Acta Geotechnica

, Volume 13, Issue 3, pp 601–618 | Cite as

Role of particle crushing on particle kinematics and shear banding in granular materials

  • Gang MaEmail author
  • Richard A. Regueiro
  • Wei Zhou
  • Qiao Wang
  • Jiaying Liu
Research Paper


The paper provides an in-depth exploration of the role of particle crushing on particle kinematics and shear banding in sheared granular materials. As a two-dimensional approximation, a crushable granular material may be represented by an assembly of irregularly shaped polygons to include shape diversity of realistic granular materials. Particle assemblies are subjected to biaxial shearing under flexible boundary conditions. With increasing percentage of crushed particles, mesoscale deformation becomes increasingly unstable. Fragmented deformation patterns within the granular assemblies are unable to form stable and distinct shear bands. This is confirmed by the sparsity of large fluctuating velocities in highly crushable assemblies. Without generating distinct shear bands, deformation patterns and failure modes of a highly crushable assembly are similar to those of loose particle assemblies, which are regarded as diffuse deformation. High degrees of spatial association amongst the kinematical quantities confirm the key role that non-affine deformation and particle rotation play in the generation of shear bands. Therefore, particle kinematical quantities can be used to predict the onset and subsequent development of shear zones, which are generally marked by increased particle kinematic activity, such as intense particle rotation and high granular temperature. Our results indicate that shear band thickness increases, and its speed of development slows down, with increasing percentage of crushed particles. As particles crush, spatial force correlation becomes weaker, indicating a more diffuse nature of force transmission across particle contacts.


Force transmission Granular materials Granular temperature Particle crushing Particle kinematics Shear banding 



This work was financially supported by the National Key Research and Development Program of China (No. 2017YFC0404801), National Natural Science Foundation of China (No. 51509190), and China Postdoctoral Science Foundation (No. 2016T907272). We also thank the anonymous reviewers for their constructive reviews.


  1. 1.
    Ai J, Langston PA, Yu HS (2014) Discrete element modelling of material non-coaxiality in simple shear flows. Int J Numer Anal Methods Geomech 38(6):615–635CrossRefGoogle Scholar
  2. 2.
    Alikarami R, Andò E, Gkiousas-Kapnisis M et al (2015) Strain localisation and grain breakage in sand under shearing at high mean stress: insights from in situ X-ray tomography. Acta Geotechnica 10(1):15–30CrossRefGoogle Scholar
  3. 3.
    Alshibli KA, Hasan A (2008) Spatial variation of void ratio and shear band thickness in sand using X-ray computed tomography. Geotechnique 58(4):249–257CrossRefGoogle Scholar
  4. 4.
    Alshibli KA, Sture S (1999) Sand shear band thickness measurements by digital imaging techniques. J Comput Civ Eng 13(2):103–109CrossRefGoogle Scholar
  5. 5.
    Alshibli KA, Sture S (2000) Shear band formation in plane strain experiments of sand. J Geotech Geoenviron Eng 126(6):495–503CrossRefGoogle Scholar
  6. 6.
    Ando E, Hall SA, Viggiani G et al (2012) Grain-scale experimental investigation of localised deformation in sand: a discrete particle tracking approach. Acta Geotechnica 7(1):1–13CrossRefGoogle Scholar
  7. 7.
    Calvetti F, Combe G, Lanier J (1997) Experimental micromechanical analysis of a 2D granular material: relation between structure evolution and loading path. Mechan Cohesive Frict Mater 2(2):121–163CrossRefGoogle Scholar
  8. 8.
    Campbell CS (2006) Granular material flows–an overview. Powder Technol 162(3):208–229CrossRefGoogle Scholar
  9. 9.
    Cheung G, O’Sullivan C (2008) Effective simulation of flexible lateral boundaries in two-and three-dimensional DEM simulations. Particuology 6(6):483–500CrossRefGoogle Scholar
  10. 10.
    Desrues J, Viggiani G (2004) Strain localization in sand: an overview of the experimental results obtained in Grenoble using stereophotogrammetry. Int J Numer Anal Meth Geomech 28(4):279–321CrossRefGoogle Scholar
  11. 11.
    Druckrey AM, Alshibli KA, Al-Raoush RI (2016) 3D characterization of sand particle-to-particle contact and morphology. Comput Geotech 74:26–35CrossRefGoogle Scholar
  12. 12.
    Fu P, Dafalias YF (2011) Fabric evolution within shear bands of granular materials and its relation to critical state theory. Int J Numer Anal Methods Geomech 35(18):1918–1948CrossRefGoogle Scholar
  13. 13.
    Gu X, Huang M, Qian J (2014) Discrete element modeling of shear band in granular materials. Theoret Appl Fract Mech 72:37–49CrossRefGoogle Scholar
  14. 14.
    Guo P (2012) Critical length of force chains and shear band thickness in dense granular materials. Acta Geotechnica 7(1):41–55CrossRefGoogle Scholar
  15. 15.
    Guo N, Zhao J (2014) A coupled FEM/DEM approach for hierarchical multiscale modelling of granular media. Int J Numer Methods Eng 99(11):789–818MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Guo N, Zhao J (2016) 3D multiscale modeling of strain localization in granular media. Comput Geotech 80:360–372CrossRefGoogle Scholar
  17. 17.
    Hall SA, Bornert M, Desrues J et al (2010) Discrete and continuum experimental study of localised deformation in Hostun sand under triaxial compression using X-ray µCT and 3D digital image correlation. Géotechnique 60(5):315–322CrossRefGoogle Scholar
  18. 18.
    Hall SA, Wood DM, Ibraim E et al (2010) Localised deformation patterning in 2D granular materials revealed by digital image correlation. Granul Matter 12(1):1–14CrossRefGoogle Scholar
  19. 19.
    Hasan A, Alshibli KA (2010) Experimental assessment of 3D particle-to-particle interaction within sheared sand using synchrotron microtomography. Géotechnique 60(5):369CrossRefGoogle Scholar
  20. 20.
    Hurley RC, Hall SA, Andrade JE et al (2016) Quantifying interparticle forces and heterogeneity in 3D granular materials. Phys Rev Lett 117(9):098005CrossRefGoogle Scholar
  21. 21.
    Iwashita K, Oda M (2000) Micro-deformation mechanism of shear banding process based on modified distinct element method. Powder Technol 109(1):192–205CrossRefGoogle Scholar
  22. 22.
    Jiang MJ, Yu HS, Harris D (2005) A novel discrete model for granular material incorporating rolling resistance. Comput Geotech 32(5):340–357CrossRefGoogle Scholar
  23. 23.
    Karatza Z, Andò E, Papanicolopulos SA et al (2017) Evolution of deformation and breakage in sand studied using X-ray tomography. Géotechnique 1:1–11Google Scholar
  24. 24.
    Kuhn MR (1999) Structured deformation in granular materials. Mech Mater 31(6):407–429CrossRefGoogle Scholar
  25. 25.
    Kuhn MR, Bagi K (2004) Contact rolling and deformation in granular media. Int J Solids Struct 41(21):5793–5820CrossRefzbMATHGoogle Scholar
  26. 26.
    Liu Y, Sun WC, Yuan Z et al (2015) A nonlocal multiscale discrete-continuum model for predicting mechanical behavior of granular materials. Int J Numer Methods Eng 106:129–160MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Lois G, Lemaître A, Carlson JM (2007) Spatial force correlations in granular shear flow. II. Theoretical implications. Phys Rev E 76(2):021303CrossRefGoogle Scholar
  28. 28.
    Løvoll G, Måløy KJ, Flekkøy EG (1999) Force measurements on static granular materials. Phys Rev E 60(5):5872CrossRefGoogle Scholar
  29. 29.
    Ma G, Zhou W, Chang XL et al (2013) Combined FEM/DEM modeling of triaxial compression tests for rockfills with polyhedral particles. Int J Geomech 14(4):04014014CrossRefGoogle Scholar
  30. 30.
    Ma G, Chang XL, Zhou W et al (2014) Mechanical response of rockfills in a simulated true triaxial test: a combined FDEM study. Geomech Eng 7(3):317–333CrossRefGoogle Scholar
  31. 31.
    Ma G, Zhou W, Chang XL (2014) Modeling the particle breakage of rockfill materials with the cohesive crack model. Comput Geotech 61(9):132–143CrossRefGoogle Scholar
  32. 32.
    Ma G, Zhou W, Ng TT et al (2015) Microscopic modeling of the creep behavior of rockfills with a delayed particle breakage model. Acta Geotechnica 10(4):481–496CrossRefGoogle Scholar
  33. 33.
    Ma G, Zhou W, Chang X et al (2016) Formation of shear bands in crushable and irregularly shaped granular materials and the associated microstructural evolution. Powder Technol 301:118–130CrossRefGoogle Scholar
  34. 34.
    Ma G, Zhou W, Chang XL et al (2016) A hybrid approach for modeling of breakable granular materials using combined finite-discrete element method. Granul Matter 18(1):1–17CrossRefGoogle Scholar
  35. 35.
    Ma G, Zhou W, Regueiro RA et al (2017) Modeling the fragmentation of rock grains using computed tomography and combined FDEM. Powder Technol 308:388–397CrossRefGoogle Scholar
  36. 36.
    Mahmood Z, Iwashita K (2010) Influence of inherent anisotropy on mechanical behavior of granular materials based on DEM simulations. Int J Numer Anal Methods Geomech 34(8):795–819zbMATHGoogle Scholar
  37. 37.
    Mahmood Z, Iwashita K (2011) A simulation study of microstructure evolution inside the shear band in biaxial compression test. Int J Numer Anal Methods Geomech 35(6):652–667CrossRefzbMATHGoogle Scholar
  38. 38.
    Majmudar TS, Behringer RP (2005) Contact force measurements and stress-induced anisotropy in granular materials. Nature 435(7045):1079–1082CrossRefGoogle Scholar
  39. 39.
    Miehe C, Dettmar J, Zäh D (2010) Homogenization and two-scale simulations of granular materials for different microstructural constraints. Int J Numer Methods Eng 83(8–9):1206–1236CrossRefzbMATHGoogle Scholar
  40. 40.
    Mohamed A, Gutierrez M (2010) Comprehensive study of the effects of rolling resistance on the stress–strain and strain localization behavior of granular materials. Granul Matter 12(5):527–541CrossRefzbMATHGoogle Scholar
  41. 41.
    Munjiza AA, Knight EE, Rougier E (2011) Computational mechanics of discontinua. Wiley, New YorkCrossRefGoogle Scholar
  42. 42.
    Nemat-Nasser S (2000) A micromechanically-based constitutive model for frictional deformation of granular materials. J Mech Phys Solids 48(6):1541–1563MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    Nemat-Nasser S, Okada N (2001) Radiographic and microscopic observation of shear bands in granular materials. Geotechnique 51(9):753–766CrossRefGoogle Scholar
  44. 44.
    Nguyen GD, Einav I (2010) Nonlocal regularisation of a model based on breakage mechanics for granular materials. Int J Solids Struct 47(10):1350–1360CrossRefzbMATHGoogle Scholar
  45. 45.
    Nguyen T, Combe G, Caillerie D et al (2014) FEM × DEM modelling of cohesive granular materials: numerical homogenisation and multi-scale simulations. Acta Geophys 62(5):1109–1126CrossRefGoogle Scholar
  46. 46.
    Oda M, Takemura T, Takahashi M (2004) Microstructure in shear band observed by microfocus X-ray computed tomography. Geotechnique 54(8):539–542CrossRefGoogle Scholar
  47. 47.
    O’Sullivan C, Bray JD, Li S (2003) A New approach for calculating strain for particulate media. Int J Numer Anal Methods Geomech 27(10):859–877CrossRefzbMATHGoogle Scholar
  48. 48.
    Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41(8):1329–1364CrossRefGoogle Scholar
  49. 49.
    Qian J, You Z, Huang M et al (2013) A micromechanics-based model for estimating localized failure with effects of fabric anisotropy. Comput Geotech 50:90–100CrossRefGoogle Scholar
  50. 50.
    Radjai F, Roux S (2002) Turbulentlike fluctuations in quasistatic flow of granular media. Phys Rev Lett 89(6):064302CrossRefGoogle Scholar
  51. 51.
    Rechenmacher AL (2006) Grain-scale processes governing shear band initiation and evolution in sands. J Mech Phys Solids 54(1):22–45CrossRefzbMATHGoogle Scholar
  52. 52.
    Sadrekarimi A, Olson SM (2009) Shear band formation observed in ring shear tests on sandy soils. J Geotech Geoenviron Eng 136(2):366–375CrossRefGoogle Scholar
  53. 53.
    Sibille L, Hadda N, Nicot F et al (2015) Granular plasticity, a contribution from discrete mechanics. J Mech Phys Solids 75:119–139CrossRefGoogle Scholar
  54. 54.
    Silbert LE, Grest GS, Landry JW (2002) Statistics of the contact network in frictional and frictionless granular packings. Phys Rev E 66(6):061303CrossRefGoogle Scholar
  55. 55.
    Tatone BSA, Grasselli G (2015) A calibration procedure for two-dimensional laboratory-scale hybrid finite–discrete element simulations. Int J Rock Mech Min Sci 75:56–72Google Scholar
  56. 56.
    Tordesillas A, Muthuswamy M, Walsh SD (2008) Mesoscale measures of nonaffine deformation in dense granular assemblies. J Eng Mech 134(12):1095–1113CrossRefGoogle Scholar
  57. 57.
    Tordesillas A, Lin Q, Zhang J et al (2011) Structural stability and jamming of self-organized cluster conformations in dense granular materials. J Mech Phys Solids 59(2):265–296CrossRefzbMATHGoogle Scholar
  58. 58.
    Tordesillas A, Walker DM, Andò E et al (2013) Revisiting localized deformation in sand with complex systems. Proc R Soc A R Soc 469(2152):20120606CrossRefGoogle Scholar
  59. 59.
    Utter B, Behringer RP (2004) Self-diffusion in dense granular shear flows. Phys Rev E 69(3):031308CrossRefGoogle Scholar
  60. 60.
    Voyiadjis GZ, Alsaleh MI, Alshibli KA (2005) Evolving internal length scales in plastic strain localization for granular materials. Int J Plast 21(10):2000–2024CrossRefzbMATHGoogle Scholar
  61. 61.
    Wang J, Dove JE, Gutierrez MS (2007) Discrete-continuum analysis of shear banding in the direct shear test. Géotechnique 57(6):513–526CrossRefGoogle Scholar
  62. 62.
    Williams JR, Rege N (1997) The development of circulation cell structures in granular materials undergoing compression. Powder Technol 90(3):187–194CrossRefGoogle Scholar
  63. 63.
    Yang Y, Misra A (2012) Micromechanics based second gradient continuum theory for shear band modeling in cohesive granular materials following damage elasticity. Int J Solids Struct 49(18):2500–2514CrossRefGoogle Scholar
  64. 64.
    Zhou B, Huang R, Wang H et al (2013) DEM investigation of particle anti-rotation effects on the micromechanical response of granular materials. Granul Matter 15(3):315–326CrossRefGoogle Scholar
  65. 65.
    Zhou W, Ma G, Chang X et al (2013) Influence of particle shape on behavior of rockfill using a three-dimensional deformable DEM. J Eng Mech 139(12):1868–1873CrossRefGoogle Scholar
  66. 66.
    Zhou W, Yang L, Ma G et al (2017) DEM modeling of shear bands in crushable and irregularly shaped granular materials. Granul Matter 19(2):25CrossRefGoogle Scholar
  67. 67.
    Zhu H, Nguyen HNG, Nicot F et al (2016) On a common critical state in localized and diffuse failure modes. J Mech Phys Solids 95:112–131CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.State Key Laboratory of Water Resources and Hydropower Engineering ScienceWuhan UniversityWuhanChina
  2. 2.Department of Civil, Environmental, and Architectural EngineeringUniversity of Colorado BoulderBoulderUSA

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