# Adaptive Optimization Method for Piled Raft Foundations Based on Variable Pile Spacing
## 7 Conclusions  
An adaptive optimization method is developed for the pile arrangement of a piled raft foundation in this paper. In the method, the pile spacing is adjusted according to the settlement of the raft from an initial design (designed by the traditional design method). Pile groups subjected to uniform and non-uniform loads and different shapes of the rafts use the proposed optimization algorithm via the finite element method. During this process, the soil inhomogeneity and nonlinearity are also considered. According to the research results, the following conclusions are drawn:  
1. Without increasing the consumption of total pile material, varying the pile spacing across the pile group can affect the overall foundation behaviour, as the maximum settlements of the raft in three cases are reduced compared with that in the initial design. The optimization rates of the differential settlement of the raft are all more than 80%, and only need few iterations during the optimization process. The minimum pile top stresses are increased in three cases, which indicates that more bearing capacity is utilized after optimization design compared with the initial design. The compared \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Model** & **Min-S (m)** & **Max-S (m)** & **Diff-S (m) (F)** & \begin{tabular}{c} **Min-Stress** \\ **(MPa)** \\ \end{tabular} & \begin{tabular}{c} **Max-Stress** \\ **(MPa)** \\ \end{tabular} & \
\begin{tabular}{c} **Diff-Stress** \\ **(MPa)** \\ \end{tabular} &
\begin{tabular}{c} **UBC** \\ **(MPa)** \\ \end{tabular} \\ \hline C1-94-O & 0.0398 & 0.0417 & 0.0019 (82\%) & 3.96 & 4.57 & 0.61 & 9.7 \\ C2-97-O & 0.0428 & 0.0445 & 0.0018 (92\%) & 4.19 & 4.92 & 0.73 & 9.7 \\ C3-173-O & 0.0526 & 0.055 & 0.0024 (90\%) & 7.07 & 7.77 & 0.7 & 9.7 \\ \hline \hline \end{tabular} Note: “Min” is short for Minimum; “Max” is short for Maximum; “S” is short for settlement; “Diff” is short for differential.  
\end{table} 
Table 7: Comparison of settlements of the rafts and pile top stress for different cases after AOM-ES. Figure 12: Raft settlements of the three cases after optimization design: (**a**) C1-94-O; (**b**) C2-97-O; (**c**) C3-173-O. results indicate that the AOM method proposed in this paper has high optimization efficiency and robustness. 2. For the case where the maximum bearing capacity of the piles after optimization design is less than that in the initial design or does not exceed the design value in the code (1/2 UBC), an economic optimization design of the piled raft foundation under certain safety conditions can be achieved by reducing the number of piles. The results show that no pile top stress from different PRFs exceeds the UBC after optimization design, and the bearing capacity of the piles with minimum pile top stress are all more utilized than that in the initial design. The reduction of the number of piles does not affect the differential stress on top of the pile group significantly compared with those in optimization designs only by AOM, and the optimization rates of the differential settlement of the raft are still more than 80%. These benefits can not only be translated into economic savings but also reduce the environmental impacts, as less construction materials will be consumed. 3. The lower limit of pile spacing during the optimization process is a problem requiring engineering judgment. Twice the pile diameter as the low limit of the pile spacing in this paper is a suggestion based on existing experience, and it can be adjusted according to construction technology and engineering requirements. On the other hand, in order to reduce the limitation of the lower limit of pile spacing on the optimization efficiency (constraint 1), piles as long as possible (with larger pile spacing) can be selected under a given load during the initial design to ensure sufficient optimization space to achieve a higher optimization rate. Conceptualization, methodology, software, validation, formal analysis, investigation, data curation, writing original draft, C.Y.