Shear strength of angular granular materials with size and shape polydispersity
Open Geomechanics, Volume 4 (2023), article no. 1, 14 p.

Shear strength characterization of coarse granular materials often requires modifying the original material in order to fit samples in standard testing devices. This is done, however, at the expense of changing the particle size distribution (psd), employing scaling-down techniques such as parallel grading or scalping methods. Such procedures hide, nevertheless, another challenge. As a given particle size can present a characteristic grain shape, altering the grain size distribution can strongly modify the distribution of grain shapes. While the effects of grain shape on shear strength have been vastly covered in the literature, the effect of having different shapes along grain sizes has yet to be systematically assessed and understood. This article explores the critical shear strength of samples composed of particles with size-shape correlations using 2D discrete element simulations. Two cases of particle shape variability across grain sizes are studied: (1) the sharpness of grains’ corners - modeled via the number of sides of regular polygons - and (2) the geometric irregularity of grains - where the corners of a polygon are not necessarily evenly spaced. The effects of these geometrical properties on the shear strength are assessed through a series of numerical simple shearing tests up to large levels of deformation. We find that granular materials presenting different number of sides across grain sizes can strongly modify their mechanical response depending on the grain-size correlation. On the contrary, grain shape irregularity turns out not to have a major effect on the critical shear strength. Microstructural analyses allow us to identify how each correlation affects load transmission mechanisms between grains, and the contribution of each grain shape class to the macroscopic shear strength. This work shows that particle sizes are not the only sample descriptor to consider when applying scaling-down techniques. It is equally key to characterize particle shapes across grain sizes to capture the material’s mechanical response adequately.

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DOI: 10.5802/ogeo.15
Keywords: shear strength, particle shape, polydispersity, discrete-element modeling, grain size distribution
Carrasco, Sergio 1, 2; Cantor, David 1, 2; Ovalle, Carlos 1, 2; Quiroz-Rojo, Paula 1, 2, 3

1 Department of Civil, Geological and Mining Engineering, Polytechnique Montréal, Québec, Canada
2 Research Institute of Mining and Environment (RIME), UQAT-Polytechnique, Québec, Canada
3 LMGC, Université de Montpellier, CNRS, Montpellier, France
License: CC-BY-NC-SA 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Carrasco, Sergio; Cantor, David; Ovalle, Carlos; Quiroz-Rojo, Paula. Shear strength of angular granular materials with size and shape polydispersity. Open Geomechanics, Volume 4 (2023), article  no. 1, 14 p. doi : 10.5802/ogeo.15. https://opengeomechanics.centre-mersenne.org/articles/10.5802/ogeo.15/

[1] Altuhafi, F. N.; Coop, M. R.; Georgiannou, V. N. Effect of Particle Shape on the Mechanical Behavior of Natural Sands, J. Geotech. Geoenviron., Volume 142 (2016) no. 12, 04016071 | DOI

[2] Azéma, E.; Estrada, N.; Radjai, F. Nonlinear effects of particle shape angularity in sheared granular media, Phys. Rev. E, Volume 86 (2012) no. 4, 041301 | DOI

[3] Andreotti, B.; Forterre, Y.; Pouliquen, O. Granular media: between fluid and solid, CUP, 2013 | DOI

[4] Amirpour Harehdasht, S.; Hussien, M. N.; Karray, M.; Roubtsova, V.; Chekired, M. Influence of particle size and gradation on shear strength–dilation relation of granular materials, Can. Geotech. J., Volume 56 (2019) no. 2, pp. 208-227 | DOI

[5] Acevedo, M.; Hidalgo, R. C.; Zuriguel, I.; Maza, D.; Pagonabarraga, I. Influence of the feeding mechanism on deposits of square particles, Phys. Rev. E, Volume 87 (2013), 012202, 9 pages https://link.aps.org/doi/10.1103/PhysRevE.87.012202 | DOI

[6] Amirpour, H. S.; Karray, M.; Hussien, M.; Chekired, M. Influence of particle size and gradation on the stress-dilatancy behavior of granular materials during drained triaxial compression, Int. J. Geomech., Volume 17 (2017) no. 9, 04017077 | DOI

[7] Al-Hussaini, M. Effect of particle size and strain conditions on the strength of crushed basalt, Can. Geotech. J., Volume 20 (1983) no. 4, pp. 706-717 | DOI

[8] 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, Volume 96 (2017), 28950486 | DOI

[9] Azéma, E.; Radjai, F. Stress-strain behavior and geometrical properties of packings of elongated particles, Phys. Rev. E, Volume 81 (2010) no. 5, 051304 | DOI

[10] Standard Test Method for Consolidated Undrained Direct Simple Shear Testing of Fine Grain Soils (2017) (Standard) | DOI

[11] Bard, E.; Anabalón, M. E.; Campaña, J. Waste rock behavior at high pressures: dimensioning high waste rock dumps, Wiley Online Library, 2011, pp. 83-112

[12] 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, Volume 87 (2013), 032206, 12 pages | DOI

[13] Barton, N.; Kjærnsli, B. Shear strength of rockfill, J. Geotech. Eng., Volume 107 (1981) no. 7, pp. 873-891

[14] Cantor, D.; Azéma, E.; Preechawuttipong, I. Microstructural analysis of sheared polydisperse polyhedral grains, Phys. Rev. E, Volume 101 (2020), 062901, 12 pages | DOI

[15] Cantor, D.; Azéma, E.; Sornay, P.; Radjai, F. Rheology and structure of polydisperse three-dimensional packings of spheres, Phys. Rev. E, Volume 98 (2018) no. 5, 052910 | DOI

[16] Carrasco, S.; Cantor, D.; Ovalle, C. Effects of particle size-shape correlations on steady shear strength of granular materials: The case of particle elongation, Int. J. Numer. Anal. Methods. Geomech., Volume 46 (2022) no. 5, pp. 979-1000 | DOI

[17] Cho, G.-C.; Dodds, J.; Santamarina, J. C. Particle Shape Effects on Packing Density, Stiffness, and Strength: Natural and Crushed Sands, J. Geotech. Geoenviron., Volume 132 (2006) no. 5, pp. 591-602 | DOI

[18] Cao, P.; Jiang, M.; Ding, Z. Effects of particle size on mechanical behaviors of calcareous sand under triaxial conditions, Jpn. Geotech. Soc. spec. publ., Volume 8 (2020) no. 5, pp. 182-187

[19] Cerato, A. B.; Lutenegger, A. J. Specimen size and scale effects of direct shear box tests of sands, Geotech. Test. J., Volume 29 (2006) no. 6, pp. 507-516

[20] Dubois, F.; Acary, V.; Jean, M. The Contact Dynamics method: A nonsmooth story, C. R. Mécanique, Volume 346 (2018) no. 3, pp. 247-262 | DOI

[21] Dubois, F.; Jean, M.; et al LMGC90 wiki page, https://git-xen.lmgc.univ-montp2.fr/lmgc90/lmgc90_user/wikis/home, 2023 ([Online; accessed 15-Mar-2023])

[22] Dubois, F.; Jean, M.; Renouf, M.; Mozul, R.; Martin, A.; Bagnéris, M. LMGC90, 10e colloque national en calcul des structures, 10e colloque national en calcul des structures (2011), 8 pages

[23] Deiminiat, A.; Li, L. Experimental study on the reliability of scaling down techniques used in direct shear tests to determine the shear strength of rockfill and waste rocks, CivilEng, Volume 3 (2022) no. 1, pp. 35-50 | DOI

[24] Deiminiat, A.; Li, L.; Zeng, F.; Pabst, T.; Chiasson, P.; Chapuis, R. Determination of the Shear Strength of Rockfill from Small-Scale Laboratory Shear Tests: A Critical Review, Adv. Civ. Eng., Volume 2020 (2020), pp. 1-18 | DOI

[25] Deng, Y.; Yilmaz, Y.; Gokce, A.; Chang, C. Influence of particle size on the drained shear behavior of a dense fluvial sand, Acta Geotech., Volume 16 (2021) no. 7, pp. 2071-2088 | DOI

[26] Estrada, N.; Azéma, E.; Radjai, F.; Taboada, A. Identification of rolling resistance as a shape parameter in sheared granular media, Phys. Rev. E, Volume 84 (2011) no. 1, 011306 | DOI

[27] Frossard, E.; Ovalle, C.; Dano, C.; Hicher, P-Y.; Maiolino, S.; Hu, W. Size effects due to grain crushing in rockfills shear strength, be published in 18th International Conference for Soil Mechanics and Geotechnical Engineering (2013)

[28] GDR-MiDi On dense granular flows, Eur. Phys. J. E, Volume 14 (2004), pp. 341-365 | DOI

[29] Hardin, B. O. Crushing of soil particles, J. Geotech. Eng., Volume 111 (1985) no. 10, pp. 1177-1192 | DOI

[30] Hu, W.; Dano, C.; Hicher, P-Y.; Le Touzo, J-Y.; Derkx, F.; Merliot, E. Effect of sample size on the behavior of granular materials, Geotech. Test. J., Volume 34 (2011) no. 3, pp. 186-197

[31] Hidalgo, R. C.; Zuriguel, I.; Maza, D.; Pagonabarraga, I. Role of particle shape on the stress propagation in granular packings, Phys. Rev. Lett., Volume 103 (2009) no. 11, 118001 | DOI

[32] Indraratna, B.; Ionescu, D.; Christie, H.D. Shear behavior of railway ballast based on large-scale triaxial tests, J. geotechn. geoenviron., Volume 124 (1998) no. 5, pp. 439-449 | DOI

[33] Jean, M.; Moreau, J. J. Unilaterality and dry friction in the dynamics of rigid body collections, 1st Contact Mechanics International Symposium, 1st Contact Mechanics International Symposium (1992), pp. 31-48

[34] Jullien, R.; Pavlovitch, A.; Meakin, P. Random packings of spheres built with sequential models, J. Phys. A Math. Theor., Volume 25 (1992) no. 15, 4103

[35] Kawamoto, R.; Andò, E.; Viggiani, G.; Andrade, J. E. All you need is shape: Predicting shear banding in sand with LS-DEM, J. Mech. Phys. Solids, Volume 111 (2018), pp. 375-392 | DOI

[36] Kanzaki, T.; Acevedo, M.; Zuriguel, I.; Pagonabarraga, I.; Maza, D.; Hidalgo, R.C. Stress distribution of faceted particles in a silo after its partial discharge, Eur. Phys. J. E, Volume 34 (2011) no. 12, pp. 1-8 | DOI

[37] Linero, S; Azéma, E.; Estrada, N.; Fityus, S.; Simmons, J.; Lizcano, A. Impact of grading on steady-state strength, Geotech. Lett., Volume 9 (2019) no. 4, pp. 328-333 | DOI

[38] Linero, S.; Fityus, S.; Simmons, J.; Lizcano, A.; Cassidy, J. Trends in the evolution of particle morphology with size in colluvial deposits overlying channel iron deposits, EPJ Web of Conferences, Volume 140, EPJ Web of Conferences (2017), 14005 | DOI

[39] Liu, Y.; Guillard, F.; Marks, B.; Rognon, P.; Einav, I. The perpetual shearing of granular soils under low stresses using the stadium shear device, Open Geomechanics, Volume 3 (2022), pp. 1-19 | DOI

[40] Li, G.; Ovalle, C.; Dano, C.; Hicher, P.-Y. Influence of grain size distribution on critical state of granular materials, Constitutive modeling of geomaterials, Springer, 2013, pp. 207-210 | DOI

[41] Linero, S.; Palma, C.; Apablaza, R. Geotechnical characterisation of waste material in very high dumps with large scale triaxial testing, Proceedings of the 2007 International Symposium on Rock Slope Stability in Open Pit Mining and Civil Engineering, Australian Centre for Geomechanics (2007), pp. 59-75

[42] Lade, P. V.; Yamamuro, J. A.; Bopp, P. A. Significance of particle crushing in granular materials, J. Geotech. Eng., Volume 122 (1996) no. 4, pp. 309-316 | DOI

[43] Marsal, R. Large scale testing of rockfill materials, J. Soil Mech. Found. Div., Volume 93 (1967) no. 2, pp. 27-43 | DOI

[44] Matsushima, T.; Chang, C. S. Quantitative evaluation of the effect of irregularly shaped particles in sheared granular assemblies, Granul. Matter, Volume 13 (2011) no. 3, pp. 269-276 | DOI

[45] Marachi, N.; Chan, C.; Seed, H. Evaluation of properties of rockfill materials, J. Soil Mech. Found. Div., Volume 98 (1972) no. 1, pp. 95-114 | DOI

[46] Matsuoka, H.; Liu, S.; Sun, D.; Nishikata, U. Development of a new in-situ direct shear test, Geotech. Test. J, Volume 24 (2001) no. 1, pp. 92-102

[47] Moreau, J. J Unilateral contact and dry friction in finite freedom dynamics, Nonsmooth mechanics and Applications, Springer, 1988, pp. 1-82 | Zbl

[48] Muir Wood, D.; Maeda, K. Changing grading of soil: Effect on critical states, Acta Geotech., Volume 3 (2008), pp. 3-14 | DOI

[49] Nguyen, D. H.; Azéma, E.; Sornay, p.; Radjai, F. Effects of shape and size polydispersity on strength properties of granular materials, Phys. Rev. E, Volume 91 (2015), 032203 | DOI

[50] Nicot, F.; Hadda, N.; Guessasma, M.; Fortin, J.; Millet, O. On the definition of the stress tensor in granular media, Int. J. Solids Struct., Volume 50 (2013) no. 14-15, pp. 2508-2517 | DOI

[51] Nouguier-Lehon, C. Effect of the grain elongation on the behaviour of granular materials in biaxial compression, C. R. Mécanique, Volume 338 (2010) no. 10, pp. 587-595 (Micromechanics of granular materials) | DOI | Zbl

[52] Ovalle, C.; Dano, C. Effects of particle size–strength and size–shape correlations on parallel grading scaling, Geotech. Lett., Volume 10 (2020) no. 2, pp. 191-197 | DOI

[53] Ovalle, C.; Dano, C.; Hicher, P.-Y.; Cisternas, M. Experimental framework for evaluating the mechanical behavior of dry and wet crushable granular materials based on the particle breakage ratio, Can. Geotech. J., Volume 52 (2015) no. 5, pp. 587-598 | DOI

[54] Ovalle, C.; Frossard, E.; Dano, C.; Hu, W.; Maiolino, S.; Hicher, P. Y. The effect of size on the strength of coarse rock aggregates and large rockfill samples through experimental data, Acta Mech., Volume 225 (2014), pp. 2199-2216 | DOI | Zbl

[55] Ovalle, C.; Linero, S.; Dano, C.; Bard, E.; Hicher, P.-Y.; Osses, R. Data Compilation from Large Drained Compression Triaxial Tests on Coarse Crushable Rockfill Materials, J. Geotech. Geoenviron., Volume 146 (2020), 06020013 | DOI

[56] Rothenburg, L.; Bathurst, R. J. Analytical study of induced anisotropy in idealized granular materials, Geotechnique, Volume 39 (1989) no. 4, pp. 601-614 | DOI

[57] Radjai, F.; Richefeu, V. Contact dynamics as a nonsmooth discrete element method, Mech. Mater., Volume 41 (2009) no. 6, pp. 715-728 (Advances in the Dynamics of Granular Materials) | DOI

[58] Saussine, G.; Cholet, C.; Gautier, P.E.; Dubois, F.; Bohatier, C.; Moreau, J.J. Modelling ballast behaviour under dynamic loading. Part 1: A 2D polygonal discrete element method approach, Comput. Methods Appl. Mech. Eng., Volume 195 (2006) no. 19, pp. 2841-2859 | DOI | Zbl

[59] Schuhmacher, P. Rhéologie des écoulements granulaires : variables internes et effets d’échelle, Thesis, Université Montpellier (2016)

[60] Visscher, W. M.; Bolsterli, M. Random packing of equal and unequal spheres in two and three dimensions, Nature, Volume 239 (1972), pp. 504-507 | DOI

[61] Verdugo, R.; de La Hoz, K. Strength and stiffness of coarse granular soils, Soil stress-strain behavior: Measurement, modeling and analysis, Springer, 2007, pp. 243-252

[62] Voivret, C.; Radjai, F.; Delenne, J. Y.; El Youssoufi, M. S. Space-filling properties of polydisperse granular media, Phys Rev. E, Volume 76 (2007), 021301 | DOI

[63] Voivret, Charles; Radjai, Farhang; Delenne, J-Y; El Youssoufi, Moulay Saıd Space-filling properties of polydisperse granular media, Phys. Rev. E, Volume 76 (2007) no. 2, 021301 | DOI

[64] Varadarajan, A.; Sharma, KG.; Venkatachalam, K.; Gupta, AK. Testing and modeling two rockfill materials, J. Geotech. Geoenviron., Volume 129 (2003) no. 3, pp. 206-218 | DOI

[65] Wadell, Hakon Sphericity and roundness of rock particles, The Journal of Geology, Volume 41 (1933) no. 3, pp. 310-331 | DOI

[66] Xiao, Y.; Liu, H.; Chen, Y.; Zhang, W. Particle size effects in granular soils under true triaxial conditions, Géotechnique, Volume 64 (2014) no. 8, pp. 667-672 | DOI

[67] Xiao, Y.; Long, L.; Matthew Evans, T.; Zhou, H.; Liu, H.; Stuedlein, A. W. Effect of particle shape on stress-dilatancy responses of medium-dense sands, J. Geotech. Geoenviron., Volume 145 (2019), 04018105 | DOI

[68] Yang, J.; Luo, X. D. The critical state friction angle of granular materials: does it depend on grading?, Acta Geotech., Volume 13 (2018), pp. 535-547 | DOI

[69] Youd, T. L.; Nichols, D.R.; Helley, E.J.; LaJoie, K.R. Liquefaction potential of unconsolidated sediments in the southern San Francisco Bay Region, California (1973) (Technical report)

[70] Zheng, J.; Hryciw, R. D. Index void ratios of sands from their intrinsic properties, J. Geotech. Geoenviron., Volume 142 (2016) no. 12, 06016019 | DOI

[71] Zeller, J.; Wullimann, R. The shear strength of the shell materials for the Go-Schenenalp Dam, Switzerland, 4th International Conference on Soil Mechanics and Foundation Engineering, Volume 2 (1957), pp. 399-415

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