<p>A novel stress-based hybrid phase-field model is developed to describe mixed-mode cracking in frictional rock-like materials, with particular attention to gravitational stress-gradient effects. To capture tensile-shear competition, the formulation introduces two physically motivated driving forces: the tensile stress-related elastic strain energy governing tensile cracking, and an equivalent shear stress-related energy driving shear cracking while incorporating internal friction. Their interaction is embedded in a mixed damage evolution criterion. In addition, a damage-hardening law is proposed to describe the evolution of shear fracture toughness with accumulated local compressive strain, enabling transition between tensile and shear dominated cracking modes. Implemented within a finite element framework, the model is first validated against four representative benchmarks. It is then applied to plate specimens with multiple pre-existing flaws under uniaxial compression subjected to both normal gravity and hypergravity conditions. The results indicate that, under normal gravity, cracks may initiate at different locations and a transition from shear to tensile dominated cracking can occur, whereas under hypergravity cracks preferentially initiate in the lower region of the specimen and propagate upward as tensile wing cracks. Moreover, the crack initiation angle and peak strength are influenced by the gravitational stress gradient. Hypergravity exhibits a clear suppressing effect on shear cracking.</p>

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Modeling of Mixed Cracking Process in Rock-Like Materials Incorporating Gravitational Stress Effect with a Hybrid Phase-Field Model

  • Kuan Zhang,
  • Zhan Yu,
  • Jinlong Li,
  • Wenjie Xu,
  • Yunmin Chen,
  • Jianfu Shao

摘要

A novel stress-based hybrid phase-field model is developed to describe mixed-mode cracking in frictional rock-like materials, with particular attention to gravitational stress-gradient effects. To capture tensile-shear competition, the formulation introduces two physically motivated driving forces: the tensile stress-related elastic strain energy governing tensile cracking, and an equivalent shear stress-related energy driving shear cracking while incorporating internal friction. Their interaction is embedded in a mixed damage evolution criterion. In addition, a damage-hardening law is proposed to describe the evolution of shear fracture toughness with accumulated local compressive strain, enabling transition between tensile and shear dominated cracking modes. Implemented within a finite element framework, the model is first validated against four representative benchmarks. It is then applied to plate specimens with multiple pre-existing flaws under uniaxial compression subjected to both normal gravity and hypergravity conditions. The results indicate that, under normal gravity, cracks may initiate at different locations and a transition from shear to tensile dominated cracking can occur, whereas under hypergravity cracks preferentially initiate in the lower region of the specimen and propagate upward as tensile wing cracks. Moreover, the crack initiation angle and peak strength are influenced by the gravitational stress gradient. Hypergravity exhibits a clear suppressing effect on shear cracking.