关键词: 瞬态响应, 精确解, 饱和, 多孔介质, 不可压缩

Abstract: Based on the Biot theory, exact solution for one-dimensional transient response of single-layer fluid-saturated porous media loaded arbitrarily at its top surface is developed, where the inertial, viscous and mechanical couplings are taken into account and the solid particles and fluid are assumed to be incompressible. Firstly, the dimensionless governing equations in terms of displacement of solid skeleton are derived; and the boundary conditions are homogenized. Then, the eigen-value problem for the corresponding nonviscous system is solved to get an orthogonal function base in spatial domain. Applying variation coefficient method and making use of the orthogonality of the base functions, a series of decoupled second-order ordinary differential equations together with its corresponding initial conditions are obtained in time domain. To get the solutions for displacement components, the second-order ordinary differential equations are solved by the state-space method. By integrating the dynamic equilibrium equation of porous media and using the boundary condition, total stress and fluid pressure are determined in turn. Finally, two examples are given to demonstrate the correctness of the presented solution

Key words: transient response, exact solution, saturated, porous media, incompressiblility