BRITTLE PLASTIC PERTURBATION SOLUTIONS OF PLASTIC ZONE RADIUS FOR CIRCULAR TUNNELS UNDER NON-HYDROSTATIC PRESSURES BASED ON THE UNIFIED STRENGTH THEORY

Based on the unified strength theory and the elastic-brittle-plastic model to comprehensively account for the intermediate principal stress effect and brittle softening of surrounding rock strength, an analytical solution of plastic zone radius for a circular tunnel under non-hydrostatic pressures was presented by using the perturbation method. Application ranges of the proposed perturbation solution were then discussed. It was validated against reported results from the complex variable function method, the perturbation method, numerical simulations, and the constant assumption of total loads. Finally, the influence of each factor on plastic tunnel shape and size was analyzed. It is found herein that the proposed perturbation solution of plastic zone radius for circular tunnels is a series of analytical ones considering different extents of the intermediate principal stress effect, and reduces to that of the elastic-perfectly plastic model. It should be applied to a plastic zone boundary with the biaxial symmetric elliptical-like completely surrounding tunnel perimeter, and the correctness and rationality of the perturbation solution is demonstrated by comparing with four methods available in the literature. Therefore, it has extensive theoretical significance and engineering application value. The perturbation parameter can significantly affect the size and long/short axis variation of tunnel elliptical-like plastic zone. The plastic zone range decreases obviously with both the increase of the intermediate principal stress effect and the post-peak strength parameters of surrounding rocks. The perturbation solution of Mohr-Coulomb strength criterion is shown to be conservative due to not take the intermediate principal stress effect into consideration, and the elastic-brittle-plastic model is more appropriate for tunnel plasticity analysis than the elastic perfectly-plastic model.