A Closed-Form Approximation to Adaptive Structural Fragility to Aftershocks

Structural vulnerability assessment to aftershocks is particularly challenging due to the cumulative damage induced in the structure. In an adaptive approach to aftershock vulnerability assessment, the structural model can be updated in a daily manner so that the damage caused by the previous aftershocks is taken into account. In such a context, the forecasting or prediction interval reduces to 24 hours. The daily aftershock fragility curves may be defined as conditional first-excursion probabilities given seismic intensity for prescribed structural limit states. Exploiting the basic probability theory rules, the structural fragility to aftershocks is derived, taking into account sequence of events that may occur during the prediction interval. Herein, a closed-form approximation to the sequence-based daily aftershock fragility is derived. As a numerical example, daily aftershock vulnerability and risk is calculated for a typical RC infilled frame subjected to the L’Aquila 2009 aftershock sequence (central Italy), for two distinct limit states. The approximate closed-form fragility curves reveal remarkable agreement with the complete sequence-dependent fragility curves. Furthermore, the adaptive daily risk prediction, obtained based on the approximate closed-form formulation, manages to properly predict the first-excursion of prescribed limit states during the days elapsed after the main-shock.