Hydraulic stability of antifer block armour layers … Hydraulic stability of antifer block armour...

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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 ρm is the density of armour units (kg/m3), ρw 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), Δ 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 α 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 α

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

3˂ξm˂6 (ξm – 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 (-), υ 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 Técnico. 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 (3×18cm=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

ρc

(kg/m3)

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

ρr

(kg/m3)

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


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

ρr

(kg/m3)

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


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 (KΔ) 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 (nº of blocks /

nº 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

ΔX (cm) 8.06 KΔ (-) 0.993

ΔY (cm) 4.67 ϕ (%) 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 (ΔX=8.1cm)

Fig. 15: Thickness of armour layer (t=H+Dn)




Table 13.

8

Table 11: Layer properties for regular placement method 1


y (-) 1.08 P (%) 49.8

ΔX (cm) 8.06 KΔ (-) 0.993

ΔY (cm) 4.67 ϕ (%) 49.8


Table 12: Wave series for regular placement method 1

Hs,input


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 (-)


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


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 (ΔX=8.8cm)

Fig. 18: Thickness of armour layer (t≈1.85H, increase of 20% in the

distance between blocks when compared with regular placement

method 1)




Table 16.

Table 14: Layer properties for regular placement method 2


y (-) 1.08 P (%) 49.9

ΔX (cm) 8.75 KΔ (-) 0.917

ΔY (cm) 4.67 ϕ (%) 45.9


9

Table 15: Wave series for regular placement method 2

Hs,input


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 (-)


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


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., Memória Nº 670 - "Dimensionamento

Hidráulico 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.

[3] Coastal Engineering Research Center, "Shore

Protection Manual", 2nd ed., Vol. 2, Ch. 7, U.S.

Government Printing Office, Washington, DC,

1975.

[4] Coastal Engineering Research Center, "Shore

Protection Manual", 4th ed., Vol. 2, Ch. 7, U.S.

Government Printing Office, Washington, DC,

1984.

[5] Van der Meer, J.; Heydra, G., Journal of Coastal

Engineering - "Rocking armour units: Number,

location and impact velocity", Elsevier Science

Publishers B. V., Amsterdam, 1991.

[6] U. S. Army Corps of Enginners, "Coastal

Engineering Manual", Part VI, Ch.5,

Washington, DC, 2011.

[7] Hughes, S., "Physical Models and Laboratory

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