Stability, instability and design of pillar workings

Abstract

The stability of a laboratory compression test of a brittle rock specimen depends on the stiffness of the loading machine and on the slope of the complete force-displacement relation of the specimen. The stability of pillar workings is discussed by generalizing the simple mechanism of the laboratory test to the mining situation. This is achieved by assuming that the rock mass is linearly elastic and by replacing the stresses exerted by the pillars on the roof and floor by statically equivalent forces. It is shown that pillar workings will be stable if the real symmetric matrix K + λ is positive definite. Here, K is the stiffness matrix of the mining layout and λ is the slope matrix of the complete load-convergence relations of the pillars. It is proved that the workings will remain stable, regardless of the magnitude of the convergence experienced by the pillars, if the minimum slope of the load-convergence relations is greater than the smallest eigenvalue of K taken with a negative sign. Also, methods of determining matrix K and the approximate values of average pillar loads are discussed. Finally, a design criterion is introduced which is aimed at the improvement of mineral extraction by pillar mining at moderate and large depths.