Report - PEER - University of California, Berkeley

economic and functional loss that should not be overlooked (Comerio 2003, 2004).Evaluation of the other two main decision variables, downtime and casualty risks,are more complicated and not as far advanced as modeling of repair costs. Repairdurations are an obvious contributor to downtime predictions, though experiencesuggests that other factors may be more significant, including post-earthquake safetyof the structure and its impact on accessibility to the building, availability of financialand other necessary resources for repairs, plus a host of even less predictable issues,such as the influence of external management or socio-political factors. Research iscurrently under way in PEER to provide a framework to clearly articulate thedowntime issues and suggest approaches for decision making on a case-by-case basis.The prediction of casualty rates is another problematic area, due in large part tothe lack of verifiable data. Available models and data, developed by PEER and otheragencies, suggest occupancy fatality rates on the order of 1% to 1.5% for partiallycollapsed buildings and 10% to 20% for fully collapsed buildings (Krawinkler 2004).These rates are based on the actual building occupancy. For mean annual frequencypredictions, these should be adjusted for the likely occupancy.3. PROBABILISTIC BASIS AND EQUATIONS FOR THE FRAMEWORKThe probabilistic expressions of the PBEE methodology components (IM, EDP, DM,and DV) can be integrated by the total probability theorem, expressed conceptually as:λ DV = G DV DM | dG DM EDP | dG EDP IM | dλ(IM (1)( ) )∫∫∫where λ(IM) represents the mean annual frequencies of exceedence (MAF) for IM,the intermediate terms G〈A| B〉 are conditional probabilities for the methodologycomponents EDP, DM, and DV, and λ(DV) is the probabilistic (MAF) description ofthe performance metrics, e.g., the mean annual frequency, Y, that the direct economicloss will exceed X percent of the building replacement cost, i.e., Y = λ (Loss > X%replacement cost). The bold font reminds us that most of the terms in (1) are vectors.Implied by (1) is that the assessment can be modeled as a Markov process, where theconditional probabilities are independent and can each be evaluated as such.While conceptually straightforward, there are many details associated with theimplementation of the framework that are fairly complex. A few implementationdetails are elaborated on in the next two sections; for further explanations the reader isreferred to Krawinkler and Miranda (2004), Krawinkler (2004), Miranda and Aslani(2003, 2004), Baker and Cornell (2003) Comerio (2004), Ibarra and Krawinkler(2004), Miranda et al. (2004), Porter et al. (2001).3.1 Collapse PredictionIt is useful to distinguish collapse mechanisms between ones that occur primarilythrough global sidesway instability versus a local gravity load collapse. In concept,either of these modes can be simulated by inelastic time history analyses, though in22