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Sediment transport

Sediment transport is the movement of solid particles (sediment), typically due to a combination of the force of gravity acting on the sediment, and/or the movement of the fluid in which the sediment is entrained.

An understanding of sediment transport is typically used in natural systems, where the particles are clastic rocks (sand, gravel, boulders, etc.), mud, or clay; the fluid is air, water, or ice; and the force of gravity acts to move the particles due to the sloping surface on which they are resting. Sediment transport due to fluid motion occurs in rivers, the oceans, lakes, seas, and other bodies of water, due to currents and tides; in glaciers as they flow, and on terrestrial surfaces under the influence wind. Sediment transport due only to gravity can occur on sloping surfaces in general, including hillslopes, scarps, cliffs, and the continental shelf—continental slope boundary.

Sediment transport is important in the fields of sedimentary geology, geomorphology, civil engineering and environmental engineering (see applications, below). Knowledge of sediment transport is most often used to know whether erosion or deposition will occur, the magnitude of this erosion or deposition, and the time and distance over which it will occur.

A plume of dust blows off of the Sahara Desert and sails over Atlantic Ocean towards the Canary Islands.

Mesquite Dunes, Death Valley, California. Ripples and dunes form as a natural self-organizing response to sediment transport.

Content Table

Mechanisms
Applications
Initiation of motion
Modes of entrainment
- Rouse number
- Settling velocity
Transport rate
Related Articles
References
Links

Mechanisms

Aeolian

Sand blowing off a crest in the Kelso Dunes of the Mojave Desert, California.

Aeolian or eolian (depending on the parsing of æ) is the term for sediment transport by wind. This process results in the formation of ripples and sand dunes. Typically, the size of the transported sediment is fine sand (<1 mm) and smaller, because air is a fluid with low density and viscosity, and can

therefore not exert very much shear on its bed.

Aeolian sediment transport is common on beaches and in the arid regions of the world, because it is in these environments that vegetation does not prevent the presence and motion of fields of sand.

Wind-blown very fine-grained dust is capable of entering the upper atmosphere and moving across the globe. Dust from the Sahara deposits on the Canary Islands and islands in the Caribbean,^[1] and dust from the Gobi desert has deposited on the western United States.^[2] This sediment is important to the soil budget and ecology of several islands.

Soil formed from wind-blown glacial sediment is called loess.

Fluvial

Toklat River, East Fork, Polychrome overlook, Denali National Park, Alaska. This river, like other braided streams, rapidly changes the positions of its channels through processes of erosion, sediment transport, and deposition.

In geology, physical geography, and sediment transport, fluvial processes relate to flowing water in natural systems. This encompasses rivers, streams, periglacial flows, flash floods and glacial lake outburst floods. Sediment moved by water can be larger than sediment moved by air because water has both a higher density and viscosity. In typical rivers the largest carried sediment is of sand and gravel size, but larger floods can carry cobbles and even boulders.

Fluvial sediment transport can result in the formation of ripples and dunes, in fractal-shaped patterns of erosion, in complex patterns of natural river systems, and in the development of floodplains.

Coastal

Sand ripples, Laysan Beach, Hawaii. Coastal sediment transport results in these evenly-spaced ripples along the shore. Monk seal for scale.

Coastal sediment transport takes place in near-shore environments due to the motions of waves and currents. At the mouths of rivers, coastal sediment and fluvial sediment transport processes mesh to create river deltas.

Coastal sediment transport results in the formation of characteristic coastal landforms such as beaches and barrier islands. In coastal-fluvial systems, river deltas form.

Glacial

A glacier joining the Gorner Glacier, Zermatt, Switzerland. These glaciers transport sediment and leave behind lateral moraines.

Glaciers can carry the largest sediment, and areas of glacial deposition often contain a large number of glacial erratics, many of which are several meters in diameter.

Hillslope

In hillslope sediment transport, a variety of processes move regolith downslope. These include:

Soil creep
Tree throw
Movement of soil by burrowing animals
Slumping and landsliding of the hillslope

These processes generally combine to give the hillslope a profile that looks like a solution to the diffusion equation, where the diffusivity is a parameter that relates to the ease of sediment transport on the particular hillslope. For this reason, the tops of hills generally have a parabolic concave-down profile, which grades into a concave-up profile around valleys.

Applications

Suspended sediment from a stream emptying into a fjord (Isfjorden, Svalbard, Norway).

Sediment transport is applied to solve many environmental, geotechnical, and geological problems.

Movement of sediment is important in providing habitat for fish and other organisms in rivers. Therefore, managers of highly-regulated rivers, which are often sediment-starved due to dams, are often advised to stage short floods to refresh the bed material and rebuild bars. This is also important, for example, in the Grand Canyon of the Colorado River, to rebuild shoreline habitats also used as campsites.

Sediment discharge into a reservoir formed by a dam forms a reservoir delta. This delta will fill the basin, and eventually, either the reservoir will need to be dredged or the dam will need to be removed. Knowledge of sediment transport can be used to properly plan to extend the life of a dam.

Geologists can use inverse solutions of transport relationships to understand flow depth, velocity, and direction, from sedimentary rocks and young deposits of alluvial materials.

Flow in culverts, over dams, and around bridge piers can cause erosion of the bed. This erosion can damage the environment and expose or unsettle the foundations of the structure. Therefore, good knowledge of the mechanics of sediment transport in a built environment are important for civil and hydraulic engineers.

Initiation of motion

Stress balance

For a fluid to begin transporting sediment that is currently at rest on a surface, the boundary (or bed) shear stress τ_b exerted by the fluid must exceed the critical shear stress τ_c for the initiation motion of grains at the bed. This basic criterion can be for the initiation of motion can be written as:

τ_b = τ_c.

This is typically represented by a comparison between a dimensionless shear stress (τ_b * )and a dimensionless critical shear stress (τ_c * ). The nondimensionalization is in order to compare the driving forces of particle motion (shear stress) to the resisting forces that would make it stationary (particle density and size). This dimensionless shear stress, τ * , is called the Shields parameter and defined as:

$\tau*=\frac{\tau}{(\rho_s-\rho)(g)(D)}$ .

And the new equation to solve becomes:

τ_b * = τ_c * .

The equations included here describe sediment transport for clastic, or granular sediment. They do not work for clays and muds because these types of floccular sediments do not fit the geometric simplifications in these equations, and also interact thorough electrostatic forces. They were also designed fluvial sediment transport of particles carried along in a liquid flow, such as that in a river, canal, or other open channel.

Critical shear stress

The Shields diagram empirically shows how the dimensionless critical shear stress required for the initiation of motion is a function of a particular form of the particle Reynolds number, Re_p or Reynolds number related to the particle. This allows us to rewrite the criterion for the initiation of motion in terms of only needing to solve for a specific version of the particle Reynolds number, which we call Re_p * .

$\tau_b*=f\left(Re_p*\right)$

This equation can then be solved by using the empirically-derived Shields curve to find τ_c * as a function of a specific form of the particle Reynolds number called the boundary Reynolds number.

Particle Reynolds Number

In general, a particle Reynolds Number has the form:

$Re_p=\frac{U_p D}{\nu}$

Where U_p is a characteristic particle velocity, D is the grain diameter (a characteristic particle size), and ν is the kinematic viscosity, which is given by the dynamic viscosity, μ, divided by the fluid density, ρ.

$\nu=\frac{\mu}{\rho}$

The specific particle Reynolds number of interest is called the boundary Reynolds number, and it is formed by replacing the velocity term in the Particle Reynolds number by the shear velocity, u _* , which is a way of rewriting shear stress in terms of velocity.

$u_*=\sqrt{\frac{\tau_b}{\rho_w}}=\kappa z \frac{\partial u}{\partial z}$

where τ_b is the bed shear stress (described below), and κ is the von Kármán constant, where

κ = 0.407.

The particle Reynolds number is therefore given by:

$Re_p*=\frac{u* D}{\nu}$

Bed shear stress

The boundary Reynolds number can be used with the Shields diagram to empirically solve the equation

$\tau_c*=f\left(Re_p*\right)$ ,

which solves the right-hand side of the equation

τ_b * = τ_c * .

In order to solve the left-hand side, expanded as

$\tau_b*=\frac{\tau_b}{(\rho_s-\rho)(g)(D)}$ ,

we must find the bed shear stress, τ_b. There are several ways to solve for the bed shear stress. First, we develop the simplest approach, in which the flow is assumed to be steady and uniform and reach-averaged depth and slope are used. Due to the difficulty of measuring shear stress in situ, this method is also one of the most-commonly used. This method is known as the depth-slope product.

Depth-slope product

Main article: Depth-slope productFor a river undergoing approximately steady, uniform equilibrium flow, of approximately constant depth h and slope θ over the reach of interest, and whose width is much greater than its depth, the bed shear stress is given by some momentum considerations stating that the gravity force component in the flow direction equals exactly the friction force ^[3]. For a wide channel, it yields:

τ_b = ρghsin(θ)

For shallow slopes, which are found in almost all natural lowland streams, the small-angle formula shows that sin(θ) is approximately equal to tan(θ), which is given by S, the slope. Rewritten with this:

τ_b = ρghS

Shear velocity, velocity, and friction factor

For the steady case, by extrapolating the depth-slope product and the equation for shear velocity:

τ_b = ρghS

$u_*=\sqrt{\left(\frac{\tau_b}{\rho}\right)}$ ,

We can see that the depth-slope product can be rewritten as:

$\tau_b=\rho u_*^2$ .

u * is related to the mean flow velocity, $\bar{u}$ , through the generalized Darcy-Weisbach friction factor, C_f, which is equal to the Darcy-Weisbach friction factor divided by 8 (for mathematical convenience).^[4] Inserting this friction factor,

$\tau_b=\rho C_f \left(\bar{u} \right)^2$ .

Unsteady flow

For all flows that cannot be simplified as a single-slope infinite channel (as in the depth-slope product, above), the bed shear stress can be locally found by applying the Saint-Vennant equations for continuity, which consider accelerations within the flow.

Solution

Set-up

The criterion for the initiation of motion, established earlier, states that

τ_b * = τ_c * .

In this equation,

$\tau*=\frac{\tau_b}{(\rho_s-\rho)(g)(D)}$ , and therefore

$\frac{\tau_b}{(\rho_s-\rho)(g)(D)}=\frac{\tau_{c}}{(\rho_s-\rho)(g)(D)}$ .

τ_c * is a function of boundary Reynolds number, a specific type of particle Reynolds number.

$\tau_c*=f \left(Re_p* \right)$ .

For a particular particle Reynolds number, τ_c * will be an emprical constant given by the Shields Curve or by another set of empirical data (depending on whether or not the grain size is uniform).

Therefore, the final equation that we seek to solve is:

$\frac{\tau_b}{(\rho_s-\rho)(g)(D)}=f \left(Re_p* \right)$ .

Solution

We make several assumptions to provide an example that will allow us to bring the above form of the equation into a solved form.

First, we assume that the a good approximation of reach-averaged shear stress is given by the depth-slope product. We can then rewrite the equation as

ρghS = 0.06(ρ_s − ρ)(g)(D).

Moving and re-combining the terms, we obtain:

${h S}={\frac{(\rho_s-\rho)}{\rho}(D)}\left(f \left(Re_p* \right) \right)=R D \left(f \left(Re_p* \right) \right)$

where R is the submerged specific gravity of the sediment.

We then make our second assumption, which is that the particle Reynolds number is high. This is typically applicable to particles of gravel-size or larger in a stream, and means that the critical shear stress is a constant. The Shields curve shows that for a bed with a uniform grain size,

τ_c * = 0.06.

Later researchers^{[citation needed]} have shown that this value is closer to

τ_c * = 0.03

for more uniformly-sorted beds. Therefore, we will simply insert

$\tau_c*=f \left(Re_p* \right)$

and insert both values at the end.

The equation now reads:

hS = RDτ_c *

This final expression shows that the product of the channel depth and slope is equal to the Shield's criterion times the submerged specific gravity of the particles times the particle diameter.

For a typical situation, such as quartz-rich sediment $\left(\rho_s=2650 \frac{kg}{m^3} \right)$ in water $\left(\rho=1000 \frac{kg}{m^3} \right)$ , the submerged specific gravity is equal to 1.65.

$R=\frac{(\rho_s-\rho)}{\rho}=1.65$

Plugging this into the equation above,

hS = 1.65(D)τ_c * .

For the Shield's criterion of τ_c * = 0.06. 0.06 * 1.65 = 0.099, which is well within standard margins of error of 0.1. Therefore, for a uniform bed,

hS = 0.1(D).

For these situations, the product of the depth and slope of the flow should be 10% of the diameter of the median grain diameter.

The mixed-grain-size bed value is τ_c * = 0.03, which is supported by more recent research as being more broadly applicable because most natural streams have mixed grain sizes. Using this value, and changing D to D_50 ("50" for the 50th percentile, or the median grain size, as we are now looking at a mixed-grain-size bed), the equation becomes:

hS = 0.05(D₅₀)

Which means that the depth times the slope should be about 5% of the median grain diameter in the case of a mixed-grain-size bed.

Modes of entrainment

The sediments entrained in a flow can be transported along the bed as bed load in the form of sliding and rolling grains, or in suspension as suspended load advected by the main flow ^[3]. Some sediment materials may also come from the upstream reaches and be carried downtream in the form of wash load.

Rouse number

The location in the flow in which a particle is entrained is determined by the Rouse number, which is determined by the density ρ_s and diameterd of the sediment particle, and the density ρ and kinematic viscosity ν of the fluid, determine in which part of the flow the sediment particle will be carried.^[5]

$\textbf{P}=\frac{w_s}{\kappa u_*}$

Here, the Rouse number is given by P. The term in the numerator is the (downwards) sediment the sendiment settling velocity w_s, which is discussed below. The upwards velocity on the grain is given as a product of the von Kármán constant, κ = 0.407, and the shear velocity, u _* .

The following table gives the approximate required Rouse numbers for transport as bed load, suspended load, and wash load.^[5][6]

Mode of Transport	Rouse Number
Initiation of motion	>7.5
Bed load	7.5>2.5
Suspended load: 50% Suspended	>1.2, <2.5
Suspended load: 100% Suspended	>0.8, <1.2
Wash load	<0.8

Settling velocity

Streamlines around a sphere falling through a fluid. This illustration is accurate for laminar flow, in which the particle Reynolds number is small. This is typical for small particles falling through a viscous fluid; larger particles would result in the creation of a turbulent wake.

The settling velocity (also called the "fall velocity" or "terminal velocity") is a function of the particle Reynolds number. Generally, for small particles (laminar approximation), it can be calculated with Stokes' Law. For larger particles (turbulent particle Reynolds numbers), fall velocity is calculated with the turbulent drag law. Dietrich (1982) compiled a large amount of published data to which he empirically fit settling velocity curves.^[7] Ferguson and Church (2006) analytically combined the expressions for Stokes flow and a turbulent drag law into a single equation that works for all sizes of sediment, and successfully tested it against the data of Dietrich.^[8] Their equation is

$w_s=\frac{RgD^2}{C_1 \nu + (0.75 C_2 R g D^3)^{(0.5)}}$ .

In this equation w_s is the sediment settling velocity, g is acceleration due to gravity, and D is mean sediment diameter. ν is the kinematic viscosity of water, which is approximately 1.0 x 10⁻⁶ m²/s for water at 20°C.

C₁ and C₂ are constants related to the shape and smoothness of the grains.

Constant	Smooth Spheres	Natural Grains: Sieve Diameters	Natural Grains: Nominal Diameters	Limit for Ultra-Angular Grains
C₁	18	18	20	24
C₂	0.4	1.0	1.1	1.2

The expression for fall velocity can be simplified so that it can be solved only in terms of D. We use the sieve diameters for natural grains, g = 9.8, and values given above for ν and R. From these parameters, the fall velocity is given by the expression:

$w_s=\frac{16.17D^2}{1.8\cdot10^{-5} + (12.1275D^3)^{(0.5)}}$

Transport rate

A schematic diagram of where the different types of sediment load are carried in the flow. Dissolved load is not sediment: it is composed of disassociated ions moving along with the flow.

Formulas to calculate sediment transport rate exist for sediment moving in several different parts of the flow. These formulas are often segregated into bed load, suspended load, and wash load. They may sometimes also be segregated into bed material load and wash load.

Bed Load

Bed load moves by rolling, sliding, and hopping (or saltating) over the bed, and moves at a small fraction of the fluid flow velocity. Bed load is generally thought to constitute 5-10% of the total sediment load in a stream, making it less important in terms of mass balance. However, the bed material load (the bed load plus the portion of the suspended load which comprises material derived from the bed) is often dominated by bed load, especially in gravel-bed rivers. This bed material load is the only part of the sediment load that actively interacts with the bed. As the bed load is an important component of that, it plays a major role in controlling the morphology of the channel.

Bed load transport rates are usually expressed as being related to excess dimensionless shear stress raised to some power. Excess dimensionless shear stress is a nondimensional measure measure of bed shear stress about the threshold for motion.

$(\tau^*_b-\tau^*_c)$ ,

Bed load transport rates may also be given by a ratio of bed shear stress to critical shear stress, which is equivalent in both the dimensional and nondimensional cases. This ratio is called the "transport stage" (T_s or φ) and is an important in that it shows bed shear stress as a multiple of the value of the criterion for the initiation of motion.

$T_s=\phi=\frac{\tau_b}{\tau_c}$

When used for sediment transport formulae, this ratio is typically raised to a power.

The majority of the published relations for bedload transport are given in dry sediment weight per unit channel width, b ("breadth"):

$q_s=\frac{Q_s}{b}$ .

Due to the difficulty of estimating bed load transport rates, these equations are typically only suitable for the situations for which they were designed.

Notable bed load transport formulae

Meyer-Peter Müller and derivatives

The transport formula of Meyer-Peter and Müller, originally developed in 1948,^[9] was designed for well-sorted fine gravel at a transport stage of about 8.^[5] The formula uses the above nondimensionalization for shear stress,^[5]

$\tau*=\frac{\tau}{(\rho_s-\rho)(g)(D)}$ ,

and Hans Einstein's nondimensionalization for sediment volumetric discharge per unit width^[5]

$q_s* = \frac{q_s}{D \sqrt{\frac{\rho_s-\rho}{\rho} g D}} = \frac{q_s}{Re_p \nu}$ .

Their formula reads:

$q_s* = 8\left(\tau*-\tau*_c \right)^{3/2}$ .^[5]

Their experimentally-determined value for τ * _c is 0.047, and is the third commonly used value for this (in addition to Parker's 0.03 and Shields' 0.06).

Because of its broad use, some revisions to the formula have taken place over the years that show that the coefficient on the left ("8" above) is a function of the transport stage:^{[5][10][11][12]}

$T_s \approx 2 \rightarrow q_s* = 5.7\left(\tau*-0.047 \right)^{3/2}$ ^[10]

$T_s \approx 100 \rightarrow q_s* = 12.1\left(\tau*-0.047 \right)^{3/2}$ ^[11][12]

The variations in the coefficient were later generalized as a function of dimensionless shear stress:^[5][13]

$\begin{cases} q_s* = \alpha_s \left(\tau*-\tau_c* \right)^n \\ n = \frac{3}{2} \\ \alpha_s = 1.6 \ln\left(\tau*\right) + 9.8 \approx 9.64 \tau*^{0.166} \end{cases}$ ^[13]

Wilcock and Crowe

In 2003, Peter Wilcock an Joanna Crowe published a sediment transport formula that works with multiple grain sizes across the sand and gravel range.^[14] Their formula works with surface grain size distributions, as opposed to older models which use subsurface grain size distributions (and thereby implicitly infer a surface grain sorting).

Their expression is more complicated than the basic sediment transport rules (such as that of Meyer-Peter and Müller) because it takes into account multiple grain sizes: this requires consideration of reference shear stresses for each grain size, the fraction of the total sediment supply that falls into each grain size class, and a "hiding function".

The "hiding function" takes into account the fact that, while small grains are inheriently more mobile than large grains, on a mixed-grain-size bed, they may be trapped in deep pockets between large grains. Likewise, a large grain on a bed of small particles will be stuck in a much smaller pocket than if it were on a bed of grains of the same size. In gravel-bed rivers, this can cause "equal mobility", in which small grains can move just as easily as large ones.^[15] As sand is added to the system, it moves away from the "equal mobility" portion of the hiding function to one in which grain size again matters.^[14]

Their model is based on the transport stage, or ratio of bed shear stress to critical shear stress for the initiation of grain motion. Because their formula works with several grain sizes simultaneously, they define the critical shear stress for each grain size class, $\tau_{c,D_i}$ , to be equal to a "reference shear stress", τ_ri.^[14]

They express their equations in terms of a dimensionless transport parameter, $W_i^*$ (with the " * " indicating nondimensionality and the "_i" indicating that it is a function of grain size):

$W_i^* = \frac{R g q_{bi}}{F_i u*^3}$

q_bi is the volumetric bed load transport rate of size class i per unit channel width b. F_i is the proportion of size class i that is present on the bed.

They came up with two equations, depending on the transport stage, φ. For φ < 1.35:

$W_i^* = 0.002 \phi^{7.5}$

and for $\phi \geq 1.35$ :

$W_i^* = 14 \left(1 - \frac{0.894}{\phi^{0.5}}\right)^{4.5}$ .

This equation asymptotically reaches a constant value of $W_i^*$ as φ becomes large.

Suspended load

Suspended load is carried in the lower to middle parts of the flow, and moves at a large fraction of the mean flow velocity in the stream.

A common characterization of suspended sediment concentration in a flow is given by the Rouse Profile. This characterization works for the situation in which sediment concentration c₀ at one particular elevation above the bed z₀ can be quantified. It is given by the expression:

$\frac{c_s}{c_0} = \left[\frac{z \left(h-z_0\right)}{z_0\left(h-z\right)}\right]^{-P/\alpha}$

Here, z is the elevation above the bed, c_s is the concentration of suspended sediment at that elevation, h is the flow depth, P is the Rouse number, and α relates the eddy viscosity for momentum K_m to the eddy diffusivity for sediment, which is approximately equal to one.^[16]

$\alpha = \frac{K_s}{K_m} \approx 1$

Experimental work has shown that α ranges from 0.93 to 1.10 for sands and silts.^[17]

Bed material load

Bed material load comprises the bed load and the portion of the suspended load that is sourced from the bed.

Three common bed material transport relations are the "Ackers-White",^[18] "Engelund-Hansen", "Yang" formulae. The first is for sand to granule-size gravel, and the second and third are for sand^[19] though Yang later expanded his formula to include fine gravel. That all of these formulae cover the sand-size range and two of them are exclusively for sand is that the sediment in sand-bed rivers is commonly moved simultaneously as bed and suspended load.

Engelund-Hansen

The bed material load formula of Engelund and Hansen is the only one to not include some kind of critical value for the initiation of sediment transport. It reads:

$q_s* = \frac{0.05}{c_f} \tau*^{2.5}$

where q_s * is the Einstein nondimensionalization for bed shear stress, c_f is a friction factor, and τ * is the Shields stress.

Wash load

Wash load is carried within the water column as part of the flow, and therefore moves with the mean velocity of main stream. Wash load concentrations are approximately uniform in the water column, and are perfectly uniform for the endmember case in which the Rouse number is equal to 0.

References

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^ Whipple, Kelin (2004). "Hydraulic Roughness". 12.163: Surface processes and landscape evolution. MIT OCW. http://ocw.mit.edu/NR/rdonlyres/Earth--Atmospheric--and-Planetary-Sciences/12-163Fall-2004/E81558F3-0A45-4106-87D7-B1C1194D307E/0/roughnes_handout.pdf. Retrieved 2009-03-27.
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^ Ferguson, R. I., and M. Church (2006), A Simple Universal Equation for Grain Settling Velocity, Journal of Sedimentary Research, 74(6) 933-937, doi: 10.1306/051204740933
^ Meyer-Peter, E; Müller, R. (1948). Formulas for bed-load transport. Proceedings of the 2nd Meeting of the International Association for Hydraulic Structures Research. pp. 39–64.
^ ^ahttp://en.wikipedia.org/wiki/Sediment_transport#cite_ref-f-l_9-0 ^bhttp://en.wikipedia.org/wiki/Sediment_transport#cite_ref-f-l_9-1 Fernandez-Luque, R; van Beck, R (1976). "Erosion and transport of bedload sediment.". Jour. Hyd. Research 14 (2).
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^ ^ahttp://en.wikipedia.org/wiki/Sediment_transport#cite_ref-wiberg_smith_12-0 ^bhttp://en.wikipedia.org/wiki/Sediment_transport#cite_ref-wiberg_smith_12-1 Wiberg, Patricia L.; Dungan Smith, J. (1989). "Model for Calculating Bed Load Transport of Sediment". Journal of Hydraulic Engineering 115: 101. doi:10.1061/(ASCE)0733-9429(1989)115:1(101).
^ ^ahttp://en.wikipedia.org/wiki/Sediment_transport#cite_ref-wilcock_crowe_13-0 ^bhttp://en.wikipedia.org/wiki/Sediment_transport#cite_ref-wilcock_crowe_13-1 ^chttp://en.wikipedia.org/wiki/Sediment_transport#cite_ref-wilcock_crowe_13-2 . doi:10.1061/(ASCE)0733-9429(2003)129:29(120).
^ Parker, G.; Klingeman, P. C., and McLean, D. G. (1982). "Bedload and Size Distribution in Paved Gravel-Bed Streams". Journal of the Hydraulics Division (ASCE) 108 (4): 544–571. http://cedb.asce.org/cgi/WWWdisplay.cgi?8200331.
^ Harris, Courtney K. (March 18, 2003). "Lecture 9: Suspended Sediment Transport II". Sediment transport processes in coastal environments. Virginia Institute of Marine Science. http://www.vims.edu/ckharris/MS698_03/lecture_09.pdf. Retrieved 23 December 2009.
^ Moore, Andrew. "Lecture 21—Suspended Sediment Transport". Lecture Notes: Fluvial Sediment Transport. Kent State. http://www.personal.kent.edu/amoore5/FST_L_21.pdf. Retrieved 25 December 2009.
^ Ackers, P.; White, W.R. (1973). "Sediment Transport: New Approach and Analysis". Journal of the Hydraulics Division (ASCE) 99 (11): 2041–2060. http://cedb.asce.org/cgi/WWWdisplay.cgi?7300122.
^ Ariffin, J.; A.A. Ghani, N.A. Zakaira, and A.H. Yahya (14–16 October 2002). "Evaluation of equations on total bed material load". International Conference on Urban Hydrology for the 21st Century (Kuala Lumpur). http://redac.eng.usm.my/html/publish/2002_07.pdf.

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Sediment transport

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Sediment transport

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Hillslope

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