The generation and propagation of initial cracks induced by frost heave loads result in the fracture of lining structures, which is a primary factor contributing to the occurrence of frost heave damage in canals located in cold regions. Based on existing research, a frost-heaving fracture mechanics model for concrete lining of trapezoid canals in frozen soil areas with high groundwater table is developed by integrating the analysis method of frost-heaving mechanics with the theory of linear elastic fracture mechanics. The proposed model reduces the complex process of initial crack propagation and fracture failure of the lining structure to a simplified type I fracture mechanics problem, so as to obtain a determination method for stress intensity factor and vulnerable sections. Taking a canal in Tarim Irrigation District as an example, the effects of different groundwater depth w on the distribution of stress intensity factor KFⅠ(x) and reasonable lining plate thickness dr of the lining sections were analyzed. The results show that the magnitude of stress intensity factor is significantly influenced by groundwater recharge conditions. The decrease in w leads to a nonlinear increase in the magnitude of KFⅠ(x), thereby amplifying the vulnerability of canal linings to frost heave-induced cracking, which is consistent with engineering practices. As w decreases, the reasonable lining plate thickness dr increases. When the groundwater table w is at a depth of 3.0 m, it is recommended to use a plate thickness of 9.0 cm. The study can provide valuable insights for the design of frost-heaving resistant trapezoidal canals.