Darcian Seepage through a Parallelogrammic Ramp: Toth’s Model Revisited
Publication: Journal of Irrigation and Drainage Engineering
Volume 138, Issue 4
Abstract
Fully saturated, 2-D steady seepage in a homogeneous, isotropic, parallelogrammic ramp is studied using the methods of complex analysis (a conformal mapping and integral representation of mixed boundary-value problem). A porous medium flow is induced by an overland free-surface flow with the latter determining the “shearing” pressure (hydraulic head) of the former through a boundary condition along one side of the polygon serving as a conjugation line. For a uniform overland flow, the stream function along the conjugation line has a single maximum corresponding to the Toth hinge line. The inflow rate into the ramp is divided into a part exfiltrating through the toe and through a toe-adjacent segment of the conjugation boundary. A wavy free surface is shown to generate a more complex seepage topology.
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Acknowledgments
The helpful comments of two anonymous referees are highly appreciated.
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Published In
Journal of Irrigation and Drainage Engineering
Volume 138 • Issue 4 • April 2012
Pages: 377 - 381
Copyright
© 2012. American Society of Civil Engineers.
History
Received: Sep 30, 2009
Accepted: Oct 20, 2011
Published online: Oct 24, 2011
Published in print: Apr 1, 2012
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