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

摘要

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.