Instability Mechanism of Pillar Burst in Asymmetric Mining Based on Cusp Catastrophe Model

Pillars are often reserved asymmetrically in the mining process. The roof deflection curve under non-equal span conditions of adjacent stopes is derived by considering the roof-pillar system as a rock beam-pillar model. The pillar instability condition under asymmetric mining is determined based on instability theory and cusp catastrophe theory. Pillar burst represents the equilibrium stability of the roof-pillar system. The pillar failure may be in a violent manner or a gentle manner, depending on the post-peak stiffness ratio of the roof-pillar system. By calculating the factor of safety (FOS) and roof-pillar stiffness ratio K, the pillar stability with different stope spans can be evaluated. The theoretical results are validated by comparison with a case study and numerical simulation. When the stope spans are not equal, the pillar is affected by small-eccentric compression. Four pillar failure patterns under eccentric compression are proposed and explained. The main factors affecting pillar burst appear to include the geometric parameters and mechanical properties of the roof-pillar system. It is difficult to change the mechanical properties, but the stiffness ratio K can be increased by improving the geometric parameters, so as to minimize the burst tendency. Once K < 1 and the critical compression failure load is reached, the pillar on the larger stope span side fails first, and then, the whole pillar loses its stability. Considering the external work during the pillar unstable failure, the rockburst energy index is optimized.