基于广义Winkler弹性地基梁理论的梯形渠道冻胀力学模型

寒区渠道衬砌冻胀破坏现象普遍，而渠道的防冻工程设计大多依赖工程实践经验和定性认识，具有一定的随意性和盲目性，对衬砌结构所受的冻胀力计算缺乏简明、合理的方法。考虑冻土与衬砌的相互作用和冻土地基的连续性，基于广义Winkler地基梁理论并结合有限差分法，推导了渠道衬砌板冻胀挠曲线微分方程，建立了梯形渠道冻胀力学模型，给出了衬砌渠道法向冻胀力及切向冻结力的计算方法。同时，考虑渠道衬砌冻胀破坏的极限承载力以及冻胀过程中坡脚上抬位移对实际冻胀力的削减和释放效应，避免了冻胀力及衬砌结构内力计算值过大。为验证模型的合理性，以甘肃省靖会总干渠梯形渠道为研究对象，对其进行冻胀破坏计算。结果表明：模型由于考虑了衬砌结构与冻土间的相互作用，渠道衬砌板法向冻胀力呈非线性分布，修正了工程力学模型线性分布假设；与工程力学模型相比，冻胀力数值在坡脚处增大、跨中减小、底板上增大，计算结果更符合工程实际。研究提出的冻胀力学模型科学合理，简便快捷，具有更好的通用性，可为寒区渠道的抗冻胀设计提供参考。

Mechanical model of frost heaving force in trapezoidal canal based on generalized Winkler elastic foundation beam theory

The frost heaving damage of canal lining is common in cold regions. The anti-freezing engineering design of the canal mostly depends on engineering practical experience and qualitative understanding， which has a certain randomness and blindness. Therefore， there is a lack of concise and reasonable method to calculate the frost heaving force on the lining structure. In this paper， considering the interaction between frozen soil and lining and the continuity of frozen soil foundation， the difference equation of frost heave deflection curve of canal lining plate is derived based on the generalized Winkler foundation beam theory and the finite difference method. Then， the mechanical model of frost heaving force of trapezoidal canal is established. The calculation methods of normal and tangential frost heaving force of lined canal are given. At the same time， this paper considers the ultimate bearing capacity of the frost heaving failure of the canal lining and the influence of the uplift displacement of the slope toe on the actual frost heaving force in the process of frost heaving， so as to avoid the excessive calculated value of the frost heaving force and the internal force of the lining structure. In order to verify the rationality of this model， taking the trapezoidal canal of Jinghui Main Canal in Gansu Province as the research object， the frost heave damage is calculated. The results show that because the interaction between lining structure and frozen soil is considered in this model， the normal frost heaving force of canal lining plate presents a nonlinear distribution， and the linear distribution assumption of engineering mechanics model is modified. The frost heaving force increases at the foot of the slope， decreases in the middle of the span and increases on the bottom plate than that of the engineering mechanical model， so that the calculation results are more in line with the engineering practice. Therefore， the frost heaving force mechanical model proposed in this paper is scientific， reasonable， simple and fast， and has better universality， which can provide a reference for the frost heaving resistance design of canals in cold regions.