A Macroscopic Analytical Model for Pressure Wave Propagation in the Water of a Variably Saturated Porous Medium

A macroscopic one-dimensional analytical model has been developed for the attenuation of low-frequency pressure waves in the water of a variably saturated porous medium. The developed model associates pressure amplitude attenuation with pore scales. Pressure propagation in a single pore size is described by a linear wave equation, and the composition of characteristic pore sizes are combined for representing the porous medium. The capillary bundle approach allows for a geometrical abstraction of the pore sizes and the definition of the water-filled capillaries under different water content states. This approach allows the pore water pressure attenuation to be addressed directly with readily available soil properties and parameters. Theoretical findings backed by experimental observations in three soils under saturated conditions indicate that the pressure wave attenuates more rapidly in the water of fine-textured soils than coarser ones. Furthermore, the results indicate that the effect of larger pores on pressure attenuation is significant at high water contents, but the pore-size distribution and the smaller pores dominantly control the pressure attenuation as the water content decreases. The developed model is consistent with previous studies and with the theory of Biot for waves in composite media.