岩石变形破坏的熵突变过程与破坏判据
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摘要
在岩石的变形破坏过程中,当进入不稳定的破裂发展阶段之后,系统不断调整结构抵抗外力的扰动,裂纹向局域集中的有序方向发展,应变能不断耗散,并以应变能的耗散为媒介,使系统与外扰动所追加的负熵流产生能量流通,也使系统熵值和系统的维数逐次降低,这一阶段岩石系统远离平衡态,岩石的破坏是系统熵的突变过程。基于这一认识,并在验证应变能分布与结构块度分布模式的一致性的基础上,推导出包含了结构因素和能量分布的熵表达式;对熵表达式进行平衡分析获得局部突变的分岔集,得到了岩石局部破坏的熵折迭突变破坏准则;同时,探讨了熵表达式所表征的结构有序度的尖点突变性,解出岩石系统的分岔集,这个分岔集就是岩石系统熵突变的整体破坏准则。
It is well known that in the deformation and failure process of rocks,a rock system will constantly readjusts its structure to resist the external pressure when it develops to an unstable crack propagation period.Thus,the cracks are gradually concentrated to a local area orderly;and the strain energy is continuously dissipated.The system will have an energy circulation with the negentropy flow that is produced and added by an external disturbing.At the same time,the entropy of the system,which shows the chaotic degree of the structure and energy,is decreased;meanwhile,the dimension of the system shows that the uniform degree of the structure and spatial distribution of energy is decreased too.The rock system is far from the equilibrium state in this period;and the failure process means a catastrophic process of the system entropy.Based on the realization which is discussed above,the paper derives an entropy equation which contains structural factors and energy distribution on the basis of testifying the uniform of strain energy distribution and structural block distribution mode.By giving an equilibrium analysis of the entropy equation,the bifurcation set shows the local catastrophe is obtained;so,the entropy fold catastrophic failure criterion shows a local failure of rocks is obtained.Meanwhile,the cusp-catastrophe represents the degree of order of rock structure by entropy equation is discussed;By finding the solution of the bifurcation set of a rock system,the bifurcation set is the integrated failure criterion which is shown the entropy catastrophe of a rock system.
It is well known that in the deformation and failure process of rocks,a rock system will constantly readjusts its structure to resist the external pressure when it develops to an unstable crack propagation period.Thus,the cracks are gradually concentrated to a local area orderly;and the strain energy is continuously dissipated.The system will have an energy circulation with the negentropy flow that is produced and added by an external disturbing.At the same time,the entropy of the system,which shows the chaotic degree of the structure and energy,is decreased;meanwhile,the dimension of the system shows that the uniform degree of the structure and spatial distribution of energy is decreased too.The rock system is far from the equilibrium state in this period;and the failure process means a catastrophic process of the system entropy.Based on the realization which is discussed above,the paper derives an entropy equation which contains structural factors and energy distribution on the basis of testifying the uniform of strain energy distribution and structural block distribution mode.By giving an equilibrium analysis of the entropy equation,the bifurcation set shows the local catastrophe is obtained;so,the entropy fold catastrophic failure criterion shows a local failure of rocks is obtained.Meanwhile,the cusp-catastrophe represents the degree of order of rock structure by entropy equation is discussed;By finding the solution of the bifurcation set of a rock system,the bifurcation set is the integrated failure criterion which is shown the entropy catastrophe of a rock system.
引文
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[2]陈顒.分形与地球科学[J].华南地震,1994,14(3):85-92.CHEN Yong.Fractal geometry and geoscience[J].South China Journal of Seismology,1994,14(3):85-92.
[3]谢和平,陈忠辉,段法兵.综放顶煤爆破的能量分形研究[J].力学与实践,2002,22(1):16-18.XIE He-ping,CHEN Zhong-hui,DUAN Fa-bing,Fractal study on blasting energy of top coal[J].Mechanics and Engineering,2000,22(1):16-18.
[4]许传华.围岩稳定分析的非线性理论研究[J].岩土工程技术,2003,3,142-146.
[5]周翠英,邓毅梅.软岩饱水过程中微观结构变化规律研究[J].中山大学学报(自然科学版),2003,42(4):98-102.
[6]许传华,任青文.地下工程围岩稳定性分析方法研究进展[J].金属矿山,2003,(2):34-37.
[7]谢应齐,曹杰.非线性动力学数学方法[M].北京:气象出版社,2001,10.
[8]同济大学数学教研室高等数学[M].上海:高等教育出版社,1996,4.
[9]陈建军,曹一波,段宝岩.结构信息熵与极大熵原理[J].应用力学学报,1998,15(4):116-121.CHEN Jian-jun CAO Yi-bo Duan BAO-yan,Informational Entropy of Structure and Maximum Entropy Principle[J].Chinese Journal of Applied Mechanics,1998,15(4):116-121.
[10]Ishido T,Nishizawa O.Effects of zeta potential on micro-crack growth in rock under relatively low uniaxial compression[J].Jourmal of Geophysical.Research,1984,89(B6):4 153-4 159.
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