Determining the optimal sampling interval for 3D morphology measurements of different-sized natural rock joints

Abstract

Efficiently studying the scale effect of surface roughness and peak shear strength of natural rock joints, especially unfilled and well-matched ones, requires an optimal sampling interval to realize cost-effective three-dimensional morphology measurements for different-sized natural rock joints with advanced non-contact optical devices. However, rationally determining such an optimal sampling interval remains controversial. To this end, inspired by digital signal processing, the optimal sampling interval is creatively determined by Shannon's sampling theorem using the Fourier series' optimum order. An empirical formula relating the joint size to the optimum order is correspondingly developed. The proposed empirical formula was found to work well under conditions of high normal stress, where the relative errors for the surface roughness and peak shear strength of series-sized natural rock joints were mostly less than 10% and 5%, respectively, but should be used cautiously under conditions of low normal stress. Furthermore, different from previous perceptions, a higher joint roughness level was discovered to not necessarily imply the need for a smaller optimal sampling interval, and conversely. The proposed empirical formula can facilitate the determination of the optimal sampling interval for measuring different-sized natural rock joints' surface morphologies in engineering practice.