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

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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