Approximate solution of plastic zone boundary of surrounding rock of circular roadway considering axial stress

In order to study the boundary of plastic zone of surrounding rock of a roadway considering axial stress, based on Mohr-Coulomb criterion, the implicit equation of plastic zone boundary of surrounding rock of circular roadway considering axial stress is derived by introducing Lode angle parameter. The size and shape of plastic zone of surrounding rock under different stress fields are analyzed by changing the horizontal stress σ_x and axial stress σ_y of roadway, and the reliability of theoretical analysis is further illustrated by numerical simulation. In addition, the influence of cohesion C, internal friction angle φ, roadway radius R and Poisson’s ratio v on the stability of surrounding rock is studied. The results show that : ① Under the condition of fixed axial lateral pressure while changing horizontal lateral pressure, the size change of plastic zone of surrounding rock can be divided into sensitive zone and insensitive zone, and in the changing process of horizontal lateral pressure, the plastic zone of surrounding rock shows three forms: circular, elliptical and butterfly-shaped. ② Under the condition of fixed horizontal lateral pressure while changing axial lateral pressure, the plastic zone at each position of surrounding rock shows a strong interval effect. By comparing the size of plastic zone under plane strain problem, the region is divided into axial stress-affected zone and axial stress-unaffected zone. In the influence zone of axial stress, the change of axial lateral pressure has great influence on the size of plastic zone of surrounding rock. ③ The failure mode of roadway surrounding rock is determined by the horizontal lateral pressure η₁, and the axial lateral pressure η₂ has little effect on the shape of plastic zone, but has great influence on the size. ④ The increase of surrounding rock C and φ will reduce the size of plastic zone of roadway surrounding rock to varying degrees, and the increase of R will increase the plastic zone at different positions of surrounding rock in an equal number sequence. In the axial stress-unaffected zone, v has no effect on the size of plastic zone of surrounding rock. In the axial stress-affected zone, the size of plastic zone at the wing corner is not affected by v, and the size of plastic zone at other locations is affected to different degrees.