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Limit Equilibrium Analysis Incorporating the Generalized Hoek–Brown Criterion
Rock Mechanics and Rock Engineering ( IF 6.2 ) Pub Date : 2021-06-05 , DOI: 10.1007/s00603-021-02518-8
Youn-Kyou Lee , S. Pietruszczak

Both the limit analysis and the limit equilibrium approach require the formulation of a failure criterion in terms of components of stress vector acting on a potential failure plane. For applications in Rock Mechanics, the generalized Hoek–Brown (GHB) criterion is commonly used, for which no analytical form of the Mohr failure envelope is, in general, available. In this work, a new approximation of the Mohr envelope for the GHB criterion is developed, which is valid in a broad range of GSI (i.e. Geological Strength Index) values. The approach is based on the orthogonal projection of a function for best-fitting the quadratic or cubic polynomials to the Balmer’s equations that define the relationship between the normal stress acting on the failure plane and the minor principal stress. The methodology is illustrated by a limit equilibrium analysis, which involves assessment of the safety factor of a rock slope that has a vertical tension crack embedded in the upper horizontal surface. The analysis employs an approximate Mohr envelope based on the cubic polynomial fitting as the failure condition along the rupture surface. The results indicate that the safety factor for stability of the slope is very sensitive to the geometry of the crack (i.e. its location and depth) as well as the selection of the value of GSI.



中文翻译:

结合广义 Hoek-Brown 准则的极限平衡分析

极限分析和极限平衡方法都需要根据作用在潜在失效平面上的应力矢量分量来制定失效准则。对于岩石力学中的应用,通常使用广义 Hoek-Brown (GHB) 准则,通常无法获得莫尔破坏包络的分析形式。在这项工作中,开发了 GHB 标准的莫尔包络的新近似值,该近似值适用于广泛的 GSI(即地质强度指数)值。该方法基于函数的正交投影,以将二次或三次多项式最佳地拟合到 Balmer 方程,该方程定义了作用在破坏平面上的法向应力与次主应力之间的关系。该方法通过极限平衡分析来说明,这涉及评估具有嵌入在上部水平表面的垂直张力裂缝的岩石边坡的安全系数。该分析采用基于三次多项式拟合的近似莫尔包络作为沿破裂面的破坏条件。结果表明,边坡稳定性的安全系数对裂缝的几何形状(即裂缝的位置和深度)以及GSI值的选择非常敏感。

更新日期:2021-06-05
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