In geological engineering, the unsaturation and non-uniformity of soil have significant influence on slope stability. However, they were common neglected in published literature. Based on the three-dimensional (3D) rotational failure mechanism, this paper introduces a method that combines the gravity increase method and the upper bound theorem, to evaluate the factor of safety (FS) of 3D stepped slope in non-uniform and unsaturated soils. The soil cohesion increases linearly with depth, and three nonlinear unsaturated shear strength models are adopted in this study. After the calculations of internal energy dissipation rate and external work rate, the analytical formula of FS is derived, and the lowest FS value is obtained through optimization. To prove the validity of the proposed method, the present results are compared with previously published solutions. A parametric study is carried out, and the influences of a number of factors on FS are discussed. For non-uniform and unsaturated soils, the new formula for calculating the FS of 3D two-stage slopes is presented for practical use in geological engineering.

在地质工程中，土体的不饱和度和不均匀度对边坡稳定性有显着影响。然而，它们在出版的文献中普遍被忽视。本文基于三维（3D）旋转破坏机理，引入重力增加法和上界定理相结合的方法，评估非均匀非饱和土中3D阶梯边坡的安全系数（FS）。 . 土壤黏聚力随深度线性增加，本研究采用三种非线性非饱和抗剪强度模型。通过计算内耗能率和外功率，推导出FS的解析公式，最低FS值是通过优化获得的。为了证明所提出方法的有效性，将当前结果与以前发布的解决方案进行了比较。进行了参数研究，并讨论了许多因素对FS的影响。对于非均匀和非饱和土，提出了用于地质工程实际应用的 3D 两级边坡FS计算新公式。