Équations et modèles mathématiques pour le calcul des tranferts d'eau dans la zone de sol non saturée

Chercheures au C.N.R.S. Laboratoire de Mécanique des Fluides, Domaine Universitaire, 38 - Saint-Martin d'Hères.

Résumé

If one attempts to approximate the study of flow in unsaturated porous media to the well-known and long-developed physical theory of flow in saturated porous media, one runs into three basic difficulties which notably concern the following : - 1. The definition and physical meaning of the system of generalised forces generating flow (in a saturated medium, this system reduces to friction and gravity forces). 2. The definition and measurement of transfer coefficients and their very considerable variation with the basic variable, i.e. the water content of the considered medium (in a saturated medium the transfer -i.e. permeability - coefficient is a constant). 3. The influence of hysteresis effects, as the "history" of the material directly governs its subsequent evolution. A relatively complete system of transfer equations is developed, followed by a study confirmed to isothermal pure water movement between the ground surface and a water table. A simple case of an analytical solution is presented to begin with, namely unidimensional infiltration into dry ground. As the transfer equations are very distinctly parabolic, this limits to some extent the possibilities of an analytical solution. The numerical solution methods generally in use are descrihed. Finally, a schematic method of approaching the hydrodynamics of free-surface aquifers and flow in the unsaturated zone by means of a single equation is suggested, in which the boundary conditions are the ground surface and bottom of the aquifer. This method notably enables allowance to be made in aquifer recharge or evaporation problems for variations in the amount of water stored in the unsaturated zone and for their effect on the water table level.