# Analysis on the Spatial-Temporal Distribution Patterns of Major Mine Debris Flows in China
## 5 Regional Comprehensive Evaluation of Mine Debris Flow Distribution
### Selection of Impact Factors and Determination of Their Weights  
Influencing factors mainly come from two aspects, natural environmental factors include: 1 topography and geomorphology: landform types and distribution, elevation, gully bed ratio and shape, slope, gully density; 2 Geological conditions: rock formations, geological structure, stratigraphy, regional mineral profile, tectonic movements, lithologic characters; 3 meteorology and hydrology: surface runoff, watershed area, unit rainfall, frequency and intensity of heavy rainfall; and 4 vegetation cover. Anthropogenic factors include: intensity of mining activities, changes in ground structure, unreasonable piling and discharging of mining waste, stability of structures, ecological impact, input of prevention, and control measures. Many factors are interrelated and work together to make the spatial and temporal distribution of major mine debris flows complex and variable. In order to explore their intrinsic links, the geological environment, tectonic conditions, multi-year average daily maximum precipitation, vegetation cover, and human factors of major mine debris flow occurrence were selected as evaluation factors based on the collected data combined with the relevant literature [30; 31; 32]. The AHP hierarchical analysis was applied to compare the importance of the factors in the hierarchical model using the \"1-9 Scale Method\" (Table 2); moreover, psychological experiments have shown that this method can reflect the ability of most people to discriminate between different things of the same attributes and is widely known and applied. The judgment matrix formed by scoring relative importance is shown in Table 3. \begin{table}
\begin{tabular}{c c} \hline
**Importance Scale** & **Description** \\ \hline
1 & Indicates that two elements are equally important \\
3 & Indicates that the former of two elements is slightly more important than the latter \\
5 & Indicates that the former of two elements is significantly more important than the latter \\
7 & Indicates that the former of two elements is strongly more important than the latter \\
9 & Indicates that the former of two elements is extremely more important than the latter \\
2, 4, 6, 8 & Indicates the middle value of the above adjacency judgment \\
1/k & If the relative importance ratio of element \(x_{i}\) to element \(x_{j}\) is a\({}_{ij}\). \\ k = 1, \(\ldots\), 9 & then the relative importance ratio of element \(x_{j}\) to element \(x_{i}\) is a\({}_{ji}\) = 1/a\({}_{ij}\) \\ \hline \end{tabular}
\end{table} 
Table 2: 1–9 Scale Method. The results of the AHP hierarchical analysis based on the judgment matrix are listed in Table 4. The detailed calculation process is as follows:  
1. The judgment matrix is normalized by column vector to obtain the new matrix. 2. The new matrix is summed by rows to obtain the column vector \(\omega\), which is the eigenvector of the judgment matrix. 3. The column vector changes to the weight vector \(W\) after normalization, i.e., the vector composed of the weight values \(W_{i}\). From Table 4, it can be seen that a fifth order judgment matrix was constructed for a total of five items: geological environment, tectonic conditions, multi-year average daily maximum precipitation, vegetation cover, and anthropogenic factors. The eigenvector were \(\omega\) (0.672, 0.339, 2.514, 0.174, 1.301)\({}^{\rm T}\). For better understanding and operation, the weighting factors are defined as total 100% in this method (i.e., normalization), and the corresponding weight values \(W_{i}\) of the five items are: 13.435, 6.778, 50.282, 3.482 and 26.023%. Consistency testing of the judgment matrix is required to obtain each weight value using the AHP hierarchical analysis:  
1. Combined with the eigenvector \(\omega\), the maximum eigenroot \(\lambda_{max}\) = 5.243 can be calculated. 2. Then, the \(CI\) = 0.061 is calculated using the maximum eigenroot value. 3. The query obtains the average random consistency index \(RI\) = 1.120 for the fifth order judgment matrix. 4.