Nonlocal scale effect on Rayleigh wave propagation in porous fluid-saturated materials

Abstract

In this paper, a Rayleigh wave model in fluid saturated porous materials based on a nonlocal Biot theory is proposed. The general characteristic equations expressed in terms of the Rayleigh wavenumbers are obtained. A specific fluid saturated porous material is used for numerical analysis. The present study shows that the nonlocal parameter does not have significant influence on the characteristics of Rayleigh waves within a low frequency range when comparing with the prediction of using the classical Biot theory. However, the influence of the nonlocal scale effect on the Rayleigh wave velocity and the displacement field becomes stronger as the response frequency increases. When the frequency exceeds a critical value, the Rayleigh wave velocity exhibits a negative dispersion. The displacement fields induced by the Rayleigh wave propagating in porous materials are also presented. An interesting phenomenon of the displacement fields is observed that the major axis of the displacement field ellipse will have a contra-rotation with respect to the vertical direction with increasing depth. This is different from the classical prediction in homogeneous materials. The presence of the nonlocal scale effect can also change the geometry property of displacement fields. In addition, the amplitude of the vertical displacement is attenuated along the depth, while the increment of the nonlocal parameters can strengthen the attenuation.