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<p>Strain localization, typically manifesting as shear bands, is a critical mechanism in the deformation and failure of quasi-brittle rocks. This study aims to develop an enhanced, thermodynamically consistent constitutive model that explicitly accounts for localization effects. The proposed model incorporates an enriched strain formulation to distinguish between the strains outside and inside the localization band, effectively representing the localized binary structure of rock failure. A three-dimensional (3D) Hoek–Brown type strength criterion, grounded in fracture mechanics, is reformulated to capture strain hardening and softening behaviors through a damage-driven internal mechanism. An incremental constitutive formulation is derived and implemented via a specialized numerical integration algorithm. The model is validated by reproducing the mechanical responses of sandstone under both conventional and true triaxial compression conditions, demonstrating its capability to quantitatively predict key metrics such as the evolution of localization band width and the complete stress–strain responses, including both pre-peak hardening and post-peak softening. The proposed framework extends continuum damage mechanics (CDM) to the simulation of discontinuous deformation and failure in quasi-brittle rocks, offering improved predictive accuracy for complex geotechnical applications.</p>

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A New Enhanced Localized Constitutive Model of Quasi-Brittle Rocks From Thermodynamic Perspective

  • 期刊论文

  • 发表日期：

    2026年3月30日

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  • Susheng Wang,
  • Shengqi Yang,
  • Changdong Ding,
  • Chaojun Jia,
  • Wanqing Shen

摘要

Strain localization, typically manifesting as shear bands, is a critical mechanism in the deformation and failure of quasi-brittle rocks. This study aims to develop an enhanced, thermodynamically consistent constitutive model that explicitly accounts for localization effects. The proposed model incorporates an enriched strain formulation to distinguish between the strains outside and inside the localization band, effectively representing the localized binary structure of rock failure. A three-dimensional (3D) Hoek–Brown type strength criterion, grounded in fracture mechanics, is reformulated to capture strain hardening and softening behaviors through a damage-driven internal mechanism. An incremental constitutive formulation is derived and implemented via a specialized numerical integration algorithm. The model is validated by reproducing the mechanical responses of sandstone under both conventional and true triaxial compression conditions, demonstrating its capability to quantitatively predict key metrics such as the evolution of localization band width and the complete stress–strain responses, including both pre-peak hardening and post-peak softening. The proposed framework extends continuum damage mechanics (CDM) to the simulation of discontinuous deformation and failure in quasi-brittle rocks, offering improved predictive accuracy for complex geotechnical applications.