Propagation characteristics of Rayleigh wave in non-homogeneous saturated foundation

In this study, a model of non-homogeneous saturated foundation is established by considering the transverse isotropy and non-homogeneity of foundation. In this model, the porosity, density, shear modulus and permeability coefficient change along the depth, and the coupling effect between parameters are also considered. Meanwhile, a parameter, non-uniform factor, is introduced to characterize the degree of non-homogeneity of foundation. The governing equation is established based on the Biot porous media theory. The differential operator method is applied to solve the control equation, and then the dispersion equation of Rayleigh wave in non-homogeneous saturated foundation is deduced. Results are verified by degrading the deduced results to homogeneous saturated foundation and single elastic foundation, respectively. Moreover, the propagation velocity, attenuation coefficient and displacement distribution of Rayleigh wave are analyzed using numerical examples. Results show that the non-homogeneity of saturated ground has significant influence on Rayleigh wave propagation velocity, attenuation, and displacement. Additionally, the particle trajectory is changed accordingly. This effect gradually decreases with an increase in the frequency. As the frequency approaches infinity, the Rayleigh wave velocity converges to the wave velocity in homogeneous elastic foundation. The non-homogeneity of foundation increases the impedance of Rayleigh wave propagation and accelerates the attenuation of Rayleigh wave displacement. In addition, the propagation depth is less than that of homogeneous saturated foundation. With the increase in non-homogeneity, the attenuation of vertical displacement of particles is more affected and the attenuation speed is faster than that of horizontal displacement. This difference leads to a small oblateness of the elliptical particle trajectory. Moreover, a smaller thickness of the non-homogeneity soil layer results in more non-homogeneous foundation, which has greater impacts on Rayleigh wave propagation.