Fractal analysis of joint patterns in granite

Two approaches for determining the stability of fractal dimensions (D) for fracture patterns in granite are examined. First, the stability of fractal dimensions for 1-D field measurements of joint spacing was investigated with respect to the number of measurements needed. At least 100–150 spacing measurements per joint set produced stable or accurate fractal dimensions where joints were regularly clustered and relatively regularly and widely spaced. Other spatial patterns require greater numbers of measurements per set. The stability of D for 1-D data is thus likely to depend on the spatial distribution of the joints within each joint set. Second, an alternate approach to estimate stable fractal dimensions based on scale invariance was explored. A combination of 1-D field data and 1- and 2-D image data was used. Fractal dimensions for the field data, which are unstable, ranged from 0.70–0.84, and for the image patterns, D ranged from 1.63–1.69, suggesting a 2-D fractal dimension of 1.7 for fractures in this area. These results suggest that the combined use of different data types with different dimensionality may overcome the problem of unstable fractal dimensions and allow reasonable estimates of stable fractal dimensions to be made.