Granular Matter

, 21:10 | Cite as

Stress fluctuations during monotonic loading of dense three-dimensional granular materials

  • Matthew R. Kuhn
  • Ali Daouadji
Original Paper


The paper examines the sudden and irregular fluctuations of stress that are commonly observed in DEM and laboratory tests of slow monotonic loading of granular materials. The stresss fluctuations occur as stress-drops that are spaced in an irregular, random manner as the material is loaded, and occur at an average rate of about 0.05 drops per particle per one percent of strain. Each fluctuation is accompanied by a drop in the number of contacts and in the number of sliding contacts, a brief increase in the particles’ kinetic energy, a reduction in the elastic energy of the contacts, and a reduction in bulk volume. Stress-drops are shown to originate within small regions of the larger assembly and are likely the result of a multi-slip mechanism. An advanced discrete element method (DEM) is used in the study, with non-convex non-spherical particles and an exact implementation of the Hertz-like Cattaneo–Mindlin contact model. The simulations reveal differences with the avalanche phenomenon of amorphous solids, in particular the different scalings of stress-drop magnitude with assembly size and drop frequency.


Granular material Instability Micro-mechanics Energy dissipation Second-order work Plasticity Discrete element method 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material


  1. 1.
    Roux, J.-N., Combe, G.: On the meaning and microscopic origins of quasistatic deformation of granular materials, In: Proceedings of the 16th ASCE Engineering Mechanics Conference, vol. 759, ASCE, pp. 1–5 (2003)Google Scholar
  2. 2.
    Alshibli, K., Alramahi, B.: Microscopic evaluation of strain distribution in granular materials during shear. J. Geotech. Geoenviron. Eng. 132(1), 80–91 (2006). CrossRefGoogle Scholar
  3. 3.
    Kuhn, M.R., Bagi, K.: Specimen size effect in discrete element simulations of granular assemblies. J. Eng. Mech. 135(6), 485–492 (2009)CrossRefGoogle Scholar
  4. 4.
    Sun, W., Ostien, J.T., Salinger, A.G.: A stabilized assumed deformation gradient finite element formulation for strongly coupled poromechanical simulations at finite strain. Int. J. Numer. Anal. Methods Geomech. 37(16), 2755–2788 (2013)Google Scholar
  5. 5.
    Nicot, F., Hadda, N., Sibille, L., Radjai, F., Hicher, P.-Y., Darve, F.: Some micromechanical aspects of failure in granular materials based on second-order work. Comptes Rendus Mécanique 342(3), 174–188 (2014)ADSCrossRefGoogle Scholar
  6. 6.
    Denisov, D.V., Lörincz, K.A., Uhl, J.T., Dahmen, K.A., Schall, P.: Universality of slip avalanches in flowing granular matter. Nat. Commun. 7, 10641 (2016)ADSCrossRefGoogle Scholar
  7. 7.
    Cui, D., Wu, W., Xiang, W., Doanh, T., Chen, Q., Wang, S., Liu, Q., Wang, J.: Stick-slip behaviours of dry glass beads in triaxial compression. Granul. Matter 19(1), 1 (2017)ADSCrossRefGoogle Scholar
  8. 8.
    Peters, J.F., Walizer, L.E.: Patterned nonaffine motion in granular media. J. Eng. Mech. 139(10), 1479–1490 (2013)CrossRefGoogle Scholar
  9. 9.
    Thornton, C.: Numerical simulations of deviatoric shear deformation of granular media. Géotechnique 50(1), 43–53 (2000)CrossRefGoogle Scholar
  10. 10.
    Michlmayr, G., Cohen, D., Or, D.: Sources and characteristics of acoustic emissions from mechanically stressed geologic granular media–a review. Earth Sci. Rev. 112(3), 97–114 (2012)ADSCrossRefGoogle Scholar
  11. 11.
    Michlmayr, G., Cohen, D., Or, D.: Shear-induced force fluctuations and acoustic emissions in granular material. J. Geophys. Res. Solid Earth 118(12), 6086–6098 (2013)ADSCrossRefGoogle Scholar
  12. 12.
    Ingraham, M.D., Issen, K.A., Holcomb, D.J.: Use of acoustic emissions to investigate localization in high-porosity sandstone subjected to true triaxial stresses. Acta Geotech. 8(6), 645–663 (2013)CrossRefGoogle Scholar
  13. 13.
    Daouadji, A., Hicher, P.Y., Jrad, M., Sukumaran, B., Belouettar, S.: Experimental and numerical investigation of diffuse instability in granular materials using a microstructural model under various loading paths. Géotechnique 63(5), 368 (2013)CrossRefGoogle Scholar
  14. 14.
    Nicot, F., Daouadji, A., Hadda, N., Jrad, M., Darve, F.: Granular media failure along triaxial proportional strain path. Eur. J. Environ. Civil Eng. 17(9), 777–790 (2013)CrossRefGoogle Scholar
  15. 15.
    Nguyen, H.N.G., Prunier, F., Djeran-Maigre, I., Nicot, F.: Kinetic energy and collapse of granular materials. Granul. Matter 18(1), 1–10 (2016)CrossRefGoogle Scholar
  16. 16.
    Lerner, E., Procaccia, I.: Locality and nonlocality in elastoplastic responses of amorphous solids. Phys. Rev. E 79(6), 066109 (2009)ADSCrossRefGoogle Scholar
  17. 17.
    Hentschel, H.G.E., Karmakar, S., Lerner, E., Procaccia, I.: Size of plastic events in strained amorphous solids at finite temperatures. Phys. Rev. Lett. 104(2), 025501 (2010)ADSCrossRefGoogle Scholar
  18. 18.
    Dasgupta, R., Karmakar, S., Procaccia, I.: Universality of the plastic instability in strained amorphous solids. Phys. Rev. Lett. 108(7), 075701 (2012)ADSCrossRefGoogle Scholar
  19. 19.
    Zhang, D., Dahmen, K.A., Ostoja-Starzewski, M.: Scaling of slip avalanches in sheared amorphous materials based on large-scale atomistic simulations. Phys. Rev. E 95(3), 032902 (2017)ADSCrossRefGoogle Scholar
  20. 20.
    Daouadji, A., Darve, F., Al Gali, H., Hicher, P.Y., Laouafa, F., Lignon, S., Nicot, F., Nova, R., Pinheiro, M., Prunier, F., et al.: Diffuse failure in geomaterials: experiments, theory and modelling. Int. J. Numer. Anal. Methods Geomech. 35(16), 1731–1773 (2011)CrossRefGoogle Scholar
  21. 21.
    Kuhn, M.R.: Implementation of the Jäger contact model for discrete element simulations. Int. J. Numer. Methods Eng. 88(1), 66–82 (2011)CrossRefGoogle Scholar
  22. 22.
    Kuhn, M.R., Renken, H., Mixsell, A., Kramer, S.: Investigation of cyclic liquefaction with discrete element simulations. J. Geotech. Geoenviron. Eng. 140(12), 04014075 (2014). CrossRefGoogle Scholar
  23. 23.
    Arulmoli, K., Muraleetharan, K.K., Hossain, M.M., Fruth, L.S.: VELACS verification of liquefaction analyses by centrifuge studies laboratory testing program soil data report, Technical Report Project No. 90-0562, The Earth Technology Corporation, Irvine, CA, data available through (1992). Accessed 21 Dec 2011
  24. 24.
    Sibille, L., Hadda, N., Nicot, F., Tordesillas, A., Darve, F.: Granular plasticity, a contribution from discrete mechanics. J. Mech. Phys. Solids 75, 119–139 (2015)ADSCrossRefGoogle Scholar
  25. 25.
    Laouafa, F., Prunier, F., Daouadji, A., Al Gali, H., Darve, F.: Stability in geomechanics, experimental and numerical analyses. Int. J. Numer. Anal. Methods.eomech 35(2), 112–139 (2011)CrossRefGoogle Scholar
  26. 26.
    Cabalar, A.F.: Stress fluctuations in granular material response during cyclic direct shear test. Granul. Matter 17(4), 439–446 (2015)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Roux, J.-N., Combe, G.: Quasistatic rheology and the origins of strain. C. R. Phys. 3(2), 131–140 (2002)ADSCrossRefGoogle Scholar
  28. 28.
    Lin, J., Lerner, E., Rosso, A., Wyart, M.: Scaling description of the yielding transition in soft amorphous solids at zero temperature. Proc. Natl. Acad. Sci. 111(40), 14382–14387 (2014)ADSCrossRefGoogle Scholar
  29. 29.
    Nicot, F., Hadda, N., Bourrier, F., Sibille, L., Wan, R., Darve, F.: Inertia effects as a possible missing link between micro and macro second-order work in granular media. Int. J. Solids Struct. 49(10), 1252–1258 (2012)CrossRefGoogle Scholar
  30. 30.
    Combe, G., Roux, J.-N.: Strain versus stress in a model granular material: a devil’s staircase. Phys. Rev. Lett. 85(17), 3628–3631 (2000)ADSCrossRefGoogle Scholar
  31. 31.
    Dahmen, K.A., Ben-Zion, Y., Uhl, J.T.: Micromechanical model for deformation in solids with universal predictions for stress-strain curves and slip avalanches. Phys. Rev. Lett. 102(17), 175501 (2009)ADSCrossRefGoogle Scholar
  32. 32.
    Dahmen, K.A.: Mean field theory of slip statistics. In: Salje, E., Planes, A. (eds.) Avalanches in Functional Materials and Geophysics, pp. 19–30. Springer, Berlin (2017)CrossRefGoogle Scholar
  33. 33.
    Sun, Q., Jin, F., Liu, J., Zhang, G.: Understanding force chains in dense granular materials. Intl. J. Modern Phys. B 24(29), 5743–5759 (2010)ADSCrossRefGoogle Scholar
  34. 34.
    Salerno, K.M., Maloney, C.E., Robbins, M.O.: Avalanches in strained amorphous solids: does inertia destroy critical behavior? Phys. Rev. Lett. 109(10), 105703 (2012)ADSCrossRefGoogle Scholar
  35. 35.
    Lin, J., Wu, W., Borja, R.I.: Micropolar hypoplasticity for persistent shear band in heterogeneous granular materials. Comput. Methods Appl. Mech. Eng. 289, 24–43 (2015)ADSMathSciNetCrossRefGoogle Scholar
  36. 36.
    Michlmayr, G., Or, D.: Mechanisms for acoustic emissions generation during granular shearing. Granul. Matter 16(5), 627–640 (2014)CrossRefGoogle Scholar
  37. 37.
    Li, J., Spaepen, F., Hufnagel, T.C.: Nanometre-scale defects in shear bands in a metallic glass. Philos. Mag. A 82(13), 2623–2630 (2002)ADSCrossRefGoogle Scholar
  38. 38.
    Tordesillas, A.: Force chain buckling, unjamming transitions and shear banding in dense granular assemblies. Philos. Mag. 87(32), 4987–5016 (2007)ADSCrossRefGoogle Scholar
  39. 39.
    Tordesillas, A., Muthuswamy, M.: On the modeling of confined buckling of force chains. J. Mech. Phys. Solids 57(4), 706–727 (2009)ADSMathSciNetCrossRefGoogle Scholar
  40. 40.
    Tordesillas, A., Steer, C.A.H., Walker, D.M.: Force chain and contact cycle evolution in a dense granular material under shallow penetration. Nonlinear Process. Geophys. 21(2), 505–519 (2014)ADSCrossRefGoogle Scholar
  41. 41.
    Kuhn, M.R.: Contact transience during slow loading of dense granular materials, J. Eng. Mech. 143(1), 1–9 (2016).
  42. 42.
    Sethna, J.P., Dahmen, K.A., Myers, C.R.: Crackling noise. Nature 410(6825), 242 (2001)ADSCrossRefGoogle Scholar
  43. 43.
    Tordesillas, A., Zhang, J., Behringer, R.: Buckling force chains in dense granular assemblies: physical and numerical experiments. Geomech. Geoeng Int. J. 4(1), 3–16 (2009)CrossRefGoogle Scholar
  44. 44.
    Kuhn, M.R., Bagi, K.: Contact rolling and deformation in granular media. Int. J. Solids Struct. 41(21), 5793–5820 (2004)CrossRefGoogle Scholar
  45. 45.
    Radjai, F., Wolf, D.E., Jean, M., Moreau, J.-J.: Bimodal character of stress transmission in granular packings. Phys. Rev. Lett. 80(1), 61–64 (1998)ADSCrossRefGoogle Scholar
  46. 46.
    Karmakar, S., Lerner, E., Procaccia, I.: Statistical physics of the yielding transition in amorphous solids. Phys. Rev. E 82(5), 055103 (2010)ADSCrossRefGoogle Scholar
  47. 47.
    Hentschel, H.G.E., Jaiswal, P.K., Procaccia, I., Sastry, S.: Stochastic approach to plasticity and yield in amorphous solids. Phys. Rev. E 92(6), 062302 (2015)ADSCrossRefGoogle Scholar
  48. 48.
    Calvetti, F., Viggiani, G., Tamagnini, C.: A numerical investigation of the incremental behavior of granualr soils. Rivista Italiana di Geotecnica 3, 11–29 (2003)Google Scholar
  49. 49.
    Plassiard, J.-P., Belheine, N., Donzé, F.-V.: A spherical discrete element model: calibration procedure and incremental response. Granul. Matter 11(5), 293–306 (2009)CrossRefGoogle Scholar
  50. 50.
    Kuhn, M.R., Mitchell, J.K.: Modelling of soil creep with the discrete element method. Eng. Comput. 9(2), 277–287 (1992)CrossRefGoogle Scholar
  51. 51.
    Jäger, J.: Uniaxial deformation of a random packing of particles. Arch. Appl. Mech. 69(3), 181–203 (1999)ADSCrossRefGoogle Scholar
  52. 52.
    Walton, K.: The oblique compression of two elastic spheres. J. Mech. Phys. Solids 26(3), 139–150 (1978)ADSCrossRefGoogle Scholar
  53. 53.
    da Cruz, F., Emam, S., Prochnow, M., Roux, J.-N., Chevoir, F.: Rheophysics of dense granular materials: discrete simulation of plane shear flows. Phys. Rev. E 72(2), 021309 (2005)ADSCrossRefGoogle Scholar
  54. 54.
    Ng, T.-T.: Input parameters of discrete element methods. J. Eng. Mech. 132(7), 723–729 (2006)MathSciNetCrossRefGoogle Scholar
  55. 55.
    Suzuki, K., Kuhn, M.R.: Uniqueness of discrete element simulations in monotonic biaxial shear tests. Int. J. Geomech. 14(5), 06014010 (2014). CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Donald P. Shiley School of EngineeringUniversity of PortlandPortlandUSA
  2. 2.University of Lyon, INSA-Lyon, GEOMASLyonFrance

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