Energy-based index for evaluating dynamic stability of surrounding rock in deep caverns

Deep high-energy rock masses are susceptible to dynamic and static disasters in underground caverns when stress waves superimpose on them. Scientifically evaluating the stability of surrounding rock mass under such conditions is fundamental for predicting and preventing related hazards. This study combines laboratory dynamic disturbance tests with numerical simulations to analyze changes in the three-dimensional stress state of surrounding rock caused by stress waves. It was found that stress waves not only alter the magnitude of unit stresses but also cause rotation of the principal stress axes. Based on the failure approach index (FAI), a new dynamic response evaluation index for brittle surrounding rock—the Energy Hazard Index (FAI_E) is proposed from an energy perspective. This index can derive functional expressions based on different strength criteria, offering good extensibility. Using the Mohr-Coulomb strength criterion as an example, the specific functional expression of FAI_E is provided. Comparison with experimental results confirms that the evaluation outcomes align with the dynamic response characteristics of surrounding rock mass, simultaneously considering both tensile and shear failure modes. Parameter sensitivity tests demonstrate the applicability of the index under complex conditions. Furthermore, the relationship between FAI_E and commonly used dynamic disturbance evaluation parameters—such as Peak Particle Velocity (PPV)—has been examined, demonstrating that FAI_E provides a more accurate and direct assessment of stability. Finally, a rapid engineering application method for FAI_E is presented. The research findings hold significant importance for future stability evaluation and support design of surrounding rock in deep underground engineering projects.