Seepage of steady rainfall through soil into drains

Abstract

Theoretical formulas for the height of all points of an arch‐shaped water table are derived for steady rainfall seeping into homogeneous soil drained by tubes or ditches. The soil is underlain by an impermeable layer and the drains are taken to be equally spaced and equally deep. The solution is based on exact mathematical procedures, but utilizes a physical assumption that the height of the water table as measured from a reference plane passing through the lowest points of the water table is small compared to the depth of the impermeable layer. For tube drains running half full and when the impermeable layer is at great depth, the theoretical height H of the water table midway between drain tubes takes the particularly simple form, H = (2sR/πk)ln(2s/πγ) where H is height above the reference plane, 2r is the diameter of the drain tube, 2s is the spacing between drain tubes, R is the rainfall rate, and k the hydraulic conductivity. Flow nets for tube and ditch drainage are presented; a table for making practical computations has been prepared. The theory is compared with field data of Kirkham and De Zeeuw; good agreement was obtained. Finally, the interesting point is brought out that the Dupuit‐Forchheimer (DF) theory emerges from the general theory for the special case of very large ratio of drain spacing to height of water saturated soil and for an essentially flat water table. Thus the analysis presents a rational foundation for DF theory which has heretofore been lacking.