Experimental and Analytical Investigation of Ponded Ditch Drainage System with Temporal Boundaries

Abstract

An analytical solution is proposed for a two-dimensional, fully-penetrating ditch drainage system by considering the boundaries at the ditch face and at the soil surface to change with time. The general assumption of instantaneous boundary impositions at the ditch face and at the surface of the soil is replaced by continuous time-varying boundary impositions at these faces, as they are expected to be more realistic and readily realized in actual field situations, as compared to static and instantaneous boundaries at the ditches and at the surface of the soil. However, the proposed analytical model is a versatile one, capable of tackling both instantaneous and continuous boundary impositions alike. To ascertain the validity of the solution, a few experiments on them have also been carried out. Further, the correctness of the proposed model is also checked for a simplified flow scenario by comparing it with an existing analytical solution to the problem. The study highlights that with the imposition of time-dependent boundaries, the maximum top discharge value gets reduced by multiple folds as compared to ponded drainage situations in which boundaries have been instantaneously imposed. It is also observed that the time taken by a ponded drainage system to reach a steady-state has a direct correlation with the time required to create steady water depths at the different boundaries of the problem. Further, the pathline and travel time of water particles are both found to be sensitive to the nature and distribution of the time-dependent boundaries of the problem.