Abstract:Based on the discontinuity and abruptness of the pillar instability, the sufficient and necessary conditions for the failure of the column are deduced by the catastrophe theory, and the release of the instability of the column Energy mechanism. The results show that the energy difference before and after the failure of the pillar is independent of the external disturbance, and only depends on the internal characteristics of the roof - pillar system. The discussion of this paper provides a strong reference for the rational layout of the mine and the optimization of the parameters of the roof and pillar.