## 3 Case Study
### Project Specification
#### 3.2.2 Distribution Types of the Duncan-Chang Model Parameters  
Based on the test data samples of high core rockfill dams and foundation material parameters, the K-S and A-D test methods were used to evaluate the marginal distribution types of the Duncan-Chang E-B model parameters. The results are shown in Tables 4-6, in which indicates that the parameter follows a distribution form, and indicates that the parameter does not follow a distribution form. The marginal distribution is not always consistent across the K-S and A-D test methods, and some parameters may conform to more than one distribution. As a result, the marginal distribution remains unclear for some parameters. To address this, the Akaike information criterion (AIC) was employed in this study. Here, the result with the minimum AIC value is the optimal marginal distribution, as shown in Tables 7-9. The parameters in the core wall obey a Weibull distribution, except, which obeys a lognormal distribution. The internal friction angle \(\varphi_{0}\) in the rockfill follows a truncated normal distribution, and \(R_{f}\) and \(n\) obey a lognormal distribution, and the other parameters follow a Weibull distribution. The parameter \(m\) in the overburden obeys a lognormal distribution, and \(K_{b}\) and \(n\) follow a Weibull distribution, and other parameters obey a truncated normal distribution. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multicolumn{5}{c}{**K-S Test**} & \multicolumn{5}{c}{**A-D Test**} \\ \cline{2-10}  & \begin{tabular}{c} **Truncated** \\ **Normal** \\ **Distribution** \\ \end{tabular} & \begin{tabular}{c} **Lognormal** \\ **Distribution** \\ \end{tabular} & \begin{tabular}{c} **Extremal** \\ **Distribution** \\ \end{tabular} & \begin{tabular}{c} **Weibull** \\ **Distribution** \\ \end{tabular} & \begin{tabular}{c} **Truncated** \\ **Normal** \\ **Distribution** \\ \end{tabular} & \begin{tabular}{c} **Lognormal** \\ **Distribution** \\ \end{tabular} & \
\begin{tabular}{c} **Extremal** \\ **Distribution** \\ \end{tabular} &
\begin{tabular}{c} **Weibull** \\ **Distribution** \\ \end{tabular} \\ \hline \(c/k\mathrm{Pa}\) & \(\mathcal{K}\) & \(\checkmark\) & \(\mathcal{X}\) & \(\checkmark\) & \(\mathcal{X}\) & \(\checkmark\) & \(\mathcal{X}\) & \(\checkmark\) & \(\checkmark\) \\ \(\varphi/^{\circ}\) & \(\checkmark\) & \(\mathcal{X}\) & \(\checkmark\) & \(\checkmark\) & \(\checkmark\) & \(\checkmark\) & \(\checkmark\) & \(\checkmark\) \\ \(R_{f}\) & \(\mathcal{X}\) & \(\checkmark\) & \(\checkmark\) & \(\checkmark\) & \(\checkmark\) & \(\checkmark\) & \(\checkmark\) & \(\checkmark\) \\ \(K_{b}\) & \(\checkmark\) & \(\mathcal{X}\) & \(\checkmark\) & \(\checkmark\) & \(\checkmark\) & \(\checkmark\) & \(\mathcal{X}\) & \(\mathcal{X}\) \\ \(m\) & \(\mathcal{K}\) & \(\checkmark\) & \(\mathcal{X}\) & \(\mathcal{X}\) & \(\checkmark\) & \(\mathcal{X}\) & \(\mathcal{X}\) & \(\mathcal{X}\) \\ \(n\) & \(\mathcal{K}\) & \(\mathcal{X}\) & \(\mathcal{X}\) & \(\checkmark\) & \(\mathcal{X}\) & \(\mathcal{X}\) & \(\mathcal{X}\) & \(\checkmark\) \\ \(R_{f}\) & \(\checkmark\) & \(\mathcal{X}\) & \(\mathcal{X}\) & \(\checkmark\) & \(\checkmark\) & \(\mathcal{X}\) & \(\mathcal{X}\) & \(\checkmark\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The marginal distribution of the Duncan–Chang model in the core wall.