Fractal characteristics of rocks fractured under tension

Fractal geometry can be useful for explaining the fracture behavior and rock properties. The fractal properties of rock fracture surface developed under tension were examined. Seven different rock samples were selected for the tests. An automated surface scanning device was used to map the fractured surfaces. Variogram analysis (VA) (for 1D self-affine sets) and power spectral density (PSD) measurement (for 2D self-affine sets) were applied to calculate the fractal dimension. On a comparative basis, there exists a trend between the fractal dimension and loading rate. The profiles in the loading direction yield higher fractal dimensions indicating the anisotropic feature of fractal. The fractal dimensions obtained by PSD and VA display a relationship for grain size and porosity. Higher porosity samples give different fractal dimensions for upper and lower fractures surfaces.