A calculation method for the embedded depth of stabilizing piles in reinforced slopes

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.