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A Mathematical Solution to a Hillside Seepage Problem¹

ABSTRACT

A solution is presented for a two-dimensional hillside seepage problem. The soil is assumed to be water-saturated to the soil surface where the soil water is at atmospheric pressure. Seepage occurs into the flow medium along the upper part and out along the lower part of the sloping soil surface. The flow medium is infinitely deep and bounded laterally by vertical stream-lines. Conformal transformations are used to find the hydraulic head and stream functions. Although the solution is analytic, a complex integral must be evaluated numerically for application. Numerical data presented includes flownets, seepage velocities, infiltration angles, and volume of flow as a function of slope.

¹ Technical Paper 1618, Arizona Agr. Exp. Sta., Tucson. Contribution from the Dept. of Agricultural Chemistry & Soils. Support was from Arizona Project 0800-155-705. Presented before Div. S-1, Soil Science Society of America, Nov. 10, 1969 at Detroit, Mich.

² Assistant Professor, University of Arizona, Tucson 85721.

Received for publication March 26, 1970. Accepted for publication July 20, 1970.