Heterogeneous perturbation of fluid density and solid elastic strain in consolidating porous media

The occurrence of heterogeneous perturbations of fluid mass density and solid elastic strain of a porous continuum, as a consequence of its undrained response is a very important topic in theoretical and applied poromechanics. The classical Mandel-Cryer effect provides an explanation of fluid overpressure in the central region of a porous sample, immediately after the application of the loading. However this effect fades away when the fluid leaks out of the porous network. Here this problem is studied within the framework of a second gradient theory and a thorough description of the static and the dynamics of the phenomenon is given. We study how the presence of an impermeable wall affects the formation of the interface between two phases differing in the fluid content. Moreover, we show that the late time interface motion towards its stationary position is not affected by the impermeable wall and is characterized by a common seepage velocity profile.