## 2 Comprehensive Ground Surface Damage Forecast Method
### Forecast and Assessment Indexes  
#### 2.2.1 Coal-Mining-Induced Building Damage Assessment Indexes  
An accurate, comprehensive and rational assessment factor and index system serves as the key for a reasonable assessment of coal-mining-induced civilian building and cropland damages [37]. The main causes for building and cropland damages in the mining area are displacement and deformation triggered by coal mining. The displacement and deformation of ground surface comprise the subsidence, inclined deformation and curvature deformation in the vertical direction, and the displacement, stretching and deformation in the horizontal direction. Among them, building damage is mainly subject to the inclined deformation, horizontal deformation and curvature deformation of the ground surface [38]; cropland damage is mainly subject to the subsidence, horizontal deformation and inclined deformation of the ground surface. The relationship between each displacement and deformation index is as follows:  
As shown in Figure 3, points 2, 3 and 4 are points on the ground surface before coal mining, while points 2\({}^{\prime}\), 3\({}^{\prime}\) and 4\({}^{\prime}\) are the corresponding points on the ground surface after surface deformation due to coal mining. The displacement and deformation of ground surface can be characterized through researching position changes in those points on the ground surface before and after coal mining. The horizontal displacement quantities of points 2, 3 and 4 are recorded as \(\overset{\rightarrow}{l_{2}}\), \(\overset{\rightarrow}{u_{3}}\) and \(\overset{\rightarrow}{u_{4}}\), respectively, and their subsidence quantities are recorded as \(\overset{\rightarrow}{w_{2}}\), \(\overset{\rightarrow}{w_{3}}\) and \(\overset{\rightarrow}{w_{4}}\). Then, the inclined deformation \(i_{2-3}\), mm/m, from point 2 to point 3 on the ground surface, the curvature deformation \(k_{3}\), \(10^{-3}\)/m of point 3 and the horizontal deformation value \(\varepsilon_{2-3}\), \(10^{-3}\)/m from point 2 to point 3 are calculated using the following Equations (3)-(5):  
\[i_{2-3}=\frac{w_{3}-w_{2}}{l_{2-3}} \tag{3}\]  
Figure 2: Space coordinate system by probability integration method. \[k_{3}=\frac{i_{3-4}-i_{2-3}}{\frac{1}{2}(l_{3-4}+l_{2-3})} \tag{4}\] \[\varepsilon_{2-3}=\frac{u_{3}-u_{2}}{l_{2-3}} \tag{5}\]  
The coal-mining-induced inclined deformation, curvature deformation and horizontal deformation of the ground surface have great influences upon the structural stability of buildings. Building damage characteristics vary depending on causative displacements. (1) The influence of horizontal deformation upon buildings; buildings present a weak tensile strength so tensile deformation will affect their walls and result in tensile cracks (as shown in Figure 4a), while compressive deformation will arch the ground surface and roof up and warp windows and door frames (as shown in Figure 4b). (2) The influence of curvature deformation upon buildings; the positive curvature generated on the ground surface will sink both sides of a wall and stretch the upper wall to form inverted \"/\(\wedge\)-shaped\" cracks (as shown in Figure 4c), while the negative curvature will sink the middle part of a wall and stretch the lower wall part to form \"\(\vee\)-shaped\" cracks (as shown in Figure 4d). (3) The influence of inclined deformation upon buildings; the inclined deformation of the ground surface and the movement in the center of gravity of a building form additional torque, break the original equilibrium state and generate a horizontal shear force that destroys a building (as shown in Figure 4e). According to the classification standard for building damages in coal mining areas in _the Code for Coal Pillar Retention and Coal Mining under Buildings, Water Bodies and Railways and in Main Shaffs and Lanes_, the buildings in the coal-mining-influenced area were classified into four damage levels, as shown in Table 1.