Skip to main content
SpringerLink
Log in

Critical Hydraulic Gradient of Piping Erosion Under Free Flow and Seepage Flow Coupling Model

  • SOIL MECHANICS
  • Published:
Soil Mechanics and Foundation Engineering Aims and scope

This paper proposes a coupling model for evaluating the occurrence of piping erosion under free flow and seepage flow. The model employs the Navier–Stokes equation to describe free water flow in a pore channel and the Brinkman-extended Darcy equation to describe seepage flow in soft soils. The expression of the critical hydraulic gradient of piping erosion was derived based on the force limit equilibrium of a single soil particle within the pore channel. The results of the theoretical calculation of the proposed model are in good agreement with the results obtained by two classical piping tests. However, compared with existing formulas, the proposed formula has better generalization and accuracy. Moreover, the critical hydraulic gradient varies linearly with the soft soil porosity (negative correlation), the soil particle diameter (positive correlation) inside the pore channel, and the stress jump coefficient (positive correlation) at the interface between the pore channel and the soft soils.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. Fell and J. J. Fry, “The state of the art of assessing the likelihood of internal erosion of embankment dams, water retaining structures and their foundations,” Intern. Erosion Dams Th. Found., Taylor & Francis, London (2007).

  2. J. E. Costa, “Floods from dam failures,” U. S. Geo. Surv., Denver, Open-File Rep, 85-560 (1985).

  3. M. Foster, R. Fell, and M. Spannagle, “The statistics of embankment dam failures and accidents,” Can. Geotech. J., 37(5), 1000-1024 (2000).

    Article  Google Scholar 

  4. K. S. Richards and K. R. Reddy, “Critical appraisal of piping phenomena in earth dams,” Bull. Eng. Geol. Environ., 66(4), 381-402 (2007).

    Article  Google Scholar 

  5. K. Fujisawa, A. Murakami, and S. I. Nishimura, “Numerical analysis of the erosion and the transport of fine particles within soils leading to the piping phenomenon,” Soils Found., 50(4), 471-482 (2010).

    Article  Google Scholar 

  6. Y. Liang, C. Zeng, J. Wang, et al., “Constant gradient erosion apparatus for appraisal of piping behavior in upward seepage flow,” Geotech. Test. J., 40(4), 630-642 (2017).

    Article  Google Scholar 

  7. G. Hoffmans and L. V. Rijn, “Hydraulic approach for predicting piping in dikes,” J. Hydraul. Res., 56(2), 268-281 (2018).

    Article  Google Scholar 

  8. M. F. Ahlinhan and C. E. Ahlinhan, “Combined geometric hydraulic criteria approach for piping and internal erosion in cohesionless soils,” Geotech. Test. J., 42(1), 180-193 (2018).

    Article  Google Scholar 

  9. M. S. Fleshman and J. D. Rice, “Constant gradient piping test apparatus for evaluation of critical hydraulic conditions for the initiation of piping,” Geotech. Test. J., 36(6), 834-846 (2013).

    Article  Google Scholar 

  10. W. G. Bligh, “Dams, barrages and weirs on porous foundations,” Eng. News, 64(26), 708 (1910).

    Google Scholar 

  11. E. W. Lane, “Security from under seepage: Masonary dams on earth foundations,” Trans. Am. Soc. Civ. Eng., 100(1), 1235-1272 (1935).

    Article  Google Scholar 

  12. J. Tammy, “An analysis on soil properties on predicting critical hydraulic gradients for piping progression in sandy soils,” M. Sc. thesis, Utah State Univ., Logan, U. S. (2013).

  13. J. Liu, “Theoretical basis of seepage control of Earth and rockfill dams and Engineering experience and lessons,” China Water & Power Press, Beijing (2006).

    Google Scholar 

  14. B. Indraratna and S. Radampola, “Analysis of critical hydraulic gradient for particle movement in filtration,” J. Geotech. Geoenviron. Eng., 128(4), 347-350 (2002).

    Article  Google Scholar 

  15. J. Zhou, Y. F. Bai, and Z. X. Yao, “A mathematical model for determination of the critical hydraulic gradient in soil piping,” Geoshanghai Int. Conf. (2010).

  16. J. X. Sha, “Research on piping in porous media,” Hydro-Sci. Eng., 1(03), 89-93 (1981).

    Google Scholar 

  17. G. Kovacs, “Seepage Hydraulics,” Elsevier Sci. Publ. Co., New York (1981).

    Google Scholar 

  18. P. Ming, J. Lu, and X. Cai, et al., “Multi-Particle model of the critical hydraulic gradient for dike piping,” Soil Mech. Found. Eng., 57(3), 200-210 (2020).

    Article  Google Scholar 

  19. Z. V. Terzaghi, “Experimental investigation of the pressure of a loose medium on retaining walls with a vertical back face and horizontal backfill surface,” Soil Mech. Found. Eng., 2(4), 197-200 (1965).

    Article  Google Scholar 

  20. S. Wang, J. S. Chen, Q. M. Zhong, et al., “Study on critical hydraulic gradient for piping in granular soils,” Water Resour. Power, 36(09), 114-117 (2008).

    Google Scholar 

  21. A. W. Skempton and J. M. Brogan, “Experiments on piping in sandy gravels,” Geotechnique, 44(3), 449-460 (1994).

    Article  Google Scholar 

  22. B. Q. Xu, J. S. Chen, and Y. Liang, “Failure test and seepage deformation analysis of fine sand piping,” Water Resour. Power, 30(6), 66-69 (2012). J. A. Ochoa-Tapia and S. Whitaker, “Momentum transfer at the boundary between a porous medium and a homogeneous fluid—I. Theoretical development,” Int. J. Heat Mass Transf., 38(14), 2635-2646 (1995).

    Article  Google Scholar 

  23. J. A. Ochoa-Tapia and S. Whitaker, “Momentum transfer at the boundary between a porous medium and a homogeneous fluid—II. Comparison with experiment,” Int. J. Heat Mass Transf., 38(14), 2647-2655 (1995b).

    Article  MATH  Google Scholar 

  24. C. S. P. Ojha and V. P. Singh, “Influence of porosity on piping models of levee failure,” J. Geotech. Geoenviron. Eng., 127(12), 1071-1074 (2001).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Hydraulic and Mountain River Engineering, School of Water Resource and Hydropower, Sichuan University, Chengdu, China

    S. Zhang, F. Ye, Y. Liu & W.-X. Fu

  2. Chengdu Surveying Geotechnical Research Institute Co., Ltd. of MCC, Chengdu, China

    H.-Y. Liao

Authors
  1. S. Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. Ye
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Y. Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. W.-X. Fu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. H.-Y. Liao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to F. Ye.

Additional information

Translated from Osnovaniya, Fundamenty i Mekhanika Gruntov, No. 5, September-October, 2023.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, S., Ye, F., Liu, Y. et al. Critical Hydraulic Gradient of Piping Erosion Under Free Flow and Seepage Flow Coupling Model. Soil Mech Found Eng 60, 419–427 (2023). https://doi.org/10.1007/s11204-023-09910-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11204-023-09910-2

Search

Navigation