The authors examine whether or not the fractures in the rock mass are statistically self-similar by using the box counting method and the method using the distribution function of fracture trace length. Further, a method to estimate the fracture distribution of the universal set from a certain subset, are proposed. In order to obtain the data over a wide range, fracture maps at some different scales are used.
The objective districts were Asahi Mountain-land (here after called Gr. H) in Yamagata Prefecture and Hatsukari in Yamanashi Prefecture, in which granite and andesite are distributed, respectively. At some different scales of those rock mass, the fractal properties of the fracture trace length and the spatial distribution of fractures (fracture pattern) were investigated.
The results are surmmarized as follows:
1) The distribution of fracture trace length shows the fractal distribution, and the fracture pattern on a 2-D plane is described by the fractal geometry. The fracture trace length has the fractal property in the range from 10-2 m to 105 m.
2) In estimating the fractal dimension Dl by using the distribution of fracture trace length, the data from the mean length of the fracture trace to 0.8 times the side length of the measured area give a meaningful result. Using the box counting method, the fractal dimension Dg of fracture pattern should be estimated on the side length of box ranging from 1/2 times grid side length to 1/32 times one.
3) The fracture pattern has a statistical self-similarity. The fractal dimension Dg of the pattern is generally smaller than two. Hence, there is a non-uniformity of the spatial fracture distribution.
4) The fracture trace length distribution N of universal set at ηu×ηu area is expressed by the equation N=N′ (ηu/ηs) Dg. (N′ : Average distribution of the subsets, ηs×ηs: Area of the subset)
