Probabilistic inelastic displacement demand estimation for SDOF self-centering viscous systems subjected to near-fault forward-directivity ground motions

This study focuses on developing probabilistic inelastic displacement ratio CR demand spectra for single-degree-of-freedom (SDOF) self-centering viscous damper (SC-VD) systems subjected to near-fault forward-directivity ground motions. In addition, this study presents a procedure for calculating the mean annual frequency (MAF) of the maximum inelastic displacement demand exceeding a specific displacement while considering the forward-directivity pulse effect to determine the maximum inelastic displacement demand hazard of the SC-VD structural system under near-fault forward-directivity ground motions. First, the effect of ground motion characteristics on CR demand is investigated. A probabilistic distribution model describing the probabilistic distribution of CR demand is then established. The effect of structural characteristics on key parameters in the probabilistic distribution of CR demand is investigated, and calculation models for key parameters are established. Based on the probabilistic distribution model and the calculation models for key parameters, the probabilistic CR demand spectra are developed. Finally, by combining the probabilistic CR demand spectra and the probabilistic seismic hazard analysis with the forward-directivity pulse effect, the procedure for calculating the MAF of the maximum inelastic displacement demand exceeding a specific displacement is presented to determine the maximum inelastic displacement demand hazard. The results indicate that the effects of ground motion characteristics should be treated as random variables, and that the Gamma distribution can reasonably describe the probabilistic distribution of CR demand. The proposed probabilistic CR demand spectra can reasonably estimate the actual CR demand, especially when R is large. Besides, the procedure for calculating the MAF of the maximum inelastic displacement demand exceeding a specific displacement is demonstrated to be effective in assessing the maximum inelastic displacement demand hazard through a set of SDOF SC-VD example systems.