Surface‐Wave Dispersion in Partially Saturated Soils: The Role of Capillary Forces

Abstract

AbstractImproving our understanding of the relation between the water content and the seismic signatures of unconsolidated superficial soils is an important objective in the overall field of hydrogeophysics. Current approaches to constrain the water content in the vadose zone from seismic data are based on computing the ratio between compressional and shear wave velocities Vp/Vs. While this allows for the detection of pronounced changes in saturation, such as the groundwater table, it is essentially insensitive to variations in the saturation‐depth profile. Conversely, evidence shows that surface waves are sensitive to both the location of the water table and the saturation‐depth profile. Classic rock physics models are unable to explain the corresponding observations. We propose to estimate surface‐wave signatures accounting for capillary suction effects. We extend the Hertz‐Mindlin model using Bishop's effective stress definition, thus accounting for stiffness changes associated with capillary stresses acting on the soil's frame. We then compute the elastic properties of the partially saturated medium using the Biot‐Gassmann‐Wood model. Considering a 1D unconsolidated porous medium under steady‐state saturation conditions, as given by Richards' equation, we simulate body‐wave travel times and surface‐wave dispersion characteristics for different water table depths and overlying soil textures. Our results illustrate that surface‐wave phase velocity dispersion curves are remarkably sensitive to capillary effects in partially saturated soils, exhibiting velocity changes of up to 20% in the 10–100 Hz frequency range. These effects, which are particularly important in medium‐to fine‐grained soils, are virtually nonexistent in the corresponding Vp/Vs profiles.