A calculational model for 3D fault complexity based on curvature analysis and fractal dimensions

Objective and Methods Faults are identified as one of the most threatening geological structural factors among hidden disaster-causing factors in coal mines. However, the 3D quantitative assessment of them remains challenging. Considering that existing quantitative indicators fail to fully reflect fault morphologies and there is a lack of 3D methods, this study proposed a calculational model for 3D fault complexity based on curvature analysis and fractal dimensions. This model improved the morphologies of traditional measurement volumes of fractal dimensions by employing the Delaunay tetrahedralization algorithm, thus effectively reducing the invalid values in calculating the 3D fractal dimensions of faults. Moreover, the model modified fault parameters by introducing fault plane curvatures, thereby retaining the structural characteristics of faults. To validate its effectiveness, this model was applied to the faults revealed in a coal mine in Shaanxi Province. Using this model, this study conducted a qualitative assessment of the complexity of geological structures and examined the data on the spatial distributions of the historical water inrush points in the mining face and roadways. Results and Conclusions Using this model, 75 partitioning intervals with nonzero statistics were identified in the mine field. Calculations revealed that the average 3D fractal dimension of faults and 3D fault complexity values integrated with Gaussian and mean curvatures were 0.9394, 1.1362, and 1.2199, respectively. Compared to a single fractal dimension, the fault complexity integrated with curvatures enjoyed significant advantages in revealing the differences in fault strikes and fault concentration zones. Based on the Pearson correlation coefficients calculated using the 3D fault complexity and the distance between sample points and water inrush points as two correlation indicators, water inrush points can be categorized into two types: those in the mining face and those in roadways. For water inrush points in the mining face, the average coefficients of their correlations with 3D fractal dimension of faults and 3D fault complexity integrated with Gaussian and mean curvatures were 0.7843, 0.8386, and 0.9072, respectively, while these average coefficients were 0.7718, 0.8324, and 0.8903, respectively, for water inrush points in roadways. These data indicate that fault complexity is highly correlated with water inrush points in the mining face compared to water burst points in roadways. In other words, the production activities in the mining face within the study area are more significantly affected by faults. Additionally, the Pearson correlation coefficients all exceeded 0.77 regardless of the curvature integrated, suggesting a strong correlation between the 3D fault complexity and the water hazard conditions of coal mines. The qualitative assessment reveals that the overall structural complexity of the coal mine is relatively low and is primarily affected by faults. The fault complexity values of the coal mine were determined at around 1, exceeding 2 in very few zones. This result implies the overall low fault complexity of the coal mine despite local fault concentration, aligning with the qualitative assessment results. The above methods validate the effectiveness of the proposed model, which provides a new modeling approach for the calculation of 3D fault complexity.