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Mathematical Analysis of Steady Saturated Flow through a Multilayered Soil with a Sloping Surface¹

ABSTRACT

An analytical solution is presented for a two-dimensional multilayered hillside seepage problem. The soil is horizontally stratified with each layer having a different permeability. The flow medium is assumed to be water-saturated to the soil surface, bounded below by an impermeable barrier at a finite depth, and bounded laterally by vertical streamlines. Seepage occurs into the flow medium along the upper part and out along the lower part of the sloping soil surface. Two situations are analyzed, one with a constant slope soil surface and another with an abritrarily shaped soil surface. The potential and stream functions for the problem are developed by starting with a general series solution to Laplace's equation and using a modified Gram-Schmidt method to determine the series coefficients. Solutions are derived for two-layered and three-layered soils. From these derivations, solutions for soils with more than three layers can be readily deduced. The results presented include flow nets, seepage velocities and infiltration rates for two-layered and three-layered soils.

¹ Journal Paper J-7031 of the Iowa Agr. and Home Econ. Exp. Sta., Ames, Iowa 50010. Project 1888. Research supported in part by National Science Foundation Grant No. GK-31137. Presented before Div. S-1, Soil Science Society of America, Las Vegas, Nevada, 12 Nov. 1973.

² Research Associate, Dept. of Soil Science, Univ. of Florida, Gainesville; Assistant Professor of Chemical Engineering, College of Petroleum & Minerals, Dhahran, Saudi Arabia; and Professor of Agronomy, Iowa State Univ., Ames, Iowa.

Received for publication August 20, 1974. Accepted for publication January 9, 1975.