## 2 Materials and Method
### Model Piles and Sand Tank  
In model tests, the dimensions of the test tank should be determined so that the boundary effects will have the least effect on the test results. In the literature, many studies have been carried out on the selection of the dimensions of the pile and the test tank in order to ensure semi-infinite medium conditions where the boundary effects do not change the experimental results. As a result of these studies, if there is a 2B (B is the dimension of the foundation) gap between the edge points of the pile and the tank sides, the boundary conditions will not affect the test, and thus, semi-infinite conditions will be provided [54; 55; 56]. In this study, the diameter of the pile was determined as 5 cm since the side length of the experiment tank was 75 cm in order to provide semi-infinite conditions. Due to the stress-dependent soil properties, it is important to accurately model the prototype stress conditions in small-scale modeling experiments. One of the common ways to apply gravity (g) in model experiments is re-establish full-size stress levels. Details of the rules and modeling practices used in laboratory modeling can be found in [57]. Information about the scaling laws used in this study is given in Table 2.  
In this study, an in-plane strain condition of the test system is assumed. The dimensions of the test system and the pile are similar in all experiments. While the pile diameter was 50 mm (The equivalent in the prototype was 1 m), the thickness of the soil layer was constant and 900 mm (The equivalent in the prototype was 18 m). The width of the system was 750 mm (The equivalent in the prototype was 15 m), according to the scaling law given in Table 3. \begin{table}
\begin{tabular}{c c} \hline
**Property** & **Value** \\ \hline D\({}_{\text{Sol}}\), (mm) & 0.475 \\ Uniformity Coefficient, (C\({}_{\text{c}}\)) & 2.895 \\ Curvature coefficient, (C\({}_{\text{c}}\)) & 0.980 \\ USC Classification & SP \\ Specific gravity, (G\({}_{\text{c}}\)) & 2.77 \\ \(\gamma_{\text{max}}\), (kN/m\({}^{3}\)) & 17.66 \\ \(\gamma_{\text{min}}\), (kN/m\({}^{3}\)) & 14.32 \\ Maximum void ratio (\(\epsilon_{\text{max}}\)) & 0.898 \\ Minimum void ratio (\(\epsilon_{\text{min}}\)) & 0.539 \\ Maximum – Minimum grain size, (D\({}_{\text{max}}-\text{D}_{\text{min}}\)) (mm) & \(1-0.074\) \\ \hline \end{tabular}
\end{table} 
Table 1: Physical properties of sand used in the study. \begin{table}
\begin{tabular}{c c} \hline
**Physical Parameters** & **Scaling Factor (Model/Prototype)** \\ \hline Gravity (m/s\({}^{2}\)) & 1 \\ Force (N) & 1/n\({}^{3}\) \\ Length (m) & 1/n \\ Displacement (m) & 1/n\({}^{2-\alpha}\) \\ Area (m\({}^{2}\)) & 1/n\({}^{2}\) \\ Stiffness (N) & 1/n\({}^{\alpha}\) \\ Strain & 1/n\({}^{1-\alpha}\) \\ Density (kg/m\({}^{3}\)) & 1 \\ Stress (kPa) & 1/n \\ \(\alpha\) & 1 \\ \hline \end{tabular}
\end{table} 
Table 2: Scaling Laws. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Properties** & **Steel** & **Wood** & **FRP** & **PVC** & **Unit** \\ \hline Density & 78.5 & 5.5 & 19.60 & 5.90–13.30 & kN/m\({}^{3}\) \\ Elasticity modulus & 210,000 & 12,600 & 15,700 & 1800–2410 & Mpa \\ Flexultural modulus & 16,400–106,000 & 8550 & 10,000 & 1520–2540 & Mpa \\ Ultimate Tensile strength & 360–510 & 5.24 & 160 & 90–53.8 & Mpa \\ Yield strength & 300 & 31 & 300–1000 & 30.0–65.0 & Mpa \\ Shear strength & 230 & 8.34 & 35–300 & 0.460–5.0 & Mpa \\ \hline \end{tabular}
\end{table} 
Table 3: Physical and chemical properties of model piles. In this study, four model piles with different materials were used, including closed-end steel pipe piles, timber piles, concrete-filled PVC and FRP pipe piles. The diameter and length of the test piles were 50 mm and 600 mm, respectively, and the pile was 500 mm embedded into the sand during the test. Plain concrete with a compressive strength of 16 MPa was used to fill the FRP and PVC pipe piles because examining the model piles' shaft friction resistance is the primary goal of the study.