Anti-frost heave design method for a parabolic canal based on the hydraulic optimal solution set in seasonally frozen regions

Parabolic canals are commonly used in seasonally frozen regions because of their excellent hydraulic characteristics and frost heave resistance. However, severe frost damage can still occur, mainly because the design of canals is based on experience, and the analytical mechnical models and design methods are limited. First, the frost heave characteristics of parabolic canals were analysed, and the canal lining was simplified as an arched thin shell structure under the normal frost heave force, tangential freezing force, and gravity. Second, an analytical mechanical model of frost damage to the lining was established, and the equations for the axial force, bending moment, tensile stress were derived; the accuracy of the model was verified by field measurements and numerical simulations of a canal case. Third, the effects of groundwater depth and canal size were analysed, and the frost damage mechanism was investigated. Fourth, the anti-frost heave design method of a canal based on the hydraulic optimal solution set was proposed, and the method was encapsulated into digital design software with Python language. This mechanical model can explain the frost damage of the canal, and the nonuniform frost heave of foundation soil caused by different groundwater depths in different parts of the canal is the cause of lining damage. The bi-objective optimization design method can consider the hydraulic performance and anti-frost heave performance of the canal, and the digital design software can assist engineers with developing a quick and accurate design approach. The research results can provide a theoretical basis and technical means for cold-region canal design.