## 1 Introduction  
Thick, soft soil layers are widely distributed in coastal areas of China. These soil layers are characterized by a high void ratio, high water content, low permeability coefficient, and low strength. To build structures on such soft soil, it is necessary to reinforce the foundation. The vacuum preloading method is a mature and low-cost technique used to strengthen soft foundations in the field of drain consolidation. This method was first proposed by [PERSON] in 1952 [1], and since then, civil engineering scholars at home and abroad have conducted practical applications, tests, and theoretical research on this method. In terms of theoretical analysis, various researchers, such as [PERSON] [2], [PERSON] [3], [PERSON] [4], [PERSON] and [PERSON] [5], [PERSON] [6], [PERSON] [7], [PERSON] et al. [8], [PERSON] et al. [9], etc., have developed sand drain consolidation theory with reference to the consolidation calculation method of surcharge preloading, changing the load boundary conditions to derive accurate analytical solutions of consolidation suitable for vacuum preloading. However, these methods are not convenient for practical application and promotion due to their simplification of assumptions, obscure and complex derivation processes, large numbers of parameters, and extensive requirements. In terms of numerical calculations, many researchers, such as [PERSON] et al. [10], [PERSON] et al. [11], [PERSON] and [PERSON] [12], [PERSON] et al. [13], [PERSON] et al. [14],[PERSON] et al. [15], [PERSON] et al. [16], [PERSON] et al. [17], and [PERSON] et al. [18], have conducted extensive research, including two-dimensional simulation, three-dimensional simulation, and sand drain simplification, considering smearing and other factors. However, few studies have been conducted on the negative pressure distribution mode of the vertical drain body under vacuum preloading. The plane strain model is usually used to represent the actual three-dimensional situation in the concrete implementation process. Although many engineering examples have been used to obtain relatively ideal results, the seepage and mechanical effects of soft foundations under vacuum preloading are three-dimensional, so a three-dimensional model should be applied in research. In the process of theoretical exploration and practical application, the mechanical and fluid disturbances of soft foundations strengthened by vacuum preloading are significant. Therefore, it is essential to analyze the settlement and pore pressure of soft foundations under this construction method using the fluid-solid coupling method, as suggested by [PERSON] et al. [19] and [PERSON] et al. [20]. FLAC3D finite-difference method software based on the LaGrangian continuum method is a suitable option for conducting such analysis. This software has a strong analytical ability, making it suitable for complex engineering problems involving the mechanical seepage coupling of geotechnical materials. Compared to other finite element software, FLAC3D has the following advantages. (1) FLAC3D adopts the \"mixed discrete method\", which is more accurate and reasonable than the \"discrete integration method\" commonly used in the finite element method. (2) There are no numerical barriers to simulating physically unstable processes with FLAC3D. (3) FLAC3D uses an explicit difference method to solve differential equations. It can conveniently calculate stress increments and unbalanced forces and track the evolution process of the system. (4) FLAC3D can simulate a large number of units with less memory, making it particularly suitable for operation on microcomputers. In the present study, fluid-solid coupling analysis of soft soil under the combined action of vacuum and surcharge was simulated Using FLAC3D. We utilized the FLAC3D finite-difference method software to model and calculate the soil consolidation process under vacuum preloading for specific projects while varying the negative pressure distributions of the drainage body and keeping other conditions constant.