Leaky-layer seepage

The Verigin function revisited

A. R. Kacimov, Yurii V. Obnosov

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

An explicit analytical solution to the problem of steady Darcian seepage into a constant-head subsurface gallery (a straight line segment) placed in a homogeneous rock under a leaky layer of silt deposited in a reservoir is obtained. The third-type boundary condition (linear relation between the head and normal component of the Darcian velocity) along the interface between sediments and rock is tackled by the Verigin function, which satisfies the mixed boundary-value problem conditions in a domain obtained by a conformal mapping of the physical plane (quadrangle) onto an auxiliary plane. This function has three integrable singularities and, unlike Verigin's attempt to construct the second conformal mapping, we use a Signorini-type integral representation. The gallery flow rate is plotted as a function of the gallery size, location under the leaky layer, and the leakage factor, which combines the hydraulic conductivities of the rock and silt, the difference in hydraulic head between the reservoir bottom above the leaky layer and the gallery contour and the silt thickness.

Original languageEnglish
Pages (from-to)345-354
Number of pages10
JournalJournal of Engineering Mathematics
Volume62
Issue number4
DOIs
Publication statusPublished - 2008

Fingerprint

Seepage
Silt
Conformal mapping
Rocks
Conformal Mapping
Hydraulic Conductivity
Mixed Boundary Value Problem
Linear Relation
Hydraulic conductivity
Sediment
Line segment
Leakage
Straight Line
Integral Representation
Hydraulics
Flow Rate
Boundary value problems
Analytical Solution
Sediments
Flow rate

Keywords

  • Analytic functions
  • Boundary-value problems
  • Leaky layer
  • Seepage

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

Cite this

Leaky-layer seepage : The Verigin function revisited. / Kacimov, A. R.; Obnosov, Yurii V.

In: Journal of Engineering Mathematics, Vol. 62, No. 4, 2008, p. 345-354.

Research output: Contribution to journalArticle

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