岩体准静态运动失稳的 CUSP 型突变模型
A CUSP CATASTROPHE MODEL TO INTERPRET LOSS OF STABLE EQUILIBRIUM IN ROCK QUASI-STATIC MOVEMENT
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摘要: 为了研究岩体在水平力(N)和垂直力(P)作用下运动的稳定性问题,本文对简化的岩体系统建立了突变理论模型,用以定量描述引起运动失稳的应力条件.文中导出了系统的总势能函数表达式,证明了该系统可由 CUSP 型突变模型描述,确定了N-P 控制空间中使系统失去稳定平衡的分叉集 B.得到的主要结果是:对 N-P 控制空间中使岩体运动保持稳定平衡和失稳的区域进行了划分;分析了作用力的渐变导致状态突变的过程,和点(N,P)在控制空间的运动途径对岩体运动稳定性的影响;讨论了势能发生突变时,所要求的应力变化量级.并根据这些初步结果,讨论了地震过程的某些现象.Abstract: In order to study the stability in motion of a rock mass acted on by horizontal force(N) and vertical forces(P), a catastrophe theoretical model of a simplified rock mass system is proposed to interpret quantitatively the conditions of the stress which may cause the loss of stable equilibrium in motion.An expression of the total potential energy function for the rock mass model is derived. It has been proved that the above-mentioned system can be described by the CUSP catastrophe model. At. the same time, a bifurcation set B which makes the system to lose its stable equilibrium in the N-P control space is delimited.The primary results obtained are as follows: demarcation of the stability and unsta-bility regions in motion of the rock mass in the N-P control space, analysis of the process of sudden state variation due to the gradually changing forces and the influence of the paths of the point (N,P) in the control space on the stability in motion of the rock mass; and order of magnitude of the stress variation necessary for the sudden change of potential energy is discussed. On the basis of these preliminary results some earthquake phenomena are reviewed.
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[2] 王仁、丁中一、殷有泉,固休力学基础,地质出版社,88——137, 1979.
[3] 许绍燮、沈佩文,北京周围地区地震的分布特点与地壳屈曲,地震学报,2, 2, 1:3——167, 1980,
[4] Henley, 5., Catastrophe theory models in geology, Mathematical Geology, 8, 6, 1976,
[5] 郭增建等,从水平和垂直力的相互作用讨论我国境内地震孕育和发生,地球物理学报,20, 3, 1977.
[6] 罗焕炎,从大陆地壳动力学观点试论我国地震的成因和机制,地震地质,1, 1, 1979.
[7] 丁文镜,地慢快速隆起对构造地震的触发作用,西北地震学报,4, 2, 1982.
[8] 陈应天,突变理论在力学中的应用,力学与实践,1, 3, 1979.
[9] Tim Poston and Ian Stewart, Catastrophe theory and .its applications, Pitman, 1978,
[10] 丁国瑜、梅世蓉、马宗晋,地震预报问题,地震科学研究,1, 1979.
[11] 康仲远、陆松澄,地震过程的几个突变理论模型,地震统计预报论文集,地震出版社,1982.
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