## 1 Introduction  
With the rapid development of urbanization, the availability of construction land resources is becoming increasingly restricted, and the use of underground space has become the key direction of research. Therefore, the excavation and support of the foundation pit is a pressing issue for research. The pile-anchor support structure method is a tie-back method in which the retaining structure is braced through anchors embedded into the neighboring grounds. Such a method allows the foundation pit to be obstacle-free, thereby ensuring sufficient working space for construction. Hence, it is widely used in foundation pit projects [1; 2; 3]. Recently, with the continuous development of computer technology, numerical simulation methods have become an important tool to deal with the problem of foundation pits, and they are widely used in foundation pit design and engineering [4; 5; 6; 7; 8; 9]. Compared with the traditional empirical formula method [10] and physical model method [11], the numerical simulation method [11], the complex three-dimensional model and invert the real pit to a certain degree but also carry out the design optimization work, which saves a large amount of money and time.  
In numerical analysis, the pile support structure plays an important role and influences all relevant results [12]. Regarding the pile equivalent calculation methods, considerable results have been reported. In general, the pile equivalent calculation methods can be divided into four types. The first type is equivalent to linear elastic solid elements [13; 14; 15]. The equivalent stiffness criterion is selected to transfer the piles to a diaphragm wall [16; 17],as shown in Equation (1), in which \(D\) is the diameter of the pile, m; \(t\) is the pile spacing of the piles, m; and \(h\) is the thickness of the retaining wall, m.  
\[\frac{th^{3}}{12}=\frac{\pi D^{4}}{64} \tag{1}\]  
The second type is the same as the first type, with an additional pile-soil interface element. The third type involves one-dimensional structural elements [18; 19], and the fourth type is equivalent to two-dimensional plate elements [14; 20; 21], wherein the thickness of the wall is equated according to Equation (1). Based on the above equivalent method, [PERSON] et al. [14] carried out a study of pit deformation by considering the outer piles of the pile structure as equivalent solid elements and the inner piles as equivalent two-dimensional plate elements. [PERSON] et al. [15] considered the piles as solid elements and the influence of the pile-soil interface to analyze the deformation of the foundation pit. [PERSON] et al. [19] considered the pile structure as a one-dimensional structural element to study an ultra-deep pile-anchored support foundation pit. From the studies described above, it can be found that researchers typically use one or two pile equivalent calculation methods to conduct relevant studies [13; 14; 15; 20; 21]. However, the mechanisms behind different pile equivalent calculation methods in a numerical model have remained unclear.  
The main objective of this study is to explore the differential effects and mechanistic differences brought about by different pile-body equivalent calculation methods in numerical modeling, and to address the gaps in previous studies. Based on the abovementioned goals, in this work, four pile equivalent calculation methods were evaluated from the perspective of soil displacement and stress, special points' stress paths, and the plastic zone based on a typical pile-anchor foundation profile using FLAC3D. The findings of this work can provide an in-depth understanding of the numerical simulation in pile-anchored foundation work.