Post-earthquake reliability assessment of structures subjected to after-shocks: An application to L'Aquila earthquake, 2009

The post-earthquake assessment of existing structures can be further complicated by the progressive damage induced by the occurrence of a sequence of after-shocks. This work presents a simple methodology for the calculation of the probability of exceeding a certain limit state in a given interval of time. The time-decaying mean daily rate of occurrence of significant after-shock events is modeled by employing a site-specific after-shock model for the L'Aquila 2009 after-shock sequence (central Italy). The occurrence of after-shock events is modeled using a non-homogenous Poisson model. An equivalent single-degree of freedom structure with cyclic stiffness degradation is used in order to evaluate the -progressive damage caused by a sequence of after-shock events. Given the time history of the main-shock and the residual damage caused by it, the probability of exceeding a set of discrete limit states in a given interval of time is calculated. Of particular importance is the time-variant probability of exceeding the limit state in a 24-hour (a day) interval of time which can be used as a proxy for the life-safety considerations regarding the re-occupancy of the structure. The method presented herein can also be used in an adaptive manner, progressively conditioned on the time-histories of after-shock events following the main-shock and on the corresponding residual damage caused by them.