Determination of Intervening Pillar Thickness Based on the Cusp Catastrophe Model

For the stability of the intervening pillar of the sublevel drilling open-stope subsequent filling mining method, the multifactor stability mechanical model of the intervening pillar under two different constraint conditions (Model 1 and Model 2) was established based on the elastic thin plate theory. Then, the cusp catastrophe equation and the necessary and sufficient conditions for the instability of the intervening pillar under two different constraint conditions were obtained by using the cusp catastrophe theory. Furthermore, the minimum thickness formula for the intervening pillar without instability under two different constraint conditions was derived, and the relationships between the minimum thickness of the intervening pillar and the factors, including the depth of the stope, the inclination of the orebody, the thickness of the orebody, the height of the stage, the length of the stope, and the mechanical properties of the orebody, were analyzed. Finally, the formula was used in the design of an intervening pillar between stopes 4-1 and 4-2 in Panlong Lead-Zinc Mine. The designed thickness of the pillar was 6.01 m by calculation, its actual thickness was 6.35–7.25 m in the mining process, and its average thickness was 6.5 m. Compared with the previously designed thickness of 7-8 m at the same stage, the pillar was 0.5–1.5 m smaller, which more effectively improved the recovery rate of the ore under the premise of ensuring the stability of the intervening pillar. This example of industrial application proves that it is feasible to use the cusp catastrophe theory to analyze the stability and parameter design of the intervening pillar under different constraints.

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