Abstract: To address the limitations of the existing Winkler model which fails to account for the continuity of frozen soil in the channel bed, we introduce the Pasternak shear layer to describe the interaction between independent soil springs, and further develop a novel analytical method for analyzing the mechanics of frost heave in trapezoidal channels with a frozen permafrost foundation. Analytical formulas are derived for the normal stress on contact surface, the frost heave displacement of lining plates, and the internal force distribution within the cross-section of a trapezoidal channel with uniformly frozen foundation soil and no top cover constraint. With a trapezoidal channel in Gansu Province as a case study, we compare the calculated results of frost heave displacement of the lining plates and the distribution of normal stress on the contact surface obtained from our proposed model with those from the Winkler model. The results demonstrate a good agreement between our model and the observed values, indicating that our model provides a more accurate representation and is closer to the actual observations compared to the Winkler model. This highlights the rationality and reliability of our proposed model. Moreover, the model effectively captures the dynamics of normal frost heave force, including its release and attenuation in response to the deformation of the lining plates. It also accounts for the non-linear and differential distribution of the normal frost heave force on the middle and lower parts of the slope plate, the tendency for detachment and uplift in the middle and upper parts due to the action of normal freezing force, and the exclusive impact of normal frost heave force on the bottom plate. These research findings offer valuable insights and serve as a practical reference for the design of frost heave resistance in trapezoidal channels.

Key words: frozen soil engineering, concrete lining canal, frost heave deformation, mechanical model, Pasternak foundation