## 6 Case Study
### Comprehensive Evaluation of Compaction Quality
#### 6.3.3 Comprehensive Evaluation Results  
For the index \(HCl^{I}\), the median of the interval number is adopted as the ultimate evaluation criterion. Based on the real-time calculated \(HCl\) and the Kriging interpolation, the contour map of \(HCl\) can be obtained as shown in Figure 8f. The mean \(HCl\) of Block 1 is 44.07, and that of Block 2 is 40.16. It indicates that the compaction quality of Block 1 is better than Block 2 with consideration of all the physical and mechanical indices, which is consistent with the individual physical and mechanical index evaluation. Moreover, the \(HCl\) takes both the physical and mechanical indices into consideration, so it is more synthetic than the individual index. For example, for Zone X marked in Figure 8, we can judge from the contour maps that \(K_{30}\) is not that great, but \(K\), \(\rho_{d}\), \(E_{vd}\) and \(E_{0}\) are visibly larger than those of the adjacent area. This shows that the relationship between indices is nondeterministic, and hybrid evaluation for these indices is necessary. Zone Y marked in Figure 8f shows a compaction weak area and needs to be recompacted. To compare with the \(i\)-AHP method, the traditional AHP method is utilized and the mean \(HCl\) of each block is 44.12 and 40.28, respectively. The results are very close to those of the \(i\)-AHP method and indicate that the two methods have high consistency. However, the \(i\)-AHP method takes both the subjectivity and uncertainty into account, and the important degree is employed for the importance comparison. Moreover, the \(i\)-AHP method transforms the uncertainty problem into a determination problem and simplifies the calculation process. Furthermore, the \(i\)-AHP method can obtain the interval \(HCl\). For any two points A and B in the working face, when the interval \(HCl\) overlaps with each other, the compaction quality at Point A is not necessarily better than that at Point B even if the mean of the former is greater than the latter. Considering the repetitive region of the interval makes it possible for Point B to be better than A when considering the uncertainty in construction, which avoids the arbitrariness of the tradition AHP.  
The semivariograms of \(HCl\) for each block are as shown in Figure 9f. The sill \(C\) is 17.45 in Block 1 and is 37.40 in Block 2. The range \(a\) is 4.012 in Block 1 and is 3.880 in Block 2. These indicate the greater compaction uniformity and geospatial continuity of Block 1 when taking both the physical and mechanical indices into account. Through the analysis of the rolling compaction calibration test and referring to Reference [26], \(a\geq 3.8\) and C \(\leq 30\) are determined as the eligibility criteria for the compaction homogeneity for \(HCl\).  
Based on the above study, the compaction quality report of a randomly selected working face can be obtained as shown in Figure 10.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Indices**} & **Criteria (\(P_{1}\))** & **Criteria (\(P_{2}\))** & **Total Weight Vectors** \\ \cline{2-3}  & [0.2432,0.2781] & [0.6877,0.7865] & \\ \hline \(A_{1}\) & [0.7609,0.8272] & & [0.1850,0.2300] \\ \(A_{3}\) & [0.1965,0.2136] & & [0.0478,0.0594] \\ \(A_{4}\) & & [01183,0.1266] & [0.0814,0.0996] \\ \(A_{5}\) & & [0.2537,0.2905] & [0.1745,0.2285] \\ \(A_{6}\) & & [0.5791,0.6293] & [0.3983,0.4950] \\ \hline \hline \end{tabular}
\end{table}
Table 4: Interval total weight vectors of the \(i\)-AHP model.