Propagation and attenuation of Rayleigh waves in a partially-saturated porous solid with impervious boundary

Abstract

Abstract Propagation of Rayleigh waves is studied in a three-phase porous solid half-space, which is bounded above by an impervious plane surface. In this dissipative medium, Rayleigh wave propagates as an inhomogeneous wave, which decays with distance from the stress-free plane boundary. The impervious boundary restricts the flow of pore-fluids to the interior of porous solid only. This is ensured by fixing the fluid-pressure gradient in pores at boundary or with the sealing of surface pores. In either case, the existence and propagation of inhomogeneous wave are represented by a dispersion equation, which happens to be complex and irrational. This equation is rationalized into an algebraic equation of degree 24, which is solved for a numerical example. Solutions of the dispersion equation are checked to represent an inhomogeneous wave decaying with depth. Each qualified solution is resolved to define the phase velocity and attenuation coefficient of a Rayleigh wave in the medium. Numerical example compares the velocity and attenuation of Rayleigh wave in porous sandy loam for the two representations of the impervious boundary, one with sealed pores and other with no fluid-pressure gradient. Effects of saturation degree, porosity, capillary pressure, pore-fluids viscosity and frame anelasticity are observed on the propagation characteristics of Rayleigh waves. Existence of second Rayleigh wave is checked numerically. Such a wave is possible only when the porous frame is highly anelastic and saturated enough.