Discrete element modelling is commonly used for particle-scale modelling of granular or particulate materials. Developing a DEM model requires the determination of a number of micro-structural parameters, including the particle contact stiffness and the particle-particle friction. These parameters cannot easily be measured in the laboratory or directly related to measurable, physical material parameters. Therefore, a calibration process is typically used to determine the values for use in simulations of physical systems. This paper focuses on how to define the particle stiffness for the discrete element modelling in order to perform realistic simulations of granular materials in the case of linear contact model. For that, laboratory tests and numerical discrete element modelling of triaxial compression tests have been carried out on two different non-cohesive soils i.e. poorly graded fine sand and gap graded coarse sand. The results of experimental tests are used to calibrate the numerical model. It is found that the numerical results are qualitatively and quantitatively in good agreement with the laboratory tests results. Moreover, the results show that the stress dependent of soil behaviour can be reproduced well by assigning the particle stiffness as a function of the particle size particularly for gap graded soil.
KeywordsGrain Size Dependent StiffnessExperimentDiscrete Element ModellingTriaxial Compression TestNon-Cohesive Soils Materials
Belheine, N., Plassiard, J.P, Donzé, F.V., Darve, F. and Seridi, A. (2009) Numerical Simulation of Drained Triaxial Test Using 3D Discrete Element Modelling. Computers and Geotechnics, 36, 320-320. https://doi.org/10.1016/j.compgeo.2008.02.003
Hu, M., O’Sullivan, C., Jardine, R.R. and Jiang, M. (2010) Stress-Induced Anisotropy in Sand under Cyclic Loading. Granular Matter, 12, 469-476. https://doi.org/10.1007/s10035-010-0206-7
Arthur, J.R.F. and Menzies, B.K. (1972) Inherent Anisotropy in a Sand. Géotechnique, 22, 115-128. https://doi.org/10.1680/geot.1972.22.1.115
Cundall, P.A. (1971) A Computer Model for Simulating Progressive Largescale Movements in Blocky Rock Systems. Proceedings of the Symposium of the International Society of Rock Mechanics, 2, 2-8.
Cundall, P.A. and Hart, R.D. (1979) The Development of Constitutive Laws for Soil Using the Distinct Element Method. In: Wittke, W., Ed., Numerical Methods in Geomechanics, Routledge, Aachen, Germany, 289-298.
Cundall, P.A. and Hart, R.D. (1992) Numerical Modelling of Discontinua. Engineering Computations. International Journal for Computer-Aided Engineering and Software, 9, 101-113. https://doi.org/10.1108/eb023851
Cundall, P.A. (2001) A Discontinuous Future for Numerical Modelling in Geomechanics? Proceedings of the Institution of Civil Engineers, Geotechnical Engineering, 149, 41-47. https://doi.org/10.1680/geng.2001.149.1.41
Cundall, P.A. and Strack, O.D.L. (1979) A Discrete Numerical Model for Granular Assemblies. Géotechnique, 29, 47-65. https://doi.org/10.1680/geot.1979.29.1.47
Bagi, K. (2005) An Algorithm to Generate Random Dense Arrangements for Discrete Element Simulations of Granular Assemblies. Granular Matter, 7, 31-43. https://doi.org/10.1007/s10035-004-0187-5
Coetzee, C.J. and Els, D.N.J. (2009) The Numerical Modelling of Excavator Bucket Filling Using DEM. Journal of Terramechanics, 46, 217-227. https://doi.org/10.1016/j.jterra.2009.05.003
Harkness, J., Zervos, A., Le Pen, L., Aingaran, S. and Powrie, W. (2016) Discrete Element Simulation of Railway Ballast: Modelling Cell Pressure Effects in Triaxial Tests. Granular Matter, 18, 65. https://doi.org/10.1007/s10035-016-0660-y
Stahl, M. and Konietzky, H. (2011) Discrete Element Simulation of Ballast and Gravel under Special Consideration of Grain-Shape, Grain-Size and Relative Density. Granular Matter, 13, 417-428. https://doi.org/10.1007/s10035-010-0239-y
Indraratna, B., Thakur, P.K. and Vinod, J.S. (2009) Experimental and Numerical Study of Railway Ballast Behavior under Cyclic Loading. International Journal of Geomechanics, 10, 136-144. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000055
Lu, M. and McDowell, G. (2010) Discrete Element Modelling of Railway Ballast under Monotonic and Cyclic Triaxial Loading. Géotechnique, 60, 459-467. https://doi.org/10.1680/geot.2010.60.6.459
Suhr, B. and Six, K. (2017) Friction Phenomena and Their Impact on the Shear Behaviour of Granular Material. Computational Particle Mechanics, 4, 23-34. https://doi.org/10.1007/s40571-016-0119-2
Chen, C., McDowell, G.R. and Thom, N.H. (2012) Discrete Element Modelling of Cyclic Loads of Geogrid-Reinforced Ballast under Confined and Unconfined Conditions. Geotextiles and Geomembranes, 35, 76-86. https://doi.org/10.1016/j.geotexmem.2012.07.004
Van Lysebetten, G., Vervoort, A., Maertens, J. and Huybrechts, N. (2014) Discrete Element Modeling for the Study of the Effect of Soft Inclusions on the Behavior of Soil Mix Material. Computers and Geotechnics, 55, 342-351. https://doi.org/10.1016/j.compgeo.2013.09.023
Grima, A.P. and Wypych, P.W. (2010) Discrete Element Simulation of a Conveyor Impact-Plate Transfer: Calibration, Validation and Scale-Up. Australian Bulk Handling Review, 3, 64-72.
Grima, A.P., Fraser, T. and Hastie, D.B. (2011) Discrete Element Modelling: Trouble-Shooting and Optimisation Tool for Chute Design. Beltcon, 16, 1-26.
Boac, J.M., Ambrose, R.P.K., Casada, M.E., Maghirang, R.G. and Maier, D.E. (2014) Applications of Discrete Element Method in Modeling of Grain Postharvest Operations. Food Engineering Reviews, 6, 128-149. https://doi.org/10.1007/s12393-014-9090-y
Coetzee, C.J. and Els, D.N.J. (2009) Calibration of Discrete Element Parameters and the Modelling of Silo Discharge and Bucket Filling. Computers and Electronics in Agriculture, 65, 198-212. https://doi.org/10.1016/j.compag.2008.10.002
Coetzee, C.J. and Els, D.N.J. (2009) Calibration of Granular Material Parameters for DEM Modelling and Numerical Verification by Blade-Granular Material Interaction. Journal of Terramechanics, 46, 15-26. https://doi.org/10.1016/j.jterra.2008.12.004
Coetzee, C.J., Els, D.N.J. and Dymond, G.F. (2010) Discrete Element Parameter Calibration and the Modelling of Dragline Bucket Filling. Journal of Terramechanics, 47, 33-44. https://doi.org/10.1016/j.jterra.2009.03.003
Alian, M., Ein-Mozaffari, F. and Upreti, S.R. (2015) Analysis of the Mixing of Solid Particles in a Plowshare Mixer via Discrete Element Method (DEM). Powder Technology, 274, 77-87. https://doi.org/10.1016/j.powtec.2015.01.012
Cleary, P.W. (2015) A Multiscale Method for Including Fine Particle Effects in DEM Models of Grinding Mills. Minerals Engineering, 84, 88-99. https://doi.org/10.1016/j.mineng.2015.10.008
Cleary, P.W., Sinnott, M.D. and Pereira, G.G. (2015) Computational Prediction of Performance for a Full Scale Isamill: Part 1—Media Motion and Energy Utilisation in a Dry Mill. Minerals Engineering, 79, 220-238.
Coetzee, C.J. (2016) Calibration of the Discrete Element Method and the Effect of Particle Shape. Powder Technology, 297, 50-70. https://doi.org/10.1016/j.powtec.2016.04.003
Marigo, M. and Stitt, E.H. (2015) Discrete Element Method (DEM) for Industrial Applications: Comments on Calibration and Validation for the Modelling of Cylindrical Pellets. KONA Powder and Particle Journal, 32, 236-252. https://doi.org/10.14356/kona.2015016
Coetzee, C.J. (2017) Review: Calibration of the Discrete Element Method. Powder Technology, 310, 104-142. https://doi.org/10.1016/j.powtec.2017.01.015
Plassiard, J.P., Belheine, N. and Donzé, F.V. (2009) A Spherical Discrete Element Model: Calibration Procedure and Incremental Response. Granular Matter, 11, 293-306. https://doi.org/10.1007/s10035-009-0130-x
De Bono, J.P. and McDowell, G.R. (2014) DEM of Triaxial Tests on Crushable Sand. Granular Matter, 16, 551-562. https://doi.org/10.1007/s10035-014-0500-x
McDowell, G.R. and Li, H. (2016) Discrete Element Modelling of Scaled Railway Ballast under Triaxial Conditions. Granular Matter, 18, 66. https://doi.org/10.1007/s10035-016-0663-8
Zhao, X. and Evans, T.M. (2011) Numerical Analysis of Critical State Behaviors of Granular Soils under Different Loading Conditions. Granular Matter, 13, 751-764. https://doi.org/10.1007/s10035-011-0284-1
Lommen, S., Schott, D. and Lodewijks, G. (2014) DEM Speedup: Stiffness Effects on Behavior of Bulk Material. Particuology, 12, 107-112. https://doi.org/10.1016/j.partic.2013.03.006
Li, S., Li, D., Cao, L. and Shangguan, Z. (2011) Parameter Estimation Approach for Particle Flow Model of Rockfill Materials Using Response Surface Method. ICCM, Cambridge, 1-12.
Derakhshani, S.M., Schott, D.L. and Lodewijks, G. (2015) Micro-Macro Properties of Quartz Sand: Experimental Investigation and DEM Simulation. Powder Technology, 269, 127-138. https://doi.org/10.1016/j.powtec.2014.08.072
Barrios, G.K.P., de Carvalho, R.M., Kwade, A. and Tavares, L.M. (2013) Contact Parameter Estimation for DEM Simulation of Iron Ore Pellet Handling. Powder Technology, 248, 84-93. https://doi.org/10.1016/j.powtec.2013.01.063
González-Montellano, C., Ramírez, á., Gallego, E. and Ayuga, F. (2011) Validation and Experimental Calibration of 3D Discrete Element Models for the Simulation of the Discharge Flow in Silos. Chemical Engineering Science, 66, 5116-5126. https://doi.org/10.1016/j.ces.2011.07.009
Vu-Quoc, L., Zhang, X. and Walton, O.R. (2000) A 3-D Discrete-Element Method for Dry Granular Flows of Ellipsoidal Particles. Computer Methods in Applied Mechanics and Engineering, 187, 483-528. https://doi.org/10.1016/S0045-7825(99)00337-0
González-Montellano, C., Fuentes, J.M., Ayuga-Téllez, E. and Ayuga, F. (2012) Determination of the Mechanical Properties of Maize Grains and Olives Required for Use in DEM Simulations. Journal of Food Engineering, 111, 553-562. https://doi.org/10.1016/j.jfoodeng.2012.03.017
Gonzalez-Montellano, C., Gallego, E., Rami-rez-Gomez, A. and Ayuga, F. (2012) Three Dimensional Discrete Element Models for Simulating the Filling and Emptying of Silos: Analysis of Numerical Results. Computers & Chemical Engineering, 40, 22-32. https://doi.org/10.1016/j.compchemeng.2012.02.007
Paulick, M., Morgeneyer, M. and Kwade, A. (2015) A New Method for the Determination of Particle Contact Stiffness. Granular Matter, 17, 83-93. https://doi.org/10.1007/s10035-014-0537-x
DIN 18123 (2011) Baugrund, Untersuchung von Bodenproben-Bestimmung der Korngrößenverteilung. Beuth Verlag, Berlin.
DIN 18126 (1996) Baugrund, Untersuchung von Bodenproben-Bestimmung der Dichte nichtbindiger Böden bei lockerster und dichtester Lagerung. Beuth Verlag, Berlin.
DIN 18137 (1990) Bestimmung der Scherfestigkeit, Teil 2, Triaxialversuch. Beuth Verlag, Berlin.
Ahlinhan, M.F., Wouya, E.K., Tankpinou, Y.K., Koube, M.B. and Adjovi, C.E. (2016) Experimental and Numerical Investigation of Stress Condition in Unstable Soil. Open Journal of Civil Engineering, 6, 370-380. https://doi.org/10.4236/ojce.2016.63031
Tom Woerden, F., Achmus, M. and Abdel-Rahman, K. (2004) Finite Element and Discrete Element Modelling for the Solution of Spatial Active Earth Pressure Problems. Proceedings of the 2nd International PFC Symposium on Numerical Modelling in Micromechanics via Particle Methods, Kyoto, 45-50.
Hakuno, M. and Tarumi, Y.A. (1988) Granular Assembly Simulation for the Seismic Liquefaction. Structural Engineering and Earthquake Engineering, 5, 333-342. https://doi.org/10.2208/jscej.1988.398_129
Hakuno, M. and Tarumi, Y.A. (1988) Granular Assembly Simulation for the Dynamic Liquefaction of the Sand. Natural Disaster Science, 1, 45-59.
Pohl, M. (2005) Modellierung von granularen Böden und biegsamen Bauwerken mit Hilfe der DEM am Beispiel einer eingebetteten Spundwand. PhD Berichte aus Bodenmechanik und Grundbau der Bergischen Universität-GH Wuppertal FB Bauingenieurwesen, Bericht 28.
Biarez, J. and Hicher, P. (1994) Elementary Mechanics of Soil Behaviour, Saturated Remoulded Soils. A. A. Balkema, Rotterdam.
De Bono, J.P., McDowell, G.R. and Wanatowski, D. (2014) DEM of Triaxial Tests on Cemented Sand. Granular Matter, 16, 563-572. https://doi.org/10.1007/s10035-014-0502-8
Utili, S. and Nova, R. (2008) DEM Analysis of Bonded Granular Geomaterials. International Journal for Numerical and Analytical Methods in Geomechanics, 32, 1997-2031. https://doi.org/10.1002/nag.728
Camusso, M. and Barla, M. (2009) Microparameters Calibration for Loose and Cemented Soil When Using Particle Methods. International Journal of Geomechanics, 9, 217-229. https://doi.org/10.1061/(ASCE)1532-3641(2009)9:5(217)
Bolton, M.D., Nakata, Y. and Cheng, Y.P. (2008) Micro- and Macro-Mechanical Behaviour of DEM Crushable Materials. Géotechnique, 58, 471-480. https://doi.org/10.1680/geot.2008.58.6.471
Harireche, O. and Mcdowell, G.R. (2002) Discrete Element Modelling of Yielding and Normal Compression of Sand. Géotechnique, 52, 299-304. https://doi.org/10.1680/geot.2002.52.4.299
Kozicki, J., Tejchman, J. and Mróz, Z. (2012) Effect of Grain Roughness on Strength, Volume Changes, Elastic and Dissipated Energies during Quasi-Static Homogeneous Triaxial Compression Using DEM. Granular Matter, 14, 457-468. https://doi.org/10.1007/s10035-012-0352-1