*4.3. Parametric Study*

Based on the above FE model, the critical parameters in the preliminary design and service process of the cantilever anti-slide pile were analyzed, including the material strength and anchored length.

#### 4.3.1. Effect of Concrete Strength and Steel Bars' Strength

The concrete strength and steel bar strength of the cantilever anti-slide pile were in a time-varying evolution states during the service period. Figures 24 and 25, respectively, show the distributions of pile displacement and bending moment for different concrete strengths (40, 35, 30, 25, and 20 MPa) and reinforcement yield strengths (The yield strengths of reinforcement N1 (*fy*N1) were 460, 432, 402, 371, and 340 MPa, and the yield strengths of reinforcement N2 (*fy*N2) were 438, 411, 381, 352, and 323 MPa). It can be obtained that the maximal lateral displacements at the pile top of the cantilever anti-slide pile with different concrete strengths under the same thrust load were 55.20 mm, 58.52 mm, 61.04 mm, 67.54 mm, and 86.02 mm, respectively, and the ultimate bending moments when the pile was destroyed are 4.689, 4.58, 4.524, 4.431, and 4.333 kN·m, respectively, indicating that the pile top lateral displacement was negatively related to the concrete strength, and the smaller the concrete strength, the greater the lateral displacement at pile top. However, the reduction of the ultimate bending capacity of the pile is not obvious. The pile top lateral displacements of cantilever anti-slide pile with different steel bars' strengths under the same thrust load were 52.48, 61.04, 72.009, 99.02, and 121.42 mm, respectively, and the ultimate bending moments when the pile was destroyed were 4.812, 4.524, 4.287, 4.112, and 3.705 kN·m, respectively, indicating that the pile top lateral displacement was negatively correlated with the steel bars' strength, and the maximum bending capacity of the pile decreased obviously with the gradual deterioration of steel bars' strength. It can be concluded that the lateral displacement at pile top can be reduced by improving the concrete or steel bars' strength during the preliminary design. However, increasing the concrete strength makes no difference to the pile bearing capacity, while increasing the reinforcement strength has obvious effect. In other words, the pile displacement gradually increases with the deterioration of the material strength during the service life, and the deterioration of the steel bar strength has a stronger deterioration effect on the maximum bearing capacity of the pile than concrete strength.

**Figure 23.** Comparison of the experimental and numerical simulation results. (**a**) Displacement; (**b**) thrust load-pile top displacement; (**c**) distribution of bending moment.

#### 4.3.2. Effect of Anchor Ratio

The anchor ratio (AR) is another crucial parameter for the structural design of a cantilever anti-slide pile. Figure 26 shows the distributions of the pile displacement and bending moment under five anchor ratios (1/5, 1/4, 1/3, 4/11, 2/5, 1/2). It can be concluded that the pile displacement and bending moment under different anchor ratios changed little. The reason is that the anchored section was set as a fixed constraint in the ABAQUS numerical simulation to simulate the anchored section, indicating that when the strength of the rock formation embedded in the pile anchored section is large enough, blindly increasing the length of the pile anchored section cannot significantly improve the bearing capacity, which is in agreement with the results by [26]. In summary, the length of pile anchored section should be designed reasonably by combining economic factors and safety factors in this case.

**Figure 24.** Variations of the pile displacement and bending moment with respect to concrete strength. (**a**) Pile displacement; (**b**) pile bending moment.

**Figure 25.** Variations of the pile displacement and bending moment with respect to steel bars' strength. (**a**) Pile displacement; (**b**) pile bending moment.

#### 4.3.3. Discussion

The lateral displacement and bending moment of the cantilever anti-slide pile under the trapezoidal load (TL) and uniform load (UL) were further compared, as shown in Figure 27. When the resultant force of the trapezoidal load (*FT*) reached 6 kN, the lateral displacements at the pile top under the trapezoidal load and uniform load were 0.47 mm and 0.9 mm, respectively, and the maximum bending moments at the sliding surface were 0.78 kN·m and 0.97 kN·m, respectively. When *Fl* reached 28.2 kN, the lateral displacements at pile top under the trapezoidal load and uniform load were 9.3 mm and 49.15 mm, respectively, and the maximum bending moments were 3.42 kN·m and 4.21 kN·m, respectively. This shows that the lateral displacement and bending moment of the anti-slide pile under the uniform load and trapezoidal load have little difference when the external thrust load is small. As the external thrust load increases, the lateral displacement and bending moment of the anti-slide pile under the uniform load are gradually larger than those under the trapezoidal load, especially the lateral displacement, and the gaps under the two loads gradually increase with the external thrust load. In summary, the distribution form of the external thrust load behind the cantilever anti-slide pile will significantly affect its stress and deformation. In the process of the structural design of the cantilever anti-slide pile, the distribution form of the external thrust load should be judged as accurately as possible to make it more consistent with the actual stress distribution, so as to make the structural design of the anti-slide pile more reasonable and economical.

**Figure 26.** Variations of the pile displacement and bending moment with respect to anchor ratio. (**a**) Pile displacement; (**b**) pile bending moment.

**Figure 27.** Displacement and bending moment comparisons for the anti-slide pile under trapezoidal load and uniform load. (**a**) Displacement; (**b**) bending moment.
