Ellipsoid reconstruction and tensor characterization of planar fractures incoal obtained by CT scanning and the applications

CT scanning technique provides an important means to observe the internal fractures of coal. However，due to the high complexity of the CTscanned fracture field in coal，the accurate and quantitative description for the fracture field remains tough and unsolved in our field. Through CT scanning，it was found that the mesofractures in coal mainly consist of planar fractures. Herein，a solution based on ellipsoid model was proposed for quantitatively describing the planar fractures in coal obtained by CT scanning. Firstly，the CTscanned planar fracture structures in coal were discretized into triangular meshes which were simplified and repaired afterwards by using Geomagic Wrap software，and multiple triangular fracture surfaces were obtained and used to replace the original fracture structure. Then，a special ellipsoid，namely rotary oblate ellipsoid，was used to fit each triangular planar fracture，and thus the ellipsoid model reconstruction for the entire fracture structure was accomplished. The governing equations and solving strategies of the reconstruction for the planar ellipsoid in twodimensional and threedimensional spaces were given in detail，which was verified by a specific case，and its reconstruction accuracy analysis was given. Further，by using the reconstructed ellipsoidal fracture field，the planar fracture orientation tensor and fabric tensor were coined respectively to quantitatively characterize the CTscanned planar fractures in coal，and a simplified calculation method for the planar fracture orientation tensor and fabric tensor was provided. As for the application of fracture tensor theory，we selected three specific cases，such as simple planar fractures，real complex fracture structure obtained by CTscanning，and evolution process of the real fracture structure，which verified the effectiveness of fracture tensor theory to describe the complex fracture structures in coal. The differences between fracture tensor theory and porosity，fractal dimension description methods were clarified as well. As for the application of ellipsoid reconstruction method，we introduced its application prospect in theoretically prediction of the equivalent elastic modulus of fractured coal，verifying its applicability through numerical simulation analysis.