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Experimental observations showed that in a compound channel, the free surface elevation transverse to the flow direction in the main channel is different to that in the floodplain in the vicinity of the end section. The non-horizontal transverse free surface profile (sagging at the main channel zone) is due to the differential accelerated flow velocities in the main channel and the floodplains. In this paper, free overfall in compound channels is theoretically modeled, considering vertical subdivisions of flow area into three zones: main channel, left floodplain, and right floodplain. The Froude number in a compound channel should be estimated on the basis of the flow in subdivided zones rather than for the whole cross-section. The finding that the critical depth in the main channel and the floodplains do not coincide has important implications for the determination of the Froude number in compound channels. Applying a momentum equation based on the Boussinesq approximation, equations of end depth that are related to the discharge are developed separately for the subdivided zones. A method to estimate the discharge from the end depths in the main channel and the floodplain is presented through computational steps. The streamwise flow profiles in the main channel and the floodplain, upstream of the end section, are computed using the streamline curvature at free surface. Experiments were conducted in three different shaped symmetrical compound channels to verify the model. The results, obtained using the model, agree satisfactorily with the experimental data. © 2006 International Association of Hydraulic Engineering and Research.

Department of Civil & Infrastructure Engineering

World University root node

Journal of Hydraulic Research

Discharge prediction in compound channels by end depth method

This paper addresses how the turbulent flow field in submerged wall jets responds to an abrupt change from smooth to rough beds. Experiments were conducted for submerged wall jets having different submergence factors and jet Froude numbers. The bed configurations investigated consisted of different combinations of the lengths of smooth beds and the roughness of rough beds. The vertical profiles of time-averaged velocity components, turbulence intensity components and Reynolds stress were detected by an acoustic Doppler velocimeter at different streamwise distances; and the horizontal distributions of bed shear stress were estimated from the Reynolds stress profiles. The flow field displays the decay of jet velocity due to abrupt changes from smooth to rough beds. The boundary layer grows more quickly with increase in roughness of rough beds. The change in bed roughness induces an increased depression of the free surface over the smooth bed. The Reynolds and bed shear stresses are also computed by solving the Navier-Stokes equations. The response of the turbulent flow characteristics of submerged wall jets to abrupt changes from smooth to rough beds is analysed from the point of view of similarity, growth of the length scale, and decay of the velocity and turbulence characteristics scales. The significant observation is that the flow in the fully developed zone is plausibly self-preserving on both smooth and rough beds. Also, the use of a common length scale makes it possible to collapse all the flow data onto a single band; and there is a gradual variation of flow at the junction of the smooth and rough beds. The equilibrium scour profiles downstream of a smooth apron due to submerged wall jets are computed from the threshold condition of the sediment particles on the scoured bed. Use of the modified bed shear stress for the downstream variation of scoured bed permits the computation of the equilibrium scour profiles. The time-variation of maximum scour depth is computed from the bed shear stress with a modification for the time dependence. The agreement between the results obtained from the model and the experimental data is satisfactory. © 2006 Cambridge University Press.

Journal of Fluid Mechanics

Response of velocity and turbulence in submerged wall jets to abrupt changes from smooth to rough beds and its application to scour downstream of an apron

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. © 2006 ASCE.

Journal of Hydraulic Engineering

Scour downstream of an apron due to submerged horizontal jets

An experiment was conducted in a laboratory flume to measure the three-dimensional turbulent flow field, using an acoustic Doppler velocimeter, in a scour hole at a vertical-wall abutment under a clear water scour condition. The distributions of time-averaged velocity components, turbulence intensity components and Reynolds stresses at different vertical sections are presented. In the upstream, a large primary vortex associated with the downflow exists inside the scour hole. On the other hand, in the downstream, the flow field is chaotic due to the vortex shedding. The data presented in this paper would be useful for the development and validation of a flow field model, which can be used for the estimation of scour depth at bridge abutments. © 2005 Elsevier Ltd. All rights reserved.

Flow Measurement and Instrumentation

Velocity and turbulence in a scour hole at a vertical-wall abutment

Closure to "time variation of scour at abutments" by Subhasish Dey and Abdul Karim Barbhuiya

Expressions for the Reynolds stress and bed shear stress are developed for nonuniform unsteady flow in open channels with streamwise sloping beds, assuming universal (logarithmic) velocity distribution law and using the Reynolds and continuity equations of two-dimensional open-channel flow. The computed Reynolds stress distributions are in agreement with experimental data. © ASCE.

Reynolds stress and bed shear in nonuniform unsteady open-channel flow

Results of an experimental investigation into local scour at piers and abutments in uniform gravels under a clear water scour condition are presented. Two types of pier, namely circular and square, and two types of short abutment (abutment length/upstream flow depth < I, for short abutments), namely wing-wall and vertical-wall, were tested. Although scour at piers and abutments has been studied widely in sand beds, it remains almost unexplored in gravel beds. Therefore, different gravel sizes, ranging from 4-1 mm to 14-25 mm, were used in this experimental study. The influence of gravel size on equilibrium scour depth at piers and abutments is prominent. From the experimental results, it is observed that the equilibrium scour depth increases with decrease in gravel size and with increase in pier width and abutment length. The variations of equilibrium scour depth with gravel size for both pier and abutment scour depart considerably from the variations of equilibrium scour depth with sand size. Consequently, for scour at piers and abutments, the resulting sediment size factors for gravels, evaluated by fitting envelope curves, are significantly different from the existing sediment size factor for sands. Combining pier and abutment scour data, an integrated approach to estimating the equilibrium scour depth at a bridge foundation is proposed. Scaling of distorted experimental model results to prototype is also discussed.

Proceedings of the Institution of Civil Engineers: Water Management

Scour of gravel beds at bridge piers and 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. © ASCE.

Time variation of scour at abutments

Nonuniform-unsteady flow in open channels with streamwise sloping beds having uniform upward seepage is theoretically analyzed. Expressions for the Reynolds stress and bed shear stress are developed, assuming a modified logarithmic law of velocity profile due to upward seepage, and using the Reynolds and continuity equations of two-dimensional open channel flow. The computed Reynolds stress profiles are in agreement with the experimental data. © ASCE.

Journal of Engineering Mechanics

Reynolds stress in open channel flow with upward seepage

The characteristics of scour holes in uniform and nonuniform sediments downstream of an apron due to a submerged horizontal jet issuing from a sluice opening are studied experimentally. Attempts are made to explain the similarity existing in the scour profiles (including the dune downstream of the scour hole). From the scour profiles, the characteristic lengths of the scour hole which are determined are: horizontal distance of dune crest from the edge of the apron; dune height; horizontal distance of maximum scour depth from the edge of the apron; horizontal extension of scour hole from the edge of the apron and maximum equilibrium scour depth. For uniform sediments, the horizontal distance of the dune crest from the edge of the apron, the horizontal distance of maximum scour depth from the edge of the apron, the horizontal extension of scour hole from the edge of the apron and the maximum equilibrium scour depth were all found to increase with increase in densimetric Froude number; whereas the dune height decreases with increase in densimetric Froude number. In addition, for nonuniform sediments, the aforementioned characteristic lengths of the scour hole are related to the geometric standard deviation of sediments. The characteristic lengths of the scour hole decrease with an increase in geometric standard deviation of sediments. The application of the findings of the paper to the prototype is discussed, which would assist the practising civil engineer to ascertain the dimensions of a scour hole (scour depth, position of maximum scour depth, extension of scour hole etc.) in uniform and nonuniform sediments downstream of an apron. Importantly, these are the key parameters for designing apron foundations and protective measures for scour downstream of an apron. Future work will focus on field work to prove the scalability of the derived relationship.

Scour downstream of aprons caused by sluices

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. © ASCE.

Scour in long contractions

An experimental investigation on scour at circular and square piers in uniform and non-uniform gravels (fine and medium sizes) under clear-water scour at limiting stability of gravels is presented. From the experimental results, it is observed that the equilibrium scour depth increases with decrease in gravel size. The variation of equilibrium scour depth with gravel sizes departures considerably from that with sand sizes. Consequently, the resulting sediment size factors for gravels, obtained from envelope curve fitting, are significantly different from the existing sediment size factor for sands. The influence of gravel gradation on scour depth is also prominent in non-uniform gravels. The time scales to represent the time variation of scour depth in uniform and non-uniform gravels are determined. For uniform gravels, the non-dimensional time scale increases with increase in pier Froude number and gravel size, whereas for non-uniform gravels, it decreases with increase in geometric standard deviation of particle size distribution of gravels. © 2005 NRC Canada.

Canadian Journal of Civil Engineering

Clear-water scour at bridge piers in fine and medium gravel beds

Experiments were conducted to measure the three-dimensional turbulent flow field, using the acoustic Doppler velocimeter, at a short vertical-wall abutment (ratio of abutment length to approach flow depth less than unity) before and after the development of a scour hole under a clear water scour condition. In the upstream, the presentation of flow field through vectors at vertical sections shows a primary vortex associated with the downflow. In the downstream, the upward flow is comprised of with irregularities owing to the vortex shedding. The flow separation near the bed and within the scour hole is evident from the turbulent kinetic energy distribution. Using Reynolds stresses, the bed shear stresses are calculated. © ASCE.

Flow field at a vertical-wall abutment

This study presents a simplified approach to determine the end depth of a free overfall in horizontal U-shaped channels. The flow over the free overfall is simulated by that over a sharp-crested weir to calculate the end-depth ratio (EDR). The theoretical model is calibrated by the experimental data by considering the coefficient of velocity a free parameter. The EDR is 0.745 up to nondimensional critical depth 0.50; and then it decreases gradually as the nondimensional critical depth increases. A method to estimate discharge from the end depth is presented. The results obtained using the model agree satisfactorily with the experimental data and results obtained from the previous model of the author. Journal of Hydraulic Engineering © ASCE.

End depth in u-shaped channels: A simplified approach

This paper presents a comparative study between the results obtained from the mathematical model and the experimental data of free overfall in circular channels (with and without flat base), following statistical and error analyses of data to ascertain the adequacy of the mathematical model. For the discharge predictions, the mathematical model tuned by an adjustable parameter is found to be accurate one, while the regression (empirical) formula fails to estimate discharge precisely. © 2005 International Association of Hydraulic Engineering and Research.

Free overfall from circular channels with flat base

The three-dimensional turbulent flow field in a scour hole at a semicircular abutment under a clear water regime was experimentally measured in a laboratory flume using an acoustic Doppler velocimeter. The distributions of time-averaged velocity components, turbulent intensity components, turbulent kinetic energy, and Reynolds stresses at different azimuthal planes are presented. Upstream, presentation of flow field through vector plots at azimuthal and horizontal planes shows the existence of a large primary vortex associated with the downflow inside the scour hole. On the other hand, downstream, the flow field is irregular. The bed shear stresses are determined from the Reynolds stresses and velocity gradients. The data presented in this paper would be useful for the development and validation of flow field models, which can be used to determine the strength of the primary vortex that is used to estimate scour depth at bridge abutments. © 2005 NRC Canada.

Turbulent flow field in a scour hole at a semicircular abutment

Measurement of three-dimensional turbulent flow field at a vertical semicircular cylinder, attached to the sidewall of a rectangular channel, was taken in the laboratory using an Acoustic Doppler Velocimeter (ADV). The distributions of time-averaged velocity components, turbulent intensity components, turbulent kinetic energy and Reynolds stresses at different azimuthal planes are presented. The vector plots of flow field at azimuthal and horizontal planes show the presence of a primary vortex upstream of the cylinder. The bed shear stresses in the vicinity of the cylinder are determined from the Reynolds stresses and velocity gradients. © 2003 Elsevier Ltd. All rights reserved.

Measurement of turbulent flow field at a vertical semicircular cylinder attached to the sidewall of a rectangular channel

Experiments on local scour at short abutments (ratio of abutment length to approaching flow depth less than unity), namely vertical-wall, 45° wing-wall, and semicircular, embedded in a bed of relatively fine noncohesive sediment overlain by a thin armor-layer of coarser sediment, were conducted for different flow conditions, thickness of armor-layers, armor-layer, and bed sediments. The abutments were aligned with the approaching flow in a rectangular channel. The armor-layer and the bed underneath it were composed of different combinations of uniform sediments. In the experiments, the approaching flow velocities were restricted to the clear-water scour condition with respect to the armor-layer particles. Depending on the approaching flow conditions, three cases of scour at abutments in armored beds were identified. Effects of different parameters pertaining to scour at abutments are examined. The comparison of the experimental data shows that the scour depth at an abutment with an armor-layer in clear-water scour condition under limiting stability of the surface particles (approaching flow velocity nearly equaling critical velocity for the threshold motion of surface particles) is always greater than that without armor-layer for the same bed sediments. The characteristic parameters affecting the maximum equilibrium nondimensional scour depth (scour depth-abutment length ratio), identified based on the physical reasoning and dimensional analysis, are excess abutment Froude number, flow depth-abutment length ratio, armor-layer thickness-armor particle diameter ratio, and armor particle-bed sediment diameter ratio. The experimental data of clear-water scour condition in thinly armored beds under limiting stability of surface particles were used to determine the equation of maximum equilibrium scour depth through regression analysis. The estimated scour depths were in agreement with the experimental scour depths. Also, an equation of maximum equilibrium scour depth in uniform sediments was obtained. © ASCE.

Clear-water scour at abutments in thinly armored beds

Laboratory experimental results on local scour at short abutments (abutment length:flow depth ratio ≤ 1), namely vertical-wall, 45° wing-wall and semicircular, in uniform and non-uniform sediments under a clear water scour condition are presented. The equilibrium scour depth is related to the sediment size and approaching flow depth relative to the abutment length. The equilibrium scour depth increases with decrease in abutment length and increase in sediment size and flow depth. The scour depth is independent of flow depth at higher flow depths. The effect of sediment gradation on scour depth is pronounced for non-uniform sediments, which reduces scour depth significantly due to the formation of an armour layer in the scour hole. The time variation of scour depth for uniform sediments shows a family of parallel lines for different abutment lengths and sediment sizes. For non-uniform sediments, the time variation of scour depth reduces with increase in non-uniformity of the particle size distribution of sediments. The characteristic parameters affecting the maximum equilibrium non-dimensional scour depth (scour depth:abutment length ratio), 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. The experimental data in clear water scour condition under limiting stability of upstream bed sediments are used to determine the equations of maximum equilibrium scour depth through regression analysis. The estimated scour depths are in agreement with the experimental data.

Clear water scour at abutments

An experimental study on critical bed shear-stress for initial movement of non-cohesive sediment particles under a steady-uniform stream flow on a combined lateral (across the flow direction) and longitudinal (streamwise direction) sloping bed is presented. The aim of this paper is to ascertain that the critical bed shear-stress on a combined lateral and longitudinal sloping bed is adequately represented by the product of critical bed shear-stress ratios for lateral and longitudinal sloping beds. Experiments were carried out with closed-conduit flow, in two ducts having a semicircular invert section, with three sizes of sediments. In laboratory flumes, the uniform flow is a difficult - if not impossible - proposition for a steeply sloping channel, and is impossible to obtain in an adversely sloping channel. To avoid this problem, the experiments were conducted with a closed-conduit flow. The critical bed shear-stresses for experimental runs were estimated from side-wall correction. The experimental data agree satisfactorily with the results obtained from the proposed formula. © IWA Publishing 2004.