Abstract: The deformation and failure of deep tunnels in a high in-situ stress field are driven by energy, which results from the dissipation and release of energy exceeding the storage limit in the surrounding rock. Existing theoretical studies mainly focus on calculating the elastic strain energy of the surrounding rock during the elastic unloading of deep circular tunnels. Few authors have conducted theoretical research on energy calculation and evolution in deep circular tunnels under elastic-plastic unloading. Firstly, this study clarifies the definitions of elastic strain energy, dissipated energy, and released energy based on the energy evolution of rocks. Subsequently, utilizing elastic-plasticity theory and Hoek-Brown strength criteria, the radius increment method is proposed to calculate the unloading stress path of the surrounding rock, taking into account strain-softening behavior. Finally, an energy calculation method for deep circular rock tunnels based on the unloading stress path is established, mathematically proving the energy conservation relationship of the surrounding rock. The research results indicate that energy is input from the remote surrounding rock after tunnel excavation. During the elastic deformation phase, input energy is all converted into elastic strain energy, with higher elastic strain energy density closer to the tunnel wall. In the plastic deformation stage, the total elastic strain energy continues to increase with ongoing energy input. However, the elastic strain energy density near the tunnel reaches the energy storage limit of the surrounding rock, leading to a plastic zone. Subsequently, the energy storage limit in the plastic zone decreases due to strain softening behavior, resulting in an exponential increase in the dissipated and released energy of the surrounding rock. For deep rocks with high peak strength, energy release dominates during plastic deformation, leading to rockbursts caused by the energy release mechanism. Rocks with low peak strength exhibit plastic deformation primarily driven by energy dissipation, leading to the initiation of tunnel squeezing deformation.

Key words: deep tunnel, unloading stress path, energy evolution, dissipated energy, released energy