Time-dependent safety of lining structures of circular tunnels in weak rock strata

Following tunnel excavation and lining completion, fractured surrounding rock deforms gradually over time; this results in a time-dependent evolution of the pressure applied to the lining structure by the surrounding rock. Thus, the safety of the tunnel lining in weak strata is strongly correlated with time. In this study, we developed an analytical method for determining the time-dependent pressure in the surrounding rock and lining structure of a circular tunnel under a hydrostatic stress field. Under the proposed method, the stress–strain relationship of the fractured surrounding rock is assumed to conform to that of the Burgers viscoelastic component, and the lining structure is assumed to be an elastomer. Based on these assumptions, the viscoelastic deformation of the surrounding rock, the elastic deformation of the lining structure, and the coordinated deformation between the surrounding rock and lining structure were derived. The proposed analytical method, which employs a time-dependent safety coefficient, was subsequently used to estimate the durability of the lining structure of the Foling Tunnel in China. The derived attenuation curve of the safety coefficient with respect to time can assist engineers in predicting the remaining viable life of the lining structure. Unlike existing analytical methods, the method derived in this study considers the time dependency of the interaction between the surrounding rock and tunnel lining; hence, it is more suitable for the evaluation of lining lifetime.