# Experimental Study on Mechanical Properties of Highway
## 3 Experiment Results and Analysis
### Effect of Freezing Temperature on Mechanical Properties  
Figure 8 shows the stress-strain curves of thawed subgrade soil under different freezing temperatures (\(-5\)\({}^{\circ}\)C, \(-10\)\({}^{\circ}\)C, \(-15\)\({}^{\circ}\)C) after one freeze-thaw cycle, with a water content of 10% and a peripheral pressure of 100 kPa. From the figure, it can be seen that as the freezing temperature decreases, the stress-strain relationship curves of the roadbed  
Figure 7: The curve of the relationship between limit deviation stress and freezing–thawing times. \begin{table}
\begin{tabular}{c c} \hline \hline
**Freezing and Thawing Times (Time)** & \(\mathrm{R_{f}}\) \\ \hline
0 & 0.88177 \\
1 & 0.90806 \\
3 & 0.91116 \\
5 & 0.92186 \\
7 & 0.93801 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Damage ratio of soil under different freeze–thaw cycles. soil have the same morphology, which is hardened curves. Additionally, as the axial strain increases, the axial bias stress also gradually increases without a peak bias stress. Furthermore, the decrease in freezing temperature does not significantly affect the strength change, indicating a weak influence of freezing temperature. Based on the destructive stress corresponding to a 15% axial strain, the influence of freezing temperature on the destructive stress and modulus of elasticity of the roadbed soil was determined, as shown in Figure 9. As observed from the figure, the destructive stress of the subgrade soil exhibits a slight decreasing trend as the freezing temperature decreases. Specifically, the destructive stress decreases from 303.9 kPa to 290.1 kPa when the freezing temperature drops from \(-5\)\({}^{\circ}\)C to \(-15\)\({}^{\circ}\)C, resulting in a decrease of 13.8 kPa, which corresponds to about 4.5%. The modulus of elasticity of the subgrade soil also decreases in a roughly linear manner with the decrease in freezing temperature. For instance, as the freezing temperature decreases from \(-5\)\({}^{\circ}\)C to \(-15\)\({}^{\circ}\)C, the modulus of elasticity of the subgrade soil drops from 0.765 MPa to 0.753 MPa, representing a decrease of 0.012 MPa, which is about 1.6%. Analyzing the test results, it can be concluded that freezing temperature has a weak influence on the destructive stress and elastic modulus of the roadbed soil. The relationship between \(\varepsilon_{1}/(\sigma_{1}-\sigma_{3})\) and \(\varepsilon_{1}\) under different freezing temperatures, as shown in Figure 10.  
A linear fit to each curve in Figure 10 gives the values of the test parameters \"a\" and \"b\" in the model, as shown in Table 6. As can be seen from the table, the coefficient of determination R\({}^{2}\) is greater than 0.98, indicating a high fit. \begin{table}
\begin{tabular}{c c c c} \hline
**Freezing Temperature (\({}^{\circ}\)C)** & **a** & **b** & **Adjusted R Square** \\ \hline \(-5\) & 1.07915 & 2.98762 & 0.99929 \\ \(-10\) & 1.17915 & 3.04751 & 0.99863 \\ \(-15\) & 1.21915 & 3.13235 & 0.98912 \\ \hline \end{tabular}
\end{table} 
Table 6: Parameters under different loading rate. Figure 8: Influence of loading rate on stress–strain relations. By taking the inverse of the parameters \"a\" and \"b\", the initial tangential modulus and ultimate deviatoric stress versus freezing temperature are obtained, as shown in Figure 11. As can be seen from the Figure, the initial tangent modulus of the soil gradually decreases as the freezing temperature decreases, and the rate of decrease increases. The parameter 1/a decreased by 11.5% when the freezing temperature was reduced from \(-5\)\({}^{\circ}\)C to \(-15\)\({}^{\circ}\)C. The ultimate deviatoric stress 1/b of the soil decreased approximately linearly, with a decrease of about 4.6%. Further calculations to obtain the damage ratio \(\mathrm{R_{f}}\) of soil at different freezing temperatures are shown in Table 7. It can be seen that as the freezing temperature increases, the damage ratio \(\mathrm{R_{f}}\) of the soil fluctuates between 0.90 and 0.91 with no significant trend.