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

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 K_S=2.33 (A) and K_S=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.

Keywords

strength reduction method / cusp catastrophic model / deep rock engineering / strain energy density / generalized H-B criterion / geo-mechanical model test

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