Stochastic Characterization and Decision Bases under Time-Dependent Aftershock Risk in Performance-Based Earthquake Engineering

This report addresses the broad role of aftershocks in the Performance-based Earthquake Engineering (PBEE) process. This is an area which has, to date, not received careful scrutiny nor explicit quantitative analysis. We begin by introducing Aftershock Probabilistic Seismic Hazard Analysis (APSHA). APSHA, similar to conventional mainshock PSHA, is a procedure to characterize the timevarying aftershock ground motion hazard at a site. We next show a methodology to quantify, in probabilistic terms, the multi-damage-state capacity of buildings in different postmainshock damage states. A time-dependent building “tagging” policy (permitting or restricting occupancy) is then developed based on the quantification of life-safety threat in the aftershock environment using the probability of collapse as a proxy for fatality risk. We also develop formal stochastic financial life-cycle cost models in both the postand pre-mainshock environment. We include both transition and disruption costs in our model. Transition costs can be attributed to one-time financial losses due to structural and nonstructural damage to the building, and can also include the costs of evacuation of the occupants of a building. Disruption costs can be attributed to the downtime and limited functionality of the damaged building. We begin with the traditional Poisson model for temporally homogeneous mainshocks and extend it to nonhomogeneous aftershocks. Further, the model is generalized to include renewal processes for modeling mainshock occurrences and Markov-chain descriptions of the damage states of a building. The analysis procedures are nonhomogeneous Markov and semi-Markov decision analysis and stochastic dynamic programming (Howard (1971)). Finally, we introduce a decision analytic framework under improving states of information for both the postand pre-mainshock environment. We emphasize the role of information in potentially improving our decision-making capability. Decision bases include the expected life-cycle cost and rate of collapse in the aftershock environment. We also introduce the concept of the value of information to determine if obtaining more information is financially desirable, which can potentially improve the quality of the decision.