Seepage Under a Rectangular Dam

A solution to the problem of seepage under a rectangular dam, founded in an homogeneous stratum of finite depth, is obtained. Use is made of potential theory, the theory of complex variables, elliptic integrals, the Jacobian Zeta function, Heuman's Lambda function, and of the process of conformal transformation. The solution is shown to agree with established solutions for a surface dam and for a sheet pile cutoff wall; and, when the depth of permeable soil is large, it is easily verified that numerical solutions tend towards values given by the established solution for infinite depth. Graphs are presented that independently relate problem geometry, discharge, and pertinent values of total head and hydraulic gradient with two parameters. The use of the graphs and parameters is illustrated by the solution of a typical problem. Also illustrated is a method of obtaining a good approximation to the distribution of total bead around the dam.