Plane strain dynamic responses of a multi-layered transversely isotropic saturated half-space

An exact dynamic stiffness matrix method is proposed to evaluate the plane strain responses due to time-harmonic loads and pore fluid pressure applied in the interior or on the surface of a multi-layered transversely isotropic (TI) saturated half-space. First, the governing equations of the TI saturated medium are solved analytically by using the Fourier transform and the exact global dynamic stiffness matrix in the wavenumber domain is established describing the relationship between the generalized displacement and force vectors. Then, solutions of the multi-layered system for discrete wavenumbers are obtained by using the dynamic stiffness matrix method, which are then synthesized to retrieve the responses in the physical domain. The accuracy of the method is confirmed by comparison with existing solutions for the TI elastic as well as isotropic saturated media that are special cases of the more general problems addressed. Selected numerical results are presented to investigate the effects of material anisotropy, layering, surface drainage condition, buried depth of the source and permeability on the responses. It is found that material anisotropy is very important for the accurate assessment of the dynamic responses subjected to time-harmonic sources. In addition, the presented solutions form a complete set of Green's functions which is required in the application of plane strain boundary methods for multi-layered TI saturated medium.