Quantification of rock joint surface heterogeneity and its influence on roughness scale effect

Accurate characterization of joint surface morphology is critical for predicting the mechanical, hydraulic, and thermal behavior of jointed rock masses, yet reported scale effects for joint roughness remain inconsistent. This study investigated the role of surface heterogeneity on the roughness scale effect and proposed a morphology-based heterogeneity index that combines rotation-invariant local binary patterns (RI-LBP) with Shannon entropy. Performance assessment using synthetic surfaces, represented by hemispherical asperities, revealed that RI-LBP entropy is capable of distinguishing surface heterogeneity arising from asperity size, spatial arrangement, and noise. Entropy correlated with conventional roughness parameters (fractal dimension D, fractal amplitude A, 3D version of Z2, and CLA), showing positive relationships with D, A, and Z2s, but a weak negative relationship with CLAs. For self-affine surfaces, synthesized via inverse FFT, entropy increased monotonically with D, and was well described by bilinear or logarithmic models. Results showed that the proposed index could be utilized as an indicator of heterogeneity and partially of roughness. The heterogeneity index was itself subject to scale effects. A negative scale effect under random sampling was found in a large self-affine surface with convergence thresholds that decreased as D increased. Field scale natural rock joints exhibited similar trends but larger thresholds, reflecting natural variability of joints. As a practical guideline, analyzing about 15% of the mapped area yielded representative entropy across a wide roughness range (≤ 2% was sufficient when D ≥ 2.2). This study revealed the relationship between morphological heterogeneity of rock joint and its roughness scale effect (particularly the convergence scale), providing a practical guidance for sampling schemes and for interpreting laboratory to field scale translations in various analyses of rock joint.