## 4 Results and Discussion
### Effect of freeze-soak-scour Cycles on Properties of NHISS-AC
#### 4.2.3 Scouring Cycles Test
If the reference sequence is set as  
\[X_{0}=\{x_{0}(1),x_{0}(2),\cdots\cdots x_{0}(n)\} \tag{21}\]  
and the comparison sequence is set as  
\[X_{i}=\{x_{i}(1),x_{i}(2),\cdots\cdots x_{i}(n)\} \tag{22}\]  
The grey correlation degree value of point \(\gamma(x_{0}(k),x_{i}(k))\) is calculated as  
\[\gamma(x_{0}(k),x_{i}(k))=\frac{\min\limits_{i}\min\limits_{k}|x_{0}(k)-x_{i}( k)|+\rho\max\limits_{i}\max\limits_{k}|x_{0}(k)-x_{i}(k)|}{|x_{0}(k)-x_{i}(k)|+ \rho\max\limits_{i}\max\limits_{k}|x_{0}(k)-x_{i}(k)|} \tag{23}\]  
where \(k\) = 1, 2,..., n, \(\rho\) is the distinguishing coefficient and it value follows the principle of minimum information \(\rho\in(0,1)\). The grey correlation degree \(\gamma(X_{0},X_{i})\) between \(X_{i}\) and \(X_{0}\) is written as  
\[\gamma(X_{0},X_{i})=\frac{1}{n}\sum\limits_{k=1}^{n}\gamma(x_{0}(k),x_{i}(k)) \tag{24}\]  
A larger grey correlation degree value indicates the reference sequence has more effect on the comparison sequence, and vice versa. In this paper, the gray rational degree theory was applied to explore the influence of three separate factors on the pavement properties of NHSS-AC in spring-thawing season. The voids content (durability), freeze-soak-scour splitting tensile ratio (water stability), Marshall stability (high temperature mechanical property), \(-10\)\({}^{\circ}\)C splitting tensile strength (low-temperature mechanical property) of NHSS-AC after 0, 5, 10, 15, and 20 freeze-soak-scour cycles are the systematic characteristic behavior sequence. The same of NHSS-AC with 0, 5, 10, 15, and 20 soaking cycles, freezing cycle, and scouring cycle act separately are correlation factor sequence. The correlation degree between the systematic characteristic behavior sequence and correlation factor sequences is calculated according to the gray rational degree theory, the results are as shown in Figure 12.  
A larger grey correlation degree value indicates the reference sequence has more effect on the comparison sequence, and vice versa. As is shown in Figure 12, the freezing cycles have a more significant impact on the properties of NHSS-AC compared with the soaking and scouring cycles. The impact of the scouring cycles on the durability of NHSS-AC is more significantly than that of the soaking cycle. The effect of scouring and soaking on low-temperature mechanical property of NHSS-AC under freeze-soak-scour cycles is similar. From the perspective of single factor to analyze, the freezing and scouring factor has the highest correlation degree with the durability of NHSS-AC in spring-thawing season, and the soaking factor has the highest correlation degree with the high-temperature mechanical properties of NHSS-AC in spring-thawing season. It can be seen that the effect of multiple freezing cycles on the internal structure of the NHSS-AC is the most drastic, and the freezing cycles will accelerate the development of microcracks. The soaking cycles is a process of deterioration of material. Especially in the spring-thaw season, various impurities and snow melt agent accelerates the mechanical performance loss of the asphalt binder. The scouring cycle removes the falling mortar particles and accelerates the development of water damage of pavement.