Triangular Ditch of Fastest Infiltration into Porous Substratum
Publication: Journal of Irrigation and Drainage Engineering
Volume 147, Issue 7
Abstract
Surface water impoundment in an unlined triangular ditch during a single managed aquifer recharge (MAR) infiltration pulse lasts for time , after which all initially disposed water seeps into a homogenous isotropic coarse soil. In ditches with initial water with depth and length , the dyad vanishes at . The ditch slope that minimizes an objective function involving a linear combination of , , and with arbitrary cost coefficients was found. The analytical expression for 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 and 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.
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Data Availability Statement
All data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This work was funded by the Grant No. IG/AGR/SWAE/18/01, Sultan Qaboos University. The support of the Research Group DR\RG\17 is appreciated. Comments and critique by the anonymous referees and editors are greatly appreciated.
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Journal of Irrigation and Drainage Engineering
Volume 147 • Issue 7 • July 2021
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© 2021 American Society of Civil Engineers.
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Received: Feb 21, 2020
Accepted: Feb 6, 2021
Published online: Apr 21, 2021
Published in print: Jul 1, 2021
Discussion open until: Sep 21, 2021
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