Computational framework for obtaining volumetric fracture intensity from 3D fracture network models using Delaunay triangulations

Fracture intensity, the degree of fracturing in rock masses, is one of the fundamental parameters used in characterizing rock mass as a fracture network. Among fracture intensity measures, volumetric fracture intensity (P32) is the most useful, since it directly reflects the degree of rock mass fracturing, independent of fracture orientation and size distribution. P32 represents the total area of fractures per cubic meter, and it can simultaneously reflect the spacing and size component of fractures. Because P32 cannot be directly measured in the field, previous works have developed various inference methods based on available 1D and 2D measures collected from field surveys. At present, discrete fracture network (DFN) models are deemed to be a suitable method for the characterization of fractured rock mass. Hence, calculating P32 from a DFN model is also a widely accepted approach. However, the geometry-based method cannot effectively address the irregular simulation space, and the methods employed are ill-suited if polygonal fractures appear in the DFN model. To solve these deficiencies, a computational framework based on the Delaunay triangulation of 3D uniformly distributed random points is introduced, and a detailed description is presented. The proposed computational framework is suitable for various types of DFN models, such as Baecher disk models, elliptical disk models and Dershowitz polygon models. A simulated example was generated to verify the proposed computational framework. Finally, a DFN model is built based on fracture data acquired from the Songta hydropower station, and the proposed computational framework was used to calculate P32 for the DFN model.