Rockbolts are a critical reinforcement ways which widely used in tunnel engineering. In this paper, an analytical solution of circular tunnel with rockbolts was proposed based on homogenization method, and then the stability of a circular tunnel was investigated by considering the uncertainty based on the proposed analytical solution. Elastoplastic analytical solution for unsupported circular tunnel was presented briefly in hydrostatic stress field with a linear Mohr-Coulomb yield criterion and a non-associated flow rule. An analytical solution of circular tunnel with rockbolts was proposed through considering rock mass and rockbolts as a new homogeneous, isotropic, parameters strengthened equivalent composite material. A numerical example is used to verify the proposed analytical solution. The results show that the proposed solution can effectively characterize the mechanical behavior of rock mass and rockbolts in tunnel. Then, the proposed solution is adopted to calculate reliability index and failure probability of tunnel. The results show that the proposed method can also be effectively used to perform the stability and reliability analysis of tunnel and rockbolts have an important effect on plastic zone size and displacement of tunnel.
Analytical solution of circular tunnel in elastic-viscoplastic rock mass
