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On the solution of steady unconfined seepage towards semi‐infinite slopes
Author(s) -
Muleshkov Angel,
Banerjee Sunirmal
Publication year - 1991
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.1610150405
Subject(s) - conformal map , dimensionless quantity , mathematics , phreatic , ordinary differential equation , mathematical analysis , partial differential equation , variable (mathematics) , parametric statistics , point (geometry) , geometry , differential equation , geology , geotechnical engineering , mechanics , physics , statistics , aquifer , groundwater
Analytical solutions for the two‐dimensional problem of unconfined seepage towards semi‐infinite slopes are described. The analysis employs complex variable techniques. Conformal mappings have been used to reduce the problem to solving an ordinary differential equation. The resulting integrals are presented in terms of special functions. The solutions for the location of the phreatic surface and the exit point have been obtained in parametric form. Some additional results and asymptotic expansions of the solutions are also presented. The numerical results have been calculated and plotted for different values of the slope angle in dimensionless co‐ordinate space.