Analytical Steady-State Solution for a Three-Dimensional Partially Penetrating Ditch Drainage System Receiving Water from an Uneven Ponding Field

Abstract

A steady-state analytical solution is proposed for computing three-dimensional seepage into a partially penetrating ditch drainage system receiving water from an uneven ponding field of finite size. The draining soil is assumed to be saturated, homogeneous, and anisotropic, resting on an impervious stratum. The correctness of the proposed model was checked with the analytical and experimental results for a simplified case. A numerical comparison was also carried out between the proposed analytical model and the corresponding finite-difference model for a given flow condition. The study highlights the significance of drain width, penetration depth, ponding distribution, and anisotropic ratio on the discharge distribution from the side and bottom face of the drains. In ditches of shallow depth, a significant rise in the percentage of bottom flow was found in soil with a low anisotropic ratio. With the introduction of the uneven ponding field, considerable enhancement in the contribution of flow discharge from the bottom face of the drain was observed. Travel time and orientation of flow paths were found sensitive to the point of release at the soil surface. Moreover, partially penetrating ditches promote a highly curved flow path from the surface to the recipient drain which in turn increases the travel time of the water particle.