Phsw. Kulatilake et J. Um, Requirements for accurate quantification of self-affine roughness using the roughness-length method, INT J ROCK, 36(1), 1999, pp. 5-18
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
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