Approximation of subsurface drainage discharge by De Zeeuw-Hellinga theory and its verification in heavy soils of fluvial landscape of the Cerhovice brook

Abstract

The subsurface drainage discharge is one of the most important indicators of the impact of the drainage systems on the water management. The procedure adopted in this study is based on the application of the De Zeeuw-Hellinga theory to derive the final expression for the estimation of the value of the subsurface drainage discharge. A simple analytical approximation of the Bussinesq’s Equation was used to verify theoretically the validity of the De Zeeuw-Hellinga assumptions and to confirm the correctness of other corresponding processes. The formulas describing the subsurface drainage discharge were derived in the conditions of the unsteady state subsurface flow to drains. These conditions included the approximately horizontal impervious layer and the Dupuit’s assumptions and Darcy’s law. No recharge to the groundwater table was realised during the drainage testing. The applicability of the De Zeeuw-Hellinga formula and the accuracy of the analytical approximation of the subsurface drainage discharge by the Bussinesq’s Equation were verified by the real field measurements on the heavy soils of the experimental watershed area of the Research Institute for Soil and Water Conservation (RISWC) Prague-Zbraslav, Czech Republic. The same data were successfully used also for the confirmation of the accuracy of the method for the derivation of a simple analytical approximation of the subsurface total drainage quantity. It was demonstrated that this approximation of the subsurface drainage discharge by De Zeeuw-Hellinga theory could satisfactorily serve in the area of water engineering practice as an elementary tool for the immediate estimation of the values of the subsurface drainage discharges from the pipe drainage systems in the saturated porous environment. The advantage of this approximation is particularly the minimum amount of the input data, e.g. the basic soil hydrology data and drainage system basic design parameters. The sphere of the use of the De Zeeuw-Hellinga equations is certainly very wide. The verifications of the field test results and measurements demonstrated that the possibilities of applications and their perceived benefits to the user can be fulfilled.