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<p>In this study, a semi-analytical elastoplastic solution method is developed for circular tunnel stability analysis, taking into account strain-softening effects. The proposed approach utilizes the distribution regularities of plastic deviatoric strain under various conditions to establish a calculation framework that replaces traditional finite difference iterations. This method aims to address the low accuracy and high computational complexity commonly associated with conventional techniques. Additionally, new determination procedures are introduced for three key parameters: the radius of the plastic loosening zone, the radius of the plastic softening zone, and the displacement of the surrounding rock. The accuracy of the method is validated through comparative analysis with existing case studies and real-world engineering applications. The main findings are as follows: (1) Under the same conditions, the method achieves high accuracy in strain-softening analysis. The relative error in the plastic softening zone radius is only 0.82%, and the computation time is negligible. (2) Considering intermediate principal stress improves the accuracy of bearing capacity predictions and reduces deformation overestimation. The relative error between predicted and measured displacements decreases from 29.2% to 10.1%. (3) The model’s fit to actual projects is significantly improved. Prediction errors for the plastic softening zone and plastic loosening zone are reduced from 0.309&#xa0;m and 1.085&#xa0;m to 0.132&#xa0;m and 0.144&#xa0;m, respectively.</p>

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Semi-analytical Model for Strain-Softening Tunnel Behavior with Intermediate Principal Stress Effects

  • 期刊论文

  • 发表日期：

    2025年10月31日

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  • Shijun Liao,
  • Shujie Wen,
  • Longji Zhu,
  • Hongyu Guo,
  • Hongfei Gao

摘要

In this study, a semi-analytical elastoplastic solution method is developed for circular tunnel stability analysis, taking into account strain-softening effects. The proposed approach utilizes the distribution regularities of plastic deviatoric strain under various conditions to establish a calculation framework that replaces traditional finite difference iterations. This method aims to address the low accuracy and high computational complexity commonly associated with conventional techniques. Additionally, new determination procedures are introduced for three key parameters: the radius of the plastic loosening zone, the radius of the plastic softening zone, and the displacement of the surrounding rock. The accuracy of the method is validated through comparative analysis with existing case studies and real-world engineering applications. The main findings are as follows: (1) Under the same conditions, the method achieves high accuracy in strain-softening analysis. The relative error in the plastic softening zone radius is only 0.82%, and the computation time is negligible. (2) Considering intermediate principal stress improves the accuracy of bearing capacity predictions and reduces deformation overestimation. The relative error between predicted and measured displacements decreases from 29.2% to 10.1%. (3) The model’s fit to actual projects is significantly improved. Prediction errors for the plastic softening zone and plastic loosening zone are reduced from 0.309 m and 1.085 m to 0.132 m and 0.144 m, respectively.