Effects of the Absence of Friction in Coarse-Grained Molecular Dynamics Simulations of Clay
Publication: International Journal of Geomechanics
Volume 24, Issue 10
Abstract
Coarse-grained molecular dynamics (CGMD) simulations can advance the understanding of clay behavior. In CGMD simulations, the interactions between clay platelets are modeled and the data generated can be used to quantitatively link the clay fabric to the overall material behavior and examine its sensitivity to changes in the pore-fluid chemistry. A key element of a CGMD model is the potential function employed for particle interactions. One approach is to use Derjaguin–Landau–Verwey–Overbeek (DLVO) theory to calibrate the contact models; however, DLVO theory does not account for a frictional component in the interaction. This contribution shows that omitting a frictional force results in an unexpected overall system response. The conclusion is developed by considering CGMD data generated during one-dimensional compression tests of assemblies of 10,000 kaolinite particles modelled as flat ellipsoids. When the Gay–Berne potential function, calibrated against DLVO predictions, is used to simulate the interactions and interparticle friction is not explicitly modeled, the resulting coefficient of earth pressure at rest is equal to 1. Furthermore, the packing density obtained in the CGMD is lower than that observed experimentally. Additional data generated using DEM simulations on assemblies of spherical particles demonstrate the sensitivity of K0 and packing density to the interparticle friction coefficient. Data presented here clearly support the need to explicitly consider a frictional-type component in particle interactions when simulating systems of clay platelets.
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Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
Dr. Bandera’s research was funded by the Leverhulme Trust with Project No. RPG-2017-055. Dr. Morimoto’s contribution to this manuscript was supported thanks to funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement MATHEGRAM No. 813202. Simulations were carried out using the High-Performance Computer (HPC) facilities at Imperial College London.
Notation
The following symbols are used in this paper:
- Cc [−]
- compression index;
- D50 [mm]
- mean particle diameter;
- e [−]
- void ratio;
- e100kPa [−]
- void ratio at the end of 1D compression (i.e., );
- G [Pa]
- shear modulus;
- h12 [nm]
- closest distance between particle surfaces used in repulsive GB potential function;
- coefficient of lateral earth pressure at rest;
- Lx, Ly, Lz [nm]
- specimen dimensions along Cartesian axes;
- [J]
- repulsive component of the pairwise Gay–Berne potential energy computed using γsb;
- γsb [−]
- pairwise shift of the potential minimum used in repulsive GB potential function;
- energy scale used in repulsive GB potential function;
- relative well depth value for face–face interaction;
- relative well depth value for edge–edge interaction;
- η [−]
- shape anisotropy used in repulsive GB potential function;
- μ [−]
- friction coefficient;
- ν [−]
- Poisson’s ratio;
- σ [nm]
- length scale used in repulsive GB potential function;
- horizontal normal stress;
- vertical normal stress;
- σij [kPa]
- component of stress tensor in Cartesian coordinate system, for example, σxx, σxy, and so forth;
- [kPa]
- initial vertical effective stress considered for the evaluation of the compression index Cc;
- final vertical effective stress considered for the evaluation of the compression index Cc; and
- χ [−]
- energy anisotropy used in repulsive GB potential function.
References
Allen, M. P., and D. J. Tildesley. 1987. Computer simulation of liquids. New York: Oxford Science Publications.
Aminpour, P., and K. J. Sjoblom. 2019. “Multi-scale modelling of kaolinite triaxial behaviour.” Géotechnique Lett. 9: 178–185. https://doi.org/10.1680/jgele.18.00194.
Amontons, G. 1699. De la Resistance Causée dans les Machines: Mémoires de l’Académie Royale, A, Chez Gerard Kuyper, 257–282. Amsterdam, Netherlands: Springer.
Anandarajah, A. 2000. “Numerical simulation of one-dimensional behaviour of a kaolinite.” Géotechnique 50: 509–519. https://doi.org/10.1680/geot.2000.50.5.509.
Atkinson, J. H., D. Richardson, and P. J. Robinson. 1987. “Compression and extension of K0 normally consolidated Kaolin Clay.” J. Geotech. Eng. 113: 1468–1482. https://doi.org/10.1061/(ASCE)0733-9410(1987)113:12(1468).
Azéma, É., F. Radjaï, and J.-N. Roux. 2018. “Inertial shear flow of assemblies of frictionless polygons: Rheology and microstructure.” Eur. Phys. J. E 41: 2. https://doi.org/10.1140/epje/i2018-11608-9.
Bandera, S. 2022. “Fundamental analysis of the influence of structure on clay behaviour.” Ph.D. thesis, Dept. of Civil and Environmental Engineering, Imperial College London.
Bandera, S., C. O’Sullivan, P. Tangney, and S. Angioletti-Uberti. 2021. “Coarse-grained molecular dynamics simulations of clay compression.” Comput. Geotech. 138: 104333. https://doi.org/10.1016/j.compgeo.2021.104333.
Bandera, S., C. O’Sullivan, P. Tangney, and S. Angioletti-Uberti. 2022. Modified LAMMPS Gay-Berne subroutine to simulate purely repulsive colloidal systems. Geneva, Switzerland: Zenodo.
Brown, W. M., M. K. Petersen, S. J. Plimpton, and G. S. Grest. 2009. “Liquid crystal nanodroplets in solution.” J. Chem. Phys. 130 (4): 044901. https://doi.org/10.1063/1.3058435.
Cundall, P. A., and O. D. L. Strack. 1979. “A discrete numerical model for granular assemblies.” Géotechnique 29: 47–65. https://doi.org/10.1680/geot.1979.29.1.47.
de Bono, J., and G. McDowell. 2023. “Simulating multifaceted interactions between kaolinite platelets.” Powder Technol. 413: 118062. https://doi.org/10.1016/j.powtec.2022.118062.
de Bono, J. P., and G. R. McDowell. 2022a. “Discrete element modelling of normal compression of clay.” J. Mech. Phys. Solids 162: 104847. https://doi.org/10.1016/j.jmps.2022.104847.
de Bono, J. P., and G. R. McDowell. 2022b. “Some important aspects of modelling clay platelet interactions using DEM.” Powder Technol. 398: 117056. https://doi.org/10.1016/j.powtec.2021.117056.
Derjaguin, B., and L. Landau. 1993. “Theory of the stability of strongly charged lyophobic sols and of the adhesion of strongly charged particles in solutions of electrolytes.” Prog. Surf. Sci. 43: 30–59. https://doi.org/10.1016/0079-6816(93)90013-L.
Ebrahimi, D., A. J. Whittle, and R. J.-M. Pellenq. 2014. “Mesoscale properties of clay aggregates from potential of mean force representation of interactions between nanoplatelets.” J. Chem. Phys. 140: 154309. https://doi.org/10.1063/1.4870932.
Everaers, R., and M. R. Ejtehadi. 2003. “Interaction potentials for soft and hard ellipsoids.” Phys. Rev. E 67: 041710. https://doi.org/10.1103/PhysRevE.67.041710.
Frenkel, D., and B. Smit. 2002. Understanding molecular simulation: From algorithms to applications. 2nd ed. Computational Science Series. San Diego: Academic Press.
Gao, J., W. D. Luedtke, D. Gourdon, M. Ruths, J. N. Israelachvili, and U. Landman. 2004. “Frictional forces and amontons” Law: from the molecular to the macroscopic scale.” J. Phys. Chem. B 108: 3410–3425. https://doi.org/10.1021/jp036362l.
Gao, J., W. D. Luedtke, and U. Landman. 1997. “Structure and solvation forces in confined films: Linear and branched alkanes.” J. Chem. Phys. 106: 4309–4318. https://doi.org/10.1063/1.473132.
Gay, J. G., and B. J. Berne. 1981. “Modification of the overlap potential to mimic a linear site–site potential.” J. Chem. Phys. 74: 3316–3319. https://doi.org/10.1063/1.441483.
Göncü, F., O. Durán, S. Luding, M. Nakagawa, and S. Luding. 2009. “Jamming in frictionless packings of spheres: Determination of the critical volume fraction.” AIP Conf. Proc. 1145: 531–534. https://doi.org/10.1063/1.3179980.
Guo, Y., and X. Yu. 2019. “A holistic computational model for prediction of clay suspension structure.” Int. J. Sediment Res. 34: 345–354. https://doi.org/10.1016/j.ijsrc.2018.12.002.
Gupta, V., M. A. Hampton, J. R. Stokes, A. V. Nguyen, and J. D. Miller. 2011. “Particle interactions in kaolinite suspensions and corresponding aggregate structures.” J. Colloid Interface Sci. 359: 95–103. https://doi.org/10.1016/j.jcis.2011.03.043.
Hanley, K. J., X. Huang, and C. O’Sullivan. 2018. “Energy dissipation in soil samples during drained triaxial shearing.” Géotechnique 68: 421–433. https://doi.org/10.1680/jgeot.16.P.317.
Huang, X. 2014. “Exploring critical-state behaviour using DEM.” Ph.D. thesis, Dept. of Civil and Environmental Engineering, Univ. of Hong Kong and Imperial College London.
Israelachvili, J. N. 2011. Intermolecular and surface forces. 3rd ed. Burlington, MA: Academic Press.
Jaradat, K. A., and S. L. Abdelaziz. 2019. “On the use of discrete element method for multi-scale assessment of clay behavior.” Comput. Geotech. 112: 329–341. https://doi.org/10.1016/j.compgeo.2019.05.001.
Keishing, J., X. Huang, and K. J. Hanley. 2020. “Energy dissipation in soil samples during cyclic triaxial simulations.” Comput. Geotech. 121: 103481. https://doi.org/10.1016/j.compgeo.2020.103481.
Kumar, N., M. P. Andersson, D. van den Ende, F. Mugele, and I. Siretanu. 2017. “Probing the surface charge on the basal planes of kaolinite particles with high-resolution atomic force microscopy.” Langmuir 33: 14226–14237. https://doi.org/10.1021/acs.langmuir.7b03153.
Lennard-Jones, J. E. 1931. “Cohesion.” Proc. Phys. Soc. 43: 461–482. https://doi.org/10.1088/0959-5309/43/5/301.
Liu, J., C.-L. Lin, and J. D. Miller. 2015. “Simulation of cluster formation from kaolinite suspensions.” Int. J. Miner. Process. 145: 38–47. https://doi.org/10.1016/j.minpro.2015.07.004.
Mitchell, J. K., and K. Soga. 2005. Fundamentals of soil behavior. 3rd ed. Hoboken, NJ: Wiley.
O’Sullivan, C., and J. D. Bray. 2004. “Selecting a suitable time step for discrete element simulations that use the central difference time integration scheme.” Eng. Comput. 21: 278–303. https://doi.org/10.1108/02644400410519794.
Otsubo, M. 2016. “Particle scale analysis of soil stiffness and elastic wave propagation.” Ph.D. thesis, Dept. of Civil and Environmental Engineering, Imperial College London.
Ouaguenouni, S., and J.-N. Roux. 1997. “Force distribution in frictionless granular packings at rigidity threshold.” Europhys. Lett. 39: 117–122. https://doi.org/10.1209/epl/i1997-00324-1.
Pagano, A. G., F. Alonso-Marroquin, K. Ioannidou, F. Radjaï, and C. O’Sullivan. 2023. “Clay micromechanics: Mapping the future of particle-scale modelling of clay.” In Proc., 8th Int. Symp. on Deformation Characteristics of Geomaterials. London, UK: ISSMGE.
Pagano, A. G., V. Magnanimo, T. Weinhart, and A. Tarantino. 2020. “Exploring the micromechanics of non-active clays by way of virtual DEM experiments.” Géotechnique 70: 303–316. https://doi.org/10.1680/jgeot.18.P.060.
Pedrotti, M., and A. Tarantino. 2018. “An experimental investigation into the micromechanics of non-active clays.” Géotechnique 68: 666–683. https://doi.org/10.1680/jgeot.16.P.245.
Peyneau, P.-E., and J.-N. Roux. 2008. “Frictionless bead packs have macroscopic friction, but no dilatancy.” Phys. Rev. E 78: 011307. https://doi.org/10.1103/PhysRevE.78.011307.
Ringlein, J., and M. O. Robbins. 2004. “Understanding and illustrating the atomic origins of friction.” Am. J. Phys. 72: 884–891. https://doi.org/10.1119/1.1715107.
Santamarina, C. J., K. A. Klein, and M. A. Fam. 2001. Soils and waves: Particulate materials behavior, characterization and process monitoring. Hoboken, NJ: Wiley.
Senetakis, K., M. R. Coop, and M. C. Todisco. 2013. “The inter-particle coefficient of friction at the contacts of Leighton Buzzard sand quartz minerals.” Soils Found. 53: 746–755. https://doi.org/10.1016/j.sandf.2013.08.012.
Shinoda, W., M. Shiga, and M. Mikami. 2004. “Rapid estimation of elastic constants by molecular dynamics simulation under constant stress.” Phys. Rev. B 69: 134103. https://doi.org/10.1103/PhysRevB.69.134103.
Sjoblom, K. J. 2016. “Coarse-grained molecular dynamics approach to simulating clay behavior.” J. Geotech. Geoenviron. Eng. 142: 06015013. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001394.
Thompson, A. P., et al. 2022. “LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales.” Comput. Phys. Commun. 271: 108171. https://doi.org/10.1016/j.cpc.2021.108171.
Tuckerman, M. E. 2010. Statistical mechanics: Theory and molecular simulation. Oxford, UK: Oxford University Press.
Verwey, E. J. W., and J. T. G. Overbeek. 1948. Theory of the stability of lyophobic colloids: The interaction of sol particles having an electric double layer. Amsterdam, Netherlands: Elsevier Publishing Company Inc.
Wang, Y.-H., and W.-K. Siu. 2006. “Structure characteristics and mechanical properties of kaolinite soils. II. Effects of structure on mechanical properties.” Can. Geotech. J. 43: 601–617. https://doi.org/10.1139/t06-027.
Yao, M. 2001. “Three-dimensional discrete element method analysis of cohesive sols.” Ph.D. thesis, Dept. of Civil Engineering, John Hopkins Univ.
Yao, M., and A. Anandarajah. 2003. “Three-Dimensional discrete element method of analysis of clays.” J. Eng. Mech. 129: 585–596. https://doi.org/10.1061/(ASCE)0733-9399(2003)129:6(585).
Yesufu-Rufai, S., M. Rücker, S. Berg, S. F. Lowe, F. Marcelis, A. Georgiadis, and P. Luckham. 2020. “Assessing the wetting state of minerals in complex sandstone rock in-situ by Atomic Force Microscopy (AFM).” Fuel 273: 117807. https://doi.org/10.1016/j.fuel.2020.117807.
Youd, T. L. 1973. Factors controlling maximum and minimum densities of sands. ASTM Special Technical Publications. West Conshohocken, PA: ASTM.
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Published In
International Journal of Geomechanics
Volume 24 • Issue 10 • October 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: May 22, 2023
Accepted: Mar 25, 2024
Published online: Jul 22, 2024
Published in print: Oct 1, 2024
Discussion open until: Dec 22, 2024
ASCE Technical Topics:
- Clays
- Coarse-grained soils
- Continuum mechanics
- Dynamics (solid mechanics)
- Engineering materials (by type)
- Engineering mechanics
- Friction
- Geomechanics
- Geotechnical engineering
- Material mechanics
- Material properties
- Materials engineering
- Particles
- Soil dynamics
- Soil mechanics
- Soil properties
- Soils (by type)
- Solid mechanics
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