Safety assessment is one critical issue for constructions of tunnels and requires a reliable and accurate stability analysis. At present, a large number of researches in stability analyses of tunneling in rock masses have been conducted; however, a lack of an accurate and reliable design equation for the tunnel stability prediction is obvious. This paper presents a new design equation for stability analyses of shallow unlined circular tunnels in rock masses obeying the Generalized Hoek-Brown failure criterion. Because of the complexity of the problem’s nature, a closed-formed analytical solution of the problem is not possible to be achieved. Hence, the computational framework of the finite element limit analysis is selected to numerically derive the upper and lower bound solutions of the problem. A complete set of the dimensionless parameters covering the shallow cover-depth ratios of tunnels, the normalized uniaxial compressive strength of intact rocks, and the Hoek-Brown material parameters are comprehensively investigated. A new design equation for stability analyses of shallow unlined circular tunnels in rock masses is developed by employing a nonlinear regression analysis to the numerically derived average bound solutions. It is found that the proposed new design equation is highly accurate and provides a convenient and reliable tool for stability analyses of shallow unlined tunnels in rock masses in practice.

安全评估是隧道建设的关键问题，需要可靠，准确的稳定性分析。目前，在岩体隧道掘进稳定性分析方面已经进行了大量的研究。但是，对于隧道稳定性的预测，缺乏准确可靠的设计方程是显而易见的。本文提出了一种新的设计方程式，该方程式适用于岩体中浅无衬砌圆形隧道的稳定性，遵循广义Hoek-Brown破坏准则。由于问题性质的复杂性，不可能实现问题的封闭形式的解析解决方案。因此，选择有限元极限分析的计算框架，以数值方式得出问题的上限和下限解。全面研究了覆盖隧道浅层深度比的完整无量纲参数，完整岩石的规范化单轴抗压强度以及Hoek-Brown材料参数。通过对数值推导的平均界解进行非线性回归分析，建立了岩体中浅浅圆形隧道稳定性分析的新设计方程。结果表明，提出的新设计方程具有较高的精度，为岩体中浅浅衬砌隧道的稳定性分析提供了方便，可靠的工具。通过对数值推导的平均界解进行非线性回归分析，建立了岩体中浅浅圆形隧道稳定性分析的新设计方程。结果表明，所提出的新设计方程具有较高的精度，为岩体中浅浅衬砌隧道的稳定性分析提供了方便，可靠的工具。通过对数值推导的平均界解进行非线性回归分析，建立了岩体中浅浅圆形隧道稳定性分析的新设计方程。结果表明，提出的新设计方程具有较高的精度，为岩体中浅浅衬砌隧道的稳定性分析提供了方便，可靠的工具。