## 4 Discussion  
Previous studies on the mechanical behaviors of Ioess in Northwest China have often been limited to a single WD or FT cycle [8, 9, 10, 11, 12, 13]. However, canal projects often undergo the coupling effect of wet and dry alternation as well as repeated freezing and thawing during the operation. There is a lack of research on the mechanical response of Ioess under the WD-FT cycles, and there is even a gap in the study of sliding damage on Ioess canal slopes. Therefore, it is necessary to analyze the stability of a collapsible Ioess canal in cold and arid areas. In this work, the strength characteristics of collapsible Ioess under the condition of the WD-FT cycle are consistent with the expectation and previous research results [14, 15]. The decay amplitude also displays a gradual decline with increasing cycles. The strength parameters tend to the residual values after nine WD-FT cycles. This is due to the irreversible structural damage of Ioess after repeated freezing and thawing, water absorption, water loss, and the weakening of the cementation between soil particles.  
The numerical model in this study considers the change rule of Ioess strength parameters under the coupling cycles and also considers the influence of the seepage on the stability of canal slopes, which is consistent with the previous study [30]. In this study, the influence of the seepage overflow point height on the change in the water level behind the impermeable membrane on the canal slope is relatively small, while the water level in the operation period of the canal significantly affects the water level behind the impermeable membrane. The water level behind the impermeable membrane rises with the increase in the water level in the operation period of the canal. Compared with previous studies [7], these considerations are more in line with the actual state of canal engineering. However, there are still some limitations. For example, the influence of temperature and soluble salt on the stability of canal slopes is neglected. The canal is not a single closed-field system  
Figure 13: The displacement programs of canal slope with different replacement depths.  
but a coupled system of multiple physical fields such as water, heat, and force [45; 46]. In addition, the seepage water behind the slope impermeable membrane is simplified to the water behind the membrane at a certain level rather than the actual infiltration line within the canal slope.  
In the numerical model, it is first necessary to divide the canal model into a series of meshes and then to calculate the stresses and strains of each point. According to the Mohr-Coulomb model, the elastic modulus and yield strength of the material can be calculated from the relationship between stress and strain [47]. When the stress exceeds the yield strength of the material, the strength reduction method is used to adjust the strength according to the damage state of the material. This is achieved with a reduction factor, which is typically based on the damage criteria and the intrinsic parameters of the material. The stability analysis of the canal slope involves complex mechanical calculations and numerical simulations, so the constitutive relationship of the loess at the base of the canal still needs to be further refined. In addition, when the stability of the channel slope is lower than the limit equilibrium state, the numerical calculation will not converge. The results of the \(F_{s}\) and displacements in the study are only used as the criterion of the soil stability condition, but not for the quantification of the actual sliding displacements in the project.  
In future work, we will focus on further research on the constitutive relation of loess and the multi-field coupling of canals. Despite these limitations, this preliminary investigation is expected to provide a theoretical basis and reference for the design, construction, operation, and maintenance of collapsible loess canal slopes in cold and arid regions.