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