduction earthquakes (Frankel, 2017, 2013) were used to validate the resulting ground motion characteristics, which can have severe consequences on the built environment due to their damaging spectral shapes and long durations (Marafi, 2018). The response spectrum of the M9 scenario considered, at the site of 25 interest, has its spectral accelerations bounded by the 475-yr and 975-yr intensity level spectral accelerations as observed in Table 2.1. Sample nonlinear response history analysis results, including story drift ratios (SDR) and peak floor accelerations (PFA) are illustrated in Figure 2. While the structural response was evaluated using 2D models in the cantilevered direction, loss estimation requires inputs in both orthogonal directions. As a result, demand parameters were assumed to be the same in both building directions (i.e., cantilevered and coupled) as outlined in Kourehpaz et al. (2021). (a) (b) (c) (d) Figure 2.3 Sample nonlinear analysis results of the 12-story RCSW archetype: (a) story drift ratios (SDR) and (b) peak floor accelerations (PFA) across intensity levels, as well as (c) SDRs and (d) PFAs for all building heights at the 475-year intensity level. 2.4.3 Damage and Repair Time Assessment To conduct the FEMA P-58 analysis, we leverage building performance models from Kourehpaz et al. (2021) for all archetype buildings, as well as the EDPs obtained from nonlinear analysis 26 simulations presented in above, to evaluate expected damage and direct economic losses at the 100- to 4975-year intensity levels and for the M9 CSZ earthquake scenario. The building performance models originally developed by Kourehpaz et al. (2021) were recreated to be compatible with the SimCenter’s open-source loss estimation software, i.e., Pelicun (Zsarnoczay and Kourehpaz, 2021). Relevant building performance models for all archetype buildings can be found in Electronic Supplement S2.1. In the FEMA P-58 methodology, to characterize demands, simulated EDPs are sampled from probability distributions fit to a finite set of structural analysis results. To characterize the capacities of structural and nonstructural components, fragility functions, also characterized probabilistically, are employed to relate component demand to anticipated damage levels. Lastly, the expected damage in each component is translated to possible impacts, such as repair cost and time, by means of consequence functions, which are also defined in a probabilistic manner. To carry out the damage and repair time assessments, 2000 Monte Carlo realizations are generated to propagate the uncertainty associated with the demands, the capacities and the consequences of all building components. In every realization, relevant probability distributions are sampled to represent a wide range of plausible outcomes. These component-level damage and repair time estimates are then used to infer the initial loss of function of the archetype buildings and to map the repairs required to achieve a functional recovery state. In the loss assessments, we account for collapse and irreparable damage instances in addition to realizations with repairable damage. Irreparable damage is assumed to occur due to excessive residual drifts using the criteria outlined in FEMA P-58 (FEMA, 2018a). Figure 2.4a summarizes the mean loss ratios for all building heights under all intensity levels considered in the assessment, as well as the M9 earthquake scenario. As seen in the figure, the expected losses under the M9 scenarios are approximately 10%, 27 when averaged across all archetypes, which is almost equivalent to the 975-year intensity-based assessment results. While the contribution of collapse to expected losses is negligible, as expected for a modern building design with a collapse risk of less than 1% in 50-years (ASCE/SEI, 2016), irreparable damage is the greatest contributor to the losses at higher intensity levels, e.g., at the 4975-year assessment, as seen in Figure 2.4b. Figure 2.4b also indicates that the contribution of collapse and irreparable damage to expected losses is negligible under the M9 earthquake scenario considered. (a) (b) Figure 2.4 (a) Direct economic loss estimates for all archetypes and (b) percent of realizations that result in reparable damage, irreparable damage, or collapse for the 12-story RCSW archetype at intensity levels ranging from 100 to 4975 years and the M9 scenario considered in the assessment. 2.4.4 Functional Recovery Time Assessment The estimated damage and repair time from a FEMA P-58 (FEMA, 2018a) assessment are used as inputs to the TREADS downtime estimation framework developed by Molina Hutt et al. (2022b). Downtime estimates to achieve functional recovery performance, DTFR, include the time necessary to repair damaged structural and nonstructural components that hinder functionality, as well the time associated with relevant impeding factors, which delay the initiation of repair activities. TREADS uses damage estimates from FEMA P-58, as implemented in Pelicun (Zsarnoczay and Kourehpaz, 2021), to determine the initial loss of function immediately following an earthquake. 28 TREADS then probabilistically models building recovery using a stochastic process. For each damage realization from the FEMA P-58 assessment, TREADS determines the necessary repairs to achieve the desired recovery state, i.e., functional recovery, and the associated factors that may delay the initiation of repairs, i.e., impeding factor delays. Probability distributions are used to characterize all impeding factor delays. These distributions are sampled to develop probabilistic recovery trajectories for each damage realization obtained from the FEMA P-58 methodology. For irreparable damage realizations, a lognormal distribution of demolition times is sampled coupled with a building reconstruction time of 35 days per story. The recovery trajectory shows the building functionality over time following the earthquake event, as shown in Figure 2.5. The building functionality drops to 0% immediately after the event until the building is inspected and returns to 100% when the building has fully achieved the desired recovery state. The TREADS framework assumes repairs are carried out in groups of three stories based on interviews with contractors following the 1994 Northridge earthquake (Terzic et al., 2016). Four repair paths are assumed to take place in parallel, i.e., structure, stairs, elevator, and exterior component damage. In any given floor, interior repairs occur only after structural repairs are complete. For each realization, four distinct recovery trajectories are modeled to reflect each repair path. The governing recovery trajectory for each realization is taken as the upper bound of all repair paths in every story. Further details of the downtime assessment framework are provided by Molina Hutt et al. (2022b) and Vahanvaty (2021). Recovery trajectories for functional recovery were developed for all archetypes at all intensity levels, as well as for the M9 scenario considered. For repairable realizations, the recovery trajectory is a stepwise function mapping the floor-by-floor functionality over time. For irreparable and collapse realizations, the building functionality drops to zero and returns to 100% only after 29 building demolition and reconstruction is complete. Example recovery trajectories to functional recovery for the 12-story archetype are illustrated in Figure 2.5 at the 475-year intensity level and for the M9 scenario, highlighting the large uncertainty in the downtime estimates. The uncertainty in these estimates is large because all uncertainty in building response, damage estimates, repair times, and impeding factors is propagated through in the calculations. Relevant downtime assessment models for all archetype buildings can be found in Electronic Supplement S2.2. (a) (b) Figure 2.5 Histogram of downtime and recovery trajectories for the 12-story archetype at the (a) 475-year intensity level and (b) M9 earthquake scenario. Table 2 summarizes the median downtime to functional recovery for all archetype buildings and intensity levels considered in the assessment. The downtime estimates calculated using TREADS (Kourehpaz and Molina Hutt, 2022) align with results from other frameworks at the 475-year intensity level (DeBock, 2022; Kolozvari and Terzic, 2023), which predict recovery times between 6 months to over one year. At the 100-year intensity level, however, downtime 30 estimates using the current TREADS framework range from 82 to 108 days. These long downtimes at the 100-year intensity level are driven by damage to the elevator and the associated impeding factor delays. In the absence of other data, TREADS utilizes impeding factor delays for elevator repairs from (Paul et al., 2018), which estimates a mean of 19 weeks of impeding factor delays for low levels of damage if no elevator contractor is on retainer. Further efforts are needed to validate such results at low levels of ground motion shaking. Table 2.2 Median downtime (in days) to achieve functional recovery (FR) under the intensity levels considered and the simulated M9 earthquake scenario. Archetype Intensity Level Scenario 100-yr 475-yr 975-yr 2475-yr 4975-yr M9 8-story (T1 = 1.93 s) 84 215 310 473 535 318 12-story (T1 = 2.70 s) 82 214 285 516 615 359 16-story (T1 = 3.53 s) 108 213 290 568 671 335 20-story (T1 = 4.36 s) 96 218 293 601 723 397 24-story (T1 = 5.11 s) 93 207 290 597 781 305 To illustrate key downtime contributors, functional recovery times are disaggregated for the 475-year and the M9 scenario assessments. The disaggregation presented in Figure 2.6 is conducted by calculating the average time across all repairable realizations of downtime associated with contractor, stabilization, engineering, and financing activities for each repair path. At the 475-year intensity downtime estimates are governed by contractor mobilization delays associated with the elevator repairs (denoted as Repair Path C in the figure). In the 475-year assessment, elevator repair times are considerably larger than those associated with other repair paths. By contrast, in the M9 scenario, downtime estimates are governed by the repairs associated with structural, interior, and equipment repairs (denoted as Repair Path A in the figure), although contractor mobilization delays related to the elevator repairs are significant. The downtime disaggregation results of the M9 scenario-based assessment are more balanced, i.e., similar across the different repair paths, than those of the 475-year intensity-based downtime assessment because the 31 simulated M9 motions result in more widespread damage, as also evidenced by the expended economic losses previously reported in Figure 2.4a. Disaggregation data for all intensity levels are provided in the Electronic Supplement S2.2. (a) (b) Figure 2.6 Disaggregation of mean downtime to functional recovery for repairable realizations for the (a) 475-year intensity level and (b) the M9 earthquake scenario as obtained from TREADS. 2.5 Functional Recovery Performance Evaluation 2.5.1 Scenario-based Functional Recovery Performance The first formulation to assess functional recovery compliance we present for the case study is the scenario-based method, as outlined in Section 2.3.1. The M9 Cascadia Subduction Zone earthquake scenario is used to evaluate the functional recovery performance of the archetype buildings. The median downtime estimated for the archetype RCSW buildings range from 305 to 397 days (refer to Table 2.2). An empirical CDF of downtime to functional recovery is developed by leveraging the 2000 Monte Carlo recovery realizations using TREADS, as shown in Figure 2.7. 32 The probability of achieving downtime to functional recovery within Y days does not show a strong trend with height. Most notably, there is a significant difference in performance between the 20- and the 24-story archetypes. This difference can be attributed to deep sedimentary basin amplification. The physics-based ground motion simulation used in this scenario earthquake explicitly captures these effects. Basin amplification of spectral acceleration is period-dependent and most notable in the range of 1-4s (Kakoty et al., 2021). The period of the 24-story archetype falls outside of the range in which basin amplification effects are most significant, which helps explain how it has lower recovery times than some of the other building heights. While these basin effects make it difficult to establish trends as a function of building height, the results illustrate some of the unique phenomena that can be captured by means of scenario-based assessments. Scenario-based assessment results for all archetype buildings can be found in Electronic Supplement S2.3. Figure 2.7 Probability of achieving downtime to functional recovery of Y days for a range of archetype RCSW buildings of varying height when subjected to M9 CSZ earthquake scenario. Table 2.3 shows the probability of achieving functional recovery by pre-defined targets (i.e., one week, one month, four months, etc.). The values in Table 2.3 can be obtained by using the performance function presented in Figure 2.7 to identify the percentage of realizations in which 33 functional recovery has been achieved by a given target. For the M9 scenario considered, the probability of achieving functional recovery within four months or less is negligible for all building heights. By contrast, the probability of achieving functional recovery within one and a half years is 91% on average. Table 2.3 Probability of achieving functional recovery (FR) at varying time targets conditioned on the M9 earthquake scenario. Archetype Probability of achieving FR with time 1 month 4 months 6 months 1 year 1 ½ years 8-story (T1 = 1.93 s) 0% 0% 1% 68% 92% 12-story (T1 = 2.70 s) 0% 0% 0% 53% 91% 16-story (T1 = 3.53 s) 0% 0% 0% 64% 93% 20-story (T1 = 4.36 s) 0% 0% 0% 32% 86% 24-story (T1 = 5.11 s) 0% 0% 0% 75% 95% 2.5.2 Intensity-based Functional Recovery Performance To understand how the probabilities of achieving downtime to functional recovery by different times vary as a function of ground motion shaking intensity, we utilize TREADS downtime estimates at a range of intensity levels with return periods of 100, 475, 975, 2475, and 4975 years. Figure 2.8 shows the empirical CDF of downtime to functional recovery of all archetypes and ground motion intensities considered. Intensity-based assessment results for all archetype buildings can be found in Electronic Supplement S2.4. 34 (a) (b) (c) (d) (e) Figure 2.8 Probability of achieving a downtime to functional recovery of Y days for a range of RCSW archetype buildings of varying height when subjected to ground motion intensities with varying return periods: (a) 100, (b) 475, (c) 975, (d) 2475, and (e) 4975 years. 35 As seen in Figure 2.8, while at lower intensity levels the results across building heights are consistent, larger recovery times are observed for the taller buildings at higher intensities of shaking. At low intensity levels, height-independent impeding factor delays are triggered (e.g., contractor mobilization times for elevator repairs). By contrast, at high intensity levels, stabilization delays govern the recovery time. In the TREADS methodology, stabilization delays increase with height (Molina Hutt et al., 2022b). Furthermore, both irreparable and repairable recovery times are included in the above calculations. A greater number of irreparable realizations is observed when the buildings were subjected to ground motions with longer return periods, as was shown in Figure 2.4b. For irreparable realizations, the functional recovery time is equal to the time of demolition plus reconstruction. A reconstruction time is defined per story, which also leads to greater variability in recovery times observed as a function of building height. In Figure 2.8a, which summarizes the results at the 100-year return period, function is immediately regained in a small percentage of realizations immediately following inspection. Delays of approximately 50 days are then observed due to contractor mobilization time for interior repairs, based on data from Paul et al. (2018). After these delays are cleared, approximately 60% of realizations reach the functional recovery state. The remaining delays are primarily caused by elevator damage, which have a long contractor mobilization time and are a requirement for functional recovery state in the TREADS methodology (Molina Hutt et al., 2022b). These trends explain the jaggedness of the 100-year results in relation to those at higher intensity levels. Table 2.4 shows the probability of achieving functional recovery by pre-defined targets (i.e., one month, four months, etc.) for the 12-story archetype and a range of intensity levels. The values in Table 2.4 can be obtained by using the performance function presented in Figure 2.8 to 36 identify the percentage of realizations in which functional recovery has been achieved by a given target. The results indicate there is a 61% probability of achieving functional recovery within four months at the 100-year return period. This probability increases to 94% when results are evaluated against a one-year target. At the 475-year intensity level, the probability of achieving functional recovery by 4 months is under 10%. At the 2475-year return period, the probability of achieving functional recovery within 4 months is negligible and only reaches around 5% when the results are evaluated against a one-year threshold. Table 2.4 Probability of achieving functional recovery (FR) at varying time targets and intensity levels for the 12-story RCSW archetype. Intensity FR Probability of achieving FR with time 1 month 4 months 6 months 1 year 1 ½ years 100-year 4% 61% 70% 94% 99% 475-year 0% 6% 34% 88% 98% 975-year 0% 0% 26% 76% 95% 2475-year 0% 0% 0% 5% 58% 4975-year 0% 0% 0% 0% 29% 2.5.3 Risk-Based Functional Recovery Performance In this section, we now combine the downtime assessment results from the range of intensity levels considered in Section 2.5.2 to calculate the annualized risk of downtime to functional recovery exceeding different thresholds. While the calculations are illustrated for the 12-story archetype, as seen in Figure 2.9, risk-based assessment results for all archetype buildings can be found in Electronic Supplement S2.4. Figure 2.9a shows the seismic hazard curve, which describes the annual frequency of exceedance of the spectral acceleration at the fundamental period of vibration of the 12-story archetype. Downtime fragilities are developed for several functional recovery targets ranging from one month to one and a half years, as shown in Figure 2.9b. These downtime fragility functions are developed for each time target of Y days by fitting a lognormal CDF to the 37 probability of downtime exceedance at the intensity levels corresponding to the 100-, 475-, 975-, 2475-, and 4975-year return period. For example, to develop the downtime fragility for the one-year target, first, the probability of not having achieved functional recovery within one year is derived from the complement of the performance function (see Equation 2.4). This is repeated for the five intensity levels to obtain a set of downtime probabilities that relate to the spectral acceleration at the first mode period of the structure, SA(T1). The Probit link function, implemented using tools by Baker (2015), is used to fit the CDF to the data derived from the intensity-based assessments. (a) (b) Figure 2.9 (a) Seismic hazard curve and (b) downtime fragility to functional recovery at varying targets for 12-story RCSW archetype. We assess the adequacy of lognormal CDF assumption for downtime fragility functions by conducting goodness-of-fit tests using the method proposed by Lilliefors (1967). For the assessments, a significance level of 0.05 (α = 0.05) is used as recommended by FEMA P-58 (FEMA, 2018a). The significance level refers to a pre-defined threshold used to determine whether the observed data fits a particular statistical model. A lower significance level indicates a more stringent criterion for rejecting the null hypothesis, i.e., the fragility function fails the goodness-38 of-fit test. The results of the assessment show that the lognormal CDF passes the goodness-of-fit test for downtime fragility functions of all building heights for the target recovery times considered in this study when the tools developed by Baker (2015) are used for fitting. The resulting median (θ) and dispersions (β) of the downtime fragilities are reported in Table 2.5. Table 2.5 Median and dispersions of downtime fragilities Archetype Probability of achieving FR with time 1 month 4 months 6 months 1 year 1 ½ years θ (g) β θ (g) β θ (g) β θ (g) β θ (g) β 8-story (T1 = 1.93 s) 0.043 0.14 0.057 0.60 0.080 0.74 0.24 0.59 0.53 0.68 12-story (T1 = 2.70 s) 0.023 0.16 0.036 0.60 0.051 0.77 0.15 0.54 0.27 0.47 16-story (T1 = 3.53 s) 0.015 0.16 0.021 0.64 0.031 0.86 0.11 0.60 0.17 0.47 20-story (T1 = 4.36 s) 0.016 0.13 0.021 0.42 0.027 0.66 0.083 0.59 0.13 0.41 24-story (T1 = 5.11 s) 0.007 0.18 0.011 0.61 0.017 0.92 0.066 0.70 0.10 0.43 As described in Section 2.3.3, to conduct the annualized downtime risk calculation, the derivative of the hazard curve is integrated with the downtime fragility. Once the annualized risk is estimated, the 50-year probability of downtime exceedance can be calculated. From the risk disaggregation results shown in Figure 2.10 for the 12-story archetype building, we can observe that the risk of exceeding rapid functional recovery targets (i.e., one month to six months) is governed by lower-intensity, higher-frequency events (i.e., 100-year intensity level). At longer downtime targets, however, such as one or one and a half years, there is a greater contribution to downtime risk from the 975-year and higher intensity levels. These trends indicate that the risk of not achieving more rapid functional recovery times is impacted most by frequent events. The risk of longer functional recovery times shows a growing contribution from less frequent and more damaging events. Fragilities and disaggregation plots for all heights considered are provided in Appendix A. 39 (a) (b) (c) (d) (e) Figure 2.10 Disaggregated downtime risk for 12-story RCSW archetype for downtime targets of (a) 1 month, (b) 4 months, (c) 6 months, (d) 1 year and (e) one and a half years. 40 While the 100-year return period dominates the risk of exceeding shorter recovery targets, this result is highly dependent on the damage thresholds that trigger impeding factors and the associated delays used in the calculation methodology. The median downtimes estimated using TREADS at the 100-year return period range from 82 to 108 days (refer back to Table 2.2), which appear excessive considering the low shaking intensity. As discussed previously in Section 2.4.4, the main contribution to these downtime estimates are contractor-related impeding factors for interior repairs and for other nonstructural components, like elevators, which are based on data collected from contractors by Paul et al. (2018). The impact of the conservatism of both damage thresholds and impeding factor delay assumptions is exacerbated by the steepness of the hazard curve in this region and by the dispersion of the fragilities. These findings highlight the sensitivity of these frameworks to impeding factor delay data and the need to expand data collection in this area. These findings also highlight the need to compare functional recovery performance using different downtime estimation frameworks. As with modern seismic design provisions, which aim to limit the probability of collapse throughout the lifetime of a building (i.e., ASCE 7-16 aims to limit the probability of collapse to 1% in 50 years (ASCE/SEI, 2016)), future design provisions for functional recovery performance should aim to limit the probability of downtime to functional recovery exceeding a time frame above which negative societal consequences are expected. The 50-year probability of not reaching functional recovery by various downtime targets is summarized in Figure 2.11 for all archetypes considered. The results indicate an increase in downtime risk as building height increases. An exception is observed for the 20-story archetype. This archetype and the 24-story archetype were both designed for minimum base-shear, making the buildings stiffer relative to the 8- to 16-story archetypes. Figure 2.11 indicates that the 50-year probability of not achieving functional recovery 41 within one month is approximately 50%, averaged across the five building heights considered. The 50-year probability of not achieving functional recovery within four months and six months decreases to approximately 43% and 36%, respectively, averaged over all building heights considered. When we consider longer recovery periods of one year and one and a half years, the 50-year probability of downtime to functional recovery exceeding those targets falls to under 8% and 3%, respectively. These results are not surprising considering that buildings designed to modern standards are designed to minimize the probability of collapse under extreme ground motion shaking, but do not limit damage that impedes functionality or other recovery states. As the disaggregation results indicated, frequent earthquakes contribute more to the 50-year probability. The results presented in Figure 2.11 are therefore also reflective of the conservative impeding factor delays and consequence of damage that are used in TREADS for lower intensity events. These findings serve to benchmark the expected downtime performance of modern RCSW buildings designed following modern design standards and highlight the need to (1) explore design interventions that expedite post-earthquake recovery and (2) better quantify impeding factor delays across a range of damage states. Figure 2.11 50-year probability of downtime to functional recovery exceeding Y days for all building heights considered and target times ranging from 1 month to one and a half years. 42 As previously noted, the results of the disaggregation performed were found to be sensitive to the assumptions for damage thresholds and the impeding factor delays triggered at low intensity levels. The lack of direct observations of impeding factor delays points to the need to consider alternate sources of empirical data or, alternatively, additional resilience metrics. For instance, robustness (i.e., the initial loss of function following the earthquake) has been considered by Bruneau et al. (2003) and was implemented in the TREADS framework (Molina Hutt et al., 2022b). The use of this metric, in lieu of recovery time, would allow us to consider the post-earthquake recovery state of a building without relying on impeding factor delay assumptions. Identifying the return period that dominates the downtime risk is useful for finding effective design interventions. In this study, the risk of downtimes exceeding shorter recovery periods is dominated by frequent earthquakes. The types of damage that are triggered at these lower intensity levels are largely nonstructural. Therefore, improvements to nonstructural component design could reduce the risk of exceeding short recovery targets. When longer recovery targets are considered, however, there is a larger contribution from longer return periods. In these higher intensity events, extensive structural damage that results in stabilization delays or demolition and reconstruction is more frequently observed. This type of damage also is the type of damage that has shown to have negative societal consequences due to lengthy downtimes (Chang et al., 2014; Comerio and Blecher, 2010; Olshansky et al., 2005). While these findings are specific to this suite of archetypes and the assumptions used in the downtime analysis, they do point to the need to perhaps consider different recovery targets in future recovery-based design provisions: a short recovery time target evaluated for frequent events, and a second one aimed at reducing the probability of irreparable damage in rare events. 43 An alternative to computing the 50-year risk of downtime to functionality exceeding different thresholds is the calculation of the expected annualized downtime to functional recovery, EADFR. The EADFR, as calculated using Equation 2.8, for each building height is summarized in Table 2.6. This EADFR estimate only considers the contribution of the discrete hazard levels considered in this study (i.e., 100-year to 4975-year return periods). The EADFR is approximately 3 days for all heights considered. This EADFR is on the rough order of magnitude with previous studies that have employed early downtime estimation frameworks (Molina Hutt et al., 2019). Results vary minimally across archetype heights, but a small positive correlation is observed between building height and EADFR. While the EADFR results are independent of the target functional recovery time, this metric provides no insights into the likelihood of an undesirable outcome, i.e., downtime exceeding a limit beyond which negative societal consequences are expected. Table 2.6 Expected annual downtime to functional recovery, EADFR. RCSW Archetype Height EADFR (Days) 8-story 2.9 12-story 2.8 16-story 3.0 20-story 3.1 24-story 3.0 2.6 Conclusions, Limitations, and Future Work This paper discusses three assessment procedures to evaluate functional recovery performance using recovery time estimates: a scenario-based, an intensity-based, and a risk-based method. The formulations presented make use of recent developments in downtime estimation frameworks to further discussions of how to include functional recovery performance targets in the next generation of building codes. A series of case studies, which evaluate the performance of eight- to 24-story residential reinforced concrete shear wall buildings designed using modern design 44 standards (i.e., ASCE/SEI, 2016) for a Seattle, WA site were used to illustrate the calculations. First, the archetype buildings were analyzed under a plausible M9 Cascadia Subduction Zone earthquake scenario. The archetypes were then analyzed using the intensity-based assessment at return periods ranging from 100- to 4975-years based on the 2014 NSHM (Petersen et al., 2014). Finally, a risk-based assessment was performed for different downtime targets. Disaggregation results were used to identify the intensity levels with the greatest contribution to downtime risk. The purpose of this study was not to set downtime targets, so performance was assessed for a series of functional recovery thresholds ranging from one month to one and a half years. A summary of findings is presented below: • Scenario-based assessment: The probability of achieving functional recovery within four months of the M9 earthquake scenario considered was negligible. The probability of achieving functional recovery within one year, however, is ~60% on average across all archetypes. While spectral accelerations at the fundamental periods of vibration of the archetype buildings for this scenario earthquake were similar to the 975-year intensity level from the 2014 NSHM (Petersen et al., 2014), downtime estimates were greater for the M9 scenario due to the damaging spectral shapes and long strong ground motion duration resulting in more extensive and widespread damage. • Intensity-based assessment: The probability of downtime exceedance at different time targets showed little variation across the building heights considered because downtimes were dominated by height-independent impeding factors. Greater downtimes were observed for taller archetypes only at the 2475- and 4975-year intensity levels, where height-dependent stabilization delays were triggered. Example results for the 12-story archetype building indicate a 60% probability of achieving functional recovery within four 45 months at the 100-year return period. This probability increases to 94% when results are evaluated against a one-year target. At the 475-year intensity level, the probability of achieving functional recovery within four months is under 10%. At the 2475-year return period, the probability of achieving functional recovery within four months is negligible and only reaches 5% when the results are evaluated against a one-year threshold. • Risk-based assessment: Results of a risk-based assessment of the archetype buildings showed a 50% probability in 50 years of the building downtime to functional recovery exceeding one month, as well as a 43% in 50-year probability of the downtime exceeding four months and a 8% in 50-year probability of downtime exceeding one year. The risk of downtime exceeding one to six months was dominated by frequent, low intensity events (e.g., 100-year return period). The risk of exceeding longer recovery times show an increasingly large contribution from less frequent, higher intensity earthquakes (i.e., return periods greater than 975 years). Generally, higher downtime risk was observed as building heights increased. The expected annual downtime to functional recovery was approximately 3 days for all archetypes considered. The goal of this study was to showcase methodologies for evaluating functional recovery performance that can be used with a range of downtime estimation frameworks. By employing a risk-based approach to assess the functional recovery performance of archetype RCSW buildings, downtime risk metrics were disaggregated to identify the intensity level that dominates the downtime risk. In this study, more frequent earthquake intensities (e.g., 100-year return periods) dominated the risk of downtimes exceeding targets of one month to six months. Disaggregation of the downtime estimates at different intensity levels revealed that downtime risk can be heavily influenced by assumed impeding factor delays of a few key component repairs (i.e., elevator 46 repairs in this study). These results highlight the need to study impeding factor delays more extensively, particularly as a result of damage in low intensity events, and to benchmark functional recovery performance results against other frameworks if attempting to codify functional recovery performance in future design provisions. Ultimately, this study highlights that current life-safety standards do not ensure rapid post-earthquake recovery and the introduction of new recovery-targeted provisions into the next generation of building codes is required to minimize earthquake-induced downtime. 2.7 Application to Canadian Building Code Development This work introduces methods that could be used to evaluate current functional recovery performance for both existing and new buildings in Canada. The scenario-based assessment could similarly be performed for a location where a specific earthquake scenario is of interest for building code development or planning purposes. For example, researchers have been working in the Lower Mainland of British Columbia to quantify expected collapse performance under the M9 Cascadia Subduction Zone earthquake (Kakoty et al., 2021). These studies could be extended to evaluate recovery performance. While there are differences between the Canadian and American modern design provisions, some of the findings from this study may also be relevant to the Cascadia region in Canada, which includes Vancouver or Victoria, BC. For the case study, the recovery time is dominated by repairs to the structure and elevators, which does give an indication of where future research in Canada could focus. Next, NBCC 2020 uses a constant-hazard model, where all design checks, including the new “No Structural Damage” provisions, are performed at a specific intensity level (NRCC, 2020). The new Article 4.1.8.23 provisions target elastic structural behaviour at the 5% in 50-year (975-year return period) and the 10% in 50-year (475-year return period) for post-disaster and high 47 importance buildings respectively. Intensity-based assessments like those presented in this study for a wide range of structural systems could be conducted to explicitly verify (1) whether structural damage is limited and (2) the corresponding nonstructural component damage. Further, nonstructural component design interventions could also be assessed. Finally, to compare performance across hazards, the annualized risk is often used. To set targets for functional recovery provisions, risk-based assessments can be performed following the methods outlined in this chapter. Overall, the methods proposed in this chapter give tools to Canadian researchers and engineers to calculate current functional recovery risk, set recovery performance targets, and identify appropriate structural and nonstructural design provisions to achieve recovery performance consistent with societal expectations. 48 Chapter 3: Evaluating the Variability in Functional Recovery Performance with Risk-Targeting for Life-Safety This chapter is based on the following reference: Blowes, K., Molina Hutt, C., and Cook, D., 2024. Evaluating the variability in functional recovery performance in modern buildings across the United States. Proceedings of the 18th World Conference of Earthquake Engineering. Presented at the 18th World Conference of Earthquake Engineering, Milan, Italy. 3.1 Introduction Current seismic design provisions in the United States aim to ensure certain life-safety performance objectives, but do not provide direction to target specific levels of post-earthquake function (ASCE/SEI, 2022). Recent studies have shown that buildings designed following these minimum standards may not perform well when evaluated against resilience-based performance metrics. Estimates of functional recovery time by Molina Hutt et al. (2022a), Cook et al. (2024) and Terzic and Kolozvari (2022) all have shown that modern reinforced concrete shear wall (RCSW) buildings may take from approximately seven months to over a year to reach a functional recovery state following a 475-year intensity-level earthquake. Blowes et al. (2023) also performed a risk-based analysis of modern RCSW buildings in Seattle, WA and found an approximately 40% probability of the functional recovery time exceeding 4 months over 50 years. This expectation of lengthy recovery times points to the need to expand existing building codes to consider post-earthquake recovery. 49 In an effort to develop clear functional recovery objectives and parallel design requirements to improve recovery performance, the Building Seismic Safety Council (BSSC) in the United States is advancing the NEHRP (National Earthquake Hazard Reductions Program) provisions to include new prescriptive recovery-based design requirements (BSSC, 2023). As part of this effort, the Functional Recovery Task Committee (FRTC) has defined a new risk-targeted Functional Recovery Earthquake, FRER, which will be used by engineers to perform structural and nonstructural design checks. To support this ongoing work, there is a need to determine whether risk-targeting that is currently used for collapse is appropriate for risk-targeting for functional recovery. Further, there is a need to identify return periods that drive functional recovery risk. This study aims to quantify the functional recovery performance across 34 U.S. cities for buildings designed for current life-safety provisions using risk-based metrics (e.g., 50-year probability of the functional recovery time exceeding 4 months). To do so, we consider an 8-story RCSW archetype building that reflects modern life-safety design provisions for the relevant seismicity across the 34 cities. The functional recovery time of each archetype building is simulated using the Cook et al. (2022) methodology, which has been adopted by the ATC-138 project (ATC, 2021b), at return periods ranging from 14 to 4975 years. A risk-based assessment is then performed to benchmark the 50-year risk of exceeding various functional recovery targets ranging from two weeks to one year. In addition, risk-based assessments are also conducted for severe partition wall damage and for structural damage that hinders tenant safety (i.e., red tags). By using these measures, we can evaluate trends in the occurrence of nonstructural and structural damage across intensity levels and across the 34 sites. Further, we can use these measures to identify the return periods that drive the risk of incurring each type of damage, and how this relates to functional recovery risk over the lifetime of the building. Overall, this study adds to the existing 50 body of work on functional recovery by calculating the 50-year risk of exceeding a wide range of functional recovery targets and provides insight into the current variability of recovery risk that exists across the United States. 3.2 Literature Review While the goal to develop recovery-based design provisions has only recently been identified, meaningful work has already been conducted in this research area. Work to date has focused on developing functional recovery time estimation frameworks, such as the REDi framework (Almufti and Willford, 2013), the F-REC framework (Terzic et al., 2021), the TREADS framework (Molina Hutt et al., 2022b), and the Cook et al. (2022) methodology that has been adopted by the ATC-138 Project (ATC, 2021b). Significant efforts have also been put into collecting data on impeding factor delays (e.g., Cook et al., 2022; Paul et al., 2018) and repair sequencing (e.g., Terzic et al., 2016), as well as benchmarking the probability of unsafe placards against past events (Cook et al., 2021). Studies using these frameworks have primarily focused on RCSW buildings (Cook et al., 2024; Molina Hutt et al., 2022a, 2022b; Terzic and Kolozvari, 2022). Researchers have also used this new generation of functional recovery time estimation frameworks to consider existing buildings, other types of modern construction, or the impact of design interventions (Galvis, 2022; Issa et al., 2023; Mohammadgholibeyki et al., 2023a; Vahanvaty, 2021). Most of these studies have focused on performance at either the 475-year intensity level or the design-level earthquake (DBE), but a few have considered performance across a range of intensity levels. Blowes et al. (2023) performed a risk-based analysis for functional recovery performance of modern RCSW buildings. Vahanvaty (2021) and Cook et al. (2024) also considered the impact of design interventions to improve recovery at intensities ranging from a 100- to a 4975-year return period for reinforced concrete buildings. In addition to 51 expanding research to evaluate functional recovery performance across intensity levels, to develop a national standard in the U.S., more effort is needed to gauge current recovery performance across a wider range of geographic locations with varying seismicity. In the United States, risk-targeting was first implemented in the 2009 NEHRP design provisions (FEMA, 2009a) using the methodology outlined by Luco et al. (2007). Horspool et al. (2023) recently implemented the methodology by Luco et al. (2007) to develop a national seismic risk model for collapse risk in New Zealand. Hulsey et al. (2022) advanced the notion of risk-targeting to consider a serviceability limit state with the goal of ensuring a ensuring a uniform risk of losing serviceability. Hulsey et al. (2022) proposed using damage to partitions to perform risk-targeting for loss of serviceability. Like the work by Hulsey et al. (2022), the ongoing effort by the BSSC also targets a uniform risk of exceeding a given resilience-based criteria, specifically, the risk of exceeding various recovery time targets. 3.3 Methodology 3.3.1 Archetype Building The archetype considered in this study is an 8-story residential special RCSW building. The archetype building is regenerated to meet the minimum design requirements at 34 cites. These 34 cities were originally studied in the development of the 2009 NEHRP Provisions (FEMA, 2009a) and more recently by Luco et al. (2017) for collapse risk, as well as in the 2020 NEHRP Provisions (FEMA, 2020). The sites selected are in cities with high seismicity, with a high population, or both. The mapped spectral response acceleration parameter for short periods, Ss, and at one second, S1, for the risk-targeted Maximum Considered Earthquake, MCER, as well as additional geographic information are provided in Table 3.1. Detailed hazard information as well as structural and nonstructural design information is included in Electronic Supplement S3.1. 52 Table 3.1 Geographic and hazard information for 34 cities in the United States. City Latitude Longitude State Region Ss S1 Los Angeles 34.05 -118.25 CA Southern California 2 0.7 Century City 34.05 -118.4 CA Southern California 2.1 0.75 Northridge 34.2 -118.55 CA Southern California 1.7 0.6 Long Beach 33.8 -118.2 CA Southern California 1.7 0.61 Irvine 33.65 -117.8 CA Southern California 1.2 0.45 Riverside 33.95 -117.4 CA Southern California 1.5 0.58 San Bernardino 34.1 -117.3 CA Southern California 2.3 0.93 San Luis Obispo 35.3 -120.65 CA Southern California 1.1 0.4 San Diego 32.7 -117.15 CA Southern California 1.6 0.53 Santa Barbara 34.45 -119.7 CA Southern California 2.1 0.77 Ventura 34.3 -119.3 CA Southern California 2 0.76 Oakland 37.8 -122.25 CA Northern California 1.9 0.72 Concord 37.95 -122 CA Northern California 2.2 0.67 Monterey 36.6 -121.9 CA Northern California 1.3 0.5 Sacramento 38.6 -121.5 CA Northern California 0.57 0.25 San Francisco 37.75 -122.4 CA Northern California 1.5 0.6 San Mateo 37.55 -122.3 CA Northern California 1.8 0.74 San Jose 37.35 -121.9 CA Northern California 1.5 0.6 Santa Cruz 36.95 -122.05 CA Northern California 1.6 0.6 Vallejo 38.1 -122.25 CA Northern California 1.5 0.6 Santa Rosa 38.45 -122.7 CA Northern California 2.4 0.94 Seattle 47.6 -122.3 WA Pacific Northwest 1.4 0.49 Tacoma 47.25 -122.45 WA Pacific Northwest 1.4 0.47 Everett 48 -122.2 WA Pacific Northwest 1.2 0.43 Portland 45.5 -122.65 OR Pacific Northwest 0.89 0.39 Salt Lake City 40.75 -111.9 UT Intermountain West 1.5 0.55 Boise 43.6 -116.2 ID Intermountain West 0.31 0.11 Reno 39.55 -119.8 NV Intermountain West 1.5 0.52 Las Vegas 36.2 -115.15 NV Intermountain West 0.65 0.21 St. Louis 38.6 -90.2 MO Central 0.46 0.16 Memphis 35.15 -90.05 TN Central 1 0.35 Charleston 32.8 -79.95 SC Central 1.4 0.41 Chicago 41.85 -87.65 IL Central 0.12 0.063 New York 40.75 -74 NY Central 0.29 0.06 3.3.2 Structural Response Prediction and Damage Assessment The structural response of the archetype is determined using the SP3 Structural Response Prediction Engine within the Seismic Performance Prediction Program (SP3) (Haselton Baker Risk 53 Group (HB-Risk), 2025). An archetype representative of typical design is generated to meet minimum design requirements outlined in ASCE 7-16 (ASCE/SEI, 2016) for Risk Category II (i.e., with an importance factor of 1.0) and site class D. The Structural Response Prediction Engine generates a simplified linear multi-degree of freedom model representative of the strength and stiffness requirements using formulations outlined in (Miranda, 2000, 1999). A nonlinear response is then sampled from incremental dynamic analysis results from high fidelity nonlinear models with similar linear performance and model characteristics. This methodology is documented in detail in Cook et al. (2018) and by HB-Risk (HB-Risk, 2025). The engineering demand parameters (EDPs) output from the Structural Response Prediction Engine are sampled to estimate damage using the FEMA P-58 methodology (FEMA, 2018b), as implemented in SP3 (HB-Risk, 2025). 3.3.3 Recovery Time Assessments Damage to components is then used to determine the functional recovery time using the Cook et al. (2022) methodology. Default impeding factor delays outlined in the Cook et al. (2022) methodology are sampled to determine the functional recovery time estimates at each of the eight intensity levels considered. In addition to functional recovery times, damage to partitions that impedes function (DS3 or worse) is determined from the FEMA P-58 analysis and the red tag probability is calculated at each intensity level using fault trees outlined in Cook et al. (2021), as implemented by Cook et al. (2022). EDPs, component damage estimates, and intermediate functional recovery time results at each intensity level are included in Electronic Supplement S3.1. 3.3.4 Risk-based Assessment of Functional Recovery Time To determine the functional recovery risk across the 34 cities considered, we adopt methods presented in Chapter 2, which are also published in Blowes et al. (2023), to calculate the 50-year risk of exceeding each recovery target. Methods to calculate collapse risk (Cornell, 1968) are 54 adapted to consider the probability of failure as the probability of the functional recovery time exceeding a pre-defined recovery target. In this study, we consider five recovery targets ranging from two weeks to one year. The targets selected are intended only to determine the recovery performance that is achievable with current design provisions and do not represent the functional recovery time objectives in the upcoming 2026 NEHRP provisions. The risk-based assessment is performed by integrating the slope of the hazard curve, λIM(IM), at each of the 34 sites with a functional recovery time fragility that provides the probability of exceeding a recovery time target given an intensity measure, P(TFR>TTarget |IM). The annual risk of the functional recovery exceeding a functional recovery target, λTFR>TTarget, is outlined in Equation 3.1. λTFR>TTarget=� P(TFR > TTarget|IM) |dλIM(IM)|∞0 (3.1) The functional recovery time fragilities are developed for each site and recovery target by fitting a lognormal CDF to the probability that the recovery time will exceed a given target at each intensity level at which a recovery time assessment was performed. The Probit link function was used to fit the fragility functions, using scripts developed by Baker (2015). Finally, the 50-year risk of exceeding each recovery target was calculated to compare the uniformity of risk across the sites when current risk-targeting methods are used. 3.3.5 Safety-Critical Structural Damage and Nonstructural Damage In addition to functional recovery time, we follow a similar process for two additional parameters. First, for all intensity levels, we evaluate the probability of exceeding the third damage state (DS3) for partitions anywhere in the building to gain insights into the risk of severe nonstructural 55 component damage that impedes function. We aggregate damage to partitions at the story-level and use this as a flag over the height of the building to provide a building-level metric. This measure only provides insights into drift-sensitive components. Future work should also consider acceleration-sensitive components. Second, we consider red tag probability as a measure of safety-critical structural damage (i.e., damage must be addressed, through temporary or full repair, before the structure can safely be reoccupied). In this study, we consider the occurrence of red tags due to structural damage only using the Cook et al. (2021) methodology which was adopted by the ATC-138 project (ATC, 2021b). Structural damage is assessed on every floor and, if any story is deemed unsafe, a red tag is assigned as a building-level metric. To evaluate the risk of incurring severe partition damage or red tags, we follow the same procedure by developing partition damage and red tag fragilities. Each fragility is integrated with the hazard curve at each site to find the 50-year partition damage and red tag risk. Disaggregation by spectral acceleration is also performed to identify the return period of the ground motion that has the largest contribution to the risk of each consequence (i.e., exceeding different recovery targets, incurring severe partition damage or red tags). 3.4 Functional Recovery Risk The fragility functions seen in Figure 3.1 describe the probability of exceeding each target recovery time as a function of spectral acceleration, as well as the hazard curve at the Los Angeles, CA, site (34.05, -118.25), which are integrated to calculate the 50-year risk of exceeding each recovery target. As can be seen in Figure 3.1, fragilities overlap for the two-week and the one-month target because the probability of exceeding both targets is very similar as a result of impeding factor delays resulting in recovery times that exceed both targets. Next, hazard data for all sites was available from return periods ranging from 14 to 4975 years and a fourth-order polynomial was 56 used to fit a hazard curve over these bounds (i.e., the hazard curve was not extrapolated). While the fragility functions were fit through a spectral acceleration at the first mode period of 0g, the integration from Equation 3.4 was conducted only over the bounds of the hazard data. Neglecting the low-intensity end of the hazard curve has little impact on most sites; however, for high-seismicity sites like San Jose, it may lead to an underestimation of the 50-year risk. Unlike the calculation of collapse risk, functional recovery time fragilities are often non-zero at return periods under 100 years. For example, in this study, the probability of exceeding a 2-week target is 27% at the 14-year return period intensity level for the San Jose site. This range of intensities also corresponds to the steepest portion of the hazard curve, which makes the calculations very sensitive to functional recovery time estimates in this range. This sensitivity points to the need to explore truncating the lower tails of component fragilities because observations of damage at extremely low levels of shaking have been rare. Figure 3.1 Hazard curve and fragility functions for the probability of exceeding various functional recovery time targets as a function of the spectral acceleration at the first mode period (SA(T1)) Employing the same methodology, the 50-year probability of the functional recovery time exceeding each recovery target for the 34 cities is summarized in Table 3.2. Results align with 57 work presented in Chapter 2 (i.e., Blowes et al., 2023) that considered the functional recovery risk for a suite of reinforced concrete shear wall buildings located in Seattle, WA. For the 8-story model from Blowes et al. (2023), the risk of exceeding one month was approximately 45% and, as shown in Table 3.1, it is 51% in this study. Similarly, the risk of exceeding one year was approximately 8% and, in this study, it is 11%. Efforts were also made to compare results and trends observed in Chapter 2 using a high-fidelity model and good agreement was found between the two frameworks. A detailed comparative study between the two frameworks, that employs the same analysis model, identical components, and impeding factor delay assumptions, is beyond the scope of this thesis. From Table 3.2, the results highlight that the risk of exceeding short recovery targets is high when minimum design provisions are used. Averaging across all 34 cities, the 50-year probability of exceeding the 1-month target is approximately 50% and the 1-year target is approximately 12%. The 50-year risk of the functional recovery time exceeding 2 weeks can be as high as 90% for high hazard cities (e.g., San Jose and San Bernardino). Comparing across cities, we see also see that the risk of exceeding short recovery targets varies considerably. By contrast, the risk of exceeding longer recovery targets varies less in absolute value, but still remains highly variable. For example, the 50-year risk of exceeding the recovery target of one year range from under 1% for sites with low seismicity to approximately 25%, with the highest risk calculated at sites that are deterministically capped (e.g., Oakland and San Jose). In looking at these results, there are two effects that should be highlighted. First, many of the cities with exceptionally high functional recovery risk have also been identified by other researchers as having much higher collapse risk due to the implementation of the deterministic cap in ASCE 7-16 (Stewart et al., 2020). Stewart et al. (2020) showed that the collapse risk in San Jose is approximate 3%, 3 times higher than the 1% risk target, and that cities along the San Andreas 58 Fault can have collapse probabilities as high as 5 to 9.45%, which is nearly 10 times the risk target. Second, the results do not consider any nonstructural design improvements, such as increasing component design forces or qualifying equipment Table 3.2 50-year probability of exceeding various recovery targets across the 34 sites in the United States. 50-Year Probability of Exceeding Recovery Target City 2 weeks 1 month 4 months 6 months 1 year Los Angeles 66% 66% 55% 43% 14% Century City 72% 72% 62% 51% 17% Northridge 82% 82% 73% 61% 22% Long Beach 69% 69% 57% 45% 14% Irvine 61% 61% 48% 37% 11% Riverside 82% 82% 74% 63% 24% San Bernardino 85% 85% 77% 67% 24% San Luis Obispo 36% 36% 28% 21% 6% San Diego 39% 39% 31% 24% 7% Santa Barbara 42% 42% 32% 24% 7% Ventura 52% 52% 40% 30% 9% Oakland 81% 81% 73% 62% 24% Concord 73% 73% 59% 47% 17% Monterey 53% 53% 41% 31% 9% Sacramento 76% 76% 66% 56% 19% San Francisco 68% 68% 57% 46% 16% San Mateo 77% 77% 66% 52% 17% San Jose 89% 89% 82% 72% 29% Santa Cruz 73% 73% 61% 48% 16% Vallejo 74% 74% 62% 51% 19% Santa Rosa 68% 68% 57% 46% 16% Seattle 51% 51% 41% 33% 11% Tacoma 59% 59% 50% 41% 14% Everett 51% 51% 42% 33% 11% Portland 37% 37% 29% 23% 7% Salt Lake City 17% 17% 14% 12% 5% Boise 12% 12% 7% 5% 1% Reno 54% 54% 43% 33% 11% Las Vegas 31% 31% 24% 19% 6% St. Louis 11% 11% 9% 7% 2% Memphis 14% 14% 12% 10% 4% Charleston 18% 18% 16% 15% 7% Chicago 2% 2% 1% 1% 0% New York 7% 7% 5% 3% 1% 59 In Chapter 2, the risk of the functional recovery time exceeding short recovery targets was driven by nonstructural damage. We would therefore expect that improvements to these components could dramatically reduce these results. Confirming this hypothesis, however, is beyond the scope of this study. The variability observed, particularly for short targets, does indicate that existing trends for collapse are perhaps exacerbated when considering recovery performance. The results also indicate that separate efforts to perform risk-targeting for functional recovery are necessary. 3.5 Identifying Drivers of Functional Recovery Risk Figure 3.2 provides the disaggregation by spectral acceleration of the risk of exceeding each functional recovery target for the Los Angeles site. The plot is normalized to help identify the return periods that drive the risk of exceeding each target. The disaggregation exercise illustrates that the risk of exceeding short recovery targets is governed by frequent earthquakes (i.e., 72-year return period and lower) for this Los Angeles site. The results at the Los Angeles site also show a greater dominance of lower return periods than was found in Chapter 2. This discrepancy may be due to the difference in seismicity (i.e., Seattle vs. Los Angeles), components considered in the models, or it may be due to underlying assumptions in the different functional recovery time assessment frameworks used for each study. Recovery time disaggregation plots for all 34 cities are shown in Appendix B1. Similar to with collapse performance, there is considerable variability in the return period that drives the risk of exceeding the recovery targets. At high hazard sites, the risk of the functional recovery time exceeding targets of one year or less is dominated by return periods under 100 years. In general, we see a high contribution to risk from low-intensity events because the buildings have not been designed for recovery. Nonstructural components such as elevators and mechanical equipment are 60 damaged in much lower levels of shaking than structural components and therefore can hinder functional recovery in these more frequent earthquakes. We also see that the return periods that drive the risk are lower for high seismicity sites than for low seismicity sites because the spectral accelerations associated with these more frequent earthquakes are higher. These results reinforce the suggestion that preventing the types of damage incurred in frequent earthquakes would also be very effective in reducing the high risk of exceeding recovery targets under one year. Figure 3.2 Disaggregation by SA(T1) of the risk of exceeding functional recovery time (TFR) targets for a residential 8-story RCSW archetype building in Los Angeles, CA. 3.6 Partition Damage and Safety-Critical Structural Damage The risk of incurring partition damage that impedes function (Damage State 3, DS3, or worse in FEMA P-58), which is used here to provide insight into severe nonstructural damage, is explored next. The risk of incurring partition damage ranges from under 1% to 28%, as summarized in Table 3.3. We see that partitions are very likely to impede function in very high seismicity sites. There has been no effort to date to perform risk-targeting specifically for nonstructural components which also results in high variation in the results. 61 Table 3.3 50-year probability of incurring severe damage to partitions and red tags across the 34 sites in the United States. City 50-Year Probability of Partition Damage (DS ≥ DS3) 50-Year Probability of Red Tag Los Angeles 8% 1% Century City 9% 1% Northridge 15% 2% Long Beach 9% 1% Irvine 8% 1% Riverside 10% 1% San Bernardino 24% 6% San Luis Obispo 1% ~0% San Diego 3% 0.2% Santa Barbara 6% 1% Ventura 6% 1% Oakland 16% 3% Concord 24% 6% Monterey 1% ~0% Sacramento 5% ~0% San Francisco 9% 1% San Mateo 20% 4% San Jose 28% 5% Santa Cruz 15% 3% Vallejo 22% 5% Santa Rosa 11% 2% Seattle 4% 0.2% Tacoma 4% 0.2% Everett 3% 0.2% Portland 4% 0.3% Salt Lake City 1% ~0% Boise 1% ~0% Reno 5% 0.6% Las Vegas 1% ~0% St. Louis ~0% ~0% Memphis 1% ~0% Charleston 1% ~0% Chicago ~0% ~0% New York ~0% ~0% 62 An example fragility is shown in Figure 3.3a. The disaggregation of the risk of severe partition damage by spectral acceleration for the Los Angeles site, shown in Figure 3.3b, indicates that the risk is driven by earthquakes with return periods around 475-years. The risk of incurring damage to partitions alone is lower than the risk of exceeding short recovery targets. This trend is observed because when the functional recovery time is considered, the combined reliability of all components is evaluated. The recovery time risk therefore relies on the performance of many other acceleration-sensitive nonstructural components, some of which may have a higher likelihood of impeding function than partitions. This finding also indicates that to achieve a given functional recovery reliability target, higher individual component reliability may be necessary. Again, plots for all cities are provided in Appendix B2. From the results, we see that there is variability in the return period that drives the risk of this type of damage. For low-seismicity sites, the risk is low and is driven by rare events. For high-seismicity sites, return periods under 475 years drive the risk of this type of damage. (a) (b) Figure 3.3 (a) Hazard curve and fragility functions for the probability of nonstructural component damage as a function of the spectral acceleration at the first mode period (SA(T1)) and (b) disaggregation by SA(T1) of nonstructural component damage for a site in Los Angeles, CA. 63 Finally, we consider the risk of incurring severe structural damage by studying the 50-year risk of red tags to provide insight into structural damage that poses a safety risk to tenants. Figure 3.4a shows the fragility developed to represent the probability of red tags as a function of spectral acceleration of the first mode period. From Table 3.3, the 50-year risk of incurring red tags is low, ranging from under 1% to approximately 3% across the 34 sites considered. There are notable exceptions where the 50-year red-tag probability exceeds 5%, primarily in cities where the influence of the deterministic cap is high (e.g., San Bernardino, San Jose). While a red tag does not indicate that a building will be irreparable, it does indicate more extensive structural damage, and the triggering of lengthy impeding factor delays which increases functional recovery times. The disaggregation of the example site in Los Angeles, shown in Figure 3.4b, indicates that the risk of red tags is governed by extremely rare earthquakes with return periods greater than 2475 years. From the results in Appendix B3, however, we can see that at the deterministically capped sites, the risk of red tags is driven by significantly lower return periods, closer to the 475-year return period. (a) (b) Figure 3.4 (a) Hazard curve and fragility functions for the probability of safety-critical structural damage as a function of the spectral acceleration at the first mode period (SA(T1)) and (b) disaggregation by SA(T1) of safety-critical structural damage for a site in Los Angeles, CA. 64 3.7 Conclusions, Limitations, and Future Work In this study, a risk-based assessment was performed to evaluate the 50-year probability of the functional recovery time exceeding targets ranging from two-weeks to one year for 34 cities across the United States. Findings from this study indicate that the 50-year risk of exceeding short recovery targets is both high, with an average of 52% across all 34 cities, and nonuniform across the 34 cities analyzed. The 50-year risk of the functional recovery time exceeding one year is approximately 12% across all 34 cities, which is lower, but the risk is still variable. We also see that the risk of incurring damage to partitions and red tags also varies considerably between sites. The results were disaggregated by spectral acceleration to determine the return period that drives risk for a site with high seismicity. In general, the risk of exceeding recovery targets under one year is dominated by frequent earthquakes with return periods under 100 years for high-seismicity sites. There is, however, variability in the return periods that drive the risk from site to site. The disaggregation exercise also highlighted that the risk of severe damage to partitions is dominated by moderately frequent earthquakes in high seismicity locations. By contrast, the risk of red tags is driven by very rare earthquakes. Here, again, there is variability from site to site, in particular with deterministically capped sites. While this disaggregation exercise is useful for identifying drivers of risk, the implementation of modest design interventions (e.g., qualifying equipment) will result in a shift in the governing return periods. As we address component damage at low intensity levels, we will see a later onset of damage and disaggregation calculations will show larger return periods as governing the recovery risk. The results should be used to identify vulnerabilities and underlying damage mechanisms that are inadequately addressed in current design standards, as opposed to return periods used for design checks. 65 As discussed, the results of this study are extremely sensitive to damage at low shaking intensities. This finding highlights the need to consider truncating component fragilities to reflect the low likelihood of damage at very low intensity levels. Simplified structural analysis methods were used to be able to provide high-level insights into risk and damage mechanisms. Therefore, the data presented should be used primarily to identify vulnerabilities and relative differences between locations and caution should be used when considering the values or percentages presented. This study ultimately illustrates two key findings. First, designing buildings using current life-safety design provisions does not ensure a low risk of exceeding functional recovery targets ranging from two weeks to one year. In particular, damage in frequent earthquakes drives the risk for high seismicity sites. Second, current risk-targeting methods for collapse risk do not ensure uniform risk for functional recovery when buildings are designed for life-safety provisions. Overall, these findings highlight the importance of ongoing BSSC efforts to develop recovery-based design provisions and perform risk-targeting for recovery. This work also provides a first step towards identifying parameters such as the return period and underlying damage mechanisms that should be considered for inclusion in these provisions. 3.8 Application for Canadian Building Code Development While design requirements are different between Canada and the United States, several findings are relevant to building code development in Canada. The new Article 4.1.8.23 design provisions target elastic structural performance at the 5% and 10% in 50-year intensity levels (975- and 475-year return periods) for certain types of buildings (NRCC, 2020). The findings from this study support the approach of designing to limit safety-critical structural damage over this range of intensities to minimize the risk of very long recovery times at higher intensities. There are also 66 new requirements that the anchorage for nonstructural components must also remain elastic at these intensity levels. The results of this study indicate that a high level of reliability across all nonstructural components, not only anchorage, in frequent earthquakes may be necessary to ensure a low 50-year risk of exceeding recovery times under one year. These findings indicate a future area of research for recovery-based code development efforts in Canada. Finally, this study was conducted for a residential building and results showed a high probability that occupants will not be able to rapidly recover following a 475-year or larger event in many high seismicity cities in the United States. These new Canadian provisions currently do not consider normal occupancies buildings under 30 meters, yet this study suggests there are potential low-impact interventions (i.e., qualifying equipment, improving anchorage and bracing for nonstructural components) that could improve recovery in this category of buildings. There has also been discussion in recent years about potentially moving towards a risk-targeted ground motion for life-safety design in Canada (Allen et al., 2015). If risk-targeting were to be adopted in Canada, findings from this study suggest that separate efforts will likely be required to ensure somewhat uniform functional recovery risk across seismic regions in Canada. 67 Chapter 4: Limiting Safety-Critical Structural Damage in Recovery-Based Seismic Design Provisions This chapter is based on the following reference: Blowes, K., Molina Hutt, C., Zimmerman, R., Cook, D., Almeter, E., and Haselton, C., 2025a. Limiting safety-critical structural damage in recovery-based seismic design provisions. Earthquake Spectra (In Review). 4.1 Introduction The Functional Recovery Task Committee (FRTC) of the Building Seismic Safety Council (BSSC) in the United States has been tasked with the development of new design provisions for functional recovery to be included in the upcoming 2026 National Hazards Earthquake Reduction Program (NEHRP) recommendations for updates to ASCE 7-28 (BSSC, 2023). For the first time in the United States, these new provisions will provide practicing engineers with prescriptive provisions to ensure buildings can be used for their basic intended function within acceptable target recovery times. To inform design provisions, there is a need to develop a consistent methodology to evaluate the functional recovery performance of a structure and the efficacy of strength and stiffness design interventions. This study builds on recent advances in building-level functional recovery modeling using state-of-the-art assessment methods and simplified nonlinear modeling techniques to systematically assess response modification coefficients and drift limits for commonly used conventional lateral force-resisting systems. 68 In past earthquakes, a bifurcation in recovery trajectories has been observed – occupants of buildings with low levels of structural damage often recover quickly, while occupants of buildings with moderate to severe structural damage tend to experience lengthy, forced displacement. This trend has been observed in the United States in the 1994 Northridge and 1989 Loma Prieta earthquakes (Comerio and Blecher, 2010), where lengthy recovery times were observed for residential buildings that were red tagged. Following the 2010-2011 Canterbury earthquake sequence in New Zealand, commercial and multi-unit residential buildings assigned unsafe placards were frequently demolished due to uncertainty in post-earthquake residual capacity (Marquis et al., 2017). While Paul et al. (2025) highlight the impact of social vulnerability in predicting occupant displacement, their study shows that property damage remains a key driver of occupant displacement across a wide range of hazards in the United States. Although significant improvements to structural design provisions for life-safety have been adopted since these earthquakes, as we move to recovery-based design provisions, there is a need to address post-earthquake building safety and recovery of building function. In this study, we propose using the probability of safety-critical structural damage as a measure to evaluate the efficacy of new design requirements on recovery performance. Safety-critical structural damage is damage that must be repaired for occupants to be able to return safely to a building. In limiting the probability of safety-critical structural damage, we recognize post-earthquake safety as a requirement for recovery. That is, we aim to ensure that occupants not only will be safe during an earthquake (i.e., life safety objective), but that occupants will also be able to safely and rapidly return following an earthquake (i.e., recovery objective). To support building code development efforts, this study outlines proposed design requirements at a new risk-targeted Functional Recovery Earthquake, FRER, that aim to minimize 69 safety-critical damage. We then evaluate the probability of safety-critical structural damage at the FRER for a wide range of lateral force-resisting systems designed to have different combinations of strength, achieved by varying the design response modification coefficients, and stiffness, achieved by varying allowable design drift limits. The results are used to identify new functional recovery design parameters, including the functional recovery response modification coefficient, Rfr, and allowable drift limit, Δafr. Because the methodology employed is simplified in nature, our intent is to address what is expected to be a temporary gap in research, with the understanding that ongoing experimental and high-fidelity analytical studies will support the development of future generations of recovery-based design provisions. 4.2 Literature Review Recent studies have shown that buildings designed using life-safety provisions (e.g., ASCE 7-16) are likely to experience both structural and nonstructural damage that may lead to lengthy recovery times. At the design earthquake (DE) and similar 475-year intensity level, studies employing various frameworks have all predicted median functional recovery times from five months to over one year for a wide range of building types, locations, occupancies, and heights (Cook et al., 2024; Molina Hutt et al., 2022a, 2022b; Terzic et al., 2021). Blowes et al. (2023) performed a risk-based assessment of a suite of RCSW archetypes ranging from eight- to 24-stories and found an approximately 40% probability in 50 years of the functional recovery time exceeding 4 months. Many of these studies demonstrate that nonstructural component damage dominates recovery issues at lower intensities; and when severe structural damage occurs in higher intensity events, recovery times often exceed one year (Blowes et al., 2023; Cook et al., 2024; Terzic and Kolozvari, 2022). 70 The studies above highlight that recovery times will be long, even when designed to the same minimum standards for life safety. To improve performance, some studies have suggested using stricter drift limits or limits of deformation-controlled actions. As part of the ATC-145 project (ATC, 2021a), Murray et al. (2022) found that reinforced concrete moment frame buildings with drifts less than 2% in a maximum considered earthquake event did not see increased drift demands in subsequent events. Adding to the ATC-145 project, Opabola et al. (2023) sought to address a critical gap in evaluating the residual capacity of buildings following an earthquake by relating reinforced concrete shear wall, beam, and column damage to the loss of lateral strength of the system. Opabola and Elwood (2024) evaluated the onset of damage that would require safety-critical repair in reinforced concrete moment frames for models with various design drift limits and demonstrated the improvement to reoccupancy time. Cook et al. (2024) also studied reinforced concrete shear wall and moment frame buildings using ATC-138 and similarly found that reducing the design drift limit from 2% to 1.5% ensured a low probability of red tags at the 475-year intensity level. These studies suggest that stricter drift limits can enhance the recovery of certain lateral force-resisting systems. 4.3 Evaluating Safety-Critical Structural Damage There is a growing interest in the use of functional recovery time as the primary metric for researchers and practitioners to communicate recovery risk and to link building performance to community resilience. The BSSC has outlined both a risk and reliability target for functional recovery time (BSSC, 2024). In terms of the risk target, the provisions aim for the 50-year probability that a given functional recovery time target will be exceeded to be under 10%. The FRER ground motion used for the design checks is developed through a separate risk-targeting effort beyond that performed for life-safety that now uses this 10% risk target. This decision 71 followed a consensus-based process and is consistent with the findings from Chapter 3 that suggest that a separate risk-targeting effort is needed for functional recovery due to differences in the underlying drivers of risk (i.e., contribution of nonstructural damage in frequent earthquakes). The provisions also aim to meet a recovery time with a 25% probability of failure at the FRER. To develop functional recovery provisions, we propose separating the design interventions required to limit structural damage (e.g., increased strength and reduced drift limits) versus those required to limit nonstructural damage (e.g., improved detailing for deformation compatibility and larger anchorage design forces). The reasons for this proposal are twofold. First, when we separate the impact of structural damage on functional recovery time, we can target a specific level structural performance across systems, ensuring uniform performance across lateral force-resisting systems. Similarly, employing this strategy promotes consistent nonstructural performance across lateral force-resisting systems. Second, while structural design interventions, such as stricter drift limits, may also be useful for limiting damage to drift-sensitive nonstructural components, enhancements in detailing requirements and design forces that specifically target nonstructural components should be explored separately. An evaluation of nonstructural design requirements is provided in Chapter 5. In the calculation of functional recovery time, significant interdependencies exist between structural and nonstructural systems, both in terms of repair sequencing (e.g., certain nonstructural repairs may not take place before structural repairs) and in terms of demands (e.g., increased structural system stiffness increases peak floor acceleration demands on acceleration-sensitive nonstructural components). These interdependencies can make it difficult to clearly separate structural and nonstructural design interventions. To facilitate the development of structural 72 seismic design criteria that enables prompt post-earthquake recovery, we propose using the probability of safety-critical structural damage as a performance metric. Safety-critical structural damage is defined herein as structural damage that must be repaired before a building can be safely reoccupied. Reoccupancy is considered a recovery state prior to functional recovery which allows safe re-entry, but where critical systems essential to the building’s basic intended function may not be operating (Almufti and Willford, 2013; Cook et al., 2022). Opabola and Elwood (2024) established a damage-control limit state, which if not exceeded, ensures a low probability of significant loss of capacity in aftershock events and limits the requirement of safety-critical repair before reoccupancy. Building on this concept, we aim for a similar performance objective. In developing recommendations for design provisions that aim to ensure post-earthquake reoccupancy at the functional level earthquake, we target a low probability of safety-critical structural damage. We build on past efforts to analytically predict the occurrence of unsafe placards that make use of the FEMA P-58 methodology (FEMA, 2018b). The FEMA P-58 methodology uses Monte Carlo simulation to implement the performance-based earthquake engineering framework (Cornell and Krawinkler, 2000; Moehle and Deierlein, 2004). Fragility functions for each component are sampled to determine component damage throughout the structure, and consequence functions relate damage to expected direct financial losses and repair time. In addition to these metrics, the FEMA P-58 methodology also includes a virtual inspection process to predict unsafe placards (FEMA, 2018b). The algorithm employed, introduced by Mitrani-Reiser (2007), aims to simulate the ATC-20 (ATC, 2005) inspection process by propagating component damage, excessive residual drifts, and collapse through a fault-tree to determine the occurrence of an unsafe placard. The process considers moderate to severe structural damage, as well as severe nonstructural 73 damage to a limited number of components (e.g., cladding, ceilings). While the actual inspection process is limited by what the inspector can see, the virtual inspection process has perfect knowledge of the building damage. To benchmark these methods, Cook et al. (2021) hindcasted red tags assigned in the 1994 Northridge earthquake, simulating regional damage to over 2.6 million structures. Red tags are a subset of unsafe placards that indicate a building is unsafe to re-enter. Cook et al. (2021) found that the FEMA P-58 methodology overestimated the occurrence of red tags in the region and proposed updates to the fault trees employed in the FEMA P-58 methodology to assign red tags. To address this overestimation, the fault trees were updated by evaluating damage on each story instead of on a component basis. The methodology now considers damage to structural components only and neglects nonstructural components, such as cladding and ceilings. Safety-based concerns from nonstructural components are now considered in a separate reoccupancy check within the functional recovery time estimation methodology developed by Cook et al. (2022), which has been adopted by the ATC-138 project team (ATC, 2021). To calculate the probability of safety-critical damage, we employ the red tag algorithm within the ATC-138 methodology. In this study, we focus on predictions of safety-critical structural damage probability directly, reflecting the severity of component damage, updated damage thresholds, and the distribution of damaged components throughout the building. We aim to predict the occurrence of safety-critical damage in the structure, not to replicate the decision of a field evaluator to assign an unsafe placard in a real post-earthquake setting. Furthermore, in this study, our focus is exclusively on damage to the structure, whereas in a true post-earthquake field inspection, a more holistic building safety evaluation is carried out, including consideration of other hazards (e.g., hazardous materials, nonstructural falling hazards, blocked fire exits, etc.). 74 The fault tree algorithm in ATC-138 has three main branches that are evaluated to determine the occurrence of safety-critical damage in a building. First, for every Monte Carlo realization of the engineering demand parameters (EDPs), the algorithm determines whether partial or complete collapse has occurred using collapse fragilities for each system. Next, the residual drift is used to sample a building-level irreparable damage fragility. This limit determines whether structural system-wide irreparable damage has occurred for each realization due to excessive permanent deformations. Finally, the structural components in each story are surveyed to determine whether the structural system is unsafe. If safety-critical structural damage occurs at any story, the building is deemed unsafe to reoccupy. The fault tree used for the analysis is shown in Figure 4.1. Figure 4.1 Fault tree used to determine whether the building has safety-critical structural damage (modified after Cook et al., 2021). Structural component damage states are mapped to a safety class (SC) following Cook et al. (2021). Safety Class 0 (SC0) includes slight damage that does not impact safety. Safety Class 1 (SC1) includes moderate damage that does not cause loss of lateral load carrying capacity. Safety 75 Class 2 (SC2) includes severe damage that results in the loss of lateral load carrying capacity. Finally, Safety Class 3 (SC3) includes severe damage that results in both the loss of lateral and gravity load carrying capacity of the component. Safety class assignments may vary for a given component if, for example, the component is load-bearing or not (e.g., SC2 corresponds to Damage State, DS, 2 in load bearing shear wall components, but to DS3 in building frame shear wall components). For every story, each independent type of structural component is then assessed using fault trees. A story is determined to be unsafe if, for any independent structural component group, more than 10% of components have Safety Class 3 damage, more than 25% of components have Safety Class 2 damage, or more than 50% of components have Safety Class 1 damage. In this study, we evaluate only the probability of safety-critical damage in structural components, which allows us to remove nonstructural components from our models. If any of these three branches (collapse, excessive residual drift, or structural component damage) is triggered, safety-critical structural damage is assigned to that realization. The probability of safety-critical structural damage is then computed based on a count of realizations. The ATC-138 methodology assumes that reoccupancy cannot be achieved if there is safety-critical structural damage (ATC, 2021b; Cook et al., 2022). Therefore, the probability of not achieving immediate reoccupancy due to structural damage (i.e., reoccupancy time greater than zero days) is equal to the probability of safety-critical structural damage. The methods proposed rely on the use of FEMA P-58 fragilities, which do not reflect improvements in detailing that have been prescribed in recent code development cycles. Fragilities for some shear wall components, for example, do not reflect the latest level of detailing required in ACI 318-19 (ACI, 2019). The framework outlined, however, can be applied as new fragilities become available. Furthermore, the use of FEMA P-58 also does not allow for the explicit 76 consideration of critical force-controlled failure modes, such as shear in concrete walls or axial compression in buckling restrained braced frame columns. An underlying assumption of this work is that all critical force-controlled design requirements for life-safety are satisfied by means of capacity design principles. 4.4 Functional Recovery Earthquake and Performance Targets Current life-safety structural design provisions employ a reliability target of a 10% probability of collapse at the risk-targeted Maximum Considered Earthquake (MCER) by employing, among other strategies, minimum strength and stiffness requirements imposed using a combination of response modification coefficients, R, and allowable drift limits, Δa. In this study, we parallel current force-based procedures using safety-critical structural damage probability — in place of collapse probability — at the Functional Recovery Earthquake (FRER), with the goal of limiting structural damage that prevents reoccupancy. Similar to MCER, FRER, is a risk-targeted design response acceleration spectrum that specifies the intensity of ground motion needed for the design of buildings to meet functional recovery performance objectives, balancing target risk objectives with seismic hazard. The current FRER proposed by the BSSC, and included in the 2026 NEHRP draft provisions update recommendations, has a reliability target of a 25% probability of exceeding various recovery time targets at the FRER (FEMA, 2024). All design checks are performed at the FRER (i.e., the 2/3 factor on MCER used for life-safety design does not apply). In this study, we target a probability of safety-critical structural damage of 10% at the FRER to limit the recovery time associated with structural damage for this shaking intensity. The 10% safety-critical structural damage at the FRER parallels the 10% collapse target at MCER while reflecting the lower consequence of structural damage that leads to loss of occupancy versus collapse. 77 The FRER ground motion is approximately 60% to 75% of the design level earthquake (DE) at most sites and the return period is approximately 350 to 400 years for low-seismicity sites and 400 to 450 years for high seismicity sites. The return periods associated with the FRER selected by the BSSC are higher than those identified as driving functional recovery risk in Chapters 2 and 3 (i.e., Blowes et al., 2023, 2024). While the decision made by the BSSC may initially appear to contradict findings from Chapters 2 and 3, there are several points worth clarifying. First, the goal of Chapter 2 and 3 was to identify drivers of functional recovery risk, both in terms of return periods and underlying damage mechanisms. The focus was on performance with current design standards – not with functional recovery provisions. The return periods that were shown to drive the risk will shift to higher return periods with the implementation of provisions that target the vulnerabilities identified (e.g., qualification of equipment to reduce nonstructural damage in frequent events). Therefore, the selection of a larger ground motion for functional recovery design requirements allows engineers to ensure better performance in larger earthquakes. Second, there are two approaches that can be followed to decide the ground motion based on findings from Chapter 2 and 3. One approach would be to develop two design checks: one at the 72- or 100-year return period focused on nonstructural component performance and one at 2475-year return period focused on safety-critical structural damage. Another approach, however, is to select a single return period and develop design checks that ensure both damage mechanisms identified in Chapters 2 and 3 are addressed. In this case, the single ground motion must be large enough to expect structural damage at high hazard sites, which allows us to evaluate the efficacy of varying structural design parameters on safety-critical structural damage while reflecting the lower consequence when compared to collapse. At the same time, this ground motion must be small enough that nonstructural components will be designable but pushed to have better performance 78 in frequent earthquakes. The latter approach was adopted by the BSSC. Therefore, while the FRER does not directly reflect the return periods identified in Chapters 2 and 3, the underlying damage mechanisms that drive both short and long recovery issues are captured by the ground motion selected by the BSSC. This Chapter and Chapter 5 adopt the FRER and develop design recommendations that aim to target the structural and nonstructural vulnerabilities previously discussed. It is beyond the scope of this dissertation, however, to explicitly verify performance with the new provisions across intensities. This verification remains an important area for future research. As we move towards a qualification procedure for functional recovery performance, there is a need to define a standard hazard level that can be used to evaluate the performance of a wide range of systems. The FEMA P-695 procedure (FEMA, 2009b) defined an MCE-level Seismic Design Category Dmax spectrum (the maximum mapped spectral acceleration for Seismic Design Category D) to qualify systems for life-safety. The Dmax spectrum is used to demonstrate a 10% probability of collapse at MCE. The FEMA P-695 Dmax criteria is consistent with ASCE 7-05 (FEMA, 2009b) and there are ongoing discussions about updating the Dmax spectrum (ATC, 2024). To address the need to use more recent hazard data and measures such as the removal of the deterministic cap for the FRER, we define a new Dmax,FRE and a new Dmax,DE spectrum that reflect the FRE and DE level ground motions in ASCE 7-22 (ASCE/SEI, 2022). The following discussion on the development of the Dmax,FRE and Dmax,DE spectra is provided for context for this dissertation; however, I note that the calculations for developing both spectra were performed by Dustin Cook, a co-author on the journal article which is the foundation for this Chapter. To develop the new spectra, we use the Dmax threshold from ASCE 7-22 (ASCE/SEI, 2022) which is an S1, the mapped MCE spectral response acceleration parameter, of 79 0.75. 21 high population sites in Table C22-2 of ASCE 7-22 (ASCE/SEI, 2022) are then filtered to only consider sites with an S1 within 10% of 0.75. The data for the design spectral response acceleration parameter at short periods, SDS, and at one second, SD1, from these sites are averaged at the design-level (DE) to give an SDS and SD1 values of 1.4g and 1.2g, respectively, which define a new design-level spectrum, Dmax,DE. The SDSfr and SD1fr from the FRER at each of these remaining sites (Los Angeles, Northridge, Long Beach, Oakland, and San Mateo) are also averaged to define the functional recovery spectrum, Dmax,FRE. The new functional recovery spectral response acceleration parameters at short periods, SDSfr, and at one second, SD1fr, are 1.15g and 0.70g respectively. For comparison, at a period of 2s, the Dmax,FRE is approximately 60% of the Dmax,DE spectrum. A comparison of the Dmax,DE and Dmax,FRE spectra is shown in Figure 4.2. Figure 4.2 Comparison of the Dmax,DE and Dmax,FRE spectra. 4.5 Functional Recovery Structural Design Requirements The structural design requirements introduced next are used to design and evaluate structures at the FRER. These new functional recovery design checks are intended to be conducted by engineers independently of the life-safety requirements, and the governing of the two designs shall apply. 80 The proposed requirements below are, therefore, a standalone set of design checks at FRER that target a specific performance and must be applied in parallel with, not in lieu of, a code-compliant life-safety design. We propose a new response modification coefficient for functional recovery, Rfr, to be used in lieu of the existing response modification coefficient, R, included in ASCE 7-22 (ASCE/SEI, 2022). Rfr is used where R occurs in design equations throughout ASCE 7-22, as illustrated in Equations 4.1 and 4.2 below: V= CsW (4.1) Cs= SafrRfr (4.2) where V is the design base shear, Cs is the seismic response coefficient, W is the seismic weight, and Safr is the functional recovery earthquake spectral acceleration at the first mode period of the structure. In this study, we use the spectral accelerations from the Dmax,FRE spectrum defined above. The minimum base shear from ASCE 7-22, which employs the lower bound for Cs, is maintained, as shown in Equation 4.3: Cs=0.044SDS ≥ 0.01 (4.3) where SDS is the design level earthquake spectral acceleration at short periods. The minimum base shear requirement rarely governs but provides a lower bound on the functional recovery design requirements that is consistent, but not more stringent, than life-safety requirements. Note that in Equations 4.1 through 4.3, the seismic importance factor, Ie, has been dropped compared to the corresponding equations in ASCE 7-22 (ASCE/SEI, 2022). In current life-safety design in ASCE 7-22, Ie reduces the response modification coefficient in the calculation of base shear (i.e., R/Ie). However, in current life-safety design in ASCE 7-22, the reduction is constant across all structural systems (i.e., R/1.5 for Risk Category IV structures regardless of structural 81 system type). In this study, we intentionally investigate the appropriate Rfr to achieve a target probability of safety-critical structural damage by structural system in lieu of attempting to develop a single reduction factor (e.g., Ie) for all systems. To do so, we study a range of possible Rfr values ranging from R, as currently codified in ASCE 7-22, down to 1.0 in increments of 1.0. Additionally, Ie is dropped from Equation 4.3 to represent the assumption of a minimum Risk Category II design. We propose a new drift limit for functional recovery, Δafr, to be used in lieu of the existing allowable drift limit, Δa, included in ASCE 7-22 (ASCE/SEI, 2022). Linear responses determined using the equivalent lateral force procedure or modal response spectrum analysis are amplified by a new functional recovery deflection amplification factor, Cdfr, which is set equal to Rfr. This assumption is made to be consistent with the FEMA P-695 methodology which assumes the deformation compatibility factor, Cd, is equal to R (FEMA, 2009b). We study a range of possible Δafr values ranging from a strict drift limit of 0.5% to the current ASCE 7-22 requirement of 2%, in 0.25% increments. Current drift limits in ASCE 7-22 vary by risk category (e.g., 2% for Risk Category II versus 1% for Risk Category IV) and are the same for most lateral force-resisting systems (ASCE/SEI, 2022). This study explores the possibility of employing different allowable drift limits for different lateral force-resisting systems to reflect differences in the onset of safety-critical structural damage across systems. This reasoning is similar to that provided for why a single Ie factor across all structural systems is not pursued. We simultaneously vary Rfr and Δafr, outputting the probability of safety-critical structural damage for each combination of these two parameters. The development of this design space allows for the evaluation of a range of plausible design interventions. 82 4.6 Scope of Study This study considers a range of concrete and steel special lateral force-resisting systems. We limited analyses to building heights that are permissible in Seismic Design Category D in ASCE 7-22 below 240ft. The lateral force-resisting systems and building heights considered are summarized in Table 4.1. Table 4.1 Lateral force-resisting systems and building heights evaluated. Lateral Force-Resisting System R Heights (Stories) 3 8 16 24 REINFORCED CONCRETE SHEAR WALL SYSTEMS Special RC shear walls (Shear-governed, Bearing) 5 X Special RC shear walls (Shear-governed, Frame) 6 X Special RC shear walls (Flexure-governed, Bearing) 5 X X X Special RC shear walls (Flexure-governed, Frame) 6 X X X RC ductile coupled walls (Flexure-governed, Bearing) 8 X X X RC ductile coupled walls (Flexure-governed, Frame) 8 X X X STEEL BRACED FRAME SYSTEMS Steel buckling-restrained braced frames (no backup frame) 8 X X X NP Steel buckling-restrained braced frames (backup frame) 8 X X X NP MOMENT-RESISTING FRAME SYSTEMS Steel special moment frames 8 X X X X Special RC moment frames 8 X X X X *NP = Not permitted in ASCE 7-22 (ASCE/SEI, 2022) In this study, we evaluate the performance of common conventional lateral force-resisting systems only. Simulated responses aim to reflect new functional recovery minimum requirements and common design and detailing decisions made in professional practice today. We do not explicitly address nonbuilding structures, except those which can be considered sufficiently similar to buildings. We also do not consider enhanced component-level detailing beyond that currently captured by FEMA P-58 fragilities, nor do we consider innovative repairability systems (e.g., replaceable fuses). The effect of increased structural system redundancy is excluded other than its effect within a performance group on exceeding the safety class thresholds for triggering safety-83 critical structural damage. Seismically isolated buildings and buildings with supplemental energy dissipation are also not considered in this study. These strategies, many of which are anticipated to improve functional recovery performance, are encouraged for future study. The study of conventional design procedures and structural systems is therefore deemed a necessary, but not necessarily sufficient, first step toward functional recovery design provisions. Since the vast majority of buildings in professional practice today are designed by prescriptive design procedures (i.e., using linear design with a response modification coefficient, R, and an allowable drift limit, Δa), we see a need for a similar design process for functional recovery (i.e., using linear design with a functional recovery response modification coefficient, Rfr, and a functional recovery allowable drift limit, Δafr). Without prescriptive provisions, it is unlikely that functional recovery design will be widely accessible and implementable on building projects. 4.7 Methodology Next, we outline the steps to generate simplified multi-degree of freedom (MDOF) models meeting combinations of strength and stiffness design requirements and to evaluate the probability of safety-critical structural damage. We repeat the methodology outlined in Figure 4.3 for all combinations of imposed design drift limits and response modification coefficients considered to generate a design space. 84 Figure 4.3 Methodology to develop a design space used to evaluate the probability of safety-critical structural damage associated with various allowable drift limits, Δafr, and functional recovery response modification coefficients, Rfr. Step 1: Define Model Parameters First, we define the lateral force-resisting system type, gravity system type, and building geometry, i.e., height and floor dimensions. Step 2: Simplified MDOF Models To generate representative structural response predictions for every design variation for a system type and building height, we employ the Structural Response Prediction Engine developed by HB-Risk (2025). This process to generate the MDOF models was peer-reviewed by as part of the ATC-138 project (ATC, 2021b). HB-Risk (2025) developed the Structural Response Prediction Engine (SRPE) to create simplified linear multi-degree of freedom models using methods proposed by Miranda (1999, 2000) and calculate story-level engineering demand parameters (e.g., story drift ratios, peak floor accelerations) using limited geometric and material information. The SRPE uses coefficients from Miranda (2000) for various lateral force 85 resisting systems to determine the shear and flexural response of each model. The SRPE was adapted to this study to reflect design requirements for functional recovery. For every model, the SPRE approximates the building fundamental period using ASCE 7-22 equations, which is then used to inform the initial stiffness of the system. Design base shear equations are used to inform the initial strength. Once the initial strength and stiffness are determined, the SRPE evaluates the linear response using the equivalent lateral force procedure for low-rise models (i.e., 3-story) and using modal response spectrum analysis for mid- and high-rise models. The linear response is amplified by the functional recovery deflection amplification factor, Cdfr, to check whether the linear response meets the assigned drift limit (i.e., 0.5% to 2%) or, for strength-controlled systems, a realistic drift ratio informed by high-fidelity analyses. For drift-controlled systems, the building stiffness is then increased until the drift limit assigned to the model is met and the first mode period is recalculated using the refined model characteristics. For strength-controlled systems, the compatibility of the strength and stiffness is checked prior to recalculating the first mode period. Finally, the expected overstrength from the lateral force-resisting system is added to the model. Further information can be found by referring to documentation on the Structural Response Prediction Engine in the SP3 software (HB-Risk, 2025) and in Cook et al. (2018). A summary of key design parameters and the fundamental period of vibration are included in Electronic Supplement S4.1 and S4.2, respectively, for every structural system and design variation considered in the analysis. Step 3: Predict Nonlinear Response After the linear MDOF model is determined to satisfy the design requirements in Step 2, the SRPE scales the elastic peak story drift ratios (SDRs) to a target roof displacement for the risk-targeted Functional Recovery Earthquake, FRER, response spectrum. The nonlinear building response is estimated by adjusting this elastic response to 86 account for nonlinear dynamic properties using a series of correction factors that map elastic-to-nonlinear response. The correction factors employed by HB-Risk (2025) are developed from a large database of results from various studies of archetype models (e.g., Haselton et al., 2011) analyzed using incremental dynamic analysis (IDA) (Vamvatsikos and Cornell, 2002) using FEMA P-695 ground motions (FEMA, 2009b). The IDA results provide responses for each building type included in this study over a large range of intensity levels and for building responses ranging from elastic to highly inelastic. While the SRPE is calibrated using models with design parameters for life-safety, responses in the database capture most behaviour studied in this work due to the difference in design levels. One key area where we extrapolate beyond the database data is with heights beyond 15 stories and with extremely stiff design variations. The estimated nonlinear structural responses establish the median structural response for the FEMA P-58 simulated demand response generation process (FEMA P-58 Appendix G). Responses are sampled from a joint lognormal distribution to establish realizations of structural response that account for ground motion, modeling, and material uncertainty, as well as correlations in peak story response, as part of the probabilistic Monte Carlo framework. Generated SDR and peak floor acceleration (PFA) plots are provided in Appendix C for all models. This overall process for generating structural responses was also peer-reviewed as part of the ATC-138 project (ATC, 2021b). Step 4: Component Damage Assessment Structural components are populated and damage is assessed using the FEMA P-58 methodology (FEMA, 2018b), as implemented in SP3 (HB-Risk, 2025). Both lateral and gravity system components are included in the building performance models. Nonstructural components are not considered. Floor plate dimensions of 100ft by 100ft were employed to determine component quantities. The number of components, component quantities, and component areas are increased to reflect increased quantity requirements for models 87 with increased height. Standard FEMA P-58 Volume 2 fragilities (FEMA, 2018b) are sampled to estimate the component damage. For buckling-restrained brace frames, new fragilities included in ATC-138 (ATC, 2021) are used. Story drift ratio (SDR) was used to estimate damage in most components. For the shear walls, however, we used the chord rotation to predict the damage to shear wall elements. Using the chord rotation removes the rigid body rotation so only the damageable wall drift is considered when sampling the fragilities. With this method, damage estimates are concentrated at the base where we expect hinging to occur. Similarly, coupling beam rotations are used to estimate damage to coupling beams. Component damage is simulated using the correlation model developed by Baker et al. (2024). Building performance model assumptions, including component quantities, are included in Electronic Supplement S4.1 for every structural system considered in the analysis. Step 5: Assess Probability of Safety-Critical Damage The damage and safety classes from each Monte Carlo realization are propagated through the ATC-138 unsafe placard fault tree (ATC, 2021b; Cook et al., 2022) described previously to determine the probability of safety-critical structural damage for each structural system design variation. The results of each design variation are then used to develop a contour plot. In the development of recommendations for new response modification coefficients and drift limits, we use these contour plots to determine which design parameters provide a design that meets a target reliability with a 10% probability of incurring safety-critical structural damage at the functional level earthquake. With this reliability target, we have a high confidence that the cumulative damage in the structure will be sufficiently low to ensure reoccupancy at this intensity level. We also select the combination of Rfr and Δafr that prioritizes stiffness requirements over strength requirements, with Δafr values close to 1%. The 88 resulting probabilities of safety-critical structural damage are provided in Electronic Supplement S4.2 for every structural system and design variation considered in the analysis. 4.8 Illustrative Example An example 8-story reinforced concrete moment frame (RCMF) building, with a reinforced concrete gravity system, is provided next to illustrate the methodology outlined above. The median story drift ratios from the nonlinear analysis for the 8-story RCMF archetype are shown for all design variations in terms of the various drift limits (Figure 4.4a) and response modification coefficients (Figure 4.4b). As shown in Figure 4.4a, for this lateral force-resisting system, as the design drift limit decreases, the realized median drifts also decrease. By contrast, when we show the relationship as a function of the response modification coefficient in Figure 4.4b, the realized drifts increase for models that are less elastic (i.e., higher Rfr values). (a) (b) Figure 4.4 Median story drift ratio for a set of 56 design variations of an 8-story reinforced concrete moment frame buildings expressed in terms of (a) design drift limit and (b) response modification coefficient. Peak floor accelerations increase as stricter drift limits are imposed, as shown in Figure 4.5a and with increased strength requirements, as shown in Figure 4.5b. For example, as shown in Figure 4.5b, the realized peak floor accelerations are approximately five times higher for models with Rfr = 1 than the models with Rfr = 8. These results highlight the need to consider the impact 89 of increased floor accelerations in future studies, particularly on acceleration-sensitive nonstructural components. (a) (b) Figure 4.5 Median peak floor acceleration for a set of 56 design variations of an 8-story reinforced concrete moment frame building expressed in terms of (a) design drift limit and (b) response modification coefficient. Figure 4.6 shows the relationship between the median story drift ratio at the most critical story (i.e., the maximum value over the height of the building) and the drift limit for each of the 56 models generated. Models with Rfr values greater than 4 show a linear relationship with the allowable drift limit, which indicates that the drift limit governs over the strength requirements. Models with Rfr values equal to 4 or less result in models that are strength-governed, meaning the base shear requirements with these lower Rfr values result in a model that is stiffer than required to meet the allowable drift limit imposed. Figure 4.6 also shows that RCMF models with Rfr greater than 4 have median story drift ratios greater than the allowable drift limit due to localized hinging at the first elevated floor, as can be seen in Figure 4.4. 90 Figure 4.6 Median story drift ratio at the most critical story as a function of drift limit for a set of 56 design variations of an 8-story reinforced concrete moment frame building. Figure 4.7 shows that as the maximum story drift ratio of the median realization increases, the probability of safety-critical structural damage also increases, which highlights the need to limit drifts in order to minimize damage that may hinder rapid post-earthquake recovery. As can be seen, several design variations meet the 10% probability of safety-critical structural damage target. Figure 4.7 Relationship between the median story drift ratio at the most critical story and the probability of safety-critical structural damage for a set of 56 design variations of an 8-story reinforced concrete moment frame building. 91 Figure 4.8 shows the 56 models generated with their safety-critical structural damage probability, with contours that show combinations of functional recovery drift limits and response modification coefficients that can achieve various reliability targets (i.e., maximum target probability of safety-critical structural damage). Each point on the plot represents the probability of safety-critical structural damage derived from 5000 Monte Carlo realizations. With these contour plots, if for example, we want to impose a 1.0% drift limit, then the response modification coefficient would need to be reduced to 3 to achieve a probability of safety-critical structural damage of 10% or less. By contrast, if we want to permit a less stringent strength requirements, we could impose an Rfr of 7 and a system-specific drift limit of 0.75% to limit the probability of safety-critical structural damage to approximately 10%. In determining recommended design values, we only considered drift limits in increments of 0.25% (i.e., we did not interpolate between the allowable drift limits considered in the design space). In some cases, we interpolated between the contours for response modification coefficients to avoid adding too much conservatism. For moderate-to-high values of Rfr, the contour lines at constant probability of safety-critical structural damage are generally horizontal (i.e., invariant to Rfr). This implies a drift-, as opposed to a strength-governed, response. However, for low values of Rfr, the contour lines are generally vertical (i.e., invariant to allowable drift limit), thus implying strength-governed response. Such observations, which also apply to other structural systems, are useful in establishing allowable drift limits and response modification coefficients for functional recovery. 92 Figure 4.8 Functional recovery response modification coefficient, Rfr, and allowable drift limit combinations that achieve various safety-critical structural damage probabilities, shown for an example 8-story reinforced moment frame building. 4.9 Limiting Safety-Critical Structural Damage for a Range of Lateral Force-Resisting Systems In this section, we discuss key trends and design recommendations to limit safety-critical structural damage probability for reinforced concrete shear walls (RCSWs), buckling restrained braced frames (BRBFs), special steel moment frames (SMFs), and RCMFs. Each lateral system evaluated with various gravity systems, as outlined in in Table 4.2. Results presented herein include either a summary of all heights or highlight the most critical building height. EDP plots for all systems and heights are provided in Appendix C1. Appendix C2 contains the plots of safety-critical structural damage as a function of realized drift and Appendix C3 provides the resulting contour plots. All corresponding data is provided in Electronic Supplement S4.2. 93 Table 4.2 Lateral force-resisting systems and building heights evaluated. Lateral Force-Resisting System Gravity System Considered PT Slab RC Slab Steel Frame REINFORCED CONCRETE SHEAR WALL SYSTEMS Special RC shear walls (Shear-governed, Bearing) X X X Special RC shear walls (Shear-governed, Frame) X X X Special RC shear walls (Flexure-governed, Bearing) X X X Special RC shear walls (Flexure-governed, Frame) X X X RC ductile coupled walls (Flexure-governed, Bearing) X X X RC ductile coupled walls (Flexure-governed, Frame) X X X STEEL BRACED FRAME SYSTEMS Steel buckling-restrained braced frames (no backup frame) X Steel buckling-restrained braced frames (backup frame) X MOMENT-RESISTING FRAME SYSTEMS Steel special moment frames X Special RC moment frames X X PT Slab = post-tensioned reinforced concrete flat slab; RC Slab = conventionally reinforced concrete flat slab; Steel Frame = steel gravity beam-column frame. 4.9.1 Reinforced Concrete Shear Wall Systems Low-rise cantilever RCSW models were analyzed separately from the remaining building heights for this system to reflect their shear-dominated, as opposed to flexure-dominated, behavior. The RCSW models were evaluated in combinations with three gravity systems: post-tensioned concrete flat slab, conventionally reinforced concrete flat slab, and steel frame. Figure 4.9a shows the probability of safety-critical structural damage for the controlling gravity system (i.e., steel frame). The probability of safety-critical damage exceeds the 10% target in models when the median story drift ratio at the critical story exceeds 0.5%. While data for all design variations are plotted in Figure 4.9a, points overlap in cases where the response does not change with variations in imposed drift limits. Figure 4.9b also shows that the models are primarily strength-governed. This behavior is demonstrated by the vertical lines on the contour plot, which indicate models designed to drift limits of 0.75% to 2.0% all achieve a similar probability of safety-critical structural damage. An 94 Rfr of 4.5 gives a probability of safety-critical structural damage from to approximately 10%. The results presented in Figure 4.9 represent bearing wall systems, but the trends are comparable to those of the low-rise RCSW building frame systems, which were also analyzed and can be found in Appendix C. (a) (b) Figure 4.9 (a) Probability of safety-critical structural damage as a function of maximum story drift of the median realization and (b) contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for low-rise, shear-governed special RCSWs (bearing) models with a steel gravity system. For RCSW models eight stories and taller, flexural-dominant behaviour is modeled to simulate EDPs and component fragilities that reflect this type of behaviour. Again, three gravity systems were evaluated: post-tensioned concrete flat slab, conventionally reinforced concrete flat slab, and steel frame. Figure 4.10a shows the probability of safety-critical structural damage as a function of median story drift ratio for cantilever bearing wall systems with post-tensioned slabs, which are the controlling gravity system for all building heights considered. Figure 4.10b provides the design parameter contour plot for the controlling building height and gravity system. As shown, a low probability of safety-critical structural damage can be achieved when using Rfr equal to approximately 4 and a drift limit of 1.0% or with an Rfr equal to 3 and a drift limit of 2.0%. Figure 4.10c and Figure 4.10d show the results for coupled bearing wall systems with post-tensioned slabs. For this system, to meet a reliability target around 10%, we select an Rfr equal to 4 and drift limit of 1.0%. The results presented in Figure 4.10 represent bearing wall systems only. The trends 95 are comparable to those of the mid- and high-rise RCSW building frame systems, which were also analyzed and can be found in Appendix C. (a) (b) (c) (d) Figure 4.10 Probability of safety-critical structural damage as a function of maximum story drift of the median realization for bearing (a) cantilevered RCSWs and (c) ductile coupled RCSWs with post-tensioned slabs and contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for the controlling height of the bearing (b) cantilevered RCSWs and (d) ductile coupled RCSWs with post-tensioned slabs. 4.9.2 Steel Buckling Restrained Braced Frame Systems Buckling restrained braced frames (BRBFs) with and without a welded back-up frame were considered in this study. In our analysis, we assumed that columns and beams in the system are designed using capacity design principles. Therefore, these components can withstand deformations and forces greater than those imposed due to nonlinear behaviour in the buckling-restrained braces. Figure 4.11a and b provide the probability of safety-critical structural damage as a function of realized median story drift ratio and the contour plot resulting from various design drift limit and functional recovery response modification coefficients for the BRBF system without 96 a welded backup frame, respectively. A response modification coefficient of Rfr equal to 5 and an allowable drift limit of 1.0% result in a probability of safety-critical structural damage to below 10%. Figure 4.11c and Figure 4.11d show that if the backup frame is welded, an Rfr equal to 8 and an allowable drift limit of 1.0% are sufficient to achieve the 10% target reliability. (a) (b) (c) (d) Figure 4.11 Probability of safety-critical structural damage as a function of maximum story drift of the median realization for BRBFs (a) without a welded backup frame and (c) with a welded backup frame for all building heights and contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for the controlling height of the BRBFs (b) without a welded backup frame and (d) with a welded backup frame. 4.9.3 Moment Frame Systems The steel moment frames (SMF) analyzed in this study are assumed to adopt reduced beam section (RBS) detailing and the gravity system considered is a steel frame. Figure 4.12a shows that models with drift limits above 1.25% result in probabilities of safety-critical structural damage above 10%. Similarly, the contour plot in Figure 4.12b for the most critical building height (i.e., 8-story) shows 97 that a drift limit of 1.25% ensures a probability of safety-critical structural damage just above 10%, with an Rfr equal to 8. (a) (b) Figure 4.12 (a) Probability of safety-critical structural damage as a function of maximum story drift of the median realization for all building heights and (b) contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for the controlling height of the SMF models. Finally, we extend the RCMF case study presented previously to now consider all building heights of the RCMF models. Models were evaluated with both post-tensioned slabs and conventionally reinforced concrete slabs as the gravity system. Figure 4.13a shows the probability of safety-critical structural damage for all heights and post-tensioned slabs. Figure 4.13b shows the results for the most critical building height (i.e., 24-stories) and gravity system (i.e., post-tensioned slabs). The results in Figure 4.13b are more stringent than those presented previously in the illustrative 8-story example (refer back to Figure 4.8b). For the suite of models, a 10% probability of safety-critical structural damage can be achieved if we impose a drift limit of 0.75% and an Rfr of approximately 4. 98 (a) (b) Figure 4.13 (a) Probability of safety-critical structural damage as a function of maximum story drift of the median realization and (b) contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for controlling height of RCMF models with post-tensioned slabs. Table 4.3 provides a summary of response modification coefficients and drift limit combinations for all structural systems considered in this study that meet an approximately 10% probability of safety-critical structural damage. The values in Table 4.3 were identified by selecting the highest possible Rfr in each system with a corresponding drift limit of approximately 1%. As a reference point, the R for current Risk Category IV ranges from 3.3 to 5.3 for the lateral systems considered, and the Risk Category IV drift limit is 1%. While a direct comparison to the values in Table 4.3 cannot be made due to differences in the design spectral accelerations and the deflection amplification factors, the results suggest that for the majority of systems considered, low probabilities of safety-critical structural damage can be achieved with Rfr and allowable drift limits similar to those currently used for life-safety for Risk Category IV structures. It should be caution ed that other systems permitted in ASCE 7 but not studied here may not follow this trend. 99 Table 4.3 Recommended functional recovery response modification coefficient, Rfr, and allowable drift limit, Δafr, to achieve 10% or less probability of safety-critical structural damage across the systems considered. Lateral Force Resisting System Rfrb Δafr Recommended Design Valuesa Height PT Slab RC Slab Steel Frame PT Slab RC Slab Steel Frame Rfr Δafr REINFORCED CONCRETE SHEAR WALL SYSTEMS Special RC shear walls (Shear-governed, Bearing) 3 4.5 4.5 4.5 2% 2% 2% 4.5 2%c Special RC shear walls (Shear-governed, Frame) 3 4.5 4.5 4.5 2% 2% 2% 4.5 2%c Special RC shear walls (Flexure-governed, Bearing) 8 5 5 5 2% 2% 2% 4 1% 16 4 5 5 1% 2% 2% 24 4 5 5 1% 2% 2% Special RC shear walls (Flexure-governed, Frame) 8 5 6 6 1% 2% 2% 4 1% 16 4 5.5 6 1% 2% 2% 24 4 5.5 6 1% 2% 2% RC ductile coupled walls (Flexure-governed, Bearing) 8 5 6 6 1% 1% 1% 4 1% 16 4 6 5.5 1% 1% 1% 24 4 6 8 1% 1.5% 2% RC ductile coupled walls (Flexure-governed, Frame) 8 5 6 6 1% 1% 1% 4 1% 16 4 6 6.5 1% 1% 1% 24 4 6 8 1% 1.5% 2% STEEL BRACED FRAME SYSTEMS Steel buckling-restrained braced frames (no backup frame) 3 - - 5 - - 1% 5 1% 8 - - 5 - - 1% 16 - - 8 - - 2% Steel buckling-restrained braced frames (backup frame) 3 - - 8 - - 1% 8 1% 8 - - 8 - - 1.25% 16 - - 8 - - 2% MOMENT-RESISTING FRAME SYSTEMS Steel special moment frames 3 - - 8 - - 1.5% 8 1.25% 8 - - 8 - - 1.25% 16 - - 8 - - 2% 24 - - 8 - - 2% Special reinforced concrete moment frames 8 6 7 - 0.75% 0.75% - 4 0.75% 16 5 6 - 0.75% 0.75% - 24 4 5 - 0.75% 0.75% - Notes: a. Values are read from contour plots with priority placed on having the highest response modification coefficient for drift limits of approximately 1%. b. Values are interpolated to halfway between the contours for the response modification coefficient. c. In this study, shear-governed RCSW designs are not governed by imposed allowable drift limits. 100 As can be seen, there is variability with both height and gravity system. The general trend observed is that, with increasing height, more stringent allowable drift limits and response modification coefficients are required. In RCSWs for example, we used chord rotations as opposed to story drift ratio to predict damage as this removes the rigid body rotation in the upper floors for taller archetypes. The concentration of damage is therefore in the plastic hinge region at the base of the wall. We still observe an increase in safety-critical structural damage with height, however, because there is an increase in the overall number of components that can be damaged in taller models which is likely driving this trend. This trend was also observed in Chapter 2, where the 24-story archetypes had more slab-column connection damage overall than the shorter archetypes simply due to the higher number of stories. For the BRBFs, there was pronounced localization or hinging in the first elevated floor in the shorter archetypes. The shorter heights governed the design recommendations in this case. In terms of gravity systems, the models with PT slabs required more stringent drift limits and response modification coefficients primarily due to the vulnerability of the PT slab-column connections. The recommended design values presented in Table 4.3 correspond to the most critical height and gravity system considered for a given lateral system. The methodology presented, however, could be extended to develop a more robust qualification procedure similar to FEMA P-695 (FEMA, 2009b) that employs the notion of performance groups. Performance groups could consider variations of parameters such as coupling beam length, brace geometry, or further variations in gravity systems. The mean of the performance group could then be used to compare against the 10% probability of safety-critical structural damage, and individual results could be compared against a more relaxed target. 101 4.10 Conclusions, Limitations, and Future Work In this paper, we used the notion of safety-critical structural damage as metric to inform the development of recovery-based seismic design provisions. First, we presented a framework to evaluate the probability of safety-critical structural damage in a wide range of conventional structural systems and proposed structural seismic design interventions, i.e., drift limits and response modification coefficients, for improved recovery. Then, the probability of safety-critical structural damage was evaluated for reinforced concrete shear walls, steel buckling-restrained braced frames, and steel and concrete moment frames. Results were used to develop recommendations for allowable drift limits and response modification coefficients for these systems at a new risk-targeted Functional Recovery Earthquake. The contour plots developed for a wide range of systems provide alternate combinations of design parameters that achieve similar performance. The methods outlined provide an important first step towards developing a qualification procedure for functional recovery performance. Future work is needed, however, to extend this observation to other systems in ASCE 7 that have not been studied herein. While this study offers a comprehensive assessment of a broad range of conventional structural systems to support the development of recovery-based seismic design provisions, several limitations should be noted: (1) the use of simplified models, (2) the reliance on existing FEMA P-58 and ATC-138 fragility data and modeling assumptions, and (3) the exclusive focus on structural components. First, we use simplified nonlinear analysis models to develop estimates of engineering demand parameters for all systems considered. Higher fidelity models developed for each system with a range of building heights, while more analytically intensive, would provide a more refined evaluation of the probability of component deformations exceeding their safety-critical limits. Furthermore, studies such as those by Opabola and Elwood (2024) could be 102 conducted to more thoroughly relate experimental test data to component deformation thresholds and allowable drift limits. Second, this study relies on fragilities included in the FEMA P-58 methodology (FEMA, 2018b) as updated in the ATC-138 project (ATC, 2021b). The results therefore rely upon the assumptions of the input fragilities and their safety class mapping. This static database, however, does not reflect the latest ductility and detailing requirements. The sensitivity of updated fragilities and safety-class definitions on the design recommendations should be assessed in future work. The performance of the systems considered in this study is controlled by deformation-controlled actions and the assumption that capacity-design principles will prevent failure due to critical force-controlled actions. Hence, such failure modes are also not explicitly considered in this work. Further, the results of the FEMA P-58 assessment can be sensitive to assumptions of yield drift and residual drift, which may influence the calculation of safety-critical structural damage probabilities in certain systems. Finally, this study considers only structural lateral and gravity force-resisting system components and aims primarily to evaluate the impact of structural design interventions on safety-critical structural damage to these components and systems. While we have discussed how limiting structural component damage also improves recovery performance, future studies should evaluate overall building recovery performance and the impact of increased floor accelerations on nonstructural systems. Despite these limitations, this study establishes a performance objective for structural functional recovery design provisions – the probability of safety-critical structural damage. Further, we outline functional recovery design checks and establish preliminary design parameters for a range of structural systems, demonstrating a methodology that could inform a more rigorous 103 qualification procedure. Ultimately, this work represents a critical first step towards the development of seismic design provisions for functional recovery performance. 4.11 Application to Canadian Building Code Development One of the primary goals in the new Article 4.1.8.23 design provisions in Canada is to have “no structural damage” (NRCC, 2020). The new provisions enforce a 0.5% drift limit at the 475-year and 975-year intensity level for high-importance and post-disaster risk categories (NRCC, 2020). This study outlines a method that could be used to analytically validate the proposed drift limits in the Canadian provisions across a wide range of lateral force resisting systems and building heights. This study also demonstrates that the allowable drift limits necessary to achieve a very low probability of safety-critical structural damage vary significantly between lateral-force resisting systems. For systems such as steel special moment frames, for example, a very stringent drift limit may not be necessary to ensure the desired performance outlined in the provisions, which if adopted in Canada, may offer cost and embodied carbon savings. 104 Chapter 5: Nonstructural Design Requirements for Functional Recovery Performance This chapter is based on the following reference: Blowes, K., Molina Hutt, C., Zimmerman, R., Cook, D., Almeter, E., and Haselton, C., 2025b. Nonstructural component design requirements for functional recovery performance. Earthquake Spectra (In Review). 5.1 Introduction Seismic damage of nonstructural components has been observed to cause loss of function in modern buildings in the United States (Filiatrault et al., 2001; Fischer, 2014). While building codes have advanced to address nonstructural life-safety requirements (e.g., ASCE 7-22 Chapter 13), to date, there has been limited focus on establishing functionality requirements for such nonstructural components. In the United States, the Functional Recovery Task Committee (FRTC) of the Building Seismic Safety Council (BSSC) has begun to develop recommendations for new seismic design provisions to ensure acceptable functional recovery performance (BSSC, 2023). These recommendations will be included in the 2026 National Earthquake Hazards Reduction Program (NEHRP) provision updates that may be considered for inclusion in ASCE 7-28. The FRTC was tasked to address both structural and nonstructural damage that impedes function. The draft recommendations also include extensive provisions related to documentation, review, observations, and quality assurance and quality control (QAQC). 105 In Chapter 4 (Blowes et al., 2025), we evaluated the probability of safety-critical structural damage, i.e., structural damage that must be repaired for tenants to safely reoccupy a building, and proposed allowable drift limits, Δafr, and response modification coefficients, Rfr, for functional recovery. To establish the Δafr and Rfr limits, we targeted a probability of safety-critical structural damage at the risk-targeted Functional Recovery Earthquake (FRER) of approximately 10% using the methodology developed by Cook et al. (2022) and adopted by the ATC-138 project (ATC, 2021b). Building on this effort, we now turn our attention to nonstructural component damage, with a focus on nonstructural component design interventions and enhanced detailing requirements to achieve specific functional recovery time targets. In this study, we assess the probability of meeting functional recovery time targets considering both structural and nonstructural component damage, given the new strength and stiffness design requirements to limit safety-critical structural damage recommended in Chapter 4 (i.e., Blowes et al., 2025). For buildings with a range of lateral and gravity force-resisting systems, we evaluate (1) the probability of exceedance of different recovery targets, (2) the probability of individual components impeding function at different recovery time intervals, and (3) the efficacy of implementing two design interventions: a functional recovery component importance factor, Ipfr, and seismic qualification of equipment. Ultimately, this study aims to inform the 2026 NEHRP Functional Recovery Provisions by providing insight into the effectiveness of various nonstructural component requirements (i.e., Ipfr and seismic qualification), when adopted in buildings where structural systems have been designed to achieve a low probability of safety-critical structural damage. This study also provides component disaggregations that can be used to develop provisions on a per-component basis. Finally, we identify the nonstructural components that are likely to be damaged but cannot be 106 addressed with the two design interventions considered. This list of components will help identify the need for alternate component design or preparedness recommendations for inclusion in functional recovery provisions. All analyses are conducted for the Seismic Design Category Dmax at the FRER (Dmax,FRE), ensuring the results are general enough to be considered across most high and very high seismicity regions in the United States. This study provides recommendations for design checks that will be conducted at the FRER and independently of life-safety design checks. It is beyond the scope of this dissertation to evaluate the functional recovery performance of the life-safety provisions, but this comparison is recommended as future work. 5.2 Literature Review Nonstructural components constitute the majority of the total replacement cost of buildings and damage to these components often occurs at lower intensity levels than structural damage (Miranda and Taghavi, 2003). As we turn towards assessing functional recovery, several past earthquakes and analytical studies have highlighted how nonstructural component damage contributes to lengthy recovery times. Nonstructural damage was observed to impede function in both the 2014 Napa and 2001 Nisqually earthquakes (Filiatrault et al., 2001; Fischer, 2014). Further, various analytical studies (Blowes et al., 2023; Molina Hutt et al., 2022b; Terzic and Kolozvari, 2022) have demonstrated that nonstructural component damage, such as damage to elevators, mechanical and plumbing systems, is often the primary contributor to functional recovery times given a ground motion intensity with a return period of 475-years. There have been many advances in nonstructural component design requirements for life-safety in North America in recent years. First, Chapter 13 of ASCE 7-22 (ASCE/SEI, 2022) has been updated to reflect findings from NIST GCR 18-917-43 (NIST, 2021). NIST GCR 18-917-43 identified life-safety performance objectives for nonstructural components, new design equations 107 that reflect the ductility of the structure, and recommendations for component detailing. Fragilities that reflect improved detailing of nonstructural components, as well as seismic qualification, have also been developed and adopted into damage assessment tools and functional recovery frameworks (Haselton Baker Risk Group (HB-Risk), 2025; NIST, 2021). While these efforts represent a significant advance in life-safety performance of nonstructural components, there is a lack of clear performance targets and prescriptive provisions for recovery. Notably, there have been longstanding efforts in hospital design to address post-earthquake function through prescriptive requirements (ASCE/SEI, 2022). Engineers are required to employ more stringent structural strength and stiffness requirements, as well as design nonstructural components following ASCE 7-22 Chapter 13 with an importance factor of 1.5. In addition to this, ASCE 7-22 employs enhanced QAQC requirements. All equipment must be seismically qualified, all nonstructural component design must be reviewed, and select nonstructural components must be inspected for conformance by the Authority Having Jurisdiction (ASCE/SEI, 2022). However, current codes do not require that functional recovery performance be explicitly evaluated, and prescriptive requirements have not been evaluated for their functional recovery performance. Finally, interest in performance-based methods to evaluate nonstructural components has also grown. Filiatrault & Sullivan (2014) laid out a methodology for the performance-based design of nonstructural elements, which requires the explicit verification of component performance. More recently, Perrone et al. (2022) developed a performance-based method that aims to ensure nonstructural components are designed to withstand the anticipated drifts and accelerations explicitly derived from the nonlinear analysis of the structure. While these efforts present critical advancement and provide guidance for the explicit verification of damage to nonstructural components and systems, there is still a need to evaluate the impact of component damage on 108 function and to ultimately derive prescriptive provisions that can be implemented widely in practice. In summary, while significant work has been conducted to develop prescriptive and performance-based methods for nonstructural component life-safety requirements, there is still a need to address post-earthquake function and recovery. The recent development of new functional recovery time assessment tools, such as the ATC-138 methodology (ATC, 2021b), provides the unique opportunity to develop a data-informed methodology to propose nonstructural design provisions for functional recovery. Ultimately, the methodology outlined in this study (1) employs a consistent intensity level for all assessments, (2) considers a wide range of buildings and heights, (3) reflects proposed structural requirements, QAQC, and preparedness measures, and (4) provides disaggregations that enable identifying components likely to impact building function. The methods proposed are scalable, transferable, and allow for the explicit verification of design recommendations for functional recovery performance. 5.3 Functional Recovery Categories and Reliability Targets Buildings designed for functional recovery performance are assigned a functional recovery category based on the services or community functions provided by the building, as identified in the BSSC’s Functional Recovery Planning Committee Report (BSSC, 2023). Current proposals include four functional recovery categories, ranging from A, for buildings withs functions needed for immediate safety and survival needs, to D, for buildings with services that support quality of life but are not necessary for function (Kersting and Liel, 2024). These categories are established based on requirements for function and do not match traditional risk categories from ASCE 7. Example community functions from the current draft NEHRP recommended seismic design provisions are provided in Table 5.1. 109 Each functional recovery category has a corresponding functional recovery time target for FRER-level shaking (Kersting and Liel, 2024), also provided in Table 5.1. The targets were developed by a subcommittee of the BSSC’s Functional Recovery Task Committee that considered societal expectations for new design. In this study, we evaluate the design requirements necessary to achieve the Recovery Category B, C, and D targets. The target for buildings in Recovery Category A is 0 days, with the goal of buildings being immediately functional following an FRER level event. The performance of these buildings is expected to be evaluated explicitly and beyond the scope of this study. In this study, we determine the necessary design requirements to achieve the recovery targets in Table 5.1 with a reliability target of 25% (i.e., a probability of exceeding the recovery target is 25%) at the FRER. Table 5.1 Building functional recovery targets for each functional recovery category. Functional Recovery Category Example Community Functions* Functional Recovery Time Target A Emergency response, acute healthcare, housing of non-ambulatory populations (e.g., nursing homes) and people in custodial care (e.g., correctional facilities) 0 days B Food and water services, non-urgent healthcare, residential housing, hotels, veterinary services 3 days C Child and adult daycare, routine healthcare, education (PK-12), banking 2 months D Post-secondary education, routine local government 6 months *Community functions are taken directly from draft NEHRP 2026 provision update recommendations (FEMA, 2024). 5.4 Structural Design for Functional Recovery This work is an extension of the efforts outlined in Chapter 4 (Blowes et al., 2025), where we aimed to establish structural design requirements that limit the probability of safety-critical structural damage, which can lead to lengthy recovery times. Following work in Chapter 4, the FRTC decided to use the recommended seismic response modification coefficients for functional 110 recovery, Rfr, and allowable drift limits for functional recovery, Δafr, with the addition of a judgement-based cap (FEMA, 2024). The recommendations, which target a 10% probability of safety-critical structural damage at the FRER, were applied to buildings assigned to Recovery Category (RC) B and C. The contour plots developed in Chapter 4 were then used to develop Rfr and Δafr requirements that targeted a slightly more relaxed probability of safety-critical structural damage of 15% for RC D. The judgment-based cap employed by the FRTC and determined through a consensus-based process was Rfr ≤ R/1.5 and Δafr ≤ 1% for RC B and C and Rfr ≤ R/1.25 and Δafr ≤ 1.5%. The resulting Rfr and Δafr, which cap the results from Chapter 4, are used in this study. These design parameters are summarized in Table 5.2 for special reinforced concrete shear walls, steel buckling-restrained braced frames, and steel and reinforced concrete special moment frames. Again, building heights from three to 24 stories were considered, with heights capped at the maximum permissible for each structural system in ASCE 7-22 (ASCE/SEI, 2022), also summarized in Table 5.2. The steel buckling restrained braced frame and moment frame lateral systems were assumed to have steel frame gravity systems. The concrete systems were evaluated with post-tensioned slabs. 111 Table 5.2 Lateral force resisting systems and building heights evaluated. Seismic Force-Resisting System Rfr and Δafr by Functional Heights (Stories) Recovery Category B and C D 3 8 16 24 BEARING WALL SYSTEMS Special reinforced concrete shear walls where the shear capacity is not designed for the shear demand corresponding to the expected flexural capacity 3.3 4 X 0.01hsx 0.015hsx Special reinforced concrete shear walls where the shear capacity is designed for the shear demand corresponding to the expected flexural capacity 3.3 4 X X X 0.01hsx 0.0125hsx Reinforced concrete ductile coupled walls 4 5 X X X 0.01hsx 0.0125hsx BUILDING FRAME SYSTEMS Special reinforced concrete shear walls where the shear capacity is not designed for the shear demand corresponding to the expected flexural capacity 4 4.8 X 0.01hsx 0.015hsx Special reinforced concrete shear walls where the shear capacity is designed for the shear demand corresponding to the expected flexural capacity 4 4.8 X X X 0.01hsx 0.0125hsx Reinforced concrete ductile coupled walls 4 5 X X X 0.01hsx 0.0125hsx Steel buckling-restrained braced frames, non-moment-resisting beam-column connections 5 5 X X X 0.01hsx 0.01hsx Steel buckling-restrained braced frames, moment-resisting beam-column connections 5.3 6.4 X X X 0.01hsx 0.0125hsx MOMENT-RESISTING FRAME SYSTEMS Steel special moment frames 5.3 6.4 X X X X 0.01hsx 0.015hsx Special reinforced concrete moment frames 4.0 5 X X X X 0.0075hsx 0.0075hsx *hsx is the story height 112 5.5 Nonstructural Design for Functional Recovery We evaluate the nonstructural component design interventions necessary to achieve the performance objective for each recovery category, when coupled with the structural provisions previously introduced. In ASCE 7-22 Chapter 13 requirements, nonstructural components are designed to meet a horizontal seismic design force, Fp (ASCE/SEI, 2022). Fp is also used to set the acceleration threshold that is used in seismic qualification. In the current ASCE 7-22, Fp is a function of a single component importance factor, Ip. Components in buildings assigned to Risk Category IV are designed with Ip = 1.5, and Ip = 1.0 is used otherwise. We modify the ASCE 7-22 Chapter 13 equations to introduce a new horizontal seismic design force, Fpfr. In this study, we use this same approach outlined in ASCE 7-22, but replace the spectral acceleration from the design earthquake, SDS, with the functional level earthquake, SDSfr. Molina Hutt and Zimmerman (2024) defined a new functional recovery component importance factor, Ipfr, which is dependent on functional recovery category. We also use Ipfr in place of Ip, as shown in Equation 5.1. Fpfr has upper and lower bounds that are consistent with Chapter 13 requirements, but now employ Ipfr, as shown in Equation 5.2 and 5.3 respectively. Fpfr = 0.4SDSfrIpfrWp �HfRμ� �CARRpo � (5.1) Fpfr ≤ 1.6SDSfrIpfrWp (5.2) Fpfr ≥ 0.3SDSfrIpfrWp (5.3) where Fpfr is the seismic design force, SDSfr, is the short period spectral acceleration from the FRER spectrum. In this study, SDSfr is determined from the Dmax,FRE spectrum. Wp is the component operating weight, Hf is the force amplification factor for the height, and CAR is the component resonance ductility factor, as tabulated in Table 13.5-1 of ASCE 7-22 (ASCE/SEI, 2022). Rμ is the structure ductility reduction factor and Rpo is the component strength factor. The lower bound Fpfr 113 shown in Equation 5.3 is also evaluated using SDS in lieu of SDSfr and Ip = 1.0 in lieu of Ipfr, to reflect the minimum bound on the life-safety requirements. Rμ reflects the reduction in force to the component from the building ductility and is calculated by modifying ASCE 7-22 Chapter 13 equation, as shown in Equation 5.4. Rμ= [1.1Rfr/Ω0fr]1/2 ≤1.5 (5.4) where Rfr is the response modification coefficient for functional recovery and Ω0fr is the overstrength factor for functional recovery, which is equal to the life-safety overstrength factor, Ω0. As the structural design recommendations from Chapter 4 (i.e., Blowes et al., 2025) propose reduced Rfr and Δafr values, we also reconsider the upper bound of Rμ. For lateral force-resisting systems that have designs governed by the new, more stringent drift limit requirements, the realized strength may be higher than that required by the provisions. The FRTC therefore decided to cap the ratio of Rfr/Ω0fr of 2. This cap results in an upper bound limit on Rμ of 1.5, which is similar to the upper bound limit of 1.3 from ASCE 7-22, Chapter 13 (ASCE/SEI, 2022). 5.6 Implementation of Nonstructural Design Interventions In this study, damage assessments are performed with FEMA P-58 (FEMA, 2018b) and results are then used to simulate recovery using ATC-138 (ATC, 2021b). The capacities of both structural and nonstructural components are determined from fragilities provided in Appendix D of FEMA P-58, with updates based on the ATC-138 project (ATC, 2021b; Welch et al., 2024). Models for each recovery category are evaluated with and without seismic qualification and by varying Ipfr ranging from 1.0 to 3.0 to find the value necessary to meet the reliability target for the corresponding recovery time. The application of Ipfr to various drift- and acceleration-sensitive components is summarized in Figure 5.1 and is discussed in detail in the remainder of this section. When the fragilities are a function of the design force Fp, we replace Fp with Fpfr which varies as a 114 function of Ipfr. A detailed list of all components considered in this study with an indication of whether the components are dependent on Ipfr, seismic qualification or independent of the design variables considered can be found in Electronic Supplement S5.1. Figure 5.1 Application of component seismic importance factor for functional recovery, Ipfr, for various component types. 5.6.1 Acceleration-Sensitive Components For the majority of the acceleration-sensitive components we analyze, we employ recently developed smart fragilities (Welch et al., 2024). Smart fragilities are used to model all anchored or braced components, such as mechanical equipment or piping. As discussed in Welch et al. (2024) and Cremen and Baker (2018), the methods employed in FEMA P-58 (FEMA, 2018b) currently fail to accurately capture equipment performance because they do not capture the interaction of equipment and anchorage performance. FEMA P-58 also does not consider the impact of seismic qualification and the resulting improvement in equipment performance that can 115 be achieved. The interaction of piping and bracing components is similarly not accurately captured. To address these shortcomings, Welch et al. (2024) developed nested or “smart” fragilities as part of the ATC-138 project. When using smart fragilities, first the anchorage or bracing fragility is sampled to determine whether the anchorage has failed (refer back to Figure 5.1). If the anchorage or bracing has failed, then the unanchored or unbraced component fragility is sampled. If the anchorage or bracing has not failed, then the anchored or braced component fragilities are sampled. For anchored or braced components, the code-based design strength is used to inform the component anchorage or bracing fragility functions using Equations 5.5 and 5.6 below from FEMA P-58 (FEMA, 2018b) for ductile and brittle behavior respectively. θductile = Cqe2.054βϕRn (5.5) θbrittle = Cqe2.81βϕRn (5.6) where θductile and θbrittle are the median strengths for the ductile and brittle failure modes respectively, Cq is a coefficient used to reflect the construction quality, β is the total dispersion, and ϕRn is component design strength. The component design strength is determined using the anchorage design force, Fpfr (Equations 5.1 to 5.3 above), which is a function of Ipfr. Following recommendations in FEMA P-58, Cq is taken as 0.5 for both ductile and brittle behaviour and a default dispersion, β, of 0.5 is used (FEMA, 2018b). The average of the median derived from the ductile and brittle failure modes is used for this analysis. Fragility functions are recalculated based on the increase in the design strength Fpfr, as shown in Figure 5.2. 116 Figure 5.2 Example fragility function showing the probability of component damage given an engineering demand parameter, with median values increasing proportionally with Ipfr. The dispersion, β, is equal for all fragilities. For a limited number of conventional acceleration-sensitive components, we use fragilities already included in FEMA P-58 and available in SP3 (FEMA, 2018b; HB-Risk, 2025). For example, for suspended ceilings two fragility functions are available within the FEMA P-58 fragility database, one for Ip less than 1.5 and one for Ip greater than or equal to 1.5. In such cases, we conservatively use the first fragility when evaluating the impacts of Ipfr equal to 1.0 and 1.25, and the second fragility when evaluating the impacts of Ipfr between 1.5 and 3.0. 5.6.2 Seismic Qualification Equipment is often qualified to prevent failure at a specified level of shaking. To simulate the performance of equipment that is seismically qualified, we replace the regular equipment fragilities within the smart fragilities previously discussed. Seismically qualified equipment is assumed to be qualified exactly to the horizontal seismic design force, Fpfr, again a function of Ipfr. This behaviour is represented by fragility functions with a 1% probability of failure at the horizontal seismic design force, Fpfr, and a dispersion, β, of 0.25 (Welch et al., 2024). We assume CAR/Rpo = 1.0 in the Fpfr calculation to ensure components are qualified to the corresponding floor acceleration. 117 5.6.3 Drift-Sensitive Components Ipfr is also applied to drift-sensitive nonstructural components in the building performance model. For component fragilities that are a function of seismic relative displacements, the relative displacement is amplified by Ipfr and the component fragility updated to reflect the increased ability to accommodate deformations. This increase is accounted for in different ways depending on the component type. For instance, for stairs, the seismic gap used to define the fragility function (i.e., the design drift) is amplified by Ipfr and the corresponding fragility function rederived. For the curtain walls, the fragility is developed to reflect a 10% probability of failure at the functional recovery drift limit amplified by Ipfr to reflect the increase in seismic relative displacements, and a dispersion of 0.45. 5.6.4 Components with No Interventions There are a handful of acceleration-sensitive components that are not impacted by Ipfr or seismic qualification. The primary example in this study is the elevator system. Here we adopt the component fragilities implemented in the ATC-138 project (ATC, 2021b) with the aim to reflect enhanced component detailing from ASME 17.1 (ASME, 2022). Beyond this enhanced detailing, no further intervention is evaluated. For partitions, fragilities for components designed in seismic design categories D or greater are used. However, no further improvement is considered. 5.7 Methodology to Inform Nonstructural Design Criteria To develop nonstructural design recommendations, we assess each lateral force-resisting system type, height, and set of structural design requirements from Table 5.2, to determine the requirements necessary to meet a 25% probability of exceeding the recovery time targets. An overview of the steps used to evaluate each model is provided in Figure 5.3. Further details on the 118 structural response, damage assessments, and functional recovery time assessments are provided in the following sections. Figure 5.3 Outline of methodology to develop nonstructural design recommendations. 5.7.1 Structural Response Prediction We perform our analysis using the Seismic Performance Prediction Program (SP3) developed by HB-Risk (HB-Risk, 2025). To simulate building responses, we use the Structural Response Prediction Engine in SP3 (Cook et al., 2018; HB-Risk, 2025). We determine the base shear requirements in accordance with Chapter 12 of ASCE 7 (ASCE/SEI, 2022), with spectral accelerations from the Dmax,FRE spectrum in place of the design level spectrum and with Rfr from Table 5.2 in place of the term R/Ie, consistent with the methods described in Chapter 4. We also enforce the minimum base shear from Chapter 12 of ASCE 7 with values from the Dmax,DE 119 spectrum and impose additional Chapter 12 stability requirements as outlined in Chapter 4 (i.e., Blowes et al., 2025). We then use the Structural Response Prediction Engine (SRPE) to develop a simplified linear multi-degree of freedom model that reflect the Rfr and Δafr outlined in Table 5.2, as well as these additional strength and stability criteria. The SRPE then adjusts the linear responses to account for nonlinear behaviour based on a database of a wide range of high-fidelity archetypes analyzed following the FEMA P-695 methodology (FEMA, 2009b). We use these simulated nonlinear engineering demand parameters (EDPs), including both story drift ratio and peak floor acceleration, for each simplified model. Further details about the SRPE can be found in Chapter 4 and in Cook et al. (2018). In the development of these provisions, the functional recovery deflection amplification factor, Cdfr, is set equal to Rfr, to amplify drifts (see Chapter 4). The earthquake importance factor, Ie, is set to 1.0. 5.7.2 Component Damage Assessment The EDPs simulated for the Dmax,FRE hazard level are then used to assess component level damage using the FEMA P-58 methodology (FEMA, 2018b), as implemented in SP3 (HB-Risk, 2025). Nonstructural components were populated using SP3 for a typical office occupancy. We used updated fragilities developed in the ATC-138 project (ATC, 2021b) where available. We also use alternate EDPs where appropriate. Examples include component rotations for coupling beams and chord rotations for slender concrete walls. The assessment is then repeated, amplifying fragilities by values of Ipfr ranging from 1.0 to 3.0, for variations with and without seismic qualification. All building performance models are provided in Electronic Supplement S5.1. 5.7.3 Functional Recovery Time Assessment We use the Cook et al. (2022) methodology, which has been adopted by the ATC-138 project (ATC, 2021b), to evaluate the functional recovery performance of the models considered. The 120 Cook et al. (2022) methodology relates component damage and excessive residual drifts to loss of function using fault trees for each building system (e.g., structural, plumbing, electrical) at each floor. The restoration of building function is modeled using repair sequencing algorithms and default impeding factor delays outlined in Cook et al. (2022). In terms of mitigation strategies, for buildings assigned to Recovery Category B, we consider an inspector and engineer on retainer to represent the requirement to have a post-earthquake functionality plan in the current draft 2026 NEHRP Functional Recovery Provisions (FEMA, 2024). We also assume there is a contractor relationship. For Recovery Categories C and D, these preparedness strategies are not considered. For all recovery categories, we simulate the response assuming private financing and 5% cash on hand. A description of impeding factors and mitigation strategies is provided in Table 5.3. 121 Table 5.3 Impeding factors and mitigation strategies. Recovery Category B Recovery Category C & D FACTORS THAT DELAY START OF REPAIRS Inspection Required Required Financing Required Required Permitting Required Required Engineering Mobilization and Design Required Required Contractor Mobilization Required Required Long Lead Time On On MITIGATION STRATEGIES Inspector on Retainer Yes No Engineer on Retainer Yes No Contractor Relationship Yes No Funding Source Private financing Private financing Cash on Hand 5% cash on hand 5% cash on hand In line with the ATC-138 project, we require the HVAC, plumbing, and electrical systems to be functional (ATC, 2021b). We also allow for temporary repairs, such as shoring. As for other requirements, we require 50% of exits to be clear and a minimum of two overall. We also consider the impacts of flooding, which is a consequence of pipe fracture and can severely hinder function in the affected tenant units. While we expect surge demands for material and labor following an FRER level earthquake, we do not assume this as the default for the purpose of general provision development as this may lead to unnecessary conservatism. We also assume the building is not in a dense area for the same reason. Finally, we only require 80% of tenant units to be functional for the building to achieve its basic intended function. This assumption is an acknowledgement that tenants will be creative in how space is used following an earthquake and will find a new normal where resources and spaces are shared. Because we assign one tenant unit per story, this assumption has little effect on shorter models but allows some relaxation in taller structures. The ATC-138 requirements for function are summarized in Table 5.4. The entries in Table 5.4 are 122 on/off switches that must be defined by a user of the ATC-138 method and hence included for replicability of the analyses presented herein. Table 5.4 ATC-138 requirements for function. Description Requirements for Functional Recovery HVAC Required Plumbing Required Electrical Required Elevators No Temporary Repairs Allowed Fire Watch Allowed Egress 50% of Exits, 2 Minimum Flooding Consequences Included Surge Demand Not Considered Percentage of Functional Floor Area 80% In our preliminary analyses, there were a handful of nonstructural components that were frequently damaged and caused loss of function but that cannot be addressed via the prescriptive provisions explored (i.e., Ipfr and qualification). These components include elevators, fire-rated partitions, lighting, and doors. The design and detailing of these components often fall outside the scope of the structural engineer. With no intervention available, damage to these components made it very difficult to evaluate the efficacy of the prescriptive provisions for the components that do fall within the structural engineer’s scope. The decision was therefore made to remove a small list of components from this study, but to provide the FRTC with these preliminary findings which were used to develop draft provisions that address damage to this critical group of components. These components are discussed in detail next. First, elevator damage drove the risk of exceeding every target because of both the high probability of damage, even when meeting ASME 17.1 requirements (ASME, 2022), and the lengthy impeding factor delays for repair. When elevators were required for function, the resulting probability of exceeding the target recovery times exceeded the 25% target substantially, making 123 it very difficult to evaluate design interventions for all other components. Chapter 2 (i.e., Blowes et al., 2023) also discussed the sensitivity of the functional recovery time assessment results to both the elevator component damage thresholds and the extremely long impeding factor delays associated with this damage. Elevators are composed of various components including the passenger cabin, guide rails, and the counterweight. While improved detailing can improve some of these components, the most sensitive component is the passenger cabin, which the structural engineer has no control over. Because of this sensitivity, we decided to not require elevators for function in our analytical models, as shown in Table 5.4. This decision is not intended to suggest that these components are not important for function; vertical transportation is critical for many people to access elevated floors. Their removal indicates the need to develop provisions that address elevator component vulnerability, either through improved detailing, improved fragility functions, or preparedness strategies (e.g., having elevator contractors from other regions on contract for post-earthquake repairs to the cabins). This vulnerability is now addressed through draft provisions that require the building owner and the engineer to discuss function in elevators and plan for impacts to accessibility due to post-earthquake damage (FEMA, 2024). We also allow for damage to the fire-rated partitions walls and allow fire watch. In our preliminary analyses, we found that the fire partitions were heavily damaged, making it extremely difficult to meet the short recovery time requirements for Recovery Category B (i.e., 3 days). Few options are available to improve the capacity of these components, so we instead acknowledge that fire watch will be required. This finding has also triggered the inclusion of a fire suppression plan in the draft design provisions (FEMA, 2024). Finally, we also removed pendant lighting fragilities and door fragilities due to lack of fragility data. While this study informed decisions about provisions to address these components (i.e., elevators, fire-rated partitions, lighting, and doors), 124 damage to these components could place buildings in a recovery state between functional recovery and reoccupancy. Ultimately, the extent to which they are addressed is left to the owner and structural engineer to decide together or is simply beyond the scope of the structural engineer. 5.7.4 Modeling Uncertainty and Truncation Uncertainty in functional recovery time assessments is often large, as it reflects the wide range of building performance expected as well as the building owner’s and tenants’ ability to access resources when recovery begins. To account for improved quality control and quality assurance (QAQC) measures required in future functional recovery design provisions, we use two measures: modeling uncertainty and truncation of fragility functions. First, the modeling uncertainty is used to reflect the distribution in responses predicted using analysis models. In the FEMA P-58 methodology, the total modeling uncertainty reflects the effects of both the construction quality, βc, and the quality of the analytical model, βm, (FEMA, 2018b). For all recovery categories, we consider βc to be 0.1 (Superior Quality, New Buildings) to reflect the new construction QAQC measures imposed with new functional recovery provisions. For the analytical model, we consider βm to be 0.25 (Average Quality), which indicates the strength and stiffness of components are modeled in a way that is representative but not explicit (FEMA, 2018b). The total modeling uncertainty, combined using the square root of the sum of the squares, is 0.27. The modeling uncertainty is ultimately combined with the dispersions from record-to-record ground motion variability according to Table 5-6 of FEMA P-58 (FEMA, 2018b), which provides period-dependent recommendations for total structural response dispersion when simplified analysis methods are used. Building on observations from past earthquakes, a number of measures to improve QAQC procedures to improve recovery outcomes are included in the FRTC draft provisions for functional 125 recovery performance (Valigura et al., 2024). To analytically reflect these improved QAQC measures, we truncate the lower tails of the component fragility functions for all damage states. To do so, we cut the lower tail of the probability density function below a specific number of standard deviations from the median. The probability density is normalized such that it sums to one over the non-truncated domain. A diagram of a lognormal and a truncated lognormal distribution are shown in Table 5.4. All component fragilities in all models are truncated at -2 standard deviations, regardless of recovery category. This truncation is applied for two reasons. First, even without QAQC measures, component damage has not been observed at low intensity levels (FEMA, 2018c). The use of the full probability distribution function over the lower tail of the fragility therefore overestimates expected damage in this range. Because we are targeting a high level of reliability among a very large level of components in each model, the effect of this overestimation is further amplified. The impact of this overestimation of damage in the lower tails of the fragilities was highlighted in Chapter 3 (i.e., Blowes et al., 2024). Previous studies comparing FEMA P-58 damage estimates against observations from past earthquakes have also demonstrated the benefit of truncation for improving the accuracy of damage predictions. Cook et al. (2021) hindcasted FEMA P-58 red tag results against observed data from the 1994 Northridge earthquake and showed that, when truncation was applied, there was much better agreement between observations and predictions. Second, the additional QAQC measures in the draft functional recovery provisions further justify truncating these fragilities as we would expect the probability of very poor performance to be even lower. 126 Figure 5.4 Illustrative diagram of truncated lognormal and lognormal distributions. 5.7.5 Developing Nonstructural Component Design Recommendations The functional recovery time assessment outlined above is performed for the RC B, C, and D models. Models are evaluated with and without seismic qualification for Ipfr values ranging from 1.0 to 3.0, following the procedures documented for each component group. From the results, we find the probability that the functional recovery time exceeds the recovery time target. This process is repeated for all heights and lateral force-resisting systems in Table 5.2. The results are used to find the Ipfr required to meet the recovery target with a 25% probability of exceedance for each lateral force-resisting system type and each recovery category. 5.7.6 Probability of Individual Components Impeding Function In addition to considering the reliability target, we also performed disaggregations to evaluate the probability of individual components impeding function at each recovery time target. The Cook et al. (2022) methodology provides the probability of recovery of each damaged component at various recovery targets. We use this algorithm to identify, with and without qualification and for increasing values of Ipfr, the probability of each component impeding function. The process is repeated for models in each recovery category using their respective target (e.g., 3 days for RC B). 127 5.8 Illustrative Example: Reinforced Concrete Moment Frame Building 5.8.1 Enhanced Recovery-Based Structural Design and Damage Assessment To illustrate the implementation of the methodology, we present the results for a case study 8-story reinforced concrete moment frame (RCMF), with a post-tensioned concrete slab. The RCMF models meet the RC B and C allowable drift limit of 0.75% and response modification coefficient of 4, and RC D allowable drift limit of 0.75% and response modification coefficient of 5 (refer back to Table 5.2). The median inelastic story drifts for all recovery categories simulated using HB-Risk’s Structural Response Prediction Engine are provided in Figure 5.5a. Figure 5.5b shows the realized PFAs, estimated using HB-Risk’s structural response prediction engine (HB-Risk, 2025). We used the realized PFAs to assess the impact of the nonstructural component design interventions. The PFAs currently required for design in the ASCE 7-22 that were used to establish the Fpfr forces for design are also plotted in Figure 5.5b. We see that increased accelerations are observed in the models with increased strength requirements (i.e., RC B and C versus RC D), highlighting the need for distinct nonstructural component design requirements for different recovery categories. EDP plots of the median realization for all systems and heights are provided in Appendix D1. Corresponding data is provided in Electronic Supplement S5.1. (a) (b) Figure 5.5 (a) Median realized inelastic story drift ratios and (b) median realized peak floor accelerations and ASCE 7 design accelerations for the 8-story RCMF archetype. 128 5.8.2 Impact of Nonstructural Design Interventions on Functional Recovery Time The results of the ATC-138 functional recovery time assessment of each 8-story RCMF structural design variation are provided in Figure 5.6. Figure 5.6a shows the probability of the functional recovery time exceeding the recovery target associated with each recovery category, first without seismic qualification of equipment. For the RC B models, the probability of exceeding the 3-day target is approximately 85% for all values of Ipfr evaluated. For the RC C, the probability of exceeding the 2-month target is slightly lower, approximately 65%. Finally, the probability of exceeding the 6-month target for RC D decreases to be around 30%, still beyond the 25% target. In Figure 5.6b, however, we can see that seismic qualification reduces the probability of exceeding all the recovery targets, which highlights the need to require seismic qualification of equipment in functional recovery design provisions. For this particular structural system and height combination, the probability of exceeding the RC B target of 3 days can be achieved with an Ipfr equal to 1.5. The RC C and D recovery targets can be achieved with an Ipfr of 1.25 and 1.0, respectively. This case study demonstrates the methodology used to determine Ipfr requirements but does not represent the most critical height. Reliability data for the case study, as well as all other systems, with and without prequalification is provided in Electronic Supplement S5.2. 129 (a) (b) Figure 5.6 Impact of Ipfr on the probability of the functional recovery times exceeding the recovery time target (a) without seismic qualification of equipment and (b) with seismic qualification of equipment. 5.8.3 Component Contributions to Function Loss Next, we disaggregate the functional recovery time results to show the probability of any individual component impeding function at 3 days for RC B, at 2 months for RC C, and at 6 months for RC D in Figure 5.7. Disaggregations were performed by finding the number of realizations where each component is in a damage state that relates to a loss of function at the target time. The disaggregation was repeated to determine the probability of each component impeding function at the recovery time targeted by each recovery category. The results shown for each component are independent of the performance of another component. However, as Ipfr is increased, components, 130 including those that are not impacted by Ipfr, may have a lower contribution because they can be repaired sooner. All results are shown are with seismic qualification of equipment. Additional disaggregations without seismic qualification are provided in Appendix D2. From Figure 5.7, we see that, for RC B, when Ipfr is equal to 1.0, the curtain walls, interior components, HVAC fan, and mechanical equipment most frequently impede function. When Ipfr is increased, the curtain wall contribution decreases, and the HVAC fan and mechanical equipment have the highest probability of impeding function. As is expected, structural damage contributes to the probability of exceeding the target but is limited because the Rfr and Δafr were selected to ensure a low probability of safety-critical structural damage in Chapter 4 (Blowes et al., 2025). The RC B and C models have the same simulated EDPs and components, with the primary difference being the recovery targets. For RC C, at 2 months, the structural component contribution is similar to that at the 3-day target because repairs to these components trigger longer impeding factor delays. We also see that most nonstructural components can be repaired by the 2-month target with modest increases to Ipfr. For the RC D models, the structural components have the highest probability of impeding function at the 6-month target if Ipfr is increased. The partitions also have a high probability of impeding function because their repairs are required to follow structural repairs. 131 *Denotes smart fragility Figure 5.7 Component disaggregations for Recovery Categories B, C, and D, with the seismic qualification of equipment. Disaggregations show the probability that each component impedes function at the specified functional recovery time target for an 8-story RC moment frame. 132 5.9 Impact of Ipfr on Functional Recovery Performance 5.9.1 Shear-Governed Reinforced Concrete Shear Wall Systems We considered both bearing wall and building frame configurations of low-rise, 3-story, shear-governed reinforced concrete shear wall archetypes. The results for the bearing wall systems are shown herein, but the results of both types of systems are provided in Appendix D2. Figure 5.8 shows the impact of Ipfr on the functional recovery time, provided all equipment is seismically certified. The results show that an Ipfr of 1.5 is required for RC B, 1.25 is required for RC C, and 1.0 is required for RC D. Figure 5.8 Impact of Ipfr on the probability of exceeding recovery targets for Recovery Categories B, C, and D, with seismic certification of equipment for shear-governed RCSW bearing wall systems. 5.9.2 Flexure-Governed Reinforced Concrete Shear Wall Systems Next, we consider flexure-governed RCSW systems, with heights ranging from 8 to 24 stories. We also considered both cantilever shear wall systems and coupled shear wall systems as shown in Figure 5.9a and b, respectively, for all heights considered. An Ipfr value of 1.75 is required for RC B and 1.5 is required for RC C. For RC D, for the cantilever walls (Figure 5.9a), an Ipfr of 1.25 is required and, for the coupled walls (Figure 5.9b), an Ipfr of 1.5 is required. The results for the 133 bearing wall systems are shown herein, but the results of the building frame systems are provided in Appendix D2. (a) (b) Figure 5.9 Impact of Ipfr on the probability of exceeding recovery targets for Recovery Categories B, C, and D, with seismic certification of equipment for flexure-governed RCSW (a) cantilever systems (bearing wall) and (b) coupled wall systems (bearing wall). 5.9.3 Steel Buckling Restrained Braced Frames Buckling restrained braced frames (BRBFs), with heights ranging from 3 to 16 stories, were considered next. Figure 5.10a shows the impact of Ipfr on the performance of the BRBF without a 134 backup frame. For RC B, an Ipfr of 2.5 is required. For RC C and D, an Ipfr of 1.75 is required. By contrast, Figure 5.10b shows that considerably lower values ensure adequate performance when the BRBF has a welded backup frame. For RC B and C, the target reliability can be achieved with an Ipfr of 1.5, and an Ipfr of 1.25 is required for RC D. (a) (b) Figure 5.10 Impact of Ipfr on the probability of exceeding recovery targets for Recovery Categories B, C, and D, with seismic certification of equipment for BRBFs with (a) without and (b) with a welded backup frame. 135 5.9.4 Steel Moment Frames Steel moment frames are considered next. We evaluated a reduced beam section (RBS) moment frame as the baseline case, although many proprietary systems that are either damped or more rapidly repairable are available. The analysis of these enhanced systems is beyond the scope of this study. Figure 5.11 shows that the Ipfr required for RC B and C is 1.5, and for RC D it is 1.75. For RC D, an Ipfr as low as 1.0 would meet the target for all heights considered except for the 8-story archetype, for which the reliability performance is closer to 30 %, slightly above the 25 % target. Figure 5.11 Impact of Ipfr on the probability of exceeding recovery targets for Recovery Categories B, C, and D, with seismic certification of equipment for steel moment frames (RBS). 5.10 Reinforced Concrete Moment Frames Finally, extending the case study presented, we considered a range of heights of RCMFs. The results for all heights are shown in Figure 5.12. For RC B, an Ipfr of 1.75 is required, for RC C, an Ipfr of 1.5 is required, and for RC D, an Ipfr of 1.25 is required. 136 Figure 5.12 Impact of Ipfr on the probability of exceeding recovery targets for Recovery Categories B, C, and D, with seismic certification of equipment for RCMFs. 5.11 Summary of Ipfr Required for All Systems From the results for each system, it can be observed that often one height or one system type governs. To inform the development of prescriptive seismic design provisions functional recovery performance, for a given Ipfr, we compute the average probability of recovery time exceeding the corresponding target across the building heights considered for each lateral resisting system. We then select the controlling Ipfr across the systems considered to ensure the 25% reliability target is met for each recovery category. This method provides a somewhat conservative upper bound on Ipfr values but allows for a slight relaxation in cases like the BRBF without the welded backup where some heights slightly exceed the 25% target. The Ipfr values required across systems, assuming equipment is seismically qualified, is summarized in Table 5.5. Table 5.5 Recommended Ipfr for various recovery categories with qualified equipment. Recovery Category Ipfr B 1.75 C 1.5 D 1.25 137 5.12 Nonstructural Components Likely to Impede Function Component disaggregation for all system and height combinations, similar to those presented earlier in Figure 8, are provided in Appendix D3. Here, we summarize findings across all systems to highlight nonstructural components that are likely to impede function. While we have focused this study on strategies to address all components, this subset of components could be used to develop more targeted requirements or to focus future research on improving the fragility functions used. First, we repeat the list of components that were excluded from the analyses due to lack of data or ability of the structural engineer to address them, but that have an outsized impact on functional recovery times. This list includes elevators, fire-rated partitions, lighting, and doors. Curtain wall damage also often leads to loss of function. Next, there are several types of mechanical equipment that frequently show up in the disaggregations, e.g., HVAC fan, control panel, switchgear, distribution panel, etc. Table 5.6 summarizes nonstructural components in each recovery category. Loss of function is typically driven by damage to this small number of components. The trends vary slightly across recovery categories because certain components can be repaired as recovery time targets increase. This list is relevant to office buildings, but the same methods outlined in this study could be applied to a wide range of occupancies to identify additional components that may be likely to impede function. Table 5.6 Components most likely to impede function. Component Name Elevators Fire-rated Partitions Lighting Doors Curtain Walls HVAC Fan Control Panel Switchgear Distribution Panel 138 5.13 Conclusions This study evaluated nonstructural component design requirements necessary to meet functional recovery targets outlined by the Building Seismic Safety Council for inclusion in the upcoming NEHRP recommendations for functional recovery design. We considered nonstructural design variations including amplification of nonstructural component forces through the inclusion of a nonstructural component importance factor, Ipfr. We also considered the impact of seismically qualifying equipment based on these increased design forces. All nonstructural design strategies were evaluated in conjunction with recently proposed response modification coefficients and allowable drift limits (i.e., Blowes et al., 2025) to limit safety-critical structural damage. The key outputs of this study include recommended component importance factors and equipment qualification requirements. Results across all systems considered indicate that the recovery targets cannot be met without seismically qualifying equipment. Further, we find that to meet a 25 % probability of exceedance of a 3-day recovery target for Recovery Category B, an Ipfr of 1.75 is required. Similarly, for Recovery Category C and D models, with 2-month and 6-month targets, an Ipfr of 1.5 and 1.25, respectively, is satisfactory for nearly all systems and heights considered. Finally, we also highlight the need to perform separate studies to evaluate the impact of damage to elevators, fire break partitions, and doors on building function. These components are likely to be damaged but were not addressed through this study because they are independent of the design interventions proposed and there is a lack of underlying data to characterize their response. While this study aims to inform prescriptive nonstructural component design provisions for functional recovery, the analyses performed are purely analytical. As such, the results are conditional on the modelling assumptions e.g., the input fragility functions, systems required for 139 function, etc. We aimed to use recent advances by incorporating smart fragilities (Welch et al., 2024) and fragilities updated with more recent data by the ATC-138 project (ATC, 2021b). For this study, we considered only one occupancy (i.e., office) that allowed us to capture nonstructural components of interest for this project. This study should be extended to other occupancies to reflect other commonly damaged components. We also selected a generic Dmax,FRE spectrum, which aims to capture the maximum expected demands for a Site Class D site. We suggest exploring responses in Site Class E and very high seismicity sites. Again, to capture average conditions, we did not consider surge demands or that the generic site used was in a dense area. The impact of surge demands on recovery has been well documented and included in functional recovery modeling tools (Cook et al., 2022; Olsen and Porter, 2011) and should be studied for future development of recovery-based design provisions. Finally, to limit scope, we did not consider repairability strategies (e.g., components designed to be repaired quickly when damaged or preparedness measures to rapidly address component damage to limit lengthy loss of function), component redundancy, and other simple but effective methods to increase resilience. Each of these topics is worthy of its own in-depth study. 5.14 Application to Canadian Building Code Development This chapter outlines a methodology to explicitly verify proposed structural and nonstructural design requirements that meet intended functional recovery performance goals. This method could be adopted to quantify the functional recover performance achieved with the NBCC 2020 Article 4.1.8.23 (NRCC, 2020) provisions (i.e., more stringent drift limits and increased anchorage design forces). In addition to the method proposed, the results show that qualifying equipment is critical to ensuring rapid post-earthquake function, yet this is not currently required in the Canadian provisions. 140 Chapter 6: Conclusions 6.1 Significant and Original Contributions While the research conducted to develop each chapter of this dissertation was extremely collaborative and represents discussions from a larger consensus-based process, I led the formulation of each study, calculations and analysis, and all writing. This dissertation, and particularly the last two chapters, underpins the development of the 2026 NEHRP Functional Recovery Provisions in the following ways: 1. Identifying damage mechanisms that functional recovery design provisions should address. 2. Establishing design requirements to be performed by engineers and demonstrating compliance with performance objectives. 3. Developing preliminary design parameters including, but not limited to, response modification coefficients, allowable drift limits, component importance factors, and additional design recommendations (e.g., provisions related to elevator function). To be able to make this contribution, I worked iteratively with many collaborators to provide the data needed to evaluate, make decisions, and revise the design requirements in the draft provisions. Each of their contributions is outlined in the Preface. Finally, beyond the direct impact on the 2026 NEHRP Functional Recovery Provisions, many key takeaways from each study are useful across a wide range of applications. Damage mechanisms, drivers of risk, and recovery time estimates identified in this dissertation provide insights into vulnerabilities of modern design and areas of focus for future research. The design recommendations and methods developed can provide a starting point for more detailed analyses and qualifying procedures, as well as comparison for other international building codes. 141 6.2 Detailed Summary of Key Findings This dissertation outlines methods to calculate functional recovery risk and provides first estimates of expected functional recovery performance, as well as the damage mechanisms that drive recovery issues over a range of intensity levels. The findings demonstrate that current life-safety design procedures do not ensure rapid post-earthquake recovery. To address this vulnerability, methods are then proposed to determine allowable drift limits and response modification coefficients to limit the types of damage that prevent immediate post-earthquake reoccupancy. The impact of nonstructural design interventions (e.g., qualifying equipment, component importance factors) is evaluated. Finally, the combined structural and nonstructural design requirements are explicitly verified to show their compliance with recovery targets for a wide range of building types and heights. This dissertation aims to fill a critical gap in research on the functional recovery performance of modern buildings. Each chapter directly supports the ongoing effort by the Building Seismic Safety Council (BSSC) to develop the first generation of recovery-based design provision; however, efforts are made to relate this to ongoing work in Canada to advance functional recovery code requirements. The methods and results discussed provide important guidance as countries begin to adopt recovery-based design provisions into their building codes. A detailed summary of key findings from each chapter is provided next 6.2.1 Finding 1: The risk of exceeding short recovery time targets is high for modern buildings. The introduction of performance objectives expressed in terms of recovery time has been identified as a key goal for the next generation of building codes. Further, the development of a new generation of functional recovery time assessment tools now allows for the discussion of how to use the outputs to establish recovery-based metrics for use in future design provisions. In Chapter 142 2, methods were adapted from life-safety provisions to evaluate building functional recovery performance using recovery time simulation outputs. A scenario-based, an intensity-based, and a risk-based analysis of functional recovery performance objectives were presented. The functional recovery performance of a series of modern residential reinforced concrete shear wall archetype buildings, ranging from eight to 24 stories in height, at a site in downtown Seattle, WA, were then assessed. Results of the scenario-based assessment of an M9 Cascadia Subduction zone earthquake, comparable to an intensity-based assessment at the 975-year intensity level, show that the probability of achieving functional recovery within four months is close to zero, while the likelihood of achieving functional recovery by one year is approximately 60%. The results of the risk-based assessment of the archetype buildings show a 50% probability in 50 years of the functional recovery time exceeding one month, a 43% in 50-year probability of the functional recovery time exceeding four months and an 8% in 50-year probability of the functional recovery time exceeding one year. Finally, the expected annual functional recovery time is approximately three days for all building heights considered. Disaggregation was used to identify intensity levels that contribute most to the functional recovery risk. The risk of the functional recovery time exceeding one month to six months is dominated by frequent, low intensity earthquakes (e.g., 100-year return period). As long recovery targets are considered, the risk of exceedance is increasingly dominated by less frequent, higher intensity earthquakes (i.e., return periods greater than 975 years). While the results of the analysis are sensitive to assumed damage thresholds and impeding factor delays triggered at low intensity levels, the findings suggest that reinforced concrete shear wall buildings designed following current building codes have a high risk of lengthy functional recovery times. Ultimately, the proposed methods and results illustrate the importance of introducing recovery-based provisions into the next generation of building codes. 143 6.2.2 Finding 2: Functional recovery risk is highly variable in the United States. As building codes in the United States move toward the development of functional recovery provisions aimed at reducing recovery times following earthquakes, it is critical to evaluate how buildings designed following life-safety provisions perform in terms of new recovery-based performance metrics. In Chapter 3, the functional recovery performance of an 8-story reinforced concrete shear wall archetype, generated to represent current life-safety design, was evaluated in 34 cities across the United States. A risk-based assessment of the functional recovery performance was conducted, using functional recovery target times ranging from two weeks to one year. The risk of damage to partitions and of safety-critical structural damage (i.e., structural red tags) was also calculated. The results were disaggregated by spectral acceleration to identify drivers of recovery risk. Results from Chapter 3 indicate that the risk of exceeding short recovery targets (i.e., recovery targets ranging from two weeks to one year) varies considerably across the 34 cities evaluated with current risk-targeting methods for collapse risk. Consistent with observations for life-safety performance, at deterministically capped sites, the 50-year functional recovery risk was also significantly higher than nearby sites with no capping. Overall, Chapter 3 results highlight the need to consider damage in frequent earthquakes (i.e., nonstructural damage) to improve the likelihood of achieving short recovery times. Further results indicate the need to consider risk-targeting for functional recovery performance to reduce the geographic variability in functional recovery risk. 6.2.3 Finding 3: Structural design requirements to limit safety-critical structural damage. In the move toward design practices that facilitate recovery in the United States, structural seismic design parameters such as design drift limits and response modification coefficients are being reevaluated. In Chapter 4, design modifications were proposed to limit the occurrence of safety-144 critical structural damage, i.e., damage that must be repaired for occupants to be able to return safely to a building. For a wide range of conventional lateral force-resisting systems, the impact of designing with increased strength and stiffness on the probability of safety-critical structural damage was evaluated. Systems evaluated include reinforced concrete shear walls, reinforced concrete moment frames, buckling-restrained braced frames and steel moment frames. For each system, models were developed to reflect combinations of drift limits ranging from 0.5%-2.0% and response modification coefficients ranging from 1 to current design values in ASCE 7. A design space was developed for each lateral force-resisting system type over a range of building heights (i.e., 3-24 stories). The design space was then used to identify potential combinations of design drift limits and response modification coefficients for a target safety-critical damage probability of 10% at a representative Dmax Seismic Design Category for the risk-targeted Functional Recovery Earthquake (FRER). Gravity systems typically combined with each lateral force-resisting system were also considered. Chapter 4 ultimately outlines a framework to evaluate and establish recommended design provisions in a broad range of systems. 6.2.4 Finding 4: Nonstructural design requirements and explicit verification of recovery performance. Past earthquakes have shown that nonstructural component damage often impedes function, even in modern buildings. As such, in the United States, the Building Seismic Safety Council (BSSC) is developing design recommendations that target a 25% probability at the FRER of exceeding 0 days for Recovery Category (RC) A, 3 days for RC B, 2 months for RC C, and 6 months for RC D. Chapter 5 explores the efficacy of nonstructural component design interventions in meeting these targets for RC B to D, with the expectation that RC A buildings will be addressed through explicit methods. Building on the work presented in Chapter 4, models were developed using 145 allowable drift limits and response modification coefficients that achieve a low probability of safety-critical structural damage. The building responses were then simulated at a representative Dmax Seismic Design Category to estimate damage and the functional recovery performance using the FEMA P-58 and ATC-138 methodologies. The functional recovery performance was assessed for increasing nonstructural component design forces by varying the seismic component importance factor for functional recovery, Ipfr, which is applied to both drift- and acceleration-sensitive components, from 1.0 to 3.0. The impact of seismic qualification was also simulated. Finally, the probability of meeting the recovery time targets was explicitly evaluated for each lateral force-resisting system, height, and recovery category. The results of Chapter 5 show that an Ipfr of 1.75 for RC B, an Ipfr of 1.5 for RC C, and an Ipfr of 1.25 for RC D, are required to meet the corresponding performance objectives at the FRER across the systems and heights considered. Chapter 5 results informed the 2026 NEHRP recommended seismic provisions by identifying the Ipfr and seismic qualification requirements for nonstructural components in buildings with structural systems designed to limit safety-critical structural damage. 6.3 Translation to Canadian Building Code Development The application of findings to the Canadian context was discussed throughout this dissertation. In Chapter 2, the methods to evaluate functional recovery performance and the damage mechanisms and earthquake intensities identified as drivers of risk could be useful for developing estimates of functional recovery risk in Canada. Chapter 3 further highlighted that nonstructural component damage in frequent earthquakes is critical and should be addressed in building codes to lower overall functional recovery risk. Finally, while Chapters 4 and 5 are specific to the U.S. building code, the methods used to assess safety-critical structural damage and functional recovery performance could complement ongoing experimental and analytical work underway in Canada. 146 Furthermore, these methods could be used to explicitly evaluate the recovery performance achieved by the NBCC 2020 design provisions. 6.4 Limitations and Future Work In developing this work, there are several limitations and opportunities for future work. These limitations are summarized below: 1) Functional Recovery Provisions Development is Ongoing: First, the proposed structural and nonstructural design requirements presented in Chapters 4 and 5, as well as the supporting calculations, reflect the 2026 NEHRP Functional Recovery Provisions development process up to January 2025. The draft provisions balloted in late 2024 (FEMA, 2024) are referenced throughout this dissertation. The NEHRP provisions development process, however, is ongoing and the draft provisions will continue to be modified and updated through a consensus-based process until their final publication. Therefore, the final provisions may deviate from the proposed design requirements that are presented in this dissertation. Furthermore, the journal articles that capture this work are also in review and will continue to be updated through the peer review process. 2) Soil Conditions: For each chapter, a single site class was used. Chapters 4 and 5 employed a Dmax,FRE spectrum that aimed to capture the highest expected level of shaking that prescriptive functional recovery provisions cover. This study also employed modeling strategies that used springs at the base to reflect the expected rotational restraint. Damage estimates and therefore recovery time estimates, however, depend on whether a building is on soft soil or on rock. Therefore, future work should be conducted to evaluate the sensitivity of the results on site classes from A and D, or alternatively over a range of shear wave velocities (Vs30s). This dissertation considered only damage from ground shaking, 147 and not secondary effects, such as liquefaction. Future work should also be conducted for site class E and F sites, where liquefaction is possible. 3) Soil-Structure Interaction: Soil-structure interaction is expected to have an impact on damage estimates as well. Stiff buildings on soft soils are likely to have more rigid body behaviour and, in turn, less structural and nonstructural component damage. Softer buildings on stiffer soils, by contrast, are expected to have more nonlinearity over the height of the building. Therefore, it is necessary to conduct sensitivity analyses that vary both the structural and soil stiffness to explore the variability of damage estimates. 4) Building Irregularities: All archetypes considered through this dissertation have regular geometry. Horizontal and vertical irregularities in the lateral or gravity force-resisting systems have not been considered. The use of regular archetypes aligns with the FEMA P-695 (FEMA, 2009b) methodology, which is used to qualify systems for life-safety in the United States. This limitation is also considered in the draft 2026 NEHRP Functional Recovery Provisions (FEMA, 2024) by prohibiting certain types of irregularities. These types of irregularities are expected to increase the risk of recovery issues and should be studied in greater detail with high-fidelity models. 5) Stiffness of Nonstructural Components: This work did not consider the impact of nonstructural components on the stiffness of the building, which may impact damage estimates. This effect is expected to be greatest in the low-rise concrete buildings considered where there is expected to be greater interaction between the nonstructural and structural systems. More detailed models should be developed for these types of buildings with linear springs to model the stiffness and brittle failure of the nonstructural component to improve damage estimates. 148 6) Wood Light-Frame Structures: In past earthquakes, a large portion of recovery issues have been associated with damage to one or two-story wood light-frame structures (Comerio and Blecher, 2010). This type of building was not included in this work because there is no way to decouple structural and nonstructural stiffness and there was less confidence in the use of simplified modeling methods to represent this interaction. This remains a major gap in current research that, if addressed, has the potential to have a profound influence on post-earthquake recovery. 7) Simplified Structural Analysis: In order to study a wide range of locations, systems, heights, and structural and nonstructural design interventions, the Structural Response Prediction Engine developed by HB-Risk (Cook et al., 2018; HB-Risk, 2025) was used. This tool uses the responses of simplified linear models to interpolate nonlinear responses from a bank of nonlinear analysis results generated from high-fidelity models, from past studies that have been heavily peer reviewed. Future studies should also be performed to validate the results using high-fidelity nonlinear models directly. Further, the results do not consider the effects of torsion. 8) Fragility Functions: Next, all of this work relies on fragility functions. The results are therefore only as good as the fragilities used. While efforts were made to use the most up to date fragilities from the FEMA P-58 database and eventually smart fragilities in Chapter 5 (Welch et al., 2024), there is still the need to conduct further research in this area to make sure fragilities reflect the latest design practice and test data. In Chapter 4, the probability of safety-critical structural damage was determined analytically. The methodology employs fragilities to estimate damage and then considers the severity and distribution of 149 the damage to determine the occurrence of safety-critical structural damage. These results should be compared to results from experimental studies. The overestimation of damage at low intensities that occurs when using fragility functions was also discussed. While truncation was applied in the last chapter of this work, more work should also be done to evaluate the sensitivity of results to truncation and whether further truncation is justified when enhanced performance and review is expected. 9) Impeding Factors: Baseline impeding factor delays from Cook et al. (2022) and Molina Hutt et al. (2022b) were used throughout this work. Impeding factor delays from both studies aim to capture the median delays for a modern building. Much more work is needed in this area to collect post-earthquake data that is both longitudinal and cross-sectional (i.e., reflects a wide range of social characteristics). Data that reflects a wider range of recovery experiences will ultimately strengthen the development of building code recommendations. Secondary impacts due to material shortages and surge demands were also not considered in this study but should also be considered in future work. Future experimental work should focus on determining post-earthquake residual capacity and drift limits that correlate to the onset of safety-critical structural damage for a wide range of structural systems. In terms of analytical studies, the focus should be on developing high-fidelity models to validate the proposed design recommendations. Other suggestions for future work include updating component fragilities to reflect experimental work, collecting more post-disaster data on function loss and impeding factors, and evaluating proposed increases in materials and costs. 150 This dissertation considers recovery at the building-level and each study simulates the recovery actions related to restoring function in the building. While the intent is to limit the scope of the recommendations to design changes and preparedness strategies within the purview of the practicing engineer, these boundaries should be highlighted. Resilience cannot be achieved in a vacuum and cannot be measured by the performance of an individual building. Factors beyond the scope of the engineer will undoubtedly impact the recovery experience. Researchers have considered the interplay of individual building recovery and regional models (Blagojević and Stojadinović, 2022), as well as the social dimensions of recovery (Costa et al., 2021). The design recommendations developed in this thesis should be considered for their impact across a wider range of dimensions. The design recommendations throughout this dissertation provide an important first step to address what happens to buildings and their occupants after a large earthquake. But the results are just that – a first step. While the qualifying procedures outlined and the preliminary recommendations are expected to have broad implications on the design of buildings in North America moving forward, the limitations outlined above highlight the need for additional detailed studies. This work should, and must, be considered only as a launch pad for future work. All of the proposed design interventions should additionally be evaluated for their impact on the environment and society. A key objective in developing resilience-based design provisions is to limit the requirement for demolition in large earthquakes due to the high environmental and societal cost of demolition and reconstruction. Imposing more stringent drift limits and strength requirements, however, could also lead to a considerable increase in embodied carbon. The increase in embodied carbon from these recovery-based design requirements should be heavily weighed against the current need to address the climate crisis. 151 6.5 Closing Remarks The study of functional recovery offers a new link between earthquake engineering and the communication of earthquake risk. In many ways, the foundation of this dissertation is in traditional performance-based earthquake engineering principles. This work is novel in that it translates and expands these methods first to evaluate recovery risk and to identify existing vulnerabilities. This work then focuses on using recovery-based performance metrics to work back to prescriptive building code requirements, supporting a new design paradigm that aims to align building recovery performance with public expectation. The translation of performance-based principles to recovery, however, was and will continue to be a major undertaking. Findings from each chapter open the discussion about how we may need to modify or reconsider calculation methods, where there are currently gaps in data, and how to improve confidence despite these gaps. This work establishes groundwork for these discussions. 152 Bibliography ACI, 2014. Building code requirements for structural concrete and commentary, ACI 318-14. Farmington Hills, MI: American Concrete Institute. ACI, 2019. Building code requirements for structural concrete and commentary, ACI 318-19. Farmington Hills, MI: American Concrete Institute. Allen, T. I., Luco, N., and Halchuk, S., 2015. Exploring risk-targeted ground motions for the National Building Code of Canada. Proceedings of the 11th Canadian Conference on Earthquake Engineering. Presented at the 11th Canadian Conference on Earthquake Engineering, Victoria, BC. Almufti, I., and Willford, M., 2013. Resilience-based earthquake design initiative (REDi) for the next generation of buildings. San Francisco, CA: Arup. ATC, 2005. ATC-20-2: Procedures for Postearthquake Safety Evaluation of Buildings. Redwood City, CA: ATC. ATC, 2021a. ATC 145-2: Resilient Repair Guide Source Report: Post-Earthquake Assessment of Reinforced Concrete Buildings. Redwood City, CA: ATC. ATC, 2021b. ATC-138-3: Seismic Performance Assessment of Buildings Volume 8 – Methodology for Assessment of Functional Recovery Time. Redwood City, CA: ATC. ATC, 2024. ATC 137-7: Scoping document for update of FEMA P-695. Redwood City, CA: ATC. ASCE/SEI, 2016. Minimum design loads for buildings and other structures, ASCE/SEI 7-16. Reston, VA: American Society of Civil Engineers. ASCE/SEI, 2022. Minimum design loads for buildings and other structures, ASCE/SEI 7-22. Reston, VA: American Society of Civil Engineers. ASME, 2022. ASME A17.1-2022 Safety Code for Elevators and Escalators. Baker, J. W., 2015. Efficient analytical fragility function fitting using dynamic structural analysis. Earthquake Spectra, 31(1), 579–599. DOI: 10.1193/021113EQS025M Baker, J. W., Almeter, E., Cook, D. T., Liel, A. B., and Haselton, C. B., 2024. A model for partially dependent component damage fragilities in seismic risk analysis. Earthquake Spectra, 40(1), 609–628. DOI: 10.1177/87552930231205790 Blagojević, N., and Stojadinović, B., 2022. A demand-supply framework for evaluating the effect of resource and service constraints on community disaster resilience. Resilient Cities and Structures, 1(1), 13–32. DOI: 10.1016/j.rcns.2022.03.001 153 Blowes, K., Kourehpaz, P., and Molina Hutt, C., 2023. Risk‐targeted seismic evaluation of functional recovery performance in buildings. Earthquake Engineering & Structural Dynamics, 52(13), 4245–4264. DOI: 10.1002/eqe.3984 Blowes, K., Molina Hutt, C., and Cook, D., 2024. Evaluating the variability in functional recovery performance in modern buildings across the United States. Proceedings of the 18th World Conference of Earthquake Engineering. Presented at the 18th World Conference of Earthquake Engineering, Milan, Italy. Blowes, K., Molina Hutt, C., Zimmerman, R., Cook, D., Almeter, E., and Haselton, C., 2025. Limiting safety-critical structural damage in recovery-based seismic design provisions. Earthquake Spectra. In Review. Bruneau, M., Chang, S. E., Eguchi, R. T., Lee, G. C., O’Rourke, T. D., Reinhorn, A. M., Shinozuka, M., et al., 2003. A framework to quantitatively assess and enhance the seismic resilience of communities. Earthquake Spectra, 19(4), 733–752. DOI: 10.1193/1.1623497 BSSC, 2023. Functional Recovery Planning Committee Report: Functional Recovery Task Committee Recommended Scope, Organization and Deliverables. Washington, DC: National Institute of Building Standards. Chang, S. E., 2016. Socioeconomic impacts of infrastructure disruptions. Oxford Research Encyclopedia of Natural Hazard Science. Oxford University Press. DOI: 10.1093/acrefore/9780199389407.013.66 Chang, S. E., Taylor, J. E., Elwood, K. J., Seville, E., Brunsdon, D., and Gartner, M., 2014. Urban disaster recovery in Christchurch: The Central Business District cordon and other critical decisions. Earthquake Spectra, 30(1), 513–532. DOI: 10.1193/022413EQS050M Comerio, M. C., and Blecher, H. E., 2010. Estimating downtime from data on residential buildings after the Northridge and Loma Prieta earthquakes. Earthquake Spectra, 26(4), 951–965. DOI: 10.1193/1.3477993 Cook, D. T., Liel, A. B., DeBock, D. J., and Haselton, C. B., 2021. Benchmarking FEMA P-58 repair costs and unsafe placards for the Northridge Earthquake: Implications for performance-based earthquake engineering. International Journal of Disaster Risk Reduction, 56, 102117. DOI: 10.1016/j.ijdrr.2021.102117 Cook, D. T., Liel, A. B., Haselton, C. B., and Koliou, M., 2022. A framework for operationalizing the assessment of post-earthquake functional recovery of buildings. Earthquake Spectra, 38(3), 1972–2007. DOI: 10.1177/87552930221081538 Cook, D. T., Liel, A. B., and Safiey, A., 2024. Earthquake functional recovery in modern reinforced concrete buildings. Journal of Structural Engineering, 150(9), 04024117. DOI: 10.1061/JSENDH.STENG-12904 154 Cook, D. T., Wade, K., Haselton, C. B., Baker, J. W., and DeBock, D. J., 2018. A structural response prediction engine to support advanced seismic risk assessment. Proceedings of the 11th National Conference of Earthquake Engineering. Presented at the 11th U.S. National Conference on Earthquake Engineering, Los Angeles, CA. Cornell, C. A., 1968. Engineering seismic risk analysis. Bulletin of the Seismological Society of America, 58(5), 1583–1606. Cornell, C. A., and Krawinkler, H., 2000. Progress and challenges in seismic performance assessment. Peer Center News, 3(2), 1–3. Costa, R., Haukaas, T., and Chang, S. E., 2021. Agent-based model for post-earthquake housing recovery. Earthquake Spectra, 37(1), 46–72. DOI: 10.1177/8755293020944175 Cremen, G., and Baker, J. W., 2018. Quantifying the benefits of building instruments to FEMA P-58 rapid post-earthquake damage and loss predictions. Engineering Structures, 176, 243–253. DOI: 10.1016/j.engstruct.2018.08.017 De Iuliis, M., Kammouh, O., Cimellaro, G. P., and Tesfamariam, S., 2019. Downtime estimation of building structures using fuzzy logic. International Journal of Disaster Risk Reduction, 34, 196–208. DOI: 10.1016/j.ijdrr.2018.11.017 DeBock, J., 2022, August 17. Building Reoccupancy and Recovery Times as Measured by the ATC-138 Functional Recovery Methodology. Presented at the ATC-138 Functional Recovery Project: Functional Recovery Workshop. Eads, L., Miranda, E., Krawinkler, H., and Lignos, D. G., 2013. An efficient method for estimating the collapse risk of structures in seismic regions. Earthquake Engineering & Structural Dynamics, 42(1), 25–41. DOI: 10.1002/eqe.2191 EERI, 2019. Functional recovery: A conceptual framework with policy options. Earthquake Engineering Research Institute. Eksir Monfared, A., Molina Hutt, C., Kakoty, P., Kourehpaz, P., and Centeno, J., 2021. Effects of the Georgia Sedimentary Basin on the response of modern tall RC shear-wall buildings to M9 Cascadia Subduction Zone earthquakes. Journal of Structural Engineering, 147(8), 05021003. DOI: 10.1061/(ASCE)ST.1943-541X.0003067 FEMA, 2009a. NEHRP Recommended Seismic Provisions for New Buildings and Other Structures (FEMA P-750/2009 Edition). Washington, DC. FEMA, 2009b. FEMA P-695: Quantification of Building Seismic Performance Factors. Washington, DC. FEMA, 2018a. Seismic Performance Assessment of Buildings, Volume 2 – Implementation Guide, FEMA P-58-2. Washington, DC: Federal Emergency Management Agency. 155 FEMA, 2018b. Seismic performance assessment of buildings, Volume 1 - Methodology, FEMA P-58-1. Washington, DC: Federal Emergency Management Agency. FEMA, 2018c. Seismic Performance Assessment of Buildings, Volume 3 – Supporting Electronic Materials and Background Documentation, Third Edition, FEMA P-58-3. Washington, DC: Federal Emergency Management Agency. FEMA, 2020. FEMA P-2082-1: NEHRP recommended seismic provisions for new buildings and other structures, Volume I: Part 1 Provisions, Part 2 Commentary. Federal Emergency Management Agency. FEMA, 2024. NEHRP Recommended Seismic Provisions for New Buildings and Other Structures (Draft). Federal Emergency Management Agency. Filiatrault, A., Uang, C.-M., Folz, B., and Christopoulos, C., 2001. Reconnaissance report of the February 28, 2001 Nisqually (Seattle-Olympia) Earthquake (Report No. SSRP–2001/02). University of California, San Diego. Fischer, E., 2014. Learning from Earthquakes: 2014 Napa Valley Earthquake Reconnaissance Report. Lyles School of Civil Engineering Graduate Student Reports. Frankel, A., 2013. Rupture history of the 2011 M 9 Tohoku Japan earthquake determined from strong‐motion and high‐rate GPS recordings: Subevents radiating energy in different frequency bands. Bulletin of the Seismological Society of America, 103(2B), 1290–1306. DOI: 10.1785/0120120148 Frankel, A., 2017. Modeling strong‐motion recordings of the 2010 Mw 8.8 Maule, Chile, earthquake with high stress‐drop subevents and background slip. Bulletin of the Seismological Society of America, 107(1), 372–386. DOI: 10.1785/0120160127 Frankel, A., Wirth, E., Marafi, N., Vidale, J., and Stephenson, W., 2018. Broadband synthetic seismograms for magnitude 9 earthquakes on the Cascadia Megathrust based on 3D simulations and stochastic synthetics, Part 1: Methodology and overall results. Bulletin of the Seismological Society of America, 108(5A), 2347–2369. DOI: 10.1785/0120180034 Galvis, F., 2022. Seismic risk and post-earthquake recovery of older tall buildings with welded steel moment frames. Stanford, CA: Stanford University. Gonzalez, R. E., Stephens, M. T., Toma, C., and Dowdell, D., 2022. The estimated carbon cost of concrete building demolitions following the Canterbury earthquake sequence. Earthquake Spectra, 38(3), 1615–1635. DOI: 10.1177/87552930221082684 Haselton Baker Risk Group, 2025. Seismic Performance Prediction Program (SP3). Retrieved from www.hbrisk.com 156 Haselton, C. B., Liel, A. B., Deierlein, G. G., Dean, B. S., and Chou, J. H., 2011. Seismic collapse safety of reinforced concrete buildings. I: Assessment of ductile moment frames. Journal of Structural Engineering, 137(4), 481–491. DOI: 10.1061/(ASCE)ST.1943-541X.0000318 Horspool, N., Hulsey, A., Elwood, K., and Gerstenberger, M., 2023. Risk-targeted hazard for seismic design in New Zealand considering individual and societal risk targets. Earthquake Spectra, 39(2), 1007–1036. DOI: 10.1177/87552930231156947 Hulsey, A., Elwood, K., Horspool, N., and Gerstenberger, M. C., 2022. Risk-targeted framework for seismic design: Maintaining serviceability. Proceedings of the 2022 New Zealand Society for Earthquake Engineering Annual Technical Conference. Presented at the NZSEE 2022 Annual Conference, Wellington, New Zealand. Hulsey, A. M., Baker, J. W., and Deierlein, G. G., 2022. High-resolution post-earthquake recovery simulation: Impact of safety cordons. Earthquake Spectra, 38(3), 2061–2087. DOI: 10.1177/87552930221075364 Iervolino, I., and Giorgio, M., 2015. Stochastic modeling of recovery from seismic shocks. Proceedings of the 12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12. Presented at the 12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12, Vancouver, Canada. Issa, O., Silva Lopez, R., Baker, J., and Burton, H. V., 2023. Machine-learning-based optimization framework to support recovery-based design. Earthquake Engineering & Structural Dynamics, 52, 3256–3280. DOI: 10.1002/eqe.3860 Jalayer, F., and Cornell, C. A., 2009. Alternative non-linear demand estimation methods for probability-based seismic assessments. Earthquake Engineering & Structural Dynamics, 38(8), 951–972. DOI: 10.1002/eqe.876 Jayaram, N., Lin, T., and Baker, J. W., 2011. A computationally efficient ground-motion selection algorithm for matching a target response spectrum mean and variance. Earthquake Spectra, 27(3), 797–815. DOI: 10.1193/1.3608002 Kakoty, P., Dyaga, S. M., and Molina Hutt, C., 2021. Impacts of simulated M9 Cascadia Subduction Zone earthquakes considering amplifications due to the Georgia sedimentary basin on reinforced concrete shear wall buildings. Earthquake Engineering & Structural Dynamics, 50(1), 237–256. DOI: 10.1002/eqe.3361 Kam, W. Y., Pampanin, S., and Elwood, K., 2011. Seismic performance of reinforced concrete buildings in the 22 February Christchurch (Lyttelton) earthquake. Bulletin of the New Zealand Society for Earthquake Engineering, 44(4), 239–278. DOI: 10.5459/bnzsee.44.4.239-278 157 Kersting, R., and Liel, A. B., 2024, July 30. Process and progress toward development of design criteria for functional recovery of buildings. Presented at the 18th World Conference on Earthquake Engineering, Presentation, Milan, Italy. Kim, J. J., Elwood, K. J., Marquis, F., and Chang, S. E., 2017. Factors influencing post-earthquake decisions on buildings in Christchurch, New Zealand. Earthquake Spectra, 33(2), 623–640. DOI: 10.1193/072516EQS120M Kolozvari, K., and Terzic, V., 2023. Methodology for developing practical recovery-based design requirements for buildings. Engineering Structures, 274, 115102. DOI: 10.1016/j.engstruct.2022.115102 Kourehpaz, P., and Molina Hutt, C., 2022. TREADS: Tool for Recovery Estimation And Downtime Simulation of buildings. Retrieved from https://github.com/carlosmolinahutt/treads Kourehpaz, P., Molina Hutt, C., Marafi, N. A., Berman, J. W., and Eberhard, M. O., 2021. Estimating economic losses of midrise reinforced concrete shear wall buildings in sedimentary basins by combining empirical and simulated seismic hazard characterizations. Earthquake Engineering & Structural Dynamics, 50(1), 26–42. DOI: 10.1002/eqe.3325 Lilliefors, H. W., 1967. On the Kolmogorov-Smirnov test for normality with mean and variance unknown. Journal of the American Statistical Association, 62(318), 399–402. Taylor & Francis. DOI: 10.1080/01621459.1967.10482916 Luco, N., Ellingwood, B. R., Hamburger, R. O., Hooper, J. D., Kimball, J. K., and Kircher, C. A., 2007. Risk-targeted versus current seismic design maps for the conterminous United States. Structural Engineers Association of California 2007 Convention Proceedings. Luco, N., Liu, T. J., and Rukstales, K. S., 2017. A risk-targeted alternative to deterministic capping of Maximum Considered Earthquake ground motion maps. Proceedings of the 16th World Conference on Earthquake Engineering. Presented at the 16th World Conference on Earthquake Engineering, 16WCEE, Santiago, Chile. Marafi, N. A., 2018. Impacts of an M9 Cascadia Subduction Zone Earthquake on Structures Located in Deep Sedimentary Basins. Seattle, WA: University of Washington. Marafi, N. A., Makdisi, A. J., Berman, J. W., and Eberhard, M. O., 2020. Design strategies to achieve target collapse risks for reinforced concrete wall buildings in sedimentary basins. Earthquake Spectra, 36(3), 1038–1073. DOI: 10.1177/875529301989172410.1177/8755293019899965 158 Marafi, N. A., Makdisi, A. J., Eberhard, M. O., and Berman, J. W., 2020. Impacts of an M9 Cascadia subduction zone earthquake and Seattle basin on performance of RC core wall buildings. Journal of Structural Engineering, 146(2). American Society of Civil Engineers. DOI: 10.1061/(ASCE)ST.1943-541X.0002490 Marquis, F., Kim, J. J., Elwood, K. J., and Chang, S. E., 2017. Understanding post-earthquake decisions on multi-storey concrete buildings in Christchurch, New Zealand. Bulletin of Earthquake Engineering, 15(2), 731–758. DOI: 10.1007/s10518-015-9772-8 Miranda, E., 1999. Approximate seismic lateral deformation demands in multistory buildings. Journal of Structural Engineering, 125(4), 417–425. DOI: 10.1061/(ASCE)0733-9445(1999)125:4(417) Miranda, E., 2000. Inelastic displacement ratios for structures on firm sites. Journal of Structural Engineering, 126(10), 1150–1159. DOI: 10.1061/(ASCE)0733-9445(2000)126:10(1150) Mitrani-Reiser, J., 2007. An Ounce of Prevention: Probabilistic Loss Estimation for Performance-Based Earthquake Engineering. California Institute of Technology. DOI:10.7907/JXPV-1Q19 Moehle, J., and Deierlein, G., 2004. A framework methodology for performance-based earthquake engineering. Presented at the 13th World Conference on Earthquake Engineering, Vancouver, Canada. Mohammadgholibeyki, N., Echeverria, M., Safiey, A., Cook, D., Koliou, M., and Liel, A. B., 2023. Assessing the feasibility of achieving functional recovery goals through seismic retrofit of existing reinforced concrete buildings. Earthquake Spectra, 39(4), 2123–2151. DOI: 10.1177/87552930231197669 Mohammadgholibeyki, N., Koliou, M., and Liel, A. B., 2023. A simple network-based probabilistic method for estimating recovery of lifeline services to buildings after an earthquake. Structure and Infrastructure Engineering, 1–17. DOI: 10.1080/15732479.2023.2177876 Molina Hutt, C., Hulsey, A. M., Kakoty, P., Deierlein, G. G., Eksir Monfared, A., Wen-Yi, Y., and Hooper, J. D., 2022. Toward functional recovery performance in the seismic design of modern tall buildings. Earthquake Spectra, 38(1), 283–309. DOI: 10.1177/87552930211033620 Molina Hutt, C., Rossetto, T., and Deierlein, G. G., 2019. Comparative risk-based seismic assessment of 1970s vs modern tall steel moment frames. Journal of Constructional Steel Research, 159, 598–610. DOI: 10.1016/j.jcsr.2019.05.012 Molina Hutt, C., Vahanvaty, T., and Kourehpaz, P., 2022. An analytical framework to assess earthquake-induced downtime and model recovery of buildings. Earthquake Spectra, 38(2), 1283–1320. DOI: 10.1177/87552930211060856 159 Molina Hutt, C., Zahedimazandarani, S., Marafi, N. A., Berman, J. W., and Eberhard, M. O., 2021. Collapse risk of pre-Northridge tall steel moment-resisting frames in the Seattle basin during large-magnitude subduction earthquakes. Engineering Structures, 244, 112751. DOI: 10.1016/j.engstruct.2021.112751 Molina Hutt, C., and Zimmerman, R. B., 2024. Toward prescriptive seismic design provisions for functional recovery: Nonstructural systems. Proceedings of the 18th World Conference on Earthquake Engineering. Presented at the 18th World Conference on Earthquake Engineering, Milan, Italy. Murray, P., Liel, A. B., and Elwood, K. J., 2022. A framework for assessing impaired seismic performance as a trigger for repair. Earthquake Engineering & Structural Dynamics, 51(2), 438–456. DOI: 10.1002/eqe.3573 NIST, 2021. Recommendations for Improved Seismic Performance of Nonstructural Components (No. NIST GCR 18-917-43). Gaithersburg, MD: NIST. DOI: 10.6028/NIST.GCR.18-917-43 NRCC, 2020. National Building Code of Canada 2020. NRCC, 2025. Structural Commentaries (User’s guide – NBC 2020: part 4 of division B). Olsen, A. H., and Porter, K. A., 2011. What we know about demand surge: Brief summary. Natural Hazards Review, 12(2), 62–71. DOI: 10.1061/(ASCE)NH.1527-6996.0000028 Olshansky, R. B., Johnson, L. A., and Topping, K. C., 2005. Opportunity in chaos: Rebuilding after the 1994 Northridge and 1995 Kobe earthquakes. Urbana, IL: Department of Urban and Regional Planning, University of Illinois Urbana-Champaign. Opabola, E. A., Abdullah, S. A., Elwood, K. J., and Wallace, J., 2023. Limit states for post-earthquake assessment and recovery analysis of ductile concrete components. Earthquake Spectra, 39(2), 799–828. DOI: 10.1177/87552930231170024 Opabola, E. A., and Elwood, K. J., 2024. Seismic design of concrete structures for damage control. Earthquake Spectra, 87552930241235487. DOI: 10.1177/87552930241235487 Parker, M., and Steenkamp, D., 2012. The economic impact of the Canterbury earthquakes. Reserve Bank of New Zealand: Bulletin, 75(3). Paul, N., Galasso, C., Baker, J., and Silva, V., 2025. A predictive model for household displacement duration after disasters. Risk Analysis, risa.17710. DOI: 10.1111/risa.17710 Paul, N., Galasso, C., Silva, V., and Baker, J., 2023. Benchmarking housing damage as a driver of population displacement following earthquakes. Proceedings of the Society for Earthquake and Civil Engineering Dynamics Conference. Presented at the SECED 2023 Conference, Cambridge, United Kingdom. 160 Paul, N., Lee, J. S., Mieler, M., and Almufti, I., 2018. Improving estimates of earthquake-induced downtime in individual buildings using the REDi methodology. Structures Conference 2018 (pp. 77–86). Presented at the Structures Conference 2018, Fort Worth, TX. DOI: 10.1061/9780784481349.008 Petersen, M. D., Moschetti, M. P., Powers, P. M., Mueller, C. S., Haller, K. M., Frankel, A. D., and Zeng, Y., 2014. Documentation for the 2014 Update of the United States National Seismic Hazard Maps (Open-File Report). Open-File Report. Reston, VA: U.S. Geological Survey. Stewart, J. P., Luco, N., Hooper, J. D., and Crouse, C. B., 2020. Risk-targeted alternatives to deterministic ground motion caps in U.S. seismic provisions. Earthquake Spectra, 36(2), 904–923. DOI: 10.1177/8755293019892010 Terzic, V., and Kolozvari, K., 2022. Probabilistic evaluation of post-earthquake functional recovery for a tall RC core wall building using F-Rec framework. Engineering Structures, 253, 113785. DOI: 10.1016/j.engstruct.2021.113785 Terzic, V., Villaneuva, P., Saldana, D., and Yoo, D., 2021. F-Rec framework: Novel framework for probabilistic evaluation of functional recovery of building systems (PEER Reports). PEER Reports. Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA. DOI: 10.55461/DPBD8076 Terzic, V., Yoo, D. Y., and Aryan, A. H., 2016. Repair time model for buildings considering the earthquake hazard. Structural Engineers Association of California 2016 Convention Proceedings. Maui, HI. USGS, 2017. The HayWired Earthquake Scenario (No. 2017–5013). Menlo Park, CA: Earthquake Science Center. DOI: 10.3133/sir20175013. Vahanvaty, T., 2021. An Analytical Framework to Estimate Downtime and Model the Recovery of Buildings after an Earthquake. Vancouver, CA: University of British Columbia, Vancouver. Valigura, J., Cook, D., and Sattar, S., 2024. Construction quality assurance for functional recovery design. Structural Engineers Association of California 2024 Convention Proceedings. Portland, OR. Vamvatsikos, D., and Cornell, C. A., 2002. Incremental dynamic analysis. Earthquake Engineering & Structural Dynamics, 31(3), 491–514. DOI: 10.1002/eqe.141 Welch, D. P., Echeverria, M. J., Almeter, E., DeBock, D. J., Haselton, C. B., Cook, D. T., and Liel, A. B., 2024. Improved FEMA P-58 fragility functions for acceleration-sensitive components for functional recovery. Proceedings of the 18th World Conference on Earthquake Engineering. Presented at the 18th World Conference on Earthquake Engineering, Milan, Italy. 161 Zsarnoczay, A., and Kourehpaz, P., 2021. Pelicun: Probabilistic estimation of losses, injuries, and community resilience under natural disasters, v2.6. NHERI-SimCenter. Retrieved from doi.org/10.5281/zenodo.5812453 162 Electronic Supplements The date compiled as a companion to each chapter can be found my locating the relevant paper in the publications list found on the following web page: www.carlosmolinahutt.com/publications and accessing the supplied “Electronic Supplement” link. The relevant papers are noted at the start of each chapter and repeated below for ease of reference. The chapter numbers are provided throughout this text to ease navigation but are not included within the electronic supplement of each relevant paper. The data will be updated to reflect published journal articles. The organization of the electronic supplements is as follows: Chapter 2: Blowes, K., Kourehpaz, P., and Molina Hutt, C., 2023. Risk‐targeted seismic evaluation of functional recovery performance in buildings. Earthquake Engineering & Structural Dynamics, 52(13), 4245–4264. DOI: 10.1002/eqe.3984 o S2.1: Inputs o S2.2: Functional Recovery Time Models o S2.3: Scenario- and Intensity-based Assessment Results o S2.4: Risk-based Assessment Results Chapter 3: Blowes, K., Molina Hutt, C., and Cook, D., 2024. Evaluating the variability in functional recovery performance in modern buildings across the United States. Proceedings of the 18th World Conference of Earthquake Engineering. Presented at the 18th World Conference of Earthquake Engineering, Milan, Italy. o S3.1: Inputs o S3.2: Risk-based Assessment Results 163 Chapter 4: Blowes, K., Molina Hutt, C., Zimmerman, R., Cook, D., Almeter, E., and Haselton, C., 2025a. Limiting safety-critical structural damage in recovery-based seismic design provisions. Earthquake Spectra (In Review). o S4.1: Inputs  Building performance model assumptions (fragilities, distributions)  Dmax,FRE and Dmax,DE spectra o S4.2: Safety Critical Structural Damage Outputs  Building periods and median engineering demand parameters (EDPs)  Safety-critical structural damage data Chapter 5: Blowes, K., Molina Hutt, C., Zimmerman, R., Cook, D., Almeter, E., and Haselton, C., 2025b. Nonstructural component design requirements for functional recovery performance. Earthquake Spectra (In Review). o S5.1: Inputs  Building performance model assumptions (fragilities, distributions)  Component interventions applied o S5.2: Functional Recovery Time Outputs  Building periods and median engineering demand parameters (EDPs)  Functional recovery time data o S5.3: Component Disaggregation Data 164 Appendix A A.1 Risk-Based Assessment Results for All RCSW Archetype Heights Appendix A.1 provides hazard curves, fragility functions, and disaggregations for all RCSW archetypes considered in Chapter 2. (a) (b) Figure A.1.1 (a) Hazard curve and (b) fragility functions for various time targets for an 8-story RCSW archetype building. (a) (b) Figure A.1.2 (a) Hazard curve and (b) fragility functions for various time targets for a 12-story RCSW archetype building. 165 (a) (b) Figure A.1.3 (a) Hazard curve and (b) fragility functions for various time targets for a 16-story RCSW archetype building. (a) (b) Figure A.1.4 (a) Hazard curve and (b) fragility functions for various time targets for a 20-story RCSW archetype building. 166 (a) (b) Figure A.1.5 (a) Hazard curve and (b) fragility functions for various time targets for a 24-story RCSW archetype building. 167 (a) (b) (c) (d) (e) Figure A.1.6 Normalized risk disaggregation for an 8-story RCSW archetype with recovery time targets of (a) 1 month, (b) 4 months, (c) 6 months, (d) 1 year, and (e) 1 ½ years. 168 (a) (b) (c) (d) (e) Figure A.1.7 Normalized risk disaggregation for a 12-story RCSW archetype with recovery time targets of (a) 1 month, (b) 4 months, (c) 6 months, (d) 1 year, and (e) 1 ½ years. 169 (a) (b) (c) (d) (e) Figure A.1.8 Normalized risk disaggregation for a 16-story RCSW archetype with recovery time targets of (a) 1 month, (b) 4 months, (c) 6 months, (d) 1 year, and (e) 1 ½ years. 170 (a) (b) (c) (d) (e) Figure A.1.9 Normalized risk disaggregation for a 20-story RCSW archetype with recovery time targets of (a) 1 month, (b) 4 months, (c) 6 months, (d) 1 year, and (e) 1 ½ years. 171 (a) (b) (c) (d) (e) Figure A.1.10 Normalized risk disaggregation for a 24-story RCSW archetype with recovery time targets of (a) 1 month, (b) 4 months, (c) 6 months, (d) 1 year, and (e) 1 ½ years. 172 Appendix B B.1 Risk-Based Assessment of Functional Recovery Time for 34 Cities – Fragilities and Disaggregation Plots Appendix B.1 provides fragility functions for recovery time targets ranging from two weeks to one year for all 34 cities considered in Chapter 3. Plots of the disaggregations by spectral acceleration of at the first mode period for the 34 cities are also provided. A handful of sites have few or no realizations where recovery times exceed one year, therefore the 50-year probability is approximately zero. The one-year target is not shown for sites where this occurs. (a) (b) Figure B.1.1 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Los Angeles. (a) (b) Figure B.1.2 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Century City. 173 (a) (b) Figure B.1.3 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Northridge. (a) (b) Figure B.1.4 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Long Beach. (a) (b) Figure B.1.5 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Irvine. 174 (a) (b) Figure B.1.6 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Riverside. (a) (b) Figure B.1.7 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in San Bernardino. (a) (b) Figure B.1.8 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in San Luis Obispo. 175 (a) (b) Figure B.1.9 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in San Diego. (a) (b) Figure B.1.10 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Santa Barbara. (a) (b) Figure B.1.11 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Ventura. 176 (a) (b) Figure B.1.12 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Oakland. (a) (b) Figure B.1.13 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Concord. (a) (b) Figure B.1.14 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Monterey. 177 (a) (b) Figure B.1.15 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Sacramento. (a) (b) Figure B.1.16 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in San Francisco. (a) (b) Figure B.1.17 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in San Mateo. 178 (a) (b) Figure B.1.18 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in San Jose. (a) (b) Figure B.1.19 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Santa Cruz. (a) (b) Figure B.1.20 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Vallejo. 179 (a) (b) Figure B.1.21 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Santa Rosa. (a) (b) Figure B.1.22 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Seattle. (a) (b) Figure B.1.23 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Tacoma. 180 (a) (b) Figure B.1.24 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Everett. (a) (b) Figure B.1.25 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Portland. (a) (b) Figure B.1.26 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Salt Lake City. 181 (a) (b) Figure B.1.27 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Boise. (a) (b) Figure B.1.28 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Reno. (a) (b) Figure B.1.29 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Las Vegas. 182 (a) (b) Figure B.1.30 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in St. Louis. (a) (b) Figure B.1.31 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Memphis. (a) (b) Figure B.1.32 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Charleston. 183 (a) (b) Figure B.1.33 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Chicago. (a) (b) Figure B.1.34 (a) Hazard curve and functional recovery fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in New York. 184 B.2 Risk-Based Assessment of Severe Partition Damage Time for 34 Cities – Fragilities and Disaggregation Plots Appendix B.2 provides fragility functions for partition damage for all 34 cities considered in Chapter 3. Plots of the disaggregation by spectral acceleration of at the first mode period for the 34 cities are also provided. A handful of low-seismicity sites have few or no realizations where severe partition damage occurs, therefore the 50-year probability is approximately zero and there are no plots for these sites. (a) (b) Figure B.2.1 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Los Angeles. (a) (b) Figure B.2.2 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Century City. 185 (a) (b) Figure B.2.3 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Northridge. (a) (b) Figure B.2.4 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Long Beach. (a) (b) Figure B.2.5 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Irvine. 186 (a) (b) Figure B.2.6 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Riverside. (a) (b) Figure B.2.7 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in San Bernardino. (a) (b) Figure B.2.8 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in San Luis Obispo. 187 (a) (b) Figure B.2.9 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in San Diego. (a) (b) Figure B.2.10 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Santa Barbara. (a) (b) Figure B.2.11 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Ventura. 188 (a) (b) Figure B.2.12 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Oakland. (a) (b) Figure B.2.13 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Concord. (a) (b) Figure B.2.14 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Monterey. 189 (a) (b) Figure B.2.15 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Sacramento. (a) (b) Figure B.2.16 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in San Francisco. (a) (b) Figure B.2.17 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in San Mateo. 190 (a) (b) Figure B.2.18 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in San Jose. (a) (b) Figure B.2.19 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Santa Cruz. (a) (b) Figure B.2.20 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Vallejo. 191 (a) (b) Figure B.2.21 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Santa Rosa. (a) (b) Figure B.2.22 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Seattle. (a) (b) Figure B.2.23 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Tacoma. 192 (a) (b) Figure B.2.24 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Everett. (a) (b) Figure B.2.25 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Portland. (a) (b) Figure B.2.26 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Salt Lake City. 193 (a) (b) Figure B.2.27 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Boise. (a) (b) Figure B.2.28 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Reno. (a) (b) Figure B.2.29 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Las Vegas. 194 (a) (b) Figure B.2.30 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in St. Louis. (a) (b) Figure B.2.31 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Memphis. (a) (b) Figure B.2.32 (a) Hazard curve and partition damage (DS3) fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Charleston. 195 B.3 Risk-Based Assessment of Safety-Critical Structural Damage Time for 34 Cities – Fragilities and Disaggregation Plots Appendix B.3 provides fragility functions for structural red tags, which was used as metric for safety-critical structural damage, for all 34 cities considered in Chapter 3. Plots of the disaggregation by spectral acceleration of at the first mode period for the 34 cities are also provided. A handful of sites have few or no realizations where red tags occur, therefore the 50-year probability is approximately zero and there are no plots for these sites. (a) (b) Figure B.3.1 (a) Hazard curve and red tag fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Los Angeles. (a) (b) Figure B.3.2 (a) Hazard curve and red tag fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Century City. 196 (a) (b) Figure B.3.3 (a) Hazard curve and red tag fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Northridge. (a) (b) Figure B.3.4 (a) Hazard curve and red tag fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Long Beach. (a) (b) Figure B.3.5 (a) Hazard curve and red tag fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Irvine. 197 (a) (b) Figure B.3.6 (a) Hazard curve and red tag fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Riverside. (a) (b) Figure B.3.7 (a) Hazard curve and red tag fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in San Bernardino. (a) (b) Figure B.3.8 (a) Hazard curve and red tag fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in San Diego. 198 (a) (b) Figure B.3.9 (a) Hazard curve and red tag fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Santa Barbara. (a) (b) Figure B.3.10 (a) Hazard curve and red tag fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Ventura. (a) (b) Figure B.3.11 (a) Hazard curve and red tag fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Oakland. 199 (a) (b) Figure B.3.12 (a) Hazard curve and red tag fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Concord. (a) (b) Figure B.3.13 (a) Hazard curve and red tag fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in San Francisco. (a) (b) Figure B.3.14 (a) Hazard curve and red tag fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in San Mateo. 200 (a) (b) Figure B.3.15 (a) Hazard curve and red tag fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in San Jose. (a) (b) Figure B.3.16 (a) Hazard curve and red tag fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Santa Cruz. (a) (b) Figure B.3.17 (a) Hazard curve and red tag fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Vallejo. 201 (a) (b) Figure B.3.18 (a) Hazard curve and red tag fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Santa Rosa. (a) (b) Figure B.3.19 (a) Hazard curve and red tag fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Seattle. (a) (b) Figure B.3.20 (a) Hazard curve and red tag fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Tacoma. 202 (a) (b) Figure B.3.21 (a) Hazard curve and red tag fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Everett. (a) (b) Figure B.3.22 (a) Hazard curve and red tag fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Portland. (a) (b) Figure B.3.23 (a) Hazard curve and red tag fragility functions and (b) disaggregation by spectral acceleration for an RCSW archetype in Reno. 203 Appendix C C.1 Engineering Demand Parameter Plots for All Systems and Heights Appendix C.1 provides median story drift ratios and peak floor accelerations for all lateral force-resisting system types and heights considered in Chapter 4, which have allowable drift limits ranging from 0.5% to 2.0%. (a) (b) Figure C.1.1 (a) Story drift ratio and (b) peak floor acceleration for 3-story RC Cantilever Shear Wall (Bearing Wall) (PT slab) models. (a) (b) Figure C.1.2 (a) Story drift ratio and (b) peak floor acceleration for 3-story RC Cantilever Shear Wall (Bearing Wall) (Steel Frame) models. 204 (a) (b) Figure C.1.3 (a) Story drift ratio and (b) peak floor acceleration for 3-story RC Cantilever Shear Wall (Bearing Wall) (Standard Slab) models. (a) (b) Figure C.1.4 (a) Story drift ratio and (b) peak floor acceleration for 8-story RC Cantilever Shear Wall (Bearing Wall) (PT slab) models. (a) (b) Figure C.1.5 (a) Story drift ratio and (b) peak floor acceleration for 16-story RC Cantilever Shear Wall (Bearing Wall) (PT slab) models. 205 (a) (b) Figure C.1.6 (a) Story drift ratio and (b) peak floor acceleration for 24-story RC Cantilever Shear Wall (Bearing Wall) (PT slab) models. (a) (b) Figure C.1.7 (a) Story drift ratio and (b) peak floor acceleration for 8-story RC Cantilever Shear Wall (Bearing Wall) (Steel Frame) models. (a) (b) Figure C.1.8 (a) Story drift ratio and (b) peak floor acceleration for 16-story RC Cantilever Shear Wall (Bearing Wall) (Steel Frame) models. 206 (a) (b) Figure C.1.9 (a) Story drift ratio and (b) peak floor acceleration for 24-story RC Cantilever Shear Wall (Bearing Wall) (Steel Frame) models. (a) (b) Figure C.1.10 (a) Story drift ratio and (b) peak floor acceleration for 8-story RC Cantilever Shear Wall (Bearing Wall) (Standard Slab) models. (a) (b) Figure C.1.11 (a) Story drift ratio and (b) peak floor acceleration for 16-story RC Cantilever Shear Wall (Bearing Wall) (Standard Slab) models. 207 (a) (b) Figure C.1.12 (a) Story drift ratio and (b) peak floor acceleration for 24-story RC Cantilever Shear Wall (Bearing Wall) (Standard Slab) models. (a) (b) Figure C.1.13 (a) Story drift ratio and (b) peak floor acceleration for 8-story RC Coupled Shear Wall (Bearing Wall) (PT slab) models. (a) (b) Figure C.1.14 (a) Story drift ratio and (b) peak floor acceleration for 16-story RC Coupled Shear Wall (Bearing Wall) (PT slab) models. 208 (a) (b) Figure C.1.15 (a) Story drift ratio and (b) peak floor acceleration for 24-story RC Coupled Shear Wall (Bearing Wall) (PT slab) models. (a) (b) Figure C.1.16 (a) Story drift ratio and (b) peak floor acceleration for 8-story RC Coupled Shear Wall (Bearing Wall) (Steel Frame) models. (a) (b) Figure C.1.17 (a) Story drift ratio and (b) peak floor acceleration for 16-story RC Coupled Shear Wall (Bearing Wall) (Steel Frame) models. 209 (a) (b) Figure C.1.18 (a) Story drift ratio and (b) peak floor acceleration for 24-story RC Coupled Shear Wall (Bearing Wall) (Steel Frame) models. (a) (b) Figure C.1.19 (a) Story drift ratio and (b) peak floor acceleration for 8-story RC Coupled Shear Wall (Bearing Wall) (Standard Slab) models. (a) (b) Figure C.1.20 (a) Story drift ratio and (b) peak floor acceleration for 16-story RC Coupled Shear Wall (Bearing Wall) (Standard Slab) models. 210 (a) (b) Figure C.1.21 (a) Story drift ratio and (b) peak floor acceleration for 24-story RC Coupled Shear Wall (Bearing Wall) (Standard Slab) models. (a) (b) Figure C.1.22 (a) Story drift ratio and (b) peak floor acceleration for 3-story RC Cantilever Shear Wall (Building Frame) (PT slab) models. (a) (b) Figure C.1.23 (a) Story drift ratio and (b) peak floor acceleration for 3-story RC Cantilever Shear Wall (Building Frame) (Steel Frame) models. 211 (a) (b) Figure C.1.24 (a) Story drift ratio and (b) peak floor acceleration for 3-story RC Cantilever Shear Wall (Building Frame) (Standard Slab) models. (a) (b) Figure C.1.25 (a) Story drift ratio and (b) peak floor acceleration for 8-story RC Cantilever Shear Wall (Building Frame) (PT slab) models. (a) (b) Figure C.1.26 (a) Story drift ratio and (b) peak floor acceleration for 16-story RC Cantilever Shear Wall (Building Frame) (PT slab) models. 212 (a) (b) Figure C.1.27 (a) Story drift ratio and (b) peak floor acceleration for 24-story RC Cantilever Shear Wall (Building Frame) (PT slab) models. (a) (b) Figure C.1.28 (a) Story drift ratio and (b) peak floor acceleration for 8-story RC Cantilever Shear Wall (Building Frame) (Steel Frame) models. (a) (b) Figure C.1.29 (a) Story drift ratio and (b) peak floor acceleration for 16-story RC Cantilever Shear Wall (Building Frame) (Steel Frame) models. 213 (a) (b) Figure C.1.30 (a) Story drift ratio and (b) peak floor acceleration for 24-story RC Cantilever Shear Wall (Building Frame) (Steel Frame) models. (a) (b) Figure C.1.31 (a) Story drift ratio and (b) peak floor acceleration for 8-story RC Cantilever Shear Wall (Building Frame) (Standard Slab) models. (a) (b) Figure C.1.32 (a) Story drift ratio and (b) peak floor acceleration for 16-story RC Cantilever Shear Wall (Building Frame) (Standard Slab) models. 214 (a) (b) Figure C.1.33 (a) Story drift ratio and (b) peak floor acceleration for 24-story RC Cantilever Shear Wall (Building Frame) (Standard Slab) models. (a) (b) Figure C.1.34 (a) Story drift ratio and (b) peak floor acceleration for 8-story RC Coupled Shear Wall (Building Frame) (PT slab) models. (a) (b) Figure C.1.35 (a) Story drift ratio and (b) peak floor acceleration for 16-story RC Coupled Shear Wall (Building Frame) (PT slab) models. 215 (a) (b) Figure C.1.36 (a) Story drift ratio and (b) peak floor acceleration for 24-story RC Coupled Shear Wall (Building Frame) (PT slab) models. (a) (b) Figure C.1.37 (a) Story drift ratio and (b) peak floor acceleration for 8-story RC Coupled Shear Wall (Building Frame) (Steel Frame) models. (a) (b) Figure C.1.38 (a) Story drift ratio and (b) peak floor acceleration for 16-story RC Coupled Shear Wall (Building Frame) (Steel Frame) models. 216 (a) (b) Figure C.1.39 (a) Story drift ratio and (b) peak floor acceleration for 24-story RC Coupled Shear Wall (Building Frame) (Steel Frame) models. (a) (b) Figure C.1.40 (a) Story drift ratio and (b) peak floor acceleration for 8-story RC Coupled Shear Wall (Building Frame) (Standard Slab) models. (a) (b) Figure C.1.41 (a) Story drift ratio and (b) peak floor acceleration for 16-story RC Coupled Shear Wall (Building Frame) (Standard Slab) models. 217 (a) (b) Figure C.1.42 (a) Story drift ratio and (b) peak floor acceleration for 24-story RC Coupled Shear Wall (Building Frame) (Standard Slab) models. (a) (b) Figure C.1.43 (a) Story drift ratio and (b) peak floor acceleration for 3-story BRBF (no backup) (Steel Frame) models. (a) (b) Figure C.1.44 (a) Story drift ratio and (b) peak floor acceleration for 8-story BRBF (no backup) (Steel Frame) models. 218 (a) (b) Figure C.1.45 (a) Story drift ratio and (b) peak floor acceleration for 16-story BRBF (no backup) (Steel Frame) models. (a) (b) Figure C.1.46 (a) Story drift ratio and (b) peak floor acceleration for 3-story BRBF (backup) (Steel Frame) models. (a) (b) Figure C.1.47 (a) Story drift ratio and (b) peak floor acceleration for 8-story BRBF (backup) (Steel Frame) models. 219 (a) (b) Figure C.1.48 (a) Story drift ratio and (b) peak floor acceleration for 16-story BRBF (backup) (Steel Frame) models. (a) (b) Figure C.1.49 (a) Story drift ratio and (b) peak floor acceleration for 3-story Steel SMF (RBS) (Steel Frame) models. (a) (b) Figure C.1.50 (a) Story drift ratio and (b) peak floor acceleration for 8-story Steel SMF (RBS) (Steel Frame) models. 220 (a) (b) Figure C.1.51 (a) Story drift ratio and (b) peak floor acceleration for 16-story Steel SMF (RBS) (Steel Frame) models. (a) (b) Figure C.1.52 (a) Story drift ratio and (b) peak floor acceleration for 24-story Steel SMF (RBS) (Steel Frame) models. (a) (b) Figure C.1.53 (a) Story drift ratio and (b) peak floor acceleration for 8-story RC Perimeter Frame (PT slab) models. 221 (a) (b) Figure C.1.54 (a) Story drift ratio and (b) peak floor acceleration for 16-story RC Perimeter Frame (PT slab) models. (a) (b) Figure C.1.55 (a) Story drift ratio and (b) peak floor acceleration for 24-story RC Perimeter Frame (PT slab) models. (a) (b) Figure C.1.56 (a) Story drift ratio and (b) peak floor acceleration for 8-story RC Perimeter Frame (Standard Slab) models. 222 (a) (b) Figure C.1.57 (a) Story drift ratio and (b) peak floor acceleration for 16-story RC Perimeter Frame (Standard Slab) models. (a) (b) Figure C.1.58 (a) Story drift ratio and (b) peak floor acceleration for 24-story RC Perimeter Frame (Standard Slab) models. 223 C.2 Relationship Between Realized Drift and Safety-Critical Structural Damage for All Heights Appendix C.2 provides the probability of safety-critical structural damage as a function of the median story drift ratio at the most critical story. Plots are provided for all lateral force-resisting system types, gravity force-resisting system types, and heights considered in Chapter 4. Results are included for models with allowable drift limits ranging from 0.5% to 2.0%. Figure C.2.1 Probability of safety-critical structural damage as a function of maximum story drift of the median realization for all RC Cantilever Shear Wall (Bearing Wall) (PT slab) models. Figure C.2.2 Probability of safety-critical structural damage as a function of maximum story drift of the median realization for all RC Cantilever Shear Wall (Bearing Wall) (Steel Frame) models. 224 Figure C.2.3 Probability of safety-critical structural damage as a function of maximum story drift of the median realization for all RC Cantilever Shear Wall (Bearing Wall) (Standard Slab) models. Figure C.2.4 Probability of safety-critical structural damage as a function of maximum story drift of the median realization for all RC Cantilever Shear Wall (Bearing Wall) (PT slab) models. Figure C.2.5 Probability of safety-critical structural damage as a function of maximum story drift of the median realization for all RC Cantilever Shear Wall (Bearing Wall) (Steel Frame) models. 225 Figure C.2.6 Probability of safety-critical structural damage as a function of maximum story drift of the median realization for all RC Cantilever Shear Wall (Bearing Wall) (Standard Slab) models. Figure C.2.7 Probability of safety-critical structural damage as a function of maximum story drift of the median realization for all RC Coupled Shear Wall (Bearing Wall) (PT slab) models. Figure C.2.8 Probability of safety-critical structural damage as a function of maximum story drift of the median realization for all RC Coupled Shear Wall (Bearing Wall) (Steel Frame) models. 226 Figure C.2.9 Probability of safety-critical structural damage as a function of maximum story drift of the median realization for all RC Coupled Shear Wall (Bearing Wall) (Standard Slab) models. Figure C.2.10 Probability of safety-critical structural damage as a function of maximum story drift of the median realization for all RC Cantilever Shear Wall (Building Frame) (PT slab) models. Figure C.2.11 Probability of safety-critical structural damage as a function of maximum story drift of the median realization for all RC Cantilever Shear Wall (Building Frame) (Steel Frame) models. 227 Figure C.2.12 Probability of safety-critical structural damage as a function of maximum story drift of the median realization for all RC Cantilever Shear Wall (Building Frame) (Standard Slab) models. Figure C.2.13 Probability of safety-critical structural damage as a function of maximum story drift of the median realization for all RC Cantilever Shear Wall (Building Frame) (PT slab) models. Figure C.2.14 Probability of safety-critical structural damage as a function of maximum story drift of the median realization for all RC Cantilever Shear Wall (Building Frame) (Steel Frame) models. 228 Figure C.2.15 Probability of safety-critical structural damage as a function of maximum story drift of the median realization for all RC Cantilever Shear Wall (Building Frame) (Standard Slab) models. Figure C.2.16 Probability of safety-critical structural damage as a function of maximum story drift of the median realization for all RC Coupled Shear Wall (Building Frame) (PT slab) models. Figure C.2.17 Probability of safety-critical structural damage as a function of maximum story drift of the median realization for all RC Coupled Shear Wall (Building Frame) (Steel Frame) models. 229 Figure C.2.18 Probability of safety-critical structural damage as a function of maximum story drift of the median realization for all RC Coupled Shear Wall (Building Frame) (Standard Slab) models. Figure C.2.19 Probability of safety-critical structural damage as a function of maximum story drift of the median realization for all BRBF (no backup) (Steel Frame) models. Figure C.2.20 Probability of safety-critical structural damage as a function of maximum story drift of the median realization for all BRBF (backup) (Steel Frame) models. 230 Figure C.2.21 Probability of safety-critical structural damage as a function of maximum story drift of the median realization for all Steel SMF (RBS) (Steel Frame) models. Figure C.2.22 Probability of safety-critical structural damage as a function of maximum story drift of the median realization for all RC Perimeter Frame (PT slab) models. Figure C.2.23 Probability of safety-critical structural damage as a function of maximum story drift of the median realization for all RC Perimeter Frame (Standard Slab) models. 231 C.3 Probability of Safety-Critical Structural Damage Plots Appendix C.3 provides contour plots that show the probability of safety-critical structural damage achieved for models with different combinations of allowable drift limits and functional recovery modification coefficients. Plots are provided for all lateral force-resisting system types, gravity force-resisting system types, and heights considered in Chapter 4. Figure C.3.1 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 3-story RC Cantilever Shear Wall (Bearing Wall) (PT slab) models. Figure C.3.2 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 3-story RC Cantilever Shear Wall (Bearing Wall) (Steel Frame) models. 232 Figure C.3.3 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 3-story RC Cantilever Shear Wall (Bearing Wall) (Standard Slab) models. Figure C.3.4 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 8-story RC Cantilever Shear Wall (Bearing Wall) (PT slab) models. 233 Figure C.3.5 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 16-story RC Cantilever Shear Wall (Bearing Wall) (PT slab) models. Figure C.3.6 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 24-story RC Cantilever Shear Wall (Bearing Wall) (PT slab) models. 234 Figure C.3.7 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 8-story RC Cantilever Shear Wall (Bearing Wall) (Steel Frame) models. Figure C.3.8 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 16-story RC Cantilever Shear Wall (Bearing Wall) (Steel Frame) models. 235 Figure C.3.9 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 24-story RC Cantilever Shear Wall (Bearing Wall) (Steel Frame) models. Figure C.3.10 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 8-story RC Cantilever Shear Wall (Bearing Wall) (Standard Slab) models. 236 Figure C.3.11 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 16-story RC Cantilever Shear Wall (Bearing Wall) (Standard Slab) models. Figure C.3.12 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 24-story RC Cantilever Shear Wall (Bearing Wall) (Standard Slab) models. 237 Figure C.3.13 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 8-story RC Coupled Shear Wall (Bearing Wall) (PT slab) models. Figure C.3.14 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 16-story RC Coupled Shear Wall (Bearing Wall) (PT slab) models. 238 Figure C.3.15 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 24-story RC Coupled Shear Wall (Bearing Wall) (PT slab) models. Figure C.3.16 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 8-story RC Coupled Shear Wall (Bearing Wall) (Steel Frame) models. 239 Figure C.3.17 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 16-story RC Coupled Shear Wall (Bearing Wall) (Steel Frame) models. Figure C.3.18 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 24-story RC Coupled Shear Wall (Bearing Wall) (Steel Frame) models. 240 Figure C.3.19 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 8-story RC Coupled Shear Wall (Bearing Wall) (Standard Slab) models. Figure C.3.20 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 16-story RC Coupled Shear Wall (Bearing Wall) (Standard Slab) models. 241 Figure C.3.21 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 24-story RC Coupled Shear Wall (Bearing Wall) (Standard Slab) models. Figure C.3.22 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 3-story RC Cantilever Shear Wall (Building Frame) (PT slab) models. 242 Figure C.3.23 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 3-story RC Cantilever Shear Wall (Building Frame) (Steel Frame) models. Figure C.3.24 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 3-story RC Cantilever Shear Wall (Building Frame) (Standard Slab) models. 243 Figure C.3.25 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 8-story RC Cantilever Shear Wall (Building Frame) (PT slab) models. Figure C.3.26 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 16-story RC Cantilever Shear Wall (Building Frame) (PT slab) models. 244 Figure C.3.27 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 24-story RC Cantilever Shear Wall (Building Frame) (PT slab) models. Figure C.3.28 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 8-story RC Cantilever Shear Wall (Building Frame) (Steel Frame) models. 245 Figure C.3.29 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 16-story RC Cantilever Shear Wall (Building Frame) (Steel Frame) models. Figure C.3.30 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 24-story RC Cantilever Shear Wall (Building Frame) (Steel Frame) models. 246 Figure C.3.31 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 8-story RC Cantilever Shear Wall (Building Frame) (Standard Slab) models. Figure C.3.32 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 16-story RC Cantilever Shear Wall (Building Frame) (Standard Slab) models. 247 Figure C.3.33 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 24-story RC Cantilever Shear Wall (Building Frame) (Standard Slab) models. Figure C.3.34 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 8-story RC Coupled Shear Wall (Building Frame) (PT slab) models. 248 Figure C.3.35 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 16-story RC Coupled Shear Wall (Building Frame) (PT slab) models. Figure C.3.36 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 24-story RC Coupled Shear Wall (Building Frame) (PT slab) models. 249 Figure C.3.37 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 8-story RC Coupled Shear Wall (Building Frame) (Steel Frame) models. Figure C.3.38 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 16-story RC Coupled Shear Wall (Building Frame) (Steel Frame) models. 250 Figure C.3.39 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 24-story RC Coupled Shear Wall (Building Frame) (Steel Frame) models. Figure C.3.40 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 8-story RC Coupled Shear Wall (Building Frame) (Standard Slab) models. 251 Figure C.3.41 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 16-story RC Coupled Shear Wall (Building Frame) (Standard Slab) models. Figure C.3.42 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 24-story RC Coupled Shear Wall (Building Frame) (Standard Slab) models. 252 Figure C.3.43 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 3-story BRBF (no backup) (Steel Frame) models. Figure C.3.44 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 8-story BRBF (no backup) (Steel Frame) models. 253 Figure C.3.45 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 16-story BRBF (no backup) (Steel Frame) models. Figure C.3.46 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 3-story BRBF (backup) (Steel Frame) models. 254 Figure C.3.47 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 8-story BRBF (backup) (Steel Frame) models. Figure C.3.48 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 16-story BRBF (backup) (Steel Frame) models. 255 Figure C.3.49 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 3-story Steel SMF (RBS) (Steel Frame) models. Figure C.3.50 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 8-story Steel SMF (RBS) (Steel Frame) models. 256 Figure C.3.51 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 16-story Steel SMF (RBS) (Steel Frame) models. Figure C.3.52 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 24-story Steel SMF (RBS) (Steel Frame) models. 257 Figure C.3.53 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 8-story RC Perimeter Frame (PT slab) models. Figure C.3.54 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 16-story RC Perimeter Frame (PT slab) models. 258 Figure C.3.55 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 24-story RC Perimeter Frame (PT slab) models. Figure C.3.56 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 8-story RC Perimeter Frame (Standard Slab) models. 259 Figure C.3.57 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 16-story RC Perimeter Frame (Standard Slab) models. Figure C.3.58 Contour plot of safety-critical structural damage probabilities for each design combination of response modification coefficient and drift limit for 24-story RC Perimeter Frame (Standard Slab) models. 260 Appendix D D.1 Engineering Demand Parameter Plots for All Systems and Heights Appendix D.1 provides median story drift ratios and peak floor accelerations for all lateral force-resisting system types and heights considered in Chapter 5. Plots show the median engineering demand parameters for models meeting the Recovery Category B, C, and D structural design requirements. (a) (b) Figure D.1.1 (a) Story drift ratio and (b) peak floor acceleration for the 3-story RC Cantilever Shear Wall (Bearing Wall) (PT slab) model. 261 (a) (b) Figure D.1.2 (a) Story drift ratio and (b) peak floor acceleration for the 8-story RC Cantilever Shear Wall (Bearing Wall) (PT slab) model. (a) (b) Figure D.1.3 (a) Story drift ratio and (b) peak floor acceleration for the 16-story RC Cantilever Shear Wall (Bearing Wall) (PT slab) model. 262 (a) (b) Figure D.1.4 (a) Story drift ratio and (b) peak floor acceleration for the 24-story RC Cantilever Shear Wall (Bearing Wall) (PT slab) model. (a) (b) Figure D.1.5 (a) Story drift ratio and (b) peak floor acceleration for the 8-story RC Coupled Shear Wall (Bearing Wall) (PT slab) model. 263 (a) (b) Figure D.1.6 (a) Story drift ratio and (b) peak floor acceleration for the 16-story RC Coupled Shear Wall (Bearing Wall) (PT slab) model. (a) (b) Figure D.1.7 (a) Story drift ratio and (b) peak floor acceleration for the 24-story RC Coupled Shear Wall (Bearing Wall) (PT slab) model. 264 (a) (b) Figure D.1.8 (a) Story drift ratio and (b) peak floor acceleration for the 3-story RC Cantilever Shear Wall (Building Frame) (PT slab) model. (a) (b) Figure D.1.9 (a) Story drift ratio and (b) peak floor acceleration for the 8-story RC Cantilever Shear Wall (Building Frame) (PT slab) model. 265 (a) (b) Figure D.1.10 (a) Story drift ratio and (b) peak floor acceleration for the 16-story RC Cantilever Shear Wall (Building Frame) (PT slab) model. (a) (b) Figure D.1.11 (a) Story drift ratio and (b) peak floor acceleration for the 24-story RC Cantilever Shear Wall (Building Frame) (PT slab) model. 266 (a) (b) Figure D.1.12 (a) Story drift ratio and (b) peak floor acceleration for the 8-story RC Coupled Shear Wall (Building Frame) (PT slab) model. (a) (b) Figure D.1.13 (a) Story drift ratio and (b) peak floor acceleration for the 16-story RC Coupled Shear Wall (Building Frame) (PT slab) model. 267 (a) (b) Figure D.1.14 (a) Story drift ratio and (b) peak floor acceleration for the 24-story RC Coupled Shear Wall (Building Frame) (PT slab) model. (a) (b) Figure D.1.15 (a) Story drift ratio and (b) peak floor acceleration for the 3-story BRBF (no backup) (Steel Frame) model. 268 (a) (b) Figure D.1.16 (a) Story drift ratio and (b) peak floor acceleration for the 8-story BRBF (no backup) (Steel Frame) model. (a) (b) Figure D.1.17 (a) Story drift ratio and (b) peak floor acceleration for the 16-story BRBF (no backup) (Steel Frame) model. 269 (a) (b) Figure D.1.18 (a) Story drift ratio and (b) peak floor acceleration for the 3-story BRBF (backup) (Steel Frame) model. (a) (b) Figure D.1.19 (a) Story drift ratio and (b) peak floor acceleration for the 8-story BRBF (backup) (Steel Frame) model. 270 (a) (b) Figure D.1.20 (a) Story drift ratio and (b) peak floor acceleration for the 16-story BRBF (backup) (Steel Frame) model. (a) (b) Figure D.1.21 (a) Story drift ratio and (b) peak floor acceleration for the 3-story Steel SMF (RBS) (Steel Frame) model. 271 (a) (b) Figure D.1.22 (a) Story drift ratio and (b) peak floor acceleration for the 8-story Steel SMF (RBS) (Steel Frame) model. (a) (b) Figure D.1.23 (a) Story drift ratio and (b) peak floor acceleration for the 16-story Steel SMF (RBS) (Steel Frame) model. 272 (a) (b) Figure D.1.24 (a) Story drift ratio and (b) peak floor acceleration for the 24-story Steel SMF (RBS) (Steel Frame) model. (a) (b) Figure D.1.25 (a) Story drift ratio and (b) peak floor acceleration for the 8-story RC Perimeter Frame (PT slab) model. 273 (a) (b) Figure D.1.26 (a) Story drift ratio and (b) peak floor acceleration for the 16-story RC Perimeter Frame (PT slab) model. (a) (b) Figure D.1.27 (a) Story drift ratio and (b) peak floor acceleration for the 24-story RC Perimeter Frame (PT slab) model. 274 D.2 Nonstructural Importance Factor Plots for Other Systems and Heights Appendix D.2 includes plots that show the probability of achieving functional recovery targets associated with each recovery category (RC). Recovery targets are 3 days for RC B, 2 months for RC C, and 6 months for RC D. Results for bearing wall RCSW systems were provided in Chapter 5 and the building frame RCSW systems are provided here. Figure D.2.1 Impact of Ipfr on the probability of exceeding recovery targets for Recovery Categories B, C, and D, with seismic certification of equipment for shear-governed RCSW building frame systems. 275 (a) (b) Figure D.2.2 Impact of Ipfr on the probability of exceeding recovery targets for Recovery Categories B, C, and D, with seismic certification of equipment for flexure-governed RCSW (a) cantilever systems (building frame) and (b) coupled wall systems (building frame). 276 D.3 Component Disaggregation Plots for All Systems and Heights Appendix D.3 includes component disaggregation plots for recovery categories and lateral force resisting systems provided in Chapter 5. These component disaggregations indicate the probability that any individual component impedes function. Structural designs meet the proposed allowable drift limits and structural response modification coefficients. The plots show the impact of increasing the functional recovery component importance factor, Ipfr, on the probability that each component impedes function. The plots can be used to identify components that commonly impede function across all lateral force-resting systems, heights, and structural design variations considered. Figure D.3.1 Component disaggregations for RC B, RC C, and RC D, with the seismic qualification of equipment for the 3-story RC Cantilever Shear Wall (Bearing Wall) (PT slab) model. 277 Figure D.3.2 Component disaggregations for RC B, RC C, and RC D, with the seismic qualification of equipment for the 8-story RC Cantilever Shear Wall (Bearing Wall) (PT slab) model. 278 Figure D.3.3 Component disaggregations for RC B, RC C, and RC D, with the seismic qualification of equipment for the 16-story RC Cantilever Shear Wall (Bearing Wall) (PT slab) model. 279 Figure D.3.4 Component disaggregations for RC B, RC C, and RC D, with the seismic qualification of equipment for the 24-story RC Cantilever Shear Wall (Bearing Wall) (PT slab) model. 280 Figure D.3.5 Component disaggregations for RC B, RC C, and RC D, with the seismic qualification of equipment for the 8-story RC Coupled Shear Wall (Bearing Wall) (PT slab) model. 281 Figure D.3.6 Component disaggregations for RC B, RC C, and RC D, with the seismic qualification of equipment for the 16-story RC Coupled Shear Wall (Bearing Wall) (PT slab) model. 282 Figure D.3.7 Component disaggregations for RC B, RC C, and RC D, with the seismic qualification of equipment for the 24-story RC Coupled Shear Wall (Bearing Wall) (PT slab) model. 283 Figure D.3.8 Component disaggregations for RC B, RC C, and RC D, with the seismic qualification of equipment for the 3-story RC Cantilever Shear Wall (Building Frame) (PT slab) model. 284 Figure D.3.9 Component disaggregations for RC B, RC C, and RC D, with the seismic qualification of equipment for the 8-story RC Cantilever Shear Wall (Building Frame) (PT slab) model. 285 Figure D.3.10 Component disaggregations for RC B, RC C, and RC D, with the seismic qualification of equipment for the 16-story RC Cantilever Shear Wall (Building Frame) (PT slab) model. 286 Figure D.3.11 Component disaggregations for RC B, RC C, and RC D, with the seismic qualification of equipment for the 24-story RC Cantilever Shear Wall (Building Frame) (PT slab) model. 287 Figure D.3.12 Component disaggregations for RC B, RC C, and RC D, with the seismic qualification of equipment for the 8-story RC Coupled Shear Wall (Building Frame) (PT slab) model. 288 Figure D.3.13 Component disaggregations for RC B, RC C, and RC D, with the seismic qualification of equipment for the 16-story RC Coupled Shear Wall (Building Frame) (PT slab) model. 289 Figure D.3.14 Component disaggregations for RC B, RC C, and RC D, with the seismic qualification of equipment for the 24-story RC Coupled Shear Wall (Building Frame) (PT slab) model. 290 Figure D.3.15 Component disaggregations for RC B, RC C, and RC D, with the seismic qualification of equipment for the 3-story BRBF (no backup) (Steel Frame) model. 291 Figure D.3.16 Component disaggregations for RC B, RC C, and RC D, with the seismic qualification of equipment for the 8-story BRBF (no backup) (Steel Frame) model. 292 Figure D.3.17 Component disaggregations for RC B, RC C, and RC D, with the seismic qualification of equipment for the 16-story BRBF (no backup) (Steel Frame) model. 293 Figure D.3.18 Component disaggregations for RC B, RC C, and RC D, with the seismic qualification of equipment for the 3-story BRBF (backup) (Steel Frame) model. 294 Figure D.3.19 Component disaggregations for RC B, RC C, and RC D, with the seismic qualification of equipment for the 8-story BRBF (backup) (Steel Frame) model. 295 Figure D.3.20 Component disaggregations for RC B, RC C, and RC D, with the seismic qualification of equipment for the 16-story BRBF (backup) (Steel Frame) model. 296 Figure D.3.21 Component disaggregations for RC B, RC C, and RC D, with the seismic qualification of equipment for the 3-story Steel SMF (RBS) (Steel Frame) model. 297 Figure D.3.22 Component disaggregations for RC B, RC C, and RC D, with the seismic qualification of equipment for the 8-story Steel SMF (RBS) (Steel Frame) model. 298 Figure D.3.23 Component disaggregations for RC B, RC C, and RC D, with the seismic qualification of equipment for the 16-story Steel SMF (RBS) (Steel Frame) model. 299 Figure D.3.24 Component disaggregations for RC B, RC C, and RC D, with the seismic qualification of equipment for the 24-story Steel SMF (RBS) (Steel Frame) model. 300 Figure D.3.25 Component disaggregations for RC B, RC C, and RC D, with the seismic qualification of equipment for the 8-story RC Perimeter Frame (PT slab) model. 301 Figure D.3.26 Component disaggregations for RC B, RC C, and RC D, with the seismic qualification of equipment for the 16-story RC Perimeter Frame (PT slab) model. 302 Figure D.3.27 Component disaggregations for RC B, RC C, and RC D, with the seismic qualification of equipment for the 24-story RC Perimeter Frame (PT slab) model.
Thesis/Dissertation
eng
Civil Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Molina Hutt, Carlos
Post-earthquake recovery performance of modern buildings and development of recovery-based seismic design provisions
Text