Insights into Modeling Small-Strain Site Response Derived from Downhole Array Data

The small-strain damping ratio (${\mathrm{D}}_{\min }$) is a key parameter in site response models and using values from laboratory tests tends to overpredict the site response because laboratory tests cannot capture the wave scattering effects that are present in the field. In this study, earthquake motions from four downhole array sites are used to investigate the increase in ${\mathrm{D}}_{\min }$, as quantified by the ${\mathrm{D}}_{\min }$ multiplier applied to the laboratory based ${\mathrm{D}}_{\min }$, required to match the site response. Empirical observations from the downhole array data are compared with theoretical results from linear-viscoelastic, one-dimensional site response analysis. Different measures of ground response are considered when evaluating the site response: the acceleration transfer function (TF), the spectral acceleration amplification factor (AF), the surface motion peak ground acceleration (PGA), peak ground velocity (PGV), and Arias Intensity (Ia), and the change in the high-frequency spectral decay parameter ($\mathrm{\Delta }\kappa$) between the downhole and surface sensors. It is recommended that the ${\mathrm{D}}_{\min }$ multiplier for a site be selected to best match the Ia rather than the TF. Across the four sites, the required ${\mathrm{D}}_{\min }$ multiplier varies from 1.5 to 5.5. It is hypothesized that the magnitude of the ${\mathrm{D}}_{\min }$ multiplier may be related to the geologic depositional environment of the site, with larger ${\mathrm{D}}_{\min }$ multipliers associated with more spatially variable geologic conditions. These conditions have more variation in shear wave velocity across a site, which leads to more wave scattering and larger ${\mathrm{D}}_{\min }$ multipliers.