## 3 Engineering Example
### Numerical Analysis Based on Dynamic Time-History Method
#### 3.3.3 Analysis of Results  
(1) Interlayer Displacement Angle  
The interlayer displacement angles under dynamic and static conditions are superimposed, and the calculation results are shown in Table 5. From the table, the maximum displacement angle is 1/9429. Moreover, within the scope of the standard requirements, the interlayer displacement angle of the middle partition wall is always greater than that of the left and right side walls. From working condition 1 to 2, the stiffness of the joint water stop gradually increases while its interlayer displacement angle is gradually reduced, indicating that the interlayer displacement angle of the joint decreases with the increase in joint stiffness. (2) Opening Value of Joints  
Joints No. 1 and No. 2 of the immersed tunnel are located on a soil layer of varying thickness, so that the opening limits of the two joints are different under the same peak ground acceleration with identical stiffness. It can be seen from Figures 18 and 19 that the opening values of joints No. 1 and No. 2 under the two working conditions show a similar trend over time. The opening value is larger between 5 and 13 s, during which its changing value is more obvious. Hence, it can have a relatively serious impact on the joint water stop, which easily leads to the weakening of the water tightness of the immersed tunnel. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Joint Stiffness Coefficient**} \\ \cline{3-6}
**Peak Ground** & **Type of Water** & **Tensile** & **Compressive** & **Longitudinal** & **Transverse** & **Working** & **Condition** \\
**Acceleration** & **Stop** & **Stiffness** & **Stiffness** & **Stiffness** & **Stiffness** & **Stiffness** & **Stiffness** \\  & & **10\({}^{6}\) (N/m)** & **10\({}^{6}\) (N/m)** & **10\({}^{11}\) (N/m\(\cdot\)rad)** & **10\({}^{10}\) (N/m\(\cdot\)rad)** & **10\({}^{10}\) (N/m\(\cdot\)rad)** & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Working conditions of calculation of seismic performance of immersed tunnel joints. Figure 17: Locations of each wall of immersed tunnel. After the superposition of dynamic and static working conditions, the comprehensive opening value is obtained. Under working condition 1, the maximum opening value of joint No. 1 is 0.85 mm, while that of joint No. 2 is 0.49 mm. Under working condition 2, the former is 0.66 mm, while the latter is 0.38 mm. On the whole, the opening value under the dynamic condition is the main influencing factor, with that under the static condition having less effect. The opening values of joint water stops No. 1 and No. 2 under each working condition is shown in Table 6.  
(3)Compression-Tension Value and Sensitivity Analysis of GINA Water Stop  
The compression and tension values of GINA water stops at each joint are shown in Figures 20 and 21. Positive values indicate tension, while negative values indicate \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{3}{*}{**Joint**} & \multirow{3}{*}{\begin{tabular}{c} **Working** \\ **Condition** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **Type of** \\ **Water Stop** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **Maximum** \\ **Opening** \\ **Value under** \\ **Condition** \\ \end{tabular} } & \multirow{3}{*}{\
\begin{tabular}{c} **Maximum** \\ **Opening** \\ **Value under** \\ **Condition** \\ \end{tabular} } & \multirow{3}{*}{
\begin{tabular}{c} **Comprehensive** \\ **Opening Value** \\ **Condition** \\ \end{tabular} } \\ \cline{1-1} \cline{3-5} \cline{7-7} Joint No. & Condition 1 & 51 & 0.797 & 0.0496 & 0.8466 \\
1 & Condition 2 & 62 & 0.611 & 0.0496 & 0.6606 \\ \hline Joint No. & Condition 1 & 51 & 0.486 & 0.0014 & 0.4874 \\
2 & Condition 2 & 62 & 0.379 & 0.0014 & 0.3804 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Maximum opening value of joints under each working condition (unit: mm). Figure 19: Opening values of joint No. 2: (a) opening value under working condition 1; (b) opening value under working condition 2.