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~ Pergamon War. Sci. T~ch. Vol. 33. No.9. pp. 61-{i7. 1996.Copyrighc C> 1996IAWQ. Published by Elsevier Science LId

Prinled In Great Briiam. All rights reserved.0273-1223196 SIH)() +0-00

SEDIMENT TRANSPORT MODELLING INCOMBINED SEWER

Huseng Lin * and Benoit Le Guennec**

• CERGRENE. Ecole Nationale des Ponts et Chaussees. La Counine. 93/67 Noisy IeGrand Cedex. France··IMFT, Institut National Polytechnique de Toulouse. Allee du Prof C. Soula.3/400. Toulouse. France

ABSTRACT

The classical solid Iranspon Iheory has been used to analyse the experimenlal results obtained from IheNo.13 combined sewer trunk of Marseille for more than two years. This study demonslraCes that the sedimentIranspon phenomena in a combined sewer trunk are nOlhing other than the classical ones. A numerical modelhas been established according to the analyses. Based on a permanent now regime. this model considers notonly the effects of the real channel geometry, non-uniform particles size. but also the coexistence of mineraland organically materials. Some particular sediment Iranspon phenomena such as the armouring of bed havealso been taken into account. It also shows that although the innuence of the suspension particles is notnecessarily considered. the simulation including the variations of particle density with each granular fractionmay be improved. Copyright ~ 1996 IAWQ. Published by Elsevier Science Ltd.

KEYWORDS

Armouring; bedload; dry weather; modelling; sediment; sewer.

INTRODUCTION

Several models of sediment transport in alluvial rivers have been developed. They are applied to themocphological development of the rivers, or to the hydraulic engineering aspects. They consider the bed loaddischarges, the suspension transport, or both, with different assumptions (steady or unsteady flows, uniformor non uniform grain sizes, ...)

The proposed model has been developed to a specific study which concerns the solid transport phenomena inthe sewer networks. Although we can find in it the same equations as in some other models; the differencescome from the fact that it has been calibrated with <in situ> data, and validated consequently for a combinedsewer trunk.

MODEL FORMULATION

In our study, the time scales for the hydraulic discharges and the deposit evolution are not in the same orderthe hydraulic and sediment equations are thus solved in an uncoupled manner; the hydrodynamic equationsare solved with a bed elevation which depend on the solid transport, but this elevation is assumed to beconstant on a large time scale.

61

62 H. LIN and B. LE GUENNEC

The in situ deposit of solids were observed for two years, with a low rate of change, and as shown in figureI, the hydraulic discharges (Q) do not vary much from day to day in dry weather, and can also be regardedas invariable during the same periods in each day, which depend on human activities.

down-stream reach (n° 13)

2016

Canebiere trunk

12II

flow rateQ(Vs) 2110

140

200

160

120

80

~

00

time (hours)

Figure I. Daily dry weather discharges.

Governing equations: We consider the water flow as steady during these daily periods and the governingequations of the one dimensional hydrodynamic model can be written in simplified forms as:

dQ=Odx (1)

dH I(x) - J(x)dx = I-F2(x) (2)

Eqn (1) is the continuity equation with no lateral inflow and outflow, Q being the water discharge in the Jt•direction, and eqn (2) is the dynamic equation of gradually varied flow without local looses, in which Ii isthe water elevation, I the bed slope, which changes in the x direction and depends on the solid deposition Orscour, but which is assumed constant (in time) during the daily period and

Q2J= K2S2R~18

the energy gradient in m1m, and

F2 _ Q2L

- gSa

is the squared flow Froude number, where Rh is the hydraulic radius, S the wet area and L the free surfacewidth.

K is the combined Strickler's coefficient, based on the Einstein's equation to evaluate the respective pan ofthe bottom and the wall shear stresses and written as:

(3)

Sediment transport modelling

where Pert.b.w are the (total, bottom and wall) wetted perimeters.

63

The bottom and wall Strickler coefficients are calculated in a special way (Lin et al., 1992), by fitting an "insitu" observed surface profile with the numerically obtained profile and suggested the following equations:

(4)

(5)

where ks is the height of wall roughness, d60 the diameter of the grain size, (such as 60% in weight arepresent in the deposit bed), which vary in x direction.

These equations permit to calculate the water level in each point x, along the sewer, for the evaluated waterdischarge during the daily period under consideration.

Bedload transport equations: The aim of the study is to understand and simulate the bedload discharge andconsecutively the deposit aggravation and classification of the grain size distribution along x direction.Using the above defined hydrodynamic conditions, the model can calculate therefore the bed load dischargein the following way:

The Meyer-Peter equation is applied for each grain size dk, as used by Wang (1977), with the approximationthat it can be used in our case (nearly steady flow).

The equation gives the unit-width volumetric bedload transport rate q\k under equilibrium conditions, andcan be written in the form, for each diameter dk:

o

q.,. = 8,ft" -"Co )3/2

~(s-l)gd: • c,"(6)

where s is the relative density of solids (s =p/Pw)' and "C*k' "C*c.k are the dimensional near bottom andcritical shear stresses, respectively, and hey are defined by the following equations:

"C~ ="C/pg(s-l)d.

where t is the mean shear stress "C = pgRh J and

(7)

(8)

(9)

where <1m is the mean diameter of the particles, and t*c.m is the non dimensional critical Shields shearstress, equals to 0.047.

64 H. LIN and B. LE GUENNEC

As in other models (<lalluvial>: Karim etal., 1982. <Carichar>: Rahuel et al.. 1989. <FCM>: Correia et al.,1992, <Tsar>: Ben Slama et al., 1992). a loading law. to take in to account the existence of a spatial delaybetween the real bedload and its equilibrium value.

We adopt the Daubert-Lebreton law (Daubert-Lebreton, 1967), which can be written as:

(10)

with qs,k the local solid discharge, in the x section, w the settling velocity of the particle of diameter d k• andu* the friction velocity (t =pu2*).

a is a coefficient, with IX = IXerosion if q*s,k > qs,k and if IX = IXdeposit if q*s.k < qs,k'

The total unit-width bedload discharge, in volume, under non equilibrium conditions. is lastly obtained by abalanced summation:

(11)

where ..:1Pk is the tate of transport (in volume) of the particles dk.

To define the bed capacities either to provide solid particles. in case of erosion, or to receive the particles incase of deposition. the model uses a mixed layer. as shown on figure 2.

Sub-layer

Figure 2. Schematic bed section.

The composition of this mixing layer. in terms of volume fraction and grain size distribution of solids,permits to manage the exchanges between the bed and the outer flow. (Exchanges with the other sub-layersare also allowed),

The behaviour of this mixing layer has to take into account the armouring and hiding phenomena. Themodel uses the Gessler's theory to determine the limit of the volume fraction of particles found in the mixinglayer (Little and Mayer. 1972).

To determine the rates variation of of the bed elevation and that of the wet flow section, the followingequation is used:

Sediment transport modelling 65

(12)

where Qs is the total bed load discharge, Cv,b the volume fraction of solids in the active mixing layer (belowthe bed surface), and Ab is the whole cross section of the deposit.

At each time step of computation, the hydrodynamic model calculates the new water level, using the newslopes and the new grain size distributions in the x direction, thus allowing to evaluate the new solidtransport, with the above equations (6), (10), (11).

CALIBRATION OF THE MODEL

The model was calibrated using the results obtained during a long "in situ" study (200 days), in one sewerreach (up-stream), and has been validated consequently on other "in situ" observations, on long duration(more than two years), and in another sewer reach (down-stream). The calibration has been made in differentstages:

For the hydrodynamic equation, because we have always sub-critical flows, the control section is locateddown-stream of each reach, where the discharge-water level laws are known.

At first, as previously mentioned, the shear stresses, near the wall and the bed, are fitted, and two Stricklercoefficients (Lin et al., 1992) - eqns 4 and 5 - are proposed.

For the bed load equations, the model needs at the beginning some enquiries on the solids entering up•stream the first reach. To obtain realistic values of the solids discharges and the associated grain size anddensity distributions, we use a specific method for the bed load measurements, as presented in a previouspaper (Lin et al., 1993a). This method allows to give the up-stream boundary conditions, and permit also toknow the entering grain size and density distributions (Lin et al., 1993b). The measures shown that the up•stream solid discharges are always the same from day to day, in dry weather (as the water discharges).

These data are required to start the computational simulation which permits to predict the depositdevelopment.

To fit the model by comparison between the numerical results and in situ observed data, the last, but notleast, parameter to be settled is the a coefficient, which appears in the Daubert-Lebreton loading law.

We found, in our investigations, that the value ct =cterosion = adeposit == 0.01 gives the best results, and tovalidate then the model, we tested it in another reach, with the observed deposit profile during two years.

TESTS AND RESULTS

We used the model on the data obtained in the no.13 sewer trunk of Marseilles. After the first stage ofcalibration, in the upper reach, with daily water discharges less than 160 lis (see in fig I: Q (upper reach) =Q (down stream) - Q (Canebiere trunk», where we observed the deposit development during 200 days, wewere able to predict the deposit development in the second downstream reach, which differs from the upperin the fact that it receives a bigger water discharge (see fig 1) coming from another trunk (Canebiere's trunk:confluence at the distance =130 m).

The model is then tested for an another long period (during 1000 days of data collection), and thecomparison of the predicted results with the observed behaviour (see fig 3) is fairly good.

66 H. LIN and B. LE GUENNEC

The only divergence is observed between the points situated at the distances of 320 and 360 m, where a bendexists in the channel. It is well known that, like in rivers, the solid transport phenomena are affected by thesecondary flows in these singularities. and a "one dimensional" model is not able to reproduce thesephenomena.

Nevertheless. the total volume (interesting for the cleaning management) is well predicted. and the meanslopes (measured and calculated) are nearly the same.

Moreover. the x direction distribution of the grain size in the deposit is also well predicted.

elevation0 ••

(m) 0 ••

0."

200th day 0 .•

0 ••

0 ••

0.2

0 ••

0"0 200 2.0..0 020

750'h day

lOOOlh day

distance (m)

... invert. _ measured profile. + calculated profile

Figure 3. Deposit profiles in the downstream reach.

CONCLUSION

The proposed model. despite the simplifying assumptions. is well adapted to describe the deposition-erosionphenomena in sewer trunks. Based on "in situ" experiments. it pennits a best understanding of the physicalcorrelation between the different involved parameters. It can be also used to test the sensitivity of the solid

Sediment transport modelling 67

transport behaviour to the entrance data characteristics, like grain size distributions, and allows to proposetherefore some technical solutions to avoid the sewer clogging.

The model needs now to·be modified to take in account the bends, in an empirical manner to represent thesecondary flows in a one dimensional model.

ACKNOWLEDGEMENT

The authors thank the SERAM (the Sewer Network Management Company of Marseille), for allowing theuse oftheir in situ measurements, and all other personnel for their contributions in this study.

REFERENCES

Ben Slama, E., Peron, S., Belleudy, P. and Rouas G. (1994). TSAR: un modele mono-dimensionnel de simulation des evolutionsdes fonds alluvionnaires des rivieres, La Houille Blanche, no.4.

Correia, L. P, Krishnappan, B. G. and Graf, W. H. (1992). Fully coupled unsteady mobile boundary flow model (FCM). JournalofHydraulic Engineering, ASCE, 118(3).

Cunge, 1. A., Holly, F. M. and Verwer. A. (1980). Practical aspects of computational mobile-bed modelling system, Pitman Ed.,London.

Daubert, A. and Lebreton, J. C. (1967). Etude experimentale sur modele mathematique de quelques aspects des processus d'erosion des lits alluvionnaires, en regime permanent et non permanent. In: Proc. of the 12th Congress of IAHR, FortCollins, Colorado, USA.

Karim, M. F. and Kennedy, J. F. (1982). IALLUVIAL: A computer based flow and sediment routing model for alluvial streamsand its application to the MISSOURI river, IIHR repon No.250, Iowa Inst.of Hyd. Research, the University of Iowa,Iowa City, Iowa, USA.

Lin, H. S., Le Guennec, B. and Dartus, D. (1992). Study of open channel flow energy gradient expressions using a numericalmodel and a speCific methodology. In: Proc. of Inter. ConJ., of Hyd. Eng. Software, Hydrosoft 92. UniversidadPolitecnica. Valencia. Spain.

Lin, H. S.. Le Guennec, B.• Dartus, D. and Bachoc, A. (I 993a). Development of a specific method for the bed-load measurementin sewer trunk. In: Proc. of the 6th Inter. Con{. on Urban Storm Drainage. Burlington, Ontario, Canada.

Lin, H. S., Le Guennec, B., Dartus, D. and Bachoc, A. (1993b). Bed-load transport in the No. 13 sewer trunk of Marseille. In:Proc. of the 6th Inter. ConJ. on Urban Storm Drainage, Burlington, Ontario, Canada.

Little, W. C. and Mayer, P. G. (1972). The role of sediment gradation on channel armoring, Repon ERC0872, School of Civ.Engrg., Georgia Inst. of Tech., Atlanta, GA. USA.

Rahuel, J. P., Holly, F. M., Chollet, J. P., Belleudy, P. J. and Yang, G. (1989). Modeling of riverbed evolution for bed loadsediment mixtures, Journal ofHydraulic Engineering, ASCE, IIS( II).

Wang, Y. F. (1977). Bed-load transport in open channel. In: Proc. of the 17th Congress o/the IAHR, Baden-Baden, Germany.