Skip to main content


You are viewing the new article page. Let us know what you think. Return to old version

Article | Open | Published:

Numerical simulation of rock fracture using three-dimensional extended discrete element method


We perform three-dimensional numerical simulation of rock fracturing under uniaxial compression by extending the discrete element method (DEM). Rock sample is modeled as an assemblage of about four thousand spheres having the same radius. Each element satisfies equations of motion for both translation and rotation. In extension of the DEM, we assume cohesion between elements and constrained rotation of the elements; these assumptions are required to treat the continuum by the DEM. We study two cases of uniaxial compression tests: A homogeneous sample having an equal cohesion force between elements and heterogeneous sample having weak parts of cohesion in one percent of the total number of the bonds of elements. We present the detail of fracturing process of model rock samples and obtain stress-strain curve for each case. The homogeneous sample shows a cone-shaped fault system, whereas the heterogeneous sample shows complex fault system consisting of major and sub faults. We find that the inner stress and rotation of elements show the negative correlation during fracturing process. The results are in good agreement with both experimental and theoretical results.


  1. Bird, P. and X. Kong, Computer simulations of California tectonics confirm very low strength of major faults, Geol. Soc. Am. Bull., 106, 159–174, 1994.

  2. Bordia, S. K., The effects of size and stress concentration on the dilatancyand fracture of rock, Int. J. Rock Mech. Min. Sci., 8, 629–640, 1971.

  3. Cundall, P. A. and O. D. L. Strack, A discrete numerical model for granular assemblies, Geotechnique, 29, 47–65, 1979.

  4. Donzé, F., P. Mora, and S. A. Magnier, Numerical simulation of faults and shear zones, Geophys. J. Int., 116, 46–52, 1994.

  5. Hawkes, I. and M. Mellor, Uniaxial testing in rock mechanics laboratories, Eng. Geol., 4, 177–285, 1970.

  6. Holland, D. and M. Marder, Ideal brittle fracture of silicon studied with molecular dynamics, Phys. Rev. Lett., 80, 746–749, 1998.

  7. Iwashita, K. and M. Oda, Rolling resistance at contacts in simulation of shear band development by DEM, J. Engrg. Mech., ASCE124(3), 285–292, 1998.

  8. Knott, J. F., Fundamentals of Fracture Mechanics, 273 pp., Butterworth, London, 1973.

  9. Lama, R. D., Elasticity and strength of coal seams in situ and an attempt to determine the energy in pressure bursting of roadsides, D. Sc. Tech. Thesis, Faculty of Mining, Academy of Min. & Metall., Cracow, Poland, 1966.

  10. Mora, P. and D. Place, Numerical simulation of earthquake faults with gouge: toward a comprehensive explanation for the heat flow paradox, J. Geophys. Res., 103(B9), 21067–21089, 1998.

  11. Paterson, M. S., Experimental Rock Deformation—the Brittle Field, 254 pp., Springer–Verlag, Berlin, 1978.

  12. Place, D. and P. Mora, The lattice solid model to simulate the physics of rocks and earthquakes: Incorporation of friction, J. Comp. Phys., 150, 373–393, 1999.

  13. Scholz, C. H., The Mechanics of Earthquakes and Faulting, 439 pp., Cambridge Univ. Press, New York, 1990.

  14. Scott, D. R., Seismicity and stress rotation in a granular model of the brittle crust, Nature, 381, 592–595, 1996.

  15. Tuckerman, M., B. J. Berne, and G. J. Martya, Reversible multiple time scale molecular dynamics, J. Chem. Phys., 97, 1990–2001, 1992.

  16. Vutukuri, V. S., R. D. Lama, and S. S. Saluja, Handbook on Mechanical Properties of Rocks: Testing Techniques and Results, 300 pp., Trans Tech Publications, Clausthal, 1974.

  17. Wawersik, W. R. and W. F. Brace, Post-failure behavior of a granite and a diabase, Rock Mech., 3, 61–85, 1971.

  18. Weertman, J., Dislocation Based Fracture Mechanics, 524 pp., World Scientific, Singapore, 1996.

  19. Wu, Z., A. Machida, and D. Gao, Development of mixed finite element method for composite discontinuous analysis, J. Geotech. Engrg., 598(I–44), 149–159, 1998.

Download references

Author information

Correspondence to Yuya Matsuda.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark


  • Uniaxial Compression
  • Discrete Element Method
  • Mora
  • Rock Fracture
  • Uniaxial Compression Test