Analysis of the Propagation of Sound Waves in Partially Saturated Soils by Means of a Macroscopic Linear Poroelastic Model

In this paper, the propagation of sound waves in partially saturated soils is investigated. A macroscopic linear model that is based on the two-component model of Biot and on the Simple Mixture Model by Wilmanski is used. For the construction of the model by a micro-macro transition, see Albers, Géotechnique, 2007. We investigate a porous medium consisting of a deformable skeleton and two compressible, chemically non-reacting, pore fluids (liquid and gas). The wave analysis of the poroelastic model reveals the number of acoustic waves and the dependence of velocities and attenuations of these waves on the initial saturation and frequency. There appear four body waves: three longitudinal waves, P1, P2, P3, and one shear wave, S. The P2-wave shows a similar feature as in air–water mixtures: from the theory of suspensions, it is well known that the existence of air bubbles in water reveals a minimum in the sonic velocity. This is also the case for the P2 -speed in the unsaturated porous medium. The P1-velocity increases very abruptly for a certain degree of saturation. This provides the hope for the development of a nondestructive testing method.