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Mathematical Analysis of Steady Saturated Flow through a Multilayered Soil with a Sloping Surface
Author(s) -
Selim H. M.,
Selim M. Sami,
Kirkham Don
Publication year - 1975
Publication title -
soil science society of america journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.836
H-Index - 168
eISSN - 1435-0661
pISSN - 0361-5995
DOI - 10.2136/sssaj1975.03615995003900030024x
Subject(s) - streamlines, streaklines, and pathlines , infiltration (hvac) , soil water , laplace transform , geology , permeability (electromagnetism) , flow (mathematics) , geotechnical engineering , soil science , mechanics , mathematics , geometry , materials science , mathematical analysis , chemistry , physics , biochemistry , membrane , composite material
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.