Analytical formulae for traverse drainage of sloping lands with constant rainfall |
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| Authors: | B Lesaffre |
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| Institution: | 1. division Drainage and Assainissement Agricoles, CEMAGREF, B.P. 121, 92164, Antony Cédex, France
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| Abstract: | To solve the problem of traverse drainage of sloping lands, the author extends continuity and motion equations to vertically heterogeneous soils and shows that the steady-state solution combines two asymptotic curves (gentle and steep slopes) and can be reduced to simple analytical equations, clearly revealing the influence of the slope; Boussinesq's first approximation (flow parallel to the impervious layer) should be used, rather than his second approximation (horizontal flow). A solution in the case of drains lying on the impervious layer is: $$\frac{L}{{H_m }}\left {4\frac{K}{R} + \left( {\frac{K}{R} - 1} \right)^2 s^2 } \right]^{1/2} $$ where K is the homogeneous and isotropic hydraulic conductivity, R the constant recharge-rate, s the slope, L the drain-spacing, Hm the maximal height of the water-table above the drains. This approximate solution yields results as accurate as other available solutions. Extensions are given for the case of drains located above the impervious layer and for vertically heterogeneous soils. |
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