Frost-heaving mechanical analysis of the trapezoidal canal with water delivery in winter using both Winkler-Pasternak model

A water delivery system can be gradually away from the normal state of the canal operation in northern China in winter. Water diversion projects can be launched to meet the harsh requirement on the large and medium-sized city's residents living water and industrial water consumption, as the guaranteed rates increased. However, the existing mechanical model of the canal with the water delivery cannot fully consider the difference between the freezing and underwater non-freezing areas in winter, particularly for the continuity of soil. It is a high demand to combine the difference in shear stiffness between frozen soil and non-frozen soil. Pasternak model with two parameters can be expected to consider the soil continuity in the freezing area, whereas, the traditional Winkler model can be adopted in the non-freezing area. By contrast, the Winkler model with only a few parameters can be easily calculated for definite physical significance. In this study, the combined Winkler-Pasternak model was proposed for the frost-heaving mechanical analysis of the trapezoidal canal with water delivery in winter. Taking a trapezoidal canal with water delivery in winter in the Manas River basin in Xinjiang of western China as a prototype, the real normal frost-heaving amount, and subsidence deformation of the canal lining plate were also calculated using the improved model, Winkler and Pasternak model. Then, the bending moment was calculated with the upper surface stress of each section of the lining plate. The results indicate that the lining plate was divided into three parts of frost heave, subsidence and frost heave-subsidence transition section. Three models better represented the basic change trend of normal displacement of the lining plate. Meanwhile, the improved model was in better agreement with the measurement. A comparative analysis showed that the improved model was much more accurate than the traditional Winkler model in the freezing area, whereas, some errors but trivial differences were compared with the Pasternak model in the non-freezing area. Furthermore, the improved model shared the excellent performance of the Winkler model, such as simple calculation, clear physical meaning, and few required parameters. The bending moment of sections decreased rapidly in the freezing area with the increase of groundwater depth. The risk of frost-heaving damage to the canal lining plate was dramatically reduced at the groundwater level by appropriate drainage measures. The position in the frozen soil area of the lining plate easy to crack was located at 10.0%~23.3% of the lining plate length away from the waterline. The optimal operation conditions were adopted in the ice-free water delivery of the trapezoidal canal in winter. The improved model can be also applied to the ever-increasingly common situation of water delivery with the ice cover. The finding can provide a strong reference to design the frost heave resistance of the trapezoidal canal with water delivery in winter.