## 3 Numerical Simulation of Pile-Anchor Support Technology for Rock Slopes of Deep Foundation Pits  
In the design and analysis of foundation pit support, it is assumed that there is a holistic penetrating failure of a single slip surface or that the breakthrough failure of a karst cave between parallel structural planes is deemed an extreme state of the foundation pit. The row piles are set with spacings of 1.5 times, 2 times, 3 times and 4 times the pile diameter. The pile is made of C35 concrete with a length of 34 m, and the anchor cable is arranged at the maximum displacement point of the pile body. This method is widely used in Tunnel Engineering [25,26]. The length of the anchor cable is 15 m, with an anchoring section length of 7 m and an inclination angle of 15\({}^{\circ}\), forming a joint pile-anchor support system in the form of one pile and one anchor. It can be seen from Figures 4 and 5 that karst cave penetration failure still occurs after the installation of the retaining piles, which shows that the slope of the foundation pit slope supported by cantilever piles does not change the failure pattern in the cave containing condition. Figure 3: Cross-sectional view of failure mode of rock mass within 50 m length of foundation pit under 60\({}^{\circ}\) dip angle of structural plane. (**a**) failure mode of the foundation pit on the bedding rock side; (**b**) failure mode of the foundation pit on the toppling rock side; (**c**) section view of failure mode of the foundation pit. Figure 6 shows the displacement curve for a cantilever pile with a 0.8 m pile diameter and 1.5 times the pile spacing, with a maximum horizontal displacement of 0.7 mm at the ultimate condition (8000 steps). The displacement curve of the pile began to bulge slightly at 4000 steps. The position of the maximum displacement increment at the top of the pile remained unchanged, with a small displacement range until 7000 steps. After 7000 steps, the displacement increases sharply between 7000 steps and 8000 steps, with an increment in displacement twice as large as the first 7000 steps. Figure 4: Pile diameter of 0.8 m, 1.5 times pile spacing, cantilever pile support (three retaining piles). Figure 5: Pile diameter of 0.8 m, 2.0 times pile spacing, cantilever pile support (three retaining piles). Figure 6: Displacement curve of cantilever piles with different pile diameters at 1.5 times pile spacing (three piles). If a pile spacing of 2.0 times the pile diameter is used to support the foundation pit, the overall deformation trend of retaining piles is similar to that of the 1.5 times pile spacing case (as shown in Figure 7), and the maximum displacement values achieved at the same analysis step are consistent between the two. For the 4 m model, when the total number of retaining piles is the same, the change in pile spacing does not affect the final deformation but only slightly affects the depth of the maximum displacement point. If the foundation pit is supported at a pile spacing of 3.0 times the pile diameter, the number of retaining piles will be reduced from 3 to 2. The extreme state is reached at 3500 steps in the calculation, as shown in Figure 8a. As shown in the working condition of the three retaining piles, there is a steep increase in the maximum displacement of the retaining piles when the foundation pit reaches extreme failure. When the crown beam is installed at the top of the retaining pile, its displacement is shown in Figure 8b. Compared with the support method without the crown beam, the occurrence time of the extreme state has shifted backward, and the displacement at the top of the retaining pile is greatly suppressed with the increase in calculation steps. After the crown beam is installed, the steep increase in pile displacement before reaching the extreme state disappears. This shows that the crown beam is necessary to avoid the collapse of the foundation pit due to the increase in instantaneous residual sliding force when the slip surface of the rock mass is penetrated.