## 3 Experimental Results and Analysis
### Displacement  
Time histories of lateral displacements of the bridge superstructure in two sites are depicted in Figure 11. Under the action of PGA = 0.10 g, the lateral displacement of the superstructure of the conventional group first experienced a slow rise, then reached a peak value about 5 s after the vibration excitation input, and remained stable until the vibration excitation input ended. The lateral displacement of the superstructure of the test group reached its peak value when the vibration excitation input was about 3 s. During the vibration excitation process, the vibration amplitude and residual displacement of the test group were smaller than those of the conventional group. After the vibration excitation, the residual displacements of the test and conventional groups were 2.07 mm and 2.59 mm, respectively. When PGA = 0.20 g, the lateral displacement of the superstructure of the test group developed rapidly and peaked within 1.5 s of the vibration excitation input, and then remained stable until the vibration excitation input stopped. However, the lateral displacement of the superstructure of the conventional group increased slowly throughout the vibration excitation input. Eventually, the residual displacement of the superstructure was 3.39 mm and 8.33 mm for the test and conventional groups, respectively. From the test results, it is known that when PGA = 0.10 g and 0.20 g, the residual displacement of the superstructure in the test group is smaller than that in the conventional group. The reason for this is that the drainage structure in the test group enabled the excess pore water to discharge in time, whereas in the conventional group it could not, resulting in a reduction in the effective stress of the soil and a reduction in shear strength, which eventually caused the bridge superstructure to produce greater lateral displacement.  
Liquefaction of soil leads to the loss some shear strength, and the lateral flow of liquefied soil also causes the lateral displacement of the sheet-pile wall, so the lateral displacement of the sheet-pile wall could also indicate the degree of liquefaction of the site. Figure 12 shows the lateral displacement of the sheet-pile wall after each round of vibration excitation input. When PGA = 0.05 g, the sheet-pile walls of the test group and the conventional group did not produce lateral displacement. With a PGA of 0.10 g, the lateral displacements of the sheet-pile wall in the conventional group and the test group were 14 mm and 8.5 mm, respectively, the former being significantly larger than the latter. This is due to the fact that in the process of vibration excitation input, the excess pore water in the conventional group could not be dissipated immediately, and the lateral flow of the liquefied soil increased the soil pressure on the sheet-pile wall, eventually leading to a greater lateral displacement of the sheet-pile wall. In contrast, the drainage structure of the test group dissipated some of the excess pore water, which better preserved the effective stress of the foundation soil and limited the lateral displacement of the sheet-pile wall. Under PGA = 0.20 g, the lateral displacement of the sheet-pile wall of the test group was still smaller than that of the conventional group, 19 mm and 19.5 mm, respectively. The reason for this is that the lateral displacement of the conventional group sheet-pile wall was greater than that of the test group under the moderate excitation load (PGA = 0.10 g), meaning that the compactness of the soil in the conventional group was greater and the soil was further stabilized after the moderate excitation load. Therefore, when PGA = 0.20 g,  
Figure 11: Lateral displacement of the bridge superstructure.  
the difference in lateral displacement between the two groups of sheet-pile walls was not significant.