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Axisymmetric critical cavities for water exclusion in “Green and Ampt” soils: use of Pologii’s integral transform

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Abstract

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.

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Authors and Affiliations

  1. Department of Soils, Water and Agricultural Engineering, Sultan Qaboos University, P.O. Box 34, Al-Khod, 123, Sultanate of Oman

    A. R. Kacimov

  2. Department of Life Sciences, Open University, Walton Hall, Milton Keynes, MK7 6AA, UK

    E. G. Youngs

Authors
  1. A. R. Kacimov
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  2. E. G. Youngs
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Correspondence to A. R. Kacimov.

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Kacimov, A.R., Youngs, E.G. Axisymmetric critical cavities for water exclusion in “Green and Ampt” soils: use of Pologii’s integral transform. J Eng Math 64, 105–112 (2009). https://doi.org/10.1007/s10665-008-9264-9

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  • DOI: https://doi.org/10.1007/s10665-008-9264-9

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