# Optimization of Uplift Piles for a Base Plate Considering Local Anti-Floating Stability
## 4 Case Study  
In this section, the design methods of uplift piles proposed in Section 3.4 are applied to practical projects. A foundation pit of the Beijing sub-center transportation hub was selected to investigate. Most of the structures in this project are underground stations and underground commercial areas near the North Canal, so the structures have high requirements for anti-floating stability. The bottom of this pit has no structures such as crossing tunnels or shield wells, and the base elevation is the same. The layout and design parameters of the uplift piles of the original design and the two optimized designs are shown in Figure 12 and Table 2:  
In the original design, the piles are designed with the large diameter and sparse spacing. Based on the same total volume of piles, the same pile diameters and the same pile spacings, the pile lengths is dispersion in optimization design 1. Although the BESO process can significantly reduce the deformation of the base plate by optimizing the distribution of pile lengths, the pile lengths after optimization are extremely uneven, which is inconvenient for engineering construction. Therefore, only three different pile lengths are selected for optimization design 1. The piles in the center area of the base plate are the longest, the piles \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Design**} & **Pile Spacing** & **Pile Diameter** & **Pile Length** & **Column Spacing** \\  & **(m)** & **(mm)** & **(m)** & **(m)** \\ \hline Original design & 4.5 & 1400 & 32 & 9 \\ Optimization design 1 & 4.5 & 1400 & 50, 38, 25 & 9 \\ Optimization design 2 & 3 & 1000 & 30 & 9 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of uplift piles. Figure 12: The layout of the uplift piles: (**a**) original design; (**b**) optimization design 1; (**c**) optimization design 2.  
at the edge area and under the column loads are the shortest. The shortest pile length is half of the longest pile length. There is a transition area between the long pile area and the short pile area, and the pile lengths in that area are selected at 1.5 times the shortest pile length. For optimization design 2, the total volume of the piles remains unchanged; the piles are designed with a small diameter and dense spacing. The numerical models shown in Figure 13 are established based on the three designs, and the parameters of the models are shown in Table 3.  
Due to a large number of piles in this model, the pile elements are used to replace solid elements of piles to improve calculation efficiency, and column loads are replaced by concentrated forces (8000 kN). The measured data of the single-pile pulling experiment are used to determine the parameters of the pile element. The diameter of the pile is 1000 mm, and the length of the pile is 30 m in the experiment. The corresponding numerical model is established; by adjusting the parameters of the pile element, the load-displacement curve of the pile crown is fitted with the measured data (Figure 14). The parameters of the pile element are shown in Table 4.  
The numerical results of the maximum uplift, maximum differential deformation, and total strain energy for the base plate are shown in Table 5, and the vertical deformation contours are shown in Figure 15. Compared with the original design, the three indicators in optimization design 1 are reduced by 34.4%, 55.8%, and 19.24%, respectively, and those in optimization design 2 are reduced by 25.2%, 35.5%, and 26.0%, respectively. Optimization design 2 (small pile diameter and dense spacing) has the smallest total strain energy, which proves that the deformation degree of the base plate in this design is the smallest among the three designs. Compared with the original design, the maximum uplift is significantly reduced, the deformation is more uniform, and the differential deformation is smaller in  
Figure 13: Numerical models.