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An algorithm to generate dense and stable particle assemblies for 2D DEM simulation. (English) Zbl 07214839
Summary: The generation of discrete elements into certain domain is the first step of DEM simulation. Geometric constructive methods are becoming increasingly popular because of their high efficiency, but the tangency problem between the generated particles and the boundaries has not been well solved yet. In this paper, the complete algorithm to achieve the boundary tangency is developed. Several packings are created to evaluate the applicability of the algorithm. It shows that the generated particles are closely tangent to the boundaries, forming a dense and stable assembly. Through the uniaxial and the Brazilian tests, the particle assemblies generated by this algorithm are verified to be able to recover the mechanical behavior of rocks. Furthermore, it is verified that the stress and deformation around the borehole can be accurately simulated by using this particle model.
MSC:
65 Numerical analysis
94 Information and communication theory, circuits
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[1] Cundall, P. A.; Strack, O. D.L., A discrete numerical model for granular assemblies, Geothechnique, 29, 30, 331-336 (1979)
[2] Lee, C.; Cundall, P. A.; Potyondy, D. O., Modeling rock using bonded assemblies of circular particles, (Proceedings of North American rock mechanics symposium (1996))
[3] O’Sullivan, C., Particulate discrete element modelling: a geomechanics perspective (2011), Spon Press/Taylor & Francis
[4] Shi, Y.; Zhang, Y., Simulation of random packing of spherical particles with different size distributions, Appl Phys A, 92, 3, 621 (2008)
[5] Hitti, K.; Bernacki, M., Optimized dropping and rolling (ODR) method for packing of poly-disperse spheres, Appl Math Model, 37, 8, 5715-5722 (2013) · Zbl 1311.68171
[6] Siiriä, S.; Yliruusi, J., Particle packing simulations based on newtonian mechanics, Powder Technol, 174, 3, 82-92 (2007)
[7] Jiang, M. J.; Konrad, J. M.; Leroueil, S., An efficient technique for generating homogeneous specimens for dem studies, Comput Geotech, 30, 7, 579-597 (2003)
[8] Han, K.; Feng, Y. T.; Owen, D. R.J., Sphere packing with a geometric based compression algorithm, Powder Technol, 155, 1, 33-41 (2005)
[9] Cundall, P. A., PFC2D users’ manual (version3. 1), 325 (2004), Itasca Consulting Group Inc.: Itasca Consulting Group Inc. Minnesota
[10] Cui, L.; O’Sullivan, C., Analysis of a triangulation based approach for specimen generation for discrete element simulations, Granul Matter, 5, 3, 135-145 (2003) · Zbl 1049.74526
[11] Jerier, J. F.; Imbault, D.; Donze, F. V., A geometric algorithm based on tetrahedral meshes to generate a dense polydisperse sphere packing, Granul Matter, 11, 1, 43-52 (2009) · Zbl 1258.74211
[12] Jerier, J. F.; Richefeu, V.; Imbault, D., Packing spherical discrete elements for large scale simulations, Comput Methods Appl Mech Eng, 199, 25, 1668-1676 (2010) · Zbl 1231.74480
[13] Feng, Y. T.; Han, K.; Owen, D. R.J., Filling domains with disks: an advancing front approach, Int J Numer Methods Eng, 56, 5, 699-713 (2003) · Zbl 1078.74679
[14] Bagi, K., An algorithm to generate random dense arrangements for discrete element simulations of granular assemblies, Granul Matter, 7, 1, 31-43 (2005) · Zbl 1094.74058
[15] Zsaki, A. M., An efficient method for packing polygonal domains with disks for 2D discrete element simulation, Comput Geotech, 36, 4, 568-576 (2009)
[16] Benabbou, A.; Borouchaki, H.; Laug, P., Geometrical modeling of granular structures in two and three dimensions. Application to nanostructures, Int J Numer Methods Eng, 80, 4, 425-454 (2010) · Zbl 1176.74051
[17] Liu, J.; Yun, B.; Zhao, C., An improved specimen generation method for dem based on local delaunay tessellation and distance function, Int J Numer Anal Methods Geomech, 36, 5, 653-674 (2012)
[18] Zsaki, A. M., Filling 2D domains with disks using templates for discrete element model generation, Granul Matter, 15, 1, 109-117 (2013)
[19] Rahmani, H., Packing degree optimization of arbitrary circle arrangements by genetic algorithm, Granul Matter, 16, 5, 751-760 (2014)
[20] Lozano, E.; Roehl, D.; Celes, W., An efficient algorithm to generate random sphere packs in arbitrary domains, Comput Math Appl, 71, 8, 1586-1601 (2016)
[21] Ouyang, Y. P.; Yang, Q.; Yu, L., An efficient dense and stable particular elements generation method based on geometry, Int J Numer Methods Eng, 110, 11, 1003-1020 (2017)
[22] Potyondy, D. O.; Cundall, P. A., A bonded-particle model for rock, Int J Rock Mech Min Sci, 41, 8, 1329-1364 (2004)
[23] Wawersik, W. R.; Fairhurst, C., A study of brittle rock fracture in laboratory compression experiments, Int J Rock Mech Min Sci Geomech Abstr, 7, 5, 561-575 (1970)
[24] Hallbauer, D. K.; Wagner, H.; Cook, N. G.W., Some observations concerning the microscopic and mechanical behaviour of quartzite specimens in stiff, triaxial compression tests, Int J Rock Mech Min Sci Geomech Abstr, 10, 6, 713-726 (1973)
[25] Jaeger, J. C.; Cook, N. G.W.; Zimmerman, R., Fundamentals of rock mechanics (2009), John Wiley & Sons
[26] Guo, H.; Aziz, N. I.; Schmidt, L. C., Rock fracture-toughness determination by the Brazilian test, Eng Geol, 33, 3, 177-188 (1993)
[27] Mahabadi, O. K.; Cottrell, B. E.; Grasselli, G., An example of realistic modelling of rock dynamics problems: fem/dem simulation of dynamic Brazilian test on barre granite, Rock Mech Rock Eng, 43, 6, 707-716 (2010)
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