Darcian Seepage through a Parallelogrammic Ramp: Toth's Model Revisited

A. R. Kacimov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)377-381
Number of pages5
JournalJournal of Irrigation and Drainage Engineering
Issue number4
Publication statusPublished - Apr 26 2012


  • Analytical solution
  • Conformal mappings
  • Overland flow
  • Seepage
  • Singular integrals

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Water Science and Technology
  • Agricultural and Biological Sciences (miscellaneous)


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