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<p>The extension of primary fissures within surrounding rock poses significant risks to the construction and operational safety of deep rock engineering. Quasi-state-based peridynamics (QSBPD) offer an effective means of capturing the complex initiation of secondary cracks. However, the diversity and abundance of these cracks often induce nonlinear behaviors, such as deflection, branching, and convergence, that challenge the accuracy and efficiency of existing peridynamic algorithms. To address these challenges, this paper introduces an enhanced QSBPD framework incorporating an exponential fictitious crack model, enabling more realistic simulations of secondary crack propagation in both brittle and semi-brittle rocks. A novel embedded crack spatial parameter identification algorithm is also developed to precisely determine crack type, length, thickness, branch number, extension velocity, and duration. In addition, an optimal memory structure informed by the spatiotemporal correlation of material points is derived, significantly improving the efficiency of contact retrieval on crack surfaces. The proposed method is validated through simulations of fourteen sandstone specimens with prefabricated cracks under compressive loading, covering various crack geometries and inclination angles. Results demonstrate that the algorithm successfully captures 11 types of secondary cracks and six key physical quantities, with prediction errors for macroscopic mechanical parameters below 4%. Contact retrieval tasks are reduced by 10% to 31%, while retrieval efficiency is improved by a factor of 5.86 to 6.53. Furthermore, a peridynamic damage statistical function based on penetrating cracks is proposed. The accuracy, robustness, and computational advantages of the approach are confirmed through experimental and numerical comparisons. This study advances the capacity of peridynamic modeling to simulate the nonlinear evolution of multi-type secondary cracks, offering a powerful numerical tool for investigating disaster mechanisms in deep rock engineering.</p>

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Modeling nonlinear propagation behavior of multi-type secondary cracks in rocks with contact retrieval by quasi-state-based peridynamics

  • 期刊论文

  • 发表日期：

    2026年5月8日

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  • Feng Tian,
  • Zaobao Liu,
  • Seokwon Jeon,
  • Yubo Wang,
  • Enda Zhang,
  • Hongbo Li

摘要

The extension of primary fissures within surrounding rock poses significant risks to the construction and operational safety of deep rock engineering. Quasi-state-based peridynamics (QSBPD) offer an effective means of capturing the complex initiation of secondary cracks. However, the diversity and abundance of these cracks often induce nonlinear behaviors, such as deflection, branching, and convergence, that challenge the accuracy and efficiency of existing peridynamic algorithms. To address these challenges, this paper introduces an enhanced QSBPD framework incorporating an exponential fictitious crack model, enabling more realistic simulations of secondary crack propagation in both brittle and semi-brittle rocks. A novel embedded crack spatial parameter identification algorithm is also developed to precisely determine crack type, length, thickness, branch number, extension velocity, and duration. In addition, an optimal memory structure informed by the spatiotemporal correlation of material points is derived, significantly improving the efficiency of contact retrieval on crack surfaces. The proposed method is validated through simulations of fourteen sandstone specimens with prefabricated cracks under compressive loading, covering various crack geometries and inclination angles. Results demonstrate that the algorithm successfully captures 11 types of secondary cracks and six key physical quantities, with prediction errors for macroscopic mechanical parameters below 4%. Contact retrieval tasks are reduced by 10% to 31%, while retrieval efficiency is improved by a factor of 5.86 to 6.53. Furthermore, a peridynamic damage statistical function based on penetrating cracks is proposed. The accuracy, robustness, and computational advantages of the approach are confirmed through experimental and numerical comparisons. This study advances the capacity of peridynamic modeling to simulate the nonlinear evolution of multi-type secondary cracks, offering a powerful numerical tool for investigating disaster mechanisms in deep rock engineering.