On anisotropic fractal and multi fractal properties of rock fracture surfaces

The multifractal behavior of rock fracture surfaces is studied,with fractal heterogeneity and anisotropy of surface structure taken into account. A roughness probability is introduced as a measure of irregularity of fracture surface. A projective covering method (PCM) is proposed and used to directly estimate the fractal dimension D ∈2,3) of fracture surface. The study indicates that the multifractal spectrum of the fracture surfaces provides much information on the fracture mechanism. The fracture surfaces induced in rocks under different failure mechanisms display distinct multifractal properties.