Elastic–plastic solutions of reserved deformation for soft rock circular tunnel under high stress

The determination of reserved deformation is typically based on referring to relevant codes or the engineering analogy method, lacking a certain theoretical approach. The purpose of this study is to provide a theoretical basis for determining reserved deformation and to analyze the variation law of the surrounding rock affected by reserved deformation. Considering the reserved deformation under the condition of asymmetric load, the expression of optimal reserved deformation, the expression of support resistance reflecting the strength of surrounding rock, the strength of support material and the magnitude of in situ stress, the displacement expression of surrounding rock are derived by approximate solution based on the classical elastic–plastic theory. Numerical simulation software is used to simulate the displacement expression of the surrounding rock considering the reserved deformation and the expression of the optimum reserved deformation under the condition of asymmetric load. The results of the numerical simulation were compared with those of the analytical solutions, and the analytical results show that the errors between the two are within 12% and that the consistency is good.