Probable loss model and spatial distribution of damage for probabilistic financial risk assessment of structures
Deficiencies in current seismic risk analysis procedures are assessed and measures to overcome these drawbacks proposed. A methodology for representing Lifetime Loss (LL), expressed in dollars, as a function of an exceedance probability is established. The methodology incorporates aleatoric variability and epistemic uncertainty in the relationship between intensity measures and engineering demand parameters, producing a probabilistic demand model. A continuous probable loss model is developed by integrating to-gether fragility curves for damage states given demand and loss given damage state. The common form of seismic hazard relationship that specifies the annual frequency of hazard occurrence is reinterpreted in terms of probability of hazard exceedance in the service life of the structure in order to allow comparisons of seis-mic risk to be made based on whole life costs. Combining with the continuous probable loss model and seis-mic hazard model, the probabilistic demand model can be transformed to a probabilistic loss hazard model, which can be used to determine the Expected Lifetime Loss (ELL) and LL for a given exceedance probability. Recognising the fact that in MDOF systems demand parameters (which signify critical structural response) will be different for different degrees of freedom, a simplified method of evaluating ELL while giving due consideration to the spatial distribution of demand response parameters is presented. A ten-storey reinforced concrete building is used as a case study to illustrate the application of the ELL assessment procedure, the ef-fect of spatial distribution of demand on ELL, and variation in LL with exceedance probability.