Computational Particle Mechanics

, Volume 6, Issue 2, pp 195–211 | Cite as

Dilation angle in bonded particle simulation of rock

  • A. FakhimiEmail author
  • S. Norouzi


A model that allows micromechanical parameters to soften as a measure of plastic deformation is discussed. In particular, a microdilation angle is involved to help for calibration of macroscopic volumetric deformation. Through biaxial and shear tests numerical simulations, it is shown that macrodilation angle of bonded particle system can be controlled only when small particles are used. The genesis pressure that causes small overlap of particles has an impact on dilation angle as well and can be utilized as a controlling factor to calibrate a bonded particle material for dilation angle and post-peak behavior.


Micromechanical model Numerical simulation Bonded particle model Dilation angle 


Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


  1. 1.
    Cundall PA (1971) A computer model for simulating progressive, large scale movement in blocky rock systems. In: Proceedings of the international symposium on rock mechanics, vol 2, pp 129–136Google Scholar
  2. 2.
    Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Geotechnique 29(1):47–65CrossRefGoogle Scholar
  3. 3.
    Rojek J, Onate E, Labra C, Kargl H (2011) Discrete element simulation of rock cutting. Int J Rock Mech Min Sci 48(6):996–1010CrossRefGoogle Scholar
  4. 4.
    Rojek J (2014) Discrete element thermomechanical modelling of rock cutting with valuation of tool wear. Comput Part Mech 1(1):71–84CrossRefGoogle Scholar
  5. 5.
    Huang H, Lecampion B, Detournay E (2013) Discrete element modeling of tool-rock interaction I: rock cutting. Int J Numer Anal Meth Geomech 37(13):1913–1929CrossRefGoogle Scholar
  6. 6.
    Oñate E, Zárate F, Miquel J, Santasusana M, Celigueta MA, Arrufat F, Gandikota R, Valiullin K, Ring L (2015) A local constitutive model for the discrete element method. Application to geomaterials and concrete. Comput Part Mech 2(2):139–160CrossRefGoogle Scholar
  7. 7.
    Fakhimi A, Lanari M (2014) DEM–SPH simulation of rock blasting. Comput Geotech 55:158–164CrossRefGoogle Scholar
  8. 8.
    Lanari M, Fakhimi A (2015) Numerical study of contributions of shock wave and gas penetration toward induced rock damage during blasting. Comput Part Mech 2(2):197–208CrossRefGoogle Scholar
  9. 9.
    Fakhimi A, Hemami B (2015) Axial splitting of rocks under uniaxial compression. Int J Rock Mech Min Sci 79:124–134CrossRefGoogle Scholar
  10. 10.
    Hemami B, Fakhimi A (2014) Numerical simulation of rock-loading machine interaction. In: ARMA 14-7488, 48th US rock mechanics/geomechanics symposium, Minneapolis, MN, June 1–4Google Scholar
  11. 11.
    Tarokh A, Kao CS, Fakhimi A, Labuz JF (2016) Insights on surface spalling of rock. Comput Part Mech 3(3):391–405CrossRefGoogle Scholar
  12. 12.
    Tarokh A, Blanksma DJ, Fakhimi A, Labuz JF (2016) Fracture initiation in cavity expansion of rock. Int J Rock Mech Min Sci 85:84–91CrossRefGoogle Scholar
  13. 13.
    Wang M, Feng YT, Pande GN, Chan AHC, Zuo WX (2017) Numerical modelling of fluid-induced soil erosion in granular filters using a coupled bonded particle lattice Boltzmann method. Comput Geotech 82:134–143CrossRefGoogle Scholar
  14. 14.
    Zhang P, Galindo-Torres SA, Tang H, Jin G, Scheuermann A, Li L (2017) An efficient discrete element lattice Boltzmann model for simulation of particle-fluid, particle-particle interactions. Comput Fluids 147:63–71MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Damjanac B, Cundall P (2016) Application of distinct element methods to simulation of hydraulic fracturing in naturally fractured reservoirs. Comput Geotech 71:283–294CrossRefGoogle Scholar
  16. 16.
    Zhang Q, Zhang XP (2017) A numerical study on cracking processes in limestone by the b-value analysis of acoustic emissions. Comput Geotech 92:1–10CrossRefGoogle Scholar
  17. 17.
    Han D, Zhang D, Jing H, Yang L, Cui T, Ding Y, Wang Z, Wang Y, Zhang T (2018) DEM-CFD coupling simulation and optimization of an inside-filling air-blowing maize precision seed-metering device. Comput Electron Agric 150:426–438CrossRefGoogle Scholar
  18. 18.
    Bennett KC, Luscher DJ, Buechler MA, Yeager JD (2018) A micromechanical framework and modified self-consistent homogenization scheme for the thermoelasticity of porous bonded-particle assemblies. Int J Solids Struct 139:224–237CrossRefGoogle Scholar
  19. 19.
    Norouzi S, Baghbanan A, Khani A (2013) Investigation of grain size effects on micro/macro-mechanical properties of intact rock using Voronoi element—discrete element method approach. Part Sci Technol 31(5):507–514CrossRefGoogle Scholar
  20. 20.
    Liu Q, Jiang Y, Wu Z, Xu X, Liu Q (2018) Investigation of the rock fragmentation process by a single TBM cutter using a Voronoi element-based numerical manifold method. Rock Mech Rock Eng 51(4):1137–1152CrossRefGoogle Scholar
  21. 21.
    Liu Q, Jiang Y, Wu Z, He J (2018) A Voronoi element based-numerical manifold method (VE-NMM) for investigating micro/macro-mechanical properties of intact rocks. Eng Fract Mech 199:71–85CrossRefGoogle Scholar
  22. 22.
    Liu Q, Jiang Y, Wu Z, Qian Z, Xu X (2018) Numerical modeling of acoustic emission during rock failure process using a Voronoi element based-explicit numerical manifold method. Tunn Undergr Space Technol 79:175–189CrossRefGoogle Scholar
  23. 23.
    He J, Liu Q, Wu Z, Jiang Y (2018) Geothermal-related thermo-elastic fracture analysis by numerical manifold method. Energies 11(6):1380CrossRefGoogle Scholar
  24. 24.
    Peng J, Wong LNY, Teh CI (2017) Effects of grain size-to-particle size ratio on micro-cracking behavior using a bonded-particle grain-based model. Int J Rock Mech Min Sci 100:207–217CrossRefGoogle Scholar
  25. 25.
    Farahmand K, Diederichs MS (2015). A calibrated Synthetic Rock Mass (SRM) model for simulating crack growth in granitic rock considering grain scale heterogeneity of polycrystalline rock. In: 49th US rock mechanics/geomechanics symposium. American Rock Mechanics AssociationGoogle Scholar
  26. 26.
    Potyondy DO (2017). Simulating perforation damage with a flat-jointed bonded-particle material. In: 51st US rock mechanics/geomechanics symposium. American Rock Mechanics AssociationGoogle Scholar
  27. 27.
    Dinç Ö, Scholtès L (2018) Discrete analysis of damage and shear banding in argillaceous rocks. Rock Mech Rock Eng 51(5):1521–1538CrossRefGoogle Scholar
  28. 28.
    Liakas S, O’Sullivan C, Saroglou C (2017) Influence of heterogeneity on rock strength and stiffness using discrete element method and parallel bond model. J Rock Mech Geotech Eng 9(4):575–584CrossRefGoogle Scholar
  29. 29.
    Khani A, Baghbanan A, Norouzi S, Hashemolhosseini H (2013) Effects of fracture geometry and stress on the strength of a fractured rock mass. Int J Rock Mech Min Sci 60:345–352CrossRefGoogle Scholar
  30. 30.
    Torkan M, Baghbanan A, Norouzi S, Amrollahi H, Hashemolhosseini H (2017) Evaluating modes I, II, and mixed mode I–II fracture toughnesses of crystalline rocks using discrete element method. Part Sci Technol. Google Scholar
  31. 31.
    Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41(8):1329–1364CrossRefGoogle Scholar
  32. 32.
    Fakhimi A (2004) Application of slightly overlapped circular particles assembly in numerical simulation of rocks with high friction angles. Eng Geol 74(1):129–138CrossRefGoogle Scholar
  33. 33.
    Lisjak A, Grasselli G (2014) A review of discrete modeling techniques for fracturing processes in discontinuous rock masses. J Rock Mech Geotech Eng 6(4):301–314CrossRefGoogle Scholar
  34. 34.
    Ding X, Zhang L (2014) A new contact model to improve the simulated ratio of unconfined compressive strength to tensile strength in bonded particle models. Int J Rock Mech Min Sci 69:111–119CrossRefGoogle Scholar
  35. 35.
    Schöpfer MP, Abe S, Childs C, Walsh JJ (2009) The impact of porosity and crack density on the elasticity, strength and friction of cohesive granular materials: insights from DEM modelling. Int J Rock Mech Min Sci 46(2):250–261CrossRefGoogle Scholar
  36. 36.
    Diederichs MS (2000) Instability of hard rock masses, the role of tensile damage and relaxation. PhD dissertation, University of Waterloo, CanadaGoogle Scholar
  37. 37.
    Particle flow code in 2 dimensions (1999) Itasca consulting group, Inc, Minneapolis, MNGoogle Scholar
  38. 38.
    Cho N, Martin CD, Sego DC, Christiansson R (2004) Modelling dilation in brittle rocks. In: Gulf rocks 2004, the 6th North America rock mechanics symposium (NARMS). American Rock Mechanics AssociationGoogle Scholar
  39. 39.
    Zhao XG, Cai M (2010) A mobilized dilation angle model for rocks. Int J Rock Mech Min Sci 47(3):368–384CrossRefGoogle Scholar
  40. 40.
    Fakhimi A, Riedel JJ, Labuz JF (2006) Shear banding in sandstone: physical and numerical studies. Int J Geomech 6(3):185–194CrossRefGoogle Scholar
  41. 41.
    Norouzi S, Fakhimi A (2017) A micromechanical model for studying the effect of ductility and micro-crack intensity on rock strength characteristics. In: ARMA 17-596, 51st US rock mechanics/geomechanics symposium, San Francisco, CA, June 25–28Google Scholar
  42. 42.
    Vermeer PA, de Borst R (1988) Non-associated plasticity for soils, concrete and rock. Heron 29(3):1–64Google Scholar
  43. 43.
    Norouzi S (2017). A micro mechanical model for numerical study of rock dilation and ductility. MS thesis, Department of Mineral Engineering, New Mexico Tech, NM, USAGoogle Scholar
  44. 44.
    Fakhimi A, Villegas T (2007) Application of dimensional analysis in calibration of a discrete element model for rock deformation and fracture. Rock Mech Rock Eng 40(2):193–211CrossRefGoogle Scholar
  45. 45.
    Ivars D, Potyondy DO, Pierce M, Cundall PA (2008) The smooth-joint contact model. In: Proceedings of WCCM8-ECCOMASGoogle Scholar
  46. 46.
    Fakhimi A, Hosseinpour H (2011) Experimental and numerical study of the effect of an oversize particle on the shear strength of mined-rock pile material. Geotech Test J 34(2):131–138Google Scholar

Copyright information

© OWZ 2018

Authors and Affiliations

  1. 1.Department of Mineral EngineeringNew Mexico Institute of Mining and TechnologySocorroUSA
  2. 2.School of Civil and Environmental EngineeringTarbiat Modares UniversityTehranIran

Personalised recommendations