Fractal analysis of fractures in rocks: the Cantor's Dust method

Abstract The Cantor's Dust method of fractal analysis has been used to describe the regularity of fracture patterns in geological materials seen on a two-dimensional surface. This linear method of analysis is well adapted to a determination of two-dimensional phenomena. The determination of the fractal dimension, D, indicates that it varies regularly as a function of the orientation of the analysis direction. This is taken to indicate that there is a relation, unexplained as yet, between the regularity of the fracture pattern and the forces which produced it. The use of the Cantor's Dust method on naturally fractured materials ranging in dimension from 3 mm to 45 m in maximum dimension indicates the fractal nature of the fractures found in natural materials. The analysis method can also be used to identify local variations in the stress field which caused failure, such as the fractures in a feldspar compared to those in the host granite, etc. The method appears to be a sensitive descriptive measure of the failure patterns in rocks.