Matrix-based predictive model of residual drift and analytical resilience design approach for self-centering columns

Residual displacement serves as a crucial indicator in evaluating the safety and reparability of structures following seismic events. As a novel self-centering structure, the unbonded prestressed reinforced concrete (UBPRC) column has demonstrated its effectiveness in reducing residual displacement. However, there remains a lack of quantitative research concerning the influence of various structural and material parameters on residual displacement. For the quick and convenient evaluation of the seismic performance and resilience of UBPRC columns, in this paper, the influence of various parameters on the residual drift ratio of UBPRC columns was investigated by establishing a logarithmic linear relationship between the parameters and the residual drift ratio. These parameters include the longitudinal reinforcement and concrete strength (fy and fc), reinforcement ratio of longitudinal and transverse (rho l and rho s), prestressed strand ratio (rho p), aspect ratio (Ar), axial load ratio (alpha c), and prestressing force ratio (alpha ps). Among the two parameters related to prestressed strands, increasing the prestressing force ratio significantly reduces RDr, while the influence of the prestressed strand ratio on RDr is relatively small. On this basis, a matrix-based probabilistic predictive model for the residual drift ratio was established. According to various physical parameters, the proposed mathematical model accurately predicts the residual drift ratio and describes the influence of each parameter on it. Furthermore, an analytical resilience design approach was proposed, and an analytical expression in matrix form for a multi-parameter resilience design was derived. Lastly, the impact of parameters on the damage state was investigated, and the range of parameter values under investigation was established, according to the analytical resilience design approach.