When trying to replicate in-situ behaviour by computational techniques, a number
of different physical phenomena (Gens, 2001) need to be considered, including:
• The non-linear solid mechanics and especially granular unbound or bound material mechanics: we consider the relations between displacements, strains, stresses and forces within solids. The material behaviour is described by a constitutive model, which can take into account elasto-plasticity or elasto-visco-plasticity;
• The fluid flow within porous media: fluid can be a single phase of various natures (water, air,…) or it can be an association of two fluids, leading to unsat
urated media (water and air,…). In the second case, partial saturation leads to permeability and storage terms depending on the saturation degree or on the suction level, involving non-linear aspects;
• The thermal transfers within porous media: conduction is the leading process in a solid (in the geomaterial matrix), but convection can also occur in the porous volume, as a consequence of the fluid flow. Radiation transfer could also occur inside the pores, but it will be neglected here. Conduction coefficients and latent heat may depend on the temperature; and
• The pollutant transport or any spatial transfer of substance due to the fluid flow: the pollutant concentration may be high enough to modify the densities, involving non-linear effects.
All these problems are non-linear ones, and can be formulated with sets of partial
differential equations. However, only three types of differential equations have to be
considered, concerning respectively:
i) solid mechanics;
ii) diffusion; and
iii) advection-diffusion problems.
