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Essay on Sediment Transportation
Essay Contents:
- Essay on the Introduction to Sediment Transportation
- Essay on the Regimes of Flow
- Essay on the Quantities of Sediment Transport Rates
- Essay on the Resistance to Flow in Alluvial Rivers
- Essay on the Bed Level Changes in Alluvial Channels
Essay # 1. Introduction to Sediment Transportation:
Sediments are generated due to erosion in the upper catchments of a river and their transport by the river towards the sea. On the way, some of this sediment might get deposited, if the stream power is not sufficient enough. The shear stress at the river bed causes the particles near the bed to move provided the shear is greater than the critical shear stress of the particle which is proportional to the particle size.
Hence, the same shear generated by a particular flow may be able to move of say, sand particles, but unable to cause movement of gravels. The particles which move due to the average bed shear stress exceeding the critical shear stress of the particle display different ways of movement depending on the flow condition, sediment size, fluid and sediment densities, and the channel conditions.
At relatively slow shear stress, the particles roll or slide along the bed. The particles remain in continuous contact with the bed and the movement is generally intermittent. Sediment material transported in this manner is termed as the contact load. On increasing the shear stress, some particles loose contact with the bed for some time, and hop or bounce from one point to another in the direction of flow. The sediment particles moving in this manner fall into the category of saltation load.
Contact load and saltation load together is generally termed as bed load, that is, the sediment load that is transported on or near the bed.
The further increase in shear stress, the particles may go in suspension and remain thus due to the turbulent fluctuations and get carried downstream by stream flow. These sediment particles are termed as suspension load. In most natural rivers, sediments are mainly transported as suspended load.
Bed load and suspended load together constitute, what is termed as, total load. A knowledge of the rate of total sediment transport for given flow, fluid and sediment characteristics is necessary for the study of many alluvial river processes. Engineers always need to bear in mind the fact that alluvial streams carry not only water but also sediment and the stability of a stream is closely linked with the sediment and transport rate.
Alluvial channels must be designed to carry definite water and sediment discharges. In effect, the rate of total load transport must be treated as a variable affecting the design of a channel in alluvium. Knowledge of total sediment transport rate is essential for estimating the amount of siltation in the reservoir upstream of a dam or the erosion and scour of the river bed below a dam.
Analysis of suspended load and the corresponding bed materials of various streams for their size analysis have shown that the suspended load can be divided into two parts depending on the sizes of material in suspension vis-a-vis the size analysis of the bed material.
One part of the suspended load is composed of these sizes of sediment found in abundance in the bed. The second part of the load is composed of those fine sizes not available in appreciable quantities in the bed. These particles, termed as the wash load, actually originate from the channel bank and the up slope area.
Essay # 2. Regimes of Flow:
When the average shear stress due to moving water on the river bed exceeds the critical shear stress, individual particles or grains making up the bed start moving. Since the particles are generally not exactly alike in size, shape or weight and also since a flow in a river with random turbulent fluctuations, all the bed particles do not start moving at the same time. Some particles move more than the rest, some slide and some hop depending on the uncertainties associated with the turbulent flow field and also the variation of drag due to particle shape.
Gradually, a plane channel bed develops irregular or regular shapes of unevenness which are called bed forms which vary according to the flow conditions and are termed as “Regimes of flow. Regimes of flow will considerably affect the velocity distribution, resistance relation and the transport of sediment in an alluvial river or channel.
The regimes of flow can be divided into the following categories:
1. Plane bed with no motion of sediment particles.
2. Ripples and dunes.
3. Transition, and
4. Antidunes.
1. Plane Bed with No Motion of Sediment Particles:
When the sediment and flow characteristics are such that the average shear stress on the bed is less than the critical shear stress, the sediment particle on the bed does not move. The water surface remains fairly smooth, if the Froude number is low. Resistance offered to the flow is on account of the grain roughness only, and the Manning’s equation can be used for prediction of the mean velocity of flow.
2. Ripples and Dunes:
The sediment particles on the bed start moving when the average shear stress of the flow exceeds the critical shear stress. This results in small triangular undulations as the channel bed and is known as ripples (Fig. 3.1).
Ripples do not occur for sediment particles coarser than 0.6 mm. The distance between the successive crests of the ripples is usually less than 0.4m and the height from the crest to the trough is usually less than 0.04m. The sediment movement is confined in the region near the channel bed. With increase in discharge, and consequently the average bed shear stress, the ripples grow in sizes which are then termed as dunes (Fig. 3.2).
Dunes are also triangular in shape but are larger than ripples. The triangular sections are not symmetric and the upstream face is inclined at about 10 to 20 degrees and downstream face at an angle of about 30 to 40 degrees with the horizontal. In rivers, dunes may be quite long and also the height (vertical distance between the crest and troughs) may be great.
For example, the dunes found in Lower Mississippi river have been found to be about 12 m height on an average and length of the order of few hundred meters. These bed forms are not static, which means that they gradually move forward with time, of course at a very slow and creeping velocity much less than the velocity of flow.
3. Transition:
With further increase in discharge over the dune bed, the ripples and dunes are washed away, and only some very small undulations are left. In some cases, the bed may become nearly flat but the sediment particles remain in motion. With slight increase in discharge, the bed and water surfaces attain a shape of sinusoidal wave form, which are called standing waves (Fig. 3.3).
These waves form and disappear and their size doesn’t increase much. Thus, in transition regime, rapid changes in bed and water configuration occur with relatively small changes in flow conditions. The Froude number is relatively high but the flow conditions are sub-critical.
4. Antidunes:
When the discharge is increased further and the Froude number increases to more than one, indicating super critical flow, the standing waves, which are symmetrical sand and water waves in the phase, move slowly upstream and break intermittently. These are called antidunes because the movement of the direction of dunes is backwards compared to the direction of flow. Since supercritical flow is rare in case of natural streams and channels, this type of bed forms do not occur generally in nature.
Essay # 3. Quantities of Sediment Transport Rates:
There are various formulae predicting the amount of sediment transported as:
i. Bed Load.
ii. Suspended Load.
iii. Total Load.
In many practical situations, the suspended load is measured or estimated, through the equation proposed by Hans Albert Einstein (1942), as this constitutes about 80 to 90 percent of the total load. After estimating suspended load a certain percentage of it is added to estimate total load.
Though there are probably over a dozen total load relationships essentially using a single representative size of the sediment mixture. While some of the methods may be considered semi-empirical, most of them are based on dimensional analysis and graphical plotting or regression analysis.
Hence the basis for the choice of an appropriate sediment transport relation in practice can only be the relative accuracy of these methods. Yang (1996) has shown through examples that the prediction of total load by different formulae may vary by as much as four times of one another.
According to Garde and Ranga Raju (2000), the methods proposed by the following researchers give better results than other methods:
(a) Ackers-White Method (1973).
(b) Engelund-Hansens Method (1967).
(c) Brownlie Method (1981).
(d) Yang Method (1973).
(e) Karim-Kennedy Method (1990).
There are other methods like that proposed by Van Rijn (1984 a and b) which estimated the bed load and suspended load components of the total load separately.
Some of the methods to calculate total load are mentioned in the following sections:
A. Ackers and White (1973) Method:
Ackers and White (1973) postulated that one part of the shear stress on the channel bed is effective in causing motion of coarse sediment, while in the case of fine sediment, suspended load movement predominates for which total shear stress is effective in causing sediment motion.
This method can be applied by following the steps mentioned below:
1. Determine the value of d*, the dimensional particle diameter, defined as:
Where the parameters on the right hand size of equation are:
i. d: Average particle diameter
ii. g: Acceleration due to gravity
iii. v: Kinematic Viscosity of water
iv. ϒs: Specific weight of sediment
v. ϒ: Specific weight of water
2. Determine the values of the coefficients c1, c2, c3 and c4 as:
3. Compute the value of particle mobility number Fg, given by the following expression:
τo = Bed shear stress
V = Average flow velocity
h = Water depth
4. Compute the value of dimensionless sediment transport function Gg, from the following expression:
5. Compute Sediment concentration, X, in p.p.m. (parts pre million) by weight of fluid using the following expression:
6. Compute total sediment load QT by multiplying sediment concentration (X), with discharge of the following water Q that is:
B. Engelund and Hansen’s Method:
Engelund and Hansen (1967) proposed a total load equation relating the sediment transport to the shear and the friction factor of the bed.
The following steps illustrate the method of application of their theory:
1. Compute the parameter 0, the dimensionless shear stress parameter by the following equation:
Where,
τ0 is the bed shear stress
ϒs is the density of sediment particles
ϒ is the density of water
d is the diameter of bed particles
2. Compute f1 the friction factor of the bed using the following expression:
Where,
g is the acceleration due to gravity
Sf is the energy slope
h is the depth of flow
V is the average flow velocity
3. Obtain the total sediment load gT from the following equation:
Essay # 4. Resistance to Flow in Alluvial Rivers:
Open channels with movable beds and boundaries are commonly encountered in water resources engineering. In contrast, some artificial channels and hydraulic structures with solid floors constitute a relatively smaller portion where the roughness coefficient can be treated as constant. In these cases, a resistance formula can be applied directly for the computation of velocity, slope, or depth, once a roughness coefficient has been determined.
Although this concept is also used for natural channels but strictly speaking, for these kinds of channels, a resistance formula cannot be applied directly without knowledge of how the resistance coefficient will change under different flow and sediment conditions. Extensive studies have been made by different researchers for determination of roughness coefficients of alluvial beds. Their results differ from each other.
Most of these studies have been based on limited laboratory data. Uncertainties remain regarding the applicability and accuracy of laboratory results to field conditions. The resistance equation expresses relationship among the mean velocity of flow V, the hydraulic radius R, and characteristics of the channel boundary.
For steady and uniform flow in rigid boundaries boundary channels, the Keulegan’s equations (logarithmic type) or power-law type of equations (like the Chezy’s and the Manninqs equations) are used.
Keulegan (1938) obtained the following logarithmic relations for rigid boundary channels:
Where,
τ0 is the bed shear stress
R is the hydraulic radius
ρ is the density of water
v is the Kinematic viscosity
ks is the grain roughness height
V is the average velocity at a point
For the range of 5 < R/ks < 700, the Manings equation is:
This has been found to be as satisfactory as the Keulegan’s equation for rough boundaries, n is the Manning’s roughness coefficient, which can be calculated using the Stickler’s equation;
Where, ks is the grain roughness height in metres.
Another power law type of equation is given by Chezy in the following form:
Where c is the Chezy’s coefficient of roughness. Comparing Manning’s and Chezy’s equations, one obtains:
In case of alluvial channels, where the bed is composed of mobile material, like sand, so long as average bed shear stress to on the boundary of the channel is less than the critical shear the channel boundary can be considered rigid and any of the resistance equations valid for rigid boundary channels would yield results for alluvial channels too.
However, as soon as sediment movement starts, undulations appear on the bed, thereby increasing the boundary resistance. Besides, some energy is required to move the grains. Further, the sediment particles in suspension also affect the resistance of alluvial streams. The suspended sediment particles dampen the turbulence or interfere with the production of turbulence near the bed where the concentration of these particles as well as the rate of turbulence production is maximum.
It is therefore, obvious that the problem of resistance in alluvial channels is very complex and the complexity further increases if one includes the effect of channel shape, non-uniformity of sediment size, discharge variation, and other factors on channel resistance. None of the resistance equations developed so far takes all these factors into consideration.
The methods for computing resistance in alluvial channels can be grouped into two broad categories:
i. Those which deal with the overall resistance offered to the flow using either a logarithmic or power type relationship for the mean velocity, and
ii. Those in which the 0 total resistance is separated into the resistance given by the grains of sand forming the channel bed and the resistance of the undulations in the bed. Thus, in this method, the total resistance is studied as a combination of grain resistance and form resistance.
These two methods are discussed in the following sections:
i. Formula for Total Resistance in Alluvial Channels:
One of the earliest resistance relationships for alluvial channel flow was proposed by Lacey on the basis of stable canal data from northern India.
The equation for mean velocity in SI units is:
V = 10.8 R2/3 S1/2
where R is the hydraulic radius, S is the friction slope; V is the average velocity. This equation, however, is not applicable at all stages of the river and hence, it cannot be used reliably for all types of alluvial rivers and channels.
Another relation obtained by Indian researchers is that by Garde and Ranga Raju and is expected to yield results with accuracy ± 30 percent. The method can be applied by following the procedural steps mentioned below. Remember that the average velocity V to be obtained for a given friction slope Sf. Another parameter that is related to the roughness of the bed material is d50, or the mean diameter of bed grains.
(a) For a particular water level, find out the hydraulic radius R and the area of cross section A.
(b) From Fig. 3.4 and 3.5 determine factors k1, and k2 corresponding to d50.
Where,
D is the water depth
Sf is the friction slope
Δϒs is equal to ϒs – ϒ in which
ϒs is the specific weight of sediment and
ϒ is the specific weight of water
Corresponding of f1 computed in step (c)
(e) Knowing f2 compute the value of V.
ii. Formula for Separate Resistance due to Grain and Form:
Here too, there are several methods.
One of the formula is quoted here, due to van Rijin (1984), states the following:
where,
V is the average velocity
τ0 is the bed shear stress
R is the hydraulic radius
Ks is the sum of the roughness corresponding to grain and form resistance, that is in which
Ks2 is related to the height of undulation (h) and the length of the dunes (L) as given by the formula:
Essay # 5. Bed Level Changes in Alluvial Channels:
Fig. 3.7 shows alluvial stream bed changes due to construction of a dam.
As water resource engineers, one is interested to find a quantitative assessment to the amount of sediment deposition in the reservoir on the dam upstream or the extent of riverbed scour in the reach downstream.
Other situations in which alluvial riverbed levels get changed due to the presence of a structure in the river are given in the following examples:
a. Scour around Bridge Piers:
Bridges, crossing alluvial rivers and channels have their piers resting on foundations within the rivers. As may be seen from the figure, the foundation well extends within the river bed and determination of its depth depends to what extent the riverbed would scour during floods (Fig. 3.8).
Some bridges are constructed on piles, instead of wells but there too the length of the piles depends on the extent of scour that is expected during floods.
It may be mentioned that the deepening of riverbed around bridge foundations occurs only during the passage of a high flood. Once the flood peak passes and the flood starts receding the scoured riverbeds start getting filled up with sediment carried by the river.
b. Sediment Movement near Intakes:
Water intakes for irrigation or water supply are often faced with the problem of excess sediment removal or deposition near its vicinity (Fig. 3.9). Sometimes, the gates of the intake and that of the barrage are not properly coordinated which results at undesirable sediment erosion and deposition.
