The accurate evaluation of the Joint Roughness Coefficient (JRC) is crucial for rock mechanics engineering. Existing JRC prediction models based on a single fractal parameter often face limitations in physical consistency and predictive accuracy. This study proposes a novel two-parameter JRC prediction method based on fractal topology theory. The core innovation of this method lies in extracting two distinct types of information from a roughness profile: the scale-invariant characteristics of its frequency distribution, quantified by the Hurst exponent (H), and the amplitude-dependent scale effects, quantified by the coefficient (C). By integrating these two complementary aspects of roughness, a comprehensive predictive model is established: JRC = 100.014H−1.5491C1.2681. The application of this model to Atomic Force Microscopy (AFM)-scanned coal rock surfaces indicates that JRC is primarily controlled macroscopically by amplitude-related information (reflected by C), while the scale-invariant frequency characteristics (reflected by H) significantly influence local prediction accuracy. By elucidating the distinct roles of scale-invariance and amplitude attributes in controlling JRC, this research provides a new theoretical framework and a practical analytical tool for the quantitative evaluation of JRC in engineering applications.
Wang et al. (Thu,) studied this question.