Probability-Based Residual Deformation Modeling for SDOF System Subjected to Mainshock–Aftershock Seismic Excitation

To evaluate the seismic performance of single-degree-of-freedom (SDOF) systems under mainshock–aftershock (MS–AS) seismic excitation, nonlinear time-history analyses were conducted on SDOF systems with various parameter combinations, using 50 sets of real MS–AS sequences and 150 sets of artificial sequences generated by repetition, random, and attenuation methods. The results indicate that the ground motion characteristics of MS–AS sequences generated by the repetition, random, and attenuation methods differ from those of real MS–AS sequences, with the repetition and random methods tending to overestimate the peak ground motion parameters and acceleration response spectra of MS–AS sequences, and the attenuation method potentially underestimating them, while all three methods for generating MS–AS sequences are prone to overestimating the ground motion duration of MS–AS sequences. Residual deformation is influenced by relative yield strength coefficient (η), aftershock relative intensity (χ), post-yield stiffness ratio (r), natural vibration period (T) and the hysteresis model under MS–AS seismic excitation, and residual deformation exhibits a positive dependence on aftershock intensity (χ) and a negative dependence on post-yield stiffness ratio (r), while the relationship between residual deformation and relative yield strength coefficient (η) is influenced by the natural vibration period (T), showing a positive correlation in the short-period range and a negative correlation in the mid-to-long period range. A log-normal distribution can be adopted to describe the probability distribution of the ratio of residual deformation to peak elastic-plastic deformation subjected to MS–AS seismic excitation with different parameters. Finally, a probabilistic prediction model for residual deformation under MS–AS seismic excitation was proposed which can effectively predict residual deformation under MS–AS seismic excitation.