One-dimensional consolidation modelling for unlayered soil

In this work, one-dimensional problem has a well-known linear solution and, thus, provides a simple verification of the consolidation capability using numerical solution. The coupling is approximated by the effective stress principle, which treats the saturated soil as a continuum, assuming that the total stress at each point is the sum of an effective stress carried by the soil skeleton and a pore pressure in the fluid permeating the soil. This fluid pore pressure can change with, and the gradient of the pressure through the soil that is not balanced by the weight of fluid between the points in question will cause the fluid to flow: the flow velocity is proportional to the pressure gradient in the fluid according to Darcy's law. A typical case is a consolidation problem. Here the addition of a load to a body of soil causes pore pressure to raise initially; then, as the soil skeleton takes up the extra stress, the pore pressures decay as the soil consolidates. The Terzaghi problem is the simplest example of such a process. For illustration purposes, the problem is treated with and without finite-strain effects. The numerical solution agrees reasonably well with the analytical solution, with some loss of accuracy at later times.