Conditional simulation of spatially variable seismic ground motions based on evolutionary spectra

摘要

This paper proposes a computational procedure for the conditional simulation of spatially variable seismic ground motions for long span bridges with multiple supports. The seismic ground motions, with part of their time histories measured at some supports, are regarded as zero-mean nonstationary random processes characterized by predefined evolutionary power spectral density. To conditionally simulate unknown seismic ground motion time histories at other supports, the Kriging method is first described briefly for the conditional simulation of a random vector comprised of zero-mean Gaussian variables. The multivariate oscillatory processes characterized by the evolutionary power spectral density matrix are then introduced, and the Fourier coefficients of the oscillatory processes and their covariance matrix are derived. By applying the Kriging method to the random vector of the Fourier coefficients and using the inverse Fourier transform, unknown nonstationary seismic ground motion time histories can be simulated. A numerical example is selected to demonstrate capabilities of the proposed simulation procedure, and the results show that the procedure can ensure unbiased time-varying correlation functions, especially the cross correlation between known and unknown time histories. The procedure is finally applied to the Tsing Ma suspension bridge in Hong Kong to generate ground accelerations at its multiple supports using limited seismic records.