Rayleigh waves in a partially saturated poroelastic solid

Abstract

SUMMARY Propagation of Rayleigh waves is studied in a porous medium, which is not fully saturated. The porous medium is assumed to be a continuum consisting of a solid skeletal with connected void space occupied by a mixture of two immiscible viscous fluids. This model also represents a case when liquid fills only a part of the pore space and gas bubbles span the remaining void space. In this isotropic medium, potential functions identify the existence of three dilatational waves coupled with a shear wave. For propagation of plane harmonic waves restricted to a plane, these potentials decay with depth from the plane boundary of the medium. Rayleigh wave in this dissipative medium is an inhomogeneous wave which decays with depth and ensures the vanishing of stresses at the plane boundary of the medium. The existence and propagation of such a wave is represented by a secular equation, which happens to be complex and irrational. This irrational equation is resolved into a polynomial form so as to find its exact roots and hence to analyse the existence and propagation of Rayleigh wave. The velocity and amplitude of Rayleigh wave are used further to calculate the averaged polarization of aggregate displacement in the medium. Existence of Rayleigh wave in a particular porous medium depends on the values of various parameters involved in secular equation. Hence, a numerical example is studied to find pertinent saturation levels for which Rayleigh waves exist in the considered numerical model of the porous medium. Variations in valid saturation range, velocity, quality factor and polarization of Rayleigh waves are studied with the changes in wave frequency, capillary pressure, liquid viscosity and frame anelasticity.