2002 3D Modelling of Sediment Transport Effects of Dregging

7/31/2019 2002 3D Modelling of Sediment Transport Effects of Dregging

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Three-dimensional modelling of sediment transport

and the effects of dredging in the Haihe Estuary

Yuchuan Baia,b,*, Zhaoyin Wangc, and Huanting Shenb

aInstitute for Sedimentation on River and Coast Engineering, Tianjin University, Tianjin 300072, Peoples Republic of ChinabThe State Key Laboratory of Estuarine and Coastal Research, East China Normal University, Shanghai 200062, Peoples Republic of China

cDepartment of Hydraulic Engineering, Tsinghua University, Beijing 100084, Peoples Republic of China

Received 3 August 2000; received in revised form 4 January 2002; accepted 4 January 2002

Abstract

The Haihe Tide Lock was constructed on the Haihe River in 1958 to stop salty and muddy water intrusion. Nevertheless, tidal

currents carry sediment, which is eroded from the surrounding silty coast, into the river mouth and, thus siltation of the channel

downstream of the tide lock becomes a major problem. Employed are trailer dredges, which stir up the silt and subsequently moves

it out of the mouth with ebb tidal currents. While the application of this method is encouraging there are still problems to be studied:

how high is the dredging efficiency, how far can the resuspended sediment be transported by the ebb currents, and is the sediment

carried back by the next flood tide? This paper develops a 3-D model to answer these questions. The model employs a special

element-interpolating-function with the r-coordinate system, triangle elements in the horizontal directions and the up-wind finite

element-lumping-coefficient matrix. The results illustrate that the efficiency of dredging is high. Sediment concentration is 420 times

higher than the flow without dredging. About 4060% of the resuspended sediment by the dredges is transported towards the sea

3.2 km off the river mouth and 1030% is transported 5 km away from the mouth. Calculations also indicate that the rate of siltation

of the river mouth is about 0.6 Mm3 per year. If the average discharge of the river runoff is 0, 200 or 400 m3 s1 the mouth has to be

dredged for 190, 99 or 75 days every year so to maintain it in equilibrium. The dredging efficiency per day is 0.531.31%. 2003 Elsevier Science B.V. All rights reserved.

Keywords: 3D-model; Trailer dredging; r-Coordinate system; Sediment transport; Haihe River mouth

1. Introduction

The Haihe River flows into the Bohai Bay at Tianjin,

the third largest city of China. The Bohai Bay is

surrounded by a silty coast composed of fine sediment of

median diameter 0.0030.01 mm, which is eroded and

resuspended by waves and currents. Sediment trans-

portation in the estuarine area has an impact on the

environment and affects coastal engineering projects.

Tidal currents carry the sediment eroded from the

surrounding silty coast into the Haihe River mouth and

causes continuous siltation of the river channel. The

Haihe Tide Lock was constructed in 1958 to stop salty

and muddy water intrusion into the river. Nevertheless,

the suspended sediment deposits in the channel down-

stream of the tide lock and siltation of the river mouth

become a major problem.

In the 1970s1980s, the mouth and the channel were

dug frequently to maintain the flood-discharge capacity.

In the 1990s, a new dredging technology was employed.

Trailer dredges stir the deposit into suspension and the

tidal currents carry the sediment out of the mouth

during ebb tides. The method is found effective and

more economically feasible than other dredging meth-

ods from engineering practices (Bai, 1998a; Mackinnon,

Chen, & Thompson, 1998). While the application of the

method is encouraging there are still problems to be

studied: how high is the efficiency of the trailer dredging,

how far can the resuspended sediment be transported by* Corresponding author.

E-mail address: [email protected] (Y. Bai).

Estuarine, Coastal and Shelf Science 56 (2003) 175186

0272-7714/03/$ - see front matter 2003 Elsevier Science B.V. All rights reserved.

doi:10.1016/S0272-7714(02)00155-5


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the ebb currents, and is the sediment carried back by the

next flood tide? This paper develops a 3-D model to

answer these questions, which is calibrated with the data

collected in 1996, 1997 and 1999.

The physical process is complex. Sediment trans-

portation occurs in the flow of the river channel, erosion

of the silty coast by waves and storm surges, dispersionof sediment suspension dredged from the river mouth,

and longshore drift of silt with tidal currents. Several

numerical models have been developed to study the

sediment transportation in the estuarine area. Unfortu-

nately, most of them are two-dimensional and not able

to simulate the complicated 3-D flow at the river mouth.

Sediment concentration and transportation is a function

of variables such as waves, currents, bottom shear stress,

turbulence intensity, size and mineral composition,

erosion and deposition of sediment. The flow field

is three-dimensional and, therefore, only 3-D models are

adequate.

Many 3-D-finite-difference hydrodynamic models

were developed employing the ADI method (Alternat-

ing-Direction-Implicit) based on the assumption of

hydrostatic pressure to study estuarine flows (Casulli

& Cattani, 1994; Casulli & Cheng, 1992; Casulli &

Stelling, 1996; De Goede, 1991; Madala & Piacsek,

1997; Stelling & Leendertse, 1992). Such kind of 3-D

models are also applied for the Hangzhou Bay (Li &

Zhang, 1998) and Bohai Bay (Dou & Ozer, 1993; Yu &

Zhang, 1987). However, the models use finite-difference

method and rectangular grids in computation, which are

not adequate to simulate irregular coastlines. Moreover,

the space steps in these models are not flexible. In fact,small space steps are needed for special areas like

harbours, river channels and beaches when large space

steps may be used for areas far away from the coast-

line. Overcoming these defects some 3-D or quasi-3-

D models have been developed using finite-element

method (Bai, 1997; Bai, 1998b; Li & Zhang, 1998).

The current 3-D model writes the equations of flow

and sediment transport by employing a special element

interpolating function with the r-coordinate system,

triangle elements in the horizontal directions and the

up-wind finite element lumping coefficient matrix (Pepper

& Carrington, 1999; Raviart, 1973; Thomee, 1983; Tou

& Arumugam, 19861987). In the vertical direction the

computation is performed with the finite-difference

method. The r-coordinate transformation is executed

to the equations of tidal currents and sediment transport

and the irregular free surface and sea bed are trans-

formed into a series of planes in the r-coordinates.

Thus, all the computational areas have equal calculation

points in the vertical direction. Therefore, the model

exhibits high precision for the flow and sediment

transport in any water area. With the triangle grids this

model is adequate for irregular coastlines and flexible to

change the space step whenever it is needed.

2. Theoretical basis

2.1. Equations of flow

qu

qx qvqy

qwqz

0 1

qu

qt u qu

qx v qu

qy wqu

qz

1q

qp

qxfv 1

q

qTxx

qx qTxy

qy qTxz

qz

2

qv

qt u qv

qx v qv

qy w qv

qz

1q

qp

qyfu 1

q

qTyx

qx qTyy

qy qTyz

qz

3

1

q

qp

qz g 0 4

in which x and y are the Cartesian coordinates in thehorizontal plane and z is the vertical coordinate, u, v and

w are the velocity components in the x, y and z

directions, respectively, p is the pressure, Txx. . .Tyz are

turbulent stresses, and f is the Coriolis parameter.

2.2. Equation of sediment transport

qc

qt u qc

qx v qc

qy w qc

qz q

qxkxqc

qx

qqy

kyqc

qy

qqz

kzqc

qz

! xs qc

qz Sx 5

in which c is the concentration of suspended sediment,

kx, ky and kz are the diffusion coefficients in the x, y and z

directions, respectively, xs is the fall velocity of sediment

in water (Wang & Gu, 1987) and Sx is a parameter

representing the source of sediment, for instance, the

rate of sediment stirred up by the trailer dredges per

time.

2.3. Equation for bed surface process

The following equation of riverbed deformation is

used to calculate the change of the bed topography,

which is indeed the boundary of the flow (Wang & Gu,1990):

c0b

qzb

qt qucH

qx qvcH

qy qqbx

qx qqby

qy 0 6

in which zb is the bed elevation, c0b is the dry weight of

the deposit per volume, qbx and qby are the rates of

transportation of fluid mud layer in the x and y

directions, respectively, given by:

qbx S8

Cbd UU; qby S8

CbdVV

176 Y. Bai et al. / Estuarine, Coastal and Shelf Science 56 (2003) 175186


3/12

S* is a coefficient and is empirically given as a function

of the median diameter as follows:

S 0:033d0:60550The over-bar represents the average value over the

depth, and UUand VVare the average velocity components

in the x and y directions, respectively, as given in Eq.(11); Cb is the concentration of suspended sediment at

the bottom; d is the thickness of the fluid mud layer,

given by:

d H 10 1

2:3k

2E

E 1

in which E is the Composite average velocity, given by:

Effiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

UU2 VV2p

and E* is the composite shear velocity:

E ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiUU2 VV2qand k is the Karman constant.

To simplify the calculation, however, the change of

the bed topography is not considered in the continuity

equation of the flow because the change in topography is

very small compared with that in the water depth.

3. Coordinate transformation

Fig. 1 shows the Cartesian coordinate system and r-

coordinate system. The transformation between the two

systems is:

a x; b y; r z gH g ; t

r t;

in which r is a dimensionless coordinate, re[1, 0]. Wemay derive the following relations:

q

qx q

qa r

D

qD

qb 1

D

qg

qa

q

qr

q

qy q

qb r

D

qD

qb 1

D

qg

qb

q

qr;

q

qz 1

D

q

qr

q

qt q

qtr r

D

qD

qtr 1

D

qg

qtr

q

qr

in which D H g. For convenience the coordinates(a, b, r, tr) are written as (x, y, r, t).

3.1. Equations of flow

In the (x, y, r, t) system the equations of flow are

written as follows:

qDuqx

qDvqy

qxqr

qDqt

e 0 7

qDuqt

qDuuqx

qDuvqy

quxqr

gD qgqx

fv

D

q

qx

Kxqu

qx

q

qy

Kyqu

qy !

q

qr

Kz

D

qu

qr ex

8

qDvqt

qDuvqx

qDvvqy

qvxqr

gD qgqy

fu

D qqx

Kxqv

qx

qqy

Kyqv

qy

! qqr

Kz

D

qv

qr

ey

9In the equations, e, ex and ey are high orders of

minuteness generated from the coordinate transforma-

tion. These terms are much smaller than other terms, so

that may be ignored. x is the vertical velocity in the r-

coordinate system, see Eq. (12).

There are four unknown variables, namely D, u, v, x

in the three equations. Therefore, another equation is

needed to solve the equations. In the r-coordinate

system, integration of the continuity equation over the

depth of water yields:

qD UUqx

qDVV

qy qD

qt 0 10

Fig. 1. (a) Cartesian-coordinate; (b) r-coordinate system.

177Y. Bai et al. / Estuarine, Coastal and Shelf Science 56 (2003) 175186


4/12

where U and V are the velocity components averaged

over the water depth, given by:

UU R01 u dr P0b DrkukVV R01 v dr P0b Drkvk

(11

The vertical velocity in the r-coordinate, x, is related to

the vertical velocity in the Cartesian coordinate, w, asfollows:

x D drdt

w u r qDqx

qgqx

v r qD

qy qg

qy

r qDqt

qgqt

12

3.2. Equation of sediment transport

The equation of sediment transport is written in the

(x, y, r, t) system as:

qDcqt

qDucqx

qDvcqy

qx xscqr

D qqx

kxqc

qx

qqy

kyqc

qy

q

Dqrkz

qc

Dqr

!DSx ec 13

in which ec is a high order of minuteness generated from

the coordinate transformation, which can be ignored

because it is small compared with the other terms.

3.3. Boundary conditions

(1) Boundary conditions for the equations of flow

Dynamic boundary conditions:

The wind stress components Tsx and Tsy are set to zero

in the calculation because wind-induced currents

are out of the scope of the study.

At the bottom, the surface friction Tbx and Tby are

taken to be the Chezy frictional stresses given by:

Tbx gUUffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

UU2 VV2p

c2D; Tby g

VVffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

UU2 VV2p

c2D; c 1

nD

1

6;

in which n is the Mannings roughness coefficient.Kinematic boundary conditions:

At the free surface, xx; y; s; tjr0 0:On the sea bed, xx; y; s; tjr1 0:At the coastal line, the velocity component perpen-

dicular to the coastline is zero.

(2) Boundary conditions for sediment transport

At the free surface:

Kz1

D

qc

qrKxqcqg

qxqxKy qcqg

qyqy xsc 0; r 0

At the interface between the fluid mud layer and the

overlying water:

Kz 1D

qc

qrKxqcqh d

qxqxKy qcqh d

qyqy P;

r

D d

DThe sediment flux into the water from the mud layer

is equal to the pick-up rate P, which is an external

variable to be determined by the local flow conditions,

especially the turbulence intensity generated by the tidal

currents and waves (Nadaoka, Yagi, & Kamata, 1991;

OConnor & Nicholson, 1988). In this paper the pick-up

rate P is given by an empirical formula (Bai, personal

communication; Bai, 1996a):

P apCb0:38bzE 1

ffiffiffiffiffiffi2p

p ea212 a1 1 U0a1

& 'cs

where

ap 0:001350:53p ; Rp ffiffiffiffiffiffiffiffi

gDsp Ds

cs;

Ds = sediment diameter (in mm), cs = the weight of the

deposit per volume, Cb = the concentration of moving

sediment on the bed, E* = friction velocity, and U0(x) =

the Error-function. The function b(z+) is given by:

bz ffiffiffiffiffiffi

vv02p

E

1

2500x 502 1; z 50

1 z > 50

(

and

z d

m=E ;

in which v0 is the fluctuating velocity. The coefficients a1and Cb are given by:

a1 0:548 dDs

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

0:301d

Ds

2h

s;

and

h U2c

gDscs c

Cb

MIN 0:0064 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4:1 105 0:392Tbp

0:196 ;Ck

& ';

Ds\0:02mm

MIN0:0064 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4:1 105 0:392Tbp

0:196;Cm

& ';

Ds ! 0:02mm

8>>>>>>>>>>>>>:

in which

Ck 15:4Ds 0:070; Cm 0:755 0:222 log10 Ds;and

Tb ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiTbx Tbyp gf=cm2



5/12

4. Numerical scheme of the model

4.1. Interpolation function

In the r-coordinate system, a series of planes parallel

to the xy plane is introduced. A triangular grid is used

to compose the computational mesh on the horizontaldomain at all levels. Define ui(x, y) the coordinate

functions of linear triangle elements:

/x;y 12D

yj ykx xk xjy xiyk yjxk

in which i 1, 2, 3, j 1, 2, 3, k 1, 2, 3, they arereplaced by each other in anti-clockwise turn, D is the

area of the element and (xi, yi), (xj, yj), (xk, yk) are the

three apex coordinates of the element. The interpolation

functions are given as follows:

u uir; t/ix;yv

vi

r; t

/i

x;y

w wir; t/ix;yD Dit/ix;y

g git/ix;y

8>>>>>>>:14

For the horizontal domains the equations of flow and

sediment transport are discretized with finite-elements

method by using the above interpolation functions,

while the finite differences scheme is employed for the

vertical direction (r-coordinate).

4.2. Numerical simulation of the 3-D flow field

In the r-coordinate system, the computational mesh

on a series of planes parallel to the xy plane is estab-

lished with the triangular grid. Substitution of Eq. (14)

into Eqs. (7)(10) with employment of the Galerkin

method yields the following finite-element equations:

/i/jqx

qr

D ukq/k

qx

/i/j u Dk

q/kqx

/i/j

D vkq/kqy

/i/j v Dk

q/kqy

/i/j

/i/jqD

qt 0 15

/i/jqu

qt u ukr; tq/

k

qx /i/j

v ukr; t q/kqy

/i/j x

1

D

quk

qr/k

2kvq/j

qx;q/iqx

u kv

q/j

qy;q/iqy

u

kvq/j

qy;q/iqx

v gg /j

q/iqx

/i/j fv/i/j

1D

q

qr

Kz

D

qu

qr

/i/j

Zsxxcosm;x

sx cosm;y /jdC 16

/i/jqv

qt u vkr; t q/k

qx

/i/j

v vkr; t q/kqy

/i/j x

1

D

qvk

qr/k

2kv

q/j

qx

;q/iqx

v kvq/j

qy

;q/iqy

v kv

q/j

qy;q/iqx

u gg /j

q/iqy

/i/j fu/i/j

1D

q

qr

Ky

D

qv

qr

/i/j

Zscosm;y

sx cos m;x/jdC 17

/i/jqD

qt UU Dkq/k

qx

/i/j VV Dk

q/kqy

/i/j

D UUkq/kqxr

/i/j D VVk

q/iqy

/i/j 0 18

Similarly, substituting Eq. (14) into Eq. (12), the

transformation between w and x is then given by:

w/i/j x/i/j urD gkq/kqx

!/i/j

vrD gk

q/kqy

!/i/j r

qD

qt qg

qt

/i/j 19

In Eqs. (15)(19), (/i, /j) represents the integration of

the inner-product. Eqs. (15)(19) can be rewritten as

Eqs. (20)(24), respectively.

Aq/

qrB1r; tD B4u C2r; tD C4v A qD

qt 0

20

Aqu

qtB1r; tu C1r; tv E1r; tx Afv D1g

A 1D

q

qr

vz

D

qu

qr

21

Aqv

qtB2r; tu C2r; tv E2r; tx Afu D2g

A 1D

qqr

vzD

quqr

22AqD

qt BB1tD B4 UU CC2tD C4 VV 0 23

wA Ax B01u B02v A rqD

qt qg

qt

24

where A, B1, C1, D1, E1; B2, C2, D2, E2; B4, C4; BB1, CC2;

B01B02 are coefficient matrices. By using the finite elementmass lumping matrix method, the coefficient matrices

are transformed into diagonal matrix except for D1and D2.



6/12

By adopting the semi-implicit finite-difference

scheme, formulae (21) and (22) give ukn+1 and vk

n+1 as

functions ofukn, vk

n, wkn, g etc., in which n is the time-level

index and k the depth-level index, ukn+1 and vk

n+1 are in

the k th-calculation-layer at the n l th-time-step andukn, vk

n, wkn are in the k th-calculation-layer at the n th-

time-step. Then, the integration formula (11) producesthe mean velocities U and V. Substituting them into

Eq. (23), we have the value of Dn+1.

With the values ofDn, Dn+1, ukn+1, vk

n+1 the Eq. (20) is

solved yielding the value ofxkn+1 for every layer. Finally,

using the relation between w and w, or the formula (24),

we obtain the value of wkn+1.

4.3. Calculation of the sediment concentration

Using the Galerkin finite element method, we rewrite

the sediment transport Eq. (13) into non-conservative

type. Substituting C Cir; tuix;y into Eq. (13)yields:

AidC

dt

XNj1

ZD

K1rUirUjdD" #

Ci

Aix xs 1D

qCi

qrAi 1

D

q

qr

Kz

D

qC

qr

AiSx 25

where D represents the area of an element, Kl represents

the diffusion coefficient in x or y direction. Here non-

conservative type implies that the continuity equation

of flow is not included. Since the continuity equation hasbeen used in the calculation of the flow filed, the non-

conservative type rather than conservative type is

used herein. Then, among the relative elements of the

calculation point pi, search for the upwind one and

discretize dC/dt for the calculation point. Let (xi, yi),

(xib, yib), (xic, yic) be three apex coordinates of the

upwind element and Di be area of the element. Thus,

we obtain:

dC

dt

ni

Cn1 CnDt

i

r rCni

Cn

1

Cn

Dt

i

aiir; tCni aiibr; tCniib aiicr; tCniic 26

where:

aiir; t 12Di

unir; tyib yic vni r; txiv xib

aiibr; t 12Di

unir; tyiv yi vni r; txi xiv

aiicr; t 12Di

unir; tyi yib vni r; txib xi

and ~VV represents the horizontal velocity vector, i.e.~VV u; v: Thus, from formula (26), we obtain:

cn1i;r cni;r 1 aii biirDt

Xnik1

aiik biikrDt" #

cniik;r

x xs1

D

qCi;r

qr !

Dt cni;r

1

D

qxi;r

qr !

Dt

1D

q

qr

kz

D

qCni;r

qr

!Dt SmDt 27

5. Application of the model to the Haihe River Estuary

5.1. The modelling area

Fig. 2a shows the Bohai Bay and the location of the

Haihe Estuary; and Fig. 2b shows the modelling area ofthe Haihe Estuary from 1.5 km upstream of the Haihe

Tide Lock to 11 km off the river mouth. The calcu-

lation area extends 4 km southward from the north

Fig. 2. (a) The Bohai Bay and the Haihe Estuary. (b) The modelling

area of the Haihe Estuary.



7/12

boundarythe south wave breaker of the Tianjin New

Harbour. The model is calibrated with the data

measured at the 11 points shown in Fig. 2b. The

measurement was performed for the diurnal-tide-cycles

in the period 19831993.

5.2. Sediment transport during flood and ebb tide

Sediment measurement was performed in 1983 and

the data are complete and reliable. The measurements

of flow and sediment for the neap tides were conducted

on 34 September; those for the mean tides on 12

September and the spring tides on 1011 September

1983. The model is calibrated and validated with the

data. The modelling results are compared with the

measurements, as shown in Figs. 3 and 4:

(a) Vertical distribution of sediment concentration. The

calculated concentration distributions are compared

with the measurements, as shown in Fig. 3a,b. Over

most part of the flow depth the calculated concen-

tration distributions agree well with the measure-

ments. The sediment concentration near the seabed

was not measured, thus no comparison can be made

for the region although the concentration near the

bed is important.

(b) Typical flow fields of ebb and flood tides. The

calculated flow fields for ebb and flood tides are

shown in Fig. 4a,b. The calculated velocities of tidal

currents at the point 2 and 9 for two cycles of tide

are compared with the measurements, as shown in

Fig. 4c,d. The calculations agree with the measure-

ments very well.

5.3. Sediment transport induced by dredging

Modelling of the sediment transport induced by

dredging is performed for mid-tide cycles. The param-

eters of runoff discharge and dredging of sediment

appear as the source terms in the continuity equation of

flow and the equation of sediment transport (Bai,

1998a). Sediment transportation is calculated for differ-

ent discharges (0, 200, 400 m3 s1) and positions of the

dredged section. The results are presented for all the

scenarios in Tables 2 and 3.

Fig. 5 shows the result for runoff discharge

=200m3 s1, and the dredged section from 0 700 to1 500 (see Fig. 6). Fig. 5ad clearly shows that sedi-ment is transported out of the river mouth by the tidal

currents and runoff flow. The calculated concentration

is averaged over the depth and compared with the mea-

surements at selected sections, as presented in Table 1.

In the table 1 800, 2 200 etc. indicate the locationsof the measurement section at 1800, 2200 m etc. down-

stream of the Haihe Tide Lock. For the calculations

and measurements the runoff discharge is 200 m3 s1.

The comparison shows a good agreement between the

model and the measurements.

Fig. 3. Triangular grid layout of the Haihe Estuary.



8/12

6. Effects of the trailer dredging

6.1. Short term effects of dredging

One purpose of the study is to investigate the effects

of the trailer dredging in the estuary at different

locations and under various runoff discharges. The

sediment concentration from the model is averaged over

the period of dredging at each measurement section, as

shown in Table 2. The average percentage of trans-

portation of the dredged sediment through the sections

is also calculated and presented in Table 3.

The results show that the efficiency of dredging is

high. The trailer dredging makes the sediment in

suspension and thus enhances the concentration 420

times higher. About 1030% of the dredged silt is

transported into the sea 5 km away from the river mouth

and more than 4060% of the dredged silt is transported

3.2 km down from the mouth.

6.2. Long term effects

The tide in the Bohai Bay is a typical semi-diurnal-

cycle tide. The Haihe river mouth receives 705 tidal

cycles per year, among them 137.5 are spring tides, 342

mid tides and 225.5 neap tides. The model employs the

wave ray method in the calculation, which takes into

account the effects of waves, the currents and the

variation in tidal level (Bai, 1996b). Let V(w, c) be the

quantity of sediment returning during a tidal cycle,

V(q, c) the quantity of sediment scoured and discharged

by the flow during a tidal cycle, V(q, t) the quantity of

sediment transported by the tidal currents due to

Fig. 4. (a) Vertical distributions of sediment concentration at Point 4 during ebb tide (h = water depth of different tidal phases; t is the time). (b)

Vertical distributions of sediment concentration at Point 4 during flood tide (h = water depth of different tidal phases; t is the time). Calculated,

d Measured.



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Fig. 5. (a) Typical flow field of ebb tide. (b) Typical flow field of flood tide. (c) Comparison of the calculated and measured velocity of tidal current

at the Point 2. (d) Comparison of the calculated and measured velocity of tidal current at the Point 9.Calculated, d Measured.



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dredging in a tidal cycle, t1 (h) the period of time with

runoff discharge in a tidal cycle, t2 (h) the period of time

during which dredging is performed in a tidal cycle, Nstotal number of tide cycles, Nt total number of tidal

cycles during which dredging is performed, Nes total

number of tidal cycles with effective runoff discharge,

Net total number of effective tidal cycles during which

Fig. 6. (a) Sediment concentration contours T 2:5 h. (b) Sediment concentration contours T 3:0 h. (c) Sediment concentration contoursT 3:5 h. (d) Sediment concentration contours T 4:0 h.

Table 1

Comparison of calculated average concentration with the measure-

ments

Measurement section 1+ 800 2 +200 3+ 200 4 +100 5+ 000

Calculated sediment

concentration (kg m3)

0.86 0.86 0.59 0.34 0.14

Measured sediment

concentration (kg m3)

0.7 0.53 0.46

Table 2

Calculated sediment concentration averaged over the period of dredging (in kg m

3

)Location of the dredged section Discharge (m3 s1) 1 + 800 2 + 200 3 + 200 4 + 100 5 + 000

Upper section (0 + 7001 + 500) 0.00 0.44 0.35 0.26 0.12 0.08200 0.95 0.80 0.65 0.40 0.16

400 1.20 1.10 0.83 0.48 0.36

Lower section (1 + 5002 + 400) 0.0 0.52 0.36 0.28 0.12 0.04200 0.76 0.68 0.54 0.28 0.12

400 1.30 1.10 0.78 0.36 0.26

Both upper and lower sections

(0+7002+400)0.00 0.86 0.52 0.40 0.24 0.10

200 1.50 1.26 0.92 0.49 0.30

400 1.90 1.80 1.32 0.80 0.37

Note: The measured sediment concentration is only 0.1 kg m3 at 1 800, 0.05kg m3 at 3 200 and 0.01kg m3 at 5 000 when there is nodredging.



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dredging is performed. The yearly volume of returning

sediment V(w,c) is given by the following equation:

Vw; c 705Vw; c Vq; c Vw; c Nes Vq; t Vw; c Net 28

where

Nes t1Ns12:34

; Net t2NT12:34

:

Taking the returning silt quantity into account, the

dredging efficiency of the whole year is:

gtotal 1 Vw; c

705Vw; c % !

29

It is calculated that in the channel section from

2 200 (the Green Lamp) to the Haihe Tide Lock thevolume of returning silt is about 858 m3 per tidal cycle.

Thus, the total volume of returning silt is 605 000 m3

a year. Taking for example the dredging in the upper

section, if the runoff discharge is 0.0, 200 and 400

m3 s1, the quantity of the dredged sediment passing the

section 2 200 per day is 3180, 6062 and 8089m3,respectively. So in order to maintain the channel bed

between 0 700 and 2 400 sections in equilibrium, thedredging days required per year are 190, 99 and 75 days,

respectively. Therefore, the efficiency per dredging day is

0.53 (1/190), 1.01 (1/99), 1.31% (1/75), correspondingly(see Table 4). Table 4 presents the days of dredging

required for maintaining the channel upper from the

Green Lamp or the reach between 0 700 and 2 400sections in equilibrium from the model calculation.

The efficiency per dredging day is shown in the table as

well.

7. Conclusions

Sedimentation of the Haihe River mouth is eased at

low cost by employing the trailer dredges, which makesuse of the tidal currents to carry the sediment into

the sea. This paper develops a 3-D model to simulate the

sediment transportation induced by dredging in the

estuary. The model employs the r-coordinate system, a

special element interpolating function, triangle elements

in the horizontal directions and the up-wind finite

element lumping coefficient matrix. The modelling

results of flow field and sediment concentration agree

well with the measurements.

Sediment is transported out of the river mouth by the

tidal currents and runoff flows. Calculations show that

the efficiency of dredging is high. Trailer dredging makes

sediment in suspension and thus enhances the concen-

tration by 420 times. About 1030% of the dredged silt

is transported into the sea 5 km away from the river

mouth and more than 4060% is transported 3.2 km

down from the mouth.

Sediment from the sea caused siltation of the river

mouth at the rate about 0.6 Mm3 per year. The model

indicates that the river mouth has to be dredged for

190, 99 or 75 days per year to maintain the river mouth

in equilibrium if the runoff discharge is 0, 200 or

400m3 s1. The efficiency per dredging day is 0.53

1.31%.

Table 3

Calculated transport rate of dredged sediment at the selected sections (in %)

Location of the dredged section Runoff discharge(m3 s1) 1+800 2+200 3+200 4+100 5+000

Upper section (0 + 7001 + 500) 0.00 100 79.5 59.1 27.3 18.2200 100 84.2 67.9 42.1 16.0

400 100 91.7 69.2 40.0 30.0

Lower section (1 + 500

2 + 400) 0.0 100 69.2 53.8 23.1 7.7

200 100 89.5 69.9 36.8 15.8

400 100 84.9 60.1 27.7 20.0

Both upper and lower sections (0 + 7002 + 400) 0.00 100 60.5 46.5 27.9 11.6200 100 84.0 61.0 32.7 20.0

400 100 94.0 69.0 42.1 19.5

Table 4

Dredging days required for bed equilibrium and the efficiency per

dredging day

Location of

dredging section

Discharge

(m3

s1

)

Dredging

days

Efficiency per

dredging day (%)

Upper section

(0+7001+500)0.00 190 0.53

200 99 1.01

400 75 1.33

Lower section

(1+5002+400)0.0 219 0.46

200 94 1.6

400 89 1.12

Both upper and

lower sections

(0+7002+400)

0.00 152 0.66

200 51 1.96

400 41 2.44



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Acknowledgements

This research work is supported by the National

Natural Science Foundation of China (NSFC) and The

Hong Kong Research Grants (Numbers 59809006 and

59890200).

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2002 3D Modelling of Sediment Transport Effects of Dregging

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