Skip to main content
SpringerLink
Log in

Transient Evolution of Rheological Properties of Dense Granular Inertial Flow Under Plane Shear

  • Original Paper
  • Published:
Tribology Letters Aims and scope Submit manuscript

Abstract

Exploration of the transient evolution of the rheological properties of dense inertial flow can reveal the equilibrium mechanism of granular materials maintaining their own stability under shear. Here, discrete element method simulations are performed to study the transient flow characteristics of a dense granular system under plane shear in the inertial regime. We quantitatively analyze the changes in the system’s flow state, interfacial friction coefficient, effective friction coefficient, microstructure anisotropy, and internal shear strength. Simulation results show that the evolution of the horizontal flow experiences three typical stages, namely transmission, adjustment, and stabilization. Moreover, the shear dilatancy caused by the vertical movement of particles, gradually weakens the spatial geometric constraint and reduces the system’s tangential load-bearing capacity, thereby decreasing the interfacial friction coefficient \({\mu }^{^{\prime}}\), which represents the boundary driving strength. On the other hand, the shear flow induces variations in the anisotropies of both contact orientation and contact forces, thus improving the system’s internal shear strength \({\mu }^{*}\) and increasing the effective friction coefficient \({\mu }_\text{e}\). By comparison, \({\mu }^{^{\prime}}\) is greater than \({\mu }_\text{e}\) until approximately equal in the steady flow state. Therefore, during the evolution of the flow state, the boundary driving strength is reduced while the system’s shear resistance is enhanced, and eventually a balance between them is achieved. Distinguished from the micromechanical behaviors, the internal shear strength always mainly originates from the anisotropies in contact orientation and in normal contact force. Moreover, the contribution of the anisotropy in contact orientation becomes more predominant with increasing shear velocity.

Graphical abstract

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

Similar content being viewed by others

References

  1. Forterre, Y., Pouliquen, O.: Flows of dense granular media. Annu. Rev. Fluid Mech. 40, 1–24 (2008)

    Article  Google Scholar 

  2. Andreotti, B., Forterre, Y., Pouliquen, O.: Granular media: between fluid and solid. Cambridge University Press, Cambridge (2013)

    Book  Google Scholar 

  3. Zhang, Y., Campbell, C.S.: The interface between fluid-like and solid-like behaviour in two-dimensional granular flows. J. Fluid Mech. 237, 541–568 (1992)

    Article  CAS  Google Scholar 

  4. Lherminier, S., Planet, R., dit Vehel, V.L., Simon, G., Vanel, L., Måløy, K.J., et al.: Continuously sheared granular matter reproduces in detail seismicity laws. Phys. Rev. Lett. 122, 218501 (2019)

    Article  CAS  Google Scholar 

  5. Zhang, H., Liu, S., Xiao, H.: Sliding friction of shale rock on dry quartz sand particles. Friction 7, 307–315 (2019)

    Article  CAS  Google Scholar 

  6. Scholz, C.H.: Earthquakes and friction laws. Nature 391, 37 (1998)

    Article  CAS  Google Scholar 

  7. Iordanoff, I., Khonsari, M.: Granular lubrication: toward an understanding of the transition between kinetic and quasi-fluid regime. J. Tribol. 126, 137–145 (2004)

    Article  Google Scholar 

  8. Ciamarra, M.P., Dalton, F., de Arcangelis, L., Godano, C., Lippiello, E., Petri, A.: The role of interstitial impurities in the frictional instability of seismic fault models. Tribol. Lett. 48, 89–94 (2012)

    Article  Google Scholar 

  9. Wang, W., Liu, X., Xie, T., Liu, K.: Effects of sliding velocity and normal load on tribological characteristics in powder lubrication. Tribol. Lett. 43, 213–219 (2011)

    Article  CAS  Google Scholar 

  10. Singla, N., Brunel, J.-F., Mège-Revil, A., Kasem, H., Desplanques, Y.: Experiment to investigate the relationship between the third-body layer and the occurrence of squeals in dry sliding contact. Tribol. Lett. 68, 4 (2020)

    Article  Google Scholar 

  11. Fannon, J.S., Moyles, I.R., Fowler, A.C.: Application of the compressible I-dependent rheology to chute and shear flow instabilities. J. Fluid Mech. 864, 1026–1057 (2019)

    Article  CAS  Google Scholar 

  12. Azéma, E., Radjai, F., Roux, J.-N.: Inertial shear flow of assemblies of frictionless polygons: rheology and microstructure. Eur. Phys. J. E 41, 2 (2018)

    Article  CAS  Google Scholar 

  13. Chialvo, S., Sun, J., Sundaresan, S.: Bridging the rheology of granular flows in three regimes. Phys. Rev. E 85, 021305 (2012)

    Article  CAS  Google Scholar 

  14. MiDi, G.: On dense granular flows. Eur. Phys. J. E 14, 341–365 (2004)

    Article  CAS  Google Scholar 

  15. Szabó, B., Török, J., Somfai, E., Wegner, S., Stannarius, R., Böse, A., et al.: Evolution of shear zones in granular materials. Phys. Rev. E 90, 032205 (2014)

    Article  CAS  Google Scholar 

  16. Massoudi, M., Phuoc, T.X.: The effect of slip boundary condition on the flow of granular materials: a continuum approach. Int. J. Non Linear Mech. 35, 745–761 (2000)

    Article  Google Scholar 

  17. Bagnold, R.A.: The shearing and dilatation of dry sand and the ‘singing’ mechanism. Proc. R Soc. London Ser. A 295, 219–232 (1966)

    Article  Google Scholar 

  18. Lemaître, A.: Rearrangements and dilatancy for sheared dense materials. Phys. Rev. Lett. 89, 195503 (2002)

    Article  CAS  Google Scholar 

  19. Bandi, M.M., Das, P., Gendelman, O., Hentschel, H.G.E., Procaccia, I.: Universal scaling laws for shear induced dilation in frictional granular media. Granular Matter 21, 40 (2019)

    Article  Google Scholar 

  20. Thompson, P.A., Grest, G.S.: Granular flow: friction and the dilatancy transition. Phys. Rev. Lett. 67, 1751 (1991)

    Article  CAS  Google Scholar 

  21. Azéma, E., Radjai, F.: Internal structure of inertial granular flows. Phys. Rev. Lett. 112, 078001 (2014)

    Article  CAS  Google Scholar 

  22. Jop, P.: Rheological properties of dense granular flows. CR Phys. 16, 62–72 (2015)

    Article  CAS  Google Scholar 

  23. 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, 021309 (2005)

    Article  CAS  Google Scholar 

  24. Fall, A., Ovarlez, G., Hautemayou, D., Mézière, C., Roux, J.-N., Chevoir, F.: Dry granular flows: rheological measurements of the μ (I)-rheology. J. Rheol. 59, 1065–1080 (2015)

    Article  CAS  Google Scholar 

  25. Schaeffer, D., Barker, T., Tsuji, D., Gremaud, P., Shearer, M., Gray, J.: Constitutive relations for compressible granular flow in the inertial regime. J. Fluid Mech. 874, 926–951 (2019)

    Article  Google Scholar 

  26. Divoux, T., Géminard, J.-C.: Friction and dilatancy in immersed granular matter. Phys. Rev. Lett. 99, 258301 (2007)

    Article  CAS  Google Scholar 

  27. Chevoir, F., Roux, J.-N., da Cruz, F., Rognon, P.G., Koval, G., Jr.: Friction law in dense granular flows. Powder Technol. 190, 264–268 (2009)

    Article  CAS  Google Scholar 

  28. Tang, Z., Brzinski, T.A., Shearer, M., Daniels, K.E.: Nonlocal rheology of dense granular flow in annular shear experiments. Soft Matter 14, 3040–3048 (2018)

    Article  CAS  Google Scholar 

  29. Weinhart, T., Hartkamp, R., Thornton, A.R., Luding, S.: Coarse-grained local and objective continuum description of three-dimensional granular flows down an inclined surface. Phys. Fluids 25, 070605 (2013)

    Article  CAS  Google Scholar 

  30. Campbell, C.S.: Granular shear flows at the elastic limit. J. Fluid Mech. 465, 261–291 (2002)

    Article  CAS  Google Scholar 

  31. Dsouza, P.V., Nott, P.R.: A non-local constitutive model for slow granular flow that incorporates dilatancy. J. Fluid Mech. 888, R3 (2020)

    Article  CAS  Google Scholar 

  32. Bathurst Richard, J., Rothenburg, L.E.O.: Investigation of micromechanical features of idealized granular assemblies using DEM. Eng. Comput. 9, 199–210 (1992)

    Article  Google Scholar 

  33. Estrada, N., Azéma, E., Radjai, F., Taboada, A.: Identification of rolling resistance as a shape parameter in sheared granular media. Phys. Rev. E 84, 011306 (2011)

    Article  CAS  Google Scholar 

  34. Binaree, T., Azéma, E., Estrada, N., Renouf, M., Preechawuttipong, I.: Combined effects of contact friction and particle shape on strength properties and microstructure of sheared granular media. Phys. Rev. E 102, 022901 (2020)

    Article  CAS  Google Scholar 

  35. Koval, G., Chevoir, F., Roux, J.-N., Sulem, J., Corfdir, A.: Interface roughness effect on slow cyclic annular shear of granular materials. Granular Matter 13, 525–540 (2011)

    Article  CAS  Google Scholar 

  36. Siavoshi, S., Orpe, A.V., Kudrolli, A.: Friction of a slider on a granular layer: nonmonotonic thickness dependence and effect of boundary conditions. Phys. Rev. E 73, 010301 (2006)

    Article  CAS  Google Scholar 

  37. Trulsson, M., DeGiuli, E., Wyart, M.: Effect of friction on dense suspension flows of hard particles. Phys. Rev. E 95, 012605 (2017)

    Article  CAS  Google Scholar 

  38. Azéma, É., Radjai, F., Roux, J.-N.: Internal friction and absence of dilatancy of packings of frictionless polygons. Phys. Rev. E 91, 010202 (2015)

    Article  CAS  Google Scholar 

  39. Meng, F., Liu, H., Hua, S., Pang, M.: Experimental research on sliding friction of dense dry particles lubricated between parallel plates. Tribol. Lett. 69, 33 (2021)

    Article  Google Scholar 

  40. Zhang, X., Sun, W., Wang, W., Liu, K.: Experimental investigation of granular friction behaviors during reciprocating sliding. Friction (2021). https://doi.org/10.1007/s40544-021-0488-2

    Article  Google Scholar 

  41. Kuwano, O., Ando, R., Hatano, T.: Crossover from negative to positive shear rate dependence in granular friction. Geophys. Res. Lett. 40, 1295–1299 (2013)

    Article  Google Scholar 

  42. Degiuli, E., Mcelwaine, J.N., Wyart, M.: Phase diagram for inertial granular flows. Phys. Rev. E 94, 012904 (2016)

    Article  CAS  Google Scholar 

  43. Hatano, T.: Power-law friction in closely packed granular materials. Phys. Rev. E 75, 060301 (2007)

    Article  CAS  Google Scholar 

  44. Boyer, F., Guazzelli, É., Pouliquen, O.: Unifying suspension and granular rheology. Phys. Rev. Lett. 107, 188301 (2011)

    Article  CAS  Google Scholar 

  45. Berger, N., Azéma, E., Douce, J.-F., Radjai, F.: Scaling behaviour of cohesive granular flows. EPL 112, 64004 (2016)

    Article  CAS  Google Scholar 

  46. Wu, W., Ma, G., Zhou, W., Wang, D., Chang, X.: Force transmission and anisotropic characteristics of sheared granular materials with rolling resistance. Granular Matter 21, 88 (2019)

    Article  Google Scholar 

  47. Majmudar, T.S., Behringer, R.P.: Contact force measurements and stress-induced anisotropy in granular materials. Nature 435, 1079–1082 (2005)

    Article  CAS  Google Scholar 

  48. Sufian, A., Russell, A., Whittle, A.: Anisotropy of contact networks in granular media and its influence on mobilised internal friction. Geotechnique 67, 1067–1080 (2017)

    Google Scholar 

  49. Zhang, J., Majmudar, T., Tordesillas, A., Behringer, R.: Statistical properties of a 2D granular material subjected to cyclic shear. Granular Matter 12, 159–172 (2010)

    Article  CAS  Google Scholar 

  50. Mollon, G.: Solid flow regimes within dry sliding contacts. Tribol Lett 67, 120 (2019)

    Article  Google Scholar 

  51. Voivret, C., Radjai, F., Delenne, J.-Y., El Youssoufi, M.S.: Multiscale force networks in highly polydisperse granular media. Phys. Rev. Lett. 102, 178001 (2009)

    Article  CAS  Google Scholar 

  52. Azéma, E., Linero, S., Estrada, N., Lizcano, A.: Shear strength and microstructure of polydisperse packings: the effect of size span and shape of particle size distribution. Phys. Rev. E 96, 022902 (2017)

    Article  Google Scholar 

  53. Cantor, D., Azéma, E., Sornay, P., Radjai, F.: Rheology and structure of polydisperse three-dimensional packings of spheres. Phys. Rev. E 98, 052910 (2018)

    Article  CAS  Google Scholar 

  54. Pena, A., Garcia-Rojo, R., Herrmann, H.J.: Influence of particle shape on sheared dense granular media. Granular Matter 9, 279–291 (2007)

    Article  Google Scholar 

  55. Azéma, E., Estrada, N., Radjai, F.: Nonlinear effects of particle shape angularity in sheared granular media. Phys. Rev. E 86, 041301 (2012)

    Article  CAS  Google Scholar 

  56. Azéma, E., Radjai, F., Dubois, F.: Packings of irregular polyhedral particles: strength, structure, and effects of angularity. Phys. Rev. E 87, 062203 (2013)

    Article  CAS  Google Scholar 

  57. Boton, M., Azéma, E., Estrada, N., Radjai, F., Lizcano, A.: Quasistatic rheology and microstructural description of sheared granular materials composed of platy particles. Phys. Rev. E 87, 032206 (2013)

    Article  CAS  Google Scholar 

  58. Boton, M., Estrada, N., Azéma, E., Radjai, F.: Particle alignment and clustering in sheared granular materials composed of platy particles. Eur. Phys. J. E 37, 116 (2014)

    Article  CAS  Google Scholar 

  59. Vo, T.-T.: Rheology and granular texture of viscoinertial simple shear flows. J. Rheol. 64, 1133–1145 (2020)

    Article  CAS  Google Scholar 

  60. Chèvremont, W., Chareyre, B., Bodiguel, H.: Quantitative study of the rheology of frictional suspensions: influence of friction coefficient in a large range of viscous numbers. Phys. Rev. Fluids 4, 064302 (2019)

    Article  Google Scholar 

  61. Macaulay, M., Rognon, P.: Viscosity of cohesive granular flows. Soft Matter 17, 165–173 (2021)

    Article  CAS  Google Scholar 

  62. Shojaaee, Z., Roux, J.-N., Chevoir, F., Wolf, D.E.: Shear flow of dense granular materials near smooth walls. I. Shear localization and constitutive laws in the boundary region. Phys. Rev. E 86, 011301 (2012)

    Article  CAS  Google Scholar 

  63. Macaulay, M., Rognon, P.: Inertial force transmission in dense granular flows. Phys. Rev. Lett. 126, 118002 (2021)

    Article  CAS  Google Scholar 

  64. Cundall, P.A., Strack, O.D.: A discrete numerical model for granular assemblies. Geotechnique 29, 47–65 (1979)

    Article  Google Scholar 

  65. Fillot, N., Iordanoff, I., Berthier, Y.: Modelling third body flows with a discrete element method—a tool for understanding wear with adhesive particles. Tribol. Int. 40, 973–981 (2007)

    Article  CAS  Google Scholar 

  66. Roux, J.-N., Combe, G.: Quasistatic rheology and the origins of strain. CR Phys. 3, 131–140 (2002)

    Article  CAS  Google Scholar 

  67. Luding, S.: Constitutive relations for the shear band evolution in granular matter under large strain. Particuology 6, 501–505 (2008)

    Article  CAS  Google Scholar 

  68. Singh, A., Magnanimo, V., Saitoh, K., Luding, S.: The role of gravity or pressure and contact stiffness in granular rheology. New J. Phys. 17, 043028 (2015)

    Article  CAS  Google Scholar 

  69. Lätzel, M., Luding, S., Herrmann, H.J.: Macroscopic material properties from quasi-static, microscopic simulations of a two-dimensional shear-cell. Granular Matter 2, 123–135 (2000)

    Article  Google Scholar 

  70. Luding, S.: Introduction to discrete element methods: basic of contact force models and how to perform the micro-macro transition to continuum theory. Eur. J. Environ. Civ. Eng. 12, 785–826 (2008)

    Article  Google Scholar 

  71. Volfson, D., Tsimring, L.S., Aranson, I.S.: Partially fluidized shear granular flows: continuum theory and molecular dynamics simulations. Phys. Rev. E 68, 021301 (2003)

    Article  CAS  Google Scholar 

  72. Rothenburg, L., Bathurst, R.: Analytical study of induced anisotropy in idealized granular materials. Geotechnique 39, 601–614 (1989)

    Article  Google Scholar 

Download references

Funding

This work was financially supported by the National Natural Science Foundation of China under Grant Nos. 51975174 and 51875154.

Author information

Authors and Affiliations

  1. Institute of Tribology, School of Mechanical Engineering, Hefei University of Technology, Hefei, 230009, Anhui, China

    Xuejie Zhang, Wei Wang, Xiaojun Liu & Kun Liu

Authors
  1. Xuejie Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wei Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiaojun Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Kun Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kun Liu.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interest or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file1 (DOCX 1081 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, X., Wang, W., Liu, X. et al. Transient Evolution of Rheological Properties of Dense Granular Inertial Flow Under Plane Shear. Tribol Lett 70, 38 (2022). https://doi.org/10.1007/s11249-022-01578-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11249-022-01578-3

Keywords

Search

Navigation