联合Winkler-Pasternak模型的冬季输水梯形渠道冻胀力学分析

为克服现有冬季输水梯形渠道冻胀力学模型未充分考虑冻结区与水下非冻结区差异，以及未考虑土体连续性的不足，该研究根据冻土与非冻土剪切刚度的不同，冻结区采用Pasternak双参数弹性地基梁模型，而非冻结区采用Winkler模型，综合Pasternak模型考虑土体连续性及Winkler模型易于求解、所需参数少的优点，提出联合Winkler-Pasternak模型的冬季输水梯形渠道冻胀力学分析方法。以新疆玛纳斯河流域某冬季输水梯形渠道为例，计算渠坡衬砌板法向变形，并将本文模型、Winkler模型、Pasternak模型计算结果与观测值进行了对比分析，最后计算了衬砌板截面弯矩及上表面应力分布。结果表明：衬砌板法向变形可分为冻胀段、沉降段及冻胀-沉降过渡段三个部分，三种模型计算结果均能较好地反映衬砌板法向位移基本变化趋势，且本文模型计算结果与实测值更加接近，表明了模型合理性。衬砌板易开裂位置位于冻土区距离水位线10.0%～23.3%坡板长处，与工程实际相符。本研究可为寒区冬季输水梯形渠道抗冻胀设计提供科学参考与理论依据。

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.