# Soil and Rockfill Dams Safety Assessment for Henan Province: Monitoring, Analysis and Prediction
## 3 Methods  
### PS-InSAR Technique  
[PERSON] et al. proposed the PS-InSAR technique in 2000, which effectively overcame the effects of temporal decorrelation and atmospheric delay errors [44]. The PS-InSAR technique is based on the identification of stable points with high reflectivity and little variation in space-time. By selecting a large number of PS points, the atmospheric delay phase can be estimated accurately, and the final deformation with millimeter accuracy is obtained. PS-InSAR mainly includes main image selection, co-registration, interference, inversion, geocoding and so on [45; 46; 47]. Its flow chart is shown in Figure 3.  
Figure 2: Sentinel-1A data coverage.  
Generally, the final results of InSAR are presented according to the deformation in the line-of-sight (LOS) direction, but the upstream slope dam and downstream slope dam of different soil and rockfill dams have different slopes. The different location directions of the dam body and the satellite incidence angle will lead to different local incidence angles of different slope dams, which will change the direction and size of the results [35]. The appearance of the dam body is similar to a multi-sided landslide. According to the characteristics of local earth rock materials and foundation geology, the slope angles of the upstream and downstream faces of the dam will be adjusted accordingly. Therefore, it is crucial to obtain the correct vertical deformation of slope dams for exploring the stability of soil and rockfill dams. Figure 4 shows the relationship between the true vertical deformation of soil and rockfill dam, slope, and incidence angle:  
Figure 3: Flow chart of PS-InSAR processing.  
\(e_{a},e_{b},e_{c}\) is the incidence angle of different slope surfaces. \(H\) is the height of the dam. \(\Delta h_{a},\ \Delta h_{b},\ \Delta h_{c}\) is the true vertical deformation of the slope dam. \(\Delta T_{a},\ \Delta T_{c}\) is the deformation perpendicular to the direction of the dam slope. \(O_{1},\ O_{2}\) is the projection distance of the upstream and downstream slope dams on the level surface. \(K_{a},\ K_{b},\ K_{c}\) represents deformation along the satellite LOS. The formula for calculating the locality incidence angle of different slope dams is as follows in Equation (1):  
\[\left\{\begin{array}{l}\varepsilon_{a}=\theta-\alpha\\ \varepsilon_{b}=\theta\\ \varepsilon_{c}=\theta+\beta\end{array}\right. \tag{1}\]  
where \(\theta\) is the satellite incidence angle, which will be provided in general image information, \(\alpha,\ \beta\) is the true slope angle of soil and rockfill dam, which are the ratio of \(H\) to \(O_{1},\ O_{2}\). Therefore, the true vertical deformation of the slope dam is shown in Equation (2).  
\[\left\{\begin{array}{l}\Delta\mathrm{h}_{a}=\frac{\Delta T_{a}}{\cos\varepsilon _{a}}=\frac{K_{a}\times\cos\varepsilon_{a}}{\cos\alpha}\\ \Delta\mathrm{h}_{b}=\frac{K_{b}}{K_{b}}\times\cos\varepsilon_{b}\\ \Delta I_{c}=\frac{\Delta T_{c}}{\cos\varepsilon_{c}}=\frac{K_{c}\times\cos \varepsilon_{c}}{\cos\beta}\end{array}\right. \tag{2}\]  
It can be seen that the influence of the dam slope and incidence angle on the deformation results needs to be considered for the polyhedral slope building. Through the above calculation, the true vertical deformation of soil and rockfill dam can be obtained, and the dam deformation survey can be carried out more accurately.