Seismic fragility analysis of girder bridges under mainshock-aftershock sequences based on input-output hidden Markov model

Current seismic design codes for bridge structures do not account for the influence of aftershock sequences, which, to some extent, overestimate the seismic performance for bridges subjected to mainshock-aftershock (MS-AS) scenarios. To address the great need for ground motion sequences tailored to specific research sites for fragility analysis, this study proposes a method for generating artificial MS-AS ground motion sequences based on the evolutional bimodal Kanai–Tajimi model and the Epidemic–Type Aftershock Sequence model. We establish a framework for MS-AS fragility analysis using an input–output Hidden Markov Model (IOHMM), where the damage states (DS) of bridge piers are considered unobservable and are inferred statistically through damage indices in an unsupervised manner. Model parameters are trained using intensity measure (IM) sequences and damage index (DI) sequences. Fragility curves for both the mainshock and state-dependent aftershocks considering multiple aftershocks are formulated based on the initial state probability and state transition probabilities of the proposed IOHMM. The fragility analysis results reveal that as the initial seismic damage level increases, the probability of aftershocks causing higher damage levels in the structure also increases, highlighting the significant impact of aftershocks on structural damage increments. Furthermore, we extend the proposed model to a bivariate seismic intensity measure and develop fragility surfaces. The proposed framework provides a novel approach and insights for tackling seismic fragility under multiple aftershocks.