Residual displacement ratios of structures under mainshock-aftershock sequences

Residual displacement demand is a key indicator of seismic damage and plays a pivotal role in post-earthquake decision making on damaged structures. This parameter can be effective as an estimator of the residual capacity of structural systems damaged under seismic sequences. Residual displacement ratio (Cr) is a conventional approach to predict the residual displacement demand from maximum linear displacement. This study investigates the residual displacement ratios of structures as bi-linear SDOF systems subjected to mainshock-aftershock sequences. Constant-strength spectra based on Cr are developed taking into account the effects of ground motion parameters (such as site condition, magnitude, epicentral distance, and duration), and of structural characteristics (such as strength modification factor and post-yield stiffness ratio). Several analytical equations are proposed to predict the residual displacement ratio as function of the elastic vibration period and the strength modification factor for different levels of the post-yield stiffness ratio and also various aftershock intensities. The proposed equations can be employed for seismic assessment of structures against mainshock-aftershock sequences.