A novel system for multivariate analysis of discontinuities in fractured rock masses based on manifold learning and fractal models

The engineering-geological characteristics of fractured rock masses depend on the discontinuity properties, which can be analyzed by the stereonet-based system. However, this system faces challenges in describing orientations, which are spherical data, and it cannot incorporate other scalar parameters (e.g., trace length, aperture, etc.) that affect engineering practice. Therefore, a novel system based on manifold learning is proposed to analyze the distribution patterns of orientation data and characterize multiple discontinuity properties. The proposed system uses manifold learning to explore and visualize the manifold structure of orientation data by a two-dimensional kernel density estimation (2D-KDE) technique. It also integrates other parameters into the manifold structure to capture multiple properties. To quantify the manifold structure and reveal the real fractal behaviors of orientation data, a detailed analysis process including monofractal and multifractal models is proposed. The effectiveness of the proposed system is verified by comparison with the stereonet-based system in several aspects. The equivalent manifold structure is also proposed to enhance the engineering applicability of the system, and one of its applications is demonstrated. Finally, the proposed system is applied to a significant road project and further developed by unmanned aerial vehicle (UAV) photogrammetry. The proposed system provides new insights for research on fractured rock masses and has great potential for solving multi-parameter problems in engineering geology.