Analytical Solutions for Long-Term Behavior of Rock Tunnels with Cyclic Internal Pressure Considering Damage

Compressed air energy storage (CAES) tunnels undergo daily inflation and deflation cycles during operation. It is inevitable that the surrounding rock will undergo fatigue damage when subjected to long-term cyclic loading. This damage leads to cumulative plastic deformation and a reduction in bearing capacity. Based on the Mohr-Coulomb criterion incorporating fatigue damage and stress path theory, this study presents an analytical solution for the mechanical response of surrounding rock during tunnel excavation, initial inflation, initial deflation, and cyclic inflation-deflation. The findings of the study suggest that the minimum air storage pressure, herein referred to as q min , exerts a significant influence on the mechanical response of the surrounding rock. In circumstances where the q min is elevated (7.5 MPa), the surrounding rock transitions into a stable cyclic stage of plastic unloading-reloading, characterized by the formation of closed stress paths. Conversely, when q min decreases to 1.5 MPa, the substantial pressure differential engenders a plastic reloading state during the process of deflation. The stress path subsequently becomes non-closed and gradually shifts toward strength degradation with increasing cycle numbers, accelerating cumulative plastic deformation and reducing load-bearing capacity. Damage parameters exert a staged influence on mechanical behavior: during air storage, they intensify circumferential stress concentration and increase displacement; during deflation, they amplify stress fluctuations and rebound deformation. These findings provide a theoretical basis for determining the operational pressure range and assessing the long-term stability of rock tunnels.