Report - PEER - University of California, Berkeley

E [ L T| IM ]$10 M$8 M$6 M$4 Mσ [ L T| IM ]$10 M$8 M$6 M$4 MCorrelat edNon-correlat edν ( L T > $ )$2 M$2 M0.001(a) (b) (c)$0 M$0 M0.00010 20 40 60 80 100 0 20 40 60 80 100 $ 0 $ 4 $ 8 $ 12 $ 16IM [ S d(cm) ]IM [ S d(cm) ]L T [ million $ ]Figure 7. (a) Expected loss at different levels of intensity, (b) dispersion ofloss at different levels of intensity, (c) building loss curve.Figure 6 presents examples of each of the correlation at each of the above threelevel. Figure 6a shows how the correlation between different types of EDP varies asthe ground motion intensity increase. Shown in Figure 6b is an example of the jointprobability distribution of two components being at different damage states. Figure 6cshows the correlation between repair costs for a column and a beam-columnconnection.3.6 Building Loss EstimationFigure 7a presents the variations of the expected loss at different levels of intensity,E[L T |IM], estimated for the case study building. It can be seen that for this buildinglosses rapidly increase at small levels of ground motion intensity. Figure 7b presentsthe variations of the dispersion of the loss of the building with increasing level ofground motion intensity for two cases: when losses in individual components areassumed to be correlated and when they are assumed non-correlated. It can be seenthat correlation has significant effects on the uncertainty of the loss. For example, atS d =20 cm assuming that the losses are uncorrelated leads to an underestimation of25% of the dispersion of the loss.The loss curve for the case study building is shown in Figure 7c where it can beseen that losses smaller than $1,000,000 have relatively high mean annual frequenciesof exceedance.4. LOSS DEAGGREGATIONSimilarly to seismic hazard deaggregation (McGuire, 1995) building losses can alsobe disaggregated. In particular, it is interesting to investigate the ground motionintensities that most contribute to expected annual losses in a building. Figure 8provides three examples of loss deaggregation. Figure 8a presents the contribution ofcollapse and non-collapse expected loss to the total loss at different levels of intensity.It can be seen in the figure that at small levels of intensity, (S d