A comparative study on joint roughness description by fractal, scaling and statistical methods

In a recent study of the relationships between geometric and mechanical properties of rock joints, a computer numerically controlled (CNC) milling machine was used to create reproducible joint surfaces with controlled parameter variations. In order to provide representative surface profiles to the CNC machine for rock joint manufacture, three different mathematical approaches were used for joint surface description: fractal (spectral), geometric scaling, and a statistical method. Rock joints were manufactured using each of the three description approaches, and visually compared. It was found that the rough surfaces generated by the fractal method using parameter values derived from profile measurements on natural joint surfaces were very close in appearance to the original joints. In the geometric mapping approach, a measured joint profile was scaled down isotropically. The resulting surface had a texture that was significantly different than the prototype natural rock joint surface, demonstrating that the surface is not self–similar. The statistical approach involved synthesis of a surface that had the same auto–correlation function as the prototype natural joint. It did not yield a satisfactory description of a joint surfaces. While the auto–correlation function was adequately duplicated in the resulting surface, its appearance was not at all like a natural rock joint.