Introduction
Sediment transport is paramount in considering restoration techniques for both watershed and river restoration. It is responsible for erosion, bank undercutting, sandbar formation, aggradation, gullying, and plugging. However, sediment transport cannot be understood without considering the hydrology, geomorphology, and ecosystem. As Luna Leopold, the father of fluvial geomorphology stated, “So complex are the details of interrelations in this organized system that to describe adequately any single portion tends to make one lose sight of other equally important features,” (Leopold, Wolman, & Miller, 1992). Therefore this paper aims to discuss sediment transport relationships, the necessity of sediment transport in restoration, an overview of how to incorporate sediment transport techniques into practice, and will reiterate its importance through presentation and discussion of case studies.
Background
Bridging Relationships in the Hydrosphere
Sediment transport is a function of slope, velocity, discharge, vegetation, mean sediment inflow rate and channel morphology. When each of these allows a river to become stable, a river is said to have reached dynamic equilibrium. This symbiotic relationship is shown in Lane’s work, Equation 1.
Equation 1
Qsd∝QS
Where Qs is the sediment discharge, d is the median particle diameter, Q is the water flow, and S is the slope of the channel. The equation shows that the sediment discharge and median particle diameter are proportional to the stream power (Lane, 1955).
Defining Erosion and Sediment Transport Processes
Sediment transport can be defined as the movement of soil particles downstream caused by gravity and the force of moving fluid imparted. The ability of a particle to move is then related to shear stresses, frictional forces, water depth, and specific weight. These components can be classified into two general categories hydraulics and hydrology, and sediment physics.
Fundamentally, erosion of sediment from a watershed begins the process of sediment transport or through human activities. While elements such as wind and chemical reactions can cause erosion, the main proponent of erosion is water, either in a flowing stream or as precipitation falling on earth’s surface. Once a particle has been eroded, water becomes the “principal vehicle for transport of the eroded material,” (Linsley, Kohler, & Paulhus, 1975).
Sediment transport and yield can be accelerated by many human activities. In the past, our reliance on wood has led to clear cutting and building roads close to streams that caused significant degradation of forests. In urban settings, construction and straightening of channels among other things has a tendency to increase the amount of sediment fed into a system, increasing the rate of degradation. A reduction of sediment load from urban areas can be realized by using techniques such as buffering ripararian zones and rivers. For more information see The Landscape Perspective.
The effects of human interference with the sediment transport process has resulted in measureable impacts on water quality. One example of the changes to sediment loads relates to dams. Dams have served as a way of trapping sediment and therefore starving streams of their natural sediment load. The result is armoring at the head of the dam, sorting of materials, and incision and widening of the channel. To learn more about the impacts of dams, see Dams and Other Impoundments.
Hydrology and Hydraulics
Hydrology and hydraulics are relevant to sediment transport because they provide the basis for quantifying the amount, depth, and velocity of water at a point whether in a watershed or river, which translates into when and how much sediment will be moved. Other physical characteristics of importance are slope, channel geometry and geomorphology. One of the most prevalent velocity and flow equations used is Manning’s Equation, shown below.
Equation 2
U=1n R2/3S 1/2
Where,
U = Velocity (m/s)
n = roughness coefficient (unitless)
R = Hydraulic Radius (m2/m)
S = slope (m/m)
Another equation that is frequently used is Chezy’s equation. It is empirical in nature
Equation 3
U=C(RS)1/2
Where,
U= Velocity (m/s)
C= Chezy’s coefficient ()
R = Hydraulic Radius (m2/m)
S = slope (m/m)
Manning’s equation and Chezy’s equation are useful tools when trying to determine average velocity in a stream. In the upcoming sections, velocity will be discussed in relation to shear stress. For more information see Hydraulics.
Effective Discharge and Bankfull Discharge
Another fundamental concept of sediment transport in rivers is effective discharge (ED), also called bankfull discharge. ED is the discharge at which a river moves a sufficient amount of sediment to maintain the width, depth and overall dynamic equilibrium. The ED correlates with the point at which overtopping occurs in a stream that is not degraded and generally occurs at regular intervals of 1.5 to 2 years (Rosgen, 1996). See Hydrology for more details.
Sediment Movement
Shear Stress and Friction
The predominate determinates in sediment transport are related to the forces acting on a particle and the shear stresses required to overcome those forces. As can be seen in Figure 1 the weight of the particle must be counterbalanced by shear force in order to resist motion. The equilibrium equation assuming steady and uniform flow is:
Equation 4
WS-τdx=0
The W component can be substituted with γ(D-z)dx. W is the fluid weight, τ is the internal shear stress acting on BC, γ is the specific weight of fluid, D is depth and dx is the length of the channel being considered. If the above equations are rearranged, the equilibrium equation is transformed to:
Equation 5
τ=γD-zS,
where it is apparent that shear stress varies linearly (Chang, 1988).
Figure 3: Schematic of Forces on Control Volume
(Chang, 1988)
Particle Motion
As discussed in the “Shear Stress and Friction” section, sediment must overcome a certain shear stress in order to move. Shields equation (See Equation 6) and diagram (See Figure 4) are often used to determine incipient motion of a uniform sediment on a level bed (Chang, 1988).
Equation 6
τc(γs-γ)=FU*cdv
Where τc is the critical shear stress, γs is the specific weight for the sediment, γ is the specific weight of water, U*c is the critical shear velocity, d is the particle diameter, and v is the kinematic viscosity.
The left side of Equation 6 is referred to as the critical Shields stress and the right hand side is referred to as the critical boundary Reynolds number. For more information on Reynolds number click here. In the instance of the Shields Diagram, see Figure 4, Reynolds number relates particle size to and flow region (laminar, transition, and turbulent).
Knowing the point of incipient motion is important to stream restoration for several reasons. If specific objectives have been set such as bank stabilization or improving flood plain connectivity, it will be critical to know if the materials used will potentially be moved downstream under the design criteria. Furthermore, if the sediment gradation is known for a particular reach, then it can be understood how the channel may respond to changes and how sediment will travel downstream.
Figure 4: Shields Diagram for Incipient Motion
(Shields, 1936)
Sediment Size and Channel Formations
Whether a channel forms dunes and antidunes or pools and riffles is a function of sediment size. For an alluvial stream with sand sized particles and smaller, it is expected that in low flow conditions, the stream bed will be composed of dunes and antidunes. In larger storm events, an alluvial system will become a flat bed channel and erode materials downstream. On the Rio Grande, dune and antidune formations can be seen in shallow riffle areas. In a gravel bed stream, the formation of pools, runs and riffles is expected. The formation and approximate geometry of pools, runs, and riffles can be estimated.
In the instance of implementing a restoration project where a stream is being placed back in a remnant channel, the use of a reference stream would be used. Reference streams have similar geomorphological and hydrologic conditions as the stream to be restored as well as being near pristine. Typically, several different reference reaches are analyzed to find the closest match before proceeding with the design stage. The chosen reference reach is then used to design the features in the remnant channel. Although there is a remnant channel, it should not expected that feature spacing and channel geometry will be the same as it was when the remnant channel was still a segment of the stream. Understanding how sediment size and channel geometry in a reference reach apply to the remnant channel restoration are useful tools, because they provide the designer an opportunity to check the design of a project.
Whether the stream sediment is sand or cobble, being able to predict the success of a particular restoration method can be supported by understanding the fundamental idea that channel shape will vary with its sediment size.
Sediment Classification
To take the previously expressed knowledge a step further, two typical approaches exist for classifying sediment loads of streams (Chang, 1988). The first classification differentiates bed load, suspended load, and saltation. Suspended sediment particles are those that are carried in suspension by flowing water. Bed load are material that are transported by sliding and rolling along the bottom of a channel. Finally, saltation refers to those particles that bounce along the bottom of a riverbed.
The second is wash load and bed-material load (Chang, 1988). Bed- material load relates to the material of a stream bed. Finally, wash load is composed primarily of silt and clay.
Sediment Discharge Equations
Sediment transport is much like hydrology in that there is not a “one size fits all” equation. Indeed, there are a plethora of sediment transport equations and algorithms that are based on different premise and that try to predict a variety of parameters. For the purposes of this paper, discussion will begin with sediment yield in watersheds and then will be limited to sediment discharge in rivers. Discussion of sediment discharge equations will be based on the sediment classifications: bed load, suspended sediment load, bed material load, and wash load.
Watersheds
According to Schumm, a fluvial system can be divided into three components. First there is the watershed, where a majority of the sediment and water in a river system originates. The middle reach is where a river channel is most stable. The last portion is near the outlet, where variations in the channel occur due to variations in tides, and base level (ie. at the inlet of reservoirs), (Chang, 1988).
Sediments from watersheds can be correlated to many factors such as climate, soil type, land use, and topography (Linsley, Kohler, & Paulhus, 1975). It is undoubtedly difficult to relate all of the factors contributing to sediment yield to one specific equation and yield accurate results. Existing efforts include those of Langbein and Schumm, and Fleming which relate sediment yield to watershed characteristics.
Bed Load and Shields Equation
Shields equation, Equation 7, is a dimensionless formula that relies on overabundance of shear stress to determine sediment discharge for bed load (Chang, 1988) and (Shields, 1936).
Equation 7
qb(γsγ-1)qγs=10τ0-τcγs-γd
Where q is the water discharge per unit width, qb is the bed load discharge per unit width, and d is the particle diameter. The left hand side of Equation 7 represents the bed load discharge and the right hand side contains both excess shear stress and the submerged weight of sediment particles (Chang, 1988).
Shields equation can be used to evaluate sediment discharge in gravel bed channels. An example where Shields equation might be used would be in a river where hydraulic mining has been completed upstream. If a reach of that river was to be restored, it would be useful to evaluate the reduction of sediment discharge before and after the project and to set goals in reaches suffering the same impairment.
Suspended Load and Einstein’s Suspended Load Method
Suspended sediment concentrations and velocity vary within the water column. To evaluate suspended sediment Einstein integrated the following equation:
Equation 8
qss=aDCudz
Where qss is the suspended sediment discharge, D is the depth, a is the lowest point at which suspension occurs, C is the concentration, and u is the velocity. This equation is then permutated with Rouse’s equation, shown in Equation 9.
Equation 9
CCa=D-zz*aD-az*
The result is
qss=aDCaD-zz*aD-az*5.75U*'log30.2z∆dz
Where Ca is the concentration at depth the lower limit of where suspension begins, and U*' is the velocity as a result of grain roughness (Chang, 1988). Finally, substitute a and z for the respective values of A=a/z and η=z/D. The results are shown in Equation 10, Equation 11, and Equation 12.
Equation 10
qss=11.6CaU*'a2.303 log30.2D∆I1+I2
Where,
Equation 11
I1=0.216Az* -11-Az*A11-ηηz*dη
And
Equation 12
I2=0.216Az* -11-Az*A11-ηηz*lnηdη
(Chang, 1988)
Einstein’s suspended sediment equation would be particularly useful in the southwestern part of the U.S., where in a large number of streams sand particles are prevalent. This equation can be used to determine how suspended sediment discharge might change with time.
Like the example used in the bed load section, determining the suspended sediment can be used to set goals. It can also be useful in reducing effects on fisheries that are sensitive to suspended sediment and have a clear threshold.
Bed-Material Load
As discussed earlier, bed-material load is simply the total of the bed load and suspended load, excluding wash load. Several relationships between bed-material load, stream power and shear stress exist. The Colby relations relate bed-material per unit channel width in terms of temperature, mean flow velocity, depth, sediment size and fine particle concentration (Chang, 1988).
Wash Load
Wash load has been accepted as not being linked to flow hydraulics with the exception of rain events (Yang & Simoes, 2005). It is considered a function of supply from a watershed and does not interact within the same bounds as other sediment types. However, Yang found a strong correlation between bed-material load and wash load on the Yellow River in China and that wash load can effect bed-material transport rates in the Yellow River’s sediment laden system. The relationship of wash load and bed-material load on the Yellow River were related through development of an algorithm. See Figure XX (crienglish.com) to view picture of Yellow River at Hukou Falls.
When wash load is an issue in a reach, developing an algorithm would be a good solution if properly developed. The use of a reasonable algorithm could aid in identifying areas that would benefit from restoration. This not only holds true for wash load but also suspended load and bed load.