Geoscience Reference
In-Depth Information
Figure 3.8 Definition of exposure height of bed material.
The total hidden and exposed probabilities, p hk and p ek , of particles d k are then
obtained by summing Eqs. (3.40) and (3.41) over all size classes, respectively:
N
d j
p hk =
p bj
(3.42)
d k
+
d j
j
=
1
N
d k
d k +
p ek =
p bj
(3.43)
d j
j
=
1
where N is the total number of particle size classes in the non-uniform sediment
mixture.
A relation p hk +
=
=
=
0.5,
which means the hidden and exposed probabilities are equal. In a non-uniform sed-
iment mixture, p ek
p ek
1 exists. For uniform sediment particles, p hk
p ek
p hk for fine particles.
This can be demonstrated with a simple example. For a sediment mixture with two
size classes d 1
p hk for coarse particles, and p ek
=
1 mm, p b 1
=
0.4 and d 2
=
5 mm, p b 2
=
0.6, one can obtain
p h 1 =
0.6333. It is shown that more coarse
particles are exposed and more fine particles are hidden.
By using the hidden and exposed probabilities, a hiding and exposure correction
factor is defined as (Wu et al ., 2000b)
0.7
>
p e 1
=
0.3, p h 2 =
0.3667
<
p e 2
=
p ek
p hk
m
η
=
(3.44)
k
where m is an empirical parameter. The criterion for sediment incipient motion
proposed by Shields (1936) is then modified as
c p ek
p hk
m
τ ck
d k =
(3.45)
γ)
s
where
=
0.03 and m
=
0.6, which are calibrated using laboratory and field data, as
c
 
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