Elastic foundation plate model for the frost heave damage of trapezoidal canal lining

Frost heave can seriously damage the trapezoidal concrete-lined canal with an open system in cold regions. In this study, the frost heave failure model of canal lining was established to consider the frost heave force and adfreeze force. The Winkler elastic foundation plate theory was also used to describe the relationship between the canal lining and frozen soil foundation. Specifically, the top of the canal slope and the soil of the channel foundation were frozen together, and the foot of the slope and the bottom plate were set as the mutual hinge constraints. The two ends of the plate at the depth direction were assumed to be simply supported boundaries. The adjacent canal lining joints were mostly filled with soft elastic waterproof materials, particularly for the relatively large deformation. The adjacent canal lining board joints were then assumed to be free boundaries. The analytical solution of the model was obtained to clarify the influence of groundwater depth and geometric parameters of canal lining. A comparison was finally made to verify the field observation and calculation. The results show that the bottom plate was subjected to the uniform force of frost heaving. There was an uneven distribution of the internal force and stress along the height direction of the plate. The stress at the free boundary was also slightly larger than that at other positions. The bending moment and shear force of the slope plate were unevenly distributed, where the maximum deflection was 2/3 from the top to the foot of the slope, and the maximum bending moment was close to the bottom plate. A similar distribution of the stress and internal force was also better consistent with the existing research. The maximum stress occurred at the maximum deflection position. The torque was distributed symmetrically along the center of the canal lining, where the maximum was at four corners. It infers that it was easy to produce a stress concentration at the corners. Compared with the beam theory, the plate theory showed that the deflection and internal force of the lining plate were not uniformly distributed along the plate width direction, where the deflection and bending moment were greater at the free boundary (longitudinal expansion joint), and the torque was distributed at the corner of the canal lining. The tangential force posed little influence on the frost heaving of the canal. The maximum deflection of the canal only increased by 0.7 mm, when adding the tangential force. But the adfreeze force produced an eccentric bending moment on the canal lining, indicating a great increase in the overall bending moment of the canal lining. Therefore, the adfreeze force should be considered in the antifreeze design of the canal lining. The relationship between groundwater and frost heave was dominant in the prevention of frost damage to the canal. Different thicknesses of lining plate should be selected for the working conditions of different groundwater depths. The frost heave displacement of the slope plate gradually decreased with the increase of groundwater depth. There was no variation in the position of the maximum frost heave displacement section. Therefore, the increasing thickness of the canal lining can also effectively prevent frost heave damage to the canal. The thick canal lining or high concrete strength can also be expected to prevent freezing damage, particularly for the high water table. As such, the safe range of canal lining thickness can be obtained, according to the canals with different groundwater levels. The finding can provide a strong referent and theoretical basis for the frost-heave-resistant design of cast-in-place concrete trapezoidal canals.