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<p>To reduce the subjectivity of conventional instability criteria in deep rock engineering, this study develops an energy-driven criterion grounded in cusp catastrophe theory and embeds it within an improved nonlinear Hoek-Brown (H-B) strength-reduction framework. We derive an explicit algebraic transformation that maps a quartic energy potential to the standard cusp form and introduce the mutation eigenvalue <i>Δ</i> as a physically interpretable measure of proximity to the vanishing of the energy barrier. Building on this, failure staging is diagnosed in practice by the concurrence of a slope mutation in displacement-reduction-factor curves, a threshold jump of total plastic strain-energy increment typically exceeding threefold between adjacent reduction steps, and video-confirmed crack through-connection. Integrating <i>Δ</i> with the nonlinear reduction scheme yields reproducible integral safety factors. Two representative cavern layouts (Model A/B) are validated by scaled physical model tests and companion simulations: global failure occurs at <i>K</i><sub><i>S</i></sub>=2.33 (A) and <i>K</i><sub><i>S</i></sub>=2.73 (B), with relative deviations from tests (2.30 and 2.90) of +1.3% and −5.9%, respectively, coinciding with the energy-jump threshold and the multi-evidence diagnosis. Compared with the equivalent Mohr-Coulomb parameter approach, the improved nonlinear scheme produces smaller (more conservative) safety factors by 5.7% and 2.5%, while better matching the observed destabilization process. The framework clarifies the role of <i>Δ</i> as an energy-based instability indicator and offers a practical, verifiable criterion for cavern stability assessment.</p>

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Transformation of strain energy increment in catastrophe model and its application to stability analysis of host rock in nuclear waste disposal caverns

  • 期刊论文

  • 发表日期：

    2026年3月16日

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  • Rui-xin Zhang,
  • Qiang-yong Zhang,
  • Chuan-cheng Liu,
  • Kang Duan,
  • Zhi-jie Wen,
  • Xi-kui Sun,
  • Peng-fei Wang

摘要

To reduce the subjectivity of conventional instability criteria in deep rock engineering, this study develops an energy-driven criterion grounded in cusp catastrophe theory and embeds it within an improved nonlinear Hoek-Brown (H-B) strength-reduction framework. We derive an explicit algebraic transformation that maps a quartic energy potential to the standard cusp form and introduce the mutation eigenvalue Δ as a physically interpretable measure of proximity to the vanishing of the energy barrier. Building on this, failure staging is diagnosed in practice by the concurrence of a slope mutation in displacement-reduction-factor curves, a threshold jump of total plastic strain-energy increment typically exceeding threefold between adjacent reduction steps, and video-confirmed crack through-connection. Integrating Δ with the nonlinear reduction scheme yields reproducible integral safety factors. Two representative cavern layouts (Model A/B) are validated by scaled physical model tests and companion simulations: global failure occurs at KS=2.33 (A) and KS=2.73 (B), with relative deviations from tests (2.30 and 2.90) of +1.3% and −5.9%, respectively, coinciding with the energy-jump threshold and the multi-evidence diagnosis. Compared with the equivalent Mohr-Coulomb parameter approach, the improved nonlinear scheme produces smaller (more conservative) safety factors by 5.7% and 2.5%, while better matching the observed destabilization process. The framework clarifies the role of Δ as an energy-based instability indicator and offers a practical, verifiable criterion for cavern stability assessment.