Frost heave mechanical model of concrete lining trapezoidal canal considering nonuniform frost heave of foundation soil based on elastic foundation beam theory

In areas with high groundwater levels in cold regions, due to the different distances between the calculation points of the canal slope lining slab and the groundwater level, the frost heave of the foundation soil under the slope lining slab presents a different distribution from the canal top to the canal bottom. The slope lining slab has a large amount of frost heave in the bottom area of the canal, and a small amount of frost heave in the canal top area. To explore the effect of nonuniform frost heave of foundation soil caused by high groundwater level in cold areas on the frost heave of concrete lining trapezoidal cannal, the interaction effect between the lining slab and the foundation soil was disintegrated into the uneven free frost heave displacement of the foundation soil, the displacement produced by the reaction of the lining slab and frozen soil, and the relative rotational displacement of the slope lining slab produced by the restraint of the slope foot. Thus, an elastic foundation beam model that satisfied the coordination of deformation at both ends was established based on the elastic foundation beam model proposed earlier. Taking the canal with slope coefficient of 1 and groundwater level of 5 m as an example, this canal was surrounded by the high liquid limit soil in the Gansu Province. The interaction between the different lengths of slope lining slabs and the nonuniform frost heave foundation soil in the process of frost heave was explored. The results showed that for every 1-m increase in the length of the slope lining slab, the maximum value of frost heave reaction force at the slope foot increased by 142%, and the maximum value of bending moment averagely increased by 223%. Meanwhile, the position of the maximum value of the bending moment moved from the original one-third of the slope foot to the slope foot. Therefore, it was recommended that the cross section should better be designed as wide and shallow as possible in order to reduce the influence of nonuniform frost heave of the foundation soil caused by the groundwater level on the canal lining slabs. For trapezoidal canal with narrow and deep cross-sections, it was recommended to set joints within one-third to one-fifth of the length of the slope lining slab from the slope foot to release the frost heave force. The specific location should be comprehensively considered and determined according to the groundwater level, the length of the slope lining slab and the slope coefficient. Meanwhile, taking the slope lining slab length of 4 m as an example, the difference between the effects of nonuniform frost heave and uniform frost heave on the slope lining slab was explored, and maximum frost heave reaction force and maximum bending moments were 264% and 170% greater than the uniform frost heave of the foundation soil, respectively. Therefore, when designing the anti-freeze-heave canal lining slabs in the cold area with high groundwater, the calculation should be based on the nonuniform frost heave elastic foundation beam model. This study can guide the design of anti-frost heave of canal lining slabs in cold areas with high groundwater.