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International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 962963, 14 pages
Research Article

Free-Boundary Seepage from Asymmetric Soil Channels

1Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, Calea 13 Septembrie 13, 010702 Bucharest, Romania
2Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, 010014 Bucharest, Romania

Received 30 March 2012; Accepted 28 May 2012

Academic Editor: Petru Jebelean

Copyright © 2012 Adrian Carabineanu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present an inverse method for the study of the seepage from soil channels without lining. We give integral representations of the complex potential, velocity field, stream lines, free phreatic lines, and contour of the channel by means of Levi-CivitΓ‘'s function πœ”. For different values of the Taylor coefficients of πœ”, we calculate numerically the contour of the channel, the phreatic lines, the seepage loss, the velocity field, the stream lines, and the equipotential lines. Examples are given for various symmetric or asymmetric channels, with smooth contours or with angular points.