Transport in Porous Media

, Volume 116, Issue 2, pp 777–796 | Cite as

Sloping Saturated–Unsaturated Flow with Outflow at Seepage Face

  • L. KarantgisEmail author
  • P. Broadbridge
  • V. Lemiale


Analytic series solutions are constructed for the phreatic free surface problem of two-dimensional steady downslope saturated–unsaturated flow, with water exiting at a seepage face. The region in free parameter space is delineated for which the water table intersects the upper surface, and the steady state with uniform constant irrigation rate, ceases to exist. The flow solution is extended to a case of the domain being more general than a parallelogram, with the upper and lower boundaries being piecewise linear. This geometry resembles that of large-scale rainfall simulators that are designed to test slope stability of wetted soil beds.


Saturated–unsaturated flow Sloping media Free surface Analytic solution 



LK is grateful to CSIRO for a vacation scholarship, to Dr Naoki Sakai of NIED Japan for helpful discussions and to La Trobe University and IMI Kyushu University for some support. PB is grateful for the support of the Japan Society for the Promotion of Science Short-Term Visiting Fellowship and for the hosts at consecutive sites: the Australian Mathematical Science Institute, the Courant Institute of Mathematical Sciences and the Institute of Mathematics for Industry at Kyushu University. We are grateful to Associate Professor Leong Eng Choon for his assistance and expertise in constructing FEM comparisons to analytical soil water flow models.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsLa Trobe UniversityBundooraAustralia
  2. 2.CSIRO Data61ClaytonAustralia

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