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A Micromechanical Model for Simulation of Rock Failure Under High Strain Rate Loading


Quasi-brittle materials such as rock are rate sensitive materials and their behaviour under dynamic loading is not identical with that under static loading. In this study, numerical Brazilian tensile tests are conducted using a Split Hopkinson Pressure Bar system in an attempt to reproduce the dynamic increase factors (DIF) of the experimental tests. The rock is modelled by a bonded particle system made of spherical particles which interact at the contact points. The numerical results indicate that while the bonded particle system with a simple contact bond model can closely mimic the static behaviour of the sandstone specimens, it lacks what is needed for a rate dependent material. Therefore, a micromechanical model in which the contact bond strength is allowed to vary in proportion to the relative velocity of the involved particles is introduced. It is shown that the modified model can reproduce the physical tests data reported in the literature. In particular, with the application of strength enhancement coefficients in the range of 0–16 × 105, DIF values of 1.1–13 are obtained in the indirect tensile Brazilian tests, and the induced strain rate in the specimen is in 10–1000 s−1 range. Our preliminary study indicates that the model, consistent with the fact reported for the quasi-brittle materials, shows different rate-dependent sensitivity and dynamic strength enhancement in tension and compression. The micromechanical parameters in the proposed model can be adjusted to reproduce the physical rock strength, and that the shape of the reflected and transmitted numerical waves can be modified to approach those in the physical tests.

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  1. 1.

    Brown ET (1981) Rock characterization testing and monitoring. ISRM suggested methods. Rock Charact. Test. Monit. ISRM Suggest. methods

  2. 2.

    Xia K, Yao W (2015) Dynamic rock tests using split Hopkinson (Kolsky) bar system—A review. J Rock Mech Geotech Eng 7:27–59.

    Article  Google Scholar 

  3. 3.

    Lindholm US (1964) Some experiments with the split hopkinson pressure bar∗. J Mech Phys Solids 12:317–335.

    Article  Google Scholar 

  4. 4.

    Hughes ML, Tedesco JW, Ross CA (1993) Numerical analysis of high strain rate splitting-tensile tests. Comput Struct 47:653–671.

    Article  Google Scholar 

  5. 5.

    Dai F, Huang S, Xia K, Tan Z (2010) Some fundamental issues in dynamic compression and tension tests of rocks using Split Hopkinson Pressure Bar. Rock Mech Rock Eng 43:657–666.

    Article  Google Scholar 

  6. 6.

    Das S (2016) A strain-rate dependent tensile damage model for brittle materials under impact loading. Ph.D. Thesis, University of Sydney

  7. 7.

    Li X, Mao H, Xu K, Miao C (2018) A SHPB experimental study on dynamic mechanical property of high-damping rubber. Shock Vib 2018:1–10.

    Article  Google Scholar 

  8. 8.

    Ai D, Zhao Y, Wang Q, Li C (2020) Crack propagation and dynamic properties of coal under SHPB impact loading: experimental investigation and numerical simulation. Theor Appl Fract Mech 105:102393.

    Article  Google Scholar 

  9. 9.

    Feng W, Liu F, Yang F et al (2019) Experimental study on the effect of strain rates on the dynamic flexural properties of rubber concrete. Constr Build Mater 224:408–419.

    Article  Google Scholar 

  10. 10.

    Gálvez F, Rodríguez J, Sánchez V (1997) Tensile strength measurements of ceramic materials at high rates of strain. Le J Phys IV 07:C3-151–C3-156.

    Article  Google Scholar 

  11. 11.

    Tedesco JW, Ross CA, McGill PB, O’Neil BP (1991) Numerical analysis of high strain rate concrete direct tension tests. Comput Struct 40:313–327.

    Article  Google Scholar 

  12. 12.

    Meng H, Li QM (2003) Correlation between the accuracy of a SHPB test and the stress uniformity based on numerical experiments. Int J Impact Eng 28:537–555.

    Article  Google Scholar 

  13. 13.

    Zhong WZ, Rusinek A, Jankowiak T et al (2015) Influence of interfacial friction and specimen configuration in Split Hopkinson Pressure Bar system. Tribol Int 90:1–14.

    Article  Google Scholar 

  14. 14.

    Binesh SM, Eslami-Feizabad E, Rahmani R (2018) Discrete element modeling of drained triaxial test: flexible and rigid lateral boundaries. Int J Civ Eng 16:1463–1474.

    Article  Google Scholar 

  15. 15.

    Wang W, Sun S, Le H et al (2019) Experimental and numerical study on failure modes and shear strength parameters of rock-like specimens containing two infilled flaws. Int J Civ Eng 17:1895–1908.

    Article  Google Scholar 

  16. 16.

    Hoormazdi G, Küpferle J, Röttger A et al (2019) a concept for the estimation of soil-tool abrasive wear using ASTM-G65 test data. Int J Civ Eng 17:103–111.

    Article  Google Scholar 

  17. 17.

    Cundall PA (1971) A computer model for simulating progressive, large-scale movement in blocky rock system. In: Proc Int Symp Rock Mech 1971

  18. 18.

    Rojek J, Oñate E, Labra C, Kargl H (2011) Discrete element simulation of rock cutting. Int J Rock Mech Min Sci 48:996–1010.

    Article  Google Scholar 

  19. 19.

    Rojek J (2014) Discrete element thermomechanical modelling of rock cutting with valuation of tool wear. Comput Part Mech 1:71–84.

    Article  Google Scholar 

  20. 20.

    Fakhimi A, Wan F (2016) Discrete element modeling of the process zone shape in mode I fracture at peak load and in post-peak regime. Int J Rock Mech Min Sci 85:119–128.

    Article  Google Scholar 

  21. 21.

    Tarokh A, Kao C-S, Fakhimi A, Labuz JF (2016) Insights on surface spalling of rock. Comput Part Mech 3:391–405.

    Article  Google Scholar 

  22. 22.

    Lanari M, Fakhimi A (2015) Numerical study of contributions of shock wave and gas penetration toward induced rock damage during blasting. Comput Part Mech 2:197–208.

    Article  Google Scholar 

  23. 23.

    Fakhimi A, Riedel JJ, Labuz JF (2006) Shear banding in sandstone: physical and numerical Studies. Int J Geomech 6:185–194.

    Article  Google Scholar 

  24. 24.

    Brara A, Camborde F, Klepaczko JR, Mariotti C (2001) Experimental and numerical study of concrete at high strain rates in tension. Mech Mater 33:33–45.

    Article  Google Scholar 

  25. 25.

    Li X, Zou Y, Zhou Z (2014) Numerical Simulation of the Rock SHPB Test with a Special Shape Striker Based on the Discrete Element Method. Rock Mech Rock Eng 47:1693–1709.

    Article  Google Scholar 

  26. 26.

    Yin T, Zhang S, Li X, Bai L (2018) A numerical estimate method of dynamic fracture initiation toughness of rock under high temperature. Eng Fract Mech 204:87–102.

    Article  Google Scholar 

  27. 27.

    Du H, Dai F, Xu Y et al (2020) Mechanical responses and failure mechanism of hydrostatically pressurized rocks under combined compression-shear impacting. Int J Mech Sci 165:105219.

    Article  Google Scholar 

  28. 28.

    Mahabadi OK, Cottrell BE, Grasselli G (2010) An example of realistic modelling of rock dynamics problems: FEM/DEM simulation of dynamic Brazilian test on barre granite. Rock Mech Rock Eng 43:707–716.

    Article  Google Scholar 

  29. 29.

    Munjiza A (2004) The combined finite-discrete element method, 1st edn. Wiley, Chichester

    Book  Google Scholar 

  30. 30.

    Rougier E, Knight EE, Broome ST et al (2014) Validation of a three-dimensional finite-discrete element method using experimental results of the Split Hopkinson Pressure Bar test. Int J Rock Mech Min Sci 70:101–108.

    Article  Google Scholar 

  31. 31.

    Osthus D, Godinez HC, Rougier E, Srinivasan G (2018) Calibrating the stress-time curve of a combined finite-discrete element method to a Split Hopkinson Pressure Bar experiment. Int J Rock Mech Min Sci 106:278–288.

    Article  Google Scholar 

  32. 32.

    O’Sullivan C (2011) Particulate discrete element modelling: a geomechanics perspective. CRC Press, Boca Raton

    Book  Google Scholar 

  33. 33.

    Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Géotechnique 29:47–65.

    Article  Google Scholar 

  34. 34.

    Fakhimi A, Azhdari P, Kimberley J (2018) Physical and numerical evaluation of rock strength in Split Hopkinson Pressure Bar testing. Comput Geotech 102:1–11.

    Article  Google Scholar 

  35. 35.

    Fakhimi A (2009) A hybrid discrete–finite element model for numerical simulation of geomaterials. Comput Geotech 36:386–395.

    Article  Google Scholar 

  36. 36.

    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 40:193–211.

    Article  Google Scholar 

  37. 37.

    Lu YBB, Li QMM, Ma GWW (2010) Numerical investigation of the dynamic compressive strength of rocks based on split Hopkinson pressure bar tests. Int J Rock Mech Min Sci 47:829–838.

    Article  Google Scholar 

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The third author acknowledges the support he received in developing CA3 program during his years of service at New Mexico Tech.

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Correspondence to Ali Fakhimi.

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Majedi, M.R., Afrazi, M. & Fakhimi, A. A Micromechanical Model for Simulation of Rock Failure Under High Strain Rate Loading. Int J Civ Eng 19, 501–515 (2021).

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  • Split Hopkinson Pressure Bar
  • Bonded particle system
  • Rock strength
  • Strength enhancement
  • Micromechanical model