BED LOAD SEDIMENT TRANSPORT
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1 BED LOAD SEDIMENT TRANSPORT Kamal EL KADI ABDERREZZAK EDF-R&D, Laboratoire National d Hydraulique et Environnement (LNHE) September 2009 UNL, Santa Fe, Argentina
2 OUTLINE I. Bed load II. Settling velocity III. Incipient motion of sediment particles IV. Sediment sorting V. Bedload sediment transport capacity formulas 2
3 OUTLINE I. Bed load II. Settling velocity III. Incipient motion of sediment particles IV. Sediment sorting V. Bedload sediment transport capacity formulas 3
4 MODES OF SEDIMENT TRANSPORT (1/3) Bed material load is that part of the sediment load that constantly exchanges with the bed Significant contribution to the channel morphology Bed material load is subdivided into bedload and suspended load Bedload: sliding, rolling or saltating in ballistic trajectory just above bed Suspended load: moves through the fluid 4
5 MODES OF SEDIMENT TRANSPORT (2/3) Wash load is transported through without interaction with the bed Material finer than mm (silt and clay) Washload moves in suspension and does exchange with the floodplain Definition of bedload, suspended load and wash load depends on flow and sediment conditions Bedload may become suspended load under rapidly flow Some wash load in upstream channels may become bed-material load in downstream channels due to the weakening of flow strength 5
6 MODES OF SEDIMENT TRANSPORT (3/3) Hjulstrom described the relationship between particle size and flow velocity required for erosion, Transport suspended or bed load and 6
7 BED LOAD (1/2) Bed load generally constitutes between 5 and 20% of the total load Particles move discontinuously by rolling or sliding at a slower velocity than the stream water, but may move short distances by saltation (series of short intermittent jumps) (Mode A) At larger stresses (Mode B), sediment particles move in several layers (sheet flow layer) At much more large stresses, some finer particles may go into suspension (Mode C) Sheet flow layer Video clip from the experiments of Miguel Wong 7
8 BED LOAD (2/2) Sheet flow When τ 0 > τ 0,sheet (τ 0 is the Shields number) the bedload layer devolves into a sliding layer of grains Sheet flows occur in unidirectional river flows Values of τ 0,sheet have been variously estimated as 0.5 ~ 1.5 (Gao, 2003) τ 0,sheet appears to decrease with increasing Froude number Wilson (1987): distribution of concentration (C) is approximately linear; Thickness 10d Channel lope= d = mm V = 1.05 m/s Fr = 1.85 τ sheet * = Video clip courtesy P. Gao and A. Abrahams; Gao (2003)
9 OUTLINE I. Bed load II. Settling velocity III. Incipient motion of sediment particles IV. Sediment sorting V. Bedload sediment transport capacity formulas 9
10 SETTLING VELOCITY (1/2) The seteling (or fall) velocity depends on particle size, shape, submerged specific weight, water viscosity, sediment concentration Navier-Stokes formula for a spherical particle under laminar flow condition 2 1 ρ s ρ d ωs = g 18 ρ υ van Rijn s (1984) formula for natural rivers Stokes law for d<0.1 mm Zanke (1977) formula for 0.1<d<1 mm 1/ 2 3 υ ρ s gd ωs = d ρ υ For d>1 mm ρ s ωs = gd ρ 1/ 2 ρ, ρ s =density of the water and sediment, respectively, ν =viscosity of water Relation of fall velocity with particle size, shape factor, and temperature (U.S. Interagency Committee, 1957) 10
11 SETTLING VELOCITY (2/2) Influence of sediment concentration on the settling velocity The settling velocity in turbid water is strongly reduced in comparison with that in clear water (hindered settling effect) ω = ( 1 ) n sm c ωs Richardson and Zaki (1954) Comparison between selected formulas for the fall velocity ω sm = sediment settling velocity in turbid water,,c =sediment concentration, n =exponent ranging between 2.3 and 4.9 She et al. (2005) R e = ω sd υ 11 d 3 g ( ρ / ρ 1) s 2 υ
12 OUTLINE I. Bed load II. Settling velocity III. Incipient motion of sediment particles IV. Sediment sorting V. Bedload sediment transport capacity formulas 12
13 SHIELDS DIAGRAM (1/2) The Shields number τ 0 τ τ 0 = g( ρ s ρ)d τ = bed shear stress Shields (1936) determined experimentally that a minimum, or critical Shields number τ 0,cr is required to initiate motion of the grains of a bed composed of non-cohesive particles The original Shields curve using wider ranges of laboratory data τ 0 13 U * d Re p = υ Shields curve modified by Chien and Wan (1983)
14 SHIELDS DIAGRAM (2/2) The relation between τ 0,cr and Re p is not explicit Guo (1990) fitted a curve to the experimental line of Shields τ 0, cr 0.23 = exp * d * ( d ) d=d[(ρ/ρ s 1)g/ν 2 ] 1/3 =non-dimensional particle size In the limit of sufficiently large Re p (fully rough flow), τ 0,cr becomes equal to 0.03 (Brownlie 1981) (=0.045 Yalin et Karahan (1979), =0.06 Guo (1990)) τ 0,cr deceases when bed slope, side slope or h/d increase (h=flow depth) τ τ 0, cr 0, cr( Shields) τ τ 0, cr 0, cr( Shields) 14 Side slope Parker (2007)
15 THRESHOLD OF NON- UNIFORM SEDIMENT PARTICLES (1/3) The Shields curve is no longer valid when the bed sediment consists of a larger range of grain sizes In a non-uniform sediment mixture, large grains are more exposed to the flow, thus having lower critical shear stresses (exposure phenomena) Smaller grains are hiding in the wake of larger grains and therefore have hiher critical shear stress (hiding phenomena) 15 Video clip by Alain Recking; Recking et al. (2008)
16 THRESHOLD OF NON- UNIFORM SEDIMENT PARTICLES (2/3) 16 The effect of exposure and hiding on the entrainment of sediments was first quantified by Egiazaroff (1965): theoretical correction for all grain size d k τ 0, cr ( d ) = τ k 0, cr ( d 50 ) log 19 d k d 50 2 In practice, the critical shear stress is corrected with an empirical relation of the form τ d = τ k 0, cr ( dk ) 0, cr ( d50 ) d50 γ γ = 0 yields the case of grain independence: there are no hiding effects γ = 1 yields the equal threshold condition: hiding is so effective that it completely counterbalances mass effects, all grains in a mixture move at the same critical boundary shear stress, and critical Shields number increases as grain size d k to the -1 power Buffington and Montgomery (1997) (Water Resources Research) provide an overview of several relations for correcting the critical shear stress of a particle d k due to the hiding-exposure effect
17 THRESHOLD OF NON- UNIFORM SEDIMENT PARTICLES (3/3) In the most general way, the threshold conditions in a given mixture can be represented, in the Re p plane, by a deformed Shields curve, which intersects the Shields curve for uniform sediment at a point P where no correction is needed Many formula for assume that the point P is given by the diameter d 50 The degree of deformation away from the Shields curve depends upon the degree of non-uniformity of the sediment mixture 17 Bettess and Frangipane (2003)
18 OUTLINE I. Bed load II. Settling velocity III. Incipient motion of sediment particles IV. Sediment sorting V. Bedload sediment transport capacity formulas 18
19 VERTICAL SORTING In low flow, only finer sediment transport can be transported A coarse surface may develop that inhibits the entrainment of finer, underlying sediment. This surface is called armour Gravel-bed rivers often display a coarse surface armor or pavement In sand rivers with dunes, the coarsest sediment are usually placed in a layer corresponding to the base of the dunes Armour layer in the Rhine river Video clip by Alain Recking; Recking et al. (2008) 19 Kleinhans (2002)
20 HORIZONTAL SORTING Horizontal sorting is often observed in cross-sectional direction, e.g. meander bends, tops of bars Laboratory experiments by Lisle et al. (1993) The response of a channel with a topography and bed material size typical of gravel bed rivers to reductions in sediment supply Laboratory flume filled and fed with a sand-gravel mixture After a series of quasi-stationary alternate bars were formed, feed rate was reduced. 20 Plan View showing of a rectangular channel the horizontal sorting of channel bed material. Laboratory experiments by Lisle et al. (1993)
21 DOWNSTREAM FINING 21 The size of river sediment normally decreases in the downstream direction, from boulders in mountain streams to silt and sand The sediment material composing bed load is gradually reduced in size by selective transport and abrasion Sternberg formulation (1875): an exponential decrease in the sediment diameter in the Rhine River Depends on the flow condition, sediment transport rate, bed meterial size (Robinson and Slingerland 1998) Seal et al. (1997) found that is in the range m -1 for natural rivers The formulation is not valid in all cases (e.g. Cosmunes Rivers) Abrupt change in channel bed slope, role of tributaries Median diameter of bed material in the Cosmunes River (USA) (Constantine et al., 2003)
22 OUTLINE I. Bed load II. Settling velocity III. Incipient motion of sediment particles IV. Grain sorting V. Bedload sediment transport capacity formulas 22
23 BEDLOAD SEDIMENT TRANSPORT CAPACITY Potential rate of sediment that can be transported for given flow conditions Many formulas exist, derived using different laboratory and field datasets and usually under simplifying assumptions about flow Most bedload formulas are expressed as a function of the excess in shear stress (τ 0 -τ 0,cr ) 23 After Garica (2007), pp 72-73
24 COMPARISON BETWEEN BEDLOAD FORMULAS Chien (1980) compared the formulas of Einstein (1942), Meyer-Peter and Mueller (1948), Bagnold (1966), and Yalin (1972) with measured data For weak sediment transport (τ 0 <0.5),the Yalin formula underpredicts the bedload transport rate, while the other formulas provide reasonably good predictions For strong sediment transport (τ 0 >0.5), the predictions of these formulas are significantly different 1/ τ 0 3 ( gρ s ( ρ s / ρ 1) ) / gd Chien (1980) 24 q s
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