## 4 Inversion of the Penetration Parameters of a High Core Rockfill Dam
### The Initial Calculated Sepage Parameter  
It has been shown that [PERSON]'s law is also adapted in unsaturated flow; in the water storage stage, some parts of the dam body are still in an unsaturated state, so it is necessary to carry out saturated-unsaturated seepage analysis. It can be seen in Equation (8) that in the van Genuchten model (hereinafter referred to as the vg model), the permeability coefficient of porous media in the unsaturated state is jointly determined by the water content, the saturated permeability coefficient and the shape parameters \(\alpha\) and \(n\). The default calculated permeability coefficient is as Table 1, \(\alpha=0.02\) and \(n=2\):  
There are three stages for the initial water storage of the reservoir. The initial water storage speed is 2 m/d and lasts for 30 days, the mid-term storage speed is 2 m/d and lasts for 40 days, the late water storage speed is 1 m/d and lasts for 80 days, the total water storage period is 150 days, and the water storage elevation is 220 m. The water storage process line is as Figure 8:  
In the transient analysis, the total time length is 150 days of total water storage time, and the step size is 1 day. In the first calculation with preset penetration parameter values, the observed result and calculated result are as follows (in this paper, several of the observation points are analyzed: 1, 2, 3, 4, 5, 10, 14). It can be seen in Table 2 that the pore water pressure shows an increasing trend from top to bottom in the dam body. However, there exists a large error between the calculated value and the observed value at each observation point, so it is necessary to conduct inversion to understand the seepage parameters in the dam body. The distribution of the pressure water head is as Figure 9. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **k(cm/s)** & \(\alpha\) & \(n\) \\ \hline gravel core wall & 7.00 \(\times\) 10\({}^{-6}\) & 0.02 & 2 \\ upstream rock & 1.00 \(\times\) 10\({}^{-1}\) & 0.02 & 2 \\ downstream rock & 1.00 \(\times\) 10\({}^{-1}\) & 0.02 & 2 \\ curtain grouting & 1.00 \(\times\) 10\({}^{-7}\) & 0.02 & 2 \\ transition layer & 3.00 \(\times\) 10\({}^{-2}\) & 0.02 & 2 \\ filter layer & 8.00 \(\times\) 10\({}^{-3}\) & 0.02 & 2 \\ sand layer & 3.00 \(\times\) 10\({}^{-3}\) & 0.02 & 2 \\ bed rock & 1.00 \(\times\) 10\({}^{-5}\) & 0.02 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The default calculated permeability coefficient. Figure 7: Distribution of the pore water pressure observer. It can be seen based on the foregoing that the pressure water head distributed in the dam body is connected to the material's shape parameters, moisture content, and saturation seepage parameters. Since the case simulates the storage process of a core rockfill dam without the impact of rainfall infiltration, the main influence factors are shape parameters and saturation seepage parameters. Since the upstream rock and gravel core wall are different, it is not accurate enough to allow them to be calculated using the same shape parameters. Figure 1 shows that the filter layer and transition layer have little influence on pressure head changes, and the effects of the two are ignored for now. In enumerating a series of parameters to discuss the impact of shape parameters, the result is as Table 3: \begin{table}
\begin{tabular}{c c c} \hline \hline
**Observation Point Number** & \
\begin{tabular}{c} **Pore Water Pressure** \\ **Observed (m)** \\ \end{tabular} &
\begin{tabular}{c} **Pore Water Pressure** \\ **Calculated (m)** \\ \end{tabular} \\ \hline
1 & 5.81 & 6.41 \\
2 & 19.82 & 18.81 \\
3 & 30.24 & 28.84 \\
4 & 46.63 & 45.76 \\
5 & 53.62 & 59.81 \\
10 & 161.51 & 163.85 \\
14 & 245.35 & 244.09 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The result of the first calculation with preset penetration parameter values. Figure 8: Water storage process line. Figure 9: The distribution of the pressure water head.