Improvement of random vibration theory site response analysis
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Random Vibration Theory (RVT) site response analysis is a standard in seismic hazard analysis for nuclear facilities to compute the dynamic response of soil deposits. However, studies have shown that the RVT analysis predicts site amplification at natural site frequencies that are considerably larger than the time series (TS) analysis. The objectives of this research are to identify improvements to the current approaches used in RVT site response analysis and to incorporate these improvements so that the discrepancy between RVT and TS site amplification are reduced. This research first investigates a critical part of the RVT approach – the peak factor, defined as the peak to root-mean-square (rms) ratio of a signal. It is shown that by accounting for the statistical dependence between peaks, the peak factor model developed by Vanmarcke (1975) is superior to the model developed by Cartwright and Longuet-Higgins (1956) when applied to seismic site response analysis. The use of the Vanmarcke peak factor model reduces the RVT site amplification at the natural site frequencies and makes the RVT amplification more similar to the TS analysis. This research also investigates the duration used in the computation of the rms value from the Fourier Amplitude Spectrum. It is shown that by accounting for the influence of the dynamic site response on the duration of the oscillator response, the RVT analysis generally predicts site amplification within +/- 10% of TS analysis. To apply the modification of duration to RVT without the use of time series, a duration model is developed that empirically predicts the change of duration at the ground surface due to site response. In the last part of the research, the improved RVT approach, which utilizes the Vanmarcke (1975) peak factor and incorporates the change in duration due to site response, is applied to more complex and realistic shear wave velocity profiles and for strain-compatible properties associated with equivalent-linear analysis. The site amplification results indicate that the improved RVT site response analysis generally works well to reduce the discrepancy between RVT and TS amplification for a wide range of situations.