## 3 Results and Analysis
### Gray Correlation Analysis of Factors Affecting Permeability Coefficient  
The factors affecting the permeability coefficient are very complex. The interaction mechanism of various influencing factors is complex and unclear for improved loess materials, so it is difficult to determine a reasonable prediction model by analytical methods. Empirical formulas have certain limitations and cannot thoroughly consider various influencing factors. Therefore, this paper uses gray correlation analysis to determine the degree of influence of each factor on the permeability coefficient.  
In the gray correlation analysis, the permeability coefficient of the improved loess obtained from the test is used as the reference sequence (i.e., parent factor sequence). Its corresponding C\({}_{\text{c}}\), d\({}_{10}\), dry density, d\({}_{50}\), d\({}_{60}\), C\({}_{\text{u}}\), admixture type, and admixture content are used as the comparison sequence (i.e., sub-factor sequence). Figures 11 and 12 display the correlation coefficients and degree of association according to the grain size characteristics, gradation characteristics, dry density, admixture type, and admixture content with the permeability coefficient of improved loess materials.  
Figure 11: Correlation coefficient of each specimen.  
Figure 10: C\({}_{\text{u}}\)\(\times\) C\({}_{\text{c}}\) versus permeability coefficient curve.  
The gray degree of association between the permeability coefficient and the type of admixture is the largest, as seen in Figure 11. This suggests that the addition of admixture is the primary factor contributing to the decrease in the permeability of the improved loess material. Therefore, it can be considered as the optimal influencing factor for the permeability coefficient of the improved loess material under the given condition. The correlation between the admixture content and the permeability coefficient is the smallest, 0.774. In this paper, the admixture types are cement and lime, and the designed admixture contents are 5%, 9%, 12%, and 15% for cement, and 6%, 9%, and 12% for lime. This indicates that the addition of admixture in the improved loess material can reduce the permeability coefficient to a large extent. The content of the admixture should be controlled in the interval of 6-15%, beyond which it is not significant for the reduction in the permeability coefficient. The degree of association of C\({}_{\rm c}\) and the permeability coefficient is only 0.001 smaller than the type of admixture, which becomes the second-best influencing factor. Combined with the contents of Section 3.1.4 of this paper, reducing C\({}_{\rm c}\)*C\({}_{\rm u}\) can significantly reduce the permeability. The type of admixture and C\({}_{\rm c}\) have the most significant effect on the permeability coefficient of the improved loess material. This is mainly because reasonable grading characteristics can improve the compaction performance of the improved loess, and the pores are smaller under the same compaction work, and because of the cementing effect formed by the admixture in the pores, which further blocks the pore channels and blocks the seepage path, thus reducing the permeability coefficient.