A. Bayram et al. / Coastal Engineering 44 (2001) 7999
97
A.4. Bailard and Inman (1981, 1984) formula
A.5. Van Rijn (1984, 1993) formula
Bailard and Inman (1981) extended the formula
Van Rjin (1984) presented comprehensive formu-
introduced by Bagnold to oscillatory flow in combi-
las for calculating the bed load and suspended load,
nation with a steady current over a plane sloping
and only a short description of the method is given in
bottom. The instantaneous bed load ( q0b,BI) and sus-
the following. For the bed load he adapted the
pended load ( q0s,BI) transport rate vectors are ex-
approach of Bagnold assuming that sediment particles
pressed as,
jumping under the influence of hydrodynamic fluid
"
#
forces and gravity forces dominate the motion of the
02 0 tanb 03
0:5f wqeb
bed load particles. The saltation (jumps) character-
U U
q0b;BI
t t tanc Ut ib
qs qg tan c
istics were determined by solving the equation of
motion for an individual sediment particle. The bed
"
5 #
load can be defined as the product between the
3
0:5f wqes 0 0 es
particle concentration (cb; a reference concentration
U U tanbU 0 ib
q0s;BI
q qgw t t w
t
for the bed load different from the reference concen-
s
tration for suspended load ca), the particle velocity
in which tanb is the local bottom slope, tanc a
(ub), and the layer thickness (db; taken to be equal to
the reference level a) according to,
vector near the bed (wave and current) and ib is a unit
qb;VR cbubdb
vector in the direction of the bed slope. Averaging
over a wave period, the total transport rate and
where,
direction are obtained containing both the wave- and
cb
T
current-related contributions. Assuming that a weak
0:18
longshore current prevails, neglecting effects of the
D
c0
slope term on the total transport rate for near-normal
!1=3
incident waves, the local time-averaged longshore
s 1g
D d50
sediment transport rate is (Bailard, 1984),
v2
dv
eb
d3
qt;BI 0:5qfwu3
s0b;wc sb;cr
v
0
qs q g tanc 2
T
sb;cr
es
dvu
0:5qfwu4
0
3
qs q gws
in which c0 ( = 0.65) is the maximum bed load
concentration, D * the dimensionless grain diameter,
where eb and es are efficiency factors, and:
T the excess bed shear stress parameter, and s0b,wc is
the effective bed shear stress for waves and current
V
dv
combined (calculated according to Van Rijn's own
u0
method, not discussed here). Substituting the above
expressions into the bed load transport formula
hjUt0j3i
u
together with some other relationships not given
3
u0
yields,
sffiffiffiffiffiffiffiffiffi "
#1:5
s0b;wc s0b;wc sb;cr
The following coefficient values are typically used
qb;VR 0:25cqsd50D0:3
in calculations: eb = 0.1, es = 0.02, tanc = 0.63. Thus,
q
sb;cr
the efficiency factors are assumed to be constant,
although work has indicated that eb and es are related
where,
rffiffiffiffiffi
to the bed shear stress and the particle diameter. It
Hs
should also be noted that the formula is derived for
c1
h
plane bed conditions.
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