Normalized Residual Displacements for Single-Degree-of-Freedom Systems Subjected to Mainshock–Aftershock Sequences

Post-earthquake structural rehabilitation faces critical challenges from aftershock-induced cumulative damage, particularly through residual displacement accumulation that compromises structural realignment feasibility. While residual displacements serve as pivotal indicators for repair-or-replace decisions, the amplification effects of aftershocks on such displacements remain systematically underexplored. This study investigates residual displacement demands of bilinear single-degree-of-freedom (SDOF) systems subjected to mainshock–aftershock sequences. A novel metric is proposed, defined as the maximum residual displacement considering both isolated mainshock and full sequence scenarios, normalized against peak inelastic displacements (termed residual displacement ratio) for predictive analysis. The influence of sequence characteristics (duration, frequency content, aftershock intensity) and structural properties (post-yield stiffness ratio, displacement ductility, natural period) on residual displacement ratios is evaluated. Statistical analysis reveals that aftershocks amplify mainshock-induced residual displacements in the statistical mean sense, with an observed maximum increase reaching up to 72%. The mainshock with stronger aftershocks tends to result in larger residual displacement ratios. A constant-ductility residual displacement ratio response spectrum is finally developed for the repairability assessment of structures against mainshock–aftershock sequences in terms of residual displacements.