Steady Subsurface Drainage of Ponded Surface by an Array of Parallel Ditches

Abstract

An array of ditches method of subsurface drainage is advantageous for various playgrounds, golf courses, parks, and also for orchard plantation where there is little farming operations. A comprehensive analytical solution for the problem of subsurface drainage of a ponded surface by an array of parallel ditches has been obtained by conformal mapping. The symmetry about the vertical axis has been considered in obtaining the solution for half of the drainage domain. The presented solution is applicable for the two dimensional steady drainage from a horizontal ponded surface of finite depth to an array of parallel ditches in homogeneous and isotropic porous medium having an impervious layer lying at finite depth or at infinite depth. The solution includes equations for the quantity of drainage from the seepage face part as well as the water depth part of the ditch. The solution also comprises expressions for the variation in seepage velocity at various locations along the porous medium. Further, particular solutions (e.g., single ditch, empty ditch, ditch of negligible width, impervious layer at infinite depth, or at the bottom of ditch) have been deduced from the proposed generalised solution. The single-ditch solutions have been verified with the existing results of previous work.