Abstract At present, almost all stability charts are designed for uniform slopes with straight surfaces. In this study, the main purpose is to provide a new stability chart analysis method, which is applicable to assess the stability of a non-straight slope with one convex fold angle. First, critical failure state charts (CFSCs) are proposed to represent the relationship among the slope height, unit weight, soil cohesion and friction angle for different slope angles when the slopes are in a critical failure state. Second, based on the CFSCs, the safety factors for any non-straight slope with one convex fold angle can be directly determined by solving quadratic equations with one unknown. Finally, the reliability and accuracy of the proposed method is tested against the limit equilibrium method (LEM) and finite-difference strength-reduction method (SRM) via 12 slope examples. The results show that the average relative errors, compared with the LEM and SRM, are 3.84% and 3.16%, respectively. Thus, it can be concluded that the proposed method has good performance in terms of calculating the FOS.

中文翻译：

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一种单凸折角非直边坡安全系数及临界稳定图的快速估计方法

摘要 目前，几乎所有的稳定性图都是针对平直面的均匀坡度设计的。本研究的主要目的是提供一种新的稳定性图分析方法，适用于具有一个凸折角的非直边坡的稳定性评估。首先，提出了临界破坏状态图（CFSCs）来表示边坡处于临界破坏状态时不同坡角下坡高、单位重量、土壤黏聚力和摩擦角之间的关系。其次，基于CFSCs，任何具有一个凸折角的非直边坡的安全系数都可以通过求解一个未知数的二次方程直接确定。最后，通过 12 个斜率实例，针对极限平衡法 (LEM) 和有限差分强度折减法 (SRM) 测试了所提出方法的可靠性和准确性。结果表明，与 LEM 和 SRM 相比，平均相对误差分别为 3.84% 和 3.16%。因此，可以得出结论，所提出的方法在计算FOS方面具有良好的性能。