Steady flow to tile drains above an impervious layer -- a theoretical study

Abstract

Existing analytical solutions for vertical influent seepage flow to an infinite series of tile drains underlain by an impervious layer do not adequately consider the free surface nor give solutions for the drain diameter (see Figure 1). The theoretical investigations described herein basically sought to find a method whereby an engineer could find the required diameter, depth, and spacing of an adequate tile drainage system when given the ratio of infiltration to soil hydraulic conductivity and the depth of the impervious layer. From a study of the available literature it was decided the problem would be exceedingly difficult to solve exactly but it seemed as if an approximate solution of good accuracy could be obtained by approximating the shape of the impervious layer, where the flow is sluggish, and satisfying the conditions exactly at the free surface, a critical region of flow. Previously published solutions invariably adopt the opposite viewpoint, with a consequent loss in accuracy. The solution to the problem when the impervious layer is at infinite depth had been solved exactly using the rather laborious hodograph technique. This work employs to advantage an image method developed by Davison and Rosenhead (1940). Detailed results are obtained herein for the condition when no water stands over the tile lines and these are given in a graphical form which enables a ready computation of drain depth diameter and spacing when the field data are known (ratio of rate of infiltration to hydraulic conductivity and the depth of the impervious layer). A comparison with field results shows that the solutions are probably as accurate as could be desired. The case which occurs when water stands over the tile lines has not been extensively tabulated for reasons explained in the report. A method is given whereby adequate tile drainage systems may be designed on a long term basis. The design curves given are not for intermittent unsteady flows such as irrigation schemes (a more difficult problem) but should prove exceedingly useful for engineers concerned with land reclamation schemes and marsh drainage.

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