冻胀反力系数在渠道衬砌冻胀弹性地基梁模型中的应用

为了探究渠道基土在冻胀过程中的非线性变形特性对渠道衬砌冻胀的影响，基于冻土三轴试验结果，建立考虑围压和温度的邓肯-张本构模型，参考室内三轴试验测定基床系数方法，应用数值模拟法建立冻胀反力系数随被约束冻胀量变化的计算式，并基于有限差分法离散弹性地基梁平衡微分方程。模型考虑衬砌不同点因被约束冻胀量不同引起冻胀反力系数不同的取值问题，克服以往模型中冻胀反力系数取常量的不足。应用解析解验证模型的合理性，探究冻胀反力系数分别为变量与常量时在梯形渠道衬砌冻胀力学响应计算结果上的差异。结果表明，对于边坡和渠底衬砌板，常量冻胀反力系数计算出的最大冻胀反力是变量的1.43倍，计算出的弯矩最大值平均是变量的1.12倍。因此在采用弹性地基梁理论分析渠道衬砌冻胀问题时，若冻胀反力系数采用常量，不考虑冻土的非线性变形，会使得计算结果偏大。研究结果可为大型梯形渠道衬砌抗冻胀设计提供参考。

Application of reaction force coefficient in the mechanical model for the elastic foundation beam of canal lining during frost heave

Canal foundation soil is generally characterized by the nonlinear deformation during the frost heaving process. In this study, a Duncan-Chang constitutive model was established considering the confining pressure and temperature, according to the frozen soil triaxial test. A numerical simulation was conducted to establish the calculation formula for the frost heave reaction force coefficient with the constrained frost heave change, particularly referring to the bed coefficient in the indoor triaxial test. The balance differential equation of elastic foundation beam was discretized to adapt to the change of frost heave reaction coefficient using the finite difference method. Since the frost heave reaction coefficient greatly varied at different points of lining, the model increased significantly the much more constants than before. Analytical solutions were also applied to verify the new model. In addition, the difference was also determined, when the frost heave reaction force coefficients were variable and constant, particularly for the frost heave mechanical response of trapezoidal canal lining. The results showed that the frost heave reaction force increased by 0.15 MPa on average, while the frost heave reaction force coefficient decreased by 1.12 MPa/m on average at the same freezing temperature for every 1 cm increase in the constrained frost heave. The frost heave reaction force increased by 0.21 times on average for every 5°C decrease at freezing temperature under the same restricted frost heave amount. As such, the hyperbolic function was used to represent this change suitable for engineering applications. In slope and canal bottom lining slabs, the maximum frost heave reaction force calculated by the constant frost heave reaction force coefficient was 1.43 times the variable, and the maximum bending moment was 1.12 times the variable on average. Therefore, the nonlinear deformation of frozen soil was not considered to avoid a larger value than before, if the frost heave reaction coefficient was constant. Moreover, the significant influence of frost heave reaction coefficient was closely related to the length of lining slab. The maximum bending moment gradually increased and then became stable, while the position of the maximum shifted to the tip of slope, as the length of slope lining slab increased. By contrast, the position of the maximum bending moment changed from the middle to two sides, and the midpoint bending moment first increased and then decreased, as the length of lining slab at the bottom of canal increased. This finding can provide a strong technical support to the design of large-scale trapezoidal canal lining. The frost heave reaction force coefficient was relatively smaller than the actual value, due mainly to the model without considering water migration well. At the same time, it is also necessary to consider the effect of the separation of lining board from the foundation, and the freezing shrinkage of lining board, on the bending in the future research.