# Adaptive Optimization Method for Piled Raft Foundations Based on Variable Pile Spacing
## 1 Introduction  
Pile foundations are preferred for supporting tall buildings and important structures [1; 2; 3; 4; 5] (e.g., high-rise buildings, nuclear power plants, and tall wind turbines), because pile foundations are good at controlling the differential and total settlement and improving the bearing capacity. However, the selection of suitable related parameters of pile foundations and the corresponding geotechnical design requires a complex process [6; 7; 8; 9; 10]. A larger design load or complex superstructure can always result in a more complex foundation design, e.g., making the foundations larger or more irregular, which will result in more resources being allocated for foundation design and construction to meet safety requirements. The foundation design and construction usually account for a large proportion of the total cost of the building, so it is necessary to improve the economic benefits of the foundation by optimizing the design. Through a large number of studies, it has been found that the optimal design can reduce the total and differential settlement of the raft, and improve the utilization of the bearing capacity of the pile foundation [11; 12; 13; 14; 15; 16; 17; 18]. For the design of large and irregular pile groups, the control of the differential settlement is particularly important [19; 20; 21]. To address this issue, [PERSON] and [PERSON] [22] proposed a method intended to enhancethe performance of the pile group by changing the geometries of each pile. [PERSON] et al. [23] determined the optimal pile locations in a piled raft design applying the genetic algorithm. [PERSON] [17; 18] gave a parametric study for the optimal design of large pile foundations on sand and commented that adding piles in the centre of a raft can reduce the differential settlement effectively. [PERSON] et al. [24] proposed an optimization analysis method for the pile foundation, which uses the compression matrix of the bending characteristics of the superstructure to consider the stiffness of the superstructure and the foundation model at the same time. [PERSON] et al. [25] introduced a geotechnical design method and its corresponding optimization program for a wind turbine tower pile-raft foundation. This method provides a robust design optimization program based on reliability based on the design parameters under simplified site conditions. [PERSON] et al. [13], [PERSON] et al. [26], [PERSON] et al. [27], and [PERSON] et al. [28] studied the application of the evolutionary algorithm in basic optimization design. Previous studies on the optimization of design basis by numerical methods mostly used traditional gradient methods or genetic algorithms, but these methods have certain limitations, such as the requirement that the design problem should be mathematically formulated and differentiable, and the calculation cost is very high (especially for large-scale pile groups). Therefore, it is necessary to propose new methods to change this limitation and give full play to the bearing capacity of pile groups. [PERSON] and [PERSON] [29] proposed a simple optimization method to achieve an optimized design of foundation stiffness to reduce the value of the differential settlement. The optimized design fully mobilizes the bearing capacity of each pile by using different pile diameters and different pile spacing. However, the method can be regarded as a semi-automatic optimization method; the existence of human factors will affect the optimization efficiency, and economic optimization was not considered. In this study, an adaptive optimization method (AOM) is presented for piled raft foundations (PRFs), which apply each pile in an appropriate location to accommodate the differential settlement of the raft. PRFs with different loads and raft shapes are optimized to verify this method. The nonlinear elasticity and inhomogeneity of the soil properties and soil-raft-pile interaction are considered through three-dimensional (3D) finite element analysis during the analysis.