REQUIREMENTS FOR ACCURATE ESTIMATION OF FRACTAL PARAMETERS FOR SELF-AFFINE ROUGHNESS PROFILES USING THE LINE SCALING METHOD

A new concept of feature size range of a roughness profile is introduc ed in the paper. It is shown that this feature size range plays an imp ortant role in estimating the fractal dimension, D, accurately using t he divider method. Discussions are given to indicate the difficulty of using both the divider and the box methods in estimating D accurately for self-affine profiles. The line scaling method's capability in qua ntifying roughness of natural rock joint profiles, which may be self-a ffine, is explored. Fractional Brownian profiles (self-affine profiles ) with and without global trends were generated using known values of D, input standard deviation, sigma, and global trend angles. For diffe rent values of the input parameter of the line scaling method (step si ze a(0)), D and another associated fractal parameter C were calculated for the aforementioned profiles. Suitable ranges for no were estimate d to obtain computed D within +/-10% of the D used for the generation. Minimum and maximum feature sizes of the profiles were defined and ca lculated. The feature size range was found to increase with increasing D and sigma, in addition to being dependent on the total horizontal l ength of the profile and the total number of data points in the profil e. The suitable range for no was found to depend on both D and sigma, and then, in turn, on the feature size range, indicating the importanc e of calculating feature size range for roughness profiles to obtain a ccurate estimates for the fractal parameters. Procedures are given to estimate the suitable no range for a given natural rock joint profile to use with the line scaling method in estimating fractal parameters w ithin +/-10% error. Results indicate the importance of removal of glob al trends of roughness profiles to obtain accurate estimates for the f ractal parameters. The parameters C and D are recommended to use with the line scaling method in quantifying stationary roughness. In additi on, one or more parameters should be used to quantify the non-stationa ry part of roughness, if it exists. The estimated C was found to depen d on both D and sigma and seems to have potential to capture the scale effect of roughness profiles.