Initial Motion Problem in Porous Media

The Lagrangian equations of fluid mechanics are used to solve the problem of rapid drawdown adjacent to a steep earth embankment. The equations are solved for the pressure and the shape of the free surface in the embankment. The pressures can then be used to compute the stability of the embankment while the values of the fluid displacement are used to compute the drainage hydrography. The Lagrangian equations have the advantage that the domain of solution remains unchanged for all time although the problem is one of unsteady flow involving a free surface. Thus, this type of representation is often useful for such initial problems. The results are presented in a dimensionless, tabular form so that calculation can be easily performed.