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基于不完全自相似原理和量纲分析的渭河高精度挟沙力计算

A high-precision calculation formula for the sediment carrying capacity of Weihe River based on incomplete self-similarity principle combined with dimensional analysis

  • 摘要: 水流挟沙力是河流动力学的核心问题之一。受制于含沙水流运动的复杂性,以往的研究倾向采用实测资料率定部分系数,同时对水力泥沙特征的考虑不够全面,因此计算模型的精度和普适性有待进一步提升。为进一步寻求在渭河水沙特性下有效的挟沙力计算式,该研究收集了下游3个水文站2006—2023年746组准平衡状态的观测资料,采用量纲分析构建了以无量纲参量为基础的挟沙力基本表达式,阐明了二者间的不完全自相似关系,确定多个待定常数,以此得到挟沙力计算公式,最后引入含沙量对模型进行修正。结果表明,该研究提出的最优模型相关系数r为0.98,相对误差δ为0.07,而集中系数和偏离系数则分别为1.01和0.07,具有较高的预测精度;由于不同河流特性存在差异,这一模型优于以往几个基于实测资料构建的半理论公式。研究成果扩宽了已有挟沙力计算思路,可为渭河河道管理工作提供理论支撑。

     

    Abstract: The capacity of water flow to transport sediment is one of the most fundamental indicators of river dynamics. Previous studies often use the measured data to determine the part of the coefficient, due to the complexity of the sediment-bearing flow movement. It is often required to consider the hydraulic sediment characteristics. The accuracy and universality of the model also need to be further improved in recent years. This study aims to predict the high-resolution sediment-carrying capacity of the Weihe River using incomplete self-similarity with dimensional analysis. A total of 746 sets of quasi-equilibrium observation data were gathered from three hydrological stations in the lower sections of the Weihe River from 2006 to 2023. Specifically, the flood data was measured from three hydrological stations in Xianyang, Lintong, and Huaxian City. The simple processing was carried out to obtain the characteristic parameters, such as the water depth, velocity, sediment content, median particle size, and settling velocity. A precise formula was developed to calculate the sediment transport capacity considering the specific water and sediment properties of the river. The sediment transport capacity was derived using dimensional analysis. An expression was also involved using nondimensional parameters. The relationship between the dimensionless parameter and sediment transport capacity was explained using ideal assumptions. The incomplete self-similarity was also highlighted. Additionally, several undetermined constants were determined to refine the calculation formula, according to measured data. Given the current performance of the calculation, the model was adjusted to incorporate the sediment content. The results indicate that the Velikanov parameter R was more suitable for the prediction model, compared with the Froude number Fr. The sediment transport capacity was obtained using the Velikanov parameter, indicating the strong prediction under the fundamental principles of water flow dynamics; Specifically, the rougher river bed was, the smaller sediment carrying capacity of the water flow was. The multi-factor incomplete self-similar relationship was dominated by the interaction of variables. The exponential term of the incomplete self-similar model was the interaction of dimensionless parameters in the formula structure. The complex sediment transport was then simulated to enhance the performance of the model using conventional regression. The sediment content was one of the crucial influencing factors on the capacity of the water flow to transfer sediment. However, the mathematical derivation was used to define the incomplete self-similar relationship between sediment concentration and sediment carrying capacity; Once the sediment concentration approached 0, the sediment carrying capacity was converged at the same time. The prediction error substantially decreased to consider this variation. Three components were considered for the highest performance, with a correlation coefficient of 0.98 and a relative error of only 0.07. The concentration coefficient and deviation coefficient were 1.01 and 0.07, respectively. This model also surpassed the several prior formulas after river test data, due to the variations in the features of different rivers. Excellent prediction accuracy was achieved at both high and low sediment content. Thus, the model can be utilized to forecast the sediment-transport capacity of the lower Weihe River, which is characterized as a sediment-laden river. Due to the clarity of the formula structure, the coefficients of the other types of rivers can still be re-calibrated by the measured data for the feasible calculation of sediment carrying capacity. At the same time, this finding can also provide some research examples for the sediment carrying capacity on the estuary flow slope.

     

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