## 3 Test Results and Discussion
### Freeze-Thaw Cycles Tests
#### 3.4.2 Results at \(-20\)\({}^{\circ}\)C  
To study the efficacy of magnesium chloride (MgCl\({}_{2}\)) solutions as antifreeze agents in soil stabilization under extreme cold conditions, F-T tests were repeated at \(-20\)\({}^{\circ}\)C. The stress-strain properties of both the untreated and treated soil samples across 7 F-T cycles are illustrated in Figure 8. The results indicate that the untreated samples and those treated with a 4% MgCl\({}_{2}\) solution exhibit significant strength reductions across F-T cycles (Figure 8a,b). However, the samples treated with a 9% MgCl\({}_{2}\) solution show a less severe decline in strength at \(-20\)\({}^{\circ}\)C (Figure 8c), indicating a concentration-dependent response to freezing conditions. It is evident that the samples treated with a 14% MgCl\({}_{2}\) solution maintain consistent strength across the F-T cycles (Figure 8d).  
At \(-20\)\({}^{\circ}\)C, similar to the findings at \(-10\)\({}^{\circ}\)C, the treated samples consistently demonstrate higher unconfined compressive strength (UCS) compared to the untreated samples across all F-T cycles, as illustrated in (Figure 9a). For example, after the third cycle, the untreated soil exhibited a strength of 121.42 kPa, whereas the soil treated with 4%, 9%, and 14% MgCl\({}_{2}\) solutions demonstrated strengths of 202.52 kPa, 238.03 kPa, and 318.38 kPa, respectively. An essential distinction at \(-20\)\({}^{\circ}\)C was observed in the performance of the samples treated with a 9% MgCl\({}_{2}\) solution, which, unlike their behavior at \(-10\)\({}^{\circ}\)C, exhibited a reduction in strength with an increasing number of cycles. However, this decline was less significant than the 4% treated and untreated samples. The samples treated with a 14% MgCl\({}_{2}\) solution maintained a consistent strength throughout the cycles.  
Figure 7: Impact of MgCl\({}_{2}\) solution at \(-10\)\({}^{\circ}\)C on: (**a**) Unconfined compressive strength (UCS) values and (**b**) durability index values.  
Figure 8: Stress-strain relations for treated and untreated samples at \(-20\)\({}^{\circ}\)C with different MgCl\({}_{2}\) solution: (**a**) Untreated, (**b**) treated with 4% MgCl\({}_{2}\), (**c**) treated with 9% MgCl\({}_{2}\), and (**d**) 14% MgCl\({}_{2}\).  
Figure 9: Impact of MgCl\({}_{2}\) Solution at \(-20\)\({}^{\circ}\)C on: (**a**) Unconfined compressive strength (UCS) values and (**b**) durability index values.  
Regarding DI values, in contrast to the experiments at \(-10\)\({}^{\circ}\)C, where the durability index (DI) values for samples treated with a 9% MgCl\({}_{2}\) solution remained stable across seven freeze-thaw (F-T) cycles, a different trend was observed at \(-20\)\({}^{\circ}\)C (Figure 9b). Both untreated and 4% MgCl\({}_{2}\) solution-treated samples, as well as those treated with a 9% solution, exhibited a decline in DI. Specifically, after 7 F-T cycles, the DI values decreased to 0.31 for untreated samples and 0.55 and 0.70 for samples treated with 4% and 9% MgCl\({}_{2}\) solutions, respectively. In contrast, the DI values for the samples treated with a 14% MgCl\({}_{2}\) solution showed stability, as was the case for the tests at \(-10\)\({}^{\circ}\)C, maintaining consistent levels before and after 7 F-T cycles. This difference in performance underscores the pivotal influence of MgCl\({}_{2}\) concentration on enhancing the stability of soil samples under severe thermal conditions. It highlights the importance of carefully tailoring antifreeze treatments to meet specific environmental demands, demonstrating the complex interplay between additive concentration and soil durability.