Critical Shields Stress Research Articles

Sediment transport on rippled beds

We conduct an Euler-Lagrange, direct numerical simulation of a turbulent channel flow at a shear Reynolds number of Reτ=180 over an erodible particle bed. The particle bed consists of approximately 1.3 × 106 monodisperse particles, resulting in a bed thickness of around 12–13 particles. The particle density and size are chosen to achieve a ratio of 4 for the Shields stress to the critical Shields stress necessary for incipient motion such that particle transport occurs primarily as bedload. The simulation is run long enough for ripples to form. We track the temporal evolution of the particle flux and excess Shields stress for the entire bed as well as for the four regions of a ripple, namely, the crest, trough, lee side, and stoss side. We find that the particle flux and excess Shields stress closely match the Wong and Parker correlation when the particle bed is featureless at early time but diverge from the correlation when ripples form. This deviation primarily arises from particle transport in the trough and lee side regions. Conversely, particle transport in the crest and stoss side regions remains largely consistent with the Wong and Parker correlation. A root mean square-based correction for the bed is proposed to be used in conjunction with the Wong and Parker correlation. Additionally, ripples attain a self-similar profile in the shape and near-bed shear stress when they are sufficiently distant from their upstream neighbor. Any departure from self-similarity occurs when the upstream neighbor gets within close proximity.

Controls of local grain size distribution, bed structure and flow conditions on sediment mobility

AbstractSteep, boulder bed streams often contain sediment patches, which are areas of the bed with relatively well‐defined boundaries that are occupied by distinct grain size distributions (GSD). In sediment mixtures, the underlying GSD affects the critical Shields stress for a given grain size, which is commonly predicted using hiding functions. Hiding functions may vary with reach‐wide bed GSD, but the effect of local GSD on relative sediment mobility between sediment patches is poorly understood. We explore the effects of patch‐scale GSD on sediment mobility using tracer particles combined with local shear stresses to develop hiding functions for different patch classes within a steep stream. Hiding functions for all tested patch classes were similar, which indicates that the same hiding function can be used for different patches. However, the critical Shields stress for a given grain size generally decreased with lower patch median grain size (D50) suggesting that patches control the relative mobility of each size through both the underlying GSD and local shear stresses. The effects of the underlying GSD partly depend on grain protrusion, which we measured for all grain sizes present on each patch class. Protrusion was generally greater for larger grains regardless of patch class, but for a given grain size, protrusion was increased with smaller patch D50. For a given grain size, higher protrusion results in greater applied fluid forces and reduced resisting forces to partly explain our lower critical Shields stresses in finer patches. Patches therefore can importantly modulate relative sediment mobility through bed structure and may need to be included in reach‐scale sediment transport and channel stability estimates.

Uncertainties in Models Predicting Critical Bed Shear Stress of Cohesionless Particles

Our data show large scatter in the critical Shields stress values for initial sediment motion. The main sources of dispersion are related to the methodological procedures defining the inception of movement (i.e., visual observations or extrapolation of sediment transport rate) and to the estimation of the bed shear stress. The threshold for sediment motion varies with many factors related not only to grain size but also to bed composition (e.g., presence of fine sediments in a coarse matrix), arrangement (e.g., bed roughness, grain orientation, and characteristic lengths of bed structures) and slope. New models to estimate the critical Shields number are proposed using grain size or bed slope or a combination of both. Model parameters and uncertainty are estimated through Bayesian inference using prior knowledge of these parameters and measured data. Apart from the uncertainty in observations, two types of uncertainty can be evaluated: one related to the parameter estimation (i.e., parametric) and one related to the choice of the model (i.e., structural). Finally, a four-parameter model based on the grain size and bed slope yields the best results and demonstrates potential interaction between these two parameters. Model uncertainty, however, remains large, which indicates that other input parameters may be needed to improve the proposed model.

Qcthreshold departs from theoreticalQcin urban watersheds: The role of streambed mobility data in managing the urban disturbance regime

The threshold discharge (Qc) for streambed mobilization is both biologically and geomorphically relevant to stream ecosystems. Excess streambed mobilization can disturb benthic organisms and initiate cycles of channel instability. The mechanistic relevance of Qc gives it great utility for aquatic ecosystem studies, stormwater management, and stream restoration design. However, field and laboratory data document considerable variability in Qc across hydrogeomorphic settings, underscoring the importance of using field data to calibrate the Qc estimate for a given stream or region. This paper shows how both high- and low-tech monitoring protocols can be used to constrain a Qc estimate, depending on monitoring program goals and budgets. Data from 3 hydrogeomorphically distinct settings in the USA and Australia show that the departure of Qc from theoretical estimates increases with watershed imperviousness. Although Qc estimates derived from conventional critical Shields stress values tend to be a reasonable and conservative starting point for stormwater management in streams that lack site-specific or regional data, streambed mobility monitoring is recommended to calibrate and validate Qc estimates for a stream or region prior to making large investments in stormwater interventions aimed at mitigating the urban streambed disturbance regime.

The Presence and Widespread Distribution of Dark Sediment in Greenland Ice Sheet Supraglacial Streams Implies Substantial Impact of Microbial Communities on Sediment Deposition and Albedo

AbstractMelting on the Greenland Ice Sheet leads to extensive supraglacial stream networks. These streams accumulate low‐albedo sediments disproportionately contribute to melting. Studies analyzing supraglacial sediment distribution and hydrodynamic properties are rare. Here, we examine a 130‐m supraglacial stream reach in southwest Greenland using drone imagery, bathymetry, and hydrology measurements from 2017. Sediment covered 24% of the channel and had a mass‐median diameter of 0.027 mm. We applied calculations of critical Shields stress to determine the minimum water depth needed to initiate sediment movement. In order for theoretical critical water depths to match observed depths, sediment grains would need to be 2.48 mm (near the grain size for cryoconite granules) indicating that microbial growth within sediment caused extensive flocculation. Without flocculation, sediment would flush out of floodplains and supraglacial streams would have significantly higher albedos. Supraglacial stream albedo might therefore be sensitive to changing stream chemistry, temperature, and meltwater supply.

Resistance Is Not Futile: Grain Resistance Controls on Observed Critical Shields Stress Variations

AbstractEstimates of the onset of sediment motion are integral for flood protection and river management but are often highly inaccurate. The critical shear stress (τ*c) for grain entrainment is often assumed constant, but measured values can vary by almost an order of magnitude between rivers. Such variations are typically explained by differences in measurement methodology, grain size distributions, or flow hydraulics, whereas grain resistance to motion is largely assumed to be constant. We demonstrate that grain resistance varies strongly with the bed structure, which is encapsulated by the particle height above surrounding sediment (protrusion, p) and intergranular friction (ϕf). We incorporate these parameters into a novel theory that correctly predicts resisting forces estimated in the laboratory, field, and a numerical model. Our theory challenges existing models, which significantly overestimate bed mobility. In our theory, small changes in p and ϕf can induce large changes in τ*c without needing to invoke variations in measurement methods or grain size. A data compilation also reveals that scatter in empirical values of τ*c can be partly explained by differences in p between rivers. Therefore, spatial and temporal variations in bed structure can partly explain the deviation of τ*c from an assumed constant value. Given that bed structure is known to vary with applied shear stresses and upstream sediment supply, we conclude that a constant τ*c is unlikely. Values of τ*c are not interchangeable between streams, or even through time in a given stream, because they are encoded with the channel history.

Modeling Streambank and Artificial Gravel Deposit Erosion for Sediment Replenishment

Sediment replenishment by artificial gravel deposits is a measure to increase sediment supply in gravel-bed rivers. Thereby, streambank erosion is the dominant process for gravel entrainment. In this contribution, we quantitatively validate a numerical morphodynamic 2D model and the relevant model approaches to reproduce non-cohesive streambank erosion. Therefore, a calibration and a sensitivity analysis of the relevant model approaches and parameters are carried out based on a reference laboratory experiment on streambank erosion in a straight channel from the literature. The relevant model approaches identified to successfully reproduce lateral streambank erosion are the gravitational bank collapse, the lateral bed slope effect on the bed load transport direction and the local bed slope effect on the critical Shields stress. Based on these findings, the numerical model was compared against data from laboratory experiments on gravel deposit erosion. Thereby, the focus was on the influence of the hydraulic discharge, the grain size distribution of the sediment and the geometrical quantities of the gravel deposits, such as the width, height and length of the deposit. It is shown that the dynamics of the erosion process were well reproduced by the numerical model using non-uniform sediment. Furthermore, the erosion rates were in good agreement with the laboratory experiments, except for the initial phase of the experiments, where the erosion rates were highest and settling of the gravel deposit was observed in the laboratory experiments. Overall, the numerical model proved to be a suitable tool to predict the erosion process of artificial gravel deposits, and hence, can be recommended for the design of sediment replenishment measures.

Effects of sand content on initial gravel motion in gravel‐bed rivers

AbstractWhen fine sediments are present in gravel streambeds (gravel‐framework beds), the gravel can be more easily removed from its original position, compared with gravel in a streambed without fine sediment but otherwise under the same hydraulic conditions. In this study, the effect of the presence of sand on the initiation of gravel motion in gravel riverbeds was investigated using flume experiments. The relationship between the critical Shields stress for gravel motion initiation and the fraction of sand in the bed was determined experimentally. The results can be summarized as follows. (1) When the fraction of sand in the bed is smaller than about 0.4, the critical Shields stress for the initiation of gravel motion decreases with increasing fraction of sand. The critical Shields stress increases, however, with increasing fraction of sand when it is larger than about 0.4. (2) The difference between the value of the critical Shields stress predicted by the Egiazaroff equation and the value obtained from the experimental data becomes maximum at about 0.4 of the fraction of sand. Here an empirical relation between the critical Shields stress and the fraction of sand is proposed so as to consider the effects of the ratio of the characteristic gravel size to the mean size of the bed material on the critical Shields stress. (3) Gravel in armored beds can be more easily mobilized by supplying sand as part of a sediment augmentation scheme. The sand fraction in the subsurface layer of the bed appears to reduce the friction angle of exposed particles. Sediment augmentation using sand has been recently demonstrated to be a viable alternative for mobilizing gravel for the restoration of gravel‐bed rivers downstream of dams. The quantitative evaluation obtained through the experiments reported here may be useful for the design of augmentation schemes. Copyright © 2017 John Wiley & Sons, Ltd.

Bedload Model for Nonuniform Sediment

AbstractIn this study, a bedload model for nonuniform sediment is developed considering the density function of sediment entrainment with no active layer. The model is formulated based on physical considerations, dimensional reasoning, regression analysis, and laboratory data. Four parameters are incorporated in the model formulation, namely the Shields stress τ*g′, the critical Shields stress τ*cg, the Kramer coefficient of uniformity cu, and the relative grain size (size of the jth grain fraction to the geometric mean size, dj/dg). The model collectively accounts for the hiding effects and the variation of the transported bedload material fractions from the surface and subsurface material. The findings of the study show that at low values of τ*g′/τ*cg fractions within the range of 0.3<dj/dg<3.0 are present with larger amounts in the transported bedload material than in the substrate, whereas fractions finer or coarser than that range are present with larger amounts in the surface layer than in the subst...

Unraveling bed slope from relative roughness in initial sediment motion

AbstractUnderstanding incipient sediment transport is crucial for predicting landscape evolution, mitigating flood hazards, and restoring riverine habitats. Observations show that the critical Shields stress increases with increasing channel bed slope, and proposed explanations for this counterintuitive finding include enhanced form drag from bed forms, particle interlocking across the channel width, and large bed sediment relative to flow depth (relative roughness). Here we use scaled flume experiments with variable channel widths, bed slopes, and particle densities to separate these effects which otherwise covary in natural streams. The critical Shields stress increased with bed slope for both natural gravel (ρs = 2.65 g/cm3) and acrylic particles (ρs = 1.15 g/cm3), and adjusting channel width had no significant effect. However, the lighter acrylic particles required a threefold higher critical Shields stress for mobilization relative to the natural gravel at a fixed slope, which is unexpected because particle density is accounted for directly in the definition of Shields stress. A comparison with model predictions indicates that changes in local velocity and turbulence associated with increasing relative roughness for lighter materials are responsible for increasing the critical Shields stress in our experiments. These changes lead to concurrent changes in the hydraulic resistance and a nearly constant critical stream power value at initial motion. Increased relative roughness can explain much of the observed heightened critical Shields stresses and reduced sediment transport rates in steep channels and also may bias paleohydraulic reconstructions in environments with exotic submerged densities such as iron ore, pumice, or ice clasts on Titan.

An entrainment model for non‐uniform sediment

AbstractA model was developed for the prediction of the entrainment rate of non‐uniform sediment considering the movement of bedforms. Laboratory experiments were conducted to advance the formulations of the proposed model and to validate and estimate the model parameters. The model parameters were related to the hydraulic conditions of the flow and the properties of the sediment mixtures using dimensional analysis and gene expression programming. The model incorporated four parameters on its formulation, namely the Shields stress and critical Shields stress to describe the hydraulic and sediment conditions of the flow, the Kramer coefficient of uniformity to describe the grain size distribution of a particular sediment mixture, and the relative position of a particular grain size fraction to the geometric mean to describe the entrainment rate of that fraction within the sediment mixture. The proposed model provided satisfactorily predictions with a deviation less than 25% between the measured and predicted values for most of the fractions, which confirms the validity of the proposed approach and model in predicting of the entrainment rates of various fractions. The model predictions were also compared with other models available for the prediction of the entrainment rate of non‐uniform sediment. The model predictions were within the same order of magnitude of the other models’ predictions. Copyright © 2015 John Wiley &amp; Sons, Ltd.

Dynamics and mechanics of bed-load tracer particles

Abstract. Understanding the mechanics of bed load at the flood scale is necessary to link hydrology to landscape evolution. Here we report on observations of the transport of coarse sediment tracer particles in a cobble-bedded alluvial river and a step-pool bedrock tributary, at the individual flood and multi-annual timescales. Tracer particle data for each survey are composed of measured displacement lengths for individual particles, and the number of tagged particles mobilized. For single floods we find that measured tracer particle displacement lengths are exponentially distributed; the number of mobile particles increases linearly with peak flood Shields stress, indicating partial bed load transport for all observed floods; and modal displacement distances scale linearly with excess shear velocity. These findings provide quantitative field support for a recently proposed modeling framework based on momentum conservation at the grain scale. Tracer displacement is weakly negatively correlated with particle size at the individual flood scale; however cumulative travel distance begins to show a stronger inverse relation to grain size when measured over many transport events. The observed spatial sorting of tracers approaches that of the river bed, and is consistent with size-selective deposition models and laboratory experiments. Tracer displacement data for the bedrock and alluvial channels collapse onto a single curve – despite more than an order of magnitude difference in channel slope – when variations of critical Shields stress and flow resistance between the two are accounted for. Results show how bed load dynamics may be predicted from a record of river stage, providing a direct link between climate and sediment transport.

Incipient sediment motion across the river to debris-flow transition

Sediment transport in mountain channels controls the evolution of mountainous terrain in response to climate and tectonics and presents major hazards to life and infrastructure worldwide. Despite its importance, we lack data on when sediment moves in steep channels and whether movement occurs by rivers or debris flows. We address this knowledge gap using laboratory experiments on initial sediment motion that cross the river to debris-flow sediment-transport transition. Results show that initial sediment motion by river processes requires heightened dimensionless bed shear stress (or critical Shields stress) with increasing channel-bed slope by as much as fivefold the conventional criterion established for lowland rivers. Beyond a threshold slope of ∼22°, the channel bed fails, initiating a debris flow prior to any fluvial transport, and the critical Shields stress within the debris-flow regime decreases with increasing channel-bed slope. Combining theories for both fluvial and debris-flow incipient transport results in a new phase space for sediment stability, with implications for predicting fluvial sediment transport rates, mitigating debris-flow hazards, and modeling channel form and landscape evolution.

Influence of Vertical Motion on Initiation of Sediment Movement

This paper makes an attempt to answer why the observed critical Shields stress for incipient sediment motion deviates from the Shields curve. The measured dataset collected from literature show that the critical Shields stress widely deviates from the Shields diagram’s prediction. This paper has re-examined the possible mechanisms responsible for the validity of Shields’ diagram and found that, among many factors, the vertical velocity in the sediment layer plays a leading role for the invalidity of Shield’s prediction. A closer look of the positive/negative deviation reveals that they correspond to the up/downward vertical velocity, and the Shields diagram is valid only when flow is uniform. Therefore, this diagram needs to be modified to account for hydraulic environments when near bed vertical velocities are significant. A new theory for critical shear stress has been developed and a unified critical Shields stress for sediment transport has been established, which is valid to predict the critical shear stress of sediment in both uniform and nonuniform flows.

Near bed turbulence measurement with acoustic doppler velocimeter (ADV)

Acoustic Doppler Velocimeter (ADV) has become prominent device in flow and turbulence measurement. The in situ turbulence measurement requires laboratory-quality data to be obtained in the field. Thus, ADV vector type provides a better choice for flow measurement at field scale. A field study was undertaken at sand-gravel bed rivers to observe the flow field and turbulence characteristics in the presence of protuberant clast. Profile measurements were executed at near bed region to characterize the flow and turbulence characteristics at the proximity of clast reference. Four major areas were identified as sampling location relative to clast reference namely stoss side, adjacent area, wake area and the downstream area. Besides, bed load measurement was carried out concurrently to elucidate the possible relation between flow variation and transport rates. Physical meaning of flow field is expressed in term of mean velocity, turbulent intensity, turbulent kinetic energy, Reynolds stresses and horizontal-vertical interaction, local bed shear stress and quadrant analysis. It is postulated that the presence of protuberant clast modifies flow field and affect transport rates. Possible occurrences of transport rates are subject to accurate estimation of acting forces on moving particles. Estimation of critical Shields stress from Reynolds extrapolation provides better comparison with actual transport rates. Besides, contribution rate to Reynolds stress analysis compliment the importance of sweeps and ejection events to occurrence of bed load transport.

Influence of bed patchiness, slope, grain hiding, and form drag on gravel mobilization in very steep streams

AbstractSteep streams are a major portion of channel networks and provide a link to transport sediment from hillslopes to lower gradient rivers. Despite their importance, key unknowns remain, perhaps foremost of which is evaluating in steep streams empirical laws for fluvial sediment transport developed for low‐gradient rivers. To address this knowledge gap, we painted sediment in situ over 3 years to monitor incipient sediment motion and sediment‐patch development in five small (drainage areas of 0.04–2 km2) and steep (slopes of 5–37%) tributaries of Elder Creek, California, United States. We found that channel beds organized into size‐sorted sediment patches which displayed active fluvial transport of gravel annually, consistent year‐to‐year patch median grain sizes, partial transport of bed material, and significantly higher values of critical Shields stress for incipient sediment motion compared to that observed for lower gradient rivers. The high critical Shields stresses (up to ≈0.5 for the median grain size) agree within a factor of ~3 to theoretical predictions which account for slope‐dependent hydraulics, grain hiding, and sediment patches. For grains of approximately the same size as the roughness length scale, slope‐dependent hydraulics and bed patchiness are the dominant controls on critical Shields stress values, while grain hiding is important for grains larger or smaller than the roughness length scale. Form drag exists in our monitored tributaries but has a smaller influence than the above effects. Our field observations show fluvial processes contribute to sediment mobilization in steep channels which are often considered to be dominated by debris flows.

Experimental study on coarse grain saltation dynamics in bedrock channels

AbstractSaltation of bed load particles on bedrock surfaces is important for landscape evolution and bedrock incision in steep landscapes. However, few studies have investigated saltation in bedrock channels where, unlike alluvial channels, the bed roughness height and the sediment size may be independent. To address this data gap, we measured the saltation hop height, hop length, and velocity of gravel saltating over a planar bed using 80–160 readings from high‐speed photography and direct measurements. Two separate dimensional analyses are used: one leading to a bed shear stress scaling and another leading to a Froude number (Fr) scaling. Our new saltation data coupled with numerous data from previous studies suggest that both shear stress and Fr‐scaling analyses are valid in characterizing bed load saltation dynamics with bed roughness ranging from smooth to alluvial beds. However, the Fr approach has the advantages that (1) there is no need to estimate a critical Shields stress , which alone can vary up to 2 orders of magnitude (e.g., 0.001–0.1) due to changes in relative bed roughness and slope and (2) the Fr‐based scaling fits the saltation data set better in a least squares sense. Results show that the saltation velocity of bed load is independent of grain density and grain size and is linearly proportional to flow velocity. Saltation height has a nonlinear dependence on grain size. Saltation length increases primarily with flow velocity, and it is inversely proportional to submerged specific density. Our results suggest that either or bed roughness coefficient must be properly estimated to yield accurate results in saltation‐abrasion models.

Width adjustment in experimental gravel‐bed channels in response to overbank flows

We conducted a series of flume experiments to investigate the response of self‐formed gravel‐bed channels to floods of varying magnitude and duration. Floods were generated by increasing the discharge into a channel created in sand‐ and gravel‐sized sediment with a median grain size of 2 mm. Flooding increased the Shields stress along the channel perimeter, causing bank erosion and rapid channel widening. The sediment introduced to the channel by bank erosion was not necessarily deposited on the channel bed, but was rather transported downstream, a process likely facilitated by transient fining of the bed surface. At the end of each experiment, bank sediments were no longer in motion, “partial bed load transport” characterized the flat‐bed portion of the channel, and the Shields stress approached a constant value of 0.056, about 1.2 times the critical Shields stress for incipient motion. Furthermore, the discharge was entirely accommodated by flow within the channel: the creation of a stable channel entirely eliminated overbank flows. We speculate that similar processes may occur in nature, but only where bank sediments are non‐cohesive and where channel‐narrowing processes cannot counteract bank erosion during overbank flows. We also demonstrate that a simple model of lateral bed load transport can reproduce observed channel widening rates, suggesting that simple methods may be appropriate for predicting width increases in channels with non‐cohesive, unvegetated banks, even during overbank flows. Last, we present a model for predicting the equilibrium width and depth of a stable gravel‐bed channel with a known channel‐forming Shields stress.

Lateral sediment sources and knickzones as controls on spatio‐temporal variations of sediment transport in an Alpine river

AbstractModern mixed alluvial‐bedrock channels in mountainous areas provide natural laboratories for understanding the time scales at which coarse‐grained material has been entrained and transported from their sources to the adjacent sedimentary sink, where these deposits are preserved as conglomerates. This article assesses the shear stress conditions needed for the entrainment of the coarse‐bed particles in the Glogn River that drains the 400 km2 Val Lumnezia basin, eastern Swiss Alps. In addition, quantitative data are presented on sediment transport patterns in this stream. The longitudinal stream profile of this river is characterized by three ca 500 m long knickzones where channel gradients range from 0·02 to 0·2 m m−1, and where the valley bottom confined into a &lt;10 m wide gorge. Downstream of these knickzones, the stream is flat with gradients &lt;0·01 m m−1 and widths ≥30 m. Measurements of the grain‐size distribution along the trunk stream yield a mean D84 value of ca 270 mm, whereas the mean D50 is ca 100 mm. The consequences of the channel morphology and the grain‐size distribution for the time scales of sediment transport were explored by using a one‐dimensional step‐backwater hydraulic model (Hydrologic Engineering Centre – River Analysis System). The results reveal that, along the entire trunk stream, a two to 10 year return period flood event is capable of mobilizing both the D50 and D84 fractions where the Shields stress exceeds the critical Shields stress for the initiation of particle motion. These return periods, however, varied substantially depending on the channel geometry and the pebble/boulder size distribution of the supplied material. Accordingly, the stream exhibits a highly dynamic boulder cover behaviour. It is likely that these time scales might also have been at work when coarse‐grained conglomerates were constructed in the geological past.

River channel slope, flow resistance, and gravel entrainment thresholds

River beds are traditionally assumed to become mobile at a fixed value of nondimensional shear stress, but several flume and field studies have found that the critical value is higher in steep shallow flows. Explanations for this have been proposed in terms of the force balance on individual grains. The trend can also be understood in bulk‐flow terms if total flow resistance has “base” and “additional” components, the latter due to protruding immobile grains as well as any bedforms, and the stress corresponding to “additional” resistance is not available for grain movement in threshold conditions. A quantitative model based on these assumptions predicts that critical Shields stress increases with slope, critical stream power is near‐invariant with slope, and each has a secondary dependence on bed sorting. The proposed slope dependence is similar to what force‐balance models predict and consistent with flume data and most field data. Possible explanations are considered for the inability of this and other models to match the very low critical values of width‐averaged stress and power reported for some low‐gradient gravel bed rivers.