Skip to main content
SpringerLink
Log in

Rock initiation and propagation simulation under compression-shear loading using continuous-discontinuous cellular automaton method

  • Published:
Acta Mechanica Solida Sinica Aims and scope Submit manuscript

Abstract

A continuous-discontinuous cellular automaton method is developed for rock initiation and propagation simulations, in which the level set method, discontinuous enrichment shape functions and discontinuous cellular automaton are combined. No remeshing is needed for crack growth analysis, and all calculations are restricted to cells without an assembled global stiffness matrix. The frictional contact theory is employed to construct the contact model of normal pressure and tangential shear on crack surfaces. A discontinuous cellular automaton updating rule suitable for frictional contact of rock is proposed simultaneously with Newton’s iteration method for nonlinear iteration. Besides, a comprehensive fracturing criterion for brittle rock under compression-shear loading is developed. The accuracy and effectivenesss of the proposed method is proved by numerical simulation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Griffith, A.A., The phenomena of rapture and flow in solids. Philosophical Transactions of the Royal Society A, 1921, 221: 163–197.

    Article  Google Scholar 

  2. Brace, W.F., Brittle fracture of rocks. In: State of Stress in the Earth’s Crust. (ed Judd). New York, U.S.A.: American Elsevier Publishing Co, 1964: 111–180.

    Google Scholar 

  3. Hoek, E. and Bieniawski, Z.T., Application of the photoelastic coating technique to the study of the stress redistribution associated with plastic flow around notches. The South African Institution of Mechanical Engineering, 1963, 12(8): 222–226.

    Google Scholar 

  4. Jaeger, G.C. and Cook, N.G.W., Foundamental of rock mechanics (2nd Edn). London, U.K.: Chapman and Hall, 1976: 20–55.

    Google Scholar 

  5. Lajtai, E.Z., A theoretical and experimental evaluation of Griffith theory of brittle fracture. Techonophysics, 1971, 11: 129–156.

    Article  Google Scholar 

  6. Bazant, Z.P., Crack band theory for fracture of concrete. Materials and Structures, 1983, 16: 155–177.

    Google Scholar 

  7. Santiago, S.D. and Hilsdorf, H.K., Fracture mechanism of concrete under compressive loads. Cement and Concrete Research, 1973, 3: 363–388.

    Article  Google Scholar 

  8. Blakey, F.A., Mechanism of fracture of concrete. Nature, 1952, 170: 1120.

    Article  Google Scholar 

  9. Hawkes, I. and Mellor, M., Uniaxial testing in rock mechanics laboratories. Engineering Geology, 1970, 4: 177–285.

    Article  Google Scholar 

  10. Chsu, T.T., Slate, G.M., Sturman, G.M. and Winter, G., Microcracking of plain concrete and the shape of the stress-strain curve. ACI Journal proceeding, 1963, 60: 209–224.

    Google Scholar 

  11. Peng, S.D. and Johnson, A.M., Crack growth and faulting in cylindrical specimens of chelmsford granite. International Journal of Rock Mechanics and Mining Sciences & Geomechanics, 1972, 9: 37–86.

    Article  Google Scholar 

  12. Al-Chalabi, M. and Huang, C.L., Stress discontribution within circular cylinders in compression. International Journal of Rock Mechanics and Mining Sciences & Geomechanics, 1974, 11: 45–56.

    Article  Google Scholar 

  13. Lee, H. and Jeon, S., An experimental and numerical study of fracture coalescence in pre-cracked specimens under uniaxial compression. International Journal of Solids and Structures, 2011, 48: 979–999.

    Article  Google Scholar 

  14. Park, C.H. and Bobet, A., Crack initiation, propagation and coalescence from frictional flaws in uniaxial compression. Engineering Fracture Mechanics, 2010, 77: 2727–2748.

    Article  Google Scholar 

  15. Sagong, M. and Bobet, A., Coalescence of multiple flaws in a rock-model material in uniaxial compression. International Journal of Rock Mechanics and Mining Science, 2002, 39: 229–241.

    Article  Google Scholar 

  16. Sih, G.C., Some basic problems in fracture mechanics and new concepts. Journal of Engineering Fracture, 1973, 5: 365–377.

    Article  Google Scholar 

  17. Glucklich, Fracture of plain concrete. Journal of Engineering Mechanics, 1963, 89: 127–138.

    Google Scholar 

  18. Shen, B. and Stephansson, O., Numerical analysis of mixed mode I and II fracture propagation. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1993, 30: 861–867.

    Article  Google Scholar 

  19. Dobroskok, A., Ghassemi, A. and Linkov, A., Extended structural criterion for numerical simulation of crack propagation and coalescence under compressive loads. International Journal of Fracture, 2005, 133: 223–246.

    Article  Google Scholar 

  20. Miao, Y., He, T.G., Yang, Q. and Zheng, J.J., Multi-domain hybrid boundary node method for evaluating top-down crack in asphalt pavements. Engineering Analysis for Boundary Elements, 2010, 34(9): 755–760.

    Article  Google Scholar 

  21. Horii, H. and Nemat-Nasser, S., Brittle failure in compression splitting, faulting and brittle-ductile transition. Philosophical Transactions of the Royal Society A, 1986, 319: 337–374.

    Article  Google Scholar 

  22. Reyes, O. and Einstein, H.H., Failure mechanisms of fractured rock—a fracture coalescence model. In 7th Int. Congress on Rock Mech., 1, ed. Balkema: Wittke W. Rotterdam, 1991, 333–340.

  23. Shen, B. and Stephansson, O., Modification of the G-criterion for fracture propagation subjected to compression. International Journal of Rock Mechanics and Mining Science, 1993, 30: 681–687.

    Article  Google Scholar 

  24. Nemat-Nasser, S. and Horii, H., Compression-induced non-planar crack extension with application to splitting, exfoliation and rockbursts. Journal of Geophysical Research, 1982, B87: 6805–6821.

    Article  Google Scholar 

  25. Zaitsev, Y.V. and Wittmann, F.H., Simulation of crack propagation and failure of concrete. Materials and Structures, 1981, 14: 357–365.

    Google Scholar 

  26. Carpinteri, A., Scavia, C. and Yang, G.P., Microcrack propagation, coalescence and size effects in compression. Engineering Fracture Mechanics, 1996, 54(3): 335–347.

    Article  Google Scholar 

  27. Han, B.C. and Swobada, G.A., A damage mechanics model with wing cracks propagation. In: Computer Methods and Advances in Geomechanics, 2, eds. Siriwardane HJ, Zaman MM. Balkema: Rotterdam, 1993: 1555–1559.

    Google Scholar 

  28. Tang, C.A. and Kou, S.Q., Crack propagation and coalescence in brittle materials under compression. Engineering Fracture Mechanics, 1998, 61: 311–324.

    Article  Google Scholar 

  29. Feng, X.T., Pan, P.Z. and Zhou, H., Simulation of the crack microfracturing process under uniaxial compression using an elasto-plastic cellular automaton. International Journal of Rock Mechanics and Mining Science, 2006, 43: 1091–1108.

    Article  Google Scholar 

  30. Bobet, A. and Einstein, H.H., Numerical modeling of fracture coalescence in a model rock material. International Journal of Fracture, 1998, 92: 221–252.

    Article  Google Scholar 

  31. Wu, Z. J. and Wong, L.N.Y., Frictional crack initiation and propagation analysis using the numerical manifold method. Computers and Geotechnics, 2012, 39: 38–53.

    Article  Google Scholar 

  32. Steen, B.V., Vervoort, A. and Napier, J.A.L., Numerical modeling of fracture initiation and propagation in biaxial tests on rock samples. International Journal of Fracture, 2001, 108: 165–191.

    Article  Google Scholar 

  33. Stolarska, M., Chopp, D.L., Moes, N. and Belytschko, T., Modelling crack growth by level sets in the extended finite element method. International Journal for Numerical Methods in Engineering, 2001, 51: 943–960.

    Article  Google Scholar 

  34. Sethian, J., Evolution, implementation and application of level set and fast marching methods for advancing fronts. Journal of Computational Physics, 2001, 169: 503–555.

    Article  MathSciNet  Google Scholar 

  35. Moes, N. and Belytschko, T., Extended finite element method for cohesive crack growth. Engineering Fracture Mechanics, 2002, 69: 813–833.

    Article  Google Scholar 

  36. Shen, C., Dai, S., Yang, J. and Tang, X., Cellular automata for analysis of plane problem in theory of elasticity. Journal of Tsinghua University (Science & Technology), 2001, 41: 35–38 (in Chinese).

    MATH  Google Scholar 

  37. Gurdal, Z. and Tatting, T., Cellular automata for design of truss structures with linear and non-linear response. In: Proceedings of 41st AIAA/ASME/ASCE/AHS/ASC Structural Dynamics and Materials Conference, GA: Atlanta, 2000.

    Google Scholar 

  38. Pan, P.Z., Yan, F. and Feng, X.T., Modeling the cracking process of rocks from continuity to discontinuity using a cellular automaton. Computers and Geosciences, 2012, 42: 87–99.

    Article  Google Scholar 

  39. Yan, F., Feng, X.T., Pan, P.Z. and Li, Y.P., A continuous-discontinuous cellular automaton method for regular frictional contact problems. Archive of applied mechanics, 2013, 83(8): 1239–1255.

    Article  Google Scholar 

  40. Rao, Q.H., Sun, Z.Q., Stephansson, O., et al., Shear fracture (Mode II) of brittle rock. International Journal of Rock Mechanics and Mining Science, 2003, 40: 355–375.

    Article  Google Scholar 

  41. Pan, P.Z., Ding, W.X., Feng, X.T., et al., Research on influence of pre-existing crack geometrical and material properties on crack propagation in rocks. Chinese Journal of Rock Mechanics and Engineering, 2008, 27(9): 1882–1889.

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Fei Yan, Xiating Feng, Pengzhi Pan & Shaojun Li

Authors
  1. Fei Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiating Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pengzhi Pan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shaojun Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fei Yan.

Additional information

Project supported by the National Key Technologies R&D Program of China (No. 2013BAB02B01) and the National Natural Science Foundation of China (Nos. 41272349, 41172284 and 51322906).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yan, F., Feng, X., Pan, P. et al. Rock initiation and propagation simulation under compression-shear loading using continuous-discontinuous cellular automaton method. Acta Mech. Solida Sin. 28, 384–399 (2015). https://doi.org/10.1016/S0894-9166(15)30024-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1016/S0894-9166(15)30024-0

Key Words

Search

Navigation