The 3-D non-axisymmetrical Lamb's problem in transversely isotropic saturated poroelastic media

Based on Biot's theory on fluid-saturated porous media, the displacement functions are adopted to convert the 3-D Biot's wave equations in the cylindrical coordinate for transversely isotropic saturated poroelastic media into two-one 6-order and one 2-order uncoupling differential governing equations. Then, the differential equations are solved by the Fourier expanding and Hankel integral transform method. Integral solutions of soil skeleton displacements and pore pressure as well as the total stresses for poroelastic media are obtained. Furthermore, the systematic study on Lamb's problems for the transversely isotropic saturated poroelastic media is performed. Integral solutions for surface radial, vertical and circumferential displacements are obtained in both cases of drained surface and undrained surface under the vertical and horizontal harmonic excitation force. In the end of this paper, the numerical examples are presented. The calculation results indicate that the difference between the model of isotropic saturated poroelastic media and that of transversely isotropic saturated poroelastic media is obvious.