## 1 Introduction  
Pile foundations are commonly used basic forms of foundations in engineering, which have the advantages of a high degree of mechanized construction, strong stability, high carrying capacity, and small soil settlement. Usually, pile foundations in actual engineering applications are based on pile group foundations, and basic soil settlement calculations of the pile groups are essential to pile foundation design. A large number of studies show that the base soil-settlement characteristics of piles are substantially different from those of a single pile, whereas the basic soil-settlement characteristics of pile groups are related to a single pile. At present, the commonly used calculation methods for the soil-settlement characteristics of the pile group load-settlement are the empirical method, the equivalent replacement method, the analytical method, and the numerical simulation method. Among them, an empirical method represented by [PERSON] [1] and [PERSON] [2] established the relationship between single pile-soil settlement and pile groups based on engineering measures. The equivalent replacement method, represented by [PERSON] et al. [3] and [PERSON] [4], proposed that the pile group foundation should be equivalent to a simple basic form, effectively simplifying the calculation of pile group soil settlement. The analyses of [PERSON] and [PERSON] [5], [PERSON] and [PERSON] [6], [PERSON] and [PERSON] [7], and [PERSON] [8] are also represented, and the main consideration in those studies is the interaction of a pile-soil surface. With developments in technology, numerical simulation methods are widely used in the analysis of the soil-settlement characteristics of pile groups under loading. By using the boundary element method (BEM) to analyse the factors that influence the pile group interactions, [PERSON] and [PERSON] [9] produced the nonlinear characteristics of pile group soil settlement by assuming that the pile was rigid and by overlaying the single pile soil-settlement characteristics in the pile groups using the superposition principle. [PERSON] [10]proposed that the pile-pile interaction factors of the pile groups in the finite soil layer were reduced with the reduction in the axial load-transfer coefficient. Based on the theory of elastic continuity, [PERSON] and [PERSON] [11] proposed the calculation method of pile group soil settlement with load transfer, which considers the compression characteristics of soil in a non-homogeneous soil layer. [PERSON] et al. [12] described the interaction characteristics of pile groups and soil in the form of a single pile analogy, which produced the nonlinear characteristics of the settlement of the pile groups under loading. Combined with the stiffness matrix theory and the integral interaction factors of pile groups, [PERSON] and [PERSON] [13] proposed a nonlinear analysis method of the soil settlement of the vertical load under the pile groups. Based on the sedimentation characteristics of the single pile and the pile groups under loading in layered soil, a simple method of analysis of the soil-settlement characteristics of the pile groups was proposed by [PERSON] et al. [14]. [PERSON] et al. [15] used finite element methods to analyse the displacement characteristics of a pile group foundation in a sand base under vertical and lateral loads. Others, [PERSON] et al. [16], [PERSON] et al. [17], [PERSON] et al. [18], and [PERSON] et al. [19] have all used numerical simulation methods to analyse the soil-displacement characteristics of piles under loading. The abovementioned research shows that soil settlement of the pile groups under vertical loading is nonlinear and there is a certain connection between the single pile and the pile groups. However, previous research did not consider the sedimentation characteristics of the settlement of the soil of the next pile due to vertical loading or the influence of the interaction between the raft plate, pile foundation, and the soil on the sedimentation characteristics of the pile groups.