## 2 Analysis and Experimental Methods of Correlating Toughness and Hydraulic Resistance
### Prediction Result of Hydraulic Response  
By substituting the average toughness analyzed in Section 3.3 into the hydrostatic pressure equation (hydrostatic resistance) of Figure 3, the expected underground depth can be converted as shown in Table 6 below.  
Based on the results shown in Table 6 above, it is judged that the low-viscosity Type A should be used only in the very shallow underground of 1 m or less under the assumption that the temperature at the depth of the underground is maintained at an average of 10 \({}^{\circ}\)C. It is judged that Type B of medium intensity can be used from 2 m to 7 m underground. It is judged that the high viscosity Type C can be used from 3 m to 32 m underground.  
Based on the above results, trend lines and equations were obtained as shown in Figure 13 based on the average toughness value of 10 \({}^{\circ}\)C for each SPRG viscosity type, and then the toughness values according to thickness were checked. It was confirmed that the low-viscosity Type A, regardless of the increase in toughness, decreased as the thickness of the material increased, and converted to a negative region around 22 mm in thickness. It means that the viscosity is low in spite of applying a thickness greater than that, which means that it cannot resist water pressure and is lost. Since Type B of medium strength does not have a large increase in toughness with increasing thickness, it is predicted that a thickness of 30 mm or more should be secured to cope with water pressure of 20 m. If it is to be used at a depth of 100 m or more, it is predicted that the SPRG must be constructed with a thickness of about 165 mm or more to cope with water pressure of 100 m. It can be confirmed from Figure 13 that the increase in toughness of Type C with high viscosity is proportional to the increase in the thickness of the material, and the increase is confirmed to be very large.  
Figure 12: Toughness comparison according to thickness and temperature.  
Therefore, it is predicted that it is possible to respond when the thickness is about 28 mm or more at a depth of 100 m or more. Thus, it was found that it is possible to use SPRG having a quality and viscosity equal to or higher than that of Type C in order to block water leakage in an actual deep underground tunnel, etc.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Specimen Type** & **Thickness (mm)** & **Temperature** & **Average** & **Expected Resistance** \\  & & (\({}^{\circ}\)C)** & **Toughness** & **Capacity Relative to** \\  & & & **[N/mm\({}^{2}\)]** & **Underground Depth [m]** \\ \hline \multirow{4}{*}{Type A} & & 5 & 0.0123 & 1.2 \\  & 2 & 10 & 0.0117 & 1.2 \\  & & 20 & 0.0033 & 0.3 \\ \cline{2-5}  & & 5 & 0.0192 & 1.9 \\  & 10 & 10 & 0.0071 & 0.1 \\  & & 20 & 0.0067 & 0.1 \\ \hline \multirow{4}{*}{Type B} & & 5 & 0.0294 & 2.9 \\  & 2 & 10 & 0.0270 & 2.7 \\  & & 20 & 0.0057 & 0.6 \\ \cline{2-5}  & & 5 & 0.1229 & 12.3 \\  & 10 & 10 & 0.0747 & 7.5 \\  & & 20 & 0.0352 & 3.5 \\ \hline \multirow{4}{*}{Type C} & & 5 & 0.0309 & 3.1 \\  & 2 & 10 & 0.0295 & 3.0 \\  & & 20 & 0.0368 & 3.7 \\ \cline{2-5}  & & 5 & 0.2062 & 20.6 \\ \cline{2-5}  & 10 & 10 & 0.3220 & 32.2 \\  & & 20 & 0.2703 & 27.0 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comprehensive toughness of specimen types in accordance with thickness and temperature.  
Figure 13: Prediction depth and toughness according to thickness by each SPRG type.