Analytical solution for surrounding rock of circular roadway based on generalized SMP criterion considering seepage and dilatancy

Based on the generalized spatially mobilized plane(SMP) criterion, considering intermediate principal stress, pore water pressure and dilatancy characteristics of surrounding rock, an ideal elastic-plastic model of roadway surrounding rock is established. According to the elastic-plastic theory, the unified analytical solutions of stress field, displacement field and radius of plastic zone under seepage flow are obtained. Then, the stress distribution of surrounding rock and the radius of plastic zone calculated by SMP criterion are compared with those calculated by Mohr-Coulomb(M-C) criterion, and the influencing factors such as pore water pressure and dilatancy angle of surrounding rock are analyzed. It is shown that the radius of plastic zone based on the SMP criterion are smaller than that of the M-C criterion, and the calculation results of M-C criterion are more conservative than those of generalized SMP criterion. The pore water pressure has a great influence on the displacement field of the roadway surrounding rock. The increase of displacement near roadway wall is influenced by the larger pore water pressure. Meanwhile, the change of radius of plastic zone of surrounding rock and the peak tangential stress variations at elastic-plastic interface are proportional to the pore water pressure. The strength of the surrounding rock will be underestimated by using the correlation flow rule, and the actual deformation of the surrounding rock will be underestimated without considering the dilatancy.