Mechanical Analysis of Bolt-Lining Combined Support in Deeply Buried Circular Tunnel

The proposal of the NATM has changed people's understanding of the support principle. Therefore, how to improve the self-supporting capacity of surrounding rock has become an important issue in support research. Bolts and lining are widely used together in various support projects because their bearing and reinforcement effects are in line with the concept of the NATM. This paper puts forward a model to analyze the mechanical behavior of a deeply buried circular tunnel jointly supported by lining and point-anchored rock bolts. Rock mass, lining, and bolts maintain an elastic state and are in full contact with each other. In addition, point-anchored rock bolts are replaced by pairs of concentrated forces of equal magnitude that act in opposite directions. By using the complex function method, the linear equations for calculating the axial force of the bolts and the relevant analytical function coefficients can be established, based on the stress condition of the inner boundary of the lining, the continuity conditions at the interface between the lining and the surrounding rock, and the compatibility condition of the displacement between the bolts and the surrounding rock. Then, using the analytical functions, the stress and displacement of any point in the lining and surrounding rock can be calculated. The results were compared with the numerical solutions. Moreover, the effects of the bolts and the Young's modulus of the lining on the whole support system are discussed.