Skip to main content
SpringerLink
Log in

Scale separation between grain detachment and grain transport in granular media subjected to an internal flow

  • Original Paper
  • Published:
Granular Matter Aims and scope Submit manuscript

Abstract

Based on a discrete element method, this paper investigates the basic mechanisms and the associated scales related to grain detachment and grain transport processes at stake in widely graded poly-disperse assemblies of spheres subjected to internal fluid flows. From the identification of force chains, particles sensitive to grain detachment are identified. Based on the computation of autocorrelation lengths, a typical length scale associated with this phenomenon is then defined. From the characterization of the void space as a pore network, particles eligible for grain transport are identified among the detachable particles. Based on the definition of a mean travel distance, the typical length scale associated with grain transport is finally characterized. The comparison between the two length scales highlights a scale separation between grain detachment and grain transport.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  1. Šmilauer, V. et al.: Yade Documentation 2nd ed. The Yade Project (2015). doi:10.5281/zenodo.34073. http://yade-dem.org/doc/

  2. Bonelli, S.: Erosion of Geomaterials. Wiley, London (2012)

    Book  Google Scholar 

  3. Cambou, B., Jean, M., Radjai, F.: Micromechanics of Granular Materials. Wiley, London (2013)

    MATH  Google Scholar 

  4. Chareyre, B., Cortis, A., Catalano, E., Barthélemy, E.: Pore-scale modeling of viscous flow and induced forces in dense sphere packings. Transp. Porous Media 94(2), 595–615 (2012). doi:10.1007/s11242-011-9915-6

    Article  MathSciNet  Google Scholar 

  5. Corson, P.B.: Correlation functions for predicting properties of heterogeneous materials. II. Empirical construction of spatial correlation functions for two-phase solids. J. Appl. Phys. 45(7), 3165–3170 (1974). doi:10.1063/1.1663742

    Article  ADS  Google Scholar 

  6. Cundall, P.A., Strack, O.D.: A discrete numerical model for granular assemblies. Geotechnique 29(1), 47–65 (1979). doi:10.1680/geot.1979.29.1.47

    Article  Google Scholar 

  7. Edelsbrunner, H., Shah, N.R.: Incremental topological flipping works for regular triangulations. Algorithmica 15(3), 223–241 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  8. Fonseca, J., Sim, W., Shire, T., O’Sullivan, C.: Microstructural analysis of sands with varying degrees of internal stability. Géotechnique 64(5), 405–411 (2014). doi:10.1680/geot.13.T.014

    Article  Google Scholar 

  9. Hadda, N.: Aspects micromécaniques de la rupture dans les milieux granulaires. Ph.D. thesis, Ecole Doctorale Ingénierie - Matériaux Mécanique Environnement Energétique Procédés Production (\(\text{I-MEP}^2\)) (2006)

  10. Hill, R.: Elastic properties of reinforced solids: some theoretical principles. J. Mech. Phys. Solids 11(5), 357–372 (1963)

    Article  ADS  MATH  Google Scholar 

  11. Kanit, T., Forest, S., Galliet, I., Mounoury, V., Jeulin, D.: Determination of the size of the representative volume element for random composites: statistical and numerical approach. Int. J. Solids Struct. 40(13), 3647–3679 (2003). doi:10.1016/S0020-7683(03)00143-4

    Article  MATH  Google Scholar 

  12. Kenney, T., Lau, D.: Internal stability of granular filters. Can. Geotech. J. 22(2), 215–225 (1985). doi:10.1139/t85-029

    Article  Google Scholar 

  13. Kézdi, Á.: Soil Physics: Selected Topics, vol. 25. Elsevier, Amsterdam (2013)

    Google Scholar 

  14. Langroudi, M.F., Soroush, A., Shourijeh, P.T.: A comparison of micromechanical assessments with internal stability/instability criteria for soils. Powder Technol. 276, 66–79 (2015). doi:10.1016/j.powtec.2015.02.014

    Article  Google Scholar 

  15. Lantuejoul, C.: Ergodicity and integral range. J. Microsc. 161(3), 387–403 (1991). doi:10.1111/j.1365-2818.1991.tb03099.x

    Article  Google Scholar 

  16. Li, W., Vincens, E., Reboul, N., Chareyre, B.: Constrictions and filtration of fine particles in numerical granular filters: Influence of the fabric within the material. In: Proceedings of the 7th International Conference on 2-4 December 2014. Scour and Erosion, p. 241. CRC Press, Perth, Australia, (2014)

  17. Matheron, G.: Eléments pour une théorie des milieux poreux. Masson, Paris (1967)

    Google Scholar 

  18. Matheron, G.: Random Sets and Integral Geometry. Wiley, New York (1975)

    MATH  Google Scholar 

  19. O\(^{\prime }\)Sullivan, C., Bluthé, J., Sejpar, K., Shire, T., Cheung, L.: Contact based void partitioning to assess filtration properties in dem simulations. Computers Geotech. 64, 120–131 (2015). doi:10.1016/j.compgeo.2014.11.003

  20. Peters, J.F., Muthuswamy, M., Wibowo, J., Tordesillas, A.: Characterization of force chains in granular material. Phys. Rev. E 72(4), 041,307 (2005). doi:10.1103/PhysRevE.72.041307

    Article  Google Scholar 

  21. Radjai, F., Wolf, D.E., Jean, M., Moreau, J.J.: Bimodal character of stress transmission in granular packings. Phys. Rev. Lett. 80(1), 61 (1998)

    Article  ADS  Google Scholar 

  22. Reboul, N., Vincens, E., Cambou, B.: A statistical analysis of void size distribution in a simulated narrowly graded packing of spheres. Granul. Matter 10(6), 457–468 (2008). doi:10.1007/s10035-008-0111-5

    Article  MATH  Google Scholar 

  23. Schofield, A., Wroth, C.: Critical state soil mechanics. McGrow-Hill, London (1968)

    Google Scholar 

  24. Scholtès, L., Hicher, P.Y., Sibille, L.: Multiscale approaches to describe mechanical responses induced by particle removal in granular materials. Comptes Rendus Méc. 338(10), 627–638 (2010). doi:10.1016/j.crme.2010.10.003

    Article  ADS  MATH  Google Scholar 

  25. Shire, T., O’Sullivan, C.: Micromechanical assessment of an internal stability criterion. Acta Geotech. 8(1), 81–90 (2013). doi:10.1007/s11440-012-0176-5

    Article  Google Scholar 

  26. Sibille, L., Marot, D., Sail, Y.: A description of internal erosion by suffusion and induced settlements on cohesionless granular matter. Acta Geotech. 10(6), 735–748 (2015). doi:10.1007/s11440-015-0388-6

    Article  Google Scholar 

  27. Sjah, J., Vincens, E.: Determination of the constriction size distribution of granular filters by filtration tests. Int. J. Numer. Anal. Methods Geomech. 37(10), 1231–1246 (2013)

    Article  Google Scholar 

  28. Terzaghi, K.: 45th james forrest lecture, 1939. Soil mechanics-a new chapter in engineering science. J. ICE 12(7), 106–142 (1939)

    Google Scholar 

  29. Terzaghi, K., Peck, R.B., Mesri, G.: Soil Mechanics in Engineering Practice. Wiley, New York (1996)

    Google Scholar 

  30. To, H., Scheuermann, A.: Separation of grain size distribution for application of self-filtration criteria in suffusion assessment. In: Proceedings of the 7th International Conference on 2-4 December 2014. Scour and Erosion, p. 121. CRC Press, Perth, Australia (2014)

  31. To, H.D., Scheuermann, A., Galindo-Torres, S.A.: Probability of transportation of loose particles in suffusion assessment by self-filtration criteria. Journal of Geotechnical and Geoenvironmental Engineering (2015a). doi:10.1061/(ASCE)GT.1943-5606.0001403

  32. To, H.D., Torres, S.A.G., Scheuermann, A.: Primary fabric fraction analysis of granular soils. Acta Geotech. 10(3), 375–387 (2015b). doi:10.1007/s11440-014-0353-9

    Article  Google Scholar 

  33. Tordesillas, A., Walker, D.M., Lin, Q.: Force cycles and force chains. Phys. Rev. E 81(1), 011,302 (2010)

    Article  Google Scholar 

  34. Vincens, E., Witt, K.J., Homberg, U.: Approaches to determine the constriction size distribution for understanding filtration phenomena in granular materials. Acta Geotech. 10(3), 291–303 (2015). doi:10.1007/s11440-014-0308-1

    Article  Google Scholar 

  35. Voivret, C., Radjai, F., Delenne, J.Y., El Youssoufi, M.S.: Multiscale force networks in highly polydisperse granular media. Phys. Rev. Lett. 102(17), 178,001 (2009). doi:10.1103/PhysRevLett.102.178001

    Article  MATH  Google Scholar 

  36. Wang, X., Li, J.: On the degradation of granular materials due to internal erosion. Acta Mech. Sin 31(5), 685–697 (2015). doi:10.1007/s10409-015-0466-x

    Article  ADS  MathSciNet  MATH  Google Scholar 

  37. Zhu, H., Nguyen, H.N., Nicot, F., Darve, F.: On a common critical state in localized and diffuse failure modes. J. Mech. Phys. Solids (2016). doi:10.1016/j.jmps.2016.05.026

Download references

Author information

Authors and Affiliations

  1. AgroParisTech-ENGREF, 19 avenue du Maine, 75732, Paris, France

    Antoine Wautier

  2. Irstea, UR ETGR, Université Grenoble Alpes, 2 rue de la Papeterie-BP 76, 38402, St-Martin-d’Hères, France

    Antoine Wautier & François Nicot

  3. Irstea UR RECOVER, 3275 Rte Cézanne, CS 40061, 13182, Aix-en-Provence Cedex 5, France

    Antoine Wautier & Stéphane Bonelli

Authors
  1. Antoine Wautier
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stéphane Bonelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. François Nicot
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Antoine Wautier.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this article. Publication has been approved by all authors. None of the material presented in the paper is submitted or published elsewhere.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wautier, A., Bonelli, S. & Nicot, F. Scale separation between grain detachment and grain transport in granular media subjected to an internal flow. Granular Matter 19, 22 (2017). https://doi.org/10.1007/s10035-017-0706-9

Download citation

  • Received:

  • Published:

  • DOI: https://doi.org/10.1007/s10035-017-0706-9

Keywords

Search

Navigation