Shear Stress For Incipient Motion Research Articles

Hazards due to large wood accumulations: Local scour and backwater rise

Large wood (LW) in rivers increases the flow variability and provides habitats for various species. During flood events, transported logs can accumulate at river infrastructures and increase the flood hazard. LW accumulations result in an upstream backwater rise and may increase local scour, for instance at bridge piers. Consequently, estimates of the resulting backwater rise and local scour are necessary to improve the flood hazard assessment. This study presents the findings of flume experiments with a movable bed on local scour and backwater rise due to LW accumulations. The approach flow conditions and the bed material were varied systematically for a specific LW accumulation volume. For all experiments, the initial condition for the bed material was defined as weak transport, since the bed shear stress was slightly below the critical bed shear stress for incipient motion. The inflow Froude number was identified as the governing parameter for backwater rise due to LW accumulations. The present study confirms the hypothesis that the resulting local scour reduces backwater rise. For the local scour, the unit discharge and the grain size diameter are the decisive parameters.

Critical bed shear stress and threshold of motion of maerl biogenic gravel

A determination of the critical bed shear stress of maerl is a prerequisite for quantifying its mobility, rate of erosion and deposition in conservation management. The critical bed shear stress for incipient motion has been determined for the first time for samples from biogenic free-living maerl beds in three contrasting environments (open marine, intertidal and beach) in Galway Bay, west of Ireland. The bed shear stress was determined using two methods, Law of the Wall and Turbulent Kinetic Energy, in a rotating annular flume and in a linear flume. The velocity profile of flowing water above a bed of natural maerl grains was measured in four runs of progressively increasing flow velocity until the flow exceeded the critical shear stress of grains on the bed. The critical Shields parameter and the mobility number are estimated and compared with the equivalent curves for natural quartz sand. The critical Shields parameters for the maerl particles from all three environments fall below the Shields curve. Along with a previously reported correlation between maerl grain shape and settling velocity, these results suggest that the highly irregular shapes also allow maerl grains to be mobilised more easily than quartz grains with the same sieve diameter. The intertidal beds with the roughest particles exhibit the greatest critical shear stress because the particle thalli interlock and resist entrainment. In samples with a high percentage of maerl and low percentage of siliciclastic sand, the lower density, lower settling velocity and lower critical bed shear stress of maerl results in its preferential transport over the siliciclastic sediment. At velocities ∼10 cm s−1 higher than the threshold velocity of grain motion, rarely-documented subaqueous maerl dunes formed in the annular flume.

DEPOSITION THICKNESS AND ITS EFFECT ON CRITICAL SHEAR STRESS FOR INCIPIENT MOTION OF SEDIMENTS

There are evidences in existing literatures suggesting the incipient motion values for any particle size is substantially lower for rigid boundary condition as compared to loose boundary condition. The objective of the current study is to determine the effect of sediment deposition thickness on the critical shear stress for incipient motion. Experimental works for incipient motion were carried out in a rectangular flume with varying sediment deposits thickness. Results showed that the sediment deposits thickness has effect on the critical shear stress at low sediment deposits thickness and the effect will slowly diminish as the sediment deposits thickness increases. Multiple linear regression analysis was performed on the experimental data to develop a new critical shear stress equation. The best regression model has value of 0.69; value of 0.60; value of 0.009 and Mallow’s value of 3.00. The new equation appears to be more consistent as compared to existing incipient motion equations for rigid boundary condition by having 80% of the predicted data falls within the acceptable discrepancy ratio when tested with data from other authors. The new equation can be used to determine critical shear stress values for self-cleansing sewerage design and other related engineering applications

Critical shear stress for incipient motion of non‐cohesive particles in open‐channel flows of pseudoplastic fluids

AbstractThe results of a theoretical and experimental study on the conditions of incipient motion of non‐cohesive solid particles in laminar flows of pseudoplastic fluids are presented in the article. It is concluded that, for practical purposes, using a modified particle Reynolds number that includes the consistency coefficient and the flow index, the motion threshold condition is well defined by the Shields diagram, with a slight modification to that presented by Mantz for low Reynolds numbers. The range of particle Reynolds numbers covered in the study was from 0.026–12.56.

Closure to “Three-Dimensional Numerical Modeling of Dam-Break Flows with Sediment Transport over Movable Beds” by Reza Marsooli and Weiming Wu

The authors of the discussed paper appreciate the discussers’ interest in this paper and their sharing their opinions about 3D nonhydrostatic pressure modeling of dam-break flows and sediment transport. For the benefit of readers, the authors of the discussed paper would like to clarify some of the issues addressed by the discussers. The discussers are acknowledged for agreeing with the necessity of considering the effects of nonhydrostatic pressure and 3D flow features on dam-break fluvial processes. The importance of these factors has been proven in the original paper by comparing the results of the present 3D model with those of the past 1D and depth-averaged 2D models in the test cases. As stated in the original paper’s conclusions, a 3D nonhydrostatic pressure model is preferred for more accurately calculating the sediment transport and morphological changes in the initial stage of dam-break flow, near the wavefront, and around instream structures. The vertical dynamic pressure gradient in Eq. (25) of the original paper, ∂pd=∂z, is near, not at the bed. It is determined using the vertical gradient at the center of the first cell near the bed, as shown in Fig. 1. The bottom face of the cell, denoted as b, represents the bed surface, and a ghost cell, B, outside of the computational domain is used for the convenience of numerical implementation. The present 3D model solves the governing equations on a collocated mesh with all variables, including the pressure, stored at cell centers. It is true that the Neumann condition, Eqs. (3) or (4) in the discussers’ paper, gives a zero gradient of dynamic pressure at the river bed, i.e., on the b face. However, the dynamic pressure gradient at Cell Center P is calculated by ðpd;t − pd;bÞ=Δz. The Neumann condition indicates that the dynamic pressure at the bottom face of the cell, pd;b, is equal to the dynamic pressure at Center P, whereas the dynamic pressure at the top face of the cell, pd;t, is calculated by linear interpolation between the values at Cell Centers P and T. Since pT can be different from pP, the dynamic pressure gradient at the Cell Center P is not necessarily zero. The discussers proposed an approach expressed in Eq. (5) in their paper to determine the vertical dynamic pressure gradient ∂pd=∂z. However, their formulation considers the sediment layer below the bed surface, which is not susceptible for motion or entrainment. The approach in the original paper for ∂pd=∂z applies to the sediment particles on the bed surface, which are subject to transport. These two approaches are totally different. As demonstrated on page 316 of Wu (2007), in the case of jet impinging to the bed or flow around a bridge pier, localized dynamic pressure is built up at the impinging point and at the bed front of the bridge pier. The vertical dynamic pressure gradient near the bed has a negative value, which leads to a reduction of the net weight of the sediment particles and in turn the critical shear stress for incipient motion. However, the formulation proposed by the discussers leads to a positive gradient of dynamic pressure in the bed sediment layer, which increases the critical shear stress for incipient motion. One can see these two approaches can have opposite effects. Readers should be aware of this difference. The authors of the original paper believe the discussers’ approach may not be applicable for the sediment transport in the water column near the bed surface. By assuming that the thickness of the first vertical layer of the computational mesh is equal to the bed-load layer thickness, it could be possible to avoid solving the hydrodynamic and suspended-load transport equations on two distinct computational

Discussion of “Three-Dimensional Numerical Modeling of Dam-Break Flows with Sediment Transport over Movable Beds” by Reza Marsooli and Weiming Wu

The authors of the discussed paper appreciate the discussers’ interest in this paper and their sharing their opinions about 3D nonhydrostatic pressure modeling of dam-break flows and sediment transport. For the benefit of readers, the authors of the discussed paper would like to clarify some of the issues addressed by the discussers. The discussers are acknowledged for agreeing with the necessity of considering the effects of nonhydrostatic pressure and 3D flow features on dam-break fluvial processes. The importance of these factors has been proven in the original paper by comparing the results of the present 3D model with those of the past 1D and depth-averaged 2D models in the test cases. As stated in the original paper’s conclusions, a 3D nonhydrostatic pressure model is preferred for more accurately calculating the sediment transport and morphological changes in the initial stage of dam-break flow, near the wavefront, and around instream structures. The vertical dynamic pressure gradient in Eq. (25) of the original paper, ∂pd=∂z, is near, not at the bed. It is determined using the vertical gradient at the center of the first cell near the bed, as shown in Fig. 1. The bottom face of the cell, denoted as b, represents the bed surface, and a ghost cell, B, outside of the computational domain is used for the convenience of numerical implementation. The present 3D model solves the governing equations on a collocated mesh with all variables, including the pressure, stored at cell centers. It is true that the Neumann condition, Eqs. (3) or (4) in the discussers’ paper, gives a zero gradient of dynamic pressure at the river bed, i.e., on the b face. However, the dynamic pressure gradient at Cell Center P is calculated by ðpd;t − pd;bÞ=Δz. The Neumann condition indicates that the dynamic pressure at the bottom face of the cell, pd;b, is equal to the dynamic pressure at Center P, whereas the dynamic pressure at the top face of the cell, pd;t, is calculated by linear interpolation between the values at Cell Centers P and T. Since pT can be different from pP, the dynamic pressure gradient at the Cell Center P is not necessarily zero. The discussers proposed an approach expressed in Eq. (5) in their paper to determine the vertical dynamic pressure gradient ∂pd=∂z. However, their formulation considers the sediment layer below the bed surface, which is not susceptible for motion or entrainment. The approach in the original paper for ∂pd=∂z applies to the sediment particles on the bed surface, which are subject to transport. These two approaches are totally different. As demonstrated on page 316 of Wu (2007), in the case of jet impinging to the bed or flow around a bridge pier, localized dynamic pressure is built up at the impinging point and at the bed front of the bridge pier. The vertical dynamic pressure gradient near the bed has a negative value, which leads to a reduction of the net weight of the sediment particles and in turn the critical shear stress for incipient motion. However, the formulation proposed by the discussers leads to a positive gradient of dynamic pressure in the bed sediment layer, which increases the critical shear stress for incipient motion. One can see these two approaches can have opposite effects. Readers should be aware of this difference. The authors of the original paper believe the discussers’ approach may not be applicable for the sediment transport in the water column near the bed surface. By assuming that the thickness of the first vertical layer of the computational mesh is equal to the bed-load layer thickness, it could be possible to avoid solving the hydrodynamic and suspended-load transport equations on two distinct computational

Critical shear stress for incipient motion of a particle on a rough bed

The main objectives of the present study are to obtain improved models of hydrodynamic forces and torque on a particle sitting on a bed and to use these models for the investigation of incipient motion and resuspension of particles. The improved models for force and torque are obtained from numerical simulations of a particle sitting on a bed with a turbulent flow of logarithmic mean velocity profile approaching the particle. Since the mean turbulent velocity profile can depart from the logarithmic profile in case of macroscale rough beds or flow down steep slopes, we have also considered forces and torque on a particle due to both linear and uniform mean flow profiles. The computed drag and lift coefficients and the predicted critical shear stress for incipient particle motion and resuspension are compared against available experimental results. The improved force and torque models are also used to evaluate the effect of turbulent velocity fluctuations on the critical shear stress for incipient motion and resuspension. The present results are of direct relevance to cases where the particle is mostly exposed to the ambient flow. In cases where the particle protrusion is small and is submerged mostly within a pocket of other particles, the above formulation can be used with a redefined area of exposure and flow velocity seen by the particle. However, the drag, lift, and torque coefficients and the resisting forces will be influenced by the partial exposure and the details of pocket geometry, which require further investigation.

Velocity profiles and incipient motion of frazil particles under ice cover

A series of experiments for the incipient motion of frazil particles under ice cover have been carried out in laboratory under different flow and boundary conditions. Measurements on flow velocities across the measuring cross-section at different water depths have been conducted. Based on these experiments under both ice-covered and open flow conditions, the impacts of solid boundary (such as ice cover and flume sidewall) on the distribution of flow velocity profiles have been discussed. The criteria for the incipient motion of frazil particles under both smooth covered and rough covered conditions have been investigated. The influence of the roughness of ice cover has been assessed. The relation between shear Reynolds number and dimensionless shear stress for incipient motion of frazil particles under ice cover have been established compared with the incipient motion of sediment particles under ice covered condition. A diagram describing the relationship between critical shear Reynolds number and dimensionless shear stress for incipient motion of frazil particle under both smooth covered and rough covered conditions has been established. Additionally, it is found that the steeper the slope of ice cover is, the greater the critical shear stress for incipient motion of frazil particles becomes. However, the steeper the riverbed slope, the less the critical shear stress for incipient motion of river sediment.

The stability of marine sediments at a tidal basin in San Francisco Bay amended with activated carbon for sequestration of organic contaminants

Recent laboratory studies show that adding activated carbon to marine sediments reduces the bioavailability of persistent organic contaminants, such as polychlorinated biphenyls, to benthic organisms. The present work investigates how mixing activated carbon into cohesive sediment affects the stability of sediment obtained from the intertidal zone at the Hunters Point Naval Shipyard Superfund site in South Basin, San Francisco Bay, CA. Our results show for these sediments that mixing activated carbon into sediment does not significantly affect stability of surface sediments, as measured by sediment erosion rate and critical shear stress for incipient motion, thus supporting the potential field application of this technique for in situ stabilization of persistent organic contaminants. Hydrodynamic modeling was used to estimate the maximum bottom shear stress encountered during high-wind storm events at the estuarine inlet from which the sediments were obtained. Comparison of estimated bottom shear stresses with measured critical shear stresses shows that surface sediments will not erode under normal, non-storm conditions. Bottom shear stresses caused by large waves under infrequent high-wind storm conditions may erode surface sediments for short periods of time. We conclude from sediment stability tests and hydrodynamic modeling that mixing activated carbon amendment with cohesive sediment at selected locations within South Basin will not reduce surface sediment stability nor result in significant erosion of treated sediments.

INCIPIENT MOTION CHARACTERISTICS OF COHESIVE SEDIMENTS

ABSTRACT Results of an experimental study on incipient motion characteristics of cohesive sediments are presented. Cohesive sediments used consisted of medium sand mixed with Illite clay in different proportions. Incipient motion condition of thus formed cohesive sediment bed was identified through visual observations. Antecedent moisture content, clay content, plasticity index and void ratio/dry density are found to be significant parameters affecting the incipient motion characteristics in these cohesive sediments. A functional relationship between shear stress for incipient motion and sediment characteristics has been proposed based on dimensional considerations which account for both the plastic as well as non-plastic sediments. An empirical relation is also proposed for computation of Critical Shear Stress (CST) with certain limitations related to the type of clay used for experimentation and other factors.

Mobility of bed material in Harris Creek

The mobility of bed material is investigated in a small gravel bed river in which the bed is weakly bimodal in texture and relatively stable. The bed surface remained intact throughout the freshet, and scour was limited to small areas of the bed. Observations of bedload caught in pit traps and displacement of magnetically tagged particles during two spring freshets permit analysis of the mobility of each size fraction. Fractional transport rates plot up to three orders of magnitude below the reference transport rate suggested in the literature. At low flows, no size fraction was fully mobile. At intermediate flows (shear stress >27 Pa) sand was fully mobile while larger material remained partially mobile. At high flows (>43 Pa) the division between the full and partial mobility regimes occurred around 16 mm, which remains finer than the median size of the subsurface material. The largest material scarcely moves at mean annual flood. Magnetic tracers confirmed results obtained from the pit traps. Three distinct zones of mobility can be defined in fractional transport plots: partial mobility, full mobility, and overpassing/suspended. Critical shear stress for incipient motion varied over an order of magnitude; a qualitatively similar result for bimodal sediment was reported by Wilcock and McArdell [1993]. Incipient motion analysis based on the largest grain observed to move yielded an upper envelope implying transport similarity for sizes found on the bed surface, and a lower envelope that corresponds with our (nonsimilar) entrainment criterion.

Critical shear stress for incipient motion of sand/gravel streambeds

Results of an experimental study of the incipient motion of streambeds composed of sand/gravel sediment mixtures are reported and compared with the earlier findings for uniform sediments. The experiments were conducted in an 8 m long by 0.30 m wide glass‐walled tilting flume and an 18 m long by 0.80–1.10 m wide trapezoidal concrete channel. A reference transport method is used to define the beginning of bed material movement. The experiments demonstrate that the incipient motion of individual size fractions within a mixture is controlled by their relative size with respect to median size (intergranular effects), mixture standard deviation (effect of the shape of grain‐size distribution), absolute value of median size (absolute size effect), and bed slope (effect of relative depth on overall flow resistance). The shear stress at incipient motion of median‐sized grains in mixtures is found to be the same as for uniform sediment of this size. The present findings are consistent with available flume and field data. A technique for calculating the critical shear stress of different grain sizes in coarse uniform sediments and unimodal/weakly bimodal sediment mixtures is proposed.

The components of fractional transport rate

Fractional transport rates are defined as the product of spatial grain entrainment, displacement length, and displacement frequency. Grain entrainment is defined relative to the population of grains on the bed surface at an initial time in order to account for partial transport, a condition in which only a portion of the exposed grains of a single size Di are mobilized over the duration of a transport event. A relation for grain displacement frequency is calculated from an assumed relation for displacement length and observed values of fractional transport rate, bed surface size distribution, and spatial entrainment in flume experiments. Fractional transport rates are independent of Di for fully mobilized fractions and decrease rapidly with Di for partially mobile fractions; the latter results from a decrease in both the displacement frequency and the mobilized proportion of each fraction. These two terms, which together determine the fractional entrainment rate, have different relations with flow strength and Di and should be independently included in a general fractional transport model. Grain‐size similarity in fractional transport rates does not hold for conditions of partial transport. Partial transport is a grain‐scale representation of incipient motion and can be directly related to the reference shear stress τri a surrogate for the critical shear stress for incipient motion based on transport rate rather than grain mobility. Fractional mobilization at different flows may be predicted from τri, and partial transport appears to be the general condition at the reference transport rate. Using τri as input, the transport component relations are used to predict the bed mobilization and fractional transport rates for a field case.

Flow competence: A criticism of a classic concept

AbstractThe largest grains found in samples of transported sediment are commonly used to estimate flow competence. With samples from a range of flows, a relationship between the flow and the largest mobile grain can be derived and used to estimate the critical shear stress for incipient motion of the different grain sizes in the bed sediment or, inversely, to estimate the magnitude of the flow from the largest grain found in a transport sample. Because these estimates are based on an extreme value of the transport grain‐size distribution, however, they are subject to large errors and are sensitive to the effect of sample size, which tends to vary widely in sediment transport samples from natural flows. Furthermore, estimates of the critical shear stress based on the largest sampled moving grain cannot be scaled in a manner that permits reasonable comparison between fractions. The degree to which sample size and scaling problems make largest‐grain estimates of fractional critical shear stress deviate from a true relationship cannot be predicted exactly, although the direction of such a deviation can be demonstrated. The large errors and unknown bias suggest that the largest sampled mobile grain is not a reliable predictor of either critical shear stress or flow magnitude. It is possible to define a single flow competence for the entire mixture, based on a central value of the transport grain‐size distribution. Such a measure is relatively stable, does not require between‐fraction scaling, and appears to be well supported by observation.

Experimental study of incipient motion in mixed‐size sediment

Transport rates of five sediments were measured in a laboratory flume. Three of these sediments had the same mean size, the same size distribution shape, and different values of grain size distribution standard deviation. The critical shear stress for incipient motion of the individual size fractions within these sediments was estimated as that shear stress that produced a small dimensionless transport rate. The sorting of the sediment mixture had little effect on the critical shear stress of individual fractions, once the median size (D50) of the mixture and a fraction's relative size (Di/D50) are accounted for. Our data, combined with previously published data, show a remarkably consistent relation between the critical shear stress of individual fractions and the fraction's relative grain size, despite a broad variation in the available data of mixture sorting, grain size distribution shape, mean grain size, and grain shape. All fractions in a size mixture begin moving at close to the same value of bed shear stress during steady state transport conditions. This result is apparently true for transport systems where the transport rates of individual fractions are determined solely by the flow and bed sediment (recirculating systems), as well as for systems where the fractional transport rates are imposed on the system (feed systems). This equivalence in initial‐motion results is important because natural transporting systems often show attributes of both types of behavior in an unknown combination.