## 4 Case Analysis
### Regional Distribution Results of Comprehensive Damages  
The damage range distribution of the single displacement indexes was determined using the above damage level classification method, and the damage ranges of each index were superimposed to obtain the damaged area, integrating all displacement indexes. Then, the extraction damage quantity was attainable through comparing the damaged area with the building and cropland distribution on the ground surface. The superposition and comparison process was as shown in Figure 10; the regional distribution and results of the obtained building damage were as shown in Figure 11a; and the regional distribution and results of the cropland damage were as shown in Figure 11b.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Coal Seam**} & \multirow{2}{*}{**Subsidence Factor**} & \multirow{2}{*}{\begin{tabular}{c} **Horizontal** \\ **Movement Factor** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Uphill Angle** \\ **of Critical** \\ **Deformation (\({}^{\circ}\))** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Downhill Angle** \\ **of Critical** \\ **Deformation (\({}^{\circ}\))** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Offset Distance** \\ **of Inflection Point** \\ \end{tabular} } \\ \hline
21 & 0.6 & 0.3 & 69 & 65 & 0.1 H \\
17 & 0.72 & 0.3 & 69 & 65 & 0.1 H \\ \hline \hline \end{tabular}
\end{table}
Table 3: Probability integration parameter selection.  
The raster field was extracted and processed in terms of the comprehensive damage risk area distribution in Figure 11. According to the statistics, the total risk area of coal-mining-induced building damage area on the ground surface was 107.25 \(\mathrm{hm}^{2}\); of this, Level-I damage range accounted for the lowest percentage of 6.23% and the percentages of Level-II, III and IV damages were 32.36%, 30.75% and 20.79%, respectively. The total coal-mining-induced cropland damage and destruction risk area was 106.85 \(\mathrm{hm}^{2}\); of this, 45.86% of the area was lightly damaged while 42.24% of the area was moderately damaged and 11.90% of the area was severely destroyed.  
Figure 10: Schematic of damage range superposition and damage level judgment.  
Figure 9: The cloud chart on ground surface subsidence due to coal mining on the work face.  
Through the comparison of the building and cropland distribution in terms of damage range, the coal-mining-induced building and cropland damage quantities are shown in Table 4:  
According to the table, the damaged buildings on Levels II and III, due to the coal mining on the work face, was the maximum with a total of five buildings holding, followed by damaged buildings on Level IV where a total of three buildings held, and the damaged building on Level I was the minimum with only one building holding. The mildly damaged croplands area on the ground surface was 11.96 hm\({}^{2}\), accounting for 36.60%; the  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline Damage level & I & II & III & IV & Total \\ \hline Number of building & & & & & \\ damages/size & 1 & 5 & 5 & 3 & 14 \\ \hline Damage level & Mildly damaged & Moderately damaged & Severely destroyed & & Total \\ \hline Cropland area/hm\({}^{2}\) & 11.96 & 15.34 & 5.37 & & 32.67 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The statistical table on coal-mining-induced damages on the ground surface.  
Figure 11: The forecast of building and cropland damage range and level integrating multiple displacement indexes: (**a**) Building; (**b**) Cropland.  
moderately damaged croplands area was 15.34 \(\mathrm{hm}^{2}\), accounting for the largest proportion of 46.94%; and the severely destroyed croplands area was 5.37 \(\mathrm{hm}^{2}\), accounting for the minimum proportion of 16.45%.