Theoretical analysis of breaking strength of mine pillars and test specimens

This paper presents a theoretical analysis of the effect of shape and size on strength of geologic materials. The results indicate that the shape effect is caused by the development of confining pressure at the interfaces. The linearization of the obtained formula is of the same form determined by experiments. The size effect is attributed to the fact that the geologic materials contain discontinuities in the form of fractures, bedding planes, and cleats. The maximum reduction factor for the size effect is the one-sixth power of the volume of a cubic test specimen. The results of this work are particularly useful in determining the strength of coal pillars in underground mines.