Contributing to a Study of the Influence of Soil Parameter Variability on Flow in Porous Media

The paper presents a finite element study of the influence of spatial variations in soil properties on the progress of water flow and solute transport in partially saturated porous media. Four parameters were retained as random variables: the saturation hydraulic conductivity K_sat and the saturation water content θ_sat given their common interdependence of soil and flow as well as the two parameters of the VAN GENUCHTEN model, α and η. Log-Normal distribution laws were used. The probabilistic study was carried out using the Monte Carlo method. The results of three hundred and fifty (350) flow and solute transport calculations were analyzed in terms of variability of hydraulic loads to show the influence of the structure of soil variability. Three cases of variability were retained: o The first is statistically homogeneous (150 calculations) o The second is stratified (150 calculations per horizontal layers) o The third and last is heterogeneous (50 calculations in both the vertical and horizontal directions).

The reduction in variability of results when the soil also varies in the horizontal direction was shown quantitatively. Comparison with classical deterministic solutions was also carried out. It indicates that the average evolution of flow and transport can be reproduced by a deterministic calculation. The probabilistic treatment cannot therefore explain the existence of a bias in relation to field observations.