Reliability analysis method for soil slopes permanent displacement under mainshock–aftershock sequences

After a primary seismic event, subsequent aftershocks frequently induce progressive damage to slopes. Evaluating the response of slopes to mainshock–aftershock sequences (MAS) from a probabilistic perspective is crucial for disaster prevention and mitigation. Current research primarily focuses on single mainshock events, and commonly adopts peak ground acceleration (PGA), with limited consideration of the cumulative aftershock effects. This study proposes a PDEM-based reliability framework for soil slopes subjected to MAS. First, the random input field of the MAS is first constructed by integrating theoretical models with real data. Then, considering the peak, cumulative, and spectral characteristics of the MAS, correlation analysis is conducted to identify cumulative absolute velocity (CAV) as the controlling parameter for the soil slope response among the 21 candidate parameters. Finally, based on the probability density evolution method (PDEM), a reliability assessment framework for soil slope behavior under MAS is constructed. Compared with existing methods, the proposed approach more effectively incorporates the effects of aftershocks and enables more accurate reliability assessment of slope permanent displacement under MAS. This study provides a probabilistic framework and methodological approaches for assessing slope stability under MAS.