Estimation of relative hydraulic conductivity of sandy soils based on a sheet flow model

Abstract

The sophistication of numerical methods that are available to solve the governing equation of unsaturated flow in soils (Richards’ equation) far exceeds the ability to accurately estimate parametric functions of the equation. One of these parametric functions that defines the relationship between the capillary pressure and saturation (retention function) is usually obtained by fitting one of a number of available models to measured laboratory or field data. A second relationship, the hydraulic conductivity–saturation function can also be obtained by fitting to measured data. More often, the measured data of hydraulic conductivity is not available and a model of hydraulic conductivity–saturation function is obtained by using measured capillary pressure–saturation data. Such a hydraulic conductivity model that is widely used in soil physics applications was developed by Mualem (Mualem, Y., 1976 Water. Resour. Res. 12 (3), 513–522). An empirical parameter in this model was obtained by fitting to retention data from non-sandy, agricultural field soils. This model also conceptualizes unsaturated flow to occur in pipes that assume no air–water interfaces. In most aquifer contamination problems sandy soils are encountered and the unsaturated flow in these soils is dominated by air–water interfaces. In a laboratory sand column experiment we have demonstrated that the Mualem's model under-predicts the hydraulic conductivity of sandy soils. A new model of unsaturated hydraulic conductivity that is specifically applicable for sandy soils is developed. This model approximates the sand grains by uniform spheres, and uses a flow geometry that allows for the incorporation of an air–water interface at the pore-scale. The model was then applied to predict the capillary pressure head in a laboratory sand column under conditions of vertical infiltration. The proposed model matched the observations much better compared to Mualem's model.