Seepage from a Rectangular Ditch to the Groundwater Table

Abstract

This study presents both a numerical and an experimental solution to seepage from a rectangular ditch or elongated pond to a groundwater table of infinite horizontal extent. Because of the unknown location of the free surface, the flow domain is transformed into the complex potential plane using the inverse formulation method, where the free surface becomes a straight line. The method of finite differences was used to solve the boundary value problem. The problem was also investigated experimentally using a sand tank model. For comparison purposes, a one-dimensional analytical solution is also presented. The results were compared with each other and with those available in the literature obtained with other solution techniques. The parameters affecting the seepage rate were investigated and the resulting relationships are presented in dimensionless graphs. It is believed that these graphs may be of use in design problems. The conditions for which the simplified one-dimensional analytical solution agrees well with the results of the sophisticated two-dimensional numerical solution are identified.