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15.1 SEDIMENT PROPERTIES
Rainfall and surface runoff are the agents responsible for the detachment and movement of soil particles on the land surface. These soil particles are referred to as sediments. The study of sediment detachment and movement is an important subject in engineering hydrology. Indeed, the subject of sediment transcends engineering hydrology to encompass the related fields of fluvial geomorphology, sediment transport, and sedimentation and river engineering [2, 4, 25, 40]. The study of sediments in the hydrologic cycle can be divided into the following three processes:
These can be linked to the various liquidtransport phases of the hydrologic cycle. At the catchment level, sediment production by soil particle detachment is primarily the result of raindrop impact. Once detachment has taken place, surface runoff acts to transport sediment downslope, first as overland flow (sheet and rill flow), and eventually as stream and river flow. Deposition of sediment occurs at any point downstream where the kinetic energy of the flow is insufficient to support sediment entrainment in the flowing water. Sediment production refers to the processes by which sediment is produced, the identification of sediment sources and amounts, and the determination of sediment yields. The source of sediment can usually be traced back to the upland catchments, although these are by no means the only source. In certain cases, streambank erosion in the lower valleys may constitute an important source of sediment. Sediment from upland catchments is delivered to streams and rivers, wherein sediment transport takes place. Sediment transport refers to the mechanisms by which sediment is moved downstream by flowing water, either in suspension or by rolling and sliding along the river bottom. The transport of sediment continues in the downstream direction until the flow is no longer able to carry the sediment, at which time sediment deposition occurs. Typically, the first opportunity for sediment deposition is at the entrance to reservoirs and water impoundments, where the flow is decelerated by the action of structures. Deposition is also likely to occur naturally, for instance, downstream of sudden decreases in energy slope or in situations where the capacity of the flow to carry sediment is substantially diminished. In the absence of these natural or humanmade features, sediment transport by the flow may continue unabated until it reaches the estuary or ocean, at which time the flow loses its kinetic energy and sediment deposition goes on to contribute to delta growth. Sediment Formation Sediments are the products of disintegration and decomposition of rocks. Disintegration includes all processes by which rocks are broken into smaller pieces without substantial chemical change. The disintegration of rocks is caused either by large temperature changes or by alternate cycles of freezing and thawing. Decomposition refers to the breaking down of mineral components of rocks by chemical reaction. Decomposition includes the follwing processes: (1) carbonation, (2) hydration, (3) oxidation, and (4) solution. Carbon dioxide (CO_{2}), present in the atmosphere and organic sources, readily unites with water to form carbonic acid (H_{2}CO_{3}). Carbonic acid reacts with feldspars to produce clay minerals, silica, calcite, and other relatively soluble carbonates containing potassium, sodium, iron, and magnesium. The addition of water to many of the minerals present in igneous rocks results in the formation of clay minerals such as aluminum silicates. Many secondary minerals are formed from igneous rocks by oxidation, which is accelerated by the presence of moisture in the air. Solution is another important mechanism in the alteration of igneous rock. Oxygen combines with other elements to form sulfates, carbonates, and nitrates, most of which are relatively soluble. The amount (by weight) of dissolved solids carried by streams in the contiguous United States has been estimated at more than 50 percent of the amount of suspended sediment [32]. Particle Characteristics The characteristics of mineral grains help describe the properties of sediments. Among them are:
Size. Particle size is a readily measured sediment characteristic. A widely accepted classification of sediments according to size is shown in Table 151. Five groups of sizes are included in this table:
Boulders and cobbles can be measured individually. Gravelsize particles can be measured individually or by sieving. Sandsize particles are readily measured by sieving. A No. 200 screen is used to separate sand particles from finer particles such as silt and clay. Silt and clay particles are separated by measuring the differences in their rate of fall in still water.
Shape. Particle shape is numerically defined in terms of its sphericity and roundness. True sphericity is the ratio of the surface area of a sphere having the same volume as the particle to the surface area of the particle. The practical difficulty of measuring true sphericity has led to an alternate definition of sphericity as the ratio of the diameter of a sphere having the same volume as the particle (i.e., the nominal diameter) to the diameter of a sphere circumscribing the particle. Accordingly, a sphere has a sphericity of 1, whereas all other shapes have a sphericity of less than 1.
Roundness is defined as the ratio of the average radius of curvature of the particle edges to the radius of the largest inscribed circle. It refers to the sharpness of the edges of sediment particles and is commonly used as an indicator of particle wear. In sediment studies, the shape factor is often used as an indicator of particle shape:
in which SF = shape factor and a, b, and c are three orthogonal particle length dimensions. According to Corey [12], a is the longest, b is the intermediate, and c is the shortest length dimension. However, according to McNown and Malaika [34], c is measured in the direction of motion, and a and b are perpendicular to c. Specific Weight and Specific Gravity. The specific weight of a sediment particle is its weight per unit volume. The specific gravity of a sediment particle is the ratio of its weight to the weight of an equal volume of water. Most sediment particles consist of either quartz or feldspar, which are about 2.65 times heavier than water. Therefore, the specific gravity of sediments is generally considered to be about 2.65. Exceptions are heavy minerals (for instance, magnetite, with specific gravity of 5.18), but these occur rather infrequently. Fall Velocity. The fall velocity of a sediment particle is its terminal rate of settling in still water. Fall velocity is a function of size, shape, and specific weight of the particle, and the specific weight and viscosity of the surrounding water. For spherical particles, the fall velocity (derived from a balance of submerged weight and drag) can be expressed as follows:
in which w = fall velocity, g = gravitational acceleration, d_{s} = particle diameter, C_{D} = drag coefficient (dimensionless), γ_{s} = specific weight of sediment particles, and γ = specific weight of water. The drag coefficient is a function of the particle Reynolds number R, defined as follows:
in which ν = kinematic viscosity of the fluid. For particle Reynolds numbers less than 0.1, the drag coefficient is equal to C_{D} = 24/R. Substituting this value of C_{D} into Eq. 152 leads to Stokes' law:
For particle Reynolds numbers greater than 0.1, the drag coefficient is still a function of Reynolds number, but the relationship cannot be expressed in analytical form. The relationship of C_{D} versus R for a wide range of particle Reynolds numbers is shown in Fig. 151 [38].
In many applications, the drag coefficient is not known a priori; in this case, an iterative solution is warranted.
A particle Reynolds number is assumed, and the drag coefficient is obtained from A fall velocity is calculated with Eq. 152, and a Reynolds number with Eq. 153. The iteration is continued untill there is sufficient agreement between assumed and calculated Reynolds numbers. The procedure is illustrated by Example 152.
Standard fall velocity. Since fall velocities vary with fluid temperature and viscosity, two particles of the same size, shape, and specific gravity, falling on two fluids of different viscosity, or in the same fluid at different temperatures, will have different fall velocities. To provide a measure of comparison, the concept of standard fall velocity was developed [23]. The standard fall velocity of a particle is the average rate of fall that it would attain if falling alone in quiescent water of infinite extent at the temperature of 24°C. Likewise, the standard fall diameter of a particle is the diameter of an equivalent sphere having the same standard fall velocity and specific gravity. Size Distribution of Sediment Deposits An important property of sediment deposits is the size distribution of its individual particles. Particle size distribution is a key to predicting the behavior of a sediment deposit and estimating its specific weight. A sediment sample containing a wide range of particle sizes is well graded, or poorly sorted. Conversely, a sediment sample consisting of particles in a narrow range of particle sizes is poorly graded, or well sorted. The size distribution of sediments can be measured in several ways. The coarsest fraction can be separated by direct measurement for boulders and cobbles and by sieving for sands and gravels. For most applications involving sediments in the sand size, the visual accumulation (VA) tube is a fast, economical, and accurate method of determining the size distribution of sediment samples. In the VA tube method, the particles start falling from a common source and become stratified according to their relative settling velocities. At a given instant, the particles coming to rest at the bottom of the tube are of a certain sedimentation size, finer than particles that have already settled and coarser than those still remaining in suspension. See [19] for a description of laboratory methods for sediment analysis. Specific Weight of Sediment Deposits The specific weight of a sediment deposit is the dry weight of sedimentary material per unit volume. Due to the voids between sediment particles, the specific weight of a sediment deposit is always less than the specific weight of individual particles. A knowledge of the specific weight of a sediment deposit allows the conversion of sediment weights to sediment volumes and vice versa. In particular, the specific weight of a sediment deposit is useful in studies of reservoir storage depletion by deposition of fluvial sediments. Factors influencing the specific weight of a sediment deposit are: (1) its mechanical composition, (2) the environment in which the deposits are formed, and (3) time. Coarse materials, e.g., boulders, gravel, and coarse sand, are deposited with specific weights very nearly equal to their ultimate value and change very little with time. However, fine materials such as silts and clays may have initial specific weights that are only a fraction of their ultimate value. Lane and Koelzer [29] have developed an empirical relationship to account for the variation of the specific weight of sediment deposits in reservoirs with time. Their relationship is:
in which W = specific weight of the deposit after T years; W_{1} = initial specific weight of the deposit, measured after 1 y of consolidation; and B = a constant. Table 152 shows values of W_{1} and B as a function of sediment size and mode of reservoir operation. For mixed deposits, a weighted average of specific weight is appropriate.
Drying or aeration of a sediment deposit helps to accelerate consolidation through removal of the water from the pore spaces. Table 153 shows the effect of aeration on the specific weight of sediment deposits for several types of soil mixtures [18].
15.2 SEDIMENT PRODUCTION
The presence of sediment in streams and rivers has its origin in soil erosion. Erosion encompasses a series of complex and interrelated natural processes that have the effect of loosening and moving away soil and rock materials under the action of water, wind, and other geologic factors. In the long term, the effect of erosion is the denudation of the land surface, i.e., the removal of soil and rock particles from exposed surfaces, their transport to lower elevations, and eventual deposition. The rate of landscape denudation can be quantified from a geological perspective. For instance, the number of centimeters of denudation per 1000 y can be used as a measure of the erosive activity of a region. Geologic measures of landscape denudation appear insignificant when compared to the typical timespan of human activity, say 25 to 100 y. However, the quantities of sediment moved may be important when considering the impact that sediment loads have on the operation and design life of reservoirs and hydraulic structures. At the outset of the study of sediment production, a distinction should be made between the amount of sediment eroded at the source(s) and the amount of sediment delivered to a downstream point. Gross sediment production refers to the amount of sediment eroded and removed from the source(s). Sediment yield refers to the actual delivery of eroded soil particles to a given downstream point. Since eroded particles may be deposited before they reach the downstream point of interest, sediment yield quantities are generally less than gross sediment production quantities. The ratio of sediment yield to gross sediment production is the sediment delivery ratio (SDR). Gross sediment production is commonly measured in terms of weight of sediment per unit drainage area per unit timefor instance, metric tons per hectare per year, or tons per acre per year. Sediment yield is expressed in terms of weight per unit time past a certain point; for instance, metric tons per day at the catchment outlet. Normal and Accelerated Erosion According to the timespan involved, erosion may be classified as:
Normal erosion has been occurring at variable rates since the first solid materials formed on the surface of the earth. Normal erosion is extremely slow in most places and is largely a function of climate, parent rocks, precipitation, topography, and vegetative cover. Accelerated erosion occurs at a much faster rate than normal, usually through reduction of vegetative cover. Deforestation, overgrazing, overcultivation, urban sprawl, and the systematic destruction of natural vegetation result in accelerated erosion. Sediment Sources According to its source, erosion may be classified as:
Rill erosion is the removal of soil by small concentrations of flowing water (rills). Gully erosion is the removal of soil from incipient channels that are large enough so that they cannot be removed by normal cultivation. Channel erosion refers to erosion occurring in stream channels in the form of streambank erosion or streambed degradation. For practical purposes, a distinction is made between upland and channel erosion. Upland erosion is mostly made up of sheet and rill erosion, whereas channel erosion encompasses all other sediment sources, specifically excluding sheet and rill erosion. Upland Erosion and the Universal Soil Loss Equation In the United States, the prediction of upland erosion (i.e., sheet and rill erosion) is commonly made by the Universal Soil Loss Equation (USLE), developed by the USDA Agricultural Research Service in cooperation with the USDA Soil Conservation Service (now Natural Resources Conservation Service) and certain state experiment stations. The universal soil loss equation is [46]:
in which A = (annual) soil loss due to sheet and rill erosion in tons per acre per year: R = rainfall factor; K = soil erodibility factor; L = slopelength factor; S = slopegradient factor; C = crop management factor; and P = erosion control practice factor. Rainfall Factor. When factors other than rainfall are held constant, soil losses from cultivated fields are shown to be directly proportional to the product of the storm's total kinetic energy E and its maximum 30minute intensity I. The product EI reflects the combined potential of raindrop impact and runoff turbulence to transport dislodged soil particles. The sum of EI products for a given year is an index of the erosivity of all rainfall for that year. The rainfall factor R is the average value of the series of annual sums of EI products. Values of R applicable to the contiguous United States are shown in Fig. 152.
Soil Erodibility Factor. The soil erodibility factor K is a measure of the resistance of a soil surface to erosion. It is defined as the amount of soil loss (in tons per acre per year) per unit of rainfall factor R from a unit plot. A unit plot is 72.6 ft long, with a uniform lengthwise gradient of 9 percent, in continuous fallow, tilled up and down the slope. Values of K for 23 major soils on which erosion plot studies were conducted since 1930 are listed in Table 154. Soil erodibility factors for other soils have been estimated by comparing their characteristics with those of the 23 soils listed in Table 154. A method for determining the soil erodibility factor based on soil characteristics has been proposed by Wischmeier et al. [47].
Slopelength and Slopegradient Factors. The rate of soil erosion by flowing water is a function of slope length (L) and gradient (S). For practical purposes, these two topographic characteristics are combined into a single topographic factor (LS). The topographic factor is defined as the ratio of soil loss from a slope of given length and gradient to the soil loss from the unit plot (of 72.6 ft length and 9 percent gradient). Figure 153 shows values of LS as a function of slope length and gradient.
Cropmanagement Factor. The cropmanagement factor C is defined as the ratio of soil loss from a certain combination of vegetative cover and management practice to the soil loss resulting from tilled, continuous fallow. Values of C range from as little as 0.0001 for undisturbed forest land to a maximum of 1.0 for disturbed areas with no vegetation. Values of C for cropland are estimated on a local basis. Table 155 shows values of C for permanent pasture, grazed forest land, range, and idle land. Table 156 shows values of C for undisturbed forest land.
Erosion Control Practice Factor. The erosion control practice factor P is defined as the ratio of soil loss under a certain erosioncontrol practice to the soil loss resulting from straightrow farming. Practices for which P have been established are contouring and contour stripcropping. In contour stripcropping, strips of sod or meadow are alternated with strips of row crops or small grains. Values of P used for contour stripcropping are also used for contourirrigated furrows. Table 157 shows values of P for contourfarmed terrace fields.
Use of the Universal Soil Loss Equation. The USLE computes upland erosion from small watersheds on an average annual basis. It includes the detachment and transport components, but it does not account for the deposition component. Therefore, the USLE cannot be used to compute sediment yield. For example, in a 1000mi^{2} drainage basin, only 5 percent of the soil loss computed by the USLE may appear as sediment yield at the basin outlet. The remaining 95 percent is redistributed on uplands or flood plains and does not constitute a net soil loss from the drainage basin.
Channel Erosion Channel erosion includes gully erosion, streambank erosion, streambed degradation, floodplain scour, and other sources of sediment, excluding upland erosion. Gullies are incipient channels in process of development. Gully growth is usually accelerated by severe climatic events, improper land use, or changes in stream base levels. Most of the significant gully activity, in terms of the quantities of sediment produced and delivered to downstream locations, is found in regions of moderate to steep topography having thick soil mantles. The total sediment outflow from gullies is usually less than sheet and rill erosion [33]. Streambank erosion and streambed degradation can be significant in certain cases. Changes in channel alignment and/or removal of natural vegetation from stream banks may cause increased bank erosion. Streambed degradation, typically downstream of reservoirs, can also constitute an additional source of sediment (Fig. 154).
Methods for determining soil loss due to the various types of channel erosion include the following:
Field surveys can often provide sufficient data to estimate streambank erosion as follows [44]:
in which S = annual volume of streambank erosion; H = average height of bank; L = length of eroded bank, each side of channel if both sides are eroding; and R = annual rate of bank recession (net rate if one side is eroding while the other is depositing). Streambed degradation can be estimated as follows [44]:
in which S = annual volume of streambed degradation; W = average bottom width of degrading channel reach; L = length of degrading channel reach; and D = annual rate of streambed degradation. Accelerated Erosion Due to Stripmining and Construction Activities Stripmining and construction activities greatly accelerate erosion rates. For instance, Collier et al. [10] found that a watershed with 10.4 percent of its area stripmined eroded 76 times more sediment than a similar undisturbed watershed. Wolman and Shick [48] found that sediment concentrations in streams draining construction areas ranged from 3000 to 150,000 ppm, compared to concentrations of 2000 ppm in comparable natural settings. These studies indicate that humaninduced land disturbances have a substantial impact on sediment production. With a careful choice of factors, the USLE can be used to compute soil loss from disturbed lands. Sediment Yield In engineering applications, the quantity of sediment eroded at the sources is not as important as the quantity of sediment delivered to a downstream point, i.e., the sediment yield. The sediment yield is calculated by multiplying the gross sediment production, which includes all types of erosion (sheet, rill, gully, and channel erosion) by a sediment delivery ratio that varies in the range 0 to 1 (it can also be expressed as a percentage). Therefore, a calculation of sediment yield hinges upon an estimate of gross sediment production (from the various sources) and an appropriate sediment delivery ratio. Sediment Delivery Ratio The sediment delivery ratio (SDR) is a function of the following factors:
The sediment source has an influence on the delivery ratio. Not all sediments originating in sheet and rill erosion are likely to enter the fluvial transport system; however, sediments produced by channel erosion are generally closer to the transport system and are more likely to be delivered to downstream points. The proximity of the sediment source to the transport system is also an important variable in the estimation of the SDR. The amounts of sediment delivered to downstream points will depend to a large extent on the ability of the fluvial transport system to entrain and hold on to the sediment particles. Silt and clay particles can be transported much more readily than sand particles; therefore, the delivery of silts and clays is more likely to occur than that of sands. Catchment characteristics also affect sediment delivery ratios. High relief often indicates both a high erosion rate and a high SDR. High channel density is usually an indication of an efficient transport system and, consequently, of a high SDR. Estimation of Sediment Delivery Ratios. The SDR is the ratio of sediment yield to gross sediment production. Sediment yield can be evaluated by one of several methods. At reservoir locations, estimates of sediment yield can be obtained by reservoir sedimentation surveys. Alternatively, sediment yield can be evaluated by direct measurement of sediment load at the point of interest. Estimates of gross sediment production from upland sources can be obtained using either the USLE formula or a regionally derived formula for sheet and rill erosion. When warranted, this estimate can be augmented by field estimates of gully and channel erosion. In the absence of actual measurements, statistical analysis can be used to develop regional regression equations to predict SDR. The simplest SDR prediction equation is that based solely on drainage area, as shown in Fig. 154. This figure shows that SDR varies approximately in inverse proportion to the 1/5 power of the drainage area. Other sources, however, have quoted values of this power as low as 1/8 [2]. The fact remains that the greater the drainage area, the smaller the catchment relief and the greater the chances for sediment deposition within the catchment; consequently, the smaller the catchment's SDR.
Rough estimates of SDR can be obtained from
An example of the use of statistical analysis for the estimation of sediment delivery ratios is given by Roehl [37]. Using data from the southeast Piedmont region of the United States, he developed the following predictive equation:
in which:
Values of SDR measured by Roehl in the Piedmont area were in the range 3.7 to 59.4 percent. Empirical Formulas for Sediment Yield
As with the SDRs, statistical analysis can be used to develop regional equations for the prediction of sediment yield. A study by Dendy and Bolton [13] showed that sediment yield can be related to catchment area and mean annual runoff. Sediment Yield versus Drainage Area. Dendy and Bolton studied sedimentation data from about 1500 reservoirs, ponds, and sediment detention basins. In developing their formulas, they used data from about 800 of these reservoirs with drainage areas greater than or equal to 1 mi^{2}. The smaller watersheds (those of drainage area less than 1 mi^{2}) were excluded because of their large variability of sediment yield, reflecting the diverse effects of soils, local terrain, vegetation, land use, and agricultural practices. For drainage areas between 1 and 30,000 mi^{2}, Dendy and Bolton found that the annual sediment yield per unit area was inversely related to the 0.16 power of the drainage area:
in which:
Sediment Yield versus Mean Annual Runoff. Dendy and Bolton studied sedimentation data from 505 reservoirs having mean annual runoff data. Annual sediment yield per unit area was shown to increase sharply as mean annual runoff Q increased from 0 to 2 in. Thereafter, for mean annual runoff from 2 to 50 in. annual sediment yield per unit area decreased exponentially. This led to the following equations. For Q < 2 in.:
For Q ≥ 2 in.:
in which Q_{R} = reference mean annual runoff, Q_{R} = 2 in. Dendy and Bolton combined Eqs. 1510 and 1511 into a set of equations to express sediment yield in terms of drainage area and mean annual runoff. For Q < 2 in.:
For Q ≥ 2 in.:
For S_{R} = 1645 tons/mi^{2}/y, Q_{R} = 2 in., and A_{R} = 1 mi^{2}, Eq. 1512 reduces to the following: For Q < 2 in.:
For Q ≥ 2 in.:
Equations 512 and 513 are based on average values of grouped data; therefore, they should be used with caution. In certain cases, local factors such as soils, geology, topography, land use, and vegetation may have a greater influence on sediment yield than either mean annual runoff or drainage area. Nevertheless, these equations provide a first approximation to the regional assessment of sediment yield for watershed planning purposes.
Other widely used sediment yield prediction formulas are the modified universal soil loss equation (MUSLE), developed by Williams [45], and the Flaxman formula [17]. Unlike the USLE, which is based on annual values, the MUSLE is intended for use with individual storms. The Flaxman formula was developed using data from the western United States and is therefore particularly applicable to that region. 15.3 SEDIMENT TRANSPORT
Sediment transport refers to the entraInment and movement of sediment by flowing water. An understanding of the principles of sediment transport is essential for the interpretation and solution of many hydraulic, hydrologic, and water resources engineering problems. The study of sediment transport can be divided into:
Sediment transport mechanics refers to the fundamental processes by which sediment is entrained and transported by flowing water. Sediment transport prediction refers to the methods and techniques to predict the equilibrium or steady rate of sediment transport in streams and rivers. The prediction of sediment transport is accomplished by means of a sediment transport formula. Sediment routing refers to the nonequilibrium or unsteady sediment transport processes, the net result of which is either the aggradation or degradation of stream and river beds. The description of sediment transport is based on principles of fluid mechanics, river mechanics, and fluvial geomorphology. The energy and turbulence of the flow gives streams and rivers the capacity to entrain and transport sediment. The sediment being transported can originate in either:
A significant feature of sediment transport is the entrainment and transport by the flow of the material constituting the channel bed. Thus, sediment transport serves not only as the means for the movement of sediment from upstream to downstream but also as the mechanism by which streams and rivers determine their own crosssectional shape and boundary roughness. While the transport of sediment is a fluid mechanics subject, the interaction between flowing stream and its boundary is a river mechanics subject. Sediment Transport Mechanics Sediment load or sediment discharge is the total amount of sediment transported by a stream or river past a given point, expressed in terms of weight per unit time. Based on the predominant mode of transport, sediment load can be classified into:
Bed load is the fraction of sediment load that moves by saltation and rolling along the channel bed, primarily by action of bottom shear stresses caused by vertical velocity gradients. Suspended load is the fraction of sediment load that moves in suspension by the action of turbulence. Particles transported as bed load are coarser than particles transported as suspended load. However, the distinction between bed load and suspended load is not allexclusive; some particles may move as bed load at one point, as suspended load at another, and vice versa. Based on whether the particle sizes are represented in the channel bed, sediment load can be classified into:
Bedmaterial load is the fraction of sediment load whose particle sizes are significantly represented in the channel bed. Conversely, finematerial load (commonly referred to as wash load) is the fraction of sediment load whose particle sizes are not significantly represented in the channel bed. Stated in other terms, bedmaterial load is the coarser fraction of sediment load that may have originated in the channel bed and that may be subject to deposition under certain flow conditions. Wash load is the finer fraction of sediment load that has not originated in the channel bed and that is not likely to deposit. Wash load is then, washed through the reach, largely unaffected by the hydraulics of the flow. The relationship between the two classifications of sediment load is shown in Fig. 156 [11]. This figure shows that the concepts of bed load and wash load are mutually exclusive. The middle overlap is the suspended bedmaterial load, i.e., the fraction of sediment load that moves in suspended mode and is composed of particle sizes that are represented in the channel bed.
Initiation of Motion. Water flowing over a streambed has a marked vertical velocity gradient near the streambed. This velocity gradient exerts a shear stress on the particles lying on the streambed, i.e., a bottom shear stress. For wide channels, the bottom shear stress can be approximated by the following formula [5]:
in which τ_{o} = bottom shear stress; γ = specific weight of water; d = flow depth; and S_{o} = equilibrium or energy slope. There is a threshold value of bottom shear stress above which the particles actually begin to move. This threshold value is referred to as critical bottom shear stress, or critical tractive stress. Determinations of critical tractive stress for given flow and sediment conditions are largely empirical in nature. The Shields curve, shown in Fig. 157, represents the earliest attempt to combine theoretical and empirical approaches to estimate critical tractive stress [2]. The Shields curve depicts the threshold of motion, i.e., the condition separating motion (above the curve) from no motion (below the curve) [39].
The abscissa in the Shields diagram is the boundary Reynolds number, defined as:
in which R_{*} = boundary Reynolds number; U_{*} = shear velocity; d_{s} = mean particle diameter; and v = kinematic viscosity of water. The shear velocity is defined as follows:
in which ρ = density of water. The ordinate in the Shields diagram is the dimensionless tractive stress, defined as follows:
in which τ_{*} = dimensionless tractive stress. The Shields diagram indicates that, within a midrange of boundary Reynolds numbers (approximately 2200), the dimensionless critical tractive stress can be taken as a constant for practical purposes. Therefore, within this range, the critical tractive stress is proportional to the sediment particle size. For instance, assuming a value of dimensionless critical tractive stress τ_{*} = 0.04 (from the Shields diagram, Fig. 157), Eq. 1517 leads to:
in which τ_{c} = critical tractive stress. For quartz particles (γ_{s} = 2.65 × 62.4 lb/ft^{3}), Eq. 1518 reduces to:
in which critical tractive stress is given in pounds per square foot and particle diameter in inches. Extensive experimental studies by Lane [30] have shown that the coefficient in Eq. 1519 is around 0.5. Lane, however, used the d_{75} particle size (i.e., the diameter for which 75% by weight is finer) instead of the mean diameter (d_{50}) used by Shields.
Forms of Bed Roughness. Streams and rivers create their own geometry. In particular, alluvial rivers determine to a large extent their crosssectional shape and boundary friction as a function of the prevailing water and sediment discharge. An inherent property of river flows is their tendency to minimize changes in stage caused by changes in discharge. This is accomplished through a continuous adjustment in boundary friction in such a way that high values of friction prevail during low flows, while low values of friction prevail during high flows [27]. Bed forms are threedimensional configurations of bed material, which are formed in streambeds by the action of flowing water. Adjustments in boundary friction are made possible by the existence of these bed forms, which develop during low flows (lower flow regime) only to be obliterated during high flows (upper flow regime) [40]. Boundary friction consists of two parts:
Grain roughness is a function of particle size; form roughness is a function of size and extent of bed forms. Grain roughness is essentially a constant when compared to the variation in form roughness that can be attributed to bed forms. Studies have shown that several forms of bed roughness can exist on river bottoms, depending on the energy and bedmaterial transport capacity of the flow. In the absence of sediment movement, the bed configuration is that of plane bed with no sediment motion. With sediment movement, the following forms of bed roughness have been identified:
Sketches of these bed configurations are shown in Fig. 158 [40].
Figure 158 Forms of bed roughness in alluvial channels [40]. The occurrence of different forms of bed roughness can be shown to be related to the median fall diameter of the particles forming the bed and to the stream power of the flow. Stream power is defined as the product of bottom shear stress and mean velocity.
Such a relationship is shown in For low values of stream power, i.e., below the critical tractive stress, there is no bed load transport, and the streambed remains essentially flat. This is the condition of plane bed with no sediment motion. An increase in stream power leads first to ripples, then to dunes with superposed ripples, and, subsequently, to dunes. Ripples, however, are a rare occurrence for sediments coarser than 0.6 mm. Dunes are longer and bigger than ripples and occur at flow velocities and sediment loads that are generally greater than those of ripples. The plane bed with sediment motion represents the condition at which the flow's stream power is large enough to obliterate the dunes, essentially eliminating the form roughness. The plane bed, then, represents the condition of minimum boundary friction. For high values of stream power, antidunes (upper regime) form in conjunction with surface waves, with the tendency for upstream movement, usually under supercritical flow conditions. For even higher values of stream power, e.g., in very steep streams, the bed configuration resembles a sequence of chutes and pools [40].
The assessment of bedform type has practical implications for engineering hydrology. Bedforms determine boundary roughness; in turn, boundary roughness determines river stages. For instance, ripples are associated with values of Manning n in the range 0.018 to 0.030, with form roughness usually a fraction of grain roughness. Dunes, however, are associated with n values in the range 0.020 to 0.040, with form roughness of the same order as grain roughness. Moreover, plane bed with sediment motion is associated with relatively low n values, in the range 0.012 to 0.015, and in this case, form roughness is minimal. The proper assessment of boundary friction, including its variation as the flow changes from lower regime (ripples, ripples on dunes, and dunes) to upper regime (plane bed with sediment movement, antidunes, and chutes and pools) is an important subject in engineering hydrology and fluvial hydraulics. Concentration of Suspended Sediment. For a given volume of watersediment mixture, the suspendedsediment concentration is the ratio of the weight of dry sediment to the weight of the watersediment mixture, expressed in parts per million. To convert the concentration in ppm to milligrams per liter (mg/ L), the applicable factor ranges from 1.0 for concentrations between 0 and 15,900 ppm, to 1.5 for concentrations between 529,000 and 542,000 ppm, as shown in Table 158.
The suspendedsediment concentration varies with the flow depth, usually being higher near the stream bed and lower near the water surface. The coarsest sediment fractions, typically those in the sand size, exhibit the greatest variation in concentration with flow depth. The finer fractions, i.e., silt and clay particles, show a tendency for a nearly uniform distribution of suspendedsediment concentration with flow depth. Figure 1510 shows the variation of suspendedsediment concentration along the flow depth. In this figure, y is the fraction of flow depth measured from the channel bottom, a is the reference distance measured from the channel bottom, and d is the flow depth. The abscissas show the dimensionless ratio C/C_{a}, in which C_{a} is the sediment concentration at the reference distance and C is the sediment concentration at a distance (y  a). The value of a is small compared to d. The plot of Fig. 1510 is specifically for the case of a/d = 0.05. The ordinates show the dimensionless ratio (y  a)/(d  a). The curve parameter z is the Rouse number, defined as follows:
in which z = Rouse number (dimensionless); w = fall velocity of sediment particles; β = a coefficient relating mass and momentum transfer (β ≅ 1 for fine sediments); κ = von Karman's constant (κ = 0.4 for clear fluids); and U_{*} = shear velocity, Eq. 1516. From Fig. 1510, it is seen that for high Rouse numbers the variation of suspended sediment concentration along the flow depth is quite marked. Conversely, for low Rouse numbers there is a tendency for greater uniformity of suspendedsediment concentration along the flow depth.
Sediment Transport Prediction Sediment load, sediment discharge, and sediment transport rate are synonymous in practice. However, bed load, suspended bedmaterial load, and wash load are mutually exclusive. Sediment transport prediction refers to the estimation of sediment transport rates under equilibrium (i.e., steady uniform) flow conditions. There are numerous formulas for the prediction of sediment transport [2]. Most formulas compute only bedmaterial load, consisting of bed load and suspended bedmaterial load. A few compute total sediment load, which consists of bed load, suspended bedmaterial load, and wash load. Yet some may compute bed load and suspended bedmaterial load separately. Invariably, sediment transport formulas have some empirical components and, therefore, are most applicable within the range of laboratory and/ or field data used in their development. Duboys Formula. The Duboys formula is widely recognized as one of the earliest attempts to develop a sediment transport predictor. The Duboys formula is [14]:
in which:
Values of ψ_{D} and critical tractive stress for use in the Duboys equation are shown in Fig. 1511 [3].
MeyerPeter Formula. The development of the MeyerPeter formula was based on flume data, with uniform bed material size in the range 3 to 28 mm. Such coarse sediments do not produce appreciable bed forms; therefore. the formula is applicable to coarse sediment transport where form roughness is negligible. The MeyerPeter formula is [2, 35]:
in which q_{s} = bedmaterial transport rate per unit channel width, in pounds per second per foot; q = water discharge per unit channel width, in cubic feet per second per foot; S_{o} = equilibrium channel slope; and d_{50} = median particle size, in feet.
Einstein Bedload Function. In 1950, Einstein published a procedure for the computation of bed material transport rate by size fractions [15]. The method was developed based on theoretical considerations of turbulent flow, supported by laboratory and field data. Einstein is credited with the introduction of several novel concepts in sediment transport theory, including the separation of boundary friction into grain and form roughness and the use of statistical properties of turbulence to explain the mechanics of sediment transport. Einstein's bedload function first computes the bedload transport rate. Then it uses the bedload transport rate to aid in the integration of the product of the suspended sediment concentration profile and the flow velocity profile, to determine the suspended bedmaterial transport rate, per individual size fraction. Several stepbystep procedures have been reported in the literature [2]. Modified Einstein Procedure. The modified Einstein procedure was developed by Colby and Hembree [6] in order to include actual measurements of suspended load into the framework of the original Einstein method. Typically, measurements of suspended load do not include:
The modified Einstein procedure calculates the total sediment load by size fractions based on measurements of suspended load and relevant geometric and hydraulic characteristics of the stream or river.
Details of the method are reported in the literature [2, 6].
Colby's 1957 Method. Colby's 1957 method is based on some of the same measurements that led to the development of the modified Einstein procedure. However, unlike the latter, it does not account for sediment transport rate by size fractions. Instead, it provides the total bedmaterial discharge, i.e., the sum of measured and unmeasured bedmaterial discharges. The following data are needed in an application of the Colby 1957 method:
The procedure is as follows [7]:
in which:
and 0.0027 is the conversion factor for the indicated units. Table 158 shows a factor to convert concentration in parts per million to milligrams per liter.
Colby's 1964 Method. In 1964, Colby published a method to calculate discharge of sands (i.e., bedmaterial discharge) in sandbed streams and rivers. The development of the method was guided by the Einstein bedload function and supported by large amounts of laboratory and field data. The method has been shown to provide a reasonably good prediction of sediment transport rates, particularly for sandsized particles. The following data are needed:
The procedure is as follows [8]:
Other Methods for the Calculation of Sediment Discharge. Many other methods have been proposed for the calculation of sediment discharge. Notable among them are the methods of Ackers and White [1], EngelundHansen [16], Toffaleti [42], and Yang [49]. The various procedures vary in complexity and range of applicability. For details on these and other sediment transport formulas, see [2, 4, 25, 41].
Sediment Rating Curves A useful curve in sediment analysis is the sediment rating curve, defined as the relationship between water discharge and sediment discharge at a given gaging site (Fig. 1517). For a given water discharge, the sediment rating curve allows the estimation of sediment discharge, assuming steady equilibrium flow conditions. The sediment rating curve is an xy plot showing water discharge in the abscissas and sediment discharge in the ordinates. This plot is obtained either by the simultaneous measurement of water and sediment discharge or, alternatively, by the use of sediment transport formulas. For lowwater discharges, the sediment rating curve usually plots as a straight line on logarithmic paper, showing an increase of sediment concentration with water discharge. However, for high water discharges, the sediment rating curve has a tendency to curve slightly downward, approaching a line of equal sediment concentration (i.e., a line having a 45° slope in the xy plane) (Fig. 518).
Like the singlevalued stagedischarge rating, the singlevalued sediment rating curve is strictly valid only for steady equilibrium flow conditions. For strongly unsteady flows, the existence of loops in both water and sediment rating curves has been demonstrated [2]. These loops are complex in nature and are likely to vary from flood to flood. In practice, loops in water and sediment rating are commonly disregarded. Sediment Routing The calculation of sediment yield is lumped, i.e., it does not provide a measure of the spatial or temporal variability of sediment production within the catchment. Sediment transport formulas are invariably based on the assumption of steady equilibrium flow. Sediment routing, on the other hand, refers to the distributed and unsteady calculation of sediment production, transport and deposition in catchments, streams, rivers, reservoirs, and estuaries. Of necessity, sediment routing involves a large number of calculations and, therefore, it is ideally suited for use with a computer. Sediment routing should be used, in addition to sediment yield and sediment transport evaluations, in cases where the description of spatial and temporal variations of sediment production, transport, and deposition is warranted. Sediment routing methods are particularly useful in the detailed analysis of sediment transport and deposition in rivers and reservoirs. For example, the computer model HECRAS, "River Analysis System," has a sediment routing component [21]. Several other sediment routing models have been developed in the last two decades; see, for instance, [4] and [25]. The Lane Relation Lane [31] pioneered the development of quantitative fluvial geomorphology by relating water and sediment discharge to the stream slope and mean particle diameter. The Lane relation is:
which states the proportionality between the product of sediment discharge and sediment particle diameter (Q_{s} d_{s}) and the product of water discharge and stream slope (Q_{w} S_{o}). The Lane relation is dimensional and was derived from experience. Ponce [36] has improved the Lane relation by expressing it in dimensionless form, as follows:
in which R = hydraulic radius, and γ = specific weight of water. In Eq. 1526, Q_{s} is given in [F T^{1}] units, d_{s} and R in the same units [L], γ in [F L^{3}] units, Q_{w} in [L^{3} T^{1}] units, and S_{o} is dimensionless. The general unitwidth sediment discharge is [36]:
in which k_{1} and m are coefficient and exponent, respectively, of the unitwidth sediment discharge vs mean velocity relation. For the special case of m = 3, Eq. 1527 reduces to:
in which k_{1} is dimensionless. For m = 3, Eq. 1526 reduces to the sediment transport relation [36]:
Equation 529 is dimensionless; therefore, independent of the system of units. Applications. Assume pre and postdevelopment conditions, with subscripts 1 and 2, respectively. Further define the ratios: a = Q_{s2}/Q_{s1}; b = d_{s2}/d_{s1}; c = R_{2}/R_{1}; d = Q_{w2}/Q_{w1}; and e = S_{o2}/S_{o1}. From Eq. 1526:
Thus, the stream slope change from pre to postdevelopment is (Fig. 1519):
15.4 SEDIMENT DEPOSITION IN RESERVOIRS
The concepts of sediment yield and sediment transport are essential to the study of sediment deposition in reservoirs. Sediment is first produced at upland and channel sources and then transported downstream by the action of flowing water. If the flowing water is temporarily detained, as in the case of an instream reservoir, its ability to continue to entrain sediment is substantially impaired, and deposition takes place. Sediment deposition occurs in the vicinity of reservoirs. typically as shown in Fig. 1520 [20]. First, deposition of the coarsersize fractions takes place near the entrance to the reservoir. As water continues to flow into the reservoir and over the dam, the delta continues to grow in the direction of the dam until it eventually fills the entire reservoir volume. The process is quite slow but relentless. Typically, reservoirs may take 50 to 100 y to fill, and in some instances, up to 500 y or more.
The rate of sediment deposition in reservoirs is a matter of considerable economic and practical importance. Since reservoirs are key features of hydroelectric and water resources development projects, the question of the design life of a reservoir is appropriate, given that most reservoirs will eventually fill with sediment. In an extreme example, the filling can occur in a single storm event, as in the case of a small sediment detention basin located in a semiarid region (Fig. 1521). On the other hand, the reservoir can take hundreds of years to fill, as in the case of a large reservoir located in a predominantly humid or subhumid environment.
Reservoir Trap Efficiency The difference between incoming and outgoing sediment is the sediment deposited in the reservoir. The incoming sediment can be quantified by the sediment yield, i.e. , the total sediment load entering the reservoir. The outgoing sediment can be quantified by the trap efficiency. Trap efficiency refers to the ability of the reservoir to entrap sediment being transported by the flowing water. It is defined as the ratio of trapped sediment to incoming sediment, in percentage, and is a function of:
The following procedure is used to determine trap efficiency [44]:
Reservoir Design Life The design life of a reservoir is the period required for the reservoir to fulfill its intended purpose. For instance, structures designed by the Soil Conservation Service for watershed protection and flood prevention programs have a design life of 50 to 100 y. Due to reservoir sedimentation, provisions are made to guarantee the fulldesign reservoir waterstorage capacity for the planned design life. This may entail either:
Typically, calculations of sedimentfilling rates and sediment accumulation are part of the design of reservoir storage projects. Distribution of Sediment Deposits The distribution of sediment deposits may be such as to materially affect the operation and maintenance of the dam and reservoir. The amount and types of sediment deposits vary with the nature of the sediment itself, the shape of the reservoir, the topography (bathymetry) of the reservoir floor, the nature of the approach channel, detention time, and purpose of the reservoir. The coarser sediment sizes are the first to deposit in the vicinity of the reservoir entrance (Fig. 1523). Finer sediment sizes are able to travel longer distances inside the reservoir and deposit at locations close to the dam. However, very fine sediments are usually uniformly distributed in the reservoir bed.
Sediment retention, or Debris, Basins Sediment retention basins, or debris basins, are small reservoirs located in upland areas with the specific purpose of trapping sediment and debris before they are able to reach the main fluvial network system. Debris is a general term used to describe the assortment of cobbles, boulders, branches, and other vegetative material that may clog channels and hydraulic structures, causing them to reach a critical design condition prematurely and often resulting in structural failure. Debris basins are placed upstream of channels or reservoirs with the specific purpose of temporary detainment of debris. Debris basins are usually small and designed to be cleaned out from time to time. Some basins are sized to fill up during one or two major storms. Others may have a 50 or 100y design life. Project costs and site conditions determine the size of debris basins. Sediment yield determinations for debris basin design should include both shortterm and longterm analyses. The longterm sediment yield is determined from the appropriate sediment rating curve. For infrequent storms, however, sediment concentrations may exceed longterm averages by a factor of 2 or 3 [43].
15.5 SEDIMENT MEASUREMENTS
The measurement of fluvial sediments is often necessary to complement sediment yield and sediment transport studies. The accuracy of the measurement, however, is dependent not only on the equipment and techniques but also on the application of basic principles of sediment transport. As sediment enters a stream or river, it separates itself into bedmaterial load and wash load. In turn, the bedmaterial load is transported as either bed load or suspended load. The suspended bedmaterial load plus the wash load constitutes the total suspended sediment load of the stream or river. The term sampled suspended sediment discharge is used to describe the fraction of suspended sediment load that can be sampled with available equipment. Generally, it excludes the unsampled suspended sediment discharge, i.e., the fraction of suspended sediment ioad that is carried too close to the stream bed to be effectively sampled. The suspended sediment discharge is the sum of sampled plus unsampled suspended sediment discharges. Sediment Sampling Equipment Sediment sampling equipment can be classified as follows:
Suspended sediment samplers. Suspendedsediment samplers can be classified as:
Depthintegrating samplers accumulate a watersediment sample in a pintsize milk bottle as they are lowered to the streambed and raised back to the surface at a uniform rate of transit. They are designed so that the velocity in the intake nozzle is nearly equal to the local stream velocity. Samples may be collected by wading in a stream, by hand from a suitable support, or mechanically with a cableandreel setup (Fig. 1525).
The US DH48 sampler (3.5 lb) (Fig. 1526) is a lightweight handheld depthintegrating sampler used for the collection of suspended sediment samples in wadeable streams. It is designed to sample isokinetically, meaning that water and sediment enter the nozzle at the same velocity as the stream being sampled, in order to collect a representative sample. This sampler is used in shallow streams when the product of flow depth (in feet) and mean velocity (in feet per second) does not exceed 10 [22].
The US DH59 and US DH76 samplers (22 and 25 lbs, respectively) with handline suspension are used in streams with low velocities but with depths that do not permit samples to be collected by wading (Figs. 1527 and 1528). The US D74 sampler (aluminum, 42 lbs; brass, 62 lbs) with cableandreel suspension is designed for use in streams beyond the range of handoperated equipment. Depthintegrating samplers were developed to improve sampling accuracy and to reduce the cost of collecting suspended sediment data.
Pointintegrating samplers accumulate a watersediment sample that is representative of the mean concentration at any selected point in a stream during a short interval of time. The intake and exhaust characteristics of pointintegrating samplers are identical to those of depthintegrating samplers. A rotary valve that opens and closes the sampler is operated by a solenoid energized by batteries at the surface. The current flows to the solenoid by a currentmeter cable, which suspends the sampler. Pointintegrating samplers can be used to collect depthintegrating samples by leaving the valve open as the sampler is moved through the stream vertical. This permits depthintegration in streams that are too deep to be appropriately sampled with a depthintegrating sampler. The US P61A1 (105 lb), US P63 (202 lb), and US P72 (41 lb) pointintegrating samplers are in current use. The singlestage sampler was developed to obtain suspended sediment data in flashy streams, particularly those in remote areas [24]. It is used to sample sediment at a specific depth and on the rising stage only. The sampler operates on the siphon principle, and therefore the velocity in the intake is not equal to the stream velocity. With careful operation, the singlestage sampler can be used to obtain supplemental data on suspendedsediment concentration at selected points. Bedload samplers. The US BLH84 is a wadingtype handheld bedload sampler (Fig. 1529). The sampler consists of an expanding nozzle, a sample bag, and a wading rod assembly.
The ratio of nozzle area to entrance area is 1.4. A polyester mesh bag with mesh openings of The sampler is constructed of aluminum and it weighs 10 lbs.
The US BL84 is a cablesuspended bedload sampler used to collect samples from streams that cannot be waded (Fig. 1530). The sampler consists of an expanding nozzle mounted in a frame and a sampler bag. The sampler is constructed of stainless steel and aluminum and it weighs 32 lbs.
Bedmaterial samplers. Bedmaterial samplers are of three types:
The dragbucket sampler consists of a weighted section of cylinder with an open mouth and cutting edge. As the sampler is dragged upstream along the bed, it collects a sample from the top layer of bed material. The grabbucket sampler is similar to the dragbucket, consisting of a cylinder section attached to a rod, and used primarily in shallow streams. The vertical pipe, or core sampler, consists of a piece of metal or plastic pipe that can be forced into the stream by hand. Generally, the dragbucket and grabbucket samplers do not obtain representative samples of bed material because of the loss of fine material. The core sampler is satisfactory for use in shallow streams. The US BMH53 sampler consists of a 8in.long, 2in.diameter brass or stainless steel pipe with a cutting edge and suction piston attached to a control rod. The sampler weighs 7.5 lbs (Fig. 1531). The piston is retracted as the cutting cylinder is forced into the streambed. The partial vacuum that develops in the sampling chamber as the piston is withdrawn assists in holding the sample in the cylinder. The sampler can be used only in streams shallow enough to be waded.
The US BMH60 bed material sampler is designed to scoop up a sample of bed sediment about 3 in. wide and 2 in. deep. At the close of the sampling operation, the cutting edge rests against a rubber stop, which prevents any sediment from being lost. The sampler is made out of aluminum, it is 22 in. long and it weighs 32 lbs (Fig. 1532). It is used to collect bedmaterialsediment samples in streams with low velocities but with depths beyond the range of the BMH53 sampler.
The US BM54 bedmaterial sampler (100 lb) with cable suspension is similar in design to the BHM60 sampler.
The sampler is made out of cast iron, it is 22 in. long and it weighs
100 lbs It is used in deep streams where a heavier sampler is necessary.
Table 1510 lists sediment samplers in common use, developed by the U.S. Federal Interagency Sedimentation Project.
Suspendedsediment Discharge Measurements Suspendedsediment samplers are used to determine sediment concentration at a point in a stream (i.e., a stream vertical), except for a small unmeasured zone located just above the stream bed. With wading equipment, measurements can generally be made down to within 0.3 ft of the stream bed. For cablesupported equipment, the unmeasured zone varies between 0.5 and 1.0 ft, depending on the size of sampler used. Suspendedsediment discharge measurements include:
The streamflow depth and velocity and the facilities at the sampling site (bridge, cableway, and so on) have an influence on the choice of sampler. Stream depth determines whether hand samplers, such as the DH48 or DH59, or a cablesuspended sampler, such as the D74, should be used. Flow depths over 15 ft require the use of pointintegrating samplers to avoid overfilling of the sampling bottles. The larger the product of flow depth times mean velocity, the heavier the sample required for proper measurement. The number of sampling verticals depends on the desired accuracy and the variation of sediment concentration across the stream. For streams with a stable cross section and essentially uniform sediment concentration across the width, sampling at a single vertical is usually adequate. Depthintegrating samplers produce a suspendedsediment concentration, which can be measured in parts per million and converted to milligrams per liter. The suspendedsediment discharge is given by the following formula:
in which:
Table 158 shows a factor to convert concentration in parts per million to milligrams per liter. There are two techniques to measure suspendedsediment discharge:
In the EDI method, sampling is done at the centroids of equaldischarge increments. In the ETR method, sampling is done at the centroids of equallength increments. The EDI method requires a knowledge of the lateral distribution of streamflow prior to the selection of sampling verticals. The ETR method is applicable to shallow streams where the crosssectional distribution of streamflow is not stable. Generally, the EDI method requires fewer sampling verticals than the ETR method. The ETR method, however, does not require a prior discharge measurement. The suspendedsediment concentration in the EDI method is the average obtained from several depthintegrating samples. In the ETR method, the suspended sediment concentration is that of a composite sample encompassing several depthintegrating samples. The error in suspendedsediment discharge provided by the measurement varies with the depth of the unsampled zone and the size distribution of suspended load. The error tends to be smallest in the cases where the vertical concentration gradient in the unsampled zone is small. The concentration gradient near the bed is small for silt and clay particles and large for coarser sand particles. Corrections in sampled suspended sediment discharge to account for the unsampled portion are usually obtained through appropriate sediment transport predictors such as the Colby 1957 method or the Modified Einstein Procedure [7, 9]. QUESTIONS
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