Étude du régime transitoire de l'écoulement de l'eau pendant le drainage des nappes à surface libre

A study of transient flow conditions during the drainage of free-surface aquifers

Attaché de Recherches au C.N.R.S., Laboratoire de Mécanique des Fluides, Grenoble.

Résumé

The objective of the study was to examine the validity of some of the current assumptions and models used to describe the drainage of unconfined aquifers. A γ-ray attenuation technique was used to follow rapid water content changes in the sail during drainage. The first aim of drainage experiments was to evaluate the effect of time, depth of the water table and drawn down on the value of the storage coefficient. This coefficient has often been assumed to be constant and equal to the specific yield when considering problems of free-surface flow in ground water hydrodynamics. Taking into account the flow of water in the unsaturated zone, it could be easily shown that the specific yield ε has to be considered only as an asymptotic limit of the value of the storage coefficient S. During the drainage of a water table aquifer initially at a certain depth H, it is important to note that the maximum drainable volume of water V∞ will be given, per unit surface of soil, by the area limited by the drainage branches of the capillary pressures curves corresponding to the initial and final positions of the water table. From the analysis of how the drained volume of water varies for different drawdown values and a water table initially at a soil surface, it is possible to make a comparative study of the drainage duration. Considering as a criterion that the experiments ended for the time t99, for which 99 % of the total drainable volume of water had flowed away, we obtained an empirical relation between t99, drawdown Z and saturatec1 permeability Ko. An attempt was then made to adapt capillary models to drainage problems. We considered three series of models: - the gravity model, neglecting the unsaturated zone; - the "single capillary" model, already developed by E. G. Youngs and considering the analogy between a unique family of capillary tubes whose diameter is defined by the capillary fringe of the soil, and the sail; - the "multi-capillary" model, considering the analogy between a series of different families of capillary tubes and the sail, the capillary rise in each family being equal to the capillary rise for the corresponding values of pore range. Comparing experimental values of the drained volume of water with theoretical ones, obtained by analysis of capillary models, it is shown that the single capillary model is very satisfactory at the beginning of a drainage experiment. However, when the position of the maximum water content θo tends towards the capillary fringe corresponding to the equilibrium position of the drained water table; the multi-capillary model gives a good approximation of values of the drained volume of water. We finally describe a method for determining the hydraulic conductivity function k(θ) from a transient flow analysis of the water content profiles. The generalized Darcy's law used to describe the flow of water in unsaturated soils is found to be valid. For different values of the water content θ, k is given by the ratio between unit discharge q and capillary ,potential gradient. It is necessary to emphasize the importance of the unsaturated zone between the water table and the sail surface in unconfined aquifer problems.