Embedded stabilizing piles are a significant optimization measure for traditional piles used to reinforce slopes or landslides. The determination of the embedded depth of the pile top is essential for engineering design. On the basis of the potential overtop‐sliding failure mechanism for a piled slope, the corresponding overall slip surface is assumed to consist of the upper part from the original slip surface of the landslide, and the lower part occurs in the local slide mass upslope of the piles. The imbalanced thrust force method is used to determine the thrust force of the upper slide mass, and a variational calculus method within the framework of limit equilibrium for the lower slide mass is provided to calculate its limit resistance. According to the equilibrium relationship between the thrust force and the limit resistance under a design factor of safety of the piled slope, a closed‐form solution to the piled‐slope stability is specifically derived. It can quantitatively exhibit the influences of some important factors, including the embedded depth on the factor of safety and the corresponding slip surface of the slope. The analysis results of some practical examples show that the factor of safety decreases nonlinearly as the embedded depth increases. The proposed method can be applied in practical engineering.

中文翻译：

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加筋边坡稳定桩嵌入深度的一种计算方法。

嵌入式稳定桩是用于加固斜坡或滑坡的传统桩的重要优化措施。确定桩顶的嵌入深度对于工程设计至关重要。根据堆积斜坡的潜在的上滑破坏机理，假定相应的整体滑移面由滑坡原始滑移面的上部组成，而下部则发生在滑坡的局部滑移质量上坡中。堆。不平衡推力法用于确定上滑动块的推力，并提供了下滑动块的极限平衡框架内的变分计算法，以计算其极限阻力。根据在堆积安全边坡的设计安全系数下推力与极限阻力之间的平衡关系，具体推导了堆积边坡稳定性的封闭解。它可以定量显示一些重要因素的影响，包括埋深对安全系数和相应的斜坡滑移面的影响。一些实例的分析结果表明，安全系数随着埋入深度的增加而非线性减小。该方法可应用于实际工程中。包括关于安全系数的嵌入深度和相应的斜坡滑移面。一些实际例子的分析结果表明，随着嵌入深度的增加，安全系数会非线性降低。该方法可应用于实际工程中。包括关于安全系数的嵌入深度和相应的斜坡滑移面。一些实例的分析结果表明，安全系数随着埋入深度的增加而非线性减小。该方法可应用于实际工程中。