Characterization of a jointed rock mass based on fractal geometry theory

Characterization of a jointed rock mass is a fundamental step in the design of a geotechnical engineering project. In this paper, fractal descriptions for joint properties and discrete fracture network (DFN) modelling for a field rock mass are presented. Based on the field investigation in an open-pit mine, traditional probability density functions are used to describe the distributions of joint orientation, spacing and trace length. A special meshing method of Schmidt projection is firstly introduced to calculate the fractal dimension for joint orientation. Comparison between the Fisher parameter and the fractal dimension suggests that the latter is a better indicator since it contains more information on the joint orientation (i.e. joint number and dispersion level). Then, the calculation procedures of the fractal dimensions for joint spacing and trace length are provided, and the corresponding fractal probability density functions are deduced by introducing the minimum spacing/trace length value and the fractal dimension value. Based on fractal analysis, the DFN module embedded in 3DEC 5.0 is used to reconstruct the field rock mass. Considering the limitations of traditional distribution functions and the complexity associated with field joint data, the fractal geometry theory could serve as a more rational tool to delineate the discontinuous, non-homogenous and anisotropic features for rock materials.