Seismic vulnerability analysis of step-terrace frame-shear wall structure under mainshock-aftershock sequence

Abstract Step-terrace frame-shear wall structures are widely adopted in mountainous regions of China, where complex terrain imposes uneven foundation conditions and irregular structural configurations that challenge conventional seismic design approaches. However, the seismic vulnerability of such structures under mainshock-aftershock sequences remains insufficiently studied. This paper presents a systematic seismic fragility analysis of step-terrace frame-shear wall structures with varying setback configurations under mainshock and mainshock-aftershock ground motion sequences. Six structural models with different numbers of step-terrace stories and spans were established using both ETABS and YJK software, and their accuracy was validated through comparison of fundamental periods, mode shapes, and mass participation coefficients. Ten sets of real mainshock-aftershock ground motion records were selected from the Pacific Earthquake Engineering Research Center NGA-West2 database based on a target response spectrum consistent with Chinese seismic design codes. Incremental dynamic analysis was performed at eight peak ground acceleration levels ranging from 0.055 g to 0.8 g, yielding a total of 320 nonlinear time-history analyses. Seismic fragility curves were derived based on a lognormal distribution assumption, with the maximum inter-story drift angle adopted as the structural damage measure. The results indicate that: (1) mainshock-aftershock sequences significantly elevate the exceedance probability of each damage state (DS) compared with mainshock-only loading, with an average increase of 9.35% at the life safety limit state (DS3) under rare earthquake intensity; (2) increasing the number of step-terrace stories reduces the exceedance probability at all DS, while the number of step-terrace spans has a negligible effect; and (3) the failure probability distribution is sensitive to the vertical step ratio but not to the horizontal area ratio under minor and moderate earthquake intensities. The findings provide quantitative guidance for the performance-based seismic design of step-terrace frame-shear wall structures in mountainous regions.