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A. Bayram et al. / Coastal Engineering 44 (2001) 7999
tion of motion was included in the original formula-
characteristics as well as references to the original
tion. The same coefficient values are used for
publications. Also, Van De Graaff and Van Oveerem
monochromatic and random waves.
(1979) can be consulted for a comprehensive sum-
mary of some formulas. They compared three formu-
2.3. The Ackers and White formula
las for the net longshore sediment transport, namely
the formulas by Bijker, Engelund Hansen, and
Ackers and White (1973) developed a total load
Ackers White, although they focused on the gross
sediment transport formula for coarse and fine sedi-
rate and made comparisons for a number of selected
ment exposed to a unidirectional current. Coarse
hypothetical cases.
sediment is assumed to be transported as bed load
with a rate taken to be proportional to the shear stress,
2.1. The Bijker formula
whereas fine sediment is considered to travel in
suspension supported by the turbulence. The turbu-
Bijker's (1967, 1971) sediment transport formula is
lence intensity depends on the energy dissipation
one of the earliest formulas developed for waves and
generated by bottom friction, which makes the sus-
current in combination. It is based on a transport
pended transport rate related to the bed shear stress.
formula for rivers proposed by Kalinske Frijlink
The empirical coefficients in the Ackers White for-
(Frijlink, 1952). Bijker distinguishes between bed
mula (hereafter, called AW formula) were calibrated
load and suspended load, where the bed load transport
against a large data set covering laboratory and field
depends on the total bottom shear stress by waves and
cases (HR Wallingford 1990; reported in Soulsby,
currents. The suspended load is obtained by integrat-
1997). Van De Graaff and Van Overeem (1979)
ing the product of the concentration and velocity
modified the AW formula to account for shear exerted
profiles along the vertical, where the reference con-
by waves.
centration for the suspended sediment is expressed as
a function of the bed load transport. In its original
2.4. The Bailard and Inman formula
form, the bed-load formula does not take into account
a critical shear stress for incipient motion, implying
Bailard and Inman (1981) derived a formula for
that any bed shear stress and current will lead to a net
both the suspended and bed load transport based on
sediment transport. The Bijker transport formula
the energetics approach by Bagnold (1966). Bagnold
(hereafter, called the B formula) is, in principle,
assumed that the work done in transporting the sedi-
applicable for both breaking and non-breaking waves.
ment is a fixed portion of the total energy dissipated
However, different empirical coefficient values are
by the flow. The Bailard Inman formula (hereafter,
needed in the formula.
called BI formula) has frequently been used by
engineers because it is computationally efficient, takes
2.2. The Engelund and Hansen formula
into account bed load and suspended load, and the
flow associated with waves (including wave asymme-
Engelund and Hansen (1967) originally derived a
try) and currents can be incorporated in a straightfor-
formula to calculate the bedload transport over dunes
ward manner. A reference level for the velocity
in a unidirectional current by considering an energy
employed in the formula (normally taken to be 5.0
balance for the transport. Later, this formula (here-
cm above the bed) must be specified.
after, called EH formula) was applied to calculate the
total sediment transport under waves and currents, and
2.5. The Van Rijn formula
modifications were introduced to account for wave
stirring (Van De Graaff and Van Overeem, 1979).
Van Rijn (1984) proposed a comprehensive theory
However, their theory has limitations when applied to
for the sediment transport rate in rivers by considering
graded sediments containing large amount of fine
both fundamental physics and empirical observations
fractions, causing predicted transport rates to be
and results. The formulations were extended to estua-
smaller than the actual transport rates. Similar to the
ries as summarized by Van Rijn (1993) (hereafter,
Bijker formula, no threshold conditions for the initia-
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