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The present study proposes two analytical solutions for a layered ponded ditch drainage system with Dirichlet and lagging Robin boundary conditions. The flow domain is assumed to be saturated, layered, and anisotropic. The first analytical model considers flow to a ditch drainage network from a ponded field through a two-layered soil considering the Dirichlet boundary condition, whereas the second model is developed considering a lagging Robin condition at the ditch face and surface of the soil. The study highlights that the lagging Robin condition can better mimic the actual flow scenario as compared to the standard Robin boundary condition. A comparison study has been carried out to assess the top layer’s permissible depth under which a homogeneous drainage system with Robin boundary condition can approximate a layered drainage system. Further, the residence time distributions are observed to follow power-law-like distributions with heavier tails for both single and two-layered ditch drainage systems.

Analytical solutions for predicting seepage in a layered ditch drainage system under Dirichlet and lagging Robin boundary conditions