Unveiling the mystery of scale dependence of surface roughness of natural rock joints

Scale dependence of surface roughness of natural rock joints has long been an outstanding issue in rock mechanics. Controversial results were reported by various studies; however, the nature of scale dependency and the underlying mechanism for the conflicting observations remain unclear. Rock joints at different scales characterise two-order asperities, namely, waviness and unevenness; thus understanding how the individual roughness of waviness and unevenness vary as the joint size increases from the laboratory-scale to the large-scale is crucial for revealing the scale effect mystery. Here we digitise three natural granite joint surfaces with the same dimension of 1000 mm × 1000 mm through a high-resolution, three-dimensional scanner. Waviness and unevenness of each rock joint surface are quantitatively separated by selecting an appropriate sampling interval. The respective fractal dimensions of waviness and unevenness of joint surfaces sized from 100 mm × 100 mm to 1000 mm × 1000 mm are estimated through an improved roughness-length method. We find that the fractal dimensions of two-order roughness are scale-dependent but without generalised trends. The stationarity threshold beyond which the scale-dependency of roughness vanishes is absent for all the three joint samples, suggesting that the roughness of natural rock joints be assessed at the specific scale of the rock mass in-situ. We reveal that previous controversial results regarding scale effect are likely due to the composition of the roughness scaling of waviness and unevenness. Thus, accurate stability analysis of rock-engineering projects should consider separate contributions of multi-order asperities across scales to the strength and deformation of jointed rock masses.