Inferring fracture forming processes by characterizing fracture network patterns with persistent homology

Persistent homology is a mathematical method to quantify topological features of shapes, such as connectivity. This study applied persistent homology to analyze fracture network patterns in rocks. We show that persistent homology can detect paths connecting from one boundary to the other boundary constituting fractures, which is useful for understanding relationships between fracture patterns and flow phenomena. In addition, complex fracture network patterns so-called mesh textures in serpentine were analyzed by persistent homology. In previous studies, fracture network patterns for different flow conditions were generated by a hydraulic-chemical-mechanical simulation and classified based on additional data and on expert's experience and knowledge. In this study, image analysis based on persistent homology alone was able to characterize fracture patterns. Similarities and differences of fracture network patterns between natural serpentinite and simulation were quantified and discussed. The data-driven approach combining with the persistent homology analysis helps to infer fracture forming processes in rocks. The results of persistent homology analysis provide critical topological information that cannot be obtained by geometric analysis of image data only.