Strain-softening behavior occurs when the surrounding rock reaches its peak load, complicating the prediction of stress and displacement. The linear Mohr-Coulomb yield criterion and semi-linear Hoek-Brown yield criterion are widely used in elastoplastic analysis. However, the established criteria struggle to universally describe the nonlinear behavior of various rock types. This study aims to overcome the difficulty and propose the solution of surrounding rock in a circular tunnel following any nonlinear yield criterion and plastic potential function. The derivation of the equivalent cohesive strength and frictional angle for an arbitrary nonlinear yield criterion in the form of using the secant method, along with the determination of the equivalent dilatancy angle for any nonlinear plastic potential functions, was conducted. Concerning the elastoplastic solution of a thick-cylinder, a numerical strain-softening solution for a circular tunnel in nonlinear yield rock masses was derived. Verification of the proposed solution was performed against the established analytical and/or numerical elasto-(brittle-)plastic and strain-softening solutions in rock masses following the Mohr-Coulomb, (generalized) Hoek-Brown, and unified strength criteria. The impact of critical plastic shear strain on displacement, plastic radius, and residual radius was further analyzed. The predictions of displacement and residual region for the Jinping II project also meet the field test results.

中文翻译：

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非线性屈服岩体中圆形开口的应变软化数值解


当围岩达到峰值载荷时，就会发生应变软化行为，从而使应力和位移的预测变得复杂。线性莫尔-库仑屈服准则和半线性Hoek-Brown屈服准则广泛应用于弹塑性分析中。然而，既定标准很难普遍描述各种岩石类型的非线性行为。本研究旨在克服这一困难，并提出了遵循任意非线性屈服准则和塑性势函数的圆形隧道围岩的解决方案。使用割线法推导了任意非线性屈服准则的等效内聚强度和摩擦角，并确定了任意非线性塑性势函数的等效剪胀角。针对厚圆柱体的弹塑性解，推导了非线性屈服岩体中圆形隧道的应变软化数值解。根据 Mohr-Coulomb、（广义）Hoek-Brown 和统一强度标准，针对岩体中已建立的分析和/或数值弹（脆）塑性和应变软化解决方案对所提出的解决方案进行了验证。进一步分析了临界塑性剪应变对位移、塑性半径和残余半径的影响。锦屏二期工程的位移和残余区域预测也符合现场试验结果。