# Evaluation of the Strength Characteristics of Sility-Clayey Soils during Freezing-Thawing Cycles
## 2 Materials and Methods  
The southern area of the Tyumen region of the Russian Federation contains silty-clayey soils which are considered as frost-susceptible soils, resulting in severe frost heave during the winter time. Remolded clay loam samples with the particle density 2.70 g/cm\({}^{3}\) were compacted in accordance with the Russian State Standard GOST 30416-2012 \"Soils. Laboratory testing. General\" [29]. The samples were compacted in three layers, with the required density and moisture content. The specimens were prepared as cylinders in metal rings of 71.5 mm in diameter and 35 mm in height. Physical characteristics of the soils are presented in Table 1.  
In the experiment, four paired samples were considered for testing with varied initial settings (Table 1). However, only one sample of the pair was subjected to 10 freeze-thaw cycles and the second remained in its original state.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**No.** & **Designation** & **Indicator** & **Unit** & **Value** \\ \hline
1 & \(\rho_{s}\) & Density of soil particles & g/cm\({}^{3}\) & 2.70 \\
2 & \(w_{P}\) & Plastic limit & - & 0.15 \\
3 & \(w_{L}\) & Liquid limit & - & 0.27 \\
4 & \(I_{P}\) & Plasticity index & - & 12.1 \\
5 & \(I_{L}\) & Liquidity index & - & 0.375 \\ \hline \end{tabular}
\end{table}
Table 1: Physical characteristics of the soil.  
The engineering properties of soil samples after freeze-thaw cycles were determined using a direct shear apparatus, according to GOST 12248-2010 \"Soils. Laboratory methods for determining the strength and strain characteristics\" [31]. Four shear tests were conducted with normal stresses 100, 150, 200, and 300 kPa. After conducting experiments under each set of conditions and processing the results of the direct shear test, the data were analyzed to determine the influence of each of the studied factors [32].  
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 is presented in Figure 2. In this case, we have four pairwise comparisons for each parameter that give the effect grade values. As an example, the main effect of the parameter \(\mathbf{X_{1}}\) is considered, which is calculated as the average of these four comparisons. The effect of \(\mathbf{X_{1}}\) is regarded as the average of the four \(\mathbf{Y}\)s at the high level of \(\mathbf{X_{1}}\) minus the average of the four \(\mathbf{Y}\)s at the low level of \(\mathbf{X_{1}}\). The results of the eight experiments carried out were used to calculate the \(\mathbf{X_{2}}\) and \(\mathbf{X_{3}}\) effects in a similar way (by subtracting the average \(\mathbf{Y}\) value at the low parameter level from the average \(\mathbf{Y}\) value at the high parameter level). Here, \(\mathbf{Y}\) parameters are the results of the direct shear test in terms of angle of internal friction and cohesion.  
Thus, the actual effect of parameters \(\mathbf{X_{1}}\), \(\mathbf{X_{2}}\), and \(\mathbf{X_{3}}\) was calculated using Equations (A2)-(A4).  
The most important advantage of factorial design of an experiment is that it allows one to evaluate the interactions between parameters. Interaction means that the influence of one parameter depends on the value (level) of one or more other parameters. The simplest type of interactions are two-factor (\(\mathbf{X_{1}X_{2}}\), \(\mathbf{X_{1}X_{3}}\) and \(\mathbf{X_{2}X_{3}}\)); the interaction of higher-order factors here is \(\mathbf{X_{1}X_{2}X_{3}}\).