Interactive Role of Rolling Friction and Cohesion on the Angle of Repose through a Microscale Assessment
Publication: International Journal of Geomechanics
Volume 23, Issue 1
Abstract
Cohesion and rolling friction play key roles in governing the behavior of soil; however, only a limited number of studies have been able to assess the simultaneous contributions of these two microparameters on the macroproperties of soil. In this respect, the innovation of the current study includes an attempt to examine the interplay of these two primary parameters on the angle of repose (AoR) based on the discrete-element method (DEM). Lifting cylinder tests on cohesive wet sand have been carried out in DEM, while the cohesion and rolling friction are captured through proposed computational models. In this paper, macroparameters, such as the geometry and developmental stages of sand piles obtained in DEM simulation, are compared with experimental data, while their microevolution is quantified in detail. The results show that a large AoR can only be obtained when the cohesive and rotational frictional forces work in tandem. Increasing the cohesion and rolling friction results in smaller contact numbers, with increasing chain-like connections between particles and larger pore spaces to account for a larger AoR. For the first time, this study distinctly identifies three major stages that contribute to the AoR, based on the development of contact numbers and the transformation of energy. Accordingly, the linkage between macroscale AoR and the microstructural coordination number is formulated with varying levels of cohesion and rolling friction. The DEM results prove that the more cohesive the particles are, the greater the delay in the dissipation of kinetic energy.
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Acknowledgments
This research was supported by Transport Research Centre (TRC, UTS), and the Australian Government through the Australian Research Council’s Linkage Projects funding scheme (project LP160101254). Technical and financial support from industry partners including SMEC, Sydney Trains, ACRI and Coffey are greatly appreciated.
References
Ai, J., J.-F. Chen, J. Rotter, and J. Ooi. 2011. “Assessment of rolling resistance models in discrete element simulations.” Powder Technol. 206: 269–282. https://doi.org/10.1016/j.powtec.2010.09.030.
Amberger, S., M. Friedl, C. Goniva, S. Pirker, and C. Kloss. 2012. “Approximation of objects by spheres for multisphere simulations in DEM.” In ECCOMAS Congress. Vienna, Austria: ECCOMAS.
Barthel, E. 2008. “Adhesive elastic contacts: JKR and more.” J. Phys. 41 (16): 163001.
Beakawi Al-Hashemi, H. M., and O. S. Baghabra Al-Amoudi. 2018. “A review on the angle of repose of granular materials.” Powder Technol. 330: 397–417. https://doi.org/10.1016/j.powtec.2018.02.003.
Behjani, M. A., N. Rahmanian, N. Fardina bt Abdul Ghani, and A. Hassanpour. 2017. “An investigation on process of seeded granulation in a continuous drum granulator using DEM.” Adv. Powder Technol. 28 (10): 2456–2464. https://doi.org/10.1016/j.apt.2017.02.011.
Belheine, N., J. P. Plassiard, F. V. Donzé, F. Darve, and A. Seridi. 2009. “Numerical simulation of drained triaxial test using 3D discrete element modeling.” Comput. Geotech. 36 (1): 320–331. https://doi.org/10.1016/j.compgeo.2008.02.003.
Campillo, M., P. Pérez, J. Daher, and L. Pérez. 2021. “Percentage porosity computation of three-dimensional non-convex porous geometries using the direct Monte Carlo simulation.” Eng. Comput. 37: 951–973. https://doi.org/10.1007/s00366-019-00866-2.
Carstensen, J. T., and P.-C. Chan. 1976. “Relation between particle size and repose angles of powders.” Powder Technol. 15 (1): 129–131. https://doi.org/10.1016/0032-5910(76)80037-X.
Castellanos, A. 2005. “The relationship between attractive interparticle forces and bulk behavior in dry and uncharged fine powders.” Adv. Phys. 54 (4): 263–376. https://doi.org/10.1080/17461390500402657.
Chen, J., and A. Anandarajah. 1996. “Van der Waals attraction between spherical particles.” J. Colloid Interface Sci. 180 (2): 519–523. https://doi.org/10.1006/jcis.1996.0332.
Chen, J., J. S. Vinod, B. Indraratna, N. T. Ngo, R. Gao, and Y. Liu. 2022. “A discrete element study on the deformation and degradation of coal-fouled ballast.” Acta Geotech. 17 (9): 3977–3993. https://doi.org/10.1007/s11440-022-01453-4.
Deng, X. L., and R. N. Davé. 2013. “Dynamic simulation of particle packing influenced by size, aspect ratio and surface energy.” Granular Matter 15 (4): 401–415. https://doi.org/10.1007/s10035-013-0413-0.
Derakhshani, S. M., D. L. Schott, and G. Lodewijks. 2015. “Micro–macro properties of quartz sand: Experimental investigation and DEM simulation.” Powder Technol. 269: 127–138. https://doi.org/10.1016/j.powtec.2014.08.072.
Derjaguin, B. V., V. M. Muller, and Y. P. Toporov. 1975. “Effect of contact deformations on the adhesion of particles.” J. Colloid Interface Sci. 53 (2): 314–326. https://doi.org/10.1016/0021-9797(75)90018-1.
Einav, I. 2007. “Fracture propagation in brittle granular matter.” Proc. R. Soc. A: Math. Phys. Eng. Sci. 463: 3021–3035. https://doi.org/10.1098/rspa.2007.1898.
El-Kassem, B., N. Salloum, T. Brinz, Y. Heider, and B. Markert. 2021. “A multivariate regression parametric study on DEM input parameters of free-flowing and cohesive powders with experimental data-based validation.” Comput. Part. Mech. 8 (1): 87–111. https://doi.org/10.1007/s40571-020-00315-8.
El Shamy, U., and M. Zeghal. 2005. “Coupled continuum-discrete model for saturated granular soils.” J. Eng. Mech. 131 (4): 413–426. https://doi.org/10.1061/(ASCE)0733-9399(2005)131:4(413).
Gentilini, C., L. Govoni, S. Miranda, G. Gottardi, and F. Ubertini. 2012. “Three-dimensional numerical modelling of falling rock protection barriers.” Comput. Geotech. 44: 58–72. https://doi.org/10.1016/j.compgeo.2012.03.011.
Goniva, C., C. Kloss, N. G. Deen, J. A. M. Kuipers, and S. Pirker. 2012. “Influence of rolling friction on single spout fluidized bed simulation.” Particuology 10 (5): 582–591. https://doi.org/10.1016/j.partic.2012.05.002.
Goudarzy, M., D. Sarkar, W. Lieske, and T. Wichtmann. 2022. “Influence of plastic fines content on the liquefaction susceptibility of sands: Monotonic loading.” Acta Geotech. 17: 1719–1737. https://doi.org/10.1007/s11440-021-01283-w.
Gratchev, I. B., K. Sassa, V. I. Osipov, and V. N. Sokolov. 2006. “The liquefaction of clayey soils under cyclic loading.” Eng. Geol. 86 (1): 70–84. https://doi.org/10.1016/j.enggeo.2006.04.006.
Grima, A. P. 2011. “Quantifying and modelling mechanisms of flow in cohesionless and cohesive granular materials.” Ph.D. thesis, School of Mechanical, Materials & Mechatronic Engineering, Univ. of Wollongong.
Hamaker, H. C. 1937. “The London—van der Waals attraction between spherical particles.” Physica 4 (10): 1058–1072. https://doi.org/10.1016/S0031-8914(37)80203-7.
Hassanzadeh, V., C. M. Wensrich, and R. Moreno-Atanasio. 2020. “Elucidation of the role of cohesion in the macroscopic behavior of coarse particulate systems using DEM.” Powder Technol. 361: 374–388. https://doi.org/10.1016/j.powtec.2019.07.070.
He, Y., A. Hassanpour, M. Alizadeh Behjani, and A. E. Bayly. 2021. “A novel stiffness scaling methodology for discrete element modelling of cohesive fine powders.” Appl. Math. Modell. 90: 817–844. https://doi.org/10.1016/j.apm.2020.08.062.
Hertz, H. 1881. “On the contact of elastic solids.” Z. Reine Angew. Math. 92: 156–171.
Hoshishima, C., S. Ohsaki, H. Nakamura, and S. Watano. 2021. “Parameter calibration of discrete element method modelling for cohesive and non-spherical particles of powder.” Powder Technol. 386: 199–208. https://doi.org/10.1016/j.powtec.2021.03.044.
Huang, H., and E. Tutumluer. 2011. “Discrete element modeling for fouled railroad ballast.” Constr. Build. Mater. 25 (8): 3306–3312. https://doi.org/10.1016/j.conbuildmat.2011.03.019.
Indraratna, B., M. Phan Nghi, T. Nguyen Thanh, and J. Huang. 2021. “Simulating subgrade soil fluidization using LBM-DEM coupling.” Int. J. Geomech. 21 (5): 04021039. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001997.
Iwashita, K., and M. Oda. 1998. “Rolling resistance at contacts in simulation of shear band development by DEM.” J. Eng. Mech. 124 (3): 285–292. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:3(285).
Johnson, K. L., and J. A. Greenwood. 1997. “An adhesion map for the contact of elastic spheres.” J. Colloid Interface Sci. 192 (2): 326–333. https://doi.org/10.1006/jcis.1997.4984.
Johnson, K. L., K. Kendall, A. D. Roberts, and D. Tabor. 1971. “Surface energy and the contact of elastic solids.” Proc. R. Soc. A: Math. Phys. Sci. 324 (1558): 301–313. https://doi.org/10.1098/rspa.1971.0141.
Kermani, E., and T. Qiu. 2020. “Simulation of quasi-static axisymmetric collapse of granular columns using smoothed particle hydrodynamics and discrete element methods.” Acta Geotech. 15: 423–437. https://doi.org/10.1007/s11440-018-0707-9.
Kermani, E., T. Qiu, and T. Li. 2015. “Simulation of collapse of granular columns using the discrete element method.” Int. J. Geomech. 15 (6): 04015004. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000467.
Kloss, C., and C. Goniva. 2011. “LIGGGHTS – open source discrete element simulations of granular materials based on lammps.” In Vol. 2 of Supplemental Proc.: Materials, Fabrication, Properties, Characterization and Modeling, 781–788. Hobokan, NJ: John Wiley & Sons.
Lajeunesse, E., A. Mangeney-Castelnau, and J. P. Vilotte. 2004. “Spreading of a granular mass on a horizontal plane.” Phys. Fluids 16 (7): 2371–2381. https://doi.org/10.1063/1.1736611.
Li, S., J. S. Marshall, G. Liu, and Q. Yao. 2011. “Adhesive particulate flow: The discrete-element method and its application in energy and environmental engineering.” Prog. Energy Combust. Sci. 37 (6): 633–668. https://doi.org/10.1016/j.pecs.2011.02.001.
Li, Y., Y. Xu, and C. Thornton. 2005. “A comparison of discrete element simulations and experiments for ‘sandpiles’ composed of spherical particles.” Powder Technol. 160 (3): 219–228. https://doi.org/10.1016/j.powtec.2005.09.002.
Liu, Y., H. Liu, and H. Mao. 2018. “The influence of rolling resistance on the stress-dilatancy and fabric anisotropy of granular materials.” Granular Matter 20: 12. https://doi.org/.1007/s10035-017-0780-z.
Lommen, S., D. Schott, and G. Lodewijks. 2014. “DEM speedup: Stiffness effects on behavior of bulk material.” Particuology 12: 107–112. https://doi.org/10.1016/j.partic.2013.03.006.
Louati, H., X. Bednarek, S. Martin, A. Ndiaye, and O. Bonnefoy. 2019. “Qualitative and quantitative DEM analysis of cohesive granular material behavior in FT4 shear tester.” Chem. Eng. Res. Des. 148: 155–163. https://doi.org/10.1016/j.cherd.2019.05.059.
Mason, T., A. Levine, D. Ertaş, and T. T. C. Halsey. 1999. “Critical angle of wet sandpiles.” Phys. Rev. E: Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 60: R5044–R5047. https://doi.org/10.1103/PhysRevE.60.R5044.
Matsusaka, S., H. Maruyama, T. Matsuyama, and M. Ghadiri. 2010. “Triboelectric charging of powders: A review.” Chem. Eng. Sci. 65 (22): 5781–5807. https://doi.org/10.1016/j.ces.2010.07.005.
Meier, C., R. Weissbach, J. Weinberg, W. A. Wall, and A. John Hart. 2019. “Modeling and characterization of cohesion in fine metal powders with a focus on additive manufacturing process simulations.” Powder Technol. 343: 855–866. https://doi.org/10.1016/j.powtec.2018.11.072.
Mitarai, N., and F. Nori. 2006. “Wet granular materials.” Adv. Phys. 55 (1–2): 1–45. https://doi.org/10.1080/00018730600626065.
Muftah, A., and M. Gutierrez. 2010. “Comprehensive study of the effects of rolling resistance on the stress–strain and strain localization behavior of granular materials.” Granular Matter 12: 527–541. https://doi.org/10.1007/s10035-010-0211-x.
Nakashima, H., Y. Shioji, T. Kobayashi, S. Aoki, H. Shimizu, J. Miyasaka, and K. Ohdoi. 2011. “Determining the angle of repose of sand under low-gravity conditions using discrete element method.” J. Terramech. 48 (1): 17–26. https://doi.org/10.1016/j.jterra.2010.09.002.
Nase, S. T., W. L. Vargas, A. A. Abatan, and J. J. McCarthy. 2001. “Discrete characterization tools for cohesive granular material.” Powder Technol. 116 (2): 214–223. https://doi.org/10.1016/S0032-5910(00)00398-3.
Nguyen, N. H. T., H. H. Bui, G. D. Nguyen, and J. Kodikara. 2017. “A cohesive damage-plasticity model for DEM and its application for numerical investigation of soft rock fracture properties.” Int. J. Plast. 98: 175–196. https://doi.org/10.1016/j.ijplas.2017.07.008.
Nguyen, T. T., and B. Indraratna. 2020a. “A coupled CFD–DEM approach to examine the hydraulic critical state of soil under increasing hydraulic gradient.” Int. J. Geomech. 20 (9): 04020138. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001782.
Nguyen, T. T., and B. Indraratna. 2020b. “The role of particle shape on hydraulic conductivity of granular soils captured through Kozeny–Carman approach.” Géotech. Lett. 10 (3): 398–403. https://doi.org/10.1680/jgele.20.00032.
Nguyen, T. T., and B. Indraratna. 2022. “Fluidization of soil under increasing seepage flow: An energy perspective through CFD-DEM coupling.” Granular Matter 24 (3): 80. https://doi.org/10.1007/s10035-022-01242-6.
O’Sullivan, C. 2011. “Particle-based discrete element modeling: Geomechanics perspective.” Int. J. Geomech. 11 (6): 449–464. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000024.
Parteli, E. J. R., J. Schmidt, C. Blümel, K.-E. Wirth, W. Peukert, and T. Pöschel. 2014. “Attractive particle interaction forces and packing density of fine glass powders.” Sci. Rep. 4 (1): 6227. https://doi.org/10.1038/srep06227.
Phan, Q. T., H. H. Bui, G. D. Nguyen, and A. Bouazza. 2021. “Effect of particle rolling resistance on drained and undrained behavior of silty sand.” Acta Geotech. 16 (8): 2657–2682. https://doi.org/10.1007/s11440-020-01128-y.
Potyondy, D. O., and P. A. Cundall. 2004. “A bonded-particle model for rock.” Int. J. Rock Mech. Min. Sci. 41 (8): 1329–1364. https://doi.org/10.1016/j.ijrmms.2004.09.011.
Prokopovich, P., and S. Perni. 2011. “Comparison of JKR- and DMT-based multi-asperity adhesion model: Theory and experiment.” Colloids Surf., A 383 (1): 95–101. https://doi.org/10.1016/j.colsurfa.2011.01.011.
Rackl, M., F. E. Grötsch, M. Rusch, and J. Fottner. 2017. “Qualitative and quantitative assessment of 3D-scanned bulk solid heap data.” Powder Technol. 321: 105–118. https://doi.org/10.1016/j.powtec.2017.08.009.
Roessler, T., and A. Katterfeld. 2019. “DEM parameter calibration of cohesive bulk materials using a simple angle of repose test.” Particuology 45: 105–115. https://doi.org/10.1016/j.partic.2018.08.005.
Rognon, P., J.-N. Roux, D. Wolf, M. Naaim, and F. Chevoir. 2007. “Rheophysics of cohesive granular materials.” Europhys. Lett. 74: 644. https://doi.org/10.1209/epl/i2005-10578-y.
Roy, S., A. Singh, S. Luding, and T. Weinhart. 2016. “Micro–macro transition and simplified contact models for wet granular materials.” Comput. Part. Mech. 3 (4): 449–462. https://doi.org/10.1007/s40571-015-0061-8.
Rumpf, H. 1962. “The strength of granules and agglomerates.” In Proc., 1st Int. Symp. on Agglomeration, 379–418. New York: Wiley Interscience.
Schwarze, R., A. Gladkyy, F. Uhlig, and S. Luding. 2013. “Rheology of weakly wetted granular materials: A comparison of experimental and numerical data.” Granular Matter 15 (4): 455–465. https://doi.org/10.1007/s10035-013-0430-z.
Shan, T., and J. Zhao. 2014. “A coupled CFD-DEM analysis of granular flow impacting on a water reservoir.” Acta Mech. 225 (8): 2449–2470. https://doi.org/10.1007/s00707-014-1119-z.
Tao, J., and H. Tao. 2017. “Factors affecting piping erosion resistance: Revisited with a numerical modeling approach.” Int. J. Geomech. 17 (11): 04017097. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000999.
Terzaghi, K. 1943. Theoretical soil mechanics. New York: Wiley.
Thakur, S. C., J. P. Morrissey, J. Sun, J. F. Chen, and J. Y. Ooi. 2014. “Micromechanical analysis of cohesive granular materials using the discrete element method with an adhesive elasto-plastic contact model.” Granular Matter 16 (3): 383–400. https://doi.org/10.1007/s10035-014-0506-4.
Thoeni, K., A. Giacomini, C. Lambert, S. W. Sloan, and J. P. Carter. 2014. “A 3D discrete element modelling approach for rockfall analysis with drapery systems.” Int. J. Rock Mech. Min. Sci. 68: 107–119. https://doi.org/10.1016/j.ijrmms.2014.02.008.
Thornton, C. 2000. “Numerical simulations of deviatoric shear deformation of granular media.” Géotechnique 50 (1): 43–53. https://doi.org/10.1680/geot.2000.50.1.43.
Tsuji, Y., T. Tanaka, and T. Ishida. 1992. “Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe.” Powder Technol. 71 (3): 239–250. https://doi.org/10.1016/0032-5910(92)88030-L.
Ucgul, M., J. M. Fielke, and C. Saunders. 2014. “Three-dimensional discrete element modelling of tillage: Determination of a suitable contact model and parameters for a cohesionless soil.” Biosyst. Eng. 121: 105–117. https://doi.org/10.1016/j.biosystemseng.2014.02.005.
Wensrich, C. M., and A. Katterfeld. 2012. “Rolling friction as a technique for modelling particle shape in DEM.” Powder Technol. 217: 409–417. https://doi.org/10.1016/j.powtec.2011.10.057.
Wiącek, J., M. Molenda, J. Y. Ooi, and J. Favier. 2012. “Experimental and numerical determination of representative elementary volume for granular plant materials.” Granular Matter 14 (4): 449–456. https://doi.org/10.1007/s10035-012-0351-2.
Wu, S., Y. Chen, Y. Zhu, P. Zhang, A. Scheuermann, G. Jin, and W. Zhu. 2021. “Study on filtration process of geotextile with LBM-DEM-DLVO coupling method.” Geotext. Geomembr. 49 (1): 166–179. https://doi.org/10.1016/j.geotexmem.2020.09.011.
Xu, J. Q., R. P. Zou, and A. B. Yu. 2007. “Analysis of the packing structure of wet spheres by Voronoi–Delaunay tessellation.” Granular Matter 9 (6): 455–463. https://doi.org/10.1007/s10035-007-0052-4.
Yang, R. Y., R. P. Zou, and A. B. Yu. 2000. “Computer simulation of the packing of fine particles.” Phys. Rev. 62 (3): 3900–3908. https://doi.org/10.1103/PhysRevE.62.3900.
Yimsiri, S., and K. Soga. 2010. “DEM analysis of soil fabric effects on behavior of sand.” Géotechnique 60 (6): 483–495. https://doi.org/10.1680/geot.2010.60.6.483.
Yin, Y., Y. Cui, Y. Tang, D. Liu, M. Lei, and D. Chan. 2021. “Solid–fluid sequentially coupled simulation of internal erosion of soils due to seepage.” Granular Matter 23: 20. https://doi.org/10.1007/s10035-020-01076-0.
Yu, A., L. Liu, Z. Zhang, R. Yang, and R. Zou. 2003a. “Computer simulation of the packing of particles.” Int. J. Mater. Prod. Technol. 19 (3–4): 324–336. https://doi.org/10.1504/IJMPT.2003.002516.
Yu, A. B., C. L. Feng, R. P. Zou, and R. Y. Yang. 2003b. “On the relationship between porosity and interparticle forces.” Powder Technol. 130 (1): 70–76. https://doi.org/10.1016/S0032-5910(02)00228-0.
Zhao, J., and T. Shan. 2013. “Coupled CFD–DEM simulation of fluid–particle interaction in geomechanics.” Powder Technol. 239: 248–258. https://doi.org/10.1016/j.powtec.2013.02.003.
Zhou, B., J. Wang, and H. Wang. 2017. “Three-dimensional sphericity, roundness and fractal dimension of sand particles.” Géotechnique 68 (1): 18–30. https://doi.org/10.1680/jgeot.16.P.207.
Zhou, Y. C., B. D. Wright, R. Y. Yang, B. H. Xu, and A. B. Yu. 1999. “Rolling friction in the dynamic simulation of sandpile formation.” Phys. A: Stat. Mech. Appl. 269 (2): 536–553. https://doi.org/10.1016/S0378-4371(99)00183-1.
Zhou, Y. C., B. Xu, A. Yu, and P. Zulli. 2001. “Numerical investigation of the angle of repose of monosized spheres.” Phys. Rev. E: Stat. Nonlinear Soft Matter Phys. 64: 021301. https://doi.org/10.1103/PhysRevE.64.021301.
Zhu, H. P., Z. Y. Zhou, R. Y. Yang, and A. B. Yu. 2007. “Discrete particle simulation of particulate systems: Theoretical developments.” Chem. Eng. Sci. 62 (13): 3378–3396. https://doi.org/10.1016/j.ces.2006.12.089.
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Published In
International Journal of Geomechanics
Volume 23 • Issue 1 • January 2023
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Apr 7, 2022
Accepted: Aug 8, 2022
Published online: Oct 28, 2022
Published in print: Jan 1, 2023
Discussion open until: Mar 28, 2023
ASCE Technical Topics:
- Business management
- Cohesive soils
- Continuum mechanics
- Discrete element method
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering materials (by type)
- Engineering mechanics
- Friction
- Geomechanics
- Geotechnical engineering
- Innovation
- Material mechanics
- Materials engineering
- Mathematics
- Methodology (by type)
- Micromechanics
- Numerical methods
- Parameters (statistics)
- Particles
- Practice and Profession
- Soil mechanics
- Soil properties
- Soils (by type)
- Solid mechanics
- Statistics
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- Corné J. Coetzee, Otto C. Scheffler, Review: The Calibration of DEM Parameters for the Bulk Modelling of Cohesive Materials, Processes, 10.3390/pr11010005, 11, 1, (5), (2022).