Analytically computed rates of seepage flow into drains and cavities

N. Fujii, A. R. Kacimov

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

The known formulae of Freeze and Cherry, Polubarinova - Kochina, Vedernikov for flow rate during 2-D seepage into horizontal drains and axisymmetric flow into cavities are examined and generalized. The case of an empty drain under ponded soil surface is studied and existence of drain depth providing minimal seepage rate is presented. The depth is found exhibiting maximal difference in rate between a filled and an empty drain. 3-D flow to an empty semi-spherical cavity on an impervious bottom is analysed and the difference in rate as compared with a completely filled cavity is established. Rate values for slot drains in a two-layer aquifer are 'inverted' using the Schulgasser theorem from the Polubarinova-Kochina expressions for corresponding flow rates under a dam. Flow to a point sink modelling a semi-circular drain in a layered aquifer is treated by the Fourier transform method. For unsaturated flow the catchment area of a single drain is established in terms of the quasi-linear model assuming the isobaric boundary condition along the drain contour. Optimal shape design problems for irrigation cavities are addressed in the class of arbitrary contours with seepage rate as a criterion and cavity cross-sectional area as an isoperimetric restriction.

Original languageEnglish
Pages (from-to)277-301
Number of pages25
JournalInternational Journal for Numerical and Analytical Methods in Geomechanics
Volume22
Issue number4
Publication statusPublished - 1998

Fingerprint

Seepage
drain
seepage
cavity
Aquifers
Flow rate
Irrigation
Catchments
Dams
Fourier transforms
Boundary conditions
Soils
aquifer
unsaturated flow
rate
Fourier transform
soil surface
boundary condition
dam
irrigation

Keywords

  • Drain
  • Flow rate
  • Optimization
  • Seepage
  • Tunnel

ASJC Scopus subject areas

  • Geotechnical Engineering and Engineering Geology
  • Computational Mechanics
  • Mechanics of Materials
  • Materials Science(all)

Cite this

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abstract = "The known formulae of Freeze and Cherry, Polubarinova - Kochina, Vedernikov for flow rate during 2-D seepage into horizontal drains and axisymmetric flow into cavities are examined and generalized. The case of an empty drain under ponded soil surface is studied and existence of drain depth providing minimal seepage rate is presented. The depth is found exhibiting maximal difference in rate between a filled and an empty drain. 3-D flow to an empty semi-spherical cavity on an impervious bottom is analysed and the difference in rate as compared with a completely filled cavity is established. Rate values for slot drains in a two-layer aquifer are 'inverted' using the Schulgasser theorem from the Polubarinova-Kochina expressions for corresponding flow rates under a dam. Flow to a point sink modelling a semi-circular drain in a layered aquifer is treated by the Fourier transform method. For unsaturated flow the catchment area of a single drain is established in terms of the quasi-linear model assuming the isobaric boundary condition along the drain contour. Optimal shape design problems for irrigation cavities are addressed in the class of arbitrary contours with seepage rate as a criterion and cavity cross-sectional area as an isoperimetric restriction.",
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AU - Fujii, N.

AU - Kacimov, A. R.

PY - 1998

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AB - The known formulae of Freeze and Cherry, Polubarinova - Kochina, Vedernikov for flow rate during 2-D seepage into horizontal drains and axisymmetric flow into cavities are examined and generalized. The case of an empty drain under ponded soil surface is studied and existence of drain depth providing minimal seepage rate is presented. The depth is found exhibiting maximal difference in rate between a filled and an empty drain. 3-D flow to an empty semi-spherical cavity on an impervious bottom is analysed and the difference in rate as compared with a completely filled cavity is established. Rate values for slot drains in a two-layer aquifer are 'inverted' using the Schulgasser theorem from the Polubarinova-Kochina expressions for corresponding flow rates under a dam. Flow to a point sink modelling a semi-circular drain in a layered aquifer is treated by the Fourier transform method. For unsaturated flow the catchment area of a single drain is established in terms of the quasi-linear model assuming the isobaric boundary condition along the drain contour. Optimal shape design problems for irrigation cavities are addressed in the class of arbitrary contours with seepage rate as a criterion and cavity cross-sectional area as an isoperimetric restriction.

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KW - Flow rate

KW - Optimization

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KW - Tunnel

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