On the influence of the hysteretic behavior of the capillary pressure on the wave propagation in partially saturated soils

It is well known that the capillary pressure curve of partially saturated soils exhibits a hysteresis. For the same degree of saturation it has different values depending on the initial state of the soil, thus for drying of a wet soil or wetting of a dry soil. The influence of these different values of the capillary pressure on the propagation of sound waves is studied by use of a linear hyperbolic model. Even if the model does not contain a hysteresis operator, the effect of hysteresis in the capillary pressure curve is accounted for. In order to obtain the limits of phase speeds and attenuations for the two processes the correspondent values for main drying and main wetting are inserted into the model separately. This is done for two examples of soils, namely for Del Monte sand and for a silt loam both filled by an air-water mixture. The wave analysis reveals four waves: one transversal wave and three longitudinal waves. The waves which are driven by the immiscible pore fluids are influenced by the hysteresis in the capillary pressure curve while the waves which are mainly driven by the solid are not.