Analytical Solution and Change Law of Circular Tunnel Surrounding Rock Displacement in Plane Three-directional Stress Field

In order to reveal the evolution law of surrounding rock displacement in complex stress field, based on the analytical solution of surrounding rock stress of circular tunnel in plane three-directional stress field, the analytical solution of surrounding rock displacement was derived, and the change law of surrounding rock displacement with stress field was studied by Matlab programming. Results show that: The influence of various factors on the plastic zone radius in plane three-directional stress field is similar to that in bidirectional stress field. In the plane three-directional stress field, when the stress field proportion coefficient λ₁ =1.0, and λ₂ increases from 1.0 to 3.6 or decreases from 1.0 to 0.35, the surrounding rock displacement distribution shape shows an evolution law of vertical thin waist gourd → similar butterfly → asymmetric butterfly. Moreover, compared with bidirectional stress field, the surrounding rock displacement in the three-directional stress field is not limited to the arch shoulders and arch feet of the tunnel, and the displacement in the different directions of the tunnel may be significantly different. Research results can directly show the variation law of surrounding rock displacement with stress field, and also provide reference for the prevention and control of surrounding rock disaster in similar projects.