Application of fractal geometry and electrical impedance measurement for the assessment of strength of granular materials

Data demonstrating a relationship between crushing strength of a variety of limestones and their fractal dimension are presented and a theoretical interpretation of the data proposed. The fractal dimension is determined from height variance measurements made on sawn surfaces of limestone hand specimens for a number of limestones commonly used as dimension stone in the U.K. Preliminary data measurements on the same limestone samples suggest that the fractal dimension, and therefore strength, can be determined by measuring the frequency dependance of their dielectric properties. In addition to strength, the fractal dimension is related to other physical properties. Thus, the relationship between fractal dimension and electrical impedance, in conjunction with the broad base of properties related to the fractal dimension, has practical implications for rapid assessment of granular materials in terms of their bulk physical properties.