Sediment transport

Sediment transport is the movement of solid particles ("sediment") due to the movement of the fluid in which they are immersed. This is typically studied in natural systems, where the particles are clastic rocks (sand, gravel, boulders, etc.) or clay, and the fluid is air, water, or ice.

Sediment transport is important in the fields of sedimentary geology, geomorphology, civil engineering and environmental engineering (see [applications] , below). Our understanding of it is most often used to know whether erosion or deposition will occur, and in what magnitude it will occur.

=Mechanisms for Sediment Transport=

Eolean

Eolean 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 is a fluid with low density and viscosity, and can therefore not exert very much shear on its bed.

Aeolean sediment transport is common on beaches and in the arid regions of the world, because it is in these enviornments 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 CarribbeanFact|date=September 2008, and dust from the Gobi desert has deposited on the western United StatesFact|date=September 2008. This sand is important to the soil budget and ecology of several islands; the soil formed by this wind-blown sediment is called loess.

Fluvial

In geology, physical geography, and sediment transport, fluvial processes relate to flowing water in natural systems. This encompasses rivers, streams, periglacial processes, 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 maximum size of this sediment is of sand and gravel (<32 mm), but larger floods can carry boulders.

Glacial

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.

=Modes of Entrainment=

Sediment entrained in a flow can be Sediment can be transported along the bed as bed load, in suspension as suspended load, or along the top (air-water) surface of the flow as wash-load.

The location in the flow in which a particle is entrained is determined by the Rouse number, which is determined by the density $ho\_s$ and diameter$d$ of the sediment particle, and the density $ho$ and kinematic viscosity $u$ of the fluid, determine in which part of the flow the sediment particle will be carried.

$extbf\{Rouse\}=frac\{w\_s\}\{kappa\; u\_*\}$

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 von Kárman's constant,

$kappa\; =\; \{0.407\}$

and the shear velocity

$u\_*=sqrt\{(frac\{tau\_b\}\{\; ho\_w\})\}=kappa\; z\; frac\{partial\; u\}\{partial\; z\}$

The following table gives the required Rouse numbers for transport as bed load, suspended load, and wash load.

ettling velocity

The settling velocity (also called the "fall velocity") can be calculated with Stokes' Law for small particles and with the Drag Law for large particles. Ferguson and Church (2006) [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] analytically combined these two expressions into a single equation that works for all sizes of sediment.

$w\_s=frac\{RgD^2\}\{C\_1\; u\; +\; (0.75\; C\_2\; R\; g\; D^3)^(0.5)\}$

In this equation "w_s" is the sediment settling velocity, "g" is acceleration due to gravity, and "D" is mean sediment diameter. R is the submerged specific gravity of the sediment, which is given by:

$R=frac\{\; ho\_s-\; ho\_w\}\{\; ho\_w\}$

where "&rho;" is density and the subscripts "s" and "w" indicate sediment and water, respectively. For quartz grains in water (a typical situation),

$ho\_s\; =\; 2650\; kg/m^3$

$ho\_w\; =\; 1000\; kg/m^3$

$R=1.65$

u is the kinematic viscosity of water, which is approximately 1.0 x 10^-6 m²/s for water at 20ºC.

C_1 and C_2 are constants related to the shape and smoothness of the grains.

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, $g=9.8$, $u=1.0$, and $R=1.65$. From these parameters, the fall velocity is given by the expression:

$w\_s=frac\{16.17D^2\}\{18\; +\; (12.1275D^3)^(0.5)\}$

Below are explanations of some standard equations that relate to sediment transport. These equations describe the initiation of sediment motion and the vertical location within the flow in a channel, such as a river, that sediment will occupy. These equations are designed for the transport of sediment in water or air. They only work for clastic, granular sediment: floccular sediment (including clays and muds) do not fit the geometric simplifications in these equations, and also interact thorough electrostatic forces.

=Initiation of motion=

For a fluid to begin transporting sediment in rest on a surface, the boundary, or bed, shear stress $au\_b$ exerted by the fluid must exceed the critical shear stress $au\_c$ for the motion of grains at the bed.

Bed shear stress

Depth-slope product

For a river of approximately constant depth "h" and slope &theta over the reach of interest, and not involving a backwater, the bed shear stress is given by the depth-slope project:

$au\_b=\; ho\; g\; h\; sin(\; heta)$

For shallow slopes, the small-angle formula shows that $sin(\; heta)$ is approximately equal to $an(\; heta)$, which is given by "S", the slope. Rewritten with this:

$au\_b=\; ho\; g\; h\; S$

Other methods of calculating bed shear stress

For all flows that cannot be simplified as a single-slope infinate channel (above), the bed shear stress can be found by

Critical shear stress

The critical shear stress that a particle must overcome to enter motion can be given by a variety of formulas. Shield's Diagram

=Applications of Sediment Transport=

References

http://ocw.mit.edu/OcwWeb/Earth--Atmospheric--and-Planetary-Sciences/12-090Fall-2006/CourseHome/index.htm