Time-Dependent Reliability Analysis of Deep-Buried Tunnels in Rheological Rock Considering Degradation of Secondary Lining Performance

In deep-buried tunnels, the loads acting on supporting structures continuously increase due to the rheological behavior of surrounding rock, while the performance of the secondary lining gradually degrades under environmental effects. These delayed features have significant implications for tunnel safety but are rarely incorporated into the reliability evaluation of tunnels. In this study, the surrounding rock is modeled using the Burgers model, and an analytical solution is developed by incorporating the degradation and damage of the secondary lining. Parametric analysis is conducted to identify the key factors governing tunnel response. Subsequently, limit state functions are established, and a time-dependent system reliability analysis is performed. Results indicate that tunnel response and reliability are highly sensitive to rheological parameters. Among the rheological parameters, the elastic shear modulus of the Maxwell elements Ge has the most pronounced influence on deformation, whereas the elastic shear modulus of the Kelvin elements Gk governs the stress response of the secondary lining. The time-dependent failure probability increases rapidly in the early stage and gradually stabilizes thereafter. Insufficient initial support strength is identified as the dominant failure mode of system failure. Furthermore, Ge and Gk are the key parameters affecting tunnel reliability, and increasing Gk improves the reliability index by more than 1500%. Meanwhile, the variation in system reliability is mainly affected by the failure mode of insufficient initial support strength. These findings provide quantitative guidance for the design, construction, and long-term maintenance of deep-buried tunnels in rheological rock.