## 2 Materials and Methods
### Conducted Tests  
Understanding the behavior of fine-grained soils, such as clay, necessitates the assessment of their Atterberg limits, which comprise the liquid limit (LL), plastic limit (PL), and plasticity index (PI). This assessment was carried out through liquid and plastic limit tests on all samples in accordance with the ASTM D4318 standards [47]. Additionally, standard Proctor compaction tests, guided by the ASTM D698 guidelines [52], were performed on soil samples treated with various concentrations of magnesium chloride (MgCl\({}_{2}\)) solution. These tests aimed to determine the samples' maximum dry density (MDD) and optimum water content (OWC). To explore the effect of the MgCl\({}_{2}\) solutions on the strength of treated samples, unconfined compressive strength (UCS) tests were conducted following ASTM D2166M [53] on samples cured for 7 and 28 days in a humidity-controlled environment, as well as on uncured samples for baseline strength comparison.  
This study further investigated the impact of F-T cycles on the mechanical properties of soil stabilized with a MgCl\({}_{2}\) solution at concentrations of 4%, 9%, and 14% under different freezing temperatures (\(-20\)\({}^{\circ}\)C and \(-10\)\({}^{\circ}\)C), using an experimental setup compliant with the ASTM D560 standards [54]. The experiment aimed to determine whether adjustments in the MgCl\({}_{2}\) solution concentration are necessary to optimize soil stabilization effectiveness in response to different temperature exposures and to assess the treated soil's response to various environmental freeze conditions.  
Two identical sets of soil specimens, including both treated and untreated samples, were prepared as per guidelines and underwent a 28-day curing period before freeze-thaw testing. These specimens were measured for height, diameter, and weight, enabling an analysis of volume changes and an assessment of mechanical behavior after F-T cycles.  
In the initial phase, one set of specimens was exposed to \(-10\)\({}^{\circ}\)C for 24 h in a controlled freezer to simulate moderate freeze conditions, while the other set was subjected to \(-20\)\({}^{\circ}\)C to represent severe freeze scenarios. After each freeze phase, the specimens were moved to a humidity chamber maintained at 23 \({}^{\circ}\)C with 100% relative humidity for 24 h, completing one 48-h F-T cycle. This process was repeated up to 7 times for both sets.  
Following the 1 st, 3 rd, 5 th, and 7 th cycles, unconfined compressive strength tests were conducted, providing insights into the samples' mechanical strength through repeated cycles. Volume changes were also measured after each freezing and thawing stage to evaluate the F-T cycles' effect on soil volume. This approach facilitated the evaluation of the MgCl\({}_{2}\) solution's effectiveness in soil stabilization under varying temperature conditions, intending to develop more durable infrastructure solutions in cold climates.  
Additionally, a subset of the samples underwent microstructural analysis using field emission scanning electron microscopy (FESEM), X-ray diffraction (XRD), and Fourier transform infrared spectroscopy (FTIR) tests. This provided more profound insights into the microstructural changes made by the freeze-thaw cycles.