A homogenization method to analyze circular tunnel with rock bolts is presented

which can simplify this kind of complex mechanical coupling problem through considering the composite material of rock mass and rock bolts as a new homogeneous

isotropic

parameters strengthened equivalent material. Rock bolt density parameter is defined to reflect the influence of high density rock bolt support pattern; Mohr-Coulomb criterion is applied to the new equivalent material; the increasement of key coefficients for Mohr-Coulomb criterion is considered to related to rock bolt density parameter; thus equivalent Young’s modulus

equivalent cohesion and equivalent friction angle for circular tunnel with rock bolts can be derived. Displacements of tunnel with and without rock bolts are compared through the existed displacement solution. Based on this solution

the reliability index and failure probability of tunnel are calculated by considering allowable ultimate displacement as instability criterion. The results show that the tunnel with rock bolts is much reliable. It is shown that the proposed method is simple and feasible and the rock bolt can improve the stability and reliability of tunnel.