Towards Quantifying the Effect of Aftershocks in Seismic Risk Assessment

The state of the art in seismic design and assessment of structures implicitly relies on structural redundancy in order to deal with the effect of the triggered sequence of aftershock events on a building. Calculating the time-dependent limit state exceedance probability for a structure considering both the main event and the triggered sequence of aftershocks is complicated both by the time-dependent rate of aftershock occurrence and also the cumulative damage caused by the sequence of events. Taking advantage of a methodology developed in previous works by the authors for postmainshock risk assessment, the limit state probability due to a sequence of a mainshock and the triggered aftershocks is calculated herein. Moreover, a closed- and analytic-form approximation to the post-mainshock limit state probability given the mainshock magnitude is derived. This closed- and analytic formulation facilitates the estimation of the limit state probability by employing the standard tools in risk assessment such as the fragility curve for the intact structure. Applying the proposed methodology for a reinforced concrete (RC) concrete moment-resisting frame with infills subjected to the main event and the triggered sequence emphasizes the importance of taking into account the cumulative damage caused by the triggered sequence for the case-study model. Moreover, it is demonstrated that the proposed analytical approximation based on the fragility curve for the intact structure leads to a surprisingly close agreement with the best-estimate results obtained by considering the time- and event-dependent degradation in the structure