Analysis of three-dimensional transient seepage into ditch drains from a ponded field

Abstract

An analytical solution in the form of infinite series is developed for predicting time-dependent three-dimensional seepage into ditch drains from a flat, homogeneous and anisotropic ponded field of finite size, the field being assumed to be surrounded on all its vertical faces by ditch drains with unequal water level heights in them. It is also assumed that the field is being underlain by a horizontal impervious barrier at a finite distance from the surface of the soil and that all the ditches are being dug all the way up to this barrier. The solution can account for a variable ponding distribution at the surface of the field. The correctness of the proposed solution for a few simplified situations is tested by comparing predictions obtained from it with the corresponding values attained from the analytical and experimental works of others. Further, a numerical check on it is also performed using the Processing MODFLOW environment. It is noticed that considerable improvement on the uniformity of the distribution of the flow lines in a three-dimensional ponded drainage space can be achieved by suitably altering the ponding distribution at the surface of the soil. As the developed three-dimensional ditch drainage model is pretty general in nature and includes most of the common variables of a ditch drainage system, it is hoped that the drainage designs based on it for reclaiming salt-affected and waterlogged soils would prove to be more efficient and cost-effective as compared with designs based on solutions developed by making use of more restrictive assumptions. Also, as the developed model can handle three-dimensional flow situations, it is expected to provide reliable and realistic drainage solutions to real field situations than models being developed utilizing the two-dimensional flow assumption. This is because the existing two-dimensional solutions to the problem are actually valid not for a field of finite size but for an infinite one only.