## 3 Damping Effect of Saturated Sandy Soil
### Results Analysis  
Finite-element dynamic time history analysis was conducted on four schemes, including the conventional gravity dam and models with \(c\) = 70,98,163 m/s. Comparative analysis was performed on relevant data from the same characteristic points in different models. Set A of characteristic points is defined as a series of five equidistant points along a 15 m path at the central section of the dam crest, aligned with the direction of water flow. Set B \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Characteristic wave velocity \(c\) (m/s)** & 70 & 98 & 163 \\ \hline
**Soil thickness \(h\) (m)** & 7 & 5 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Characteristic wave velocity and soil thickness correspondence table. Figure 4: Artificial seismic wave time history curves. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Bulk Sound Speed \(k_{0}\) (m/s)** & **Characteristic Wave Velocity** & **Dynamic Viscosity** & **Kinematic Viscosity** \\  & \(c\) (m/s) & \(\eta\) (N \(\times\) s/m\({}^{2}\))** & **Coefficient \(\mu\) (N \(\times\) s \(\times\) m/kg)** \\ \hline
144 & 70/98/163 & 1.96 \(\times\) 10\({}^{9}\) & 9.8 \(\times\) 10\({}^{5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The fluid parameters of liquefied saturated sandy soil. of characteristic points is similarly arranged as five equidistant points along a 1515 path on the upstream face of the dam crest, perpendicular to the water flow direction. These configurations are illustrated in Figure 5.  
The time histories of displacement for each characteristic point during the seismic loading process are recorded. The relative displacement of these points is determined by subtracting the displacement-time history of a reference point at the base. The maximum displacements at each point are subsequently extracted and illustrated in Figures 6 and 7. Figures 6 and 7 illustrate that at the three characteristic wave speeds, the displacement of characteristic points on the crest of the new-type dam, along both paths in the direction of water flow, is significantly reduced compared to that of the conventional gravity dam. Analyzing the maximum displacement of characteristic points along Path A in the direction of water flow, the reductions are 21.53% to 21.62% at \(c\) = 70 m/s, 20.09% to 20.18% at \(c\) = 98 m/s, and 19.39% to 19.59% at \(c\) = 163 m/s. Regarding Path B, the corresponding reductions are approximately 21.28% to 21.83% at \(c\) = 70 m/s, 19.84% to 20.65% at \(c\) = 98 m/s, and 19.36% to 19.63% at \(c\) = 163 m/s. Upon comprehensive analysis, it is evident that the presence of liquefied saturated sandy soil can reduce the displacement of the gravity dam crest along the direction of water flow by about 20%. This reduction is inversely proportional to the characteristic wave speed of the saturated sandy soil, indicating that the thicker the layer of liquefied sand, the greater the reduction in displacement and the more effective the seismic damping becomes. The data indicate that the hollow gravity dam with saturated sandy soil of different characteristic wave speeds exhibits similar trends in displacement- and velocity-time histories. Additionally, the maximum displacement and velocity values observed in these dams are lower than those in conventional gravity dams. This similarity suggests that using saturated sandy soil as a damping material is relatively stable. The peak displacement occurs approximately 0.8 s after the initiation of the seismic load, after which the values begin to decrease, indicating the rapid response capability of the saturated sandy soil. The time history peak values for displacement and velocity suggest that under the condition of \(c\) = 70 m/s, the damping performance is superior to the other two scenarios, with \(c\) = 98 m/s being the next best. This pattern is consistent with the maximum displacement results for characteristic points along paths A and B, demonstrating a trend where the damping effect diminishes as the characteristic wave speed increases.