Proposal of a New Comprehensive Parameter to Characterize Directional Multi-Scale Morphological Complexity of Discontinuity in Rock Tunnel

In rock tunnel engineering, the discontinuity roughness plays a crucial role in rock mass stability. Nevertheless, no suitable parameter is currently available to describe the multi-scale morphological complexity associated with varying shear directions. Improved 1D and 3D fractal dimensions are proposed and systematically evaluated for their ability to characterize the anisotropy and morphology complexity. The results show that the trends of improved 1D and 3D fractal dimensions are consistent with the Grasselli parameter GP(θ) along the orthogonal direction of the major and minor axes, which effectively characterizes the anisotropy. Meanwhile, they effectively characterize the profile and discontinuity morphology complexity, respectively. On the basis of the evaluation results, a comprehensive parameter is proposed to quantify directional multi-scale morphological complexity, which characterizes the discontinuity anisotropy, local roughness, and global morphological complexity simultaneously. Furthermore, the proposed parameter is compared with GP(θ) based on the Huashansong tunnel, using the concordance correlation coefficient and macro-trend similarity as evaluation criteria. The results show a moderate correlation between the two parameters, with a concordance correlation coefficient of 0.716. The overall similarity score of 85.8 and the macroscopic trend similarity of 71.0 indicate strong consistency in morphological features. In addition, the RMSE and MAE of γ(θ) are 0.25 and 0.19, which is lower than that of the existing GP(θ) and PSD-based methods in the study of characterizing the dominant morphology complexity direction.