Three-dimensional fractal distribution of the number of rock-mass fracture surfaces and its simulation technology
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 (DS) of the fracture surfaces and the fractal parameter (DL) of the fracture trajectory in a 2D profile, DL=DS?1, has been derived. It has further been proved that the 2D fractal dimension (DL) is not related to the initial value of the fracture-surface distribution. The initial value of the 2D fractal distribution (NL) shows a linear relation with the initial value of the 3D fractal distribution (NS), NL=kNS, where k is determined by the projection relation between the rock-mass profile and the 3D fracture surface. The program developed in this research to simulate fractal analysis of rock-mass fractures and the correlation between 2D and 3D fractal characteristics could facilitate study of the fracture-trajectory distribution on any rock-mass profile and that of the fracture surfaces in any subblock. This work provides theoretical and technical support for stability analysis in geological engineering.
fractal fracture surface simulation technology distribution type 2d-3d correlation