An H/V Geostatistical Approach for Building Pseudo-3D Vs Models to Account for Spatial Variability in Ground Response Analyses I: Model Development

Abstract

<p>Many recent studies have shown that we are generally unable to accurately replicate recorded ground motions at most borehole array sites using available subsurface geotechnical information and one-dimensional (1D) ground response analyses (GRAs). When 1D GRAs fail to accurately predict recorded site response, the site is often considered too complex to be effectively modeled as 1D. While 3D numerical GRAs are possible and believed to be more accurate, there is rarely a 3D subsurface model available for these analyses. The lack of affordable and reliable site characterization methods to quantify spatial variability in subsurface conditions, particularly regarding shear wave velocity (Vs) measurements needed for GRAs, has pushed researchers to adopt stochastic approaches, such as Vs randomization and spatially correlated random fields. However, these stochastically generated models require the assumption of generic, or assumed, input parameters, introducing significant uncertainties into the site response predictions. This paper describes a new geostatistical approach that can be used for building pseudo-3D Vs models as a means to rationally account for spatial variability in GRAs, increase model accuracy, and reduce uncertainty. Importantly, it requires only a single measured Vs profile and a number of simple, cost-effective, horizontal-to-vertical spectral ratio (H/V) noise measurements. Using Gaussian geostatistical regression, irregularly sampled estimates of fundamental site frequency from H/V measurements (f0,H/V) are used to generate a uniform grid of f0,H/V across the site with accompanying Vs profiles that have been scaled to match each f0,H/V value, thereby producing a pseudo-3D Vs model. This approach is demonstrated at the Treasure Island and Delaney Park Downhole Array sites (TIDA and DPDA, respectively). While the pseudo-3D Vs models can be used to incorporate spatial variability into 1D, 2D, or 3D GRAs, their implementation in 1D GRAs at TIDA and DPDA is discussed in a companion paper.</p>

An H/V Geostatistical Approach for Building Pseudo-3D Vs Models to Account for Spatial Variability in Ground Response Analyses II: Application to 1D Analyses at Two Downhole Array Sites

“…Thus, the f0,H/V semivariograms (Figure 4) provide quantitative evidence that supports the presence of more complex subsurface conditions at the DPDA site than at the TIDA site. This is also in line with findings presented in the companion paper (refer to Figure 11a in Hallal and Cox 2020), which show that the standard deviation in f0,H/V is higher at DPDA beyond a specific area around the downhole arrays. Additionally, if the degree of spatial variability determines the extent of wave scattering, then Figure 4 suggests that the variability at distances relatively far from the site may be of interest.…”

“…While these effects can also extend over significant distances, we do not believe they are influencing the small-strain ground motions recorded at either downhole array site. As highlighted in Hallal and Cox (2020) and this paper, the mapped f0,H/V values at each downhole array site underscore the importance of incorporating site-specific spatial variability to capture true site response. Measurements of site-specific variability should reflect both its magnitude and skewness; we refer to skewness as variability being favored in a certain direction, such as having mostly stiffer or softer conditions in a certain area or direction around the site.…”

“…The two downhole array sites for which pseudo-3D Vs models were developed in the companion paper (Hallal and Cox, 2020), the TIDA and DPDA, are investigated in this study regarding their recorded versus predicted linear-viscoelastic site response. Importantly, these two sites are distinct in that TIDA is believed to be an archetype of 1D conditions, where 1D GRAs are expected to provide a satisfactory match to empirical/recorded ground motions, whereas DPDA is the antithesis of such conditions, where even highly modified 1D GRAs fail to accurately represent empirical ground motions (Tao and Rathje, 2019).…”

“…The H/V geostatistical approach proposed in the companion paper (Hallal and Cox, 2020) uses site-specific, simple measurements to develop reasonable and representative pseudo-3D Vs models that can be used to incorporate spatial variability into 1D, 2D, and 3D GRAs. In this paper we focus exclusively on incorporating these pseudo-3D Vs models into 1D GRAs, with the ultimate goal of modeling 3D response in the future, at least for sites where the 1D approach is shown to not be adequate.…”

“…Furthermore, investigating an approach that could be used within the 1D framework is desirable, as 1D GRAs are easier to perform and within the proverbial comfort zone of most engineers. In a companion paper (Hallal and Cox, 2020), a new framework called the 'H/V geostatistical approach' was proposed for developing pseudo-3D Vs models that capture key aspects of site-specific spatial variability using a single measured Vs profile and estimates of fundamental site frequency (f0; a key parameter governing site effects) from horizontal-to-vertical spectral ratio (H/V) noise measurements (f0,H/V). This paper incorporates this 3D site-specific spatial variability in a meaningful and practical way into 1D GRAs.…”