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: ychbai@tju.edu.cn (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
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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.
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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
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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.
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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.
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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.
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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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