## 5 Conclusions  
The numerical simulations and laboratory tests are conducted in this paper to study the stability response of a water conveyance canal in Xinjiang, China. We examine the stability of the canal slope under various conditions and investigate the damage and destabilization mechanism of the collapsible loess canal slope in cold and arid regions. The following conclusions can be drawn:  
The c, \(\varphi\), and E of the soil exponentially decrease with the increase in the number of WD-FT cycles. The degree of decline after the first cycle is the most obvious, and their decrease rates are 25.4%, 8.3%, and 17.9%, respectively. Then, the amplitude of decline gradually decreases and finally stabilizes, resulting in the deterioration in the strength of the loess.  
The height of the infiltration line and the change in pore water pressure during the operation period of the canal are not significantly affected by the height of the seepage overflow point of the canal slope. The height of the infiltration line and pore water pressure are significantly influenced by the water level in the operation period of the canal. During the operation period, the pore water pressure below the infiltration line is uniformly distributed, and the water level behind the impermeable membrane is set up to be 2 m above the base of the canal.  
In general, the \(F_{s}\) of the canal slope decreases during the water conveyance period, but it is always greater than 1.05, and the canal slope is in a relatively stable state. This is due to the hydrostatic pressure acting on the surface of the lining structure improving the anti-slide capacity of the canal slope, which protects the canal slope. During the shutdown period, the water level of 4.5 m behind the membrane was in an unstable state after three cycles. This is due to the coupling effect between the reduction in water loading, the change in pore water pressure caused by water seepage behind the membrane, and the reduction in the mechanical characteristics of loess on the channel base.  
By replacing the surface layer of deteriorated loess with gravel, the mechanical properties of the collapsible loess are improved, and the \(F_{s}\) values of the collapsible loess slope are continuously improved with the increase in the replacement depth. If the replacement depth of gravel for the canal slope is 0.3 m, the slope will be unstable after three cycles, and there will be a risk of landslides. It is recommended to use a gravel replacement depth of 0.9-1.2 m. This is because, in this scenario, the canal slope can remain in a relatively stable state after nine WD-FT cycles, which meets the needs for the safe operation of the project.  
Conceptualization, H.X. and L.Z.; methodology, H.X. and L.Z.; software, H.X. and C.S.; validation, L.Z. and C.S.; formal analysis, H.X. and L.Z.; investigation, H.X.; resources, L.Z. and C.S.; data curation, H.X. and C.S.; writing--original draft preparation, H.X.; writing--review and editing, L.Z. and C.S.; visualization, L.Z.; supervision, L.Z. and C.S.; project administration, L.Z. and C.S.; funding acquisition, L.Z. and C.S. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Outstanding Youth Science Fund Project of Xinjiang Uygur Autonomous Region of China, grant number 2022D01E45; Key R & D Tasks of Xinjiang Uygur Autonomous Region of China, grant number 2022B03024-3; and Research Project of Key Laboratory of Water Conservancy Project Safety and Water Disaster Prevention and Control in Xinjiang, China, grant number ZDSYS-YS-2023-18.  
Not applicable.  
The data presented in this study are all available in the manuscript.  
The authors declare no conflicts of interest.