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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 of fine its surrounding fluid. It can be directly calculated on plains increases the fertility of farmlands. from the dimensionless particle diameter d , which In urban areas, high suspended 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 , 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 , 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 . load and (2) . 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: , on whether the size fractions can be found in large mixed load, and . In most , 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 . 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 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

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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 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 , 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 -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 , 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

changes in sedi ment trans port capaci ty in velocitthe down-y from eqn [2] is o ¼ ;1 0.027(3) the m ratios o ¼ stream directio n, the trap efficienc y descru* / ibes a4.2, and the Rouse numb er is 0.59 assuming greater potent ial for coarse sedi ment to deposik ffi t.0.4, It thusis most of the sediment is trans ported also interes ting to note that the trap efficiencin suspen y at sion;a (4) the suspende d sediment concentra- given reach length and flow disch arge increasetion s 1 withm below the free surfa ce1 obtaiis 19ned mg l increasi ng sedi ment size o and chann el widfrom th CaW .I¼ti s400 mg1at al ¼ 0.5 m, h ¼ 10 m, a nd therefore noticeabl e at a given discharge thatthe concentriver ration at z ¼ 9 m from eqn [3]; and (5) wideni ng will induce settlin g of suspende dthe seditrap ment efficienc y over a reach lengt h of 500 m from (Julie n, 2002). eqn [5] isE ¼ T0.55, which means that about ha lf Wh en calculating the trap efficienc y of siltthe ansuspende d d sedi ment load would dep osit withi n particl es in backw ater areas like reservoi rshalf and a estu-kilomet er if the trans port cap acity of this river aries, careful consi deration must also be wouldgive n beto suddenl y reduce d. densi ty cu rrents and pos sible floccul ation. ThisFlocc examplula- e is quite instruct ive becau se most of tion of and clay s is a complex su bject,the suspendebut in d itssediment load woul d dep osit very rap- essen ce, the settli ng veloc ity of floc of siltsidly anddespite clays the is fact that most of the sediment is fine 1 typical ly around 0.6 mm. The s settling velocit yand of trans ported in susp ension. EThe indi highcates T flocs incr eases with floc siz e but will rarelythat mostexcee dof the sedi ment woul d also easily be 1 5mm s . trappe d on the flood plai n within sho rt distan ce of As an example to illustrat e the concept s thecovere main d channin el dur ing major floods. Thi s river this article, consid er the Rhine River data fromwould Julienbe very dynami c an d could chan ge morph ol- (2002 ). The flow depth is appro ximately ogy10 m,if itthe wer e not con strained with a series of dikes. main naviga ble ch annel constraine d betw eenFinall ay , seriesthe susp ended sediment concentrat ion near of dikes is ab out 260 m wide, the mean theflow freeveloc su ityrface is only 119compar mg edl with is 1.68 m1 , s an d the friction slope 13.2 .1 cm400 kmmg 1 lne ar the bed, and water inta kes should 1 The sediment co ncentratio n at mid dep ,th definitis 38 elymg bel located near the free surface. 1 and the near-bed concent ration is 400at mga l distan ce of 0.5 m abo ve the rive r bed . If the grai n diamete r of the sediment in suspens ion is 0.2 mm, the follow ing param eters can be calculat edFurther from theReading metho ds covere d in this article: (1) the shear velo- 0 :5 Julien PY (1995) and Sedimentation, 280p. New York: ¼ð Þ city obtai ned from ghSu is approx imately Cambridge University Press. ¼ 1 u* 0.11 m ; s(2) the dimensi onles s particl Juliene diame- PY (2002) River Mechanics, 434p. New York: Cambridge ter is approxim ately 5 from eqn [1] and theUniversity settling Press.

Encyclopedia of Inland Waters (2009), vol. 1, pp. 681-683

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Julien P Y. (2009) Fluvial Transport of Suspended Solids. In: Gene E. Likens, (Editor) Encyclopedia of Inland Waters. volume 1, pp. 681-683 Oxford: Elsevier.