Requirements for accurate quantification of self-affine roughness using the roughness-length method

Self-affine fractals have the potential to represent rock joint roughness p rofiles. Fractional Brownian profiles (self-affine profiles) with known val ues of fractal dimension, D, input standard deviation, sigma, and data dens ity, d, were generated. For different values of the input parameter of the roughness-length method (window length, w), D and another associated fracta l parameter A were calculated for the aforementioned profiles. The calculat ed D was compared with the D used for the generation to determine the accur acy of calculated D. Suitable ranges for w were estimated to produce accura te D (within +/-10% error) for the generated profiles. The results showed t hat to obtain reliable estimates for fractal parameters of a natural rock j oint profile, it is necessary to choose a unit for the profile length to sa tisfy a data density (ti) gl eater than or equal to 5.1. For roughness prof iles having 5.1 less than or equal to d less than or equal to 51.23 and 1.2 less than or equal to D less than or equal to 1.7, w values between 2.5% a nd 10% of the profile length were found to be highly suitable to produce ac curate fractal parameter estimates. It is recommended to use at least seven w values between the estimated minimum and maximum suitable w values in es timating fractal parameters of a natural rock joint profile. It was found t hat D and a global trend of a roughness profile have no effect on calculate d D. The estimated A was found to increase with both D and a. The parameter D captures the auto-correlation and ii captures the amplitude of a roughne ss profile at different scales. Therefore, the parameters D and A are recom mended to use with the roughness-length method in quantifying rock joint ro ughness. In addition, at least one more parameter is required to quantify t he global trend of a roughness profile, if it exist, in many cases just the inclination or declination angle of the roughness profile in the direction considered would be sufficient to estimate the global trend. Calculated cr oss-over lengths (segment length of a profile at which a self-affine profil e becomes self similar) for the profiles investigated were found to be extr emely small (less than 0.6% of the profile length) indicating that laser pr ofilometers are required to make roughness measurements at interval lengths comparable to the cross-over lengths of the natural rock joint profiles. T o calculate rock joint roughness parameters accurately using the self-simil ar techniques, it is necessary to have roughness measurements made at inter val lengths comparable to the cross-over length of the profile. This indica te clearly the difficulty of using self-similar techniques such as the divi der method in estimating rock joint roughness accurately. (C) 1999 Elsevier Science Ltd. All rights reserved.