Seismic damage accumulation in multiple mainshock–aftershock sequences

Earthquakes are generally clustered, both in time and space. Conventionally, each cluster is made of: foreshocks, the mainshock, and aftershocks. Seismic damage can possibly accumulate because of the effects of multiple earthquakes in one cluster and/or because the structure is unrepaired between different clusters. Typically, the performance-based earthquake engineering (PBEE) framework neglects seismic damage accumulation. This is because: (a) probabilistic seismic hazard analysis (PSHA) only refers to mainshocks and (b) classical fragility curves represent the failure probability in one event, of given intensity, only. However, for life-cycle assessment, it can be necessary to account for the building-up of seismic losses because of damage in multiple events. It has been already demonstrated that a Markovian model (i.e., a Markov chain), accounting for damage accumulation in multiple mainshocks, can be calibrated maintaining PSHA from the classical PBEE framework, and replacing structural fragility with a set of state-dependent fragility curves. In fact, the Markov chain also works when damage accumulates in multiple aftershocks from a single mainshock of known magnitude and location, if aftershock-PSHA replaces classical PSHA. Herein this model is extended further developing a Markovian model that accounts, at the same time, for damage accumulation: (i) within any mainshock-aftershock seismic sequence and (ii) among multiple sequences. The model is illustrated through applications to a series of six-story reinforced-concrete moment-resisting-frame buildings designed for three sites with different seismic hazard levels in Italy. The time-variant reliability assessment results are compared to the classical PBEE approach and the accumulation model that only considers mainshocks, so as to address the relevance of aftershocks for life-cycle assessment.