## 4 Case Study
### Characteristics Analysis of the Dam Deformation Zoning
#### 4.2.2 Water Level Characteristics Analysis of the Dam Deformation  
According to the above clustering and zoning results, the time series from the beginning of 2013 to the middle of 2015 is taken as the time series, and one representative measuring point is selected from each of the six types of deformation zones (in which two representative measuring points are selected in Zone VI, i.e., one at the dam crest and one at the dam foundation) to form the panel data time series, as shown in Figure 11. In the figure, the deformation along the river is positive and the deformation against the river is negative. The seven measuring points selected are PL13-5, PL16-4, PL13-3, PL13-2, PL16-2, PL5-1, and IP13-2, which can directly and efficiently reflect the corresponding relationship between water level, dam height, and dam deformation. Meantime, the correlation between water level and displacement is calculated by the maximum information coefficient (MIC) algorithm. The results are shown in Table 4. Where MIC = 1 indicates complete correlation and MIC = 0 means completely irrelevant.  
Figure 10: Deformation zoning of the ultra-high arch dam in different operation phases.  
From the above dam deformation clustering results and the time series of representative measuring points, it can be concluded that:  
* Dam deformation is greatly affected by water levels. With the rise of the water level, the deformation of the dam changes obviously, which also proves the rationality of the water pressure component in the statistical model.
* There is an obvious positive correlation between water level and deformation, and the influence of water level on dam deformation is hysteretic. In addition, with the rise of the water level, the cluster center area also rises, indicating that the trend of the expansion and upward movement of the maximum deformation area of the dam body is consistent with the engineering practice.
* The maximum deformation of the dam is the dam section of the middle riverbed. Because the absolute height of the dam body is large and the bearing water pressure is correspondingly larger, the deformation is more obvious. Similarly, due to low water pressure, the deformation of dam sections on both banks is not as significant as that of dam sections in the middle of the riverbed.
* In different elevations of the same dam section, because the water pressure is linearly distributed with the water depth from top to bottom, the water depth pressure in the middle and lower part is large, and the corresponding deformation is more obvious. Although the water depth near the dam bottom is the largest, the dam bottom is equivalent to the constraint of the fixed end due to the existence of the foundation cementation surface, so the deformation is the smallest. For example, the deformation of measuring point IP13-2 is basically unchanged due to its proximity to the dam foundation. However, it can also be seen from the clustering zoning that the gradient of dam bottom zoning changes greatly, and the deformation increases rapidly at the part far away from the dam bottom constraint area.  
In general, the dam deformation shows an obvious positive correlation with the change of water level. The maximum deformation occurs in the middle of the dam, that is, between the elevation of 1660 m and 1740 m, which should be regarded as the key observation part. In addition, with the rapid rise of the water level, the maximum deformation part of the dam rises and expands, and the fluctuation expansion range is between 10 m and 20 m.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Measuring Point** & **PL13-5** & **PL16-4** & **PL13-3** & **PL13-2** & **PL16-2** & **PL5-1** & **IP13-2** \\ \hline
**MIC** & 0.596 & 0.595 & 0.632 & 0.426 & 0.500 & 0.417 & 0.429 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Zoning results of deformation measuring points of the ultra-high arch dam during the third phase.  
Figure 11: Relationship between the deformation of representative monitoring points and variation of reservoir water level.