岩体系统动力失稳的总势能函数诠释
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摘要
定量阐述了在岩体系统准静态形变路径不同的位置处,系统有不同的总势能;岩体系统动力失稳释放的能量?Π与失稳起始点j、终止点s之间的能量关系为Πs=Πj+△Π,其中△Π<0;发现折迭突变模型势函数的微分是全微分,利用全微分的积分值与路径无关的性质,对在普通试验机上加载发生脆性破坏的岩样,在伺服试验机上通过油缸排油对外界输出能量,使岩样以渐进形式破裂的现象进行阐述。计算表明,油缸排油对外界输出的能量与岩样脆性破坏时系统以动力形式释放的能量相同;利用格林公式算得,系统平衡位置在折迭突变平衡路径上沿直线跳跃时释放的弹性能,等于直线与准静态平衡路径围成面积D的负值。分析表明,处于极限状态的岩体系统,不论是在准静态还是动力失稳的形变增大过程中,系统总势能总是向减小的方向发展。所得结果深化了对岩体动力失稳现象的认识、提高了量化描述水平。
It had been expatiated quantitatively that the rock system had different values of the total potential energy at different positions on the quasi-static deformation path.The relationship between the energy,?Π,released by rock system dynamic failure and that at the failure starting point j and the failure halting point s was Π s= Π j + ?Π,and it was essential that ?Π <0.It had also been discovered that the differential of the potential function of fold catastrophe model was the total differential.Based on the characteristic that the integration value of the total differential was not related to the path of integration,the phenomenon that the rock sample failed in stepped form as a result of energy output to environment by oil drainage of the cylinder on a servo experimental machine had been expatiated,and the rock sample failed in brittle form while it was loaded on an ordinary experimental machine.It was indicated that the energy output to environment by oil drainage of the cylinder was equal to the energy released by the system in dynamic form while the rock sample failued in brittle form.By using Green formula,it was obtained that the released elastic energy while the equilibrium position of system leaping along straight line on fold catastrophe equilibrium path could be expressed by negative value of the area D enclosed by the straight line and quasi-static equilibrium path.Furthermore,it was also obtained that the total potential energy of the rock system in limit state always changed towards decreasing direction no matter whether it was in quasi-static or dynamic course of deformation.
It had been expatiated quantitatively that the rock system had different values of the total potential energy at different positions on the quasi-static deformation path.The relationship between the energy,?Π,released by rock system dynamic failure and that at the failure starting point j and the failure halting point s was Π s= Π j + ?Π,and it was essential that ?Π <0.It had also been discovered that the differential of the potential function of fold catastrophe model was the total differential.Based on the characteristic that the integration value of the total differential was not related to the path of integration,the phenomenon that the rock sample failed in stepped form as a result of energy output to environment by oil drainage of the cylinder on a servo experimental machine had been expatiated,and the rock sample failed in brittle form while it was loaded on an ordinary experimental machine.It was indicated that the energy output to environment by oil drainage of the cylinder was equal to the energy released by the system in dynamic form while the rock sample failued in brittle form.By using Green formula,it was obtained that the released elastic energy while the equilibrium position of system leaping along straight line on fold catastrophe equilibrium path could be expressed by negative value of the area D enclosed by the straight line and quasi-static equilibrium path.Furthermore,it was also obtained that the total potential energy of the rock system in limit state always changed towards decreasing direction no matter whether it was in quasi-static or dynamic course of deformation.
引文
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[3]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 process in rock[J].Chinese Journal of Geotechnical Engineering,1999,21(3):299–303.(in Chinese))
[4]潘岳,刘瑛,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))
[5]潘岳,王志强.狭窄煤柱岩爆的折迭突变模型[J].岩土力学,2004,25(1):23–30.(PAN Yue,WANG Zhi-qiang.Fold catastrophe model of rockburst in narrow coal pillar[J].Rock and Soil Mechanics,2004,25(1):23–30.(in Chinese))
[6]潘岳,张勇,于广明.圆形硐室岩爆机制及其突变理论分析[J].应用数学和力学,2006,27(6):741–749.(PAN Yue,ZHANG Yong,YU Guang-ming.Mechanism and catastrophe theory analysis of circular tunnel rockburst[J].Applied Mathematics and Mechanics[J].2006,27(6):741–749.(in Chinese))
[7]KARCINOVIC D.Statistial aspects of the continuous damage theory[J].Int J Solids Structures,1982,18(7):551–562.
[8]陈应天.突变理论在力学中的应用[J].力学与实践[J].1979,1(3):9–14.(CHEN Ying-tian.Application of catastrophe theory in mechanics[J].Mechanics in Engineering,1979,1(3):9–14.(in Chinese))
[9]郑颖人,沈珠江,龚晓南.岩土塑性力学[M].北京:中国建筑工业出版社,2002.(ZHING Ying-ren,SHEN Zhu-jiang,GONG Xiao-nan.Rock and soil plastic mechanics[M].Beijing:China Architecture and Building Press,2002.(in Chinese))
[10]窦林名,田京城,陆菜平.组合煤岩冲击破坏电磁辐射规律研究[J].岩石力学与工程学报,2005,24(19):3541–3544.(DOU Lin-ming,TIAN Jing-cheng,LU Cai-ping.Reseach on electromagnetic radiation rules of composed coal-rock burst failure[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(19):3541–3544.(in Chinese))
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