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JOURNAL OF MATERIALS & CONSTRUCTION

ISSN: 2734-9438

Website: www.jomc.vn

An investigation of seepage flow through homogenous embankment dams using an iteration technique for determining the free surfaces

Giang Vo Tuyet , Nguyen Vo Trong

Abstract

This paper presents the application of the finite element method into solving the balance equation of seepage flows within the porous media. More specifically, these seepage flows occur within homogenous embankment dams. With the specific boundary conditions of water levels in the upstream and downstream sides, the seepage mechanism takes place, generating the unsaturated zones and the saturated ones as well. The demarcation surfaces between the un-saturated and saturated zones are called the free surfaces. For determining these free surfaces, an algorithm of loop is employed, and the convergence is required to locate the free surfaces. This paper combines the relevant ideas into a sub-routine using the programming language Python. Next, a case is shown using the current sub-routine considering the convergence of the solution and comparing it to the outcome of a popular software of seepage analysis SEEP/W. The results show that the algorithm used for locating the free surface is acceptable when dealing with this type of seepage mechanism.

References

  1. S. P. Neuman and P. A. Witherspoon, "Finite Element Method of Analyzing Steady Seepage with a Free Surface," Water Resources Research, vol. 6, no. 3, pp. 889-897, 1970, doi: https://doi.org/10.1029/WR006i003p00889.
  2. C. S. Desai, "Finite element residual schemes for unconfined flow," International Journal for Numerical Methods in Engineering, vol. 10, no. 6, pp. 1415-1418, 1976, doi: https://doi.org/10.1002/nme.1620100622.
  3. K.-J. Bathe and M. R. Khoshgoftaar, "Finite element free surface seepage analysis without mesh iteration," International Journal for Numerical and Analytical Methods in Geomechanics, vol. 3, no. 1, pp. 13-22, 1979, doi: https://doi.org/10.1002/nag.1610030103.
  4. S. J. Lacy and J. H. Prevost, "Flow through porous media: A procedure for locating the free surface," International Journal for Numerical and Analytical Methods in Geomechanics, vol. 11, no. 6, pp. 585-601, 1987, doi: https://doi.org/10.1002/nag.1610110605.
  5. A. Cividini and G. Gioda, "On the variable mesh finite element analysis of unconfined seepage problems," Géotechnique, vol. 39, no. 2, pp. 251-267, 1989, doi: 10.1680/geot.1989.39.2.251.
  6. A. Leontiev and W. Huacasi, "Mathematical programming approach for unconfined seepage flow problem," Engineering Analysis with Boundary Elements, vol. 25, no. 1, pp. 49-56, 2001/01/01/ 2001, doi: https://doi.org/10.1016/S0955-7997(00)00067-9.
  7. J.-P. Bardet and T. Tobita, "A practical method for solving free-surface seepage problems," Computers and Geotechnics, vol. 29, no. 6, pp. 451-475, 2002/09/01/ 2002, doi: https://doi.org/10.1016/S0266-352X(02)00003-4.
  8. D. G. Fredlund, H. Rahardjo, and M. D. Fredlund, Unsaturated Soil Mechanics in Engineering Practice, 1st ed. Wiley-Interscience, 2012.
  9. S. P. Neuman, "Saturated-Unsaturated Seepage by Finite Elements," Journal of the Hydraulics Division, vol. 99, no. 12, pp. 2233-2250, 1973, doi: doi:10.1061/JYCEAJ.0003829.
  10. C. S. Desai and G. C. Li, "A residual flow procedure and application for free surface flow in porous media," Advances in Water Resources, vol. 6, no. 1, pp. 27-35, 1983/03/01/ 1983, doi: https://doi.org/10.1016/0309-1708(83)90076-3.
  11. A. T. Papagianakis and D. G. Fredlund, "A steady state model for flow in saturated–unsaturated soils," Canadian Geotechnical Journal, vol. 21, no. 3, pp. 419-430, 1984, doi: 10.1139/t84-046.
  12. D. V. Hutton, Fundamentals of finite element analysis, 1 ed. Boston: McGraw-Hill, 2004.
  13. M. T. van Genuchten, "A Closed-form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils," Soil Science Society of America Journal, vol. 44, no. 5, pp. 892-898, 1980, doi: https://doi.org/10.2136/sssaj1980.03615995004400050002x.
  14. G.-S. I. Ltd., Seepage modelling with SEEP/W. Calgary, Canada: Geo-Slope International Ltd., 2012.
  15. C. Geuzaine and J.-F. Remacle. "GMSH." https://gmsh.info/ (accessed.