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Influence of Grain Size on Sediment Transport Rates with Emphasis on the Total Longshore Rate
ERDC/CHL CHETN-II-48

November 2005


Influence of Grain Size on Sediment
Transport Rates with Emphasis
on the Total Longshore Rate
by David B. King, Jr.
PURPOSE: The calculation of longshore sediment transport (LST) rates is a key component of
most coastal engineering studies. While the LST process is conceptually simple, in practice the
development of reliable rates is made difficult by problems associated with collecting accurate field
data, by limitations to model predictions, and by substantial variations of the rates in time and space.

This Coastal and Hydraulic Engineering Technical Note (CHETN) summarizes the state of
understanding of the influence of grain size on surf zone sediment transport and is a companion to
Smith et al. (2004). This CHETN discusses details of bed-load and suspended load transport, and the
classical bed-load regime is shown to encompass two distinct modes of transport. Four LST models
with varying levels of complexity are discussed to show how they incorporate the physics of grain
size variation and its effect on the transport rate. In addition, a relationship between the K coefficient
in the CERC formula (Coastal Engineering Manual (2002), Section III-2-3-a) and grain size is
presented. Finally, some inconsistencies between theory and data are discussed in the context of the
interrelationship between grain size and beach slope.

The final conclusion is repeated here. In general, an increase in the median grain size will decrease
LST rates in the surf zone. If a simple exponential relationship between transport rate and grain size
(D) is needed (Equation 7: LST rate
D
n
), the most appropriate value for the exponent n should be
of the order of -1, as seen from Equation 23. However, this tech note argues that this is clearly a
simplistic view of surf zone sediment dynamics. A more realistic (though still highly simplified)
approach would be that, for fine grain sediments (D
50
on the order of 0.15 to 0.30 mm), suspended
load transport should dominate and n should be somewhere within the range of -0.5 to -3.0. For
coarse sands (D
50
around 1.0 mm), sheetflow bed-load transport should dominate (Figure 6), and the
transport rate should be nearly independent of grain size (n = 0). For large gravel and shingle (D
50

> 20 mm), the dominant transport should be in the IM (Initial Motion) bed-load regime, with n
within the range of -0.5 to -2.0. To state this another way, the exponent n in Equation 7 is itself a
function of grain size.


BACKGROUND: Though most researchers recognize the median grain size as a parameter of first
order importance in its effects on the magnitude of sediment transport, its variation is not as easily
studied as the variation of many of the other primary parameters. In the field, it is easy to obtain data
for a range of values for wave heights and periods, for instance, as these vary constantly in time.
However, the grain size on a beach typically shows no (or insignificant) variations in time. Similar
problems can occur in the laboratory. Changing the wave height or period in a laboratory study is
usually as simple as reprogramming a wave paddle. However, usually, changing the grain size in a
large model is infrequently done because of the large cost in both time and money. ERDC/CHL CHETN-II-48
November 2005

Consequently, the effects of grain size on sediment transport rates is not as well understood as for
some other parameters. Grain size has occasionally been incorporated into models to make expres-
sions dimensionally correct, rather than based upon theory or data.

Relationship of Grain Size to Fall Velocity and Shear Stress. The fall velocity is the
terminal velocity reached by a sediment particle as it falls through an infinite, quiescent fluid, where
the fluid drag retarding the particle is equal to the downward gravitational pull. Many sediment
transport relationships (particularly suspended load relationships) contain a fall velocity parameter
(w
s
) with or without a separate grain-size parameter (D or D
50
, the median grain diameter). Fall
velocity increases with grain diameter. For silts and clays, w
s
varies as D
2
and for gravels it varies as
D
½
. For sand-size particles, w
s
falls in a transition region where it varies as the grain size to a power
between ½ and 2 (Coastal Engineering Manual 2002, Section III-1). For convenience, this
relationship can be crudely approximated as a variation to the first power for sand-size particles, but
to obtain accurate values, a formula such as those of Hallermeier (1981) or Ahrens (2000) should be
used.

An important parameter in sediment transport is the shear stress (
), which is the tangential force per
unit area that a moving fluid exerts on the sediment bed, which causes transport. In a wave
dominated environment, it is generally related to the horizontal fluid velocity just above the top of
the boundary layer (u) by the expression:


2
½
w
f u
= (1)
where
is the fluid density, and f
w
is the friction factor. The stress on the bed is strongly affected by
the nature of the flow within the boundary layer. The boundary layer flow can be laminar or
turbulent; it is affected by the bed roughness and the presence of bed forms such as ripples; and it is
substantially different in steady versus oscillatory flow. Generally, an attempt is made to represent
these effects as variations in the f
w
term. In oscillatory flow, the f
w
term is usually inversely related to
the dimensionless term (a/k
s
), where a is the orbital excursion amplitude and k
s
is the bed roughness.
For flat beds with sand or larger grain sizes, k
s
is directly related to the grain size. Several equations
have been proposed for this relationship (e.g., Jonsson 1966; Swart 1974; Kamphuis 1975; Nielsen
1979). For the purposes of this discussion, the important result is that, for sand- and gravel-sized
particles, an increase in the sediment grain size will cause a small increase in the shear stress on the
bed, which will lead directly to a slightly greater sediment transport rate for the same free-stream
flow conditions. While this effect is important, it can be easily masked by other greater influences
that the size of the sediment has on the transport rate, as discussed in the following paragraphs.

Minimum and Maximum Beach Sediment Sizes. The lower grain-size limit for the material
composing most beaches is in the 0.10- to 0.15-mm range. This value is largely controlled by
ambient near-bottom turbulence levels. There are two primary sources of turbulence in the surf zone:
breaking wave turbulence and turbulence generated within the wave or wave/current bottom
boundary layer. The turbulence generated by breaking waves is substantially larger, but is generated
at the top of the water column and its effect on the bed is highly episodic on both wave and storm
time scales. Sediment picked up by breaking wave suspension events will at least occasionally have
enough time to settle back to the bed before the next event. However, small grains (slits and clays,
with low fall velocities) are mobilized by the turbulence generated in the bottom boundary layer and
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ERDC/CHL CHETN-II-48

November 2005

kept in suspension throughout a half wave cycle. The same thing occurs on next half cycle, and the
material never settles to the bed. Instead, the material is kept in suspension and slowly diffuses or is
transported into quiescent waters elsewhere, either offshore or into back bays and estuaries. This
process is analogous to that which supports wash loads in rivers. Beaches with grain sizes smaller
than about 0.10 mm are usually only found near large river deltas (such as many sections of the coast
of Louisiana), where the system is overwhelmed by the presence of fine sediments and coarser
material is unavailable.

Few beaches are composed of material whose median grain size is larger than 100-300 mm. The
maximum size of beach materials is governed by the rate at which large materials can be delivered to
a beach by rivers, eroding bluffs, etc., compared with the rate at which these materials weather
(ablate) once they are on the beach. The weathering of cobble-sized materials can be quite rapid in a
geological sense. In comparison, the fine quartz sands (0.15 to 0.3 mm) that compose most beaches
have so little mass that they are almost totally resistant to further weathering. For additional
discussion, see Coastal Engineering Manual (2002), Section III-1.

SEDIMENT TRANSPORT REGIMES: The theory leading to the development of the CERC
formula was based upon the concept that waves deliver a certain amount of energy to the surf zone,
and that a constant proportion of this energy is available to mobilize and transport sediment
(Bagnold 1963; Inman and Bagnold 1963; Bagnold 1966). Though remarkable, this development
had been found to have limitations. As waves break and release energy across the surf zone, the
proportion of this energy used to transport sediment is not constant, but varies substantially through
surf zone parameter space. The understanding that surf zone sediment transport is not a simple
process that can be described by a simple one-term equation has led to the develo