Geoscience Reference
In-Depth Information
the sediment transport capacity under rapidly varied flow conditions. After having
analyzed the mechanism of local scour at bridge piers, Dou (1997) related the sediment
transport capacity for local scour to the mean flow, downward flow, vorticity, and
turbulence intensity as follows:
a
1
U
3
gh
a
2
|
W
|−|
W
|
a
3
(
−
)
b
a
4
i
−
i
app
ω
app
app
C
∗
=
s
+
+
+
(7.62)
ω
U
U
∗
s
where
C
is the sediment transport capacity for local scour,
U
is the depth-averaged
velocity,
U
∗
∗
is the bed shear velocity,
|
W
|
is the magnitude of downward flow,
is the vorticity,
b
is the pier width,
i
is the turbulence intensity,
a
i
)
are empirical coefficients, and the subscript “
app
” denotes the approaching flow
quantities.
In Eq. (7.62), the non-dimensional parameter
U
3
(
i
=
1, 2, 3, 4
represents the contribution
of mean flow, which is used in the Zhang formula for general sediment transport
capacity, as introduced in Section 3.5.3. The term
/(
gh
ω
)
s
(
|
W
|−|
W
|
)/
U
represents the
app
influence of downward flow,
(
−
)
b
/
U
∗
accounts for the effect of vorticity, and
app
(
i
app
)/ω
s
takes into account the effect of turbulence intensity. Eq. (7.62) considers
the significant factors that affect the local scour process. However, in reality, it is
difficult to use the linear formulation in Eq. (7.62) to reflect all factors reasonably,
and the empirical coefficients
a
i
need to be calibrated extensively.
Based on the analysis of the forces acting on sediment particles near the bed exerted
by rapidly varied flows, Wu and Wang (2005) modified the van Rijn (1984a & b)
formulas (3.70) and (3.95) of equilibrium bed-load transport rate and near-bed
suspended-load concentration for the simulation of local scour by determineing the
transport stage number
T
with
T
i
−
=
τ
be
/τ
−
1. Here,
τ
be
is the effective tractive force
cr
and
τ
cr
is the critical shear stress for sediment incipient motion in rapidly varied flows.
τ
cr
is determined by
τ
=
K
p
K
d
K
g
τ
(7.63)
cr
c
where
c
is the critical shear stress for sediment incipient motion, determined using the
Shields curve; and
K
p
,
K
d
, and
K
g
are the correction factors for the effects of vertical
dynamic pressure gradient, downward flow, and bed slope, respectively.
Fig. 7.12 depicts the localized dynamic pressure field due to the impingement of a
jet onto a channel bed. This localized dynamic pressure also exists in front of bridge
piers, abutments, and spur-dikes. The gradient of fluid pressure causes a pressure-
difference force on sediment particles, which is also called the general buoyancy. This
pressure-difference force on a single particle is determined by (Liu, 1993)
τ
1
6
π
f
p
d
3
=−
∇
p
(7.64)
where
d
is the particle diameter.
The vertical component of the pressure-difference force changes the effective weight
of sediment inwater and, in turn, the critical shear stress required for sediment incipient
