Seepage Through an Earth Dam Computed by the Relaxation Technique

The problem of seepage flow through a homogeneous earth dam is investigated on the assumption that the flow is plane, steady, and governed by Darcy's law. In this case the governing equation for the pressure head is the Laplace equation, and the boundary conditions are straightforward except at the phreatic surface, which is a free streamline with location initially unknown. The problem is solved by adapting the relaxation method for machine computation. In particular, the intuition of the hand calculator is replaced by automatic procedures more suited for the machine. Closely agreeing solutions were obtained for separate executions having widely different initial (guessed) positions of the free streamline. These solutions, execution of each of which took from 50 to 70 seconds on an IBM 7090, are in excellent agreement with the longhand solutions of Shaw and Southwell. Computer flow rates agreed very well with the theoretical discharge given by the Dupuit formula.