Determination of design spectrum compatible evolutionary spectra via Monte Carlo peak factor estimation

The problem of generating ensembles of artificial non-stationary earthquake accelerograms compatible with a given (target) response/design spectrum is cast on a stochastic basis. The design spectrum of the European aseismic code provisions (EC8) for various soil conditions and damping ratios is used as a paradigm of a design/target spectrum. The generated accelerograms are construed as realizations of a non-stationary random process; they are char-acterized in the frequency domain by a parametrically defined evolutionary power spectrum (EPS). An appropriate least squared optimization problem is formulated for the determination of the parameters of the EPS. The solution of this problem involves the incorporation of a “peak factor” which is used to re-late the target spectrum to the EPS in a probabilistic context. To this end, a comprehensive Monte Carlo study is undertaken to estimate numerically the statistical properties of the peak factor from appropriately computed popula-tions, and to derive polynomial expressions for the median frequency-dependent peak factors (peak factor spectra). These expressions are used in conjunction with the herein adopted optimization problem to determine EPSs compatible with the EC8 design spectrum. The derived median peak factor spectra yield an excellent level of agreement between the EC8 spectrum and the ensemble average and median response spectra of simulated EPS-compatible ensembles of accelerograms