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


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.


Backward erosion piping Embankments Erosion Groundwater flow 

List of symbols


Cross section (mm2)


Pipe width (mm)


Coupled fluid dynamics


Coefficient of uniformity (−)


Coefficient of gradation (−)


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


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


Average grain size (mm)


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


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


Pipe depth (m)


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)


Discrete element method


Hydraulic head difference (m)


Critical hydraulic head for progression (m)


Pressure drop per meter (Pa/m)


Distance from pipe tip (m)


Finite-element method


Unit density of water (N/m3)


Submerged unit density of particles (N/m3)


Hydraulic permeability (m/s)


Pipe length (m)


Correction factor (−)


Dynamic viscosity (Pa s)


Coefficient of white (−)


Wetted perimeter (m)


Effective friction angle of the sand (°)


Flow rate (mm3/s)


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


Unit density (kg/m3)


Reynolds number (−)


Hydraulic radius (m)


Bedding angle (°)


Flow velocity (m/s)


Horizontal coordinate along piping direction (m)


Horizontal coordinate perpendicular to piping direction (m)


Vertical coordinate



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


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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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