Modified Solution of Convergence Deformation of Bolt Supported Circular Tunnel Based on Composite Rock Mass Method

This paper investigates the interaction between bolts and surrounding rock mass and introduces the inhomogeneity of the bolts’ reinforcement effect. This study is based on the homogenized composite rock mass method. The equivalent stiffness calculation method of composite rock mass is modified according to its degree of restraint on the deformation of the composite rock mass to obtain the modified solution of convergence deformation of a circular tunnel under the bolt reinforcement. The correctness of the modified solution is verified by comparing it with the existing solution and numerical analysis results. The modified solution reasonably reduces the overestimation of the bolt restraint effect by the previous composite rock stiffness calculation method. The analysis using the modified solution shows that: the bolt support reduces the tunnel convergence deformation by increasing the equivalent stiffness of the composite rock; it is more effective to reduce the tunnel convergence by increasing the bolt density than by increasing the bolt length; under the regular bolt arrangement, the reduction of the final tunnel convergence by bolts does not exceed 20%, and it is not easy to rely entirely on system bolts to limit the convergence deformation of tunnels in soft rock mass. The modified solution proposed in this paper can reasonably reflect the restraining effect of bolts on the convergence deformation of the surrounding rock, and it can provide a concise and accurate calculation method for the quantitative analysis of the tunnel convergence deformation under bolt support.