Reflection and Refraction of an Acoustic Wave at a Surface of a Partially Saturated Porous Medium

Abstract This article is concerned with the reflection and refraction of an acoustic wave at the interface between a fluid and a partially saturated porous material filled by two immiscible fluids. The governing equations of the displacement potentials for wave propagation under the plane strain conditions are presented based on the Berryman–Thigpen–Chin (BTC) model which predicts two compressional waves (the fast P1 and the slow P2 waves) as in the classical Biot's poroelastodynamics theory for fluid-saturated porous media. The reflection and refraction coefficients of a harmonic acoustic wave incident on the surface of a partially saturated medium are determined. Numerical analyses are conducted for wave reflection and refraction at the surface of a soil of loamy sand texture to examine the effect of soil moisture on the wave behavior. The results show that for a given incident frequency and angle, the reflection coefficient slightly increases with an increase in the degree of water saturation. At a given water saturation, the reflection coefficient decreases with an increase in the incident frequency. The refraction coefficients for the fast P1 and shear waves monotonically decrease with increasing water saturation. For the slow P2 wave, the refraction coefficient first increases slightly with an increase in water saturation, reaches a peak value, and then decreases rapidly when the water saturation approaches the critical value corresponding to the saturated water content.