## 2 Selection of Model Materials for the Pile-Soil Shaking Table Test  
Soft soil from Tianjin, China, was used in this test, which focused on its dynamic properties; thus, a model soft soil with similar dynamic properties to the prototype soft soil in the Binhai area of Tianjin was used [25]. The results of a large number of tests on the dynamic properties of soils show that the dynamic stress-dynamic strain characteristics of soils under cyclic loading are mainly characterized by three aspects: hysteresis, nonlinearity, and strain accumulation. The results of the influence of these three aspects can be reflected to varying degrees by the G/Gmax-\(\gamma\) curve of the relationship between the dynamic shear modulus ratio and the shear strain. Therefore, in this paper, we first identified model soft soils with similar G/Gmax-\(\gamma\) curves to those of the prototype soft soils in the Binhai area of Tianjin. In this test, kaolin and quartz sand were chosen as the raw materials of the model soil. To determine the model soft soil ratio, the test used the STX200 electrohydraulic servo-controlled bidirectional dynamic triaxial instrument manufactured by GCTS, USA (with a maximum axial loading force of 100 kN, a maximum surrounding pressure of 2 MPa, and a loading frequency of 0.01-20 Hz), to measure the dynamic parameters of the model soft soil.  
The test was first designed with the model soft soil ratio table, as shown in Table 1. Model soft soils with different kaolin to quartz sand powder ratios and different moisture contents were prepared according to the proportioning table, as shown in Figure 1. Their densities were measured by the ring-knife method, as shown in Figure 2. Then, soil sample columns with a diameter of 38 mm and a height of 76 mm were made using a three-valley membrane, as shown in Figure 3. The consolidation pressure was applied to 50 kPa in a graded manner, the axial dynamic load was applied in a graded manner after 6 h of isobaric consolidation, and the dynamic elastic modulus E\({}_{\text{d}}\) and axial strain \(\varepsilon_{\text{d}}\) of the model soft soil under different axial strains were measured, as shown in Figure 4. After that, the axial strain and dynamic elastic modulus of the model soft soil with different mix ratios were converted into the shear strain and dynamic shear modulus ratio (data results are detailed in Appendix A), and then the dynamic shear modulus ratio versus shear strain curves of the model soft soils were plotted, as shown in Figure 5. Finally, the dynamic shear modulus ratio versus shear strain curves of the model soft soils with different mix ratios were compared with the dynamic shear modulus ratio versus shear strain curve of the prototype soft soil in the Binhai area of Tianjin. The model soft soil with a 1:1 ratio of kaolin and quartz sand powder and a 33% water content has a dynamic shear modulus ratio versus shear strain curve closest to that of the prototype soft soil; i.e., the dynamic properties of the two are the most similar, so the model soft soil with this ratio was used as the soft soil in the pile-soil shaking table test. In addition, the test used a reduced scale model that incorporated piles and soil. The main purpose of the test was to provide a qualitative analysis of the mechanism and law of negative friction resistance generation based on the test data. Model similarity relationships were not the focus. If the test law needs to be reflected to the prototype, a basic prediction can also be made based on the similarity relationship.  
Figure 3: Dynamic triaxial sample.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Test Number** & **Kaolin: Quartz Sand Powder** & **Moisture Content** \\ \hline
1 & 1:1 & 30\% \\
2 & 1:1 & 33\% \\
3 & 1:1 & 36\% \\
4 & 1:1.5 & 30\% \\
5 & 1:1.5 & 33\% \\
6 & 1:1.5 & 36\% \\
7 & 1:2 & 30\% \\
8 & 1:2 & 33\% \\
9 & 1:2 & 36\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: The ratio table of the model soft soil.  
Figure 2: Density Experiment.