Exact solution for one-dimensional transient response of single-layer fluid-saturated porous media under arbitrary vertical loadings

Based on the Biot's Theory, considering the inertial, viscous and mechanical couplings and the compressibility of fluid and solid particles, exact solution for one-dimensional transient response of single-layer fluid-saturated porous media under arbitrary loadings applied on its top surface are developed. Firstly, the dimensionless displacement governing equations in matrix form are derived and the boundary conditions is homogenized. Then, by using the separate variable method the eigen-value problem for the corresponding nonviscous problem is solved to get a series of orthogonal function base with respect to space. After this, by applying the variation coefficient method and making use of the orthogonality of the function base, a series of decoupling second-order ordinary differential equations with respect to time together with their corresponding initial conditions, which can be solved by the state-space method, are obtained. Finally, two examples are given to demonstrate the correctness of the present solution.