## 4 Comprehensive Evaluation Model of Coal Mine Goaf Ground Considering High-Speed Railway Load
### Comprehensive Evaluation Model  
(1) Determination of classical and nodal domains  
To clarify the evaluation system of the catastrophe progression method-extension comprehensive evaluation model, firstly, the classical domain and the joint domain are determined, and let  
\[R_{0j}=(N_{0j},C,V_{0j})= \begin{bmatrix}N_{0j}&c_{1}&v_{0j1}\\ &c_{2}&v_{0j2}\\ &\ldots&\ldots\\ &c_{n}&v_{0 jn}.\end{bmatrix} \]  
Figure 8: Activation evaluation system of high-speed railway coal mine goat ground. \begin{table}
\begin{tabular}{c c} \hline \hline
**Grade** & **Embankment Height Below Subgrade Bed** \\ \hline I & \(H\leq 3.75\) \\ II & \(3.75<H\leq 4.0\) \\ III & \(4.0<H\leq 4.5\) \\ IV & \(4.5<H\leq 5.5\) \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Classification of subgrade height influence degree. The \(N_{0j}\) level is expressed as the j level, where \(c_{n}\) denotes each model's evaluation index, and the \(V_{0 ji}\) reflects the value range of each evaluation index at the j level. Based on the classification value of the catastrophe progression method and the division of Tables 7-9, the classical domain is constructed. The classical domain matter-elements of each grade affected by the coal mine goaf are as follows:  
\[ \begin{array}{l}R_{01}=\left[\begin{array}{cc}N_{01}&\text{stability grade of coal mine goaf}&(0.961,1)\end{array}\right]\\ R_{02}=\left[\begin{array}{cc}N_{02}&\text{stability grade of coal mine goaf}&(0.893,0.961)\\ N_{03}&\text{stability grade of coal mine goaf}&(0.737,0.893)\end{array}\right]\\ R_{04}=\left[\begin{array}{cc}N_{04}&\text{stability grade of coal mine goaf}&(0,0.737)\end{array}\right]\end{array} \]  
The nodal domain matter-element is:  
\[R_{D}=\left[ \begin{array}{cc}D&\text{stability grade of coal mine goaf}&(0,1) \end{array} \right]\]  
The classical domain matter-elements of each grade affected by the train are as follows:  
\[R_{01}=\left[ \begin{array}{cc}N_{01}&\text{train axle}&(14,18)\\ &\text{train speed}&(120,150)\\ &\text{subgrade height}&(3.35,3.75)\end{array} \right]\]  
\[R_{02}=\left[ \begin{array}{cc}N_{02}&\text{train axle}&(18,22)\\ &\text{train speed}&(150,200)\\ &\text{subgrade height}&(3.75,4.0)\end{array} \right]\]  
\[R_{03}=\left[ \begin{array}{cc}N_{03}&\text{train axle}&(22,26)\\ &\text{train speed}&(200,300)\\ &\text{subgrade height}&(4.0,4.5)\end{array} \right]\]  
\[R_{04}=\left[ \begin{array}{cc}N_{04}&\text{train axle}&(26,30)\\ &\text{train speed}&(300,350)\\ &\text{subgrade height}&(4.5,5.5)\end{array} \right]\]  
The nodal domain matter-element is:  
\[R_{D}=\left[ \begin{array}{cc}D&\text{train axle}&(14,30)\\ &\text{train speed}&(120,350)\\ &\text{subgrade height}&(3.35,5.5)\end{array} \right]\]
2. Determination of matter-element to be evaluated  
The data of the object being evaluated, \(a_{i}\), are represented using matter-elements. Through this representation, the matter-element \(R_{i}\), which is the object that needs to be evaluated, is derived. \[R_{i}=\left(p_{i},C,V_{i}\right)=\left[ \begin{array}{ccc}p_{i}&c_{1}&v_{i1} \\ c_{2}&v_{i2}\\ \ldots&\ldots&\ldots\\ c_{n}&v_{in}\end{array} \right]\]  
\(P_{i}\) is represented as the \(i\)-th evaluation object, and \(v_{ij}\) is the value of \(p_{i}\) on the characteristic index \(c_{j}\). (3) Determination of index weight  
The three factors of axle load, vehicle speed, and subgrade height are independent of each other. At present, the main parameters of trains in China are as follows: the load is 14-30 tons, the speed is 120-350 km/h, and the subgrade height is 3.35-5.5 m. The influence of the upper and lower bounds of the factor interval is calculated via the fitting formula of each factor, and the influence of each factor on the disturbance depth is analyzed. \[\left|y_{i}(x_{\max(i)}-x_{\min(i)})\right|=E_{i} \tag{17}\]  
where \(E_{i}\) is the influence range of \(i\) factor, \(y_{i}\) is the fitting equation of \(i\) factor, \(x_{max(i)}\) is the minimum value of \(i\) factor, and \(x_{min(i)}\) is the maximum value of \(i\) factor.