Rheology of granular materials composed of crushable particles

  • Duc-Hanh Nguyen
  • Émilien Azéma
  • Philippe Sornay
  • Farhang Radjaï
Regular Article
First Online:
Received:
Accepted:

Abstract.

We investigate sheared granular materials composed of crushable particles by means of contact dynamics simulations and the bonded-cell model for particle breakage. Each particle is paved by irregular cells interacting via cohesive forces. In each simulation, the ratio of the internal cohesion of particles to the confining pressure, the relative cohesion, is kept constant and the packing is subjected to biaxial shearing. The particles can break into two or more fragments when the internal cohesive forces are overcome by the action of compressive force chains between particles. The particle size distribution evolves during shear as the particles continue to break. We find that the breakage process is highly inhomogeneous both in the fragment sizes and their locations inside the packing. In particular, a number of large particles never break whereas a large number of particles are fully shattered. As a result, the packing keeps the memory of its initial particle size distribution, whereas a power-law distribution is observed for particles of intermediate size due to consecutive fragmentation events whereby the memory of the initial state is lost. Due to growing polydispersity, dense shear bands are formed inside the packings and the usual dilatant behavior is reduced or cancelled. Hence, the stress-strain curve no longer passes through a peak stress, and a progressive monotonic evolution towards a pseudo-steady state is observed instead. We find that the crushing rate is controlled by the confining pressure. We also show that the shear strength of the packing is well expressed in terms of contact anisotropies and force anisotropies. The force anisotropy increases while the contact orientation anisotropy declines for increasing internal cohesion of the particles. These two effects compensate each other so that the shear strength is nearly independent of the internal cohesion of particles.

Graphical abstract

Open image in new window

Keywords

Flowing Matter: Granular Matter 
This is a preview of subscription content, log in to check access

References

  1. 1.
    L. Elghezal, M. Jamei, I.-O. Georgopoulos, Granular Matter 15, 685 (2013)CrossRefGoogle Scholar
  2. 2.
    Yukio Nakata, Masayuki Hyodo, Adrian F.L. Hyde, Yoshinori Kato, Hidekazu Murata, Soils Found. 41, 69 (2001)CrossRefGoogle Scholar
  3. 3.
    Y.P. Cheng, Y. Nakata, M.D. Bolton, Géotechnique 53, 633 (2003)CrossRefGoogle Scholar
  4. 4.
    Y.P. Cheng, M.D. Bolton, Y. Nakata, Géotechnique 54, 131 (2004)CrossRefGoogle Scholar
  5. 5.
    D.W. Fuerstenau, O. Gutsche, P.C. Kapur, Confined particle bed comminution under compressive loads, in Comminution 1994, edited by K.S.E. Forssberg, K. Schnert (Elsevier, Amsterdam, 1996) pp. 521--537Google Scholar
  6. 6.
    C. Hosten, H. Cimilli, Int. J. Min. Process. 91, 81 (2009)CrossRefGoogle Scholar
  7. 7.
    Arghya Das, Giang D. Nguyen, Itai Einav, J. Geophys. Res.: Solid Earth 116, B08203 (2011)ADSGoogle Scholar
  8. 8.
    O. Ben-Nun, I. Einav, A. Tordesillas, Phys. Rev. Lett. 104, 108001 (2010)ADSCrossRefGoogle Scholar
  9. 9.
    V.P.B. Esnault, J.-N. Roux, Mech. Mater. 66, 88 (2013)CrossRefGoogle Scholar
  10. 10.
    Poul V. Lade, Jerry A. Yamamuro, Paul A. Bopp, J. Geotech. Eng. 122, 309 (1996)CrossRefGoogle Scholar
  11. 11.
    Fawad A. Chuhan, Arild Kjeldstad, Knut Bjørlykke, Kaare Høeg, Mar. Pet. Geol. 19, 39 (2002)CrossRefGoogle Scholar
  12. 12.
    N. Cho, C.D. Martin, D.C. Sego, Int. J. Rock Mech. Min. Sci. 45, 1335 (2008)CrossRefGoogle Scholar
  13. 13.
    Gang Ma, Wei Zhou, Xiao-Lin Chang, Comput. Geotech. 61, 132 (2014)CrossRefGoogle Scholar
  14. 14.
    M.R. Coop, K.K. Sorensen, T. Bodas Freitas, G. Georgoutsos, Géotechnique 54, 157 (2004)CrossRefGoogle Scholar
  15. 15.
    Charles Sammis, Geoffrey King, Ronald Biegel, Pure Appl. Geophys. 125, 777 (1987)ADSCrossRefGoogle Scholar
  16. 16.
    Luis E. Vallejo, Sebastian Lobo-Guerrero, Kevin Hammer, Int. J. Geomech. 6, 435 (2006)CrossRefGoogle Scholar
  17. 17.
    Junyu Huang, Songlin Xu, Shisheng Hu, Mech. Mater. 68, 15 (2014)CrossRefGoogle Scholar
  18. 18.
    K.H. Wohletz, M.F. Sheridan, W.K. Brown, J. Geophys. Res.: Solid Earth 94, 15703 (1989)CrossRefGoogle Scholar
  19. 19.
    Sidney Redner, Statistical theory of fragmentation, in Disorder and Fracture (Springer, 1990) pp. 31--48Google Scholar
  20. 20.
    J.A. Astrom, H.J. Herrmann, Eur. Phys. J. B 5, 551 (1998)ADSCrossRefGoogle Scholar
  21. 21.
    M. Gorokhovski, Fragmentation under the scaling symmetry and turbulent cascade with intermittency, Technical Report, DTIC Document, 2003Google Scholar
  22. 22.
    Itai Einav, J. Mech. Phys. Solids 55, 1274 (2007)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    Predrag Elek, Slobodan Jaramaz, FME Trans. 37, 129 (2009)Google Scholar
  24. 24.
    N.R.A. Bird, C.W. Watts, A.M. Tarquis, A.P. Whitmore, Vadose Zone J. 8, 197 (2009)CrossRefGoogle Scholar
  25. 25.
    Ferenc Kun, Imre Varga, Sabine Lennartz-Sassinek, Ian G. Main, Phys. Rev. E 88, 062207 (2013)ADSCrossRefGoogle Scholar
  26. 26.
    Ferenc Kun, Imre Varga, Sabine Lennartz-Sassinek, Ian G. Main, Phys. Rev. Lett. 112, 065501 (2014)ADSCrossRefGoogle Scholar
  27. 27.
    Francesca Casini, Giulia M.B. Viggiani, Sarah M. Springman, Granular Matter 15, 661 (2013)CrossRefGoogle Scholar
  28. 28.
    Benjy Marks, Itai Einav, Geophys. Res. Lett. 42, 274 (2015)ADSCrossRefGoogle Scholar
  29. 29.
    Luis E. Vallejo, Sebastian Lobo-Guerrero, Zamri Chik, A network of fractal force chains and their effect in granular materials under compression, in Fractals in Engineering (Springer, 2005) pp. 67--80Google Scholar
  30. 30.
    F. Radjaï, M. Jean, J.-J. Moreau, S. Roux, Phys. Rev. Lett. 77, 274 (1996)ADSCrossRefGoogle Scholar
  31. 31.
    Olivier Tsoungui, Denis Vallet, Jean-Claude Charmet, Stphane Roux, C. R. Acad. Sci., Ser. IIB 325, 457 (1997)ADSGoogle Scholar
  32. 32.
    F. Radjaï, D.E. Wolf, M. Jean, J.J. Moreau, Phys. Rev. Lett. 80, 61 (1998)ADSCrossRefGoogle Scholar
  33. 33.
    C. Thornton, M.T. Ciomocos, M.J. Adams, Powder Technol. 140, 258 (2004)CrossRefGoogle Scholar
  34. 34.
    Ivana Agnolin, Jean-Noël Roux, Phys. Rev. E 76, 061302 (2007)ADSMathSciNetCrossRefGoogle Scholar
  35. 35.
    Vincent Richefeu, Moulay Saïd El Youssoufi, Farhang Radjai, Phys. Rev. E 73, 051304 (2006)ADSCrossRefGoogle Scholar
  36. 36.
    C. Voivret, F. Radjaï, J.-Y. Delenne, M.S. El Youssoufi, Phys. Rev. Lett. 102, 178001 (2009)ADSCrossRefGoogle Scholar
  37. 37.
    C. Thornton, K.K. Yin, M.J. Adams, J. Phys. D: Appl. Phys. 29, 424 (1996)ADSCrossRefGoogle Scholar
  38. 38.
    R. Moreno, M. Ghadiri, S.J. Antony, Powder Technol. 130, 132 (2003)CrossRefGoogle Scholar
  39. 39.
    L. Liu, K.D. Kafui, C. Thornton, Powder Technol. 199, 189 (2010)CrossRefGoogle Scholar
  40. 40.
    Wei Zhou, Lifu Yang, Gang Ma, Kun Xu, Zhiqiang Lai, Xiaolin Chang, Granular Matter 19, 25 (2017)CrossRefGoogle Scholar
  41. 41.
    Ming Xu, Juntian Hong, Erxiang Song, Comput. Geotech. 89, 113 (2017) (Supplement C)CrossRefGoogle Scholar
  42. 42.
    D.O. Potyondy, P.A. Cundall, Int. J. Rock Mech. Min. Sci. 41, 1329 (2004)CrossRefGoogle Scholar
  43. 43.
    N. Cho, C.D. Martin, D.C. Sego, Int. J. Rock Mech. Min. Sci. 44, 997 (2007)CrossRefGoogle Scholar
  44. 44.
    Manoj Khanal, Wolfgang Schubert, Jurgen Tomas, Miner. Eng. 20, 179 (2007)CrossRefGoogle Scholar
  45. 45.
    M.D. Bolton, Y. Nakata, Y.P. Cheng, Géotechnique 58, 471 (2008)CrossRefGoogle Scholar
  46. 46.
    Steffen Abe, Karen Mair, Geophys. Res. Lett. 36, L23302 (2009)ADSCrossRefGoogle Scholar
  47. 47.
    Jianfeng Wang, Haibin Yan, Soils Found. 52, 644 (2012)CrossRefGoogle Scholar
  48. 48.
    G. Timár, F. Kun, H.A. Carmona, H.J. Herrmann, Phys. Rev. E 86, 016113 (2012)ADSCrossRefGoogle Scholar
  49. 49.
    Matthew J. Metzger, Benjamin J. Glasser, Powder Technol. 217, 304 (2012)CrossRefGoogle Scholar
  50. 50.
    Takao Ueda, Takashi Matsushima, Yasuo Yamada, Granular Matter 15, 675 (2013)CrossRefGoogle Scholar
  51. 51.
    S.A. Galindo-Torres, D.M. Pedroso, D.J. Williams, L. Li, Comput. Phys. Commun. 183, 266 (2012)ADSCrossRefGoogle Scholar
  52. 52.
    Gang Ma, Wei Zhou, Richard A. Regueiro, Qiao Wang, Xiaolin Chang, Powder Technol. 308, 388 (2017)CrossRefGoogle Scholar
  53. 53.
    Ferenc Kun, Hans J. Herrmann, Comput. Methods Appl. Mech. Eng. 138, 3 (1996)CrossRefGoogle Scholar
  54. 54.
    Bart Van de Steen, André Vervoort, J.A.L. Napier, Int. J. Fract. 108, 165 (2001)CrossRefGoogle Scholar
  55. 55.
    G.A. D’Addetta, F. Kun, E. Ramm, Granular Matter 4, 77 (2002)CrossRefGoogle Scholar
  56. 56.
    S.A. Galindo-Torres, D.M. Pedroso, D.J. Williams, L. Li, Comput. Phys. Commun. 183, 266 (2012)ADSCrossRefGoogle Scholar
  57. 57.
    Duc-Hanh Nguyen, Emilien Azéma, Philippe Sornay, Farhang Radjai, Phys. Rev. E 91, 022203 (2015)ADSMathSciNetCrossRefGoogle Scholar
  58. 58.
    E. Azema, N. Estrada, F. Radjai, Phys. Rev. E 86, 041301 (2012)ADSCrossRefGoogle Scholar
  59. 59.
    J.J. Moreau, Eur. J. Mech. A Solids 13, 93 (1994)Google Scholar
  60. 60.
    M. Jean, Comput. Methods Appl. Mech. Eng. 177, 235 (1999)ADSCrossRefGoogle Scholar
  61. 61.
    Farhang Radjai, Vincent Richefeu, Mech. Mater. 41, 715 (2009)CrossRefGoogle Scholar
  62. 62.
    Farhang Radjaï, Frédéric Dubois, Discrete Numerical Modeling of Granular Materials (Wiley-ISTE, New-York, 2011) ISBN: 978-1-84821-260-2Google Scholar
  63. 63.
    L. Staron, J.-P. Vilotte, F. Radjaï, Phys. Rev. Lett. 89, 204302 (2002)ADSCrossRefGoogle Scholar
  64. 64.
    A. Taboada, K.J. Chang, F. Radjaï, F. Bouchette, J. Geophys. Res. 110, B09202 (2005)ADSCrossRefGoogle Scholar
  65. 65.
    M. Renouf, P. Alart, Comput. Methods Appl. Mech. Eng. 194, 2019 (2005)ADSCrossRefGoogle Scholar
  66. 66.
    E. Azéma, F. Radjaï, R. Peyroux, F. Dubois, G. Saussine, Phys. Rev. E 74, 031302 (2006)ADSCrossRefGoogle Scholar
  67. 67.
    E. Azéma, F. Radjaï, R. Peyroux, V. Richefeu, G. Saussine, Eur. Phys. J. E 26, 327 (2008)CrossRefGoogle Scholar
  68. 68.
    Nicolas Estrada, Alfredo Taboada, Farhang Radjaï, Phys. Rev. E 78, 021301 (2008)ADSCrossRefGoogle Scholar
  69. 69.
    E. Azéma, F. Radjaï, Phys. Rev. E 81, 051304 (2010)ADSCrossRefGoogle Scholar
  70. 70.
    E. Azéma, F. Radjaï, Phys. Rev. E 85, 031303 (2012)ADSCrossRefGoogle Scholar
  71. 71.
    N. Estrada, E. Azéma, F. Radjaï, A. Taboada, Phys. Rev. E 84, 011306 (2011)ADSCrossRefGoogle Scholar
  72. 72.
    B. Saint-Cyr, J.-Y. Delenne, C. Voivret, F. Radjai, P. Sornay, Phys. Rev. E 84, 041302 (2011)ADSCrossRefGoogle Scholar
  73. 73.
    Juan Carlos Quezada, Pierre Breul, Gilles Saussine, Farhang Radjai, Phys. Rev. E 86, 031308 (2012)ADSCrossRefGoogle Scholar
  74. 74.
    C. Voivret, F. Radjaï, J.-Y. Delenne, M.S. El Youssoufi, Phys. Rev. Lett. 102, 178001 (2009)ADSCrossRefGoogle Scholar
  75. 75.
    Dirk Kadau, Guido Bartels, Lothar Brendel, Dietrich E. Wolf, Comput. Phys. Commun. 147, 190 (2002)ADSCrossRefGoogle Scholar
  76. 76.
    Ivar Bratberg, Farhang Radjai, Alex Hansen, Phys. Rev. E 66, 031303 (2002)ADSCrossRefGoogle Scholar
  77. 77.
    Duc-Hanh Nguyen, Emilien Azéma, Farhang Radjai, Philippe Sornay, Phys. Rev. E 90, 012202 (2014)ADSCrossRefGoogle Scholar
  78. 78.
    Duc-Hanh Nguyen, Florian Fichot, Vincent Topin, Nucl. Eng. Des. 313, 96 (2017)CrossRefGoogle Scholar
  79. 79.
    Eric Clement, Curr. Opin. Colloid Interface Sci. 4, 294 (1999)CrossRefGoogle Scholar
  80. 80.
    GDR-MiDi, Eur. Phys. J. E 14, 341 (2004)CrossRefGoogle Scholar
  81. 81.
    J.J. Moreau, Numerical investigation of shear zones in granular materials, in Friction, Arching, Contact Dynamics, edited by D.E. Wolf, P. Grassberger (World Scientific, Singapore, 1997) pp. 233--247Google Scholar
  82. 82.
    L. Staron, F. Radjaï, Phys. Rev. E 72, 041308 (2005)ADSCrossRefGoogle Scholar
  83. 83.
    Da-Mang Lee, The angles of friction of granular fills, PhD Thesis, University of Cambridge, 1992Google Scholar
  84. 84.
    J.P. Bardet, J. Proubet, Géotechnique 41, 599 (1991)CrossRefGoogle Scholar
  85. 85.
    J.P. Bardet, J. Proubet, J. Eng. Mech. 118, 397 (1992)CrossRefGoogle Scholar
  86. 86.
    A.N.B. Poliakov, H.J. Herrmann, Geophys. Res. Lett. 21, 2143 (1994)ADSCrossRefGoogle Scholar
  87. 87.
    H.J. Herrmann, J.A. Astrom, R. Mahmoodi Baram, Physica A: Stat. Mech. Appl. 344, 516 (2004)ADSCrossRefGoogle Scholar
  88. 88.
    J. Desrues, G.S. Viggiani, Int. J. Numer. Anal. Methods Geomech. 28, 279 (2004)CrossRefGoogle Scholar
  89. 89.
    D.L. Turcotte, J. Geophys. Res.: Solid Earth 91, 1921 (1986)CrossRefGoogle Scholar
  90. 90.
    H.J. Herrmann, A.N.B. Poliakov, S. Roux, Fractals 3, 821 (1995)CrossRefGoogle Scholar
  91. 91.
    G.R. McDowell, M.D. Bolton, D. Robertson, J. Mech. Phys. Solids 44, 2079 (1996)ADSCrossRefGoogle Scholar
  92. 92.
    Tetsuo Akiyama, Keiko M. Aoki, Tatsusaburo Iguchi, Kazuo Nishimoto, Chem. Eng. Sci. 51, 3551 (1996)CrossRefGoogle Scholar
  93. 93.
    Leo Rothenburg, R.J. Bathurst, Géotechnique 39, 601 (1989)CrossRefGoogle Scholar
  94. 94.
    F. Radjaï, Multicontact dynamics, in Physics of Dry Granular Media, edited by H.J. Herrmann (Kluwer Academic Publishers, Netherlands, 1998) pp. 305--312Google Scholar
  95. 95.
    H. Ouadfel, L. Rothenburg, Mech. Mater. 33, 201 (2001)CrossRefGoogle Scholar
  96. 96.
    E. Azéma, F. Radjaï, R. Peyroux, G. Saussine, Phys. Rev. E 76, 011301 (2007)ADSCrossRefGoogle Scholar
  97. 97.
    E. Azema, F. Radjai, B. Saint-Cyr, J.-Y. Delenne, P. Sornay, Phys. Rev. E 87, 052205 (2013)ADSCrossRefGoogle Scholar
  98. 98.
    Duc-Hanh Nguyen, Emilien Azéma, Philippe Sornay, Farhang Radjai, Phys. Rev. E 91, 032203 (2015)ADSCrossRefGoogle Scholar
  99. 99.
    Farhang Radjai, Vincent Richefeu, Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci. 367, 5123 (2009)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Duc-Hanh Nguyen
    • 1
    • 2
    • 3
  • Émilien Azéma
    • 1
  • Philippe Sornay
    • 2
  • Farhang Radjaï
    • 1
    • 4
  1. 1.LMGCUniv. Montpellier, CNRSMontpellierFrance
  2. 2.CEA, DEN, DEC, SFER, LCUSaint-Paul-les-DuranceFrance
  3. 3.Faculty of Hydraulic EngineeringNational University of Civil EngineeringHanoiVietnam
  4. 4.MSE2, UMI 3466 CNRS-MITMIT Energy InitiativeCambridgeUSA

Personalised recommendations