EROSION OF SEDIMENT LAYER OVER RIGID BED

M.H. Omid¹ and R. Narayanan²

¹Postgraduate Student, Department of Civil and Construction Eng., UMIST, Manchester.

²Reader, Department of Civil and Construction Eng., UMIST, Manchester.

Abstract: The erosion of a layer of sediment of nearly uniform size on a rigid smooth bed due to clear and sediment-laden water has been investigated. The erosion takes place as a wave travelling downstream. The speed of the wave front is related to the upstream velocity of flow. The thickness of the erosion wave is found to be a function of the upstream specific energy. The structure of sediment motion with sediment-laden water is different from that with clear water particularly in the region upstream of the erosion front. The studies are expected to be useful in determining the time required to flush out a layer of deposited sediments in channels.

Keywords: erosion, deposited sediment, hydraulics, irrigation, sewers

1 INTRODUCTION

The transport of sediments along rigid channels is of importance to the design and operation of sewers, lined irrigation canals and channel in treatment works. For the design of sewers, the sediment transporting capacity of flow in a rigid circular channel is determined for the case of the so-called limit of deposition (Novak and Nalluri, May et al, Mayerle and Ackers et al). Nalluri et al, Ab Ghani, May and Perrusquia and Nalluri provide empirical equations for sediment transport in circular channels with deposited bed.

The purpose of the present investigations is to study how a layer of uniform sediments of limited extent resting on the rigid bed of a rectangular channel is eroded by flow of clear water and water with different sediment concentrations. The study is restricted to steady incoming flow and sediments of nearly uniform size moving purely along the bed.

2 EXPERIMENTAL INVESTIGATIONS

Experiments were carried out in a tilting flume 305 mm wide and 12.2 m long with glass sides and smooth bed, and of rectangular cross-section (Figure 1). The flume is provided with a sediment trap at its downstream end. The sediments collected in the basket were weighed by a digital weighing scale. A tailgate consisting of a set of rotating flaps provided various degrees of openings without causing undue backwater effects into the channel. Experiments were carried out both with clear water and with water with sediments at different concentrations. In the latter experiments, an electromagnetic vibrator placed at 5 m upstream of the test reach is used to inject sediment at desired uniform rates. Different diameters of sediments, thickness of sediment layer, flow rates, water depths, channel slopes and rates of sediment injection have been considered in the experiments.

3 EROSION PATTERNS WITH SEDIMENT-LADEN AND CLEAR WATER

Figure 2 shows typically the bed profiles assumed by a stretch of sediment layer at different stages of erosion due to clear water. Figure 2a shows simply the initial condition of the sediment bed of uniform thickness. As the erosion starts to occur, a raised bed develops at the front very quickly (Figure 2b). In Figure 2b are also shown the main features of the erosion wave in cross-section and the symbols used in this paper to denote various quantities. After an elapse of certain time depending on the velocity of flow and the sediment diameter, the layer of sediments attains a developed state as shown in Figure 2b and 2c. The front of this erosion wave in plan is V-shaped (Figure 2d). Sediments eroded at the front travel along the nearly flat crest of the erosion wave and deposit at the downstream end at a sloping step.

When the incoming flow carries sediments, the sediment layer on the rigid bed behaves similar to that with clear water but the leading edge of the layer takes up a V-shape with its vertex pointing upstream as shown in Figure 2 by breaker line. The structure of erosion and the movement of the sediments at the layer of sediments are essentially the same as with clear water. However for a given velocity, as the sediment concentration increases, the vertex of the erosion front moves forward because some of the incoming sediments are deposited over there. The remaining sediments along with those eroded at the front of the erosion wave move along the crest of the wave to be deposited downstream. Further increase of sediment supply produces pockets of sediment deposit upstream of the triangular front of the erosion wave. With elapse of time these deposits grow bigger to occupy the whole width of the flume. However these upstream deposits of injected sediments are separated from the layer which is placed before the start of the experiments and whose erosion is of concern in this paper.

The back of the wave moves faster than the front so that the crest length increases with time. The frontal speed decreases with increase of sediment concentration in the incoming flow. In the developed state of erosion, as seen in Figure 2b d_S1 remains essentially constant. Temporal variations of thickness of the erosion wave is shown in Figure 3. The region downstream of the wave is slowly eroded away and is a flat bed or is made up of dunes depending on the sediment diameter, initial thickness of the bed and the flow velocity. When the flow velocity is sufficiently large, the dunes disintegrate to form sediment pockets separated by clear rigid bed of the channel.

4 EROSION WAVE

As mentioned already, the leading edge of the sediment deposit erodes to assume a form similar to a moving wave, which in its developed state is of nearly uniform mean thickness d_S1. In Figure 4 d_S1 is shown as a function of the specific energy E_Supstream of the erosion wave. d_S1 and E_S are made dimensionless with respect to D₅₀. D₅₀ is sediment diameter for which 50% of the sediment is finer. Figure 4 includes all the data collected for various sediment diameters, initial thickness, slopes and flow rates considered in our investigations. Erosion wave thickness was found to be almost independent of the concentration of sediment inflow upstream of the deposited bed. This is demonstrated in Figure 5 where the thickness of the erosion wave is plotted against the upstream specific energy for different inflow sediment concentrations.

The speed at which the erosion front V_S1 in clear water conditions moves downstream is shown as dependent on the upstream velocity of the flow V_up in Figure 6a, 6b and 6c. Both V_S1 and V_up are non-dimensionalised using [g (S_S-1) D₅₀]^0.5. g is the gravitational acceleration and S_s is the relative density of the sediments. Each of the figures is relevant to a range of d_i/D₅₀ as shown in Figure 6, d_i being the initial thickness of the sediment bed before the erosion starts. Knowledge of this speed is important from the point of view of time required to flush out a given layer of sediment from the rigid channel.

When sediments are injected into the flow upstream of deposited bed, the velocity of erosion wave decreases with the increase of sediment concentration of the incoming flow. Figure 7 shows the erosion wave velocity as a function of the upstream flow velocity for different sediment concentration. Evidently, larger flow velocity and less concentration of sediment inflow cause greater speed of retreat of the front of sediment deposit. The results shown in Figure 7 are relevant to sediment size of 1.33 mm and initial bed thickness of 20mm.

5 CONCLUSIONS

The erosion of a layer of nearly uniform sediments on a rigid bed in a rectangular channel by incoming flow of different concentrations has been investigated experimentally. Only the motion of the sediments purely along the bed is considered.

(1) An erosion wave is formed with a V-shaped front followed by a raised bed over the initial bed of nearly uniform thickness and then a step at the downstream end. Sediments eroded at the front move along the raised bed to be deposited at the step downstream. The length of the wave (crest length) increases with time till the downstream step reaches the sediment trap.

(2) The thickness of the raised bed is shown to be a function of the specific energy of the flow and the diameter of the sediment.

(3) The wave front moves downstream with speed that is related to the upstream flow velocity, diameter of sediments, sediment concentration of incoming flow and initial thickness of the bed.

(4) The results presented in this paper can be used to find the time required to flush out cohesion less deposited sediments from rectangular channels by means of clear water.

References

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