Catastrophe Theory Analysis on Asymmetric Mining Pillar Dynamic Failure
Based on the simplified analytic model of asymmetric mining rock beam-pillar system, the catastrophe model of dynamic failure of the rock beam-pillar system in asymmetric mining has been established by way of the differential form of total potential function deduced by law of conservation of energy. Analysis and illustration show it is consistent in discriminating the system stability by energy importing rate J—presenting the descending or increasing tendency. Outside or suroundings imports energy into rock beam-pillar system when J> 0; and the system exports energy to outside or surroundings when J<0.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.
Dongye Sun, Wen-Pei Sung and Ran Chen
Z. Q. Wang et al., "Catastrophe Theory Analysis on Asymmetric Mining Pillar Dynamic Failure", Applied Mechanics and Materials, Vols. 71-78, pp. 4662-4667, 2011