Quantifying the Error Associated with the Elastic Halfspace Assumption in Site Response Analysis

Abstract

One of the fundamental decisions when performing one-dimensional (1D) site response analyses (SRA) involves the selection of the depth and dynamic properties of the elastic halfspace (EHS). This boundary condition assumes linear and homogenous material underlying the soil column for an infinite depth. This assumption implies that waves refracted into the EHS are fully absorbed, and as a result, energy from waves that are potentially reflected back toward the surface from deeper impedance contrasts in the actual geologic profile are not accounted for in the SRA. If a strong soil-rock seismic impedance contrast is present at the site of interest, the EHS boundary is typically set at that depth. However, the actual geologic profile below this impedance contrast may not be in accord with the assumed properties of the EHS, which can lead to systematic errors in the SRA. An analytical expression to quantify these errors is derived in this study, verified using an idealized three-layer profile, and compared to case studies of nine real sites in Charleston, South Carolina. Our results show that the presence of a single strong impedance contrast does not suffice as the sole condition to define the EHS boundary. Frequency-dependent errors in site amplification associated with the assumptions inherent to the EHS used in the SRA can be evaluated as a function of multiple impedance contrasts present in the profile. Smaller errors are associated with strong impedance contrasts at shallower layers and/or minimal impedance contrast among layer interfaces at depth. We also find that strong impedance contrasts located at great depths within deep soil deposits introduce nonnegligible errors to site response results.