Maximum Local Scour Depth at Bridge Piers under Unsteady Flow

The temporal effect of hydrograph on local scour depth is investigated under clear-water scour condition. By analyzing the characteristics of scour-depth evolutions at bridge piers for different rising hydrographs, a relation for estimating the maximum scour depth in uniform sediment is proposed. In the relation, the flow unsteadiness effect is taken into account by an unsteady flow parameter combining the peak-flow intensity and time-to-peak factors. For nonuniform sediment with d84 employed as the effective sediment size, this relation can yield reasonably good results of the maximum scour depth under rising hydrograph.     

Bridge Pier Scour under Flood Waves

The effect of a single-peaked flood wave on pier scour is investigated both theoretically and experimentally. The conditions considered involve clear-water scour of a cohesionless material of given median sediment size and sediment nonuniformity, an approach flow characterized by a flow depth and velocity, a circular-shaped cylindrical bridge pier, and a flood hydrograph defined by its time to peak and peak discharge. A previously proposed formula for scour advance under a constant discharge was applied to the unsteady approach flow. The generalized temporal scour development along with the end scour depth are presented in terms of mainly the densimetric particle Froude number based on the maximum approach flow velocity and the median sediment size. The effect of the remaining parameters on the end scour depth is discussed and predictions are demonstrated to be essentially in agreement with model observations.     

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.     

Temporal Variation of Scour Depth at Nonuniform Cylindrical Piers

The paper proposes a semiempirical model to estimate the temporal development of scour depth at cylindrical piers with unexposed foundations. A cylindrical pier with a foundation is considered as nonuniform pier. The concept of primary vortex and the principle of volumetric rate of sediment transport are used to develop a methodology to characterize the rate of evolution of the scour hole at nonuniform cylindrical piers. The model also simulates the entire scouring process at nonuniform cylindrical piers having the discontinuous surface located below the initial bed level. The scouring process includes three zones; viz Zone 1 having the scouring phenomenon similar to that of a uniform pier, Zone 2 in which the scour depth remains unchanged with its value equal to the depth of the top level of foundation below the initial bed level while the dimensions of the scour hole increase, and in Zone 3 the geometry pier foundation influences the scouring process. A concept of superposition using an effective pier diameter is proposed to simulate the scouring process in Zone 3. In addition, the laboratory experiments were conducted to utilize the laboratory results for the validation of the model. The simulated results obtained from the proposed model are in good agreement with the present experimental results and also other experimental data. Also, the effect of unsteadiness of flow is incorporated in the model and the results of the model are compared with the experimental data. The model agrees satisfactorily with the experimental data.     

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.     

Effect of Sediment Size Scaling on Physical Modeling of Bridge Pier Scour

Local pier scour experiments were performed in the laboratory to investigate the effect of relative sediment size on pier scour depth using three uniform sediment sizes and three bridge pier designs at different geometric model scales. When the data from a large number of experimental and field investigations are filtered according to a Froude number criterion, the effect of relative sediment size on dimensionless pier scour depth is brought into focus. The choice of sediment size in the laboratory model distorts the value of the ratio of pier width to sediment size in comparison with the prototype which in turn causes larger values of scour depth in the laboratory than in the field. This model distortion due to sediment size is shown to be related to the scaling of the large-scale unsteadiness of the horseshoe vortex by studying the relevant time scales of its coherent structure upstream of a bridge pier using acoustic Doppler velocimeter measurements. Observations of sediment movement, probability distributions of velocity components, and phase-averaging of velocity measured upstream of a bridge pier reveal properties of coherent motions that are discussed in terms of their contribution to the relationship between dimensionless pier scour depth and the ratio of pier width to sediment size over a large range of physical scales.     

Field Measurements and Simulation of Bridge Scour Depth Variations during Floods

An understanding of bridge scour mechanisms during floods in a fluvial river is very important for cost-effective bridge foundation design. Reliable bridge scour data for flood events are limited. In this study, field experiments were performed at the Si-Lo Bridge in the lower Cho-Shui River, the longest river in Taiwan, to collect scour-depth data using a sliding magnetic collar, a steel rod, and a numbered-brick column. By separating each scour component, a methodology for simulating the temporal variations of the total scour depth under unsteady flow conditions is proposed. The proposed total-scour model integrates three scour components, namely general scour, contraction scour, and local scour. The collected field data, comprising both general scour and total scour depths, are used to validate the applicability of the proposed model. Based on the peak flow discharges during floods, a comparison of the local scour depths calculated using several commonly used equilibrium local scour formulas indicates that most equations may overestimate the local scour depth.     

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.     

Riprap Failure at Circular Bridge Piers

Riprap of bridge piers is placed to prevent scour and to secure the pier from failure. Riprap is therefore an addition to a pier to increase its performance against scour. The present research intends to present three basic scour mechanisms associated with circular-shaped bridge piers in rivers first, to introduce then a number of selected experiments for a range of hydraulic, geometric, and sedimentologic conditions, and finally to describe a novel procedure for assessing the safety of these river elements against failure. This procedure is based on the Shields diagram relating to sediment entrainment in a uniform and flat sediment bed subjected by a water flow. The Shields approach is extended for the presence of a circular-shaped pier that is protected by a circular-arranged riprap layer of equal size elements. The design procedure presented in the following thus reduces to the entrainment condition of a pier for equal riprap and the sediment sizes and to the Shields entrainment condition when the pier diameter degenerates to 0.     

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.     

Scour Downstream of an Apron Due to Submerged Horizontal Jets

The results of an experimental investigation on scour of noncohesive sediment beds (uniform and nonuniform sediments) downstream of an apron due to a submerged horizontal jet issuing from a sluice opening are presented. Attempts are made to explain the similarity existing in the scour process and profiles (including dune in the downstream of the scour hole). The scour profiles at different times follow a particular geometrical similarity and can be expressed by the combination of two polynomials. Using experimental scour depth at different times, the time variation of scour depth is scaled by an exponential law, where time scale increases linearly with densimetric Froude number. The equilibrium scour depth, related to the sediment size relative to the sluice opening, decreases with increase in sediment size and sluice opening. On the other hand, the equilibrium scour depth increases with increase in densimetric Froude number. The variation of equilibrium scour depth with tailwater depth indicates a critical tailwater depth corresponding to a minimum equilibrium scour depth. The effect of sediment gradation on scour depth is pronounced for nonuniform sediments, which reduce scour depth significantly due to formation of an armor layer, and therefore prompted study of the reduction of scour depth by a launching apron placed downstream of the rigid apron. The results show that the average reduction of scour depth by placing a launching apron was 39%, having a maximum of 57.3% and a minimum of 16.2%. The characteristic parameters affecting maximum equilibrium scour depth are identified based on the physical reasoning and dimensional analysis. Equation of maximum equilibrium scour depth obtained empirically agrees well with the experimental data.     

Time Variation of Scour at Abutments

A semiempirical model is presented to compute the time variation of scour depth in an evolving scour hole at short abutments (abutment length/flow depth ? 1), namely the vertical wall, 45° wing wall, and semicircular, in uniform and nonuniform sediments under a clear water scour condition. The methodology developed for computing the time variation of scour depth is based on the concept of the conservation of the mass of sediment, considering the primary vortex system as the main agent of scouring, and assuming a layer-by-layer scouring process. For an equilibrium scour hole, the characteristic parameters affecting the nondimensional equilibrium scour depth (scour depth/abutment length), identified based on the physical reasoning and dimensional analysis, are excess abutment Froude number, flow depth—abutment length ratio, and abutment length—sediment diameter ratio. Experiments were conducted for time variation and equilibrium scour depths at different sizes of vertical walls, 45° wing walls and semicircular abutments in uniform and nonuniform sediments under limiting clear water scour conditions (approaching flow velocity nearly equal to the critical velocity for bed sediments). The present model corresponds closely with the data of time variation of scour depth in uniform and nonuniform sediments obtained from the present experiments and reported by different investigators.     

3D Unsteady RANS Modeling of Complex Hydraulic Engineering Flows. II: Model Validation and Flow Physics

A chimera overset grid flow solver is developed for solving the unsteady Reynolds-averaged Navier-Stokes (RANS) equations in arbitrarily complex, multiconnected domains. The details of the numerical method were presented in Part I of this paper. In this work, the method is validated and applied to investigate the physics of flow past a real-life bridge foundation mounted on a fixed flat bed. It is shown that the numerical model can reproduce large-scale unsteady vortices that contain a significant portion of the total turbulence kinetic energy. These coherent motions cannot be captured in previous steady three-dimensional (3D) models. To validate the importance of the unsteady motions, experiments are conducted in the Georgia Institute of Technology scour flume facility. The measured mean velocity and turbulence kinetic energy profiles are compared with the numerical simulation results and are shown to be in good agreement with the numerical simulations. A series of numerical tests is carried out to examine the sensitivity of the solutions to grid refinement and investigate the effect of inflow and far-field boundary conditions. As further validation of the numerical results, the sensitivity of the turbulence kinetic energy profiles on either side of the complex pier bent to a slight asymmetry of the approach flow observed in the experiments is reproduced by the numerical model. In addition, the computed flat-bed flow characteristics are analyzed in comparison with the scour patterns observed in the laboratory to identify key flow features responsible for the initiation of scour. Regions of maximum shear velocity are shown to correspond to maximum scour depths in the shear zone to either side of the upstream pier, but numerical values of vertical velocity are found to be very important in explaining scour and deposition patterns immediately upstream and downstream of the pier bent.     

Experimental Investigation of Clear-Water Local Scour at Pile Groups

Experiments of local scour around pile groups are carried out under steady clear-water scour conditions. A variety of conditions including different pile group arrangements, spacing, flow rates, and sediment grain sizes are considered. In total, 112 experiments are carried out. It is observed that the scour-hole depth for some cases of pile groups increases as much as two times more than its magnitude for the case of single piles. The data from this study and some laboratory experiment data from previous works are used to derive a correction factor to predict the maximum local scour depth for the pile groups. Two well-known equations, i.e., Federal Highway Administration, Hydraulic Engineering Circular No. 18, HEC-18 (reported by Richardson and Davis in 2001) and the New Zealand pier scour equation (reported by Melville and Coleman in 2000) are considered. The prediction of scour hole based on the present correction agrees well with the observations.     

Temporal Evolution of Clear-Water Pier and Abutment Scour

Scour related to bridge hydraulics received much attention in the past decade, including its relation to flood hydrology and hydraulic processes in addition to steady flow. This paper presents new research on bridge pier and abutment scour based on a large data set collected at ETH Zurich, Switzerland. In total six different sediments were tested, of which three were uniform. Also a large variety of scour elements were considered, from 1 to 60% of the channel width, and flow depths ranging from 1 to about 40% of the channel width. Using similarity arguments and the analogy to flow resistance, an equation for temporal scour evolution is proposed and verified with the available literature data. The agreement of the present scour equation with both the VAW data and the literature data were considered sufficient in terms of river engineering accuracy, provided limitations relating to hydraulic, granulometric, and geometrical parameters are satisfied. These limitations are discussed and refer particularly to effects of viscosity, which were excluded in the present scour equation.     

Similitude of Large-Scale Turbulence in Experiments on Local Scour at Cylinders

The writers’ experiments on local scour at vertical cylinders placed in a sand bed show that similitude of large-scale turbulence is an important consideration influencing equilibrium depth of local scour. For the range of cylinder diameters used in their experiments, the writers identify a direct trend between equilibrium scour depth (normalized with cylinder diameter) and the intensity and frequency of large-scale turbulence shed from each cylinder; values of normalized scour depth increased when cylinder diameter decreased. The writers offer a scour-depth adjustment factor to account for this trend, which essentially is a scale effect incurred with experiments involving three independent length scales: cylinder diameter, bed-particle diameter, and flow depth. The consequent similitude consideration, or scale effect, has general significance for laboratory studies of local scour associated with hydraulic structures in sediment beds.     

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.     

Riprap Protection at Bridge Piers

Although riprap is the most commonly employed countermeasure against scouring around bridge piers, few studies exist of riprap performance under live-bed conditions. In this study, failure mechanisms, stability, and placement level effects for riprap at bridge piers are considered experimentally. Under clear-water conditions, riprap is subject to shear, winnowing, and edge failure. Under live-bed conditions, a fourth failure mechanism, destabilization by bed-form progression, becomes important. Destabilization by bed-form progression is dependent on the destabilizing influence of bed-form troughs as they pass the pier. Experiments were used to assess the ability of riprap stones to protect bridge piers under a wide range of flow conditions. The effects of placing the riprap layer at depth within the sediment bed, rather than level with the bed surface, were investigated also. The study showed that, as the flow velocity increases, the ability of riprap stones to protect a pier decreases asymptotically until the scour depth in the riprap layer reaches that of an equivalent unprotected pier. In addition, it was found that the deeper the placement level the less exposed the riprap was to destabilizing bed forms and the better the protection against local scour. Lowering the placement level also meant that the riprap performed better than for surface-placed layers as the flow velocity increased. The mode of riprap failure is also changed as the placement level below the bed surface is lowered. A pier riprap size-prediction equation is proposed, including a parameter to account for placement level.     

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.     

Depth-Averaged Two-Dimensional Numerical Modeling of Unsteady Flow and Nonuniform Sediment Transport in Open Channels

A depth-averaged two-dimensional (2D) numerical model for unsteady flow and nonuniform sediment transport in open channels is established using the finite volume method on a nonstaggered, curvilinear grid. The 2D shallow water equations are solved by the SIMPLE(C) algorithms with the Rhie and Chow’s momentum interpolation technique. The proposed sediment transport model adopts a nonequilibrium approach for nonuniform total-load sediment transport. The bed load and suspended load are calculated separately or jointly according to sediment transport mode. The sediment transport capacity is determined by four formulas which are capable of accounting for the hiding and exposure effects among different size classes. An empirical formula is proposed to consider the effects of the gravity on the sediment transport capacity and the bed-load movement direction in channels with steep slopes. Flow and sediment transport are simulated in a decoupled manner, but the sediment module adopts a coupling procedure for the computations of sediment transport, bed change, and bed material sorting. The model has been tested against several experimental and field cases, showing good agreement between the simulated results and measured data.