# Impact Analysis and Optimization of Key Material Parameters of Embedded Water-Stop in Tunnels
## 2 Optimization of Key Parameters for Water-Stop Materials
### Analysis of the Influence of Water-Stop Hardness on Its Deformation Force State  
Hardness is the ability of a material to resist local penetration by a hard object on its surface, and it is a comprehensive indicator of the mechanical properties of a material, such as elasticity, plasticity, strength, and toughness. The specifications have made clear provisions for the hardness of some waterproof materials: for water-swelling rubber strips, the specifications stipulate a hardness range of 32-58; for rubber sealing gaskets, the specifications stipulate a hardness range of 50-70; and for rubber water-stops, the specifications stipulate a hardness range of 60 \(\pm\) 5. To explore the influence of different hardness on the force deformation of water-stops, a wider hardness range than specified in the specifications is selected, and different water-stop hardness values are set. The rubber parameters are shown in Table 1. A plane strain finite element model of embedded water-stops is established using ABAQUS/Standard. The calculation results of the deformation stress of the water-stops are shown in Figures 4-6. It can be observed from the results that: \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Working Condition** & **Hardness/HA** & **E\({}_{0}\)/MPa** & **C\({}_{10}\)/MPa** & **C\({}_{01}\)/MPa** \\ \hline
1 & 40 & 1.696 & 0.226 & 0.057 \\
2 & 45 & 2.045 & 0.273 & 0.068 \\
3 & 50 & 2.465 & 0.329 & 0.082 \\
4 & 55 & 2.978 & 0.397 & 0.099 \\
5 & 60 & 3.619 & 0.483 & 0.121 \\
6 & 65 & 4.443 & 0.592 & 0.148 \\
7 & 70 & 5.542 & 0.739 & 0.185 \\
8 & 75 & 7.080 & 0.944 & 0.236 \\
9 & 80 & 9.388 & 1.252 & 0.313 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material parameters of rubber water-stops. Figure 3: Finite element analysis model. Figure 4: Tensile deformation stress of water-stops with different hardness. Figure 5: Compressive deformation stress of water-stops with different hardness. Figure 6: Settlement deformation stress of water-stops with different hardness. 1 During tensile deformation, the deformation stress of the water-stop increases with the increase in hardness, and the deformation stress exceeds the dangerous stress value when the hardness exceeds 70 in working condition 7;
2 During compressive deformation, the deformation stress of the water-stop increases with the increase in hardness, and the deformation stress exceeds the dangerous stress value when the hardness exceeds 65 in working condition 1;
3 During settlement deformation, the deformation stress of the water-stop also increases with the increase in hardness, and the deformation stress exceeds the dangerous stress value when the hardness exceeds 60 in working condition 5. At the same time, after working condition 7, when the hardness reaches 70, the settlement deformation of the water-stop causes tensile damage to the concrete lining, as shown in Figure 7. With the increase in hardness, the tensile damage value DAMAGET of the concrete lining changes from 0.667 to 0.998 (when the hardness of the water-stop is 80, i.e., in working condition 9, only part of the curve is shown in the figure due to excessive concrete damage). From the above analysis, it can be concluded that the deformation stress of the water-stop will increase with the increase in the material hardness of the water-stop. When the hardness of the water-stop reaches 60, the settlement deformation stress exceeds the dangerous stress value; when the hardness of the water-stop reaches 65, the compressive deformation stress exceeds the dangerous stress value; when the hardness of the water-stop  
Figure 7: Settlement deformation concrete lining stiffness damage cloud map. (**a**) Working condition 7. (**b**) Working condition 8. (**c**) Working condition 9.  
reaches 70, the tensile deformation stress exceeds the dangerous stress value. At the same time, when the hardness of the water-stop reaches 70, the settlement deformation will cause tensile damage to the concrete lining.