A note on modelling of coupled flow-deformation in unsaturated soils

In the first part of the paper the equations of continuity of water and air within an unsaturated deformable soil are derived in terms of flux velocities measured relative to the soil skeleton. This is the form in which the continuity equations should be presented if they are to be combined with Darcy's law for water and air flows. A simple numerical study shows the consequences of incorrectly combining Darcy's law with the continuity equations expressed in terms of absolute flux velocities. The second part of the paper focuses on the numerical implementation of the equations of flow in a finite element code. If an elasto-plastic stress-strain model is employed and if degree of saturation depends on net stress state, residual flux terms must be included in the two equations of flow during the convergency process for each elasto-plastic load step, analogous to residual forces in the equilibrium equation. A simple numerical example shows that substantial errors can arise from omission of these residual flux terms.