ATwo-dimensional Mono-fractal Approach to Natural Fracture Networks in Rocks

摘要

The mono-fractal dimension and geometric features of outcropping fractures in welded tuff and tuffaceous mudstone, and aritifcial 2D network models have been investigated. The fractal dimension of observed fracture sets were determined using the box-counting method, and several geometric characteristics including length distribution, orientation, connectivity, number of fractures, and total length of fractures were quantified in order to construct a two-dimensional fracture network model. The space filling fracturing of a welded tuff was represented by a single fractal dimension from 1.6mm through 10 m square scales, however, an universal fractal property could not be observed in the case of tuffaceous mudstone in spite of fractal behavior at each scale. These differences of fractal features between the welded tuff and the tuffaceous mudstone are considered to be related to the mechanism of fracture generation and different fracture mechanical characteristics. Computer-generated two-dimensional fracture network patterns of the welded tuff utilizing the observed fractal dimension and geometric relationship have been found capable of simulating the natural fracture patterns. This artificial model, which is founded on the uniform fractal property of a given fracture set from microscopic to 10 m scales in the welded tuff, is capable of being expanded to larger scales on the basis of self-similarity.