INCIPIENT MOTION OF COARSE PARTICLES IN HIGH GRADIENT RIVERS

1 INTRODUCTION To data, there are about 100 formulae for the incipient motion of sediment, among which, only about ten are convenient and practical. In 1936, using nondimensional drag force and the sediment’s Reynolds number, Shields (1936) presented the…     

A probabilistic model for sediment entrainment:The role of bed irregularity

A generalized probabilistic model is developed in this study to predict sediment entrainment under the incipient motion, rolling, and pickup modes. A novelty of the proposed model is that it incorporates in its formulation the probability density function of the bed shear stress, instead of the near-bed velocity fluctuations, to account for the effects of both flow turbulence and bed surface irregularity on sediment entrainment. The proposed model incorporates in its formulation the collective effects of three para-meters describing bed surface irregularity, namely the relative roughness, the volumetric fraction and relative position of sediment particles within the active layer. Another key feature of the model is that it provides a criterion for estimating the lift and drag coefficients jointly based on the recognition that lift and drag forces acting on sediment particles are interdependent and vary with particle protrusion and packing density. The model was validated using laboratory data of both fine and coarse sediment and was compared with previously published models. The study results show that all the examined models perform adequately for the fine sediment data, where the sediment particles have more uniform gra-dation and relative roughness is not a factor. The proposed model was particularly suited for the coarse sediment data, where the increased bed irregularity was captured by the new parameters introduced in the model formulation. As a result, the proposed model yielded smaller prediction errors and physically acceptable values for the lift coefficient compared to the other models in case of the coarse sediment data.     

Generalized algorithms for particle motion and collision with streambeds

Recent theoretical and numerical models for the motion of saltating particles close to stream beds are constituted of three sub-models: a) a set of equations describing the particle “free flight”, b) a sub-model to calculate the post-collision particle velocity, and c) a mathematical representation of the bed roughness. In this paper, a comprehensive three-dimensional (3-D), theoretical/numerical model for bedload motion at large Reynolds numbers is presented. By using geometric considerations and stochastic parameters to characterize collisions with the wall, five new sub-models for representation of bed roughness are, for the first time to the best of our knowledge, proposed and implemented. The emphasis of this paper is on the particle model, for which Basset, Magnus, drag, submerged weight, virtual mass, and lift forces are included. For the range of particle sizes (sands) analyzed herein, it is found that the stream-wise contribution of the Basset force, compared to other forces, may be as large as 60%. Whereas in the wall-normal direction, the Basset force is equally important as the drag force, and it is exceeded only by the submerged weight. It is also found that the best agreement between numerical and experimental results in terms of jump length, jump height, and stream-wise particle velocity is achieved for restitution and friction coefficients of 0.65 and 0.1, respectively. Important conclusions are obtained regarding the lack of realistic prediction with available “roughness” models with small ranges of angles.     

Issues in Eulerian–Lagrangian modeling of sediment transport under saltation regime

The saltation regime is very important for understanding the sediment transport mechanism. However,there is no consensus on a model for the saltation regime. This study answers several questions raised with respect to the Eulerian-Lagrangian modeling of sediment transport. The first question is why the previous saltation models that use different combinations of hydrodynamic forces yielded acceptable results? The second question is which shear lift model(i.e. a shear lift expression and its coefficient) is more appropriate? Another important question is which hydrodynamic forces have greater contributions to the saltation characteristics of a sediment particle? The last question is what are the contributions of the turbulence fluctuations as well as effects of using two-and three-dimensional(2 D and 3 D) models on the simulation results? In order to fairly answer these questions, a systematic study was done by considering different scenarios. The current study is the first attempt to clearly discuss these issues. A comprehensive 3 D saltation model for non-cohesive sediment was developed that includes all the hydrodynamic forces acting on the particle. The random nature of sediment transport was included using turbulent flow and bed-particle collision models. The eddy interaction model was applied to generate a3 D turbulent flow field. Bed-particle collisions were considered using the concept of a contact zone and a corresponding contact point. The validation of the model was done using the available experimental data for a wide range of sediment size(0.03 to 4.8 cm). For the first question, the results indicated that some of the hydrodynamic effects show opposing trends and some have negligible effects. With these opposing effects it is possible to adjust the coefficients of different models to achieve acceptable agreement with the same experimental data while omitting some aspects of the physics of the process. A suitable model for the shear lift force was developed by linking the lift coefficient to the drag coefficient and the contributions of the hydrodynamic forces and turbulence fluctuations as well as the consequences of using of 2 D and 3 D models were studied. The results indicate that the shear lift force and turbulent flow fluctuations are important factors for the saltation of both sand and gravel, and they cannot be ignored.     

Effects of sizes and shapes of gravel particles on sediment transports and bed variations in a numerical movable-bed channel

The paper presents a numerical movable-bed channel capable of simulating three-dimensional motions of flows and gravel particles in different shapes. At first, the numerical channel was tested against results of fixed-bed channel experiments in which gravel particles were transported. Simulated particle motions were validated in comparison with those in the laboratory experiment. Next, numerical movable-bed experiments with sphere particles and gravel particles were conducted. The results of these experiments clearly elucidated the difference in motion between the large and the small particles, effects of shapes of gravel particles on sediment-transport rates, and hydrodynamic forces and contact forces at incipient motion and at settling.     

THE FLUCTUATING CHARACTERISTICS OF HYDRODYNAMIC FORCES ON BED PARTICLE

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An improved formula for incipient sediment motion in vegetated open channel flows

Quantifying incipient sediment motion in vegetated open channel flow is pivotal for estimating bed load transport and the aquatic ecological environment in rivers.A new formula is developed to predict the critical flow velocity for incipient sediment motion in the presence of emergent vegetation,by incorporating the influence of vegetation drag that characterizes the effects of mean flow and turbulence on sediment movement.The proposed formula is shown to agree with existing experimental data.Mo...     

A heuristic probabilistic approach to estimating size-dependent mobility of nonuniform sediment

This paper presents a heuristic probabilistic approach to estimating the size-dependent mobilities of nonuniform sediment based on the pre- and post-entrainment particle size distributions (PSDs), assuming that the PSDs are lognormally distributed. The approach fits a lognormal probability density function to the pre-entrainment PSD of bed sediment and uses the threshold particle size of incipient motion and the concept of sediment mixture to estimate the PSDs of the entrained sediment and post-entrainment bed sediment. The new approach is simple in physical sense and significantly reduces the complexity and computation time and resource required by detailed sediment mobility models. It is calibrated and validated with laboratory and field data by comparing to the size-dependent mobilities predicted with the existing empirical lognormal cumulative distribution function approach. The novel features of the current approach are: (1) separating the entrained and non-entrained sediments by a threshold particle size, which is a modified critical particle size of incipient motion by accounting for the mixed-size effects, and (2) using the mixture-based pre- and post-entrainment PSDs to provide a continuous estimate of the size-dependent sediment mobility.     

细颗粒泥沙成团起动及其流速的研究

文中首选指出当水深很大时,考虑薄膜水附加下压力的起动流速公式计算的单颗细泥沙的起动流速很大,甚至于远超过３ｍ／ｓ,这与实际资料有相当出入。此外,实际现象还表明这些粘土及细颗粒起动时常常不是单颗的,则是成团进行。由此出发,再考虑粘着力及薄膜水附压力下分析了土块成团起动的临界条件,得到了成团起动的起动流速。     

Threshold criterion for debris flow initiation in seasonal gullies

A series of flume experiments were done to investigate the effect of grain composition on the critical gradient and discharge of debris flows initiated in seasonal gullies. The results indicated that the critical gradient and discharge for debris flow initiation decrease initially, and then increase as the mass content of fine particles (<2 mm) increases. As the mass content of fine particles increases, the angle of repose, permeability of widely graded gravel soils, and the incipient motion conditions of the coarse grains in non-uniform sediments decrease at first, and then increase. The mass content of fine particles of all inflection points is the same. The theoretical model based on the combination of hydrodynamic force and shear stress is more applicable to the prediction of the critical gradient for debris flow initiation. The critical discharge model considering the effect of non-homogeneity of the soil and the size of coarse and fine grains provides a more accurate prediction of debris flow initiation than other models based on the mean diameter.     

Non-uniform sediment incipient velocity

Based on the mechanism of non-uniform sediment incipient motion, the dragging force and uplift force coefficient expressions are put forward for the non-uniform bed material exposure and close alignment state. The incipient velocity formula of the non-uniform sediment is then established. It is shown that the formula structure is reasonable, and fine particles of the non-uniform sediment are more difficult to set into motion than the same sized uniform particles, whereas coarser particles are easier to set into motion than their uniform equivalents. The validity of the formula is verified by field and experiment data.     

LOCAL SCOUR DEPTH AROUND SPURS IN THE LOWER YELLOW RIVER

1 INTRODUCTION The Lower Yellow River is a suspended river channel bed much higher than the adjacent ground behind the dikes, well known all over the world. The floods flow east into the sea under the constraints of dikes. The safety of the dikes or embankments mainly relies on the protection provided by the river training works that have been constructed and maintained for several thousand years. There are three types of river training works and they are spurs, guide banks, and reve…     

Flume experiments on wood entrainment in rivers

A flume experiment on entrainment of woody debris is carried out. Woody debris is modeled using smooth, cylindrical dowels, in touch with the flume bed. The water depth and velocity are evaluated that initiate the motion of the partially submerged dowels. On the basis of the experimental finding, a theoretical model of log entrainment is developed, providing in dimensionless form the equilibrium equation for incipient motion. The experiment shows that the equilibrium equation must keep into account the modification of the local water profile, affecting the force balance at incipient motion. This issue has been apparently neglected in the wood entrainment models so far developed. The entrainment model is less sensitive to the choice of the apparent drag coefficient. The capability of the model in predicting the critical log diameter for initiation of motion is discussed and compared with that from the recent entrainment model from Braudrick and Grant, 2000. The comparison shows interesting results and provide evidence of the needs for further studies on wood entrainment in rivers.     

Effect of seepage on initiation of cohesionless sediment transport

This paper presents theoretical analyses and experimental results of seepage effects, especially downward seepage, on the initiation of cohesionless sediment particles. The theoretical analysis examines how the additional seepage force acts to modify the critical shear stress for sediment entrainment. Laboratory experiments were conducted using medium sand with diameter of 0.9 mm with downward seepage to quantitatively show suction effects on sediment entrainment. The critical shear stresses with different suction rates were calculated using the experimental results. The measured data together with published results provide an overall view on seepage effects on the initiation of cohesionless sediment transport. Depending on whether seepage is in the form of injection or suction, it will either increase or decrease the critical shear stress. The result reveals that the ratio of drag force at the threshold condition with seepage to that without seepage is dependent on the ratio of the hydraulic gradient with seepage to its value at the quick condition.     

Laboratory and theoretical evaluation of impact of packing density,particle shape,and uniformity coefficient on erodibility of coarse-grained soil particles

Sedimentation – including erosion, transport, and deposition of coarse-grained particles – is a primary and growing environmental, engineering, and agricultural issue around the world. Soil erosion occurs when the hydrodynamic force induced by flowing water exceeds the geotechnical resistance of soils, as measured by critical shear stress for initiation of soil-particle motion. Even though various quantitative methods have been suggested with respect to different types of soil, the most widely accepted formula to estimate critical shear stress for coarse-grained soil is a direct function of the median grain size of the soil particles; however, the erosion resistance of soils also varies with other geotechnical properties, such as packing density, particle shape, and uniformity coefficient. Thus, in this study, a combined rolling–lift model for particle detachment was derived based on theoretical analysis. A series of experimental flume tests were conducted with specimens prepared with standard soil types, as well as laboratory-prepared mixtures of coarse-grained soil to validate the theoretical model and determine the effect of other geotechnical properties on the erosion characteristics of coarse grains, coupled with the effect of median particle size. The results indicated that the median grain size is the primary variable determining the resistance of coarse grains, but the critical shear stress also varies with the packing density of the soil matrix. In addition, angular particles show more erosion resistance than rounded particles, and the erosion potential of a soil decreased when the grain is well graded (higher value of uniformity coefficient). Additionally, regression analysis was performed to quantify the effect of each parameter on the critical shear stress of coarse grains. © 2020 John Wiley & Sons, Ltd.     

Biofilm effects on size gradation,drag coefficient and settling velocity of sediment particles

Sediment particles are often colonized by biofilm in a natural aquatic ecological system, especially in eutrophic water body. A series of laboratory experiments on particle size gradation, drag coefficient and settling velocity were conducted after natural sediment was colonized by biofilm for 5, 10, 15 and 20 days. Particle image acquisition, particle tracking techniques of Particle Image Velocimetry and Particle Tracking Velocimetry were utilized to analyze the changes of these properties. The experimental results indicate that the size gradation, the drag force exerted on bio-particles, and the settling velocity of bio-particles underwent significant change due to the growth of biofilm onto the sediment surface. The study proposes a characteristic particle size formula and a bio-particle settling velocity formula based on the regression of experiment results, that the settling velocity is only 50% to 60% as the single particle which has the same diameter and density. However, biofilm growth causes large particle which the settling velocities are approximately 10 times larger than that of primary particles. These results may be specifically used in the low energy reservoir or lake environment.     

Adaptive criterion curves describing incipient motion of sediment under wave and current conditions

Sediment incipient motion is a fundamental issue in sediment transport theory and engineering practice. Whilst Shields curve often is used to determine the threshold of sediment movement under unidirectional current conditions, it is unclear whether it can be directly applied for the wave or combined wave-current conditions. The study developed adaptive criterion curves describing incipient motion of sediment under wave and current conditions based on the flow pattern around the sediment particles. Firstly, the flow pattern law for fixed particles was recognized based on the friction law under various dynamic conditions (wave, current, and their combinations), and the flow pattern demarcations for incipient sediment motion were obtained with the threshold conditions for sediment movement under various dynamic conditions combined. Secondly, the exact shape of the Shields curve in each flow regime was derived under the current condition. By combining the flow pattern demarcations for incipient sediment motion under the wave condition, the criterion curve under the wave condition was derived. By combining the flow pattern demarcations for incipient sediment motion under the combined current-wave condition, the criterion curve for sediment incipient motion under the combined current-wave condition was derived. The results indicated that the flow pattern around incipient particles includes laminar, laminar-rough turbulent transition, and rough turbulent regimes. The criterion curves for sediment incipient motion under various dynamic conditions stayed the same in the laminar and rough turbulent regimes, but different in the transition regime. Depending on the relative strengths of the currents and waves, the shape of the criterion curve under the combined current-wave condition transitions adaptively between the criterion curve under the current condition and the criterion curve under the wave conditions.     

STOCHASTIC THEORY OF THE DISTRIBUTION OF SEDIMENT PARTICLES SUSPENDED IN A TURBULENT FLOW

The random motion of sediment particles suspended in a turbulent flow is studied by means of stochastic process. Results of analysis of particle's frequency response to the random force exerted on the particle due to fluid turbulence suggest that only the lower part of the whole frequency range of the eddy motion will govern the motion of the particle. The mean values of particle velocity and displacement in the vertical direc- tion are calculated and it is found that particle velocity vp- can be decomposed into a mean motion and a velocity fluctuation vp- , where is equal to the fall velocity in tranquil fluid. An Ito^ random differential equation for particle dis- placement Yp is developed, from which a Fokker-Planck equation for the probability density function p(y,t) is derived on the basis of the theory of Markov process, where y denotes the vertical coordinate. The vertical distribution of the particle is thus interrelated to the random motion of the particle. The an effect that a particle will be subject to in the neighborhood or the bottom boundary is taken into consideration and a corresponding Fokker-Planck equation is developed. Analytical solution of the Fok- ker-Planck equation including the lift force effect shows that probability density p(y,t) for the particle displacement has a maximum value at y = H where the perpen- dicular component of the lift force balances the particle gravity. This theoretical result agrees with experimental observations as reported in literature.     

On the mechanisms of the saltating motion of bedload

Saltation of sediment particles is an important pattern of bedload transport.Based on force analysis for sediment particles,a Lagrangian model was proposed for the saltating motion of bedload in river flows,which was then solved with numerical method.Simulation results on the saltating trajectories neglecting particle rotation and turbulence effects compare fairly well with experimental observations.The mean values of the saltation parameters (saltation height,length and velocity) also agree well with the previous experimental data.Based on the numerical results,regression equations for the dimensionless saltation height,length and velocity were presented.Using the numerically achieved characteristics of the sediment saltation,we also obtained mathematical expression for the sediment transport rate.The studies in this paper are significant for its contribution to mechanism of the bedload motion and the computation of sediment transport rate.