Unified plastic solutions to a circular tunnel under two-way unequal pressures and their applications

Various unified plastic solutions to a circular tunnel under two-way unequal pressures are presented corresponding with the in-situ stress distributions, such as the stress, displacement and radius of plastic zone and the ground response curve, where the elastic perfectly-plastic model is assumed for surrounding rock. The unified strength theory and a non-associated flow rule are adopted to account for the effects of the intermediate principal stress and dilatancy, respectively. Discussions and applications of the proposed solution are then performed. The results show that the unified plastic solutions of this study are the serialized and ordered ones with simple expressions, which reasonably consider the effects of three factors to have certain theoretical significance and good engineering application prospect. The two-way unequal pressures and the intermediate principal stress significantly affect the range of plastic zone, displacement of tunnel wall and the ground response curve. The supports with different bearing performances (or installation time) should be applied for different azimuth angles. The displacement of tunnel wall and stable deformation of surrounding rock increase with the increase of the dilatancy coefficient.