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Groundwater withdrawal from a hill with uniformly sloped seepage faces
Author(s) -
Maas C.
Publication year - 1992
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 - 10.1029/91wr02576
Subject(s) - phreatic , hodograph , boundary (topology) , groundwater , geology , plane (geometry) , boundary value problem , geotechnical engineering , surface (topology) , geometry , transformation (genetics) , mathematics , hydrology (agriculture) , mathematical analysis , aquifer , biochemistry , chemistry , gene
A new kind of free boundary is introduced, namely, the projection on the horizontal plane of the interzonal boundary between a seepage face and a phreatic surface. This “seepage boundary” is demonstrated to show certain mathematical similarities to a phreatic surface, viewed in a vertical plane. A variation on Zhukovsk's method is employed to derive a formula for the deformation of the seepage boundary on the side of a hill due to groundwater withdrawal. The modified Zhukovski function, being many valued, is handled by Strack's extension of the Schwartz‐Christoffel transformation. It is finally pointed out that more complicated problems could be solved by a modified hodograph method.