laboratory experiments and numerical modelling of the scouring ...

Engineering Applications of Computational Fluid Mechanics Vol. 4, No. 3, pp. 365–373 (2010)

LABORATORY EXPERIMENTS AND NUMERICAL MODELLING OF THE SCOURING EFFECTS OF FLUSHING WAVES ON SEDIMENT BEDS S. Todeschini*, C. Ciaponi and S. Papiri Department of Hydraulic and Environmental Engineering, University of Pavia, Via Ferrata, 1 - 27100 - Pavia, Italy * E-Mail: [email protected] (Corresponding Author) ABSTRACT: This paper presents an investigation on the scouring effects of flushing waves on sewer sediment deposits in order to derive guidelines on the design and set-up of flushing devices in sewer systems and in stormwater storage tanks. The investigation comprises both laboratory experiments and numerical modelling. The experimental campaign was carried out on a channel at the laboratory of the Department of Hydraulic and Environmental Engineering of the University of Pavia adopting a simple flushing device. The first set of experiments is carried out without sediment and the water levels during the flushing processes are monitored by a digital videocamera. The second set of tests is carried out with uniform layers of sediment at the bottom of the channel and the effects on sediment beds produced by flushes are analysed. The numerical model solves the De Saint Venant equations describing unsteady flow in open channel and the continuity equation of Exner for the conservation of the sediment mass. For this purpose, the MacCormack explicit finite difference scheme is introduced. A sediment erosion relationship linking the rate of erosion to an excess of shear stress at the bottom is included in the model. The comparison between the experimental and computed water depths shows good agreement for different flushing conditions and longitudinal slopes of the channel. The tests with different sediment beds allow the calibration of the parameters that globally describe the erosion process produced by flushes. Keywords: laboratory flushing waves, sand-clay mixtures, erosion-transport model, sewer system, stormwater storage tank

determines the quick release of the upstream stored water volume and generates flushing waves that are able to scour and transport the deposited sediments downstream. Some experimental studies have investigated the scouring effects produced by flushes in laboratory channels and in sewer collectors (Lorenzen et al., 1996; Linehan, 2001; Tait et al., 2003; Guo et al., 2004). Also numerical models for erosion and sediment transport of flushing waves have been developed (Lin and Guennec, 1996; Saiedi, 1997; Kassem and Chaudhry, 1998; Campisano et al., 2004). These models mainly adopt the traditional sediment transport formulas of fluvial hydraulic for unsteady flow conditions. Nevertheless not exhaustive results are available in the scientific literature for the evaluation of the efficiency of these devices. Further experimental data are necessary for the comprehension of the mechanics of sediment erosion and transport during flushes and furthermore for the calibration of the numerical models. In this paper an investigation of the scouring effects of flushing waves on sediment deposits is

1. INTRODUCTION The accumulation of deposits inside sewer systems causes both hydraulic and environmental problems, such as reduction of flow capacity, gas and corrosive acid production and stronger first flush pollution discharged through Combined Sewer Overflows (CSOs) into water bodies (Ashley and Verbanck, 1996; Arthur and Ashley, 1997; 1998; Fan et al., 2003). Also deposits at the bottom of stormwater storage tanks are critical as they cause sanitary problems and odours. The periodical removal of deposits is necessary in order to avoid or reduce these problems. For this purpose, several techniques based on the use of different mechanical and hydraulic devices have been developed (Chebbo et al., 1996; Lorenzen et al., 1996; Pisano et al., 2003; Fan et al., 2003; Bertrand-Krajewski et al., 2003, 2004; Guo et al., 2004). Many studies have focused on the use of hydraulic flushing devices, in particular mobile gate devices (Pisano et al., 2003; BertrandKrajewski et al., 2003, 2004). Their operation is based on the sudden opening of a gate which Received: 18 Dec. 2009; Accepted: 15 Mar. 2010 365

Engineering Applications of Computational Fluid Mechanics Vol. 4, No. 3 (2010)

Storage tank

Channel

generate flushing waves propagating downstream (after the gate opening). The atmospheric pressure acts on the water surface. A basket equipped with a synthetic cloth is inserted into the tank at the downstream end of the channel in order to intercept the scoured sand. The first set of experiments is developed without sediment and the water levels during the flushing processes are monitored by a digital video-camera. Two different initial values of water head (0.15 m and 0.25 m) upstream the gate and four different slopes of the channel (0.5-1-1.5-2%) are considered during the tests. The flushing waves are generated by the sudden opening of the sluice gate, which is 0.1 m high. The second set of experiments is carried out with uniform layers of sediment at the bottom of the channel. These experiments consider a water level upstream the gate equal to 0.25 m and a longitudinal slope of the channel equal to 0.02. First tests are carried out with a cohesionless sediment. Three different types of sand (type I: grain size 0.2-0.35 mm, d50=0.25 mm, bulk 3 density 1 520 kg/ m ; type II: grain size 0.4-0.6 3 mm, d50=0.48 mm, bulk density 1 530 kg/ m ; type III: grain size 0.8-1.2 mm, d50=0.90 mm bulk 3 density 1 560 kg/ m ) are used. In further experiments different clay contents 3 (montmorillonite: bulk density 1 080 kg/ m ) are added to these three types of sand. Table 1 summarises the initial sediment bed conditions of the tests. Experiments are carried out both with dry (D) and wet (W) sediment beds. Sediments are placed at

Basket

0.1 m 0.3 m 0.15-0.25 m

1m

Fig. 1

Sluice gate

0.1 m

4.5 m

Sketch of the laboratory channel and of the experimental set-up.

presented. The investigation comprises both laboratory experiments and numerical modelling (Todeschini, 2007; Todeschini et al., 2008). In particular, the study focuses on the removal efficacy of a single flushing wave on a sediment bed (i.e. the removal efficacy of a flushing device inside a stormwater storage tank).

Laboratory experiments provide data that allow the defination of a suitable correlation between calibration parameters and sediment properties (grain size distribution and clay content). 2. LABORATORY EXPERIMENTS The experimental system (figure 1) is made up of a 5.5 m long laboratory channel with Plexiglas bottom and side walls characterised by a Manning -1/3 roughness coefficient equal to 0.0082 s m . The channel has a rectangular cross section 0.1 m wide and 0.3 m deep, the longitudinal slope can be varied. The entrance section is closed and a steel sluice gate, positioned 1 m from the upstream end, can activate in-line storage (when closed) and

Table 1 Sediment bed conditions of the experiments. Tb (cm)

Sediment condition

0.5 1.0 0.5 1.0 0.5 1.0 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

W/D W/D W/D W/D W/D W/D W W W W W W W W W W W W W W W W

Sand type I Sand type II Sand type III Sand type I - II - III (equal %) Sand type I – clay 7.5% Sand type II - clay 7.5% Sand type III - clay 7.5% Sand type I - II - III (equal %) - clay 7.5% Sand type I - clay 15% Sand type II - clay 15% Sand type III - clay 15% Sand type I - II - III (equal %) - clay 15% Sand type I – clay 20% Sand type II - clay 20% Sand type III - clay 20% Sand type I - II - III (equal %) - clay 20% Sand type I – clay 25% Sand type II - clay 25% Sand type III - clay 25%

366

nb (s m-1/3)

p

0.0143

0.43

0.0154

0.42

0.0175

0.41

0.0157 0.0143 0.0154 0.0175 0.0157 0.0143 0.0154 0.0175 0.0157 0.0143 0.0154 0.0175 0.0157 0.0143 0.0154 0.0175

0.40 0.40 0.40 0.39 0.39 0.39 0.39 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.37


[m3/(m s)]; Sf the friction slope [m/m]; x the distance along the channel [m]; t the time [s]; p the porosity of the bed layer; ε the rate of erosion [kg/(s m2)]; ρs the sediment density [kg/m3]; εm [kg/(s m2)] and α two parameters; τb the bottom shear stress [N/m2]; τcr the critical bottom shear stress [N/m2]. The friction slope Sf is evaluated using the ChézyManning relation:

the bottom of the channel and levelled with a steel plate. Two different bed thicknesses (Tb) are considered (0.5 - 1 cm). Homogeneous mixed sediments are obtained mixing dry sand and clay mechanically: percentages from 0 to 25% clay by weight are added to sand. The consolidation time for the wet sediment beds is one night. The values of the Manning roughness coefficient at the bottom (nb) for each type of sand given in Table 1 are obtained by preliminary experiments in steady state conditions. The same roughness coefficient is used for a mixed sediment of a certain type of sand, assuming that clay content does not change significantly bed roughness (Table 1). The sediment porosity (p) is evaluated with a laboratory test.

Sf = (q2 n2)/(h2 R4/3)

(5)

with R [m] the hydraulic radius and n [s/m1/3] the Manning roughness coefficient which is evaluated by the Einstein relation, taking into account the different roughness values on the wetted perimeter P [m]:

3. MATHEMATICAL MODEL 3.1

n=[ (Psw nsw3/2 + Pb nb3/2 ) / P ]2/3

Mathematical equations

The numerical model solves the De Saint Venant equations (1) and (2) describing unsteady flow in open channel and the continuity equation of Exner (3) for the conservation of the sediment mass. The sediment erosion relationship of Parchure and Metha (1985) (Equ. 4) is included in the computations. This formula links the rate of erosion to an excess of shear stress at the bottom and has some successful applications for mixed cohesive/non-cohesive sediments (Torfs, 1995; Ashley and Verbanck, 1996; Skipworth, 1996). In this model, the relationship of Parchure and Metha (1985) is directly applied to the evolution of the bed elevation involving sediment erosion. 



with sw and b referring to the channel side walls and to the channel bottom, respectively. The bottom shear stress τb is obtained by the following expression: τb = ρw g R Sf (nb/n)3/2 3

(1)

Momentum equation for water:

3.2 Numerical scheme and boundary conditions

∂q/∂t + ∂/∂x (q2/h + gh2/2) + gh ∂z/∂x + ghSf = 0 (2) 



Equations (1) (2) (3) are numerically solved using the second order MacCormack scheme (Bhallamudi and Chaudhry, 1991). An additional step based on the theory of the total variation diminishing (TVD) is also applied to the hydraulic variables in order to reduce the numerical oscillations generated in correspondence with high gradients in water levels and flow rates (Sweby, 1984; GarciaNavarro and Saviron, 1992). Boundary conditions for the hydraulic variables q and h are imposed by applying the theory of

Continuity equation for sediment:

∂/∂t [(1-p) z + qs h/q ] + ∂qs /∂x = 0

(3)

Evolution of the bed elevation and sediment erosion relationship of Parchure and Metha (1985):

∂z/∂t= ε/ρs

ε = εm [(τb – τcr) / τcr]α

(7)

in which ρw [kg/ m ] is the water density. The flushing process produces both bed load and suspension load transport but the model does not distinguish between them. Moreover, this model does not include loading law equations for the lag between sediment transport capacity and sediment discharge (hypothesis of immediate adaptation), assuming the transport essentially a bed load transport.

Continuity equation for water:

∂h/∂t + ∂q/∂x = 0

(6)

(4)

in which h [m] is the flow depth; q the water discharge per unit width [m3/(m s)]; z the bed elevation [m]; qs the unit sediment discharge 367


4. NUMERICAL AND EXPERIMENTAL RESULTS 4.1

Hydraulic validation of the model

The numerical code is first applied to the set of experiments without sediment. The initial condition is the sluice gate in the closed position with water levels in the storage upstream the gate equal to 0.15 m (flush A) and to 0.25 m (flush B). Different longitudinal slopes S are considered: 0.5-1-1.5-2%. A spatial step Δx of 0.1 m is used for the numerical integration, while each time step Δt is determined imposing a Courant-Friedrichs-Lewy number (CFL) equal to 0.9 for the scheme stability. Figure 2 shows the comparison between computed and experimental water depths at different channel sections (cell 7 is 0.4 m upstream the gate, while cells 12 - 22 - 47 are respectively 0.1 - 1.1 - 3.6 m downstream the gate) for flush A - S equal to 0.01 and for flush B - S equal to 0.02 . The comparison shows very good agreement between the experimental data and the model results for both the flushing conditions and all the monitored cells upstream and downstream the gate.

Flush A - S=0.01

Flush B - S=0.02

Cell 7

Cell 7

0.2 0.15 0.1 0.05 0

h [m]

h [m]

characteristics (Abbot and Minns, 1998). For supercritical flow the values of both variables must be imposed at the upstream end (actually the upstream end is always in subcritical condition being q equal to zero at the side wall of the storage chamber), none at the downstream end. For subcritical flow a condition must be imposed at the upstream end (q equal to zero) and one at the downstream end (Froude number equal to 1). A boundary condition for the sediment is imposed at the upstream end for subcritical flow (variable qs equal to zero, the water stored in the chamber being clean) and one at the downstream end for supercritical flow (variable z, function of the excess of shear stress at the bottom). The second order accuracy in time and space integral continuity equation for sediment furnishes the variable not imposed (Cao et al., 2002). Being in the neighbourhood of the gate, the basic De Saint Venant hypotheses are violated and internal boundary conditions across the discontinuity are used. Also these internal conditions are imposed using the theory of characteristics: the end of the domain upstream the gate is treated as a downstream boundary whereas the beginning of the downstream domain is treated as an upstream boundary (GarciaNavarro and Saviron, 1992; Todeschini, 2007).

0.0

2.0

4.0

6.0

0.3 0.2 0.1 0 0.0

Time [s]

h [m]

h [m] 4.0

0.09 0.06 0.03 0

6.0

0.0

Time [s]

h [m]

h [m] 4.0

6.0

0.0

h [m]

h [m] 6.0

8.0

6.0

0.09 0.06 0.03 0 0.0

Time [s]

Fig. 2

4.0

Cell 47

0.09 0.06 0.03 0 4.0

2.0

Time [s]

Cell 47

2.0

6.0

0.09 0.06 0.03 0

Time [s]

0.0

4.0

Cell 22

Cell 22

2.0

2.0

Time [s]

0.09 0.06 0.03 0.00 0.0

6.0

Cell 12

0.09 0.06 0.03 0.00 2.0

4.0

Time [s]

Cell 12

0.0

2.0

2.0

4.0

6.0

Time [s]

Comparison between measured (dots) and simulated water depths (solid line). 368

Engineering Applications of Computational Fluid Mechanics Vol. 4, No. 3 (2010) Table 3 Results of the experiments with sand.

Table 2 Minimum, mean and maximum values of RMSE of the hydraulic tests.

RMSE [m] Flush A

S=0.01

MIN MED MAX

0.0005 0.0043 0.0092

Flush B

S=0.02

MIN MED MAX

0.0017 0.0052 0.0091

Sand type I

Sand type II

Sand type III Sand type I - II - III (equal %)

Tb (cm) D/W 0.5 D 0.5 W 1.0 D 1.0 W

Vs_w [dm3] 1.42 1.28 1.46 1.34

0.5 0.5 1.0 1.0 0.5 0.5 1.0 1.0

D W D W D W D W

0.5

W

Fig. 3

0.09 0.06 0.03 0.00

0.97 0.90 1.03 0.94 0.80 0.75 0.85 0.77

43.4 39.7 23.0 20.7 35.3 33.2 18.7 17.0

0.60 0.65 0.60 0.65 0.80 0.85 0.80 0.85

5.0 10-5 5.0 10-5 5.2 10-5 5.2 10-5 5.0 10-5 5.1 10-5 5.3 10-5 5.2 10-5

0.89

41.0

0.70

5.1 10-5

0.06 0.04 0.02 0.00

1 6 11 16 21 26 31 36 41 46

1 6 11 16 21 26 31 36 41 46

Cell

Cell

Comparison between measured (dots) and simulated water depths (solid line) after a fixed time from the opening of the sluice gate (flush B - S=0.02).

For the same experiments, Table 2 shows the range of the root mean square error (RMSE) evaluated for each spatial cell as:

RMSE 

ker [m/s] 5.0 10-5 4.9 10-5 4.9 10-5 5.1 10-5

t = 4 sec h [m]

h [m]

t = 2 sec

61.9 56.6 31.8 29.6

τcr [N/m2] 0.40 0.43 0.40 0.43

%w



1 K k h s , i  h k e, i  K k 1

i=1,2,…,N+1

4.2 Scouring effects of flushing tests on sediment beds and calibration of the model

The numerical code can model the evolution of the sediment bed during the flushing operations. However, a continuous monitoring of the erosion process is impossible because the initial sediment layer is very thin. For this reason, only the global effects of flushing waves produced by the opening of the gate are studied.



2

(8)

in which k is the time index, K is the time index indicating the end of flush, hks,i is the simulated water depth for cell i at time k and hke,i is the experimental water depth for cell i at time k. The low values of RMSE confirm the good performance of the hydraulic part of the model. Referring to flush B and to a longitudinal slope of 0.02 figure 3 shows a comparison between numerical and experimental water levels in each cell after a fixed time from the opening of the sluice gate. Experimental water depths are very close to those obtained with the code both after 2 and 4 seconds from the gate opening.

4.2.1 Experiments with sand

Table 3 summarises the experimental results for different initial conditions in terms of washed sediment volume (Vs_w) and washed sediment percentage (%w). The washed sediment volume is obtained by dividing the weight of the washed sediment (Ws_w) drained in the synthetic cloth by the bulk density of such a wet sediment (ρwet) obtained with a laboratory test. The washed sediment percentage is obtained by the following formula: %w = 100 Ws-w / [Ws-i (ρwet / ρdry) ]

369

(9)


account the compactness of a wet sediment (Table 3). The parameter α is assumed equal to 1 (Mitchener and Torfs, 1996; Skipworth et al., 1999). The parameter ker=εm/ρs is evaluated for each test by imposing the global continuity of the sediment mass at the downstream end of the channel:

2.5

Ws_w [kg]

2 1.5 1 Type I Type II Typer III Type I - II - III (equal %)

0.5

qs kN 1  qs kN11   t  Vs _ w 1  p    k 2 k 1 

K 1

0 0

Fig. 4

5

10 15 Clay Content [%]

20

25

(10)

Washed sediment weight (Ws_w) for different clay content.

where k is the time index, K is the time index indicating the end of flush in the last spatial cell (cell N+1), Δtk is the time interval between the instants denoted by k and k+1 and p the porosity of the washed sand. The left term of equation (10) comes from the numerical simulation, the right one from the flushing experiment. According to the Shields formula, the parameter τcr increases as the grain size of the sediment increases, while the parameter ker is almost equal for all the experiments with sand supporting the adopted sediment erosion relationship.

in which ρdry is the bulk density of the dry sediment and Ws_i the initial weight of the dry sediment placed at the bottom of the channel. For the same type of sand and equal thickness, dry sand has higher volume and percentage scoured than wet sand because the wet sediment is more compact and so more difficult to remove. As expected the percentage of the washed sand decreases as the grain size of sand increases. The volume and the percentage scoured for the mixture of the three types of sand are almost the same as those of sand type II. Visual observations show that the sediment is essentially transported as bedload. Table 3 also shows the adopted values for the calibration parameters of the numerical model. The critical bottom shear stress τcr comes from the Shields formula (Yalin and Karahan, 1979) for dry sand. A higher value of critical shear stress is adopted for the wet sand in order to take into Table 4

4.2.2 Experiments with sand and clay mixtures

Figure 4 shows the washed sediment weight (Ws_w) of the experiments carried out with sand and clay mixtures, while table 4 furnishes the washed sediment volume (Vs_w) and the washed sediment percentage (%w) of these experiments. These values are obtained adopting the same

Results of the experiments with sand and clay mixtures. ker [m/s] 0.83 10-4

Sand type I – clay 7.5%

0.5

W

Vs_w [dm3] 1.26

53.5

τcr [N/m2] 0.7

Sand type II - clay 7.5%

0.5

W

0.91

38.7

1.0

0.84 10-4

Sand type III - clay 7.5%

0.5

W

0.72

30.5

1.3

0.83 10-4

Sand type I - II - III (equal %) - clay 7.5 %

0.5

W

0.87

37.1

1.1

0.84 10-4

Sand type I – clay 15%

0.5

W

1.21

49.0

0.78

0.84 10-4

Sand type II - clay 15%

0.5

W

0.90

36.0

1.05

0.84 10-4

Sand type III - clay 15%

0.5

W

0.70

27.9

1.4

0.85 10-4

Sand type I - II - III (equal %) - clay 15 %

0.5

W

0.81

33.1

1.15

0.84 10-4


0.5

W

0.66

25.4

1.4

1.06 10-4


0.5

W

0.63

24.0

1.6

1.08 10-4


0.5

W

0.54

20.4

1.9

1.06 10-4

Sand type I - II - III (equal %) - clay 20 %

0.5

W

0.63

24.0

1.6

1.08 10-4


0.5

W

0.54

20.2

1.65

1.07 10-4


0.5

W

0.51

18.9

1.8

1.06 10-4


0.5

W

0.49

18.0

2.1

1.08 10-4

Tb (cm) D/W

370

%w


procedure described in the previous paragraph. However, some modifications are necessary because the synthetic cloth is not able to retain all the clay washed. The weight of washed clay (Wc_w) is provided by the following expression assuming that the washed clay percentage by weight and that of the washed sediment are the same. Wc_w = %w Wc_i

the mode of erosion of a cohesive sediment is characterised by a rapid dislodgement of large pieces of sediment, immediately removed by the flow when the shear strength of the material is exceeded (mass erosion). The material being detached from the bed is mostly transported as bedload. The parameter ker for mixtures with a clay content of 7.5% and 15% assumes a value intermediate between that of sand and that of sand with a clay content of 20 and 25%. This result is due to the intermediate erosive behaviour of mixtures with a clay content of 7.5% and 15% between a noncohesive behaviour and a cohesive one. Also Torfs (1995) has found the transition between non-cohesive and cohesive behaviour for a montmorillonite content in a sandy bed of around 7-13%.

(11)

in which Wc_i is the initial weight of the clay placed at the bottom of the channel. The weight of washed clay passing through the cloth is assumed equal to the total weight of the washed clay. This assumption comes from the visual observation of the washed sediment retained in the synthetic cloth and of the water passing through the cloth. Washed sediment volume and percentage decrease as clay content increases for each type of sand. This result confirms other experimental studies carried out on cohesive/non-cohesive mixtures (Mitchener and Torfs, 1996). Table 4 also shows the adopted values for the calibration parameters of the numerical model. The values of critical bottom shear stress τcr are those found in previous laboratory experiments with sand and clay mixtures: the experiments of Torfs (1995) for sand types I, II and for the mixture of the three types of sand; those of Campisano et al. (2008) for sand type III (Table 4). The critical bottom shear stress increases significantly when clay is added to sand because sand and clay mixtures develop binding forces between particles which are broken by higher shear stresses than those that characterise the start of the erosion process in a sediment of sand only. These binding forces increase with time while the consolidation process of the sediment occurs. The parameter αis assumed equal to 1 according with the findings of Torfs (1995). The parameter ker is evaluated for each test by the Equ. (10) taking into account the clay being not retained in the synthetic cloth. The values of parameter ker are equal in the experiments with a clay content of 20 and 25%. However, these values are greater (almost double) than that of a sand without clay. This is due to the fact that the erosion behaviour of a cohesive sediment (sand with a clay content of 20 and 25%) is different from that of a non-cohesive sediment (sand without clay). While the erosion of a noncohesive sediment is a particle-by-particle erosion,

5. CONCLUSIONS

An experimental and numerical investigation on the scouring effects of flushing waves on sediment deposits is presented. The experiments were carried out at the laboratory of the Department of Hydraulic and Environmental Engineering of the University of Pavia on different uniform layers of sediment. The numerical code based on the solution of the De Saint Venant - Exner equations was developed adopting the TVD-McCormack scheme. The sediment erosion relationship of Parchure and Metha (1985) was implemented in the code in order to obtain the bed evolution during the flushing process. The comparison between the numerical results and the laboratory measurements allows the calibration of the parameters that globally describe the erosion process consequent to the flushing operations. Variations in the sediment composition affect the erosion process and the mode of erosion. The erosion process of a sediment bed occurs with increasing bottom shear stress as clay is added to sand, but once this process is started the rate of erosion is greater for a cohesive sediment (sand with a clay content of 20 and 25%) than for a non-cohesive one (sand without clay). While the mode of erosion of a non-cohesive sediment is a particle-by-particle erosion, the erosion of a cohesive sediment is characterised by a rapid dislodgement of large pieces of sediment, immediately removed by the flow when the shear strength of the material is exceeded.

371


Mixtures with a clay content of 7.5% and 15% show an intermediate erosive behaviour between a non-cohesive behaviour and a cohesive one. Both for sand and for sand and clay mixtures the material being detached from the bed is mostly transported as bedload. The results of this study can be adopted for deriving guidelines on the set-up and design of flushing devices in sewer systems and particularly in stormwater storage tanks. However, further laboratory investigations are necessary in order to consider homogeneous and layered sediment beds with different grain size distributions, cohesive characteristics and consolidation times. Also some field campaigns should be carried out as some factors affecting the erosion resistance in sewer sediment deposits cannot be simulated in artificially produced beds, such as the history of the bed, chemical and biological effects and environmental processes.

Tb x Vs_w %w W Ws_i Ws_w Wc_i Wc_w z α Δt Δtk Δx ε εm ρdry ρw ρwet ρs τb τcr

NOTATION D d50 g h hke,i hks,i hs k K ker n nb nsw

N+1 p P Pb Psw q qs R RMSE S Sf t

dry sediment condition sediment particle size for which 50% of the sediment mixture is finer (m) gravity acceleration (m/s2) water level (m) experimental water depth for cell i at time k (m) simulated water depth for cell i at time k (m) sediment height (m) time index time index indicating the end of flush ratio between the parameter of erosion εm and the sediment density ρs (m/s) Manning roughness coefficient (s/m1/3) Manning roughness coefficient of bottom (s m-1/3) Manning roughness coefficient of side walls (s m-1/3) last spatial cell sediment porosity wetted perimeter (m) wetted perimeter of bottom (m) wetted perimeter of side walls (m) flow rate per unit width (m3/s/m) sediment transport rate per unit width (m3/s/m) hydraulic radius (m) root mean square error (m) longitudinal slope (m/m) friction slope (m/m) temporal independent variable (s)

bed thickness (cm) spatial independent variable (m) washed sediment volume (dm3) washed sediment percentage wet sediment condition initial weight of dry sediment (kg) washed sediment weight (kg) initial weight of the clay placed at the bottom of the channel (kg) weight of washed clay (kg) bed elevation (m) parameter time step (s) time interval between the instants denoted by k and k+1 (s) spatial step (m) rate of erosion (kg/s/m2) parameter of erosion (kg/s/m2) bulk density of dry sediment (kg/m3) water density (kg/m3) bulk density of a wet sediment (kg/m3) sediment density (kg/m3) bottom shear stress (N/m2) critical bottom shear stress [N/m2]

REFERENCES

1. Abbott MB, Minns AW (1998). Computational hydraulics. Ashgate Publishing. 2. Arthur S, Ashley RM (1997). Near bed solids transport rate prediction in a combined sewer network. Water Science and Technology 36(8):129–134. 3. Arthur S, Ashley RM (1998). The influence of near bed solids transport on first foul flush in combined sewers. Water Science and Technology 37(1):131–138. 4. Ashley RM, Verbanck MA (1996). Mechanics of sewer sediment erosion and transport. Journal of Hydraulic Research 34(6):753–769. 5. Ballamudi SM, Chaudhry MH (1991). Numerical modelling of aggradation and degradation in alluvial channels, Journal of Hydraulic Engineering, ASCE 117(9):1145– 1164. 6. Bertrand-Krajewski JL, Bardin JP, Gibello C, Laplace D (2003). Hydraulics of a sewer flushing gate. Water Science and Technology 47(4):129–136. 7. Bertrand-Krajewski JL, Campisano A, Creaco E, Modica C (2004). Experimental study and modelling of the hydraulic behaviour of a

372


8.

9.

10.

11.

12.

13.

14.

15.

16. 17.

18.

Hydrass flushing gate. Novatech2004, Lyon, France. Campisano A, Creaco E, Modica C (2004). Experimental and numerical analysis of the scouring effects of flushing waves on sediment deposits. Journal of Hydrology 299:324–334. Campisano A, Creaco E, Modica C (2008). Laboratory investigation on the effects of flushes on cohesive sediment beds. Urban Water Journal 5(1):3–14. Cao Z, Day R, Egashira S (2002). Coupled and decoupled numerical modelling of flow and morphological evolution in alluvional rivers. Journal of Hydraulic Engineering 128(3):306–321. Chebbo G, Laplace D, Bachoc A, Sanchez Y, Le Guennec B (1996). Technical solutions envisaged in managing solids in combined sewer networks. Water Science and Technology 33(9):237–244. Fan CY, Field R, Lai F (2003). Sewer sediment control: overview of an environmental protection agency wet-weather flow research program. Journal of Hydraulic Engineering, ASCE 129(4):253–259. Garcia–Navarro P, Saviron JM (1992). Mc Cormack’s method for the numerical simulation of one-dimensional discontinuous unsteady open channel flow. Journal of Hydraulic Research, ASCE 30(1):95–104. Guo Q, Fan C, Raghaven R, Field R (2004). Gate and vacuum flushing of sewer sediment: laboratory testing. Journal of Hydraulic Engineering, ASCE 130(5):463–466. Kassem A, Chaudhry MH (1998). Comparison of semi coupled numerical models for alluvial channels. Journal of Hydraulic Engineering, ASCE 124(8):794– 802. Lin H, Le Guennec B (1996). Sediment transport modelling in combined sewer. Water Science and Technology 33(9):61–67. Linehan P (2001). The design of flushing gates to transport sewer sediment. Dissertation, Department of Civil and Structural Engineering, University of Sheffield. Lorenzen A, Ristenpart E, Pfuhl W (1996). Flush cleaning of sewers. Water Science and Technology 33(9):221–228.

19. Mitchener H, Torfs H (1996). Erosion of mud/sand mixtures. Journal of Coastal Engineering 29:1–25. 20. Parchure TM, Metha AJ (1985). Erosion of soft cohesive sediment deposits. Journal of Hydraulic Engineering 111(10):1308–1326. 21. Pisano WC, O’Riordan OC, Ayotte FJ, Barsanti JR, Carr DL (2003). Automated sewer and drainage flushing system in Cambridge, Massachusetts. Journal of Hydraulic Engineering, ASCE 129(4):260– 266. 22. Saiedi S (1997). Coupled modelling of alluvial flows. Journal of Hydraulic Engineering, ASCE 123(5):440–446. 23. Skipworth PJ (1996). The erosion and transport of cohesive-like sediment beds in sewers. Ph. D. thesis, University of Sheffield, UK. 24. Skipworth PJ, Tait SJ, Saul AJ (1999). Erosion of sediments beds in sewers: model Journal Environ. Eng. development, 125(6):566–573. 25. Sweby PK (1984). High resolution schemes using flux limiters for hyperbolic conservation laws. Journal of Numerical Analysis 21(5):995–1011. 26. Tait SJ, Chebbo G, Skipworth PJ, Ahyerre M, Saul AJ (2003). Modelling in-sewer deposit erosion to predict sewer flow quality. Journal of Hydraulic Engineering, ASCE 129(4):316– 324. 27. Todeschini S (2007). Il controllo degli scarichi fognari in tempo di pioggia mediante vasche di prima pioggia: aspetti progettuali e gestionali, Ph. D. Thesis, Università degli Studi di Pavia. 28. Todeschini S, Ciaponi C, Papiri S (2008). Experimental and numerical analysis of erosion and sediment transport of flushing waves, XI Int. Conference on Urban Drainage, Edinburgh, UK, 2008. 29. Torfs H (1995). Erosion of mud / sand mixtures, Ph. D. thesis, Katholieke Universiteit Leuven. 30. Yalin MS, Karahan E (1979). Interception of sediment transport, Journal of Hydraulic Div., ASCE 105:1433–1443.

373