Geostatistical analyses for relating rock joint roughness to shear strength

Surface roughness of clean joints in hard rock has a major influence on the shear-strength characteristics of those joints. Geostatistical tools, in particular the semivariogram and the spatial covariance functions, can be used to help characterize directional surface roughness, because they can be computed in a directional fashion by averaging over data pairs in specified orientations. Roughness measures derived from these directional geostatistical analyses that have shown promise in predicting directional shear strength include the sill-to-range ratio and the scaled area beneath the spatial covariance function, as well as the fractal dimension derived from directional semivariograms and from the spectrum of directional spatial covariance models. Directshear test results, where shear strength is described by a friction angle, have been related to these geostatistical roughness measures, yielding linear regression models with correlation coefficients as high as 0.98. Thus, such surface roughness measures can provide useful predictions of directional shear strength along clean rock joints.