Three-dimensional fundamental solution for unsaturated transversely isotropic half-space under surface time-harmonic load

An analytical solution of unsaturated poroelastic transversely isotropic (TI) half-space under surface time-harmonic load with consideration of compressibility, viscous and inertial coupling of soil skeleton, pore-water and pore-air, as well as the capillary pressure is investigated in this paper. Firstly, the governing equations of unsaturated TI soil are established in cylindrical coordinate system. Then, the displacement function and operator theory are introduced to decouple the general solution. Secondly, Fourier expansion and Hankel transform are applied to the circumferential and radial coordinates, and the integral general solutions of soil skeleton displacement, pore-water displacement and pressure, pore-air displacement and pressure, and the total stress components are derived in the transformed domain. Combined with boundary conditions and continuity conditions, the fundamental solution of unsaturated TI half-space is obtained. Finally, the proposed solution is verified by benchmarking with two existing solutions. The influence of the TI parameters, vibration frequency and the degree of saturation on the dynamic response of unsaturated poroelastic half-space is investigated.