To study the distribution law of frost heave in base soil with a concrete lining structure and compound geomembrane, the coupled heat–moisture–stress, capillary action, and membrane water migration were considered, and multi-field coupling software was used to simulate the frost heaving of the channel. A 67-day frost heaving process of the foundation soil considering the change of groundwater level around a channel was also considered. The displacement fields at different positions on the base soil were obtained. The results showed that the frost heave was the largest at about one-third of the slope from the bottom of the channel, and the maximum is 8.243 cm. A compound geomembrane on the lower side of the lining can reduce the frost heaving of the foundation soil to some extent, and the maximum normal displacements of the lining along the slope and at the top of the channel decreased by 14.3% and 15.5% after adding the compound geomembrane.

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Hydraulic performance and frost-heaving resistance should be considered simultaneously in the channel design of seasonally frozen soil areas. Quadratic parabolic channels have good water and sand transport capacities and high frost-heaving resistances. The width–depth ratio of a parabola determines its section structural form, which in turn determines the hydraulic performance and frost-heaving resistance. In this research, based on the current lack of a comprehensive optimization method that accounts for the hydraulic performance and frost-heaving resistance of the cross-section structures of parabolic channels, a multi-objective optimization model was established with the goal of achieving a minimum cross-sectional flow area and a uniform channel section force. Taking the flow velocity, the width–depth ratio and the crack resistance of concrete lining plate as constraints, the α method of the linear weighted sum method was used to optimize the calculation, and the comprehensive optimal quadratic parabolic channel section was obtained. The comprehensive optimal section of an actual parabolic channel in the Shijin Irrigation District was determined using this method, and the comprehensive optimal section was analyzed and compared to the original design section and two typical parabolic channel sections. The comprehensive optimal section was compared with the original design section in the Shijin Irrigation District. The force uniformity of the optimal section was 23.2% better, the hydraulic performance was 1.96% better, and the land use was 12.35% less. Compared with the values for the hydraulic optimal section, the maximum positive and negative bending moments of the comprehensive optimal section decreased by 5.6% and 11.89%, respectively, and the force uniformity increased by 7.62%. Additionally, compared with the values for the practical economic section, the force uniformity and the hydraulic performance of the comprehensive optimal section increased by 1.79% and 0.2%, respectively, and the land use decreased by 4.49%. Thus, the comprehensive optimal section met the engineering requirements and it could provide a reference for the design and selection of parabolic channels in seasonally frozen soil areas.