## 1 Introduction  
Since [PERSON] and [PERSON] [1] proposed an analytical method in 1972 to solve problems involving it, the pile-raft foundation is widely used in Europe and Asia. However, in a conventional pile-raftfoundation, the connection between the pile and the raft is governed by rigid constraints. In particular, when the number of piles is small and the pile spacing is large, large bending moments may be easily generated in the raft, even leading to the cracking of the raft and the concentration of stress on top of the pile [2]. To solve this problem of structural stress, a cushion of a certain thickness can be set between the raft and the top of the pile [3]. It helps use the bearing capacity of soil between the piles to adjust their load-transfer mechanism [4; 5; 6; 7]. Many researchers studied the performance of connected and disconnected piled rafts in sand using centrifugal model tests [8; 9; 10; 11; 12; 13]. [PERSON] et al. [8] and [PERSON] [9] carried out extensive static load tests to study the behavior of connected and disconnected piled rafts under vertical and eccentric loads. [PERSON] and [PERSON] [10], [PERSON] [11], and [PERSON] et al. [12] studied the mechanical and settlement-related characteristics of connected and disconnected piled rafts through a series of centrifugal model tests. Based on the transfer mechanism of load in the case of disconnected pile (DP) rafts, a simplified failure mode involving a cushion and the corresponding theoretical analysis were proposed by [PERSON] [13]. Moreover, [PERSON] et al. [14] and [PERSON] et al. [15] highlighted the importance of the cushion layer in adjusting the ratio of load sharing of the pile to that of the soil, based on field static load tests. The DP raft involves multiple interactions among the raft, cushion, pile, and soil. For this complex structural system, the finite element method (FEM) is an effective analytical tool. [PERSON] et al. [16], [PERSON] et al. [17], [PERSON] et al. [18], [PERSON] et al. [19], [PERSON] et al. [20], [PERSON] et al. [21], and [PERSON] et al. [22] studied the load-transfer mechanism and settlement characteristics of piled rafts with cushions using three-dimensional (3D) finite element analysis. It was assumed in these studies that the pile was in homogeneous soil, and a solid element was used to simulate the pile. With increasing number of piles, the number of model meshes increase significantly, which eventually leads to an increase in the time needed for numerical computation [19]. To overcome these shortcomings, [PERSON] and [PERSON] [23] proposed an improved embedded pile simulation method, and [PERSON] and [PERSON] [24] further improved it. In this method, the embedded pile element was not dealt with in the soil meshing, which could reduce the number of degrees of freedom of the computational model and improve the efficiency of calculation. [PERSON] et al. [25] studied the applicability and accuracy of the embedded pile to DP rafts for the first time, and noted that the settlement in the embedded pile method was usually close to that in the solid pile method. [PERSON] et al. [7] proposed a simplified analytical model for the optimal selection of cushion stiffness. [PERSON] et al. [26] developed a settlement calculation method for a long-short pile composite pile-raft foundation. [PERSON] and [PERSON] [27] constructed a mechanical model of a pile-piercing cushion and a method to calculate pile-soil interaction. They used them to propose a method to theoretically calculate the pile-soil stress ratio. Most of the above studies focused on the bearing capacity and deformation performance of single-building pile-raft foundations under ideal and simplified conditions. Analyses of the geometric parameters of the pile, raft, and cushion formed the main work reported in them. However, the area of the raft and the number of piles used were largely different from those employed in practice. Little attention was further paid to situations involving basements.