基于能坡划分原理的大比降山区河流阻力特性

在山区河流水沙灾害河道修复中，河道阻力系数是一个非常重要的参数。普通天然河道的达西阻力系数是水深h与泥沙粒径d比值的函数，而在山区大比降粗糙河道中，其值随着坡降的改变而变化。为探究大比降河道达西阻力变化规律，该研究通过变坡水槽试验设置3种坡度（10°、25°、35°）更大的河道，试验时床面铺设中值粒径为0.5、1和1.85 mm的3种天然沙，流量设定为0.5～2.5 L/s，淹没度范围h/d为0.84～7.27，采取试验数据和经典文献数据共计48组，涵盖河道坡度范围0.97°～35°（对应比降S范围为17‰～573.6‰），进而建立能够反映滚波影响的适用于山区大比降河流的达西阻力表达式。结果表明：1）大比降河道水流表面会产生滚波，使得达西阻力系数增大；2）大比降河流的能坡可划分为两部分：正常河道无滚波时的能坡以及河道水面滚波产生的额外能坡，前者及其对应的达西阻力系数可以利用传统的对数公式进行求取，后者可以利用总能坡与无滚波时的能坡相减得到；3）将建立的比降达西阻力公式计算结果与实测数据比较，可以发现绝大部分数据落在±20%误差线中，说明该研究提出的公式的计算精度较高。研究建立的大比降河流阻力计算模型可以揭示大比降河道水流能量消耗机理，为后续研究大比降河流问题提供理论基础。

Friction factor of river channel flows in rough steep slope mountaineous areas using energy slope division

Abstract: The corridor restoration of mountain river channels has been a considerable object over the past four decades. Among them, the friction factor of river channels can be one of the most important variables in the theory of stream corridor restoration. The Daycy friction factor is a function of the depth-to-sediment diameter (h/d) ratio for the traditional open channel flows. However, the friction factor formula is not applicable for the open channel flows on the rough steep slope mountain. The friction factor is dependent on both the h/d and energy slope S. In this study, an impervious flume with the adjustable slope was designed to investigate the river resistance of the steep slope mountain in the laboratory. The flume bottom was covered with uniform sediment in the diameter of 0.5, 1, and 1.85 mm. The flow discharge varied from 0.5 to 2.5 L/s. The h/d (divergence) was within the range of 0.84-7.27. Three slopes with the degree of 10°, 25°, and 35° were used to test the effect of the slope on the resistance factor. Experimental results show that the Darcy friction factor was larger than that for the traditional open channels, due to the roll waves on the water surface of the mountain rivers channels. The variable roll waves modified the flow resistance, leading to the stage-discharge relationship of the channel conveyance. Assume that the energy slope in a steep slope mountain channel was divided into two major components, i.e., the energy slope S1 without the roll waves, and the other S2 related to the roll waves. The energy slope S2 was caused by the roll waves that were created on the water''s surface. The rolling wave occurred on the much larger slope of open channel. The Colebrook-White formula was used to calculated the energy slope without the roll waves S1 or related friction factor f1. An indirect empirical treatment was carried out to measure the roll wave with the energy slope S2. The formula of S2 and the related friction factor f2 were derived from the energy slope S2 using present experimental data. Among them, the energy slope S2 increased with the total slope S. Finally, a semi-analytical model was developed to compute the Darcy friction factor for the steep slope open channels. The total Darcy friction factor was set as the sum of two friction components, corresponding to the traditional open channel and roll wave resistance: f=f1+f2. A total of 48 datasets of measured flume data were selected to test the validity of the present energy division formula. Each data set included the complete records of flow discharge, channel width, water depth, energy slope, median sediment size, and specific gravity of sediment. The comprehensive database covered a wide range of slopes in the mountain river channels. A comparison was made between the present formula with the measured data. Nearly all the data lay within the ±20% error band, indicating excellent consistency. Furthermore, the present formula was also developed on the basis of the mechanism of steep slope mountain river energy dissipation. The finding can provide a fundamental theory for the mountain river.