Investigation of Relationship between the Response and Fourier Spectral Ratios Based on Statistical Analyses of Strong-Motion Records

Abstract

In both seismic design and probabilistic seismic-hazard analyses, site effects are typically characterized as the ratio of the response spectral ordinate on the ground surface to that on the bedrock based on the scaling law borrowed from the Fourier spectral ordinate. Recent studies have shown that different from the Fourier spectral ratio (FSR), the response spectral ratio (RSR) does not purely reflect the site effects but also depends on the earthquake scenario even for linear analysis. However, previous studies are limited to theoretical analysis. This study statistically compares the two spectral ratios by analyzing many actual seismic ground motions recorded at nearby soil and rock sites. It is observed that the average RSR and FSR have similar overall shapes, and their maximum values occur at approximately the same period; however, the values around the peak are clearly different with FSRs consistently exceeding the RSRs. The RSR–FSR relationship depends on the earthquake scenario and the oscillator damping; their difference at periods longer than the site’s fundamental period decreases as the magnitude and epicentral distance increase, and the RSRs generally approach the FSRs as the oscillator damping decreases.