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

Kacimov, A. R. and Youngs, E. G. (2009). Axisymmetric critical cavities for water exclusion in “Green and Ampt” soils: use of Pologii’s integral transform. Journal of Engineering Mathematics, 64(2) pp. 105–112.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1007/s10665-008-9264-9
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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.

Item Type: Journal Article
Copyright Holders: 2009 Springer Science+Business Media B.V.
ISSN: 0022-0833
Keywords: axisymmetric flow; free boundary; integral transform; seepage
Academic Unit/Department: Science > Environment, Earth and Ecosystems
Item ID: 16504
Depositing User: Colin Smith
Date Deposited: 26 May 2009 12:23
Last Modified: 14 Nov 2012 13:40
URI: http://oro.open.ac.uk/id/eprint/16504
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