Hydraulic performance of sewer pipes with deposited sediments

Q IWA Publishing 2008 Water Science & Technology—WST | 57.11 | 2008

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Hydraulic performance of sewer pipes with deposited sediments Robert Banasiak

ABSTRACT This paper investigates in-sewer sediment deposit behaviour and its influence on the hydraulic performance of sewer pipes. This evaluation is based on experimental results regarding the mobility of non-cohesive and partly cohesive deposits in a partially full circular pipe. The focus of these tests is on the development of bed forms and friction characteristics. In particular, it is

Robert Banasiak Hydraulics Laboratory, Ghent University, Sint-Pietersnieuwstraat 41, 9000 Ghent, Belgium E-mail: [email protected]

investigated to what extent the bed forms from the non-cohesive and (partly) cohesive sediments affect a sewer’s discharge capacity. Based on the laboratory study results and on the existing criteria for sewer design, a generic assessment of a sewer’s hydraulic performance is made. The relative discharge factor for a pipe with sediment deposit is analysed in terms of the thickness and roughness of the deposit. Key words

| bed forms, bed roughness, discharge capacity, sediment, sewer pipes

INTRODUCTION The efficiency and economical performance of sewer

designed according to self-cleansing criteria, with an under-

systems is an essential issue in urban drainage engineering.

standing that the conveyance is kept clean from sediment

It is generally known to be strongly affected by the in-sewer

deposits. This concept is defined as “limit deposition” or “no

sediment transport processes, which are considered as the

deposition”. However, designing sewers so as to have

major uncertainties in sewer hydraulics and water quality

velocities that do not maintain sediment (solids) deposition

modelling (Jack et al. 1996).

can impose severe conditions on sewer design, as this would

It has been noted (Skipworth et al. 1999) that many

require large slopes and high flow velocities (Ota & Nalluri

existing combined sewers have a shallow gradient and

2003). On the other hand, a number of studies show that

experience a wide range of hydraulic conditions (i.e. mostly

designing sewers with limited loose bed deposits can lead to

repeated phases of deposition, erosion, and transport). If an

more economical solutions. As a consequence, the former

initially clean sewer, flowing partially full, is subjected to a

criteria for sewer design were evaluated and renewed in the

sediment-laden flow and the conditions are not optimal to

CIRIA report (Ackers et al. 1996). The new definition of self-

prevent deposition, a sediment bed will develop, potentially

cleansing does not require sewers to be designed to operate

with bed forms. This sediment bed may substantially

completely free from sediment deposits:

increase the bed’s resistance, causing the depth of flow to increase and the velocity to decrease. For combined sewers,

“An efficient self-cleansing sewer is one having a

this can lead to the premature operation of combined-sewer

sediment-transporting capacity that is sufficient to

overflows – which is undesirable.

maintain a balance between the amounts of deposition

The influence of the sediment bed on the flow character-

and erosion, with a time-averaged depth of sediment

istics in sewer pipes is particularly interesting in view of a new

deposit that minimises the combined costs of construc-

design approach. To date, most of the sewers have been

tion, operation, and maintenance.”

doi: 10.2166/wst.2008.287

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R. Banasiak | Hydraulic performance of sewer pipes with sediments

Water Science & Technology—WST | 57.11 | 2008

Allowing some deposition to occur appears to be a viable alternative, because the presence of the deposited bed can

significantly

increase

the

sediment

transporting

capacity of the pipe, despite the adverse effect it might

rough flow regime, the friction factor can be determined on the basis of the equivalent roughness height ks:   1 12R pffi ¼ 2:03 log ks f

ð3Þ

have on the geometry and hydraulic roughness (Butler Despite the advantage of the friction factor f being

et al. 2003).

dimensionless and conceptually sound, n coefficient in Manning’s formula is widely used in engineering practice. However, one must not forget that the use of a constant

SEWER SEDIMENTS: FROM NON-COHESIVE TO COHESIVE

value of n in Manning’s formula is limited to flows in rough channels at moderate velocities and with large hydraulic

When attempting to analyse the hydraulic performance of

radii (conditions that may not be fulfilled in sewer

sewer pipes with sediment deposits, it is important to first

flows). Consequently, the relationship between the Darcy –

recognise the variety of sediment types that can be

Weisbach friction factor and Manning’s coefficient is: sffiffi f R1=6 n¼ pffiffi 8 g

encountered in these systems. The sewer sediments may exhibit a wide range of variation, both in granulometric

ð4Þ

composition and organic components. This depends primarily on the drained area from which the sediments are

When a sediment deposit is present in a pipe, the overall

supplied, on the sewer type and on the pipe’s location in the

resistance consists of two components: one determined by

system. According to Butler et al. (2003), in storm sewers,

the roughness of the pipe wall, and the other determined by

sediments are mainly inorganic and non-cohesive. Yet, some

the roughness of the sediment bed. This composite

deposits may be cementitious and become permanent if they

resistance can be calculated by different methods, as

are left undisturbed for a long period. Sediments in sanitary

summarized by Yen (2002). For pipe flows, the geometrical

sewers generally have cohesive-like properties, due to the

features (i.e. the ratio between the deposit depth t, pipe

nature of the particles and the presence of greases and

diameter D, and flow depth H) are essential in an initial

biological slimes. In combined sewers, the sediments tend to

estimate of how the bed may contribute to the overall

be a combination of the first two types.

resistance. Furthermore, the bed’s roughness depends on its composition and can be considerably increased by the presence of bed forms. According to the concept introduced by Einstein & Barbarossa (1952), the total resistance of the

FLOW FORMULAS AND FRICTION FACTORS

bed is the sum of the grain and form resistances. Using The flow in sewer pipes can be calculated using either the Darcy-Weisbach formula sffiffiffiffiffiffiffi sffiffi 8gRS 8 U¼ ¼ u f f *

Manning’s roughness coefficient, this is written as: 0

00

nb ¼ nb þ nb ð1Þ

ð5Þ

where the primed part is to assign for the plane bed resistance and the double-primed part for the bed form part.

or the Manning formula U¼

1 2=3 1=2 R S n

Alternatively, in the same linear way, Equation 5 can be written using the friction factor f. ð2Þ

where U is stream velocity, g is gravitational acceleration, R is hydraulic radius, S is energy slope, up is shear velocity

BED FORMS

and f is friction factor, which can be determined by the well

A special feature of flow over a loose sediment bed is the

known Colebrook –White equation. In the turbulent, fully

interaction between the flow and the bed when sediment

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R. Banasiak | Hydraulic performance of sewer pipes with sediments

Water Science & Technology—WST | 57.11 | 2008

transport takes place. The flow activity over a non-cohesive sediment is responsible for the occurrence of a variety of bed forms: ripples at low shear stress, progressively developing dunes, washed-out dunes, and flat beds with increasing flow velocities. At upper flow regimes, anti-dunes and standing waves have been reported. This standard classification, based on observation in open channels, also applies to the flow activity in pipes. Moreover, unlike in open channels, in a single sewer pipe carrying sediments, one can expect the full range of mentioned flow regimes with corresponding bed topographies. The equilibrium ripple dimensions are generally accepted to be principally determined by sediment size, insensitive to the depth of the flow. The appearance of

Figure 1

|

Bed forms for sand (left) and partly cohesive sediment (mixture of sand, clay and organic material) in a semi-circular flume (D ¼ 0.4 m, U ¼ 0.4 m/s, Fr ¼ 0.42).

ripples is restricted to fine sands; coarser sands (larger than

with a mean diameter d50 ¼ 0.19 mm and mixtures of the

, 0.6 mm) are ‘non-rippling’ sediments that form dunes

same sand with kaolinite clay (3– 10% by weight of clay),

(Raudkivi 1990). The equilibrium dune dimensions are

related to the Froude number Fr (Fr ¼ U/(gA/B)0.5, where

primarily a function of flow characteristics (Coleman et al.

A-total water cross-section area, B - free surface width). The

2003). Kleijwegt (1992) suggested that dimensions of ripples

figure also includes a mixture of sand, clay and an organic

and dunes in circular pipes can be successfully predicted,

material (mix s-c-o) that was to mimic real sewer sediment.

using predictors that are derived from open channel

For these mixtures, it has been observed that a drastic

hydraulics. On the other hand, Banasiak & Verhoeven

change in the bed form’s size appears when the clay content

(2007) noted that dunes in pipes appear to be shorter. Torfs

increases from 3 to 6%. This corresponds to a rise in the

et al. (1994) also reported that dunes in the circular cross-

critical shear stress for these mixes with respect to the pure

section are markedly different, compared to flows in a

sand by a factor of about 2. These figures also show that with

rectangular flume. In the circular cross-section, the loose

increasing flow (Fr . 0.5), the transition regime is reached

bed boundary interacts with the side walls, becomes very

and the bed forms flatten; the dunes of sand bed become

irregular, and deeply localized holes appear at points along

longer and lower and the ripples of sand-clay mixtures are

the walls. This was further linked to the specific feature of

washed out.

the shear stress distribution in a circular cross-section (Alvarez-Hermandez 1990). The presence of cohesive particles in the sediment deposit has a considerable effect on the development of bed

BED ROUGHNESS

forms. The cohesive particles increase the deposit’s resistance

The appearance of different bed forms as the flow changes

against erosion, with a more thinly mobilised (active) bed

results in a variation of the bed roughness. Figure 3 presents

layer as a result. The erosion of partly cohesive sediment

the values of Manning’s roughness coefficient correspond-

deposits features the elutriation of fine particles from the

ing to the data shown above. The roughness coefficient

sediment bed and produces a granular layer on top of it.

increases by some 60% with respect to a flat bed when the

Provided that equilibrium sediment transport is reached, this

ripples and dunes are formed from non-cohesive beds.

layer forms ripples of a few millimetres in height. Dunes are

n decreases later, as dunes are washed out, and approaches

inhibited in such a situation. Figure 1 illustrates the different

the value for a flat bed (nb ¼ 0.01). In the case of partly

bed topographies under the same flow conditions for non-

cohesive beds, the rise in roughness is clearly smaller,

cohesive and partly cohesive sediment beds. In addition,

reaching approximately 20%, also having a narrower band

Figure 2 shows the bed form sizes for beds made of sand

due to higher critical shear stresses for beginning of motion.

R. Banasiak | Hydraulic performance of sewer pipes with sediments

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Figure 2

|

Water Science & Technology—WST | 57.11 | 2008

Relative height (left) and length of the bed forms as a function of the Froude number (dots–average, bars –maximum values).

For the transition regime, when the ripples are washed out,

decrease by a potentially increased deposit roughness

the roughness decreases notably towards the value for a flat

(relative to the roughness of the pipe’s walls). The first

granular bottom, but still remains slightly higher than that

influence can easily be assessed, provided that no distinction

for the sand bed.

is made between the roughness of the bed and the wall. When

The variability in flow resistance with regards to flow

the thickness of the deposit increases, the bed surface

rate and the effect of bed forms can also be illustrated by

contributes to a larger extent to the overall n. The bed

means of the water surface’s slope. Figure 4 shows that for

roughness affects only a part of the flow field, in which the

non-cohesive sediment beds, the slope increases signifi-

flow velocity is reduced, and which increases as the bed

cantly due to the development of bed forms and for certain

roughness increases. It might therefore be interesting to have

flow conditions (U between 0.3 and 0.5 m/s) reaches values

a clear insight in the geometrical flow characteristics in a pipe

nearly twice as large as that for partly cohesive beds.

with deposited beds. These geometrical characteristics are the bed hydraulic radius Rb, related to the flow depth H, and the bed water cross-section area Ab as a fraction of the total

IMPLICATION FOR THE SEWER’S PERFORMANCE

water cross-section area. They are presented in Figure 5 for a deposit thickness t equal to 0.1D. It can be seen that the

The reducing factor for the discharge carrying capacity of

influence of the bed on the total flow characteristics

sewer pipes is primarily related to the sedimentation/erosion

diminishes with increasing flow depth; in the current case

processes. This influence can be divided into two categories.

Ab for a half-full flow is less than 0.5A.

First, the discharge carrying capacity can decrease directly by

An assessment of the potential impact of the sediment

reducing the flow cross-sectional area. Second, it can

bed on the flow capacity from a practical perspective

Figure 3

|

Manning’s bed roughness factor versus Froude number (sand d50 ¼ 0.19 mm, deposit thickness t ¼ 0.1D).

Figure 4

|

Water surface slope as a function of mean flow velocity.

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Water Science & Technology—WST | 57.11 | 2008

friction should be less significant. Consequently, the negative effect of the sediment bed on the pipe’s conveyance capacity should be limited. The magnitude of flow reduction in a pipe with deposited beds with varying thickness and deposit roughness is further investigated in Figure 7. In this figure, the relative discharge factor (i.e. the discharge Q for a pipe with deposit related to the discharge for a clean pipe Qt¼0) is plotted against the water depth. The value of pipe wall roughness nw is equal to 0.012 and the bed roughness Figure 5

|

coefficient is assumed to be 0.012 and 0.018. The lower Hydraulic parameters for a pipe with a sediment deposit: t/D ¼ 0.1 and ks,w /ks,b < 1.5.

value of nb stands for a relatively smooth bed that can be expected for a finely graded, (nearly) flat sediment bed. The

requires the estimates of both the sediment bed thickness

upper value of the bed roughness is to account for the

and the bed form development at design or storm

development of bed forms and/or possibly coarser material

conditions. Therefore, an analysis is made by using the

forming the sediment bed. The ratio between the roughness

minimum design criteria in the literature and combining

for pipe walls and the sediment bed nw:nb is then 1:1 and

them with the presented experimental results. The mini-

1.5, respectively. Obviously, as can be seen in Figure 7, the

mum flow velocities in a function of sewer pipe diameter,

discharge reduction increases with the sediment deposit

and an assumption of 2% allowable deposition depth is

thickness and with the bed roughness. However, this

adopted after Butler et al. (2003). The Froude number for

reduction is less than 5% of the clean pipe discharge

these conditions is then calculated, assuming that the pipe is

when the sediment deposit thickness is up to 0.05D and

run half-full. Figure 6 shows that for these assumptions, the

when the deposit has a relatively low roughness height. One

values of Froude number vary between 0.4 and 0.6,

can conclude that the presence of such deposits does not

indicating possible dunes (for a pipe diameter smaller

affect the discharge capacity of the sewer pipe very much.

than 1.0 m) or a bed at transition regime (for larger pipe

To do this, the sediment deposits would need to be thicker,

diameters) if a sediment bed is present. The friction factor

composed of coarser particles, or they would have to be

may then be increased considerably by the possible bed

in the flow regime, allowing them to develop bed forms.

forms. However, if flow velocities are larger than those

As discussed above, however, this cannot always be the case

minimally required at the design, the bed may be expected

in storm conditions.

to be in a higher bed form regime, so the rise in the bed’s

Figure 6

|

Design velocities and Froude number for storm sewers with high sediment loading and 2% allowable deposition.

Figure 7

|

Relative discharge factor for pipe with sediment deposit thickness t ¼ 0.02D, 0.05D and 0.1D (nw ¼ 0.012).

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Water Science & Technology—WST | 57.11 | 2008

discharge capacity reduction may be smaller, in the range

CONCLUSIONS

of 5 – 10%.

Sediment transport and deposition, either undesired or

The final conclusion is that it may indeed be rational

allowed, is an integral part of sewer systems. The influence

and appropriate to design sewer pipelines with an allowable

of sediment deposit on the hydraulic performance may

deposit, as has been proposed in recent literature. However,

be significant, and therefore, its assessment is crucial.

the appearance of bed forms should be analysed and, at

However, such an evaluation should be based on thorough

best, avoided.

knowledge of the nature and behaviour of sediments appearing in sewer pipes. The mobility of non-cohesive sediments induces extra friction to flow, due to bed forms appearing during typically widely varying flow conditions in sewer pipes. The presence of fine sediment fraction in the sediment deposit makes the deposit (partly) cohesive and reduces or even inhibits the formation of these bed forms. Therefore, in terms of the bed roughness—not its erodibility—one can conclude that cohesive-like beds are more favourable to the flow than granular ones. An exception may be made for the transition regime, when the washed-out ripples appear slightly rougher than the washed-out dunes. A prediction of the flow capacity of sewer pipes should include an analysis of the flow regime and the bed topography. It has been shown that the transition regime for bed forms starts at Froude number larger than 0.5, with washed-out bed forms and diminishing bed roughness as a result. Therefore, under sufficiently high flow velocities, the bed forms may be of negligible importance. This paper provides a non-dimensional analysis of the influence of sediment deposit on a sewer’s discharge capacity. Under given conditions, a substantial increase in the sediment depth (from 2 to 10%) results in a 10 –20% reduction of the full pipe discharge capacity relative to a clean pipe, and bed forms (dunes) are expected to be developed.

However,

as

this

dune

development

is

likely to be restricted in many sewers working under storm conditions and carrying cohesive sediments, the

REFERENCES Ackers, J. C., Butler D. & May R. W. P. 1996 Design of sewers to control sediment problems. CIRIA Report R141, London. Alvarez-Hermandez, E. M. 1990 The influence of cohesion on sediment movement in channels of circular cross-section. PhD thesis, University of Newcastle upon Tyne. Banasiak, R. & Verhoeven, R. 2008 Transport of sand and partly cohesive sediments in a circular pipe run partially full. J. Hydraulic Eng., 134, 216– 224. Butler, D., May, R. & Ackers, J. 2003 Self-cleansing sewer design based on sediment transport principles. J. Hydraulic Eng. 129(12), 276 –282. Coleman, S. E., Fedele, J. J. & Garcia, M. H. 2003 Closed-conduit bed-form initiation and development. J. Hydraulic Eng. 129(12), 956 –965. Einstein, H. A. & Barbarossa, N. L. 1952 River channel roughness. Trans. Am. Soc. Civ. Eng. 117, 1121 – 1146. Jack, A. G., Petrie, M. M. & Ashley, R. M. 1996 The diversity of sewer sediments and the consequences for sewer flow quality modelling. Water Sci. Technol. 33(9), 207 –214. Kleijwegt, R. A. 1992 Sediment transport in circular sewers with non-cohesive deposits. PhD thesis, TU Delft. Ota, J. J. & Nalluri, C. 2003 Urban storm sewer design: approach in consideration of sediments. J. Hydraulic Eng. 129(4), 291–297. Raudkivi, A. J. 1990 Loose Boundary Hydraulics, 3rd edition, Pergamon, Oxford, UK. Skipworth, P. J., Tait, S. J. & Saul, A. J. 1999 Erosion of sediment beds in sewers: Model development. J. Environ. Eng. 125(6), 566 –573. Torfs, H., Huygens, M. & Tito, L. 1994 Influence of the cross section on the erosion criteria of partly cohesive sediments. Water Sci. Technol. 29(1 –2), 103 –111. Yen, B. C. 2002 Open channel flow resistance. J. Hydraulic Eng. 128(1), 20 –39.