Estimation of Tunnel Pressure Arch Zone Based on Energy Density Difference of Surrounding Rock

The pressure arch effect limits the influence range of excavation on the surrounding rock, reduces the geological pressure on underground structures, and serves as an important indicator for evaluating the stability of underground engineering. By accounting for the energy transfer process in surrounding rock during the tunnel-induced pressure arch formation, this paper proposes a novel approach for determining the range of the pressure arch around tunnels—the energy density difference (EDD) method. Numerical analysis is conducted to evaluate the effects of tunnel span, internal friction angle, and lateral pressure coefficient on post-excavation energy density fields and pressure arch zones in tunnels. Comparative studies with three existing approaches confirm the EDD method’s efficacy in identifying the arch zones of tunnel-surrounding rock. Critically, the proposed approach addresses the controversy regarding the determination of the deviation degree of principal stress vectors and provides a physically meaningful interpretation of the formation and evolution mechanisms of pressure arches.