## 3 Materials and Methodology
### Surface Subsidence Prediction and Impact Analysis  
#### 3.4.1 Probability Integral Method (PIM)  
Due to its superior accuracy and simplicity, the PIM stands out as one of the most commonly employed techniques for predicting mining subsidence in China, and one requiring fewer parameters compared to other methods [26]. This theory is used in both caving mining and backfilling mining for subsidence prediction. According to the principle of the PIM, the subsidence of any surface point in a rectangle of mining whose coordinates are \((x,y)\) caused by the whole backfilling working face can be calculated as follows [1; 23; 24; 25]:  
* The surface subsidence value at any point \(A(x,y)\) on the surface is as shown in Equation (1): \[W(x,y)= W_{cm}C_{x}^{\prime}C_{y}^{\prime}\left\{ \begin{array}{l}W_{cm}=mqcos \alpha\\ C_{x}^{\prime}=\frac{1}{\sqrt{\pi}}\left(\int_{-\sqrt{\pi}}^{0}e^{-\lambda^{2 }}d\lambda+\int_{0}^{\sqrt{\pi}\frac{l-x}{\tau}}e^{-\lambda^{2}}d\lambda \right)\\ C_{y}^{\prime}=\frac{1}{\sqrt{\pi}}\left(\int_{-\sqrt{\pi}\frac{\tau}{n_{1}}}^ {0}e^{-\lambda^{2}}d\lambda+\int\limits_{0}^{\sqrt{\pi}\frac{l-x}{\tau^{2}}} e^{-\lambda^{2}}d\lambda\right)\end{array} \right.\] (1) where \(W_{cm}\) is the full mining maximum subsidence value; \(C_{x}^{\prime}\) and \(C_{y}^{\prime}\) are the subsidence distribution coefficients of point \(A(x,y)\) in the main strike and dip sections; \(m\) is the thickness of the coal seam; \(q\) is the surface subsidence coefficient; \(\alpha\) is the dip angle of the coal seam; \(q\) is the subsidence coefficient; \(r_{1}\) is the major influence radius of the dip direction in the downhill area; \(r_{2}\) is the major influence radius of the dip direction in the uphill area; \(l\) and  
Figure 6: Arrangement of ground deformation measuring lines S and E.  
\(L\) are the calculated mining widths in the strike and dip directions after considering the inflection point offset; and \(x\) and \(y\) are the coordinates of any surface point to be found. * The tilt deformation value \(T(x,y)_{j}\) of any point \(A(x,y)\) on the surface in the \(\varphi\) direction is shown in Equation (2): \[ \begin{array}{c}T(x,y)_{j}=T_{x}C_{y}^{\prime}cos\varphi+T_{y}C_{x}^{\prime} sin\varphi\\ T(x,y)_{j+90}=-T_{x}C_{y}^{\prime}cos\varphi-T_{y}C_{x}^{\prime}sin\varphi\\ T(x,y)_{m}=T_{x}C_{y}cos\varphi_{T}+T_{y}C_{x}^{\prime}sin\varphi_{T}\end{array} \] (2) where \(\varphi_{T}=arctg(T_{y}C_{x}^{\prime}/T_{x}C_{y}^{\prime})\); \(T(x,y)_{m}\) is the maximum tilt value of the point to be determined, mm/m; \(\varphi_{T}\) is the angle between the direction of the maximum tilt value and the OX axis (rotating in the counterclockwise direction), degrees; and \(T_{x}\) and \(T_{y}\) are the tilt deformation values superimposed at the projection points on the main section along the strike and dip of the point to be determined, mm/m. * The curvature deformation value \(K(x,y)_{j}\) of any point \(A(x,y)\) on the surface in the \(\varphi\) direction is shown in Equation (3): \[ \begin{array}{c}K(x,y)_{j}=K_{x}C_{y}^{\prime}cos^{2}\varphi+K_{y}C_{x}^{ \prime}sin^{2}\varphi+\big{(}T_{x}T_{y}/W_{0}\big{)}sin2\varphi\\ K(x,y)_{j+90}=K_{x}C_{y}^{\prime}cos^{2}\varphi+K_{y}C_{x}^{\prime}sin^{2} \varphi+\big{(}T_{x}T_{y}/W_{0}\big{)}sin2\varphi\\ K(x,y)_{max}=K_{x}C_{y}^{\prime}cos^{2}\varphi+K_{y}C_{x}^{\prime}sin^{2} \varphi+\big{(}T_{x}T_{y}/W_{cm}\big{)}sin2\varphi_{k}\\ K(x,y)_{min}=K(x,y)_{j}+K(x,y)_{j+90}-K(x,y)_{max}\end{array} \] (3) where \(K(x,y)_{max}\) and \(K(x,y)_{min}\) are the maximum and minimum curvature deformation values of the point to be determined and \(K_{x}\) and \(K_{y}\) are the curvature values of the point to be determined after its superposition along the strike and dip at the projection of the main section. * The horizontal displacement value \(U(x,y)\) of any point \(A(x,y)\) on the surface in the \(\varphi\) direction is shown in Equation (4): \[