断层是煤矿隐蔽致灾因素中威胁最大的地质构造因素之一，其三维量化评价一直是个难题。针对现有量化指标无法全面反映断层形态及缺乏三维方法的不足，提出了一种结合曲率分析与分形维数的断层三维复杂度计算模型。该模型利用Delaunay算法改进了传统分形维数测量体形态，有效减少在断层三维分形维数计算中存在的无效值，并引入断层面曲率来修正断层参数量，从而保留了断层自身结构特征。为验证模型的有效性，选取陕西某煤矿实际揭露的断层，地质构造复杂程度定性评价以及工作面、巷道历史突水点空间分布数据开展模型应用及验证。

模型识别出煤矿井田空间内共有75个剖分区间具有非零统计值，计算得出断层三维分形维数、两种融合断层面曲率(高斯曲率和平均曲率)的断层三维复杂度的均值，分别为0.9394、1.1362、1.2199，与单一的分形维数相比，融合曲率的复杂度指标在揭示断层走向差异及分布集中区方面表现出明显优势。此外，将断层三维复杂度、样本点与各突水点间的距离作为2个相关性指标计算皮尔逊相关系数，结果可分为工作面及巷道突水点两类，其平均值按断层三维分形维数、融合断层面高斯曲率以及平均曲率的断层三维复杂度排序，前者为0.7843、0.8386以及0.9072，后者为0.7718、0.8324、0.8903。数据表明，断层复杂度与工作面突水点的相关性均大于与巷道突水点的相关性，即在研究区内，断层对工作面的生产活动影响更大。此外，无论融合何种断层面曲率，相关系数均在0.77以上，即提出的断层三维复杂度与矿井水害条件有强相关关系。另一方面，结合该煤矿构造复杂程度定性评价为总体较低，且主要受断层影响，而该煤矿的断层复杂度在1左右，极少区域在2以上，反映了该煤矿断层分布虽在部分区域较为集中，但总体的断层复杂程度较低，与该煤矿已有的构造复杂程度定性分析相符。两种方式均验证了提出的断层三维复杂度计算模型的有效性，经过验证有效，为三维断层复杂度计算提供了一种新的模型构建思路。

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.

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.