To describe the evolution law of tunnel plastic zone and the principle of support design under in-situ stress field

this paper presented equations of plastic zone radius at horizontal and vertical axes of a circular tunnel under non-hydrostatic pressure with the total load invariant method. The two equations were based on the Mohr-Coulomb criterion and the elastic-brittle-plastic model

and a stress perturbation solution in the elastic zone was introduced. Then

the equations were extended to other azimuth angles according to the geometric similarity principle. The obtained equations of plastic zone radius were compared with the results of the total load invariant method (based on the Kirsch stress formulation)

Kastner method

complex variable function method

and measured data. An analytical solution of plastic zone displacement was derived using the non-associated flow law. Finally

parametric studies were performed to investigate the effects of lateral pressure coefficient and brittle softening on the plastic boundary

distribution of plastic zone displacement

and ground response curve. Results showed that the second-order perturbation solution taken as the stress equation in the elastic zone of a non-hydrostatic tunnel was more reasonable than the total load invariant method and the Kastner method

and it was verified against the complex variable function method. Lateral pressure coefficient had an obvious influence on the shape and range of tunnel plastic boundary

so support type and size should be determined for specific azimuth angles to control support pressure and stable rock deformation at the intersection point of convergence-confinement analysis. Plastic zone radius and tunnel wall displacement increased significantly with the decrease in rock post-peak strength

so the elastic-brittle-plastic model was suggested to calculate ground response curve.