Prediction of Mode I Fracture Behavior of Granite Under NSCB Configuration Using a Multi-task Conditional Generative Adversarial Network and Phase-Field Method

Predicting rock fracture performance is crucial for engineering safety assessment. However, traditional experimental methods are time-consuming and costly, while numerical simulations incur high computational costs, making it difficult to meet real-time assessment requirements. This paper proposes an end-to-end prediction framework that integrates phase-field method with a multi-task conditional generative adversarial network (MT-cGAN) for predicting crack propagation paths, displacement fields, and fracture toughness of granite. First, based on the statistical features of real granite polarized-light micrographs, 1,600 numerical samples were generated through stochastic reconstruction. The phase-field method (PFM) was employed to simulate the notched semi-circular bend (NSCB) test configuration, establishing a high-fidelity dataset linking mesostructure, crack paths, displacement fields, and fracture toughness. Second, an improved MT-cGAN model was designed, taking rock mesostructure images as input to simultaneously predict crack propagation paths and displacement fields, with fracture toughness KIC via inversion of the Williams series. Furthermore, Brazilian splitting tests on semi-circular disc specimens were conducted on granite to validate the effectiveness and accuracy of the proposed method. Finally, through multi-parameter sensitivity analysis, the influence mechanisms of the proportions and distribution characteristics of mineral components on rock fracture toughness were quantified. Results demonstrate that the crack path prediction achieved an intersection over union (IoU) of 89.33%, with an average relative error of 5.82% for KIC prediction. Single-sample inference time was 85 ms, representing a speedup of over 20,000 times compared to phase-field method (0.5 h). This method leverages physics-informed datasets generated by phase-field simulations while retaining the computational efficiency of deep learning, providing a novel and promising approach for rock fracture mechanism analysis and rapid engineering evaluation.