A 2.5-D dynamic model for a saturated porous medium: Part I. Green’s function

Based on Biot’s theory, the dynamic 2.5-D Green’s function for a saturated porous medium is obtained using the Fourier transform and the potential decomposition methods. The 2.5-D Green’s function corresponds to the solutions for the following two problems: the point force applied to the solid skeleton, and the dilatation source applied within the pore fluid. By performing the Fourier transform on the governing equations for the 3-D Green’s function, the governing differential equations for the two parts of the 2.5-D Green’s function are established and then solved to obtain the dynamic 2.5-D Green’s function. The derived 2.5-D Green’s function for saturated porous media is verified through comparison with the existing solution for 2.5-D Green’s function for the elastodynamic case and the closed-form 3-D Green’s function for saturated porous media. It is further demonstrated that a simple form 2-D Green’s function for saturated porous media can be been obtained using the potential decomposition method.