Factors affecting confluence scour

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1 & Wang (eds) River Sedimentation 1999., Balkema, Rotterdam. ISBN Factors affecting confluence scour R. B. Rezaur & A. W. Jayawardena. Department of Civil Engineering, The University of Hong Kong, Hong Kong, China. M. M. Hossain Bangladesh University of Engineering and Technology, Bangladesh ABSTRACT: Confluence scour represents a critical component of drainage system geometry and are points at which river morphology and hydrology can change drastically. To understand flow patterns in channel confluences and to isolate the major controls of confluence scour, laboratory experiments in a sand bed flume were conducted on a model stream with tributaries. Using the similarity relationships, dimensionless groups representing scour depth were formulated. It was found that scour depth was a function of confluence angle, relative tributary discharge and relative sediment discharge through the confluence. Confluence angle was found to be the major control of scour depth. Tributary discharge and sediment loads were found to have less influence on scour depth. Scour depth increased rapidly as confluence angle increased from 1 to 7, and more slowly up to 1. Scour depth was found to be a maximum when the angle of incidence of the tributaries was symmetrical and discharges in the tributaries were equal. Scour depth decreased as the relative discharge in the tributary or sediment discharge in the tributaries increased. Angle of incidence studied in this experiment covers the most common naturally occurring confluence angles. Key words: Confluence scour, confluence angle, scour depth, tributary 1 INTRODUCTION The scour occurring downstream of confluence of two channels is called confluence scour (Klassen and Vermeer, 19). Such a confluence can be either the part of a braiding channel system, or it can be the confluence of two rivers. The scour pattern that develops downstream of such a confluence can be characterised as an elongated reach of relatively low bed levels in the middle of the combined downstream channel. Confluence scour is geomorphologically important as nodes in channel network which controls the distribution of sediment downstream and hence the pattern of bar formation and channel migration (Ashmore and Parker, 193). At present it can be said that no comprehensive field measurements are available with which to determine the main controls on scour depth and form, and on which design relationship could be based. The reason for this lack of attention is probably because channel confluences exhibit extremely complex phenomena. The flow patterns in straight unbranched channel are still incompletely understood and flow at the confluence of two channel is not at present susceptible to analysis, except at a rather gross level (Mosley, 191). Scour measurement from large streams at high flows and high velocities can be extremely hazardous. Often it is impossible to gain access to suitable confluences, and the turbid water during high stage makes it impossible to see the form of channels and scour holes. However, if a model stream with tributaries can be produced in the laboratory, confluence scour can be studied under more manageable conditions. Such a model allows an understanding of the dependence of confluence scour on tributary migration and bifurcation. For successful planning and design of scour control, correct prediction of the depth of scour is required. Aiming at identifying the mechanism responsible for this phenomenon and to arrive at methods to predict the maximum scour depth, the objectives of the present studies were to understand flow patterns and processes in channel confluences and to isolate the major controls of confluence scour. 17

2 & Wang (eds) River Sedimentation 1999., Balkema, Rotterdam. ISBN THEORY Major factors affecting confluence scour may be grouped into three categories: (1) flow properties, () sediment properties and (3) a system representation, as presented in scour erosion studies (ASCE, 197; Barr, 193). Sediment properties may be defined by sediment load, density and the mean diameter of particles. Fluid properties of importance are density, mass and velocity. The system representation includes characteristic lengths describing the size and shape of the system; confluence angle, water depth, scour depth, and slope gradient. The process of confluence scour may be expressed as: f1 ( ρ s, D, Qs1, Qs, Qst, v, ρ, µ, Q1, Q, Qt, hs, h, g, θ, δ ) = [1] Sediment Fluid System properties properties representation where, hs = confluence scour depth h = cross sectional average depth of upstream tributaries, h = (h 1 +h )/, suffix 1 and are for left and right tributary g = acceleration due to gravity (cm s ) θ = angle of incidence of tributaries at confluence ( ) δ = average water surface slope v = average tributary flow velocity (cm sec 1 ) ρ = density of water (g cm 3 ) µ = viscosity of fluid (g cm 1 sec 1 ) ρ s = density of soil particle (g cm 3 ) D = bed material size D Q 1, Q, Q t are the discharge in left, right tributaries and total discharges downstream of confluence (cm 3 s 1 ) and Q s1,q s,q st are the sediment discharge in left, right tributaries and total sediment discharge (g min 1 ). After dimensional analysis, Eq. [1] may be reduced to (Hossain, 197; Rezaur, 1991); hs v ρvh ρ s f (,,,, δ, θ, ε1, ε ) = [] h gh µ ρ where, ε 1 = Q 1 Q /.Q t and ε = Q s1 Q s /.Q st are respectively the dimensionless relative water discharge and sediment discharge. Identifying standard parameters, Eq. [] can be written as h s = f 3 ( F, R, δ, θ, ε1, ε ) [3] h where F is the Froude number and R is the Reynolds number. The effects of F, R and δ has no significant influence on scour depth (Mosley, 197; Ashmore and Parker, 193), and for a specific soil and nearly constant temperature the ratio ρ s /ρ becomes constant and therefore can be neglected. Eq. [3] can be simplified as h s = f ( θ, ε1, ε ) [] h where f indicates a functional relationship. Eq. [] describes a general confluence scour model related to confluence angle, relative water and sediment discharges in the tributaries. 3 EXPERIMENTAL APPARATUS Data on confluence scour were collected from a laboratory model of a simple Y shaped confluence on a sand bed flume. The sand bed flume contained well sorted sand with D of.13 mm, and measured 1 m in length, m in width and 1 m in depth. Water was supplied to the tributaries from a constant head water tank by two pumps, two supply lines whose discharges were independently controlled through a series of valves and flow meters. Two sand feeders were used to feed dry sediment at measured rates at the upstream end of the tributaries. Flow depths, 1

3 & Wang (eds) River Sedimentation 1999., Balkema, Rotterdam. ISBN scour depths, longitudinal and cross sectional profile readings were taken by a point gauge mounted on a movable platform. Flow velocities were measured by timing three surface floats (plastic beads) over a cm reach. EXPERIMENTAL PROCEDURE The sand bed flume was filled with a sand silt clay mixture which has been passed through a mm screen to remove pebbles and clay lumps. The final bed surface was given a slope of.1. A channel with two tributaries meeting at a confluence (Figure 1) was then excavated on the sand bed using a wooden form. The tributaries and the main channel were cm wide and 1 cm deep. Water was then supplied to the tributaries. Discharges in the tributaries were adjusted and monitored for every run by the flow meters and valves. At the same time dry sediment was fed at the upstream end of the tributaries at measured rates by two sand feeders. The sediment feed into the tributaries was of the same type as the bed material. Runs were terminated when the tributaries and confluence had reached a state of dynamic equilibrium. This equilibrium was defined in terms of sediment discharge in which all sediment feed at the upstream was transported through and significant erosion and deposition had ceased. From this point on, measurement on cross sectional average water surface, water depth, tributary and scour parameters commenced. Run times for each experiment were between three to four hours. At the end of each experiment, position of maximum scour depth was located and measured. Cross sectional profile and longitudinal profile readings were also taken. After each experimental run, the old channel and bank material was removed and fresh material added, compacted and graded into a smooth surface in preparation for the next run. Figure 1 shows the schematic diagram of the set up of instruments and model confluence in the laboratory flume used in the study. P1 P F Sand feeder Tributary V V1 Scour hole W F1 θ P W Sand feeder θ 1 Tributary 1 Figure 1. Schematic diagram of model confluence and experimental set up on a sand bed flume. P: Pumps; V: Valves; F: Flow meters; W: Water tanks; θ: Confluence angle; P: Moveable platform on rails for gauging stations; Suffix 1 are for left and right tributaries. Three set of runs were carried out. In series A runs, the confluence angle θ was varied between 1 to 1 with symmetrical distribution, Q 1, Q were variables and Q s1, Q s were held constant at g min 1 (Table I). In series B runs, the discharge Q 1, Q and sediment loads Q s1, Q s of tributary 1 and were kept 7 cm 3 s 1 and g min 1 respectively, and initial confluence angle θ was varied between 1 9 with asymmetrical distribution. These runs were carried out with an intention to see the effect of equal and unequal distribution of confluence angle on scour depth. In series C runs, confluence angle was held constant at, and tributary discharge and sediment loads were varied from run to run. Table I, gives a summary of the parameters that were varied, kept constant in different runs. Most of the information that would have been provided by a complete factorial design was thereby obtained. Visual observations with dye injection were made during the runs with a view to study the flow pattern and processes in the channel confluence. 19

4 & Wang (eds) River Sedimentation 1999., Balkema, Rotterdam. ISBN Table I. Summary of parameter combination of experiments θ 1 + θ Q Q 1 ε 1 Q s1 :Q s ε Series ( ) (cm 3 s 1 ) ( ) (g min 1 ) ( ) A B = 1 + 3= 3 + = + = + 7= = 9 C :. [ 7 7]. :. 7 7 = 3 = 1 9 = 3 1 = : :. 7. :. 7. : : 19. Within each series of run, all combination of factor levels (within braces) have been studied RESULTS AND DISCUSSION.1 Relation between scour depth and confluence angle In all the runs of series A and B, sediment discharges in the tributaries were equal, and interest was concentrated on the varying confluence angle θ between 1 1 for each relative tributary discharge of ε 1 =.,.,.. Although erosion and deposition occurred at the bed and banks of the channels, final confluence angle was almost unchanged from the initial confluence angles. Figure and 3 show the cross sectional and longitudinal profile of scour holes for an experiment with symmetrical angle of incidence and equal tributary discharge. An increase in shape and scour depth with increasing confluence angle is observed. The form of the scour hole changes with the angle of incidence. At lower angles the scour is an elongated trough, while at higher angles the scour is more basinlike. Super elevation of water surface over the centre of the scour is also more evident at higher angles water surface 1 3 θ = 3 o θ = o θ = 9 o θ = 1 o Distance from left bank 1 3 Figure. Cross sectional profile of scour hole showing variation of scour depth depending on angle of incidence of the tributaries. h s - -1 water surface θ = 3 o θ = o θ = 9 o θ = 1 o Distance down stream of confluence Figure 3. Longitudinal profiles of scour hole showing variation in scour hole form and depth depending on the angle of incidence of tributaries h s 19

5 & Wang (eds) River Sedimentation 1999., Balkema, Rotterdam. ISBN Scour depth data from series A and B runs along with Mosley (197) data are plotted as a function of confluence angle in Figure. The graph represents a general non linear trend. Scour depth increases rapidly as confluence angle increases from 1 to 7 and then increases slowly up to 1. Scour depths from Mosley (197) are less than that from the present study. However, the general trend is almost the same. This is probably due to the influence of bed material size on scour depth. Mosley (197) used bed materials with a D of.3 mm whereas the present study uses bed material with a D of.13 mm. This suggests that, there is a tendency for scour to be deeper in fine non cohesive bed materials than in larger bed materials. Figure shows a plot of dimensionless scour depth h s /h versus confluence angle θ for data of series A and B experiments (replicate means). The graph shows that the data of series B runs (θ 1 θ ) lies below that of series A (θ 1 =θ ). This suggests that scour depth are greater with symmetrical angle of incidence than with asymmetrical angle of incidence. A regression fit to the data sets reveal a coefficient of determination of.7, suggesting that about 7% of the variation in scour depths can be accounted for variations in confluence angle. This reveals that scour depth may be estimated from a knowledge of confluence and tributary water depths only. However, the applicability of such approach has not been verified with field observations because of scanty field data on confluence scour. 1 Trend line Mosley (197) Confluence angle θ ( ο ) Figure. Scour depth vs. confluence angle (all data) Dimensionless scour depth h s /h 1 1 h s /h = 3.73ln(θ) 9.31, (θ 1 = θ ) h s /h = 3.33ln(θ) 1.137, (θ 1 /= θ ) Confluence angle θ ( o ) Figure. Dimensionless scour depth vs. confluence angle (replicate means, series{a and B runs) 1 1. Relation between scour depth and relative tributary discharge In all the runs of series C, overall confluence angle was held constant at, relative discharge and sediment load were varied to identify their effects on scour depth. Figure shows a plot of series C dimensionless scour depths h s /h as a function of upstream tributary relative discharges ε 1 for different sediment loads. The general trend is linear. This might be due to the reason that the channel reaches an equilibrium either by erosion or deposition in the upstream tributaries as required by the flow condition such that the tributary dept h and scour depth h s adjust among themselves for an equilibrium. The graph also shows that when the relative discharge is a maximum, flow is mostly concentrated in one channel and the scour is relatively less. As the relative discharge decreases the scour depth increases and is a maximum when the tributary discharges are equal. Scour depth also increases as the sediment load decreases. This is probably because flow with less sediment load has more transport capacity and are more erosive than flows with high sediment load (Renard et al., 199)..3 Relation between scour depth and sediment discharge Scour depths from series C experiments are plotted as a function of total sediment discharge Q st through the confluence in Figure 7. This figure shows a non linear trend between scour depth and total sediment discharge through the confluence. The scour depth decreases as the total sediment discharge passing through the confluence increases. However when series C dimensionless scour depths h s /h were plotted against relative sediment discharge ε of upstream tributaries they revealed no consistent trend. This result suggests scour depth may not be 191

6 & Wang (eds) River Sedimentation 1999., Balkema, Rotterdam. ISBN related to the relative amount of sediment passing through each tributary instead scour depth adjusts to the total sediment passing through the confluence rather than the relative amount from each tributary. 1 1 Dimensioless scour depth h s /h Q s1 :Q s = 1:1 Q s1 :Q s = 1: Q s1 :Q s = 1: Dimensionless relative tribytary discharge ε 1 Total sediment load Q st (g min 1 ) Figure. Dimensionless scour depth vs. dimensionless relative tributary discharge (replicate means, Series C) Figure 7. Scour depth vs. total sediment load (Series{C) CONCLUSIONS The experimental study has provided insight on the factors that control confluence scour. The major control of relative scour depth has been shown to be the angle of incidence of the upstream tributaries, with only minor contributions from the relative discharge ε 1 and relative sediment load ε of the two tributaries. Thus the local geometry dominates over hydraulic parameters. Turbulence are relatively poorly developed at confluence angle less than 3. Maximum scour depth occurs when both channels have equal discharge and undergo the same amount of turning and angle of incidence are symmetrical. Scour depth increases rapidly for angle of incidence 1 to 7 and slowly up to 1. The analysis suggests that a reasonable estimate of scour depth can be obtained from a knowledge of only the average depth of the upstream tributaries and the angle of confluence. However, the applicability of such approach needs testing with field data. 7 REFERENCES American Society of Civil Engineers, (197). Sedimentation Engineering, ASCE, New York, NY. p. 7. Ashmore, P., and Parker, G. (193). Confluence scour in course braided stream, Water Resou. Res., 19(): 39. Barr, D. I. H. (193). A survey of procedures for dimensional analysis, International Journal of Mechanical Engineering Education, 11, (3), Hossain, M. M. (197). Introduction to dimensional analysis and similarity models, Paper presented at the Workshop on Similarity Application Resistance, Sediment Transport and Channel Geometry. March 7 9, BUET, Dhaka. Mosley, M. P. (197). An experimental study of channel confluence: J. Geology, : 3 Mosley, M. P. (191). Scour depths in branch channel confluence, Ohau River, Rep. WS39. Water and Soil Sci. Center, Min. of Works and Dev., Christchurch, New Zeland, p.1. Renard, K. G., Lane, L. J., Foster, G. R., and Laflen, J. M. (199). Soil loss estimation, in Agassi, M. (ed.), Soil Erosion Conservation and Rehabilitation, Marcel Dekker, New York. p. 19. Rezaur, R. B. (1991). An experimental study of confluence scour, Unpublished M.Sc. Engineering Thesis, Bangladesh University of Engineering and Technology, Dhaka. Klassen G. J. and Vermeer, K. (19). Confluence scour in large braided rivers with fine bed material, International Conference on Fluvial Hydraulics, Budapest. 19

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