Experimental investigation of bedload transport processes under unsteady flow conditions

Hydraulic engineering is usually based on theoretical analysis and/or numerical modelling simulation. As the dynamic behaviour of sediment movement under unsteady flow is still unclear, and field measurement is comparatively difficult during a large flood, prior investigations through flume experiments are required. A series of flume experiments, conducted using different inflow hydrographs without sediment supply from upstream, was carried out to investigate the sediment transport process under unsteady flow conditions. A series of triangular hydrographs were performed in the experiments. The results indicate that a temporal lag was found between the flow hydrograph peak and the sediment hydrograph peak because large size sand dunes lasted for a short period in the falling limb of the flow hydrograph. The temporal lag was found to be about equal to 6–15% of the flow hydrograph duration. Owing to the temporal lag, the total bedload yield in the rising period was less than that in the falling period. Furthermore, the measured total bedload yield in the unsteady flow experiments was larger than the predicted value, which was estimated by using the results obtained from the equivalent steady flow experiment. The peak bedload transport rate for unsteady flow conditions was also larger than the predicted value. The ratios of the measured to the predicted quantities mentioned above were found to be constant values for different shapes of hydrographs. It is, therefore, expected that the analytical results of sediment transport from equivalent steady flow can be a good reference for sediment transport under unsteady flow conditions. Copyright © 2004 John Wiley & Sons, Ltd.     

Bridge pier failure probabilities under combined hazard effects of scour, truck and earthquake. Part I: occurrence probabilities

In many regions of the world, a bridge will experience multiple extreme hazards during its expected service life. The current American Association of State Highway and Transportation Officials (AASHTO) load and resistance factor design (LRFD) specifications are formulated based on failure probabilities, which are fully calibrated for dead load and nonextreme live loads. Design against earthquake loads is established separately. Design against scour effect is also formulated separately by using the concept of capacity reduction (or increased scour depth). Furthermore, scour effect cannot be linked directly to an LRFD limit state equation, because the latter is formulated using force-based analysis. This paper (in two parts) presents a probability-based procedure to estimate the combined hazard effects on bridges due to truck, earthquake and scour, by treating the effect of scour as an equivalent load effect so that it can be included in reliability-based bridge failure calculations. In Part I of this series, the general principle of treating the scour depth as an equivalent load effect is presented. The individual and combined partial failure probabilities due to truck, earthquake and scour effects are described. To explain the method of including non-force-based natural hazards effects, two types of common scour failures are considered. In Part II, the corresponding bridge failure probability, the occurrence of scour as well as simultaneously having both truck load and equivalent scour load are quantitatively discussed.     

Bridge pier failure probabilities under combined hazard effects of scour, truck and earthquake. Part II: failure probabilities

In many regions of the world, a bridge will experience multiple extreme hazards during its expected service life. The current American Association of State Highway and Transportation Officials (AASHTO) load and resistance factor design (LRFD) specifications are formulated based on failure probabilities, which are fully calibrated for dead load and non-extreme live loads. Design against earthquake load effect is established separately. Design against scour effect is also formulated separately by using the concept of capacity reduction (or increased scour depth). Furthermore, scour effect cannot be linked directly to an LRFD limit state equation because the latter is formulated using force-based analysis. This paper (in two parts) presents a probability-based procedure to estimate the combined hazard effects on bridges due to truck, earthquake and scour, by treating the effect of scour as an equivalent load effect so that it can be included in reliability-based failure calculations. In Part I of this series, the general principle for treating the scour depth as an equivalent load effect is presented. In Part II, the corresponding bridge failure probability, the occurrence of scour as well as simultaneously having both truck load and equivalent scour load effect are quantitatively discussed. The key formulae of the conditional partial failure probabilities and the necessary conditions are established. In order to illustrate the methodology, an example of dead, truck, earthquake and scour effects on a simple bridge pile foundation is represented.     

Effect of pier shape and pier alignment on the equilibrium scour depth at single piers

The equilibrium scour depth at uniform single bridge piers depends on a large number of variables,including the pier horizontal cross-section shape and its alignment angle towards the flow direction.The influence of these variables has been studied by only a few researchers,mostly,on the basis of tests that were far from approaching equilibrium.This experimental study aims at revisiting the influence of piers' shape and alignment on local scouring for length-width ratios smaller than or equal to 4,by increasing the experimental evidence.Fifty five long-duration laboratory tests were run under steady,clear-water flow,close to the threshold for initiation of sediment motion.Five pier shapes were considered:circular,rectangular square-nosed,rectangular round-nosed,oblong,and zero-spacing(packed) pile-groups;the tested skew-angles were 0°,30°,45°,60°,and 90°.It was concluded that i) the shape factor can be taken as 1.0,for rectangular round-nosed and oblong cross-section piers,and as 1.2,for rectangular squarenosed and packed pile-group cross-section piers,ii) the shape factor does not vary significantly with the duration of tests,this way confirming the robustness of the shape factors reported to date,iii) the effect of shape is present at skewed piers although the associated coefficients remain in the narrow range of1.0-1.2,and iv) for length-width ratios smaller than 4,the shape factor is of the same order of magnitude as the skew angle factor and should not be neglected.     

Local scour around two side-by-side cylindrical bridge piers under ice-covered conditions

In the current study, 108 flume experiments with non-uniform, cohesionless sediments have been done to investigate the local scour process around four pairs of side-by-side bridge piers under both open channel and ice-covered flow conditions. Similar to local scour around bridge piers under open channel conditions and a single bridge pier, it was observed in the experiments that the maximum scour depth always occurred at the upstream face of the pier under ice-covered conditions. Further, the smaller the pier size and the greater the spacing distance between the bridge piers, the weaker the horseshoe vortices around the bridge piers, and, thus, the shallower the scour holes around them. Finally, empirical equations were developed to estimate the maximum scour depth around two side-by-side bridge piers under both open channel and ice-covered flow conditions.     

Computational fluid dynamics modeling of abutment scour under steady current using the level set method

The scour and deposition pattern around an abutment under constant discharge condition is calculated using a three dimensional(3D) Computational Fluid Dynamics(CFD) model.The Reynolds-Averaged Navier Stokes(RANS) equations are solved in three dimensions using a CFD model.The Level Set Method(LSM) is used for calculation of both free surface and bed topography.The two-equation turbulence model(k-ε and k-ω) is used to calculate the eddy viscosity in the RANS equations.The pressure term in the RANS...     

A novel platform to evaluate the dampening of water and solute transport in an experimental channel under unsteady flow conditions

This paper presents a novel platform to study the dampening of water and solute transport in an experimental channel under unsteady flow conditions, where literature data are scarce. We address the question about what could be the smallest size of experimental platform that is useful for research, project studies, and teaching activities and that allows to do rational experiments characterized by small space occupation, short experimental duration, high measurement precision, high quality and reproducible experimental curves, low water and energy consumption, and the possibility to test a large variety of hydrograph scenarios. Whereas large scale hydraulic laboratories have focused their studies on sediment transport, our platform deals with solute transport. The objectives of our study are (a) building a platform that allows to do rational experiments, (b) enriching the lack of experimental data concerning water and solute transport under unsteady state conditions, and (c) studying the dampening of water and solute transport. We studied solute transport in a channel with lateral gain and lateral loss under different experimental configurations, and we show how the same lateral loss flow event can lead to different lateral loss mass repartitions under different configurations. In order to characterize water and solute dampening between the input and the output of the channel, we calculate dampening ratios based on peak coordinates of time flow curves and time mass curves and that express the decrease of peak amplitude and the increase of peak occurrence time between the input and output curves. Finally, we use a solute transport model coupling the diffusive wave equation for water transfer and the advection–diffusion equation for solute transport in order to simulate the experimental data. The simulations are quite good with a Nash–Sutcliffe efficiency NSE > 0.98 for water transfer and 0.84 < NSE < 0.97 for solute transport. This platform could serve hydrological modellers because it offers a variety of measured parameters (flow, water height, and solute concentration), at a fine time step under unsteady flow conditions.     

Evolution of scouring process downstream of grade‐control structures under steady and unsteady flows

For many incised channels, one of the most common strategies is to install some hard structures, such as grade‐control structures (GCSs), in the riverbed to resist further incision. In this study, a series of experiments, including both steady and unsteady flow conditions, were conducted to investigate the scouring process downstream of a GCS. Three distinct phases, including the initial, developing and equilibrium phases, during the evolution of scour holes were identified. In addition, a semi‐empirical method was proposed to predict the equilibrium scour‐hole profile for the scour countermeasure design. In general, the comparisons between the experimental and simulated results are reasonably consistent. As the studies on temporal variation of the scour depth at GCSs caused by floods are limited, the effect of flood hydrograph shapes on the scour downstream of GCSs without upstream sediment supply was also investigated experimentally in this study. Based on the dimensional analysis and the concept of superposition, a methodology is proposed to simulate the time evolution of the maximum scour depth downstream of a GCS for steady flows. Moreover, the proposed scheme predicts reasonably well the temporal variations of the maximum scour depth for unsteady flows with both single and multiple peak. Copyright © 2012 John Wiley & Sons, Ltd.     

Numerical model of local scour considering the unsteady sediment inflow and sediment sorting: Application to scour upstream of slit weir

The current study proposes a novel framework for the numerical model for estimating the temporal scour considering unsteady sediment inflow and the sediment sorting process. The framework was applied to local scour upstream of a slit weir. The scour model is based on an ordinary nonlinear differential equation derived from sediment continuity and scour rate equations. A one-dimensional(1-D)Boussinesq-type model coupled with nonequilibrium sediment transport was incorporated in the scour model to...     

Estimation of maximum scour depth around bridge piers under ice-covered conditions using data-driven methods

The scouring around bridge foundations is a significant concern in civil engineering. Several research has been conducted experimentally and numerically to study the maximum scour depth around the foundations of a bridge in open channel conditions. In cold regions, where ice forms on lakes, reservoirs, and rivers, the interaction between ice and hydraulic structures is further complicated. The flow distribution varies significantly leading to deeper and larger scouring around bridge foundations....     

Coherent structure dynamics and sediment particle motion around a cylindrical pier in developing scour holes

Recent investigations on the dynamics of the turbulent horseshoe vortex system (THV) around cylindrical piers have shown that the rich coherent dynamics of the vortical structures is dominated by low-frequency bimodal fluctuations of the velocity field. In spite of these advances, many questions remain regarding the changes of the flow and sediment transport dynamics as scour progresses. In this investigation we carry out laboratory experiments to register the development of the scour hole around a cylindrical pier in a fine-sand bed (d ₅₀ = 0.36 mm). We use the bathymetry measured in the experiment to simulate the flow field employing the detached-eddy simulation approach (DES), which has shown to resolve most of the turbulent stresses around surface-mounted obstacles. From these simulations we compare the dynamics of the THV to the flat-bed case, and analyze the effects on particle transport and sediment flux using the Lagrangian particle model of Escauriaza and Sotiropoulos (2011b) to study the impact of the changes of the flow on the sediment dynamics.     

Reduction of bend scour with an air-bubble screen-morphology and flow patterns

The interplay between streamwise flow,curvature-induced secondary flow,sediment transport and bed morphology leads to the formation of a typical bar-pool bed morphology in open-channel bends.The associated scour at the outer bank and deposition at the inner bank may endanger the outer bank’s stability or reduce the navigable width of the channel.Previous preliminary laboratory experiments in a sharply curved flume with a fixed horizontal bed have shown that a bubble screen located near the outer bank can generate an additional secondary flow located between the outer bank and the curvature-induced secondary flow and with a sense of rotation opposite to the latter.This bubble-induced secondary flow redistributes velocities and bed shear stresses.The reported study investigates the implications of a bubble screen on the flow and the morphology in configurations with mobile bed.Velocity measurements show that the bubble-induced secondary flow shifts the curvature-induced secondary flow in inwards direction and reduces its strength.The bubble screen considerably reduces morphological gradients.Maximum bend scour is reduced by about 50%and occurs further away from the outer bank where it does not endanger the bank stability anymore.The location of maximum scour coincides with the junction of the curvature-induced and bubble-induced secondary flows.At this same location,the maximum streamwise velocities and maximum vertical velocities impinging on the bed also occur,which indicates their importance with respect to the formation of bend scour.The bubble screen also substantially reduced deposition at the inner bank.These preliminary experiments show the potential of a bubble screen to influence and modify the bed morphology.     

On unsteady flow of a viscous fluid between two parallel plates under variable surface charges

Summary The equations of electricity and the equations of hydrodynamics have been used to solve the problem of unsteady flow of a viscous fluid under variable surface charges.     

Mobility of lowland stream Trichoptera under experimental habitat and flow conditions

The species-specific mobility of six species of lowland stream Trichoptera was studied in flume experiments with different habitats and current flows. The test species were selected according to their occurrence along the environmental gradient from more natural towards highly disturbed sandy, lowland streams of the North-West European plain. Two groups of species were distinguished, three species occurring more frequently towards the natural end versus three occurring more frequently towards the disturbed end of the stream disturbance gradient. Experiments were conducted in a temperature and light controlled environment in indoor, re-circulating, man-made stream channels with four replicate gutters each. The bottom of each gutter held ten trays filled with five selected habitat materials (two trays each), which provided refugia and food. Three flow treatments with constant current velocities of 10, 30, or 50 cm/s were applied. Movements were scored based on visual observations of the position of each individual at fixed time points. The first day after release, individuals moved around very actively; this ‘release effect’ was removed from further analyses. The trichopteran species occurring near the more natural end of the disturbance gradient exhibited significantly less mobility (on average 10-15% of individuals actively moved around) than the species from the more disturbed end of the gradient (on average 30-40% of individuals actively moved around). The first group of trichopteran species also spent significantly longer times in the leaves habitat compared to the other three species, which moved more or less independent of habitat. With increasing current velocity, all test species moved more frequently, particularly the species from the more disturbed end of the gradient. This could indicate behavior to avoid dislodgement. The mobility of all species exceeded the mobility needed to use habitat resources of food and shelter, both present in excess. Therefore, short-term movement could also be (partly) a random behavior. Overall, the more tolerant species from the disturbed end of the gradient showed more mobility and flexibility than the species occurring under more or less natural stream conditions. This was consistent with the hypothesis that mobility is an adaptation of tolerant, ubiquitous species. Mobility is an adaptation of r-strategists.     

Closed-form solutions for unsaturated flow under variable flux boundary conditions

It is shown that from any solution of the linear diffusion equation, we may construct a solution of a realistic form of the Richards equation for unsaturated flow. Compared to the usual direct linearization method, our inverse approach involves a quite different sequence of transformations. This opens the possibility of exact solutions with a wider variety of continuously varying flux boundary conditions. Closed-form solutions are presented for two examples. In these, the varying water flux boundary conditions resemble (i) the passage of a peaking storm and (ii) the continuous opening of a valve preceding a steady water supply. Unlike earlier more systematic approaches to this problem, our method does not require the numerical solution of an integral equation.     

Particle accumulation in a cylindrical sediment trap under laminar and turbulent steady flow: An experimental approach

The hydrodynamical, fluid and particle parameters which control flushing rates, flow cells, and accumulation rates of particulate matter in cylindrical (MultiPIT) sediment traps were quantified in a flume simulation using a seeding technique for 25–45 µm particles. Particle collection was found to be a trap- and particle-specific filtering process encompassing advective and gravitational entry of particles over a reduced trap aperture area, and gravitational-turbulent removal of particles at the bottom of the internal flow cell. Trapping efficiency increased up to 10-fold with increasing horizontal flow velocity (1–30 cm · s^–1). For given flow velocity, the trap over-and undercollected particles relative to their weight, i.e. (theoretical) Stokes settling velocity. The trapping efficiency increased with increasing trap Reynolds number Re_T, changed by the approaching velocity in our experiments. Opposite findings from earlier experiments using the flume seeding technique and changing Re_T by altering the trap diameter (Butman, 1986) are discussed. Semi-empirical equations are derived for the accumulation process of light, heavy and intermediate particles. From these, measured trap fluxes can be converted into in-situ verticle particle flux except for light particles.     

The impact of lateral flow contraction on the rock plucking process under sub-critical flow conditions

Rock plucking is the vertical removal of chunks of rock along intersection joint planes by flowing water. The plucking of durable jointed rock in a natural stream alters stream morphology and potentially damages a bridge substructure situated on a rock foundation by local erosion. Despite its importance, the mechanics of bedrock erosion by plucking are not well understood. In this study, we conduct laboratory experiments to investigate the threshold of block entrainment through plucking near a flow obstruction under sub-critical conditions. In a laboratory flume, we reproduce a wide range of typical lateral flow contraction scenarios that occur around a large rock or bridge substructure and investigate the process of the vertical entrainment of blocks near the obstruction. Two different modes of block removal process (impulsive plucking and accumulative plucking) are observed near the bluff structure. We find that under severe flow contraction, blocks are more likely to escape quickly via impulsive plucking because higher flow contraction and the resulting strong local turbulence around the structure generate large instantaneous uplift force that removes the block within a short period of time; however, we observe accumulative plucking under weaker flow contraction near the bluff structure. From the experimental results, we develop a formula for the threshold point of block dislocation caused by plucking with respect to the degree of lateral flow contraction. The results indicate that increasing the flow contraction ratio reduces block stability because of higher flow acceleration and the increased turbulence effect near the upstream edge of the obstruction. The results of this study should be useful to those who estimate the rate of rock erosion by plucking in natural open channels around a bluff structure.     

Experiment and simulation of turbulent flow in local scour around a spur dyke

The turbulent flow in the local scour hole around a single non-submerged spur dyke is investigated with both experimental and numerical methods. The experiments are conducted under clear-water scour regime with an impermeable spur dyke. The scour geometry and flow velocities are measured in details with a high-resolution laser displacement meter, electro-magnetic velocimetries and PIV （Particle image velocimetry）. A 3D non-linear k-ε model is developed to simulate the complex local flow field around the scour area. The numerical model is formulated using FVM （Finite volume method） on a collocated unstructured mesh, capable of resolving complex geometries and boundaries. It is found that the simulation results are reasonably consistent with those of the experimental measurements. Based on the study results, the nature of the flow structure around a spur dyke with local scour hole is analyzed.     

Effective dispersion in a chemically heterogeneous medium under temporally fluctuating flow conditions

We investigate effective solute transport in a chemically heterogeneous medium subject to temporal fluctuations of the flow conditions. Focusing on spatial variations in the equilibrium adsorption properties, the corresponding fluctuating retardation factor is modeled as a stationary random space function. The temporal variability of the flow is represented by a stationary temporal random process. Solute spreading is quantified by effective dispersion coefficients, which are derived from the ensemble average of the second centered moments of the normalized solute distribution in a single disorder realization. Using first-order expansions in the variances of the respective random fields, we derive explicit compact expressions for the time behavior of the disorder induced contributions to the effective dispersion coefficients. Focusing on the contributions due to chemical heterogeneity and temporal fluctuations, we find enhanced transverse spreading characterized by a transverse effective dispersion coefficient that, in contrast to transport in steady flow fields, evolves to a disorder-induced macroscopic value (i.e., independent of local dispersion). At the same time, the asymptotic longitudinal dispersion coefficient can decrease. Under certain conditions the contribution to the longitudinal effective dispersion coefficient shows superdiffusive behavior, similar to that observed for transport in s stratified porous medium, before it decreases to its asymptotic value. The presented compact and easy to use expressions for the longitudinal and transverse effective dispersion coefficients can be used for the quantification of effective spreading and mixing in the context of the groundwater remediation based on hydraulic manipulation and for the effective modeling of reactive transport in heterogeneous media in general.