Groundwater flow over a sloping impermeable layer: 1. Application of the Dupuit-Forchheimer assumption

Abstract

THE PROBLEM OF SEEPAGE FLOW IN A SATURATED LAYER, BOUNDED BELOW BY A SLOPING IMPERMEABLE SUBLAYER AND WITH THE UPPER SURFACE FREE, IS TREATED BY AN EXTENDED FORM OF THE DUPUIT- FORCHHEIMER ASSUMPTION IN WHICH THE STREAMLINES ARE ASSUMED PARALLEL TO THE SLOPING SUBLAYER. CALCULATED VALUES OF THE SLOPE OF THE PHREATIC SURFACE AT THE HIGHEST POINT OF THE FLOW REGION AND FAR DOWNSTREAM ARE IN AGREEMENT WITH EXACT VALUES OBTAINED BY CONSIDERATION OF THE FLOW HODOGRAPH. BY CONTRAST, THE RESULTS OBTAINED USING THE CLASSICAL DUPUIT- FORCHHEIMER ASSUMPTION /THAT STREAMLINES ARE HORIZONTAL/ EXHIBIT INCREASING DISCREPANICES AS THE SLOPE INCREASES. A SIMPLE METHOD OF CHECKING THE EFFECTIVENESS OF THE EXTENDED FORM OF DUPUIT-FORCHHEIMER ASSUMPTION, BY COMPARISON WITH THE HODOGRAPH, IS NOTED. THE EXTENDED FORM OF THE THEORY IS USED TO OBTAIN RELATIONS BETWEEN THE MAXIMUM HEIGHT OF WATER TABLE ABOVE THE IMPERMEABLE BASE, THE SPACING OF DRAINS, THE STEADY RATE OF INFLOW, AND THE SLOPE OF THE IMPERMEABLE BASE. /AUTHOR/