A numerical comparison of random vibration theory and time histories based methods for equivalent-linear site response analyses

Dynamic site response is usually implemented using an equivalent-linear approach through analyses based on time-histories or random vibration theory (RVT). In the RVT approach the input motion is characterized in the frequency domain by means of Fourier Amplitude Spectra (FAS) or power spectral densities so that the need for selecting/developing multiple suitable time-histories is avoided. Nevertheless, past studies have found that RVT may produce results that differ significantly from empirically determined site amplification functions and from the time history approach. This work is aimed to further understand the potential differences in the results from RVT and time-histories based approaches by performing a comprehensive numerical evaluation that takes into account the effect of the input intensity level, input spectral shape, site conditions, and the methodology used to produce the input FAS. The results obtained corroborate that RVT over-predictions occur mainly at the site fundamental frequencies and are larger for relatively soft soil deposits with significant impedance contrast at the soil/rock interface. However, in the soft site evaluated the magnitude of the over-prediction was rather insensitive to the increase in the inelastic demand, conversely, the over-prediction in the stiffer site increased as the site softened due to the rising inelastic demand.