## 4 Results
### Analysis of Soil Erosion Effect of Slope Deformation  
#### 4.3.1 Soil Erosion Effect Under Annual Erosion Rainfall Scale  
(1) The variation characteristics of soil erosion modulus under the same natural slope shape  
According to Table 4, the contrast diagram of the increment of and increase in the soil erosion modulus of the loess slope with the same natural slope shape after coal mining subsidence under the annual erosion rainfall scale is drawn; this is shown in Figure 9.  
Figure 8: The change curve of slope length after full mining under the same slope. From Figure 9, it can be seen that no matter what the slope shape, coal mining subsidence will lead to an increase in the soil erosion modulus on the loess slope. Specifically:  
First, under the condition of full mining, when the natural slope is [5\({}^{\circ}\), 15\({}^{\circ}\)], the average increase in the soil erosion modulus of the linear, concave, convex, and composite loess slopes is 10.33%, 9.62%, 10.76%, and 9.56%, respectively. When the natural slope is (15\({}^{\circ}\), 25\({}^{\circ}\)), the average increase in the soil erosion modulus of these four loess slopes is 6.42%, 6.55%, 5.98%, and 6.03%, respectively. When the natural slope was (25\({}^{\circ}\), 45\({}^{\circ}\)], the average increase in the soil erosion modulus of the four loess slopes was 4.26%, 4.43%, 4.37%, and 4.18%, respectively. In addition, the increment of the soil erosion modulus of the linear, concave, convex, and complex loess slopes with a natural slope of 15\({}^{\circ}\) is the largest, which is 1.67 times, 1.12 times, 1.24 times, and 1.26 times that of the average increment of the soil erosion modulus of the four slopes with natural slopes of 5\({}^{\circ}\), 25\({}^{\circ}\), 35\({}^{\circ}\), and 45\({}^{\circ}\). Second, according to the data of the slope increase, slope length decrease, and soil erosion modulus increase of the loess slope in different models, the quantitative relationship between the soil erosion modulus increase (\(R_{M_{1}}\)) and slope increase (\(R_{s}\)) and slope length decrease (\(R_{l}\)) under the annual erosion rainfall scale was constructed by using a multiple linear fitting method, as shown in Equation (9). \[R_{M_{1}}=1.007R_{s}-0.279R_{l}+0.644\ \ \ \ \ R^{2}=0.9325 \tag{9}\]  
In the formula: \(R_{M_{1}}\)--The increase in soil erosion modulus under the scale of one-year erosion rainfall, %; \(R_{s}\)--slope gradient increase, %; \(R_{l}\)--slope length decrease, %. Figure 9: Comparison of soil erosion modulus increment and increase after full mining under CSLE model. It can be seen, firstly, that under the scale of annual erosion rainfall, the increase in the soil erosion modulus of the loess subsidence slope with any slope shape shows a decreasing trend with the increase in natural slope. Secondly, the natural slope of 15\({}^{\circ}\) is the key point of the abrupt change in soil erosion intensity on the loess slope of the coal mining subsidence area in northern Shaanxi under the annual erosion rainfall scale. Thirdly, under the scale of annual erosion rainfall, the increase in the slope gradient has a positive effect on the increase in the soil erosion modulus, and the decrease in the slope length has a negative effect on the increase in the soil erosion modulus. The contribution of the slope increase was 92.9%, and the contribution of the slope length decrease was 7.1%. Therefore, the increase in the slope is the main factor of the increase in the soil erosion modulus. (2) The variation characteristics of soil erosion modulus under the same natural slope angle According to Table 4, the curve of the soil erosion modulus increment of and the increase in the linear, concave, convex, and composite loess slopes with the same natural slope after coal mining subsidence under the annual erosion rainfall scale is drawn; this is shown in Figures 10 and 11.