岩体失稳前兆阶段准静态形变平衡方程和加载参数——能量输入率
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摘要
由能量守恒原理导得的岩体失稳前兆阶段准静态形变平衡方程中包括Ι体的弹性能释放率、II体的能量耗散率和环境对系统的能量输入率(或广义地称为“环境与岩体系统能量交换率”),包涵了岩体系统准静态形变过程的完整信息量。阐述了用能量输入率J呈递减或递增趋势,来判别系统稳定性与用Dirichlet势函数2阶导数正负法则判别系统稳定性的结果完全一致;J>0是环境对系统输入能量;J<0是系统对环境输出能量;J=0是岩体系统动力失稳的临界条件,可用于确定岩体系统失稳起始点和终止点;这些可为准确计算地震、岩爆时释放的地震能等问题提供科学依据。首次从仿照弹性稳定理论得到的系统总势能全量函数形式,正确导得岩体系统准静态形变的平衡方程。
Rock′s quasi-static deformation equilibrium equation in premonitory phase of rock destabilization,which is induced by the energy conservation principle,includes body I′s elastic energy releasing rate,body II′s energy dissipation rate and energy importing rate (or generally titled“energy exchanging rate of surroundings and rock”)which is surroundings acting on the system;and full information of rock′s quasi-static deformation course is covered. Analysis and illustration show it is consistent in discriminating the system stability by energy importing rate J — presenting the descending or increasing tendency,and by Dirichlet discrimination law. Outside or surroundings imports energy into rock system when J >0;and the system exports energy to outside or surroundings when J< 0;J =0is the dynamic destabilization critical condition of rock,and which can be applied to determine the starting point and ending point of rock destabilization. They can offer scientific basis for calculating releasing energy of earthquake when earthquake or rockburst happens. The quasi-static strain equilibrium equation of rock system is deduced correctly for the first time from whole amount form of totalpotential energy obtained by imitating elastic stabilization theory.
Rock′s quasi-static deformation equilibrium equation in premonitory phase of rock destabilization,which is induced by the energy conservation principle,includes body I′s elastic energy releasing rate,body II′s energy dissipation rate and energy importing rate (or generally titled“energy exchanging rate of surroundings and rock”)which is surroundings acting on the system;and full information of rock′s quasi-static deformation course is covered. Analysis and illustration show it is consistent in discriminating the system stability by energy importing rate J — presenting the descending or increasing tendency,and by Dirichlet discrimination law. Outside or surroundings imports energy into rock system when J >0;and the system exports energy to outside or surroundings when J< 0;J =0is the dynamic destabilization critical condition of rock,and which can be applied to determine the starting point and ending point of rock destabilization. They can offer scientific basis for calculating releasing energy of earthquake when earthquake or rockburst happens. The quasi-static strain equilibrium equation of rock system is deduced correctly for the first time from whole amount form of totalpotential energy obtained by imitating elastic stabilization theory.
引文
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[9]潘岳,王志强.圆形硐室岩爆的折迭突变模型[J].岩土力学,2005,26(2):175–181.(Pan Yue,Wang Zhiqiang.Fold catastrophe model of circular tunnel rockburst[J].Rock and Soil Mechanics,2005,26(2):175–181.(in Chinese))
[10]Karcinovic D.Statistical aspects of the continuous damage theory[J].International Journal of Solids and Structures,1982,18(7):551–562.
[11]陈忠辉,唐春安,傅宇方.岩石失稳破裂的变形突跳研究[J].工程地质学报,1997,5(2):143–149.(Chen Zhonghui,Tang Chun′an,Fu Yufang.Study on sudden jump of deformation in unstable failure of rock[J].Journal of Engineering Geology,1997,5(2):143–149.(in Chinese))
[2]Tang C A,Xu X H.Sudden jump of deformation in unstable failure of rock[A].In:The International Congress on Rock Mechanics[C].[s.l.]:[s.n.],1995.197–199.
[3]林鹏,唐春安,陈忠辉,等.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,Chen Zhonghui,et al.Numerical and experiment study on deformation and failure behavior in a double rock specimen system[J].Earthquake,1999,19(4):413–418.(in Chinese))
[4]Das S,Aki K.Fault planes with barriers:versatile earthquake model[J].J.Geophys.Res.,1977,82:5658–5670.
[5]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 Jianxin,Tang Chun′an,Zhu Wancheng.Rock-coal model for studying the rockburst[J].Chinese Journal of Geotechnical Engineering,2004,26(2):276–280.(in Chinese))
[6]潘岳.岩石破裂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 Shanfa.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,张孝武.狭窄煤柱岩爆的折迭突变模型[J].岩石力学与工程学报,2004,23(1):23–30.(Pan Yue,Zhang Xiaowu.The catastrophe theory analysis of rockburstin narrow coal pillar[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(1):23–30.(in Chinese))
[9]潘岳,王志强.圆形硐室岩爆的折迭突变模型[J].岩土力学,2005,26(2):175–181.(Pan Yue,Wang Zhiqiang.Fold catastrophe model of circular tunnel rockburst[J].Rock and Soil Mechanics,2005,26(2):175–181.(in Chinese))
[10]Karcinovic D.Statistical aspects of the continuous damage theory[J].International Journal of Solids and Structures,1982,18(7):551–562.
[11]陈忠辉,唐春安,傅宇方.岩石失稳破裂的变形突跳研究[J].工程地质学报,1997,5(2):143–149.(Chen Zhonghui,Tang Chun′an,Fu Yufang.Study on sudden jump of deformation in unstable failure of rock[J].Journal of Engineering Geology,1997,5(2):143–149.(in Chinese))
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