Axisymmetric critical cavities for water exclusion in "green and ampt" soils: Use of Pologii's integral transform

A. R. Kacimov, E. G. Youngs

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An analytical solution of Laplace's equation is obtained for the flow of water in the tension-saturated zone of a "Green and Ampt" soil, subject to uniform vertical infiltration from above, around an axisymmetric cavity of critical shape that just excludes water. The solution is obtained by converting a line-source potential in a plane seepage flow into a line source in an axisymmetric flow (the Polubarinova-Kochina solution) using Pologii's integral transform combined with a unit-gradient potential for downward seepage flow. The analysis shows that both the cavity surface and the capillary fringe boundary are paraboloids between which is sandwiched a tension-saturated region. The critical cavity obtained for the Green and Ampt soil and Philip's paraboloidal cavity obtained for a "Gardner" soil allow the estimates of the soil parameters used in the two soil models to be related.

Original languageEnglish
Pages (from-to)105-112
Number of pages8
JournalJournal of Engineering Mathematics
Issue number2
Publication statusPublished - 2009



  • Axisymmetric flow
  • Free boundary
  • Integral transform
  • Seepage

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

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