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Acta Mechanica Solida Sinica

, Volume 25, Issue 2, pp 177–185 | Cite as

Strength Properties of Jointed Rock Masses Based on the Homogenization Method

  • Hongtao Zhang
  • Jianming Zhu
  • Yinghua Liu
  • Bingye Xu
  • Xiaochun Wang
Article

Abstract

This paper aims to determine the strength properties of jointed rock masses by means of the homogenization method. To reflect the microstructure of jointed rock masses, a representative element volume (REV) is selected. Assuming being rigid and perfectly plastic and utilizing the Mohr-Coulomb yield criterion for rock and joints, an upper bound limit analysis method is proposed based on the homogenization theory. By using the finite element method and Goodman joint element, a nonlinear mathematical programming with equality constraints is formulated, which can be solved by a direct iterative algorithm. Numerical results show the strength of jointed rock masses behaves anisotropy with different joint directions. This method presents an effective tool for the strength analysis of jointed rock masses.

Key words

jointed rock mass homogenization representative element volume (REV) upper bound limit analysis anisotropy 

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References

  1. [1]
    Goodman, R.E., Taylor, R.E. and Breeke, T., A model for the mechanics of jointed rock. ASCE Journal of the Soil Mechanics and Foundations Division, 1968, 94(3): 637–659Google Scholar
  2. [2]
    Singh, B., Continuum characterization of jointed rock masses. International Journal of Rock Mechanics and Mining Sciences, 1973, 10: 311–335.CrossRefGoogle Scholar
  3. [3]
    Gerard, C.M., Elastic models of rock masses having one, two and three sets of joints. International Journal for Numerical and Analytical Methods in Geomechanics Abstract, 1982, 19: 15–23.Google Scholar
  4. [4]
    Morland, L.W., Elastic anisotropy of regularly jointed rock media. Rock Mechanics, 1976, 8: 35–48.CrossRefGoogle Scholar
  5. [5]
    Zhang, W. and Zhang, X.H. Elastic models of jointed rock mass. Chinese Journal of Geotechnical Engineering, 1987, 9(4): 33–44 (in Chinese).Google Scholar
  6. [6]
    Yang H.T, and Wang G., Numerical analysis of jointed rock with two models. Chinese Journal of Geotechnical Engineering, 1999, 21(3): 273–276 (in Chinese).Google Scholar
  7. [7]
    Zhang, Y.J., Equivalent model and numerical analysis and laboratory test for jointed rock masses. Chinese Journal of Geotechnical Engineering, 2006, 28(1): 29–32 (in Chinese).Google Scholar
  8. [8]
    Hoek, E. and Brown, E.T., Practical estimates of rock mass strength. International Journal of Rock Mechanics and Mining Sciences, 1997, 34(8): 1165–1186.CrossRefGoogle Scholar
  9. [9]
    Cai, M. and Horii, H., A constitutive model and FEM analysis of jointed rock masses. International Journal for Numerical and Analytical Methods in Geomechanics Abstract, 1993, 30(4): 351–359.Google Scholar
  10. [10]
    Ren, Q. and Xu W.Y., Homogenizaiton-based method for predicting effective elastic properties of jointed rock. Engineering Mechanics, 2008, 25(4): 75–79 (in Chinese).Google Scholar
  11. [11]
    De, B.H., Freard, J., Garnier, D. and Maghous, S., Failure properties of fractured rock masses as anisotropic homogenized media. Journal of Engineering Mechanics ASCE, 2002, 128: 869–875.CrossRefGoogle Scholar
  12. [12]
    Maghous, S., Bernaud, D. and Garnier, D., Elastoplastic behavior of jointed rock masses as homogenized media and finite element analysis. International Journal of Rock Mechanics and Mining Sciences, 2008, 45(8):1273–1286.CrossRefGoogle Scholar
  13. [13]
    Pouya, A. and Ghoreychi, M., Determination of rock mass strength properties by homogenization. International Journal for Numerical and Analytical Methods in Geomechanics, 2001, 25(13):1285–1303.CrossRefGoogle Scholar
  14. [14]
    Francescato, P. and Pastor, J., Lower and upper numerical bounds to the off-axis strength of unidirectional fiber-reinforced composite by limit analysis methods. European Journal of Mechanics A/Solids, 1997, 16: 213–234.Google Scholar
  15. [15]
    Zhang, H.T., Liu, Y.H. and Xu, B.Y., Lower bound limit and shakedown analysis of orthotropic structures. Engineering Mechanics, 2006, 23(1): 11–16 (in Chinese).Google Scholar
  16. [16]
    Li, H., Liu, Y., Feng, X. and Cen, Z., Limit analysis of ductile composites based on homogenization theory. Proceedings of the Royal Society London A, 2003, 459(2031): 659–675.CrossRefGoogle Scholar
  17. [17]
    Zhang, H.T., Liu, Y.H. and Xu B.Y., Plastic limit analysis of ductile composite structures from micro-to macro-mechanical analysis. Acta Mechanica Solida Sinica, 2009, 22(1): 73–84.CrossRefGoogle Scholar
  18. [18]
    Milani, G., Lourenço, P. and Tralli, A., Homogenization Approach for the limit analysis of out-of-plane loaded masonry walls. Journal of Structural Engineering, 2006, 132(10): 1650–1663.CrossRefGoogle Scholar
  19. [19]
    Hill, R., Continuum micromechanics of elastoplastic polycrystals. Journal of the Mechanics and Physics of Solids, 1965, 13: 89–101.CrossRefGoogle Scholar
  20. [20]
    Gong, X.N., Soil Plasticity. Zhejiang University Press, 1999 (in Chinese).Google Scholar
  21. [21]
    Yu, H.S and Sloan, S.W., Bearing capacity of jointed rock. In: Proceedings of the 8th International Conference on Computer Methods and Advances in Geomechanics, West Virginia: Balkema Publishers, 1994: 2403–2408.Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2012

Authors and Affiliations

  • Hongtao Zhang
    • 1
  • Jianming Zhu
    • 1
  • Yinghua Liu
    • 2
  • Bingye Xu
    • 2
  • Xiaochun Wang
    • 1
  1. 1.Department of Civil EngineeringNorth China University of TechnologyBeijingChina
  2. 2.Department of Engineering MechanicsTsinghua UniversityBeijingChina

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