How to Achieve Representative Roughness Measurement of a 3D Rock Discontinuity Surface

The roughness of rock discontinuities is a critical property that significantly affects rock mass behavior. While various parameters have been proposed in numerous studies for roughness measurement, recent advancements enable the assessment of roughness using 3D digital elevation models (DEMs) obtained through digital cameras, drones, and LiDAR technology. Despite these advancements, challenges remain in ensuring the representativeness of roughness measurements due to scale effects and the inherent limitations of 2D profile-based parameters. Although some 3D roughness parameters have been applied to better represent the three-dimensional characteristics of rock discontinuities, these parameters often fall short of capturing the full complexity of such surfaces and do not adequately correlate with conventional 2D parameters, such as the Joint Roughness Coefficient (JRC) or Z2. In this study, we present an innovative methodology for effectively quantifying roughness from 3D DEMs of rock discontinuities, taking into account scale effects and enabling conversion to conventional 2D parameters like Z2. We determined the minimum relevant size of the discontinuity required for roughness measurements to stabilize, thereby ensuring the acquisition of representative roughness values. Beyond addressing scale effects, our approach emphasizes the evaluation of roughness from 3D DEMs, which reflects morphological variations more effectively and facilitates conversion to traditional 2D parameters. This study introduces a formula for calculating Z2 using single-value roughness parameters, specifically Rq and Fractal Dimension, derived from 3D DEMs of various synthetic discontinuity surfaces. Furthermore, we validate the proposed formula through 3D modeling and evaluation of natural rock discontinuities. In conclusion, this approach aims to overcome the limitations of 2D roughness assessments, providing greater objectivity and consistency across evaluators in roughness measurement