Technical Papers
Jan 6, 2022

Mesoscale Investigation of Fine Grain Contribution to Contact Stress in Granular Materials

Publication: Journal of Engineering Mechanics
Volume 148, Issue 3

Abstract

Fine grains play an important role in mechanical properties of granular materials as they control how plastic strain may develop, which has a noticeable impact on mechanical stability. In this work, we use numerical simulations based on a discrete element method (DEM) to analyze the stress contribution of fine grains to the total stress. Different from usual DEM simulations, the analysis is conducted directly at the mesoscopic scale by considering an idealized grain assembly. The results show how fine grains get progressively jammed and increasingly participate in stress transmission. Fine contribution to contact stress is shown to be nonisotropic. The principal anisotropy direction coincides with the principal direction of contraction and the anisotropy ratio (i.e., the ratio between the largest and the smallest eigenvalues of the fine stress) is shown to be limited (σmax/σmin2). By performing strain controlled directional analyses, an analytical model is proposed to account for the stress contribution of fine grains along various loading paths. Its simple form will help to enrich advanced micromechanically-based constitutive formulations and better account for the constitutive behavior of widely graded granular materials.

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Data Availability Statement

The data that support the findings of this study were generated using the DEM code LIGGGHTS. Data are available upon request.

Acknowledgments

This work was financially supported by the China Scholarship Council (No. 201906270111). This enabled Qirui Ma to spend one year as a visiting Ph.D. Candidate at INRAE under the supervision of Dr. A. Wautier. Revision work was done while Qirui Ma was financially supported by the Key research and development plan of Hubei Province, China (No. 2020BCA083).

References

Ahmadi, M., T. Shire, A. Mehdizadeh, and M. Disfani. 2020. “DEM modelling to assess internal stability of gap-graded assemblies of spherical particles under various relative densities, fine contents and gap ratios.” Comput. Geotech. 126 (Oct): 103710. https://doi.org/10.1016/j.compgeo.2020.103710.
Behringer, R. P., and B. Chakraborty. 2019. “The physics of jamming for granular materials: A review.” Rep. Prog. Phys. 82 (1): 012601. https://doi.org/10.1088/1361-6633/aadc3c/meta.
Bi, D., J. Zhang, B. Chakraborty, and R. P. Behringer. 2011. “Jamming by shear.” Nature 480 (7377): 355–358. https://doi.org/10.1038/nature10667.
Cabalar, A. F. 2011. “The effects of fines on the behaviour of a sand mixture.” Geotech. Geol. Eng. 29 (1): 91–100. https://doi.org/10.1007/s10706-010-9355-z.
Cao, X., Y. Zhu, and J. Gong. 2021. “Effect of the intermediate principal stress on the mechanical responses of binary granular mixtures with different fines contents.” Granular Matter 23 (2): 1–19. https://doi.org/10.1007/s10035-021-01110-9.
Ciamarra, M. P., R. Pastore, M. Nicodemi, and A. Coniglio. 2011. “Jamming phase diagram for frictional particles.” Phys. Rev. E: Stat. Nonlinear Soft Matter Phys. 84 (4): 041308. https://doi.org/10.1103/PhysRevE.84.041308.
Cui, Y. F., Y. Jiang, and C. X. Guo. 2019. “Investigation of the initiation of shallow failure in widely graded loose soil slopes considering interstitial flow and surface runoff.” Landslides 16 (4): 815–828. https://doi.org/10.1007/s10346-018-01129-9.
Cui, Y. F., X. J. Zhou, and C. X. Guo. 2017. “Experimental study on the moving characteristics of fine grains in wide grading unconsolidated soil under heavy rainfall.” J. Mountain Sci. 14 (3): 417–431. https://doi.org/10.1007/s11629-016-4303-x.
Cundall, P. A., and O. D. L. Strack. 1979. “A discrete numerical model for granular assemblies.” Géotechnique 29 (1): 47–65. https://doi.org/10.1680/geot.1979.29.1.47.
Deng, Y., Z. Wu, Y. Cui, S. Liu, and Q. Wang. 2017. “Sand fraction effect on hydro-mechanical behavior of sand-clay mixture.” Appl. Clay Sci. 135 (Jan): 355–361. https://doi.org/10.1016/j.clay.2016.10.017.
Edwards, S. F., and D. V. Grinev. 2001. “Statistical physics of the jamming transition: The search for simple models.” In Jamming and rheology: Constrained dynamics on microscopic and macroscopic scales. London: Taylor & Francis.
Gong, J., and J. Liu. 2017. “Mechanical transitional behavior of binary mixtures via DEM: Effect of differences in contact-type friction coefficients.” Comput. Geotech. 85 (May): 1–14. https://doi.org/10.1016/j.compgeo.2016.12.009.
Gong, J., J. Liu, and L. Cui. 2019a. “Shear behaviors of granular mixtures of gravel-shaped coarse and spherical fine particles investigated via discrete element method.” Powder Technol. 353 (Jul): 178–194. https://doi.org/10.1016/j.powtec.2019.05.016.
Gong, J., X. Wang, L. Li, and Z. Nie. 2019b. “DEM study of the effect of fines content on the small-strain stiffness of gap-graded soils.” Comput. Geotech. 112 (Aug): 35–40. https://doi.org/10.1016/j.compgeo.2019.04.008.
Hicher, P. Y. 2013. “Modelling the impact of particle removal on granular material behaviour.” Géotechnique 63 (2): 118–128. https://doi.org/10.1680/geot.11.P.020.
Jiang, M. D., Z. X. Yang, D. Barreto, and Y. H. Xie. 2018. “The influence of particle-size distribution on critical state behavior of spherical and non-spherical particle assemblies.” Granular Matter 20 (4): 1–15. https://doi.org/10.1007/s10035-018-0850-x.
Jiang, X., P. Cui, and Y. Ge. 2015. “Effects of fines on the strength characteristics of mixtures.” Eng. Geol. 198 (Nov): 78–86. https://doi.org/10.1016/j.enggeo.2015.09.011.
Kloss, C., C. Goniva, A. Hager, S. Amberger, and S. Pirker. 2012. “Models, algorithms and validation for opensource DEM and CFD–DEM.” Int. J. 12 (2–3): 140–152. https://doi.org/10.1504/PCFD.2012.047457.
Lade, P. V., and J. A. Yamamuro. 1997. “Effects of nonplastic fines on static liquefaction of sands.” Can. Geotech. J. 34 (6): 918–928. https://doi.org/10.1139/t97-052.
Liu, D., C. O’Sullivan, and J. A. H. Carraro. 2021. “Influence of particle size distribution on the proportion of stress-transmitting particles and implications for measures of soil state.” J. Geotech. Geoenviron. Eng. 147 (3): 04020182. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002466.
Liu, J., F. Nicot, and W. Zhou. 2018. “Sustainability of internal structures during shear band forming in 2D granular materials.” Powder Technol. 338 (Oct): 458–470. https://doi.org/10.1016/j.powtec.2018.07.001.
Liu, J., A. Wautier, S. Bonelli, F. Nicot, and F. Darve. 2020. “Macroscopic softening in granular materials from a mesoscale perspective.” Int. J. Solids Struct. 193 (Jun): 222–238. https://doi.org/10.1016/j.ijsolstr.2020.02.022.
Love, A. E. H. 2013. A treatise on the mathematical theory of elasticity. Cambridge, MA: Cambridge University Press.
Luding, S. 2016. “So much for the jamming point.” Nat. Phys. 12 (6): 531–532. https://doi.org/10.1038/nphys3680.
Majmudar, T. S., M. Sperl, S. Luding, and R. P. Behringer. 2007. “Jamming transition in granular systems.” Phys. Rev. Lett. 98 (5): 058001. https://doi.org/10.1103/PhysRevLett.98.058001.
Mehrabadi, M. M., S. Nemat-Nasser, and M. Oda. 1982. “On statistical description of stress and fabric in granular materials.” Int. J. Numer. Anal. Methods Geomech. 6 (1): 95–108. https://doi.org/10.1002/nag.1610060107.
Minh, N. H., and Y. P. Cheng. 2013. “A DEM investigation of the effect of particle-size distribution on one-dimensional compression.” Géotechnique 63 (1): 44–53. https://doi.org/10.1680/geot.10.P.058.
Minh, N. H., Y. P. Cheng, and C. Thornton. 2014. “Strong force networks in granular mixtures.” Granular Matter 16 (1): 69–78. https://doi.org/10.1007/s10035-013-0455-3.
Monkul, M. M., and G. Ozden. 2007. “Compressional behavior of clayey sand and transition fines content.” Eng. Geol. 89 (3): 195–205. https://doi.org/10.1016/j.enggeo.2006.10.001.
Morgan, J. K. 1999. “Numerical simulations of granular shear zones using the distinct element method: 2. Effects of particle size distribution and interparticle friction on mechanical behavior.” J. Geophys. Res. Solid Earth 104 (2): 2721–2732. https://doi.org/10.1029/1998JB900055.
Ng, T.-T., W. Zhou, and X.-L. Chang. 2017. “Effect of particle shape and fine content on the behavior of binary mixture.” J. Eng. Mech. 143 (1): C4016008. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001070.
Nicot, F., and F. Darve. 2005. “A multi-scale approach to granular materials.” Mech. Mater. 37 (9): 980–1006. https://doi.org/10.1016/j.mechmat.2004.11.002.
Nicot, F., and F. Darve. 2011. “The H-microdirectional model: Accounting for a mesoscopic scale.” Mech. Mater. 43 (12): 918–929. https://doi.org/10.1016/j.mechmat.2011.07.006.
Papadopoulou, A., and T. Tika. 2008. “The effect of fines on critical state and liquefaction resistance characteristics of non-plastic silty sands.” Soils Found. 48 (5): 713–725. https://doi.org/10.3208/sandf.48.713.
Peters, J. F., M. Muthuswamy, J. Wibowo, and A. Tordesillas. 2005. “Characterization of force chains in granular material.” Phys. Rev. E: Stat. Nonlinear Soft Matter Phys. 72 (4): 1–8. https://doi.org/10.1103/PhysRevE.72.041307.
Radjai, F., D. E. Wolf, M. Jean, and J. J. Moreau. 1998. “Bimodal character of stress transmission in granular packings.” Phys. Rev. Lett. 80 (1): 61. https://doi.org/10.1103/PhysRevLett.80.61.
Rahman, M. M., S. R. Lo, and M. A. L. Baki. 2011. “Equivalent granular state parameter and undrained behaviour of sand-fines mixtures.” Acta Geotech. 6 (4): 183–194. https://doi.org/10.1007/s11440-011-0145-4.
Scholtès, L., P.-Y. Hicher, and L. Sibille. 2010. “Multiscale approaches to describe mechanical responses induced by particle removal in granular materials.” Comptes Rendus Mécanique 338 (10–11): 627–638. https://doi.org/10.1016/j.crme.2010.10.003.
Shi, X. S., K. Liu, and J. Yin. 2021. “Analysis of mobilized stress ratio of gap-graded granular materials in direct shear state considering coarse fraction effect.” Acta Geotech. 16 (6): 1801–1814. https://doi.org/10.1007/s11440-020-01107-3.
Shi, X. S., J. Zhao, J. Yin, and Z. Yu. 2019. “An elastoplastic model for gap-graded soils based on homogenization theory.” Int. J. Solids Struct. 163 (May): 1–14. https://doi.org/10.1016/j.ijsolstr.2018.12.017.
Shire, T., and C. O’Sullivan. 2013. “Micromechanical assessment of an internal stability criterion.” Acta Geotech. 8 (1): 81–90. https://doi.org/10.1007/s11440-012-0176-5.
Shire, T., C. O’Sullivan, K. J. Hanley, and R. J. Fannin. 2014. “Fabric and effective stress distribution in internally unstable soils.” J. Geotech. Geoenviron. Eng. 140 (12): 04014072. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001184.
Thevanayagam, S., T. Shenthan, S. Mohan, and J. Liang. 2002. “Undrained fragility of clean sands, silty sands, and sandy silts.” J. Geotech. Geoenviron. Eng. 128 (10): 849–859. https://doi.org/10.1061/(ASCE)1090-0241(2002)128:10(849).
Tordesillas, A. 2007. “Force chain buckling, unjamming transitions and shear banding in dense granular assemblies.” Philos. Mag. 87 (32): 4987–5016. https://doi.org/10.1080/14786430701594848.
Ueda, T., T. Matsushima, and Y. Yamada. 2011. “Effect of particle size ratio and volume fraction on shear strength of binary granular mixture.” Granular Matter 13 (6): 731–742. https://doi.org/10.1007/s10035-011-0292-1.
Vallejo, L. E. 2001. “Interpretation of the limits in shear strength in binary granular mixtures.” Can. Geotech. J. 38 (5): 1097–1104. https://doi.org/10.1139/t01-029.
Wang, D., J. Ren, J. A. Dijksman, H. Zheng, and R. P. Behringer. 2018. “Microscopic origins of shear jamming for 2D frictional grains.” Phys. Rev. Lett. 120 (20): 208004. https://doi.org/10.1103/PhysRevLett.120.208004.
Wang, T., S. Liu, A. Wautier, and F. Nicot. 2021. “An updated skeleton void ratio for gravelly sand mixtures considering the effect of grain size distribution.” Can. Geotech. J. 2021 (Mar): 10. https://doi.org/10.1139/cgj-2020-0570.
Wang, T., A. Wautier, S. Liu, and F. Nicot. Forthcoming. “How fines content affects granular plasticity of under-filled binary mixtures.” Acta Geotech.
Wautier, A., S. Bonelli, and F. Nicot. 2017. “Scale separation between grain detachment and grain transport in granular media subjected to an internal flow.” Granular Matter 19 (2): 22. https://doi.org/10.1007/s10035-017-0706-9.
Wautier, A., S. Bonelli, and F. Nicot. 2019. “DEM investigations of internal erosion: Grain transport in the light of micromechanics.” Int. J. Numer. Anal. Methods Geomech. 43 (1): 339–352. https://doi.org/10.1002/nag.2866.
Wautier, A., G. Veylon, M. Miot, M. Pouragha, F. Nicot, R. Wan, and F. Darve. 2021. “Multiscale modelling of granular materials in boundary value problems accounting for mesoscale mechanisms.” Comput. Geotech. 134 (Jun): 104143. https://doi.org/10.1016/j.compgeo.2021.104143.
Xiong, H. 2017. Multiscale modeling of granular materials in application to geotechnical engineering problems. Grenoble, France: Université Grenoble Alpes.
Xiong, H., Z. Y. Yin, and F. Nicot. 2019. “A multiscale work-analysis approach for geotechnical structures.” Int. J. Numer. Anal. Methods Geomech. 43 (6): 1230–1250. https://doi.org/10.1002/nag.2893.
Xiong, H., Z.-Y. Yin, F. Nicot, A. Wautier, M. Marie, F. Darve, G. Veylon, and P. Philippe. 2021. “A novel multi-scale large deformation approach for modelling of granular collapse.” Acta Geotech. 2021 (Jan): 1–18. https://doi.org/10.1007/s11440-020-01113-5.
Yin, Z. Y., J. Zhao, and P. Y. Hicher. 2014. “A micromechanics-based model for sand-silt mixtures.” Int. J. Solids Struct. 51 (6): 1350–1363. https://doi.org/10.1016/j.ijsolstr.2013.12.027.
Zhang, F., M. Li, M. Peng, C. Chen, and L. Zhang. 2019. “Three-dimensional DEM modeling of the stress–strain behavior for the gap-graded soils subjected to internal erosion.” Acta Geotech. 14 (2): 487–503. https://doi.org/10.1007/s11440-018-0655-4.
Zhao, C., K. Tian, and N. Xu. 2011. “New jamming scenario: From marginal jamming to deep jamming.” Phys. Rev. Lett. 106 (12): 125503. https://doi.org/10.1103/PhysRevLett.106.125503.
Zhou, W., Q. Ma, G. Ma, X. Cao, and Y. Cheng. 2020. “Microscopic investigation of internal erosion in binary mixtures via the coupled LBM-DEM method.” Powder Technol. 376 (Oct): 31–41. https://doi.org/10.1016/j.powtec.2020.07.099.
Zhou, W., W. Wu, G. Ma, T. Ng, and X. Chang. 2018. “Undrained behavior of binary granular mixtures with different fines contents.” Powder Technol. 340 (Dec): 139–153. https://doi.org/10.1016/j.powtec.2018.09.022.
Zhu, H., F. Nicot, and F. Darve. 2016. “Meso-structure organization in two-dimensional granular materials along biaxial loading path.” Int. J. Solids Struct. 96 (Oct): 25–37. https://doi.org/10.1016/j.ijsolstr.2016.06.025.

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Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 148Issue 3March 2022

History

Received: Mar 10, 2021
Accepted: Oct 28, 2021
Published online: Jan 6, 2022
Published in print: Mar 1, 2022
Discussion open until: Jun 6, 2022

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Qirui Ma
Formerly, Ph.D. Candidate, State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan Univ., Wuhan 430072, China; presently, Research Scholar, Changjiang Institute of Survey, Planning, Design and Research, Wuhan 430010, China.
Researcher, Aix-Marseille Univ., Institut National de Recherche pour l'Agriculture, l'Alimentation et l'Environnement, Unité Mixte de Recherche Risques, ECOsystèmes, Vulnérabilité, Environnement, Résilience, 3275 Rte Cézanne, CS 40061, 13182 Aix-en-Provence Cedex 5, France (corresponding author). ORCID: https://orcid.org/0000-0002-2551-103X. Email: [email protected]
François Nicot
Research Director, Université Grenoble Alpes, Institut National de Recherche pour l'Agriculture, l'Alimentation et l'Environnement, Unité de Recherche Erosion Torrentielle Neige et Avalanche, 2 rue de la Papeterie-BP 76, F-38402 Saint Martin d'Hères Cedex, France.

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  • Effect of Particle Shape on Contact Network and Shear-Induced Anisotropy of Granular Assemblies: A DEM Perspective, Journal of Geotechnical and Geoenvironmental Engineering, 10.1061/JGGEFK.GTENG-11762, 150, 3, (2024).

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