Steady-state ditch-drainage of two-layered soil regions overlying an inverted V-shaped impermeable bed with examples of the drainage of ballast beneath railway tracks

Water-table heights due to steady surface accretion in drained two-layered soil regions overlying an inverted V-shaped impermeable bed are obtained using both the Dupuit–Forchheimer approximate analysis with flow assumed parallel to the bed and also from numerical solutions of Laplace’s equation for the head distribution. For illustration, water-table profiles obtained by the two procedures are compared for surface accretion draining to ditches in a typical two-layered ballast foundation for a railway track where a very permeable ballast material overlies a less permeable sub-grade on top of an inverted V-shaped impermeable bed that slopes away both sides from a central line to drainage ditches. These results are found to be in good agreement except very near the drainage ditches where the Laplace numerical solution takes into consideration a surface of seepage that is ignored in the Dupuit–Forchheimer analysis. The Dupuit–Forchheimer analysis is also in good agreement with results of a laboratory model experiment. It is concluded that the approximate Dupuit–Forchheimer analysis can be used with confidence in these situations. It is used to investigate the effect on the water-table elevation caused by the reduction of hydraulic conductivity of the porous materials due to clogging.