## 3 Methodology
### Landslide Risk Evaluation  
Figure 8 is the theoretical curve of a gradual change type landslide, which has three stages [51]. In the first stage, from A to B, represents the initial deformation stage. At the beginning of this stage, the deformation curve shows a relatively large slope, then, the deformation will gradually tend to be normal, and the slope of the curve has slowed down. In the second stage, from B to C, the slope continues to deform at essentially the same rate. In the third stage, from C to F, the deformation rate will show a trend of increasing until the overall instability of the slope. As the slope is easily affected by complex factors such as soil type, human engineering activities, etc. Therefore, the overall trend of its deformation conforms to the above-mentioned three-stage evolution law and oscillatory or step type locally. Figure 7: Flow chart of background value optimization. There are many ways to assess landslide risk such as the TOPSIS-Entropy weight theory [52; 53], the speed division method, and so on. However, these methods are mainly based on ground displacement in combination with other relevant factors such as rainfall and water level. Each method has its own disadvantages. For example, the TOPSIS-Entropy weight theory is uncertain about how many indicators should be selected. Furthermore, there must be more than two research subjects to be used for it. The velocity division method is a kind of landslide-stage division method mainly based on surface displacement. Although the method has a relatively clear evaluation criterion for different soil types, it cannot be well adapted to different cases due to the high randomness, complexity, and uncertainty of the landslide deformation evolution process. Because of the hysteresis of surface deformation, the surface displacement-based stage prediction is only applicable to the short-term forecast of landslide risk. In comparison, stage discrimination based on deep displacement is more important and reliable. However, limited by the slow development of deep displacement instruments, related studies to judge the landslide risk through deep displacement are still rare. The current method of judging risk through deep displacements is mainly based on the data of horizontal displacement measured by borehole inclinometers. However, this risk assessment method can be flawed, because the rock and soil mass usually not only has horizontal displacement but also vertical displacement when a landslide occurs. In this subsection, a method for judging slope stability with multiple parameters is proposed, based on horizontal displacements, vertical displacements, and the angle between the two displacement directions. Accompanying the continuous deformation of rock and soil, every sensing unit will have corresponding horizontal and vertical displacement with the deformation of surrounding rock and soil. In other words, the movement of each unit represents the displacement of the rock and soil at its buried depth. Assuming that each sensing unit has its accumulative horizontal displacement \(R_{i}\)(_i_ = 1, 2,..., _n_) and accumulative vertical displacement \(Z_{i}\)(_i_ = 1, 2,..., _n_). Then the orientation vector angle \(\gamma_{i}\) can be calculated as follow  
\[\gamma_{i}=\tan^{-1}\frac{Z_{i}}{R_{i}} \tag{29}\]  
Since the initial cumulative vertical displacement of each sensing unit is close to 0, the \(\gamma_{i}\) will approach 0 degrees. In the first and second stages, \(\gamma_{i}\) fluctuate around 0 because  
Figure 8: Sketch of three stages of slope deformation. the displacement does not change tremendously. When entering the third stage, the Ri will gradually increase and the \(Z_{i}\) will suddenly increase, and the trend is more and more obvious, thus, the \(\gamma_{i}\) will also produce a significant increase along with these variables, and the whole curve shows exponential growth. Therefore, the process of \(\gamma_{i}\) can be roughly illustrated in Figure 9, which basically shows an exponential increase.