Optimization and analysis of advective travel times beneath hydraulic structures

Anvar R. Kacimov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


Steady, 2D Darcian seepage in a homogeneous isotropic porous medium under an impervious structure is studied by the methods of complex analysis. The geometry of the structure is studied focusing on the travel time of a marked (neutral tracer) particle from the upper pool to the tailwater. In the Verigin problem, the angle of inclination of a sheetpile resulting in minimal time along the bounding streamline is π2. If the maximum of the minimum of the travel time is searched between all streamlines originated in the upper pool, then the optimal angles are found to be 0.404π and 0.596π. The minimization of the total volume of fluid that arrives from the upper pool to the tailwater during a prescribed time span is also considered. For arbitrary geometry, structure optimization with respect to travel time is carried out explicitly for the bounding streamline with a constraint on the wetted perimeter of a depressed structure. The minimal-time shape is found to be the Voshinin semicircular structure, which is mathematically generated by a line vortex.

Original languageEnglish
Pages (from-to)1311-1317
Number of pages7
JournalJournal of Hydraulic Engineering
Issue number9
Publication statusPublished - Sept 2008


  • Hydraulic structures
  • Optimization
  • Porous media
  • Seepage
  • Travel time
  • Vortices

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Water Science and Technology
  • Mechanical Engineering


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