## 2 Materials and Methods
### Test Device
#### 2.2.2 U-Shape Sheet Pile Model  
To accurately represent the pile-soil interaction of the retaining structure during excavation in the model test, the model pile had to exhibit cross-section characteristics and geometric similarities like the prototype while accurately displaying the details of the sheet pile's interlocking structure. Therefore, the U-shape model sheet pile was innovatively formed using 3D printing SLA (stereo lithography appearance) technology, provided by \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Physical Property** & **Abbreviation** & **Unit** & **Dimension** & **Similarity Relation** & **Similarity Constant** \\ \hline Elastic modulus & \(E\) & Pa & [F][L]\({}^{-2}\) & \(S_{E}\) & 80.93 \\ Length & \(L\) & m & [L] & \(S_{L}\) & 10.31 \\ Area & \(A\) & m\({}^{2}\) & [L]\({}^{2}\) & \(S_{A}={S_{L}}^{2}\) & 106.30 \\ Section factor & \(W\) & m\({}^{3}\) & [L]\({}^{3}\) & \(S_{W}={S_{L}}^{3}\) & 1095.91 \\ Moment of inertia & \(I\) & m\({}^{4}\) & [L]\({}^{4}\) & \(S_{I}={S_{L}}^{4}\) & 11,298.86 \\ Moment of inertia per & \(I^{\prime}\) & m\({}^{4}\)/m & [L]\({}^{3}\) & \(S_{I^{\prime}}={S_{L}}^{3}\) & 1095.91 \\ Line load & \(q\) & N/m & [F][L]\({}^{-1}\) & \(S_{q}={S_{E}}{S_{L}}\) & 834.39 \\ Bending moment & \(M\) & N-m & [F][L] & \(S_{M}={S_{E}}{S_{L}}^{3}\) & 8602.54 \\ Flexural rigidity & \(EI\) & N-m\({}^{2}\) & [F][L]\({}^{2}\) & \(S_{EI}={S_{E}}{S_{L}}^{4}\) & 914,416.81 \\ Stiffness & \(K\) & N/m & [F][L]\({}^{-1}\) & \(S_{K}={S_{E}}{S_{L}}\) & 834.39 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Similarity relations and constants. Figure 3: YT-3000 pseudo-static underground geotechnical engineering comprehensive model test system. (**a**) front view; (**b**) vertical view. Vistar 3D Printing Industry Co., Ltd. (Xiamen, China). The model pile was made of Vistar 6335 UV-curable resin, and its specific parameters are listed in Table 3. Among them, the elongation at break was assessed using the ASTM D638-22 [19] test method, and it was determined to be within the range of 10-13%, very close to that of steel (\(\geq\)15%). This indicated that the material was pliable and capable of undergoing significant plastic deformation. The tensile modulus was 2100 MPa-2200 MPa, which agreed with the elastic modulus calculated using the similarity ratio. All parameters met the expectations of the experiment's design. A single model pile measured 38.737 mm in length, 16.463 mm in width, 1.8 m in height, and 2 mm in thickness, with interlocking structures on both sides. Figure 4 depicts the cross-section dimensions, and Table 4 lists the specific geometric characteristics of the cross-section. In the table, area (\(S\)) is the cross-section area of the model sheet pile. The centroid moment of inertia (\(I_{c}\)) is the second moment calculated by the cross-section area based on the neutral axis passing through the centroid point, and it is closely related to the flexural rigidity of the sheet piles. The maximum centroid distance (\(I_{max}\)) is the maximum vertical length of a point in the cross-section from the neutral axis. The section factor (\(W\)) is the ratio of the centroid moment of inertia to the maximum centroid distance (\(I_{c}\)/\(I_{max}\)), which was used to verify the maximum stress on the surface of the sheet pile. To ensure the correctness of the sheet pile design, it was also necessary to verify the physical and mechanical properties of the materials. The materials' flexural stiffness \(EI\) was verified through a simply supported beam test, as described in Figure 5. We applied a concentrated load to the mid-span in four stages, increasing the load by 5 N at each stage. The dial indicator measured the deflection at the quarter point, which increased by 0.1 mm