Key Takeaways & Executive Findings
- •• Introduces a novel energy-driven instability criterion based on cusp catastrophe theory, reducing subjectivity in deep rock engineering stability assessments. • Derives an explicit algebraic transformation linking quartic energy potential to standard cusp form, enabling the mutation eigenvalue Δ as a physically interpretable instability measure. • Validates the framework through scaled physical model tests and simulations, achieving conservative safety factors (K=2.33 and 2.73) with deviations under 6% from experimental results. • Demonstrates that the improved nonlinear H-B strength reduction method yields more conservative safety factors than equivalent Mohr-Coulomb approach, better matching observed failure processes.
Abstract
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 the overload safety factor K=2.33 for Model A and K=2.73 for Model B, with relative deviations from tests (2.4P0 and 2.9P0) 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.
1. Introduction
With the rapid development of computational techniques, numerical methods are used to solve the elastic-plastic theoretical solutions and numerical solutions of the stability of surrounding rock in deep tunnel. The strength reduction method is one of the most commonly used methods in the safety evaluation of deep tunnel surrounding rocks [1−4]. The strength reduction method was first proposed by ZIENKIEWICZ et al [5]. The traditional idea is to use linear strength criterion (M-C criterion, Drucker-Prager criterion) for analysis [6, 7]. In recent years, the strength reduction methods have been gradually extended by applying non-linear strength criteria and a certain amount of studies have been carried out.
In the reduction of rock strength, we should first consider the influence of constitutive parameters. YUAN et al [8] presented a new nonlinear strength reduction method based on the generalized Hoek-Brown (H-B) criterion and provided a reduction strategy to find optimal parameters. HAMMAH et al [9] used the technique of directly reducing the nonlinear strength envelope to study the law between the reduction of H-B strength parameters and the stability of surrounding rock. ZHANG et al [10] and XU et al [11] explored the influence of parameters such as shear direction and crack inclination angle on strength reduction. GALINDO et al [12], KE et al[13], and JIANG et al [14] also discovered the nonlinear variation law of constitutive parameters in the process of strength reduction through bond connection model or finite element model.
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ZHANG Rui-xin, ZHANG Qiang-yong, LIU Chuan-cheng, DUAN Kang, WEN Zhi-jie, SUN Xi-kui, WANG Peng-fei (2026). Transformation of strain energy increment in catastrophe model and its application to stability analysis of host rock in nuclear waste disposal caverns. Journal of Central South University. https://doi.org/10.1007/s11771-026-6266-6
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Frequently Asked Questions
What is the main contribution of this paper?
The paper develops an energy-driven instability criterion based on cusp catastrophe theory, integrated with an improved nonlinear Hoek-Brown strength-reduction framework, providing a more objective and conservative approach for assessing cavern stability in deep rock engineering.
How does the proposed method improve upon traditional strength reduction methods?
It replaces linear strength criteria with a nonlinear H-B criterion and introduces a mutation eigenvalue Δ as a physically interpretable measure of instability, leading to more conservative safety factors and better agreement with observed failure processes.
What are the key validation results?
The method was validated using scaled physical model tests and simulations for two cavern layouts, yielding safety factors of 2.33 and 2.73 with relative deviations of 1.3% and -5.9% from tests, respectively.
What is the significance of the mutation eigenvalue Δ?
Δ serves as an energy-based instability indicator that quantifies proximity to the vanishing of the energy barrier, enabling objective failure staging in practical applications.
How does the proposed method compare to the equivalent Mohr-Coulomb approach?
The improved nonlinear scheme produces smaller (more conservative) safety factors by 5.7% and 2.5% compared to the equivalent Mohr-Coulomb approach, while better matching the observed destabilization process.
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