THRESHOLD FOR SEDIMENT MOTION IN V-SHAPED CHANNELS

 

MIRALI MOHAMMADI and DONALD W KNIGHT

 

School of Civil Engineering, The University Birmingham, Edgbaston,

Birmingham B15 2TT, England, UK.

Tel : (44) 121 414 5075; Fax : (44) 121 414 5075; email : d.w.knight@bham.ac.uk

 

 

ABSTRACT

Sediment threshold experiments were conducted in two types of rigid boundary V-shaped drainage channels, commonly used in bridge kerbside drainage units. Sand and gravel particles were used and the slope-discharge relationships found for threshold conditions. Comparisons were made with the Shields (1936) threshold criterion and the Ackers & White (1973) total load function. The latter equation was found to be more appropriate for design purposes.

 

Keywords: sediment threshold, open channels, bridge deck drainage.

 

INTRODUCTION

The removal of sediment in bridge deck drainage channels is a complex process. In many theories, the boundary shear stress is used as the main parameter defining a stream's transporting power. Since the rate of transport is very sensitive to the transporting power, any inaccuracy in the shear separation procedure may give large errors in the predicted transport rate or threshold condition. The majority of research work on sediment transport has focused on beds formed of the same mobile sediment and only a few researchers have investigated sediment motion over rigid boundaries, e.g. Pedroli (1963), Novak & Nalluri (1975 & 1984), Mayerle et al (1991), Butler et al (1996), Okabe et al (1996) and Mohammadi (1996 &1998).

 

MECHANISMS FOR INCIPIENT SEDIMENT MOTION

The threshold condition for particles requires certain parameters to be considered, namely bed shear stress, critical velocity, cross-sectional shape, fall velocity, material size, and boundary conditions. When the value of the bed friction velocity just exceeds the critical value for initiation of motion, the particles will begin to move. The following approaches are often applied in practice :

 

Critical Velocity Approach - The initiation of motion is assumed to depend upon the critical bed velocity, U_bc, or the critical mean velocity, U_c. A combination of the Shields criterion with Strickler's equation for Manning's n (=0.04d^1/6) gives

(1)

in which d = particle median diameter; R = hydraulic radius; s = relative density ratio; and a = parameter which is a function of the particle shear Reynolds number.

 

Critical Shear Stress Approach - An alternative approach was given by Shields, who assumed that the threshold condition was related to the frictional drag of the flow acting on a layer of sediment particles. He defined those physical parameters which influenced the sediment transport and gave a functional relationship as :

(2)

Thus for a flat bed, when the form drag is absent, then , which is a key assumption in the Shields approach and has been used by many researchers.

 

Lift Force Approach - In this approach it is assumed that incipient motion occurs when the upward force on a sediment particle is just greater than the particle's submerged weight. Vanoni (1975) states the most early work on initiation of particle motion considered only the bed shear stress and completely ignored the lift force on particles, despite both analytical and experimental studies indicating its presence.

 

ACKERS & WHITE TOTAL LOAD FUNCTION

Ackers & White (1973) proposed a total load sediment transport function, based on dimensional analysis as well as some physical arguments. The function relates the sediment transport parameter, G_gr, to the excess of a mobility parameter, F_gr, over its value at initial motion, A. F_gr takes account of the effective shear stress acting on the bed. The basic formulation for a rectangular channel is given by

(3a)

where D_gr = dimensionless grain size parameter, varying from 1.0 for fine sediments (d»0.04mm for quartz bed material) to 60 for coarse sediments (d»2.50mm);

(3b)

where n = a transition parameter lying between zero and 1, and a = a parameter related to the roughness, estimated to lie between 10 & 12;

(3c)

where, G_gr = the general transport parameter and C_v = the volumetric sediment concentration. The following power relationship was obtained :

(3d)

Updated values of empirical parameters are given in Ackers (1993).

 

EXPERIMENTAL APPARATUS AND METHODOLOGY

 

Apparatus

The experiments were carried out under uniform flow conditions in a 15m long glass-walled rigid tilting flume having a working cross section of 460 mm wide ´ 380 mm deep. The flume rotated about a central pivot, and was supported by two hydraulic jacks which formed part of a motorised slope control system. Two experimental channels were built inside the flume. The first was made from a number of 0.5m long commercially available 300mm bridge deck drainage units, manufactured by Cast Iron Services (CIS), with a cross section of 278mm wide ´ 76mm deep, and the second was made from PVC sheets into a V-shaped channel with a cross section of 460mm wide ´ 300mm deep (see Fig. 1).

 

Fig. 1 : Cross sectional shape of the channels

a) CIS 300mm: B=278mm, H=56mm & Dh=20mm

b) V-shaped 460mm: B=460mm, H=250mm & Dh=50mm

 

Water discharges were measured by Venturi, electromagnetic or Dall tube flow meters, depending on the required flow. The test section consisted of a 12m long zone and water depths were measured at 0.5m intervals along the flume by means of a pointer gauge attached to a roving instrument carriage. Stage-discharge curves were produced for five slopes of 0.1%, 0.2%, 0.4%. 0.9% and 1.6%. A Preston tube with a 4.075mm outer diameter was used for the boundary shear stress measurements and a miniature 13mm diameter propeller meter was used for the velocity measurements.

 

Threshold condition measurements for sediment particles

A series of tests was carried out for two sizes of materials, a sand size of d₃₅=0.80mm and a road/concrete aggregate size of d₃₅=7.22mm. A total of seven channel bed slopes were used (0.1%, 0.2%, 0.4%, 0.5%, 0.6%, 0.9%, and 1.6%). For each bed slope, a discharge was set and uniform flow established. The threshold condition was then studied visually, increasing the discharge in 1 l/s increments. When the threshold condition occurred, the discharge and slope were recorded. Previously obtained stage-discharge results were then used to estimate the corresponding normal depths. Measurements of velocity and boundary shear stress were also made in both channels. See Fig. 2 for a typical isovel plot.

 

Fig. 2 : An example of Isovel plots (u/U) in a V-shaped channel; S0=0.2%, Q=125.89 l/s & U=1.253 m/s

 

Observations

It was observed that after placing sand particles over the whole width of the channel bed, most particles tended to move/slide towards the centreline and the lowest part of the V-shape. Transport then took place in distinct isolated mounds, and it was generally difficult to observe different modes of individual particle movement. By contrast, various modes of particle movement (at the threshold condition) were observed for the gravel particles. The shape of the side of a particle in contact with the bed at times of critical motion determined the mode of movement. It was also observed that in many tests the movement of a particle took place in front (upstream) of rows of particles settled on the bed. Therefore particles tended to jump onto the others and cause an obstacle (by locking together) against the flow.

 

DISCUSSION OF RESULTS

 

Fig. 3 : Comparison of the threshold condition results for two types of sediment

 

CIS channel - Fig. 3 shows the threshold conditions for both sand and gravel for the 300mm CIS units. The best fit equations for sand (d₃₅=0.80mm) and gravel (d₃₅=7.22mm) were as follows :

(4a) and (4b)

where S₀ = channel bed slope times 10³ and Q = discharge in ls^-1. The Shields (1936) and Ackers & White (1973) incipient motion equations for both materials were also examined and are shown with the experimental data in Fig. 4 for sand and Fig. 5 for the aggregate material. As can be seen from these two Figures, both materials show close agreement with the Ackers & White equation. The Shields approach is good for small sediment sizes but less so for large aggregate particles.

 

Fig. 4 : Comparison of the threshold condition results of sand size d35=0.8mm with Ackers & White and Shields equations

 

 

Fig. 5 : Comparison of the threshold condition results of aggregate size d35=7.22mm with Ackers & White and Shields equations

 

V-shaped channel - In order to understand the behaviour of flow in V-shaped channels in more detail, some measurements of boundary shear stress and velocity were undertaken in the larger 460mm wide V-shaped channel. Typical lateral distributions of local boundary shear stress are shown in Fig. 6 for selected slopes and a discharge of around 10 ls^-1.

Fig. 6 : Distribution of boundary shear stress adjusted to mean energy slope value

 

As can be seen, for mild slopes (S₀ = 0.1%) the distribution is very uniform, whereas for steeper channels and higher flow rates some perturbations were observed, indicating the presence of secondary currents and shape effects. Both of these affect the threshold of sediment motion. Fig. 7 shows the threshold conditions and best fit equations for both sand and gravel in the 460mm V-shaped channel.

 

Fig. 7 : Slope-Discharge results for incipient motion condition (V-shaped channel)

 

Fig. 8 shows a comparison between the threshold conditions for sand and gravel in both types of V-shaped channel. This Figure indicates that for a given channel bed slope and particle size, the CIS channel needs a higher flow discharge than the V-shaped channel in order to exceed the threshold condition.

Fig. 8 : A comparison of the results of CIS 300mm & V-shaped bottom channels

 

CONCLUSIONS

1) A power law relationship between S0 and Q, is suitable for defining the incipient motion of both sand and gravel particles in V-shaped channels.

2) The critical velocity and shear stress for particles resting on a smooth rigid bed are substantially lower than for particles of the same size forming a movable bed. The Shields criterion thus overestimates threshold conditions for rigid beds.

3) The Shields (1936) threshold criterion and the Ackers & White (1973) sediment transport equation, with the imposed condition of A = Fgr, reveal that the Ackers & White equation is more suitable than the Shields one.

4) The discharge required for incipient motion in the CIS 300mm channel is a little higher than that for the V-shaped bottom channel for both sand and gravel particles (see Fig. 8). However the effect of cross sectional shape, resistance and boundary shear stress distribution also influence this particular result.

 

ACKNOWLEDGEMENTS

The first author acknowledges the assistance of the Ministry of Culture and Higher Education of Iran, and The University of Urmia, who sponsored his PhD studies.

 

REFERENCES

Ackers, P., 1993, "Sediment transport in open channels: Ackers and White Update", Proc. Instn. Civ. Engrs., Wat., Marit. & Energy, 101, Dec., Technical Note 619, pp. 247-249.

Ackers, P. and White, W.R., 1973, "Sediment transport: new approach and analysis", J. Hydraulics Div., ASCE, Vol. 99, HY11, November, pp 2041-2060.

Butler, D., May R.W.P; and Ackers, J.C., 1996, "Sediment transport in sewers Part 1: Background", Proc. Instn Civ. Engrs., Wat, Marit. & Energy, Paper 10956, June, pp 103-112.

Mayerle, R., Nalluri, C. and Novak, P., 1991, "Sediment transport in rigid bed conveyances", J. of Hydr. Research, IAHR, Vol. 29, No. 4, pp 475-495.

Mohammadi, M., 1996, "An introduction to bridge drainage hydraulics", Proc. 2nd Int. Conf. on Bridges, AmirKabir University of Technology (Tehran Polytechnic), 10-12 September, Tehran, Iran.

Mohammadi, M., 1998, "Resistance to flow and the Influence of boundary shear stress on sediment transport in smooth rigid boundary channels; PhD Thesis, School of Civil Engineering, The University of Birmingham, England.

Novak, P. and Nalluri, C., 1975, "Sediment transport in smooth fixed bed channels", J. Hydraulics Div., ASCE, Vol. 101, HY9, September, pp 1139-1154.

Novak, P. and Nalluri, C., 1984, "Incipient motion of sediment particles over fixed beds", J. Hydr. Research, IAHR, Vol. 22, No. 3, pp 181-197.

Okabe, T., Anase, Y. and Yamashita, H., 1996, "A formula for bed load capacity of flow on smooth and fixed beds", J. of Hydroscience and Hydr. Eng., JSCE, Vol. 14, No. 1, June, pp. 25-35.

Pedroli, R., 1963, "Bed load transportation in channels with fixed and smooth inverts", Mitteillung des Eidg. Amtes fur Wasserwirtschaft, Dienst Exemplar, No. 43, Bern, Switzerland.

Shields, A., 1936, "Application of similarity principles and turbulence research to bed load movement", Versuchsant fur Wasserbau und Schiffbau, Berlin, No. 26. (in German).

Vanoni, V.A., 1975, Sedimentation Engineering, Manual No. 54, ASCE, New York.