# 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
This can be explained by the fact that an increase in temperature with an increase in salinity is a local effect only for small values of initial salinity. In general, chalk is characterized by a decrease in temperature with an increase in salinity. This is explained by the fact that, if the soil is more saline, then less heat must be removed from the soil to lower its temperature by a given value, \(\Delta T\), since less unfrozen water content needs to be frozen. It is worth noting that, in fact, a decrease in temperature with an increase in initial salinity is also characteristic of clay, but this is manifested to a much lesser extent due to more gently sloping curves for unfrozen water content (see Figure 7a). When comparing the unfrozen water content in clay and chalk, it can be noted that the unfrozen water content near the heat source in chalk is lower than in clay. Therefore, with the same salinity of chalk and clay, it is easier to freeze porewater in chalk. The case of sand (Figure 13) differs significantly from clay and chalk. First, this is due to the presence of porewater flow. Due to the convective transfer of porewater, the dependence of the temperature distribution on the initial salinity is more pronounced. As in the case of clay and chalk, an increase in temperature can be observed with an increase in initial salinity from 0.01 g/100 g to 3.46 g/100 g, but with a further increase in initial salinity, the temperature decreases significantly. Additionally, in general, it is possible to observe a more complex distribution of temperature, unfrozen water content, and salinity due to the presence of the flow of porewater. For this reason, the design, construction, and monitoring of FWs in highly permeable soils can be complicated because, in this case, there is the problem of selecting a criterion for assessing the thickness of the FW due to a highly asymmetric freezing pattern. Based on the obtained simulation results, the dependencies of an FW's thickness on time for all three layers were also determined (see Figures 14 and 15). However, as noted above, in the case of sand, the criterion for estimating the FW's thickness is complicated due to the asymmetric distribution of the temperature field. For this reason, we considered three FW thicknesses for sand: (1) the thickness of the inner frozen zone (to the left of the heat source), (2) the thickness of the outer frozen zone (to the right of the heat source), and (3) the total FW's thickness. It is also worth noting that an FW's thickness is usually determined by reaching the ground temperature of a certain isotherm. In this case, the FW's thickness was calculated from the isotherm of the freezing temperature of the porewater. The choice of this isotherm was based on the fact that it directly varies, depending on the amount of salinity, and it allows one to more accurately assess the variation in the FW's thickness with a change in salinity. If we estimate the FW's thickness using the constant isotherm, then we can arrive at an erroneous conclusion about the beneficial effect of salinity on an FW's growth over time. The fallacy lies in the fact that, as has been shown, with an increase in initial salinity, the soil temperature decreases, and, accordingly, the FW's thickness, as calculated from the constant isotherm, will grow. Figure 14a shows the expected result for clay; with an increase in initial salinity, the FW's thickness decreases. However, in the case of chalk (Figure 14b), interesting results can be observed; for cases of initial salinity of 3.46 g/100 g and 6.9 g/100 g, the FW's thickness practically does not change, and with a further increase in the initial salinity, the FW's thickness decreases again. This result can be explained by balancing two factors for initial salinities of 3.46 g/100 g and 6.9 g/100 g: a decrease in soil temperature with an increase in salinity, and a decrease in freezing temperature with an increase in salinity.