## 3 Results
### Quantitative Analysis of \(Z\) and \(H\)
#### 3.1.2 The Range of Top Elevation of the Water-Retaining Structure H  
During the design phase of the Qianping Reservoir, based on the actual engineering conditions and in accordance with relevant requirements such as the \"Specifications for Construction Planning of Water Resources and Hydropower Projects (SL 303-2017)\" [35] of China, three construction progress plans were formulated for comparison and selection. The planned elevations before each flood season during the construction period are determined. Taking into account factors such as construction intensity, current construction technology, mechanical failure rate, material yard distribution, road traffic, variations in work area, and local precipitation patterns for each schedule, and leveraging expert experience, the interval elevations for each schedule are determined as shown in Figure 6. Among them, schedule 1 in Figure 6a is the conventional one, which conforms to the average advanced level of current construction technology; schedule 2 in Figure 6b is the slower-paced one; and schedule 3 in Figure 6c is the more aggressive one.  
The flood season of Qianping Reservoir is from May to September each year, with the main flood season occurring from 25 June to 15 August. Therefore, the elevation range (\(H_{1},H_{2}\)) of the water-retaining structure during the flood season is determined based on the elevation range of the dam/weir by the end of May. The three construction schedules all aim to have the top elevation of the cofferdam reach 374.4 m by the end of May 2017 (before the flood season). Therefore, the elevation range of the retaining structure (\(H_{1},H_{2}\)) before the flood season in 2017 is taken as the elevation range of the cofferdam top. In the 2018 flood season, the water-retaining structure elevation range H varied depending on the construction progress. For example, both schedule 1 and schedule 2 were constructed under the protection of cofferdams, and, at this time, the top elevation of the cofferdam had reached 374.4 m, meaning that at this point \(H_{1}=H_{2}\). However, in schedule 3, the elevation of the dam top exceeded the cofferdam elevation before the 2018 flood season, so the elevation range (\(H_{1},H_{2}\)) for the water-retaining structure is taken as the dam top elevation range.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Flood** & **Flood Frequency** & **Upstream Water** & **Flood** & **Flood Frequency** & **Upstream Water** \\
**Return Period** & **(\%)** & **Level (m)** & **(Years)** & **(\%)** & **Level (m)** \\ \hline
1 & 100.00 & 344.12 & 100 & 1.00 & 387.69 \\
2 & 50.00 & 347.20 & 200 & 0.50 & 393.48 \\
5 & 20.00 & 353.06 & 500 & 0.20 & 401.55 \\
10 & 10.00 & 360.28 & 1000 & 0.10 & 407.35 \\
20 & 5.00 & 372.60 & 5000 & 0.02 & 416.67 \\
50 & 2.00 & 381.62 & & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Flood frequency and upstream flood water level of the Qianping reservoir during the construction period.  
In order to measure the likelihood of construction progress lagging behind during different construction schedules, the progress risk \(R_{p}\) is defined as shown in Equation (6). The progress risk \(R_{p}\) ranges from 0 to 1. When the value is from 0 to 0.5, there is a greater possibility of construction progress being ahead; when the value is from 0.5 to 1.0, there is a greater possibility of construction progress being behind.  
\[R_{p}=\frac{H_{0}-H_{1}}{H_{2}-H_{1}},H_{1}\
eq H_{2}, \tag{6}\]  
where \(H_{0}\) represents the planned elevation, \(H_{1}\) represents the lower limit of the interval elevation, and \(H_{2}\) represents the upper limit of the interval elevation.  
Figure 6: Construction schedules for Qianping Reservoir: (**a**) schedule 1; (**b**) schedule 2; (**c**) schedule 3.  
As shown in Figure 6, the elevations of the top of the water-retaining structures for the three construction schemes during each flood season are known, and the corresponding progress risks are calculated using Equation (6), with the results shown in Table 3.