Linear site responses from U.S. borehole arrays: Primary site-response parameters and proxies

Abstract

Site response, site resonance in particular, is a great concern in earthquake engineering. However, scientists and engineers have yet to reach a consensus on the most important parameters or proxies to characterize or quantify site response. In this investigation, we identified the most important parameters at 12 borehole arrays in the United States by analyzing weak-motion empirical and theoretical site responses in terms of soil-to-rock spectral ratios and ratios of response spectra at each site in the frequency range of engineering interest, 0.1–10 Hz (i.e., a period range of 0.1–10 s). From these ratios, we extracted two sets of parameter pairs: the fundamental and peak mode frequencies, f0 and fp, respectively, and their corresponding amplifications, A0 and Ap, respectively. We also characterized the Vs profiles using the shear-wave velocity ratio (Rj) and impedance ratio IRj and determined the maximum velocity and impedance ratios (Rmax and IRmax) for these borehole arrays. Both the linear empirical and theoretical results confirm that site response is site-specific and controlled predominantly by each site's in situ shear-wave velocity (Vs) profile in terms of shear-wave velocity ratios or impedance ratios, the maximum velocity or impedance ratio in particular. Our studies suggest that a minimum bedrock-sediment shear-wave velocity ratio of about 2.5 (i.e., Rmax≥2.5) or impedance ratios of about 3.0 (i.e., IRmax ≥ 3.0) is required to generate site resonance. Our results show that the fundamental mode is the most important mode for quantifying site response for engineering purposes at sites where amplifications are controlled by site resonance because it is the dominant mode on the ratios of response spectra. We also compared five proxies derived from each site's velocity profile—the time-averaged shear-wave velocity for the top 30 m (VS30), depth to bedrock or basin depth (Zb), time-averaged shear-wave velocity of sediment (Vs‾), ratio of bedrock shear-wave velocity (Vsb) to Vs‾ (Rmax), and ratio of bedrock impedance to the average sediment impedance (IRmax)—with the empirical fundamental resonant mode parameters. The comparisons revealed that Zb and Rmax (or IRmax) are the best pair of proxies to parameterize the fundamental resonant mode parameters. The comparisons also show that VS30 is not the best proxy and that no single proxy is sufficient to parameterize the fundamental resonant mode parameters.