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Offshore structures are deployed extensively to harvest marine resources. Due to the harsh marine environments and heavy-duty working conditions, the risks associated with failure due to scour are high, and the need for accurate prediction of these risks is increasing. Often, pipelines and cables are critical elements of subsea energy transportation and telecommunication, and they are highly susceptible to scour-induced failure. The scour around spheres is relevant to the offshore industry as a simplified three-dimensional representation of subsea structures. This paper presents a numerical study, using FLOW-3D HYDRO, of the scour around on-bottom cylinders and spheres. Whereas most published research investigated scour around stationary solid objects, this paper presents numerical results of a more challenging case of scour around sagging cylinders and spheres. The model was validated against published experimental and numerical results. The scour depth was found to increase with the decrease of the sagging velocity of the solid object. For sagging horizontal cylinders, the scour depth reaches a plateau of 1.1 times the cylinder diameter when the dimensionless sagging velocity is smaller than 0.094. For sagging spheres, the maximum scour depth reaches 0.37 times the sphere diameter when the dimensionless sagging velocity is reduced to 0.0103. The findings provide guidelines for future research on more complicated interactions between flow, solid objects, and the seabed, accounting for the deformation of infrastructure over time. Practical Applications: This paper concerns the flow, sediment transport, and scour around horizontal cylinders and spheres undergoing slow downward motion, which resembles the sagging of on-bottom infrastructure under the influence of gravity and bed erosion. Offshore structures are deployed extensively to harvest marine resources. Pipelines and cables are critical subsea infrastructures that are susceptible to scour-induced failure. Spherical objects are commonplace in the offshore industry, so a sphere can be deemed as an idealized three-dimensional body. This paper provides detailed FLOW-3D simulations and developed empirical relationships between the dimensionless scour depth and dimensionless sagging speed. Most previous research considered only the scour around fixed objects, so this paper provides a novel addition to the existing knowledge on the scour phenomenon. The computational methods established in this study are useful for simulating more-complicated scenarios. The findings provide guidelines for more-realistic predictions of scour and for the design of scour mitigation measures. [ABSTRACT FROM AUTHOR]

By incorporating horizontal sediment transport and bed erosion into the two-layer depth-averaged shallow water system, one can construct a hydro-sediment-morphodynamic mathematical model in which a variable sediment concentration in a denser layer and interaction between underflows and ambient water are taken into account. Numerically solving such a promising system presents challenges due to its inherent mathematical properties of being conditionally hyperbolic and nonconservative. These properties may result in instability and incorrect results near sharp hydraulic gradients in numerical solutions. The major contribution of this paper is to develop a novel numerical scheme to overcome these issues and to allow the system to be extended to a wider range of engineering applications. To this end, for a one-dimensional two-layer hydro-sediment-morphodynamic system, (1) its mathematical model is first reformulated to a novel relaxation format, which is mathematically equivalent and unconditionally hyperbolic, by relaxing interlayer surface level, and (2) this relaxation system is then solved using a novel path-conservative numerical algorithm with new discrete formulas for the fluxes and nonconservative terms. Thus, the proposed numerical scheme ensures the well-balanced property, and has a major advantage in its ability to accurately and stably handle sharp hydraulic/density gradients with second-order accuracy. Several numerical and laboratory tests are conducted to demonstrate the performance of the proposed new scheme. [ABSTRACT FROM AUTHOR]

Resuspension and redistribution of sediments induced by propeller wash may significantly influence aquatic ecosystems at contaminated sediment sites. This study describes a numerical modeling method developed to predict the sediment resuspension and subsequent transport processes resulting from ship traffic, with a fully coupled simulation of hydrodynamics, sediment transport, and propeller wash. By including propeller momentum effects in the flow field computation, the advection and dispersion of resuspended sediments are better represented than in previously available methods. To achieve this improvement, a computational algorithm was first developed to calculate the propeller wash effects from one or more ships (e.g., erosion rate and momentum flux); these results were then dynamically linked to a hydrodynamic and sediment transport computation using Environmental Fluid Dynamics Code Plus (EFDC+). This modeling framework was evaluated using a field experiment conducted by the US Navy. The model was calibrated with flow velocities and sediment erosion depths, and then validated with resuspended sediment concentrations in the water column. The model results reproduced the horizontal and vertical distributions of resuspended sediments better when the propeller-induced momentum was incorporated into the flow field computation. The sensitivity test indicated that the increased flow energy from propeller momentum resulted in significant dispersion of resuspended sediments in both longitudinal and lateral directions. The maximum scour was dependent on the propeller revolution speed, the ship engine power, and the distance between the propellers and the sediment bed. [ABSTRACT FROM AUTHOR]

Understanding the complex flow and sediment transport on vegetated slopes is important for ecological restoration and conservation projects. This study quantifies the erodibility of sand infill through densely vegetated engineered turf on steep slopes. Flume testing was conducted on four different sand infill materials. The initially lain bed material had artificially high mobility due to the infill application method. Grains were elevated by the vegetation and protruded into the flow. Then, the bed material gradation during subsequent flows became progressively coarser. Two regimes were identified. Poorly sorted infill soils underwent noticeable changes to gradation and had decreasing mobility with increasing shear stress. Conversely, well-sorted soils had minimal changes to gradation and resulted in the expected trend of increasing sediment flux with increasing shear stress. Existing predictive formulas performed poorly, in particular for the soils with evolving gradation. An updated formulation to predict sediment flux is proposed based on a reduction to the effective bed shear stress and dimensionless parameters relating to the flow, sediment, and vegetation characteristics. The proposed modification results in greatly improved predictions for both sediment flux magnitude and trend. [ABSTRACT FROM AUTHOR]

Erosion of rock masses by water typically involves unraveling of blocks of rock along existing defects in a manner that is not represented by analytical solutions for sediment transport or rockfill (rip-rap). A pragmatic approach to this complex problem is found by using a rock mass index to represent the erodibility of the rock-mass. The likelihood of erosion is then assessed by comparison against case studies in similar rock masses. A new independent data set of rock-mass erosion was gained from inspection of 26 unlined spillways in Australia, South Africa, and the United States. It was found that erosion can be usefully correlated against various published rock mass indices and hydraulic indices. A modified rock mass index, developed specifically to represent erodibility, is presented, and is applied to prepare a new comparative erosion assessment method for rock masses. [ABSTRACT FROM AUTHOR]

Natural bedrock rivers exhibit diverse erosional morphologies. Although the formation of alternate bars on bedrock has been noted in previous studies, the influence of these alternate bars on bedrock erosion has not been clarified. In this study, the authors propose a model for bedrock-alluvial channels that reproduces both bar formation and erosional morphology. In addition, the authors report on numerical simulations to evaluate the influence of sediment supply on the state of the bed at and over the bedrock surface. The numerical results illustrate the formation of different morphologies for different supply rates. When the sediment supply rate is close to transport capacity, mixed alluvial-bedrock alternate bars form. These bars are analogous to purely alluvial alternate bars. A meandering thread of alluvial material migrates downstream over a uniformly eroding bedrock surface. When the sediment supply rate is well below capacity, however, multiple incisional troughs (grooves) form on the bedrock surface, and alluvial cover tends to concentrate in the troughs. [ABSTRACT FROM AUTHOR]

Due to a complex three-dimensional flow pattern, the outer banks of river bends are predisposed to erosion. When endangering civil structures, preventing measures to mitigate this erosion are thus required. Vertical ribs at protection walls for scour reduction have been applied to several flood protection projects in mountain rivers; nevertheless, no systematic and intensive study has been presented so far to evaluate their effect. This paper investigates experimentally the effect of vertical ribs, placed as macroroughness elements on the outer vertical wall of a 90° laboratory channel bend. Systematic tests were performed using a wide and coarse grain-size distribution. Scour formation and velocity distribution were assessed in the channel in the presence of a macrorough outer bank, materialized in the laboratory by vertical elements placed on the outer vertical wall along the channel bend. Experiments showed that the macrorough outer bank changed considerably the bed morphology under equilibrium conditions. Maximum scour depth is considerably reduced by the vertical ribs placed at an optimal spacing on the bend outer wall. A considerable grain sorting process occurs across the cross section in the bend, which influences the scour process; differences are observed between situations with and without macrorough banks. The distribution of the time-averaged velocity field across the section shows the influence of the channel rough wall. An optimal macroroughness configuration in terms of scour reduction is discussed and proposed. It was observed that when spacing between vertical ribs is too reduced, these ribs act as uniformly distributed wall roughness, contributing to the width reduction due to the occupation of the cross section and increasing consequently the flow velocity with negative effects in scour reduction. [ABSTRACT FROM AUTHOR]

A numerical model for simulation of embankment dams' gradual breaching because of overtopping, named embankments breach software (EBS), is introduced in this paper. The model solves the equations for the depth-averaged flow (modified for shallow water flow on steep slopes), the turbulence model, the sediment transport, and the bed elevation change in a coupled manner. An upwind cell center finite volume method is applied for developing the discrete form of the differential equations. A linearized scheme with second-order accuracy in space and explicit time integration on unstructured triangular meshes is utilized in this model. To simulate the flow over dry sloping surfaces of the embankment dam configuration, the developed model considers a powerful wetting and drying technique. Furthermore, the abilities of the model enhanced simulation of sudden bank failure of the breach channel because of the base erosion and transport of the failed solid material. [ABSTRACT FROM AUTHOR]

The flow characteristics around two partially buried objects, a short cylinder (SC) and a truncated cone (TC) were examined experimentally and numerically. Experiments were conducted in a large tilting flume with vertical walls made of acrylic plastic and steel floor covered by a 24-m long sand pit. For each experiment, the object was placed on a flat sandy bed, the flume was filled to a water depth of 41 cm, and a steady unidirectional current was established at high Reynolds numbers while sinking of the object was tracked over time. Velocity records were taken with an acoustic Doppler velocimeter (ADV) probe at the final stage of burial and scour hole evolution. The flow structure around each object was further investigated using a model that solves the Reynolds-averaged Navier-Stokes (RANS) equations coupled with a turbulence closure model, and results were compared to the experimental measurements. Measurements and numerical simulations allowed identification of regions of high and low velocity and turbulent kinetic energy accounting for zones of potential sediment erosion and deposition that dictate the burial of the object. The turbulence closure model was shown to reproduce the experimental mean flow velocity and turbulent kinetic energy with acceptable accuracy. [ABSTRACT FROM AUTHOR]

The sediment erosion rate flume (SERF) is used to evaluate various methods to estimate shear stresses in a flume-style erosion rate testing device. Results show that direct shear stress measurements most closely correspond to shear stress estimates obtained from the Colebrook equation using a roughness height of approximately 77% of the sediment particle diameter. Using pressure drops to estimate shear stress appears to underestimate rough sample (grain sizes ) stresses. Likewise, smooth-wall assumptions and analytical methods also appear to produce lower than expected results for similar heights. Colebrook equation results should be interpreted as 'instrument specific' because of the different devices' hydraulic diameters. [ABSTRACT FROM AUTHOR]

Many rivers in Taiwan have steep slopes, are subject to typhoon-induced flood flows, and contain soft bedrock that is exposed at many locations and easily erodible. The occurrence of extensive bedrock erosion has been a major threat to river infrastructure at many locations. Soft bedrock erosion, therefore, is an important process to consider for river projects in Taiwan. In this study, bedrock erosion models are reviewed. A specific model is proposed by combining two existing models incorporating both the hydraulic and abrasive scour mechanisms. The proposed bedrock erosion model is incorporated into a two-dimensional mobile-bed model, and the integrated model is tested by simulating bedrock erosion downstream of the Chi-Chi weir on the Choshui River in Taiwan. A calibration study is performed to determine appropriate values of the model parameters based on two and a half years of measured data. The model is then assessed based on a verification study that compares model predictions of bedrock erosion of the same reach to two additional years of measured data. The bedrock erosion model is found to be suitable for the river reach studied. Further improvement, however, is still necessary, which points to potential future research. [ABSTRACT FROM AUTHOR]

In dredging practice sand is eroded at very high flow velocities using water jets. Breaching of dikes or dams is another process where sediments are eroded under the influence of high flow velocities. The existing pick-up functions were developed for relative low values of bed shear stress and hence overestimate erosion. Conventional pick-up functions can be made suitable for dealing with high-velocity erosion by taking the permeability of the sediment into account. This can be achieved by modifying the critical Shields parameter. The procedure is demonstrated using the van Rijn pick-up function. The theory is compared with experiment, and agreement is found to be good. [ABSTRACT FROM AUTHOR]

Experiments have been carried out in a mobile-bed laboratory flume in order to study the sediment exchange process between the main channel and the groyne fields. The flume represented half the width of a schematized river reach with a series of groynes. The experiment was designed to represent typical dimensions of the Dutch River Waal at a geometrical scale of 1:100. The conditions were set to guarantee bed load as well as suspended load sediment transport. Conditions with submerged and emerged groynes were investigated. In addition to traditional measurements, viz., bed-level changes, suspended sediment concentrations, and flow velocities, bed-form propagation was measured in two dimensions using a the particle image velocimetry technique. The results were analyzed with focus on sediment exchange mechanisms and sediment transport patterns. The results demonstrate that under all flow conditions there is a net import of sediment into the groyne fields. The prevailing transport mechanisms vary with the flow stage: if the groynes are emerged it is mainly advection by the primary circulation cell, whereas if the groynes are submerged it is rather residual advection by large-scale coherent flow structures (in a straight reach). Additional entrainment of sediment by enhanced turbulence complicates the erosion/deposition patterns. [ABSTRACT FROM AUTHOR]

The article reviews the article "Sediment Transport Modeling Review-Current and Future Developments," by M. Elhakeem and colleagues, published in the January 2008 issue of the journal.

Live-bed scour at a vertical-wall abutment is experimentally investigated with specific attention paid to the conceptual issues concerning the temporal development of local scour phenomenon. First explored are the time scales for the initial rising phase of the time variation of scour depth. An appropriate identification of such scales and of their normalizing parameters makes it possible to recognize a quantitative dependency of nondimensional time scales on flow intensity. Second, the time scales for the subsequent fluctuations around a mean equilibrium value are considered. Experimental results indicate that the quasiperiodical fluctuations of scour depths do not always correspond to those of bed forms. A conceptual model is outlined to explain this aspect. [ABSTRACT FROM AUTHOR]

The paper presents a study on the influence of gravity on the incipient motion and the bed-load transport of sediment. The computation of critical bed-shear stress is revisited considering the balance of forces (hydrodynamic forces and submerged self-weight) acting on a solitary sediment particle lying on an arbitrary sloping bed. Modified effective bed-shear stress and the corresponding critical bed-shear stress, which are defined to assess the incipient motion of sediment in the direction of resultant force, are applied for the estimation of bed-load transport rate in the direction of resultant force. The sediment transport induced by the gravitational force, which is oblique to the direction of the drag force induced by flow, is incorporated into the bed-load transport equation. This modified model provides a reasonable prediction of the critical bed-shear stress and the bed-load transport rate. The model is validated by experimental data. It can be applied to steep slopes and can also avoid the problem of singularity that arises in numerically calculation of sediment transport rate. Additionally, the vectorial transport rate obtained in the model calculation can be implemented in a numerical simulation of channel bed evolution. [ABSTRACT FROM AUTHOR]

Fine particle deposition in coarser sediment beds plays an important role in biogeochemical cycling in sediments by (1) supplying organic matter, attached microorganisms, and nutrients and (2) mediating interfacial fluxes through changes in permeability. In some cases, particles could be associated with contaminants or particles could clog pores in the sediment resulting in ecological impacts through changes in porewater chemistry (e.g., dissolved oxygen profiles). We compare two mechanisms for fine particle deposition to permeable sediments. First, for flat beds, particle delivery by sediment grain-scale flows coupled with particle retention within the sediment could result in deposition in excess of the gravitational settling. Second, pressure-driven flows across ripples may deliver additional particles directly into the sediment, although sediment transport can counteract deposition. Flume experiments were used to measure deposition rates over a range of particle and sediment sizes for both flat and rippled beds. Flat bed deposition rates were greater than the particle settling velocities and comparable to the deposition rates to rippled beds under similar flow conditions. An empirical expression based on parameters for flow, sediment, and particle conditions predicts where each mechanism dominates the deposition rate. This result illustrates the potential importance of grain-scale processes for the deposition of fine particles to permeable sediments regardless of bed roughness. Predictions of particle fate, penetration into the sediment, and degradation following the deposition still require a description of bed topography in addition to sediment properties. [ABSTRACT FROM AUTHOR]

This note, using a three-dimensional model of river flow and sediment transport, examines the effect of the vertical resolution and the choice a nonequilibrium adaptation length Ls in predicting flow and sediment transport around groins in China’s Yongding River. The results show that a fine vertical grid and nonequilibrium sediment transport model provide good predictions, especially on the river bed profile with an obvious main channel and flood plain. [ABSTRACT FROM AUTHOR]

An experimental study was conducted to determine the influence of length, width, and protrusion of noncontinuous riprap protections on shear failure conditions. The incipient motion of particles as a failure criterion and the reference transport method as the threshold of motion were used. In each test, riprap transport rates were measured at different time intervals using a sediment trap placed immediately downstream from the test reach so that time dependence could be well described. Results reveal that incipient motion conditions of transverse (cross-sectional) protections are strongly influenced by both the protrusion and length of bed protection, which indicates that stability significantly increases as protection length increases and decreases as protrusion increases. In the case of longitudinal protections, almost the same failure conditions were found as in the case of continuous protection. Furthermore, these conditions are unrelated to the width of the protection. A coefficient to correct design formulas obtained by other authors is proposed to take into account the effect of the geometry of transverse protections on their stability. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to develop an unsteady 2D depth-averaged model for nonuniform sediment transport in alluvial channels. In this model, the orthogonal curvilinear coordinate system is adopted; the transport mechanisms of cohesive and noncohesive sediment are both embedded; the suspended load and bed load are treated separately. In addition, the processes of hydraulic sorting, armoring, and bed consolidation are also included in the model. The implicit two-step split-operator approach is used to solve the flow governing equations and the coupling approach with iterative method are used to solve the mass-conservation equation of suspended sediment, mass-conservation equation of active-layer sediment, and global mass-conservation equation for bed sediment simultaneously. Three sets of data, including suspension transport, degradation and aggradation cases for noncohesive sediment, and aggradation, degradation, and consolidation cases for cohesive sediment, have been demonstrated to show the rationality and accuracy of the model. Finally, the model is applied to evaluate the desilting efficiency for Ah Gong Diann Reservoir located in Taiwan to show its applicability. [ABSTRACT FROM AUTHOR]

The standard k-ω turbulence model and two versions of blended k-ω/k-[variant_greek_epsilon] models have been used to study the characteristics of a one-dimensional oscillatory boundary layer on a rough surface. The wall boundary condition for the specific dissipation rate of turbulent kinetic energy at the wall is specified in terms of a function based on wall roughness. A detailed comparison has been made for mean velocity, turbulent kinetic energy, Reynolds stress, and wall shear stress with the available experimental data. The three models predict the above properties reasonably well. In particular, the prediction of turbulent kinetic energy for the rough case by the blended models is much better than that for smooth oscillatory boundary layers as reported in previous studies. As a result of the present study, the use of one of the blended models in calculating the sediment transport in coastal environments may be recommended. [ABSTRACT FROM AUTHOR]

This study proposes relationships between mean streamflow depth and cohesionless particle bed characteristics at the beginning of the sediment transport at high slopes in low submergence conditions. The inception of sediment transport is theoretically approached by the incipient motion condition. A previous theoretical analysis of the equilibrium of a gravel particle based on the exposure of the particle itself to the streamflow is generalized by introducing the relative position of the exposed part of the particle with respect to the bottom and by considering the case of a partially submerged particle. Using a low-submergence flow velocity profile in the particle balance of forces at the limit of equilibrium leads to a relationship between the mean flow depth and the sediment size. Another velocity profile of low-submergence flow is added to that used in the previous study, and two analytical expressions of flow depths corresponding to the beginning of sediment transport are obtained for both fully submerged particles and partially submerged particles. The theoretical flow depths given by the analytical expressions are then compared with those from previous experimental tests at the beginning of sediment transport at high slopes with fully submerged particles. The comparison shows a satisfactory agreement between theoretical and experimental values of flow depth corresponding to the degree of exposure and the relative position of the exposed part of the surface layer bed particles. [ABSTRACT FROM AUTHOR]

Analytical predictions of numerical errors in method of characteristics analyses using time-line interpolation in a rectangular grid are obtained for (1) both time-line and space-line interpolation and (2) both rectangular and diamond grids. Amplitude and frequency errors are investigated for each of these four cases using purpose-developed polynomial transfer matrices. Both semiinfinite and finite pipes are investigated. The time-line analysis permits reach back in time and the space-line analysis permits reach out in space. A common definition is adopted for the Courant number in the four cases and it is shown why stability can be achieved in reach-out analyses with Courant numbers greater than 1. In contrast with most work on error estimation, the predicted errors are obtained analytically, not numerically. This is made possible by restricting the analysis to special, but important, cases such as liquid-filled pipes in which the waves may be assumed to propagate at constant speed. Furthermore, the development is restricted to inviscid flows, thereby enabling interpolation errors to be assessed in the absence of complicating influences of discretization errors. In contrast with the latter, it is found that interpolation errors are more sensitive to the shape of numerical grids (i.e., Courant number and rectangular versus diamond grid) than to the size of the numerical time step. [ABSTRACT FROM AUTHOR]

This paper analyzes the effect of flume test section length on sediment erodibility measurements. A modular flume was constructed and experiments were conducted with two test section lengths: 0.15 and 1.10 m. The internal height and width of the flume were 0.11 and 0.13 m, respectively. A fine (7 μm) commercially available quartz sediment was used for the tests. The expectation was that the shorter flume test section would experience a significantly higher erosion rate (per unit surface area) due to its greater sensitivity to edge effects (i.e., scour) at the entrance and exit of the flume test section. However, the measured erosion rates at comparable bottom stresses were only 35% greater in the short test-section tests. These results were consistent with the lack of significant scour development at the entrance or exits of the test sections. Hence, flume test section length alone does not appear to significantly affect erodibility measurements provided edge effects (i.e., scour) are minor. [ABSTRACT FROM AUTHOR]

A theoretical model is developed to describe the process of fine sediment infiltration into immobile coarse sediment deposits. The governing equations are derived from mass conservation and the assumption that the amount of fine sediment deposition per unit vertical travel distance into the deposit is either constant or increases with increasing fine sediment fraction. Model results demonstrate that fine sediment accumulation decreases rapidly with depth into coarse substrate initially void of fine sediment, which is consistent with experimental observations that significant fine sediment infiltration occurs to only a shallow depth. Comparisons of the theory with flume data indicate that the model adequately reproduced the weighted-averaged fine sediment fraction values from experiments. An early model developed by Sakthivadivel and Einstein for fine sediment infiltration is in part based on the generally incorrect assumption that intragravel flow remains constant following fine sediment infiltration. Applying a correction to the Sakthivadivel and Einstein model based on alternate hypothesis that introgravel flow is driven by a constant head gives similar results as the proposed model. [ABSTRACT FROM AUTHOR]

Local scour below a piggyback pipeline in steady currents is investigated numerically. A piggyback pipeline comprises two pipelines that are arranged in the so-called piggyback configuration with the small pipeline being located directly above the large pipeline. The Reynolds-averaged Navier–Stokes equations and the transport equation for suspended sediment concentration are solved using a finite element method. The bed scour profile is determined through solving sediment mass conservation equation. The numerical model is validated against experimental data available in literature on scour below a single pipeline. Computations are carried out for the diameter ratio [the small pipe diameter (d) to the larger one (D)] of 0.2 and the gap (G, between the two pipelines) to the large diameter ratio G/D ranging from 0.0 to 0.5. It is found that the flow and the scour profiles are influenced significantly by the gap ratio. [ABSTRACT FROM AUTHOR]

Recent empirical and numerical evidence shows that the Basset force plays an important role in the description of acceleration of relatively small sediment particles moving close to solid boundaries. This force can make the numerical solution of the equations of motion computationally time and memory consuming. This technical note presents a two-stage methodology to deal with the difficulties associated with computing the Basset force. The Basset term is first approximated based on a semiderivative (fractional mathematics), and then the integration time is redefined in terms of appropriate flow and particle time scales, thus, avoiding unnecessary computations. Important savings in computational time are reported. [ABSTRACT FROM AUTHOR]

The paper reports on an experimental investigation concerning two important issues: (1) local scour and (2) riprap stability at a 45° wing-wall abutment in a degrading river bed of noncohesive sediment. The abutment considered was short (that is abutment length/flow depth <1). From the experimental observations, no influence of abutment inclusion on bed degradation was evident, as bed profiles with and without abutment were quite identical apart from the immediate vicinity of the abutment. Total scour depth at an abutment is found to be the maximum abutment scour depth in addition to the reduction of bed elevation due to bed degradation. The maximum abutment scour depth can be estimated from the equation given by Kandasamy and Melville in their 1998 paper. For scouring time beyond 24 h, the local abutment scour depth remains independent of time. In a degrading bed, the bed forms cause edge failure of the riprap at an abutment when the dunes propagate over the riprap layer. Initially, the dune height is significant causing the maximum damage of riprap layer. As the flow velocity reduces, the resulting bed-shear stress diminishes with the degrading bed and gradually the formation of dunes ceases. An additional experiment reveals that the damaged riprap layer is significantly vulnerable against a subsequent flood accompanied by large dunes. [ABSTRACT FROM AUTHOR]

Experiments were conducted over uniform gravel bed materials to obtain 143 friction factor values under bed-load equilibrium flow conditions in an attempt to add to the scarce data available on slopes between 1 and 9% for Shields numbers between 0.08 and 0.29. Analyses showed that when only flows over flat beds are considered, a distinction must be made between flows with and without bed load. More particularly, fitting flow resistance equations indicated that the roughness parameter increases by a factor of 2.5 from clear water flow to intense bed-load transport. Between these two states, the flow resistance can be approximated by a constant for a given slope. [ABSTRACT FROM AUTHOR]

The original derivation of the Einstein bed-load formula involves several oversimplified assumptions concerning step length of a particle, exchange time, and probability of being lifted into motion. A modified version of the Einstein formula that relaxes these assumptions and incorporates a nonuniform sediment model is proposed and tested with both field and laboratory data. The modified formula shows promise as being more reliable than the original version in estimating bed-load transport rates. [ABSTRACT FROM AUTHOR]

A two-dimensional depth-averaged model was used for the simulation of scour and deposition in sand-bed meandering channels with fixed banks. The model employs unstructured meshes based on triangular elements and incorporates the effects of curvature-induced helical flow and transverse bed slope in the direction of bed-load sediment transport. The model was tested using experimental data from a well-known laboratory curved channel and a full scale meandering river. The numerical results agreed well with observed data, demonstrating that the model can reproduce the main features of bed profiles along meandering rivers, such as the formation of point bars and pools. [ABSTRACT FROM AUTHOR]

Four in situ experiments on sediment erosion characteristics were conducted at the Anacostia River that runs through Washington, D.C. Supplemental erosion rate data were also obtained by carrying out five laboratory experiments using sediment samples collected at the field. In laboratory experiments, the sediment samples were mixed with tap water and placed in the flume to form beds for finding the difference in terms of erosion characteristics caused by different sediment composition among the five samples. This approach enables the finding of erosion characteristics for the entire tidal Anacostia River with limited resources. The in situ measured critical bed-shear stresses τcr for erosion at the water-sediment interface z=0 varies from 0.03 to 0.08 Pa. Field results indicated that τcr(z) increases with the depth z and becomes more than 0.6 to 0.7 Pa with an erosion thickness of less than 1 cm. Sediment beds prepared at a laboratory appear having an upper limit on how much τcr(z) can be developed. [ABSTRACT FROM AUTHOR]

An unsteady total load equation is derived for use in depth-averaged sediment transport models. The equation does not require the load to be segregated a priori into bed and suspended but rather automatically switches to suspended load, bed load, or mixed load depending on a transport mode parameter consisting of local flow hydraulics. Further, the sediment transport velocity, developed from available data, is explicitly tracked, and makes the equation suitable for unsteady events of sediment movement. The equation can be applied to multiple size fractions and ensures smooth transition of sediment variables between bed load and suspended load for each size fraction. The new contributions of the current work are the consistent treatment of sediment concentration in the model equation and the empirical definition of parameters that ensure smooth transitions of sediment variables between suspended load and bed load. [ABSTRACT FROM AUTHOR]

One-dimensional numerical sediment transport models (DREAM-1 and DREAM-2) are used to simulate seven experimental runs designed to examine sediment pulse dynamics in a physical model of forced pool-riffle morphology. Comparisons with measured data indicate that DREAM-1 and -2 closely reproduce the sediment transport flux and channel bed adjustments following the introduction of fine and coarse sediment pulses, respectively. The cumulative sediment transport at the flume exit in a DREAM-1 simulation is within 10% of the measured values, and cumulative sediment transport at flume exit in a DREAM-2 simulation is within a factor of 2 of the measured values. Comparison of simulated and measured reach-averaged aggradation and degradation indicates that 84% of DREAM-1 simulation results have errors less than 3.3 mm, which is approximately 77% of the bed material geometric mean grain size or 3.7% of the average water depth. A similar reach-averaged comparison indicates that 84% of DREAM-2 simulation results have errors less than 7.0 mm, which is approximately 1.7 times the bed material geometric mean grain size or 11% of the average water depth. Simulations using measured thalweg profiles as the input for the initial model profile produced results with larger errors and unrealistic aggradation and degradation patterns, demonstrating that one-dimensional numerical sediment transport models need to be applied on a reach-averaged basis. [ABSTRACT FROM AUTHOR]

A robust computational model for simulating the long-term evolution of incised and restored or rehabilitated stream corridors is presented. The physically based model simulates the three main processes that shape incised streams: hydraulics, sediment transport, and streambed and bank adjustments. A generalized implicit Preissmann scheme is used for the spatial and temporal discretization of the flow governing equations to accommodate large time steps and cross sections spaced at irregular intervals. The solution method introduces several enhancements that increase its robustness, specifically to simulate flashy flows. Transport of cohesive or cohesionless graded bed material is based on a total-load concept, and suspended and bed load transport modes are accounted for through nonequilibrium effects. The model simulates channel width adjustment by hydraulic erosion and gravitational mass failure of heterogeneous bank material. The present paper focuses mainly on the treatment of streamflow hydraulics and evolution of graded streambeds, and reports simulations of published experiments on degrading and aggrading channels with graded bed material. Description and validation of the model’s streambank erosion component and the application of the model to incised stream systems are presented elsewhere. [ABSTRACT FROM AUTHOR]

Experiments on clear-water scour below underwater pipelines (initially laid on the sediment bed) in uniform and nonuniform sediments under steady flow were conducted. Equilibrium scour profiles were modeled by a cubic polynomial. The experimental results are examined to describe the influence of various parameters on equilibrium scour depth. The equilibrium scour depth ds increases with increase in approach flow depth h for shallow flow depths, becoming independent of higher flow depths when h/b>5, where b=pipe diameter. However, the curves of scour depth versus sediment size d and Froude number Fb have a maximum value of ds/b=1.65 at b/d=27 and Fb=0.6. The influence of sediment gradation on scour depth is prominent for nonuniform sediments, which reduce scour depth to a large extent due to the formation of armor layer within the scour hole. The influence of different shaped cross sections of pipes on the scour depth was investigated, where the shape factors for circular, 45° (diagonal facing) and 90° (side facing) square pipes obtained as 1, 1.29, and 1.91, respectively. Using the data of scour depths at different times, the time variation of scour depth is scaled by an exponential law, where the nondimensional time scale increases sharply with increase in Froude number characterized by the pipe diameter. In addition, clear-water scour below circular pipelines laid on a thinly armored sand bed (the sand bed is overlain by a thin armor layer of gravels) was experimentally studied. Depending on the pipe diameter, armor gravel, and bed-sand sizes, three cases of scour holes were recognized. The comparison of the experimental data reveals that the scour depth below a pipeline with an armor layer under limiting stability of the surface particles (approach flow velocity nearly equaling critical velocity for surface particles) is greater than that without armor layer for the same sand bed, if the secondary armoring formed within the scour hole is scattered. In contrast, the scour depth with an armor layer is less than that without armor layer for the same sand bed, when the scour hole is shielded by the secondary armor layer. [ABSTRACT FROM AUTHOR]

The paper presents the application of a two-dimensional depth-averaged numerical model to simulate the lateral migration processes of a meandering reach in the West Jordan River in the state of Utah. A new bank erosion model was developed and then integrated with a depth-averaged two-dimensional hydrodynamic model. The rate of bank erosion is determined by bed degradation, lateral erosion, and bank failure. Because bank material in the West Jordan River is stratified with layers of cohesive and noncohesive materials, a specific bank erosion model was developed to consider stratified layers in the bank surface. This bank erosion model distinguishes itself from other models by relating bank erosion rate with not only flow but also sediment transport near the bank. Additionally, bank height, slope, and thickness of two layers in the bank surface were considered when calculating the rate of bank erosion. The developed model was then applied to simulate the processes of meandering migration in the study reach from 1981 to 1992. Historical real-time hydrographic data, as well as field survey data of channel geometry and bed and bank materials, were used as the input data. Simulated cross-sectional geometries after this 12-year period agreed with field measurements, and the R2 value for predicting thalweg elevation and bank shift are 0.881 and 0.706, respectively. [ABSTRACT FROM AUTHOR]

Many sediment deposits contain not only a granular but also a mineral and/or organic cohesive fraction, which has the potential to change significantly the erosion response when compared to noncohesive sediment deposits. Sediment deposits containing a low proportion of cohesive sediment display a specific, transitional behavior between cohesive and noncohesive sediments. In the past, several studies have examined partly cohesive sediment, however, the quantification of its erosion behavior is still unsatisfactory. In an attempt to advance the understanding and qualitative description of erosion and transport of mixed sediments in pipes, a comprehensive experimental investigation on the erosion behavior was designed. Tests were conducted in a flume with semicircular cross section with a diameter of 0.39 m using fine sand with a d50=0.19 mm and partly cohesive sediment deposits being a mixture of sand and clay with proportion of 3–10% by weight of clay. Tests covered a range of flow conditions with Froude numbers up to 0.6. Data on bed form geometries, friction characteristics, and sediment transport rates were collected. In steady sediment transport conditions the eroded partly cohesive bed produces an active granular top layer over an intact substrate, the thickness of which is up to ten times smaller than in the case of a granular bed. The cohesion of the substrate reduces the height and length of bed forms, bed form friction, and sediment transport rates. A comparison of the mobility of noncohesive sediments in circular pipes obtained in other studies is presented to indicate the generality of these results. [ABSTRACT FROM AUTHOR]

The article intends to examine the developmental stages of one-dimensional, two-dimensional, and three-dimensional models and elucidate their key applications, strength, as well as limitations. It also offers perception about future trends and needs concerning hydrodynamic and sediment transport models. It also concentrates on multidimensional computational models which are the two- and three-dimensional models. It also highlights an overview of the one-dimensional models to provide a comparison of the one-dimensional model features with the main features of the two- and three-dimensional models.

Results of an experimental study on clear-water scour at submerged cylindrical obstacles (circular cylinders) in uniform bed sediments under steady flow are presented. The scour depths at submerged circular cylinders are compared with the scour depths at corresponding unsubmerged cylinders (extended above the free surface of flow) of the same diameters under similar flow and bed sediment conditions. The scour depth decreases with an increase in submergence ratio. A submergence factor is introduced to determine the scour depth at a submerged cylinder from the information of the scour depth at an unsubmerged cylinder of the same diameter. In addition, the flow fields along the upstream vertical plane of symmetry of unsubmerged and submerged cylinders are presented through vector plots, which reveal that the dimension and strength of the horseshoe vortex decreases with an increase in submergence ratio. The horseshoe vortex circulations, which decrease with an increase in submergence ratio, are computed from the vorticity contours by using the Stokes theorem. [ABSTRACT FROM AUTHOR]

Technical note discusses a detailed approach to dimensional analysis for the bridge pier scour phenomenon and the introduction of flow intensity. It demonstrates the dependence of critical upstream velocity on the rest of the parameters describing the process and its implications on dimensional analysis. Assuming that the viscous effects are negligible in the local scour phenomenon, it is concluded that the flow intensity of the approaching undisturbed flow is not an adequate parameter to describe the process in usual laboratory conditions. A new proposal is established. [ABSTRACT FROM AUTHOR]

The results of an experimental investigation of riprap stability at wing-wall abutments are reported. The aim of the experiments was the determination of the size of riprap stones necessary to resist shear failure by the flow. The results, which were obtained under a wide range of mobile-bed conditions, are compared with predictions of riprap stone size given by existing equations. Two existing methods, with the addition of suitable factors of safety, are shown to give stable stone size for riprap layers at wing-wall abutments under mobile-bed conditions. It is noted that consideration needs also to be given to filter protection, edge effects, and the effects of bed-form undermining in the design of such riprap layers. [ABSTRACT FROM AUTHOR]

The process of breach erosion of river embankments depends on the interaction among flow, sediment transport, and the corresponding morphological changes. Levees often consist of noncohesive material with a wide range of grain sizes. The dam material is mainly eroded due to the transport capacity of the overtopping water. Both bed load and suspended load are of importance. For breach formation, the lateral erosion due to slope instabilities has a significant impact. A depth averaged, two-dimensional numerical model was developed to account for these processes. The sensitivity of the discharge through the breach related to different processes and material parameters was investigated and compared to experimental and field data. The results show that the most sensitive parameter of an erosion-based dike-breach simulation is the breach side-slope angle which determines the lateral erosion. The application of the described Model 2dMb to different embankment failures at the Elbe River illustrates its capability in simulating overtopping breaching. [ABSTRACT FROM AUTHOR]

Clear-water scour at circular and square piers, embedded in a sand bed overlain by a thin armor layer of gravels, was experimentally studied. Depending on the pier width, flow depth, armor gravel, and bed-sand sizes, three cases of scour holes at piers in armored beds were recognized. A comparison of the experimental data shows that the scour depth at a pier with an armor layer under limiting stability of the surface particles is greater than that without an armor layer for the same bed sediments, if the secondary armoring formed within the scour hole is scattered. The equations of maximum equilibrium scour depths at piers in armored beds for these cases are proposed. On the other hand, the scour depth with an armor layer is less than that without an armor layer for the same bed sediments, when the scour hole is shielded by the compact secondary armor layer. [ABSTRACT FROM AUTHOR]

Experimental results on scour below a high vertical drop (drop height/critical depth >1) in uniform sands and gravels are presented. The experimental results are used to describe the effects of important parameters, identified from the dimensional analysis, on equilibrium scour depth. The important observations are that the equilibrium scour depth increases with increase in densimetric Froude number, whereas the scour depth decreases with increase in sediment size and tailwater depth. The time scale of scour depth that follows an exponential law is determined. The nondimensional time scale decreases with increase in densimetric Froude number. [ABSTRACT FROM AUTHOR]

The flow characteristics around short, bottom-mounted cylinders were examined with a three-dimensional nonhydrostatic model for Reynolds numbers of 300–3,900 and different obstacle geometries. Simulations using a large-eddy simulation closure scheme reproduce the vortex shedding in the wake, with reasonable Strouhal number comparisons to available laboratory data. The length of the recirculation region is also in good agreement with the data. The sensitivity of the flow to obstacle cross section and length is investigated for a Reynolds number of 500 with square and circular cylinder geometries for nondimensional lengths of 1–15. Model predicted upstream separation was found to be most sensitive to cross section. The predicted downstream recirculation lengths reproduced the nondimensional length dependency of available observations. To highlight the processes relevant to scour, the time-dependent bed shear was evaluated with the mean and peak Shields parameters. Significant wake variability was found which would not be described by the mean alone, indicating that sediment transport models assuming a mean shear will underpredict the transport in the wake. [ABSTRACT FROM AUTHOR]

Sediment management in reservoirs with the help of water jets has motivated this work. Erosion caused by single and multiple submerged circular turbulent wall jets on a noncohesive sediment bed of finite thickness lying on a fixed boundary was studied with the help of laboratory experiments. Different combinations of jet diameter, jet separation, and sediment thickness to jet diameter ratio were tested. Results show a relation between dimensionless parameters characterizing the steady state bed profile and the densimetric particle Froude number F0 given by the velocity at the nozzle and the effective diameter and submerged specific density of the sediment. Evolution of scour with time confirms previous studies where the erosion was found to initially grow with the logarithm of time up to a certain reference time t*. This time, made dimensionless with a time scale tc involving the volume of sediment scoured and the rate of erosion, was also related to the densimetric Froude number. A comparison with studies regarding erosion of a semiinfinite layer of sediment is also presented. [ABSTRACT FROM AUTHOR]

A new model for the critical shear stress and the transport of graded sediment is presented. The model is based on the size distribution of the bed surface and can be used to compute sediment transport rates in numerical simulations with an active layer model. This model makes a distinction between unimodal and bimodal sediments. It is assumed that all size fractions of unimodal sediments have the same critical shear stress while there is selective transport for the gravel fractions of bimodal sediments. A recently published laboratory transport data set is used to calibrate our model. [ABSTRACT FROM AUTHOR]