## 5 Evaluation of Material Factors and Performance Indicators by One-Way Standard Deviation and GRA
### GRA-Based Evaluation of Impact Factors  
Grey Relational Analysis (GRA) was used to assess the relevance of each performance indicator on the grouting material and to determine the optimal mix ratio [51; 52]. It was found that, according to the relevant specifications [22; 32; 35] and field requirements [53; 54] for the setting time, flowability, bleeding rate, and compressive strength, among the 18 ratio groups, the initial setting times of Groups 1 to 7, 11, and 14 did not meet the minimum standards. Groups 15 and 16 did not meet the minimum requirements for the initial setting time and flowability. The bleeding rate of Group 18 exceeded the upper limit, and the compressive strength of Group 17 did not meet the specified minimum standards. Five groups satisfied the specified criteria, and the GRA evaluated only these five groups. The following details were provided:  
According to the stipulated specifications, the performance indicators (initial setting time, final setting time, flowability, bleeding rate, and compressive strength) of the selected ratio group (1-18) had to be met. This was achieved by constructing a comparative series \(D_{i}(j)\), where \(j=1\), 2,\(\ldots\), \(m\) (\(m\) is the number of groups meeting the specification) and \(I=1\), 2,\(\ldots\), \(n\) (\(n\) is the number of control performance indicators). To ensure the accuracy of the results and avoid the effects of significant differences between the data, the data were preprocessed by normalization, as shown in Equation (2). \[d_{i}(j)=\frac{\frac{D_{i}(j)-\min_{i}}{\max_{i}-\min_{i}}}{\frac{n}{\sum\limits _{i=1}^{n}D_{i}(j)}} \tag{2}\]  
According to the standard [22; 32; 52] and site requirements, the optimal range for the performance indicators is as follows: initial setting time of 45-120 min, final setting time of 150-600 min, flowability of 26-33 cm, bleeding rate of 0-5%, and compressive strength of 12-18 MPa. The construction of the referenced series \(Z_{0}(j)\) is shown in Equation (3). \[Z_{0}(j)=\max(d_{1j},d_{2j},\ldots,d_{nj}) \tag{3}\]  
The grey relational coefficient \(\xi_{i}\) is shown in Equation (4). \[\xi_{i}[Z_{0}(j),d_{i}(j)]=\left|\frac{\min\limits_{i}  
The degree of serial correlation between the series \(D_{i}(j)\) and the reference series \(Z_{i}\) was compared using the correlation \(r_{i}\), as shown in Equation (5). The correlation degree of each performance index of the grouting material was then determined.  
\[r_{i}=\frac{1}{n}\sum_{j=1}^{n}\zeta_{i}[Z_{0}(j),d_{i}(j)] \tag{5}\]  
where the closer the correlation \(r_{i}\) is to 1, the better the series \(D_{i}(j)\) is correlated to the performance metrics. The indicator weights \(W_{i}\), as shown in Equation (6), should be used. The optimal mix ratio group was then determined, as shown in Table 3.  
\[W_{i}=\frac{r_{i}}{\sum_{j=1}^{n}r_{j}}\;(i=1,2,\ldots,n) \tag{6}\]  
As shown in Figure 10, the correlation of the alkali-activated GGBFS-zeolite powder slurry was investigated. The correlation of the compressive strength was found to be the highest and closest to 1, indicating that this performance indicator had the greatest correlation with optimum proportioning. Except for the compressive strength correlation, which exceeded 0.7, the correlations of the other four performance indicators were all greater than 0.5, and all were correlated with the optimal mix ratio. The weights of the performance indicators (initial setting time, final setting time, flowability, bleeding rate, and compressive strength) on the mix ratio were 19.71%, 19.72%, 19.98%, 19.67%, and 20.92%, respectively. The correlation of each performance index of the grouting material on the optimal mix ratio was, in descending order, as follows: compressive strength, flowability, final setting time, initial setting time, and bleeding rate. Figure 10: Correlation of different performance indicators.