EXPERIMENTAL STUDY OF STAGE-DISCHARGE RELATIONSHIPS AND SEDIMENT TRANSPORT RATES IN A COMPOUND CHANNEL 

Xiaonan Tang and Donald W. Knight

The University of Birmingham,

Edgbaston, Birmingham, B15 2TT, UK

E-mail: xntang@hotmail.com & d.w.knight@bham.ac.uk 

Abstract: Experimental results are presented concerning stage-discharge relationships, resistance and sediment transport rates for compound channels with a mobile main channel bed and rigid smooth or roughened floodplains.  The variation of resistance with depth, the effect of bed forms, and the abrupt reduction in resistance at the bankfull stage, are all linked to the stage-discharge relationships.  The sediment transport rates G_s (g/s) are shown to gradually increase with increasing flow rate, but the concentration X (ppm) only increases up to the bankfull stage, after which it gradually decreases as the overbank flow increases.  The effect of floodplain roughness on G_s is also described. 

Keywords: overbank flow, compound channel, sediment transport, flow resistance

1    INTRODUCTION

In the practice of river engineering, sediment movement has been receiving more attention in recent years, as indicated by Jayawardena et al (1999).  Despite this, our understanding of alluvial hydraulics is still not very good, even for uniform sand and inbank flows.  Our understanding of flood flows and morphological response is inevitably weaker, mainly due to the complexity of two-phase flow and the difficulty of measurement under extreme conditions.  However, in the last few decades, a considerable amount of research has been undertaken on overbank flows, especially concerning the main channel/floodplain interaction effect on the conveyance capacity of the channel, the flow resistance, and the proportional distribution of discharge between the main channel and any associated floodplains. See Knight & Shiono (1996) and Knight (1999). Of the several methods for predicting the stage-discharge relationship in compound channels, the 1-D model developed by Ackers (1993) and the analytically based solution to the depth-averaged Navier-Stokes equation, developed by Shiono & Knight (1991), are perhaps among the most promising methods currently available.

Due to the complexity of the flow-sediment interaction, the majority of research on sediment movement has been undertaken in simple channels with inbank flow. More recently, some research has been undertaken on sediment transport in compound channels with overbank flow (Ayyoubzadeh, 1997; Brown, 1997; Atabay & Knight, 1999; Knight et al, 1999). Although this has enhanced our understanding of the interaction of the floodplain flow with the main channel flow and its impact on the flow resistance, sediment bed forms, transport rate and channel geomorphology, most studies have been carried out with smooth floodplains.  In order to rectify this, a systemic series of laboratory experiments have recently been conducted in a compound channel with different floodplain roughnesses, and are the subject of paper.  Particular attention is paid to the stage-discharge relationships, the variation of resistance with depth, and the sediment transport rates.

2    EXPERIMENTAL PROCEDURES

The experiments were performed in a non-tilting 22m long flume with a test length of 18m at the University of Birmingham. The flume was 1213 mm wide, and configured into a two stage channel with a 398mm wide, 50mm deep sand main channel and two 407.3mm wide floodplains, as shown in Fig. 1. The flume had a water circulation system, where the water was supplied through 50mm, 100mm and 150mm pipelines, with discharges measured by an electro-magnetic flow meter, a Venturi meter and a Dall tube respectively.  Sand, with a d₃₅ = 0.80mm was re-circulated in the flume via a slurry pump and the 50mm pipeline.  Water surface profiles were measured directly using pointer gauges, and uniform flow was set up through adjustments to three tailgates until the mean water surface slope was equal to the valley slope of the floodplain, fixed at 2.204 x 10^-3. A preliminary development of bed was allowed for in establishing normal depth flow. The floodplains were made of smooth PVC material for the study of smooth floodplains, whereas for the study of roughened floodplains, four different floodplain roughnesses were created using metal meshes. These meshes had a width of 355mm, a height of 145mm and an angle of 30 degrees, as shown in Fig. 2, and were placed at 4 different interval spacings (l = 3m, 1m, 0.5m and 0.25m) on each floodplain.

For a required test discharge, preliminary experiments were undertaken and the tailgates were calibrated so that the mean water surface slope and the mean longitudinal bed slope would be set equal to the valley slope of the channel, fixed at 2.024 x 10^-3. These settings were found be very reliable and the experiments could be repeated at will. During each experiment measurements were made of velocity and transport rates. Velocity measurements were taken at 0.4 of the local depth on the sand main channel and the floodplains. Sediment samples were collected manually over 5 ~ 6 minute intervals for at least 5 times for each experiment whilst the dune migrations movements are recorded manually over at least 1 hour.  For large discharges, bed profiles were also measured at the conclusion of each experiment with an automatic touch-sensitive bed profiler.

3    EXPERIMENTAL RESULTS

STAGE-DISCHARGE RELATIONSHIPS

It is of interest to compare the differences between the stage-discharge relationships for alluvial channels with inbank and overbank flows with different floodplain roughness.  The measured H~Q relationships are shown in Fig. 3, with the experimental data for rigid compound channels (Atabay & Knight, 1999) included as well. In each case, the data are best fitted by a power function, in a form of H = aQ^b, where a and b are constants, given in Table 1, in which H is the flow depth (m) and Q is the discharge (m³/s). As can be seen from Fig. 3, there is not a

Table 1    Values of a and b of H~Q relationships

discontinuity in the H~Q relationship at the bankfull depth of 0.05m for compound channels with mobile beds, whereas comparable data for rigid compound channels do show sharp discontinuities, as reported by Knight & Demetriou (1983), Knight, Shiono & Pirt (1989), Atabay & Knight (1999) and Myers et al. (1999). As would be expected, the discharges are reduced for mobile bed channels compared with the rigid channels, for both inbank and overbank flows. Furthermore, for the mobile bed compound channels, the discharge decreases as the roughness on the floodplains increases for the same flow depth.

4    RESISTANCE RELATIONSHIPS

Standard hydraulic laws were used to represent the resistance to flow, as used by most practising engineers, given by the following equivalent forms:

U = R^2/3 S^1/2 / n           or   U = [(8g/f) RS ]^1/2              (1)

where U is the channel mean velocity, R is the hydraulic radius, S is the friction slope (equal to the valley slope S_o for uniform flow), g is the gravitational acceleration, and n & f are the Manning and the Darcy-Weisbach resistance coefficients respectively.

The experimental results for n are shown in Fig. 4, together with some data for the rigid channels for the purpose of comparison. Figs. 4 shows that the resistance coefficient has an abrupt transition at the bankfull stage, whether the channel is rigid or mobile. The overall values of n (and f) are much larger for the mobile channels than for the rigid channels at the same flow depth. In the mobile bed cases, n increase as the roughness of the floodplain increases, i.e. l from infinity (smooth) to 0.25 m (roughest).

5    VELOCITY DISTRIBUTION AND ZONAL DISCHARGE RELATIONSHIPS

The lateral distribution of mean streamwise velocity was measured over the cross-section, including the sand-bed main channel and the rigid floodplains.  A typical transverse velocity distribution is shown in Fig. 5, which shows that the velocity distribution is symmetric, and that there is a minimum value around the centre of the main channel.

The zonal discharges can be calculated by integrating the velocity data over the cross-section. The proportions of the total flow within the main channel and on the floodplains were thus determined and are shown in Fig. 6 for both smooth and rough cases. Despite some scatter in the data, largely due to the effect of dune movement, certain trends are apparent.  The best-fit equations through the data for the proportion of flow occurring on the floodplain are:

Smooth:

Q_fp% = -435.03 Dr³ +352.63 Dr² + 40.167 Dr – 0.3645    R² = 0.9851  (2)

Rough:

Q_fp% = a Dr² + b Dr +c                         (3)

Where

and Dr = (H-h)/H, Q_fp% = Q_fp/Q_t x 100, Q_fp = the discharge on the floodplain, and Q_t = the total flow.  Thus the proportion of main channel discharge, Q_mc%, can be obtained from

Q_mc% = 100 - Q_fp%                            (4)

As might be expected, Fig. 6 clearly indicates that the proportion of discharge in the main channel increases as the roughness of the floodplain increases.

Sediment Transport Rates and Bed Forms

An important objective of these experiments was to investigate how the flow structure affects the sediment transport rate.  The determination of the sediment transport rate is important in river engineering because it governs the behaviour of the river bed.  It also helps in understanding the non-equilibrium state, and in specifying the sediment capacity of a channel once an equilibrium state is reached.

The measured sediment transport rates, expressed either in term of weight per second, G_s (g/s) or ppm, X, are shown in Fig. 7 and Fig. 8 respectively, where the sediment transport rates are shown plotted against the total discharge, Q_t.  As can be seen from these Figures, G_s increases as the flow rate increases, but X (ppm) only increases up to around the bankfull stage, after which it gradually decreases with increasing overbank flow.  As would be expected, Gs decreases as the roughness of the floodplain increases.  A preliminary analysis on the measured data gives the following function:

ln G_s = k₁ + k₂ ln Q + k₃ /Q                            (5)

where G_s is in g/s, Q is in m³/s and the coefficients are as follows:

For an alluvial river various bed forms, such as ripples, dune, bars and riffles, occur on the channel bed, depending on the intensity of the flow.  Ripples are small bed forms and occur during very low flows.  Dunes are more common, and are much larger than ripples but smaller than bars and riffles.  The dimensions of a typical dune were found for all the experiments, as indicated in Fig. 9.  This Figure shows that for a comparable discharge, the dune size for the compound channel with a roughened floodplain is much bigger than that for the channel with a smooth floodplain.  The data also shows that the dune height increases as the floodplain roughness increases, for the more or less same discharge.

6    CONCLUSIONS

(1) A simple power function relationship exists for the stage-discharge relationship of flow in mobile compound channels, with either smooth or rough floodplains.

(2) The flow resistance changes abruptly at the bankfull stage, and varies significantly with depth. For overbank flow, it generally increases as the flow depth increases, particularly for a rough floodplain.

(3) The transverse distribution of depth-averaged velocity is quite symmetric, with a minimum value occurring at the centre of the main channel for rough floodplain cases.

(4) The sediment transport rate Gs increases as the flow rate increases, but X (ppm) only increases up to the bankfull stage, after which it gradually decreases with increasing overbank flow. Gs decreases as the roughness of the floodplain increases.

(5) Dune size increases as the roughness of floodplain in a compound channel increases, for the more or less same discharge.

References

Ackers, P (1983), "Stage-discharge functions for two-stage channels: The impact of new research", J. Instn.Water & Environmental Management, Vol.7 (1), 52-61.

Atabay, S. and Knight, D.W., 1999, "Stage discharge and resistance relationships for laboratory alluvial channels with overbank flow", In River Sedimentation [Eds A W Jayawardena, J H W Lee & Z Y Wang], Proc. Seventh International Symposium on River Sedimentation, Hong Kong, December 1998, pp 223-229.

Ayyoubzadeh, S A (1997), "Hydraulic aspects of straight compound channel flow and bed load sediment transport", PhD thesis, The University of Birmingham, UK.

Brown, F. A. (1997), "Sediment transport in river channels at high stage", PhD thesis, The University of Birmingham, UK.

Jayawardena, A.W., Lee, J.H.W. and Wang, Z.Y., (1999), “River Sedimentation”, Proc. 7^th Int. Symp. on River Sedimentation, Hong Kong, December 1998, Balkema, pp 1- 1015.

Knight D. W. & J D Demetriou (1983), "Flood plain and main channel flow interaction", J. of Hydraulic Division, ASCE, Vol.108, No.3, 443-452.

Knight D. W, Shiono K & J Pirt (1989), "Prediction of depth mean velocity and discharge in natural rivers with overbank flow", Proc. Int. Conf. On Hydraulic and Environmental Modelling of Coastal, Estuarine and River Waters, University of Bradford, Sept. 419-428.

Knight, D.W. and Shiono, K., 1996, "River channel and floodplain hydraulics", in Floodplain Processes, (Eds Anderson, Walling & Bates), Chapter 5, J Wiley, pp 139-181.

Knight, D.W., Brown F.A., Ayyoubzadeh S.A. & Atabay, S., 1999, "Sediment transport in river models with overbank flow", In River Sedimentation [Eds A W Jayawardena, J H W Lee & Z Y Wang], Proc. Seventh International Symposium on River Sedimentation, Hong Kong, 16 - 18 December 1998, Balkema, pp 19-25.

Knight, D.W., 1999, "Flow mechanisms and sediment transport in compound channels", Proc. 1st Sino-US Workshop on Sediment Transport and Disasters, 15-17 March, Special Issue of International Journal of Sediment Research, [Eds Z. Y. Wang, T. W. Soong, & B.C. Yen], Vol. 14, No. 2, Beijing, China, pp 217-236.

Knight, D.W., Brown, F.A., Valentine, E.M., Nalluri, C., Bathurst, J.C., Benson, I.A., Myers, W.R.C., Lyness, J.F., and Cassells, J.B., 1999, "The response of straight mobile bed channels to inbank and overbank flows", Proc. Instn. of Civil Engineers, Water, Maritime and Energy Division, London, Vol. 136, Dec., pp 211-224.

Myers W. RC, Knight D. W, Lyness J F, Cassells J, and Brown F A (1999), "Resistance coefficients for inbank and overbank flows", Proc. Instn. of Civil Engineers, Water Maritime & Energy, Vol.136, June, 105-115.

Shiono K. & Knight D. W (1991), "Turbulent open channel flows with variable depth across the channel", J. of Hydraulic Research. IAHR, Vol.19, No.1, 43-59.

Fig. 1    Schematic cross section of the flume at University of Birmingham

Fig. 2    Schematic of metal mesh for the roughness on the floodplain

Fig. 3    Comparison of H~Q relationship for mobile compound channels with smooth & rough floodplains

Fig. 4    Relationship of manning's coefficient (n) versus flow depths

Fig. 5    Laterial variation of depth-averaged velocity (Ud) with a roughened loodplain (l=0.25m)

Fig. 6    Zonal discharge percentage (%Q) for mobile compound channels with rough floodplains

Fig. 7    Comparison of sediment transport rate G_s for smooth & rough floodplains

Fig. 8    Sediment concentration vs discharge for smooth & rough floodplain compound channel

 Fig. 9    Standarised bed level variance for the smooth (Q=27.15l/s) and rough (l=3m, Q=27.20l/s) floodplains