This paper introduces a novel closed‐form equation (surrogate model) for approximating the Morgenstern–Price estimate of the factor of safety of homogeneous dry finite slopes with circular failure surfaces. Unlike typically used methods, the proposed equation does not require the definition of a critical failure surface, splitting the soil mass into slices, or the iterative reduction of soil resistance to the limit state. It can be easily programmed into calculators or computers and accurately determines the minimum factor of safety based on the shear strength parameters and slope geometry—meaning that it is ideally suited for integration into reliability calculations. The equation is determined parametrically for various soil parameters and slope geometry using the Morgenstern–Price method and compares favorably with conventional techniques, such as slope stability charts, limit equilibrium, and strength reduction methods (SRM). From a practical perspective, the proposed equation greatly simplifies the analysis of the slope stability as the creation of a numerical model is not required and is suited to use in the feasibility stage of a project, for example, for large linear infrastructure projects with differing slope geometries or in situations where a quick assessment is desired.

中文翻译：

---

用于估计均匀干燥有限边坡安全系数的新型稳定性方程

本文介绍了一种新颖的封闭式方程（代理模型），用于近似具有圆形破坏表面的均质干燥有限斜坡的安全系数的 Morgenstern-Price 估计。与通常使用的方法不同，所提出的方程不需要定义临界破坏面、将土体分割成切片或将土体阻力迭代降低到极限状态。它可以轻松地编程到计算器或计算机中，并根据抗剪强度参数和坡度几何形状准确确定最小安全系数，这意味着它非常适合集成到可靠性计算中。该方程是使用 Morgenstern-Price 方法针对各种土壤参数和边坡几何形状进行参数确定的，并且与边坡稳定图、极限平衡和强度折减法 (SRM) 等传统技术相比具有优势。从实际角度来看，所提出的方程大大简化了边坡稳定性的分析，因为不需要创建数值模型，并且适合在项目的可行性阶段使用，例如具有不同坡度的大型线性基础设施项目几何形状或需要快速评估的情况。