Comparison of State-of-the-Art Approaches Used to Account for Spatial Variability in 1D Ground Response Analyses

A significant amount of seismic site response research over the past decade has focused on our abilities to replicate recorded ground motions at borehole array sites, where both the input (rock) and output (surface) ground motions are known. When viewed in aggregate, these studies have found that approximately 50% of borehole array sites are poorly modeled using one-dimensional (1D) ground response analyses (GRAs) based on a single shear wave velocity ($Vs$ ) profile, with individual studies reporting values between approximately 30%–80%. While there is no doubt that some sites are indeed too variable to be modeled using 1D GRAs, it is possible that simple 1D analyses could still be effectively used at many sites if spatial variability is accounted for via a rational, site-specific approach. In this study, we investigate five alternative approaches that can be used to account for spatial variability in 1D GRAs: (1) $Vs$ randomization, (2) shear wave travel time randomization, (3) utilization of $Vs$ suites derived from surface wave testing covering a large area, (4) incorporation of a pseudo-3D $Vs$ model derived from a horizontal-to-vertical spectral ratio geostatistical approach, and (5) damping modifications. These approaches are investigated at two US borehole array sites (the Treasure Island and Delaney Park Downhole Arrays) so that the GRA results can be compared with recorded small-strain ground motions. Spatial variability is accounted for by generating approximately 250 $Vs$ profiles for each approach, except for damping modifications, wherein only a single $Vs$ profile is used, but with increased damping to account for wave scattering originating from spatial discontinuities. Through qualitative and quantitative comparisons, we assess the relative and absolute effectiveness of each approach, highlight their limitations, and propose potential improvements that can help overcome these limitations in practice.