Constant-ductility residual displacement ratios

This paper presents a predictive model for evaluating the central tendency and related record-to-record variability for the residual displacements of simple inelastic oscillators under seismic excitation. For this study, yielding single-degree-of-freedom systems were considered, with bilinear backbones and non-degrading hysteretic rule characterized by peak-oriented reloading stiffness. Systems with natural periods belonging to the 0.3 s to 2.0 s range and exhibiting post-yield hardening ratios ranging from 0 to 10%, were analyzed via incremental dynamic analysis to obtain the residual displacements as a function of the ductility demand. A set of fifty acceleration records was used for the dynamic analysis, coming from medium-to-large magnitude events, recorded at the closest distance to the rupture surface ranging from 3.5 km to 43.7 km on firm soil or rock and devoid of apparent directivity effects of interest for seismic response. The model fitted on these results, consists of two regression equations: one equation for the period elongation given ductility demand and another for the residual displacement ratio given period elongation and ductility demand. In this context, the residual displacement ratio is defined as residual-to-peak inelastic displacement. Thus, the model allows to assess the joint conditional distribution of period elongation and residual displacement at fixed ductility levels. These results could be useful for seismic reliability assessment for structures accumulating damage, for example during seismic sequences, where the seismic fragility of a structure damaged during a mainshock earthquake comes into play for risk calculations during the ensuing aftershock sequence.