alternative placement technique for antifer blocks used on breakwaters

Ocean Engineering 30 (2003) 1433–1451 www.elsevier.com/locate/oceaneng
Technical Note
Alternative placement technique for antifer
blocks used on breakwaters
O. Yagci
∗
, S. Kapdasli
Istanbul Technical University, Civil Engineering Faculty, Division of Hydraulics, 80626 Maslak,
Istanbul, Turkey
Received 5 May 2002; accepted 21 August 2002
Abstract
In this study, a placement technique named as “alternative placement technique” was
developed for antifer blocks and the results of its application to a breakwater model were
presented. This placement technique was compared with the existing techniques such as the
“regular placement technique”, the “irregular placement technique” and the “sloped wall place-
ment technique” by experiments. The comparison was carried out considering armor layer
stability, prototype placement, clarity of the placement technique’s definition, armor layer cost,
and wave runup. As a result of this investigation the “alternative placement technique” was
found to be superior to the other existing placement techniques.
2003 Elsevier Science Ltd. All rights reserved.
Keywords: Antifer blocks; Armor units; Breakwaters; Damage ratio; Placement technique; Stability
1. Introduction
Transportation and availability of stone limit natural stone utilization in the break-
water construction. Various artificial block types, such as dolosse, tetrapod, tribar,
hexapod, accropode, core-loc, quadripod etc. are used as alternative. The antifer
block is also widely used. The placement technique of the blocks on the armor layer
is one of the most significant parameters affecting the stability (Hudson et al., 1979).
Some difficulties were experienced during the placement stage of antifers on the
armor layer at some applications in Turkey (Kefken NATO breakwater and Rumeli-
∗
Corresponding author. Tel.: [phone]; fax: [phone].
E-mail address: [email protected] (O. Yagci).
0029-8018/03/$ - see front matter 2003 Elsevier Science Ltd. All rights reserved.
doi:10.1016/S0029-8018(02)00134-8

1434 O. Yagci, S. Kapdasli / Ocean Engineering 30 (2003) 1433–1451
Nomenclature
aBase width of antifer (m)
D
n50
Nominal diameter of the stone (m)
dAntifer block dimension (m)
eAntifer block dimension (m)
HCharacteristic wave height (m)
hAntifer block dimension (m)
K
D
Empirical stability coefficient
k
⌬
Layer coefficient
l
x
Grid dimension along slope (m)
l
y
Grid dimension along upslope (m)
M
50
Median mass from mass distribution curve (kg)
N
s
Hudson’s stability number (-)
nNumber of layers
PPorosity of armor layer (-)
RLBN Rolling block number (-)
RBN Rocking block number (-)
S
r
Solid ratio of armor layer (-)
TBN Turning block number (-)
t
ave
Average thickness of two antifer unit layers (m)
t
max
Maximum thickness of two antifer unit layers (m)
t
min
Minimum thickness of two antifer unit layers (m)
VVolume of concrete to be used at the armor per square meter of
slope (m
3
)
V
0
Volume of single block (m
3
)
V
1
Gross volume per block (m
3
)
WWeight of an armor unit (kg)
W
50
Median weight from weight distribution curve (N)
aSlope angle (°)
g
s
Specific weight of armor unit (N/m
3
)
g
w
Specific weight of water (N/m
3
)
⌬ Relative submerged mass density (-)
r
s
Mass density of armor unit (kg/m
3
)
r
w
Mass density of water (kg/m
3
)
fPacking density angle between the upper surface of the first armor
layer and the diagonal of a side surface with semi cylindrical hole
or the antifer cube diagonal on the second layer (°)

1435O. Yagci, S. Kapdasli / Ocean Engineering 30 (2003) 1433–1451
Fig. 1. The oblique, plan view and cross-section of the antifer block.
feneri Breakwater). Furthermore, low porosity and low roughness have resulted from
placement in these applications. This was the motivation of developing a new place-
ment technique described herein. The performance of the presented technique is com-
pared with other existing placement techniques.
2. Antifer cube blocks
The antifer blocks were used for the first time on the Antifer Harbor of France
between 1976 and 1978. The antifer shape has appeared as a result of the investi-
gations for this breakwater and does not have any patent. The damages on the break-
waters in Sines (Portugal) and Arzew (Algeria) have been repaired using antifer
blocks. Its first application in Turkey was the Kefken NATO Breakwater
(Gu
¨nbak, 1999).
Antifer blocks have a geometric shape close to a cube. The oblique, plan view
and the cross-section of the antifer blocks are presented in Fig. 1. The characteristics
of the antifer cube blocks are presented in Table 1. The geometric characteristics of
antifer blocks are related to block base width. The base width is calculated by Eq. (1).
a⫽
冉
W
0.8g
s
冊
1/3
(1)
Table 1
The characteristics of the model antifer cube blocks
a(cm) b(cm) h(cm) r(cm) s(cm) WV(cm
3
)g
s
(kN/m
3
)
(N)
5.40 0.9254 h=0.921 0.0877 0.022 3.24 0.8 25.90
a=5.00 a=4.97 a=0.47 a=0.12 a
3
=125

1436 O. Yagci, S. Kapdasli / Ocean Engineering 30 (2003) 1433–1451
where W=weight an armor unit; and g
s
=specific weight of armor unit.
It is sufficient that the unit specific weight is between 2.2 t/m
3
and 2.4 t/m
3
and
the compression resistance is within the range 200–250 kg/cm
2
. There is no necessity
to use high strength concrete (Gu
¨nbak, 1999). Antifer block use is also advantageous
since it provides better settlement for the cast concrete providing low concrete
porosity. According to Gu
¨nbak (1999) it is advisable to cast the concrete with 50%
or higher blast furnace cement and water/cement ratio lower than 0.45.
3. Earlier studies
Hudson et al. (1979) determined the parameters affecting the armor layer stability
and obtained Eq. (2) by solving these using dimensional analysis (Buckingam
Theorem). Artificial block types and the corresponding stability coefficient values
are presented in Shore Protection Manual (1984).
W⫽g
s
H
3
K
D
(g
s
g
w
⫺1)
3
cota
(2)
where W=weight of an armor unit; H=characteristic wave height; g
s
and g
w
are
specific weights of armor unit and water, respectively; a=the slope angle; and K
D
=the empirical stability coefficient.
The packing density, f(the number of armor units to be used per unit square
meter of breakwater slope), may be used to calculate the volume of concrete to be
used at the armor per square meter of the slope, V(Gu
¨nbak, 2000).
V⫽fD(3)
D⫽(W
g
s
)
1/3
(4)
The porosity of the armor layer, P, may be written in terms of fas:
f⫽k
⌬
n(1⫺P) (5)
where n=number of layers; k
⌬
=layer coefficient defined in Shore Protection Manual
(1984). For some artificial armor units, fvalues are presented in Table 2 (Gu
¨nbak,
2000). Table 2 shows that the amount of concrete used at the armor in case of using
antifer is almost twice more than core-loc. However, antifer blocks have specific
applications where they are useful; for example; if construction quality is expected
Table 2
The packing density values for the corresponding placement technique
Unit type Antifer Cube Rock Tetrapod Accropode Core-loc
f1.21 1.32 1.26 1.04 0.66 0.58

1437O. Yagci, S. Kapdasli / Ocean Engineering 30 (2003) 1433–1451
to be difficult to control or uncertainty in the wave climate is high, or foundation
instability is expected, then interlocking blocks, like dolosse or core-loc, may be
unreliable because of potential breakage. Burcharth et al. (2000) proposed an empiri-
cal formula for breakage of dolosse and tetrapods.
The H/
⌬ D
n50
parameter can be used to define the relationship between different
structures. Structures such as caissons or structures with large armor units are charac-
terized by small values of H/
⌬ D
n50
. Large values imply gravel beaches and sand
beaches (Van der Meer, 1988).
N
s
⫽H
⌬D
n50
(6)
where N
s
=Hudson’s stability number; H=characteristic wave height; ⌬ =
(ρ
s⫺
r
w
)/r
w
=relative submerged mass density; r
s
and r
w
=mass densities of armor
unit and water, respectively; and D
n50
=nominal diameter of the stone determined
from median mass from mass distribution curve or median weight from weight distri-
bution curve and it is computed as:
D
n50
⫽
冉
W
50
g
s
冊
⫽
冉
M
50
r
s
冊
(7)
where W
50
=median weight from weight distribution curve; g
s
=the specific weight
of armor unit; M
50
=median mass from mass distribution curve.
Losada et al. (1986) defined three different damage levels based on the visual
evaluation. These are “Initiation of Damage”,“Iribarren’s Damage”and “Destruc-
tion”. Vidal et al. (1991) mentioned an additional damage level naming it as
‘Initiation of Destruction’. These four damage levels are briefly explained below.
Initiation of This state is defined as situation attained when a certain number of
Damage: armor units were displaced from their original places to a new position
at a distance longer than a side of the unit.
Iribarren’s This state occurs when there is failure covering area so extensive in
Damage: the upper layer of the armor as to allow the extraction of units from
the lower one (two-layer armor).
Initiation of A small number of units, two or three, in the lower armor layer are
Destruction: forced out and the waves work directly on pieces of the second layer.
Destruction: In this case, the failure is large enough to uncover the underlayer. The
armor units leave the mound continuously, and if the test is not
stopped, the whole cross-section will be destroyed after a sufficiently
long period.
4. Theoretical approach
Three different types of block movement were considered and it was assumed that
each type has different contribution to damage (Yagci, 2000). The movement types
are as follows: