Steady flow to tile drains above an impervious layer -- a theoretical study
Creators: name: List, E. John
Publisher: name: California Institute of Technology
Year: 1965

description: 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.
description: © The work reported herein was originally a portion of a thesis submitted to the University of Auckland, New Zealand in partial fulfillment of the requirements for the degree of Master of Engineering. The major part of the computation was completed as a laboratory research project at the California Institute of Technology, Pasadena, California. 

The author is indebted to Fletcher Industries, and the University of Auckland, Auckland, New Zealand for financial assistance during 1962 and the California Institute of Technology for the use of its computing facilities. Numerous suggestions and assistance by Dr. C. M. Segedin (University of Auckland) and Dr. N. H. Brooks (California Institute of Technology) are gratefully acknowledged. The assistance of Mrs. Pat Rankin, Mr. F. C. Cammack and Mr. Paul Kochendorfer in the preparation of the manuscript is also gratefully acknowledged.
description: Submitted - KH-R-9.pdf