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Analytical solutions for deep tunnels in strain-softening rocks modeled by different elastic strain definitions with the unified strength theory

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Abstract

This paper presents the analytical solutions for the responses of tunnels excavated in rock masses exhibiting strain-softening behavior. Since previous analyses give little consideration to the effect of the intermediate principal stress on the strain-softening rock behavior, the unified strength theory was introduced to analyze the tunnel response. Four cases of different definitions of the elastic strain in the softening and residual regions, used in the existing solutions, were considered. The tunnel displacements, stresses, radii of the softening and residual zones and critical stresses were deduced. The proposed solutions were verified by comparing with numerical simulations, model tests and existing solutions. Furthermore, the solutions of the four cases were compared with each other to investigate the influence of the elastic strain expressions on the tunnel responses. The results showed that the intermediate principal stress coefficient b has a significant effect on the tunnel displacements, stress fields, and plastic radii. Parametric studies were performed to analyze the influences of the softening and residual dilatancy coefficients, softening modulus and residual strength on the tunnel responses. The parametric analysis indicated that the existing models should be carefully evaluated in the analysis of tunnels constructed through average-quality rocks; the proposed solutions outperformed the existing models in solving the mentioned problem.

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Authors and Affiliations

  1. Key Laboratory for Urban Underground Engineering of Ministry of Education, Beijing Jiaotong University, Beijing, 100044, China

    ZhenYu Sun, DingLi Zhang, Qian Fang & GuanSuo Dui

  2. School of Civil Engineering, Wuhan University, Wuhan, 430072, China

    ZhaoFei Chu

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  1. ZhenYu Sun
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  2. DingLi Zhang
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  4. GuanSuo Dui
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  5. ZhaoFei Chu
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Correspondence to DingLi Zhang.

Additional information

This work was supported by the Fundamental Research Funds for the Central Universities (Grant No. 2021RC202), and the National Natural Science Foundation of China (Grant No. 51738002).

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Sun, Z., Zhang, D., Fang, Q. et al. Analytical solutions for deep tunnels in strain-softening rocks modeled by different elastic strain definitions with the unified strength theory. Sci. China Technol. Sci. 65, 2503–2519 (2022). https://doi.org/10.1007/s11431-022-2158-9

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  • DOI: https://doi.org/10.1007/s11431-022-2158-9

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