Geoscience Reference
In-Depth Information
3.2.4 Incipient motion of non-uniform sediment
particles
Interactions exist among different size classes of a non-uniform sediment mixture on
the bed. Coarse particles have higher chances of exposure to flow, while fine particles
are more likely sheltered by coarse particles. Therefore, it is necessary to consider the
effect of this hiding and exposure mechanism on non-uniform sediment transport. The
widely used approach is to introduce correction factors into the existing formulas of
uniform sediment incipient motion and transport, as discussed below.
Qin formula
Qin (1980) proposed the following formula for the incipient motion of non-uniform
sediment particles:
1
/
6
0.786
h
d
90
gd
k
1
γ
−
γ
γ
2.5
m
d
m
d
k
s
U
ck
=
+
(3.34)
where
U
ck
is the critical average velocity for the incipient motion of size class
k
of
bed material (m
s
−
1
),
d
k
is the diameter of size class
k
(m),
d
m
is the arithmetic mean
diameter of bed material (m), and
m
represents the compactness of non-uniform bed
material:
·
0.6,
η
d
<
2
m
=
0.76059
−
0.68014
/(η
+
2.2353
)
,
η
≥
2
d
d
where
d
10
. A formula similar to Eq. (3.34) was also proposed by Xie and
Chen (1982; see Zhang and Xie, 1993).
η
=
d
60
/
d
Methods of Egiazaroff and others
Egiazaroff (1965), Ashida and Michiue (1971), Hayashi
et al
. (1980), and Parker
et al
.
(1982) developed formulas to determine the incipient motion of non-uniform sedi-
ment particles by introducing correction factors as functions of the non-dimensional
sediment size
d
k
/
d
m
or
d
k
/
d
50
. The Egiazaroff formula can be written as
2
log 19
ck
c
=
(3.35)
log
(
19
d
k
/
d
m
)
τ
ck
being the critical shear stress for the incipient
motion of particle
d
k
in bed material; and
ck
=
τ
ck
/
[
(γ
s
−
γ)
d
k
]
where
, with
c
can be interpreted as the critical Shields
number corresponding to
d
m
.
c
was given 0.06 by Egiazaroff. This value is too large
in general. Misri
et al
. (1984) found that
c
should be 0.023-0.0303.
