梯形断面排水输沙渠道和隧洞最佳宽深比研究

Research on optimal width-depth ratio of drainage and sediment-conveying channels and culverts with trapezoid cross-section

考虑超高与否的渠道和涵洞的最优水力断面的宽深比是不同的,结合排洪和输沙的不同情形,对加设超高的渠道和涵洞的最佳宽深比进行了讨论,并得到相应的公式。与传统的消除微分法相比,用拉格朗日乘数法求解最优宽深比可以使具有一定约束条件的方程归并统一,并使计算得到简化。与未设超高的梯形断面相比,加设超高时最佳的理论边坡系数将有所减小。求得的统一计算公式以及梯形断面排洪输沙的最佳宽深比可以作为相关设计和研究的参考依据。

The optimal width - depth ratio of channels and culverts with freeboard is discussed in the combination of two differ- ent conditions, drainage and sediment - conveying, and the corresponding formulas are obtained. Compared with the convention- al methods of eliminating the differentiation, the Lagrange multiplier method can merge the equations with certain constraint con- ditions and make the calculation simplified. Optimal theoretical slope coefficient with freeboard is smaller than the situation that the freeboard does not exist. The obtained unified computational formula and the optimal width - depth ratio of drainage and sand - conveying channels and culverts with trapezoid cross - section can provide references for relevant design and research.