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Discrete element method simulation of random Voronoi grain-based models

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Abstract

The generation of random Voronoi grain-based models for DEM simulation is proposed in this investigation. Voronoi diagram has important applications in rock engineering and geological engineering. However, the application of 3D Voronoi models has been limited due to the difficulty of generating 3D Voronoi domains. Little research has been done on the Voronoi tessellations of objects with irregular shapes. Voronoi tessellations of objects with regular and irregular shapes are investigated by using the Matlab function mpt_voronoi. The proposed models are then employed to simulate micro-fracturing and tension cracks in brittle rock. The 3D Voronoi grain-based slope model is used to investigate the dynamic response and failure mechanism of the rock slopes during earthquakes. The failures of rock slopes are actually due to the increasing and expanding of the tension cracks, the development of the tension surfaces and sliding of the blocks during earthquakes. The 2D Voronoi grain-based specimen composed of clusters is adopted to carry out rock fragmentation by TBM cutters. PFC simulation results reveal that the damaged rock undergoes some volume dilation that causes the expansion of the crushed zone and the propagation of the vertical crack. The rock fragmentations are actually caused by the increasing of the tension cracks. According to the simulation, it is believed that Voronoi grain-based models will contribute to an improved knowledge of DEM simulation.

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References

  1. Cundall, P.A., Hart, R.D.: Development of Generalized 2-D and 3-D Distinct Element Programs for Modeling Jointed Rock. Itasca Consulting Group Inc, Minneapolis (1985)

    Google Scholar 

  2. Gao, F.Q., Stead, D.: The application of a modified Voronoi logic to brittle fracture modelling at the laboratory and field scale. Int. J. Rock Mech. Min. Sci. 68, 1–14 (2014)

    Google Scholar 

  3. Potyondy, D.O.: Simulation stress corrosion with a bonded-particle model for rock. Int. J. Rock Mech. Min. Sci. 44(5), 677–691 (2007)

    Article  Google Scholar 

  4. Cundall, P.A., Strack, O.D.L.: A discrete element model for granular assemblies. Geotechnique 29(1), 47–65 (1979)

    Article  Google Scholar 

  5. Jing, L.: A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering. Int. J. Rock Mech. Min. Sci. 40, 283–353 (2003)

    Article  Google Scholar 

  6. Potyondy, D.O.: The bonded-particle model as a tool for rock mechanics research and application: current trends and future directions. Geosyst. Eng. 18(1), 1–28 (2015)

    Article  Google Scholar 

  7. Cho, N., Martin, C.D., Sego, D.C.: A clumped particle model for rock. Int. J. Rock Mech. Min. Sci. 44, 997–1010 (2007)

    Article  Google Scholar 

  8. Hsieh, H.-H., Tai, W.-K.: A simple GPU-based approach for 3D Voronoi diagram construction and visualization. Simul. Model. Pract. Theory 13(8), 681–692 (2005)

    Article  Google Scholar 

  9. Alzo’ubi, A.M.: The Effect of Tensile Strength on the Stability of Rock Slopes. Ph.D. thesis. University of Alberta. (2009)

  10. Christianson, M., Board, M., Rigby, D.: UDEC Simulation of Triaxial Testing of Lithophysal Tuffs. In: Proceedings of the 41st U.S. Rock Mechanics Symposium, ARMA-06-968. (2006)

  11. Shin, W.S.: Excavation Disturbed Zone in Lac du Bonnet Granite. Ph.D. thesis. University of Alberta. (2010)

  12. Lan, H., Martin, C.D., Hu, B.: Effect of heterogeneity of brittle rock on micromechanical extensile behavior during compression loading. J. Geophys. Res. 115, 1–14 (2010)

    Article  Google Scholar 

  13. Kazerani, T., Zhao, J.: Micromechanical parameters in bonded particle method for modeling of brittle material failure. Int. J. Numer. Anal. Methods Geomech. 34(18), 1877–1895 (2010)

    Article  MATH  Google Scholar 

  14. Fernandes, D.T., Cheng, L.Y., Favero, E.H., Nishimoto, K.: A domain decomposition strategy for hybrid parallelization of moving particle semi-implicit (MPS) method for computer cluster. Clust. Comput. 18, 1329–1364 (2015)

    Article  Google Scholar 

  15. Dorronsoro, B., Nesmachnow, S.: Special issue on soft computing techniques in cluster and grid computing systems. Clust. Comput. 17, 153–154 (2014)

    Article  Google Scholar 

  16. Damjanac, B., Fairhurst, C.: Evidence for a long-term strength threshold in crystalline rock. Rock Mech. Rock Eng. 43, 513–531 (2010)

    Article  Google Scholar 

  17. Zhang, C., Suzuki, A., Ishimaru, T., Enomoto, M.: Characterization of three-dimensional grain structure in polycrystalline iron by serial sectioning. Metall. Mater. Trans. 35(7), 1927–1933 (2004)

    Article  Google Scholar 

  18. Döbrich, K., Rau, C., Krill III, C.: Quantitative characterization of the three-dimensional microstructure of polycrystalline Al–Sn using X-ray microtomography. Metall. Mater. Trans. 35(7), 1953–1961 (2004)

    Article  Google Scholar 

  19. Quey, R., Dawson, P.R., Barbe, F.: Large-scale 3D random polycrystals for the finite element method: generation, meshing and remeshing. Comput. Methods Appl. Mech. Eng. 200, 1729–1745 (2011)

    Article  MATH  Google Scholar 

  20. Itasca Consulting Group, Inc.: Universal Distinct Element Code: Theory and Background[R]. Itasca Consulting Group, Inc., Minneapolis (2013)

  21. Itasca Consulting Group, Inc.: 3 Dimensional Distinct Element Code: Theory and Background[R]. Itasca Consulting Group, Inc., Minneapolis (2013)

  22. Ghazvinian, E., Diederichs, M.S., Quey, R.: 3D random Voronoi grain-based models for simulation of brittle rock damage and fabric-guided micro-fracturing. J. Rock Mech. Geotech. Eng. 6, 506–521 (2014)

    Article  Google Scholar 

  23. Itasca Consulting Group, Inc.: Particle Flow Code in 2 Dimensions (PFC2D), Version 4.0. ICG, Minneapolis (2008)

  24. Itasca Consulting Group, Inc.: Particle Flow Code in 3 Dimensions (PFC3D), Version 4.0. ICG, Minneapolis (2008)

  25. Potyondy, D.O., Cundall, P.A.: A bonded-particle model for rock. Int. J. Rock Mech. Min. Sci. 41(8), 1329–1364 (2004)

    Article  Google Scholar 

  26. Keefer, D.K.: Landslides caused by earthquakes. Geol. Soc. Am. Bull. 95, 406–421 (1984)

    Article  Google Scholar 

  27. Keefer, D.K.: Rock avalanches caused by earthquakes: source characteristics. Science 223, 1288–1290 (1984)

    Article  Google Scholar 

  28. Keefer, D.K.: Investigating landslides caused by earthquakes—a historical review. Surv. Geophys. 23, 473–510 (2002)

    Article  Google Scholar 

  29. Liu, Y.Q., Li, H.B., Zhao, J., Li, J.R., Zhou, Q.C.: UDEC simulation for dynamic response of a rock slope subject to explosions. Int. J. Rock Mech. Min. Sci. 41(1), 599–604 (2004)

    Article  Google Scholar 

  30. Cook, N.G.W., Hood, M., Tsai, F.: Observations of crack growth in hard rock loaded by an indenter. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 21(2), 97–107 (1984)

    Article  Google Scholar 

  31. Alvarez Grima, M., Miedema, S.A., van de Ketterij, R.G., et al.: Effect of high hyperbaric pressure on rock cutting process. Eng. Geol. 196, 24–36 (2015)

    Article  Google Scholar 

  32. Christian, E., Robert, S., Peter, E.: A discrete element model to describe failure of strong rock in uniaxial compression. Granul. Mater. 13(4), 341–364 (2011)

    Article  Google Scholar 

  33. Li, X.B., Summers, D.A., Rupert, G., Santi, P.: Experimental investigation on the breakage of hard rock by the PDC cutters with combined action modes. Tunn. Undergr. Sp. Technol. 16(2), 107–114 (2001)

    Article  Google Scholar 

  34. Kaitkay, P., Lei, S.: Experimental study of rock cutting under external hydrostatic pressure. J. Mater. Process. Technol. 159, 206–213 (2005)

    Article  Google Scholar 

  35. Pang, S.S., Goldsmith, W.: Investigation of crack formation during loading of brittle rock. Rock Mech. Rock Eng. 23, 53–63 (1990)

    Article  Google Scholar 

  36. Hoe, E., Martin, C.D.: Fracture initiation and propagation in intact rock—a review. J. Rock Mech. Geotech. Eng. 6, 287–300 (2014)

    Article  Google Scholar 

  37. Liu, H.Y., Kou, S.Q., Lindqvist, P.A., et al.: Numerical simulation of the rock fragmentation process induced by indenters. Int. J. Rock Mech. Min. Sci. 39(4), 491–505 (2002)

    Article  Google Scholar 

  38. Kou, S.Q., Lindqvist, P.A., Tang, C.A., Xu, X.H.: Numerical simulation of the cutting of inhomogeneous rocks. Int. J. Rock Mech. Min. Sci. 36, 711–717 (1999)

    Article  Google Scholar 

  39. Su, O., Ali Akcin, N.: Numerical simulation of rock cutting using the discrete element method. Int. J. Rock Mech. Min. Sci. 48, 434–442 (2011)

    Article  Google Scholar 

  40. Cho, J.W., Jeon, S., Yu, S.H., Chang, S.H.: Optimum spacing of TBM disc cutters: a numerical simulation using the three-dimensional dynamic fracturing method. Tunn. Undergr. Space Technol. 25(3), 230–244 (2010)

    Article  Google Scholar 

  41. Linqvist, P.A.: Rock Fragmentation by Indentation and Disc Cutting. Ph.D. thesis. University of Lulea. (1982)

  42. Tan, X.C., Kou, S.Q., Lindqvist, P.A.: Application of the DDM and fracture mechanics model on the simulation of rock breakage by mechanical tools. Eng. Geol. 49(3), 277–284 (1998)

    Article  Google Scholar 

Download references

Acknowledgements

This work was financially supported by National Natural Science Funds (Nos. 50878123 and 11072257), National Natural Science Funds for Distinguished Young Scholar (No. 51025935 and No. 51009086) and Major State Basic Research Development Program of China (973 Program) (No. 2010CB732001). Young Scholars Development Fund of SWPU (201599010101).

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Authors and Affiliations

  1. School of Mechatronic Engineering, Southwest Petroleum University, Chengdu, 610500, Sichuan, China

    Yanxin Lv, Xiaohua Zhu & Weiji Liu

  2. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, 430071, China

    Yanxin Lv & Haibo Li

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  1. Yanxin Lv
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  2. Haibo Li
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Correspondence to Yanxin Lv.

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Lv, Y., Li, H., Zhu, X. et al. Discrete element method simulation of random Voronoi grain-based models. Cluster Comput 20, 335–345 (2017). https://doi.org/10.1007/s10586-016-0705-3

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