## 4 Correlation between the Microscopic Parameters and Shear Strength Parameters under F-T Cycles
### Analysis of GRA Results between Microscopic Parameters and Internal Friction Angle  
To study the correlation between the above eight microscopic parameters and internal friction angle, the GRA results are shown in Table 7.  
Table 7 displays that the correlations between the internal friction angle of S0 and C, D\({}_{\text{hs}}\), D\({}_{\text{pr}}\), H\({}_{\text{m}}\), and D\({}_{\text{h}}\) were all higher than 0.70, representing their close relationship. C was the most essential factor affecting the internal friction angle of S0. The reason might be that the internal friction angle of S0 mainly depended on the friction between particles. C reflected the shape of soil particles as a whole, which pertained to the arrangement of the particles. Furthermore, R and D\({}_{\text{p}}\) were associated with the internal friction angle of S0.  
The correlations between microscopic parameters and the internal friction angle of S2 were about 0.65. The most relevant parameter was D\({}_{\text{h}}\), and it was perceived that the internal friction angle of S2 was most affected by D\({}_{\text{h}}\). This was mainly because the structure of soil was relatively stable with the hydration reaction of the addition of cement. D\({}_{\text{h}}\) reflected the size of pores: the larger the pores, the smaller the internal friction angle.  
Comparing Table 6 with Table 7, the correlations between microscopic parameters and internal friction angle were basically higher than those with cohesion, demonstrating that the decrease of shear strength after F-T cycles was mainly caused by the change of internal friction angle. Therefore, the frictional strength was the main parameter, which played a dominate role in the shear strength.  
In order to visualize the effect of the micro parameters on the internal friction angle of S0 and S2, the variation of which with the five most relevant microscopic parameters was revealed after F-T cycles, this is shown in Figures 15 and 16, respectively. The degree of microscopic parameters associated with the internal friction angle is arranged from large to small based on the analysis of the GRA results.  
From Figure 15, the internal friction angle of S0 increased with the increase of C, D\({}_{\rm hs}\), and H\({}_{\rm m}\), and decreased as D\({}_{\rm pr}\) and D\({}_{\rm h}\) increased. The method of improving C, D\({}_{\rm hs}\), and H\({}_{\rm m}\) and reducing D\({}_{\rm pr}\) and D\({}_{\rm h}\) could increase the internal friction angle of unmodified soil after F-T, and the frictional strength could be effectively enhanced, thereby achieving the aim of improving the shear strength and frost heave resistance of soil.  
Figure 16 shows that the internal friction angle of S2 decreased with the increasing D\({}_{\rm h}\) and D\({}_{\rm pr}\) and increased as R, D\({}_{\rm ps}\), and D\({}_{\rm p}\) increased. Comparing with Figure 15 and according to the results of 3.2.5 and 3.4.1, we could conclude that the principle of cement improvement was mainly to decrease the D\({}_{\rm pr}\) and D\({}_{\rm h}\) of the unmodified soil under F-T cycles; F-T cycles weakened the soil strength mainly by increasing D\({}_{\rm h}\). Hence, the use of modifiers to reduce D\({}_{\rm h}\) could most effectively increase the shear strength after F-T cycles, reducing maintenance costs and prolonging the service life of the subgrade material.