Mechanical Model of Frost Heave Damage in Lining of Trapezoidal Canals Accounting for the Influence of Cracks

Investigating the influence of cracks on frost-heave-induced damage of water conveyance canal linings in cold regions is pivotal to the assessment and mitigation of frost hazards. Based on the two-parameter elastic foundation beam theory, this study establishes a frost heave mechanical model for canal linings that explicitly accounts for crack effects, and the model accuracy is validated against existing experimental and numerical results. The results indicate that cracks exert a pronounced influence on lining deformation and internal forces. As the crack depth increases from 0 to 8 cm, the maximum frost heave displacement and bending moment exhibit increases of approximately 25% and 17.6%, respectively. Within 0.5 m of the slope crest, the shear force first decreases and then increases with increasing crack depth, accompanied by a reversal in its direction. In the region 1.5–3 m from the slope toe, the shear force increases continuously. For relatively deep cracks, the spatial distribution of frost heave displacement becomes increasingly nonuniform, showing larger values as the crack location shifts toward the slope toe. Meanwhile, a sharp amplification of shear force is observed at the slope toe, accompanied by a substantial increase near the slope crest. Structural responses induced by a single crack are consistently more severe than those associated with a crack band, resulting in higher peak frost heave displacement, bending moment, and shear force. Within a crack band, enlarging the crack spacing leads to a gradual attenuation of these responses, highlighting that a dominant crack governs the frost-heave-induced damage of the concrete lining.