Analytical Solution And Reliability Analysis Of Circular Tunnel With Rockbolts

Tunnel is an important part of the underground engineering structures, analytical solution and failure mechanism are the basis to solve practical engineering problems for tunnels with and without rockbolts. Elastic analysis or elastoplastic analysis are too conservative for practical engineering based on ideal elastic-plastic material, solutions based on classic micromechanics are rather complex for tunnel with rockbolts. The instability criterion for tunnel reliability analysis is still vague. These problems are critical to stability analysis, design and construction of tunnel. New methods and ideas are necessary to the stability analysis for tunnels with and without rockbolts.This paper presents analytical solutions of stresses, displacements and plastic zone radius for circular tunnel with or without rockbolts. Firstly, considering a circular tunnel in hydrostatic stress filed, elastic-brittle-plastic rock mass, with a linear Mohr-Coulomb yield criterion and a non-associated flow rule, elastoplastic analytical solution for unsupported circular tunnel was derived. Based on homogenization method, considering the composite material of rock mass and rockbolt as a new homogeneous, isotropic, parameters strengthened equivalent material, bolt density parameter was defined to reflect the influence of bolt support pattern, thus equivalent Young’s modulus, equivalent cohesion and equivalent friction angle for supported circular tunnel can be derived. Bolt supporting showed a good effect on reducing plastic zone radius and displacement of circular tunnel by unsupported and supported tunnel comparison, also contrastive analysis was taken with existed results and numerical solution. Baed on this solution, the reliability index and failure probability of tunnel were calculated. The results show the proposed method is simple and feasible and rockbolt can improve the stability and reliability of tunnel.