Rayleigh wave dispersion and attenuation characterized by couple-stress-based poroelasticity

In this paper, propagation of Rayleigh waves in a fluid-saturated porous solid is studied by using the couple-stress-based gradient theory, which incorporates the rotation gradient, and its work-conjugate counterpart, the couple-stress. In the frequency domain, wave equations involving a length parameter $\ell$, that characterizes the microstructure of the material, are derived and, by using displacement potentials, coupled wave equations are reduced to four uncoupled wave equations governing the motions of $P_1$-, $P_2$-, $SV$-, and $SH$-waves. Based on the solutions of these equations, the dispersion equation for Rayleigh waves is obtained. Numerical results show that Rayleigh waves are dispersive at all frequencies in the range considered, unlike the velocity dispersion characterized by the classical theory, and the wave velocity is always higher than the conventional Rayleigh wave velocity. It is shown that the attenuation decreases as $\ell$ increases. The effects of porosity, the ratio of bulk modulus of the solid skeleton to the solid phase, and the length parameter on Rayleigh wave dispersion and attenuation are also investigated.