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Sediment Bed Forms in
Sewers
K.H.M. ALI
and R. BURROWS
Department
of Civil Engineering, University of Liverpool, U.K.
e-mail: r.burrows@liverpool.ac.at
ABSTRACT
The paper describes an
experimental and theoretical study of the development of bed forms in sediment
deposits transported within circular pipes representative of sewers. Particles
of various sizes and specific gravities were used in the laboratory experiments
performed with pipes of different diameters. Steady and unsteady water flows
were applied.
Keywords: Sewers, sediments, experiments, ripples, heights, wave length, analysis.
INTRODUCTION
Combined sewerage systems
transport domestic, industrial and storm solids and associated liquid wastes,
for treatment and disposal. Sedimentation in sewers is recognised as a major problem
by the Water Industry, placing a significant maintenance burden upon the
sewerage agencies. In the U.K., many sewers are laid to shallow gradients and
as a consequence, suffer from recurrent sediment deposition. The wash-out of
in-sewer sediment deposits through Combined Sewage Overflows (CSO's) by
rain-induced "foul flushes" further aggravates the pollution caused by storm
discharges. The movement of these solids has come under increased scrutiny in
recent years, due to pollution concerns related to this material.
Based on observation from U.K.
sewerage systems and further afield, three principal modes of solids transport
have been established, although the nature of each mode may be dependent on
site-specific characteristics: suspension, near the bed as "bed-load", and semi
permanent deposits. In addition to these three fundamental modes of transport,
where the deposited sediments are non-cohesive sands, it is possible to
consider bed forms as a mode of transport also as they have been shown to creep
slowly along the invert.
This paper is concerned with a
theoretical and experimental investigation of bed forms. Sediments of different
sizes and specific gravities were used in order to form a better understanding
of scaling laws for sediment transport.
(a) Prediction of ripple heights
Ripple heights were predicted
using two different methods:
(i) open channel relationships for bed load discharge
(ii) sediment discharge relationship for pipes
It can be shown that the momentum
equation in the x-direction, for a pipe (neglecting sediment deposit) is given
by
(1)
Where V = mean velocity; h = elevation
of water surface above the pipe invert (Figure 1); g = acceleration due to
gravity; C = Chezy coefficient; R = hydraulic radius and x = distance along the
pipe.
Using the continuity equation for
the flow of water together with the condition 
Ali (1998) used Eq. (1) to obtain
(2)
where B = width at bed elevation
z; B1 = width of the water surface; Aw = water cross
sectional area; and Q = water discharge.
The sediment continuity equation,
for a pipe, is given by Ali et al (1995)
(3)
where Az = sediment
area; p = porosity and Qs = total sediment discharge.
We have 
Also, the ripple velocity Vb is equal to 
Substituting for 
from Eq. (2) into Eq.
(3) and simplifying
(4)
where F = Froude number 
(i) Ripple height predicted from open channel relationships
After Gill (1971), the following
relationship was used for sediment discharge
(5)
where 
; t0 = boundary
shear stress; t0 = critical
shear stress, C0 and n are constants.
The sediment discharge is also
given by
(6)
where - = ripple height and I = constant depending on the shape
of the bed form (I = 0.5 for
a triangular ripple and 0.636 for a sinusoidal one)
Using Eqs. (4), (5) and (6), we
obtain (see Ali (1998))
(7)
where B0 = 
(ii) Ripple height predicted from pipe relationships
One of the most recent
relationships for sediment discharge in pipes is given by Perrusquia and
Nalluri (1995)
= 
; 
; (8)
; 
(9)
where Y = h - z, u* = shear
velocity; S = specific gravity of particles and U = kinematic viscosity of water. Using Eqs 4, 6, 8 and 9 we
obtain
(10)
EXPERIMENTAL
ARRANGEMENTS
The experiment described herein
were conducted using two pipes of 100mm and 138mm diameters. Both pipes were
about 4.5m long. Details of the experimental setups are given in Ali (1995a,
1998). Uniform particles of different sizes and densities were used in these
experiments.
In the case of sand and synthetic
particles, a level sediment bed was first established. For the crushed Olive
Stones the cohesive-like sediment was thoroughly mixed with freshwater until it
was all in suspension and then pumped into the pipe. A level bed was formed as
the sediment settled under gravity. For each type of sediment, the critical
discharge was determined by slowly increasing the flow rate until a point was
reached where a certain (critical) flow caused a few particles in the top layer
to move. Next, the discharge was slightly increased to allow bed forms to
evolve. Video records were made of the changes in bed elevations. Mean water velocities
were obtained using an ultrasonic and a miniature propeller velocity meters. Bed
elevations were also measured. Runs 1 - 4 were conducted to study the effect of
unsteady water flow on bed form development.
EXPERIMENTAL
RESULTS
For particles with median size d50
= 0.10 - 2.00mm and S = 1.35 - 2.65, the range of ripple heights observed was 5
- 40mm with wave length of 50 - 305mm. Fig. 2 shows an example of bed forms
obtained using white sand with d50 = 0.8mm understeady flow. Figs. 4
and 5 show examples of changes in bed levels produced by unsteady water flows.
THEORETICAL RESULTS
(i) Using open
channel relationships
Good agreement is obtained between
experimental steady flow observations and the theoretical relationship given by
(Eq. 7) if n = 1 and 
and if the effect of
the change in friction factor f (which defines the shear stresses) with mean
velocity is included ( 
). Similar results
were obtained from using the DuBoys formula (not discussed herein (Ali 1998)). Fig.
6 gives predicted changes of bed forms obtained from the numerical integration
of Eq. (3) (see Ali et al 1995) . For
the unsteady flow experiments, it was found that good agreement was obtained
only by selection of the value of n in accordance with the ripple steepness
(height/length) ratio as can be seen in Fig. 7.
ii) Using pipe relationships
Eq. (10) was applied for unsteady flows. The range of the experimental values of observed - was 3 - 40mm but Eq. (10) produced a lower range of only 13 - 18mm.
CONCLUSIONS
Sediments of various size and
specific gravity were used to obtain bed forms for steady and unsteady water
flows. Ripples of heights 5 - 40mm and wave length of 50 - 305mm were obtained.
The sediment discharge relationship based on the work of Gill (Eq. (5)) for
open channels has been shown to be capable of good agreement with experiment
when n is adjusted for the effect of ripple steepness. However, for a wide
range of experiments, using n = 1 gives acceptable results. Perrusquia and
Nalluri's relationship for pipes (Eq. (10)) needs to be improved upon, however,
in order to give acceptable predictions of bed changes in sewers.
REFERENCES
1. Ali,
K.H.M. (1993), "Theoretical and experimental investigation of bed load movement
in long sea outfalls", Report, Civ. Eng. Dept., Univ. of Liverpool, U.K., 1a.
2. Ali,
K.H.M., Burrows, R and Wose, A.E. (1995)", Sedimentation in long sea outfalls
", Water Science and Technology, Vol. 32, No. 2, pp 23 - 132.
3. Ali,
K.H.M. and Karim, O. (1995), "Scour and deposition downstream of hydraulic
structures", Sixth Int. Symp. on River Sedimentation, New Delhi, India, pp 1045
- 1055.
4. Ali,
K.H.M. (1998), "Bed forms in circular sewers", Report, Civ. Eng. Dept., Univ of
Liverpool, U.K., 1998.
5. Perrusquia,
G. and Nalluri, C. (1995), "Modelling of bed-load transport in pipe channels", Int.
Conf. on the Transport and Sedimentation of Solid Particles, Prague.
