狭窄煤柱岩爆的突变理论分析

CATASTROPHE THEORY ANALYSIS ON ROCKBURST IN NARROW COAL PILLAR

基于简化的狭窄煤柱岩爆分析模型和功、能增量平衡关系,导得狭窄煤柱岩爆的突变模式属折迭突变模型。该突变模型的平衡方程和平衡路径所展示的全部性态,可对煤柱以岩爆形式破坏和渐进形式破坏过程中包括系统稳定性在内的所有主要行为作一一对应的描述。首次给出的岩梁弹性能变化(释放)率曲线包含了丰富的信息量,对理解岩梁-煤柱系统在各阶段的行为规律有着重要的作用。能量输入率0=J是系统失稳的临界条件,其表达式中蕴涵了Cook刚度判据,故可视为Cook判据能量形式的动态推广。

Based on the simplified analytic model of rockburst in narrow coal pillar,the catastrophe model of rockburst in narrow coal pillar,the fold catastrophe model can be educed by equilibrium relation of work-energy increment from energy conservation principle. All the characteristics,demonstrated by the equilibrium equation and its equilibrium path of catastrophe model,can be used to describe the main behaviors of failure process in coal pillar with the forms of rockburst and gradual damage one by one correspondingly. The variation rate curve of elastic energy of rock beam,which includes abundant information,is given for the first time,which is of great significance for understanding the behavior and law of rock beam-coal pillar system in each phase. The presented study results show that energy importing rate J = 0 is the critical condition of system destabilization,which implicates Cook stiffness criterion and is a dynamic generalization of Cook criterion in the form of energy.