Internal dissipative waves in poroelastic media

Abstract

Free internal-wave solutions in poroelastic media are found by allowing for dilatational discontinuities in both the solid and fluid displacements. Physically, the displacement discontinuity sheet is shown to represent a thin layer in the state of dynamic liquefaction (i.e. a layer with zero dynamic solid-stress tensor) so that across the layer the porous medium is dynamically supported by pore pressure. Because of the associated relative motion between the viscous pore fluid and the porous solid, the resulting internal waves are dissipative in character. However, the dissipation rates are not necessarily similar for all obtained waves. In fact, two distinct wave types can be identified. One is characterized by having a dissipation-length scale that is much longer than the wavelength scale, and hence may be termed a propagating wave solution, while the other type has comparable dissipation and wave lengths, i. e. a non-propagating wave solution. It is shown that both types of waves can simultaneously exist in a poroelastic medium. Solutions are obtained for plane waves in a whole homogeneous space, giving the phase speeds, damping rates and velocity and pressure fields for both types of internal waves.