A statistical approach to generation of design spectrum compatible earthquake time histories

A statistical approach to design spectrum compatible generation of seismic motions is presented. This problem is addressed on a probabilistic basis, and an earthquake time history is considered as a realization of a nonstationary stochastic process which possesses an evolutionary power spectrum. Thus, the approach is based on relating the power spectrum of the stochastic seismic motion to the design spectrum. In determining the parameters which define the power spectrum, an approximate expression for the probability density of the response of a lightly damped linear structure to a broadband nonstationary stochastic excitation is used. For exemplification, the Newmark-Blume-Kapur (NBK) spectrum and the Housner (H) spectrum are considered. In this regard, analytical expressions of power spectra of stochastic processes which are statistically compatible with the (NBK) and the (H) spectra are derived. These expressions can prove quite useful not only for simulating acxelerograms, but for conducting, as well, stochastic dynamic analyses of structural systems exposed to seismic loads specified by regulatory agencies.