The composite lining canal is a kind of lining form which combine compound geomembrane and concrete lining structure. In order to improve the performance of the canal of antifreezing expansion damage, aimed at the lining trapezoidal canal with arc-bottom, the friction of the compound geomembrane and the concrete lining structure are considered. By analyzing the damage mechanism of frostheaving on the concrete lining of the channel with arc-bottom section, it has been indicated that the slope lining is seen as a cantilever beam under the function of frost-heaving force, frozen force and the friction. Further, it has been found that the slope lining plate and the bottom lining plate are combined deformation members under the loads of bending and compressing. The mechanics models of frost-heaving damage of composite lining canal with arc-bottom are built. The internal forces of the canal slope lining plate and the canal bottom lining plate with arc-bottom are solved and the thickness of the lining plates are assessed. Compared with the concrete canal, the tangential force of constraint of the lining canal is reduced by adding the compound geomembrane because of a number of allowable displacements of frost heave. The stress condition of the lining structure itself is improved, and the distribution of the frost-heave capacity is more balanced. These have played an important role in anti-freezing expansion damage and have disclosed the mechanism of frost-heaving damage. Compared with the trapezoidal canal, the integration of the lining canal with arc-bottom combined with the slope lining plate and the bottom lining plate is better because of its antiarching effect is obvious and it’s of more benefit to anti-freezing expansion damage. To sum up, this study provides some theory basis for the technology of anti-freezing expansion damage of the compound lining canal.