Environmental Engineering Reference
In-Depth Information
stationary. If this is not the case then alternative
methods or some pre-filtering of the data are nec-
essary. To determine design conditions, techni-
ques are available to fit probability distributions
to measurements. Extreme values corresponding
to the chosen return period are obtained by extrap-
olation (e.g. Reeve et al. 2004).
All statistical methods are dependent on good
and extensive measurements. Also, extrapolation
into the future is usually made on the basis that
past behaviour is a good indicator of future evolu-
tion, and will therefore be unable to capture be-
haviour absent from the data.
related to grain size, D, by Dean (1991), i.e.
A
¼
0.21D
0.48
with D in mm. These equations
predict that equilibrium beach slopes increase in
steepnesswith increasing grain size, in accordance
with observations. On beaches that are not well
sorted, i.e. with a range of grain sizes, there can be
uncertainty over the appropriate value of D to use.
Further, this model can describe neither the tem-
poral evolution of a beach, nor the formation of
bars and troughs. Figure 16.1 shows an example of
fitting Equation 16.1 to a measured beach profile
in Colombia. The equilibrium curve fits the gen-
eral trend of the measurements reasonably well,
but there are some notable (and large) discrepan-
cies both nearshore and further offshore.
Bays form where an erodible coastline exists
between hard, stable headlands. The shape of the
bay will depend on the wave climate and supply of
sediments. Silvester (1974) performed laboratory
experiments to investigate the equilibrium shape
of bays for different wave conditions. He found
that in the absence of sediment supply and for a
fixed wave direction, a stable bay would take the
approximate formof a cardioid; the beach adapting
its shape so that the incoming wave crests, which
are curved due to diffraction, are everywhere par-
allel to the shore (Fig. 16.2). More recent work
on this method may be found in Hsu et al. (1989),
Silvester and Hsu (1997), and Gonzalez and
Empirical models
Empirical models are usually based on equilibri-
um type arguments, and describe the shape of the
beach under particular (unchanging) wave condi-
tions. In reality, wave conditions change contin-
ually, but the predominant conditions can provide
a useful guide to the 'typical' beach shape. Bruun
(1954) found that many ocean-facing coastlines
exhibit a concave curve that can be described by
the equation:
Ax
2
=
3
h
¼
ð
16
:
1
Þ
where h is the profile depth at a distance x from
the shoreline, and A is a constant, which has been
5
Measured Profile
Dean Profile
0
0
150
300
450
600
750
900
1050
1200
1350
1500
1650
-5
-10
-15
Cross-Shore Distance (m)
Fig. 16.1
Comparison of Dean profile and measured profile of a beach in Santa Marta, Colombia (South America).
