| Summary: | Due to the unique hydrothermal environments, the frost heave failure of the concrete lining of water conveyance canals in cold regions is still frequent. The deformation of lining after frost heaving and the stress distribution calculated by the mechanical model can be the reference for the lining design. However, previous research mainly focused on the mechanical model of the cross-section while having little attention for the longitudinal nonuniform frost heave damage. In this study, a mechanical model of the bottom lining under the nonuniform frost heave deformation is built based on the Euler–Bernoulli beam and the Pasternak foundation model, and the analytical solution of the model is obtained. The internal stress of the lining is analyzed during the changes of subgrade coefficient, shear rigidity, transition section length, and frost heave amount inside the model. Also, the calculation process is proved to be correct. The result shows that dangerous cross-sections are at the start and the end of the transition sections. The maximum normal stress and the tangential stress increase when the subgrade coefficient and the frost heave amount increase and the shear modulus and transition section length decrease. The frost heave amount in the frozen ground subgrade increases constantly, while the temperature decreases, but at the same time, the shear rigidity of the subgrade increases with it. The former increases the stress of lining, and the latter decreases it. Therefore, during the frost heaving process, the internal force of lining is coupled with these two elements. By analyzing a water conveyance canal lining under the nonuniform frost heave in the Xinjiang Tarim irrigation district, the maximum normal stress of the dangerous lining cross-section is greater than its tensile strength when the transition section length smaller than 7 m at the frost heave amount is 0.031 m.
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