Effect of impermeable boundaries on the propagation of Rayleigh waves in an unsaturated poroelastic half-space

This study presents an analytical model for describing propagation of Rayleigh waves along the impermeable surface of an unsaturated poroelastic half-space. This model is based on the existence of the three modes of dilatational waves which employ the poroelastic equations developed for a porous medium containing two immiscible viscous compressible fluids (Lo, Sposito and Majer, [13]). In a twofluid saturated medium, the three Rayleigh waves induced by the three dilatational waves can be expressed as R1, R2, and R3 waves in descending order of phase speed magnitude. As the excitation frequency and water saturation are given, the dispersion equation of a cubic polynomial can be solved numerically to obtain the phase speeds and attenuation coefficients of the R1, R2, and R3 waves. The numerical results show the phase speed of the R1 wave is frequency independent (non-dispersive). Comparatively, the R1 wave speed is 93-95% of the shear wave speed, and 28% to 49% of the first dilatational wave speed for selected frequencies between 50Hz & 200Hz and relative water saturation ranging from 0.01 to 0.99. However, the R2 and R3 waves are dispersive at the frequencies examined. The ratios of R2 and R3 wave phase speeds to the second and third dilatational wave speeds fall between 56% and 90%. The R1 wave attenuates the least while the R3 wave has the highest attenuation coefficient. Furthermore, the phase speed of the R1 wave under an impermeable surface approaches 1.01-1.37 times of the R1 wave under a permeable boundary. Impermeability has significant influence on the phase speeds and attenuation coefficients of the R1 and R2 waves at high water saturation due to the existence of confined fluids.