Can modeling soil heterogeneity in 2D site response analyses improve predictions at vertical array sites?

Abstract

This study uses a database of 21 vertical borehole arrays in California to examine whether a two-dimensional (2D) site response analysis framework that accounts for soil heterogeneity via spatially correlated random fields can explain misfits observed from prior one-dimensional (1D) ground response modeling. The main hypothesis is that the overprediction of ground motion at site modal frequencies, consistently observed in many site response validation studies, is caused by soil heterogeneity and 2D/three-dimensional (3D) wave propagation effects that cannot be captured by 1D analyses. We apply classical “within” boundary conditions for borehole input motion along with equivalent incident wave motions derived using a framework developed here to help elucidate the effects of the down-going wave on observed fundamental mode resonances. Results from 2D and 1D analyses are compared to observations using a transfer-function-based taxonomy and residuals of other intensity measures (IMs) including response spectra. The uncertainty in predicted IMs is estimated from the many realizations of 2D models. This 2D approach was found capable of scattering seismic waves and producing transfer function variability resembling the observed event-to-event variability in empirical transfer functions (ETFs). For several sites that exhibit less down-going wave effects in ETFs (i.e. flatter peaks) and/or higher variability in ETFs, median transfer functions from 2D analyses provide a significantly better estimate of the median ETF than conventional 1D deterministic analyses, especially at fundamental modes. In contrast, for some of the sites that are well represented by 1D methods (e.g. Wildlife Liquefaction Array and Treasure Island), 2D methods with generic levels of spatial variability may over-represent the heterogeneity and consequently underpredict amplifications at higher mode frequencies.