差异冻胀条件下双参数地基梯形渠道冻胀变形的计算模型

Calculation model for the frost-heaving deformation of trapezoidal canal on two-parameter foundation under uneven frost heave conditions

衬砌冻胀变形便于监测且易于控制,成为《渠系工程抗冻胀设计规范SL23-2006》明确提出的渠道抗冻胀设计控制指标,但规范没有提供差异冻胀变形的具体计算方法。为便捷、合理计算差异冻胀条件下衬砌结构冻胀变形,在现有研究基础上,考虑渠道断面各点地下水位逐点不同及渠基冻土受力变形的连续性,基于双参数冻土地基理论构建了差异冻胀条件下寒区梯形渠道冻胀变形与内力计算模型。以甘肃省靖会总干渠为算例,将该模型退化为均匀冻胀条件下的Winkler模型并进行对比分析,结果表明传统Winkler模型可视为该研究模型的特殊情形。以新疆塔里木灌区某梯形渠道为原型,用幂级数方法对该研究模型进行求解,并与材料力学法、Winkler模型计算值及观测值进行了对比分析。结果表明:应用该研究模型、传统Winkler模型、材料力学方法计算的冻胀变形与观测值的平均相对误差分别为4.31%、9.23%、17.45%,均方根误差分别为0.17、0.29、0.47 cm。可见与材料力学法、传统Winkler模型相比,考虑冻土-衬砌相互作用及冻土中剪力扩散的双参数地基模型能更好地反映差异冻胀条件下梯形渠道的力学行为,计算值与观测值更加一致。通过把形式多样的渠基土自由冻胀量分布统一展开成幂级数形式,可以有效提高模型对不同复杂基土差异冻胀模式的通用性。研究为差异冻胀条件下寒区梯形渠道冻胀力学分析提供了一种有效的计算模型。

Frost-heaving resistance of canals can be designated to evaluate the control parameters in cold regions.As proposed in the national standard of SL23-2006"Design Code for Frost Heave Resistance of Canal System Engineering",the frost-heaving deformation of the canal concrete lining structure can be expected to readily monitor and control in practice.However,the specification cannot provide the specific calculation of uneven frost-heaving deformation in the canal concrete lining.This study aims to facilitate the accurate and practical calculation for the frost-heaving deformation of concrete lining structures under uneven frost-heaving deformation conditions.The fluctuation of groundwater levels was considered across different points along the canal cross-section,together with the continuous deformation within the canal foundation soil.A calculation model was developed for the frost-heaving deformation and internal force of trapezoid concrete lining canal in cold regions under differential frost heave conditions,according to the two-parameter foundation beam of frozen soil.Taking the main trunk canal of Jinghui in Gansu Province as an example,the presented model degenerated into the Winkler model under uniform frost heave conditions.Comparative analysis showed that the traditional Winkler model was regarded as a special case within the proposed model.Some measuring points were simultaneously considered for the shady slope,sunny slope,and bottom of the canal.The Root Mean Square Error(RMSE)between the presented model and observed values was determined to be 0.23,with the Mean Relative Error(MRE)of 4.82%.Taking a trapezoidal concrete lining canal in the Tarim Irrigation area of Xinjiang Uygur Autonomous Region as the prototype,the frost-heaving deformation of the concrete lining structure was calculated at the same time.The results show that the better mechanical performance of the concrete lining canal was achieved in the improved model considering the frozen soil-structure interaction and diffusion of shear force in the frozen soil foundation under uneven frost heave conditions,compared with the material mechanics and traditional Winkler model.The calculated values of the improved model were more consistent with the observation,indicating the rationality and applicability of the model.The engineering example was combined to solve the improved model.The first was the conventional analytical,while the second involved the power series.Among them,the various distributions of free frost heave deformation were expanded into the power series using the comparison coefficient.A special solution with a homogeneous solution was then obtained to introduce the boundary conditions.The general solution was derived for the original control differential equation.The MRE between the frost-heaving deformation was calculated by the power series.Among them,the observed value was 4.31%with an RMSE of 0.17,indicating a reasonable calculation.The power series was utilized to represent the natural frost-heaving displacement of canal foundation soil.Therefore,the improved model effectively enhanced the applicability for the various differential frost-heaving modes in foundation-frozen soil.The mechanical response of frost heave was found in the trapezoidal concrete lining canal under differential or uniform frost-heaving deformation.Then,some implication was gained to clarify the influence of transverse groundwater replenishment on the mechanical behavior of concrete lining structures under the frost-heaving deformation of foundation soil.In addition,the improved model can be expected to effectively capture the non-uniform and asymmetric distribution of tangential freezing force at the contact interface,due to the non-equilibrium axial force on both ends of the bottom plate that is caused by the difference between shady and sunny slopes.The finding can provide an effective computational model for the frost heave mechanics of trapezoidal canals in cold regions,especially on differential frost heave conditions.