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An approximate solution for steady vertical flux of moisture through an unsaturated homogeneous soil
Author(s) -
Salvucci Guido Daniel
Publication year - 1993
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 - 10.1029/93wr02068
Subject(s) - capillary action , surface tension , water table , mechanics , hydraulic conductivity , capillary fringe , flux (metallurgy) , percolation (cognitive psychology) , moisture , steady state (chemistry) , flow (mathematics) , capillary number , water content , homogeneous , capillary length , materials science , thermodynamics , geotechnical engineering , soil science , geology , chemistry , soil water , physics , composite material , groundwater , neuroscience , biology , metallurgy
An approximate solution is found to the differential equation governing the steady state vertical flux of moisture through an unsaturated homogeneous soil for which the dependence of hydraulic conductivity on tension head is given in the form K (Ψ) = A(B +Ψ n ) −1 . The solution expresses the depth from the water table as a function of the capillary tension for a given rate of percolation or capillary rise. It is easily inverted to obtain explicit expressions both for the capillary tension as a function of depth and flow rate, and for the steady flow rate in terms of the capillary tension at a given depth. The latter is shown to compare favorably both to existing limiting case solutions of percolation to a water table at infinite depth, and to capillary rise from a shallow water table to an infinitely dry surface. More importantly, this solution applies to the intermediate condition where the magnitude and direction of flow are sensitive to both the near‐surface capillary tension and the water table depth.