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Seepage of Steady Rainfall through Soil into Ditches of Unequal Water Level Heights¹

ABSTRACT

A theoretical solution and numerical results for the seepage of steady rainfall into soil laying above an impermeable layer and drained by ditches of unequal water level heights is obtained for the ditches just reaching or penetrating into the impermeable layer. This is done by using a finite series of orthonormal functions generated from products of trigonometric and hyperbolic functions. The theoretical solution gives the potential function and stream function for a range of water level heights, ditch spacings, and a range of ratios R/K of rainfall rate R to hydraulic conductivity K. If R/K is increased from 0 to 0.05, for 10-m spacing of ditches and for 1 ditch having water maintained 1 m above the barrier and the other ditch 1.5 m; then the maximum water table height in the soil will increase from 1.50 m to 1.82 m. Also, as R/K increases, the position of the maximum water table height will approach a position midway between the ditches. Flow nets and other results computed for a number of geometries from the theory bring out additional information.

¹ Journal Paper No. J-5520 of the Iowa Agr. & Home Econ. Exp. Sta., Ames, Iowa. Project No. 998. Part of the funds for this research were made available through the Office of Water Resources Research, US Department of Interior, as authorized under Water Resources Research Act of 1964, Public Law 88-379.

² Research Associate, Professor of Soils and Physics and Numerical Programmer respectively, Iowa State University of Science and Technology, Ames, Iowa.

Received for publication October 13, 1966. Accepted for publication February 10, 1967.