Rayleigh-Type Surface Waves in a Swelling Porous Half-Space

The present work deals with the propagation of Rayleigh-type surface waves in a swelling porous elastic half-space consisting of three phases, namely solid matrix, liquid (viscous) and gas (inviscid). Using Eringen's theory of swelling porous media, the governing equations are first solved by potential method. Frequency equation of Rayleigh-type waves has been derived, which is found to be irrational due to the presence of radicals in it. This irrational equation has been rationalized into a polynomial, which is then solved numerically for a specific porous model consisting of sandstone, water (viscous) and carbon dioxide as solid, liquid and gas phases, respectively. The nature of Rayleigh-type surface waves in the considered swelling porous medium is found to be inhomogeneous. Two modes of Rayleigh-type surface waves are noticed: One of them is the counterpart of the classical Rayleigh wave, while the second mode of Rayleigh-type surface waves arises due to the presence of either liquid or gas phases of the swelling porous medium. The variation of phase speeds and the corresponding attenuations of Rayleigh-type surface waves are depicted graphically against frequency parameter for the selected model. In the considered model, the swelling parameter has negligible effect on the propagation speeds of Rayleigh-type surface modes. It is also observed that in the absence of swelling, there still exist two modes of Rayleigh-type waves. The effect of the viscosity of the liquid constituent present in the pores is also examined on the phase speeds and attenuations. The results of Gales (Eur J Mech A Solids, 23:345-357 2004) for the cases of fluid saturation alone and gas saturation alone have also been deduced analytically as special cases from the present formulation.