Exact solutions to one-dimensional transient response of incompressible fluid-saturated single-layer porous media

Based on the Biot theory of porous media, the exact solutions to onedimensional transient response of incompressible saturated single-layer porous media under four types of boundary conditions are developed. In the procedure, a relation between the solid displacement u and the relative displacement w is derived, and the well-posed initial conditions and boundary conditions are proposed. The derivation of the solution for one type of boundary condition is then illustrated in detail. The exact solutions for the other three types of boundary conditions are given directly. The propagation of the compressional wave is investigated through numerical examples. It is verified that only one type of compressional wave exists in the incompressible saturated porous media.