Stochastic Modeling of Recovery from Seismic Shocks

One of the earthquake engineering buzzwords nowadays is resilience, which is related to the bulk of issues related to the recovery of a system of interest (e.g., a civil structure, an infrastructure, or a community) from a seismic shock. Resilience, in fact, includes and is more important than vulnerability itself, which has been the target of earthquake engineering in the last decades. From a probabilistic standpoint, the recovery path for a system should be treated as a stochastic process, as it is a function of time and affected by random variables at each point in time. The study discusses stochastic modeling of resilience to retrieve solutions for the probability of the system’s time-to-recovery. In particular, the non-monotonic Gaussian process and the monotonic gamma and inverse-Gaussian processes, typically used in the reliability assessment of deteriorating systems, are considered first to discuss their capabilities in representing the restoration path. Once the limits of these independent increments processes are acknowledged, a more powerful time- and state-dependent increments model is proposed. It is able to account for the situation in which the recovery is possibly slowed-down by aftershocks occurring in a seismic sequence, when the latter is stochastically modeled by means of the results of probabilistic aftershock hazard analysis. For this case, the recovery process is modeled as the combination of two Markov chains: one modeling the recovery effort and the second one modeling the aftershock disruption.