Mainshock-aftershock resilience assessment of an isolated curved girder bridge system based on a Copula-semi-Markov framework

To accurately assess the seismic performance and post-earthquake recovery capability of isolated curved girder bridges (ICGBs) under mainshock-aftershock (MS-AS) sequences, this study uses a three-span ICGB as a case study and proposes a system-level seismic resilience assessment framework. First, to address the issue that a single component cannot comprehensively characterize the bridge system, a multi-level nested Copula method is introduced; through bottom-up layer-by-layer recurrence and AIC/BIC criteria optimization, a dimensionality-reduced correlation structure of “component-subsystem-overall system” is constructed, achieving an accurate assessment of system-level fragility under MS-AS cumulative damage. Second, to overcome the limitation of traditional methods in adapting to dynamic damage states, a bridge performance evolution model based on the semi-Markov process (SMP) is proposed, providing a probabilistic framework for assessing bridge seismic resilience under different ground motion intensities. The results show that, compared with the traditional first-order bounding method, the multi-level nested Copula method considering the correlation between components can more accurately describe the system-level damage, revealing that the secondary damage of MS-AS sequences will significantly aggravate the damage degree of the bridge. In terms of seismic resilience evolution, MS-AS sequences will significantly accelerate bridge function degradation and prolong the recovery period. The resilience curves obtained using the SMP exhibit different recovery evolution characteristics as the probabilities of different damage states vary, demonstrating the flexibility of the proposed method in describing recovery trajectories associated with different damage states within a unified probabilistic framework. This study provides an analytical framework that accounts for state transitions and uncertainty in repair time for seismic design and post-earthquake emergency recovery decision-making of bridges under complex earthquake sequences.