On propagation characteristics of Rayleigh wave in saturated porous media based on the strain gradient nonlocal Biot theory

Abstract Based on the strain gradient nonlocal Biot theory, the semi-analytical solution of Rayleigh wave fields is obtained using the wave function expansion method. The influence of nonlocal pore size (characterized by nonlocal parameter) and heterogeneity structure effect (characterized by scale factor) on the propagation of Rayleigh wave are numerically implemented and then discussed in detail. The results show that the nonlocal parameter and scale factor have an ignorable influence on the propagation of Rayleigh wave in low frequency region while a significant influence within high frequency range by comparing with the results obtained from the classical Biot theory. A critical ratio of scale factor to nonlocal parameter defining the transition of negative dispersion to positive dispersion is observed. The Rayleigh wave velocity in saturated porous media increases with increasing nonlocal parameter and decreases with the increase of the scale factor. The length of the principal axis and minor axis of the ellipse formed by the displacement fields strongly depends on the ratio of nonlocal parameter to scale factor and the depth of the observation point. Furthermore, the displacement amplitude is intensified by increasing the nonlocal parameter and weakened by increasing the scale factor.