Abstract This study introduces a simplified semi-distinct element algorithm for discontinuous rock slopes under toppling instability assessment based on block theory. The presented algorithm is developed to investigate block, flexural and block-flexural types of toppling failures which have been coded in the Python high-level programming language. In order to investigate toppling instabilities for different modes, the three modelling steps, namely, geometrical, behavioural and mechanical simulations were conducted to appoint high-order calculation trending loops. These loops were based on the analytical description of modified second-order reliability method with first-order efficiency to determine the factor of safety values for discontinuous rock slopes. Each type of toppling failure was described based on main assumptions that were modified by geometric qualifications such as the analytical procedure, single block slip, and the Voronoi diagram algorithm for the stability analysis of the three different failure types. According to the stability assessment results of the studied slopes which were verified by the distinct numerical method via UDEC software, it has been clarified that the results obtained from the algorithm and the numerical analysis were in an appropriate trend. The used algorithm is superior in pinpointing the critical sliding zones, safety factor estimation and progressive failure analyses as compared to the numerical analyses. Moreover, the block theory based algorithm has higher processing capability and speed with respect to the numerical method.

中文翻译：

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基于关键块的不连续岩质边坡倾覆稳定性分析方法

摘要 本文介绍了一种基于块体理论的不连续岩质边坡倾覆失稳评估的简化半离散元算法。所提出的算法被开发用于研究用 Python 高级编程语言编码的块状、弯曲和块状弯曲类型的倾覆故障。为了研究不同模式的倾覆不稳定性，进行了三个建模步骤，即几何、行为和机械模拟，以指定高阶计算趋势循环。这些回路基于对具有一阶效率的修正二阶可靠性方法的分析描述，以确定不连续岩石边坡的安全系数值。每种类型的倾覆故障都是基于主要假设进行描述的，这些假设由几何限定修改，例如用于三种不同故障类型稳定性分析的分析程序、单块滑动和 Voronoi 图算法。根据UDEC软件采用不同数值方法对研究边坡的稳定性评估结果进行验证，表明该算法和数值分析的结果处于适当的趋势。与数值分析相比，所使用的算法在精确定位关键滑动区域、安全系数估计和渐进式失效分析方面具有优势。此外，基于块理论的算法相对于数值方法具有更高的处理能力和速度。