## 2 Materials and Methods
### Experimental Design and Groups  
To study the impermeability performance of the SSS-coated concrete in a high-pressure environment, we set up three experimental groups to simulate different working conditions. The experimental groups and parameters are shown in Table 4. A schematic diagram and physical images of the experimental groups are shown in Figure 4. Experimental group C-O-S\({}_{1}\) was used to study the concrete and coated concrete seepage regulation. For comparison, concrete without anti-seepage treatment, concrete coated with waterproofing agents, and SSS-coated concrete were selected to conduct 24 h impermeability tests under water pressures of 1 MPa, 2 MPa, and 3 MPa. The waterproofing agents were permeable organic sodium silicates available on the market. The SSS coating thickness was 0.5 mm. Experimental group S\({}_{1}\)-S\({}_{2}\) simulated two working conditions: the internal water pressure during the operation period of the high-pressure water conveyance tunnel and the external water pressure during the emptying period. The SSS coating was applied to the top and bottom surfaces of the specimen, simulating the external and internal water working conditions, respectively. The SSS coating thickness was 0.5 mm, and impermeability tests were conducted for 10, 20, and 30 days under a water pressure of 3 MPa. Finally, to study the effect of concrete cracks in high-pressure water environments on the impermeability of the SSS coating, impermeability tests were conducted on surfaces with different crack widths in experimental group SC\({}_{1}\)-SC\({}_{2}\). We prepared natural cracks through splitting and controlled the width of the cracks using longitudinal splitting and lateral splitting. During longitudinal splitting, steel bars were placed on the bottom and top surfaces of the specimen. Due to the influence of the steel bars' diameter, wide cracks appeared on the bottom surface of the specimen after splitting, with widths ranging from 2 mm to 5 mm. During lateral splitting, the steel bars were placed on both sides of the specimen; after splitting, thin cracks appeared on the bottom of the specimen with a width of less than 1 mm. The bottom surface of the split specimen was coated with the SSS coating with a thickness of 1 mm. The specimen was loaded in stages of 0.5 MPa per level. If the SSS coating was damaged during the pressurization process, i.e., water seeped from the top surface of the specimen, the specimen was immediately removed. After the water pressure \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Water-Binder Ratio** & **Fly Ash** &
\begin{tabular}{c} **Water-Reducing** \\ **Admixture** \\ \end{tabular} & **Percentage of Sand** \\ \hline
0.43 & 25\% & 0.25\% & 40\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mix proportion. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Water** & **Cement** & **Fly Ash** &
\begin{tabular}{c} **Water-Reducing** \\ **Admixture** \\ \end{tabular} & **Sand** & **Gravel** \\ \hline
186 & 323 & 108 & 1.08 & 603 & 904 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Unit quantity (kg/m\({}^{3}\)). was increased to the design water pressure, if there was no water seepage on the top surface of the specimen, the specimen was removed after 24 h of stabilization. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Number** & **Group** & **Crack Width (mm)** & \begin{tabular}{c} **Water Pressure** \\ **(MPa)** \\ \end{tabular} & \
\begin{tabular}{c} **Pressurization** \\ **Time** \\ \end{tabular} &
\begin{tabular}{c} **Number of** \\ **Specimens** \\ \end{tabular} \\ \hline
3 & C-O-S\({}_{1}\) & 0 & 3 & 1 d & 3 \\
4 & S\({}_{1}\)-S\({}_{2}\) & 0 & 3 & 10 d & 3 \\
5 & S\({}_{1}\)-S\({}_{2}\) & 0 & 3 & 20 d & 3 \\
6 & S\({}_{1}\)-S\({}_{2}\) & 0 & 3 & 30 d & 3 \\
7 & SC\({}_{1}\)-SC\({}_{2}\) & 2–5 & 1 & / & 3 \\
8 & SC\({}_{1}\)-SC\({}_{2}\) & 2–5 & 2 & / & 3 \\
9 & SC\({}_{1}\)-SC\({}_{2}\) & 2–5 & 3 & / & 3 \\
10 & SC\({}_{1}\)-SC\({}_{2}\) & \textless{}1 & 3 & / & 3 \\ \hline \hline \end{tabular}
\end{table}