The consolidation problem treated by a consistent (static) finite element approach

Abstract The consolidation problem in a plane strain porous elastic medium is treated by adopting a consistent formulation of the finite element model. To this purpose, the fluid‐phase behaviour is modelled in static terms through a piecewise linear description of the pore pressure field and the behaviour of the two‐phase medium is consistently modelled through rigorously equilibrated piec̀ewise linear stress distribution. Incompressibility of the pore fluid and of the skeleton grains is assumed, as is linear elastic behaviour of the solid phase. After a compact description of the model, the governing equations for the continuum problem are recalled and the solution system for the discretized problem is obtained following Galerkin's method of weighted residuals. Some examples are finally illustrated, in order to assess the reliability of the approach and to introduce possible comparisons with other methods.