## 2 Laboratory Model Test
### Pretest for the Laboratory Model Test  
Joomunjin standard sand was used in this study to measure the relative density of sandy soil. Jumunjin sand is the standard sand used for research in Korea. Many experiments and continuous studies on material properties have been conducted using this sand. Hence, in this study, model tests were performed using this sand. The particle size distribution curve of the Joomunjin standard sand is shown in Figure 7. The particle size distribution of the sand was uniform. A uniformity coefficient (C\({}_{\text{u}}\)) of 1.93 and a curvature coefficient (C\({}_{\text{c}}\)) of 1.09 were observed, with grain-size distribution D\({}_{10}\) = 0.331 mm, D\({}_{30}\) = 0.480 mm, and D\({}_{60}\) = 0.639 mm. The characteristics of the Joomunjin standard sand are as follows [19]:  
1. It has a silicon dioxide (SiO\({}_{2}\)) content 4-8% higher than that of other sand. 2. It is made of quartz, but is whiter, harder, and more resistant to fire than quartzite. 3. It is a natural silica sand, smoother than that from other areas, and retains its original shape, making it suitable for use in filtration and molding. 4. It contains few impurities, and its transparency is much higher than that of silica sand from other areas. Distinguishing between dense and loose sand is important for understanding sand behavior [20]. In general, the volume of loose sand decreases under shear force, whereas the volume of dense sand expands. In this study, uniform sandy soil was prepared during the laboratory model test using the sand pouring device, and the relative density of the soil was measured using a moisture-based technique: the unit dry weight was found using  
Figure 6: Single pile for model test. Figure 7: Particle size distribution curve for Joomunjin sand [19]. the volume of the moisture can and the measured weight of the sand (Figure 8), and the relative density was calculated by referring to the cyclic-triaxial-test measurements of [PERSON] et al. [21] (Table 2). The relative density is  
\[ \begin{array}{l}\mathrm{D}_{r}=\frac{e_{max}-e}{e_{max}-e_{min}}\times 100( \%)\\ =\frac{\gamma_{dmax}}{\gamma_{d}}\times\frac{\gamma_{d}-T_{dmin}}{\gamma_{dmax} -\gamma_{d}}\times 100(\%),\end{array} \]  
where \(e\) is the void ratio and \(\gamma_{d}\) is the unit dry weight. The average relative density of sandy soil in this study was calculated to be 52.67% (Table 3). [PERSON] et al. [22] have classified soil conditions according to the relative density of sandy soil, as shown in Table 4. Based on their classification, the soil conditions in this study were determined to be medium. Since the relative density was close to the loose state under medium conditions, it was assumed that the soil would exhibit shrinkage. Numerical analysis was conducted based on the fully-non-associated-flow rule, which does not consider the dilatancy angle. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Relative Density (D\({}_{\mathrm{r}}\))** & **Max.** & **80\%** & **70\%** & **60\%** & **50\%** & **40\%** & **30\%** & **Min.** \\ \hline Density (kN/m\({}^{3}\)) & 16.48 & 15.80 & 15.48 & 15.17 & 14.88 & 14.59 & 14.32 & 13.55 \\ \hline Void ratio & 0.608 & 0.667 & 0.712 & 0.747 & 0.782 & 0.816 & 0.851 & 0.955 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Properties of sandy soil with various relative densities [21]. Figure 8: Equipment for determining relative density. Eight strain gauges were calibrated and attached to the inside of the tunnel to investigate its behavioral characteristics. For tunnel calibration, the changing strain gauge values were measured with a data logger and a computer using the load control method (LCM), which directly applies a load to the tunnel. Load was applied to the crown of the tunnel, and the following equations were derived using the applied load and the strain gauge values. The eight equations were matched with the eight strain gauges, as shown in Figure 5. Figure 9 shows the calibration results obtained by converting the strain measured using each strain gauge into a force.