10
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].

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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.

    [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

    Techniques in Coastal Engineering", World

    Scientific, Singapore, 1993.

    [8] Quintela, A., "Hidrulica", 10 ed., Fundao

    Calouste Gulbenkian, Lisboa, 2007.

    [9] CIRIA, CUR, CETMEF, "The Rock Manual. The

    use of Rock in hydraulic engineering", 2nd ed.,

    Ch. 3, C683, CIRIA, London, 2007.

    [10] Maquet, J., Developments in Geotechnical

    Engineering, 37 - "Design and construction of

    mounds for breakwaters and coastal protection -

    Port of Antifer, France", P. Bruun, Ed., Elsevier

    Science Publishers B. V., Amsterdam, 1985.

    [11] Frens, A., "The impact of placement method on

    Antifer-block stability", Delft University of

    Technology, Delft, 2007.