Journal of Central South University of Technology

, Volume 11, Issue 4, pp 445–450 | Cite as

Analysis of progressive failure of pillar and instability criterion based on gradient-dependent plasticity

  • Wang Xue-bin Email author


A mechanical model for strain softening pillar is proposed considering the characteristics of progressive shear failure and strain localization. The pillar undergoes elastic, strain softening and slabbing stages. In the elastic stage, vertical compressive stress and deformation at upper end of pillar are uniform, while in the strain softening stage there appears nonuniform due to occurrence of shear bands, leading to the decrease of load-carrying capacity. In addition, the size of failure zone increases in the strain softening stage and reaches its maximum value when slabbing begins. In the latter two stages, the size of elastic core always decreases. In the slabbing stage, the size of failure zone remains a constant and the pillar becomes thinner. Total deformation of the pillar is derived by linearly elastic Hooke’s law and gradient-dependent plasticity where thickness of localization band is determined according to the characteristic length. Post-peak stiffness is proposed according to analytical solution of averaged compressive stress-average deformation curve. Instability criterion of the pillar and roof strata system is proposed analytically using instability condition given by Salamon. It is found that the constitutive parameters of material of pillar, the geometrical size of pillar and the number of shear bands influence the stability of the system; stress gradient controls the starting time of slabbing, however it has no influence on the post-peak stiffness of the pillar.

Key words

instability criterion strain softening pillar strain localization shear band progressive failure slabbing rock burst 

CLC number



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  1. [1]
    Linkov A M. Rockburst and instability of rock masses [J]. Int J Rock Mech Min Sci, 1996, 33(7): 727–732.CrossRefGoogle Scholar
  2. [2]
    Salamon M D G. Stability, instability and design of pillar workings[J]. Int J Rock Mech Min Sci, 1970, 7 (6): 613–631.CrossRefGoogle Scholar
  3. [3]
    Salamon M D G. Energy considerations in rock mechanics: fundamental results[J]. J South Afr Int Min Metall, 1984, 84: 237–246.Google Scholar
  4. [4]
    Vardoulakis I. Rock bursting as a surface instability phenomenon[J]. Int J Rock Mech Min Sci, 1984, 21 (3): 137–144.CrossRefGoogle Scholar
  5. [5]
    ZHANG Meng-tao. The instability theory and numerical simulation of rock burst[J]. Chin J Rock Mech Engrg, 1987, 6(3): 197–204. (in Chinese)MathSciNetGoogle Scholar
  6. [6]
    XU Zheng-he, XU Xiao-he, TANG Chun-an. Theoretical analysis of a cusp catastrophe bump of coal pillar under hard rocks[J]. Journal of China Coal Society, 1995, 20(5): 485–491. (in Chinese)Google Scholar
  7. [7]
    PAN Yi-shan, ZHANG Meng-tao, LI Guo-zheng. The study of chamber rockburst by the CUSP model of catastrophe theory[J]. Applied Mathematics and Mechanics, 1994, 15(10): 943–951.CrossRefGoogle Scholar
  8. [8]
    PAN Yue, LIU Ying, GU Shan-fa. Fold catastrophe model of mining fault rockburst[J]. Chin J Rock Mech Engrg, 2001, 20(1): 43–48. (in Chinese)Google Scholar
  9. [9]
    Vardoulakis I, Papanastasiou P. Bifurcation analysis of deep boreholes: I. Surface instabilities [J]. Int J Num Anal Meth Geomech, 1988, 12: 379–399.CrossRefGoogle Scholar
  10. [10]
    de Borst R, Muhlhaus H B. Gradient-dependent plasticity: formulation and algorithmic aspects[J]. International Journal for Numerical Methods in Engineering, 1992, 35(3): 521–539.CrossRefGoogle Scholar
  11. [11]
    WANG Gui-yao, SUN Zong-qi, QING Du-gan. Fracture mechanics analysis of rock burst mechanism and prediction[J]. The Chinese Journal of Nonferrous Metals, 1999, 9(4): 841–845. (in Chinese)Google Scholar
  12. [12]
    FENG Tao, PAN Chang-liang. Lamination spallation bucking model for formation mechanism of rock burst [J]. The Chinese Journal of Nonferrous Metals, 2000, 10(2): 287–290. (in Chinese)Google Scholar
  13. [13]
    HUANG Qing-xiang, GAO Zhao-ning. Mechanical model of fracture and damage of coal bump in the entry[J]. Journal of China Coal Society, 2001, 6(2): 156–159. (in Chinese)Google Scholar
  14. [14]
    TANG Li-zhong, WANG Wen-xing. New rock burst proneness index[J]. Chin J Rock Mech Engrg, 2002, 21(6): 874–878. (in Chinese)Google Scholar
  15. [15]
    TANG Li-zhong, PAN Chang-liang, WANG Wen-xing. Surplus energy index for analyzing rock burst proneness[J]. Journal of Central South University of Technology (Natural Science), 2002, 33(2): 129–132. (in Chinese)Google Scholar
  16. [16]
    YIN Guang-zhi, ZHANG Dong-ming, DAI Gao-fei, et al. Damage model of rock and the damage energy index of rockburst[J]. Journal of Chongqing University, 2002, 25(9): 75–79. (in Chinese)Google Scholar
  17. [17]
    JI Hong-guang, WANG Jin-an, CAI Mei-feng. Relativity and unity physical and geometrical characteristics of rockbursting events[J]. Journal of Coal Science & Engineering, 2002, 28(1): 31–36. (in Chinese)Google Scholar
  18. [18]
    FENG Xia-ting, ZHAO Hong-bo. Prediction of rock-burst using support vector machine [J]. Journal of Northeastern University (Natural Science), 2002, 23 (1): 57–59. (in Chinese)MathSciNetGoogle Scholar
  19. [19]
    FENG Xia-ting, Webber S, Ozbay M U. Neural network assessment of rockburst risks for deep gold mines in South Africa[J]. Trans Nonferrous Met Soc China, 1998, 8(2): 335–341.Google Scholar
  20. [20]
    CAI Mei-feng, LAI Xing-ping. Evaluation on stability of stope structure based on nonlinear dynamics of coupling artificial neural network[J]. Journal of University of Science and Technology Beijing, 2002, 9 (1): 1–4.CrossRefGoogle Scholar
  21. [21]
    PAN Chang-liang, ZHU Fang-cai, CAO Ping, et al. Characteristics of acoustic emission of bursting-induced rocks under unaxial compression[J]. Journal of Central South University of Technology (Natural Science), 2001, 32(4): 336–338. (in Chinese)Google Scholar
  22. [22]
    CAI Mei-feng, LAI Xing-ping. Monitoring and analysis of nonlinear dynamic damage of transport roadway supported by composite hard rock materials in Linglong Gold Mine[J]. Journal of University of Science and Technology Beijing, 2003, 10(2): 10–15.Google Scholar
  23. [23]
    WU Ai-xiang, SUN Ye-zhi, Gour S, et al. Characteristics of rockburst and its mining technology in mines [J]. Journal of Central South University of Technology (English Edition), 2002, 9(4): 255–259.CrossRefGoogle Scholar
  24. [24]
    CAI Mei-feng, WANG Jin-an, WANG Shuang-hong. Prediction of rock burst with deep mining excavation in Linglong Gold Mine[J]. Journal of University of Science and Technology Beijing, 2001, 8(4): 241–243.Google Scholar
  25. [25]
    WANG Xue-bin, YANG Xiao-bin, ZHANG Zhi-hui, et al. Dynamic analysis of fault rockburst based on gradient-dependent plasticity and energy criterion[J]. Journal of University of Science and Technology Beijing, 2004, 11(1): 5–9.Google Scholar
  26. [26]
    WANG Xue-bin, PAN Yi-shan, HAI Long. Instability criterion of fault rock burst based on gradient-dependent plasticity[J]. Chin J Rock Mech Engrg, 2004, 23(4): 588–591. (in Chinese)Google Scholar
  27. [27]
    WANG Xue-bin, PAN Yi-shan, MA Jin. Analysis of strain (or the ratio of strain) in the shear band and a criterion on instability based on the energy criterion [J]. Chinese Journal of Engineering Mechanics, 2003, 20(2): 111–115. (in Chinese)CrossRefGoogle Scholar
  28. [28]
    WANG Xue-bin, ZHAO Yang-feng, ZHANG Zhi-hui, et al. Analysis of fault rockburst considering strain rate and strain gradient[J]. Chin J Rock Mech Engrg, 2003, 22(11): 1859–1862. (in Chinese)Google Scholar
  29. [29]
    WANG Xue-bin, PAN Yi-shan, REN Wei-jie. Instability of shear failure and application for rock specimen based on gradient-dependent plasticity[J]. Chinese Journal of Rock Mechanics and Engineering, 2003, 22(5): 747–750. (in Chinese)Google Scholar
  30. [30]
    CHEN R, Stimpson B. Simulation of deformation and fracturing in potash yield pillars, vanscoy, saskatchewan[J]. Can Geotech J, 1997, 34(2): 283–292.CrossRefGoogle Scholar
  31. [31]
    ZHANG Hong-wu, Schrefler B A. Gradient-dependent plasticity model and dynamic strain localization analysis of saturated and partially saturated porous media one dimensional model[J]. Eur J Mech A/Solids, 2000, 19(3): 503–524.CrossRefGoogle Scholar

Copyright information

© Central South University 2004

Authors and Affiliations

  1. 1.Department of Mechanics and Engineering SciencesLiaoning Technical UniversityFuxinChina

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