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WOI. Sci. Tech. Vol. 31. No.7. pp. 107-115. 1995. CopYrlgbtCCll9951AWQ

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PRINCIPLES AND APPROACHES FOR NUMERICAL MODELLING OF SEDIMENT TRANSPORT IN SEWERS

Ole Mark*, Cecilia Appelgren* and Torben Larsen**

• Division/or Water and Environment. VBB- VIAK. Box 5038. S-102 41 Stockholm. Sweden .* Depanment 0/ Civil Engineering. Aalborl{ University. Sohngaardsholmvej 57. 9000 Aalborg. Denmark

ABSTRACT

A study bas been carried out with the objectives of descnbing the effect of sediment depOSits on the hydraulic capacity of sewer systems and to investigate the sediment transport in sewer systems. A result of the study is a mathematical model MOUSE ST which describes sediment transport to sewers. This paper discusses the applicability and the lunitations of various modelling approaches and sediment transport formulauons in MOUSE ST. Further. the paper presents a simple application of MOUSE ST to the Rya catchment in Gothenburg. Sweden.

KEYWORDS

Bed load; suspended load; hydraulic capacity; advection; mathematical model; sediment transport; sewer.

INTRODUCTION

At present. numerical models for sewer systems describe well the hydraulic conditions in pipes without sediment deposits. However, the hydraulic capacity of a sewer system depends strongly on whether or not sediment deposits are present. The modelling of the sediment in sewers is important as the sediment deposit~ affect the flow condition by reducing the flow area and increasing the average flow resistance in the pipe. Further, pollutants are carried through the sewer system attached to the sediments and sediment discharged from combined sewer overflows may affect the morphological regime and the water quality of the receiving waters.

The sediment transport model for sewers (MOUSE ST) is a part of a new modelling system for deterministic modelling of the transport processes in sewers (Mark et aI. 1993). MOUSE ST is based on the MOUSE package developed by the Danish Hydraulic Institute (Lindberg, 1986). The MOUSE package contains descriptions for the runoff from both pervious and impervious catchment~ and a pipe flow model which solvell the full St Venant equations for looped sewer systems. The capability of MOUSE ST to predict the resistance and the hydraulic capacity of sewers has been validated against laboratory data (Mark. 1992).

107

108 o. MARK tt 01.

This paper describes the modes of sediment transport in sewers and it discusses the modelling approaches applicable for these transport modes. Further. the paper describes the modelling approaches available in MOUSE ST and a comparison of parts of MOUSE ST to laboratory and field data.

SEDIMENT TRANSPORT IN SEWERS

The sediment transport processes in rivers and in sewers with a deposited sediment bed have many similarities. A long tradition exists for studying sediment transport in rivers and many data are available concerning the sediment transport in flumes with an "unlimited" amount of sediment in the flume. The sediment transport in sewer systems differs from traditional modelling of sediment transport in rivers in the following aspects: the sediment in sewers is often limited in supply. it often has cohesive-type properties and the hydraulic conditions cover much wider flow ranges.

A general problem is that very few experiments have been carried out with sediment transport in sewers. Hence. little knowledge is available concerning the concentration profile and the influence of the pipe wall on the sediment transport. At present. insufficient data exist to develop specific sediment transport formulae for sewers. However. the sediment transport formulae for large pipes approximate sediment transport formulate for rivers as large sewers in principle act as small rivers/flumes. Hence. the sediment transport formulae for sewers should be an extension of the existing well proven sediment transport formulate for rivers. with special considerations if the pipe is very small. the layer of sediment in the pipe is thin or the pipe is running full.

THE MODE OF SEDIMENT TRANSPORT

The transport mode of the sediments in a sewer system may change from dry weather conditions to storm conditions. Sediments which during dry weather flow are transported in close contact with the bed as a function of the local flow conditions might during storm conditions be transported in suspension at the mean flow velocity without significant interaction with the bed. At these high flow rates the sediment transport is determined by both the local and the upstream flow conditions and a space and a time lag exists between the local sediment transport capacity and the actual sediment transport. At present. there is still discussion on which transport processes actually take place in sewer systems (Ashley et al. 1994. Verbanck 1993). The current debate concerns whether or not a heavy-fluid layer (also termed fluid sediment) exists. The heavy•fluid layer is characterised as a dense suspension moving along the bed. Further. there is doubt concerning whether this layer. if it exists. is a continuous layer or a discontinuous layer and whether the layer can be described by conventional bed load theory. As insufficient information exisL.~ about this layer. no special considerations were taken to describe this phenomena. For simplicity. the sediment transport modes in sewers are. as in rivers. split into three transport modes.

• bed load • suspended load • wash load.

The Bed Load Mode of Transport

The sediment transported as bed load is controlled by the effective shear stress acting on the sand surface. The difference between a sewer and a river is that in a sewer the shear stress is derived from both the pipe and the sediment bed while the shear stress in a river is more or less only determined by the sediment bed. One way to determine the shear stress on the sediment bed in a sewer is to apply a side wall elimination procedure. Once a side wall elimination procedure has been applied to find the bed shear stress then there is no difference between computation of the bed-load transport taking place in a wide pipe with a sediment deposit and that taking place in a flume/river.

Numerical modelling of sediment transport 109

The Suspended Load Mode of nan sport

The traditional sediment transport formulate for suspended load in rivers are based on the assumption of a logarithmic velocity profile. The velocity profile in sewers changes from a logarithmic velocity profile similar to that in rivers when the pipe is flowing part full to a double logarithmic velocity profile when the pipe is flowing full. The suspended load is traditionally calculated as the integral over the cross-sectional area of the concentration multiplied by the velocity, ie:

qs = fu(y,z) ·c(y,z) da A

(1)

Little work has yet been carried out concerning the variation of the concentration profiles over the cross•section in sewers. If the concentration profile is known, the effect on the suspended load transport from the change in velocity profile can be evaluated as:

a

f u(y,z)xivex·c(y,z)xivex da A

f u (y, z) sewer· C (y, z) sewer da A

(2)

The suspended load transport is the same in rivers and sewers for small Rouse numbers, which corresponds to a uniform distribution of the concentration profile over the water depth. The integral in equation (2) has been evaluated analytically and it was found that for large Rouse numbers the suspended load transport calculated on the basis of river formulations has to be modified to be applied to full running pipes (Mark, 1994).

The Wash Load Mode of Transport

The wash load is usually assumed to be uniformly distributed over the flow depth, hence wash load has very small Rouse numbers and it is transported with the mean velocity of the flow. No major difference should be expected between the transport formulate for sewers and rivers.

SEDIMENT TRANSPORT MODELLING IN SEWERS

The selection of a sediment transport formula for a specific study of the sediment transport in a sewer system depends on the sediment characteristics and the flow characteristics. During dry weather flow, the non-cohesive sediment in the sewer system will typically be transported as bed load transport. During storms some of the sediments will be transported as bed load but most sediment will be transported in suspension, depending on the flow and the sediment characteristics. The sediment in suspension is either transported as suspended load which from time to time is in contact with the bed or it is transported as wash load, i.e. advection transport with the flow velocity. If the event is characterized by small flow velocities and the sediment has a high density, 1800 kglm3-26S0 kg/m3, i.e. the sediment has a high fall velocity, then it has been shown by e.g. Nalluri et al. (1994) and Perrusqufa (1992), that the sediment transport can be modelled by use of a bed load formula for non-cohesive sediment, e.g. Fredsle (1984), van Rijn (1984a) or Perrusqufa (1992). If high flow velocities exist and the sediment has a high fall velocity then it is necessary to use a sediment transport formula for non-cohesive sediments which describes both bed load transport and suspended load transport, e.g. Ackers and White (1973), Engelund and Hansen (1968), Engelund and Fredsle (1984), van Rijn (1984a, b). If high velocities exist and the sediment has a small density is 1000 kg/m3-ISOO kg/m3, i.e. the sediment has a small fall velocity, the sediment transport must be described as suspended transport by use of an advection model including a description for erosion and deposition, as the sediment transport locally is both a function of the local flow and the upstream conditions.

When a sediment transport formula is applied to a sewer system it is important to be aware of the assumptions and the limitations of the formula. The sediment transport formula should be applicable to the

110 O. MARK el al.

transport mode and it should be validated for the flow conditions and the sediment characteristics. e.g. particle size and density. in the study. Hence. sediment models calibrated by use of a bed load formulate during dry weather flow may not apply during storm conditions since different modelling approaches may be needed for dry weather and storm conditions.

THE MODELLING APPROACHES IN MOUSE ST

In MOUSE ST various methods for modelling of sediment transport in sewer systems have been developed. As described above the selection of modelling approach and transport formulatr depends on the scope of the study. the sediment characteristics and the hydraulic conditions. The basic modelling approaches in the MOUSE ST are:

• an implicit solution of the continuity equation for bed sediment based on non-cohesive sediment transport formulae i.e.: Ackers-White. Engelund-Hansen. Engelund-Fredsle and van Rijn.

• an implicit solution of the advection-dispersion equations with an explicit update of the bed based on a source/sink description for modelling of cohesive sediments.

• a formulation of the transport of non-uniform sediment where a range of sediment fraction can be modelled simultaneously on the basis of two models above.

• a fixed bed model which can be used to give a first indication of the non-cohesive sediment transport capacity in the sewer system.

Together these modelling approaches cover the range of sediment transport modes found in sewer systems. E.g. modelling of bed load transport can be carried out by use of non-cohesive sediment transport formulae. while the modelling of fme organic particles during storm conditions has to be modelled by use of the advection-dispersion formula.

COMPARISON OF MOUSE ST WITH LABORATORY DATA

Available laboratory experiments mostly concern the bed load transport in sewers. Very few laboratory experiments have been carried out to measure the suspended transport in pipes. Experiments with bed load in pipes have been carried out by Perrusqufa (1991) at Chalmers University of Technology. Sweden. Newcastle University. UK and Hydraulic Research Wallingford. UK. These experiments are used to evaluate the capability of the implemented sediment transport formulae to predict the bed load sediment transport in pipes. The grain sizes in the experiments were 0.72. 0.9. 1.0 and 2.5 mm and the pipe slopes were up to 0.6%. The experiments cover a range of the dimensionless bed shear stress from the critical bed shear stress (of the order of 0.03-0.05) up to 0.14. The transport process in these studies is bed load. i.e. the experiments only cover dry weather periods.

The sediment transport formulae of Ackers and White. Engelund and Fredsle. and van Rijn. all describe the bed load as a function of the criteria for the initiation of motion. The bed shear stresses in the experiments are close to the critical dimensionless bed shear stress which describes whether the sediment moves or not. As there is an uncertainty of approximately 20% in the critical bed shear stress defined by the Shields curve (Raudkivi. 1990) quite large deviations can be expected between the observed and the predicted sediment transport.

A linear regression analysis was carried out between the measurements by Perrusqufa (1991). and the sediment transport rates predicted by the four implemented sediment transport formulate. The correlation coefficient for the sediment transport formulations can be seen in Table 1. It can be seen that there is a good correlation for all the theories between the predicted and the observed sediment transport rates. The performance for the theories was evaluated on the basis of performance index proposed by van Rijn (1984). The performance index is the percentage of data within the discrepancy range 0.5<r<2. r is defined as:

Numerical modelling of sediment transport

I Bed loadcomputed

Bed loadmeasured

III

(3)

On the basis of 600 data sets Van Rijn (1984a) found the perfonnance for the bed load transport in flumes given in the last column of Table I. A common mode of calibration in sediment transport modelling is to multiply the sediment transport fonnula by a constant factor. A calibration of the sediment transport fonnulae was carried out and the perfonnance of the fonnulae was improved significantly. the perfonnance of the fonnulae with and without calibration can be seen in Table 1.

TABLE 1. Correlation coefficient from the linear regression analysis and scores (percentage) of predicted bed load in the discrepancy range 0.5<r<2

Correlation Performance Calibration Perfonnance Perfonnance coefficient without factor with in flumes by without calibration calibration van Rijn calibration

Ackers-White 0.87 7% 1.5 S7 % 77% Engelund-Hansen l 0.72 32 % 2.0 84% 76% Engelund-Hansen2 0.76 23 % 3.2 82 % Not evaluated Engelund-Fredsee I 0.77 66 % 0.7 78 % Not evaluated Engelund-Fredsee2 0.89 72% 0.8 81 % Not evaluated van Rijn3 0.73 SS % 1.0 SS % 77% van Rijn4 0.80 76 % 0.8 80 % van RijnS 0.91 10 % 3.8 76 %

I without prediction of the bed she.r Slress. 2 with prediction of the bed shear Itress.3 all grain fractions. 4 all grain fractions excepl the 2.S mm grain fraction. 5 only the 2.S mm grain fraction.

A comparison between the measured and the observed sediment transport rates is shown in Figures 1-4. The perfonnance of the Ackers-White fonnula is not good for the prediction of the sediment transport without calibration. When the model is calibrated. the perfonnance is acceptable. The model is very sensitive to the mobility parameter within the range of the experimental data. The perfonnance of the sediment transport by the Engelund-Hansen fonnula is not good without calibration. Once the fonnula is calibrated the perfonnance improves significantly. The performance of the sediment transport by the Engelund-Fredsle formula is acceptable without calibration. the performance increases when the fonnula is calibrated. The formula is sensitive to the critical bed shear stress within the range of the test data. The van Rijn formula has an acceptable prediction of the sediment transport without calibration. The performance of the formula cannot be improved by calibration of the model. If the 2.5 mm fraction is taken out of the test data the formula has a good perfonnance and it can be further improved by calibration. This may be due to the fact that the van Rijn fonnula has not been validated by van Rijn for grain fractions larger than 2.0 mm. If a calibration is carried out for the 2.5 mm fraction only. the performance of the formula is good. The formula is very sensitive to the criteria for the critical bed shear stress within the range of these experimental data.

EXAMPLE OF APPLICATION OF THE SEDIMENT TRANSPORT MODEL

The MOUSE ST has been applied to the Rya catchment in Gothenburg. Sweden. with approx. 793.000 person equivalents including industry and a daily mean flow of 321.000 m3/d in 1991. The flow capacity of the full secondary treatment is 518.000 m3/d (6 m3/s). How exceeding this capacity only receives primary treatment. The sediment transport model was applied in conjunction with an existing hydrodynamic MOUSE model of the pipe system (Gustafsson et al .• 1993). The pipe system consists of a 120 km tunnel in bed rock with cross-sectional areas of 6 m2 to 18 m2 and slope varying from 0.07 to 0.1 %. The hydrodynamic model has been calibrated and verified against water levels and discharges at the sewage treatment plant.

112 o. MARK el al.

Predicted transport, I/s

0.0000001 '-:=:-'-..L..I..LJ.J.':':::-'-....l...J...u.J~---1-L.Lll~_L...L..J...L.LllLJ':-l 0.001 0.01 0.1 1 10

Measured transport, I/s (Thousandths)

+ 0nlD oIze 0.9 mill <> 0nlD oIze 2.5 mill l> 0nlD oIze 1.0 mill

X Olalla oIze 0.72. mill

Figure I. Predicted bed load versus observed transpm for lbe Ackers-White theory.

Predicted transport, I/s 0.1...----------------------,

0.01

0.001

0.0001 +

0.00001

0.001 0.01 0.1 1 10

Measured transport, I/s (Thousandths)

+ Grain me 0.9 mm <> Grain oIze 2.5 mm l> Grain me 1.0 DUD

X 0!aiD me 0.72 mill

Figure 2. Predicted bed load versus observed transport for the Engelund-Hansen theory. withour prediction of the bed shear stress.

Very few data have been collected for the sediment transport model. The only available data were the accumulated mass of fine and coarse sediments (wet) at the sewage treatment plant for a continuous period. At present, no information is available on the density and the grain size of the fine and the coarse sediment fractions. nor is information available on the sediment properties in the sewer system, e.g. sediment depths in the tunnel system. Due to the sparse data only the sediment transport capacity of the flow was evaluated. This is obviously a rather simple approach as it neglects the influence on the sediment transport of a limited sediment supply in the sewer system and of the time of travel for the sediment within the sewer system. As no data were available the data used in the simulation were the default values found for sewer systems in the UK (Crabtree et a1. 1993). The sediment depth in the system was assessed to be 5-10% of the pipe diameter. No attempt was made to calibrate the sediment transport model as the lack of information did not justify a calibration.

Numerical modelling of sediment transport

Predicted transport, Vs 0.1

0.01

0.001

+ 0.0001

0.00001

o

0.000001 L-O.J..00-

1 .LJ..J...>.J.J..LOLL.O-I.....L....L..J...u.J.l.LO~.I:--'.-...........,u..wI~-'-......... '-'-I.J~l-=-O---'

Measured transport, Va (Thousandths)

+ Gnia aize 0.9 DUll () Gnia aize :u mm II GniD Iize 1.0 mm x Orain Iize 0.72 mm

Figure 3. Predicted bed load versus observed transport for the Engelund-Freds0e theory. without prediction of the bed shear stress.

Predicted transport, I/s 0.1

0.01 x

0.001

0.0001

0.00001

0.000001 o

0.0000001 1........;0:-'::.00::-1:-'-....L....JL.J.J.LLO~.O:-:-I-L....J...J..LU.llO~.I:---l--L....l....L..u.u.lL-...l..-.L...Lu..uwl-0-l

Measured transport, lis ('Ihousandths)

+ Oraln size 0.9 DUD 0 Gnln Iize 2.5 mm II Gnln Iize 1.0 mm x Gnln Iize 0.72 mm

Figure 4. Predicted bed load versus observed transport for the van Rijn theory.

113

The results of the hydrodynamic and the sediment transport simulations, using the Engelund-Hansen sediment transport formula. can be seen in Figures 5 and 6. From Figure 6 it can be seen that the model predicts sediment transport for the fine fraction when sediment transport is recorded at the sewage treatment plant. Further. it can be seen that the sediment transport capacity simulated for the fine fraction follows the trend of the sediment intlow at the treatment plant very well during the first 9000 minutes of the simulation. During the last part of the simulation it seems as if there is a time lag between the sediment intlow and simulated sediment transport capacity and the magnitude of the simulated sediment transport is not correct. This may be due to:

• the assumed sediment properties being wrong. • the transport time being neglected in the simulation. • only a limited supply of sediment being available in the pipe system.

114 o. MARK er al.

• the model simulating dry sediment mass while the sediment inflow measured at Rya is wet sediment, • discrepancies between the simulated and the observed discharge at the sewage treatment plant during this period. M3/S

14.0

12.0

10.0

B.O

6.0

4.0

o 2000

31/10

4000 6000 8000

SIll

10000 12000 min

9/11

- - - - - - Observed discharge at Rya Simulated discharge

Figure S. The observed and simulated discharges at the Rya sewage treabnent plant in November 1992.

I/s 1.000

0.800

0.600

0.400

. . 0.200 .. . ~ . .. .... ., . . . .. .. - ....... .

0.000 o

31/10

2000 6000 8000

SIll

10000 lim min.

9111

Obsetved sediment transport at Rya

Simulated sediment transport capacity

Figure 6. The observed sediment transport of the fine sediment (wet sediments) and simulated sediment transport capacity at the Rya sewage treabnent plant m November 1992.

CONCLUSION

Different approaches for modelling of sediment transport are applicable to different modes of sediment transport. I.e. modelling of fine organic material should during stonn conditions be modelled by use of an advection-dispersion model while bed load during dry weather flow should be modelled by use of a sediment transport fonnula for non-cohesive sediment transport.

A sediment transport model which is able to simulate the sediment transport modes in sewers has been developed. This type of model opens a wide scope for modelling of the sediment transport processes in sewer systems. However. due to a lack of data only a few aspects of the capability of the model to predict the sediment transport in sewers have been tested against laboratory and field data. When the sediment transport fonnulae in MOUSE ST were calibrated against the measurements in pipes by Perrusqufa (1991). they predicted the sediment transport with the same accuracy as when applied to rivers/flumes. The best

Nwnerical modelling of sediment transport 115

agreement between the observed and the simulated sediment transport rates was achieved by use of the Engelund-Hansen model with a calibration factor of 2.0.

The model has been set up for a catchment in Sweden. The preliminary results from the modelling of the transport capacity are not perfect. but the results must be considered acceptable based on the available data. The model shows that the simulated sediment transport follows the pattern of the sediment transport which was recorded at the sewage treatment plant. The model can be used to give an estimate of the magnitude of the transport at the sewage treatment plant and to evaluate options for management of the sewer system with respect to sediments. The results of the simulation can probably be improved if more data on the sediment properties becomes available. e.g. sediment size. density and sediment depth in the pipe system.

Field measurement~ and further laboratory experiments with suspended load transport are needed in order to evaluate the general applicability of the model to predicting the sediment transport in sewer systems.

A c(y.z) qs r u(y.z) y y z a

NOTATION

flow area. (m2). concentration. arbitrary unit.

suspended sediment transport. (m3/s). performance index.

velocity. (mls). distance above the bed. (m). water depth. (m). horizontal coordinate. (m). transport constant.

REFERENCES

Ackers. P. and White. W.R. (1973). "Sediment Transport: New approach and analysis". Proc. ASCE. JHD. 99. HYII. pp. 2041· 2060.

Ashley R. M .• Arthur. S .• Coghlan. B.P. and McGregor. I. (1993). "fluid Sediment in Combined Sewers". Wal. Sci. Tech. 29 0-2) 113-123.

Crabtree. R .• Gent, R. and Spooner. S. (1993). "MOUSE TRAP: Specification of Pollutant and Sediment Cbaracteristic Default Values". Water Researcb Centre. UC 1950.

Engelund, F. A. and Hansen. E. (1967). "A monograpb on sediment transport in allUVial streams". Teknisk Forlag. Copenhagen. Denmatk.

Fredsle. J. (\984). "Sediment Transport in current and Waves". Prog. Rep. 49, Institute of Hydrodynamics and Hydraulic Engineering. Tecbnical University of Denmark.

Gustafsson. L-G .• Lumley, D., Persson. B. and Lindeborg C. (1993). "Development of a Catchment Simulator as an On-Line Tool for Operating a Wastewater Treaunent Plant", SiXth International Conference on Urban Stonn Drainage, Niagara

Mark, O. (1992). "A Sediment Transport Model for Sewers", Wal. SCI. Tech. Vol. 25. No.8, pp. 141·149. Mark. 0 .• Larsson, J., Larsen. T. (1993). "A Sediment Transport Model for Sewers", Sixth International Conference on Urban

Stonn Drainage. Niagara. Mark, O. (1994). "Discussion of Numerical Modelling Approaches for Sediment Transport in Sewers", Ph.D thesis in prep. Nalluri, C., Ab Gbani A and EI-Zaemey. A. K. S. (1994). "Sediment Transport over Deposited Beds in Sewers", Wal. ScL Tech.

29 (1-2) 125·133. Perrusqu(a, G. S. (1991). "Bed Load Transport in Stonn Sewers. Stream Traction in Pipe Cbannels". Chalmers University of

Technology, Giiteborg, Report Series A:22 Sweden. Perrusqu(a, G. S. (1992). "Sediment Transport in Pipe Channels", Chalmers Untversity of Technology, Giiteborg, Report Senes

B:55. Sweden. Raudkivi. A. J. (\990). "Loose Boundary Hydraulics". 3rd Edition, Pergamon Press. Rijn. L. C. van. (\984a). "Part I: Bed load transport", Journal of Hydraulic Engineering, ASCE, Vol, 110. No. 10. 1431-1456. Rijn, L. C. van. (I984b). "Part II: Suspended load transport", Journal of HydraUlic Engineering, ASCE, Vol, 110. No. 10, 16\3-

1641. Verbanck, M. (\ 993). "Identification of the depth-dependent transportation of particulate solids in dry-weather sewage flows".

Sixth International Conference on Urban Stonn Drainage, Niagara.