By virtue of a pair of scalar potentials for the displacement of the solid skeleton and the pore fluid pressure field of a saturated poroelastic medium, an alternative solution method to the Helmholtz decomposition is developed for the wave propagation problems in the framework of Biot's theory. As an application, a comprehensive solution for three-dimensional response of an isotropic poroelastic half-space with a partially permeable hydraulic free surface under an arbitrarily distributed time-harmonic internal force field and fluid sources is developed. The Green's functions for the poroelastic fields, corresponding to point, ring, and disk loads, are reduced to semi-infinite complex-valued integrals that can be evaluated numerically by an appropriate quadrature scheme. Analytical and numerical comparisons are made with existing elastic and poroelastic solutions to illustrate the quality and features of the solution.Contrary to a single-phase elastic medium, the Biot's theory of poroelasticity (Biot [4]) predicts the existence of two distinct compressional waves in a fluid-saturated poroelastic medium; the compressional wave of the first kind, also known as the 'fast dilatational wave', propagates at a higher velocity and corresponds to the motions for which the displacements of the solid and the fluid are in phase. The compressional wave of the second kind, also known as the 'slow dilatational wave', propagates at a velocity close to (but usually less than) the wave velocity in the fluid. It corresponds to the motions for which the displacements of the solid and the fluid are out of phase. As in an elastic non-porous medium, the Biot's theory of poroelasticity predicts the propagation of only one shear wave in a fluid-saturated poroelastic medium. In fact, as no shear stress can be 1908 A. POOLADI, M. RAHIMIAN AND R. Y. S. PAK
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