岩体动力失稳的折迭突变模型  

Fold catastrophe model of rock dynamic destabilization

作　　者：张黎明[1] 王在泉[1] 张晓娟[1] 王志强[1] 

机构地区：[1]青岛理工大学理学院,山东青岛266033

出　　处：《岩土工程学报》2009年第4期552-557,共6页Chinese Journal of Geotechnical Engineering

基　　金：国家自然科学基金项目(50674059);山东省教育厅项目(J07YB01)

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.

关 键 词：动力失稳 突变理论 折迭突变 WEIBULL分布 

分 类 号：TU452[建筑科学—岩土工程] TD324.1[建筑科学—土工工程]