Fold catastrophe model of dynamic pillar failure in asymmetric mining

A rock burst disaster not only destroys the pit facilities and results in economic loss but it also threatens the life of the miners. Pillar rock burst has a higher frequency of occurrence in the pit compared to other kinds of rock burst. Understanding the cause, magnitude and prevention of pillar rock burst is a significant undertaking. Equations describing the bending moment and displacement of the rock beam in asymmetric mining have been deduced for simplified asymmetric beam-pillar systems. Using the symbolic operation software MAPLE 9.5 a catastrophe model of the dynamic failure of an asymmetric rock-beam pillar system has been established. The differential form of the total potential function deduced from the law of conservation of energy was used for this deduction. The critical conditions and the initial and final positions of the pillar during failure have been given in analytical form. The amount of elastic energy released by the rock beam at the instant of failure is determined as well as. A diagrammatic form showing the pillar failure was plotted using MATLAB software. This plot contains a wealth of information and is important for understanding the behavior during each deformation phase of the rock-beam pillar system. The graphic also aids in distinguishing the equivalent stiffness of the rock beam in different directions.