# Experimental Study on Mechanical Properties of Highway
## 2 Test Description
Using the static pressure sample maker, it was pressed into a cylindrical specimen with a diameter of 50 mm and a height of 100 mm. The upper surface was shaved after each layer was pressed. 4. Demolding: The specimen was wrapped with a thin layer of cling film and placed into a plexiglass cylinder. It was then wrapped with cling film again and marked to prevent moisture loss. It was put into a constant temperature environment box and quickly frozen at \(-30\)\({}^{\circ}\)C for 4 h to prevent water migration in the soil. \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Soil Sample**} & **Maximum Dry Density** & **Optimum Moisture** & **Natural Water** & **Specific** & **Natural Void** \\  & \(\rho_{d}\) (g/cm\({}^{3}\)) & **Content \(\omega\)/\%** & **Content \(\omega\)/\%** & **Content \(\omega\)/\%** & **Gravity Gs** & **Ratio e** \\ \hline silly sand & 2.01 & 10 & 4 & 2.67 & 0.423 \\ \hline \end{tabular}
\end{table} 
Table 2: Physical parameters of soil samples. Figure 1: MTS triaxial test system. * Conservation: The frozen specimens were removed for demolding. They were then re-wrapped with cling film and placed in the molds for curing. The molds were sealed well and placed in a constant temperature environment box for freeze-thaw cycles. After the freeze-thaw cycle, the specimens were further cured at room temperature (20 \({}^{\circ}\)C) for 24 h to shape them. Three parallel specimens were prepared for each test condition. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Sample Number**} & **Number of Freeze–Thaw Cycles (Time)** & **Moisture Content (\%)** & **Confining Pressure (\%)** & **Freezing Temperature (\({}^{\circ}\)C)** \\ \hline D-1 & 0 & & & \\ D-2 & 1 & & & \\ D-3 & 3 & 10 & 100 & \(-\)10 \\ D-4 & 5 & & & \\ D-5 & 7 & & & \\ H-1 & & 6 & & \\ H-2 & 1 & 8 & 100 & \(-\)10 \\ H-3 & 1 & 10 & 100 & \(-\)10 \\ H-4 & & & 12 & & \\ W-1 & & & & 50 & \\ W-2 & 1 & 10 & 100 & \(-\)10 \\ W-3 & & & & 150 & \\ F-1 & & & & \(-\)5 \\ F-2 & 1 & 10 & 100 & \(-\)10 \\ F-3 & & & & \(-\)15 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Triaxial compression test scheme. Figure 2: Particle analysis curve. Data processing. The calculation formula of axial strain \(\varepsilon_{1}\) is:  
\[\varepsilon_{1}=\frac{\Delta h}{h_{0}}\times 100 \tag{1}\]  
where \(\Delta h\) is axial deformation, mm; \(h_{0}\) is the height of the sample, mm. During the test, the sample will produce transverse deformation and the cross-sectional area will change. Therefore, the average method is adopted for the sample area when processing the data, that is, the cross-sectional area of the sample is approximately replaced by the corrected cross-sectional area of the equal volume cylinder. The correction formula of the corrected cross-sectional area \(A_{\text{a}}\) of the specimen is as follows:  
\[A_{\text{a}}=\frac{A_{c}}{1-0.01\varepsilon_{1}}=\frac{V_{0}-\Delta V}{(h_{0} -\Delta h)(1-0.01\varepsilon_{1})} \tag{2}\]  
where \(A_{\text{c}}\) is the cross-sectional area of the sample before the test, mm\({}^{2}\); \(V_{0}\) is the volume of the sample before the test, mm\({}^{3}\); and \(\Delta V\) is the volume change in mm\({}^{3}\). The axial deviatoric stress (\(\sigma_{1}-\sigma_{3}\)) is calculated according to the corrected area, and the calculation formula is:  
\[\sigma_{1}-\sigma_{3}=\Delta\sigma=\frac{F}{A_{\text{a}}} \tag{3}\]  
where \(F\) is the axial pressure, N.  
Duncan-Chang constitutive model is used to fit the stress-strain relationship of triaxial shear test by hyperbola, that is:  
\[q=\sigma_{1}-\sigma_{3}=\frac{\varepsilon_{\text{a}}}{a+b\varepsilon_{\text{ a}}} \tag{4}\]  
where \(a\) and \(b\) are test parameters.