Shields Diagram Research Articles

Influence of a Meandering Channel on the Threshold of Sediment

River meanders and channel curvatures play a significant role in sediment motion, making it crucial to predict incipient sediment motion for effective river restoration projects. This study utilized an artificial intelligence method, multiple linear regression (MLR), to investigate the impact of channel curvature on sediment incipient motion at a 180-degree bend. We analyzed 42 velocity profiles for flow depths of 13, 15, and 17 cm in a laboratory flume. The results indicate that the velocity distribution was influenced by the sediment movement threshold conditions due to channel curvature, creating a distinct convex shape based on the bend’s position and flow characteristics. Reynolds stress distribution was concave in the upstream bend and convex in the downstream bend, underscoring the bend’s impact on incipient motion. Bed Reynolds stress was highest in the first half of the bend (0 to 90 degrees) and lowest in the second half (90 to 180 degrees). The critical Shields parameter at the bend was approximately 8–61% lower than the values suggested by the Shields diagram, decreasing from 0.042 at the beginning to 0.016 at the end of the bend. Furthermore, our findings suggest that the MLR method does not significantly enhance the understanding of sediment movement, highlighting the need for a more comprehensive physical rationale and an expanded dataset for studying sediment dynamics in curved channels.

Quantitative definition of Shields criterion for incipient sediment motion

The Shields diagram has been widely used in the description of the threshold condition for incipient sediment motion. Because the current definition of the Shields criterion is generally subjective, the relevant data are subject to high uncertainty. To date, several efforts have been made to define the threshold condition quantitatively, but they are all based on certain low bedload rates that were empirically chosen. The current study aims to provide a theoretical framework to quantify the Shields criterion based on the concept of the pickup probability of sediment particles. The results show that the Shields criterion can be reasonably described with a low pickup probability (p = 1%), which can be further converted to a low dimensionless bedload rate (i.e., ϕ/θ1.5=0.13, where ϕ is the Einstein number and θ is the Shields number). The new approach is finally validated with experimental data of bedload rates published in the literature.

Effect of turbulent coherent motion on the onset of particle transport using synchronized 3D PIV and PTV

A series of laboratory experiments was conducted to understand the role of unsteady coherent motions of turbulent flow in the onset of particle motion. Turbulent eddies having coherent structures constantly interact with sediment particles within the bottom boundary layer. Therefore, a 3D turbulent flow field and grain trajectories were obtained by the simultaneous operation of three-dimensional (3D) particle image velocimetry and particle tracking velocimetry. Characteristics of the grain motions were investigated with the various particles in the various flow conditions. Based on the Stokes number of sediments, the spectral density of flow field revealed that turbulent eddies in the production subrange initiate grain motion. The proper orthogonal decomposition extracted the flow fields in the production subrange and the quadrant analysis was used to define dominant turbulent event initiating particle motions in the different flow conditions. The events of outward interaction and sweep initiated particle motion under low-velocity conditions, whereas those of sweep and ejection frequently occurred at the onset of particle motion under high-velocity conditions. Based on the results of the quadrant analysis, we proposed a transition curve that determines the dominant turbulent event depending on the flow condition on the conventional Shields diagram

Shields Diagram and the Incipient Motion of Microplastic Particles.

Incipient motion conditions for 57 regular (spheres, cylinders, disks, square plates, cubes, square prisms, rectangular prisms, tetrahedrons, and fibers) and eight irregular microplastic particle groups, having various sizes and densities, are investigated in a circular flume. The present data set is combined with additional data from the literature and systematically analyzed. A new framework is developed for predicting incipient motion conditions for foreign particles, accounting for variations in static friction, hydraulic roughness, and hiding-exposure effects. Via this framework, incipient motion conditions for microplastic particles lying on a sediment bed are, for the first time, reconciled with the classical Shields diagram.

Sediment erodibility in the Changjiang (Yangtze) subaqueous delta: spatial–temporal distribution and sedimentary significance

Delta evolution in the context of no sediment discharge has become a global concern, and an accretion-to-erosion conversion is occurring in the Yangtze estuary. This conversion could threaten Changjiang subaqueous delta development. Sediment erodibility is an important indicator of subaqueous delta vulnerability. However, the present and future erodibility of the Changjiang subaqueous delta remains unclear. In this study, 37 short cores were collected from the Changjiang subaqueous delta, and the critical shear stress of the sediment was measured using a cohesive strength meter (CSM) and compared with estimates based on an empirical Shields diagram. The sediment erodibility was analyzed by comparing the sediment critical shear stress with the bed shear stress simulated using a numerical model (i.e., FVCOM), and sediment activity was introduced to discuss the geomorphological change in the subaqueous delta. The CSM-derived critical shear stress is significantly higher than that derived from the empirical Shields formula, but it better shows the erodibility of the sediment. The annual surface sediment activity ranges from 5% to 30% based on the CSM, indicating low surface erodibility. Moreover, the critical shear stress in this region increases as water depth increases, but the bed shear stress shows the opposite trend. Therefore, the erodibility of the Changjiang subaqueous delta is lower than that of the shallow area, indicating no accretion-erosion conversion or continued vertical erosion under sediment starvation in the coming decades. These findings can provide suggestions for erosion assessment and management in large river deltas under decreasing sediment discharge.

Centrifuge modeling of scale effect on hydraulic gradient of backward erosion piping in uniform aquifer under river levees

The hydraulic gradient that causes backward erosion piping under a river levee is influenced by the scale of the levee, which is a major concern in the physical modeling. In this study, the results of 1 g and centrifuge tests performed on backward erosion piping were analyzed to facilitate a better understanding of the scale effect mechanism. The three-dimensional profile of the pipe and the flow rate of water in the pipe were observed using a transparent model levee. Although the flow in the pipe was determined to be laminar in most tests, it was found to be transient and turbulent in the coarse sand model at high g levels. The hydraulic gradient in the pipe was significantly high in the turbulent flow. Additionally, the scale effect was investigated based on the hydraulic conditions that cause sand transportation in an ideal pipe. The critical Shields number (θc), estimated for the model pipes, was consistent with that observed in the Shields diagram. The effects of centrifugal acceleration on the hydraulic gradient of the extending pipes can be explained by the change in θc with the particle Reynolds number and the hydraulic gradient in the pipe.

Incipient motion of sediment particles in the presence of bed forms under decelerating and accelerating flows

Abstract This paper investigates the incipient motion of sediment particles under non-uniform flow in river and laboratory. In rivers, the non-uniform flow is often observed due to the presence of various bed forms. Threshold condition has been examined by using the Shields diagram based on the uniform flow assumption, however, this approach can be led to fallacious results for non-uniform flows where the effect of pressure gradient is significant due to bed forms. This study investigates the chronological order of incipient motion of the particles, the average threshold velocity (Ucr ), and Shields parameter for non-uniform flows. River data collection with gravel is used for investigating the incipient motion of surface layer of river bed and the laboratory data collection is considered studying the incipient motion of sub-surface layer of river. Both river and laboratory data collections are conducted in the presence of bed forms. Results reveal that the Shields diagram underestimates the particle incipient motion under accelerating and decelerating flows for the both case of laboratory and river. In both weak and general motion in the laboratory, the values of the critical Shields parameter are located below the Shields diagram, showing no particle motion. Our analysis shows that the incipient motion in river is affected by the presence of bed forms, river width changes, and flow non-uniformity conditions. The results show that in the accelerating flow (the bed form exit with a negative slope), the incipient motion is greater than the decelerating flow (the bed form entrance with a positive slope).

Generalized Bed-Load Function Based on Empirical Data

There exist many bed-load functions in the literature to calculate bed-load transport rates, but none of them fit data from low to high shear stress conditions. This research presents a generalized bed-load function based on empirical data. Specifically, the classic power law in high shear stress conditions is extended to low shear stress conditions by applying a complimentary error function (or logistic function) and using Coles’ mathematical idea for the wake law in turbulent boundary layer velocity distribution. The resulting generalized bed-load function agrees well with the classic data sets; it reduces to Huang’s 5/3 power law in the very low and the high shear stress conditions, and it is numerically close to Paintal’s 16th power law in the transitional regime. It is found that the maximum turbulence-induced lift force and the minimum critical shear stress in the Shields diagram correspond to the inflection point (in terms of logarithmic scale) in the Einstein bed-load diagram, resulting in the most efficient bed-load transport rate. After that, this paper discusses the effects of turbulence-induced lift force, critical shear stress, viscosity, nonlinearity, and uncertainty on bed-load transport. Finally, an example with uncertainty analysis is illustrated for applications.

Closure to “Empirical Model for Shields Diagram and Its Applications” by Junke Guo

Closure to “Empirical Model for Shields Diagram and Its Applications” by Junke Guo

Discussion of “Empirical Model for Shields Diagram and Its Applications” by Junke Guo

Discussion of “Empirical Model for Shields Diagram and Its Applications” by Junke Guo

Assessment of Critical Shear Stress and Threshold Velocity in Shallow Flow with Sand Particles

In this study, the incipient motion of four groups of sand, ranging from medium to very coarse particles, was experimentally examined using an acoustic Doppler velocimeter (ADV) in different water depths under the hydraulically transitional flow condition. The transport criterion of the Kramer visual observation method was used to determine threshold conditions. Some equations for calculating threshold average and near-bed velocities were derived. Results showed that the threshold velocity was directly proportional to both sediment particle size and water depth. The vertical distributions of the Reynolds shear stress showed an increase from the bed to about 0.1 of the water’s depth, after performing a damping area, then a decrease toward the water surface. By extending the linear portion of the Reynolds shear stress in the upper zone of the damping area to the bed, the critical shear stress, particle shear Reynolds number, and critical Shields parameter were calculated. Results showed that the critical Shields parameter was located under the Shields curve, showing no sediment motion. This indicates that the incipient motion of sediment particles occurred with smaller bed shear stress than that estimated using the Shields diagram in the hydraulically transitional flow region. The reason could be related to differences between the features of the present experiment and those of the experiments used in the development of the Shields diagram, including the approaches to determine and define threshold conditions, the accuracy of experimental tools to estimate critical shear stress, and sediment particle characteristics. Therefore, the change in the specifications of experiments from those on which the Shields diagram has been based led to the deviation between the estimation using the Shields diagram and that of real threshold conditions, at least in the hydraulically transitional flow region with sand particles.

Рhysical simulation of erosion of bottom pits

The present paper is devoted to research of the erosion of large-scale sand pits in the water flow. The investigations were performed in the hydrodynamic flume with sandy bottom. To provide suitable conditions for sediment transport in the flume, the analysis of the factors leading to the motion of sediments was carried out in accordance with the Shields diagram. It was shown that the flow regime created in the laboratory channel promotes the development of natural bed forms such as ripples. Estimations of the velocity of movement of the ripples were obtained. The experiments with large sand pits on the flume bottom demonstrated that those disturb the balance of sediments and cause the reformatting of the water flow. To assess the influence of the pit configuration on the erosion process, two-dimensional triangular and trapezoidal pits were considered. It was found that the longitudinal profile of the triangular pit changes due to sediment deposition on its upper slope and erosion of the lower slope. The pit upper slope levels out and shifts forward due to the continuous flow of sediment in this region. The depth of the unevenness also decreases owing to deposition of the sediment directly on its bottom. Due to the blow of water jet to the pit lower slope, the zone of maximum erosion of the bottom surface is observed here. The bottom reformatting leads to the displacement of the pit downstream. Studies of the erosion of the trapezoidal pit have shown that its upper slope is first shifted toward the lower slope until the trapezoidal profile turns into a triangular one. The pit erosion causes also the deformation of natural forms of the channel bed and destabilization of sediment discharge. The analysis of the obtained data demonstrated that the reformation of channel bed is a durable process depending of the ratio of pit scales to the volume of sediment. The present study is useful for development of engineering solutions directed to reduction of risks caused by the interaction of sand quarries with hydraulic structures in rivers.

Condition for the Incipient Motion of Non-Cohesive Particles Due to Laminar Flows of Power-Law Fluids in Closed Conduits

The results of an experimental study on the condition of incipient transport of non-cohesive particles due to the flow of a power-law fluid in a rectangular pipe are presented in this article. The pipe can change its inclination, and experiments were carried out with positive and negative slopes. From a dimensional analysis, the parameters that define the condition of incipient motion were found and validated with experimental data. Thus, the threshold condition is well defined by a particle Reynolds number and a Galileo number, properly modified to take into account the power-law rheology of the fluid. The experimental data are also presented in a standard Shields diagram, including the data obtained in other studies carried out in open-channel laminar flows of Newtonian and power-law fluids.

Empirical Model for Shields Diagram and Its Applications

AbstractThe Shields diagram is a classic method for quantifying sand incipient motion in sediment transport. It is often expressed by empirical or semiempirical equations. This research applies the...

The Physics of Sediment Transport Initiation, Cessation, and Entrainment Across Aeolian and Fluvial Environments

AbstractPredicting the morphodynamics of sedimentary landscapes due to fluvial and aeolian flows requires answering the following questions: Is the flow strong enough to initiate sediment transport, is the flow strong enough to sustain sediment transport once initiated, and how much sediment is transported by the flow in the saturated state (i.e., what is the transport capacity)? In the geomorphological and related literature, the widespread consensus has been that the initiation, cessation, and capacity of fluvial transport, and the initiation of aeolian transport, are controlled by fluid entrainment of bed sediment caused by flow forces overcoming local resisting forces, whereas aeolian transport cessation and capacity are controlled by impact entrainment caused by the impacts of transported particles with the bed. Here the physics of sediment transport initiation, cessation, and capacity is reviewed with emphasis on recent consensus‐challenging developments in sediment transport experiments, two‐phase flow modeling, and the incorporation of granular physics' concepts. Highlighted are the similarities between dense granular flows and sediment transport, such as a superslow granular motion known as creeping (which occurs for arbitrarily weak driving flows) and system‐spanning force networks that resist bed sediment entrainment; the roles of the magnitude and duration of turbulent fluctuation events in fluid entrainment; the traditionally overlooked role of particle‐bed impacts in triggering entrainment events in fluvial transport; and the common physical underpinning of transport thresholds across aeolian and fluvial environments. This sheds a new light on the well‐known Shields diagram, where measurements of fluid entrainment thresholds could actually correspond to entrainment‐independent cessation thresholds.

Threshold of motion of bivalve and gastropod shells under oscillatory flow in flume experiments

AbstractThe threshold of motion of non‐fragmented mollusc shells was studied for the first time under oscillatory flow. In this regard, flume experiments were used to investigate the threshold of motion of three bivalve and three gastropod species, two typical mollusc classes of coastal coquina deposits. The sieve diameters ranged from 2·0 to 15·9 mm. These experiments were performed on a flat‐bottom setup under regular non‐breaking waves (swell) produced by a flap‐type wave generator. The critical Shields values for each species of mollusc were plotted against the sieve and nominal diameter. Moreover, the dimensionless Corey shape factor of the shells was evaluated in order to investigate the effect of mollusc shell shapes on the threshold of motion. According to their critical Shields parameter, the mollusc threshold data under oscillatory flow present smaller values than the siliciclastic sediments when considering their sieve diameter. In addition, the mollusc datasets are below the empirical curves built from siliciclastic grain data under current and waves. When considering the nominal diameter, the critical Shields parameter increases and the mollusc data are closer to siliciclastic sediments. Bivalves, which have a flat‐concave shape (form factor: 0·27 to 0·37), have a higher critical Shields parameter for smaller particles and more uniform datasets than the gastropod scattered data, which have a rounded shape (form factor: 0·58 to 0·62) and have varied morphologies (ellipsoidal, conical and cubic). The comparison between previous current‐driven threshold data of bioclastic sediment motion and the data of mollusc whole shells under oscillatory flow shows a fair correlation on the Shields diagram, in which all datasets are below the mean empirical curves for siliciclastic sediments. These findings indicate that the shape effect on the transport initiation is predominant for smaller shells. The use of the nominal diameter is satisfactory to improve the bioclastic and siliciclastic data correlation.

Mechanism of Phase Lag Between Current Speed and Suspended Sediment: Combined Effect of Erosion, Deposition, and Advection

To retrieve and explain the phase lag between current speed and suspended sediment concentration (SSC), erosion, deposition, and advection were isolated as primary processes of sediment movement in a three-dimensional model. The response time was proved to be one of the reasons for the phase lag, as time is needed for suspension to diffuse from bottom to surface. A fitted Shields diagram was introduced into the model to reflect the relationship between SSC and shear stress, between shear stress and critical shear stress, as well as between SSC and critical shear stress for erosion. It takes some time for shear stress to increase to the critical value after high or low tide, and this was proved to be an important contributor to the phase lag. Overall, the variation of vertically integrated SSC is influenced by erosion mass flux, deposition mass flux, and advection flux. The phase pattern of erosion mass flux is consistent with the pattern of current if there was no wave action. However, phase difference is produced by the influence of deposition mass flux and advection. In this study, SSC peak/trough mostly occurred near the moment erosion mass flux approximately equaled deposition mass flux and would be impacted by advection. The time required for instantaneous variation of suspension to get to 0 after current peak/trough represents the phase lag between current speed and SSC.

Kriteria Pergerakan Ambang Sedimen bagi Campuran Sedimen Jelekit Biologi

Shields diagram is used as the main source to determine the incipient motion of sediment. However, incipient sediment motion in the Shields diagram was developed based on non-cohesive sediment where the parameter influencing the motion of cohesive and non-cohesive sediments are different. Therefore, this study attempts to investigate the incipient sediment motion for biological extracellular polymeric substance (EPS) influenced by a cohesive sediment mixture. Percentage of silt with a median grain size of 28μm (which acts as the cohesive material) and fine sand with of 150μm were varied as 10:90, 20:80, 40:60, and 50:50, which formed the cohesive sediment mixture. Two different concentrations of EPS 0.02% (which denotes as low concentration) and 0.1% (as high concentration) were well mixed with the sediment mixture. This study utilised Xanthan gum, which acts as a substitution for EPS. The experiments were conducted in a laboratory flume and the threshold criterion for sediment motion was obtained through observation. The critical Shields parameter θ_c was calculated using the critical shear velocity and root-mean-square horizontal velocity (representing turbulent fluctuations) when few of the particles on the bed was observed to move. Obvious finding from this study is the presence of EPS clearly influence the threshold criteria based on the higher value obtained at sediment mixture with 0.1% compared to the values found for the 0.02% EPS sediment mixture. The values of the critical Shields parameter were monotonously increased as the percentage of silt in the sediment mixture increases. The presence of silt in the sediment mixture increases the sediment stability signifying more hydrodynamic forces are required for the particles to be entrained. The critical Shields parameter obtained based on the critical shear velocity and turbulent fluctuations posed similar trend as described in the well-established Shields curve indicating that the velocity scale used to describe the incipient sediment motion is not a decisive factor.

A method for simulating sediment incipient motion varying with time and space in an ocean model (FVCOM): development and validation

We modified the sediment incipient motion in a numerical model and evaluated the impact of this modification using a study case of the coastal area around Weihai, China. The modified and unmodified versions of the model were validated by comparing simulated and observed data of currents, waves, and suspended sediment concentrations (SSC) measured from July 25th to July 26th, 2006. A fitted Shields diagram was introduced into the sediment model so that the critical erosional shear stress could vary with time. Thus, the simulated SSC patterns were improved to more closely reflect the observed values, so that the relative error of the variation range decreased by up to 34.5% and the relative error of simulated temporally averaged SSC decreased by up to 36%. In the modified model, the critical shear stress values of the simulated silt with a diameter of 0.035 mm and mud with a diameter of 0.004 mm varied from 0.05 to 0.13 N/m2, and from 0.05 to 0.14 N/m2, respectively, instead of remaining constant in the unmodified model. Besides, a method of applying spatially varying fractions of the mixed grain size sediment improved the simulated SSC distribution to fit better to the remote sensing map and reproduced the zonal area with high SSC between Heini Bay and the erosion groove in the modified model. The Relative Mean Absolute Error was reduced by between 6% and 79%, depending on the regional attributes when we used the modified method to simulate incipient sediment motion. But the modification achieved the higher accuracy in this study at a cost of computation speed decreasing by 1.52%.

Critical conditions of incipient motion of cohesive sediments

AbstractThe critical condition of incipient motion of cohesive sediments was investigated in a laboratory study. One‐hundred experimental runs were performed with sediment samples by varying the yield stress to determine the relationship between the critical condition of incipient motion and the rheological properties of the cohesive sediments. The results indicate that yield stress is a factor that has a major influence on the incipient motion of cohesive sediments. In addition, the critical Shields parameter is found to be exponentially proportional to the yield stress and inversely proportional to the median grain size. The effect of yield stress on the critical Shields parameter is significant for the cohesive sediments and becomes progressively weaker with increasing median grain size. Furthermore, an empirical formula for calculating the critical Shields parameter of cohesive sediments that includes a rheological term and a gravity term is proposed by introducing the yield stress. According to this formula, a modified Shields diagram is obtained in which the values of the critical Shields parameter for cohesive sediments vary within a band that contains countless curves (instead of on a single line) to reflect the influence of the yield stress. This modification of the traditional Shields curve is effective for fine sediments, but the effects tend to vanish for coarse sediments as the behavior of sediments changes from cohesive to noncohesive. Finally, potential further investigations are discussed.