# Experimental and Theoretical Study of the Influence of Saline Soils on Frozen Wall Formation
## 2 Experimental Study on the Effect of Salinity on Soil Thermophysical Properties
### Results and Processing of Experimental Measurements
The porosity of soils can be calculated using the following equation:  
\[n=w_{0}\frac{\rho}{\rho_{w}} \tag{9}\]  
However, comparative analysis showed that it is not possible to achieve a good agreement with the experimental data when calculating the thermal conductivity according to Equation (8). It was assumed that the reasons for this are unaccounted for by physical factors. For example, these may include a change in the thermal conductivity of the solution due to a change in its salt concentration, the migration of moisture, or the limited applicability of Equation (8) for the types of soils under consideration. Another possible factor is the error (6%) in the experimental measurement of thermal conductivity, as noted earlier. In this regard, to calculate the coefficient of thermal conductivity, a correction factor, \(\xi\), is introduced into Equation (8):  
\[\lambda=\lambda_{s}^{1-\xi n}\lambda_{w}^{\xi n\gamma}\lambda_{i}^{\xi n(1- \gamma)} \tag{10}\]  
Table 6 shows the calculated porosity and thermal conductivity of the dry skeleton for the studied soils (index \"\(s\)\" in Equation (10)) from the minimum mismatch with the experimental data on thermal conductivity. The mismatch was calculated as the root-mean-square error. It was assumed that the thermal conductivities of water and ice are 0.56/2.20 W/(m\(\cdot\)\({}^{\circ}\)C), respectively. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Soil**} & \multirow{2}{*}{**0.00**} & \multirow{2}{*}{**5.46**} & \multirow{2}{*}{**5.20**} & \multirow{2}{*}{**6.90**} & \multirow{2}{*}{**0.00**} & \multirow{2}{*}{**3.46**} & \multirow{2}{*}{**5.20**} & \multirow{2}{*}{**6.90**} \\ \cline{2-2} \cline{6-9}  & & & & & & & & \\ \hline Clay & 1.00 & 1.23 & - & 1.39 & 0.36 & 0.32 & - & 0.29 \\ \hline Chalk & 0.06 & 0.72 & - & 0.85 & 0.37 & 0.36 & - & 0.30 \\ \hline Sand & 0.01 & - & 0.51 & - & 0.64 & - & 0.70 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Parameters of the approximate dependence of the unfrozen water content. Based on the measurements from Table 1 and measurements processed according to the unfrozen water content and thermal conductivity, the specific heat capacity of the soils was set according to a known dependence [30]:  
\[\rho c_{p}=\big{(}\rho c_{p}\big{)}_{s}(1-n)+n\big{[}\big{(}\rho c_{p}\big{)}_{l} \gamma+\big{(}\rho c_{p}\big{)}_{i}(1-\gamma)\big{]}, \tag{11}\]  
where \(\rho\) is the soil density (kg/m\({}^{3}\)), and \(c_{p}\) is the specific heat capacity of the soil at a constant pressure (J/(kg.\({}^{\circ}\)C)). Figure 6 shows the obtained dependencies. It was assumed that the density of water/ice is 1000/912 kg/m\({}^{3}\) and the specific heat capacity of water/ice is 4200/2100 J/(kg.\({}^{\circ}\)C). \begin{table}
\begin{tabular}{|c c c|} \hline
**Soil** & **Porosity** & **Thermal Conductivity (W/(m.\({}^{\circ}\)C))** \\ \hline
**Clay** & 0.54 & 1.95 \\ Chalk & 0.50 & 2.27 \\ \hline Sand & 0.20 & 2.75 \\ \hline \end{tabular}
\end{table} 
Table 6: Porosity, specific heat capacity, and thermal conductivity of solid soil particles. Figure 3: Dependence of the unfrozen water content (**a**) and the thermal conductivity (**b**) on temperature and salinity for clay. Figure 4: Dependence of the unfrozen water content (**a**) and the thermal conductivity (**b**) on temperature and salinity for chalk. Figure 5: Dependence of the unfrozen water content (**a**) and the thermal conductivity (**b**) on temperature and salinity for sand. Figure 6: Dependencies of specific heat capacity on temperature and salinity for clay (**a**), chalk (**b**), and sand (**c**). The comparison of thermophysical properties of soils in Figures 3-6 enabled us to observe the following similarities and differences among them:  
1. As the salt concentration increases, all the considered soils exhibit an increase in the amount of unfrozen water, ceteris paribus. In all cases, clay contains the highest proportion of unfrozen water. Even when the salt concentration is nearly zero, clay retains a significant amount of unfrozen water.