Three-dimensional fractal distribution of the number of rock-mass fracture surfaces and its simulation technology

摘要

The number of rock-mass fractures obeys a fractal distribution. In this study, numerical simulation was performed to confirm that the number of rock-mass fracture surfaces also obeys a three-dimensional fractal distribution. A simulation model is proposed here for the three-dimensional fractal distribution of the number of rock-mass fracture surfaces. Random distributions of fracture surfaces (RDFS) can be divided into three types: heavy random, weakly random, and distributed by group. By extensive calculations and theoretical deduction, the relation of the three types RDFS between the 3D fractal dimension (D-s) of the fracture surfaces and the fractal parameter (D-L) of the fracture trajectory in a 2D profile, D-L = D-s - 1, has been derived. It has further been proved that the 2D fractal dimension (D-L) is not related to the initial value of the fracture-surface distribution. The initial value of the 2D fractal distribution (N-L) shows a linear relation with the initial value of the 3D fractal distribution (N-s), N-L = kNs, where k is determined by the projection relation between the rock-mass profile and the 3D fracture surface.