Abstract: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.