## 4 Results
### Analysis of Soil Erosion Effect of Slope Deformation
#### 4.3.2 Soil Erosion Effect Under Typical Field Erosion Rainfall Scale  
(1) The variation characteristics of soil erosion modulus under the same natural slope shape  
According to Table 4, the average increment of and average increase in the soil erosion modulus of the loess slope with the same natural slope shape after coal mining subsidence were compared under the typical rainfall scale of erosion, as shown in Figure 12.  
From Figure 12, it can be seen that coal mining subsidence will lead to an increase in soil erosion modulus on loess slopes under all slope shape and rainfall conditions, and the smaller the natural slope, the greater the increase in soil erosion modulus. Specifically  
and composite loess slopes under three typical erosive rainfall conditions is 5.44%, 6.28%, 5.52%, and 5.64%, respectively. The average increment of the soil erosion modulus of the loess slopes with any slope shape in this natural slope range is not much different from that of the natural slope of 25\({}^{\circ}\), and the average increment is not more than 1.5 t-hm\({}^{-2}\). When the natural slope is (35\({}^{\circ}\), 45\({}^{\circ}\)), the average increase in the soil erosion modulus of the linear, concave, convex, and composite loess slopes under three typical erosive rainfall conditions is 3.82%, 4.19%, 3.73%, and 3.79%, respectively. In this natural slope range, the average increase in the soil erosion modulus of the loess slope with any slope shape is slightly lower than that of the natural slope of 35\({}^{\circ}\), and the average decrease is not more than 3.9 t-hm\({}^{-2}\). Secondly, according to the data of the slope increase, slope length decrease, and soil erosion modulus increase of the loess slope in the different models, the quantitative relationship between the soil erosion modulus increase (\(R_{M_{2}}\)) and slope increase (\(R_{s}\)) and slope length decrease (\(R_{l}\)) under a typical erosion rainfall scale was constructed by using the multiple linear fitting method, as shown in Equation (10). \[R_{M_{1}}=1.007R_{s}-0.279R_{l}+0.644~{}R^{2}=0.9325 \tag{10}\]  
In the formula: \(R_{M_{2}}\)--The increase in soil erosion modulus under typical field erosion rainfall scale, %; \(R_{s}\)--Slope gradient increase, %; \(R_{l}\)--Slope length decrease, %. It can be seen, firstly, that under the typical rainfall scale of erosion, the increment of the soil erosion modulus of the loess subsidence slope with an arbitrary slope shape increases first and then decreases with the increase in the natural slope. Secondly, the natural slope of 25\({}^{\circ}\) is the key point of the abrupt change in soil erosion intensity on the loess slope in the coal mining subsidence area of northern Shaanxi under the typical erosion rainfall scale. Thirdly, under the typical rainfall scale of erosion, the increase in slope and the decrease in slope length have a positive effect on the increase in the soil erosion modulus. The contribution of the slope increase is 79.1%, and the contribution of the slope length decrease is 20.9%. 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 curves of the average increment of and average increase in the soil erosion modulus of the linear, concave, convex, and compound loess slopes with the same natural slope after coal mining subsidence under a typical rainfall scale are drawn, as shown in Figures 13 and 14. Figure 13: Under three typical rainfall conditions, the average increment curve of soil erosion modulus. It can be seen from Figures 13 and 14 that under the same natural slope and three typical rainfall conditions, the influence of coal mining subsidence on the soil erosion modulus of the linear, concave, convex, and complex loess slopes is different.