Three-dimensional axisymmetric transient response of an unsaturated poroelastic transversely isotropic half-space

This paper investigates the three-dimensional (3D) axisymmetric dynamic response of an unsaturated poroelastic transversely isotropic half-space subjected to different vertical transient loading types. Taking into account the compression deformation of soil particles, pore fluid, the viscous and inertial coupling between different phases, as well as the material anisotropy of soil skeleton, the dynamic governing equations of unsaturated poroelastic transversely isotropic half-space medium in cylindrical coordinate system are established. Then, the general solutions for the soil skeleton's displacement and stress, as well as the relative displacements and pressures of pore-water and pore-air, are obtained by using Laplace-Hankel transform. Finally, the Durbin numerical inversion method and Gauss-Kronod algorithm are applied to solve the transient Lamb's problem in time domain. After validating the correctness of the proposed solution, the numerical examples focused on the effect of material anisotropy, transient loading type, the degree of saturation and distance from the loading source on the vertical and radial surface displacements of an unsaturated transversely isotropic poroelastic half-space are investigated.