Uncertainty and correlation for loss assessment of spatially distributed systems

Seismic risk assessment for a spatially distributed system, such as a lifeline network, involves characterization of ground shaking and structural damage for multiple structures in a region. The expected value of monetary loss, a common measure of the risk, has been previously formulated but with little attention to the uncertainty around this monetary loss. Furthermore, prior research on risk assessment for lifeline systems, in particular transportation networks, assumes no spatial ground motion correlation and no structure-to-structure damage correlation between sites in the network. In this paper, a framework for treating these correlations in the network risk analysis is presented. A demonstration of this methodology is carried out for two transportation networks located in the San Francisco Bay region. Coefficients of variation for network physical loss using a non-distance dependent ground motion correlation model in the framework range between 0.6 and 1.5 for the sample networks presented here. Coefficients of variation for network physical loss using a distance-dependent ground motion correlation model in the framework range between 1.0 and 1.4 for the same networks. It is demonstrated through these applications that assuming no correlation in ground motion and in damage may potentially underestimate uncertainty in the overall loss estimation.