岩体动力失稳的折迭突变模型
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摘要
讨论了目前采用突变理论研究岩体动力失稳存在的问题。尖点突变模型对同一参数最多有3个平衡状态,其中一个不稳定另两个稳定,它描述的是两个稳定平衡状态在一定条件下可以相互转换、重复的系统;折迭突变模型最多有两个平衡状态,一个稳定,一个不稳定,它描述系统不能重复的本构失稳问题。由系统在平衡位置作准静态位移时的功、能增量关系式,按能量守恒原理推导了两体系统的平衡方程,建立了两体系统动力失稳的折迭突变模型,给出了岩体动力失稳问题的一般方程,得到了系统失稳前后的变形突跳和系统能量释放的一般表达式,基于Weibull分布的岩体本构关系为其特例。
The problems existing in rock dynamic destabilization are discussed by use of the catastrophe theory. There are three equilibrium states for the cusp catastrophe model. One is unstable, the others are stable. One equilibrium state can reach another equilibrium state. For the fold catastrophe model there are two equilibrium states. One is stable, the other is unstable. One equilibrium state can not change to the other equilibrium state. According to the energy conservation principle, the equilibrium equation is established. A fold catastrophe model of rock dynamic destabilization is generalized by adopting a general form of material constitutive equation. The equations of deformation catastrophe and energy release of the material are obtained. The catastrophe material constitutive relationship of Weibull distribution is introduced into the generalized fold model.
引文
[1]蔡美峰.岩石力学与工程[M].北京:科学出版社,2002.(CAI Mei-feng.Rock mechanics and engineering[M].Beijing:Science Press,2002.(in Chinese))
    [2]张明,李仲奎.准脆性材料破裂过程失稳的尖点突变模型[J].岩石力学与工程学报,2006,25(6):1233-1239.(ZHANG Ming,LI Zhong-kui.A cusp catastrophe model of unstable process of quasi-brittle materials[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(6):1233-1239.(in Chinese))
    [3]唐春安,徐小荷.岩石破裂过程失稳的尖点突变模型[J].岩石力学与工程学报,1990,9(2):100-107.(TANG Chun-an,XU Xiao-he.A cusp catastrophic model of rock unstable failure[J].Chinese Journal of Rock Mechanics and Engineering,1990,9(2):100-107.(in Chinese))
    [4]潘一山,章梦涛.洞室岩爆的尖角型突变模型[J].应用数学和力学,1994,15(10):893-900.(PAN Yi-shan,ZHANG Meng-tao.The study of chamber rockburst by the cusp model of catastrophe theory[J].Applied Mathematics and Mechanics,1994,15(10):893-900.(in Chinese))
    [5]徐曾和,徐小荷,唐春安.坚硬顶板下煤柱岩爆的尖点突变理论分析[J].煤炭学报,1995,20(5):485-491.(XU Zeng-he,XU Xiao-he,TANG Chun-an.Theoretical analysis of a cusp catastrophe bump of coal pillar under hard rocks[J].Chinese Journal of Coal Society,1995,20(5):485-491.(in Chinese))
    [6]潘岳.岩石破坏过程的折迭突变模型[J].岩土工程学报,1999,21(3):299-303.(PAN Yue.Fold catastrophe model of damaging in rock[J].Chinese Journal of Geotechnical Engineering,1999,21(3):299-303.(in Chinese))
    [7]潘岳,刘英,顾善发.矿井断层冲击地压的折迭突变模型[J].岩石力学与工程学报,2001,20(1):43-48.(PAN Yue,LIU Ying,GU Shan-fa.Fold catastrophe model of mining fault rockburst[J].Chinese Journal of Rock Mechanics and Engineering,2001,20(1):43-48.(in Chinese))
    [8]潘岳,王志强.岩体动力失稳的功、能增量-突变理论研究方法[J].岩石力学与工程学报,2004,23(9):1433-1438.(PAN Yue,WANG Zhi-qiang.Rock coal model for studying the rockburst[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(9):1433-1438.(in Chinese))
    [9]林鹏,唐春安.二岩体系统破坏全过程的数值模拟和实验研究[J].地震,1999,19(4):413-418.(LIN Peng,TANG Chun-an.Numerical and experimental study on deformation and failure behavior in a double rock specimen system[J].Earthquake,1999,19(4):413-418.(in Chinese))
    [10]刘建新,唐春安,朱万成.煤岩串联组合模型及冲击地压机理研究[J].岩土工程学报,2004,26(2):276-280.(LIU Jian-xin,TANG Chun-an,ZHU Wan-cheng.Rock coal model for studying the rockburst[J].Chinese Journal of Geotechnical Engineering,2004,26(2):276-280.(in Chinese))
    [11]潘岳,王志强,吴敏应.岩体动力失稳终止点、能量释放量解析解与图解[J].岩土力学,2006,27(11):1915-1921.(PAN Yue,WANG Zhi-qiang,WU Min-ying.Analytic solution and illustration on destabilization end and energy releasing amount of rock dynamic destabilization[J].Rock and Soil Mechanics,2006,27(11):1915-1921.(in Chinese))
    [12]凌复华.突变理论及其应用[M].上海:上海交通大学出版社,1987.(LING Fu-hua.Catastrophe theory and its application[M].Shanghai:Shanghai Jiaotong University Press,1987.(in Chinese))

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