A Semi-analytical Solution For One Dimensional Transient Response Of Unsaturated Porous Media

The wave propagation theory of porous media is an significant foundmental problem in Civil Engineering, Earthquake Engineering, ocean engineering, Petroleum Engineering, and environmental engineering. Research on transient response problem plays a important role in the theory. This paper focuses on the one-dimensional transient response research of single-layer unsaturated porous media. Some achievements are demonstrated in the text.For the one-dimensional transient response of single-layer unsaturated porous media, based on the Biot theory and the basic equations 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 ten typical boundary conditions. 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 eigen-value problem of the governing equations is solved. After that, the variation coefficient method and the orthogonality of the characteristics functions are utilised to obtain a series of ordinary differential equations with its initial conditions. Applying the modified 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 single-layer unsaturated porous media. Among the examples, different dynamic permeability coefficients, loading frequencies, liquid saturations and boundary conditions are considered. This method is not limited by the material parameters and can be applied to any nonhomogeneous boundary conditions.Time-integration method is a high-efficiency method for solving dynamic equations, but the original method is not available when the the matrix H is singular. To solve the problem, a new precise time-integration method is introduced. This modified method will be appropriate for any equations form and also be applied to solve all kinds of boundary problems in Chapter3. Two examples are provided to show the precision and the computational efficiency of the new method.