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The seepage exclusion problem for spherical cavities
Author(s) -
Knight J. H.,
Philip J. R.,
Waechter R. T.
Publication year - 1989
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr025i001p00029
Subject(s) - dimensionless quantity , radius , roof , curvature , radius of curvature , mechanics , hydraulic conductivity , geometry , shadow (psychology) , physics , mathematics , geology , mean curvature , engineering , soil science , psychology , computer security , structural engineering , mean curvature flow , computer science , psychotherapist , soil water
The quasi‐linear problem of water exclusion from, or entry into, spherical cavities from steady uniform downward unsaturated seepage is solved. Both exact solutions and simple asymptotic results are found. These are qualitatively similar to those given previously for circular cylindrical cavities, exhibiting such features as the dry shadow and the roof‐drip lobes. A major practical result of the analysis is the function ∂ max ( s ), the dependence of the maximum potential (at the roof apex) on the dimensionless quantity s = ½ α l , with α the sorptive number and l cavity radius. ∂ max ( s ) is almost indistinguishable from ∂ max (½ s ) for circular‐cylindrical cavities. This implies that physically the most relevant configuration parameter is total curvature at the apex of the cavity surface. Our results enable us to establish, for given values of downward seepage velocity, cavity radius, saturated hydraulic conductivity K 1 and of α, whether or not seepage water will enter a spherical cavity.