Three-dimensional dynamic Green's functions for transversely isotropic saturated half-space subjected to buried loads

Abstract

Based on Biot's theory of saturated porous medium, three-dimensional (3D) dynamic Green's functions for a transversely isotropic (TI) saturated half-space is solved. The 3D Green's functions correspond to solutions of buried uniformly distributed loads acting on a circular disk of a homogeneous TI saturated half-space. First, a set of scalar potential functions are adopted to solve the governing equations of TI saturated medium in the cylindrical coordinate system. Next, by employing the Fourier series expansion and Hankel transform, the solutions for the potential functions are obtained in transformed domain, and then the displacements, stresses and pore fluid pressure are expressed via the relationships between these functions. Finally, the boundary conditions of problem are introduced, the solutions are derived for three different cases of vertical load in z-direction, horizontal load in x(y)-direction and pore fluid pressure in z-direction. The accuracy of the proposed method is validated by comparison with existing solutions for isotropic elastic and saturated as well as TI saturated (surface load) media that are special cases of the more general problems addressed. Parametric studies in both frequency and time domain are performed to investigate the influences of the material anisotropy, buried depth load frequency and drainage condition on the dynamic responses of the TI saturated half-space. Numerical results indicate that material anisotropy and surface drainage condition are significant important for the accurate assessment of the dynamic responses subjected to buried sources. In addition, The obtained Green's functions form a complete set of fundamental solutions of the TI saturated medium, by which the key to applying the BEMs to a variety of radiation, scattering and interaction problems associated with wave propagation in TI saturated half-space is solved.