A performance-based framework for adaptive seismic aftershock risk assessment

Operative seismic aftershock risk forecasting can be particularly useful for rapid decision-making in the presence of an ongoing sequence. In such a context, limit state first-excursion probabilities (risk) for the forecasting interval (a day) can represent the potential for progressive state of damage in a structure. This work lays out a performance-based framework for adaptive aftershock risk assessment in the immediate post-mainshock environment. A time-dependent structural performance variable is adopted in order to measure the cumulative damage in a structure. A set of event-dependent fragility curves as a function of the first-mode spectral acceleration for a prescribed limit state is calculated by employing back-to-back nonlinear dynamic analyses. An epidemic-type aftershock sequence model is employed for estimating the spatio-temporal evolution of aftershocks. The event-dependent fragility curves for a given limit state are then integrated together with the probability distribution of aftershock spectral acceleration based on the epidemic-type aftershock sequence aftershock hazard. The daily probability of limit state first-excursion is finally calculated as a weighted combination of the sequence of limit state probabilities conditioned on the number of aftershocks. As a numerical example, daily aftershock risk is calculated for the L'Aquila 2009 aftershock sequence (central Italy). A representative three-story reinforced concrete frame with infill panels, which has cyclic strength and stiffness degradation, is used in order to evaluate the progressive damage. It is observed that the proposed framework leads to a sound forecasting of limit state first-excursion in the structure for two limit states of significant damage and near collapse.