A Semi-Analytical Solution For One Dim-ensional Transient Response Of Single Layered Fluid-Saturated Porous Media

Based on the Biot Theory, a semi-analytical approach accounting for the inertial terms, viscous and mechanical couplings is proposed to analyze the one-dimensional transient response of single-layered saturated porous media. Ten typical arbitrary non-homogeneous boundary conditions are solved.Considering the one-dimensional governing equations, the dimensionless displacement governing equations with its initial and boundary conditions in matrix form are derived. After homogenizing the boundary condition, the characteristic problem for the governing equations is solved to get a series of eigenvalues and characteristic functions. Then, Because of the orthogonal characteristic functions, a series of ordinary differential equations with its initial conditions become solvable by precise time-integration method. Some examples are presented to demonstrate the characteristics of wave propagation and the impact of the dynamic permeability coefficient on the fluid-solid coupling. The results confirm the truth of this method.The method is valid and suitable for arbitrary non-homogeneous boundary conditions accounting for the inertial terms, viscous and mechanical couplings and the compressibility of fluid and solid particles. This systematic method can be expanded to other dynamic problems for saturated porous media.