Non-uniform Sediment Transport Research Articles

Derivation of vertical concentration profile for nonuniform sediment in suspension using Shannon entropy

This research paper introduces a novel methodology for quantifying the sediment concentration of nonuniform sediment in suspension within an open channel, employing the concept of Shannon entropy. By treating the normalized sediment concentration as a stochastic variable, a probability distribution function is formulated via the maximum entropy principle. The validity of the proposed cumulative distribution function is established through a comparison with empirical data. Additionally, the newly devised concentration profile for nonuniform suspended sediment is compared with the established deterministic concentration equation and experimental data on grain-size distribution. A relationship between model parameters and Rouse number for nonuniform sediment is also provided. This study’s significance lies in introducing a new way to understand nonuniform sediment transport and its behaviors. The utilization of Shannon entropy not only showcases the versatility of this technique but also underlines its potential for unraveling the complexities inherent in nonuniform sediment dynamics. This study is the first step to introduce the entropy notion in nonuniform sediment and encourages more research to improve it.

Modelling of phosphorus and nonuniform sediment transport in the Middle Yangtze River with the effects of channel erosion , tributary confluence and anthropogenic emission.

Phosphorus (P) transport plays a crucial role in the aquatic ecology of natural rivers. However, our understanding still remains unclear that how P transport is affected in a river-lake connected system downstream of a dam. This system usually undergoes both severe channel degradation and complex exchange of flow-sediment-phosphorus between the mainstem and tributaries. In the current study, a method was proposed firstly to determine the individual contribution of different sources to P recover based on the calculation of phosphorus budget; then an integrated model was developed, covering the modules of flow, nonuniform sediment and phosphorus transport. The application of the proposed method in the 955-km-long Middle Yangtze River (MYR) shows that the type of P transportation was predominantly changed from particulate phosphorus to dissolved phosphorus after the operation of the Three Gorges Project (TGP), but a significant longitudinal recovery of total phosphorus (TP) flux was observed. The TP flux exporting from the MYR was mainly from the Upper Yangtze River (44%), and 12%, 18% and 26% of that were originated from channel erosion, tributary confluence and anthropogenic emission. Moreover, the effects were investigated of nonuniform sediment transport and bed-material coarsening on P transport in the MYR, based on the proposed integrated model. Obtained results show that the TP transport process in the MYR was more reasonable simulated using the nonuniform sediment mode, and it is also confirmed that the process of bed-material coarsening after the TGP operation would lead to the decrease of particulate phosphorus flux in the MYR.

Numerical modeling of local scour of non-uniform graded sediment for two arrangements of pile groups

A three-dimensional (3D) non-hydrostatic numerical model is established to investigate local scour around four aligned circular piles in uniform and non-uniform sediment mixtures and to provide information for improving scour countermeasures design. In the current study, unsteady Reynolds averaged Navier–Stokes (URANS) equations along with a Re-normalization Group (RNG) k–ε model were applied to simulate the flow field. A non-uniform sediment transport model was applied to estimate the bedload transport. The simulations lasted up to 8 h. The laboratory results of a reference single pile case in uniform and non-uniform sediment were utilized to validate the simulation results of bed elevation changes and time evolution of scour depth and reflected a good agreement. The influence of pile spacing for two arrangements of pile groups, one column (tandem) and two columns (non-tandem) of four aligned piles, on spatial/temporal variations of the bed surface in both sediment bed configurations are discussed in detail. The results reveal the significant effects of the pile spacing on the flow field and patterns of scour hole formation and sediment deposition. In general, lower pile spacing results in more scour upstream of the front pile(s) and shifts deposition more downstream due to the existence of higher energy in the wake region of the piles for both sediment types. Side scouring dominates for non-uniform sediment around each pile due to flow deviating because of the presence of relatively larger particles in front of the pile(s). For non-uniform sediment, deposition begins to develop at the exit area of the scour hole and enhances boundary resistance to scour. The knowledge gained from this study is suitable for the accurate determination of riprap dimensions around the front pile(s) and rear piles in a pile group.

Applicability of Sun’s Empirical Relations for Non-Uniform Sediment in Jiaojiang Estuaries, Zhejiang, China

The numerical simulation of non-uniform sediment transport under tidal flow in estuaries is a complicated, yet important, issue in Zhejiang estuaries. In this paper, a depth-averaged two-dimensional (2D) mathematical model for non-uniform sediment transport in estuaries is established and applied in Zhejiang tidal estuaries based on several newly derived formulas by Zhlin Sun et al. The model is validated using data from several experiments, including an aggradation test and an erosion test. Good performance in the tests indicates that the present model can simulate aggradation and erosion processes of non-uniform sediment. The model is also verified by observational data from the Jiaojiang estuary, and calculations agree well with measurements. The model is thus adaptable to simulating flow and non-uniform sediment transport in tidal estuaries.

Streamwise and Vertical Dispersal of Tracer Stones in an Equilibrium Bed

AbstractModeling transport, erosion, and deposition of nonuniform sediment over temporal intervals that are short compared to those characterizing channel bed aggradation and degradation remains an open problem due to the complex quantification of the sediment fluxes between the bed material load and the alluvial deposit. Parker, Paola, and Leclair in 2000 proposed a morphodynamic (PPL) framework to overcome this problem. This framework is used here to model the dispersal of a patch of gravel tracers in three different settings, a laboratory flume, a mountain creek, and a braided river. To simplify the problem, (a) the bed slope, bedload transport rate, and bed configuration are assumed to be constant in space and time (equilibrium), (b) sediment entrainment and deposition are modeled with a constant step length formulation, and (c) the PPL framework is implemented in a one‐dimensional (laterally averaged) model. Model validation against laboratory experiments suggests that, as the transport capacity of the flow increases, the maximum elevation‐specific density of sediment entrainment may migrate downward in the deposit. The comparison between model results and field data shows that the equilibrium solution can reasonably capture tracer dispersal. The equilibrium model can also reproduce subdiffusion and superdiffusion of a patch of tracers in the streamwise direction, depending on the magnitude of the short‐term bed level changes. Finally, the average tracer elevation in a cross‐section decreases in time because particles that are buried deep in the deposit are only rarely reentrained into bedload transport.

A new criterion for critical suspension of nonuniform sediment

ABSTRACT As the lower boundary of suspended particles, the critical condition of suspension is an important component in the theory of nonuniform sediment transport and plays a significant role in the numerical computations in the suspended sediment movement. Previous studies on critical suspension are mostly based on Rouse number and Shields number. From the perspective of maximum particle size, this paper conducted research on the critical suspension of nonuniform sediment by flume experiment. A new criterion for critical suspension of nonuniform sediment is proposed according to the concept of maximum particle Reynolds number and analysis of experimental data. Sediments will not be suspended unless the particle Reynolds number is less than or equal to the maximum one related to flow and boundary conditions. A formula, established from experimental data, indicates that the maximum particle Reynolds number is proportional to 3 power of Froude number and 1/5 power of relative roughness. As a new criterion for critical suspension, this formula offers a reasonable description of the physical mechanism for the initial movement of the suspended load. Not only does the proposed formula agree well with laboratory and field data, but it also has its advantages compared with traditional criteria.

Coupled modelling of flow and non-capacity sediment transport in sewer flushing channel

Flushing is cost-effective for mitigating sediments and constraining environmental problems in sewer systems. Previous mathematical models are almost exclusively built upon simplified governing equations evoking the assumptions of slow bed evolution and sediment transport capacity, of which the applicability remains open to question. Here a 1D coupled non-capacity model is presented for non-uniform sediment transport in sewer flushing channels, as adapted from recently established shallow water hydro-sediment-morphodynamic models for fluvial processes. The present model is tested for an experimental flushing case in Paris's Des Coteaux catchment system. The computational results agree with observed data more closely than those of a previous decoupled capacity model. While the differences between decoupled and capacity models and the present coupled non-capacity model are minor for flushing processes of short-durations, they are more pronounced for sustained long-duration flushing processes. Physically, the adaptation of suspended sediments to capacity regime cannot be fulfilled quickly, though bedload sediments can adapt to capacity regime instantly. Also, the bed deformation rate is comparable to its counterpart of the flow depth. Therefore, coupled non-capacity modelling is suggested for general applications to sewer flushing channels, of which the computing cost is essentially equivalent to simplified models built upon decoupling and capacity assumptions.

A Quasi-Single-Phase Model for Debris Flows Incorporating Non-Newtonian Fluid Behavior

Debris-flow modeling is a great challenge due to its complex physical mechanism that remains poorly understood. The present research incorporates the effect of rheological features of the non-Newtonian fluid into the complete quasi-single-phase mixture model, which explicitly accommodates the interactions between flow, non-uniform sediment transport, and bed evolution. The effect of rheological features is estimated by Hersch–Bulkley–Papanastasiou model that can be simplified to Bingham or Newtonian models with specific coefficients. The governing equations are solved by a fully conservative numerical algorithm, using an explicit finite volume discretization with well-balanced slope-limited centered scheme combined with an implicit discretization method. One set of large-scaled U.S. Geological Survey debris-flow experiments is applied to investigate the influence of the non-Newtonian fluid on debris-flow modeling. It is found that the present model closed by Hersch–Bulkley–Papanastasiou model performs better than the models without considering effect of rheological features, which may facilitate the development of quasi-single-phase mixture modeling for debris flows.

Sediment Transport and Water Flow Resistance in Alluvial River Channels: Modified Model of Transport of Non-Uniform Grain-Size Sediments

The paper presents recommendations for using the results obtained in sediment transport simulation and modeling of channel deformations in rivers. This work relates to the issues of empirical modeling of the water flow characteristics in natural riverbeds with a movable bottom (alluvial channels) which are extremely complex. The study shows that in the simulation of sediment transport and calculation of channel deformations in the rivers, it is expedient to use the calculation dependences of Chézy’s coefficient for assessing the roughness of the bottom sediment mixture, or the dependences of the form based on the field investigation data. Three models are most commonly used and based on the original formulas of Meyer-Peter and Müller (1948), Einstein (1950) and van Rijn (1984). This work deals with assessing the hydraulic resistance of the channel and improving the river sediment transport model in a simulation of riverbed transformation on the basis of previous research to verify it based on 296 field measurements on the Central-East European lowland rivers. The performed test calculations show that the modified van Rijn formula gives the best results from all the considered variants.

Transport characteristics of non-uniform suspended sediment in the Jingjiang Reach after the Three Gorges Project operation

三峡工程运用后，坝下游荆江段来沙量大幅度减小，处于严重的不平衡输沙状态，次饱和水流冲刷河床使悬沙量沿程恢复.基于实测水沙资料，分析了三峡工程运用后荆江段非均匀悬沙恢复特点.提出了恢复效率的概念用以表征悬移质沿程恢复的程度，并根据实测水沙资料计算了荆江段1994-2017年非均匀悬沙的恢复效率.结果表明：三峡工程运用前，荆江段各粒径组悬沙恢复效率绝对值均接近0，故该时期内各粒径组泥沙冲淤幅度不大；三峡工程运用后，各粒径组悬沙恢复效率绝对值均明显增大，且粗沙（d>0.125 mm）恢复效率绝对值远大于细沙（d<0.125 mm），故粗沙恢复程度更高.这主要是由于荆江段床沙组成中粗沙部分含量大，而细沙含量小.最后建立了三峡水库蓄水后非均匀悬沙恢复效率与来水来沙条件（来沙系数）的关系，结果表明：各粒径组悬移质恢复效率均与来沙系数呈正相关关系，全沙、细沙和中沙的决定系数（R²）分别为0.89、0.67和0.69，相关性较高，故荆江段各粒径组悬移质泥沙恢复效率较大程度上受到来水来沙条件的影响.;The amount of suspended sediment entering the Jingjiang Reach of the middle Yangtze River has been greatly reduced owing to the operation of the Three Gorges Project (TGP), which caused the sediment transport of the reach at a severe non-equilibrium state, and the suspended sediment concentration recovered during the channel scour process. Therefore, the characteristics of non-equilibrium transport of non-uniform suspended sediment were analyzed based on the measured flow and sediment data. In addition, the recovery efficiency was proposed to represent the recovery speed for suspended sediment load, and the corresponding values were calculated annually from 1994 to 2017 based on the measured data of the Jingjiang Reach. Calculated results show that the suspended sediment recovery efficiency of all particle-size groups was very close to zero before the TGP operation, which means that the channel deformation was small during this period. However, the recovery efficiency of each particle-size group increased greatly after the operation of TGP, and the recovery efficiency of coarse sediment (d>0.125 mm) was much higher than that of fine sediment (d<0.125 mm). This is mainly because the content of coarse sediment in bed-material of Jingjiang Reach is large, while the content of fine sediment is relatively small. Finally, empirical relationship was developed between the recovery efficiency and incoming flow-sediment regime, which shows that the recovery efficiency of each group was negatively related to incoming sediment coefficient, with the correlation coefficient for the total, fine and coarse sediment being 0.89, 0.67 and 0.69, respectively. Therefore, it can be concluded that the recovery efficiency of suspended sediment was significantly affected by the incoming flow and sediment conditions.

Evolution of a delta-canyon-fan system on a typical passive margin using stratigraphic forward modelling

The present work simulated a hypothetical 4D delta-canyon-fan depositional system using stratigraphic forward modelling (SFM) to: 1) investigate the differences and linkages of the sea-level control on the evolution of each sub-environment; 2) explain the evolution under the constraints of sea-level change from the perspective of channel activities.The SFM approach LECODE applied in this study combines an open-channel flow approach with a non-uniform sediment transport algorithm, with former to simulate water dynamics of turbidity currents and river flows and latter to simulate the transportation, deposition, and erosion of sediments. The input data is calibrated via sensitivity analysis and survey of analogue records. The results are compared with three sets of actual seismic data as verification. After introducing the general characteristics of the model, this study compares the influence of sea-level change on the delta, canyon, and fan, respectively, by analysing stratigraphic framework, the architecture of channel-levee complex, channel distribution and migration, sedimentation/erosion rate, and peak velocity. Moreover, a higher sediment supply case and a lower sediment supply case are compared to test the situation when sediment supply is less dominant. Finally, the influence of sea-level change on channel migration is discussed and the system evolution, especially the canyon evolution, is explained from the view of channel activities.The results show that sea-level control will be weakened from the delta to the fan via the canyon along with sediment transport. With higher sediment supply, the weakening is stronger. With lower sediment supply, the whole system is more sensitive to the sea-level change and this sensitivity lasts longer. The channel migration is more influenced by local topography, even adjacent topography, rather than sea-level change. The inner bank erosion near the canyon head is directly related to the shelf morphology. The translation and asymmetrical distribution of turbidity channels result in the translation and asymmetrical erosion of canyon bends. The insights extracted from this study could discriminate sea-level control on submarine canyon and fan instead of regarding them as an entirety of ultimate sink in source-to-sink research. Also, the integrated investigation with both qualified perspectives and quantified data could refine sequence stratigraphic concepts and provide a prototype for hydrocarbon exploration on high-sediment-supply river-fed delta-canyon-fan systems.

Experimental Study on Uniform and Mixed Bed-Load Sediment Transport under Unsteady Flow

The scouring and deposition of sediment caused by unsteady flows (e.g., storm waves and floods) produces many secondary disasters. The resultant bed-load movement exhibits different transport laws compared with that by steady flow. In this study, the flume experiments were performed to study the bed-load movement under unsteady flow with different velocity skewness. The movement of uniform and non-uniform non-cohesive sediment under unsteady flow as well as the influence of the steady and unsteady flow on sediment transport rate are compared. Additionally, the non-uniform sediment transport formula of fine-to-coarse particle diameter ratio was investigated. The results showed that the sediment transport rate between uniform and non-uniform sand under the same median diameter is different. The non-uniform sediment transport rate is 1.27-, 3.19-, and 0.68-times as large as that in uniform sediment under d50 = 0.664, 1.333, and 2.639 mm under unsteady flow, respectively. For non-uniform sand, the transport rate of non-uniform sand with a larger adjacent particle size ratio (δ = 0.29) was 1.31-times greater than that of the non-uniform sand with a smaller adjacent particle size ratio (δ = 0.50). Moreover, theoretical deduction was carried out and the incipient sediment motion was analyzed from the force mechanism. A new unsteadiness parameter based on the acceleration concept was proposed. The relationship between the travel distance and velocity skewness of sediment particles was set up. The experimental results and theoretical analysis showed that sediment under unsteady flow were easier to start and transport than those under steady flow in the same flow effect. The travel distance of sediment particles was longer under unsteady flow than that under steady flow.

Riverbed armoring and sediment exchange process in a sand–gravel bed reach after the Three Gorges Project operation

Upstream damming greatly altered the flow and sediment regime entering downstream reaches in the Middle Yangtze River, and the bed material in a sand–gravel bed reach coarsened continuously, which had a significant influence on the sediment transport and bed evolution. In order to study the riverbed armoring, the sediment exchange process (SEP) among bed material, bed load and suspended load in a sand–gravel bed river is firstly clarified, and then, the three-state transition probability model (Markov chain) is proposed in this study, with the hiding-exposure effect of non-uniform sediment being considered. Finally, the equilibrium equation of sediment quantity in an active layer is presented to calculate the grain size distribution of bed material. In this model, the influences of flow and sediment conditions, riverbed erosion and deposition on the SEP are discussed. The results show that the composition of surface bed material at the Zhicheng station became obviously coarse, and the median grain size (d50) of surface bed material increased from 0.230 to 0.424 mm in 2003–2017, with an upward increasing trend. The proposed probabilistic model was validated against field measurements of bed material, and calculated results show reasonable agreement with the measured data at Zhicheng. Accordingly, the probabilistic model can be used to predict the riverbed armoring and to investigate the non-equilibrium transport of non-uniform sediment in a sand–gravel bed river.

A model for non-uniform sediment transport induced by flushing in sewer channels

A novel unsteady flow numerical model for the simulation of the transport of non-uniform non-cohesive sediment mixtures (SM) during flushing operation in sewers is presented in this paper. The model was applied to the case of a flush experimental test that was recently carried out in a combined sewer channel of the sewer system of Paris city that exhibits depositional problems due to relatively coarse sediments. The model output was compared to the results of the field experiments as well as to those obtained with a model for the transport of uniform sediments (US). The model for SM provided a reliable interpretation of the selective transport of the sediments deposited in the channel bed as induced by the flush. The comparison showed the model for SM to provide an enhanced description of the erosional effects of the flush on the deposits, including improved evaluation of the volume of sediments flushed out of the experimental channel in the field.

Bedload transport and temporal variation of non-uniform sediment in a seepage-affected alluvial channel

ABSTRACTUnderstanding bedload transport fluctuations in rivers is crucial for complementing the existing knowledge on sediment transport theory. In this contribution, we use a natural-scale laboratory flume to analyse bedload transport fluctuations in non-uniform sand under normal flow conditions. Based on the significance of downward seepage, we incorporate the seepage effect on bedload transport over a non-uniform sand bed channel. The weight of the dry material was measured, and the volumetric transport rate per unit width (bedload transport rate) was estimated. An important observation is that the bedload transport rate initially rapidly increases with time and reaches a maximum value. Based on experimental data, we propose an empirical expression to estimate temporal bedload transport. In addition, an empirical model for bedload transport is proposed by incorporating downward seepage among other variables. The performance of several existing bedload transport formulae was also taken into account by the experimental datasets.

Numerical Modeling of Non-Uniform Sediment Transport in River Channels

The mathematical model for simulating deformations of river channels composed of heterogeneous alluvium has been developed. The combination of shallow water equations and a three-layer model is used to describe the fluid flow and non-uniform sediment transport in bed (layer II) and suspended (layer III) loads. Changes in the fractional composition of unerodible bottom sediments (layer I) are also considered. The algorithm provides mass conservation for each fraction. The comparison of calculations results and experimental data (hydraulic washing of a desilting basin from sediments and armoring processes in heterogeneous soils) confirms the operability of the model. The model is applied to calculate the silting and hydraulic washes of the reservoir of a hydroelectric power station on a mountain river.

A framework for modeling scenario-based barrier island storm impacts

Methods for investigating the vulnerability of existing or proposed coastal features to storm impacts often rely on simplified parametric models or one-dimensional process-based modeling studies that focus on changes to a profile across a dune or barrier island. These simple studies tend to neglect the impacts to curvilinear or alongshore varying island planforms, influence of non-uniform nearshore hydrodynamics and sediment transport, irregular morphology of the offshore bathymetry, and impacts from low magnitude wave events (e.g. cold fronts). Presented here is a framework for simulating regionally specific, low and high magnitude scenario-based storm impacts to assess the alongshore variable vulnerabilities of a coastal feature. Storm scenarios based on historic hydrodynamic conditions were derived and simulated using the process-based morphologic evolution model XBeach. Model results show that the scenarios predicted similar patterns of erosion and overwash when compared to observed qualitative morphologic changes from recent storm events that were not included in the dataset used to build the scenarios. The framework model simulations were capable of predicting specific areas of vulnerability in the existing feature and the results illustrate how this storm vulnerability simulation framework could be used as a tool to help inform the decision-making process for scientists, engineers, and stakeholders involved in coastal zone management or restoration projects.

Three-dimensional simulation of non-uniform sediment transport based on multi-phase Eulerian approach: Application to debris flow

To simulate 3D flow of a non-uniform and highly concentrated sediment, a numerical model using a multi-phase Eulerian method for air, water, and particles of various class size is developed. This model accounts for turbulence in pore water, particle-particle collisions, and enduring friction. To test its performance, simulations were performed for large scale debris-flow experiments. The numerical model reproduces successfully the flow property and sediment size segregation of the debris flow.

A Novel Explicit-Implicit Coupled Solution Method of SWE for Long-term River Meandering Process Induced by Dambreak

Large amount of sediment deposits in the reservoir area can cause dam break, which not only leads to an immeasurable loss to the society, but also the sediments from the reservoir can be transported to generate further problems in the downstream catchment. This study aims to investigate the short-to-long term sediment transport and channel meandering process under such a situation. A coupled explicit-implicit technique based on the Euler-Lagrangian method (ELM) is used to solve the hydrodynamic equations, in which both the small and large time steps are used separately for the fluid and sediment marching. The main feature of the model is the use of the Characteristic-Based Split (CBS) method for the local time step iteration to correct the ELM traced lines. Based on the solved flow field, a standard Total Variation Diminishing (TVD) finite volume scheme is applied to solve the sediment transportation equation. The proposed model is first validated by a benchmark dambreak water flow experiment to validate the efficiency and accuracy of ELM modelling capability. Then an idealized engineering dambreak flow is used to investigate the long-term downstream channel meandering process with non-uniform sediment transport. The results showed that both the hydrodynamic and morphologic features have been well predicted by the proposed coupled model.

A depth-averaged 2-D model of flow and sediment transport in coastal waters

A depth-averaged 2-D model has been developed to simulate unsteady flow and nonuniform sediment transport in coastal waters. The current motion is computed by solving the phase-averaged 2-D shallow water flow equations reformulated in terms of total-flux velocity, accounting for the effects of wave radiation stresses and general diffusion or mixing induced by current, waves, and wave breaking. The cross-shore boundary conditions are specified by assuming fully developed longshore current and wave setup that are determined using the reduced 1-D momentum equations. A 2-D wave spectral transformation model is used to calculate the wave height, period, direction, and radiation stresses, and a surface wave roller model is adopted to consider the effects of surface roller on the nearshore currents. The nonequilibrium transport of nonuniform total-load sediment is simulated, considering sediment entrainment by current and waves, the lag of sediment transport relative to the flow, and the hiding and exposure effect of nonuniform bed material. The flow and sediment transport equations are solved using an implicit finite volume method on a variety of meshes including nonuniform rectangular, telescoping (quadtree) rectangular, and hybrid triangular/quadrilateral meshes. The flow and wave models are integrated through a carefully designed steering process. The model has been tested in three field cases, showing generally good performance.