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Reliability analysis of horseshoe tunnels by radial-based importance sampling method based on complex function displacement solution

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  • Yao Rong
  • Qiang Liu
  • Yang Sun
  • Xiangshen Chen
  • Xinwei Zhang
  • Songyan Li

Abstract

Tunnel reliability analysis is an important analytical method to ensure tunnel safety. In this paper, the plane elastic complex variable function theory is adopted, and the explicit displacement function of the horseshoe-shaped tunnel vault is derived through conformal mapping. This function is verified by ABAQUS numerical analysis, and the correctness of the derivation is further confirmed by degenerating it to a circular tunnel. Subsequently, based on this explicit displacement function, a comparative analysis is conducted on four methods: the advanced first-order second moment (AFORM) method, Monte Carlo sampling (MCS) method, importance sampling (IS) method, and radial-based importance sampling (RBIS) method. The results show that the RBIS method has higher calculation accuracy and better efficiency. Finally, considering the influences of the mean value of load, load variation coefficient, and surrounding rock parameters, the reliability of the horseshoe-shaped tunnel and the circular tunnel is compared and analyzed based on the derived explicit function. It is found that except for the lateral pressure coefficient, the two types of tunnels are similar in terms of the sensitivity of other parameters and the influence laws of parameters on reliability. The research results can provide a reference for the analogical design and analysis of horseshoe-shaped tunnels and circular tunnels.

Suggested Citation

  • Yao Rong & Qiang Liu & Yang Sun & Xiangshen Chen & Xinwei Zhang & Songyan Li, 2026. "Reliability analysis of horseshoe tunnels by radial-based importance sampling method based on complex function displacement solution," PLOS ONE, Public Library of Science, vol. 21(4), pages 1-20, April.
    • Handle: RePEc:plo:pone00:0346030
    DOI: 10.1371/journal.pone.0346030
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    References listed on IDEAS

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    1. Amirfakhrian, M. & Mafikandi, H., 2016. "Approximation of parametric curves by Moving Least Squares method," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 290-298.
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