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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-