Triangular Ditch of Fastest Infiltration into Porous Substratum

Surface water impoundment in an unlined triangular ditch during a single managed aquifer recharge (MAR) infiltration pulse lasts for time Te, after which all initially disposed water seeps into a homogenous isotropic coarse soil. In ditches with initial water W0 with depth H0 and length L, the dyad (W0,H0) vanishes at t→Te. The ditch slope that minimizes an objective function involving a linear combination of Te, W0, and H0 with arbitrary cost coefficients was found. The analytical expression for Te as a function of the bank slope and the sand's porosity is for soils without capillarity and mild bank slopes. An isoperimetric constraint in optimization is the volume of the water pulse released into the ditch. A global unique minimum exists if the coefficients factoring W0 and H0 are not identically zero. A numerical solution to a two-dimensional infiltration problem was obtained using HYDRUS 2D/3D and its reservoir boundary condition option for arbitrary soils and bank slopes. Optimal slopes of triangular ditches were found for an initially dry loam. The analytical and numerical optimal shapes were not sensitive to mild variations of the ditch slope.