Elastodynamic Fundamental Solutions of a Transversely Isotropic Unsaturated Half-Space Subjected to Axisymmetric Buried Vertical and Fluid Loading

This paper presents solutions for a transversely isotropic unsaturated half-space subjected to axisymmetric time-harmonic vertical and fluid pressure loading. The Biot’s coupled poroelastodynamic equations are modified to include the unsaturated case by adding the air phase into the balance equations. The resulting fully coupled field equations of the three-phase medium are analytically solved to obtain the frequency-domain general solutions by using Hankel integral transforms in the radial direction. A boundary value problem is then formulated to obtain explicit expressions for the solutions of a half-space subjected to internally applied time-harmonic vertical loading and applied fluid pressure. To validate the accuracy of the proposed formulation, a comparison is made with existing solutions for surface loading on an unsaturated half-space. Numerical results are presented to illustrate the influence of the degree of saturation and the frequency of excitation on the dynamic response of the unsaturated half-space under internal excitations. The analysis reveals significant differences in profiles of displacement, stress, and pore pressure for the unsaturated soils compared to fully saturated cases, highlighting the importance of incorporating partial saturation in dynamic poroelastic modelling for geotechnical and earthquake engineering applications.