On natural rock joint profile characterization using self-affine fractal approach

Self-affine properties of Barton’s ten standard profiles for the joint roughness coefficient (JRC) were analyzed using the theory of fractal geometry with the ultimate goal of relating the JRC values with the fractal properties of rock profiles. Four different methods were adopted in the study for calculation of fractal properties. The applicability of these methods was tested using the fractional Brownian motion functions with Hurst exponent (H) varying from 0.5 to 0.9. Against the common belief that a larger fractal dimension should correspond to a higher JRC value, all four methods consistently predict a decreasing trend of JRC values with increase in fractal dimension. This finding suggests that using fractal dimension alone for rock profile characterization is not sufficient. The intercept of the fractal model was found to be representative of the local trend (long wavelengths) of a rock profile that controls the shear behavior of rock joints at laboratory scales. To uniquely define a joint profile, both the fractal dimension and the intercept are needed. Even considering these two parameters in evaluating the ten profiles, our study has shown that not all of the ten standard profiles are representative of the roughness classes as suggested.