In part I the authors describe a new finite element algorithm for solving elastic and elastoplastic coupled consolidation problems. The procedure treats the governing consolidation relations as a system of first-order differential equations, and is based on the backward Euler-Thomas-Gladwell schemes with automatic subincrementation of a prescribed series of time increments. The prescribed time increments, which are called coarse time steps, serve to start the procedure, and they can be chosen by the user. The automatic consolidation algorithm attempts to select the time subincrements such that, for a given mesh, the time-stepping (or temporal discretisation) error in the displacements lies close to a specific tolerance. Unlike existing solution techniques, the new algorithm computes not only the displacements and pore pressures, but also their derivatives with respect to time. For the elastic case, the displacements and pore pressure may be solved directly. For elastoplastic behaviour, the relationships are nonlinear and must be solved by iterations.
In part II automatic time-stepping algorithms developed in part I are used to study several problems on the consolidation of porous media. The aim of these analyses is to demonstrate that the new procedures are robust and efficient.