## 2 Materials and Methods
### Experimental Methods
#### 2.2.2 Triaxial Tests  
In this study, the triaxial tests were carried out utilizing a triaxial testing apparatus with computerized control (see Figure 4). This apparatus comprised three primary components: a servo-controlled loading system, a multi-channel data acquisition unit equipped with precise sensors and a pressure chamber assembly.  
The servo-controlled loading system incorporated a rigid structural frame integrated with a high-precision axial actuator, enabling the applications of both stress-controlled and strain-controlled loadings. The sensors equipped into the data acquisition unit encompassed a confining pressure sensor for measuring the radial pressure applied around the  
Figure 4: Monotonic triaxial testing system configured for frozen conditions.  
Figure 3: Prepared soil samples: (**a**) \(w=19\%\); (**b**) \(w=27.5\%\); (**c**) \(w=35\%\).  
sample, an axial force transducer for measuring vertical force applied to the sample, a pore pressure transducer for monitoring the water pressure within the sample, a linear variable differential transformer (LVDT) for measuring axial displacement, and a volumetric change monitoring sensor for tracking the sample volume change.  
The triaxial pressure chamber possessed a thermal insulation capability, which enabled the liquid (ethylene glycol) inside the chamber to be kept at a consistent negative temperature throughout the testing period. This insulation was achieved by enveloping the standard chamber wall with an external thermally insulating organic shell, creating an annular gap between the two shells that was also filled with ethylene glycol. Temperature regulation was managed through a closed-loop cryogenic system. In this process, the ethylene glycol in the annular area cooled down and its temperature dropped to the target value. This cooling effect was transferred to the ethylene glycol inside the chamber, causing its temperature to decrease to the desired level as well. Note that the temperature for all the triaxial tests carried out during this study was set at \(-10\)\({}^{\circ}\)C.  
Before being introduced to the triaxial chamber, the sample underwent a 48 h freezing period at \(-10\)\({}^{\circ}\)C. Following installation of the sample, the coolant in the chamber were cooled to \(-10\)\({}^{\circ}\)C as well. Then the sample stood for over 12 h for thermal equilibrium. Each sample was subjected to triaxial shearing at a constant axial strain rate of 1 mm/min under three confining pressure levels (\(\sigma_{3}=200\) kPa, 700 kPa and 1200 kPa). The three different confining pressures used in this study were selected based on both field conditions and experimental requirements. Specifically, the confining pressure of \(\sigma_{3}=200\) kPa corresponded to a high subgrade with a height of around 20 m. The mechanical behavior of high subgrade was critically important in road and railway engineering, as the failure of such structure often led to catastrophic engineering accidents.  
The other two higher \(\sigma_{3}\) levels (\(\sigma_{3}=700\) kPa and 1200 kPa), although not directly representing typical field stress levels, were chosen to ensure reliable determination of the shear strength parameters of cohesion \(c\) and internal friction angle \(\varphi\). Due to the significantly high cohesion of frozen soils, narrow spacing between \(\sigma_{3}\) levels may diminish the detectable influence of internal friction [25], making it difficult to accurately determine \(\varphi\) from the failure envelope. At the same time, the upper limit of the confining pressure was carefully selected to prevent excessive compression that could induce pressure melting, triggering additional mechanical responses of frozen soils [26], which fell outside the focus of this study. The testing procedure used in this study was made by referring to the previous studies ([PERSON] et al., [PERSON] et al.) [27; 28]. The testing process was stopped when the axial strain \(\varepsilon_{1}\) reached 20%, which indicated that the failure had been achieved.