# Experimental and Theoretical Study of the Influence of Saline Soils on Frozen Wall Formation
## 3 Numerical Simulation of Heat and Mass Transfer on the FW Formation
### Discussion  
Figures 11-13 present the results of the simulation of the dependencies of the distributions of temperature, salinity, and unfrozen water content on the initial salinity, \(S_{0}\), for clay, sand, and chalk near the heat source. The results are presented for the final moment in time: 30 days. The dashed vertical line in the figure shows the location of the distributed heat source. From Figure 11, it can be observed that the initial salinity has a weak effect on the temperature distribution in the clay in the range from 0 to 6.9 g/100 g. At the same time, with an increase in initial salinity, the unfrozen water content increases significantly. That is, clay may contain a significant amount of unfrozen porewater despite the weak dependence of temperature on initial salinity, up to 6.9 g/100 g. It may negatively affect the FW's strength properties. However, with an increase in the initial salinity to 13.8 g/100 g, the temperature dependence on the initial salinity begins to manifest itself. In this case, with an increase in the initial salinity above 6.9 g/100 g, the temperature begins to decrease. At the same time, the maximum difference between the curves with initial salinities of 6.9 g/100 g and 13.8 g/100 g is 3 \({}^{\circ}\)C, which can be considered significant. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Dimension** & **Value** \\ \hline \multicolumn{3}{c}{**Geometry and computational mesh**} \\ \hline Radius, \(R_{1}\) & m & 0.1 \\ \hline Radius, \(R_{2}\) & m & 25 \\ \hline Radius of the freezing contour, \(R_{f}\) & m & 7.7 \\ \hline The characteristic value of the computational mesh around the freeze pipe & m & 0.0025 \\ \hline Radius of the freeze pipe, \(r_{f}\) & m & 0.073 \\ \hline The ratio of the size of neighboring computing volumes & \% & 10 \\ \hline \multicolumn{3}{c}{**Initial and boundary conditions**} \\ \hline Simulation time & day & 30 \\ \hline Temperature of the untouched soil, \(T_{0}\) & \({}^{\circ}\)C & 10 \\ \hline Temperature on the wall of the freeze pipe, \(T_{f}\) & \({}^{\circ}\)C & \(-30\) \\ \hline Heat transfer coefficient, \(\alpha\), between the freeze pipe and the soil & \(\text{W}/(\text{m}^{2,\circ}\text{C})\) & 150 \\ \hline Pressure, \(p_{1}\) & MPa & 0 \\ \hline Pressure, \(p_{2}\) & MPa & 1.79 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Basic numerical parameters. Figure 10: Schematic representation of the computational mesh. Figure 11: Distribution of temperature (**a**), unfrozen water content (**b**), salinity (**c**), and relative salinity (**d**) for clay. Figure 12: Distribution of temperature (a), unfrozen water content (b), salinity (c), and relative salinity (d) for chalk. Figure 13: Distribution of temperature (**a**), unfrozen water content (**b**), salinity (**c**), and relative salinity (**d**) for sand. It is also worth noting that, since an increase in initial salinity leads to an increase in the unfrozen water content, a natural proportional decrease in relative salinity occurs since the same volume of dissolved salt remains in a larger volume of unfrozen water. From Figure 11c,d, it can be observed that a significant jump in salinity occurs at the location of the distributed heat source. This is natural because, at the initial moment in time, the temperature of the freeze pipe is rapidly established in the local zone near the heat source. This dramatically reduces the unfrozen water content. As a result, the dissolved salt remains in a smaller unfrozen water content. For chalk (see Figure 12), one can qualitatively note the same features that were described above for clay. The exceptions are the temperature distributions. For chalk, the effect of the initial salinity on the resulting temperature curves is much stronger and appears earlier than for clay. Figure 12a shows that the temperature curve shifts higher with an increase in the initial salinity from 0.01 g/100 g to 3.46 g/100, but with a further increase in the initial salinity, the temperature curve shifts downward.