Report - PEER - University of California, Berkeley

There are many studies on seismic loss estimation. However, most previousstudies have been aimed at estimating losses on a regional basis for a large number offacilities (e.g., ATC-13, Hazus, etc.) as opposed to a more accurate estimation ofeconomic losses in individual facilities. For a comprehensive literature review ondifferent loss estimation approaches, the reader is referred to FEMA 249 (1994).The objective of this work is to summarize research conducted by the authorsaimed at quantifying the seismic performance in specific buildings in terms ofeconomic losses. In the proposed approach the total loss in a building due to physicaldamage is treated as a random variable and it is computed as the sum of the losses inindividual structural and nonstructural components. Economic losses are computedusing a fully probabilistic approach that permits the explicit incorporation ofuncertainties in the seismic hazard at the site, in the structural response, on thefragility of individual structural and nonstructural components, and on the costsassociated with the repairs or replacement of individual building components.Physical damage is estimated by combining structural response parameters such asinterstory drift ratio or peak floor acceleration with component fragility functions.The proposed approach is illustrated by applying it to a non-ductile seven-storyreinforced concrete building.2. MEASURES OF ECONOMIC LOSSThere are many possible measures of economic losses that can be used to describeseismic performance. Only two measures of economic loss are discussed here. For amore complete discussion of alternative economic losses the reader is referred toMiranda and Aslani (2003) and Krawinkler and Miranda (2004). The first economicloss measure is the expected annual loss, which corresponds to the economic loss that,on average, occurs every year in the building. The expected annual loss providesquantitative information to assist stakeholders in making risk management decisions.In particular, owners, lending institutions, insurers, and other stakeholders can useexpected annual losses to compare, for example, annual revenues versus expectedannual losses. Similarly, they can compare annual earthquake insurance premiums toannual expected losses, etc.The second measure of economic loss discussed here is the probability of havingan economic loss equal or greater than a certain amount, which provides informationof the probability of experiencing an economic loss larger than a certain amount (e.g.,the probability of loosing more than one million dollars due to earthquake damage inthe building). This second measure of economic loss also provides economic lossesassociated with particular probabilities of being exceeded (e.g., the total dollar lossthat has 1% probability of being exceeded in 50 years).The expected annual loss in a building E[L T ] over a time period t can becomputed as (Rosenblueth 1976, Wen et al. 2001)E∫∫ ∞ −λτ= t TT0 0[ L ] e E[ L | IM ] dν( IM ) dτ(1)150