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The magnitude of shear stress required to move a given particle is known as the critical shear stress (τcr ).
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Stream Geomorphic Assessment Handbooks VT Agency of Natural Resources
Particle Entrainment and Transport
What follows is an introduction to basic concepts associated with measurement and prediction of entrainment and transport of bed material in natural rivers. The purpose of this discussion is to familiarize the reader with methods for predicting particle entrainment and their limitations. This discussion does not represent the full breadth of study and research on this subject matter. Rather it introduces core principles and gives background on methods of entrainment prediction most commonly used by river management practitioners.
many applications including prediction of the effects of land use or flow regime change and channel restoration efforts (Wilcock, 2001). The relationship between discharge and bedload transport rate through a reach and the ability of the existing channel to transport the bedload (sediment transport capacity) is critical to the establishment of river equilibrium in river corridor protection and restoration efforts. Measuring the size and quantity of bedload particles moving through a reach at different discharges and developing a sediment rating curve is the ideal predictive tool for project design. Once the conditions required for bedload transport are known they can be translated into an understanding of the channel dimension, pattern, and profile that will result in sufficient transport of the expected sediment supply.
is a sporadic process that occurs through a variety of mechanisms. Its variability both spatially and temporally add to the difficulty. Bedload measurement is particularly challenging for river managers to conduct due to its high cost and the length of time over which it takes to accurately complete. Additionally, sampling devices placed in the flow may perturb local hydraulics sufficiently to create anomalously high or low transport conditions (Wohl, 2000). Despite these difficulties, efforts to understand bed-load transport and its relation to flow discharge are worthwhile and can lead to better assessment and project design.
In lieu of creating sediment rating curves on a project by project basis, practitioners have had fairly good results using empirically derived equations for the prediction of the conditions necessary to entrain bed particles and designing channels to produce those conditions. While the first efforts in this area resulted in equations that were accurate only when applied to channels with homogeneous bed sediments, more recent efforts have resulted in equations that are applicable to natural rivers.
The parameter often used as a measure of the stream’s ability to entrain bed material is the shear stress created by the flow acting on the bed material. Shear stress acts in the direction of the flow as it slides along the channel bed and banks. Critical shear stress is the shear stress required to mobilize sediments delivered to the channel. When the shear stress equals the critical shear stress, the channel will likely be in equilibrium. Where shear stress is excessively greater than critical shear stress, channel degradation will likely result. Where the shear stress is less than critical shear stress, channel aggradation will likely result. Thus the ability to calculate or measure both shear and critical shear stress is crucial in understanding channel adjustments.
Calculating Shear Stress: Unfortunately, attempts to calculate or measure shear stress values in mountain rivers are complicated by the channel bed roughness and the associated turbulence and velocity fluctuations (Wohl, 2000). Turbulence can lead to substantial variability in velocity and shear stress at a point during constant discharge. Heterogeneities caused by grains and bedforms may create substantial velocity and shear
Stream Geomorphic Assessment Handbooks VT Agency of Natural Resources
Calculating Critical Shear Stress: With the above principles in mind, Shields in 1936 conducted flume experiments to develop an expression for the critical shear stress to move a particle of a given size (Knighton, 1998). His work resulted in the following equation:
where;
τ ci is dimensionless critical shear stress,
ρ (^) ws is the density of water; and
Shields’ studies showed that in gravel bed channels of homogeneous sediment sizes and turbulent flow the value of dimensionless critical shear stress is 0.06. Shields’ still serves as a basis for defining critical shear stress (Fischenich, 2001). However, since Sheilds’ work other researchers have developed derivations of Shields’ equation in an effort to improve the prediction of critical shear in natural channels with heterogeneous substrate sizes.
Fischenich, (2001) lists the following equations presented by Julien to approximate the critical shear stress for particles of various sizes.
τ cr = 0 25. d (^) *−0 6.^ × g (ρ (^) s − ρ w ) d × Tan φ :For silts and sands τ cr = 0 06. × g ( ρ (^) s − ρ w ) d × Tan φ :For gravels and cobbles
Where;
/
2
1 3
φ is the angle of repose of the particle G is the specific gravity of sediment
ρ (^) ws is the density of water v is the kinematic velocity; and
Angles of repose are given in Table 1 (Julien, 1995). Critical shear stresses are also provided in Table 1. It is important to realize that mixtures of sediments behave differently than uniform sediments. Particles larger than the median will be entrained at shear stresses lower than those given in Table 1 and, conversely, larger shear stresses than those listed in the table are required to entrain particles smaller than the median size (Fischenich, 2001).
Stream Geomorphic Assessment Handbooks VT Agency of Natural Resources
Table 1 Limiting Shear Stress and Velocity For Uniform Noncohesive Sediments
following equation:
τ *.
.
ci
i
s
−
50
0 872
Andrews equation can be used to calculate τ * ci which can then be used in the Shields equation to determine
the critical shear stress required to move a particle of a given size in gravel-cobble bed streams. As
It is important to remember that the equations presented above, while used widely, are not used exclusively. The predictive tools presented here are understood to be general in nature and may not be appropriate for all situations. As stated above there are many variables associated with measurement or calculation of shear stress, critical shear stress and bed-load transport. Despite the uncertainties, the weighing of river management alternatives will benefit from attempts to develop as accurate an understanding as possible. Otherwise, assessment, river corridor protection, and restoration efforts are less likely to meet established goals. Careful use of prediction and application methods and an understanding of the limitations of those methods, will greatly improve project outcomes and helps explain the variables and uncertainties that are inherent in river assessment and management work. Following these guidelines will increase the likelihood of success.
where;
Stream Geomorphic Assessment Handbooks VT Agency of Natural Resources
