Abstract: Based on the theory of unsaturated porous media proposed by Zienkiewicz, considering the inertia, viscous and mechanical couplings and the compressibility of fluid and solid particles, semi-analytical solutions for one-dimensional transient response of single-layer unsaturated porous media are obtained with the example of a typical boundary condition problem. During the solution procedure, the dimensionless displacement governing equations in matrix form are derived firstly. Then the the nonhomogeneous boundary conditions are transformed into homogeneous boundary conditions and the eigenvalue problems of the governing equations are solved. After that, the variation coefficient method and the orthogonality of the characteristics functions are utilized to obtain a series of ordinary differential equations with their initial conditions. Applying the precise time-integration method, the semi-analytical solutions of the ordinary differential equations are developed. Finally, several numerical examples are provided to prove the correctness of the present solution and investigate the features of one-dimensional transient response of unsaturated single-layer porous media. This method can be extended to any other boundary conditions.

Key words: unsaturated porous media, transient response, semi-analytical solution, precise time-integration method