## 3 Case Study
### General Description of the Project
Due to the minimal impact of the connection element and the Goodman element on the internal displacement of the dam, the mechanical parameters were determined by referring to relevant references [45; 46]; the mechanical parameters for the elements under consideration are set out in Tables 2 and 3. Since the displacement of the dam originates principally from that of the rockfill materials [47; 48], only the material mechanical parameters of the upstream rockfill, the main rockfill, and the downstream rockfill are simulated in this paper with random fields. Figure 6: Finite element modeling and material zones of rockfill dams. In the actual project, there are some differences in the physical and mechanical properties of the materials in each zone of the rockfill dam, but the overall variability is not significant, and there is no order of magnitude or multiplier difference in the values of parameters. In addition, the construction method, process, and steps of each zone are basically the same in the construction of rockfill dam, so the correlation distance of each zone should not differ too much. At present, there are relatively few studies on the correlation distance of the rockfill dam. According to the references [19; 38; 49; 50], the horizontal correlation distance of the rockfill dam is generally set to 50-150 m, and the vertical correlation distance is generally 1/3\(\sim\)1/20 of the horizontal distance. The inverse analysis of the parameter of the rockfill dam in references [51; 52; 53; 54] shows that the variation coefficient of the parameter of the main rockfill is less than 0.25, and that of the secondary rockfill is less than 0.35. Therefore, considering the material parameter characteristics and construction method and other factors, the relevant distance of 10 m (vertical direction) and 100 m (horizontal and transverse river direction) for the rockfill materials is adopted, and the coefficients of variation of material parameters of the upstream rockfill and the main rockfill are 0.1, and the coefficient of variation of material parameters of the downstream rockfill is 0.2. The parameters of each material of the rockfill dam are shown in Table 4, and the eigenvalues of the parameters random fields are shown in Table 5. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Zones** & \(\rho\) **(kg/m\({}^{3}\))** & \(\mathbf{c}\) (kPa)** & \(\mathbf{\varphi_{0}}\) (\({}^{\circ}\)) & \(K\) & \(R_{f}\) & \(K_{b}\) & \(n\) & \(K_{ur}\) & \(\mathbf{\Delta\varphi}\) (\({}^{\circ}\)) & \(m\) \\ \hline Cushion & 2150 & 0 & 49.4 & 950 & 0.921 & 510 & 0.63 & 1425 & 8.7 & 0.41 \\ Transition & 2130 & 0 & 50.4 & 1180 & 0.911 & 630 & 0.53 & 1770 & 9.3 & 0.3 \\ Upstream rockfill & 2087 & 0 & 50.3 & 710 & 0.61 & 383 & 0.91 & 1065 & 9.3 & 0.19 \\ Main rockfill & 2195 & 0 & 50.5 & 845 & 0.4 & 455 & 0.853 & 1267 & 8.5 & 0.185 \\ Downstream rockfill & 2058 & 0 & 47.5 & 725 & 0.4 & 225 & 0.92 & 1087 & 8 & 0.13 \\ \hline Extrusion wall & 2400 & & & & \(E=2.17\times 10^{10}\) Pa, \(\
u=0.167\) & & & & \\ Face slab & 2400 & & & & \(E=2.17\times 10^{10}\) Pa, \(\
u=0.167\) & & & & \\ Toe slab & 2400 & & & & \(E=2.17\times 10^{10}\) Pa, \(\
u=0.167\) & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Values of material parameters for each zone. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Sress Conditions** & **Element Stiffness** & **Parameters** \\ \hline Pull up & \(a/(1-b\delta_{zz})^{2}\) & \(a=175\), \(b=47.6\) \\ Pressed & \(a/(1-b\delta_{zz})^{2}\) & \(a=650\), \(b=41\) \\ Vertical shear & \(a/(1-b\delta_{zz})^{2}\) & \(a=225\), \(b=40\) \\ Transverse shear & \(a,(\delta_{xz}\leq 12.5\mathrm{mm})\) & \(a=608\), \(b=560\) \\ & \(b,(\delta_{xz}>12.5\mathrm{mm})\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Material parameters of the connection element.