## 2 Materials and Method
### Model Pile Installation Method and Test Procedure  
Model pile tests were conducted under axial load in such a manner that the end (point) bearing capacity of the pile does not exist, and the whole pile capacity was derived by the lateral friction resistance between the pile material and sand along the pile shaft. For this purpose, a Styrofoam with dimensions (12 cm \(\times\) 12 cm \(\times\) 10 cm) was used. A hole with a diameter of 5.1 cm was cut out of the middle of the Styrofoam body to ensure there was  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Model Pile**} & **Arithmetic Mean Surface** & **Maximum Surface** & **D50, (\(\mu\)m)** & **Normalized Surface** \\  & **Roughness, R\({}_{\text{a}}\)** (\(\mu\)m)** & **Roughness, R\({}_{\text{r}}\)** (\(\mu\)m)** & **Roughness, (R\({}_{\text{r}}\)/D\({}_{\text{50}}\)), R\({}_{\text{n}}\)** (\(\mu\)m)** \\ \hline Timber & 4.17 & 24.45 & 475 & 0.051 \\ PVC & 1.78 & 12.83 & 475 & 0.027 \\ FRP & 1.63 & 8.84 & 475 & 0.019 \\ Steel & 0.55 & 3.43 & 475 & 0.007 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Table roughness parameters of the model piles used in this study.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\mathbf{D_{r}}\) & **(\(\phi\))** & **(\(\circ\))** & **(\(\delta\)) of Sand-Tibber (\(\circ\))** & **(\(\delta\)) of Sand-FPC (\(\circ\))** & **(\(\delta\)) of Sand-FRP (\(\circ\))** & **(\(\delta\)) of Sand-Steel** \\  & **(\(\circ\))** & **Material (\(\circ\))** \\ \hline
10 & 41.0 & 35.1 & 26.1 & 23.7 & 20.0 \\
40 & 44.3 & 36.2 & 28.7 & 26.2 & 21.0 \\
65 & 48.7 & 37.9 & 31.4 & 28.3 & 22.5 \\
90 & 52.4 & 35.3 & 30.3 & 28.2 & 21.0 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Internal friction angle of sand (\(\phi\)) and interface friction angles (\(\delta\)) between sand and pile materials versus relative density.  
Figure 7: Description of mean line roughness R\({}_{\text{a}}\) and maximum roughness R\({}_{\text{t}}\).  
enough space between the edges of the pile and the Styrofoam during the load test, as illustrated in Figure 8a.  
In order to install model piles, a specific kind of epoxy adhesive was used to fix the pile to a detachable shaft, which was then threaded into a load cell. The soil tank was filled with sand for each test to a depth of 30 cm, and then, a Styrofoam body was put in the middle of the soil tank, after which an additional 10 cm of sand was filled to stabilize the Styrofoam body. After that, the model pile with a detachable shaft threaded into a load cell was lowered using a hydraulic jack until the bottom of the pile protruded 2 cm into the pre-drilled hole inside the Styrofoam. Following that, a clamp was used to wrap a sponge strip around the pile bottom. To stop sand particles from leaking into the hole as illustrated in Figure 8b, the tank was filled to the depth of 90 cm. Because the model piles have been pre-installed, they are considered non-displacement (bored) piles because they do not displace the soil [PERSON] et al. [45]. A total of sixteen model pile load tests were performed in the soil model tank, four load tests for each pile with sand relative densities (10%, 40%, 65% and 90%).  
Using a hydraulic jack, the axial load was applied to the single model pile, and the two LVDTs were used for measuring pile displacement; the vertical displacement rate of the model pile was 1 mm/min. The loading machine was computer controlled, and all data from LVDTs and load cells were recorded. A two-dimensional schematic diagram of the sand tank, test setup, and experimental apparatus can be seen in Figure 9.  
Figure 8: (**a**) Styrofoam with the hole, (**b**) sponge strip wrapped around the pile bottom by using a clamp.  
Figure 9: Schematic diagram of the test setup for a typical shaft friction test.