The difficulty in the 3D analysis of a circular tunnel excavation lies in the selection of a reasonable softening equation for the out-of-plane stress (σ_z) in the plastic zone. This study developed and compared the semi-analytical solutions of a circular opening considering different approaches for obtaining σ_z, and the results were verified by the numerical results (1) The elastic approaches (e.g., generalized Hooke's law). cannot accurately reflect the mechanical properties of rock in the plastic zone and the results exhibit large differences compared with numerical results. (2) Plastic approaches demonstrate that the in-site axis stress (q) has a limited effect on the stability of surrounding rock, whereas the elastic approach-based results exhibit severe dependence on q. (3) The excavation responses based on the GZZ strength criterion and Hoek–Brown strength criteria have significant differences, reflecting the obvious effect of σ_z (σ₂) on the stability of rock mass, and an unreasonable criterion may result in inappropriate support measures (4) Different post-peak behaviors of rock mass (e.g., constitutive model, residual strength, dilatancy, etc.). significantly affect the surrounding rock stresses, and the applicability of elastic theories and shallow tunnel experiences need to be further considered in deep tunnel where the plastic zone is widely distributed.

圆形隧道开挖三维分析的难点在于为塑性区的面外应力 ( σ _{z ) 选择合理的软化方程。}本研究开发并比较了考虑到获得σ _z的不同方法的圆形开口的半解析解，并通过数值结果验证了结果 (1) 弹性方法（例如，广义胡克定律）。不能准确反映塑性区岩石的力学性质，结果与数值结果存在较大差异。(2) 塑性方法表明现场轴应力 ( q) 对围岩的稳定性影响有限，而基于弹性方法的结果表现出对q 的严重依赖性。(3) 基于GZZ强度准则和Hoek-Brown强度准则的开挖响应存在显着差异，反映了σ _z ( σ ₂ )对岩体稳定性的明显影响，不合理的准则可能导致支护措施不当(4) 岩体不同的峰后行为（如本构模型、残余强度、延展性等）。显着影响围岩应力，弹性理论和浅埋隧道经验在塑性区广泛分布的深埋隧道中的适用性需要进一步考虑。