Evaluation of previous remedial construction along the Duquesne Bluff

Abstract

Accurate quantification of roughness is important in modeling strength, deformability and fluid flow behaviors of joints. Self-affine fractals seem to have potential to represent rock joint roughness profiles. Both stationary and non-stationary fractional Brownian profiles (self-affine profiles) with known values of fractal dimension, D, and input standard deviation, σ, were generated. For different values of the input parameter of the roughness-length method (window size, w), D and another associated fractal parameter A were calculated for the aforementioned profiles. It was found that σ has no effect on calculated D. A range for w between 1 (length having about 10 roughness data points) and 20 (10% of the total profile length) was found to be highly suitable to estimate D with 10% error for roughness profiles having D between 1.3 and 1.7 and a length of 200 units. Results indicated that the given roughness-length methodology has the capability of producing accurate estimates for fractal parameters for both stationary and non-stationary profiles with a global linear trend. The estimated A was found to increase with both D and σ and seems to have potential to capture the scale effect of roughness profiles. The parameter combinations (a) D and A or (b) D and the cross-over length, are suggested to use with the roughness-length method to quantify stationary roughness. In addition, one or more parameters should be used to quantify the non-stationary part of roughness, if it exists. The calculated cross-over lengths of the profiles indicated the difficulty in measuring roughness heights of natural rock joints at measurement intervals comparable to the cross-over lengths of the profiles. The study showed the necessity to know the effect of input and profile parameter values on the estimated fractal parameters in order to calculate these parameters accurately.