Peculiarities of wave propagation processes in poroelastic media

Abstract

During analyzing of wave propagation processes in the fluid-saturated porous media unlike the theory of elasticity should be applied proposed by Biot the two phase model of media in which porous the solid elements are belonging to the first phase and the elements of pores fluid filler are belong to the second phase. Sometimes, for solving problems three phase model are used in which porous skeleton is partially saturated by fluid and partially saturated by gas. For the elastic porous media are introduced parameters such as: the porosity, the fluid viscosity, the permeability, the Biot coefficient of effective stress, the shear modulus and the bulk modulus, the mass densities and the total density of the porous material. Also the fundamental characteristic of the porous media is propagation of three different compression waves: the longitudinal fast wave, the second longitudinal slow wave, and the third transversal slow wave. One of the methods that are used for solving problems of poroelasticity is the Boundary Integral Equation Method. The algorithmic bases of it are the boundary analogues of Somiliani’s formulas for the solid displacements and the fluid pressure. The boundary integral equations and the fundamental solutions that are comprised in the poroelastic equations are different from the theory of elasticity analogues because the body with fluid-saturated pores is differ from the continuous homogeneous elastic media. Figures show that the graphs for the poroelastic region may be gradual approximated to the elastic analogues during changing some parameters. The biggest influence for displacements functions has change of the parameter R especially gradual increase of it for the some order. When for changing the functions graphs of the generalized derivatives one gradual increase of the parameter Q for one order is enough.