Quantifying surface roughness heterogeneity and its contribution to roughness scale dependency in rock joints

While the shear behavior of rock joints is influenced by multiple factors such as rock strength, normal stress, and boundary conditions, this study focuses on morphological surface roughness, specifically on two key aspects: the scale effect, which reflects the variations in surface roughness characteristics as a function of the joint surface size and the roughness heterogeneity, which reflects spatial variations in surface roughness characteristics. Although many studies have explored the scale dependency of rock joints, most have overlooked the impact of roughness heterogeneity. The objective of this work is to quantify roughness heterogeneity and demonstrate its influence on scale dependency. An 800 mm × 800 mm granite surface was scanned with a laser profilometer at a resolution of 72 μm. Heatmap and polar plot analyses were performed on eight sample sizes ranging from 100 mm × 100 mm to 800 mm × 800 mm. To achieve this, a new parameter, the roughness heterogeneity index (RHI), was proposed to measure roughness heterogeneity. The findings of this study indicate that the inconsistent results regarding roughness scale dependency reported in the literature cannot be attributed solely to the size of the sampling window, interval spacing, or scanning resolution. Instead, roughness scale dependency is primarily influenced by the surface roughness heterogeneity. This highlights the importance of carefully selecting sampling window locations and expansion directions to account for surface heterogeneity, ultimately improving the reliability of field-scale representative sampling and subsequent analyses. These findings underscore the value of including surface heterogeneity in roughness assessments, which could improve predictive modeling of joint shear strength and lead to better design practices in rock engineering and geotechnical fields.