Ground-motion prediction equations for constant-strength and constant-ductility input energy spectra

In this study, new ground motion prediction equations are proposed for both constant-ductility and constant-strength absolute and relative input energy spectra. The proposed equations are developed using mixed-effects models calibrated through empirical regressions of inelastic responses derived from nonlinear dynamic analyses on single-degree-of-freedom systems subjected to a large number of strong ground motions. Parametric analyses are carried out to show the variation on the predicted inelastic spectra produced by the level of inelastic demand in terms of constant ductility factors and strength ratios, and by the type of hysteretic model adopted to describe the nonlinear behavior of the system. It is shown that the latter has a moderate influence only on constant-strength spectra at short periods. With the increase of the inelastic demand level, the input energy decreases at long periods while increases at short periods. In general, differences between elastic and inelastic constant-strength spectra are negligible except in the very short period range. The increase in the damping ratio reduces such differences. Comparisons between the present proposals and already existing predictive equations available in the literature are finally discussed.