Abstract
This paper investigates the induced anisotropy and multi-scale shear characteristics of granular materials by quantifying force chain distribution in two-dimensional specimens of rigid particles under quasi-static loading. A new criterion is proposed and implemented into the existing algorithm which can effectively solve the identification instability of force chains at branching and merging points. Force chain is then classified into three categories according to the variation of force chain quantity and average stress with segment length: stable segments, meta-stable segments and unstable force chain segments. The stable force chain segments dominate the load-bearing behavior of the granular materials. The directional distribution of force chain segments is more anisotropic and more sensitive to the applied stress than contact normal vectors, which show obvious local peaks in both vertical and horizontal directions at high deviatoric stress. Therefore, the probability density of directional distribution of force chains needs to be described by the first two deviatoric components of Fourier expansion with deviators A1 and A2, which are indicators reflecting the intensity of the induced-anisotropy of the granular materials. As the absolute values of A1 and A2 increase, the induced anisotropy is more significant. The final shear failure types are determined by the quantities of force chains orienting in two potential shear failure directions: if there is an obvious difference between the quantities of the two directions, single shear band occurs within the direction with less force chains; otherwise, conjugated double shear bands occur and lie in the two potential shear failure directions.
Similar content being viewed by others
References
Aharonov, E., Sparks, D.: Shear profiles and localization in simulations of granular materials. Phys. Rev. E 65, 051302 (2002)
Wan, R., Guo, P., Al-Mamun, M.: Behaviour of granular materials in relation to their fabric dependencies. Soils Found. 45, 77–86 (2005)
Behringer, R., Daniels, K.E., Majmudar, T.S., Sperl, M.: Fluctuations, correlations and transitions in granular materials: statistical mechanics for a non-conventional system. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 366, 493–504 (2008)
Tordesillas, A., Zhang, J., Behringer, R.: Buckling force chains in dense granular assemblies: physical and numerical experiments. Geomech. Geoeng. 4, 3–16 (2009)
Rothenburg, L., Bathurst, R.J.: Analytical study of induced anisotropy in idealized granular materials. Géotechnique 39, 601–614 (1989)
Guo, P., Stolle, D.F.E.: On the failure of granular materials with fabric effects. Soils Found. 45, 1–12 (2005)
Zhu, H., Nicot, F., Darve, F.: Meso-structure evolution in a 2D granular material during biaxial loading. Granul. Matter 18, 3 (2016)
Oda, M., Kazama, H.: Microstructure of shear bands and its relation to the mechanisms of dilatancy and failure of dense granular soils. Géotechnique 48, 465–481 (1998)
Tordesillas, A., Muthuswamy, M.: A thermomicromechanical approach to multiscale continuum modeling of dense granular materials. Acta Geotech. 3, 225–240 (2008)
Iwashita, K., Oda, M.: Micro-deformation mechanism of shear banding process based on modified distinct element method. Powder Technol. 109, 192–205 (2000)
Guo, P.: Critical length of force chains and shear band thickness in dense granular materials. Acta Geotech. 7, 41–55 (2012)
Dantu, P.: Contribution à l’ètude mècanique et gèomètrique des milieux pulvèrulents. In: Presented at the 4th International Conference on Soil Mechanics and Foundation Engineering, London (1957)
Liu, C.H., Nagel, S.R., Schecter, D.A., Coppersmith, S.N., Majumdar, S., Narayan, O., Witten, T.A.: Force fluctuations in bead packs. Science 269, 513–515 (1995)
Ouaguenouni, S., Roux, J.-N.: Force distribution in frictionless granular packings at rigidity threshold. Europhys. Lett. 39, 117–122 (1997)
Majmudar, T.S., Behringer, R.P.: Contact force measurements and stress-induced anisotropy in granular materials. Nature 435, 1079–1082 (2005)
Goldenberg, C., Goldhirsch, I.: Force chains, microelasticity, and macroelasticity. Phys. Rev. Lett. 89, 084302 (2002)
Bigoni, D., Noselli, G.: Localized stress percolation through dry masonry walls. Part I—Experiments. Eur. J. Mech. A/Solids 29, 291–298 (2010)
Bigoni, D., Noselli, G.: Localized stress percolation through dry masonry walls. Part II—Modelling. Eur. J. Mech. A/Solids 29, 299–307 (2010)
Geng, J., Howell, D., Longhi, E., Behringer, R.P., Reydellet, G., Vanel, L., Clément, E., Luding, S.: Footprints in sand: the response of a granular material to local perturbations. Phys. Rev. Lett. 87, 035506 (2001)
Chaiamarit, C., Balandraud, X., Preechawuttipong, I., Grédiac, M.: Stress network analysis of 2D non-cohesive polydisperse granular materials using infrared thermography. Exp. Mech. 55, 761–769 (2015)
Oda, M., Nemat-Nasser, S., Konishi, J.: Stress-induced anisotropy in granular masses. Soils Found. 25, 85–97 (1985)
Vairaktaris, E., Theocharis, A.I., Dafalias, Y.F.: Correlation of fabric tensors for granular materials using 2D DEM. Acta Geotech. (2018). https://doi.org/10.1007/s11440-019-00811-z
Theocharis, A.I., Vairaktaris, E., Dafalias, Y.F.: Scan line void fabric anisotropy tensors of granular media. Granul. Matter 19, 68 (2017)
Howell, D., Behringer, R.P., Veje, C.: Stress fluctuations in a 2D granular couette experiment: a continuous transition. Phys. Rev. Lett. 82, 5241–5244 (1999)
Drescher, A., De Jong, G.D.J.: Photoelastic verification of a mechanical model for the flow of a granular material. J. Mech. Phys. Solids 20, 337–351 (1972)
Ken-Ichi, K.: Distribution of directional data and fabric tensors. Int. J. Eng. Sci. 22, 149–164 (1984)
Raihan Taha, M., Shaverdi, H.: Evolution of fabric under the rotation of the principal stress axes in the simple shear test. Mech. Mater. 69, 173–184 (2014)
Blair, D.L., Mueggenburg, N.W., Marshall, A.H., Jaeger, H.M., Nagel, S.R.: Force distributions in three-dimensional granular assemblies: effects of packing order and interparticle friction. Phys. Rev. E 63, 041304 (2001)
Kruyt, N., Rothenburg, L.: Probability density functions of contact forces for cohesionless frictional granular materials. Int. J. Solids Struct. 39, 571–583 (2002)
Oda, M.: Fabric tensor for discontinous geological materials. Soils Found. 22, 96–108 (1982)
Radjai, F., Wolf, D.E., Jean, M., Moreau, J.-J.: Bimodal character of stress transmission in granular packings. Phys. Rev. Lett. 80, 61–64 (1998)
Azéma, E., Radjaï, F.: Force chains and contact network topology in sheared packings of elongated particles. Phys. Rev. E 85, 031303 (2012)
Peters, J.F., Muthuswamy, M., Wibowo, J., Tordesillas, A.: Characterization of force chains in granular material. Phys. Rev. E 72, 041307 (2005)
Tordesillas, A., Walker, D.M., Lin, Q.: Force cycles and force chains. Phys. Rev. E 81, 011302 (2010)
Campbell, C.S.: A problem related to the stability of force chains. Granul. Matter 5, 129–134 (2003)
Hunt, G.W., Tordesillas, A., Green, S.C., Shi, J.: Force-chain buckling in granular media: a structural mechanics perspective. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 368, 249–262 (2010)
Tordesillas, A., Lin, Q., Zhang, J., Behringer, R.P., Shi, J.: Structural stability and jamming of self-organized cluster conformations in dense granular materials. J. Mech. Phys. Solids 59, 265–296 (2011)
Zhang, L., Nguyen, N.G.H., Lambert, S., Nicot, F., Prunier, F., Djeran-Maigre, I.: The role of force chains in granular materials: from statics to dynamics. Eur. J. Environ. Civil Eng. 21, 874–895 (2017)
Blumenfeld, R.: Stresses in isostatic granular systems and emergence of force chains. Phys. Rev. Lett. 93, 108301 (2004)
Muthuswamy, M., Tordesillas, A.: How do interparticle contact friction, packing density and degree of polydispersity affect force propagation in particulate assemblies? J. Stat. Mech Theory Exp. 2006, P09003 (2006)
Cates, M.E., Wittmer, J.P., Bouchaud, J.-P., Claudin, P.: Jamming, force chains, and fragile matter. Phys. Rev. Lett. 81, 1841–1844 (1998)
Van Siclen, C.D.: Force structure of frictionless granular piles. Physica A 333, 155–167 (2004)
Han, J., Bhandari, A., Wang, F.: DEM analysis of stresses and deformations of geogrid-reinforced embankments over piles. Int. J. Geomech. 12, 340–350 (2012)
Sazzad, M.M., Suzuki, K.: Micromechanical behavior of granular materials with inherent anisotropy under cyclic loading using 2D DEM. Granul. Matter 12, 597–605 (2010)
Lu, M., McDowell, G.R.: The importance of modelling ballast particle shape in the discrete element method. Granul. Matter 9, 69–80 (2006)
Zhao, S., Evans, T.M., Zhou, X.: Shear-induced anisotropy of granular materials with rolling resistance and particle shape effects. Int. J. Solids Struct. 150, 268–281 (2018)
Rui, R., van Tol, F., Xia, X.-L., van Eekelen, S., Hu, G., Xia, Y.: Evolution of soil arching; 2D DEM simulations. Comput. Geotech. 73, 199–209 (2016)
Gu, X., Huang, M., Qian, J.: Discrete element modeling of shear band in granular materials. Theor. Appl. Fract. Mech. 72, 37–49 (2014)
Sadrekarimi, A., Olson, S.M.: Shear band formation observed in ring shear tests on sandy soils. J. Geotech. Geoenviron. Eng. 136, 366–375 (2010)
Desrues, J., Viggiani, G.: Strain localization in sand: an overview of the experimental results obtained in Grenoble using stereophotogrammetry. Int. J. Numer. Anal. Meth. Geomech. 28, 279–321 (2004)
Lumb, P.: Safety factors and the probability distribution of soil strength. Can. Geotech. J. 7, 225–242 (1970)
Shi, J., Guo, P.: Induced fabric anisotropy of granular materials in biaxial tests along imposed strain paths. Soils Found. 58, 249–263 (2018)
Acknowledgements
The NSFC (National Natural Science Foundation of China) Program, Grant Nos. 51708423 and 51761135109 are greatly appreciated for providing financial support for this research. The authors also thank Mr. Zhekan Tian for his assistance in preparation of the figures.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Fu, L., Zhou, S., Guo, P. et al. Induced force chain anisotropy of cohesionless granular materials during biaxial compression. Granular Matter 21, 52 (2019). https://doi.org/10.1007/s10035-019-0899-1
Received:
Published:
DOI: https://doi.org/10.1007/s10035-019-0899-1