A comparative study on the application of phase transition theory analytical method and phase plane method to strain localization in brittle rocks

The initiation and propagation of strain localization can lead to degradation of intergranular cementation, local strength loss of materials, and accelerated deformation instability, which can induce underground engineering disasters. Describing the strain localization process from the perspective of phase transition theory is reasonable. When solving the theoretical model, two analytical methods, the perturbation method and the phase plane method, are used for analysis. Both calculation results can effectively describe the strain localization process in rock masses. This study compares and analyzes the two solution methods, describing the strain localization process in rocks separately to determine which method is more reasonable for describing the evolution of strain localization. The research finds that the phase plane analysis method can describe the strain localization evolution phenomenon in materials, offering both rationality and simplicity. Through a multi-objective optimization algorithm (NSGA-II), the optimal numerical solution for the phase plane is matched, demonstrating speed and intelligence compared to traditional approximate analytical methods.