Effect of initial stress on the propagation of plane waves in a general anisotropic poroelastic medium

Abstract

Biot's theory is used to study the wave propagation in fluid‐saturated porous medium in the presence of initial stress. The medium is a general anisotropic porous frame saturated with a viscous fluid flowing through its pores of anisotropic permeability. Propagation of plane waves in the medium is represented through two systems of equations. One is consisting of modified Christoffel equations that define the existence of the four waves in the medium. The complex phase velocities of the four waves and the corresponding polarizations of solid particles are derived from this system. The effect of initial stress on the propagation is represented through the modifications in a square matrix of order 3. The other system relates the fluid discharge in the medium to the motion of its solid particles. This relation does not involve the components of initial stress, if any, present in the medium. A particular numerical example shows that the attenuation is more sensitive to the presence of initial stress as compared to the propagation velocities. The effect of initial stress on velocities may be little more in high‐frequency regime of Biot's theory. The effect of initial stress on attenuation varies considerably with frequency, but these variations are different for different waves. The symmetries in the anisotropy may reduce the effect of initial stress on velocities and attenuations.