## 3 Damping Effect of Saturated Sandy Soil
### Computational Model  
Globally, the maximum height of constructed gravity dams has reached 305 m, with most falling within the range of 130 to 170 m. Consequently, this study models a gravity dam at 150 m in height for the purpose of our analysis. The dam model features a thickness of 30 m, stands at a height of 150 m, has a base width of 100 m, and has a top width of 15 m. The internal cavity is positioned 45 m from the crest and 91 m from the base of the dam. The steel container, which is open at the top, measures 25 m in length, 20 m in width, and 12 m in height, with a 1-meter-thick steel plate, and is filled with saturated sandy soil, bonded to the dam structure. The model is enveloped by a discrete field with dimensions of 102 by 32 by 152 cubic meters, and a conventional gravity dam of identical dimensions serves as the control model.  
The meshing diagram of the model is depicted in Figure 3, while the material parameters are detailed in Table 2. The computational process utilizes explicit dynamic analysis. The dam and the steel container are discretized using C3D8R elements, whereas the saturated sand is modeled as an Eulerian material with EC3D8R elements. The mesh density is strategically varied across the dam model: the top and middle sections feature a dense mesh with 1 m spacing in both the horizontal and vertical directions. Conversely, the mesh in other regions is coarser, with a horizontal spacing of 2.75 m and a vertical spacing of 3.75 m at the base. The transition zones' mesh is automatically generated by the software to ensure smooth gradation. To maintain computational precision, the mesh within the container and the saturated sandy soil is kept dense, adhering to a 1 m spacing in both directions. This mesh arrangement not only ensures mesh convergence but also optimizes computational efficiency.  
Numerical simulations are conducted using Abaqus 2020 software [21], where the EOS (equation of state) and viscosity subroutines are employed to endow saturated sandy soil with its properties. Furthermore, a volume fraction tool is applied to create a discrete field within the model's potential activity domain. The parameters of the saturated sandy soil are as shown in Table 3, and the corresponding values of characteristic wave velocity \(c\) and soil thickness \(h\) are presented in Table 4.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Material** & **Elastic Modulus (Pa)** & **Poisson’s Ratio** & **Density (kg/m\({}^{3}\))** \\ \hline Concrete (C50) & \(3.5\times 10\) & 0.2 & 3200 \\ Steel & \(2.06\times 10^{11}\) & 0.3 & 7800 \\ Liquefied saturated sandy soil & - & - & 2000 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Material parameters.  
Figure 3: The mesh division diagram of the finite-element calculation model.  
Movement of the model is permitted solely in the direction of water flow, with displacements in the remaining two directions being restricted. To facilitate a seamless simulation process, the steel container is rigidly bonded to the dam body through its base, in lieu of a bolted connection. The interaction between the saturated sandy soil and the steel container is characterized as a general contact. These provisions ensure the successful computation of the large-scale model, which requires approximately twenty hours for the entire calculation.