## 4 Case Analysis
### Quantitative Analysis of Influences of Displacement Indexes on Damages of Each Level  
On the basis of the obtained comprehensive damage range (Figure 11), and the damage range due to each index, the law of influence of the displacement indexes on the damage ranges of each level was calculated using Equation (7) by virtue of the Raster Calculator, and the contribution rate of the displacement indexes to the damage risk areas of each level were obtained, as shown in Table 6.  
According to Table 6, in the building damage and destruction areas, the contribution rate of curvature K was low while the contribution rates of both horizontal deformation E and inclined T were high. As building damage level was aggravated, the contribution rate of T toward building damage increased while the contribution rate of deformation index E toward building damage decreased. This indicated that the deformation index K caused fewer building damages and that, as damage level aggravated, building damages caused by deformation index T increased while building damages caused by deformation index E decreased. In the cropland damage and destruction areas, as damage level was aggravated, the contribution rate of deformation index T to damages increased while the contribution rates of displacement indexes W and E to damages decreased. And the contribution rate of deformation index W to severe destruction was 0; this indicated that, as damage level was aggravated, the damaged cropland area due to T increased while the damaged cropland \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Damage Level**} & \multicolumn{3}{c}{**Contribution Rate of Each Deformation Index to Building Damage (\%)**} \\ \cline{2-4}  & **E** & **T** & **K** \\ \hline I & 69.53 & 28.30 & 2.17 \\ II & 54.79 & 40.47 & 4.74 \\ III & 36.1 & 63.85 & 0.05 \\ IV & 32.96 & 67.03 & 0.01 \\ \hline \hline \multirow{2}{*}{**Damage Level**} & \multicolumn{3}{c}{**Contribution Rate of Each Deformation Index to Cropland Damage (\%)**} \\ \cline{2-4}  & **W** & **E** & **T** \\ \hline mildly damaged & 33.38 & 32.68 & 33.94 \\ moderately damaged & 14.4 & 29.09 & 56.51 \\ severely destroyed & 0 & 21.74 & 78.26 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The contribution rates of displacement to building and cropland damage risk areas of different severities. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline Damage reason & E & T & J & E\&T & T\&K & E\&K & E\&T\&K & Total \\ \hline Number of house & & & & & & & & & \\ damages/size & 5 & 7 & 0 & 2 & 0 & 0 & 0 & 14 \\ \hline Damage reason & W & E & T & W\&E & E\&T & W\&T & W\&E\&T & Total \\ \hline Cropland & & & & & & & & & & \\ area/hm\({}^{2}\) & 1.19 & 3.95 & 10.94 & 1.94 & 3.34 & 1.36 & 9.95 & 32.67 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The statistical table of deformation index-triggered damages on the ground surface. area caused jointly by W and E decreased, and that W failed to trigger serious cropland destruction. The causes for estimated building and cropland damages were extracted so as to draw Figure 13 for damage cause distribution analysis and to verify the accuracy of the law concerning the influence of displacement indexes on the damages obtained from contribution rate analysis. In the figure, the inner pie chart indicates the proportions of each damage level while the outer doughnut chart indicates the proportions of damage causes corresponding to their damage severities. According to the causes for 14 estimated damaged buildings in Figure 13a, those building damages were all caused by displacement indexes E and T; among those damaged buildings on Levels I and II, the damages caused by horizontal deformation E accounted for a large proportion. As damage level was aggravated, among those damaged buildings on Levels III and IV, the proportion of building damages caused by deformation index E decreased while the proportion of damages caused by inclined deformation index T increased.