An adaptive mesh refinement algorithm for stress-based phase field fracture models for heterogeneous media: Application using FEniCS to ice-rock cliff failures

Abstract

Fracture propagation in heterogeneous ice-rock cliffs and hanging glaciers is complicated by the presence of internal interfaces and material property mismatch, so their failure risk is difficult to assess. Despite recent advances, phase-field fracture modeling is computationally expensive for large-scale homogeneous and heterogeneous material media. Here, we present an adaptive mesh refinement algorithm for the stress-based phase-field fracture model for heterogeneous media, implemented within the open-source finite element software package FEniCS. The novelty of the proposed algorithm includes its ability to handle material heterogeneity by representing elastic and fracture properties as fields via material distribution functions. These properties, along with the solution fields, are then appropriately transferred during the mesh refinement process without requiring a redefinition. We present several numerical studies to benchmark the method and analyze fracture predictions in idealized homogeneous and heterogeneous rock and ice-rock domains. Through these studies, we demonstrate the method’s accuracy and efficiency of simulations in multi-dimensions, and examine the effect of material properties and the interface inclination on fracture propagation. The results indicate that the mismatch of material properties at the rock-rock and ice-rock interfaces and the critical stress for fracture initiation can have a significant influence on crack propagation, including depth, length, and orientation. In three-dimensional geological fracture simulations, non-adaptive meshes would require handling billions of elements, whereas the proposed algorithm reduces the final mesh size to fewer than a million, demonstrating substantial computational savings and making it a practical approach for geological fracture simulation.