Sediment Transport Equations Research Articles

Estimating Grain Stress and Distinguishing Between Mobility and Transportability Improves Bedload Transport Estimates in Coarse‐Bedded Mountain Rivers

AbstractEstimating sediment transport in mountain rivers is challenging because of sediment supply limitation, broad grain size distributions, complex flow hydraulics, and large form drag. Consequently, sediment transport equations are lacking for application in rivers where the bed is coarse and largely immobile, but small fractions of finer, transportable sized material contribute disproportionately to bedload transport. We introduce a framework for estimating sediment transport in mountain rivers that addresses two limitations: estimating the shear stress acting on mobile grains, and accounting for the difference between mobility of size fractions, that is, whether or not a specific grain size can move at a given flow, and transportability, which we define as how much of that size present in the bed will be recruited into transport. We use two bedload data sets to develop equations for predicting incipient motion and transport rates of each grain size fraction present in the bed. We tested the new equations against incipient motion and sediment transport data we collected from streams in the Rocky Mountains, USA, and against published regional sediment yield data. Using this method results in transport estimates where the finer fractions, despite being a small fraction of the bed surface, make up a large part of the total yield. Fractions greater than the median bed grain size are mobile only during peak flood flows, consistent with the existing mountain river bedload data sets. The approach is parsimonious, requiring only data that are often readily available or obtainable: a bed grain size distribution, hydraulic geometry measurements, and discharge.

Formal derivation and existence of global weak solutions of an energetically consistent viscous sedimentation model

The purpose of this paper is to derive a viscous sedimentation model from the Navier-Stokes system for incompressible flows with a free moving boundary. The derivation is based on the different properties of the fluids; thus, we perform a multiscale analysis in space and time, and a different asymptotic analysis to derive a system coupling two different models: the sediment transport equation for the lower layer and the shallow water model for the upper one. We finally prove the existence of global weak solutions in time for model containing some additional terms.

OPTIMIZATION OF DESIGN OF THE FISH-SPAWNING PASS OF THE BAGAEVSKY HYDROELECTRIC COMPLEX USING NUMERICAL 2D MODELING

Numerical hydrodynamic modeling of the flow of water and sediment through the fish-spawning pass of the Bagaevsky hydroelectric complex on the river Don is considered. The calculations use two-dimensional shallow water and sediment transport equations by the STREAM 2D CUDA software complex. Recommendations are made to change the longitudinal profile of the bottom and the configuration of the inlet section, as well as to increase the coefficient of roughness of the bottom and sides of the channel to ensure fish protection requirements.

Gravity‐Driven Differences in Fluvial Sediment Transport on Mars and Earth

AbstractThere is abundant evidence from fluvial landforms and deposits that Mars had rivers that actively transported sediment and shaped its surface. Sediment transport equations are playing a key role in quantifying river processes from these observations, which continue to increase in quality and quantity. In this study, we review sediment transport equations developed on Earth and isolate the effect of gravity for the case of an alluvial channel. We compare 33 formulas used to calculate the sediment transport rate, under transport‐limited conditions, for grain sizes that range from silt to boulders and a lognormal sediment distribution. Results indicate that for a given discharge, channel morphology and grain size, the lower gravity on Mars compared to Earth results in: (a) larger grains mobilized on Mars and transported in suspension, and (b) larger suspended sediment transport rates on Mars and therefore larger total transport rates. Importantly, the effect of gravity is different for bed load and suspended load, with nonlinearity at the bed load‐suspended load transition zone. Therefore, typical total‐load transport relations that do not distinguish between bedload and suspended load are not appropriate for other planets as they simplify the effect of gravity. Gravity‐driven differences in fluvial sediment transport should produce differences in sediment sorting, morphology and stratigraphy between Earth and Mars. Additionally, our results show how Earth‐derived fluvial sediment transport theory can be applied beyond Mars to other planets and moons.

Simulation of breaching of laboratory-scale earth dams by overtopping with XBeach

Catastrophic breaches of water and mine waste retaining impoundments in recent history have emphasized the severity and consequences to the downstream environment. In this study, the applicability and suitability of the XBeach numerical model for modelling earth dam failures driven by overtopping with water is explored by detailed comparison with controlled experimental data. The XBeach model is applied to simulate laboratory-scale breaches caused by overtopping failure of dams constructed with uniform sand at the Queen's University Landslide Flume by Walsh et al. (2021a). The model sensitivity to boundary conditions for different virtual flume sizes, different sediment transport equations that influence erosion rates, and the process of avalanching are investigated. The model results are in best agreement with laboratory measurements when the Soulsby-van Rijn sediment transport formulation is used, which depends on grain size, and the avalanching module is activated, indicating the importance of these processes. The model is also run for different dam geometries to investigate the influence of upstream slope angle, which is relevant for tailings dam breach analyses. The results indicate that for flatter slopes the model is in closer agreement with observations of the peak discharge, while for steeper slopes the model results are better for breach duration time. Overall, XBeach provides promising results for the prediction of the dam breach outflow hydrograph at the laboratory scale and has potential to improve understanding of earth dam failure outcomes with further investigation.

Numerical modelling of the evolution of a river reach with a complex morphology to help define future sustainable restoration decisions

Abstract. The prediction of river morphology evolution is very complicated, especially in the case of mountain and Piedmont rivers with complex morphologies, steep slopes, and heterogeneous grain sizes. The Lac des Gaves (LDG) reach, located within the Gave de Pau River in the Hautes-Pyrénées department, France, has precisely the complex morphological characteristics mentioned above. This reach has gone through severe sediment extractions for over 50 years, leading to the construction of two weirs for riverbed stabilisation. Two large floods resulted in changes in the LDG's hydromorphological characteristics as it went from a single channel river section to a braided river reach. In this study, a 2D hydromorphological model is developed with the TELEMAC-MASCARET system to reproduce the evolution of the channel following a flood that occurred in 2018. The model's validity is assessed by comparing the simulated topographic evolution to the observed one. The results reveal the challenge to choose well-fitted sediment transport equations and friction laws that would make it possible to reproduce such complex morphology. Although the exact localisation of the multiple channels forming the braided nature of the LDG was challenging to reproduce, our model was able to provide reliable volumetric predictions as it reproduces the filling of the LDG correctly. The influence of the two weirs on the river's current and future morphology is also studied. The aim is to provide decision-makers with more reliable predictions to design suitable restoration measures for the LDG reach.

An advanced check‐dam sedimentation module: Laboratory validation and implementation in a distributed sediment yield model for field application

AbstractCheck‐dams are structures used extensively around the world for soil and water conservation. However, existing models for check‐dams are unable to simulate the Sediment Trap Efficiency (STE) at the catchment scale. A numerical model was developed to simulate the SEdiment Deposition upstream of Check‐Dams (SEDCD) and integrated into a distributed sediment yield model, the Digital Yellow River Model (DYRIM). Two versions of the SEDCD model were evaluated: the SV version which used the Saint–Venant equation to simulate the unsteady flow, and the BW version, which used a modified backwater equation (based on a quasi‐steady approximation) to improve computational efficiency. Sediment deposition and the associated bed profile adjustment were simulated with the sediment conservation equation and the non‐equilibrium suspended sediment transport equation. The SEDCD model was first validated in the laboratory using experimental data from a scale‐down check‐dam. The bed profiles predicted using both versions of the SEDCD model showed good agreement with the observations, with NSE values over 0.9 in most profiles. When integrated into the DYRIM and applied to the Xiaoli River Basin (818 km2) on the Loess Plateau, which has 183 active check‐dams, the SEDCD‐DYRIM combination predicted the STE for an extreme rainstorm event in 2017 with good accuracy and high computational efficiency. The SEDCD‐BW‐DYRIM simulated the hourly discharge and sediment concentration with high accuracy (NSE values of 0.79 and 0.71, respectively) and provided single‐event STEs (R2 value of 0.99) comparable to those of the SEDCD‐SV model, with an approximately 30 times faster runtime efficiency than the SEDCD‐SV model. The SEDCD‐BW model is a powerful and efficient tool to assess the effect of check dams on sediment dynamics at the catchment scale.

Numerical Modeling of Local Scour in the Vicinity of Bridge Abutments When Covered with Ice

The occurrence of bridge collapse is frequently attributed to the prevalent erosion in the vicinity of bridge abutments. Accurate determination of the maximum scour depth in the vicinity of bridge abutments is imperative to ensure a secure and reliable bridge design. The phenomenon of local scour at bridge abutments can exhibit significant variations when compared to open-flow conditions, primarily due to the additional obstacle posed by the presence of ice cover. Research has demonstrated that the erosion of bridge abutments is more pronounced in the presence of ice. The vertical velocity distribution has a direct impact on both the bed shear stress and the resulting scour geometry in ice-covered conditions. This study aims to analyze the effects of flow through open channels and covered flow conditions on the local scour process around semi-circular and square bridge abutments using FLOW-3D V 11.2 software. The utilization of the volume of fluid (VOF) approach is employed for monitoring the free surface, while the Reynolds averaged Navier-Stokes (RANS) equations and the RNG k turbulence model are employed for simulating the flow field in the vicinity of bridge abutments. The sediment transport equations formulated by Meyer-Peter and Müller were employed for the purpose of simulating the movement of sediment particles. The numerical simulation results are compared with the experimental results. The result shows that the presence of ice cover and its roughness can increase the maximum scour depth both in numerical and experimental studies. The results also indicate that the maximum scour depth is located at the upstream section of the bridge abutments. These findings demonstrate the ability of the numerical model to predict the occurrence of local scour in the vicinity of bridge abutments under conditions of ice presence.

Numerical simulation of turbidity currents using consistent particle method

This paper expands the Consistent Particle Method (CPM) to simulation of turbidity currents with focus on turbulent water-sediment flow. A mixture model is adopted in solving the sediment transport equation to simulate the sediment mass transfer due to settling convection and turbulent diffusion. To compute the gravity-driven convection term, the proposed CPM-upwind scheme is relatively easy to implement as it avoids the use of a kernel function which has the requirements of symmetry and unity. Two sand settling problems demonstrate the good accuracy of the CPM-upwind scheme. For suspended sediment diffusion caused by turbulence, CPM is able to model anisotropic diffusion without the averaging effect caused by the isotropy requirement if a kernel function is used. The validated CPM methodology is then applied to simulate a sudden flow of water-sediment mixture into ambient water. The results of the mixture front motion and sediment deposit density agree well with published experimental results.

ESTIMATING ALONGSHORE SEDIMENT TRANSPORT FROM DREDGED ACCESS CHANNELS

Alongshore sediment transport rates are important in sediment budget studies or design of coastal structures. Underestimated transport rates give rise to severe siltation updrift from cross-shore structures and severe erosion downdrift. Overestimates may lead to over-design and thus high costs. Currently, these estimates are generally obtained from sediment transport equations, morphodynamic numerical modelling or bathymetrical changes in accumulation areas (Vandebroek et al. 2017). However, alongshore transport is difficult to estimate from regular bathymetrical surveys, since only locations with gradients in the transport will provide information via volume changes. On a straight coastline the sediment will simply pass by. Here an alternative data-based approach is proposed, studying an access channel suffering from repeated siltation. As the access channel effectively serves as a sediment trap it can be used to study alongshore sediment transport rates. The access channel is frequently dredged and even more frequently surveyed. It is therefore suitable to make estimates of sediment transport on the time-scale of weeks to months.

Integration of a numerical model in curvilinear coordinates with sand mining component for bottom morphology simulation

Numerical models for calculating bottom morphology are increasingly popular because of their long-term forecasting capabilities as well as their ability to identify causes. However, the simulation of bottom morphology, in addition to natural factors, is also governed by economic activities, especially sand mining. In this paper, we propose the development of the numerical model in curvilinear coordinates combined with a sand mining component that simulates the bottom morphology of the Tien river segment in the Mekong Delta as a study area. The modeling theory relies on the Reynolds equation system, which is combined with the suspended sediment transport equation in a two-dimensional curvilinear coordinate system. The process of averaging is performed over the depth. The suspended sediment transport equation incorporates a source function that describes the upward or downward movement of particles. In the model for bottom morphology, a component for sand mining is included, which accounts for the rate at which sand is extracted from the riverbed. This component is integrated into the equation governing the continuity of the bed load. The findings demonstrate that the numerical model effectively captures the changes in the river’s bottom morphology resulting from sand mining. Specifically, when the sand mining component is employed, the model accurately represents the actual development of the bottom morphology in river segments where sand mining occurs. Furthermore, the downstream bed alterations are significantly influenced by sand mining activities. By incorporating the sand mining component into the model, it becomes a valuable tool for simulating the bottom morphology in river segments subjected to sand mining, thus aiding in sand mining planning and the management of disaster risks associated with bank erosion.

Numerical simulation of offshore wind power pile foundation scour with different arrangements of artificial reefs

The industrial integration of offshore wind power and marine ranches has been actively explored and developed in many countries. This emerging industrial synergy can significantly improve the ecological friendliness of offshore wind power and contribute to the development of the marine economy in the region. This industrial synergy is an important development direction for future offshore engineering. Artificial reefs (ARs) are critical components of marine ranches and are widely placed around offshore wind foundations (OWFs). The ARs can block the water flow and form a complex wake region behind it, which changes the original turbulence structure and reduces scour around the OWF. Therefore, determining the arrangement of ARs for scour protection around an OWF is of great engineering significance. In this study, a three-dimensional numerical model is established using a prototype of the first offshore wind power-marine ranch demonstration project in China. The turbulent change and sediment movement between the OWF and ARs are solved using the Reynolds-averaged Navier-Stokes (RANS) and sediment transport equations. Moreover, the variations in the maximum scour depth and scour volume around the OWF at different arrangements of ARs are explored. The results demonstrate that the arrangement of ARs weakens the horseshoe vortices in front of the OWF and destroys the vortex shedding behind the OWF, thereby producing a beneficial scour protection effect. Various arrangements of ARs have different effects on scour results around the OWF. Increasing the height of the AR could significantly reduce the scour results around the OWF and play an effective role in scour protection, followed by the tandem arrangement of ARs, whereas the parallel arrangement of ARs will produce negative scour effects. This study will serve a vital guiding role in the arrangement of ARs and practical significance for scouring protection around the OWF.

NUMERICAL STUDY OF ICE AND CHANNEL PROCESSES ON THE BRIDGE SUPPORTS ACROSS THE KUIBYSHEV RESERVOIR (KAZAN)

Numerical hydrodynamic modeling of water movement at discharges of 1% and 10% supply is considered in order to study the effect of ice effects and bottom deformations on the bridge supports across the reservoir of the Kuibyshev hydroelectric complex, and to predict the general erosion of the channel. The calculations use two-dimensional shallow water and sediment transport equations implemented in the STREAM 2D CUDA software package.

Experimental investigation of sediment transport in partially ice-covered channels

It is important to understand the effects of ice cover on sediment transport in cold climates, where sub-freezing temperatures affect water bodies for a significant part of the year. The literature contains many studies on sediment transport in open channel flow, and several studies on sediment transport in completely ice-covered flow. There has been little or no research on sediment transport in partially ice-covered channels. In the current study, laboratory experiments were done in a rectangular flume to quantify the impact of border ice presence on the sediment transport rate. The effects of ice cover extent and changing flow strengths on sediment transport distribution also were investigated, and the results were compared to those for fully ice-covered and open channel flow. The ice coverage ratios considered were 0 (representing the open water condition), 0.25, 0.50, 0.67, and 1 (representing fully ice-covered flow). The partial ice cover was found to impact the sediment transport distribution within the channel. The effect of ice coverage extent on sediment transport distribution was more significant at lower flow strengths and became negligible at higher flow strengths. The conventional equations for sediment transport in open channel flow and fully ice-covered flow that relate the dimensionless bedload transport rate to the flow strength were found to be applicable to estimate the total cross-section-averaged bedload transport for partially ice-covered flow when modified appropriately. Empirical coefficients for these equations were determined using the experimental data.

Bed shear stress and sediment transport equations for predicting morphological and shoreline changes: a review

Coastal sediments can be transported as bedload and suspended-load transport by waves and currents. The waves stir up the sediments, then currents transport sediments. Waves on the bottom can generate bed-shear stress. Meanwhile, the combination of bedload and suspended-load transport is known as total sediment transport. Prediction of total sediment transport has become important related to coastal morphological change and also shoreline change. Most of the sediment transport equations and approaches are developed from the physical principles. There are so many researchers proposed some formulas and methods with some considerations and difficulties. Due to the complexity of coastal conditions, the existing sediment transport rate prediction formulas are still not finished yet. Several well-known equations of bed-shear stress, bedload-suspended transport, and cross shore-longshore sediment transport; are discussed and reviewed in the present study. Thus, an overview of approaches and formulations that are reliable and nearly accurate for calculating the total sediment transport rate based on the characteristics of each coastal waters will be obtained. Accurate estimation of sediment transport rates will provide good results for predicting and monitoring changes in coastal morphology and shoreline changes. Moreover, coastal monitoring can be used for actions related to coastal protection system and coastal management.

Some recent finite volume schemes for one and two layers shallow water equations with variable density

We propose a class of finite volume algorithms that are both simple and efficient for solving numerically the shallow water equations with varying densities; shallow water flows in single and two layers are considered. In these flow regimes, variable horizontal or vertical density is taken into account. The shallow water equations for the hydraulic variables are coupled with a suspended sediment transport equation for the concentration variable to construct the model. To approximate the numerical solution of the models under consideration, a generalized Rusanov method is proposed; this method avoids solving Riemann problems during the time integration process, and it is simple and accurate. The proposed method is divided into two stages: predictor and corrector; the presented finite volume approach is well balanced, conservative, and simple. Non‐oscillatory and suitable for shallow water equations when Riemann problems are challenging to solve. Several test problems for single‐layer and two‐layer shallow water flows are applied to the proposed method. The numerical results show that the proposed finite volume approach has high resolution and that it is capable of simulating shallow water equations with variable density in flow regimes with strong shocks accurately.

Modelling sediment trapping in vegetative filter strips on steep slopes

AbstractThe slope effects on sediment trapping process in vegetative filter strips (VFS) are usually neglected in current modelling practices for VFS operation, which hamper the VFS design and performance evaluation, especially on steep slopes. To fill the knowledge gap, 12 laboratory experiments of sediment trapping in VFS were conducted with three different inflow discharge (80, 100, and 120 ml s−1) and four slope angles (5,10, 15, and 20°). The experimental results show that, on steep slopes (10, 15, and 20°), a part of trapped sediment particles in VFS can be eroded again and then dragged to the downstream as bed load, whilst they do not move on gentle slope (5°). To describe the complex processes, a simple and effective modelling framework was developed for sloped VFS by coupling the slope infiltration, runoff, and modified sediment transport model. The model was tested against the experimental results and good agreements between the modelled and observed results were found in both runoff and sediment transport processes for all cases. On steep slopes, the sediment trapping performance of VFS decreases significantly because the erosion of deposited sediment particles can account for more than 60% of the sediment load in the outflow. The slope effect on sediment trapping efficiency of VFS varies greatly with soil, VFS, and slope properties. The model was compared with previous sediment transport equation and found that both methods can satisfactorily predict the sediment trapping of VFS on gentle slopes, but previous sediment transport equation is likely to overestimate the sediment trapping efficiency in VFS on steep slopes. This model is expected to provide a more realistic and accurate method for predicting runoff and sediment reduction in VFS on sloping surfaces.

Hydraulic Model Prediction of the Total Load of Sediment Transport in The Euphrates River at The Upstream Ramadi Barrage

Examining river engineering properties and bed erosion is one of the most challenging but crucial issues in river engineering and sediment hydraulics, so preventing erosion and sedimentation is one of the primary goals of river management and prediction of river behavior. This research aims to give hydraulic engineers and decision-makers an accurate and dependable sediment transport equation that could be utilized to govern river engineering and modify river morphology. This study evaluated the carried sediments and their estimated quantity upstream of the Ramadi Barrage on the Euphrates River in the Anbar area of western Iraq. Six formulas, including Yang, Shen, Hung, Ackers and White, Engelund and Hansen, and Bagnold's and Toffaleti's, were used to evaluate the applicability of sediment transport in the study area. The performance of these models was assessed based on the precision of the actual sediment load relative to a specified deviation ratio. The analyses indicated that the Engelund-Hansen formula is the most applicable for this section of the river; that concludes, field data indicated an annual total sediment flow of roughly 1, 536, 337 tons.

Transport equation for nonuniform suspended sediment

Theoretical research on nonuniform sediment suspension is limited due to difficulties of elucidating nonuniform particle interaction. A new transport equation is generalized for nonuniform suspended sediment based on multi-dispersed two-phase flow theory, to account for nonuniform particle interaction and its effect on sediment suspension. Instead of implementing numerical discretization, constitutive relation of drift velocity is derived by solving the momentum equations with the aid of the Sherman–Morrison–Woodbury formula and the perturbation asymptotic technique. Applied to open channel flows, concentration profiles for each grain size of sediment are derived and a satisfactory consistency is obtained in comparison with both experimental and field data. Nonuniform sediment suspension is attributed to fluid turbulence, gravity, particle inertia and nonuniform particle interaction. The nonuniform effect plays an important role in the vicinity of the riverbed and is positively correlated to sediment concentration and grain size ratios, which helps bring insight into the suspension mechanics.

Streambed Median Grain Size (D50) across the Contiguous U.S.

The streambed median grain size (D50) has been an integral part of many sediment transport and stream power equations seeking to characterize stream channel stability conditions. However, its previous usage is constrained by regional applicability, localization of datasets, and a limited number of data points. This study uses a large and geographically diverse data set (n > 2400), from five published sources, to present quantitative information and assess the distribution of D50 data across the contiguous U.S. Spatial distribution was analyzed based on the three regional frameworks: Physiographic Provinces, Level III Ecoregions, and Hydrologic Landscape Regions (HLRs). Gravel was found to be the dominant streambed material in most Physiographic Provinces. Regions with a humid climate, permeable soil, and plateaus exhibit a higher average D50 than regions with other climate, geologic texture, and landscape forms. Further analysis of all data across the U.S. using smoothed spatial maps showed the dominance of sand and fine gravel in streams located in the central and southern U.S., and the dominance of coarse gravel and cobbles in the northeastern U.S.