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.