## 4 Results and Discussion
### Parametric Study  
Different from common tunnels, water conveyance tunnels require special consideration. The interaction between inner water and the tunnel lining must be examined [23; 42], as it will affect the dynamic responses of the tunnel during earthquakes. In this study, the tunnel with full water, corresponding to normal operation conditions, is considered. However, there are also other conditions like the modification condition with an empty tunnel and the water hammer condition. With the intention of comparing and evaluating the effects of the inner water on seismic responses of the tunnel, the double-line tunnel with no water inside under the same traveling seismic excitation is also analyzed using the proposed parallel algorithm. The parameters are the same as those illustrated in Section 3 except for the removed inner water. Figure 23 shows the comparison of the largest and smallest first order principal stresses of section RS5 during the earthquake. It is shown that the tunnel with inner water suffers higher stresses than those of the empty tunnel, which means that the existence of inner water may make the tunnel more vulnerable during earthquakes. These results may be attributed to the added mass, the sloshing of the inner water and the FSI between inner water and the tunnel. Other sections show similar trends. Therefore, the simulation of the water conveyance tunnel with filled water included by this paper's study may give more reasonable guidelines for the tunnel design. The deformation joints embedded in the tunnel can prevent the tunnel from being damaged by non-uniform subsidence and accidental external forces. They can also alleviate the stress concentrations caused by sharp changes of structure and stiffness when the tunnel is subjected to earthquakes. For  
Figure 23: Effects of the inner water on dynamic responses evaluated by principal stress: (**a**) the largest one; (**b**) the smallest one. this specific tunnel, three deformation joints are embedded to connect the tunnel lining ring and the work shaft. The layout of deformation joints is shown in Figure 8d. The effects of the deformation joints on the dynamic responses of the tunnel under seismic excitation are studied here using the established three-dimensional full scale model. Figure 24 illustrates the modulus of the maximum dislocation displacement of each deformation joint, namely, \(\max\left\{\left|A_{i}-B_{i}\right|,i=1...n\right\}\) (see Figure 8d). For brevity, in this Figures S1-S5 represent the water sluice work shaft, middle work shaft, Changxing island work shaft, Pudong work shaft and Pudong #5 conduit work shaft, respectively; LE and RI mean the left side and the right side of each work shaft along the tunnel from S1 to S5, respectively; a, b and c denote the first, second and third deformation joint in the direction away from each work shaft, respectively (see Figure 8d). For instance, S1 RIa means the first deformation joint at the right side of the water sluice work shaft. As shown in Figure 24, the maximum dislocation displacements of deformation joints situated in the same location at both two sides of a work shaft are close to each other; and for deformation joints at one side of a work shaft, the smaller the distance between the deformation joint and the work shaft is, the bigger the dislocation displacement becomes. Besides, the maximum dislocation displacement occurs at S3 RIa and the maximum value is about 3 mm. To further evaluate the function of the deformation joints, cases with and without deformation joints are considered. Table 6 shows the largest compressive stresses and the largest tensile stresses of the lining at two sides of each work shaft with and without deformation joints during earthquakes. It can be seen that with deformation joints the tensile and compressive stresses decrease and the maximum decrement appears at S3 RI (right of the Changxing island work shaft) with a value of about 16.7%.