## 2 Engineering Overview and Numerical Modeling
### Pile Equivalent Calculation Methods  
According to the previous research results of scholars, four types of pile equivalent calculation methods are considered in this paper, including equivalent solid elements without the interface (Figure 4a), equivalent solid elements with the interface (Figure 4b), one-dimensional structural elements (Figure 4c), and two-dimensional plate elements (Figure 4d), respectively. Figure 3: View of numerical model: (**a**) 3D view; (**b**) plane view. (1) Equivalent solid elements without interface (Mode 1)  
For Mode 1 (Figure 4a), according to Equation (1), based on the geometric parameters of the piles shown in Figure 2, the equivalent thickness \(h\) is 0.77 m, which is simulated by solid elements. No interface elements are used at the soil-pile interface, which means that the soil-pile interface displacement is continuous [30]. A linear-elastic constitutive model is adopted for the solid elements, and the crown beam is considered by solid elements and given the same stiffness parameter values as the solid elements. Without the setting of the waist beam, the anchor head nodes are in rigid contact at the intersection with the solid elements. (2) Equivalent solid elements with interface (Mode 2)  
In Mode 2 (Figure 4b), the pile, crown beam, and anchors are considered the same as in Mode 1, but with the addition of a soil-pile interface element. The shear behavior of the soil-pile interface obeys the Mohr-Coulomb criterion. Since there is no interface between the pile and soil in Mode 1, they are considered to be in good contact [21]. For comparison with Mode 1, the interface shear strength parameters of Mode 2 are set as the soil layer parameters using the control variable method. Hence, the interface friction angle is taken as 22\({}^{\circ}\) and the cohesion is 25 kPa, which represents the shear strength index in the  
Figure 4: Support structure schematic diagram for four modes: (**a**) Mode 1; (**b**) Mode 2; (**c**) Mode 3; (**d**) Mode 4.  
second layer of soil. For the flat pit, the normal and tangential stiffness of the interface are recommended as in Equation (2) [22]. \[Kn=Ks=10\text{max}\Bigg{[}\frac{K+\frac{4}{3G}}{\Delta Z_{min}}\Bigg{]} \tag{2}\]  
where \(Kn\) and \(Ks\) represent the normal and tangential stiffness of the interface element, respectively. \(K\) and \(G\) are the bulk modulus and shear modulus of the soil layer, which can be calculated by converting the Young's modulus and [PERSON]'s ratio; \(\Delta z_{min}\) represents the dimension of the grid near the interface element along the direction of the vertical interface element. According to the relevant parameters, the normal and tangential stiffness are taken as 246 MPa. The anchors are moved halfway towards the inside wall in its X-directional horizontal position, compared to Mode 1, in order to prevent the anchors from interfering with the sliding of the interface element on this side of the pit [22]. (3) One-dimensional structural elements (Mode 3)  
In Mode 3 (Figure 4c), the pile structure is simulated with one-dimensional structural elements, namely pile elements. To prevent soil flow between piles [18], the area of reinforcement within the pile diameter of 1.2 m is considered (green part of Figure 4c), and the reinforcement area is simulated with a linear-elastic constitutive model, with a deformation parameter three times that of the surrounding soil. The crown beam and waist beam are simulated using beam elements. The beam, anchor, waist beam, and pile structure elements are in rigid contact at the intersection. (4) Two-dimensional plate elements (Mode 4)  
For Mode 4 (Figure 4d), the pile is equivalent to plate elements according to the equal stiffness method. It is simulated with two-dimensional structural elements, namely embedded liner elements, which consider the soil-pile coupling spring effect [22]. The liner thickness and the parameters of the soil-pile interface are set in the same way as in Mode 2. The crown beam is simulated by beam elements, and the waist beam is ignored.