Analytical solution of viscoelastic-plastic of roadway surrounding rock considering intermediate principal stress and supporting force

The rheological properties of rock have an important influence on the deformation of surrounding rock of roadway, which often leads to large deformation or even instability of surrounding rock. In order to comprehensively analyze the deformation characteristics of surrounding rock of circular roadway, the Burgers model is combined with the friction plate under the unified strength criterion by using the series theory of rheological model, and a viscoelastic-plastic constitutive model of surrounding rock considering the plasticity of surrounding rock is obtained. In the elastic-plastic analysis of surrounding rock, the influence of intermediate principal stress coefficient and supporting force is considered, and the analytical formula of plastic zone radius and displacement of roadway surrounding rock is obtained by using the non-associated flow rule. Combined with an example, the influence of intermediate principal stress and supporting force on the radius of plastic zone, stress field and displacement field of surrounding rock of roadway is analyzed, and the variation law of displacement with time is analyzed. The results show that the surrounding rock of roadway has experienced two stages of deceleration creep and steady creep. In the deceleration stage, the displacement growth rate of surrounding rock is large, and the early support pressure is large. In the steady speed stage, although the growth rate of surrounding rock displacement decreases slightly, it still needs support to maintain stability. By increasing the intermediate principal stress and supporting force, the radius of plastic zone and the displacement of surrounding rock can be reduced, and the stability of surrounding rock of roadway can be improved. In addition, with the increase of time, the deformation of surrounding rock increases gradually. By increasing the supporting force, the deformation speed of surrounding rock can be effectively inhibited, and the deformation of surrounding rock can be alleviated to a certain extent.