Laboratoire Hydrologie Urbaine

Cours de DEA “Hydrologie Urbaine ” Partie 9

MODELLING OF SEWER SOLIDS PRODUCTION AND TRANSPORT

Jean-Luc BERTRAND-KRAJEWSKI

OSHU3 13 Modelling of sediment transport and processes - 01/12/2006

J.-L. Bertrand-Krajewski, URGC Hydrologie Urbaine, INSA de Lyon

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CONTENTS 1. INTRODUCTION ....................................................................................................... 3 2. BASIC CHARACTERISTICS OF SEWER SOLIDS .................................................................. 3 2.1 Grain size and specific gravity............................................................................... 3 2.2 Calculated settling velocities.................................................................................. 4 2.2.1 Rubey formula (1933)..................................................................................... 4 2.2.2 Stokes formula ................................................................................................ 4 2.2.3 Zanke formula................................................................................................. 5 2.2.4 Van Rijn formula ............................................................................................ 5 2.3 Measured settling velocities................................................................................... 5 3. ACCUMULATION OF PARTICLES ON THE CATCHMENT................................. 5 3.1 The Storm Water Management Model................................................................... 6 3.2 Servat model .......................................................................................................... 6 4. WASHOFF BY RAINFALL........................................................................................ 6 4.1 Deterministic models ............................................................................................. 6 4.2 Conceptual models................................................................................................. 8 4.2.1 The SWMM .................................................................................................... 8 4.2.2 NPS model ...................................................................................................... 8 4.2.3 MOSQITO model ........................................................................................... 9 4.2.4 Servat model ................................................................................................... 9 4.2.5 Other models................................................................................................... 9 5. PASSAGE THROUGH GULLY POTS..................................................................... 10 5.1 Grottker model ..................................................................................................... 10 5.2 Fletcher and Pratt model ...................................................................................... 10 6. SEDIMENT TRANSPORT ....................................................................................... 11 6.1 Basic concepts of solid transoprt of cohesionless particles.................................. 11 6.2 Units for solid transport ....................................................................................... 13 6.3 Incipient motion and Shields parameter for bed load .......................................... 14 6.3.1 Neill formula for mean velocity for scour of bed material ........................... 16 6.4 Bed load transport formulas................................................................................. 16 6.4.1 Meyer-Peter and Müller formula .................................................................. 17 6.4.2 Einstein formula............................................................................................ 18 6.4.3 van Rijn formula ........................................................................................... 18 6.4.4 Novak and Nalluri formula ........................................................................... 19 6.4.5 Side wall elimination procedure ................................................................... 20 6.5 Suspended load transport ..................................................................................... 21 6.5.1 Inception of suspended load motion ............................................................. 21 6.5.2 Rouse formula............................................................................................... 22 6.5.3 Van Rijn formula .......................................................................................... 22 6.6 Total load transport .............................................................................................. 24 6.6.1 Macke relation for total load......................................................................... 24 6.6.2 Velikanov model for suspended and/or total load ........................................ 24 6.6.3 Ackers-White model for total load................................................................ 25 6.7 Solid transport in closed pipes ............................................................................. 26 6.8 Cohesion of sediment........................................................................................... 26 6.9 Design criteria for self-cleansing sewers ............................................................. 26 7. BRIEF PRESENTATION OF SOME SOFTWARES................................................ 29 7.1 The SWMM ......................................................................................................... 29 7.2 THALIA model.................................................................................................... 30 7.3 Combes and FLUPOL models ............................................................................. 30 7.4 MOSQITO model ................................................................................................ 31 7.5 KOSIM model...................................................................................................... 31

OSHU3 13 Modelling of sediment transport and processes - 01/12/2006

J.-L. Bertrand-Krajewski, URGC Hydrologie Urbaine, INSA de Lyon

2 7.6 Other models ........................................................................................................ 32 8. DIFFICULTIES FOR MODEL COMPARISON ....................................................... 32 9. CONCLUSION .......................................................................................................... 33 10. NOTATIONS ........................................................................................................... 33 11. REFERENCES......................................................................................................... 35

OSHU3 13 Modelling of sediment transport and processes - 01/12/2006

J.-L. Bertrand-Krajewski, URGC Hydrologie Urbaine, INSA de Lyon

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1. INTRODUCTION Hydrological and hydraulic models are now well established and are becoming more detailed (See Sections 3 to 6). Generally, they are conceptual for their hydrological part, and conceptual or physically based (mechanistic) for hydraulic transfer (Desbordes 1984, Yen 1986, Deutsch et al. 1989, Hémain 1991, Bertrand-Krajewski 1991, Bertrand-Krajewski et al. 1993). Quality models are more recent (Huber 1986) and more difficult to establish and calibrate, particularly because of the lack of good and adequate field experimental data, and, of course, because the phenomena themselves are very complex and not very well understood. Many pollutants can be taken into account : chemical oxygen demand, nitrogen, total suspended solids, heavy metals... (see Section 7). Only models for solid concentrations and loads will be presented hereafter. This choice is due to the major importance of sediment problems in urban hydrology. After a brief reminder of some basic particles characteristics, this section will describe some models used to simulate the typical four main steps usually identified : -

the accumulation of sediments over an urban catchment ; the washoff of these sediments by rainfall ; their passage through gully pots ; their transfer, erosion and deposition in sewer pipes.

For each step, the distinction will be made, if necessary and pertinent, between conceptual and physically based models. This paper simply presents the basic equations of the models, but not their detailed working or comparative simulation results (see paragraph 8). Nevertheless, the accuracy of these models is an important question. The agreement between observed and calculated values is a usual criterion of estimation, which can be quantify thanks to objective functions like least squares method. Many urban hydrologists admit that a quality model gives “satisfactory results” if the overall curve of the calculated pollutograph is similar to the observed one. Such a similarity can include discrepancies for local points, peak values or time shifts. These discrepancies are generally accepted because : - the measured values are themselves not accurate due to sampling techniques, with errors in a range of 20 to 50 % or more. - the equations are often rough approximate compared to the complexity of the physical phenomena. However the discrepancies have to be appreciated in relation to the objectives of the user : does he want an accurate value at each time step, or an overall estimation of the total load for a storm event ? Some quality models for sewer design just give an order of magnitude. The expression “satisfactory results” if then partly subjective. From a scientific point of view, it shows that further research is obviously needed to improve basic knowledge and modelling approaches, even if some models are already employed by engineers to design sewer systems. The pollution of stormwater is now a so important problem that many solutions have to be used, even if the knowledge of the phenomena and the capabilities of the models are still not well defined.

2. BASIC CHARACTERISTICS OF SEWER SOLIDS The three main characteristics of sewer solids used in solid transport basic equations are the grain size and the specific gravity (see paragraph 2.1) and/or the settling velocities. In some models, settling velocities are calculated from grain size and specific gravity, assuming that the particles are non cohesive and spherical (see paragraph 2.2). In other models, settling velocities should be given directly as a model parameter and may be issued from experimental measurements (see paragraph 2.3).

2.1 GRAIN SIZE AND SPECIFIC GRAVITY Many authors have worked on particle size distribution (e.g. Artières 1987; Brombach 1984; Chebbo et al. 1990a, b, 1991; CIRIA 1987; Göttle 1978; Laplace and Dartus 1991; Lessard et al. 1982; Marsalek 1984;

OSHU3 13 Modelling of sediment transport and processes - 01/12/2006

J.-L. Bertrand-Krajewski, URGC Hydrologie Urbaine, INSA de Lyon

4 Verbanck 1990) and, although a great variability according to the experimental site is observed, the following typical results can be given (more information is given in Section 7) : - particles deposited along roads and kerbs : their diameter is usually between 200 and 1000 μm, with a mean median diameter d50 of about 300-400 μm (specific gravity : 2,6) ; - particles in domestic sewage : the d50 is about 30-40 μm (specific gravity : 1,5) ; - particles transferred in sewers by rain weather : they are very fine, with a median diameter of 30-40 μm, and are transported essentially in suspension (specific gravity : 2,4) (Chebbo et al. 1989; Dastugue et al. 1990) ; - particles deposited in sewers : they are larger than those transported by suspension : their d50 is about 2001000 μm (Crabtree 1989; Ashley 1991), and they are transported essentially by rolling and saltating along the sewer invert (specific gravity : 2,6). Along a sewer trunk, the mean diameter of deposited particles diminishes from inlet to outlet : there is a granulometric sorting with distance (Artières and Stotz 1988; Laplace et al. 1989]. Some authors have observed an increasing median diameter of deposited particles at the same location with time, due to the consolidation of deposits by organic matter (Artières 1987; Chebbo et al. 1990b; Kleijwegt et al. 1989; Luu et al. 1990) and/or by chemical precipitation (Roberts et al. 1988).

2.2 CALCULATED SETTLING VELOCITIES Several formulas have been proposed in the literature to calculate the settling velocity of non cohesive solid particles, under the following conditions : - the particle is spherical ; - the particle is isolated in a infinite water volume. According to the formulas, and also in experimental conditions, it is important to note that the settling process of a mixture of grains leads to a sorting of the grains. This sorting effect depends on both grain diameter and density. It should also be noticed that, for graded sediments, the representative diameter d to be used in the formulas may be very different from the median d50 diameter.

2.2.1 Rubey formula (1933) Rubey (1933) proposed the following relationship : ρ −ρ w=F g s d ρ

with

g ρs ρ d F

acceleration of gravity (m/s2) density of the particle (kg/m3) density of water (kg/m3) diameter of the particle (m) factor of Rubey given by : 1/ 2

⎛ 2 36ν 2 ⎞ ⎟ F =⎜ + ⎜ 3 Δgd 3 ⎟ ⎝ ⎠

with

Eq. 2.1

1/ 2

⎛ 36ν 2 ⎞ ⎟ −⎜ ⎜ Δgd 3 ⎟ ⎝ ⎠

Eq. 2.2

ν kinematic viscosity (m2/s) ρ −ρ . Δ= s ρ

2.2.2 Stokes formula The Stokes’ law is written : w=

gd 2 (ρ s − ρ) gΔd 2 = 18μ 18ν

Eq. 2.3

with µ = νρ the dynamic viscosity (all other variables as in the above Rubey formula).

OSHU3 13 Modelling of sediment transport and processes - 01/12/2006

J.-L. Bertrand-Krajewski, URGC Hydrologie Urbaine, INSA de Lyon

5 The Stokes formula, originally established for quartz grains with d < 100-150 µm, is one of the most widely used formula thanks to its simplicity. However, sewer particles are not isolated particles and are submitted to some flocculation effects. Under such conditions, there are large discrepancies between calculated and actual settling velocities.

2.2.3 Zanke formula For sand particles which diameter d is between 100 and 1000 µm, one can use the formula proposed by Zanke (1977) : ν w = 10 d

0. 5 ⎤ ⎡⎛ 3 ⎢⎜1 + 0.01 gΔd ⎞⎟ − 1⎥ ⎢⎜ ⎥ ⎟ ν2 ⎠ ⎣⎢⎝ ⎦⎥

Eq. 2.4

2.2.4 Van Rijn formula For sand particles which diameter d is above 1000 µm, one can use the formula proposed by van Rijn (1984b) : w = 1.1 gΔd

Eq. 2.5

2.3 MEASURED SETTLING VELOCITIES The settling velocity of suspended sewer solids is frequently represented by means of the median settling velocity w50, i.e. 50 % in mass of the particles have a velocity lower than w50. Other indicators like w10, w35 or w90 are used in some models. Some typical values are given in Table 2.1.

Combined sewers Separate sewers (F) Separate sewers (USA)

Settling velocities (m/h) w50 w90 w10 < 0.06 8.1 67 0.37 7.2 89 0.10 4.9 213

Table 2.1 : typical mean values of w10, w50 and w90 for different types of sewer systems (Stahre et Urbonas 1990, Chebbo 1992)

Chebbo (1992) measured the following values of w50 in French sewer systems : - 5.5 to 9 m/h in separate sewers ; - 3.7 to 11 m/h in combined sewers. Pisano and Zukovs (1992), in the USA, measured w50 = 25.2 m/h in CSO discharges. Michelbach and Wöhrle (1992), in Germany, measured w50 = 21.6 m/h in combined sewer systems. The differences are due to two main factors : - the intrinsic local variability of the settling velocities - the various methods used to experimentally measure settling velocities, which are completely different and lead to different values for the same samples. A more detailed discussion about these protocols and their problems is given by Aiguier et al. (1996), Bertrand-Krajewski et al. (1996), Gagné and Bordeleau (1996), Lucas-Aiguier et al. (1998).

3. ACCUMULATION OF PARTICLES ON THE CATCHMENT This is the first phase of most of the models. The build-up of sediments is usually supposed to be linear or exponentially asymptotic with time. Both approaches are proposed in the literature, and experimental results do not allow to choose definitely between them.

OSHU3 13 Modelling of sediment transport and processes - 01/12/2006

J.-L. Bertrand-Krajewski, URGC Hydrologie Urbaine, INSA de Lyon

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3.1 THE STORM WATER MANAGEMENT MODEL The Storm Water Management Model (SWMM) is known worldwide. Its first version was created at the end of the sixties for the US EPA (Environment Protection Agency). The accumulation process is governed by the following equation which leads to an exponential asymptotic build-up (Alley and Smith, 1981) : dM a = ACCU - DISP M a dt

with

Ma t ACCU DISP

Eq. 3.1

accumulated mass of particles at time t (kg) time (d) daily accumulation rate (kg/d) disappearing coefficient (d-1)

DISP is a coefficient representing particle removal due to wind, traffic, biological and biochemical degradation, street sweeping. Ma increases until an upper limit equal to ACCU/DISP is reached. Sartor et al. (1974) found that this limit was reached after about 10 days, but this value is subject to great variations according to site and weather conditions. The values of ACCU and DISP depend on urbanisation, site, weather, and must be determined by calibration for each catchment. In such a model, the antecedent dry period seems to play an important role which is not easily explained. Because the SWMM is well known, several models use the same basic relation, like the French model Flupol (Bujon 1988, Bujon and Herremans 1990) and Hypocras (Bertrand-Krajewski 1992), the German one Thalia (Iossifidis 1985), and others like NPS (Litwin and Donigian 1978) or STORM (Warwick and Wilson, 1990).

3.2 SERVAT MODEL Servat (1984) studied different accumulation models (asymptotic, power, linear and parabolic functions), and he proposed to use a simple linear relation : M ai= ACCU DTSi

with

Mai ACCU

Eq. 3.2

mass of particles over the catchment (kg/ha) accumulated during a dry weather period DTSi (d) accumulation rate (kg.ha-1.d-1).

According to French field data for small catchments with separate sewers, this relation has given the best values of accumulated sediments for a long period simulation (about 1 year).

4. WASHOFF BY RAINFALL During a storm event, the accumulated particles on impervious areas (streets, kerbs, roofs) are washed off. Many parameters are involved in this phenomenon (Servat 1984) : rainfall intensity, rainfall height, rainfall duration, runoff peaks and volume, topography, particles characteristics. The most important among these parameters is the rainfall intensity, and especially the square of the maximum rainfall intensity (Shivalingaiah and James 1984, Borah 1989). According to different authors, the particles are washed off by rain drop impact, and transported into sewers by surface runoff (Young and Wiersma 1973, Servat 1984, Aalderink et al. 1990).

4.1 DETERMINISTIC MODELS Little research has been carried out on the physical process of washoff over urban catchments. The models proposed for soil erosion in agricultural or natural sites (Bubenzer and Jones 1971, Ranchet and Philippe 1982, Zhang and Cundy 1987, Tan 1989) are not easily adaptable and not used in urban hydrology. However, some of them are briefly presented hereafter because they may help urban hydrologist to identify the main driving parameters. Bubenzer and Jones (1971) have shown that soil erosion was proportional to rainfall intensity, kinetic energy of raindrops and percentage of clay in the soil, by fitting the following type of relationship for four different soils : S L = αI β E k γ Pc δ

OSHU3 13 Modelling of sediment transport and processes - 01/12/2006

Eq. 4.1

J.-L. Bertrand-Krajewski, URGC Hydrologie Urbaine, INSA de Lyon

with

SL I Ek Pc

7 soil loss (g/cm2) rainfall intensity (mm/h) kinetic energy (joules/cm2), that depends on the raindrop size and terminal velocity clay percentage (%).

Tan (1989), after a review of previous data and experiments, proposed a model to evaluate the soil loss due to rainfall. The model is based on the pressure due to the impact of a raindrop, given by : pe =

with

⎛ 3 ⎞ 4 3 ⎟ ρwr 2 exp⎜⎜ − ⎟ 3 8r 2 ⎝ 8r 2 ⎠

pe ρ wr r

Eq. 4.2

pressure generated as a result of raindrop impact (Pa) density of water (kg/m3) terminal velocity or velocity of raindrop at the moment of impact (m/s) ratio of depth of water d (m) to drop diameter D (m) (-).

The soil loss is then given by the expression : S L = K 3 exp( K 4 pe )

with

SL K3 K4

Eq. 4.3

soil loss (kg/s) numerical coefficient (kg/s) numerical coefficient (Pa-1) depending on hydraulic flow and soil properties.

The larger the raindrop, the higher is the eroding pressure pe. Moreover, the eroding pressure shows a peak value for r = (3/8)1/2 and then decreases when the depth of water increases. The terminal velocity of raindrops may be calculated according to the data and relationship given in Figure 4.1. 10

terminal velocity w r (m/s)

9 8 7 6

w r = 0.0481D 3 - 0.8037D 2 + 4.621D r 2 = 0.9991

5 4 3 2 1 0 0

1

2

3

4

5

6

7

raindrop diameter D (mm)

Figure 4.1 : terminal velocity of raindrop vs. diameter (data from Best 1950)

Best (1950), from various data series, has established a relationship between the distribution of raindrop size and the rainfall intensity : ⎛ ⎛ x ⎞n ⎞ 1 − F = exp⎜ − ⎜ ⎟ ⎟ ⎜ ⎝a⎠ ⎟ ⎝ ⎠

Eq. 4.4

a = AI p

Eq. 4.5

W = CI r

Eq. 4.6

with

F

fraction of liquid water in the air comprised by raindrops with diameter less than x mm

OSHU3 13 Modelling of sediment transport and processes - 01/12/2006

J.-L. Bertrand-Krajewski, URGC Hydrologie Urbaine, INSA de Lyon

I W

8 rainfall intensity (mm/h) amount of liquid water per unit volume of air (mm3/m3).

A, C, p, r and n are numerical coefficients, whose mean values are as follows : A = 1.30, C = 67, p = 0.232, r = 0.846, n = 2.5.

4.2 CONCEPTUAL MODELS The washoff is such a complex process that physically based models are replaced by conceptual or global models in urban hydrology. They usually do not separate erosion by rain drops and transport by runoff. Sometimes, they are reduced to a simple "washoff coefficient".

4.2.1 The SWMM The washoff process is supposed to be in direct ratio to the available mass of accumulated particles and to the rainfall intensity. This assumption is written (Jewell and Adrian 1978, Alley 1981) : dM a = -K e i (t ) M a dt

with

Ma i(t) Ke

Eq. 4.7

accumulated mass on impervious surfaces at time t (kg) rainfall intensity at time t (mm/h) washoff coefficient (mm-1)

The first authors proposed the standard value Ke = 0.18 mm-1. However it has rapidly been shown that Ke needs to be calibrated specifically for each catchment (Alley 1981). If Me is the mass of particles entering into the sewer during a time step, the relation becomes : M e (t + Δt ) = M a (t )⎛⎜1 − e − K e i (t + Δt ) Δt ⎞⎟ ⎝ ⎠

Eq. 4.8

An adaptation to very small or very strong rainfall is possible thanks to the introduction of an "availability factor" Kd : M e (t + Δt ) = K d M a (t )⎛⎜1 − e − K e i (t + Δt ) Δt ⎞⎟ ⎝ ⎠

with

Eq. 4.9

Kd = 0.057 + 0.04 i(t)1.1 for suspended particles Kd = 0.028 + 0.003 i(t)1.8 for deposited particles.

In the model Flupol (Bujon 1988), a lumped coefficient Ke' = KeKd is used and the basic equation becomes : dM a = -K e ' i (t ) M a dt

Eq. 4.10

Another refinement is the introduction of an exponent ω for rainfall intensity in Eq. 4.8, with 0,8 < ω < 2. With this last refinement, the model finally depends on the square of rainfall intensity and should allow a better calculation of peak values. In spite of all refinements and parameters introduced in Eq. 4.7, the results are not significantly improved.

4.2.2 NPS model In the NPS (Non Point Source) model, Litwin and Donigian (1978) proposed the following relation for impervious areas, where the washoff depends on the available mass and on the surface runoff : M e (t ) = K eni S b c M e (t ) = M a (t )

with

Me(t) Ma(t) Keni Sb

if M e (t ) ≤ M a (t ) if M e (t )>M a (t )

Eq. 4.11

washed off mass at time t (ton/ha) accumulated mass at time t (ton/ha) washoff coefficient surface runoff on impervious area (mm)

OSHU3 13 Modelling of sediment transport and processes - 01/12/2006

J.-L. Bertrand-Krajewski, URGC Hydrologie Urbaine, INSA de Lyon

9 c

numerical coefficient.

In spite of great discrepancies, Litwin and Donigian considered that their results were satisfactory. Models using rainfall intensity are probably more realistic for the washoff process itself.

4.2.3 MOSQITO model The MOSQITO model proposed by Hydraulics Research Wallingford (Henderson and Moys 1987, Moys et al. 1988) uses the following equation : dM a M a qb = ai i1.5 + ae (τ 0 − τ ce ) + a d (τ cd − τ 0 ) − dt Kqb + S m

with

a i, a e, a d i τ0 τce τcd qb Sm K

Eq. 4.12

Price-Mance coefficients rainfall intensity mean shear stress critical shear stress for erosion critical shear stress for deposition surface runoff soil depression storage linear reservoir parameter (the linear reservoir model is used to reproduce the rainfall runoff process)

The first calibrations (Payne et al. 1989) have shown that the second and third terms of Eq. 4.12 were negligible compared to the first and fourth ones. The relation can then be simplified and rewritten as : dM a M a qb = a i i1.5 − dt Kqb + S m

Eq. 4.13

This relation is the only one which distinguishes the washoff by rainfall and the erosion by surface runoff. However the results are not significantly better than those given by other models, probably because it needs more parameters whose calibration remains approximate.

4.2.4 Servat model Using several field data and statistical analysis, Servat (1984) proposed the following expression :

M e = K s M a a I max 5 bVr c with

Me Ma Ks Imax5 Vr a, b, c

Eq. 4.14

washed off mass (kg) accumulated mass (kg) washoff coefficient maximum rainfall intensity during a time step of 5 minutes (mm/h) runoff volume (m3) numerical coefficients

The results have an overall accuracy of about 5 % for a long period (several months), but the accuracy decreases to 10-30 % for particular events. Servat used the maximum intensity for 5 minutes, but the value for one minute (available with new devices) would be better, because the washoff phenomenon depends on instantaneous rainfall intensity peaks.

4.2.5 Other models Many other models have been proposed (Bedient et al. 1980, Brombach 1982, 1984, Geiger 1984, Göttle 1978), which are often a simple variation or an adaptation of the preceding ones. All of them need to be calibrated for each catchment before they can be used. A last category exists : the statistical models. They can only give mean results, and are unable to reproduce satisfactorily a particular event. Their domain of validity is limited to the experimental sites which were used for their establishment (Jewell and Adrian 1982).

OSHU3 13 Modelling of sediment transport and processes - 01/12/2006

J.-L. Bertrand-Krajewski, URGC Hydrologie Urbaine, INSA de Lyon

10 A example has been proposed by Driver and Troutman (1989). One of the regression equations is (for areas in the USA with annual rainfall less than 500 mm) : M e = 14.374 H t 1.211 A0.735 d p −0.463

with

Me Ht A dp

Eq. 4.15

washed off mass during the rainfall event (kg) total rainfall height (mm) catchment area (km2) rainfall duration (min)

Eq. 4.15 gives very approximate results : the discrepancy can reach 200 % or more. Such models are generally not enough precise for practical use or design : they can just give an order of magnitude.

5. PASSAGE THROUGH GULLY POTS Washed off particles enter into the sewer system through street inlets along kerbs or in parking areas. These inlets are named gully pots when they have a storage capacity of some ten litres at their bottom. Particles are partly retained and accumulated in these devices. With a runoff increase, accumulated particles are eroded again and enter into the sewer pipes with storm water. These phenomena have been studied and it appears that they depend on runoff and particle characteristics, dry weather period, season, catchment slopes and imperviousness.

5.1 GROTTKER MODEL After experimental studies, Grottker and Hurlebusch (1987) and Grottker (1990) proposed a model for both dry and wet gullies, which predicts the "passed load" (i.e. the load which cannot be retained by gully pot) as a function of the two main parameters he identified : the pollutant load and the flow rate through street inlets. This model is written : M p = aM a Q b

with

Mp Me Q a, b

Eq. 5.1

mass of particles passing through the gully pot (kg) mass of particles washed off by rainfall (kg) flow rate through the gully pot (L/s) numerical coefficients depending on the particle diameter.

Grottker showed also that this relation was time independent. Eq. 5.1 gives results with errors in a range of 10 to 30 %. However the model should be tested for other sites.

5.2 FLETCHER AND PRATT MODEL Fletcher and Pratt (1981) proposed a model to reproduce the flushing mechanism of accumulated sediments in gully pots by wet weather. This flushing out is due to the stirring action of the inflow water. Their model was tested later by Wada et al. (1987) and Wada and Miura (1988). Two phenomena can be distinguished : - for sediments already in suspension in the gully water, the concentration is given by the following relation : ⎛ −tQP ⎞ ⎜ ⎟ C = C 0 ⋅ e ⎝ 100V ⎠

with C C0 t Q V P

Eq. 5.2

suspended sediment concentration in the outflow (mg/L) initial concentration in the gully pot (mg/L) time (s) inflow (L/s) gully pot volume (L) percentage of gully pot fluid mixed (%).

if Q < 0.12 L/s then P = 664 Q + 19.7 if Q ≥ 0.12 L/s then P = 100.

OSHU3 13 Modelling of sediment transport and processes - 01/12/2006

J.-L. Bertrand-Krajewski, URGC Hydrologie Urbaine, INSA de Lyon

11 - for sediments resuspended from bottom deposited sediments, with M total mass of released sediment (kg) and Kr rate of release (mg/s), the relations are : if 0 < t < M/Kr (re-suspension is continued) : ⎛ ⎛ − tQ ⎞ ⎞ ⎜ ⎟⎟ Kr ⎜ ⎜1 − e ⎝ V ⎠ ⎟ C= Q ⎜ ⎟ ⎜ ⎟ ⎝ ⎠

Eq. 5.3

if M/Kr < t < ∞ (re-suspension is finished) : ⎛ ⎛ − MQ ⎞ ⎞ ⎛ − tQ MQ ⎞ ⎜⎜ ⎟⎟ ⎜ ⎟ ⎜ + K K V ⎟ ⎜ V K r V ⎟⎠ C = r ⎜1 − e ⎝ r ⎠ ⎟e ⎝ ⎟ Q ⎜ ⎜ ⎟ ⎝ ⎠

Eq. 5.4

Wada and Miura determined Kr and M with the following empirical equations : K r = (1.78Q + 0.22) M t

Eq. 5.5

M = (57.1Q + 0.83) M t

Eq. 5.6

with Mt the total mass of sediment in the bottom of the gully pot. The above numerical coefficients were experimentally determined by Wada and Miura. Fletcher and Pratt observed that the gully pots were efficient : with the maximum inflow that they examined (1,0 L/s), only 0,2 % of the bottom sediments was released. The results presented by the authors showed a good agreement with field data.

6. SEDIMENT TRANSPORT This step is the most complex because of : - the insufficiency of available data for sewer systems - the complexity of the physical process which involves bed and suspended loads, deposition and erosion processes - the great number of parameters to be accounted for : velocities, shear stresses, collectors geometry, particles characteristics. Many researchers have worked on sediment transport, especially for fluvial hydraulics and solid transport in closed pipes. The transposition of their results and relations to urban hydrology and especially sewer systems is problematic because site conditions are very different : particles are smaller (d < 100 μm) and partly cohesive due to organic matter, the flow is turbulent and unsteady, pipes are not filled up but present free surface flows. In the late 1980s and 1990s, significant research programs have been undertaken for pipes with free surface flows, deposits and cohesive particles to reproduce as closely as possible the actual conditions observed in sewers (Kleijwegt 1992, Nalluri 1991, Perrusquia 1992). However these studies did not lead to definitive and practical results. In the following paragraphs, the main definitions and relations for fluvial hydraulics and solid transport in pipes are briefly reminded. Some equations which are actually used in urban hydrology are then described with more details.

6.1 BASIC CONCEPTS OF SOLID TRANSOPRT OF COHESIONLESS PARTICLES According to Raudkivi (1998), « in a combined flow of fluid and sediment in an open channel, assuming tow dimensional steady uniform flow, the flow is determined by its depth y (m), slope Ir (m/m) and gravity g(m/s2), which provides the driving force [for particles transport] ». The fluid itself is characterised by its density ρ (kg/m3) and dynamic viscosity µ (kg/m/s). The particles, assuming they have a uniform size, are characterised

OSHU3 13 Modelling of sediment transport and processes - 01/12/2006

J.-L. Bertrand-Krajewski, URGC Hydrologie Urbaine, INSA de Lyon

12 by their diameter d (m) and their density ρs (kg/m3). These seven basic variables maybe combined and/or substitutre by others, using physical relationships or dimensional analysis, to give alternative variables which are very frequently used in the field of solid transport. The most frequently used alternative variables are the following ones : the kinematic viscosity ν (m2/s) : ν = μ/ρ the relative roughness (-) :

Eq. 6.1

y d

Eq. 6.2

ρ the relative density s (-) : s = s ρ

Eq. 6.3

the parameter γs (kg/m2/s2) : γ s = g (ρ s − ρ)

Eq. 6.4

ρ −ρ the parameter Δ (-) : Δ = s = s −1 ρ

Eq. 6.5

the shear velocity u* (m/s) : u* = gRh I r ≈ gyI r

with Rh = S/Pw the hydraulic radius (m) where S is the flow section (m2) and Pw the wetted perimeter (m). If the flow width is large compared to the flow depth, then Rh ≈ y. the bed shear stress τ0 (N/m2) : τ 0 = ρu *2 = ρgRh I r ≈ ρgyI r the particle Reynolds number Re (-): Re =

the Shields parameter θ (-) : θ =

Eq. 6.6

Eq. 6.7

u*d ν

Eq. 6.8

τ ρu* 2 = 0 = Fd 2 γ sd γsd

Eq. 6.9

where Fd is the grain Froude number 1/ 3

⎛ gΔd 3 ⎞ ⎟ the dimensionless grain size D* (-) : D* = ⎜ ⎜ ν2 ⎟ ⎝ ⎠

the sedimentation parameter η (-) : η =

1/ 3

⎛ gΔ ⎞ ⎟ = d ⎜⎜ ⎟ ⎝ ν2 ⎠

w κu *

Eq. 6.10

Eq. 6.11

with κ the von Karman constant (κ ≈ 0.4)

Usually, three types of solid transport are distinguished : - the bed load transport : the particles are sliding, rolling and saltating, without to leave definitely the bed (see Danel et al. 1973 about saltation) ; - the suspended load : the particles from bed material or from other sources remain in suspension in the flow without definitive deposition, but temporary deposition is possible ; - the wash load : very fine particles which are permanently transported in the flow, without any deposition. The total load is the sum of the three above loads.

Many authors simply distinguish bed and suspended load, assuming that the wash load is not really a mode of solid transport. From the modelling point of view, the wash load is usually calculated by the advectiondispersion equation used for soluble substances.

OSHU3 13 Modelling of sediment transport and processes - 01/12/2006

J.-L. Bertrand-Krajewski, URGC Hydrologie Urbaine, INSA de Lyon

13 Concerning the suspended load, one distinguishes between : - the homogeneous suspension, where the concentration C (kg/m3) is constant along the water depth y ; - the heterogeneous suspension, where the concentration C increases from the water surface to the bottom of the flume or pipe. In sewer systems with free surface flows, the suspension is heterogeneous in most cases. Another important distinction is made according to the presence of deposits : - the transport in smooth flumes or pipes without deposits over the bottom ; - the transport in flumes and pipes where fixed or loose deposits are present and may be eroded. As real physical processes are interactive and not easy to separate, the frontiers between bed load, suspended load and wash load are partly arbitrary. But their distinction facilitates theoretical and experimental approaches and works. Some authors have proposed numerical criteria to distinguish bed load and suspended load. They usually used the ratio of the particle settling velocity w (m/s) to the shear velocity u*. For example, Raudkivi (1998) indicates for fluvial hydraulics : w < 0.6 suspended load u* w saltation (i.e. particles saltating over the bed but remaining in frequent contact with the bed) 0.6 < 1 (i.e. for small particles and high concentrations), Eq. 6.33 and Eq. 6.36 give similar results. For decreasing values of φ, the divergence between the formulas increases significantly. An attempt to use the relation of Graf-Acaroglu for solid transport in sewer systems has been carried out at the University of Karlsruhe (Germany) [Beichert, personal communication].

6.4.5 Side wall elimination procedure As most of the bed load transport formulas give a transport rate per unit width, it appeared since the earlier studies that the effect of the walls should be eliminated in order to express the results as only depending on the shear stress contributing to the sediment transport, i.e. to the fraction of the shear stress linked to the bed. This separation between side walls and bed shear stress is accomplished using the so-called « side wall elimination » (or side wall correction) procedure which separates total roughness into side walls and bank roughness and conceptually divides the cross sectional area into additive components for obvious geometrical reasons. Many different procedure for side wall correction have been proposed, but the most frequently used ones are the procedures proposed by Einstein (1942) and Vanoni and Brooks (1957). Both procedures are similar in their principle, but the first one uses the Manning-Strickler roughness coefficient while the second one uses the Darcy-Weisbach friction factor. However, the Manning-Strickler roughness k, the Darcy-Weisbach friction factor f (also named λ) and the Chézy resistance coefficient Ch are related by the following relationship :

OSHU3 13 Modelling of sediment transport and processes - 01/12/2006

J.-L. Bertrand-Krajewski, URGC Hydrologie Urbaine, INSA de Lyon

21 R 1/ 6 = k h g

8 Ch = = f g

U

Eq. 6.37

gRh J

The side wall elimination is based on the assumption that the average velocity U and the energy gradient J are the same in all components of cross section. The following equation corresponds to the fact that the total cross section is divided into two virtual components which relate respectively to the wall and to the bed : S = S w + S b = Pw Rw + Pb Rb

Eq. 6.38

where S total cross section area (m2) P wetted perimeter (m) R hydraulic radius (m) and subscripts w and b correspond respectively to side wall and bed. Using the Manning-Strickler equation, the above assumption leads to the following expression of the hydraulic radius Rb corresponding to the bed only : U J

= k m Rh 2 / 3 = k b Rb 2 / 3 = k w Rw 2 / 3

Eq. 6.39

where km is the equivalent mean roughness coefficient for the whole cross section. Additionally, in case of beds with composite roughness, the calculation procedure to evaluate the contribution of each component to the total roughness has been proposed by Einstein and Banks (1950).

6.5 SUSPENDED LOAD TRANSPORT Among the most widely known relations, the following ones can be quoted : Rouse (quoted in Bouvard 1984), Van Rijn (1984b), Velikanov (Bujon 1988, Combes 1982), Wiuff (1985), Celik and Rodi (1991). These formulas are based on mechanical equilibrium, turbulence effects and energy considerations. Like bed load transport models, they are valuable for non cohesive particles with homogeneous diameters.

6.5.1 Inception of suspended load motion The transition from bed load to suspended load is more complex than the inception of bed load motion, and there is no simple criterion equivalent to the Shields criterion for bed load. The particles motion along the bed is not smooth : some of them may bounce and jump over the others. As the shear velocity u* increases, the number of particles bouncing and jumping increases until they become to be transported as suspended load. This is the reason why the threshold between bed load and suspended load is not well defined. “Considering a particle in suspension, the particle motion in the direction normal to the bed is related to the balance between the particle settling velocity component (w cosα) and the turbulent velocity fluctuation in the direction normal to the bed. Turbulence studies suggested that the turbulent velocity fluctuation is of the same order of magnitude as the shear velocity. With this reasoning, a simple criterion for the initiation of suspension (which does not take into account the effect of bed slope) is :” (Chanson 1999) u* > critical value w

One usually consider that suspension occurs when

Eq. 6.40 u* > 0.2 to 2. w

Initiation of suspension as suggested by Bagnold (1966) corresponds to u*/w = 1. Engelund (1967) considered that initiation of suspension occurs when u*/w = 0.25. Van Rijn (1984b) suggested the following formula for suspension :

OSHU3 13 Modelling of sediment transport and processes - 01/12/2006

J.-L. Bertrand-Krajewski, URGC Hydrologie Urbaine, INSA de Lyon

22 u* 4 > w D*

for 1 < D* < 10 Eq. 6.41

u* > 0.4 w

for D* > 10

Van Rijn (1984b, p. 1615) suggested that “the criterion of Bagnold may define an upper limit at which concentration profile starts to develop, while [his] criterion defines an intermediate stage at which locally turbulent bursts of sediment particles are lifted from the bed into suspension”.

6.5.2 Rouse formula Rouse (1937) established the following formula which gives the vertical concentration profile C(z) : w

⎛ y − z a ⎞ κu * ⎟⎟ C ( z ) = C (a)⎜⎜ ⎝ z y−a⎠

where a z y C(a) C(z)

Eq. 6.42

reference level (m) vertical coordinate (m) water depth (m) suspended load concentration at the reference level a (m3/m3) suspended load concentration at depth z (m3/m3).

If w/u* is high, C is high close to the bed and the profile is very significant ; if w/u* is low, C is rather uniform along the vertical axis. The main problem consists to evaluate a and C(a). This crucial question has been studied by many authors and some information will be provided in the following paragraphs. The suspended load transport rate qS (in m3/s per unit width) is then calculated by : z= y

qS =

∫ C ( z)u( z)dz

Eq. 6.43

z =a

where u(z) is the logarithmic velocity profile along the vertical axis. For turbulent flow regime over a smooth bed, u(z) is given by : log ( zu*) ⎛ ⎞ + 5.5 ⎟ u ( z ) = u * ⎜ 5.75 ν ⎝ ⎠

Eq. 6.44

For turbulent flow regime over a rough bed, u(z) is given by : ⎛ ⎛ z u ( z ) = u * ⎜ 5.75 log ⎜⎜ ⎜ ⎝ ks ⎝

⎞ ⎞ ⎟ + 8.5 ⎟ ⎟ ⎟ ⎠ ⎠

Eq. 6.45

where ks is the bed equivalent roughness of Nikuradse : ks ≈ 2d50 if the bed is flat, and ks is equal to the height of the dunes if dunes are present on the bed. The total suspended load is then calculated after integration of qS through the whole cross section S of the flow.

6.5.3 Van Rijn formula From laboratory flumes and rivers experiments, van Rijn (1984b) proposed the following method to calculate the suspended load, expressed as m3/s per unit width. One calculates successively : 1/ 3

⎛ gΔ ⎞ ⎟ D* = d ⎜⎜ ⎟ ⎝ ν2 ⎠

OSHU3 13 Modelling of sediment transport and processes - 01/12/2006

Eq. 6.10

J.-L. Bertrand-Krajewski, URGC Hydrologie Urbaine, INSA de Lyon

23 u *cr =

Eq. 6.46

gU

u*' =

T=

τ 0cr with τ0cr from the Shields curve (see Figure 6.2) ρ

⎛ 12 Rb ⎞ ⎟ 18 log ⎜⎜ ⎟ ⎝ 3 d 90 ⎠

Eq. 6.47

(u*')2 − (u *cr )2 (u *cr )2

Eq. 6.31

a = k s or a = 0.5 hd with hd the thickness of the bed load layer of the height of the dunes

Eq. 6.48

with the minimum value of a being equal to 0.01 d. ⎧⎪ ⎫⎪ dT 1.5 C (a) = min ⎨0.015 ; 0.65⎬ (m3/m3) ⎪⎩ ⎪⎭ aD *0.3

Eq. 6.49

In case of graded sediments, one calculates the geometric standard σs deviation from the grain size distribution of the sediments : σs =

1 ⎛ d 84 d16 ⎞ ⎜ ⎟ + 2 ⎜⎝ d 50 d 50 ⎟⎠

Eq. 6.50

and then the representative diameter ds to be used for further calculations : d s = d 50 (1 + 0.011 (σ s − 1)(T − 25) )

Eq. 6.51

If the grain size is uniform, ds = d50. Depending on the representative grain size ds, one uses the most appropriate of the formulas given in section 2.2 to calculate the settling velocity w. One then calculates : ⎛ w⎞ β = 1+ 2 ⎜ ⎟ ⎝ u *⎠ ⎛ w⎞ ϕ = 2.5 ⎜ ⎟ ⎝ u *⎠

2

0.8

for 0.1
Cmax

there is erosion until C = Cmin. there is sediment transport at concentration C without deposition or erosion. there is deposition until C = Cmax.

Combes proposed 0.0005 < ηmin < 0.002 and 0.002 < ηmax < 0.007, whereas Bujon used ηmin = 0.018 and ηmax = 0.022.

OSHU3 13 Modelling of sediment transport and processes - 01/12/2006

J.-L. Bertrand-Krajewski, URGC Hydrologie Urbaine, INSA de Lyon

25 This model is employed for total transport, but it seems that it gives better results for suspended load. Bujon, for Flupol, added an "efficiency coefficient" to fit the results as well as possible. The Velikanov model is easy to use, but it needs more experimental validations. The models proposed by Wiuff (1985) and Celik and Rodi (1991) for open channels have similar expressions, with refinements to calculate the efficiency coefficients. Wiuff, for example, proposed an expression of ηmax that depends on grain size and shear stress.

6.6.3 Ackers-White model for total load This model (Ackers and White 1973, 1980) was first established for sediment transport in open alluvial channels. An empirical adaptation for circular pipes has been proposed to have a better agreement with laboratory data (Ackers 1984, CIRIA 1987). The three main equations are : 1/ 3

⎛ g ( s − 1) ⎞ ⎟ D* = d 35 ⎜⎜ ⎟ ⎝ ν2 ⎠

Eq. 6.60

with d35 instead of d50 as usual 1− naw

Fgr =

⎛ ⎞ ⎜ ⎟ naw ⎜ ⎟ u* U ⎜ ⎟ ⎛ 12 Rh ⎞ ⎟ gd 35 ( s − 1) ⎜ ⎟ 32 log⎜⎜ ⎟⎟ ⎜ ⎝ d 35 ⎠ ⎠ ⎝

Eq. 6.61

m ⎛ Fgr ⎞ aw − 1⎟⎟ G gr = C aw ⎜⎜ ⎝ Aaw ⎠

qt = G gr sd 35

with

Eq. 6.62

1− n n 1 ⎛ U ⎞ aw ⎛ We Rh ⎞ aw ⎜ ⎟ ⎜ ⎟ Rh ⎝ u * ⎠ ⎝ S ⎠

Eq. 6.63

Fgr dimensionless mobility particle number Ggr dimensionless solid flow number qt total solid flow (kg particles/kg water) u* friction velocity (m/s) U mean flow velocity (m/s) Rh hydraulic radius (m) s specific gravity of particles (i.e. relative density) d35 effective diameter (for graded sediments) Aaw, Caw, naw, maw numerical coefficients depending on dimensionless particle diameter D* as given in Table 6.2. 1 < D* < 60

D* > 60 0.17

Aaw

0.23 D *−1 / 2 +0.14

Caw

log(C aw ) = 2.86 log( D*) − log( D*) 2 − 3.53 1.00 − 0.56 log( D*)

naw maw

9.66 ( D*) −1 + 1.34

0.025 0 1.50

Table 6.2 : values of the parameters in the Ackers-White formula

Aaw represents the Fgr value at which transport sediment begins. The Ackers-White formula is applicable to any bed form (flat bed, ripples, dunes, anti-dunes), but is limited to Froude numbers below 0.8.

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26 1− naw

⎛W R ⎞ The last term of Eq. 6.63 ⎜ e h ⎟ is the main corrective term for the adaptation to pipes, with ⎝ S ⎠ We = 10 d35 the effective deposited sediments width (m), and S the flow section (m2). This correction has an important effect for coarse particles (i.e. for bed load transport).

These equations have been verified by other researchers who obtained good results for laboratory experiments (Mat Suki and Nik Hassan 1990). The Ackers-White model, with this adaptation, is used in the models Mosqito and Mousetrap.

6.7 SOLID TRANSPORT IN CLOSED PIPES The transport of solids by water in closed pipes has been studied by several authors, due to its economical interest. Durand proposed a distinction between different transport regimes in relation to the particle diameter (Durand and Condolios 1952, Durand 1953), for graded sediments : - homogeneous mixture : for d < 25 μm, particles remain always in suspension without deposition and with a homogeneously distributed concentration. - intermediary mixture : this is a transition domain, for d from 25 to 50 μm. -

heterogeneous mixture : for d from 50 to 200 μm : particles are transported in suspension with heterogeneous concentrations for d from 0,2 to 2 mm : particles are transported with intermediate conditions for d > 2 mm : particles are transported by saltation.

Durand relations have been established and verified for higher concentrations and for coarser particles than those observed in sewers. A more specific model has been established directly for sewer pipes with free surface flows by Macke (1980, 1983).

6.8 COHESION OF SEDIMENT All the above-mentioned equations were established, and are valid, for non cohesive particles. Nevertheless it is clear that sewer deposits are cohesive (Nalluri 1991, Nalluri and Alvarez 1992, Wotherspoon and Ashley 1992) : the rheological properties of their fine fraction are similar to those of a clay, and especially an illite (Artières 1987, Beyer 1989). This fraction has an important influence on the deposits behaviour. Consequently, it should be necessary to take sediment cohesion into account, with some characteristics like erosion threshold shear stress, initial rigidity, sediment consolidation with time, percentage of organic matter. In estuarine sediment field, some equations have been established (Partheniades 1965, Ariathurai and Arulanandan 1978, Mehta et al. 1989a, b, Migniot 1989a, b). However, because of the lack of knowledge about sewer sediments and despite recent research (Artières 1987, Beyer 1989, Williams et al. 1989), these relations have not yet been verified or adapted for urban hydrology. Quality models then usually ignore this important aspect.

6.9 DESIGN CRITERIA FOR SELF-CLEANSING SEWERS Most of the traditional design criteria are based on minimum slopes, minimum velocities and/or minimum shear stress required to avoid deposition and/or to ensure the periodic (usually daily) erosion and scouring of temporary deposits. Examples of traditional criteria may are summarised in Table 6.3.

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27 Minimum velocity criteria for self-cleansing sewer design Source

Country

Sewer type

Minimum velocity (m/s) 0.6 0.9 0.75

Pipe conditions

American Society of Civil Engineers (1970) British Standard BS 8001 (1987)

USA

Foul Storm Storm

Minister of Interior (1977)

France

Combined Foul Combined or separate storm sewer

1.0 0.3 0.6 0.3

Europe

All sewers

Germany

Foul Storm Combined

0.7 once per day for pipes with D < 300 mm 0.7 or more if necessary in sewers larger than D = 300 mm Depends on diameter of pipe ranging from 0.48 (D=150 mm) to 2.03 (D=3000 mm)

Full Mean daily flow For a flow equal to 1/10 of the full section flow for a flow equal to 1/100 of the full section flow N/A

European Standard EN 752-4 (1997)

UK

Abwassertechnische Vereinigung ATV, Standard A 110 (1998) (replaced by ATV 110 (2001))

Full/half-full Full/half-full Full

0.3 to full for 0.1 to 0.3, velocity plus 10 %

Minimum shear stress criteria for sewer design Reference source

Country

Sewer type

Lysne (1969)

USA

Minimum shear stress (N/m2) 2.0–4.0

ASCE (1970)

USA

1.3–12.6

Yao (1974)

USA

Maguire rule (CIRIA, 1986)

UK

Storm Foul

Pipe conditions

3.0–4.0 1.0–2.0 6.2

Full/half full

Lindholm (1984)

Norway

Combined Separate

3.0 – 4.0 2.0

-

Scandiaconsult (1974)

Sweden

All

1.0 – 1.5

1.5 if sand is present

Macke (1982)

Germany

Foul Storm Combined

depending on transport capacity and transport concentration

0.1 to full typical combined systems under longterm conditions

Brombach et al. (1993)

Germany

Combined

1.6 to transport 90% of all sediments

Table 6.3 : traditional self-cleansing sewer design criteria (excerpt from Ashley et al., 2004, p. 253)

However, these traditional criteria are not satisfactory because they do not account for the complexity of real situations, as already suggested by Calvert and Francis (1970). A more comprehensive approach has been proposed by Nalluri and Ab-Ghani (1996) who suggested specific equations accounting for solid concentration, grain size and sediment depth. It appears from their calculations that a limited depth of sediment is recommended for pipes which diameter is larger than 1 m in order to maximise their transport capacity (see Figure 6.4).

OSHU3 13 Modelling of sediment transport and processes - 01/12/2006

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28

Figure 6.4 : optimum sediment depth, Cv = 1000 ppm (half-full flow, d = 1 mm) (from Nalluri and Ab-Ghani 1996)

Nalluri and Ab-Ghani (1996) proposed two equations for clean pipes and for pipes with deposited loose beds : equation for clean pipes : ⎛R ⎞ = 3.08 Cv 0.21D *− 0.09 ⎜ h ⎟ gΔd ⎝ d ⎠

U cr

0.53

λ s − 0.21

Eq. 6.64

with λ s = 1.13 λ o 0.98Cv 0.02 D *0.01 equation for pipes with deposited loose beds : ⎛W = 1.18 C v 0.16 ⎜⎜ b gΔd ⎝ yo

U cr

⎞ ⎟ ⎟ ⎠

−0.18

⎛d⎞ ⎜ ⎟ ⎝ D⎠

− 0.34

λ s − 0.31

Eq. 6.65 ⎛W with λ s = 0.0014 Cv − 0.04 ⎜⎜ b ⎝ yo

with

Ucr Cv λs λo Wb yo D

⎞ ⎟ ⎟ ⎠

0.34

⎛ Rh ⎞ ⎜ ⎟ ⎝ d ⎠

0.24

D *0.54

self-cleansing velocity (m/s) volumetric sediment concentration (-) friction coefficient with sediment (-) friction factor with clear water (-) width of sediment bed (m) mean flow depth (m) pipe diameter (m)

For the friction factor, see Eq. 6.37. From the above equations, design charts may be drawn to determine the minimum slope required to reach the critical self-cleansing velocity for given pipe diameter, grain size, roughness and solid concentration. An example is given on Figure 6.5.

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29

Figure 6.5 : design chart for pipes with loose bed (half-full flow, d = 1 mm, ys/D = 15 %) (from Nalluri and Ab-Ghani 1996)

7. BRIEF PRESENTATION OF SOME SOFTWARES 7.1 THE SWMM It is one of the first quality models in urban hydrology. The first version (Lager et al. 1971) was fairly simple : all particles with a diameter greater than dd were deposited, all particles with a diameter smaller than de were eroded; dd and de were calculated with the Shields criterion, for each time and space step. The solid transfer was simply calculated too : the particles were supposed to be homogeneously distributed in water, and they were transferred at the same velocity as water, by applying the mass conservation law. All particles are described by a single size distribution. This model is simple but some assumptions are unrealistic and lead to approximate results : same velocity for particles as for water, single and constant size distribution for deposits and suspended load despite erosion and sedimentation. Some years later, an improved and more sophisticated version was established using Sonnen transport model (1977). This model distinguishes bed load, suspended load and wash load, for 10 grain size classes (Combes 1982). It considers separately particles from domestic sewage and from storm water. The bed load is represented by a relation derived from those of Kalinske (quoted in Larras 1972) which is approximated by straight line segments with the following expression : ⎛ − bτ cr ⎜ ⎜ τ q s = aρ s u * d × 10 ⎝ 0

with

qs u* ρs d a, b τ0 τcr

⎞ ⎟ ⎟ ⎠

Eq. 7.1

bed load flow per unit width (kg/s.m) friction velocity (m/s) density of particles (kg/m3) particles diameter (m) numerical coefficients depending on τcr and τ0 mean shear stress over flow section (N/m2) critical shear stress for particles (N/m2).

For suspended load, Sonnen uses the classical equation of Rouse.

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30 The wash load is assumed to be the difference between particles entering into the sewer and particles depositing in sewer. There is deposition if the flow velocity is smaller than a critical value Uc which is given by the following relation derived from that of Durand (1953) where the pipe diameter has been replaced by the flow depth y : U c = 0.9 (2 gy ( s − 1)) 0.5

with

Uc y s

Eq. 7.2

critical flow velocity (m/s) flow depth (m) specific gravity of particles (kg/m3).

This version of the SWMM can give satisfactory results but its calibration is not easy due to the great number of parameters. Rouse and Durand equations have been modified or adapted with assumptions which are not well established. In later versions, this sophisticated approach has been pulled out.

7.2 THALIA MODEL The THALIA model (Iossifidis and Hahn 1984, Iossifidis 1985, Iossifidis and Xanthopoulos 1986), established at the University of Karlsruhe (Germany), is initially a copy of the SWMM with Sonnen model. The relation for wash load is replaced by another one derived from Bagnold studies (quoted in Macke 1980), where a critical shear stress τc is introduced. This modification should allow a better accuracy and is written : τ c = 0.4 w 2 (ρ s − ρ)

if d < 2 mm

τ c = gd (ρ s − ρ)

if d > 2 mm

with

Eq. 7.3

w settling velocity of particles (m/s) d particles diameter (m).

The solid transfer model is coupled with the hydrodynamic software HAMOKA which uses the complete St Venant equations. It appeared that the calculation duration for solid transfer was three times longer than the time required for hydraulic calculations. To reduce this difference, the authors established a simplified version, which uses an empirical bed load transport equation from Shields : qc Q

⎛ γs − γ ⎞ τ − τ cr ⎟⎟ = 10 0 ⎜⎜ I ( γ s − γ )d γ ⎝ r ⎠

with

qc Q Ir τ0 τcr d γs , γ

Eq. 7.4

volumic bed load transport rate (m3/s) flow rate (m3/s) invert slope (m/m) mean shear stress (N/m2) critical shear stress for erosion beginning (N/m2) particles diameter (m) volumic weight of particles and water (N/m3).

Contrary to the first version, the simplified one does not take the real deposits into account, but the time needed for calculations is 10 times shorter and the results are not significantly different : the divergence is about 10 %.

7.3 COMBES AND FLUPOL MODELS Both models use Velikanov equations. Only Flupol (Bujon 1988, Bujon and Herremans 1990), established by the Compagnie Générale des Eaux and the Agence de l'Eau Seine Normandie (France), was employed to reproduce real data. It is coupled with an hydrological and hydraulic model using linear reservoirs and Muskingum schemes for flow calculations. Flupol does not use several grain size classes, but it distinguishes between solids during dry and wet weather. An "efficiency coefficient" has been introduced to improve calibrations, but it is more an artful device than a hypothesis in relation to the Velikanov theory. The first calibrations for French catchments around Paris give results with a satisfactory overall agreement between calculated and observed values. However this recent model needs further validations for other catchments.

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31

7.4 MOSQITO MODEL This model (Hydraulics Research 1989, 1991), developed by Hydraulics Research (UK), is one of the most detailed at the present time but it is still in its development phase. MOSQITO, which is coupled with the hydrodynamic software Wallrus (Brown 1990), uses the Ackers-White transport model. For wash load, it makes calculations with the advection-diffusion model from Holly and Preissmann (1977). The most interesting aspect of MOSQITO is its separation of deposits into two layers : - the upper layer, named "active layer", composed of non cohesive sediments, easily eroded, with an important organic matter fraction; - the lower layer, named "storage layer", composed of consolidated deposits, with an important mineral fraction and a specific gravity greater than 2. When the whole active layer is eroded, it becomes possible to erode the storage layer if the shear stress is greater than a critical value chosen by the user. With such a solution, MOSQITO is able to take the cohesion of sediments into account. The first calibrations show that MOSQITO can give interesting results for some catchments, but it is too early to draw more precise conclusions. There is a need for further research and comparisons with field data. Nevertheless, it is important to note that (Osborne and Payne 1990, Debarbat 1991) : - Mosqito is very sensitive to deposit height in the sewer and to the particle characteristics (density and settling velocity) ; - the storage layer can be eroded but its re-building is not very well defined ; - the dry weather part of calculations is too simplified and not sufficiently realistic.

7.5 KOSIM MODEL The KOSIM (Kontinuierliche Simulation) model (Sieker 1987, Durchschlag and Harms 1989, Preul et al. 1990) was established by the Institut für Technisch-Wissenschaftliche Hydrologie in Hannover (Germany) to design storm tanks. The hydrodynamic part is composed of linear reservoirs in cascade. The Kosim model is not as deterministic or detailed as the above-mentioned ones. Its three main hypotheses are : - the TSS concentrations in storm water are supposed to be constant in time - the TSS sources are domestic sewage, storm water from impervious areas and storm water from pervious areas - the TSS load is always in direct ratio to the flow rate. The resulting TSS concentration at the outlet is written : C (t ) =

with

Qeu C eu + Q pp C pp + Q pi C pi

Eq. 7.5

Qeu + Q pp + Q pi

C(t) Qeu, Ceu Qpp, Cpp Qpi, Cpi

TSS concentration at the outlet in mixed water flow rate and TSS concentration of domestic sewage flow rate and TSS concentration of water from pervious area flow rate and TSS concentration of water from impervious area.

This model takes the "first flush" phenomenon into account, but not the erosion and deposition in sewers. A second version (Ries 1990) has been proposed with the following improvements : - a first equation represents the growing of deposits in sewers : P (t ) = Pmax − ⎛⎜ Pmax − P (t − Δt )e − K1t ⎞⎟ ⎝ ⎠

Eq. 7.6

- a second equation represents the erosion of the deposited sediments : P(t ) = P(t − Δt )e (− K 2 (Q(t ) − Qlim )t ) with

P(t) Pmax Q(t) Qlim

Eq. 7.7

solid load at time t maximum mass of deposits in sewers flow rate at time t critical flow rate under which there is no erosion

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32 Δt K1, K2

time step numerical coefficients.

K1 is determined assuming that 50 % of the TSS entering into sewers during dry weather deposit in 24 hours. K2 is determined assuming that Qlim allows the erosion of the whole deposit in five minutes. Kosim is a simple conceptual model which tries to represent the main phenomena and to give a mean load for long periods. It should be evaluated with more experimental data, especially to evaluate the importance of the hypothesis of constant TSS concentration in storm waters. This model is already used in Low Saxony (Germany) as official software for every storm tank design project.

7.6 OTHER MODELS The present review does not pretend to be exhaustive, and other models for sewer sediment transport exist (Bertrand-Krajewski 1991). Among the recent ones, the following two may be quoted : - Berndtsson et al. model : it is a conceptual model which was originally established to predict overflows from combined sewers (Hogland et al. 1984, Berndtsson et al. 1986). It can take the erosion of deposited sediments into account, with a relation proposed firstly by Göttle (1978) for surface wash off. The main assumption is that the deposited sediments are eroded only by storm water flow. This model was not initially adapted for whole sewer systems, but only for storm tank overflows. However, we think that its adaptation (Larson et al. 1990) could be interesting because of its simplicity. - Laplace (1991) has developed a model to reproduce experimental data obtained in a trunk sewer in Marseille (France).

8. DIFFICULTIES FOR MODEL COMPARISON After the above descriptions, it is evident that a comparison of the models and of their results would be very interesting. But such a task is not be easy because : - each model has been calibrated with its own data sets. A direct comparison is impossible. - each model has been calibrated only with a few data, and, sometimes, it has not been verified with other data sets (or this verification has not been published in the literature). This problem is partly due to the lack of available field data. It is then difficult to have a great confidence in the model, to evaluate its domain of validity and its accuracy, and to determine its actual facilities. It is also difficult to know the relative importance of the different parameters because sensitivity analyses are not usual. Finally, it is now impossible to give any serious criterions of choice : users have to remember that these models are new tools which are still in development stage. They need further calibrations and should be used with care. Any valuable and efficient comparison would require the use of the same field data sets. Such a comparison remains difficult because : - all models are not commercialised or public. - the available models do not need the same data and/or the same format of data. Any comparison would require a long preparation to collect enough data and to adapt them for each model. The setting of a data base with existing field data will be the first step to begin this task (Hémain et al. 1990, Osborne and Hutchings 1990, Saget 1994). The last difficulty, but not the least, is the collecting of sufficiently precise field data. The modelling approach cannot now be achieved because data about bed load and deposits are insufficient : these data are determinative and their absence hinders calibration and verification of some parts of the models. It is also necessary to develop conjunctively modelling and field experiments. In fact, many improvements are needed in sampling methodology, especially for bed load and deposits measurements, and in the field of metrology. Unfortunately, field experiments in sewers are very expensive. It is a no negligible drawback.

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9. CONCLUSION This literature review shows that sewer sediment transport models are growing in developments. However they still remain difficult to establish and calibrate because:

number, with recent

- the solid transport theories have generally been developed for fluvial hydraulics or solid transport in pipes. Their transposition to urban hydrology is not straightforward because of important differences in sewers environmental conditions. - cohesion and consolidation of sediments are important factors which have not been extensively studied and which are at the present time not well understood and described. - experimental data for models calibration are insufficient, dispersed and of varying quality and accuracy. A homogeneous database would be an interesting and important improvement. Deterministic and detailed models like Mosqito are useful to understand the phenomena involved in sewers and to predict accurately deposits and overflows. They are necessary for progress, but they remain too much complicated for practical use in management or design offices.

10. NOTATIONS a numerical coefficient a i, a e , a d Price Mance coefficients A catchment area Aaw numerical coefficient ACCU daily accumulation rate of sediment b numerical coefficient c numerical coefficient C TSS concentration Caw numerical coefficient Ceu TSS concentration in domestic sewage Cmin, Cmax limit concentrations in Velikanov model Cpi TSS concentration in water from impervious areas Cpp TSS concentration in water from pervious areas d particles diameter d50 median particles diameter dp rainfall duration DISP disappearing coefficient DTS dry weather period Fgr dimensionless mobility particle number g acceleration of gravity Ggr dimensionless solid flow number Ht total rainfall height i(t) rainfall intensity Imax5 maximum rainfall intensity during a 5 minutes time step Ir invert slope J energy line slope K linear reservoir parameter K1 numerical coefficient K2 numerical coefficient Kd availability factor in the SWMM Ke washoff coefficient in the SWMM Ke' lumped washoff coefficient in FLUPOL Keni washoff coefficient in NPS Kr rate of release in gully pot Ks washoff coefficient in Servat model

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m M Ma Me Mp Mt n P P(t) Pmax qb qc qt Q Qeu Qlim Qpi Qpp Rh s S Sb Sm t u* U Uc V Vr w We y Δt γ γs ηmin, ηmax ρ ρs ρm τc τce, τcr τcd τ0

34 numerical coefficient total mass of sediment released in gully pot accumulated mass of sediment on a catchment washed off mass of sediment amount of particles passing through the gully pot total mass of sediment in the bottom of the gully pot numerical coefficient percentage of gully pot fluid mixed solid load at time t in KOSIM maximum amount of deposits in KOSIM surface runoff bed load transport rate total sediment transport rate flow rate domestic sewage flow rate critical flow rate in KOSIM flow rate of water from impervious areas flow rate of water from pervious areas hydraulic radius specific gravity of particles flow section surface runoff on impervious surface in NPS soil depression storage time friction velocity mean flow velocity critical velocity gully pot volume runoff volume settling velocity of particles effective deposited sediment width flow depth time step volumic weight of water volumic weight of sediment efficiency coefficients in Velikanov model density of water density of sediment density of mixture (sediment + water) critical shear stress in THALIA critical shear stress for erosion critical shear stress for deposition mean shear stress

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11. REFERENCES (code clé : d13 dans biblio-3) Aalderink R.H., Van Duin E.H.S., Peels C.E., Scholten M.J.M. (1990). Some characteristics of run-off quality from a separated sewer system in Lelystad, The Netherlands. Proceedings of the 5th International Conference on Urban Storm Drainage, Osaka, Japan, 23-27 July 1990, 427-432. Acaroglou E.R., Graf W.H. (1968). Sediment transport in conveyance systems - Part 2 : the modes of sediment transport and their related bed forms in conveyance systems. Bulletin of the International Association of Scientific Hydrology, 13(3), 123-135. Ackers P. (1984). Sediment transport in sewers and the design implications. Proceedings of the International Conference on Planning, Construction, Maintenance and Operation of Sewerage Systems, September 1984, 215-230. Ackers P., White W.R. (1973). Sediment transport : a new approach and analysis. Journal of the Hydraulics Division, 99(11), 2041-2060. Ackers P., White W.R. (1980). Bed material transport : a theory for total load and its verification. Proceedings of the International Symposium on River Sedimentation, Beijing, China, 249-268. Aiguier E., Chebbo G., Bertrand-Krajewski J.-L., Hedges P., Tyack J.N. (1996). Methods for determining the settling velocity profiles of solids in storm sewage. Water Science and Technology, 33(9), 117-125. ISSN 0273-1223. Alley W.M. (1981). Estimation of impervious area washoff parameters. Water Resources Research, 17(4), 11611166. Alley W.M., Smith P.E. (1981). Estimation of accumulation parameters for urban runoff quality modelling. Water Resources Research, 17(6), 1657-1664. Ariathurai R., Arulanandan K. (1978). Erosion rates of cohesive soils. Journal of the Hydraulics Division, 104(2), 279-283. Artières O. (1987). Les dépôts en réseau d'assainissement. Thèse de doctorat : Université Louis Pasteur de Strasbourg - ENITRTS, France, 214 p. Artières O., Stotz G. (1988). Caractéristiques des dépôts en réseau d'assainissement unitaire - Conséquences sur leur transport. Actes des Journées d'étude de la Société Hydrotechnique de France, Paris, France, 16-17 novembre 1988, 9 p. Ashley R.M. (1991). Review of data on sediment in sewers. Seminar on sediment in sewers at Hydraulics Research, Wallingford, UK, 11 April 1991, 3 p. Bedient P.B., Lambert J.L., Springer N.K. (1980). Stormwater pollutant load-runoff relationships. JWPCF, 52(9), 2396-2404. Berndtsson R., Hogland W., Larson M. (1986). Mathematical modelling of combined sewer overflow quality. in "Urban Drainage Modelling", Pergamon Press, Oxford, UK, 305-315. Bertrand-Krajewski J.-L. (1991). Modélisation des débits et du transport solide en réseau d'assainissement Etude bibliographique. Strasbourg (France) : ENITRTS, Rapport ENITRTS / Lyonnaise des Eaux-Dumez, avril 1991, 207 p. Bertrand-Krajewski J.-L. (1992). Modélisation conceptuelle du transport solide en réseau d'assainissement. Thèse de doctorat : Université Louis Pasteur, Strasbourg, France, avril 1992, 206 p. Bertrand-Krajewski J.-L., Briat P., Scrivener O. (1993). Sewer sediment production and transport modelling : a litterature review. Journal of Hydraulic Research, 31(4), 435-460. Bertrand-Krajewski J.-L., Lefebvre M., Chaudriller D., Poirier J. (1996). Mesure des vitesses de chute des solides des rejets urbains de temps de pluie par les méthodes UFT et IFTS. Bordeaux (France) : CTIA Lyonnaise des Eaux, rapport, juillet 1996, 139 p. Borah D.K. (1989). Sediment discharge modell for small watersheds. Transactions of the ASAE, 32(3), 874880. Bouvard M. (1984). Barrages mobiles et ouvrages de dérivation à partir de rivières transportant des matériaux solides. Paris (France) : Eyrolles, 355 p. Briat P. (1989). Transport solide en réseau d'assainissement - Inventaire et étude comparative des modèles. Bordeaux (France) : Lyonnaise des Eaux, rapport R/D n° 97952210, juin 1989 Brombach H. (1982). Zwei Experimente zum Stofftransport im Mischwasserkanal. Korrespondenz Abwasser, 5, 284-291. Brombach H. (1984). Modell zur Berechnung des Abflusses von befestigten Flächen. Stuttgart (Deutschland) : Universität Stuttgart, Stuttgarter Berichte zur Siedlungswasserwirtschaft, Heft n° 79, 103-125.

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36 Brown A.J. (1990). WALLRUS user manual, third edition. Wallingford (UK) : Hydraulics Research, October 1990 Bubenzer G.D., Jones B.A. (1971). Drop size and impact velocity effects on the detachment of soil under simulated rainfall. Transactions of the ASAE, 14, 625-628. Bujon G. (1988). Prévision des débits et des flux polluants transités par les réseaux d'égouts en temps de pluie Le modèle FLUPOL. La Houille Blanche, 1, 11-23. Bujon G., Herremans L. (1990). Modèle de prévision des débits et des flux polluants en réseaux d'assainissement par temps de pluie - Calage et validation. La Houille Blanche, 2, 123-139. Celik I., Rodi W. (1991). Suspended sediment transport capacity for open channel flow. Journal of Hydraulic Engineering, 117(2), 191-204. Chebbo G. (1992). Solides des rejets pluviaux urbains - Caractérisation et traitabilité. Thèse de doctorat : Ecole Nationale des Ponts et Chaussées, Paris, France, 400 p. Chebbo G., Bonnefois J., Bachoc A. (1990). Caractérisation des solides transférés dans le bassin de retenue Béquigneaux. Toulouse (France) : IMFT, rapport Lyonnaise des Eaux Bordeaux-IMFT-CERGRENE n° 402.1, octobre 1990, 57 p. + annexes. Chebbo G., Bonnefois J., Faup G., Vidoux R., Briat P., Bachoc A. (1991). Caractérisation des solides des rejets pluviaux urbains du collecteur Le Limancet à Bordeaux. Actes du 71° Congrès AGHTM, Annecy, France, avril 1991, 669-689. Chebbo G., Musquère P., Bachoc A. (1990). Solides transférés dans les réseaux d'assainissement Caractéristiques hydrodynamiques et charges polluantes. Toulouse (France) : IMFT, rapport, 7 p. Chebbo G., Musquère P., Milisic V., Bachoc A. (1989). Caractérisation des solides transférés par temps de pluie dans les réseaux d'assainissement. Proceedings of the 2nd Wageningen Conference, Wageningen, NL, September 1989, 10 p. CIRIA (1987). Sediment movement in combined sewerage and stormwater drainage systems. London (UK) : CIRIA, 200 p. Combes V. (1982). Etude de modèles mathématiques de transport des matériaux solides en réseau d'assainissement. Toulouse (France) : Institut National Polytechnique, mémoire de DEA, 153 p. Crabtree R.W. (1989). Sediment in sewers. Journal of the Institution of Water and Environmental Management, 3(6), 569-578. Dastugue S., Vignoles M., Heughebaert J.C., Vignoles C. (1990). Matières en suspension contenues dans les eaux de ruissellement de la ville de Toulouse. TSM, 3, 131-143. Debarbat M. (1991). Test de Mosqito sur Entzheim. Strasbourg (France) : ENITRTS, rapport interne ENITRTSLyonnaise des Eaux Bordeaux, mai 1991, 18 p. + annexes. Desbordes M. (1984). Modélisation en hydrologie urbaine - Recherches et applications. Montpellier (France) : LHM - Université des Sciences et Techniques du Languedoc, rapport LHM 22/1984, 183 p. + annexes. Deutsch J.-C., (dir.), et al. (1989). Mémento sur l'évacuation des eaux pluviales. Paris (France) : La Documentation Française, 349 p. ISBN 2-11-002179-9. Driver N.E., Troutman B.M. (1989). Regression models for estimating urban storm runoff quality and quantity in the United States. Journal of Hydrology, 109(3/4), 221-236. Durand R. (1953). Basic relationships of the transportation of solids in pipes - Experimental research. Proceedings of the 5th IAHR Congress, Minneapolis, USA, 89-103. Durand R., Condolios E. (1952). Etude expérimentale du refoulement des matériaux en conduites, en particulier des produits de dragage et des schlamms. Actes des 2° Journées de l'Hydraulique de la Société Hydrotechnique de France, Grenoble, France, juin 1952, 27-55. Durchschlag A., Harms R.W. (1989). Mikrocomputer in der Stadtentwässerung - Mischwasserentlastungen. Hannover (Deutschland) : Institut für Wasserwirtschaft der Universität Hannover, 200 p. Einstein H.A. (1950). The bed-load function for sediment transportation in open channel flow. US Department of Agriculture, Technical Bulletin n° 1026, 71 p. + annexes. Fletcher I.J., Pratt C.J. (1981). Mathematical simulation of pollutant contributions to urban runoff from roadside gully pots. Proceedings of the 2nd International Conference on Urban Storm Drainage, Urbana, Illinois, USA, 116-124. Gagné B., Bordeleau F. (1996). Vitesses de chute des particules - Essais comparatifs des méthodes allemande et américaine. Saint Laurent, Québec (Canada) : CEGEO, février 1996, 46 p. Geiger W.F. (1984). Mischwasserabfluss und dessen Beschaffenheit - Ein Beitrag zur Kanalnetzplannung. München (Deutschland) : Berichte der Technischen Universität München, Heft n° 50, 249 p. + annexes. Göttle A. (1978). Ursachen und Mechanismen der Regenwasserverschmutzung - Ein Beitrag zur Modellierung der Abflussbeschaffenheit in städtischen Gebieten. München (Deutschland) : Berichte der Technischen Universität München, Heft n° 23, 313 p. Graf W.H., Acaroglu E.R. (1968). Sediment transport in conveyance systems - Part 1 : a physical model for sediment transport in conveyance systems. Bulletin of the International Association of Scientific Hydrology, 13, 21-39.

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37 Graf W.H., Acaroglu E.R. (1972). Sedimenttransport in Gerinnen und Rohren. Vorträge der Studienrichtung Kulturtechnik und Wasserwirtschaft, Wien, Austria, Oktober 1972, 71-88. Grottker M. (1990). Pollutant removal by catch basins in West Germany - State of the art - New design. Proceedings of "Urban Stormwater Quality Enhancement - Source control, retrofitting and combined sewer technology", New York, USA, 29 p. Grottker M., Hurlebusch R. (1987). Mitigation of stormwater pollution by gully pots. Proceedings of the 4th International Conference on Urban Storm Drainage, Lausanne, Switzerland, 31 Aug. - 4 Sept. 1987, 66-67. Hémain J.-C. (1991). Modélisation mathématique en assainissement pluvial urbain. Bulletin de Liaison des Laboratoires des Ponts et Chaussées, 172, 65-78. Hémain J.C., Bachoc A., Kovacs Y., Breuil B. (1990). The current position in France as regards urban stormwater quality data : the need for a data base. Proceedings of the 5th International Conference on Urban Storm Drainage, Osaka, Japan, 23-27 July 1990, 351-356. Henderson R.J., Moys G.D. (1987). Development of a sewer quality model for United Kingdom. Proceedings of the 4th International Conference on Urban Storm Drainage, Lausanne, Switzerland, 31 Aug. - 4 Sept. 1987, 201-207. Hogland W., Berndtsson R., Magnus L. (1984). Estimation of quality and pollution load of combined sewer overflow discharge. Proceedings of the 3rd International Conference on Urban Storm Drainage, Göteborg, Sweden, 3, 841-850. Holly F.M., Preissmann A. (1977). Accurate calculation of transport in two dimensions. Journal of Hydraulic Research, 103(11), 1259-1277. Huber W.C (1986). Deterministic modeling of urban runoff quality. in "Urban Runoff Pollution", NATO ASI Series vol. G10, edited by H.C. Torno, J. Marsalek and M. Desbordes, Berlin (Germany) : Springer-Verlag, 167-242. Hydraulics Research (1989). MOSQITO User manual. Wallingford (UK) : Hydraulics Research, October 1989, 96 p. Hydraulics Research (1991). MOSQITO Training course. Wallingford (UK) : Hydraulics Research, 13-15 March 1991, 232 p. Iossifidis V. (1985). Die Rolle der Ablagerungen bei der Schmutzfrachtberechnung in Kanalisationsnetzen. Karlsruhe (Deutschland) : Universität Karlsruhe, Schriftenreihe des Institutes für Siedlungswasserwirtschaft, Heft n° 43, 171 p. + annexes. ISSN 0722-7698. Iossifidis V., Hahn H.H. (1984). Die Rolle der Ablagerungen bei der Schmutzfrachtsimulation. Korrespondenz Abwasser, 8, 686-694. Iossifidis V., Xanthopulos C. (1986). Wie weit können Kanalablagerungen bei der Schmutzfrachtberechnung vernachlässigt werden ?. Korrespondenz Abwasser, 3, 214-224. Jewell T.K., Adrian D.D. (1978). SWMM stormwater pollutant washoff functions. Journal of the Environmental Engineering Division, 104(5), 1036-1040. Jewell T.K., Adrian D.D. (1982). Statistical analysis to derive improved stormwater quality models. JWPCF, 54(5), 489-499. Kleijwegt R.A. (1992). Sewer sediment models and basic knowledge. Water Science and Technology, 25(8), 123-130. Kleijwegt R.A., Veldkamp R.G., Nalluri C. (1989). Sediment in sewers : initiation of transport. Proceedings of the 2nd Wageningen Conference, Wageningen, NL, September 1989, 8 p. Lager J.A., Shubinski R.P., Russell L.W. (1971). Development of a simulation model for stormwater management. JWPCF, 43(12), 2424-2435. Laplace D. (1991). Dynamique du dépôt en collecteur d'assainissement. Thèse de doctorat : Institut National Polytechnique de Toulouse, France, 202 p. + annexes. Laplace D., Sanchez Y., Dartus D., Bachoc A. (1989). La dynamique des dépôts dans le collecteur n° 13 du réseau unitaire d'assainissement de Marseille. Proceedings of the 2nd Wageningen Conference, Wageningen, NL, September 1989, 10 p. Larras J. (1972). Hydraulique et granulats. Paris (France) : Eyrolles, 254 p. Larson M., Berndtsson R., Hogland W., Spangberg A., Bennerstedt K. (1990). Field measurements and mathematical modeling of pollution build-up and pipe-deposit wash-out in combined sewers. Proceedings of the 5th International Conference on Urban Storm Drainage, Osaka, Japan, 23-27 July 1990, 325-332. Lessard P., Beron P., Brière F., Rousselle J., Desjardins R. (1982). Variation de la qualité des eaux en temps de pluie dans un réseau unitaire. La Technique de l'Eau et de l'Assainissement, 430/431, 9-15. Litwin Y.J., Donigian A.S. (1978). Continuous simulation of nonpoint pollution. JWPCF, 50, 2348-2361. Lucas-Aiguier E., Chebbo G., Bertrand-Krajewski J.-L., Gagné B., Hedges P. (1998). Analysis of the methods for determining the settling characteristics of sewage and stormwater solids. Water Science and Technology, 37(1), 53-60. ISBN 0 08 043379 0.

OSHU3 13 Modelling of sediment transport and processes - 01/12/2006

J.-L. Bertrand-Krajewski, URGC Hydrologie Urbaine, INSA de Lyon

38 Luu P.N., Butler D., Karunaratne G. (1990). Sediment deposition in the sewers of the London borough of Lambeth. Proceedings of the 5th International Conference on Urban Storm Drainage, Osaka, Japan, 23-27 July 1990, 909-914. Macke E. (1980). Vergleichende Betrachtungen zum Feststofftransport im Hinblick auf ablagerungfreie Strömungszustände in Regen- und Schmutzwasserkanälen. Braunschweig (Deutschland) : Mitteilungen des Leichtweiss-Instituts für Wasserbau der Technischen Universität Braunschweig, Heft n° 69, 109-233. Macke E. (1983). Bemessung ablagerungsfreier Strömungszustände in Kanalisationsleitungen. Korrespondenz Abwasser, 7, 462-469. Marsalek J. (1984). Caractérisation du ruissellement de surface issu d'une zone urbaine commerciale. Sciences et Techniques de l'Eau, 17(2), 163-167. Mat Suki R.B., Nik Hassan N.M.K. (1990). Effective bed width of sediment transport in storm sewer design criterion. Proceedings of the 5th International Conference on Urban Storm Drainage, Osaka, Japan, 879-884. Mehta A.J., Hayter E.J., Parker W.R., Krone R.B., Teeter A.M. (1989). Cohesive sediment transport - I : process description. Journal of Hydraulic Engineering, 115(8), 1076-1093. Mehta A.J., McAnally W.H., Hayter E.J., Teeter A.M., Schoellhammer D., Heltzel S (1989). Coehseive sediment transport - II : application. Journal of Hydraulic Engineering, 115(8), 1094-1112. Michelbach S., Wöhrle C. (1992). Settleable solids in a combined sewer system - measurement, quantity, characteristics. Water Science and Technology, 25(8), 181-188. Migniot C. (1989). Tassement et rhéologie des vases - 2° partie. La Houille Blanche, 2, 95-111. Mignot C. (1989). Tassement et rhéologie des vases - 1° partie. La Houille Blanche, 1, 11-29. Misri R.L., Garde R.J., Ranga Raju K.C. (1984). Bed load transport of coarse nonuniform sediment. Journal of Hydraulic Engineering, 110(3), 312-328. Moys G.D., Osborne M.P., Payne J.A. (1988). MOSQITO 1 : Modelling Of Stormwater Quality Including Tanks and Overflows - Design specifications. Wallingford (UK) : Hydraulics Research Limited, Report no SR 184, 170 p. Nalluri C. (1991). The influence of cohesion on sediment behaviour in sewers. Seminar on sediment in sewers, Hydraulics Research, Wallingford, UK, 11 April 1991, 2 p. Nalluri C., Alvarez E.M. (1992). The influence of cohesion on sediment behaviour. Water Science and Technology, 25(8), 151-164. Novak P., Nalluri C. (1975). Sediment transport in smooth fixed bed channels. Journal of the Hydraulics Division, 101(9), 1139-1154. Novak P., Nalluri C. (1984). Incipient motion of sediment particles over fixed beds. Journal of Hydraulic Research, 22(3), 181-197. Osborne M.P., Hutchings C.J. (1990). Data requirements for urban water quality modeling and limitations of the existing UK database. Proceedings of the 5th International Conference on Urban Storm Drainage, Osaka, Japan, 23-27 July 1990, 357-364. Osborne M.P., Payne J.A. (1990). Calibartion, testing and application of the sewer flow model MOSQITO. Proceedings of the 5th International Conference on Urban Storm Drainage, Osaka, Japan, 23-27 July 1990, 377-383. Partheniades E. (1965). Erosion and deposition of cohesive soils. Journal of the Hydraulics Division, 91(1), 105139. Payne J.A., Moys G.D., Hutchings C.J., Henderson R.J. (1989). Development, calibration and further data requirements of the sewer flow quality model MOSQITO. Proceedings of the 2nd Wageningen Conference, Wageningen , The Netherlands, September 1989, 7 p. Perrusquia G. (1992). An experimental study on the transport of sediment in sewer pipes with a permanent deposit. Water Science and Technology, 25(8), 115-122. Pisano W.C., Zukovs G. (1992). Demonstration of advanced high rate treatment for CSO control in Metropolitan Toronto area. Proceedings of NOVATECH 92, Lyon, France, 3-5 November 1992, 331-340. Preul H.C., Harms R., Sieker F. (1990). Technical approaches for combined sewer overflow control in West Germany. Proceedings of the 5th International Conference on Urban Storm Drainage, Osaka, Japan, 14351440. Rakoczi L. (1987). Effect of granulometry on sediment motion : a new approach. Proceedings of the 22th IAHR Congress, Lausanne, Switzerland, 154-159. Ranchet J., Philippe J.P. (1982). Pollution véhiculée par les eaux de ruissellement en réseau unitaire - Le bassin versant de Mantes-la-Ville. Bulletin de Liaison des Laboratoires des Ponts et Chaussées, 119, 25-37. Ries J.-M. (1990). Analyse et simulation des rejets unitaires et des bassins de pollution par temps de pluie. Strasbourg (France) : ENITRTS, mémoire de Mastère, 50 p. + annexes. Roberts A.H., Ellis J.B., Whalley W.B. (1988). The progressive alteration of fine sediment along a urban storm drain. Water Research, 22(6), 775-781.

OSHU3 13 Modelling of sediment transport and processes - 01/12/2006

J.-L. Bertrand-Krajewski, URGC Hydrologie Urbaine, INSA de Lyon

39 Saget A. (1994). Base de données sur la qualité des rejets urbains de temps de pluie : distribution de la pollution rejetée, dimensions des ouvrages d'interception. Thèse de doctorat : ENPC, Paris, France, décembre 1994, 333 p. Sartor J.D., Boyd G.B., Agardy F.J. (1974). Water pollution aspects of street surface contaminants. Journal of Water Pollution Control Federation, 46(3), 458-467. Servat E. (1984). Contribution à l'étude des matières en suspension du ruissellement pluvial à l'échelle d'un petit bassin versant urbain. Thèse de doctorat : Université des Sciences et Techniques du Languedoc, Montpellier, France, 182 p. Shivalingaiah B., James W. (1984). Algorithms for build-up, washoff and routing pollutants in urban runoff. Proceedings of the 3rd International Conference on Urban Storm Drainage, Göteborg, Sweden, 4-8 June 1984, 4, 1445-1455. Sieker F. (1987). Neue Aspekte der Bemessung von Mischwasserentlastungen - Teil 2 : Bemessung nach dem Prinzip der Zweikomponenten-Methode und der Langzeitsimulation. Korrespondenz Abwasser, 6, 638-344. Simon L. (1986). Transport solide de sédiments de granulométrie non uniforme. Chatou (France) : EDF Laboratoire National d'Hydraulique, rapport n° HE/43/86-28, 41 p. Stahre P., Urbonas B. (1990). Stormwater detention for drainage, water quality and CSO management. Englewood Cliffs, New Jersey (USA) : Prentice Hall, 338 p. Tan S.K. (1989). Rainfall and soil detachment. Journal of Hydraulic Research, 27(5), 699-715. van Rijn L.C. (1984). Sediment transport, part I : bed load transport. Journal of Hydraulic Engineering, 110(10), 1431-1456. van Rijn L.C. (1984). Sediment transport, part II : suspended load transport. Journal of Hydraulic Engineering, 110(11), 1613-1641. Verbanck M. (1990). Sewer sediment and its relation with the quality characteristics of combined sewer flows. Water Science and Technology, 22(10/11), 247-257. Wada Y., Miura H. (1988). Characteristics of accumulated loads in the street inlets in urban area and its flushing. Technology Reports of Kensai University, 30, 153-166. Wada Y., Miura H., Hasegawa K. (1987). Model building and analysis of runoff water quality of flush from the street gully pots. Proceedings of the 4th International Conference on Urban Storm Drainage, Lausanne, Switzerland, 31 Aug. - 4 Sept. 1987, 60-65. Warwick J.J., Wilson J.S. (1990). Estimating uncertainty of stormwater runoff computations. Journal of Water Resources Planning and Management, 116(2), 187-204. Williams D.J.A., Williams P.R., Crabtree R.W. (1989). Preliminary investigations into the rheological properties of sewer sediment deposits and the development of a synthetic sediment material. Swindon (UK) : Water Research Centre, Foundation for Water Research, Research Report n° FR0016, 41 p. Wiuff R. (1985). Transport of suspended material in open and submerged streams. Journal of the Hydraulics Division, 111(5), 774-792. Wotherspoon D.J.J., Ashley R.M. (1992). Rheological measurement of the yield strength of combined sewer sediment deposits. Water Science and Technology, 25(8), 165-169. Yang C.T. (1972). Unit stream power and sediment transport. Journal of the Hydraulics Division, 98(10), 18051826. Yang C.T. (1985). Mechanics of suspended sediment transport. Proceedings of Euromech 192 : Transport of suspended solids in open channels, Neubiberg, Germany, 87-91. Yen B.C. (1986). Rainfall-runoff process on urban catchments and its modelling. in "Urban Drainage Modelling", London (UK) : Pergamon Press, 3-26. Young R.A., Wiersma J.L. (1973). The role of rainfall impact in soil detachment and transport. Water Resources Research, 9(6), 1629-1636. Zhang W., Cundy T.W. (1987). Laminar Einstein bed load transport equation for overland sheet flow. Journal of Hydraulic Engineering, 113(12), 1525-1538.

OSHU3 13 Modelling of sediment transport and processes - 01/12/2006

J.-L. Bertrand-Krajewski, URGC Hydrologie Urbaine, INSA de Lyon