Mechanism of Efficient Sediment Transport by Hyperconcentrated Flow in the Lower Yellow River (Part II)

1. Friction Characteristics of Hyperconcentrated Flow

The magnitude of sediment transport capacity of flow is mainly determined by the hydrodynamic condition (Qi et al., 2002). It is found that in turbulent region, the friction characteristics of hyperconcentrated flow are the same as those of the clear water flow，which can be calculated with Manning’s formula. As shown in Table 1, while sediment concentration ranges from 55 to 843 kg/m³, Manning’s coefficients of hyperconcentrated flow (S >= 200 kg/m³) and low sediment-laden flow (S < 200 kg/m³) at Xiaolangdi Station (Figure 1) on the lower Yellow River are almost the same. The average Manning’s n value for hyperconcentrated flow is 0.041, and 0.039 for low sediment-laden flow. The value of Manning’s coefficient of hyperconcentrated flow is a little bit higher, which is mainly caused by the velocity measurement device itself. 

Table 1 Comparison of Manning’s Coefficients between Hyperconcentrated Flow and Low Sediment-laden Flow at Xiaolangdi Station

Hyperconcentrated Flow (S >= 200 kg/m3)						Low Sediment-laden Flow (S < 200 kg/m3)
Date	Q (m3/s)	S (kg/m3)	H (m)	V (m/s)	n	Date	Q (m3/s)	S (kg/m3)	H (m)	V (m/s)	n
08/07/77	5,240	268	7.5	2.93	0.036	08/01/82	7,450	56.5	8.1	3.48	0.038
08/07/77	5,120	324	7.5	2.74	0.041	08/01/82	7,220	56.5	7.4	3.66	0.036
08/07/77	6,910	592	8.6	3.1	0.043	08/01/82	6,230	56.5	7.1	3.35	0.038
08/07/77	9,720	843	9.7	3.87	0.042	08/02/82	9,400	55	8.6	4.05	0.036
08/08/77	6,550	356	8.9	2.91	0.049	08/02/82	9,290	55	9.2	3.76	0.041
08/08/77	4,950	405	7.6	2.43	0.045	08/02/82	7,710	55	8.6	3.4	0.039
08/28/73	3,110	440	7.2	2.19	0.041	08/02/82	5,150	69.1	7.9	3.03	0.038
08/28/73	3,520	508	7.8	2.39	0.037	08/03/82	5,660	91.1	7.6	2.84	0.041
08/28/73	2,880	324	7.8	2.32	0.036	08/03/82	4,790	99.6	7	2.72	0.037
09/02/73	4,150	313	7.7	2.53	0.040	08/04/82	4,150	82	7.1	2.37	0.041
						08/04/82	3,550	82	6.6	2.29	0.040
						08/05/82	2,970	66.4	7.2	2.01	0.043
Average					0.041	Average					0.039

Note: in this table, Q, S, H, V and n stand for discharge (m³/s), sediment concentration  (kg/m³), average water depth (m), flow velocity (m/s) and Manning’s coefficient. Dates are expressed in MM/DD/YY notation.

2. Effect of Sediment Concentration on Its Vertical Distribution

The increase in sediment concentration and fine particle content results in the increase of flow viscosity and specific weight, and consequently decreases of particle fall velocity. In some cases even mud flow is formed. Based on 96 sets of field data collected from 9 stations along the main stream and tributaries, namely, Huayuankou, Jiahetan, Gaocun, Sunkou, Aishan, Luokou of the lower Yellow River (Figure 1), and Huaxian, Huayin of lower Weihe River (tributary), and Chaoyi of Beiluohe River (tributary), the vertical sediment concentration profile was studied by comparing value of K_s with the cross sectional average sediment concentrations S. Here K_s is the ratio of sediment concentration at the relative depth 0.2h to that at 0.8h (measured from free surface), e.g. K_s = S_0.2 / S_0.8, when median sediment grain size d₅₀ is 0.03 - 0.10 mm. As shown in Figure 2, when the average sediment concentration is lower than 200 kg/m³, even with Froude’s number (Fr) higher than 0.2, the sediment concentration is not uniformly distributed in the vertical direction, where K_s is around 0.4 to 0.8. When the average sediment concentration is higher than 300 kg/m³, the sediment concentration becomes more uniform in the vertical direction, where K_s is around 0.9 to 1.0.

 Figure 2 Relationship between Sediment Concentration Ratio (K_s) and Sediment Concentration (S)

The effect of changes in rheological characteristics of fluid on sediment transport can be analyzed as followings. The ratio of fall velocity of a particle in clear water to that in sediment-water mixture (or muddy-water) can be written with Stokes equation: 

Where ω₀ and ω_s are particle fall velocities in clear water and in sediment water, respectively. γ_s and γ_m are the specific weights of sediment particles and sediment water. μ_r is the ratio of the viscosity of sediment water over clear water. With the increase of sediment concentration, μ_r also increases, which means fall velocity of particles decreases dramatically in sediment water. When d₅₀ = 0.036 mm and percentage of sediment with grain size finer than 0.01 mm is 20% (equivalent to the average sediment gradient of the Yellow River),  calculated values of m_r and w₀/w_s corresponding to the long term average sediment and field observed sediment of lower Yellow River are listed in Table 2.

Table 2 Impact of Sediment Concentration on Fall Velocity

S (kg/m3)	0	100	200	300	400	500	600	700	800	Notes
mr	1.0	1.49	2.08	2.74	3.48	4.32	5.40	6.93	9.33	Average Sediment Data
mr	1.0	1.50	2.0	2.4	3.0	4.0	4.50	6.50	8.50	Observed Sediment Data
w0/ws	1.0	1.55	2.25	3.09	4.10	5.32	6.97	9.38	13.4

As shown in Table 2, with the increase of sediment concentration, w₀/w_s increases continuously, and the fall velocity decreases significantly. When the sediment concentration is 300 kg/m³, the fall velocity in muddy water is only one-third of that in clear water. When the sediment concentration increases to 700 kg/m³, the fall velocity in muddy water is only one-tenth of that in clear water. The above result is in good agreement with the vertical sediment concentration distribution shown in Figure 2. Both indicate that fall velocity decreases with the increasing sediment concentration, and the vertical sediment distribution also becomes more uniform, which makes the sediment particles easier to be transported.

Mechanism of Efficient Sediment Transport by Hyperconcentrated Flow in the Lower Yellow River (Part I)

The Yellow River, the second largest river in China, is well known as a highly sediment-laden river. The average annual sediment inflow entering the Lower Yellow River (Figure 1) is 1.6 billion tons. Every year, there are around 400 million tons of sediment deposit on the lower reach of the Yellow River, which results in raising of river bed with a speed of 10 cm per year. For decades, reduction of channel sedimentation has drawn attention of hydraulic engineers and geomorphologists (Xu, 2003). 

In the 1950, Soil-Water Conservation Project was initialized to control erosion in the Loess Plateau of the middle basin, which contributes 90% of the sediment loads. However, this project cannot completely solve the sediment problem, since there will be still 800 million tons of sediment yields annually after the project is finished (Qi and Li, 1996).  As early as the 1960s, the hyperconcentrated flow occurring on the Loess Plateau has been field investigated by hydraulic engineers. The research on hyperconcentrated flow of the Yellow River, which was originated by Dr. Ning Chien (Chien and Wan, 1999) in 1950’s, opens a new path by making full use of the channel for sediment transport. It has been evolved from pure theory into real engineering practices in recent years. 

Figure 1 Major Tributaries and Hydrologic Stations of Middle and Lower Yellow River in China

In the first International Workshop on Hyperconcentrated Flow held in Beijing in 1985, scientists from United States reported on the sediment transportation by lahars and hyperconcentrated flows at Mount St. Helens, Washington (Scott and Dinehart, 1985, Janda and Meyer, 1985, Pierson and Scott, 1985). Brown (1988) advanced the understanding of sediment transport of bed material discharged in sand bed channels through the developed theoretical concepts related to the effects of high concentration of suspended sediment of the water-sediment mixture along a 27-mile reach of the Cowlitz and Toutle Rivers in Washington. Julien and Lan (1991) used a physically based quadratic rheological model to test hyperconcentrated flows with experimental data. The model considers (1) cohesion between particles; (2) viscous friction between fluid and sediment particles; (3) impact of particles; and (4) turbulence. The resulting quadratic formulation of the shear stress was shown to be in excellent agreement with the experimental data sets. Rickenmann (1991) simulated fine-material slurry of a debris flow in a steep flume. The results showed that viscous effects became important below a limiting particle Reynolds number of about 10. Above this limiting value, density effects cause an increase in the bed-load transport rates as compared to similar conditions with clear water as transporting fluid.

In the book authored by Wang and Wan (1994), the rheological properties of hyperconcentrated flows were further revealed, as well as the mechanism of surface instability and drag reduction. Batalla et al. (1999) analyzed the hyperconcentrated flow occurred after collapse of a bridge in the Pyrenean Arás basin, Spain. The flood was characterized by transportation of large amounts of slope material, including debris flows. Along the main tributary, an intensive hyperconcentrated flow was observed during the rising stage, whereas in the main valley smaller flows occurred after failure of check dams. Lavigne and Suwa (2004) carried out observation of debris flows, hyperconcentrated flows, and stream flows in the Curah Lengkong River on the southeast slope of Mount Semeru in East Java, Indonesia. This study provided quantitative data for these flows in motion, and it also compared the data for different types of flow that occur in the same river. The influence of rainfall on debris flows, hyperconcentrated flows, and streamflow generation was also analyzed. A detailed case study in a small catchment on the Loess Plateau conducted by Hessel (2005) indicated that a number of corrections are necessary to be able to compare field measurements with results of soil erosion models: sediment volume should be subtracted from runoff volume and a density correction is needed to use data from a pressure transducer.

These researches above mainly focused on hyperconcentrated flow in the mountainous region with relatively steep slope. However, the sediment concentration of the lower Yellow River with a mild slope can reach above one thousand kg/m3, and the fine sediment particle content is also the highest in the world. When the sediment concentration reaches a certain threshold, the fluid characteristics of the muddy water and its sediment carrying capacities also change substantially. Such change makes it more efficient for sediment transport, and the deposition of the sediment on river bed can also be greatly reduced. Based on the field data analysis, this paper discusses efficient sediment transport mechanism of hyperconcentrated flow in the Yellow River.