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Sediment transport is the movement of solid particles (
sediment Sediment is a naturally occurring material that is broken down by processes of weathering and erosion, and is subsequently transported by the action of wind, water, or ice or by the force of gravity acting on the particles. For example, sand ...
), typically due to a combination of gravity acting on the sediment, and/or the movement of the fluid in which the sediment is entrained. Sediment transport occurs in natural systems where the particles are
clastic Clastic rocks are composed of fragments, or clasts, of pre-existing minerals and rock. A clast is a fragment of geological detritus,Essentials of Geology, 3rd Ed, Stephen Marshak, p. G-3 chunks, and smaller grains of rock broken off other rocks ...
rocks (
sand Sand is a granular material composed of finely divided mineral particles. Sand has various compositions but is defined by its grain size. Sand grains are smaller than gravel and coarser than silt. Sand can also refer to a textural class ...
,
gravel Gravel is a loose aggregation of rock fragments. Gravel occurs naturally throughout the world as a result of sedimentary and erosive geologic processes; it is also produced in large quantities commercially as crushed stone. Gravel is classifi ...
, boulders, etc.), mud, or
clay Clay is a type of fine-grained natural soil material containing clay minerals (hydrous aluminium phyllosilicates, e.g. kaolin, Al2 Si2 O5( OH)4). Clays develop plasticity when wet, due to a molecular film of water surrounding the clay pa ...
; the fluid is air, water, or ice; and the force of gravity acts to move the particles along the sloping surface on which they are resting. Sediment transport due to fluid motion occurs in
river A river is a natural flowing watercourse, usually freshwater, flowing towards an ocean, sea, lake or another river. In some cases, a river flows into the ground and becomes dry at the end of its course without reaching another body of ...
s,
ocean The ocean (also the sea or the world ocean) is the body of salt water that covers approximately 70.8% of the surface of Earth and contains 97% of Earth's water. An ocean can also refer to any of the large bodies of water into which the wor ...
s,
lake A lake is an area filled with water, localized in a basin, surrounded by land, and distinct from any river or other outlet that serves to feed or drain the lake. Lakes lie on land and are not part of the ocean, although, like the much large ...
s,
sea The sea, connected as the world ocean or simply the ocean, is the body of salty water that covers approximately 71% of the Earth's surface. The word sea is also used to denote second-order sections of the sea, such as the Mediterranean Sea, ...
s, and other bodies of water due to currents and
tide Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon (and to a much lesser extent, the Sun) and are also caused by the Earth and Moon orbiting one another. Tide tables ...
s. Transport is also caused by
glacier A glacier (; ) is a persistent body of dense ice that is constantly moving under its own weight. A glacier forms where the accumulation of snow exceeds its ablation over many years, often centuries. It acquires distinguishing features, such a ...
s as they flow, and on terrestrial surfaces under the influence of
wind Wind is the natural movement of air or other gases relative to a planet's surface. Winds occur on a range of scales, from thunderstorm flows lasting tens of minutes, to local breezes generated by heating of land surfaces and lasting a few ...
. Sediment transport due only to gravity can occur on sloping surfaces in general, including
hill A hill is a landform that extends above the surrounding terrain. It often has a distinct summit. Terminology The distinction between a hill and a mountain is unclear and largely subjective, but a hill is universally considered to be not a ...
slopes,
scarp Scarp may refer to: Landforms and geology * Cliff, a significant vertical, or near vertical, rock exposure * Escarpment, a steep slope or long rock that occurs from erosion or faulting and separates two relatively level areas of differing elevatio ...
s,
cliff In geography and geology, a cliff is an area of rock which has a general angle defined by the vertical, or nearly vertical. Cliffs are formed by the processes of weathering and erosion, with the effect of gravity. Cliffs are common on co ...
s, and the
continental shelf A continental shelf is a portion of a continent that is submerged under an area of relatively shallow water, known as a shelf sea. Much of these shelves were exposed by drops in sea level during glacial periods. The shelf surrounding an island ...
—continental slope boundary. Sediment transport is important in the fields of
sedimentary geology ''Sedimentary Geology'' is a peer-reviewed scientific journal In academic publishing, a scientific journal is a periodical publication intended to further the progress of science, usually by reporting new research. Content Articles in sc ...
, geomorphology,
civil engineering Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including public works such as roads, bridges, canals, dams, airports, sewa ...
,
hydraulic engineering Hydraulic engineering as a sub-discipline of civil engineering is concerned with the flow and conveyance of fluids, principally water and sewage. One feature of these systems is the extensive use of gravity as the motive force to cause the m ...
and environmental engineering (see applications, below). Knowledge of sediment transport is most often used to determine whether
erosion Erosion is the action of surface processes (such as water flow or wind) that removes soil, rock, or dissolved material from one location on the Earth's crust, and then transports it to another location where it is deposited. Erosion is d ...
or
deposition Deposition may refer to: * Deposition (law), taking testimony outside of court * Deposition (politics), the removal of a person of authority from political power * Deposition (university), a widespread initiation ritual for new students practiced f ...
will occur, the magnitude of this erosion or deposition, and the time and distance over which it will occur.


Mechanisms


Aeolian

''Aeolian'' or ''eolian'' (depending on the parsing of æ) is the term for sediment transport by
wind Wind is the natural movement of air or other gases relative to a planet's surface. Winds occur on a range of scales, from thunderstorm flows lasting tens of minutes, to local breezes generated by heating of land surfaces and lasting a few ...
. This process results in the formation of ripples and sand dunes. Typically, the size of the transported sediment is fine
sand Sand is a granular material composed of finely divided mineral particles. Sand has various compositions but is defined by its grain size. Sand grains are smaller than gravel and coarser than silt. Sand can also refer to a textural class ...
(<1 mm) and smaller, because air is a fluid with low
density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...
and
viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the int ...
, and can therefore not exert very much shear on its bed. Bedforms are generated by aeolian sediment transport in the terrestrial near-surface environment. Ripples and
dune A dune is a landform composed of wind- or water-driven sand. It typically takes the form of a mound, ridge, or hill. An area with dunes is called a dune system or a dune complex. A large dune complex is called a dune field, while broad, f ...
s form as a natural self-organizing response to sediment transport. 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 Dust is made of fine particles of solid matter. On Earth, it generally consists of particles in the atmosphere that come from various sources such as soil lifted by wind (an aeolian process), volcanic eruptions, and pollution. Dust in ...
is capable of entering the upper atmosphere and moving across the globe. Dust from the
Sahara , photo = Sahara real color.jpg , photo_caption = The Sahara taken by Apollo 17 astronauts, 1972 , map = , map_image = , location = , country = , country1 = , ...
deposits on the
Canary Islands The Canary Islands (; es, :es:Canarias, Canarias, ), also known informally as the Canaries, are a Spanish Autonomous communities of Spain, autonomous community and archipelago in the Atlantic Ocean, in Macaronesia. At their closest point to ...
and islands in the
Caribbean The Caribbean (, ) ( es, El Caribe; french: la Caraïbe; ht, Karayib; nl, De Caraïben) is a region of the Americas that consists of the Caribbean Sea, its islands (some surrounded by the Caribbean Sea and some bordering both the Caribbean ...
, and dust from the
Gobi desert The Gobi Desert ( Chinese: 戈壁 (沙漠), Mongolian: Говь (ᠭᠣᠪᠢ)) () is a large desert or brushland region in East Asia, and is the sixth largest desert in the world. Geography The Gobi measures from southwest to northeast a ...
has deposited on the
western United States The Western United States (also called the American West, the Far West, and the West) is the region comprising the westernmost states of the United States. As American settlement in the U.S. expanded westward, the meaning of the term ''the We ...
. This sediment is important to the soil budget and ecology of several islands. Deposits of fine-grained wind-blown glacial sediment are called
loess Loess (, ; from german: Löss ) is a clastic, predominantly silt-sized sediment that is formed by the accumulation of wind-blown dust. Ten percent of Earth's land area is covered by loess or similar deposits. Loess is a periglacial or aeoli ...
.


Fluvial

In
geology Geology () is a branch of natural science concerned with Earth and other Astronomical object, astronomical objects, the features or rock (geology), rocks of which it is composed, and the processes by which they change over time. Modern geology ...
,
physical geography Physical geography (also known as physiography) is one of the three main branches of geography. Physical geography is the branch of natural science which deals with the processes and patterns in the natural environment such as the atmosphere ...
, and sediment transport, fluvial processes relate to flowing
water Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as ...
in natural systems. This encompasses rivers, streams, periglacial flows,
flash floods A flash flood is a rapid flooding of low-lying areas: washes, rivers, dry lakes and depressions. It may be caused by heavy rain associated with a severe thunderstorm, hurricane, or tropical storm, or by meltwater from ice or snow flow ...
and glacial lake outburst floods. Sediment moved by water can be larger than sediment moved by air because water has both a higher
density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...
and
viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the int ...
. In typical rivers the largest carried sediment is of
sand Sand is a granular material composed of finely divided mineral particles. Sand has various compositions but is defined by its grain size. Sand grains are smaller than gravel and coarser than silt. Sand can also refer to a textural class ...
and
gravel Gravel is a loose aggregation of rock fragments. Gravel occurs naturally throughout the world as a result of sedimentary and erosive geologic processes; it is also produced in large quantities commercially as crushed stone. Gravel is classifi ...
size, but larger floods can carry
cobbles Cobblestone is a natural building material based on cobble-sized stones, and is used for pavement roads, streets, and buildings. Setts, also called Belgian blocks, are often casually referred to as "cobbles", although a sett is distinct f ...
and even boulders. Fluvial sediment transport can result in the formation of ripples and
dune A dune is a landform composed of wind- or water-driven sand. It typically takes the form of a mound, ridge, or hill. An area with dunes is called a dune system or a dune complex. A large dune complex is called a dune field, while broad, f ...
s, in
fractal In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as ill ...
-shaped patterns of erosion, in complex patterns of natural river systems, and in the development of
floodplain A floodplain or flood plain or bottomlands is an area of land adjacent to a river which stretches from the banks of its channel to the base of the enclosing valley walls, and which experiences flooding during periods of high discharge.Goudi ...
s.


Coastal

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 delta A river delta is a landform shaped like a triangle, created by deposition of sediment that is carried by a river and enters slower-moving or stagnant water. This occurs where a river enters an ocean, sea, estuary, lake, reservoir, or (more rare ...
s. Coastal sediment transport results in the formation of characteristic coastal landforms such as
beach A beach is a landform alongside a body of water which consists of loose particles. The particles composing a beach are typically made from rock, such as sand, gravel, shingle, pebbles, etc., or biological sources, such as mollusc s ...
es, barrier islands, and capes.


Glacial

As glaciers move over their beds, they entrain and move material of all sizes. Glaciers can carry the largest sediment, and areas of glacial deposition often contain a large number of
glacial erratics A glacial period (alternatively glacial or glaciation) is an interval of time (thousands of years) within an ice age that is marked by colder temperatures and glacier advances. Interglacials, on the other hand, are periods of warmer climate betw ...
, many of which are several metres in diameter. Glaciers also pulverize rock into " glacial flour", which is so fine that it is often carried away by winds to create
loess Loess (, ; from german: Löss ) is a clastic, predominantly silt-sized sediment that is formed by the accumulation of wind-blown dust. Ten percent of Earth's land area is covered by loess or similar deposits. Loess is a periglacial or aeoli ...
deposits thousands of kilometres afield. Sediment entrained in glaciers often moves approximately along the glacial flowlines, causing it to appear at the surface in the ablation zone.


Hillslope

In hillslope sediment transport, a variety of processes move regolith downslope. These include: *
Soil creep Downhill creep, also known as soil creep or commonly just creep, is a type of creep characterized by the slow, downward progression of rock and soil down a low grade slope; it can also refer to slow deformation of such materials as a result of ...
* Tree throw * Movement of soil by
burrow An Eastern chipmunk at the entrance of its burrow A burrow is a hole or tunnel excavated into the ground by an animal to construct a space suitable for habitation or temporary refuge, or as a byproduct of locomotion. Burrows provide a form of s ...
ing animals *
Slumping Slumping is a technique in which items are made in a kiln by means of shaping glass over molds at high temperatures. The slumping of a pyrometric cone is often used to measure temperature in a kiln. Technique Slumping glass is a highly techni ...
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-up profile, which grades into a convex-up profile around valleys. As hillslopes steepen, however, they become more prone to episodic landslides and other mass wasting events. Therefore, hillslope processes are better described by a nonlinear diffusion equation in which classic diffusion dominates for shallow slopes and erosion rates go to infinity as the hillslope reaches a critical
angle of repose The angle of repose, or critical angle of repose, of a granular material is the steepest angle of descent or dip relative to the horizontal plane to which a material can be piled without slumping. At this angle, the material on the slope fac ...
.


Debris flow

Large masses of material are moved in debris flows, hyperconcentrated mixtures of mud, clasts that range up to boulder-size, and water. Debris flows move as
granular flow A granular material is a conglomeration of discrete solid, macroscopic particles characterized by a loss of energy whenever the particles interact (the most common example would be friction when grains collide). The constituents that compose g ...
s down steep mountain valleys and washes. Because they transport sediment as a granular mixture, their transport mechanisms and capacities scale differently from those of fluvial systems.


Applications

Sediment transport is applied to solve many environmental, geotechnical, and geological problems. Measuring or quantifying sediment transport or erosion is therefore important for coastal engineering. Several sediment erosion devices have been designed in order to quantify sediment erosion (e.g., Particle Erosion Simulator (PES)). One such device, also referred to as the BEAST (Benthic Environmental Assessment Sediment Tool) has been calibrated in order to quantify rates of sediment erosion. 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
flood A flood is an overflow of water ( or rarely other fluids) that submerges land that is usually dry. In the sense of "flowing water", the word may also be applied to the inflow of the tide. Floods are an area of study of the discipline hydrol ...
s to refresh the bed material and rebuild bars. This is also important, for example, in the Grand Canyon of the
Colorado River The Colorado River ( es, Río Colorado) is one of the principal rivers (along with the Rio Grande) in the Southwestern United States and northern Mexico. The river drains an expansive, arid watershed that encompasses parts of seven U.S. s ...
, 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. When suspended sediment transport is increased due to human activities, causing environmental problems including the filling of channels, it is called siltation after the grain-size fraction dominating the process.


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 Shear stress, often denoted by ( Greek: tau), is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. '' Normal stress'', on ...
\tau_b exerted by the fluid must exceed the critical shear stress \tau_c for the initiation of motion of grains at the bed. This basic criterion for the initiation of motion can be written as: :\tau_b=\tau_c. This is typically represented by a comparison between a dimensionless shear stress \tau_b* and a dimensionless critical shear stress \tau_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, \tau*, is called the
Shields parameter The Shields parameter, also called the Shields criterion or Shields number, is a nondimensional number used to calculate the initiation of motion of sediment in a fluid flow. It is a nondimensionalization of a shear stress, and is typically denot ...
and is defined as: :\tau*=\frac. And the new equation to solve becomes: :\tau_b*=\tau_c*. The equations included here describe sediment transport for
clastic Clastic rocks are composed of fragments, or clasts, of pre-existing minerals and rock. A clast is a fragment of geological detritus,Essentials of Geology, 3rd Ed, Stephen Marshak, p. G-3 chunks, and smaller grains of rock broken off other rocks ...
, or granular sediment. They do not work for
clays Clay is a type of fine-grained natural soil material containing clay minerals (hydrous aluminium phyllosilicates, e.g. kaolin, Al2 Si2 O5( OH)4). Clays develop plasticity when wet, due to a molecular film of water surrounding the clay par ...
and
muds A MUD (; originally multi-user dungeon, with later variants multi-user dimension and multi-user domain) is a multiplayer real-time virtual world, usually text-based or storyboarded. MUDs combine elements of role-playing games, hack and slash, ...
because these types of floccular sediments do not fit the geometric simplifications in these equations, and also interact thorough
electrostatic Electrostatics is a branch of physics that studies electric charges at rest ( static electricity). Since classical times, it has been known that some materials, such as amber, attract lightweight particles after rubbing. The Greek word for ...
forces. The equations were also designed for fluvial sediment transport of particles carried along in a liquid flow, such as that in a river, canal, or other open channel. Only one size of particle is considered in this equation. However, river beds are often formed by a mixture of sediment of various sizes. In case of partial motion where only a part of the sediment mixture moves, the river bed becomes enriched in large gravel as the smaller sediments are washed away. The smaller sediments present under this layer of large gravel have a lower possibility of movement and total sediment transport decreases. This is called armouring effect. Other forms of armouring of sediment or decreasing rates of sediment erosion can be caused by carpets of microbial mats, under conditions of high organic loading.


Critical shear stress

The Shields diagram empirically shows how the dimensionless critical shear stress (i.e. the dimensionless shear stress required for the initiation of motion) is a function of a particular form of the particle Reynolds number, \mathrm_p or Reynolds number related to the particle. This allows the criterion for the initiation of motion to be rewritten in terms of a solution for a specific version of the particle Reynolds number, called \mathrm_p*. :\tau_b*=f\left(\mathrm_p*\right) This can then be solved by using the empirically derived Shields curve to find \tau_c* as a function of a specific form of the particle Reynolds number called the boundary Reynolds number. The mathematical solution of the equation was given by
Dey Dey (Arabic: داي), from the Turkish honorific title ''dayı'', literally meaning uncle, was the title given to the rulers of the Regency of Algiers (Algeria), Tripoli,Bertarelli (1929), p. 203. and Tunis under the Ottoman Empire from 1671 ...
.


Particle Reynolds number

In general, a particle Reynolds number has the form: :\mathrm_p=\frac Where U_p is a characteristic particle velocity, D is the grain diameter (a characteristic particle size), and \nu is the kinematic viscosity, which is given by the dynamic viscosity, \mu, divided by the fluid density, . :\nu=\frac 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 Shear velocity, also called friction velocity, is a form by which a shear stress may be re-written in units of velocity. It is useful as a method in fluid mechanics to compare true velocities, such as the velocity of a flow in a stream, to a veloc ...
, u_*, which is a way of rewriting shear stress in terms of velocity. :u_*=\sqrt=\kappa z \frac where \tau_b is the bed shear stress (described below), and \kappa is the von Kármán constant, where : \kappa = . The particle Reynolds number is therefore given by: :\mathrm_p*=\frac


Bed shear stress

The boundary Reynolds number can be used with the Shields diagram to empirically solve the equation :\tau_c*=f\left(\mathrm_p*\right), which solves the right-hand side of the equation :\tau_b*=\tau_c*. In order to solve the left-hand side, expanded as :\tau_b*=\frac, the bed shear stress needs to be found, . There are several ways to solve for the bed shear stress. The simplest approach is to assume the flow is steady and uniform, using the reach-averaged depth and slope. because it is difficult to measure shear stress ''in situ'', this method is also one of the most-commonly used. The method is known as the depth-slope product.


Depth-slope product

For a river undergoing approximately steady, uniform equilibrium flow, of approximately constant depth ''h'' and slope angle 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. For a wide channel, it yields: :\tau_b=\rho g h \sin(\theta) For shallow slope angles, which are found in almost all natural lowland streams, the
small-angle formula The small-angle approximations can be used to approximate the values of the main trigonometric functions, provided that the angle in question is small and is measured in radians: : \begin \sin \theta &\approx \theta \\ \cos \theta &\approx 1 - \ ...
shows that \sin(\theta) is approximately equal to \tan(\theta), which is given by S, the slope. Rewritten with this: :\tau_b=\rho g h S


Shear velocity, velocity, and friction factor

For the steady case, by extrapolating the depth-slope product and the equation for shear velocity: :\tau_b=\rho g h S :u_*=\sqrt, The depth-slope product can be rewritten as: :\tau_b=\rho u_*^2. u* is related to the mean flow velocity, \bar, through the generalized Darcy-Weisbach friction factor, C_f, which is equal to the Darcy-Weisbach friction factor divided by 8 (for mathematical convenience). Inserting this friction factor, :\tau_b=\rho C_f \left(\bar \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-Venant equations for continuity, which consider accelerations within the flow.


Example


Set-up

The criterion for the initiation of motion, established earlier, states that :\tau_b*=\tau_c*. In this equation, :\tau*=\frac, and therefore :\frac=\frac. :\tau_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, \tau_c* will be an empirical 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 to solve is: :\frac=f \left(Re_p* \right).


Solution

Some assumptions allow the solution of the above equation. The first assumption is that a good approximation of reach-averaged shear stress is given by the depth-slope product. The equation then can be rewritten as: :=f\left(\mathrm_p* \right). Moving and re-combining the terms produces: :=\left(f \left(\mathrm_p* \right) \right)=R D \left(f \left(\mathrm_p* \right) \right) where R is the submerged specific gravity of the sediment. The second assumption is that the particle Reynolds number is high. This typically applies to particles of gravel-size or larger in a stream, and means the critical shear stress is constant. The Shields curve shows that for a bed with a uniform grain size, :\tau_c*=0.06. Later researchers have shown this value is closer to :\tau_c*=0.03 for more uniformly sorted beds. Therefore the replacement :\tau_c*=f \left(\mathrm_p* \right) is used to insert both values at the end. The equation now reads: :=R D \tau_c* This final expression shows 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 \right) in water \left(\rho=1000 \frac \right), the submerged specific gravity is equal to 1.65. :R=\frac=1.65 Plugging this into the equation above, :=1.65(D)\tau_c*. For the Shield's criterion of \tau_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, :=. 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 \tau_c*=0.03, which is supported by more recent research as being more broadly applicable because most natural streams have mixed grain sizes. If this value is used, and D is changed to D_50 ("50" for the 50th percentile, or the median grain size, as an appropriate value for a mixed-grain-size bed), the equation becomes: := 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 The term bed load or bedload describes particles in a flowing fluid (usually water) that are transported along the stream bed. Bed load is complementary to suspended load and wash load. Bed load moves by rolling, sliding, and/or saltating (hop ...
in the form of sliding and rolling grains, or in suspension as
suspended load The suspended load of a flow of fluid, such as a river, is the portion of its sediment uplifted by the fluid's flow in the process of sediment transportation. It is kept suspended by the fluid's turbulence. The suspended load generally consists ...
advected by the main flow. Some sediment materials may also come from the upstream reaches and be carried downstream 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 diameter ''d'' 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. :P=\frac Here, the Rouse number is given by ''P''. The term in the numerator is the (downwards) sediment the sediment 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'' = 0.4, and the
shear velocity Shear velocity, also called friction velocity, is a form by which a shear stress may be re-written in units of velocity. It is useful as a method in fluid mechanics to compare true velocities, such as the velocity of a flow in a stream, to a veloc ...
, ''u''. The following table gives the approximate required Rouse numbers for transport as
bed load The term bed load or bedload describes particles in a flowing fluid (usually water) that are transported along the stream bed. Bed load is complementary to suspended load and wash load. Bed load moves by rolling, sliding, and/or saltating (hop ...
,
suspended load The suspended load of a flow of fluid, such as a river, is the portion of its sediment uplifted by the fluid's flow in the process of sediment transportation. It is kept suspended by the fluid's turbulence. The suspended load generally consists ...
, and wash load.


Settling velocity

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 Dietrich () is an ancient German name meaning "Ruler of the People.” Also "keeper of the keys" or a "lockpick" either the tool or the profession. Given name * Dietrich, Count of Oldenburg (c. 1398 – 1440) * Thierry of Alsace (german: Dietri ...
(1982) compiled a large amount of published data to which he empirically fit settling velocity curves. 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. Their equation is :w_s=\frac. In this equation ''ws'' is the sediment settling velocity, ''g'' is acceleration due to gravity, and ''D'' is mean sediment diameter. \nu is the kinematic viscosity of
water Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as ...
, which is approximately 1.0 x 10−6 m2/s for water at 20 °C. 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, and values given above for \nu and R. From these parameters, the fall velocity is given by the expression: :w_s=\frac


Hjulström-Sundborg Diagram

In 1935,
Filip Hjulström Henning Filip Hjulström (6 October 1902 – 26 March 1982) was a Swedish geographer. Hjulström was professor of geography at Uppsala University from 1944, and in 1949, when the subject of geography was split, he became professor of Physical ...
created the Hjulström curve, a graph which shows the relationship between the size of sediment and the velocity required to erode (lift it), transport it, or deposit it. The graph is logarithmic. Åke Sundborg later modified the Hjulström curve to show separate curves for the movement threshold corresponding to several water depths, as is necessary if the flow velocity rather than the boundary shear stress (as in the Shields diagram) is used for the flow strength. This curve has no more than a historical value nowadays, although its simplicity is still attractive. Among the drawbacks of this curve are that it does not take the water depth into account and more importantly, that it does not show that sedimentation is caused by flow velocity ''deceleration'' and erosion is caused by flow ''acceleration''. The dimensionless Shields diagram is now unanimously accepted for initiation of sediment motion in rivers.


Transport rate

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 The term bed load or bedload describes particles in a flowing fluid (usually water) that are transported along the stream bed. Bed load is complementary to suspended load and wash load. Bed load moves by rolling, sliding, and/or saltating (hop ...
,
suspended load The suspended load of a flow of fluid, such as a river, is the portion of its sediment uplifted by the fluid's flow in the process of sediment transportation. It is kept suspended by the fluid's turbulence. The suspended load generally consists ...
, and wash load. They may sometimes also be segregated into
bed material load Three components that are included in the load of a river system are the following: dissolved load, wash load and bed material load. The bed material load is the portion of the sediment that is transported by a stream that contains material derive ...
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 Three components that are included in the load of a river system are the following: dissolved load, wash load and bed material load. The bed material load is the portion of the sediment that is transported by a stream that contains material derive ...
(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 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 \text \phi) 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 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 Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the Interna ...
"): :q_s=\frac. 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, was designed for well- sorted fine
gravel Gravel is a loose aggregation of rock fragments. Gravel occurs naturally throughout the world as a result of sedimentary and erosive geologic processes; it is also produced in large quantities commercially as crushed stone. Gravel is classifi ...
at a transport stage of about 8. The formula uses the above nondimensionalization for shear stress, :\tau*=\frac, and Hans Einstein's nondimensionalization for sediment volumetric discharge per unit width :q_s* = \frac = \frac. Their formula reads: :q_s* = 8\left(\tau*-\tau*_c \right)^. Their experimentally determined value for \tau*_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: :T_s \approx 2 \rightarrow q_s* = 5.7\left(\tau*-0.047 \right)^ :T_s \approx 100 \rightarrow q_s* = 12.1\left(\tau*-0.047 \right)^ The variations in the coefficient were later generalized as a function of dimensionless shear stress: :\begin q_s* = \alpha_s \left(\tau*-\tau_c* \right)^n \\ n = \frac \\ \alpha_s = 1.6 \ln\left(\tau*\right) + 9.8 \approx 9.64 \tau*^ \end


=Wilcock and Crowe

= In 2003, Peter Wilcock and Joanna Crowe (now Joanna Curran) published a sediment transport formula that works with multiple grain sizes across the sand and gravel range. 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 inherently 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. 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. 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_, to be equal to a "reference shear stress", \tau_. 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 q_ 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, \phi. For \phi < 1.35: :W_i^* = 0.002 \phi^ and for \phi \geq 1.35: :W_i^* = 14 \left(1 - \frac\right)^. This equation asymptotically reaches a constant value of W_i^* as \phi becomes large.


=Wilcock and Kenworthy

= In 2002, Peter Wilcock and Kenworthy T.A. , following Peter Wilcock (1998), published a sediment bed-load transport formula that works with only two sediments fractions, i.e. sand and gravel fractions. Peter Wilcock and Kenworthy T.A. in their article recognized that a mixed-sized sediment bed-load transport model using only two fractions offers practical advantages in terms of both computational and conceptual modeling by taking into account the nonlinear effects of sand presence in gravel beds on bed-load transport rate of both fractions. In fact, in the two-fraction bed load formula appears a new ingredient with respect to that of Meyer-Peter and Müller that is the proportion F_i of fraction i on the bed surface where the subscript _i represents either the sand (s) or gravel (g) fraction. The proportion F_i, as a function of sand content f_s, physically represents the relative influence of the mechanisms controlling sand and gravel transport, associated with the change from a clast-supported to matrix-supported gravel bed. Moreover, since f_s spans between 0 and 1, phenomena that vary with f_s include the relative size effects producing ‘‘hiding’’ of fine grains and ‘‘exposure’’ of coarse grains. The ‘‘hiding’’ effect takes into account the fact that, while small grains are inherently 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, which the Meyer-Peter and Müller formula refers to. In gravel-bed rivers, this can cause ‘‘equal mobility", in which small grains can move just as easily as large ones. 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. Their model is based on the transport stage,''i.e.'' \phi, or ratio of bed shear stress to critical shear stress for the initiation of grain motion. Because their formula works with only two fractions simultaneously, they define the critical shear stress for each of the two grain size classes, \tau_, where _i represents either the sand (s) or gravel (g) fraction . The critical shear stress that represents the incipient motion for each of the two fractions is consistent with established values in the limit of pure sand and gravel beds and shows a sharp change with increasing sand content over the transition from a clast- to matrix-supported bed. 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 q_ 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, \phi. For \phi < \phi^': :W_i^* = 0.002 \phi^ and for \phi \geq \phi^': :W_i^* = A \left(1 - \frac\right)^. This equation asymptotically reaches a constant value of W_i^* as \phi becomes large and the symbols A,\phi^',\chi have the following values: :A = 70 ,\phi^'=1.19 ,\chi=0.908, \text :A = 115, \phi^'=1.27 ,\chi=0.923, \text In order to apply the above formulation, it is necessary to specify the characteristic grain sizes D_s for the sand portion and D_g for the gravel portion of the surface layer, the fractions F_s and F_g of sand and gravel, respectively in the surface layer, the submerged specific gravity of the sediment R and shear velocity associated with skin friction u_* .


= Kuhnle ''et al.''

= For the case in which sand fraction is transported by the current over and through an immobile gravel bed, Kuhnle ''et al.''(2013), following the theoretical analysis done by Pellachini (2011), provides a new relationship for the bed load transport of the sand fraction when gravel particles remain at rest. It is worth mentioning that Kuhnle ''et al.'' (2013) applied the Wilcock and Kenworthy (2002) formula to their experimental data and found out that predicted bed load rates of sand fraction were about 10 times greater than measured and approached 1 as the sand elevation became near the top of the gravel layer. They, also, hypothesized that the mismatch between predicted and measured sand bed load rates is due to the fact that the bed shear stress used for the Wilcock and Kenworthy (2002) formula was larger than that available for transport within the gravel bed because of the sheltering effect of the gravel particles. To overcome this mismatch, following Pellachini (2011), they assumed that the variability of the bed shear stress available for the sand to be transported by the current would be some function of the so-called "Roughness Geometry Function" (RGF), which represents the gravel bed elevations distribution. Therefore, the sand bed load formula follows as: :q^*_s = 2.29*10^ A(z_s)^\left(\frac \right)^ where :q^*_s = \frac the subscript _s refers to the sand fraction, s represents the ratio \rho_s/\rho_w where \rho_s is the sand fraction density, A(z_s) is the RGF as a function of the sand level z_s within the gravel bed, \tau_b is the bed shear stress available for sand transport and \tau_ is the critical shear stress for incipient motion of the sand fraction, which was calculated graphically using the updated Shields-type relation of Miller ''et al.''(1977).


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 c_0 at one particular elevation above the bed z_0 can be quantified. It is given by the expression: :\frac = \left frac\right 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 \alpha relates the eddy viscosity for momentum K_m to the eddy diffusivity for sediment, which is approximately equal to one. :\alpha = \frac \approx 1 Experimental work has shown that \alpha ranges from 0.93 to 1.10 for sands and silts. The Rouse profile characterizes sediment concentrations because the Rouse number includes both turbulent mixing and settling under the weight of the particles. Turbulent mixing results in the net motion of particles from regions of high concentrations to low concentrations. Because particles settle downward, for all cases where the particles are not neutrally buoyant or sufficiently light that this settling velocity is negligible, there is a net negative concentration gradient as one goes upward in the flow. The Rouse Profile therefore gives the concentration profile that provides a balance between turbulent mixing (net upwards) of sediment and the downwards settling velocity of each particle.


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", "Engelund-Hansen", "Yang" formulae. The first is for
sand Sand is a granular material composed of finely divided mineral particles. Sand has various compositions but is defined by its grain size. Sand grains are smaller than gravel and coarser than silt. Sand can also refer to a textural class ...
to granule-size gravel, and the second and third are for sand 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 \tau*^ where q_s* is the Einstein nondimensionalization for sediment volumetric discharge per unit width, c_f is a friction factor, and \tau* is the Shields stress. The Engelund-Hansen formula is one of the few sediment transport formulae in which a threshold "critical shear stress" is absent.


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. This is described by the endmember case in which the Rouse number is equal to 0 (i.e. the settling velocity is far less than the turbulent mixing velocity), which leads to a prediction of a perfectly uniform vertical concentration profile of material.


Total load

Some authors have attempted formulations for the total
sediment Sediment is a naturally occurring material that is broken down by processes of weathering and erosion, and is subsequently transported by the action of wind, water, or ice or by the force of gravity acting on the particles. For example, sand ...
load carried in water. These formulas are designed largely for sand, as (depending on flow conditions) sand often can be carried as both bed load and suspended load in the same stream or shoreface.


Bed Load Sediment Mitigation at Intake Structures

Riverside intake structures used in
water supply Water supply is the provision of water by public utilities, commercial organisations, community endeavors or by individuals, usually via a system of pumps and pipes. Public water supply systems are crucial to properly functioning societies. Th ...
,
canal Canals or artificial waterways are waterways or engineered channels built for drainage management (e.g. flood control and irrigation) or for conveyancing water transport vehicles (e.g. water taxi). They carry free, calm surface f ...
diversions, and water cooling can experience entrainment of bed load (sand-size) sediments. These entrained sediments produce multiple deleterious effects such as reduction or blockage of intake capacity, feedwater pump impeller damage or vibration, and result in sediment deposition in downstream pipelines and canals. Structures that modify local near-field secondary currents are useful to mitigate these effects and limit or prevent bed load sediment entry.


See also

* * * *


References


External links

* Liu, Z. (2001)
Sediment Transport
* Moore, A

Kent State. * Wilcock, P

January 26–28, 2004, University of California at Berkeley * Southard, J. B. (2007)

* Linwood, J,
Suspended Sediment Concentration and Discharge in a West London River.
{{Geologic Principles Fluid mechanics Sedimentology Environmental engineering Hydrology Physical geography Geological processes Transport phenomena