GROUNDWATER FLOW OVER A SLOPING IMPERMEABLE LAYER. 2 EXACT SOLUTIONS BY CONFORMAL MAPPING

EXACT SOLUTIONS ARE OBTAINED BY THE HODOGRAPH METHOD FOR SATURATED SEEPAGE FLOW OVER AN IMPERMEABLE BASE OF SLOPE 30 DEGREES TO THE HORIZONTAL, WHEN THE RATE OF REPLENISHMENT BY DISTRIBUTED INFILTRATION HAS A CRITICAL VALUE OF 0.0718 TIMES THE HYDRAULIC CONDUCTIVITY. THREE DIFFERENT PROBLEMS ARE CONSIDERED. /1/ FLOW OVER A SLOPE INTO A HORIZONTAL SLIT DRAIN. THE WIDTH OF DRAIN EFFECTIVE IN REMOVING WATER IS EQUAL TO ABOUT 4.0% OF THE DOWNSLOPE DISTANCE, AND THE MIXIMUM DEPTH OF WATER /MEASURED NORMAL TO THE IMPERMEABLE LAYER/ IS ABOUT 10% AND OCCURS AT 72% OF THE DISTANCE DOWNSLOPE. THE APPROXIMATE SOLUTION OBTAINED USING THE EXTENDED FORM OF DUPUIT-FORCHHEIMER ASSUMPTION IS IN EXCELLENT AGREEMENT WITH THE EXACT RESULT EXCEPT NEAT THE SLIT DRAIN. /2/ FLOW WITH FINITE DEPTH AT THE HIGHEST POINT. THE DUPUIT-FORCHHEIMER ASSUMPTION IS ASYMPTOTICALLY CORRECT AT LARGE DISTANCES DOWNSTREAM BUT FAILS AS THE HIGHEST POINT ON THE PHREATIC SURFACE IS APPROACHED, WHERE THE SURFACE IS HORIZONTAL. /3/ SEEPAGE SURFACE PARALLEL TO THE IMPERMEABLE LAYER /THE PERMEABLE OVERBURDEN PROBLEM/. THE DEPTH OF SATURATED FLOW INCREASES WITH DOWNSLOPE DISTANCE, UNTIL THE PHREATIC SURFACE INTERESTS THE SEEPAGE SURFACE AT A DOWNSLOPE DISTANCE OF 7.3 TIMES THE OVERBURDEN DEPTH. FLOW ACROSS THE SEEPAGE SURFACE /AN INFLOW/ DECREASES RAPIDLY WITH FURTHER DISTANCE DOWNSLOPE. THE EXTENDED DUPUIT-FORCHHEIMER ASSUMPTION LEADS TO AN EXCELLENT PREDICTION OF THE SHAPE OF PHREATIC SURFACE BUT TREATS THE THE SEEPAGE FLOW AS ZERO. /AUTHOR/

  • Supplemental Notes:
    • Vol 71, No 12, PP 2903-2910
  • Authors:
    • Wooding, R A
  • Publication Date: 1966-6-15

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  • Accession Number: 00234079
  • Record Type: Publication
  • Files: TRIS
  • Created Date: Jul 28 1994 12:00AM