Using an approach based on the theory of similitude, a general equation and related concepts were developed that provide new insights to an old problem. The load-bearing capacity (strength) of a square, retangular, or cylindrical prism of a brittle material such as rock, coal, or concrete is expressed as the mathematical product of a size effect, a shape effect, and a function of the mechanical properties (deformability, cleat-joint spacing, and friction) of the pillar, roof, and floor materials. Through an application of multivariate statistical analysis, the results of assorted tests (laboratory and in situ) and observations of failed pillars can be combined into a fundamental scaling equation, which provides a unified, consistent approach to the estimation of mine pillar strength. The form of the equation is sufficiently general to be able to incorporate refinements in the characterization of the structural parameters, as they become available through future analysis and experimentation. Analysis of the published test data suggests that pillar compressive strength (per unit of area) is proportional to the cube root of the pillar width, and that the height effect can be described as the superimposing of a variable size effect (characteristic of the material) on the constant width effect.
Trans., SME/AIME, V. 268, 1981, PP. 1749-1761