Scour of Cohesive Soil by Submerged Circular Turbulent Impinging Jets

This paper introduces a method for estimating the scour in cohesive soils produced by a submerged vertical circular turbulent impinging jet. Determining scour in cohesive soils is a complex problem, partly because the clay particles within the soil are held together by electrochemical forces that are not easily quantifiable. As well, erosion occurs in many forms, such as the removal of individual particles or as large chunks of soil. Results of a laboratory study of scour by a circular impinging jet of a cohesive soil, consisting of 40% clay, 53% silt, and 7% fine sand, are presented. Analysis based on the mechanics of the impinging jets shows that the dimensions of the scour hole at an equilibrium state of scour are a function of the momentum flux from the jet, the impingement height (for “large” impingement heights), the viscosity and density of the eroding fluid, and the critical shear stress of the soil. Mass erosion was the predominant type of erosion observed.     

Clear-Water Scour below Underwater Pipelines under Steady Flow

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.     

Clear-Water Scour at Piers in Sand Beds with an Armor Layer of Gravels

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.     

Bridge Pier Scour in Clay-Sand Mixed Sediments at Near-Threshold Velocity for Sand

Local scour at circular bridge piers embedded in a clay-sand-mixed bed was investigated in laboratory flume experiments. The effects of clay content, water content, and sand size on maximum equilibrium scour depth, equilibrium scour hole geometry, scouring process, and time variation of scour were studied at velocities close to the threshold velocities for the sand in the clay-sand mixture. It was observed that clay content and water content were the key parameters that effect the scouring process, scour hole geometry, and maximum equilibrium scour depth. The bridge pier scouring process in clay-sand mixtures involved different dominating modes for removal of sediment from scour hole: chunks-of-aggregates, aggregate-by-aggregate, and particle-by-particle. Regression-based equations for estimation of nondimensional maximum scour depth and scour hole diameter for piers embedded in clay-sand mixtures having clay content of <40% and water content of <40% were proposed as functions of pier Froude number, clay content, water content, and bed shear strength.     

Flume Tests for Scour in Clay at Circular Piers

Local scour at circular piers founded on clay was studied experimentally in the laboratory to compare the depth of scour in sand and in clay and to investigate the effects of the Reynolds number, Froude number, and approach flow depth on scour depth. The depths of scour in front, at the side, and in the back of the piers were measured as a function of time under steady, gradually varied flow conditions. The measured scour-depth-versus-time curves were fitted with a hyperbola to estimate the equilibrium scour depths. The extrapolated equilibrium scour depths were compared with values predicted by the Federal Highway Administration equation. The results showed that although the rates of scour were much slower in clay than in sand, equilibrium scour in clay was about the same as in sand. It was found that the shape of the scour hole correlates with the pier Reynolds number. At low Reynolds numbers, the depth of scour was about the same all around the piers. At higher Reynolds numbers, the scour holes developed mainly behind the piers with much less scour in front of the piers. It was also found that the extrapolated equilibrium scour depth correlates well with the pier Reynolds number and that the Froude number and relative water depth did not have a significant effect on the scour depth for these experimental conditions.     

Local Scour Caused by Submerged Square Jets under Model Ice Cover

An experimental study was carried out to understand the local scour process of noncohesive sand beds caused by submerged three-dimensional square jets under model ice covered conditions. The characteristics of asymptotic scour have been investigated by varying the tailwater depth, the densimetric Froude number, the grain size of the bed material, and three different types of water surface conditions (open-water flow, smooth ice covered flow, and rough ice covered flow). Results show that the local scour process under covered conditions is different from that under open water, especially at lower tailwater depths. Further, for the range of test conditions, the effect of the ice cover is reduced when the bed is composed of finer sand particles or when the densimetric Froude number is small.     

Characteristics of Horseshoe Vortex in Developing Scour Holes at Piers

The outcome of an experimental study on the turbulent horseshoe vortex flow within the developing (intermediate stages and equilibrium) scour holes at cylindrical piers measured by an acoustic Doppler velocimeter (ADV) are presented. Since the primary objective was to analyze the evolution of the turbulent flow characteristics of a horseshoe vortex within a developing scour hole, the flow zone downstream of the pier was beyond the scope of the investigation. Experiments were conducted for the approaching flow having undisturbed flow depth ( = 0.25?m) greater than twice the pier diameter and the depth-averaged approaching flow velocity ( = 0.357?m/s) about 95% of the critical velocity of the uniform bed sand that had a median diameter of 0.81?mm. The flow measurements by the ADV were taken within the intermediate (having depths of 0.25, 0.5, and 0.75 times the equilibrium scour depth) and equilibrium scour holes (frozen by spraying glue) at a circular pier of diameter 0.12?m. In order to have a comparative study, the ADV measurements within an equilibrium scour hole at a square pier (side facing the approaching flow) of sides equaling the diameter of the circular pier were also taken. The contours of the time-averaged velocities, turbulence intensities, and Reynolds stresses at different azimuthal planes (0, 45, and 90°) are presented. Vector plots of the flow field at azimuthal planes reveal the evolution of the characteristics of the horseshoe vortex flow associated with a downflow from intermediate stages to equilibrium condition of scour holes. The bed-shear stresses are determined from the Reynolds stress distributions. The flow characteristics of the horseshoe vortex are discussed from the point of view of the similarity with the velocity and turbulence characteristic scales. The imperative observation is that the flow and turbulence intensities in the horseshoe vortex flow in a developing scour hole are reasonably similar.     

Effect of Upward Seepage on Scour and Flow Downstream of an Apron due to Submerged Jets

The upward seepage through the bed sediment downstream of an apron of a sluice gate structure is a common occurrence due to afflux of the flow level between the upstream and downstream reaches of a sluice gate. The result of an experimental investigation on the characteristics of the scour hole and the flow-field downstream of an apron due to submerged jets under the influence of upward seepage through the bed sediment is presented. Experiments were run for the conditions of submerged jets, having submergence factors from 0.99 to 1.72 and jet Froude numbers from 3.15 to 4.87, over beds of sediments (median sizes = 0.8, 1.86, and 3?mm) downstream of an apron under upward seepage velocities. The characteristic lengths of the scour hole determined from the scour profiles are: the maximum equilibrium scour depth, the horizontal distance of the location of maximum scour depth from the edge of the apron, the horizontal extent of the scour hole from the edge of the apron, the dune height, and the horizontal distance of the dune crest from the edge of the apron, all of which were found to increase with an increase in the seepage velocity. Using experimental results, the time variation of the scour depth is scaled by an exponential law, where the nondimensional time scale decreases linearly with an increase in the ratio of the seepage velocity to the issuing jet velocity. The flow field in the submerged jets over both the apron and within the scour hole was detected using an acoustic Doppler velocimeter. The vertical distributions of time-averaged velocities, turbulence intensities and Reynolds stress at different streamwise distances, and the horizontal distribution of bed-shear stress are plotted for the conditions of scour holes with and without upward seepage. Vector plots of the flow field show that the rate of decay of the submerged jet decreases with an increase in the seepage velocity. The flow characteristics in the scour holes are analyzed in the context of the influence of upward seepage velocity on the decay of the velocity and turbulence intensities and the growth of the boundary layer.     

Scour due to Crossing Jets at Fixed Vertical Angle

Plunge pool scour is an important topic in hydraulic structures design. Numerous studies have been done in past years to understand the scour phenomenon due to plunging jets. These studies finally aimed at reducing the risk of structural undermining and collapse. Scour holes created under various hydraulic and geometrical conditions were analyzed for both two-dimensional and three-dimensional cases, and methods to reduce the scour were also investigated. In the current study, an attempt was made to quantify the feasibility of using crossing jets. The scour process was analyzed, and various relationships were presented to predict the main geometrical parameters, i.e., maximum scour hole depth, scour hole length, and scour hole width. Scour profiles were also compared with those due to an equivalent single jet. The main parameters on which the scour geometry depends were found as the densimetric Froude number of the jet, the crossing angle between the jets, the distance between the crossing point and the water surface level, and the water depth. All experiments have been carried out for a fixed vertical angle of 45°.     

Design Method of Time-Dependent Local Scour at Circular Bridge Pier

A reliable prediction of local scour depth related to hydrological characteristics such as peak discharge, and time corresponding to the equilibrium scour depth is essential for the efficient design of bridge pier foundation. In this paper, a design method to predict the local scour depth with time is proposed. An experimental program was carried out using a cylindrical pier placed in uniform beds under clear-water flows. The pier scour depth was calculated on the basis of a sediment transport equation. Equilibrium local scour depth is reached when the bed-shear stress tends to critical bed-shear stress in the scour hole. Hence, changes to bed-shear stress at the circular bridge pier should be incorporated in the sediment transport theory. The proposed method follows experimental data of various sources.     

Influence of Cohesion on Scour under Submerged Circular Vertical Jets

The results of an experimental study on scour under submerged circular vertical jets of water in cohesionless and cohesive sediments are presented. The difference between scour patterns in cohesionless and cohesive sediments is identified. In cohesive sediments, the variations of maximum depth and volume of scour have been studied with respect to the percentage of clay content, dry density, antecedent moisture content, etc. Empirical relationships have been proposed for the maximum depth and volume of scour for both nonplastic and plastic cohesive sediments. The range of data for the applicability of the proposed relationships is specified.     

Observations on Sand Jets in Air

This note presents the results of an experimental study of circular sand jets in air from three nozzles of diameter of 19.2, 31.1 and 63.8 mm. It was found that the frontal speeds of the sand jets and the steady sand jet velocity accelerate due to gravity with negligible air resistance. The sand velocity does not appear to be affected by sand particle sizes for the three sizes tested. The diameters of sand jets, as they travel downwards, decrease and gradually approach an asymptotic value after a distance of 120 times of the initial jet diameter. The sand concentration in the jet decreases as the distance from the nozzle increases. Waves were observed at the periphery of the sand jet and some preliminary results of wave speed and wavelength are reported.     

Scour in Long Contractions

Experimental results on local scour in long contractions for uniform and nonuniform sediments (gravels and sands) under clear-water scour are presented. An emphasis was given to conduct the experiments on scour in long contractions for gravels. The findings of the experiments are used to describe the effects of various parameters (obtained from dimensional analysis) on equilibrium scour depth under clear-water scour. The equilibrium scour depth increases with decrease in opening ratio and with increase in sediment size for gravels. But the curves of scour depth versus sediment size have considerable sag at the transition of sand and gravel. The scour depth decreases with increase in densimetric Froude number, for larger opening ratios, and increases with increase in approaching flow depth at lower depths. However, it becomes independent of approaching flow depth at higher flow depths. The effect of sediment gradation on scour depth is pronounced for nonuniform sediments, which reduce scour depth significantly due to the formation of armor layer in the scour hole. Using the continuity and energy equations, a simple analytical model for the computation of clear-water scour depth in long contractions is developed with and without sidewall correction for contracted zone. The models agree satisfactorily with the present and other experimental data. Also, a new empirical equation of maximum equilibrium scour depth, which is based on the experimental data at the limiting stability of sediments in approaching channel under clear-water scour, is proposed. The potential predictors of the maximum equilibrium scour depth in long contractions are compared with the experimental data. The comparisons indicate that the equations given by Komura and Lim are the best predictors among those examined.     

Probability of Exceedance Estimates for Scour Depth around Bridge Piers

Scour at a bridge pier is the formation of a hole around the pier due to the erosion of soil by flowing water; this hole in the soil reduces the carrying capacity of the foundation and the pier. Excessive scour can cause a bridge pier to fail without warning. Current predictions of the depth of the scour hole around a bridge pier are based on deterministic models. This paper considers two alternative deterministic models to predict scour depth. For each deterministic model, a corresponding probabilistic model is constructed using a Bayesian statistical approach and available field and experimental data. The developed probabilistic models account for the estimated bias in the deterministic models and for the model uncertainty. Parameters from both prediction models are compared to determine their accuracy. The developed probabilistic models are used to estimate the probability of exceedance of scour depth around bridge piers. The method is demonstrated on an example bridge pier. The paper addresses model uncertainties for given hydrologic variables. Hydrologic uncertainties have been presented in a separate paper.     

Experimental Investigation on Influence of Aeration on Plane Jet Scour

A series of experiments was conducted to investigate the influence of aeration on plane jet scour. The scour holes caused by the aerated and the nonaerated jets were compared under the same conditions of jet velocity, water discharge per unit width, and tailwater depth. A quantitative relationship between the air concentration of jet and the relative scour depth was established, which is not affected by jet velocity and water discharge per unit width. The profile of the scour hole was found to mainly depend on the scour depth under the same conditions of bed material and tailwater depth and affected very little by the air concentration itself in the test range. The aeration influences the shape of the scour hole mainly through decreasing the scour depth. The scour holes formed under aerated and nonaerated conditions are self-similar.     

Erosion of Finite Thickness Sediment Beds by Single and Multiple Circular Jets

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.     

Experimental Study of Sand and Slurry Jets in Water

This paper presents the results of an experimental study of turbulent sand jets and sand-water slurry jets impinging vertically into a stagnant water body. The jets contained silica sand with a median diameter D50 of 206?μm, and with an initial concentration 0.60 by volume for the sand jets, and 0.055–0.124 by volume for the slurry jets. The jets had densimetric Froude numbers between 2.0 and 5.94. The sand concentration and velocity profiles were measured simultaneously using a novel fiber optical probe, up to a distance of 130do for sand jets, and 65do for slurry jets, where do is the jet diameter at the water surface. The jets were found to have self-similar Gaussian profiles. The centerline sand concentration within the jets was found to decrease rapidly, following trends similar to single phase plumes. The centerline sand velocity profile decreased significantly before reaching a plateau region. The “terminal” centerline sand velocity within this region varies somewhat depending upon sand mass flux, and is between 0.32 and 0.43 m/s. The spreading rates of the jets were found to vary with the particle Froude number. Within the sand jets and the higher Froude number slurry jet, the sand concentration had a smaller spreading rate than the velocity. The other slurry jets had equal concentration/velocity spreading rates. The momentum flux of the sand within the jets was found to decrease sharply, followed by a constant flux below a depth of 25 to 30 jet diameters.     

Physically Based Model for Evaluation of Rock Scour due to High-Velocity Jet Impact

Scour of rock may occur downstream of dam spillways, as a result of the impact of high-velocity jets. The phenomenon is traditionally assessed by means of (semi-) empirical methods. These partially neglect basic physical processes responsible for rock mass breakup. Therefore, a model to evaluate the ultimate depth and time evolution of scour in jointed rock is presented. The model is based on near-prototype scaled experimental investigations of transient water pressures in artificially created rock joints and on a numerical modeling of the measured pressures. It describes two different ways of rock mass destruction, i.e., failure by instantaneous or progressive breakup of closed-end rock joints, and failure by dynamic ejection of single rock blocks. The corresponding computational methods are easily applicable to practice, without neglecting relevant physics. The basic principles are outlined and applied to the well-known scour hole at Cabora-Bassa Dam.     

Effect of Jet Air Content on Plunge Pool Scour

The effect of air discharge on plunge pool scour was investigated by using a simplified experimental configuration. Instead of considering the complete arrangement involving chute and deflector resulting in an air-water jet impinging on a sediment surface, the mixture flow was produced with a circular pipe for which the air concentration and the jet diameter close to impact on the free water surface are known. The results of this study were primarily directed to the definition of a three-phase Froude number that accounts for the combined effects of an air-water mixture jet on scour. The analysis of data allows simple estimates of the scour geometry including a generalized scour profile, the width of scour, and the temporal advance of the extreme scour depths. It was pointed out that for a certain water velocity and selected grain characteristics, the addition of air to the jet results in an increase of scour depth. However, if the reference would be the air-water mixture velocity, scour depth decreases significantly by the addition of air to the jet.     

Characteristics of Submerged Jets in Evolving Scour Hole Downstream of an Apron

This paper reports an experimental investigation on the velocity and turbulence characteristics in an evolving scour hole downstream of an apron due to submerged jets issuing from a sluice opening detected by an acoustic Doppler velocimeter. Experiments were carried out for the conditions of submerged jets, having submergence factors from 0.96 to 1.85 and jet Froude numbers from 2.58 to 4.87, over sediment beds downstream of a rigid apron. The distributions of time-averaged velocity vectors, turbulence intensities, and Reynolds stress at different streamwise distances are plotted for the conditions of initial flat bed, intermediate scour holes, and equilibrium scour hole downstream of an apron. Vector plots of the flow field show that the rate of decay of the submerged jet velocity increases with an increase in scour hole dimension. The bed-shear stresses are determined from the Reynolds stress distributions. The flow characteristics in evolving scour holes are analyzed in the context of self-preservation, growth of the length scale, and decay of the velocity and turbulence characteristics scales. The most significant observation is that the flow in the scour holes (intermediate and equilibrium) is found to be plausibly self-preserving.