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Water seepage through soils with a sloping surface

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Abstract

An analytical solution is derived for a two-dimensional soil with a sloping surface under steady and water-saturated flow conditions. The soil was assumed to consist of several layers where each layer was horizontally stratified. Moreover, the lower layer was assumed to be bounded by an impermeable barrier, whereas the soil surface was assumed to be of constant slope (terraced type) or of an arbitrary configuration. Each layer was considered anisotropic in nature where the hydraulic conductivity in the vertical and horizontal directions are dissimilar. Potential and stream functions were obtained and several flow nets are presented for two-layered soils with varying degrees of anisotropy. The results shown illustrate the significance of the degree of anisotropy of each soil layer on the water flow pattern, the relative flow rate as well as the volume of water passing through individual soil layers.

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Abbreviations

A m :

Fourier coefficients (m = 0, 1, 2,...), dimensionless

a, b, d :

distances in Figure 1, L

K :

equivalent hydraulic conductivity, L/T

L :

width of hillside of Figure 1, L

Q :

water flow rate, L/T

R :

dimensionless anisotropie parameter

υ n :

velocity normal to the soil surface given by Equation (25), L/T

ϕ :

potential function or hydraulic head, L

ϕ′ :

dimensionless potential function given by Equation (23)

ψ :

stream function, L/T

ψ′ :

dimensionless stream function given by Equation (24)

ξ :

horizontal hydraulic conductivity, L/T

κ :

vertical hydraulic conductivity, L/T

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Authors and Affiliations

  1. Department of Chemical Engineering and Petroleum Refining, Colorado School of Mines, 80401, Golden, CO, USA

    M. Sami Selim & H. M. Selim

Authors
  1. M. Sami Selim
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  2. H. M. Selim
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Contribution from the Department of Chemical Engineering and Petroleum Refining, Colorado School of Mines, Golden, CO 80401, U.S.A. and Agronomy Department, Louisiana Agric. Exp. Sta., Louisiana State Univ. Agric. Center, Baton Rouge, LA 70803. Approved by the Director of the La. Agric. Exp. Sta. as manuscript number 87-09-1069.

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Selim, M.S., Selim, H.M. Water seepage through soils with a sloping surface. Transp Porous Med 2, 363–381 (1987). https://doi.org/10.1007/BF00136442

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  • DOI: https://doi.org/10.1007/BF00136442

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