Terzaghi 1D consolidation

To validate the two phase flow, the consolidation of the excess pore water pressure of a one-dimensional soil column is studied, for which the analytical solution given by Terzaghi is known. Starting from a constant excess pore water pressure of 50 kPa, the drainage at the top of the soil column is opened, the pore water flows out, and the excess pore water pressure gradually dissipates.

The soil column of 1 m height is composed of 20 or 40 elements, depending on the interpolation order of the elements. The soil within the column is elastic. All elements are given the same elastic parameters (\(E\) = 5000 kPa, \(\nu\) = 0.35). The hydraulic conductivity is \(10^{-6}\) m/s, which is intentionally chosen low in order to trigger oscillations in the elements discretizing the pore water pressure.

Finite element model, initial conditions and loading for the 1D consolidation problem.

Input files

The input files for the benchmark simulations can be downloaded here.

Simulation results

The excess pore water pressure distribution at different times and the settlement of the column at its top are evaluated. The naming convention of the different element formulations used is as follows: the number after u indicates the number of nodes discretizing the solid displacements, the number after p indicates the number of nodes discretizing the pore water pressure and the number after (capital) U indicates the number of nodes discretizing the water displacements. -sat indicates that the element assumes fully saturated conditions and -red that the element uses a reduced integration scheme.