Drainage equations and non-Darcian modelling in coarse porous media or geosynthetic materials

In coarse porous media, Darcyʹs law is not valid because of turbulence. Different alternative laws have been proposed like Forchheimerʹs or Izbashʹs law. In the present study, these two laws were experimentally investigated and have been shown to be equally suitable to describe the flow equation in different coarse materials, namely gravel materials and geosynthetic products. Izbashʹs law (vn=−λni) has been preferred to derive drainage equations because it is in continuity with Darcyʹs law and facilitates the development of an analytical solution. It has been introduced in Boussinesqʹs equation, which has been solved by a semi-analytical semi-numerical method. General equations for the drainage of coarse porous media have been derived and incorporated into the drainage model SIDRA, which predicts water-table elevations and drain flow rates for a given net recharge. This allows for comparison (i) between predicted Darcian and non-Darcian behaviours and (ii) between predicted drainage functionings of different coarse materials. Water-table elevations are shown to be much more sensitive to non-Darcian flow equation and to the hydraulic properties of the materials than drain flow rates. Response surface maps of an objective function based on the Nash criterion show that the water-table predictions are almost not sensitive to drainable porosity values. They also indicate that the two parameters of the Izbash flow equation (λ and n) are dependent for water-table prediction. Based on this result a method is proposed to determine hydraulic properties and drainage systems yielding similar water-table elevations. The results can help choosing between classical granular materials and geocomposite products in drainage systems such as leachate collection systems of landfills.