### 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.

Original language | English |
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Pages (from-to) | 105-112 |

Number of pages | 8 |

Journal | Journal of Engineering Mathematics |

Volume | 64 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2009 |

### Keywords

- Axisymmetric flow
- Free boundary
- Integral transform
- Seepage

### ASJC Scopus subject areas

- Mathematics(all)
- Engineering(all)