Analytical Model of Mechanical Responses of Circular Tunnels Considering Rheological Behavior of Surrounding Rock and Functionally Graded Lining

The rock–lining interaction significantly affects the stability and safety of a tunnel in service. In this study, a mechanical model is proposed to explore the rock–lining interaction under hydrostatic pressure. The model takes into account the alterable mechanical property (such as the elastic modulus) of the lining in the rheological rock mass, which may be subjected to inner surface pressure along the radial direction of the highway tunnel. The alterable elastic modulus is assumed as a power function of the radius. The analytical solutions of this model are first verified by comparison with existing solutions and corresponding results are obtained by numerical simulation. Then, systematic parametric investigations are carried out to analyze the influence of the main model parameters on the radial deformation of the rock–lining interface and the normalized supporting pressure provided by the lining. The research conclusions obtained by this study can offer some valuable references for the safety evaluation of a tunnel in service.