The drainage of sloping lands

Abstract

The problem of the water table in equilibrium with the rainfall on sloping land is analyzed by solving Boussinesq's equation. It is assumed that the hillside is drained by parallel ditches which are founded in the impermeable layer. A nomegram is presented for calculating the ditch spacing as a function of rate of replenishment, soil hydraulic conductivity, and maximum height of the water table above the impermeable layer.

Steady Groundwater Flow to Drains on a Sloping Bed: Comparison of Solutions Based on Boussinesq Equation and Richards Equation

“…When applied without modification to flow over a sloping plane, as proposed by Schmid and Luthin (1964), DF theory also contravenes the boundary condition at the bed, with the error increasing as the bed slope increases. Figure 1 shows the geometrical configuration studied by Schmid and Luthin (1964), in which h m is the maximum value of h, the vertical distance between the sloping base and the free surface.…”

“…The solutions have been used to determine the maximum height (h m ) and to present this as a ratio with the length of the slope section (L). Schmid and Luthin (1964) considered that the flow was parallel to a horizontal surface. They derived a solution which is correct in its final form but has some errors in the derivation (Appendix 1).…”

“…Figure 1 shows the geometrical configuration studied by Schmid and Luthin (1964), in which h m is the maximum value of h, the vertical distance between the sloping base and the free surface. By the Dupuit assumptions, h is necessarily the same as , the pressure head on the base at that point, and so for the Schmid and Luthin solution the maximum value m is the same as h m and occurs at the same position.…”

A systems approach to evaluate nutrient and pesticide transport from artificially drained cropland

“…On flat, regularly shaped fields a gridiron system of parallel laterals located perpendicular to the main line is employed. An interceptor drain is installed to collect water coming from higher ground, thus preventing it from reaching the area to be protected (Schmid and Luthin 1964). In addition, in order to accomplish subsurface drainage a system of open ditches for carrying the outlet water is generally necessary.…”

Saturated flow models applicable to hillside surface mine reclamation

“…These authors do not include a horizontal segment in the barrier. The theory for drainage on the sloped portion of the terraces in this thesis generally follows Schmid and Luthin (1964), although somewhat different notation and coordinates have been used to permit inclusion of the hori zontal segments. Tube drains have been assumed, although the theory more nearly represents an actual situation of drainage ditches.…”