Applicability of fractal characterization and modelling to rock joint profiles

Abstract

Abstract Synthetic records of fractional Brownian motion ( f Bm) with known dimensions were generated using random midpoint displacement, spectral synthesis and deterministic fractal geometry methods. The validity of the methods used to measure the fractal dimensions of self-affine records was evaluated by examining the calculated dimensions of the synthetic f Bm records with known fractal dimensions. Two methods of fractal analysis (i.e. variogram and periodogram) were employed to determine the fractal dimensions of the profiles. Analysis of periodograms of f Bm records revealed a higher correlation between the expected and calculated dimensions of pre-whitened data. Variograms of those f Bm records indicated a better accuracy while smaller lag (i.e. approx. 10% of the profile length) of the synthetic profile length was used for determination. Laser profilometry was utilized as well to provide the measurement of joint roughness. Several natural rock joints were cored parallel to the joint faces. The cores were then analyzed with a laser profilometer for asperity measurement. The fractal dimensions of the natural joint profiles determined by using variograms and periodograms ranged from 1.3 to 1.4. The periodogram method, however, produced slightly higher dimensions than did the variogram method. Synthesized joint profiles of known dimensions were generated using fractal interpolation functions to provide a qualitative comparison with the natural joints. The computer generated profiles were found to mimic many of the visual characteristics of natural rock joints.