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<p>This study presents an efficient hybrid second-order exponential cone programming (HSOECP) framework to model Hoek–Brown (HB) yield criterion, handling the issues related to non-linearity, and stress-space singularities. This framework overcomes the requirements of yield surface smoothening, introduction of a fixed exponent and computational inefficiency of traditional and power cone programming. The HSOECP is integrated with the stress-based finite element limit analysis to estimate the required resistance of support systems against failure, and surcharge that can be applied without any support systems in the case of unsupported rock tunnels. The methodology adopted in this study yields result with superior numerical stability and reduced iteration requirements relative to other conic programming methodologies. Analyses were performed for three shapes of tunnels (circular, square, and horseshoe-shaped) to demonstrate the generalised nature and capability of the present methodology in handling complex computations. The square tunnels were less stable due to high stress concentrations at the corners, leading to higher support resistance (6–7 times) and lower surcharge carrying capacity than circular and horseshoe tunnels. The results are provided in the form of design charts, which could be directly used for the stability evaluation of lined and unlined tunnels.</p>

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Modelling of Hoek–Brown yield criterion using hybrid second order exponential cone programming for stability analysis of rock tunnels: Design charts and practical implications

  • 期刊论文

  • 发表日期：

    2026年7月4日

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  • Spandan Sahu,
  • Jagdish Prasad Sahoo,
  • Gaurav Tiwari

摘要

This study presents an efficient hybrid second-order exponential cone programming (HSOECP) framework to model Hoek–Brown (HB) yield criterion, handling the issues related to non-linearity, and stress-space singularities. This framework overcomes the requirements of yield surface smoothening, introduction of a fixed exponent and computational inefficiency of traditional and power cone programming. The HSOECP is integrated with the stress-based finite element limit analysis to estimate the required resistance of support systems against failure, and surcharge that can be applied without any support systems in the case of unsupported rock tunnels. The methodology adopted in this study yields result with superior numerical stability and reduced iteration requirements relative to other conic programming methodologies. Analyses were performed for three shapes of tunnels (circular, square, and horseshoe-shaped) to demonstrate the generalised nature and capability of the present methodology in handling complex computations. The square tunnels were less stable due to high stress concentrations at the corners, leading to higher support resistance (6–7 times) and lower surcharge carrying capacity than circular and horseshoe tunnels. The results are provided in the form of design charts, which could be directly used for the stability evaluation of lined and unlined tunnels.