A Fractal Topology-Based Method for Joint Roughness Coefficient Calculation and Its Application to Coal Rock Surfaces

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.