### 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 |
---|---|

Pages (from-to) | 105-112 |

Number of pages | 8 |

Journal | Journal of Engineering Mathematics |

Volume | 64 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2009 |

### Fingerprint

### Keywords

- Axisymmetric flow
- Free boundary
- Integral transform
- Seepage

### ASJC Scopus subject areas

- Mathematics(all)
- Engineering(all)

### Cite this

**Axisymmetric critical cavities for water exclusion in "green and ampt" soils : Use of Pologii's integral transform.** / Kacimov, A. R.; Youngs, E. G.

Research output: Contribution to journal › Article

*Journal of Engineering Mathematics*, vol. 64, no. 2, pp. 105-112. https://doi.org/10.1007/s10665-008-9264-9

}

TY - JOUR

T1 - Axisymmetric critical cavities for water exclusion in "green and ampt" soils

T2 - Use of Pologii's integral transform

AU - Kacimov, A. R.

AU - Youngs, E. G.

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

KW - Axisymmetric flow

KW - Free boundary

KW - Integral transform

KW - Seepage

UR - http://www.scopus.com/inward/record.url?scp=67349157200&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67349157200&partnerID=8YFLogxK

U2 - 10.1007/s10665-008-9264-9

DO - 10.1007/s10665-008-9264-9

M3 - Article

VL - 64

SP - 105

EP - 112

JO - Journal of Engineering Mathematics

JF - Journal of Engineering Mathematics

SN - 0022-0833

IS - 2

ER -