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Interaction of Foreland
Structures with Waves
Stephan Mai 1
, Nicole von Lieberman 2 , Claus Zimmermann 3
Research Assistant 1
, Research Assistant 2 , Professor and Director 3
Franzius-Institut for
Hydraulic, Waterways and Coastal Engineering
Nienburger Strasse 4, 30167
Hannover, Germany
Tel.: +49 - 511 762 4295 ;
Fax: +49 - 511 762 4002
e-mail:
smai@fi.uni-hannover.de
Abstract
The protection system of the
German North-Sea coast comprises a series of elements with the dike supplying
the main protection. Brushwood fences and summer dikes (submerged dikes) are
applied in front of dikes as additional protection element.
Apart from their original function for land
reclamation and protection of reclaimed land against summer storm tides both,
brushwood fences and summer dikes, cause a reduction of energy of the incoming
waves and therefore of wave run-up at the main dike. The wave reduction, i.e.
the transmission coefficients, depending on water-level, incoming wave and
design parameter of the protection elements was investigated in the wave tanks
of the Franzius-Institut, Hannover, Germany.
Transmission coefficients are described in good
agreement with empirical formulas for permeable and impermeable breakwaters
depending on freeboard and wave steepness. Numerical modelling of the
transmission process at summer dikes on the basis of energy decrease due to
wave breaking according to Battjes and Janssen using phase averaged wave models
showed good agreement with results from physical modelling.
Keywords: wave transmission, brushwood fences, summer
dikes, physical and numerical modelling
BrushWOOD
FENCES AND Summer DIKES AS WAVE REDUCING ELEMENTS
Forelands and salt marshes in
front of the man made sea dikes contribute significantly to the protection and
safety of the artificial coastline. Thus the forelands are an important element
in the coastal protection system as a
whole. To prevent the loss of sediments and even support natural sedimentation,
artificial reclamation methods are applied. At the German North Sea Coast
sedimentation was achieved for centuries by systematic reclamation works with
the installation of large-scale sedimentation fields using low brushwood fences
in combination with a regular drainage system. Wooden stake and brushwood
structures (fig. 1) create areas with lower waves and reduced currents
resulting in enhanced sedimentation.
Summer dikes protect such
reclaimed land against storm tides during summers and also the main dike in
case of winter storm tides. Summer dikes are designed as overflow dikes with a
crest height of approximately 2 m above mean high water, which corresponds to a
ratio of freeboard RC and wave height HS, RC/HS
» -1, during average winter storm tides, a crest width
of 3 m and a seaward slope of 1:7 up to 1:12 and 1:5 up to 1:10 on the land
side. Besides their function as protection against flooding during summer the
overflow dike act as a submerged breakwater during winter storm tides reducing
the height of incoming waves and therefore increases the safety for the hinterland
by reducing wave run-up and overflow at the main dike.
The interaction of waves with such additional coastal
protection elements have been studied using one dimensional physical modelling
at prototype-scale in the wave tanks of the Franzius-Institut at the University of Hannover. To analyse the effects of brushwood
fences under varying water levels different brushwood fences with variing
porosities and heights were installed in the small wave flume (110 m length,
2.20 m width and 2 m depth). Wave transmission coefficients of these fences
were obtained with orthogonal, regular and irregular waves. The effect of
standard-type submerged dikes on irregular waves was investigated for different
water-levels and wave parameters, i.e. significant wave height and mean wave
period, in the Large Wave Tank (324 m length, 5 m width and 7 m depth).
In addition to physical
modelling, numerical simulations of wave transmission at summer dikes have been
performed using the models HISWA (Holthuijsen et al., 1985), SWAN (Ris, 1997)
and MIKE 21 EMS (Madsen und
Larsen, 1987).
ANalYTICAL
Background
The interaction of waves with
brushwood fences and summer dikes can be distinguished into transmission,
reflection, dissipation and breaking of the incoming waves. This is described
by the transmission coefficient cT, reflection coefficient cR
and loss coefficient cV,
(1)
where H is the height of the
incident waves, HT the transmitted wave height and HR the
reflected wave height. The coefficients cT, cR and cV
are calculated using the significant wave height H = Hs when
performing experiments with irregular waves.
Fig. 1: Wave transmission at
brushwood fence and submerged summer dike
Wave damping at brushwood
fences and summer dikes, described by their transmission coefficients, can be
described in analogy to the transmission at permeable and impermeable
breakwaters as a function of relative freeboard RC/HS,
relative crest width B/HS and the Iribarren-parameter x=tan(a)/(HS/L)0.5 (d'Angremond
et al., 1996):
(2)
The parameters bi are for breakwaters given by
d'Angremond et al. (1996) with b1 = 0.4, b2 = 0.64, b3 = 0.31, b4 = 0.5 (for permeable
breakwaters) and b1 = 0.4, b2 = 0.64, b3 = 0.31, b4 = 0.5 (for impermeable
breakwaters) and are calculated for the coastal elements, as described here, by
least-squares-fit.
Besides the change of wave
height at coastal structures a change of the mean wave Tm period
might occur for irregular waves due to non-linear wave-wave interactions. This
change in mean wave period rT is described by the ratio of mean
period of the transmitted waves Tm,T to the incident waves Tm (Mai
et al., 1998):
(3)
Experimental
Set-Up AND PROCEDUREs
Figure 2 shows the
experimental set-up of a brushwood fence which was installed in the small wave
flume of the Franzius-Institut at prototype-scale. The fence was built with
original materials that have been applied over centuries, i.e. timber poles
with bundled brushwood in between of varying height (fig. 1). Water level
variations in front of and behind the brushwood fence were recorded with wave
gauges (fig. 2).
The model of a summer dike in
the Large Wave Tank of Franzius-Institut
(fig. 2) was built on a
"foreland" and consists of a sand core protected from erosion by a
concrete filled geo-textile mattress simulating a clay cover with grass as
applied in nature (Fig. 1, right). Waves were measured for varying water-levels
and incident wave parameters. To identify the influence of the summer dike from
the effect of the foreland the experiments were carried out on a foreland with
and without summer dike.
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Fig. 2: Prototype-scaled
model of brushwood fence (left) and summer dike (right)
Wave
Transmission
Transmission coefficients
were calculated for significant wave heights and mean wave periods according to
equation (1) and (3).
Figure 3 shows the
transmission coefficient cT measured at a brushwood fence (left) and
at a summer dike (right) as a function of relative freeboard (Rc/Hs).
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Fig. 3: Transmission cT
of waves at brushwood fences (left) and summer dikes (right) as function of
relative freeboard
The transmission at brushwood
fences increases linearly RC/Hs from 1.0 up to
approximately - 1.5. Below and above (1.0 £ Rc/Hs £ 2.0 and - 2.0 £ Rc/Hs £ - 1.5) the coefficient
remains nearly constant. The wave damping of a brushwood fence decreases for
water levels above its crest height. The transmission coefficients obtained
from physical tests are slightly higher than those obtained from field
measurements. This can be attributed to fine sediments and algae which settle
within the natural brushwood fences and reduce their permeability over long
term (von Lieberman et al., 1997).
No wave damping from summer
dikes are obtained for a relative crest height RC/HS < -1.75.
Transmission coefficients decrease linearly with decreasing water depth, i.e.
increasing relative crest height. The slope of decay 
is in good agreement
with results obtained for impermeable breakwaters, e.g. d'Angremond et al.,
1996. The measured transmission coefficients are classified using the parameter
w increasing with decreasing relative crest width B/HS and
increasing Iribarren parameter x.
Using equation (2) to
calculate the transmission coefficient a modified parameter set bi was obtained by
least-squares-fit:
·
brushwood
fences: b1 = 0.06 w = 0.68 r2
= 0.77 (4)
·
summer
dike: b1 = 0.41 b2 = 0.58 b3 = 2.59 b4 = 0.52 r2
= 0.98 (5)
Transmission at brushwood
fences is mainly affected by the relative freeboard, which includes the water
depth, and depends only slightly on the wave period (eq. (4), von Lieberman et
al., 1998) whereas the transmission coefficient at summer dikes is strongly
dependent on wave period (eq. (5), Mai et al., 1998). The fit of the formula of
d'Angremond et al. (1996, eq. (2)) to the experimental data obtained for
brushwood fences is not as good as for summer dikes as indicated by the much
lower explained variance r2.
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Fig. 4: Mean wave period Tm,T
after transmission at brushwood fences (left) and summer dikes (right) as a
function of incoming wave period Tm
The transmitted mean wave
period Tm,T is shown as a function of incoming wave period, figure
4. While the mean wave period remains nearly constant, i.e. rT = 1,
in case of wave transmission at brushwood fences (fig. 4, left) it decreases
approximately 12%, i.e. rT = 0.88, in case of transmission at summer
dikes (fig. 4, right).
COmparison
of results from physical and numerical modelling
The experiments on summer
dikes have been used to calibrate the phase averaged wave models Hindcast
Shallow Waves HISWA (Holthuijsen et al., 1985), Shallow Waves Near Shore SWAN
(Ris, 1997) and MIKE 21 Elliptic Mild Slope (Madsen und Larsen, 1987). Figure 5
shows a comparison of physical and numerical modelling of the wave transmission
at summer dikes.
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Fig. 5: Comparison of physical
and numerical modelling
The left part of figure 5
presents the change in significant wave height Hs along the foreland
with a summer dike for a water level of 4 m and incoming waves with a
significant wave height HS = 0.8 m and peak period TP =
8.0 s. All models reproduce shoaling on the foreland and energy dissipation at
the summer dike due to wave breaking quite well. Also the peak in wave height
right in front of the summer dike occurs in all simulations. The calculated
transmission coefficients using experimental and numerical data are in good
agreement as shown, figure 5 (right). Best fit of transmission coefficients
calculated on the basis of numerical simulations 
with the calculated transmission coefficients using experimental
data 
was achieved using
the model SWAN. The variation of model parameters revealed wave breaking to be
the most important process in tuning the numerical models. The mean dissipation
rate D per area due to wave breaking is described in all models according to
Battjes and Janssen (1978):
(6)
with the fraction of breaking
waves Qb, the water density r, the wave number k, the
water depth d, the root mean square Hrms and maximum wave height Hmax.
The empirical parameters a, g1, g2 were adjusted to give the
best fit of numerical and experimental data:
·
HISWA:
a = 0.95 g1 = 0.85 g2 = 0.95 (7)
·
SWAN: a = 1.45 g = 0.75 (with Hmax = g d)
·
MIKE
21 EMS: a = 1.00 g1 = 1.05 g2 = 0.85
CONCLUSION
The interaction of foreland structures, i.e. brushwood
fences and summer dikes, with waves can be described quite satisfactorily with
a modified empirical formula for the calculation of the decrease in wave height
published for impermeable and permeable breakwaters e.g. by d'Angremond et al.,
1996. At the impermeable summer dike also the mean wave period decreases while
it remains constant on transmission over the permeable brushwood fence. Due to
the reduction of wave height and some extent of the wave period the wave load
on the main dike is significantly reduced. Therefore brushwood fences and
summer dikes are important elements to increase the safety of a coastal
protection system non least because of their ecological compatibility.
ACKNOWLEDGEMENTS
We appreciate the support of
Dr.-Ing. K.-F. Daemrich during the experiments on summer dikes. The research
presented was partly supported by the German Ministry of Science and Technology
and the Council for Coastal Engineering Research (KFKI).
REFERENCES
Battjes, J.A., Janssen,
J.P.F.M.: Energy Loss and Set-up due to Breaking of Random Waves, Proc. 16th
ICCE, Hamburg, 1978
d'Angremond, K., van der Meer, J.W., De Jong, R.T.:
Wave Transmission at Low-Crested Structures, Proc. 25th ICCE,
Orlando, 1996
Holthuijsen, L.H., Booij, N.: A Numerical Model for
Wave Boundary Conditions in Port Design, Int. Conf. Numerical and Hydraulic
Modelling of Ports and Harbours, Birmingham, 1985
von
Lieberman, N., Matheja, A., Zimmermann, C.: Foreland Stabilization under Waves
in Shallow Tidal Waters, Proc. 2nd Indian National Conference on Harbour and
Ocean Engineering, Thiruvanathapuram, India, 1997
von
Lieberman, N., Matheja, A., Schwarze, H., Zimmermann, C.: Investigation on the
Effects of Brushwood Fences via Simulation of the Hydrodynamical and
Morphodynamical Interactions in Physical and Numerical Models, J of the
Franzius-Institute for Hydraulics, Waterways and Coastal Engineering of the University
of Hannover, no. 82, 1998 (original in german)
Madsen,
P.A., Larsen, J.: An Efficient Finite-Difference Approach to the Mild-Slope
Equation, Coastal Engineering, no. 11, 1987
Mai, S., Daemrich, K.-F., Zimmermann, C.: Wave
Transmission at Summer Dikes, Wasser+Boden, no. 11, 1998 (original in german)
Ris, R.C.: Spectral Modelling of Wind Waves in Coastal
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