Repair, Evaluation, Maintenance and Rehabilitation Research Program. SurfaceRoughness Characterization of Rock Masses Using the Fractal Dimension and the Variogram

摘要

Fractal dimension analysis, a branch of mathematical topology, and the variogramconstruction from the theory of regionalized variables were applied to geologic rock surface descriptive data. The purpose was to determine the technique's applicability to characterize rock surface roughness and to the semi-empirical prediction of the surface shear strengths. Both the fractal dimensions and variograms were determined from data obtained on the DS + 122 slide surface at Libby Dam, MT. The data used were a fine-scale photogrammetric contour map of the joint surface and string line profiles measured on the joint surface. Fractal dimensions were found to exactly reflect the qualitative roughness of the surface and found to be directly proportional to the roughness in a numerical comparison. Variograms of the natural surface data demonstrate that roughness elevations are spatially correlated and have a finite spatial continuity. The variogram is also useful for examining asperity magnitude differences across the joint surface. The variogram demonstrated more descriptive ambiguity than did the fractal dimension. Fractal dimensions of roughness profiles of small rock specimens were calculated and compared to the Joint Roughness Coefficient used in the empirical rock shear strength criterion. A least squares relationship: JRC = -1022.55 + (1023.92) D with D as the fractal dimension was determined. (edc)