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1
Hydraulic stability of antifer block armour layers
Physical model study
Paulo Freitas
Department of Civil Engineering, IST, Technical University of Lisbon
Abstract
The primary aim of the study is to experimentally investigate the stability performance of antifer block armour layers on a
1:1.5 slope, under the effect of irregular waves, for different placement methods. A literature review on the armour layer
stability, as well as 2 different stability formulas for different armour units, is firstly presented. The rubble mound structure
scaling requirements, scale effects in these models and the material used in rubble mound construction are discussed. The
results demonstrate that the best performing placement method corresponds to the regular placement method. However, in
this method, the reflected significant wave heights are higher than in the semi-irregular placement method.
Key words: Rubble Mound Breakwater; Antifer Block; Hydraulic Stability; Placement Method; Damage Assessment.
1. INTRODUCTION
Several evidences of the influence of placement
method on the stability of antifer block armour layers
are well known and studied. The problem of rubble
mound breakwaters stability involves a large number
of parameters. As a consequence, the studies of
hydraulic armour layer are very complex due to the
interaction between these parameters.
This extended abstract is divided into six chapters. In
the second chapter the armour layer stability is
discussed, such as the stability formulas for different
armour units.
On the third chapter, the required theory to design and
operate a scaled physical model of a rubble mound
breakwater is presented, as well as the materials used
in rubble mound construction.
In chapter four the model construction is discussed
together with the different placement methods.
On the fifth chapter, the results and the values
downscaled to the prototype are presented.
The last chapter contains the conclusion remarks and
suggestions for future work.
2. RUBBLE MOUND BREAKWATER
Rubble mound breakwaters can be found along the
coastline, to either protect the coastal area against
wave action or create sheltered areas where vessels
can navigate and berth safely. The wave energy in this
type of structure is dissipated by absorption and part
of it is reflected.
A rubble mound breakwater is usually constituted by a
core of quarry run and an under layer of random
shaped and random-placed stones, protected with an
armour layer of selected armour units.
2.1. Antifer block
The antifer cube is a massive armour unit that was
created as a result of laboratory research conducted for
the breakwaters of Antifer Harbour in France. So,
their first use was on the Antifer breakwaters and later
they have been used in the repair works of the west
breakwater of Sines harbour (Fig. 1).
Fig. 1: Use of antifer blocks in repair works of the west breakwater
in Sines harbour (Portugal)
The blocks have a geometric shape close to a cube, but
they present four grooves and a slightly tapered shape
(Fig. 2) [1].
2
Fig. 2: Geometrical characteristics of Antifer Cubes
2.2. Hydraulic stability
The hydraulic stability of the armour layer on the front
slope has been widely investigated for many years. To
understand the breakwaters performance against wave
action, it is necessary to describe some physical
processes.
Generally, the common failure mode of the armour
layer is failure of singles units when the wave
dislocating force is greater than the stabilizing force.
The instability of these units is caused by wave forces,
which tend to move the blocks once a critical value is
exceeded. Those wave-generated forces are known as
drag and lift forces that are withstood by the
interlocking effect and/or block weight.
( )
( ) (1)
where m is the density of armour units (kg/m3), w is
the density of water (kg/m3), D is the nominal
diameter (m), g is the gravitational acceleration (m/s2),
v is the flow velocity (m/s), FD is the drag force, FL is
the lift force and FG is the gravitational force.
Assuming that the velocity of a wave on the slope is
proportional to the celerity in shallow water, equation
(1) can be shortened, and the stability parameter is
obtained.
( )
(2)
where H is the characteristic wave height (m), is the
relative densiy (-) and Ns is the stability parameter.
Nowadays the most widely used equations in the
design of some concrete armour units are the Hudson
equation and Van der Meer equations.
2.3. Hudson equation
Hudson formula can be described by equation (3) for
concrete armour units [2]. Here the first term
corresponds to the stability parameter and the second
represents the slope angle and the KD factor.
( )
(3)
where Dn is the nominal diameter of the armour unit
(m), KD is the Hudson stability parameter (-) and is
the slope angle ().
The value of KD depends mainly on the type of armour
layer adopted. However, this value also depends on
the wave steepness, ratio of depth to wavelength, ratio
of wave height to depth, thickness and porosity of
cover layer, armour unit surface roughness, incident
wave angle, shape of armour unit, slope of bottom
seaward of structure, crest width, method of placing
the breakwater materials, and damage level. In Table
1, suggested KD values are presented.
This formula has, however, limitations:
- the use of regular waves only;
- no description of the damage level;
- the use of non-overtopped and permeable structures
only.
Table 1: Suggested KD values
Armour
unit
Structure trunk
Manual KD cotg
H Breaking
wave
Nonbreaking
wave
Tetrapod 7.2 8.3
1.5
to
5 H1/3
SPM
1975 [3] Modified
cube 6.8 7.8
Tetrapod 7.0 8.0 SPM
1984 [4] Modified cube
6.5 7.5
Antifer Cube
7.0 8.0 2
Rock
Manual
2007 [2]
3
2.4. Van der Meer equations
To overcome the limitations of Hudson formula, Van
der Meer conducted an extended research on the
stability of breakwater. For armour layers composed
by cubes in a double layer on a 1:1.5 slope with
3m6 (m surf similarity parameter), based on non-
depth-limited wave conditions, Van der Meer
proposed the equations (4) and (5) [5].
(
)
(4)
(
)
(5)
where Hs is the significant wave height (m), Nod is the
number of displaced units related to a width of one
nominal diameter, for displacements higher than 2Dn
(-), No,mov is the number of displaced units related to a
width of one nominal diameter, for all type of
displacements (-), sm is the mean wave steepness (-)
and Nz is the number of waves (-).
2.5. Damage
The damage in armour layers is related to the specific
conditions and duration of a sea state. It can be
characterized by counting the number of displaced
units or measuring the eroded surface profile of the
armour slope.
The damage can be expressed in terms of a relative
displacement D, which is defined as the ratio between
the number of displaced units and the total number of
units within a specific zone (usually the area between
Hs around Still Water Level is used) [4].
(6)
The KD values suggested for Hudson formula are
obtained for a level of damage smaller than 5%,
measured between Hs around Still Water Level.
Broderick defined the damage (S) as the relation
between the eroded surface profile and the square of
the nominal stone diameter [6].
(7)
where Ae is the eroded area.
In Table 2, the damage levels associated to the
structure damage classification are presented.
Table 2: Damage level by Nod and S for double layer armour
Armour unit
/ Damage
parameter
Slope Initial
damage
Intermediate
damage Failure Manual
Rock / S 1:1.5 2 3 - 5 8 USACE,
2011 [6]
Modified
cube / Nod 1:1.5
0 - 2 USACE,
2011 [6]
0.2-0.5 1 2
CIRIA
et al.,
2007 [2]
Tetrapod/
Nod 1:1.5
0 - 1.5 USACE,
2011 [6]
0.2-0.5 1 1-5
CIRIA
et al.,
2007 [2]
3. MODEL SET-UP
This chapter presents the theory to design and operate
scaled physical models of a rubble mound breakwater,
as well as the materials used in the rubble mound
construction.
3.1. Scaling requirements and scale effects
Physical modelling is based on the idea that the model
behaves in a similar way to the prototype that intends
to represent. Thus, a validated physical model can be
used to predict the prototype's behaviour under a
specified set of conditions. However, there is a
possibility that the physical model may not represent
the prototype behaviour due to scale effects and
laboratory effects [7].
Gravity forces predominate in free surface flows and
thus most hydraulic models can be designed using the
Froude criterion [8].
(8)
(9)
where Nt is the time scale (-), Nl is the length scale (-)
and NM is the mass scale (-).
In equation (9) it is assumed that relative density
relationship is the same for model and prototype.
The linear geometric scaling of material diameters that
follows from Froude scaling may lead to viscous
forces, corresponding to small Reynolds numbers.
4
This means that the flow regime in the breakwater
armour units of the model is laminar, instead of
turbulent, to avoid viscous scale effects.
However, this scale effect can be neglected if the
Reynolds number is greater than 30000, obtained by
equation (10) [7].
(10)
where Re is the Reynolds number (-), is the
kinematic coefficient of viscosity (m2/s) and Hs,i is the
incident significant wave height (m).
The results obtained in this study were downscaled
according to Froude similitude criterion using a length
scale of 1:60.
3.2. Facilities
The experimental research was performed in the wave
flume of the hydraulic and environment laboratory of
Instituto Superior Tcnico. After building the model,
the placed antifer layers were tested for a peak wave
period of 1.4s with different significant wave heights,
i.e. 10cm, 12cm, 14cm, 16cm and 18cm.
The channel has a length of 22m, a width of 0.7m and
a height of 1m and has a system of wave generation
with dynamic wave absorption (Fig. 3).
In this work, the irregular waves were produced by the
HR WaveMaker wave generation software, adjusted to
JONSWAP spectral shape.
The waves were measured with four probes and the
data was recorded and analysed by HR Data
Acquisition and Analysis software.
One camera was used to capture video of every tests
and take pictures before and after each test.
Fig. 3: Wave flume
The duration for each test was defined for 2000
waves. The water depth in the flume should be, at
least, 3Hs (318cm=54cm) to avoid breaking
conditions before the structure. However, due to issues
related with glasses safety, a value of 45cm was
chosen [2].
3.3. Materials used in the construction and
structural parameters
3.3.1. Armour Layer
About 600 antifer cubes were used in the construction
of the breakwater armour layer. The antifer blocks are
made available by LNEC (National Laboratory for
Civil Engineering) (Fig. 4). The blocks are made of
concrete, filled up with small spheres of metal and
were painted to avoid friction scale effects and to
observe more easily their eventual displacement.
The proprieties and dimensions of the block are
presented in Table 3 and Table 4.
Table 3: Block proprieties of used antifer cubes
c (kg/m
3)
Dn15
(cm)
Dn50
(cm)
Dn85 (cm)
M15
(g)
M50
(g)
M85
(g)
2450 4.30 4.33 4.36 195.25 199 203.3
Table 4: Block dimensions of used antifer cubes
H
(cm)
V
(cm3)
A
(cm)
B (cm)
C
(cm)
D
(cm)
r
(cm)
4.30 81.47 4.67 4.32 0.41 0.10 0.52
Fig. 4: Example of used antifer blocks
The gradation Dn85/Dn15 is 1.014 and the gradation
M85/M15 is 1.041.
3.3.2. Under Layer
Graded rock was used in the construction of the
breakwater under layer (granite stones) (Fig. 5). The
standard Froude scaling method for the under layer is
based on the relation between the armour layer weight
ant the under layer weight. The typical value
recommended to the weight ratio is around 10 [6].
5
The proprieties of the graded rock are presented in
Table 5.
Table 5: Graded rock proprieties of used stones
r (kg/m
3)
Dn15
(cm)
Dn50
(cm)
Dn85 (cm)
M15
(g)
M50
(g)
M85
(g)
2600 1.63 1.78 1.97 11.29 14.6 20
Fig. 5: Graded rock used in under layer
The gradation Dn85/Dn15 is 1.209 and the gradation
M85/M15 is 1.772. The nominal diameter of the rocks
should be around 19.9g, however the value obtained
after the sieve selection was smaller, corresponding to
14.6g.
3.3.3. Core
Quarry run is used as core material. Generally the top
weight pretended in rubble mound breakwaters core is
1000kg and the bottom weight is 1kg. The lowest
value is recommended to avoid geotechnical
instability [9]. Therefore, the material of the core was
constructed using 5 types of gravel with different
gradations. The proprieties of the quarry run are
presented in Table 6.
Table 6: Quarry run proprieties
r (kg/m
3)
Dn15
(cm)
Dn50
(cm)
Dn85 (cm)
M15
(g)
M50
(g)
M85
(g)
2600 0.23 0.68 0.89 0.029 0.807 1.902
The gradation Dn85/Dn15 is 3.925 and the gradation
M85/M15 is 65.586. The porosity of the core is around
30%.
3.3.4. Toe and superstructure
Rectangular concrete blocks with an edge of 10cm has
been applied in the construction of the breakwater toe
protection, as well as in the superstructure. In this
way, the instability of the armour layer induced by the
possible movements of the toe is avoided.
4. MODEL CONSTRUTION AND
PLACEMENT METHODS
Knowing the elevation of the crest and the slope, the
model dimensions were drawn on the glass of the
flume. The material of the core was placed in stages to
allow the settlement of the core (Fig. 6). During the
construction of the core, irrigations were made in
order to facilitate the settlement.
Fig. 6: Core of the model
After placing the core, the graded rock of the under
layer was placed one by one. Firstly, the first layer of
under layer was placed and then the second layer (Fig.
7).
Fig. 7: Under layer of the model under construction
After placing the core, the under layer and the
concrete blocks of the toe in a stable way, the antifer
blocks were placed one by one, for each test.
In Fig. 8, the sketch of the breakwater cross section, as
well as, material characteristics used in the model, are
presented.
6
Fig. 8: Breakwater cross section
In this study 3 different placement methods of armour
layer were analysed. Each placement method was
designed to have porosity of around 50%. For values
above 50% the stability may be insufficient and for
values below occurs a paving action (consequently
grater overtopping) [10].
The geometry of the placed antifer for each placement
method, was calculated using the formulas described
in Table 7 [9].
Table 7: Basic geometric design formulae and parameters for placed
armour units
First
step
Based on the armour layer
thickness (t), the Layer
coefficient (K) was
calculated
Second
step
Based on the
dimensionless upslope
distance (y=1,08), the
dimensionless horizontal
distance (x) was
calculated
Third
step
The horizontal and
upslope centre to centre
distance between blocks
was calculated
Fourth
step
The packing density
coefficient (n of blocks /
n of possible blocks) was
calculated
( )
Fifth
step
The numbers of antifer
blocks per unit area was
calculated
Sixth
step
The value of packing
density coefficient was
verified
The value y=1.08, means that the spacing between
blocks along the upslope does not exist.
The configuration of the first layer of the armour layer
is the same for all placement methods (Fig. 9).
However, the horizontal centre to centre distance is
different for some placement methods, leading to
different thickness of armour layer.
Fig. 9: Configuration of the first layer of armour layer (regular
pattern)
The techniques of the placement are defined as row by
row or layer by layer, see Fig. 10 and Fig. 11,
respectively.
Fig. 10: Row by Row
Fig. 11: Layer by Layer
The assessment of the damage was measured between
Hs around Still Water Level for each test.
Classification of the movements of the armour units is
required in the counting method. Such classification
was based on the displacement of each block,
measured in units of nominal diameter. In this work
distances lower than 1Dn were not considered as
damage.
5. RESULTS
In the reflection analysis, reflection coefficients for
fast Fourier transform (NFFT) with 256, 512 and 1024
points obtained in the reflection routine were analysed
and the incident significant wave heights were
calculated. To check the accuracy of the results, the
reflection coefficients were determined using the
incident and reflected wave spectral energy in order to
obtain the incident significant wave heights and
compare the results.
5.1. Semi-irregular placement method
For this experiment the antifer blocks of the first layer
are placed by the regular pattern (Fig. 9). After every
4-5 rows of the first layer, the second layer is placed
by dropping the blocks above the holes (Fig. 12). The
7
thickness of armour layer is defined as the nominal
diameter plus the height of the antifer cube.
Fig. 12: Semi-irregular placement method
The properties of the armour layer and the wave series
are presented in Table 8 and Table 9. The reflection
coefficients and Reynolds number are presented in
Table 10.
Table 8: Layer properties for semi-irregular placement method
x (-) 1.86 tmeasured (cm) 8.60
y (-) 1.08 P (%) 49.8
X (cm) 8.06 K (-) 0.993
Y (cm) 4.67 (%) 49.8
tcalculated (cm) 8.63 Nc (blocks/m2) 531.3
Table 9: Wave series for semi-irregular placement method
Hs,input
(m) Hm0,i (m) Tp (s) Tm (s) sm (-) Ns (-)
0.10 0.081 1.38 1.18 0.037 1.28
0.12 0.102 1.41 1.25 0.042 1.63
0.14 0.115 1.41 1.32 0.043 1.84
0.16 0.128 1.41 1.38 0.043 2.04
0.18 0.139 1.38 1.41 0.045 2.22
Table 10: Reflection and Reynolds number for semi-irregular
placement method
Hs,input
(m)
Reflection Re (-)
Cr (-) NFFT (points) eq. 9
0.10 0.335 512 38084
0.12 0.319 512 42936
0.14 0.300 512 45588
0.16 0.306 256 48063
0.18 0.294 256 50055
Analysing the video, is visible that in the first wave
series, the blocks are displaced around SWL. In this
placement method the effect of interlocking is low.
Consequently the hydraulic stability is mostly
guaranteed by the weight of the block.
In the Fig. 13, damage ratios for the displacements are
presented, for 2 different references areas.
Fig. 13: Damage for semi-irregular placement method
The Hudson stability parameter was calculated for a
damage of 5%, for the first wave series were the first
displacements were observed. From this follows
KD=2.1. This value is similar to the value found by
Frens [11] (KD,Frens=2.3).
5.2. Regular placement method 1
The antifer blocks are placed row by row (Fig. 10).
The blocks in the first layer are placed with their
grooves perpendicular to the slope (Fig. 14). The
blocks of the second layer are placed diagonal for the
first row directing to the left and for the second row to
the right and so on (Fig. 15).
Fig. 14: Regular placement method 1 (X=8.1cm)
Fig. 15: Thickness of armour layer (t=H+Dn)
The properties of the armour layer and the wave series
are presented in Table 11 and Table 12. The reflection
coefficients and Reynolds number are presented in
Table 13.
8
Table 11: Layer properties for regular placement method 1
x (-) 1.86 tmeasured (cm) 8.60
y (-) 1.08 P (%) 49.8
X (cm) 8.06 K (-) 0.993
Y (cm) 4.67 (%) 49.8
tcalculated (cm) 8.63 Nc (blocks/m2) 531.3
Table 12: Wave series for regular placement method 1
Hs,input
(m) Hm0,i (m) Tp (s) Tm (s) sm (-) Ns (-)
0.12 0.095 1.41 1.26 0.038 1.52
0.14 0.114 1.43 1.33 0.041 1.82
0.16 0.122 1.43 1.38 0.041 1.94
0.18 0.131 1.41 1.41 0.042 2.08
0.18 1000 waves
0.129 1.43 1.41 0.041 2.06
Table 13: Reflection and Reynolds number for regular placement
method 1
Hs,input
(m)
Reflection Re (-)
Cr (-) NFFT (points) eq. 9
0.12 0.388 512 41466
0.14 0.355 256 45392
0.16 0.373 256 46876
0.18 0.379 256 48488
0.18 1000 waves
0.370 512 48238
The first blocks were displaced only in the last test for
Hm0,i=0.129m. In this test, the blocks were not
replaced. As a result, the displacement occurs for a
total of 2000 waves plus 1000 waves. In this
placement method, the effect of interlocking is
efficient, providing a high hydraulic stability.
In Fig. 16, damage ratios for the displacements are
presented for references area 18cm.
Fig. 16: Damage for regular placement method 1
The Hudson stability parameter was calculated for a
damage of 0.8%. Therefore that value was determined
for the last test (Ns=2.06) where the displacements
observed was low, almost null. From this follows
KD=5.8. This value when associated with the value
found by Frens is almost equal, KD,Frens=6.4 [11].
5.3. Regular placement method 2
The placement of the antifer blocks is similar to the
regular placement method 1 (Fig. 17). However the
packing density is lower, and the horizontal centre to
centre distance is higher (Fig. 18).
The antifer blocks are placed row by row (Fig. 10).
The blocks in the first layer are placed with their
grooves perpendicular to the slope (Fig. 17). The
blocks of the second layer are placed diagonal for the
first row directing to the left and for the second row to
the right and so on (Fig. 18).
Fig. 17: Regular placement method 2 (X=8.8cm)
Fig. 18: Thickness of armour layer (t1.85H, increase of 20% in the distance between blocks when compared with regular placement
method 1)
The properties of the armour layer and the wave series
are presented in Table 14 and Table 15. The reflection
coefficients and Reynolds number are presented in
Table 16.
Table 14: Layer properties for regular placement method 2
x (-) 2.02 tmeasured (cm) 7.94
y (-) 1.08 P (%) 49.9
X (cm) 8.75 K (-) 0.917
Y (cm) 4.67 (%) 45.9
tcalculated (cm) 7.96 Nc (blocks/m2) 489.7
9
Table 15: Wave series for regular placement method 2
Hs,input
(m) Hm0,i (m) Tp (s) Tm (s) sm (-) Ns (-)
0.12 0.097 1.41 1.27 0.039 1.55
0.14 0.114 1.41 1.34 0.041 1.82
0.16 0.125 1.43 1.38 0.042 1.99
0.18 0.128 1.41 1.42 0.041 2.04
Table 16: Reflection and Reynolds number for regular placement
method 2
Hs,input
(m)
Reflection Re (-)
Cr (-) NFFT (points) eq. 9
0.12 0.390 512 41825
0.14 0.356 256 45375
0.16 0.359 256 47467
0.18 0.386 512 48028
The first blocks were displaced in the third wave
series for Hm0,i=0.125m. In the last test (Hm0,i=0.128m)
the blocks were not displaced. Consequently, the
reflection visualized in the basin was higher and
therefore greater reflected significant wave height was
obtained, around 5cm (wave breaking along the basin
was higher). The effect of interlocking is efficient, but
lower when compared with regular placement method
1.
In Fig. 19, damage ratios for the displacements are
presented, for 2 different references areas.
Fig. 19: Damage for regular placement method 2
The Hudson stability parameter was calculated for a
damage of 0.6%. Therefore, that value was determined
for Ns=1.99, which is associated to the lowest
displacements, almost null. From this follows KD=4.0.
This value when compared with the value obtained by
Frens is almost equal, KD,Frens=4.1 [11].
5.4. Study values Froude-scaled for a prototype
with a geometrical scale of 1:60
The scaling of the design units and time series was
adjusted using the equations (8) and (9) (Froude
similitude criterion). A length scale of 1:60 has been
applied for the breakwater model, and the unit sizes
and design storm were determined for the prototype
(see Table 17, Table 18, Table 19 and Table 20).
Table 17: Armour Unit specifications for the prototype
Antifer cubes Dn,50 M50
Prototype 2.50m 42.98ton
Model 4.33cm 199g
Table 18: Graded rock specifications for the under layer
Grades Rock Dn,50 M50
Prototype 1.07m 3.15ton
Model 1.78cm 14.60g
Table 19: Quarry run specifications for the core
Quarry Run Dn,50 M50
Prototype 0.41m 174.31kg
Model 0.68cm 0.81g
Table 20: Design Storm for the prototype (Semi-irregular placement
method)
Prototype
Hs,input (m) Hm0,i (m) Tp (s) Tm (s)
6.0 4.9 10.7 9.1
7.2 6.1 10.9 9.7
8.4 6.9 10.9 10.2
9.6 7.7 10.9 10.7
10.8 8.3 10.7 10.9
Analysing Table 9 and Table 20, the incident
significant wave height of 0.139m and the peak period
of 1.38s obtained in the model corresponds to a
Hm0,i=8.3m and a Tp=10.7s in the prototype.
6. CONCLUDING REMARKS AND
SUGGESTIONS FOR FUTURE WORK
Among the various conclusions drawn from this study,
the following ones deserve to be specially mentioned:
In the semi-irregular placement method, the
reflection coefficients are smaller than the
coefficients obtained in regular placement
methods. This value tends to decrease when
increasing incident significant wave heights,
since the damage and porosity are greater for
higher Hm0,i.
10
The regular placement methods are more
stable and the reflection coefficients are
higher. However in the regular placement
method 2, the values of reflection coefficients
are greater when compared with the regular
placement method 1, due to the fact that the
first layer is more exposed to wave breaking.
The settlement of the core in the reference
area for wave action in the regular placement
method 2 was higher.
In physical modelling, tests should be
repeated in order to check the accuracy of the
results. However in this study the tests have
not been repeated. Nevertheless, the
comparison between the Hudson stability
coefficients, obtained in this work with the
results found by Frens in 2007, allow to
verify that the values are similar.
For the semi-irregular placement method
KD=2.1 is suggested for a damage of 5%,
since in this placement method is easy to
repair the armour layer by placing a new
block in the revealed hole.
For regular placement methods 1 and 2, the
values KD=5.8 and KD=4.0 are suggested,
respectively. These values were obtained for
damage almost null, due to the fact that the
armour layer cannot be repaired by filling up
the holes, because the upper blocks tend to
slide down (chain reaction).
In conclusion, the regular placement method 1 appears
to have the best stability performance. However this
method, when compared with regular 2, has a bigger
consumption of concrete on manufacturing of antifer
blocks, due to the higher numbers of antifer blocks per
unit area.
There are some changes and studies that could be done
to consolidate the trends here presented.
Construct a model with armour layers
composed by antifer cubes in a double layer
on a 1:2 slope, for all placement methods
tested in this study.
Test the placement methods studied for
different peak wave periods and reduce the
number of waves to 1000.
Use a small scale crawler crane and pressure
clamp in the construction of the armour layer.
Study other placement methods on a 1:1.5
and 1:2 slope, as the regular placement with
smaller horizontal centre to centre distance.
7. BIBLIOGRAPHY
[1] Pita, C., Memria N 670 - "Dimensionamento
Hidrulico do Manto de Quebra-mares de
Talude", LNEC, Lisboa, 1986.
[2] CIRIA, CUR, CETMEF, "The Rock Manual. The
use of Rock in hydraulic engineering", 2nd ed.,
Ch. 5, C683, CIRIA, London, 2007.
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