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Series Solution for Richards Equation Under Concentration Boundary Conditions and Uniform Initial Conditions
Author(s) -
Salvucci Guido Daniel
Publication year - 1996
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 - 10.1029/96wr01106
Subject(s) - infiltration (hvac) , water content , soil water , richards equation , thermal diffusivity , mathematics , moisture , quadratic equation , saturation (graph theory) , power series , soil science , mechanics , mathematical analysis , geotechnical engineering , environmental science , thermodynamics , geology , geometry , physics , meteorology , combinatorics
A series solution which expresses the moisture profiles and surface fluxes during infiltration and exfiltration is derived. The solution applies for conditions of fixed surface moisture content and uniform initial moisture content within an unbounded, homogeneous, nonhysteretic soil column. The series derivation is similar to J. R. Philip's but with a transformed time variable. The series converges for infiltration problems involving soils which exhibit steep increase in capillary pressure near saturation. Under these conditions the solution captures the transition from early square root of time behavior to the longtime traveling wave solution without the use of approximate joining techniques. The soil water retention models for which convergence occurs include the widely applied Brooks‐Corey and van Genuchten models, with minor restrictions on the shape parameters of the latter. Other cases examined include infiltration and exfiltration assuming power law, linear, quadratic, and constant dependence of diffusivity and conductivity on moisture content. For these cases the convergence limits were finite. The solution is particularly well suited for infiltration into sandy soils, for which the transition between short‐time and longtime behavior occurs relatively early.