A novel 3D adaptive isogeometric phase-field approach for rock fracture failure

The phase field model is a powerful tool for modelling 3D rock mass fracture, with significant potential in geothermal energy development, shale gas extraction, and nuclear waste storage. However, its high computational cost poses a major challenge for engineering applications. To address this issue, this manuscript develops a robust and efficient 3D adaptive isogeometric phase-field approach for modeling the evolution of spatial crack surfaces. Within the isogeometric analysis framework, hierarchical B-Spline/NURBS splines are employed to construct a hierarchical mesh, allowing for real-time local refinement as cracks propagate, and to establish a complete hierarchical C¹ basis function space for solving high-order phase-field models. Additionally, a straightforward cell-marking criterion is developed to predict and identify potential crack propagation regions, along with an efficient variable transfer strategy between old and new meshes. The key components of the proposed method include the hierarchical mesh, hierarchical basis function space, cell-marking criterion, and variable transfer strategy. Four 3D numerical cases are provided to assess the effectiveness, computational advantage, and performance of the proposed method. The results show that the proposed method effectively captures detailed features of 3D irregular fracture surfaces while reducing computational time by 95.4% and memory usage by 91.6% compared to uniform meshes. This advancement lays a solid foundation for overcoming the high computational cost associated with phase-field models, thereby enhancing their practical engineering applications.