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.
Figure 1: Bank Undercutting Diagram
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.
Figure 2: Sediment Plug at the confluence of the
Green River with Rio Grande in TX
Equation 1
𝑄𝑠 𝑑 ∝ 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=
1 2/3 1/2
𝑅 𝑆
𝑛
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 3 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 = 𝛾(𝐷 − 𝑧)𝑆,
where it is apparent that shear stress varies linearly (Chang, 1988).
Figure 3: Schematic of Forces on Control Volume
dx
z
Wx
D-z
τ
D
z
E
F
x
(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
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) are often used to determine incipient motion of a uniform sediment on a level bed
(Chang, 1988).
Equation 6
𝜏𝑐
𝑈∗𝑐 𝑑
=𝐹
(𝛾𝑠 − 𝛾)
𝑣
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
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, 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 (𝛾𝑠 ⁄𝛾 − 1)
𝜏0 − 𝜏𝑐
= 10
(𝛾𝑠 − 𝛾)𝑑
𝑞𝛾𝑠
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
𝐷
𝑞𝑠𝑠 = ∫𝑎 𝐶𝑢𝑑𝑧
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
𝑧∗
𝐶
𝐷−𝑧
𝑎
=(
∗
)
𝐶𝑎
𝑧
𝐷−𝑎
The result is
𝑧∗
𝐷
𝐷−𝑧
𝑎
30.2𝑧
𝑞𝑠𝑠 = ∫ 𝐶𝑎 (
∗
) 5.75𝑈∗′ 𝑙𝑜𝑔 (
) 𝑑𝑧
𝑧
𝐷−𝑎
∆
𝑎
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
30.2𝐷
𝑞𝑠𝑠 = 11.6𝐶𝑎 𝑈∗′ 𝑎 [2.303 𝑙𝑜𝑔 (
) 𝐼1 + 𝐼2 ]
∆
Where,
Equation 11
1
𝐴𝑧∗ −1
1 − 𝜂 𝑧∗
𝐼1 = 0.216
∫ (
) 𝑑𝜂
(1 − 𝐴) 𝑧∗ 𝐴
𝜂
And
Equation 12
1
𝐴𝑧∗ −1
1 − 𝜂 𝑧∗
𝐼2 = 0.216
∫ (
) ln 𝜂 𝑑𝜂
(1 − 𝐴) 𝑧∗ 𝐴
𝜂
(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.
The Big Picture
As mentioned before, sediment transport processes are intricate. Sediment is only one
component of an elaborate system that includes: biota and fauna, water quality, geomorphology,
and much more. Table 1 illustrates how variables change spatially and are dependent on
changes within the watershed. In terms of evaluating geologic time, no predictions can be made
about how interactions will transpire and this effects a slew of variables.
Table 1: River Variables for Different Time Spans (After Schumm, 1971)
Status of Variable
Steady
Graded
(Short-Term)
(Long-Term)
Geology(lithology, structure)
I
I
Paleoclimate
I
I
Paleohydrology
I
I
Valley slope, width and depth
I
I
Climate
I
I
Vegetation (type and density)
I
I
Mean water discharge
I
I
Mean sediment inflow rate
I
I
Channel morphology
I
D
Observed discharge and load
D
X
Hydraulics of flow
D
X
I*, independent variable; D, dependent variable; X, indeterminate
(Chang, 1988)
Geologic
(Very Long-Term)
I
I
D
D
X
X
X
X
X
X
X
To get a general idea of how these are tied together, an overview is presented that relates each
system to sediment transport.
Collecting Data and Application
So, how does one incorporate sediment transport processes into a robust watershed or stream
restoration project? To begin, a plan and project should be defined. Next, field reconnaissance
should be completed that mindfully incorporates as many variables into the design as can
feasibly be allowed. In terms of sediment transport, this means assessing whether a site’s stream
composition is primarily alluvial or gravel in nature.
The collection of bed-material particle size from rivers is an important part of the reconnaissance
process. For a stream composed of mainly fine particles, a bed material sampler can be used to
obtain a representative sample of the streambed. The sample is then filtered, dried, and sent
through a set of standard sieves to determine percent by weight of particle sizes (USDA). In the
instance of larger particles, a Wolman pebble counter is used to determine the size of 100
pebbles or cobbles at minimum.
Once the collected data has been evaluated, it is generally evaluated for a particular particle size.
For instance, an engineer may decide that the d50 is the most useful particle size to use in Shields
equation. Other equations are specific about the particle size required to determine critical shear
stress.
Case Studies
Elwha Dam
The Elwha Dam in Washington is one of the largest dams removed to date. The purpose of its
removal was to provide increased spawning habitat to anadromous fish and to restore the natural
ecosystem. The Elwha River is a steep gradient river that is 45 miles long on its main stem and
has over 100 miles of tributaries. Each year the Elwha carries between 120,000 and 290,000
cubic meters of sediment downstream (Czuba & Randle, 2011). In order to understand the
potential outcomes of dam removal,
Figure 5: Elwha Dam Removal in Washington
(The Seattle Times, 2011)
Conclusion/Discussion
Assessment of sediment transport in stream restoration is of great importance in stream
restoration. There are a variety of equations available for evaluating sediment discharge loads
and it is important to choose equations carefully. Its evaluation must include the sediment
gradation, the geomorphology of the system, and understanding of the relationship between
hydraulics and channel geometry and what that means for sediment discharge. Investigating
sediment characteristics and movement is beneficial in supporting fisheries, life of a restoration
project, and setting goals for reducing sediment load. It is an essential component of analysis
and design process and should not be dismissed when considering the effects on a watershed.
References
Chang, H. H. (1988). Fluvial Processes in River Engineering. Malabar: Krieger Publishing
Company.
crienglish.com. (n.d.). crienglish.com. Retrieved March 28, 2012, from Yan'an the Cradle of
Chinese Revolution: http://english.cri.cn/4406/2008/07/02/1141s375974.htm
Czuba, C., & Randle, T. (2011). Anticipated Sediment Delivery to the Lower Elwha River During
and Following Dam Removal. Washington D.C.: USGS.
Hart, D. D., Johnson, T. E., Bushaw-Newton, K. L., & Horwitz, R. J. (n.d.). Dam Removal:
Challenges and Opportunities for Ecological Research and River Restoration.
Lane, E. (1955). The Importance of Fluvial Morphology in Hydraulic Engineering. ASCE, 1-17.
Leopold, L. B., Wolman, M. G., & Miller, J. P. (1992). Fluvial Processes in Geomorphology.
San Francisco: W.H. Freeman and Company.
Linsley, R. K., Kohler, M. A., & Paulhus, J. L. (1975). Hydrology for Engineers, 2nd edition.
New York City: McGraw-Hill Book Company.
Loveless, J., Seillen, R., Bryant, T., Wormleaton, P., Catmur, S., & Hey, R. (2000). The Effect of
Overbank Flow in a Meandering River on its Conveyance and the Transport of Graded
Sediments. J. CIWEM, 447-455.
Rosgen, D. (1996). Applied River Morphology. Minneapolis: Printed Media Companies.
Shields, A. (1936). Anwendung der Aenlichkitsmechanik und der Turbulenzforshung auf die
Geschiebebewegung. Berlin: Mitteilungen der Prevssischen Versuchsanstalt fur
Wasserbau und Schiffbau.
Simon, A., Dickerson, W., & Heins, A. (2004). Suspended-sediment transport rates at the 1.5year recurrence interval for ecoregions of the United States: transport conditions at the
bankfull and effective discharge? Elsevier, 243-262.
The Seattle Times. (2011, September 28). See It For Yourself: Dam Removal Underway on
Elwha River. Retrieved 02 26, 2012, from The Seattle Times:
http://seattletimes.nwsource.com/html/fieldnotes/2016343068_see_it_for_yourself_overl
ook_trail_for_viewing_elwha_dam_removal.html
Tockner, K., Schiemer, F., & Ward, J. (1998). Conservation by restoration: the management
concept for a river-floodplain system on the Danube River in Austria. Aquatic
Conservation: Marine and Freshwater Ecosystems, 71-86.
Trans Pecos Water and Land Trust. (n.d.). US Army Corps of Engineers Forgotten River Study,
August 2007. Retrieved 02 17, 2012, from Trans Pecos Water and Land Trust:
http://www.transpecoswatertrust.com/cschap3.html
USDA. (n.d.). Chapter 7: Analysis of Corridor Condition. In Federal Stream Corridor
Restoration Handbook.
Yang, C. T., & Simoes, F. J. (2005). Wash Load and Bed-Material Load Transport in the Yellow
River. Journal of Hydraulic Engineering, 413-418.