## 2 Model Test  
For the model test, the generalized scaling law [16] was adopted to satisfy the scale effect by the field conditions, as shown in Table 1.  
Figure 1 shows the test device set up for grasping the behavior characteristics of batter pile under vertical load in a sandy ground. The chamber used for the model test was produced with 500 mm \(\times\) 1400 mm \(\times\) 1000 mm steel maintaining sufficient distance for prevention of interference between the pile and the wall of the chamber with more than 5D (5 times of the diameter of the pile) interval. The model pile used for the test is a copper pipe with a closed front end as shown in Figure 2 and its specifications are summarized in Table 2. In consideration of analogous relationship, a circular copper pipe was used \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Scale Factor, \(\lambda\) = 19.54 Ration of** & **Iai(1989)** & **Experiment** & **Reality** \\ \hline Vertical length & \(\lambda\) & 1 & 19.54 \\ Horizontal length & \(\lambda\) & 1 & 19.54 \\ Density & 1 & 1 & 1 \\ Stress and pressure & \(\lambda\) & 1 & 19.54 \\ Time & \(\lambda^{3/4}\) & 1 & 9.29 \\ Acceleration & 1 & 1 & 1 \\ Displacement & \(\lambda^{3/2}\) & 1 & 86.36 \\ Bending moment & \(\lambda^{3}\) & 1 & 7458.84 \\ Strain & \(\lambda^{1/2}\) & 1 & 4.42 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Generalized scaling law for model tests. for the production of the model pile, and the 1 g analogue of [PERSON] (1989) [16] was used for simulation. In addition, considering that the bending rigidity of the tile is the dominant influence factor for the behavior of the pile, the thickness of the pile was adjusted at 1.27 mm to satisfy the analogous relationship of the bending rigidity. The material used as the ground was the specimen collected at Hapcheon of the Nakdong River basin. The sand which passed through #4 sieve was used and the water content percentage was 0.08%. The physical property of the specimen and the size curve are shown in Table 3 and Figure 3. For measurement of the density of the ground, a density measurement instrument was buried at the bottom of the model ground as shown in Figure 4 and the sand was sprayed. Then the vibration was given for 2, 15 and 90 s with the vibration motor installed at the bottom of the chamber for measurement of \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Vibrating Time** & \
\begin{tabular}{c} **Range of Values of** \\ **(sec.)** \\ \end{tabular} &
\begin{tabular}{c} **Avg. D\({}_{\text{r}}\)** \\ **(\%)** \\ \end{tabular} & **Classification** \\ \hline
2 & 29.26–32.15 & 31 & Loose \\
15 & 50.51–54.70 & 53 & Medium \\
90 & 69.06–75.55 & 72 & Dense \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Relative density in test ground. Figure 3: Grain size distribution curve for Hapcheon sand. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Property** & **Symbol** & **Value** \\ \hline Max. void ratio & \(\text{e}^{\text{max}}\) & 0.79 \\ Min. void ratio & \(\text{e}^{\text{min}}\) & 0.58 \\ Max. dry density & \(\gamma_{dmax}\) (\(\text{kN}/\text{m}^{3}\)) & 15.78 \\ Min. dry density & \(\gamma_{dmin}\) (\(\text{kN}/\text{m}^{3}\)) & 13.92 \\ Specific gravity & \(\text{G}_{\text{s}}\) & 2.54 \\ Average grain size & \(\text{D}_{50}\) & 0.59 \\ Effective grain size & \(\text{D}_{10}\) & 0.28 \\ Uniformity coefficient & \(\text{C}_{\text{u}}\) & 2.50 \\ Coefficient of gradation & \(\text{C}_{\text{c}}\) & 0.92 \\ Fineness modulus & F.M. & 2.59 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Physical properties of Hapcheon sand for model test. pile holder (Figure 5d). 1 Install perpendicular vertical displacement gauge and various other measuring instruments. (Figure 5e) 5 Measure the vertical displacement of the pile head until the pile displacement reaches maximum 25 mm or the vertical load becomes 20 kN at 1 mm/min of speed. 6 Remove the load to recover the elasticity of the pile. The influence of the underground water among the conditions of the model test was ignored.