<p>The phase field method (PFM) has attracted significant attention in rock fracture due to its distinct advantages in simulating complex crack propagation without explicit interface tracking. However, existing phase field models often exhibit limitations in accurately capturing the mechanical response and fracture patterns of rock, particularly under compressive-shear loading. To address these shortcomings, this study proposes an improved phase field model for rock fracture. The proposed model incorporates three key optimizations: First, a stress-based energy decomposition method is introduced to integrate the modified Mohr–Coulomb (M-C) failure criterion into the energy-driven phase field framework. Second, a generalized threshold strategy is developed to account for the tension–compression asymmetry of rock by defining distinct threshold parameters. Third, a novel compressive-shear energy driving force and its critical energy release rate are defined to characterize the influence of strength parameters (cohesion and internal friction angle) on the mechanical response during rock fracture. Subsequently, the accuracy of the proposed model is validated through two benchmark tests—the single element test and the single edge notched shear test. Furthermore, simulations of uniaxial compression tests on pre-cracked rock specimens and Brazilian disc tests demonstrate the model's capability to accurately capture the typical fracture patterns and mechanical responses of rock. Finally, the practical applicability of the proposed model is highlighted through the failure analysis of hard rock tunnels with varying cross-sections and the instability analysis of rock slopes.</p>

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A Phase Field Model for Rock Fracture Based on the Modified Mohr–Coulomb Failure Criterion

  • Mingtao Zhang,
  • Gen Li,
  • Guang Han,
  • Laigui Wang,
  • Xiangfeng Liu,
  • Qi Sun,
  • Chuang Sun,
  • Jinyang Du

摘要

The phase field method (PFM) has attracted significant attention in rock fracture due to its distinct advantages in simulating complex crack propagation without explicit interface tracking. However, existing phase field models often exhibit limitations in accurately capturing the mechanical response and fracture patterns of rock, particularly under compressive-shear loading. To address these shortcomings, this study proposes an improved phase field model for rock fracture. The proposed model incorporates three key optimizations: First, a stress-based energy decomposition method is introduced to integrate the modified Mohr–Coulomb (M-C) failure criterion into the energy-driven phase field framework. Second, a generalized threshold strategy is developed to account for the tension–compression asymmetry of rock by defining distinct threshold parameters. Third, a novel compressive-shear energy driving force and its critical energy release rate are defined to characterize the influence of strength parameters (cohesion and internal friction angle) on the mechanical response during rock fracture. Subsequently, the accuracy of the proposed model is validated through two benchmark tests—the single element test and the single edge notched shear test. Furthermore, simulations of uniaxial compression tests on pre-cracked rock specimens and Brazilian disc tests demonstrate the model's capability to accurately capture the typical fracture patterns and mechanical responses of rock. Finally, the practical applicability of the proposed model is highlighted through the failure analysis of hard rock tunnels with varying cross-sections and the instability analysis of rock slopes.