Abstract
We derive precisely the fundamental equation of the nonlinear flow in porous media based on Forchheimer's resistance equation and explain in detail how to solve this equation by the direct iterative procedure using the finite element method. We apply this procedure to seepage through embankment dams and compare the characteristics of the nonlinear flow with that of the linear flow. The results are summarized as follows:
1) The locations of the free surface of the nonlinear flow are higher than those of the linear flow and the equi-potential lines of the nonlinear flow move toward the downstream.
2) The maximum hydraulic gradient occurs near the downstream toe of dam and its value is about 0.5 and not so much different from that of the linear flow.
3) The positions of the exit point of the nonlinear flow become higher and there are more difference between the positions of the exit point of the nonlinear flow and those of the linear flow, as the constant ‘a’ of the Forchheimer's resistance equation becomes smaller and/or the constant ‘b’ becomes larger.
4) The locations of the exit point of the nonlinear flow are about 5% to 25% higher than those of the linear flow.
5) There are more difference between the discharge of the nonlinear flow and that of the linear flow, as the constant ‘a’ of the Forchheimer's resistance equation becomes smaller and/or the constant ‘b’ becomes larger.
