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Fluvial Transport of Suspended Solids
P Y Julien, Colorado State University, Fort Collins, CO, USA
ã 2009 Elsevier Inc. All rights reserved.
0:5 Introduction shear velocity u ¼ðghSÞ is approximately equal to the square root of the product of gravitational The fluvial transport of suspended solids is of great acceleration g, flow depth h, and friction slope S. interest to living communities. It has been known for The settling velocity is a property of the particle in a very long time that the deposition of fine sediments its surrounding fluid. It can be directly calculated on flood plains increases the fertility of farmlands. from the dimensionless particle diameter d , which In urban areas, high suspended sediment concen- * is defined from the particle diameter d , the specific trations adversely impact the quality of drinking s gravity G of sediment, the kinematic viscosity of the water and increase the operation cost of water treat- fluid n, and the gravitational acceleration g,as ment plants. During floods, the excessive suspended ð 1Þ 1=3 sediment concentrations can also cause major sedimen- ¼ G g ½1 d ds 2 tation problems resulting in aggradation, river naviga- v tion problems, and changes in river morphology. On Simplified calculations are obtained with the grain the other hand, riverbed degradation from a lack of fine diameter (m), the kinematic viscosity (n ¼ 1 10 6 sediment in suspension can also undermine the stability m2 s 1), g (9.81 m s 2), and G (2.65). The settling of bridges and river protection structures. o 1 velocity (m s ) of a sediment particle in clear water is then calculated from () 8 3 0:5 Equilibrium Transport of Sediment v d ! ¼ 1 þ 1 ½2 ds 72 Suspensions o There are two types of sediment sizes that contribute The ratio of shear velocity u* to settling velocity to the suspended sediment load of a river: (1) wash determines the primary mode of sediment transport. load and (2) bed material load. The difference The bed material can be subdivided into three zones between wash load and bed material load depends describing the dominant mode of transport: bed load, on whether the size fractions can be found in large mixed load, and suspended load. In most rivers, bed o quantities in the bed. The size fractions that are found load is dominant at values of u*/ less than about 0.4. Note that incipient motion corresponds to u /o ffi 0.2, in large quantities in the bed are referred to as bed * material load. In practice, all size fractions that are which means that the bed material does not move < o finer than the d10 of the bed material will be consid- when u* 0.2 . A transition zone called mixed load is found where 0.4 < u /o < 2.5 in which both the bed ered wash load. The wash load does not depend on * the sediment transporting capacity of the flow, but load and the suspended load contribute to the total o > depends on the supply of sediment from upstream load. When u*/ 2.5, most of the sediment load is sources or from the river bank. transported in suspension. Field measurements are
The quantity of wash load can only be determined necessary to determine the rate of sediment transport. from field measurements. Suspended sediment sam- The concentration of suspended sediment in rivers pling is usually done with a point sediment sampler of varies with depth. The suspended sediment concen- tration C at an elevation z above the bed for the the type P-61 or P-63. Point sediment samplers are designed to collect sediment through time at a given suspended load can be calculated from the Rouse point along the stream vertical. The sampler weight is equation as the primary difference between the P-61 (100 lb) and != h z a u P-63 (200 lb) and heavy samplers must be used in C ¼ C ½3 a z h a deep and fast-flowing rivers. Figure 1 shows a P-63 sampler on the Mississippi River. where Ca is the concentration at an elevation a above k The bed material load in suspension requires basic the bed, h is the flow depth, and is the von Karman knowledge of the properties of the flow and of the constant (k ffi 0.4). The exponent of this equation is transported sediment. In a very simplified form, called the Rouse number Ro ¼ o/ku*, which varies o two main properties describe suspended sediment with u*/ . The near-bed concentration can be obtained transport in rivers: (1) the shear velocity of the flow from point sediment concentration measurements and (2) the settling velocity of the bed material. The near the bed, or in the lower part of the water
681 Encyclopedia of Inland Waters (2009), vol. 1, pp. 681-683
Author's personal copy
682 Hydrology _ Fluvial Transport of Suspended Solids column. The Rouse number can be experimentally of the sediment flux describes the unit sediment dis- obtained as the slope of the linear fit to the con- charge or amount of sediment being transported per centration profile obtained after a logarithmic trans- unit channel width qtx. It represents a volume of formation, as shown in Figure 2. sediment per unit width.
The sediment flux per unit area is the product of the flow velocity and sediment concentration. For Nonequilibrium Transport of Sediment instance, the volumetric flux of sediment is obtained Suspensions from the product of the volumetric sediment concen- tration, the flow velocity, and the unit area. Because As rivers approach reservoirs, lakes, and estuaries, the flow velocity and sediment concentration vary the reduced sediment transport capacity in the back- with depth and width, it is necessary to integrate the water areas causes deposition of the suspended sedi- ment load. Owing to the continuity of sediment, the velocity and concentration profiles along the vertical and across the entire width of a river to determine the equation of conservation of mass determines the sediment flux. This integral is very complex and is changes in vertical elevation from settling when there is a decrease in sediment transport in the down- discu ssed in detail in Julien (1995). The depth inte gral stream direction. This equation of conservation of mass shows that the settling sediment flux in the z
direction causes a change in bed surface elevation zb:
@ @ zb ¼ TE qtx ½4
@t ð1 p0Þ @x
The porosity p0 depends on the specific weight of
sediment deposits and is approximately 0.43 for sand-bed rivers. The trap efficiency TE describes the fraction of sediment that would deposit in a given river reach of length X. It is therefore a measure of
how much sedimentation could take place in backwa- ter flow conditions. Trap efficiency is a function of the reach length X, the river width W, the flow dis-
charge Q, the mean flow velocity V, and the settling velocity o as X! WX! TE ¼ 1 exp ¼ 1 exp ½5 hV Q
This relationship for the trap efficiency of sediment can be useful. At a given flow discharge, the trap
Figure 1 Suspended sediment sampling on the Mississippi efficiency remains very small for very short reaches River. and for very fine sediment particles (low o). Under
102 Run 19 Run 55 Vanoni, 1946 h = 0.590 ft h = 0.236 ft d50 =0.10mm k d50 =0.10 mm = 0.34 k 10 = 0.33 1 1 Ro = z )/
- Ro = 0.49 Run S-16 ( h 0.63 1 Einstein and R = 1 o Chien, 1955 1.86 h = 0.390 ft
d50 =0.274mm k =0.18
− Suspension Hyper-conc. 10 1 10−2 10−1 110102 103
Concentration C (g/l )
Figure 2 Examples of sediment concentration profiles (from Julien, 1995).
Encyclopedia of Inland Waters (2009), vol. 1, pp. 681-683
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Hydrology _ Fluvial Transport of Suspended Solids 683