Bedload Layer Research Articles

Turbulent kinetic energy budget of sediment-laden open-channel flows: bedload-induced wall-roughness similarity

New experiments in highly turbulent, steady, subcritical and uniform water open-channel flows have been carried out to measure the mean turbulent kinetic energy (TKE) budget of sediment-laden boundary layer flows with two sizes (dp = 3 mm and 1 mm) of Plexiglas particles $({\rm relative\ density}\ = 1.192)$ . The experiments covered energetic sediment transport conditions (Shields number of $0.35 < \theta < 1.2$ ) ranging from non-capacity to full-capacity flows in bedload-to-suspension-dominated transport modes (suspension number of $0.5 < {w_s}/{u_\ast } < 1.3$ where ${w_s}$ is the settling velocity and $u_*$ is the friction velocity) and for weakly to highly inertial, finite size turbulence-particle conditions (Stokes number of 0.1 < St < 3.5 and dp/η > 10 where $\eta$ is the Kolmogorov length scale). It was shown that the effects of sediments on the TKE budget are very pronounced in all large particle experiments for which a bedload layer of several grain diameter thickness is developed above the channel bed. When compared with the corresponding reference clear-water flows, the TKE shear-production rate for the 3 mm particle flows is strongly reduced in the wall region corresponding to the bedload layer. This turbulence damping is seen to increase with sediment load until full capacity for flows with constant Shields value, as well as with Shields number value. Inside this damped TKE shear-production zone, a distinct peak of maximal turbulence production appears to coincide with the upper edge of the bedload layer delimited by a sharp gradient in mean sediment concentration. This vertically upshifted peak of TKE production is accompanied by an enhanced net downward oriented TKE flux when compared with the reference clear-water flows. The downward diffused TKE is found to act in the bedload layer as a local energy source in reasonable balance with the sediment transport term. The mechanism behind this downward TKE transport was further analysed on the basis of coherent flow structure dynamics controlled by ejection- and sweep-type events. The agreement between the height of downward directed mean TKE flux and the height below which sweep-type events dominate the Reynolds shear-stress contribution over ejections, revealed the leading role played by sweeps in mean TKE transport. This agreement holds for all reference clear-water flows supporting the well-known wall-roughness-induced dominance of the sweep contribution in turbulent, rough clear-water boundary layer flows. Furthermore, for all 3 mm particle flows, the two referred to transition levels were significantly and similarly upshifted to the upper edge of the bedload layer. Only for these sediment-laden flows, the bedload layer thickness is seen to exceed the wall-roughness sublayer of the reference clear-water flows. This supports a strong analogy between wall-roughness effects in clear-water flows and bedload layer effects in sediment-laden flows, on the mean TKE budget induced by a similarly modified coherent flow structure dynamics. The bedload layer-controlled wall roughness is finally confirmed by the good prediction of the wall-roughness parameter ks of the logarithmic velocity distribution. An empirical formulation fitting the presented measurements is presented, valid over the range of Shields number values covered herein.

On the vertical structure of non-buoyant plastics in turbulent transport

Plastic pollution is overflowing in rivers. A limited understanding of the physics of plastic transport in rivers hinders monitoring, the prediction of plastic fate and restricts the implementation of effective mitigation strategies. This study investigates two unexplored aspects of plastic transport dynamics across the near-surface, suspended and bed load layers: (i) the complex settling behaviour of plastics and (ii) their influence on plastic transport in river-like flows. Through hundreds of settling tests and thousands of 3D reconstructed plastic transport experiments, our findings show that plastics exhibit unique settling patterns and orientations, due to their geometric anisotropy, revealing a multimodal distribution of settling velocities. In the transport experiments, particle-bed interactions enhanced mixing beyond what established turbulent transport theories (Rouse profile) could predict in low-turbulence conditions, which extends the bed load layer beyond the classic definition of the bed load layer thickness for natural sediments. We propose a new vertical structure of turbulent transport equation that considers the stochastic nature of heterogeneous negatively buoyant plastics and their singularities.

Lateral Erosion of Bedrock Channel Banks by Bedload and Suspended Load

AbstractBedrock rivers carry large amounts of fine sediment in suspension. We developed a mechanistic model for erosion of bedrock channel banks by impacting bedload and suspended load particles that are advected laterally by turbulent eddies (advection‐abrasion model). The model predicts high lateral erosion rates near the bed, with rates decreasing up to the water surface. The model also predicts greater erosion within the suspended load layer than the bedload layer for many typical sediment supply and transport conditions explored. We compared the advection‐abrasion model with a previously derived model for lateral erosion of bedrock banks by bedload particles deflected by stationary bed alluvium (deflection‐abrasion model). Erosion rates predicted by the deflection‐abrasion model are lower, except within limited conditions where sediment is transported near the threshold of motion and the bed is near fully covered in sediment. Both processes occur in bedrock rivers at the same time, so we combined the advection‐abrasion and deflection‐abrasion models and found that the lateral erosion rate generally increases with increasing transport stage and relative sediment supply for a given grain size. Application of our combined‐abrasion model to a natural bedrock river with a wide distribution of discharge and supply events, and mixed grain sizes, indicates that finer sediment dominates the lateral erosion on channel banks in low sediment supply environments and can be as important as coarser sediment in high sediment supply environments.

A multi-dimensional two-phase mixture model for intense sediment transport in sheet flow and around pipeline

A two-phase mixture model is developed to simulate intense sediment transport covering the bed-load layer and suspended load layer. The proposed model maintains high accuracy as an Eulerian two-phase model but requires low computational cost. The proposed model applies an analytical formula for relative velocity between phases. The dense granular flow rheology is employed to close particle stress economically. The closure of Reynolds stress considers turbulence damping and small-scale fluctuation of fluid–particle interaction and particle collision. A damping function is adopted in eddy viscosity for extra turbulence damping from inter-particle interaction. The optimal exponent of the damping function refers to sediment shape and size. The sediment diffusion includes turbulence diffusion and shear-induced self-diffusion originating from dense sediment. The proposed model is validated by several sets of sheet flow cases (Shields number Θ = 0.44–2.20 and particle Reynolds number Res = 1.6–603.0) and shows a wide applicable range and good accuracy. The small-scale fluctuation and shear-induced self-diffusion improve the computation in the lower sheet flow layer where volumetric sediment concentration is larger than 0.2. Furthermore, the proposed model shows reasonable applicability on the multi-dimensional pipeline scour development. The scour profiles are well predicted and the Brier Skill Score = 0.809. However, the proposed model does not perform the wake characteristic around the pipeline sufficiently, and slight scour difference exists between the simulation and experiment.

On how defining and measuring a channel bed elevation impacts key quantities in sediment overloading with supercritical flow

The manuscript presents the results of an aggradation experiment performed in a laboratory channel with supercritical flow. The channel was fed with a stationary sediment load exceeding the transport capacity of the flow in the initial condition, thus inducing sediment aggradation and an increase of the bed slope. The experiment is part of a laboratory campaign mimicking sediment overloading in mountain rivers, a process that can determine increased hydraulic risk levels at key spots. A crucial issue in measuring sediment aggradation is the definition and determination of the bed elevation, this issue being quite relevant in experiments with a relatively large transport capacity, where a thick bed-load layer exists and hinders the possibility to determine with confidence a reference bed elevation. The determination of the bed elevation, in turn, impacts the quantification of a number of properties, including the initial sediment transport capacity of the flow, temporal scales of the aggradation process, water depth and Froude number. The manuscript presents a sensitivity analysis of the results to two extreme definitions for the bed elevation: the first one locates the bed at the upper edge of the bed-load layer, while the second one at the lower edge of the bed-load layer where the particles do not move. The presentation of the two alternatives is focused on the experimental methods they use, consistently with the intent of the special issue. Furthermore, it is demonstrated that the definition of the bed elevation also has a major impact on numerical models of the process. The experimental results have been reproduced numerically, demonstrating that the calibration parameters returning a best fit are also impacted significantly by how the bed is defined. The preferred definition for analyzing an experimental campaign is locating the bed below the bed-load layer.

Sentinel-1 Satellite Radar Images: A New Source of Information for Study of River Channel Dynamics on the Lower Vistula River, Poland

The amount of sediments transported by a river is difficult to estimate, while this parameter could influence channel geometry. It is possible to derive the bedload transport rate per unit width of the river channel by measuring the migration distance of bedform profiles over time and thickness of bedload layer in motion. Other possible methods include instrumental measurements using bedload traps and empirical formulas. It is possible to use remote-sensing techniques to measure the dynamics of bedform movements and geometries. Landsat images and aerial photographs have been used for this. A new source of remote-sensing information is radar satellite images. Sentinel-1 images have a temporal resolution of 2–3 days and spatial resolution of 25 m at middle latitudes, which make them usable on large rivers. The research area is the 814–820 km reach of the Lower Vistula River, where seven alternate sandbars were selected. The bank lines of the sandbars were delineated on Sentinel-1 images sensed during two low-flow periods of 4 August–26 September 2018 and 1 July–31 August 2019, when discharges at low flow were similar. From water stage observations at gauges, water elevations were assigned to every bank line of the alternate sandbars. The following morphometric parameters were calculated: alternate sandbar centers, volumes and longitudinal profile. Average daily movement of the sandbars in the period 4 August 2018–1 July 2019 was calculated as 0.97 m·day−1. A similar alternate sandbar movement velocity was obtained from a study of Sentinel-2 optical satellite images and hydro-acoustic measurements on the Lower Vistula River. Having depth of bedload in motion and alternate sandbar shift velocities, it was possible to calculate the rate of bedload transport according to the Exner approach formula. Rate of bedload transport was estimated as qb = 0.027 kg·s−1·m−1. This study shows a novel use of Sentinel-1 images to study the 3D geometry and movement rate of sandbars.

Entrainment and adaptation processes in the evolution of collisional bedload layers

We performed laboratory experiments which describe the evolution, from triggering until full formation, of a bedload layer. The phenomenon is driven by a turbulent open-channel flow at about constant discharge since the very initiation of the process. The flow stays uniform and the slope constant during the transient phase, during which we measured the instantaneous velocity and concentration profiles of the solid phase within the bedload layer. The timing of the process is governed by inertia and resistance forces. The bedload layer progressively thickens, fed by sediments entrained from the bed, which is progressively eroded, until the final steady uniform condition (i.e., equilibrium) is reached. We then applied a recent numerical model, able to cope with collisional suspensions using extended kinetic theories, to replicate the experimental results. The model results are used to further analyze and discuss the physical processes within the flow.

Validation of a two-layer depth-averaged model by comparison with an experimental dilute stratified pyroclastic density current

Numerical results of a two-layer depth-averaged model of pyroclastic density currents (PDCs) were compared with an experimental PDC generated at the international eruption simulator facility (the Pyroclastic flow Eruption Large-scale Experiment (PELE)) to establish a minimal dynamical model of PDCs with stratification of particle concentrations. In the present two-layer model, the stratification in PDCs is modeled as a voluminous suspended-load layer with low particle volume fractions (lesssim {10}^{-3}) and a thin basal bed-load layer with higher particle volume fractions (sim {10}^{-2}) on the basis of the source condition in the experiment. Numerical results for the suspended load quantitatively reproduce the time evolutions of the front position and flow thickness in the experimental PDC. The numerical results of the bed-load and deposit thicknesses depend on an assumed value of settling speed at the bottom of the bed load ({W}_{mathrm{sH}}). We show that the thicknesses of bed load and deposit in the simulations agree well with the experimental data, when {W}_{mathrm{sH}} is set to about 1.25times {10}^{-2} m/s. This value of the settling speed is two orders of magnitude smaller than that predicted by a hindered-settling model. The small value of {W}_{mathrm{sH}} is considered to result from decreasing in the effective deposition speed due to the erosion process accompanied by saltating/rolling of particles at the bottom of the bed load.

Quantitative Study on Bed Load Proppant Transport during Slickwater Hydraulic Fracturing

Abstract Bed load proppant transport is a significant phenomenon during slickwater hydraulic fracturing. However, the mechanism of bed load proppant transport is still unclear. In the present study, the proppant transport process during slickwater hydraulic fracturing was simulated with a coupled computational fluid dynamics- (CFD-) discrete element method (DEM) model, and the mechanism of the bed load proppant transport was analyzed. A model for calculating the mass flux of the bed load layer was proposed and verified with experimental results from the literature. The results show that bed load migration is an essential mechanism of proppant transport. When the shear force of fluid acting on the surface of the sand bank reaches the critical Shields number, the proppant in the upper layer of the sand bank begins to migrate in the form of bed load. The movement of the bed load layer increases the time for the sand bank to reach the equilibrium height. In addition, the mass flux of the bed load layer significantly affects the equilibrium height of the sand bank. The mass flux of the bed load layer decreases, and the equilibrium height increases as the proppant density, proppant diameter, or rolling friction coefficient and static friction coefficient of the proppant increase, but the mass flux of the bed load layer increases, and the equilibrium height decreases as the fluid viscosity increases.

Bedload Velocity and Backscattering Strength from Mobile Sediment Bed: A Laboratory Investigation Comparing Bistatic Versus Monostatic Acoustic Configuration

Despite the many advantages of using active ultrasound sonars, recent studies have shown that the specific acoustic geometry, signal-processing configuration, and complex surface-volume scattering process at the riverbed introduce several uncertainties in bedload estimation. This study presents a comparison of bedload velocity and bottom echo intensity measurements performed by monostatic and bistatic active ultrasound systems. The monostatic configuration is widely applied in the field to measure the apparent velocity at the riverbed with an acoustic current Doppler profiler (ADCP). Two laboratory investigations were conducted in two different hydraulic facilities deploying ADCP Stream Pro, monostatic and bistatic acoustic velocity profilers, manufactured by Ubertone. The bistatic instruments provided more accurate bedload velocity measurements and helped in understanding the acoustic sampling of the monastic systems. The bistatic profiles succeeded in measuring a profile over the active bedload layer, and the monostatic instruments resulted in different bedload velocity estimations depending on the acoustic resolution and sampling. The echo intensity increased in the cells measured within the active bedload layer with respect to the cell measuring the water column above. The cells that sampled the immobile bed surface beneath the bedload layer showed a reduction of the echo intensity compared with the cells above. The acoustic sampling, which combines the measurement volume geometry and internal processing, seems crucial for more accurate outputs. Future research about the use of monostatic instruments in the field should aim to define the best possible setting for the acoustic parameters at a given bedload condition that may be tuned by evaluating the backscattering at the river bottom together with the apparent bedload velocity.

Three-dimensional scour simulations with a two-phase flow model

In this contribution, a three-dimensional sediment scour model based on the two-phase flow Eulerian-Eulerian solver, sedFoam, is developed within the framework of the open source platform OpenFOAM. The adoption of the Eulerian approach for both fluid and sediment makes the model suitable for simulating scour process around structures with arbitrary geometry. The model is first validated with unidirectional sediment transport configurations without structures, to ensure that it can capture both flow and sediment transport processes. The validation cases show that the model can accurately simulate the sediment transport rate and bedload layer thickness as a function of the Shields number over a wide range of flow condition and sediment properties. Then, the model is applied to simulate the live-bed scour process around a vertical pile due to unidirectional current. It is a first attempt to use a two-phase model for simulating such case and its success serves as a proof-of-concept for future development. Simulated results of flow, sediment transport, and scour processes are compared with experiments and good agreement is observed. A new methodology to determine the bed shear stress in complex flow configurations is proposed. The mixture shear stress computed at the elevation of the iso-concentration ϕ0=0.08 (corresponding to top of the bedload layer) is used to define the local Shields number.Within the scour hole, a competition between fluid bed shear stress driven and gravity driven sediment transport occurs at bed angles up to β ≈ 23∘. This is lower than the repose angle (βr=32∘). The relationship between the sediment flux and the bed slope is linear below β ≈ 23∘. Above this angle the sediment flux increases nonlinearly with the bed slope while the Shields number tends to 0. This shows that, in the part of the scour hole close to the vertical cylinder, the sediment flux only result from the action of gravity: avalanching is the dominant transport mechanism and conventional power law become ineffective even with slope correction. In the lee-side of the cylinder suspended load dominant and the power law, assuming a local equilibrium between bottom shear stress and transport flux, is no longer valid. Further discussion is made on the computational cost of the proposed model and future research directions.

Acoustic sampling effects on bedload quantification using acoustic Doppler current profilers

ABSTRACT This paper provides an evaluation of a hydro-acoustic technique for efficient quantification of the bedload transport in riverine environments. Stationary bedload measurements were conducted simultaneously at different study sites, using three different acoustic Doppler current profilers (ADCP) working at four different frequencies. The raw apparent bedload velocities were de-spiked and filtered in a streamwise direction. Then, functional correlations were observed between the magnitudes of the apparent velocities and the bedload transport rates measured by the conventional bedload sampler. Each ADCP yielded different results because of the different frequency backscatter sensitivity and acoustic penetration in the active bedload layer. In addition to the frequency, other acoustic parameters such as the percentage of the filtered data, transducers width, beam opening angle, beam-grazing angle and the pulse length, contributed to the acoustic bedload sampling. The influence of these parameters is examined, and recommendations are given for the performance and limitations of each instrument.

Emplacement of massive deposits by sheet flow

AbstractTurbidity current and coastal storm deposits are commonly characterized by a basal sandy massive (structureless) unit overlying an erosional surface and underlying a parallel or cross‐laminated unit. Similar sequences have been recently identified in fluvial settings as well. Notwithstanding field, laboratory and numerical studies, the mechanisms for emplacement of these massive basal units are still under debate. It is well accepted that the sequence considered here can be deposited by waning‐energy flows, and that the parallel‐laminated units are deposited under transport conditions corresponding to upper plane bed at the dune–antidune transition. Thus, transport conditions that are more intense than those at the dune–antidune transition should deposit massive units. This study presents experimental, open‐channel flow results showing that sandy massive units can be the result of gradual deposition from a thick bedload layer of colliding grains called sheet flow layer. When this layer forms with relatively coarse sand, the non‐dimensional bed shear stress associated with skin friction, the Shields number, is larger than a threshold value approximately equal to 0·4. For values of the Shields number smaller than 0·4 the sheet flow layer disappeared, sediment was transported by a standard bedload layer one or two grain diameters thick, and the bed configuration was characterized by downstream migrating antidunes and washed out dunes. Parallel laminae were found in deposits emplaced with standard bedload transport demonstrating that the same dilute flow can gradually deposit the basal and the parallel‐laminated unit in presence of traction at the depositional boundary. Further, the experiments suggested that two different types of upper plane bed conditions can be defined, one associated with standard bedload transport at the dune–antidune transition, and the other associated with bedload transport in sheet flow mode at the transition between upstream and downstream migrating antidunes.

Estimating the Bed-Load Layer Thickness in Open Channels by Tsallis Entropy.

In the research field of river dynamics, the thickness of bed-load is an important parameter in determining sediment discharge in open channels. Some studies have estimated the bed-load thickness from theoretical and/or experimental perspectives. This study attempts to propose the mathematical formula for the bed-load thickness by using the Tsallis entropy theory. Assuming the bed-load thickness is a random variable and using the method for the maximization of the entropy function, the present study derives an explicit expression for the thickness of the bed-load layer as a function with non-dimensional shear stress, by adopting a hypothesis regarding the cumulative distribution function of the bed-load thickness. This expression is verified against six experimental datasets and are also compared with existing deterministic models and the Shannon entropy-based expression. It has been found that there is good agreement between the derived expression and the experimental data, and the derived expression has a better fitting accuracy than some existing deterministic models. It has been also found that the derived Tsallis entropy-based expression has a comparable prediction ability for experimental data to the Shannon entropy-based expression. Finally, the impacts of the mass density of the particle and particle diameter on the bed-load thickness in open channels are also discussed based on this derived expression.

CFD-DEM Two-Way Coupled Numerical Simulation of Bridge Local Scour Behavior under Clear-Water Conditions

Bridge local scour involves extremely complex interactions among the flow, the sediments, and the pier. Our understanding of the underlying mechanism, especially at the microscale, is far from complete. The newly emerged multiphase numerical simulation overcomes the technical limitations imposed on physical experiments. To advance knowledge of the sediment dynamics under turbulent junction flows, this paper employed a CFD-DEM two-way coupled numerical model to simulate the local scour behavior of uniform spherical mass particles around an oblong pier. In this coupled system, the flow phase was described as a continuum by a detached eddy simulation (DES) model, and motion of the discrete particles was governed by Newton’s laws of motion (DEM). The flow–sediment interactions were directly considered through the momentum exchange between the two phases. The two-way coupled model was shown to successfully capture microscopic sediment dynamics similar to those observed in the literature. Sediment grains in the bed-load layer were shown to be eroded in the form of sliding and saltation. The erosional forces acting on two representative target particles, together with their correspondent motions/trajectories, provide valuable insights into the mechanism that dictates the scour initiation.

Intense Granular Sheetflow in Steep Streams

AbstractQuantifying sediment transport rates in mountainous streams is important for hazard prediction, stream restoration, and landscape evolution. While much of the channel network has steep bed slopes, little is known about the mechanisms of sediment transport for bed slopes between 10% < S < 30%, where both fluvial transport and debris flows occur. To explore these slopes, we performed experiments in a 12‐m‐long sediment recirculating flume with a nearly uniform gravel bed. At 20% and 30% bed gradients, we observed a 4‐to‐10 particle‐diameter thick, highly concentrated sheetflow layer between the static bed below and the more dilute bedload layer above. Sheetflow thickness increased with steeper bed slopes, and particle velocities increased with bed shear velocity. Sheetflows occurred at Shields stresses close to the predicted bedload‐to‐debris flow transition, suggesting a change of behavior from bedload to sheetflow to debris flow as the bed steepens.

An explicit analytical expression for bed-load layer thickness based on maximum entropy principle

The present study aims to derive an analytical model on bed-load layer thickness in an open channel turbulent flow carrying sediments. Determination of the thickness of the bed-load layer is of utmost importance in the study of bed-load transport as it is required to determine the bed-load transport rate, as well as in the study of suspended load transport as it acts as reference level for the particles in suspension. Apart from the several deterministic approaches available in the literature, the work adopts probabilistic approach based on entropy theory to determine the bed-load layer thickness. The concept of entropy theory developed by Shannon is used and the method of Lagrange multipliers is employed for the maximization of entropy function to find the least biased probability distribution. To calculate the Lagrange multipliers, present in the probabilistic model of dimensionless bed-load layer thickness, two different methodologies are presented. The model of bed-load layer thickness is a function of dimensionless shear stress and also depends on three other parameters which are found to be functions of specific gravity of sediment particle and dimensionless particle diameter from a non-linear regression analysis. The proposed model is validated with wide sets of experimental data available in literature and a good agreement is achieved. Apart from comparison with data, the model is also compared with existing deterministic model and computation of relative percentage error proves the better efficiency of the present model.

Advection and dispersion of bed load tracers

Abstract. We use the erosion–deposition model introduced by Charru et al. (2004) to numerically simulate the evolution of a plume of bed load tracers entrained by a steady flow. In this model, the propagation of the plume results from the stochastic exchange of particles between the bed and the bed load layer. We find a transition between two asymptotic regimes. The tracers, initially at rest, are gradually set into motion by the flow. During this entrainment regime, the plume is strongly skewed in the direction of propagation and continuously accelerates while spreading nonlinearly. With time, the skewness of the plume eventually reaches a maximum value before decreasing. This marks the transition to an advection–diffusion regime in which the plume becomes increasingly symmetrical, spreads linearly, and advances at constant velocity. We analytically derive the expressions of the position, the variance, and the skewness of the plume and investigate their asymptotic regimes. Our model assumes steady state. In the field, however, bed load transport is intermittent. We show that the asymptotic regimes become insensitive to this intermittency when expressed in terms of the distance traveled by the plume. If this finding applies to the field, it might provide an estimate for the average bed load transport rate.

Towards a universal optimization of the performance of sand storage dams in arid and semi-arid areas by systematically minimizing vulnerability to siltation: A case study in Makueni, Kenya

Sand storage dams are hydraulic retention structures that increase the volume of coarse sediments in seasonal sandy streams by exclusively blocking the bedload transport during runoff events. However, siltation of fine grain particles, which are transported as part of the suspended load, is a major factor causing sand storage dams to perform poorly. Therefore, this study aimed to evaluate the hydrological performance and cost-efficiency of 30 sand storage dams. This study also aimed to increase the understanding of critical factors which may affect the performance and lead to siltation of sand storage reservoirs. The analysis was based on a physical survey of 30 sand storage dams that were built in one-stage in southeastern Kenya. Most of the study sites had the capacity to produce sand. However, the reservoirs suffered from severe siltation, which caused generalized low annual yields, reduced supply capacities, and low cost-efficiency. It is argued that the main factors for the poor performance were the high inter- and intra-annual variability of bedload transport, which coupled with the construction of one-stage spillways, led to siltation of the reservoirs. Thus, large volumes of fine grain particles accumulated in the reservoirs during runoff events with bedload layer heights lower than the height of the one-stage spillways. To systematically maximize the robustness to the inherent variability of bedload transport, and ensure optimal performance levels by systematically minimizing siltation, spillways should be built in stages of reduced height. Thus, the lower the stage height, the higher the probability of maximizing the accumulation of coarse sediment. It is estimated that a multi-stage construction process with stage heights of 20 cm would have produced a performance 26 times higher. This implies that the 30 reservoirs would have had the capacity to supply 8516 people as compared to the current supply capacity of 330 people. Improvements in the performance of sand storage dams can greatly assist attempts to link this technology with income-generating activities for agropastoralists in arid and semi-arid areas.

Depth-averaged modelling of granular dike overtopping

Failure of river dikes due to overtopping is a dangerous phenomenon to be avoided, and a complex unsteady sediment transport problem that is under intense scientific consideration. Mathematical modelling of these flows is conducted using one-dimensional families of models based on different conceptual approximations, including (i) a clear-water layer and bed-load layer approach; (ii) a mixture flow approach dividing the sediment transport into bed and suspended load transport modes; and (iii) a two-phase approach formulating the mass and momentum conservation equations for the water and sediment phases separately. These families of conceptual models involve a vertical momentum balance reducing to hydrostatic pressure distribution. As discussed in previous works, numerical results might be improved by relaxing this closure hypothesis. Herein, a vertically-averaged RANS model is presented for a water–sediment mixture, conceptually divided into suspended/bed-load layers, overtopping the erodible dike surface under non-equilibrium sediment transport and non-hydrostatic fluid pressure conditions. The model is critically compared with experimental data and Saint-Venant type simulations, resulting in improved predictions of the dike crest reach. However, the erosion at the dike toe is overpredicted, stating a limitation of depth-averaged modelling.