梯形渠道衬砌冻胀破坏弹性地基板模型

为探讨开放系统中梯形混凝土衬砌渠道的冻胀问题，根据衬砌板与冻土地基的相互关系，采用 Winkler弹性地基板理论建立了考虑冻胀力和冻结力作用的衬砌板冻胀破坏力学模型，使用解析法得到了衬砌板变形和内力解，对不同地下水埋深、衬砌板几何参数的影响规律进行了分析。通过与已有现场观测值和计算值进行对比，验证了弹性地基板理论计算结果的正确性。研究结果表明：坡板在非均匀分布的冻胀力作用下，挠度、弯矩和剪力也表现为非均匀分布，挠度最大值在坡顶距坡脚2/3处，弯矩最大值靠近底板位置，拉应力分布与内力分布规律一致，与已有研究结果吻合。与梁理论相比，板理论计算结果表明衬砌板的挠度和内力沿板宽方向为非均匀分布，挠度和弯矩在自由边界（纵向伸缩缝）处增大，扭矩主要分布在衬砌板的拐角处。切向冻结力对渠道冻胀影响较小，在原渠道工况下，不考虑切向冻结力与考虑最大切向冻结力之间，最大挠度相差0.7 mm。针对不同地下水位的渠道，给出了衬砌板的安全厚度，可为现浇混凝土梯形渠道的抗冻胀设计提供参考和理论依据。

Elastic foundation plate model for the frost heave damage of trapezoidal canal lining

The frost heave damage is an important aspect of trapezoidal concrete lined canal with an open system in cold regions. The Winkler elastic foundation plate theory, which could describe the relationship between canal lining and frozen soil foundation, was used to establish the frost heave failure model of l canal lining considering the frost heave force and adfreeze force. The top of the slope of the canal and the soil of the channel foundation are frozen together, and the foot of the slope and the bottom plate are mutually hinge constraints, so the two ends of the plate at the depth direction are assumed to be simply supported boundaries. The adjacent canal lining joints are mostly filled with soft elastic waterproof material, which allows relatively large deformation, so the adjacent canal lining board joints are assumed to be free boundaries. The analytical solution of the model was obtained, and the influence of groundwater depth and geometric parameters of canal lining was analyzed. Compared with the existing field observation and calculation results, the correctness of the calculation results in this paper is verified. The results show that the bottom plate is subjected to uniform frost heaving force, that generate the unevenly distributing of the internal force and stress along the height direction of the plate, also the stress at the free boundary is slightly larger than that at other positions. Bending moment and shear force of the slope plate is unevenly distributed. And the maximum deflection is 2/3 from the top of the slope to the foot of the slope, and the maximum bending moment is close to the bottom plate. The stress distribution and the internal force distribution are similarly, which is also consistent with the existing research results. The maximum stress position occurs at the maximum deflection position. Torque distributed symmetrically along the center of the canal lining, and the maximum value distributed at four corners, which are easy to produce a stress concentration at the corners. Compared with the beam theory, the results of plate theory show that the deflection and internal force of the lining plate are not uniformly distributed along the plate width direction, and the deflection and bending moment is greater at the free boundary (longitudinal expansion joint), and the torque distributed at the corner of the canal lining. The tangential force has little influence on frost heaving of the canal. The maximum deflection of the canal after adding the tangential force increased 0.7 mm, but the adfreeze force will produce an eccentric bending moment on the canal lining, which will increase the overall bending moment of the canal lining. Therefore, the influence of adfreeze force should be considered in the antifreeze design of the canal lining. The relationship between groundwater and frost heave plays an important role in preventing the frost damage of the canal. Different thicknesses of lining plate should be selected for the working conditions of different groundwater depth. With the increase of groundwater depth, the frost heave displacement of slope plate gradually decreases, and the position of the maximum frost heave displacement section has not changed. Increasing the thickness of the canal lining can also effectively prevent the frost heave damage of the canal. When the water table is high, thickening canal lining or enhancing concrete strength should be chosen to prevent freezing damage. According to the canals with different groundwater levels, the safe range of canal lining thickness is obtained, which can provide a referent and theoretical basis for the frost heave resistant design of cast-in-place concrete trapezoidal canals.