Cusp Catastrophe Model of Instability of Pillar in Asymmetric Mining

A simplified mechanical model of pillar-hang wall was established in asymmetric mining and instability of the system was discussed by means of potential energy principle and cusp catastro phe theory. The necessary-sufficient condition and the jump value of displacement of pillar and the re leased energy expressions were derived, which established foundation for quantifying of the instability of system. The results show that instability of the system is related to load and its stiffness distribu tion. The critical load increases with the increasing relative stiffness, and the system is more stable. On the contrary, the instability of system is likely to occur, and the released energy is larger in insta bility process, and the harm is more tremendous accordingly. Furthermore, an example was calculat ed, and the estimated results correspond to practical experience, which provide basis for mining order and arranging stope.