The stability of vertical unsupported circular excavations in rock media, obeying generalized Hoek-Brown yield criterion, has been investigated by using the lower bound finite elements limit analysis. An axisymmetric analysis, composed of a planar domain with a mesh of three-noded triangular elements, has been carried out. The optimization problem is dealt with by using the semidefinite programming technique avoiding the need of either smoothing the yield surface or making any assumption associated with the circumferential stress (I�I¸). A detailed parametric study has been executed, and the effects of different input material parameters, namely, geological strength index (GSI), yield parameter (mi), and the disturbance factor (D) on the results have been studied. For different height to radius ratios of the excavation, the computed results are presented in the form of nondimensional stability numbers. Failure mechanisms have also been investigated for a few typical cases. The results from the analysis have been compared with that evaluated separately with the application of the software OptumG2.

中文翻译：

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使用 Hoek-Brown 破坏准则的岩石无支护垂直圆形开挖下限分析

通过使用下界有限元极限分析，研究了岩石介质中垂直无支撑圆形开挖的稳定性，遵循广义 Hoek-Brown 屈服准则。轴对称分析由平面域和三节点三角形单元的网格组成。优化问题是通过使用半定规划技术来处理的，避免了平滑屈服面或做出与周向应力 (I I¸) 相关的任何假设的需要。已执行详细的参数研究，并研究了不同输入材料参数，即地质强度指数 (GSI)、屈服参数 (mi) 和干扰因子 (D) 对结果的影响。对于不同的开挖高度半径比，计算结果以无量纲稳定性数的形式表示。还研究了一些典型案例的失效机制。分析结果与使用 OptumG2 软件单独评估的结果进行了比较。