## 4 Results and Discussion
### Effect of freeze-soak-scour Cycles on Properties of NHISS-AC
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Mixture Type** & **Number of Cycles** & **0** & **5** & **10** & **15** & **20** \\ \hline \multirow{3}{*}{AC} & Splitting tensile strength (Mpa) & 4.02 & 3.57 & 3.78 & 3.71 & 3.63 \\  & Destruction tensile strain (\(\mu\varepsilon\)) & 2.06 & 2.00 & 1.97 & 1.88 & 1.85 \\  & Destruction stiffness modulus (Mpa) & 3361 & 3330 & 3305 & 3397 & 3383 \\ \hline \multirow{3}{*}{NHSS-AC} & Splitting tensile strength (Mpa) & 4.33 & 4.22 & 4.15 & 4.07 & 3.97 \\  & Destruction tensile strain (\(\mu\varepsilon\)) & 2.27 & 2.18 & 2.12 & 2.09 & 2.03 \\ \cline{1-1}  & Destruction stiffness modulus (Mpa) & 3282 & 3330 & 3365 & 3353 & 3369 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of \(-10\)\({}^{\circ}\)C splitting test. Overall, after 15 or 20 freeze-soak-scour cycles, the normal asphalt mixture cannot meet the requirements of specifications, and the NHSS modified asphalt mixture still meet the requirements of the specifications, which indicates that the NHSS modified can effectively improve the ability of asphalt concrete to resist the spring environment. The price of normal asphalt is about 3000 rmb/t, and the price of NHSS modified asphalt is about 3300 rmb/t. The comprehensive unit price analysis of mechanical paving NHSS modified asphalt concrete of 7 cm thick is as follows. (a) Artificial cost: 2.1 rmb/cm\({}^{2}\); (b) Materials cost (including main material and auxiliary material): 97.7 rmb/cm\({}^{2}\); (c) Mechanical cost: 2.5 rmb/cm\({}^{2}\); (d) Other cost (including safe and civilized construction costs, fees, and taxes): 7.4 rmb/cm\({}^{2}\). The total cost of NHSS modified asphalt concrete is 109.7 rmb/cm\({}^{2}\), and the total cost of normal asphalt concrete is 102 rmb/cm\({}^{2}\). The cost of mechanical paving NHSS modified asphalt concrete of 7 cm thick is 7.6% higher than normal asphalt concrete. Considering the ability of NHSS modified asphalt to improve the durability and the property of the asphalt concrete in spring-thawing season, an increase of 7.6% of the cost is still acceptable. Establishment of the freeze-soak-scour Damage Model of NHSS-AC based on the Logistic Judgment Model  
The logistic judgment model is a set of nonlinear regular regression models which are mainly used to describe and infer the relationship between two or more classified dependent variables and a set of variables. Compared with multiple linear regression, logistic regression has many unique advantages. The model does not require the normality and homogeneity of the data variables in the calculation, nor does it limit the specific type of the independent variable, and its statistical coefficient has strong interpretability, so that the logistic regression models can be widely used in metrology research. In this paper, the deterioration process of NHSS-AC under freeze-soak-scour cycles was studied based on logistic judgment model. The equation of logistic curve is used to study the increasing process of the population by biologist [PERSON] initially. The equation is expressed as  
\[\mathrm{y}=\frac{K}{1+ae^{-bt}} \tag{3}\]  
Figure 9: TSRn changes of mixtures under freeze-soak-scour cycles. The first derivative of the above equation can be found. The resulting equation is the growth velocity function of the described object. \[\mathrm{v(t)}=\frac{dy}{dt}=\frac{Kabe^{-bt}}{\big{(}1+ae^{-bt}\big{)}^{2}} \tag{4}\]  
The growth process of the logistic curve is slow-fast-slow. The first derivative of the growth velocity function can be found, then let the result be 0. \[\frac{dv(t)}{dt}=\frac{Kabe^{-bt}\Big{(}abe^{-bt}-b\Big{)}}{\big{(}1+ae^{-bt} \big{)}^{3}}=0 \tag{5}\]  
We can get  
\[t=\frac{\ln a}{b} \tag{6}\]  
So, when \(t=\frac{\ln a}{b}\), the object is at the peak of the growth. Then find the second derivative of the growth velocity function, then let the result be 0.