An analytical solution for predicting transient seepage into ditch drains from a ponded field

Abstract

An analytical solution is provided for predicting time dependent seepage into an array of equally spaced parallel ditch drains in a homogeneous and anisotropic soil medium underlain by an impervious layer and receiving water from a ponded horizontal field of infinite extent. The solution can account for both unequal levels of water in the adjacent drains and variable depths of ponding at the soil surface. The validity of the developed model is tested by first reducing it to a steady state solution and then comparing predictions obtained from it for a few flow situations with corresponding predictions obtained from the analytical works of others. A numerical comparison of the developed model for a flow situation is also carried out using MODFLOW. The surface discharge distribution is found to show relatively greater uniformity at the early stages of simulation but with the progress of time, the extent of uniformity is found to reduce particularly for cases where the soil is subjected to a uniform depth of ponding. However, even when a soil surface is subjected to a constant depth of ponding, a high anisotropy ratio (ratio of horizontal to vertical hydraulic conductivity of soil) of the soil alone may lead to a marked improvement on the uniformity of the surface discharge distribution at all times in comparison to a soil having a low anisotropy ratio. A better uniformity of surface discharge may also be achieved by suitably adjusting the depths of ponding over the surface of the soil – regions close to the ditches be provided with zero or negligible depths of ponding and the ponding depths may be made to progressively increase with the increase in distance from the ditch faces. As the developed analytical model is of a general nature, it is hoped that the solution provided herein will lead to a better and realistic design of ditch drainage networks for controlling waterlogged areas and in reclaiming salt affected soils.