Influence of heterogeneity on the flow in unconfined aquifers

This note deals with the way the heterogeneity of the hydraulic conductivity affects the behaviour of an unconfined aquifer at the local scale (Dagan, G., 1986. Statistical theory of groundwater flow and transport: pore to laboratory, laboratory to formation, formation to regional scale. Water Resour. Res., 22, 120–136.). The vertical wall dam problem has been considered as an example of this kind of aquifer and the flow corresponding to different piezometric head gradients and statistical characteristics of the hydraulic conductivity space distribution has been investigated. The consequences on the free surface position and on the total discharge have been analysed, and their statistical distributions have been evaluated. Moreover, the average values have been used to investigate the value of the effective hydraulic conductivity for two-dimensional motions with significant curvatures of trajectories and a high variance of heterogeneity. The Monte Carlo method has been used, and the delicate numerical aspects, related to the coupling between the generation of random fields and the corresponding free surface flow field simulation, have been thoroughly examined.