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Acta Geotechnica

, Volume 14, Issue 2, pp 477–486 | Cite as

Analysis of the pipe depth development in small-scale backward erosion piping experiments

  • Kristine VandenboerEmail author
  • Vera M. van Beek
  • Adam Bezuijen
Research Paper

Abstract

Backward erosion piping is an important failure mechanism for water-retaining structures. It results in the formation of shallow pipes at the interface of a sandy or silty foundation and a cohesive cover layer. This paper analyzes the depth of these erosion pipes through small-scale experiments. The development of the pipe depth reveals a lot of information on the backward erosion process, but it had never been measured systematically during the erosion process. Our analysis shows that the pipes are extremely shallow (in the order of mm) and that the pipe depth increases slightly, as piping progresses. Furthermore, a relation is found between pipe depth, grain size, soil permeability, and pipe length. The experimentally obtained depths are in good agreement with those obtained with theoretically determined pipe depths based on pipe hydraulics. Finally, the experiments are compared to 2D numerical simulations using Sellmeijer’s mathematical model and 3D numerical simulations with the correct pipe dimensions.

Keywords

Backward erosion piping Embankments Erosion Groundwater flow 

List of symbols

A

Cross section (mm2)

B

Pipe width (mm)

CFD

Coupled fluid dynamics

Cu

Coefficient of uniformity (−)

Cc

Coefficient of gradation (−)

d10

Diameter for which 10% of the particles of the distribution are smaller (mm)

d30

Diameter for which 30% of the particles of the distribution are smaller (mm)

d50

Average grain size (mm)

d60

Diameter for which 60% of the particles of the distribution are smaller (mm)

d80

Diameter for which 80% of the particles of the distribution are smaller (mm)

d

Pipe depth (m)

davg

Average (of cross section) pipe depth (mm)

\(d_{{{\text{avg}}, \Delta x}}\)

Average pipe depth at a distance Δx from the pipe tip (calculated) (mm)

DEM

Discrete element method

ΔH

Hydraulic head difference (m)

ΔHcrit

Critical hydraulic head for progression (m)

ΔP/L

Pressure drop per meter (Pa/m)

Δx

Distance from pipe tip (m)

FEM

Finite-element method

γw

Unit density of water (N/m3)

γ′p

Submerged unit density of particles (N/m3)

k

Hydraulic permeability (m/s)

L

Pipe length (m)

M0

Correction factor (−)

Μ

Dynamic viscosity (Pa s)

η

Coefficient of white (−)

Pw

Wetted perimeter (m)

φ

Effective friction angle of the sand (°)

Q

Flow rate (mm3/s)

Q2D

Flow rate in 2D (Sellmeijer) (m2/s)

ρ

Unit density (kg/m3)

Re

Reynolds number (−)

Rh

Hydraulic radius (m)

θ

Bedding angle (°)

v

Flow velocity (m/s)

x

Horizontal coordinate along piping direction (m)

y

Horizontal coordinate perpendicular to piping direction (m)

z

Vertical coordinate

Notes

Acknowledgements

The authors are grateful to Sibelco Belgium for providing some of the sands.

References

  1. 1.
    Benjasuppatananan S, Meehaln CL (2013) Analytical solutions for levee underseepage analysis: straight and curved levee sections with an infinite blanket. In: Geo-congress. pp 1129–1138Google Scholar
  2. 2.
    Bligh WG (1915) Submerged weirs founded on sand. In: Dams and weirs: an analytical and practical treatise on gravity dams and weirs; arch and buttress dams, submerged weirs; and barrages. Chicago, pp 151–179Google Scholar
  3. 3.
    De Wit JM, Sellmeijer JB, Penning A (1981) Laboratory testing on piping. In: Paper presented at the tenth international conference on soil mechanics and foundation engineering, Stockholm, SwedenGoogle Scholar
  4. 4.
    El Shamy U, Aydin F (2008) Multiscale modeling of flood-induced piping in river levees. J Geotech Geoenviron Eng 134(9):1385–1398.  https://doi.org/10.1061/(asce)1090-0241(2008)134:9(1385) CrossRefGoogle Scholar
  5. 5.
    GeoDelft (2002) MSeep User Manual. Release 6.7Google Scholar
  6. 6.
    Glynn E, Quinn M, Kuszmaul J (2012) Predicting piping potential along middle Mississippi river levees. In: ICSE6, ParisGoogle Scholar
  7. 7.
    Hanses U, Müller-Kirchenbauer H, Savidis S (1985) Zur Mechanik der rückschreitenden Erosion unter Deichen und Dämmen. Bautechnik, 62nd edn. Wilhelm Ernst & Sohn, BerlinGoogle Scholar
  8. 8.
    Lane EW (1935) Security from under-seepage-masonry dams on earth foundations. Trans Am Soc Civ Eng 100(1):1235–1272Google Scholar
  9. 9.
    Miesel D (1978) Rückschreitende Erosion unter bindiger Deckschicht. In: BerlinGoogle Scholar
  10. 10.
    Morgan RPC (2005) Soil erosion and conservation. Blackwell Publishing, HobokenGoogle Scholar
  11. 11.
    Ojha CSP, Singh VP, Adrian DD (2003) Determination of critical head in soil piping. J Hydraul Eng 129(7):511–518.  https://doi.org/10.1061/(asce)0733-9429(2003)129:7(511) CrossRefGoogle Scholar
  12. 12.
    Schmertmann JH (2000) The no-filter factor of safety against piping through sands. ASCE judgment and innovation at the heritage and future of the geotechnical engineering profession, p 68Google Scholar
  13. 13.
    Sellmeijer JB (1981) Piping due to flow towards ditches and holes. In: Verruijt A, Barends FBJ (eds) Flow and transport in porous media. In: Proceedings of Euromech 143, Delft, the Netherlands. CRC Press, Boca Raton, FL, USAGoogle Scholar
  14. 14.
    Sellmeijer JB (1988) On the mechanism of piping under impervious structures. TU Delft, DelftGoogle Scholar
  15. 15.
    Sellmeijer JB, Koenders MA (1991) A mathematical model for piping. Appl Math Model 15(11–12):646–651CrossRefzbMATHGoogle Scholar
  16. 16.
    Sellmeijer JB, Calle EOF, Sip JW (1989) Influence of aquifer thickness on piping below dikes and dams. In: International symposium on analytical evaluation of dam related safety problems, Copenhagen, Denmark, pp 357–366Google Scholar
  17. 17.
    Sellmeijer H, de la Cruz JL, van Beek VM, Knoeff H (2011) Fine-tuning of the backward erosion piping model through small-scale, medium-scale and IJkdijk experiments. Eur J Environ Civ Eng 15(8):1139–1154.  https://doi.org/10.3166/ejece.15.1139-1154 CrossRefGoogle Scholar
  18. 18.
    Shields A (1936) Anwendung der Aehnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebebewegung. BerlinGoogle Scholar
  19. 19.
    van Beek VM, Knoeff JG, Rietdijk J, Sellmeijer JB, Lopez de la Cruz J (2010) Influence of sand and scale on the piping process: experiments and multivariate analysis. In: Paper presented at the physical modelling in geotechnics, LondonGoogle Scholar
  20. 20.
    van Beek VM, Knoeff H, Sellmeijer H (2011) Observations on the process of backward erosion piping in small-, medium- and full-scale experiments. Eur J Environ Civ Eng 15(8):1115–1137.  https://doi.org/10.3166/ejece.15.1115-1137 Google Scholar
  21. 21.
    van Beek VM, Yao Q, Van M, Barends FBJ (2012) Validation of Sellmeijer’s model for backward erosion piping under dikes on multiple sand layers. In: ICSE6, Paris. pp 543–550Google Scholar
  22. 22.
    van Beek VM, Bezuijen A, Sellmeijer H (2013) Backward erosion piping. In: Bonelli S (ed) Erosion in geomechanics applied to dams and levees, vol 1. Wiley, London, pp 193–269CrossRefGoogle Scholar
  23. 23.
    van Beek VM, Vandenboer K, Bezuijen A (2014) Influence of sand type on pipe development in small- and medium-scale experiments. In: Paper presented at the ICSE2014, PerthGoogle Scholar
  24. 24.
    van Beek VM, Essen HM, Vandenboer K, Bezuijen A (2015) Developments in modelling of backward erosion piping. Géotechnique 65(9):740–754.  https://doi.org/10.1680/geot.14.P.119 CrossRefGoogle Scholar
  25. 25.
    Van Rhee C, Bezuijen A (1992) Influence of seepage on stability of sandy slope. J Geotech Eng-ASCE 118(8):1236–1246CrossRefGoogle Scholar
  26. 26.
    Vandenboer K, van Beek VM, Bezuijen A (2013) 3D FEM simulation of groudwater flow during backward erosion piping. In: 5th international young geotechnical engineers’ conference, Paris, France. Ios Press, Amsterdam, The Netherlands, pp 301–304.  https://doi.org/10.3233/978-1-61499-297-4-301
  27. 27.
    Vandenboer K, Bezuijen A, van Beek VM (2014) 3D character of backward erosion piping: small-scale experiments. In: Cheng L, Draper S, An H (eds) 7th international conference on scour and erosion, Perth. Taylor & Francis, pp 81–86Google Scholar
  28. 28.
    Vorogushyn S, Merz B, Apel H (2009) Development of dike fragility curves for piping and micro-instability breach mechanisms. Nat Hazards Earth Syst Sci 9(4):1383–1401CrossRefGoogle Scholar
  29. 29.
    Wyseure G (2002) Stroming van Vloeistoffen (trans: Wetenschappen FLeTB). Fysische transportverschijnselen. KU LeuvenGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Civil Engineering (Geotechnics)Ghent UniversityGhentBelgium
  2. 2.DeltaresDelftThe Netherlands

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