## 2 Design of the Planted Pile Foundation Model Test Based on Transparent Soil
### Preparation of Transparent Soil and Planted Pile Foundation Model  
Transparent soil is mainly composed of skeleton particle material and pore fluid with the same refractive index as the skeleton material. To better simulate natural sandy soil tests, fused quartz sand with a particle size range of 0.1 to 1.0 mm is selected as the skeleton material for the transparent soil. At room temperature (22 \({}^{\circ}\)C), n-dodecane and #15 white oil are mixed in an approximate volume ratio of 1:8 to create a pore solution. Once the solution is thoroughly mixed, its refractive index is measured using an Abbe refractometer. The ratio of the two liquids is slightly adjusted based on the refractive index of the mixed solution until it reaches 1.4585 (the same as that of quartz sand). After preparation, the pore solution is poured into the model box lined with quartz sand. Following thorough mixing, vacuum treatment is conducted for approximately 30 min. Once completed, the model box is placed in a constant temperature chamber at 22 \({}^{\circ}\)C for 1 day to allow the soil particles to fully consolidate, making it ready for subsequent experiments. To investigate the uplift bearing capacity of the pile foundation and the effect of the presence of isolated stones on this capacity, the current transparent soil model test simulates pile foundations with isolated stones at the pile tip. The test conditions are detailed in Table 1.  
Pile foundations typically consist of tubular piles and surrounding concrete. In the model test, the core pile of the foundation is made of hollow aluminum tubes, while the outer concrete is represented using epoxy resin, with a layer of quartz sand wrapped around the external surface to simulate the real pile formation effect, according to the referenced engineering and similarity ratio of the tests. The models are similarity systems constructed based on prototypes, which exhibit a proportional relationship in geometric features and physical quantities. This relationship allows us to infer the corresponding physical quantities of the prototype system by mea \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Experiment Number** & **Pile Type** & **Isolated Stone** & **Isolated Stone Location** \\ \hline
1 & Planted pile & No & - \\
2 & Planted pile & Yes & Pile bottom \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Model test plan. Figure 1: Transparent soil model test device for planted piles; they should be listed as: (**a**) schematic diagram of the test apparatus and (**b**) physical diagram of the test apparatus. suring the physical quantities in the model system, which is referred to as the similarity condition. Under elastic conditions, the similarity equations are as follows [28]:  
\[C_{\gamma}C_{l}=C_{\sigma};\ C_{e}C_{l}=C_{\delta};\ C_{\sigma}=C_{e}C_{E} \tag{1}\]  
In Equation (1), \(C_{\gamma}\) represents the unit weight similarity ratio; \(C_{l}\), the geometric similarity ratio; \(C_{\sigma}\), the stress similarity ratio; \(C_{e}\), the strain similarity ratio; \(C_{\delta}\), the displacement similarity ratio; and \(C_{E}\), the elastic modulus similarity ratio. To mitigate the impact of size effects and to account for the maximum transparency of the transparent soil, the geometric similarity ratio (\(C_{l}\)) was established at 0.01, the unit weight similarity ratio (\(C_{\gamma l}\)) of the soil at 1, and the elastic modulus similarity ratio (\(C_{EI}\)) at 0.01. Consequently, the similarity ratio of the stress fields (\(C_{\sigma l}\)) between the prototype and the model is 0.01, the strain similarity ratio (\(C_{\sigma l}\)) of the soil is 1, and the displacement similarity ratio (\(C_{\sigma l}\)) of the soil is 0.01. The diameter of the field prototype pipe pile is 1.2 m (with a wall thickness of 0.25 m), while the diameter of the planted pile is 1.8 m, and its length is 20 m. According to the geometric similarity ratio of 1:100, the diameter of the model pipe pile is 12 mm (with a wall thickness of 2.5 mm), and its length is 200 mm.