# Evaluation of the Strength Characteristics of Sility-Clayey Soils during Freezing-Thawing Cycles
## 3 Results  
The results of the direct shear test for each paired experimental sample set are presented in Table 2, where samples 2, 4, 6, 8 were those subjected to 10 freeze-thaw cycles, and samples 1, 3, 5, 7 were their analogs in the original state of density and moisture content, as presented in Table 3.  
The actual interaction effect between the factors can be calculated by multiplying the interaction factors and the subsequent sum of the products of the obtained value by the result of the experiment in Table 4. For example, the actual effect of interaction of factors  
Figure 2: The assessment of the effect of each parameter, \(\mathbf{X_{1}}\), \(\mathbf{X_{2}}\), and \(\mathbf{X_{3}}\), for the designed three-parameter two-level experiment. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multicolumn{10}{c}{**Average Effect of Factors on \(\frac{\omega_{0}\,^{\circ}}{c}\), \(\frac{\omega_{0}\,^{\circ}}{c}\)**} \\ \hline \hline \multicolumn{10}{c}{**Factor (Coded)**} & \multicolumn{1}{c}{**Level (\(-\))**} & \multicolumn{1}{c}{\(Y(-)_{\text{arg}}\)**} & \multicolumn{1}{c}{**Level (\(+\))**} & \multicolumn{1}{c}{\(Y(+)_{\text{arg}}\)} & \multicolumn{1}{c}{\(\begin{bmatrix}\textbf{Effect}\\ \textbf{Y}(+)_{\text{arg}}-\textbf{Y}(-)_{\text{arg}}\end{bmatrix}\)**} \\ \hline \(X_{1}\) & E, u.f. & 0.55 & \(\frac{11.25}{31.75}\) & 0.75 & \(\frac{13.75}{16.75}\) & \(\frac{2.50}{-15.00}\) (\(4\%\)) \\ \(X_{2}\) & W, \% & 22.6 & \(\frac{12.50}{19.00}\) & 16.5 & \(\frac{12.50}{29.50}\) & \(\frac{10.50}{10.50}\) (\(3\%\)) \\ \(X_{3}\) & Nc & 0 & \(\frac{11.00}{28.50}\) & 10 & \(\frac{14.00}{20.00}\) & \(\frac{3.00}{-8.50}\) (\(30\%\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average effect of factors \(X_{1}\), \(X_{2}\), and \(X_{3}\) on the strength characteristics of soils. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**No. **} & \multicolumn{3}{c}{**Factor**} & \multicolumn{3}{c}{**Parameters (Coded)**} & \multicolumn{3}{c}{**Additional Calculations**} & \multicolumn{3}{c}{**Result**} \\ \multicolumn{10}{c}{**e,**} & **w, \%** & **Nc, pcs** & \(X_{1}\) & \(X_{2}\) & \(X_{3}\) & \(X_{1}X_{2}\) & \(X_{1}X_{3}\) & \(X_{2}X_{3}\) & \(X_{1}X_{2}X_{3}\) & \(\varphi_{r}\,^{\circ}\) & \(\frac{\textbf{c}  
The combination of the void ratio and the number of freezing-thawing cycles also had a significant effect on the strength characteristics of the soil. (Figure 4). The angle of internal friction of soil with a void ratio of 0.55 increased by 2.5\({}^{\circ}\) (20%) during freezing-thawing cycles. The angle of internal friction of soil with a void ratio of 0.75 increased by 3.50\({}^{\circ}\) (23%) during freezing-thawing cycles. It should be noted that the angle of internal friction of soil with a void ratio of 0.55 was 2.0\({}^{\circ}\) (17%) lower, without freezing-thawing. The angle of internal friction of soil with a void ratio of 0.55 was 3\({}^{\circ}\) (19%) lower during freezing-thawing. Cohesion of the soil during freezing-thawing cycles dropped drastically by 11.50 kPa (31%) and 5.50 kPa (28%) for soil with void ratios of 0.55 and 0.75, respectively. The cohesion of soil with a void ratio of 0.55 was 18.00 kPa (48%) higher without the effect of freezing-thawing. The cohesion of soil with a void ratio of 0.55 was 12.00 kPa (46%) higher during freezing-thawing cycles. Cohesion was revealed to be the most sensitive parameter influenced by the freeze-thaw cycles. In addition, the average effect of both the initial soil moisture content and the number of freezing-thawing cycles on the cohesion and the angle of internal friction was considered. The results are shown in Figure 5.  
The angle of internal friction of soil with an initial moisture content of 16.5% did not change during freezing-thawing. However, the angle of internal friction of soil with an initial moisture content of 22.6% increased by 5\({}^{\circ}\) (33%) during freezing-thawing.