Predictive Model for Constant-Ductility Energy Factor Spectra of Near- and Far-Fault Ground Motions Based on Gauss-Newton Algorithm

Abstract

Gauss-Newton algorithm is originally applied for estimating constant-ductility energy factor spectra of near- and far-fault ground motions. First, constant-ductility energy factors are clarified, a three-parameter exponential equation relating energy factor to period is proposed and estimation of parameters of the proposed equation by means of Gauss-Newton algorithm is fully demonstrated. A set of 100 both pulse-like and non-pulse like near-fault ground motion records and 112 ordinary far-fault ground motion records is assembled as seismic input. Mean energy factor spectra of the utilized ground motions are preliminarily computed from nonlinear time history analyses for five constant ductility ratios ranging from 2 to 6, and then the same spectra are estimated by Gauss-Newton method. Very strong correlation between the computed and the estimated energy constant-ductility energy factor spectra is observed after few iteration steps.