ANALYTICAL SOLUTION FOR CIRCULAR TUNNELS WITH ROCK BOLTS

Analytical expressions of stress, displacement, and plastic zone radius in circular tunnels with or without rock bolts are presented. Considering a circular tunnel in hydrostatic stress field, with elastic-brittle-plastic rock mass, a linear Mohr-Coulomb yield criterion, and a non-associated flow rule, a new elastoplastic analytical solution for unsupported circular tunnels was derived. Based on the homogenization method, considering the composite material of rock mass and rock bolts as a new homogeneous, isotropic, parameter-strengthened equivalent material, the bolt density parameter was defined to reflect the influence of a high density support pattern of rock bolts, thus an equivalent Young’s modulus, equivalent cohesion, and equivalent friction angle for supported circular tunnels can be derived. Then an analytical solution for circular tunnel with rock bolts can be derived based on the new elastoplastic analytical solution without rock bolts. Bolt support was shown to be effective in reducing plastic zone radius and displacement of circular tunnel by comparison with an unsupported tunnel, also comparative analysis was undertaken using existing results and numerical solutions; the solutions derived provide reference for circular tunnel stability analysis in underground engineering.